Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(47,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.c (of order \(2\), degree \(1\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.14 | ||
Character | \(\chi\) | \(=\) | 276.47 |
Dual form | 276.2.c.b.47.13 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.469504 | + | 1.33400i | 0.331990 | + | 0.943283i | ||||
\(3\) | −1.64481 | − | 0.542779i | −0.949630 | − | 0.313373i | ||||
\(4\) | −1.55913 | + | 1.25264i | −0.779566 | + | 0.626320i | ||||
\(5\) | 2.34886i | 1.05044i | 0.850966 | + | 0.525220i | \(0.176017\pi\) | ||||
−0.850966 | + | 0.525220i | \(0.823983\pi\) | |||||||
\(6\) | −0.0481753 | − | 2.44902i | −0.0196675 | − | 0.999807i | ||||
\(7\) | − | 0.796368i | − | 0.300999i | −0.988610 | − | 0.150499i | \(-0.951912\pi\) | ||
0.988610 | − | 0.150499i | \(-0.0480882\pi\) | |||||||
\(8\) | −2.40305 | − | 1.49177i | −0.849605 | − | 0.527419i | ||||
\(9\) | 2.41078 | + | 1.78553i | 0.803594 | + | 0.595178i | ||||
\(10\) | −3.13338 | + | 1.10280i | −0.990863 | + | 0.348735i | ||||
\(11\) | −3.21461 | −0.969243 | −0.484621 | − | 0.874724i | \(-0.661043\pi\) | ||||
−0.484621 | + | 0.874724i | \(0.661043\pi\) | |||||||
\(12\) | 3.24438 | − | 1.21409i | 0.936571 | − | 0.350477i | ||||
\(13\) | −6.69212 | −1.85606 | −0.928030 | − | 0.372505i | \(-0.878499\pi\) | ||||
−0.928030 | + | 0.372505i | \(0.878499\pi\) | |||||||
\(14\) | 1.06236 | − | 0.373898i | 0.283927 | − | 0.0999285i | ||||
\(15\) | 1.27491 | − | 3.86342i | 0.329180 | − | 0.997530i | ||||
\(16\) | 0.861782 | − | 3.90606i | 0.215446 | − | 0.976516i | ||||
\(17\) | 0.675569i | 0.163850i | 0.996639 | + | 0.0819248i | \(0.0261067\pi\) | ||||
−0.996639 | + | 0.0819248i | \(0.973893\pi\) | |||||||
\(18\) | −1.25003 | + | 4.05431i | −0.294636 | + | 0.955610i | ||||
\(19\) | 0.720048i | 0.165190i | 0.996583 | + | 0.0825951i | \(0.0263208\pi\) | ||||
−0.996583 | + | 0.0825951i | \(0.973679\pi\) | |||||||
\(20\) | −2.94227 | − | 3.66218i | −0.657912 | − | 0.818888i | ||||
\(21\) | −0.432251 | + | 1.30987i | −0.0943250 | + | 0.285837i | ||||
\(22\) | −1.50927 | − | 4.28831i | −0.321778 | − | 0.914270i | ||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 3.14285 | + | 3.75799i | 0.641531 | + | 0.767097i | ||||
\(25\) | −0.517128 | −0.103426 | ||||||||
\(26\) | −3.14198 | − | 8.92731i | −0.616193 | − | 1.75079i | ||||
\(27\) | −2.99612 | − | 4.24538i | −0.576604 | − | 0.817023i | ||||
\(28\) | 0.997563 | + | 1.24164i | 0.188522 | + | 0.234648i | ||||
\(29\) | 1.92582i | 0.357616i | 0.983884 | + | 0.178808i | \(0.0572240\pi\) | ||||
−0.983884 | + | 0.178808i | \(0.942776\pi\) | |||||||
\(30\) | 5.75239 | − | 0.113157i | 1.05024 | − | 0.0206595i | ||||
\(31\) | 7.61577i | 1.36783i | 0.729560 | + | 0.683917i | \(0.239725\pi\) | ||||
−0.729560 | + | 0.683917i | \(0.760275\pi\) | |||||||
\(32\) | 5.61531 | − | 0.684292i | 0.992657 | − | 0.120967i | ||||
\(33\) | 5.28742 | + | 1.74482i | 0.920422 | + | 0.303735i | ||||
\(34\) | −0.901212 | + | 0.317183i | −0.154557 | + | 0.0543964i | ||||
\(35\) | 1.87055 | 0.316181 | ||||||||
\(36\) | −5.99536 | + | 0.235964i | −0.999226 | + | 0.0393274i | ||||
\(37\) | 1.89808 | 0.312043 | 0.156021 | − | 0.987754i | \(-0.450133\pi\) | ||||
0.156021 | + | 0.987754i | \(0.450133\pi\) | |||||||
\(38\) | −0.960546 | + | 0.338065i | −0.155821 | + | 0.0548414i | ||||
\(39\) | 11.0072 | + | 3.63234i | 1.76257 | + | 0.581640i | ||||
\(40\) | 3.50395 | − | 5.64441i | 0.554023 | − | 0.892460i | ||||
\(41\) | 7.63841i | 1.19292i | 0.802643 | + | 0.596460i | \(0.203426\pi\) | ||||
−0.802643 | + | 0.596460i | \(0.796574\pi\) | |||||||
\(42\) | −1.95032 | + | 0.0383653i | −0.300941 | + | 0.00591989i | ||||
\(43\) | 11.0728i | 1.68859i | 0.535879 | + | 0.844295i | \(0.319980\pi\) | ||||
−0.535879 | + | 0.844295i | \(0.680020\pi\) | |||||||
\(44\) | 5.01201 | − | 4.02676i | 0.755588 | − | 0.607056i | ||||
\(45\) | −4.19396 | + | 5.66258i | −0.625199 | + | 0.844128i | ||||
\(46\) | −0.469504 | − | 1.33400i | −0.0692246 | − | 0.196688i | ||||
\(47\) | −1.22603 | −0.178835 | −0.0894175 | − | 0.995994i | \(-0.528501\pi\) | ||||
−0.0894175 | + | 0.995994i | \(0.528501\pi\) | |||||||
\(48\) | −3.53759 | + | 5.95696i | −0.510608 | + | 0.859814i | ||||
\(49\) | 6.36580 | 0.909400 | ||||||||
\(50\) | −0.242794 | − | 0.689851i | −0.0343362 | − | 0.0975596i | ||||
\(51\) | 0.366685 | − | 1.11118i | 0.0513461 | − | 0.155597i | ||||
\(52\) | 10.4339 | − | 8.38282i | 1.44692 | − | 1.16249i | ||||
\(53\) | − | 11.3409i | − | 1.55780i | −0.627151 | − | 0.778898i | \(-0.715779\pi\) | ||
0.627151 | − | 0.778898i | \(-0.284221\pi\) | |||||||
\(54\) | 4.25666 | − | 5.99006i | 0.579258 | − | 0.815144i | ||||
\(55\) | − | 7.55067i | − | 1.01813i | ||||||
\(56\) | −1.18800 | + | 1.91371i | −0.158753 | + | 0.255730i | ||||
\(57\) | 0.390826 | − | 1.18434i | 0.0517662 | − | 0.156870i | ||||
\(58\) | −2.56905 | + | 0.904180i | −0.337333 | + | 0.118725i | ||||
\(59\) | 0.176969 | 0.0230394 | 0.0115197 | − | 0.999934i | \(-0.496333\pi\) | ||||
0.0115197 | + | 0.999934i | \(0.496333\pi\) | |||||||
\(60\) | 2.85172 | + | 7.62058i | 0.368156 | + | 0.983812i | ||||
\(61\) | 6.71562 | 0.859847 | 0.429923 | − | 0.902865i | \(-0.358541\pi\) | ||||
0.429923 | + | 0.902865i | \(0.358541\pi\) | |||||||
\(62\) | −10.1595 | + | 3.57564i | −1.29025 | + | 0.454106i | ||||
\(63\) | 1.42194 | − | 1.91987i | 0.179148 | − | 0.241881i | ||||
\(64\) | 3.54926 | + | 7.16957i | 0.443658 | + | 0.896196i | ||||
\(65\) | − | 15.7188i | − | 1.94968i | ||||||
\(66\) | 0.154865 | + | 7.87264i | 0.0190626 | + | 0.969055i | ||||
\(67\) | 9.36728i | 1.14440i | 0.820116 | + | 0.572198i | \(0.193909\pi\) | ||||
−0.820116 | + | 0.572198i | \(0.806091\pi\) | |||||||
\(68\) | −0.846246 | − | 1.05330i | −0.102622 | − | 0.127732i | ||||
\(69\) | 1.64481 | + | 0.542779i | 0.198012 | + | 0.0653429i | ||||
\(70\) | 0.878233 | + | 2.49533i | 0.104969 | + | 0.298249i | ||||
\(71\) | −9.44253 | −1.12062 | −0.560311 | − | 0.828282i | \(-0.689319\pi\) | ||||
−0.560311 | + | 0.828282i | \(0.689319\pi\) | |||||||
\(72\) | −3.12962 | − | 7.88704i | −0.368830 | − | 0.929497i | ||||
\(73\) | 0.422106 | 0.0494037 | 0.0247019 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247019 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(74\) | 0.891158 | + | 2.53205i | 0.103595 | + | 0.294345i | ||||
\(75\) | 0.850576 | + | 0.280686i | 0.0982161 | + | 0.0324108i | ||||
\(76\) | −0.901961 | − | 1.12265i | −0.103462 | − | 0.128777i | ||||
\(77\) | 2.56002i | 0.291741i | ||||||||
\(78\) | 0.322395 | + | 16.3891i | 0.0365041 | + | 1.85570i | ||||
\(79\) | − | 10.1253i | − | 1.13918i | −0.821928 | − | 0.569591i | \(-0.807101\pi\) | ||
0.821928 | − | 0.569591i | \(-0.192899\pi\) | |||||||
\(80\) | 9.17478 | + | 2.02420i | 1.02577 | + | 0.226313i | ||||
\(81\) | 2.62375 | + | 8.60906i | 0.291527 | + | 0.956562i | ||||
\(82\) | −10.1897 | + | 3.58627i | −1.12526 | + | 0.396037i | ||||
\(83\) | −8.44270 | −0.926706 | −0.463353 | − | 0.886174i | \(-0.653354\pi\) | ||||
−0.463353 | + | 0.886174i | \(0.653354\pi\) | |||||||
\(84\) | −0.966862 | − | 2.58372i | −0.105493 | − | 0.281907i | ||||
\(85\) | −1.58682 | −0.172114 | ||||||||
\(86\) | −14.7712 | + | 5.19874i | −1.59282 | + | 0.560594i | ||||
\(87\) | 1.04529 | − | 3.16760i | 0.112067 | − | 0.339602i | ||||
\(88\) | 7.72487 | + | 4.79546i | 0.823473 | + | 0.511197i | ||||
\(89\) | 11.2794i | 1.19562i | 0.801640 | + | 0.597808i | \(0.203961\pi\) | ||||
−0.801640 | + | 0.597808i | \(0.796039\pi\) | |||||||
\(90\) | −9.52299 | − | 2.93615i | −1.00381 | − | 0.309498i | ||||
\(91\) | 5.32939i | 0.558672i | ||||||||
\(92\) | 1.55913 | − | 1.25264i | 0.162551 | − | 0.130597i | ||||
\(93\) | 4.13368 | − | 12.5265i | 0.428643 | − | 1.29894i | ||||
\(94\) | −0.575627 | − | 1.63553i | −0.0593714 | − | 0.168692i | ||||
\(95\) | −1.69129 | −0.173523 | ||||||||
\(96\) | −9.60753 | − | 1.92234i | −0.980564 | − | 0.196198i | ||||
\(97\) | −7.27066 | −0.738224 | −0.369112 | − | 0.929385i | \(-0.620338\pi\) | ||||
−0.369112 | + | 0.929385i | \(0.620338\pi\) | |||||||
\(98\) | 2.98877 | + | 8.49200i | 0.301911 | + | 0.857821i | ||||
\(99\) | −7.74974 | − | 5.73980i | −0.778878 | − | 0.576871i | ||||
\(100\) | 0.806271 | − | 0.647776i | 0.0806271 | − | 0.0647776i | ||||
\(101\) | − | 7.25596i | − | 0.721995i | −0.932567 | − | 0.360997i | \(-0.882436\pi\) | ||
0.932567 | − | 0.360997i | \(-0.117564\pi\) | |||||||
\(102\) | 1.65448 | − | 0.0325458i | 0.163818 | − | 0.00322251i | ||||
\(103\) | 11.6113i | 1.14410i | 0.820219 | + | 0.572050i | \(0.193852\pi\) | ||||
−0.820219 | + | 0.572050i | \(0.806148\pi\) | |||||||
\(104\) | 16.0815 | + | 9.98308i | 1.57692 | + | 0.978922i | ||||
\(105\) | −3.07670 | − | 1.01530i | −0.300255 | − | 0.0990828i | ||||
\(106\) | 15.1288 | − | 5.32461i | 1.46944 | − | 0.517172i | ||||
\(107\) | 19.9682 | 1.93040 | 0.965198 | − | 0.261521i | \(-0.0842240\pi\) | ||||
0.965198 | + | 0.261521i | \(0.0842240\pi\) | |||||||
\(108\) | 9.98929 | + | 2.86604i | 0.961219 | + | 0.275784i | ||||
\(109\) | −14.8640 | −1.42371 | −0.711855 | − | 0.702327i | \(-0.752145\pi\) | ||||
−0.711855 | + | 0.702327i | \(0.752145\pi\) | |||||||
\(110\) | 10.0726 | − | 3.54507i | 0.960386 | − | 0.338009i | ||||
\(111\) | −3.12198 | − | 1.03024i | −0.296325 | − | 0.0977859i | ||||
\(112\) | −3.11066 | − | 0.686296i | −0.293930 | − | 0.0648489i | ||||
\(113\) | − | 11.7321i | − | 1.10367i | −0.833954 | − | 0.551834i | \(-0.813928\pi\) | ||
0.833954 | − | 0.551834i | \(-0.186072\pi\) | |||||||
\(114\) | 1.76341 | − | 0.0346885i | 0.165158 | − | 0.00324888i | ||||
\(115\) | − | 2.34886i | − | 0.219032i | ||||||
\(116\) | −2.41236 | − | 3.00261i | −0.223982 | − | 0.278785i | ||||
\(117\) | −16.1332 | − | 11.9490i | −1.49152 | − | 1.10469i | ||||
\(118\) | 0.0830878 | + | 0.236077i | 0.00764885 | + | 0.0217327i | ||||
\(119\) | 0.538002 | 0.0493185 | ||||||||
\(120\) | −8.82698 | + | 7.38210i | −0.805790 | + | 0.673891i | ||||
\(121\) | −0.666258 | −0.0605689 | ||||||||
\(122\) | 3.15301 | + | 8.95866i | 0.285460 | + | 0.811079i | ||||
\(123\) | 4.14597 | − | 12.5637i | 0.373829 | − | 1.13283i | ||||
\(124\) | −9.53983 | − | 11.8740i | −0.856702 | − | 1.06632i | ||||
\(125\) | 10.5296i | 0.941798i | ||||||||
\(126\) | 3.22872 | + | 0.995487i | 0.287637 | + | 0.0886851i | ||||
\(127\) | − | 10.7727i | − | 0.955926i | −0.878380 | − | 0.477963i | \(-0.841375\pi\) | ||
0.878380 | − | 0.477963i | \(-0.158625\pi\) | |||||||
\(128\) | −7.89784 | + | 8.10087i | −0.698077 | + | 0.716023i | ||||
\(129\) | 6.01009 | − | 18.2127i | 0.529159 | − | 1.60354i | ||||
\(130\) | 20.9690 | − | 7.38006i | 1.83910 | − | 0.647274i | ||||
\(131\) | 5.76563 | 0.503745 | 0.251873 | − | 0.967760i | \(-0.418954\pi\) | ||||
0.251873 | + | 0.967760i | \(0.418954\pi\) | |||||||
\(132\) | −10.4294 | + | 3.90283i | −0.907765 | + | 0.339698i | ||||
\(133\) | 0.573423 | 0.0497221 | ||||||||
\(134\) | −12.4960 | + | 4.39798i | −1.07949 | + | 0.379927i | ||||
\(135\) | 9.97179 | − | 7.03747i | 0.858235 | − | 0.605689i | ||||
\(136\) | 1.00779 | − | 1.62342i | 0.0864175 | − | 0.139208i | ||||
\(137\) | − | 14.4134i | − | 1.23142i | −0.787971 | − | 0.615712i | \(-0.788868\pi\) | ||
0.787971 | − | 0.615712i | \(-0.211132\pi\) | |||||||
\(138\) | 0.0481753 | + | 2.44902i | 0.00410096 | + | 0.208474i | ||||
\(139\) | − | 11.6755i | − | 0.990301i | −0.868807 | − | 0.495150i | \(-0.835113\pi\) | ||
0.868807 | − | 0.495150i | \(-0.164887\pi\) | |||||||
\(140\) | −2.91644 | + | 2.34313i | −0.246484 | + | 0.198031i | ||||
\(141\) | 2.01659 | + | 0.665464i | 0.169827 | + | 0.0560421i | ||||
\(142\) | −4.43331 | − | 12.5964i | −0.372035 | − | 1.05706i | ||||
\(143\) | 21.5126 | 1.79897 | ||||||||
\(144\) | 9.05197 | − | 7.87793i | 0.754331 | − | 0.656494i | ||||
\(145\) | −4.52347 | −0.375654 | ||||||||
\(146\) | 0.198180 | + | 0.563091i | 0.0164015 | + | 0.0466017i | ||||
\(147\) | −10.4705 | − | 3.45522i | −0.863593 | − | 0.284982i | ||||
\(148\) | −2.95936 | + | 2.37762i | −0.243258 | + | 0.195439i | ||||
\(149\) | 15.0305i | 1.23135i | 0.788000 | + | 0.615675i | \(0.211117\pi\) | ||||
−0.788000 | + | 0.615675i | \(0.788883\pi\) | |||||||
\(150\) | 0.0249128 | + | 1.26645i | 0.00203412 | + | 0.103406i | ||||
\(151\) | 0.656832i | 0.0534523i | 0.999643 | + | 0.0267261i | \(0.00850821\pi\) | ||||
−0.999643 | + | 0.0267261i | \(0.991492\pi\) | |||||||
\(152\) | 1.07414 | − | 1.73031i | 0.0871245 | − | 0.140346i | ||||
\(153\) | −1.20625 | + | 1.62865i | −0.0975196 | + | 0.131669i | ||||
\(154\) | −3.41507 | + | 1.20194i | −0.275194 | + | 0.0968549i | ||||
\(155\) | −17.8884 | −1.43683 | ||||||||
\(156\) | −21.7118 | + | 8.12483i | −1.73833 | + | 0.650507i | ||||
\(157\) | −13.6112 | −1.08629 | −0.543146 | − | 0.839638i | \(-0.682767\pi\) | ||||
−0.543146 | + | 0.839638i | \(0.682767\pi\) | |||||||
\(158\) | 13.5072 | − | 4.75386i | 1.07457 | − | 0.378197i | ||||
\(159\) | −6.15561 | + | 18.6536i | −0.488172 | + | 1.47933i | ||||
\(160\) | 1.60730 | + | 13.1896i | 0.127069 | + | 1.04273i | ||||
\(161\) | 0.796368i | 0.0627626i | ||||||||
\(162\) | −10.2527 | + | 7.54208i | −0.805525 | + | 0.592562i | ||||
\(163\) | 3.07465i | 0.240825i | 0.992724 | + | 0.120413i | \(0.0384218\pi\) | ||||
−0.992724 | + | 0.120413i | \(0.961578\pi\) | |||||||
\(164\) | −9.56818 | − | 11.9093i | −0.747150 | − | 0.929959i | ||||
\(165\) | −4.09834 | + | 12.4194i | −0.319055 | + | 0.966848i | ||||
\(166\) | −3.96388 | − | 11.2626i | −0.307657 | − | 0.874146i | ||||
\(167\) | 4.30533 | 0.333157 | 0.166578 | − | 0.986028i | \(-0.446728\pi\) | ||||
0.166578 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(168\) | 2.99274 | − | 2.50286i | 0.230895 | − | 0.193100i | ||||
\(169\) | 31.7845 | 2.44496 | ||||||||
\(170\) | −0.745017 | − | 2.11682i | −0.0571402 | − | 0.162353i | ||||
\(171\) | −1.28567 | + | 1.73588i | −0.0983175 | + | 0.132746i | ||||
\(172\) | −13.8703 | − | 17.2640i | −1.05760 | − | 1.31637i | ||||
\(173\) | 5.68962i | 0.432574i | 0.976330 | + | 0.216287i | \(0.0693947\pi\) | ||||
−0.976330 | + | 0.216287i | \(0.930605\pi\) | |||||||
\(174\) | 4.71636 | − | 0.0927770i | 0.357546 | − | 0.00703341i | ||||
\(175\) | 0.411824i | 0.0311310i | ||||||||
\(176\) | −2.77030 | + | 12.5565i | −0.208819 | + | 0.946481i | ||||
\(177\) | −0.291080 | − | 0.0960551i | −0.0218789 | − | 0.00721994i | ||||
\(178\) | −15.0468 | + | 5.29573i | −1.12780 | + | 0.396932i | ||||
\(179\) | 21.1309 | 1.57939 | 0.789697 | − | 0.613497i | \(-0.210238\pi\) | ||||
0.789697 | + | 0.613497i | \(0.210238\pi\) | |||||||
\(180\) | −0.554247 | − | 14.0822i | −0.0413111 | − | 1.04963i | ||||
\(181\) | −12.7953 | −0.951067 | −0.475533 | − | 0.879698i | \(-0.657745\pi\) | ||||
−0.475533 | + | 0.879698i | \(0.657745\pi\) | |||||||
\(182\) | −7.10942 | + | 2.50217i | −0.526986 | + | 0.185473i | ||||
\(183\) | −11.0459 | − | 3.64509i | −0.816536 | − | 0.269453i | ||||
\(184\) | 2.40305 | + | 1.49177i | 0.177155 | + | 0.109975i | ||||
\(185\) | 4.45832i | 0.327782i | ||||||||
\(186\) | 18.6512 | − | 0.366893i | 1.36757 | − | 0.0269019i | ||||
\(187\) | − | 2.17169i | − | 0.158810i | ||||||
\(188\) | 1.91154 | − | 1.53578i | 0.139414 | − | 0.112008i | ||||
\(189\) | −3.38088 | + | 2.38602i | −0.245923 | + | 0.173557i | ||||
\(190\) | −0.794067 | − | 2.25619i | −0.0576077 | − | 0.163681i | ||||
\(191\) | 8.07378 | 0.584198 | 0.292099 | − | 0.956388i | \(-0.405646\pi\) | ||||
0.292099 | + | 0.956388i | \(0.405646\pi\) | |||||||
\(192\) | −1.94636 | − | 13.7190i | −0.140467 | − | 0.990085i | ||||
\(193\) | 5.34117 | 0.384466 | 0.192233 | − | 0.981349i | \(-0.438427\pi\) | ||||
0.192233 | + | 0.981349i | \(0.438427\pi\) | |||||||
\(194\) | −3.41361 | − | 9.69909i | −0.245083 | − | 0.696354i | ||||
\(195\) | −8.53185 | + | 25.8544i | −0.610978 | + | 1.85148i | ||||
\(196\) | −9.92512 | + | 7.97406i | −0.708937 | + | 0.569576i | ||||
\(197\) | − | 1.19189i | − | 0.0849186i | −0.999098 | − | 0.0424593i | \(-0.986481\pi\) | ||
0.999098 | − | 0.0424593i | \(-0.0135193\pi\) | |||||||
\(198\) | 4.01838 | − | 13.0330i | 0.285574 | − | 0.926217i | ||||
\(199\) | 24.2553i | 1.71941i | 0.510788 | + | 0.859707i | \(0.329354\pi\) | ||||
−0.510788 | + | 0.859707i | \(0.670646\pi\) | |||||||
\(200\) | 1.24268 | + | 0.771435i | 0.0878709 | + | 0.0545487i | ||||
\(201\) | 5.08436 | − | 15.4074i | 0.358623 | − | 1.08675i | ||||
\(202\) | 9.67948 | − | 3.40670i | 0.681046 | − | 0.239695i | ||||
\(203\) | 1.53366 | 0.107642 | ||||||||
\(204\) | 0.820202 | + | 2.19180i | 0.0574256 | + | 0.153457i | ||||
\(205\) | −17.9415 | −1.25309 | ||||||||
\(206\) | −15.4896 | + | 5.45158i | −1.07921 | + | 0.379829i | ||||
\(207\) | −2.41078 | − | 1.78553i | −0.167561 | − | 0.124103i | ||||
\(208\) | −5.76715 | + | 26.1398i | −0.399880 | + | 1.81247i | ||||
\(209\) | − | 2.31467i | − | 0.160109i | ||||||
\(210\) | −0.0901146 | − | 4.58102i | −0.00621850 | − | 0.316120i | ||||
\(211\) | 18.3549i | 1.26361i | 0.775129 | + | 0.631803i | \(0.217685\pi\) | ||||
−0.775129 | + | 0.631803i | \(0.782315\pi\) | |||||||
\(212\) | 14.2061 | + | 17.6820i | 0.975679 | + | 1.21440i | ||||
\(213\) | 15.5312 | + | 5.12521i | 1.06418 | + | 0.351173i | ||||
\(214\) | 9.37514 | + | 26.6376i | 0.640871 | + | 1.82091i | ||||
\(215\) | −26.0085 | −1.77376 | ||||||||
\(216\) | 0.866709 | + | 14.6714i | 0.0589721 | + | 0.998260i | ||||
\(217\) | 6.06496 | 0.411716 | ||||||||
\(218\) | −6.97869 | − | 19.8286i | −0.472657 | − | 1.34296i | ||||
\(219\) | −0.694283 | − | 0.229110i | −0.0469153 | − | 0.0154818i | ||||
\(220\) | 9.45827 | + | 11.7725i | 0.637677 | + | 0.793701i | ||||
\(221\) | − | 4.52099i | − | 0.304115i | ||||||
\(222\) | −0.0914408 | − | 4.64843i | −0.00613710 | − | 0.311982i | ||||
\(223\) | − | 26.3795i | − | 1.76650i | −0.468899 | − | 0.883252i | \(-0.655349\pi\) | ||
0.468899 | − | 0.883252i | \(-0.344651\pi\) | |||||||
\(224\) | −0.544948 | − | 4.47186i | −0.0364109 | − | 0.298788i | ||||
\(225\) | −1.24668 | − | 0.923349i | −0.0831122 | − | 0.0615566i | ||||
\(226\) | 15.6507 | − | 5.50829i | 1.04107 | − | 0.366406i | ||||
\(227\) | −6.18899 | −0.410778 | −0.205389 | − | 0.978680i | \(-0.565846\pi\) | ||||
−0.205389 | + | 0.978680i | \(0.565846\pi\) | |||||||
\(228\) | 0.874202 | + | 2.33611i | 0.0578955 | + | 0.154712i | ||||
\(229\) | 5.28251 | 0.349078 | 0.174539 | − | 0.984650i | \(-0.444156\pi\) | ||||
0.174539 | + | 0.984650i | \(0.444156\pi\) | |||||||
\(230\) | 3.13338 | − | 1.10280i | 0.206609 | − | 0.0727164i | ||||
\(231\) | 1.38952 | − | 4.21073i | 0.0914238 | − | 0.277046i | ||||
\(232\) | 2.87287 | − | 4.62783i | 0.188613 | − | 0.303832i | ||||
\(233\) | − | 10.0481i | − | 0.658272i | −0.944283 | − | 0.329136i | \(-0.893243\pi\) | ||
0.944283 | − | 0.329136i | \(-0.106757\pi\) | |||||||
\(234\) | 8.36538 | − | 27.1319i | 0.546862 | − | 1.77367i | ||||
\(235\) | − | 2.87977i | − | 0.187856i | ||||||
\(236\) | −0.275918 | + | 0.221679i | −0.0179607 | + | 0.0144301i | ||||
\(237\) | −5.49579 | + | 16.6541i | −0.356990 | + | 1.08180i | ||||
\(238\) | 0.252594 | + | 0.717696i | 0.0163732 | + | 0.0465214i | ||||
\(239\) | 13.7376 | 0.888613 | 0.444307 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444307 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(240\) | −13.9921 | − | 8.30930i | −0.903183 | − | 0.536363i | ||||
\(241\) | −14.6530 | −0.943881 | −0.471940 | − | 0.881631i | \(-0.656446\pi\) | ||||
−0.471940 | + | 0.881631i | \(0.656446\pi\) | |||||||
\(242\) | −0.312811 | − | 0.888791i | −0.0201082 | − | 0.0571336i | ||||
\(243\) | 0.357257 | − | 15.5844i | 0.0229180 | − | 0.999737i | ||||
\(244\) | −10.4705 | + | 8.41226i | −0.670307 | + | 0.538540i | ||||
\(245\) | 14.9523i | 0.955270i | ||||||||
\(246\) | 18.7066 | − | 0.367983i | 1.19269 | − | 0.0234617i | ||||
\(247\) | − | 4.81864i | − | 0.306603i | ||||||
\(248\) | 11.3610 | − | 18.3011i | 0.721422 | − | 1.16212i | ||||
\(249\) | 13.8866 | + | 4.58252i | 0.880028 | + | 0.290405i | ||||
\(250\) | −14.0466 | + | 4.94370i | −0.888382 | + | 0.312667i | ||||
\(251\) | 0.497047 | 0.0313734 | 0.0156867 | − | 0.999877i | \(-0.495007\pi\) | ||||
0.0156867 | + | 0.999877i | \(0.495007\pi\) | |||||||
\(252\) | 0.187914 | + | 4.77451i | 0.0118375 | + | 0.300766i | ||||
\(253\) | 3.21461 | 0.202101 | ||||||||
\(254\) | 14.3709 | − | 5.05785i | 0.901709 | − | 0.317358i | ||||
\(255\) | 2.61001 | + | 0.861290i | 0.163445 | + | 0.0539361i | ||||
\(256\) | −14.5147 | − | 6.73235i | −0.907166 | − | 0.420772i | ||||
\(257\) | 15.6813i | 0.978170i | 0.872236 | + | 0.489085i | \(0.162669\pi\) | ||||
−0.872236 | + | 0.489085i | \(0.837331\pi\) | |||||||
\(258\) | 27.1175 | − | 0.533437i | 1.68826 | − | 0.0332103i | ||||
\(259\) | − | 1.51157i | − | 0.0939245i | ||||||
\(260\) | 19.6900 | + | 24.5077i | 1.22112 | + | 1.51990i | ||||
\(261\) | −3.43861 | + | 4.64273i | −0.212845 | + | 0.287378i | ||||
\(262\) | 2.70699 | + | 7.69137i | 0.167238 | + | 0.475174i | ||||
\(263\) | −27.6024 | −1.70204 | −0.851018 | − | 0.525136i | \(-0.824015\pi\) | ||||
−0.851018 | + | 0.525136i | \(0.824015\pi\) | |||||||
\(264\) | −10.1030 | − | 12.0805i | −0.621799 | − | 0.743503i | ||||
\(265\) | 26.6382 | 1.63637 | ||||||||
\(266\) | 0.269224 | + | 0.764948i | 0.0165072 | + | 0.0469020i | ||||
\(267\) | 6.12222 | − | 18.5525i | 0.374674 | − | 1.13539i | ||||
\(268\) | −11.7338 | − | 14.6048i | −0.716758 | − | 0.892131i | ||||
\(269\) | 26.6429i | 1.62444i | 0.583348 | + | 0.812222i | \(0.301742\pi\) | ||||
−0.583348 | + | 0.812222i | \(0.698258\pi\) | |||||||
\(270\) | 14.0698 | + | 9.99828i | 0.856261 | + | 0.608476i | ||||
\(271\) | 3.04363i | 0.184888i | 0.995718 | + | 0.0924438i | \(0.0294678\pi\) | ||||
−0.995718 | + | 0.0924438i | \(0.970532\pi\) | |||||||
\(272\) | 2.63882 | + | 0.582194i | 0.160002 | + | 0.0353007i | ||||
\(273\) | 2.89268 | − | 8.76582i | 0.175073 | − | 0.530531i | ||||
\(274\) | 19.2276 | − | 6.76717i | 1.16158 | − | 0.408820i | ||||
\(275\) | 1.66237 | 0.100244 | ||||||||
\(276\) | −3.24438 | + | 1.21409i | −0.195289 | + | 0.0730796i | ||||
\(277\) | 0.169013 | 0.0101550 | 0.00507749 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507749 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(278\) | 15.5751 | − | 5.48168i | 0.934134 | − | 0.328770i | ||||
\(279\) | −13.5982 | + | 18.3600i | −0.814104 | + | 1.09918i | ||||
\(280\) | −4.49503 | − | 2.79043i | −0.268629 | − | 0.166760i | ||||
\(281\) | − | 4.21550i | − | 0.251476i | −0.992064 | − | 0.125738i | \(-0.959870\pi\) | ||
0.992064 | − | 0.125738i | \(-0.0401298\pi\) | |||||||
\(282\) | 0.0590645 | + | 3.00257i | 0.00351724 | + | 0.178800i | ||||
\(283\) | 3.01367i | 0.179144i | 0.995980 | + | 0.0895719i | \(0.0285499\pi\) | ||||
−0.995980 | + | 0.0895719i | \(0.971450\pi\) | |||||||
\(284\) | 14.7222 | − | 11.8281i | 0.873599 | − | 0.701869i | ||||
\(285\) | 2.78184 | + | 0.917995i | 0.164782 | + | 0.0543773i | ||||
\(286\) | 10.1002 | + | 28.6979i | 0.597240 | + | 1.69694i | ||||
\(287\) | 6.08298 | 0.359067 | ||||||||
\(288\) | 14.7591 | + | 8.37665i | 0.869690 | + | 0.493599i | ||||
\(289\) | 16.5436 | 0.973153 | ||||||||
\(290\) | −2.12379 | − | 6.03433i | −0.124713 | − | 0.354348i | ||||
\(291\) | 11.9588 | + | 3.94636i | 0.701039 | + | 0.231340i | ||||
\(292\) | −0.658118 | + | 0.528747i | −0.0385135 | + | 0.0309426i | ||||
\(293\) | − | 9.32392i | − | 0.544709i | −0.962197 | − | 0.272355i | \(-0.912198\pi\) | ||
0.962197 | − | 0.272355i | \(-0.0878023\pi\) | |||||||
\(294\) | −0.306675 | − | 15.5899i | −0.0178856 | − | 0.909224i | ||||
\(295\) | 0.415675i | 0.0242015i | ||||||||
\(296\) | −4.56118 | − | 2.83150i | −0.265113 | − | 0.164577i | ||||
\(297\) | 9.63138 | + | 13.6473i | 0.558870 | + | 0.791894i | ||||
\(298\) | −20.0508 | + | 7.05690i | −1.16151 | + | 0.408795i | ||||
\(299\) | 6.69212 | 0.387015 | ||||||||
\(300\) | −1.67776 | + | 0.627840i | −0.0968654 | + | 0.0362483i | ||||
\(301\) | 8.81804 | 0.508263 | ||||||||
\(302\) | −0.876217 | + | 0.308386i | −0.0504206 | + | 0.0177456i | ||||
\(303\) | −3.93838 | + | 11.9347i | −0.226254 | + | 0.685628i | ||||
\(304\) | 2.81255 | + | 0.620524i | 0.161311 | + | 0.0355895i | ||||
\(305\) | 15.7740i | 0.903218i | ||||||||
\(306\) | −2.73897 | − | 0.844485i | −0.156576 | − | 0.0482760i | ||||
\(307\) | − | 4.19690i | − | 0.239529i | −0.992802 | − | 0.119765i | \(-0.961786\pi\) | ||
0.992802 | − | 0.119765i | \(-0.0382140\pi\) | |||||||
\(308\) | −3.20678 | − | 3.99140i | −0.182723 | − | 0.227431i | ||||
\(309\) | 6.30239 | − | 19.0984i | 0.358530 | − | 1.08647i | ||||
\(310\) | −8.39866 | − | 23.8631i | −0.477012 | − | 1.35534i | ||||
\(311\) | 1.57780 | 0.0894688 | 0.0447344 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447344 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(312\) | −21.0323 | − | 25.1489i | −1.19072 | − | 1.42378i | ||||
\(313\) | 7.02504 | 0.397079 | 0.198539 | − | 0.980093i | \(-0.436380\pi\) | ||||
0.198539 | + | 0.980093i | \(0.436380\pi\) | |||||||
\(314\) | −6.39052 | − | 18.1574i | −0.360638 | − | 1.02468i | ||||
\(315\) | 4.50950 | + | 3.33994i | 0.254082 | + | 0.188184i | ||||
\(316\) | 12.6833 | + | 15.7866i | 0.713493 | + | 0.888068i | ||||
\(317\) | − | 0.0798294i | − | 0.00448367i | −0.999997 | − | 0.00224183i | \(-0.999286\pi\) | ||
0.999997 | − | 0.00224183i | \(-0.000713598\pi\) | |||||||
\(318\) | −27.7741 | + | 0.546353i | −1.55749 | + | 0.0306380i | ||||
\(319\) | − | 6.19076i | − | 0.346616i | ||||||
\(320\) | −16.8403 | + | 8.33671i | −0.941401 | + | 0.466036i | ||||
\(321\) | −32.8438 | − | 10.8383i | −1.83316 | − | 0.604935i | ||||
\(322\) | −1.06236 | + | 0.373898i | −0.0592029 | + | 0.0208365i | ||||
\(323\) | −0.486442 | −0.0270664 | ||||||||
\(324\) | −14.8748 | − | 10.1360i | −0.826379 | − | 0.563114i | ||||
\(325\) | 3.46068 | 0.191964 | ||||||||
\(326\) | −4.10160 | + | 1.44356i | −0.227166 | + | 0.0799515i | ||||
\(327\) | 24.4484 | + | 8.06784i | 1.35200 | + | 0.446153i | ||||
\(328\) | 11.3947 | − | 18.3555i | 0.629169 | − | 1.01351i | ||||
\(329\) | 0.976372i | 0.0538291i | ||||||||
\(330\) | −18.4917 | + | 0.363756i | −1.01793 | + | 0.0200241i | ||||
\(331\) | − | 29.4692i | − | 1.61977i | −0.586588 | − | 0.809886i | \(-0.699529\pi\) | ||
0.586588 | − | 0.809886i | \(-0.300471\pi\) | |||||||
\(332\) | 13.1633 | − | 10.5757i | 0.722429 | − | 0.580415i | ||||
\(333\) | 4.57586 | + | 3.38909i | 0.250756 | + | 0.185721i | ||||
\(334\) | 2.02137 | + | 5.74333i | 0.110605 | + | 0.314261i | ||||
\(335\) | −22.0024 | −1.20212 | ||||||||
\(336\) | 4.74394 | + | 2.81723i | 0.258803 | + | 0.153692i | ||||
\(337\) | −12.3468 | −0.672575 | −0.336287 | − | 0.941759i | \(-0.609171\pi\) | ||||
−0.336287 | + | 0.941759i | \(0.609171\pi\) | |||||||
\(338\) | 14.9229 | + | 42.4006i | 0.811701 | + | 2.30629i | ||||
\(339\) | −6.36796 | + | 19.2971i | −0.345860 | + | 1.04808i | ||||
\(340\) | 2.47405 | − | 1.98771i | 0.134174 | − | 0.107799i | ||||
\(341\) | − | 24.4818i | − | 1.32576i | ||||||
\(342\) | −2.91929 | − | 0.900084i | −0.157857 | − | 0.0486710i | ||||
\(343\) | − | 10.6441i | − | 0.574727i | ||||||
\(344\) | 16.5181 | − | 26.6085i | 0.890595 | − | 1.43463i | ||||
\(345\) | −1.27491 | + | 3.86342i | −0.0686388 | + | 0.207999i | ||||
\(346\) | −7.58998 | + | 2.67130i | −0.408040 | + | 0.143610i | ||||
\(347\) | 17.0322 | 0.914339 | 0.457169 | − | 0.889380i | \(-0.348863\pi\) | ||||
0.457169 | + | 0.889380i | \(0.348863\pi\) | |||||||
\(348\) | 2.33812 | + | 6.24808i | 0.125336 | + | 0.334932i | ||||
\(349\) | 18.1974 | 0.974082 | 0.487041 | − | 0.873379i | \(-0.338076\pi\) | ||||
0.487041 | + | 0.873379i | \(0.338076\pi\) | |||||||
\(350\) | −0.549375 | + | 0.193353i | −0.0293653 | + | 0.0103352i | ||||
\(351\) | 20.0504 | + | 28.4106i | 1.07021 | + | 1.51644i | ||||
\(352\) | −18.0511 | + | 2.19974i | −0.962125 | + | 0.117246i | ||||
\(353\) | 9.37154i | 0.498797i | 0.968401 | + | 0.249398i | \(0.0802329\pi\) | ||||
−0.968401 | + | 0.249398i | \(0.919767\pi\) | |||||||
\(354\) | −0.00852555 | − | 0.433400i | −0.000453128 | − | 0.0230350i | ||||
\(355\) | − | 22.1792i | − | 1.17715i | ||||||
\(356\) | −14.1290 | − | 17.5861i | −0.748838 | − | 0.932061i | ||||
\(357\) | −0.884909 | − | 0.292016i | −0.0468344 | − | 0.0154551i | ||||
\(358\) | 9.92103 | + | 28.1886i | 0.524343 | + | 1.48982i | ||||
\(359\) | −34.0837 | −1.79887 | −0.899434 | − | 0.437057i | \(-0.856021\pi\) | ||||
−0.899434 | + | 0.437057i | \(0.856021\pi\) | |||||||
\(360\) | 18.5255 | − | 7.35104i | 0.976381 | − | 0.387434i | ||||
\(361\) | 18.4815 | 0.972712 | ||||||||
\(362\) | −6.00745 | − | 17.0690i | −0.315744 | − | 0.897125i | ||||
\(363\) | 1.09587 | + | 0.361631i | 0.0575180 | + | 0.0189807i | ||||
\(364\) | −6.67581 | − | 8.30922i | −0.349908 | − | 0.435521i | ||||
\(365\) | 0.991466i | 0.0518957i | ||||||||
\(366\) | −0.323527 | − | 16.4467i | −0.0169110 | − | 0.859680i | ||||
\(367\) | 31.6260i | 1.65086i | 0.564502 | + | 0.825432i | \(0.309068\pi\) | ||||
−0.564502 | + | 0.825432i | \(0.690932\pi\) | |||||||
\(368\) | −0.861782 | + | 3.90606i | −0.0449235 | + | 0.203618i | ||||
\(369\) | −13.6386 | + | 18.4145i | −0.709999 | + | 0.958623i | ||||
\(370\) | −5.94742 | + | 2.09320i | −0.309192 | + | 0.108820i | ||||
\(371\) | −9.03155 | −0.468895 | ||||||||
\(372\) | 9.24623 | + | 24.7084i | 0.479395 | + | 1.28107i | ||||
\(373\) | −10.5471 | −0.546110 | −0.273055 | − | 0.961998i | \(-0.588034\pi\) | ||||
−0.273055 | + | 0.961998i | \(0.588034\pi\) | |||||||
\(374\) | 2.89705 | − | 1.01962i | 0.149803 | − | 0.0527233i | ||||
\(375\) | 5.71525 | − | 17.3192i | 0.295134 | − | 0.894360i | ||||
\(376\) | 2.94621 | + | 1.82895i | 0.151939 | + | 0.0943211i | ||||
\(377\) | − | 12.8878i | − | 0.663756i | ||||||
\(378\) | −4.77029 | − | 3.38987i | −0.245357 | − | 0.174356i | ||||
\(379\) | 11.3796i | 0.584531i | 0.956337 | + | 0.292265i | \(0.0944091\pi\) | ||||
−0.956337 | + | 0.292265i | \(0.905591\pi\) | |||||||
\(380\) | 2.63694 | − | 2.11858i | 0.135272 | − | 0.108681i | ||||
\(381\) | −5.84721 | + | 17.7191i | −0.299562 | + | 0.907776i | ||||
\(382\) | 3.79068 | + | 10.7705i | 0.193948 | + | 0.551065i | ||||
\(383\) | −15.0762 | −0.770360 | −0.385180 | − | 0.922842i | \(-0.625861\pi\) | ||||
−0.385180 | + | 0.922842i | \(0.625861\pi\) | |||||||
\(384\) | 17.3874 | − | 9.03760i | 0.887297 | − | 0.461198i | ||||
\(385\) | −6.01311 | −0.306456 | ||||||||
\(386\) | 2.50770 | + | 7.12514i | 0.127639 | + | 0.362660i | ||||
\(387\) | −19.7709 | + | 26.6942i | −1.00501 | + | 1.35694i | ||||
\(388\) | 11.3359 | − | 9.10753i | 0.575494 | − | 0.462365i | ||||
\(389\) | 9.20298i | 0.466610i | 0.972404 | + | 0.233305i | \(0.0749540\pi\) | ||||
−0.972404 | + | 0.233305i | \(0.925046\pi\) | |||||||
\(390\) | −38.4957 | + | 0.757260i | −1.94930 | + | 0.0383454i | ||||
\(391\) | − | 0.675569i | − | 0.0341650i | ||||||
\(392\) | −15.2973 | − | 9.49629i | −0.772631 | − | 0.479635i | ||||
\(393\) | −9.48335 | − | 3.12946i | −0.478372 | − | 0.157860i | ||||
\(394\) | 1.58998 | − | 0.559597i | 0.0801023 | − | 0.0281921i | ||||
\(395\) | 23.7828 | 1.19664 | ||||||||
\(396\) | 19.2728 | − | 0.758534i | 0.968493 | − | 0.0381178i | ||||
\(397\) | −28.5280 | −1.43178 | −0.715890 | − | 0.698214i | \(-0.753979\pi\) | ||||
−0.715890 | + | 0.698214i | \(0.753979\pi\) | |||||||
\(398\) | −32.3567 | + | 11.3880i | −1.62189 | + | 0.570827i | ||||
\(399\) | −0.943170 | − | 0.311242i | −0.0472176 | − | 0.0155816i | ||||
\(400\) | −0.445652 | + | 2.01993i | −0.0222826 | + | 0.100997i | ||||
\(401\) | − | 5.92896i | − | 0.296078i | −0.988982 | − | 0.148039i | \(-0.952704\pi\) | ||
0.988982 | − | 0.148039i | \(-0.0472961\pi\) | |||||||
\(402\) | 22.9406 | − | 0.451272i | 1.14417 | − | 0.0225074i | ||||
\(403\) | − | 50.9657i | − | 2.53878i | ||||||
\(404\) | 9.08911 | + | 11.3130i | 0.452200 | + | 0.562843i | ||||
\(405\) | −20.2215 | + | 6.16281i | −1.00481 | + | 0.306232i | ||||
\(406\) | 0.720060 | + | 2.04591i | 0.0357360 | + | 0.101537i | ||||
\(407\) | −6.10160 | −0.302445 | ||||||||
\(408\) | −2.53878 | + | 2.12321i | −0.125689 | + | 0.105115i | ||||
\(409\) | 1.37988 | 0.0682306 | 0.0341153 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341153 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(410\) | −8.42362 | − | 23.9341i | −0.416013 | − | 1.18202i | ||||
\(411\) | −7.82331 | + | 23.7073i | −0.385895 | + | 1.16940i | ||||
\(412\) | −14.5448 | − | 18.1036i | −0.716573 | − | 0.891901i | ||||
\(413\) | − | 0.140933i | − | 0.00693484i | ||||||
\(414\) | 1.25003 | − | 4.05431i | 0.0614358 | − | 0.199258i | ||||
\(415\) | − | 19.8307i | − | 0.973450i | ||||||
\(416\) | −37.5783 | + | 4.57937i | −1.84243 | + | 0.224522i | ||||
\(417\) | −6.33720 | + | 19.2039i | −0.310334 | + | 0.940419i | ||||
\(418\) | 3.08778 | − | 1.08675i | 0.151028 | − | 0.0531547i | ||||
\(419\) | −15.3755 | −0.751144 | −0.375572 | − | 0.926793i | \(-0.622554\pi\) | ||||
−0.375572 | + | 0.926793i | \(0.622554\pi\) | |||||||
\(420\) | 6.06878 | − | 2.27102i | 0.296126 | − | 0.110814i | ||||
\(421\) | 25.5241 | 1.24397 | 0.621984 | − | 0.783030i | \(-0.286327\pi\) | ||||
0.621984 | + | 0.783030i | \(0.286327\pi\) | |||||||
\(422\) | −24.4855 | + | 8.61772i | −1.19194 | + | 0.419504i | ||||
\(423\) | −2.95569 | − | 2.18912i | −0.143711 | − | 0.106439i | ||||
\(424\) | −16.9180 | + | 27.2528i | −0.821612 | + | 1.32351i | ||||
\(425\) | − | 0.349356i | − | 0.0169463i | ||||||
\(426\) | 0.454897 | + | 23.1249i | 0.0220398 | + | 1.12041i | ||||
\(427\) | − | 5.34810i | − | 0.258813i | ||||||
\(428\) | −31.1330 | + | 25.0129i | −1.50487 | + | 1.20905i | ||||
\(429\) | −35.3841 | − | 11.6766i | −1.70836 | − | 0.563750i | ||||
\(430\) | −12.2111 | − | 34.6954i | −0.588871 | − | 1.67316i | ||||
\(431\) | −17.1182 | −0.824556 | −0.412278 | − | 0.911058i | \(-0.635267\pi\) | ||||
−0.412278 | + | 0.911058i | \(0.635267\pi\) | |||||||
\(432\) | −19.1647 | + | 8.04446i | −0.922063 | + | 0.387039i | ||||
\(433\) | −31.8725 | −1.53169 | −0.765846 | − | 0.643024i | \(-0.777680\pi\) | ||||
−0.765846 | + | 0.643024i | \(0.777680\pi\) | |||||||
\(434\) | 2.84752 | + | 8.09068i | 0.136685 | + | 0.388365i | ||||
\(435\) | 7.44024 | + | 2.45524i | 0.356732 | + | 0.117720i | ||||
\(436\) | 23.1749 | − | 18.6192i | 1.10988 | − | 0.891698i | ||||
\(437\) | − | 0.720048i | − | 0.0344445i | ||||||
\(438\) | −0.0203351 | − | 1.03374i | −0.000971648 | − | 0.0493942i | ||||
\(439\) | 9.98392i | 0.476507i | 0.971203 | + | 0.238253i | \(0.0765748\pi\) | ||||
−0.971203 | + | 0.238253i | \(0.923425\pi\) | |||||||
\(440\) | −11.2638 | + | 18.1446i | −0.536982 | + | 0.865010i | ||||
\(441\) | 15.3466 | + | 11.3663i | 0.730788 | + | 0.541254i | ||||
\(442\) | 6.03102 | − | 2.12262i | 0.286866 | − | 0.100963i | ||||
\(443\) | 39.5217 | 1.87773 | 0.938866 | − | 0.344284i | \(-0.111878\pi\) | ||||
0.938866 | + | 0.344284i | \(0.111878\pi\) | |||||||
\(444\) | 6.15810 | − | 2.30444i | 0.292250 | − | 0.109364i | ||||
\(445\) | −26.4937 | −1.25592 | ||||||||
\(446\) | 35.1904 | − | 12.3853i | 1.66631 | − | 0.586461i | ||||
\(447\) | 8.15826 | − | 24.7223i | 0.385872 | − | 1.16933i | ||||
\(448\) | 5.70962 | − | 2.82652i | 0.269754 | − | 0.133540i | ||||
\(449\) | 22.2438i | 1.04975i | 0.851180 | + | 0.524875i | \(0.175888\pi\) | ||||
−0.851180 | + | 0.524875i | \(0.824112\pi\) | |||||||
\(450\) | 0.646428 | − | 2.09660i | 0.0304729 | − | 0.0988345i | ||||
\(451\) | − | 24.5545i | − | 1.15623i | ||||||
\(452\) | 14.6962 | + | 18.2920i | 0.691249 | + | 0.860381i | ||||
\(453\) | 0.356515 | − | 1.08036i | 0.0167505 | − | 0.0507599i | ||||
\(454\) | −2.90576 | − | 8.25614i | −0.136374 | − | 0.387480i | ||||
\(455\) | −12.5180 | −0.586852 | ||||||||
\(456\) | −2.70593 | + | 2.26300i | −0.126717 | + | 0.105975i | ||||
\(457\) | 12.2420 | 0.572657 | 0.286329 | − | 0.958131i | \(-0.407565\pi\) | ||||
0.286329 | + | 0.958131i | \(0.407565\pi\) | |||||||
\(458\) | 2.48016 | + | 7.04689i | 0.115890 | + | 0.329280i | ||||
\(459\) | 2.86805 | − | 2.02409i | 0.133869 | − | 0.0944764i | ||||
\(460\) | 2.94227 | + | 3.66218i | 0.137184 | + | 0.170750i | ||||
\(461\) | − | 25.1325i | − | 1.17054i | −0.810840 | − | 0.585268i | \(-0.800989\pi\) | ||
0.810840 | − | 0.585268i | \(-0.199011\pi\) | |||||||
\(462\) | 6.26952 | − | 0.123330i | 0.291684 | − | 0.00573781i | ||||
\(463\) | 22.2615i | 1.03458i | 0.855810 | + | 0.517290i | \(0.173059\pi\) | ||||
−0.855810 | + | 0.517290i | \(0.826941\pi\) | |||||||
\(464\) | 7.52237 | + | 1.65964i | 0.349217 | + | 0.0770467i | ||||
\(465\) | 29.4229 | + | 9.70942i | 1.36445 | + | 0.450264i | ||||
\(466\) | 13.4042 | − | 4.71762i | 0.620937 | − | 0.218539i | ||||
\(467\) | 10.3712 | 0.479921 | 0.239960 | − | 0.970783i | \(-0.422866\pi\) | ||||
0.239960 | + | 0.970783i | \(0.422866\pi\) | |||||||
\(468\) | 40.1217 | − | 1.57910i | 1.85462 | − | 0.0729940i | ||||
\(469\) | 7.45980 | 0.344462 | ||||||||
\(470\) | 3.84163 | − | 1.35206i | 0.177201 | − | 0.0623661i | ||||
\(471\) | 22.3878 | + | 7.38787i | 1.03158 | + | 0.340415i | ||||
\(472\) | −0.425265 | − | 0.263997i | −0.0195744 | − | 0.0121514i | ||||
\(473\) | − | 35.5949i | − | 1.63665i | ||||||
\(474\) | −24.7970 | + | 0.487789i | −1.13896 | + | 0.0224049i | ||||
\(475\) | − | 0.372357i | − | 0.0170849i | ||||||
\(476\) | −0.838816 | + | 0.673923i | −0.0384471 | + | 0.0308892i | ||||
\(477\) | 20.2496 | − | 27.3405i | 0.927165 | − | 1.25184i | ||||
\(478\) | 6.44988 | + | 18.3260i | 0.295010 | + | 0.838214i | ||||
\(479\) | 14.8914 | 0.680407 | 0.340203 | − | 0.940352i | \(-0.389504\pi\) | ||||
0.340203 | + | 0.940352i | \(0.389504\pi\) | |||||||
\(480\) | 4.51531 | − | 22.5667i | 0.206095 | − | 1.03002i | ||||
\(481\) | −12.7022 | −0.579170 | ||||||||
\(482\) | −6.87963 | − | 19.5471i | −0.313359 | − | 0.890347i | ||||
\(483\) | 0.432251 | − | 1.30987i | 0.0196681 | − | 0.0596012i | ||||
\(484\) | 1.03878 | − | 0.834582i | 0.0472174 | − | 0.0379355i | ||||
\(485\) | − | 17.0777i | − | 0.775460i | ||||||
\(486\) | 20.9573 | − | 6.84034i | 0.950644 | − | 0.310284i | ||||
\(487\) | − | 13.0830i | − | 0.592848i | −0.955056 | − | 0.296424i | \(-0.904206\pi\) | ||
0.955056 | − | 0.296424i | \(-0.0957942\pi\) | |||||||
\(488\) | −16.1379 | − | 10.0181i | −0.730530 | − | 0.453500i | ||||
\(489\) | 1.66885 | − | 5.05721i | 0.0754682 | − | 0.228695i | ||||
\(490\) | −19.9465 | + | 7.02019i | −0.901090 | + | 0.317140i | ||||
\(491\) | 33.1384 | 1.49552 | 0.747758 | − | 0.663972i | \(-0.231130\pi\) | ||||
0.747758 | + | 0.663972i | \(0.231130\pi\) | |||||||
\(492\) | 9.27371 | + | 24.7819i | 0.418091 | + | 1.11725i | ||||
\(493\) | −1.30102 | −0.0585952 | ||||||||
\(494\) | 6.42809 | − | 2.26237i | 0.289213 | − | 0.101789i | ||||
\(495\) | 13.4820 | − | 18.2030i | 0.605969 | − | 0.818165i | ||||
\(496\) | 29.7477 | + | 6.56314i | 1.33571 | + | 0.294694i | ||||
\(497\) | 7.51973i | 0.337306i | ||||||||
\(498\) | 0.406730 | + | 20.6763i | 0.0182260 | + | 0.926527i | ||||
\(499\) | 41.0462i | 1.83748i | 0.394865 | + | 0.918739i | \(0.370791\pi\) | ||||
−0.394865 | + | 0.918739i | \(0.629209\pi\) | |||||||
\(500\) | −13.1898 | − | 16.4171i | −0.589867 | − | 0.734194i | ||||
\(501\) | −7.08144 | − | 2.33684i | −0.316376 | − | 0.104402i | ||||
\(502\) | 0.233366 | + | 0.663063i | 0.0104156 | + | 0.0295940i | ||||
\(503\) | 15.3234 | 0.683239 | 0.341619 | − | 0.939838i | \(-0.389025\pi\) | ||||
0.341619 | + | 0.939838i | \(0.389025\pi\) | |||||||
\(504\) | −6.28099 | + | 2.49233i | −0.279777 | + | 0.111017i | ||||
\(505\) | 17.0432 | 0.758413 | ||||||||
\(506\) | 1.50927 | + | 4.28831i | 0.0670954 | + | 0.190638i | ||||
\(507\) | −52.2793 | − | 17.2519i | −2.32181 | − | 0.766185i | ||||
\(508\) | 13.4944 | + | 16.7961i | 0.598716 | + | 0.745207i | ||||
\(509\) | − | 15.9280i | − | 0.705996i | −0.935624 | − | 0.352998i | \(-0.885162\pi\) | ||
0.935624 | − | 0.352998i | \(-0.114838\pi\) | |||||||
\(510\) | 0.0764454 | + | 3.88614i | 0.00338506 | + | 0.172081i | ||||
\(511\) | − | 0.336151i | − | 0.0148705i | ||||||
\(512\) | 2.16629 | − | 22.5235i | 0.0957374 | − | 0.995407i | ||||
\(513\) | 3.05687 | − | 2.15735i | 0.134964 | − | 0.0952494i | ||||
\(514\) | −20.9188 | + | 7.36241i | −0.922691 | + | 0.324742i | ||||
\(515\) | −27.2734 | −1.20181 | ||||||||
\(516\) | 13.4434 | + | 35.9244i | 0.591813 | + | 1.58148i | ||||
\(517\) | 3.94122 | 0.173335 | ||||||||
\(518\) | 2.01644 | − | 0.709689i | 0.0885974 | − | 0.0311820i | ||||
\(519\) | 3.08821 | − | 9.35834i | 0.135557 | − | 0.410785i | ||||
\(520\) | −23.4488 | + | 37.7731i | −1.02830 | + | 1.65646i | ||||
\(521\) | 8.57243i | 0.375565i | 0.982211 | + | 0.187783i | \(0.0601300\pi\) | ||||
−0.982211 | + | 0.187783i | \(0.939870\pi\) | |||||||
\(522\) | −7.80786 | − | 2.40734i | −0.341741 | − | 0.105366i | ||||
\(523\) | − | 18.2693i | − | 0.798860i | −0.916764 | − | 0.399430i | \(-0.869208\pi\) | ||
0.916764 | − | 0.399430i | \(-0.130792\pi\) | |||||||
\(524\) | −8.98937 | + | 7.22226i | −0.392703 | + | 0.315506i | ||||
\(525\) | 0.223529 | − | 0.677371i | 0.00975562 | − | 0.0295629i | ||||
\(526\) | −12.9594 | − | 36.8217i | −0.565059 | − | 1.60550i | ||||
\(527\) | −5.14498 | −0.224119 | ||||||||
\(528\) | 11.3720 | − | 19.1493i | 0.494903 | − | 0.833368i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 12.5068 | + | 35.5355i | 0.543259 | + | 1.54356i | ||||
\(531\) | 0.426634 | + | 0.315984i | 0.0185143 | + | 0.0137125i | ||||
\(532\) | −0.894042 | + | 0.718293i | −0.0387616 | + | 0.0311419i | ||||
\(533\) | − | 51.1172i | − | 2.21413i | ||||||
\(534\) | 27.6235 | − | 0.543389i | 1.19538 | − | 0.0235148i | ||||
\(535\) | 46.9024i | 2.02777i | ||||||||
\(536\) | 13.9738 | − | 22.5100i | 0.603576 | − | 0.972284i | ||||
\(537\) | −34.7562 | − | 11.4694i | −1.49984 | − | 0.494940i | ||||
\(538\) | −35.5417 | + | 12.5089i | −1.53231 | + | 0.539299i | ||||
\(539\) | −20.4636 | −0.881429 | ||||||||
\(540\) | −6.73191 | + | 23.4634i | −0.289695 | + | 1.00970i | ||||
\(541\) | −7.80032 | −0.335362 | −0.167681 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167681 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(542\) | −4.06022 | + | 1.42900i | −0.174401 | + | 0.0613807i | ||||
\(543\) | 21.0458 | + | 6.94501i | 0.903162 | + | 0.298039i | ||||
\(544\) | 0.462287 | + | 3.79353i | 0.0198204 | + | 0.162646i | ||||
\(545\) | − | 34.9133i | − | 1.49552i | ||||||
\(546\) | 13.0518 | − | 0.256745i | 0.558564 | − | 0.0109877i | ||||
\(547\) | 8.69373i | 0.371717i | 0.982577 | + | 0.185859i | \(0.0595066\pi\) | ||||
−0.982577 | + | 0.185859i | \(0.940493\pi\) | |||||||
\(548\) | 18.0549 | + | 22.4725i | 0.771266 | + | 0.959976i | ||||
\(549\) | 16.1899 | + | 11.9910i | 0.690968 | + | 0.511761i | ||||
\(550\) | 0.780488 | + | 2.21760i | 0.0332801 | + | 0.0945589i | ||||
\(551\) | −1.38668 | −0.0590746 | ||||||||
\(552\) | −3.14285 | − | 3.75799i | −0.133769 | − | 0.159951i | ||||
\(553\) | −8.06345 | −0.342893 | ||||||||
\(554\) | 0.0793521 | + | 0.225463i | 0.00337135 | + | 0.00957902i | ||||
\(555\) | 2.41988 | − | 7.33308i | 0.102718 | − | 0.311272i | ||||
\(556\) | 14.6252 | + | 18.2036i | 0.620246 | + | 0.772005i | ||||
\(557\) | 15.8975i | 0.673598i | 0.941577 | + | 0.336799i | \(0.109344\pi\) | ||||
−0.941577 | + | 0.336799i | \(0.890656\pi\) | |||||||
\(558\) | −30.8767 | − | 9.51998i | −1.30711 | − | 0.403013i | ||||
\(559\) | − | 74.1007i | − | 3.13412i | ||||||
\(560\) | 1.61201 | − | 7.30650i | 0.0681199 | − | 0.308756i | ||||
\(561\) | −1.17875 | + | 3.57202i | −0.0497668 | + | 0.150811i | ||||
\(562\) | 5.62349 | − | 1.97919i | 0.237213 | − | 0.0834873i | ||||
\(563\) | 22.2168 | 0.936325 | 0.468162 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468162 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(564\) | −3.97771 | + | 1.48851i | −0.167492 | + | 0.0626776i | ||||
\(565\) | 27.5571 | 1.15934 | ||||||||
\(566\) | −4.02024 | + | 1.41493i | −0.168983 | + | 0.0594739i | ||||
\(567\) | 6.85598 | − | 2.08947i | 0.287924 | − | 0.0877494i | ||||
\(568\) | 22.6908 | + | 14.0861i | 0.952087 | + | 0.591038i | ||||
\(569\) | 2.61033i | 0.109431i | 0.998502 | + | 0.0547155i | \(0.0174252\pi\) | ||||
−0.998502 | + | 0.0547155i | \(0.982575\pi\) | |||||||
\(570\) | 0.0814784 | + | 4.14199i | 0.00341276 | + | 0.173489i | ||||
\(571\) | 17.4391i | 0.729802i | 0.931046 | + | 0.364901i | \(0.118897\pi\) | ||||
−0.931046 | + | 0.364901i | \(0.881103\pi\) | |||||||
\(572\) | −33.5409 | + | 26.9475i | −1.40242 | + | 1.12673i | ||||
\(573\) | −13.2798 | − | 4.38228i | −0.554772 | − | 0.183072i | ||||
\(574\) | 2.85599 | + | 8.11472i | 0.119207 | + | 0.338702i | ||||
\(575\) | 0.517128 | 0.0215657 | ||||||||
\(576\) | −4.24500 | + | 23.6216i | −0.176875 | + | 0.984233i | ||||
\(577\) | 31.5241 | 1.31237 | 0.656184 | − | 0.754601i | \(-0.272170\pi\) | ||||
0.656184 | + | 0.754601i | \(0.272170\pi\) | |||||||
\(578\) | 7.76729 | + | 22.0692i | 0.323077 | + | 0.917959i | ||||
\(579\) | −8.78520 | − | 2.89907i | −0.365100 | − | 0.120481i | ||||
\(580\) | 7.05269 | − | 5.66629i | 0.292847 | − | 0.235280i | ||||
\(581\) | 6.72349i | 0.278937i | ||||||||
\(582\) | 0.350267 | + | 17.8060i | 0.0145190 | + | 0.738081i | ||||
\(583\) | 36.4567i | 1.50988i | ||||||||
\(584\) | −1.01434 | − | 0.629684i | −0.0419737 | − | 0.0260565i | ||||
\(585\) | 28.0665 | − | 37.8947i | 1.16041 | − | 1.56675i | ||||
\(586\) | 12.4381 | − | 4.37762i | 0.513815 | − | 0.180838i | ||||
\(587\) | −1.18762 | −0.0490183 | −0.0245092 | − | 0.999700i | \(-0.507802\pi\) | ||||
−0.0245092 | + | 0.999700i | \(0.507802\pi\) | |||||||
\(588\) | 20.6531 | − | 7.72865i | 0.851718 | − | 0.318724i | ||||
\(589\) | −5.48372 | −0.225953 | ||||||||
\(590\) | −0.554512 | + | 0.195161i | −0.0228289 | + | 0.00803466i | ||||
\(591\) | −0.646932 | + | 1.96043i | −0.0266112 | + | 0.0806412i | ||||
\(592\) | 1.63573 | − | 7.41403i | 0.0672283 | − | 0.304715i | ||||
\(593\) | − | 1.62727i | − | 0.0668238i | −0.999442 | − | 0.0334119i | \(-0.989363\pi\) | ||
0.999442 | − | 0.0334119i | \(-0.0106373\pi\) | |||||||
\(594\) | −13.6835 | + | 19.2557i | −0.561441 | + | 0.790073i | ||||
\(595\) | 1.26369i | 0.0518062i | ||||||||
\(596\) | −18.8279 | − | 23.4346i | −0.771220 | − | 0.959918i | ||||
\(597\) | 13.1653 | − | 39.8953i | 0.538818 | − | 1.63281i | ||||
\(598\) | 3.14198 | + | 8.92731i | 0.128485 | + | 0.365065i | ||||
\(599\) | −6.10795 | −0.249564 | −0.124782 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124782 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(600\) | −1.62526 | − | 1.94336i | −0.0663508 | − | 0.0793375i | ||||
\(601\) | −31.6552 | −1.29124 | −0.645621 | − | 0.763658i | \(-0.723401\pi\) | ||||
−0.645621 | + | 0.763658i | \(0.723401\pi\) | |||||||
\(602\) | 4.14011 | + | 11.7633i | 0.168738 | + | 0.479436i | ||||
\(603\) | −16.7256 | + | 22.5825i | −0.681118 | + | 0.919629i | ||||
\(604\) | −0.822775 | − | 1.02409i | −0.0334782 | − | 0.0416696i | ||||
\(605\) | − | 1.56494i | − | 0.0636240i | ||||||
\(606\) | −17.7700 | + | 0.349558i | −0.721855 | + | 0.0141998i | ||||
\(607\) | − | 16.3567i | − | 0.663898i | −0.943297 | − | 0.331949i | \(-0.892294\pi\) | ||
0.943297 | − | 0.331949i | \(-0.107706\pi\) | |||||||
\(608\) | 0.492723 | + | 4.04329i | 0.0199826 | + | 0.163977i | ||||
\(609\) | −2.52258 | − | 0.832438i | −0.102220 | − | 0.0337321i | ||||
\(610\) | −21.0426 | + | 7.40597i | −0.851990 | + | 0.299859i | ||||
\(611\) | 8.20475 | 0.331929 | ||||||||
\(612\) | −0.159410 | − | 4.05028i | −0.00644378 | − | 0.163723i | ||||
\(613\) | 35.0612 | 1.41611 | 0.708054 | − | 0.706158i | \(-0.249573\pi\) | ||||
0.708054 | + | 0.706158i | \(0.249573\pi\) | |||||||
\(614\) | 5.59867 | − | 1.97046i | 0.225944 | − | 0.0795213i | ||||
\(615\) | 29.5104 | + | 9.73828i | 1.18997 | + | 0.392685i | ||||
\(616\) | 3.81895 | − | 6.15183i | 0.153870 | − | 0.247864i | ||||
\(617\) | 30.9142i | 1.24456i | 0.782795 | + | 0.622279i | \(0.213793\pi\) | ||||
−0.782795 | + | 0.622279i | \(0.786207\pi\) | |||||||
\(618\) | 28.4364 | − | 0.559381i | 1.14388 | − | 0.0225016i | ||||
\(619\) | 31.1753i | 1.25304i | 0.779405 | + | 0.626520i | \(0.215521\pi\) | ||||
−0.779405 | + | 0.626520i | \(0.784479\pi\) | |||||||
\(620\) | 27.8903 | − | 22.4077i | 1.12010 | − | 0.899915i | ||||
\(621\) | 2.99612 | + | 4.24538i | 0.120230 | + | 0.170361i | ||||
\(622\) | 0.740784 | + | 2.10479i | 0.0297027 | + | 0.0843944i | ||||
\(623\) | 8.98256 | 0.359879 | ||||||||
\(624\) | 23.6740 | − | 39.8647i | 0.947719 | − | 1.59587i | ||||
\(625\) | −27.3182 | −1.09273 | ||||||||
\(626\) | 3.29829 | + | 9.37143i | 0.131826 | + | 0.374558i | ||||
\(627\) | −1.25636 | + | 3.80719i | −0.0501740 | + | 0.152045i | ||||
\(628\) | 21.2216 | − | 17.0499i | 0.846836 | − | 0.680367i | ||||
\(629\) | 1.28229i | 0.0511281i | ||||||||
\(630\) | −2.33826 | + | 7.58380i | −0.0931584 | + | 0.302146i | ||||
\(631\) | − | 29.0712i | − | 1.15731i | −0.815574 | − | 0.578653i | \(-0.803578\pi\) | ||
0.815574 | − | 0.578653i | \(-0.196422\pi\) | |||||||
\(632\) | −15.1046 | + | 24.3315i | −0.600827 | + | 0.967856i | ||||
\(633\) | 9.96266 | − | 30.1903i | 0.395980 | − | 1.19996i | ||||
\(634\) | 0.106493 | − | 0.0374802i | 0.00422937 | − | 0.00148853i | ||||
\(635\) | 25.3036 | 1.00414 | ||||||||
\(636\) | −13.7689 | − | 36.7942i | −0.545972 | − | 1.45899i | ||||
\(637\) | −42.6007 | −1.68790 | ||||||||
\(638\) | 8.25850 | − | 2.90659i | 0.326957 | − | 0.115073i | ||||
\(639\) | −22.7639 | − | 16.8600i | −0.900526 | − | 0.666969i | ||||
\(640\) | −19.0278 | − | 18.5509i | −0.752139 | − | 0.733289i | ||||
\(641\) | − | 1.69974i | − | 0.0671358i | −0.999436 | − | 0.0335679i | \(-0.989313\pi\) | ||
0.999436 | − | 0.0335679i | \(-0.0106870\pi\) | |||||||
\(642\) | −0.961973 | − | 48.9024i | −0.0379661 | − | 1.93002i | ||||
\(643\) | 8.93016i | 0.352171i | 0.984375 | + | 0.176086i | \(0.0563436\pi\) | ||||
−0.984375 | + | 0.176086i | \(0.943656\pi\) | |||||||
\(644\) | −0.997563 | − | 1.24164i | −0.0393095 | − | 0.0489276i | ||||
\(645\) | 42.7789 | + | 14.1168i | 1.68442 | + | 0.555850i | ||||
\(646\) | −0.228387 | − | 0.648916i | −0.00898575 | − | 0.0255312i | ||||
\(647\) | −23.1977 | −0.911997 | −0.455999 | − | 0.889981i | \(-0.650718\pi\) | ||||
−0.455999 | + | 0.889981i | \(0.650718\pi\) | |||||||
\(648\) | 6.53773 | − | 24.6020i | 0.256826 | − | 0.966458i | ||||
\(649\) | −0.568887 | −0.0223308 | ||||||||
\(650\) | 1.62481 | + | 4.61656i | 0.0637301 | + | 0.181077i | ||||
\(651\) | −9.97569 | − | 3.29193i | −0.390978 | − | 0.129021i | ||||
\(652\) | −3.85143 | − | 4.79379i | −0.150834 | − | 0.187739i | ||||
\(653\) | 18.6140i | 0.728422i | 0.931317 | + | 0.364211i | \(0.118661\pi\) | ||||
−0.931317 | + | 0.364211i | \(0.881339\pi\) | |||||||
\(654\) | 0.716076 | + | 36.4021i | 0.0280008 | + | 1.42343i | ||||
\(655\) | 13.5426i | 0.529154i | ||||||||
\(656\) | 29.8361 | + | 6.58265i | 1.16490 | + | 0.257009i | ||||
\(657\) | 1.01761 | + | 0.753684i | 0.0397006 | + | 0.0294040i | ||||
\(658\) | −1.30248 | + | 0.458411i | −0.0507761 | + | 0.0178707i | ||||
\(659\) | −9.00688 | −0.350858 | −0.175429 | − | 0.984492i | \(-0.556131\pi\) | ||||
−0.175429 | + | 0.984492i | \(0.556131\pi\) | |||||||
\(660\) | −9.16719 | − | 24.4972i | −0.356832 | − | 0.953553i | ||||
\(661\) | 7.53200 | 0.292961 | 0.146480 | − | 0.989214i | \(-0.453205\pi\) | ||||
0.146480 | + | 0.989214i | \(0.453205\pi\) | |||||||
\(662\) | 39.3120 | − | 13.8359i | 1.52790 | − | 0.537747i | ||||
\(663\) | −2.45390 | + | 7.43616i | −0.0953015 | + | 0.288797i | ||||
\(664\) | 20.2882 | + | 12.5945i | 0.787334 | + | 0.488763i | ||||
\(665\) | 1.34689i | 0.0522301i | ||||||||
\(666\) | −2.37267 | + | 7.69541i | −0.0919390 | + | 0.298191i | ||||
\(667\) | − | 1.92582i | − | 0.0745680i | ||||||
\(668\) | −6.71258 | + | 5.39304i | −0.259718 | + | 0.208663i | ||||
\(669\) | −14.3182 | + | 43.3892i | −0.553575 | + | 1.67752i | ||||
\(670\) | −10.3302 | − | 29.3513i | −0.399091 | − | 1.13394i | ||||
\(671\) | −21.5881 | −0.833400 | ||||||||
\(672\) | −1.53089 | + | 7.65113i | −0.0590555 | + | 0.295149i | ||||
\(673\) | −18.3835 | −0.708633 | −0.354316 | − | 0.935126i | \(-0.615286\pi\) | ||||
−0.354316 | + | 0.935126i | \(0.615286\pi\) | |||||||
\(674\) | −5.79689 | − | 16.4707i | −0.223288 | − | 0.634428i | ||||
\(675\) | 1.54938 | + | 2.19540i | 0.0596357 | + | 0.0845011i | ||||
\(676\) | −49.5562 | + | 39.8145i | −1.90601 | + | 1.53133i | ||||
\(677\) | 39.7266i | 1.52682i | 0.645915 | + | 0.763409i | \(0.276476\pi\) | ||||
−0.645915 | + | 0.763409i | \(0.723524\pi\) | |||||||
\(678\) | −28.7322 | + | 0.565200i | −1.10345 | + | 0.0217064i | ||||
\(679\) | 5.79012i | 0.222204i | ||||||||
\(680\) | 3.81319 | + | 2.36716i | 0.146229 | + | 0.0907764i | ||||
\(681\) | 10.1797 | + | 3.35925i | 0.390087 | + | 0.128727i | ||||
\(682\) | 32.6588 | − | 11.4943i | 1.25057 | − | 0.440139i | ||||
\(683\) | 1.64291 | 0.0628641 | 0.0314320 | − | 0.999506i | \(-0.489993\pi\) | ||||
0.0314320 | + | 0.999506i | \(0.489993\pi\) | |||||||
\(684\) | −0.169906 | − | 4.31694i | −0.00649650 | − | 0.165062i | ||||
\(685\) | 33.8551 | 1.29354 | ||||||||
\(686\) | 14.1993 | − | 4.99745i | 0.542130 | − | 0.190803i | ||||
\(687\) | −8.68871 | − | 2.86723i | −0.331495 | − | 0.109392i | ||||
\(688\) | 43.2512 | + | 9.54237i | 1.64893 | + | 0.363799i | ||||
\(689\) | 75.8948i | 2.89136i | ||||||||
\(690\) | −5.75239 | + | 0.113157i | −0.218990 | + | 0.00430781i | ||||
\(691\) | − | 43.5396i | − | 1.65632i | −0.560489 | − | 0.828162i | \(-0.689387\pi\) | ||
0.560489 | − | 0.828162i | \(-0.310613\pi\) | |||||||
\(692\) | −7.12706 | − | 8.87087i | −0.270930 | − | 0.337220i | ||||
\(693\) | −4.57099 | + | 6.17164i | −0.173638 | + | 0.234441i | ||||
\(694\) | 7.99671 | + | 22.7211i | 0.303551 | + | 0.862480i | ||||
\(695\) | 27.4240 | 1.04025 | ||||||||
\(696\) | −7.23721 | + | 6.05256i | −0.274326 | + | 0.229422i | ||||
\(697\) | −5.16028 | −0.195459 | ||||||||
\(698\) | 8.54373 | + | 24.2753i | 0.323385 | + | 0.918835i | ||||
\(699\) | −5.45388 | + | 16.5272i | −0.206285 | + | 0.625115i | ||||
\(700\) | −0.515868 | − | 0.642088i | −0.0194980 | − | 0.0242686i | ||||
\(701\) | − | 40.8332i | − | 1.54225i | −0.636684 | − | 0.771125i | \(-0.719695\pi\) | ||
0.636684 | − | 0.771125i | \(-0.280305\pi\) | |||||||
\(702\) | −28.4861 | + | 40.0862i | −1.07514 | + | 1.51296i | ||||
\(703\) | 1.36671i | 0.0515464i | ||||||||
\(704\) | −11.4095 | − | 23.0474i | −0.430012 | − | 0.868632i | ||||
\(705\) | −1.56308 | + | 4.73667i | −0.0588689 | + | 0.178393i | ||||
\(706\) | −12.5017 | + | 4.39998i | −0.470507 | + | 0.165595i | ||||
\(707\) | −5.77841 | −0.217320 | ||||||||
\(708\) | 0.574155 | − | 0.214856i | 0.0215781 | − | 0.00807480i | ||||
\(709\) | 6.73893 | 0.253086 | 0.126543 | − | 0.991961i | \(-0.459612\pi\) | ||||
0.126543 | + | 0.991961i | \(0.459612\pi\) | |||||||
\(710\) | 29.5871 | − | 10.4132i | 1.11038 | − | 0.390801i | ||||
\(711\) | 18.0790 | − | 24.4098i | 0.678016 | − | 0.915441i | ||||
\(712\) | 16.8263 | − | 27.1049i | 0.630591 | − | 1.01580i | ||||
\(713\) | − | 7.61577i | − | 0.285213i | ||||||
\(714\) | −0.0259184 | − | 1.31758i | −0.000969973 | − | 0.0493090i | ||||
\(715\) | 50.5300i | 1.88971i | ||||||||
\(716\) | −32.9458 | + | 26.4694i | −1.23124 | + | 0.989207i | ||||
\(717\) | −22.5958 | − | 7.45649i | −0.843854 | − | 0.278468i | ||||
\(718\) | −16.0024 | − | 45.4678i | −0.597205 | − | 1.69684i | ||||
\(719\) | 16.1780 | 0.603339 | 0.301670 | − | 0.953413i | \(-0.402456\pi\) | ||||
0.301670 | + | 0.953413i | \(0.402456\pi\) | |||||||
\(720\) | 18.5041 | + | 21.2618i | 0.689608 | + | 0.792380i | ||||
\(721\) | 9.24690 | 0.344373 | ||||||||
\(722\) | 8.67716 | + | 24.6544i | 0.322930 | + | 0.917543i | ||||
\(723\) | 24.1013 | + | 7.95332i | 0.896337 | + | 0.295787i | ||||
\(724\) | 19.9495 | − | 16.0279i | 0.741419 | − | 0.595673i | ||||
\(725\) | − | 0.995895i | − | 0.0369866i | ||||||
\(726\) | 0.0320972 | + | 1.63168i | 0.00119124 | + | 0.0605572i | ||||
\(727\) | 17.7372i | 0.657836i | 0.944358 | + | 0.328918i | \(0.106684\pi\) | ||||
−0.944358 | + | 0.328918i | \(0.893316\pi\) | |||||||
\(728\) | 7.95021 | − | 12.8068i | 0.294654 | − | 0.474650i | ||||
\(729\) | −9.04648 | + | 25.4394i | −0.335055 | + | 0.942199i | ||||
\(730\) | −1.32262 | + | 0.465497i | −0.0489523 | + | 0.0172288i | ||||
\(731\) | −7.48046 | −0.276675 | ||||||||
\(732\) | 21.7880 | − | 8.15336i | 0.805308 | − | 0.301357i | ||||
\(733\) | −21.9273 | −0.809903 | −0.404951 | − | 0.914338i | \(-0.632712\pi\) | ||||
−0.404951 | + | 0.914338i | \(0.632712\pi\) | |||||||
\(734\) | −42.1892 | + | 14.8485i | −1.55723 | + | 0.548070i | ||||
\(735\) | 8.11581 | − | 24.5937i | 0.299356 | − | 0.907153i | ||||
\(736\) | −5.61531 | + | 0.684292i | −0.206983 | + | 0.0252233i | ||||
\(737\) | − | 30.1122i | − | 1.10920i | ||||||
\(738\) | −30.9685 | − | 9.54827i | −1.13997 | − | 0.351477i | ||||
\(739\) | 21.5215i | 0.791682i | 0.918319 | + | 0.395841i | \(0.129547\pi\) | ||||
−0.918319 | + | 0.395841i | \(0.870453\pi\) | |||||||
\(740\) | −5.58468 | − | 6.95111i | −0.205297 | − | 0.255528i | ||||
\(741\) | −2.61546 | + | 7.92574i | −0.0960812 | + | 0.291159i | ||||
\(742\) | −4.24035 | − | 12.0481i | −0.155668 | − | 0.442300i | ||||
\(743\) | 6.40397 | 0.234939 | 0.117469 | − | 0.993076i | \(-0.462522\pi\) | ||||
0.117469 | + | 0.993076i | \(0.462522\pi\) | |||||||
\(744\) | −28.6200 | + | 23.9352i | −1.04926 | + | 0.877508i | ||||
\(745\) | −35.3046 | −1.29346 | ||||||||
\(746\) | −4.95192 | − | 14.0699i | −0.181303 | − | 0.515136i | ||||
\(747\) | −20.3535 | − | 15.0747i | −0.744696 | − | 0.551555i | ||||
\(748\) | 2.72035 | + | 3.38596i | 0.0994660 | + | 0.123803i | ||||
\(749\) | − | 15.9020i | − | 0.581047i | ||||||
\(750\) | 25.7872 | − | 0.507268i | 0.941616 | − | 0.0185228i | ||||
\(751\) | 49.9030i | 1.82099i | 0.413525 | + | 0.910493i | \(0.364297\pi\) | ||||
−0.413525 | + | 0.910493i | \(0.635703\pi\) | |||||||
\(752\) | −1.05657 | + | 4.78896i | −0.0385292 | + | 0.174635i | ||||
\(753\) | −0.817547 | − | 0.269787i | −0.0297931 | − | 0.00983158i | ||||
\(754\) | 17.1924 | − | 6.05088i | 0.626110 | − | 0.220360i | ||||
\(755\) | −1.54281 | −0.0561484 | ||||||||
\(756\) | 2.28242 | − | 7.95515i | 0.0830108 | − | 0.289326i | ||||
\(757\) | 29.0398 | 1.05547 | 0.527735 | − | 0.849409i | \(-0.323041\pi\) | ||||
0.527735 | + | 0.849409i | \(0.323041\pi\) | |||||||
\(758\) | −15.1804 | + | 5.34277i | −0.551378 | + | 0.194058i | ||||
\(759\) | −5.28742 | − | 1.74482i | −0.191921 | − | 0.0633331i | ||||
\(760\) | 4.06424 | + | 2.52301i | 0.147426 | + | 0.0915191i | ||||
\(761\) | 26.7922i | 0.971216i | 0.874177 | + | 0.485608i | \(0.161402\pi\) | ||||
−0.874177 | + | 0.485608i | \(0.838598\pi\) | |||||||
\(762\) | −26.3826 | + | 0.518981i | −0.955741 | + | 0.0188007i | ||||
\(763\) | 11.8372i | 0.428535i | ||||||||
\(764\) | −12.5881 | + | 10.1136i | −0.455421 | + | 0.365895i | ||||
\(765\) | −3.82547 | − | 2.83331i | −0.138310 | − | 0.102439i | ||||
\(766\) | −7.07836 | − | 20.1118i | −0.255751 | − | 0.726667i | ||||
\(767\) | −1.18430 | −0.0427625 | ||||||||
\(768\) | 20.2196 | + | 18.9517i | 0.729614 | + | 0.683860i | ||||
\(769\) | −35.3787 | −1.27579 | −0.637894 | − | 0.770124i | \(-0.720194\pi\) | ||||
−0.637894 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(770\) | −2.82318 | − | 8.02151i | −0.101740 | − | 0.289075i | ||||
\(771\) | 8.51145 | − | 25.7926i | 0.306532 | − | 0.928899i | ||||
\(772\) | −8.32759 | + | 6.69057i | −0.299717 | + | 0.240799i | ||||
\(773\) | 42.2942i | 1.52122i | 0.649211 | + | 0.760608i | \(0.275099\pi\) | ||||
−0.649211 | + | 0.760608i | \(0.724901\pi\) | |||||||
\(774\) | −44.8926 | − | 13.8414i | −1.61363 | − | 0.497519i | ||||
\(775\) | − | 3.93833i | − | 0.141469i | ||||||
\(776\) | 17.4717 | + | 10.8461i | 0.627199 | + | 0.389354i | ||||
\(777\) | −0.820449 | + | 2.48624i | −0.0294334 | + | 0.0891935i | ||||
\(778\) | −12.2768 | + | 4.32084i | −0.440145 | + | 0.154910i | ||||
\(779\) | −5.50002 | −0.197059 | ||||||||
\(780\) | −19.0841 | − | 50.9978i | −0.683319 | − | 1.82601i | ||||
\(781\) | 30.3541 | 1.08616 | ||||||||
\(782\) | 0.901212 | − | 0.317183i | 0.0322273 | − | 0.0113424i | ||||
\(783\) | 8.17583 | − | 5.76999i | 0.292180 | − | 0.206203i | ||||
\(784\) | 5.48593 | − | 24.8652i | 0.195926 | − | 0.888043i | ||||
\(785\) | − | 31.9708i | − | 1.14109i | ||||||
\(786\) | −0.277761 | − | 14.1201i | −0.00990741 | − | 0.503648i | ||||
\(787\) | 1.09045i | 0.0388705i | 0.999811 | + | 0.0194352i | \(0.00618682\pi\) | ||||
−0.999811 | + | 0.0194352i | \(0.993813\pi\) | |||||||
\(788\) | 1.49301 | + | 1.85831i | 0.0531862 | + | 0.0661996i | ||||
\(789\) | 45.4006 | + | 14.9820i | 1.61631 | + | 0.533373i | ||||
\(790\) | 11.1661 | + | 31.7264i | 0.397273 | + | 1.12877i | ||||
\(791\) | −9.34310 | −0.332202 | ||||||||
\(792\) | 10.0605 | + | 25.3538i | 0.357485 | + | 0.900908i | ||||
\(793\) | −44.9417 | −1.59593 | ||||||||
\(794\) | −13.3940 | − | 38.0565i | −0.475336 | − | 1.35057i | ||||
\(795\) | −43.8147 | − | 14.4587i | −1.55395 | − | 0.512796i | ||||
\(796\) | −30.3832 | − | 37.8172i | −1.07690 | − | 1.34040i | ||||
\(797\) | 17.1558i | 0.607688i | 0.952722 | + | 0.303844i | \(0.0982702\pi\) | ||||
−0.952722 | + | 0.303844i | \(0.901730\pi\) | |||||||
\(798\) | −0.0276248 | − | 1.40432i | −0.000977909 | − | 0.0497124i | ||||
\(799\) | − | 0.828269i | − | 0.0293021i | ||||||
\(800\) | −2.90384 | + | 0.353867i | −0.102666 | + | 0.0125111i | ||||
\(801\) | −20.1398 | + | 27.1922i | −0.711603 | + | 0.960789i | ||||
\(802\) | 7.90926 | − | 2.78367i | 0.279286 | − | 0.0982949i | ||||
\(803\) | −1.35691 | −0.0478842 | ||||||||
\(804\) | 11.3727 | + | 30.3910i | 0.401085 | + | 1.07181i | ||||
\(805\) | −1.87055 | −0.0659284 | ||||||||
\(806\) | 67.9884 | − | 23.9286i | 2.39479 | − | 0.842849i | ||||
\(807\) | 14.4612 | − | 43.8224i | 0.509058 | − | 1.54262i | ||||
\(808\) | −10.8242 | + | 17.4364i | −0.380794 | + | 0.613411i | ||||
\(809\) | − | 41.0217i | − | 1.44225i | −0.692806 | − | 0.721124i | \(-0.743626\pi\) | ||
0.692806 | − | 0.721124i | \(-0.256374\pi\) | |||||||
\(810\) | −17.7153 | − | 24.0820i | −0.622451 | − | 0.846156i | ||||
\(811\) | 0.995583i | 0.0349596i | 0.999847 | + | 0.0174798i | \(0.00556428\pi\) | ||||
−0.999847 | + | 0.0174798i | \(0.994436\pi\) | |||||||
\(812\) | −2.39118 | + | 1.92113i | −0.0839139 | + | 0.0674183i | ||||
\(813\) | 1.65202 | − | 5.00619i | 0.0579388 | − | 0.175575i | ||||
\(814\) | −2.86473 | − | 8.13956i | −0.100409 | − | 0.285291i | ||||
\(815\) | −7.22192 | −0.252973 | ||||||||
\(816\) | −4.02434 | − | 2.38989i | −0.140880 | − | 0.0836629i | ||||
\(817\) | −7.97296 | −0.278939 | ||||||||
\(818\) | 0.647859 | + | 1.84076i | 0.0226519 | + | 0.0643608i | ||||
\(819\) | −9.51580 | + | 12.8480i | −0.332509 | + | 0.448945i | ||||
\(820\) | 27.9732 | − | 22.4743i | 0.976867 | − | 0.784836i | ||||
\(821\) | − | 1.60669i | − | 0.0560738i | −0.999607 | − | 0.0280369i | \(-0.991074\pi\) | ||
0.999607 | − | 0.0280369i | \(-0.00892559\pi\) | |||||||
\(822\) | −35.2988 | + | 0.694373i | −1.23119 | + | 0.0242190i | ||||
\(823\) | 19.6188i | 0.683869i | 0.939724 | + | 0.341934i | \(0.111082\pi\) | ||||
−0.939724 | + | 0.341934i | \(0.888918\pi\) | |||||||
\(824\) | 17.3214 | − | 27.9026i | 0.603420 | − | 0.972033i | ||||
\(825\) | −2.73427 | − | 0.902297i | −0.0951952 | − | 0.0314140i | ||||
\(826\) | 0.188005 | − | 0.0661684i | 0.00654151 | − | 0.00230229i | ||||
\(827\) | −22.2783 | −0.774694 | −0.387347 | − | 0.921934i | \(-0.626608\pi\) | ||||
−0.387347 | + | 0.921934i | \(0.626608\pi\) | |||||||
\(828\) | 5.99536 | − | 0.235964i | 0.208353 | − | 0.00820033i | ||||
\(829\) | 37.8163 | 1.31341 | 0.656707 | − | 0.754146i | \(-0.271949\pi\) | ||||
0.656707 | + | 0.754146i | \(0.271949\pi\) | |||||||
\(830\) | 26.4542 | − | 9.31059i | 0.918239 | − | 0.323175i | ||||
\(831\) | −0.277993 | − | 0.0917364i | −0.00964347 | − | 0.00318230i | ||||
\(832\) | −23.7521 | − | 47.9796i | −0.823455 | − | 1.66339i | ||||
\(833\) | 4.30054i | 0.149005i | ||||||||
\(834\) | −28.5934 | + | 0.562470i | −0.990109 | + | 0.0194767i | ||||
\(835\) | 10.1126i | 0.349961i | ||||||||
\(836\) | 2.89946 | + | 3.60888i | 0.100280 | + | 0.124816i | ||||
\(837\) | 32.3318 | − | 22.8178i | 1.11755 | − | 0.788699i | ||||
\(838\) | −7.21888 | − | 20.5110i | −0.249372 | − | 0.708541i | ||||
\(839\) | 9.88894 | 0.341404 | 0.170702 | − | 0.985323i | \(-0.445396\pi\) | ||||
0.170702 | + | 0.985323i | \(0.445396\pi\) | |||||||
\(840\) | 5.87887 | + | 7.02953i | 0.202840 | + | 0.242542i | ||||
\(841\) | 25.2912 | 0.872111 | ||||||||
\(842\) | 11.9837 | + | 34.0492i | 0.412985 | + | 1.17341i | ||||
\(843\) | −2.28808 | + | 6.93368i | −0.0788057 | + | 0.238809i | ||||
\(844\) | −22.9921 | − | 28.6178i | −0.791422 | − | 0.985064i | ||||
\(845\) | 74.6572i | 2.56828i | ||||||||
\(846\) | 1.53258 | − | 4.97071i | 0.0526912 | − | 0.170896i | ||||
\(847\) | 0.530586i | 0.0182312i | ||||||||
\(848\) | −44.2984 | − | 9.77341i | −1.52121 | − | 0.335620i | ||||
\(849\) | 1.63575 | − | 4.95690i | 0.0561389 | − | 0.170120i | ||||
\(850\) | 0.466042 | − | 0.164024i | 0.0159851 | − | 0.00562598i | ||||
\(851\) | −1.89808 | −0.0650654 | ||||||||
\(852\) | −30.6351 | + | 11.4641i | −1.04954 | + | 0.392753i | ||||
\(853\) | 18.9941 | 0.650345 | 0.325173 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325173 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(854\) | 7.13439 | − | 2.51096i | 0.244134 | − | 0.0859232i | ||||
\(855\) | −4.07733 | − | 3.01985i | −0.139442 | − | 0.103277i | ||||
\(856\) | −47.9844 | − | 29.7879i | −1.64007 | − | 1.01813i | ||||
\(857\) | 31.1980i | 1.06570i | 0.846208 | + | 0.532852i | \(0.178880\pi\) | ||||
−0.846208 | + | 0.532852i | \(0.821120\pi\) | |||||||
\(858\) | −1.03638 | − | 52.6847i | −0.0353813 | − | 1.79862i | ||||
\(859\) | − | 30.5041i | − | 1.04079i | −0.853927 | − | 0.520393i | \(-0.825786\pi\) | ||
0.853927 | − | 0.520393i | \(-0.174214\pi\) | |||||||
\(860\) | 40.5506 | − | 32.5793i | 1.38277 | − | 1.11094i | ||||
\(861\) | −10.0053 | − | 3.30171i | −0.340981 | − | 0.112522i | ||||
\(862\) | −8.03708 | − | 22.8358i | −0.273744 | − | 0.777789i | ||||
\(863\) | −36.1335 | −1.23000 | −0.614999 | − | 0.788528i | \(-0.710843\pi\) | ||||
−0.614999 | + | 0.788528i | \(0.710843\pi\) | |||||||
\(864\) | −19.7293 | − | 21.7889i | −0.671203 | − | 0.741274i | ||||
\(865\) | −13.3641 | −0.454393 | ||||||||
\(866\) | −14.9643 | − | 42.5180i | −0.508506 | − | 1.44482i | ||||
\(867\) | −27.2110 | − | 8.97952i | −0.924136 | − | 0.304960i | ||||
\(868\) | −9.45607 | + | 7.59721i | −0.320960 | + | 0.257866i | ||||
\(869\) | 32.5489i | 1.10414i | ||||||||
\(870\) | 0.217920 | + | 11.0781i | 0.00738818 | + | 0.375581i | ||||
\(871\) | − | 62.6869i | − | 2.12407i | ||||||
\(872\) | 35.7188 | + | 22.1736i | 1.20959 | + | 0.750892i | ||||
\(873\) | −17.5280 | − | 12.9820i | −0.593232 | − | 0.439374i | ||||
\(874\) | 0.960546 | − | 0.338065i | 0.0324910 | − | 0.0114352i | ||||
\(875\) | 8.38545 | 0.283480 | ||||||||
\(876\) | 1.36947 | − | 0.512474i | 0.0462701 | − | 0.0173149i | ||||
\(877\) | −29.8694 | −1.00862 | −0.504308 | − | 0.863524i | \(-0.668252\pi\) | ||||
−0.504308 | + | 0.863524i | \(0.668252\pi\) | |||||||
\(878\) | −13.3186 | + | 4.68749i | −0.449481 | + | 0.158195i | ||||
\(879\) | −5.06082 | + | 15.3360i | −0.170697 | + | 0.517272i | ||||
\(880\) | −29.4934 | − | 6.50703i | −0.994222 | − | 0.219352i | ||||
\(881\) | − | 18.4324i | − | 0.621003i | −0.950573 | − | 0.310501i | \(-0.899503\pi\) | ||
0.950573 | − | 0.310501i | \(-0.100497\pi\) | |||||||
\(882\) | −7.95747 | + | 25.8089i | −0.267942 | + | 0.869031i | ||||
\(883\) | − | 30.3693i | − | 1.02201i | −0.859579 | − | 0.511003i | \(-0.829274\pi\) | ||
0.859579 | − | 0.511003i | \(-0.170726\pi\) | |||||||
\(884\) | 5.66318 | + | 7.04882i | 0.190473 | + | 0.237078i | ||||
\(885\) | 0.225620 | − | 0.683706i | 0.00758412 | − | 0.0229825i | ||||
\(886\) | 18.5556 | + | 52.7221i | 0.623387 | + | 1.77123i | ||||
\(887\) | 26.0710 | 0.875377 | 0.437688 | − | 0.899127i | \(-0.355797\pi\) | ||||
0.437688 | + | 0.899127i | \(0.355797\pi\) | |||||||
\(888\) | 5.96539 | + | 7.13298i | 0.200185 | + | 0.239367i | ||||
\(889\) | −8.57907 | −0.287733 | ||||||||
\(890\) | −12.4389 | − | 35.3427i | −0.416953 | − | 1.18469i | ||||
\(891\) | −8.43433 | − | 27.6748i | −0.282561 | − | 0.927141i | ||||
\(892\) | 33.0441 | + | 41.1291i | 1.10640 | + | 1.37711i | ||||
\(893\) | − | 0.882801i | − | 0.0295418i | ||||||
\(894\) | 36.8100 | − | 0.724102i | 1.23111 | − | 0.0242176i | ||||
\(895\) | 49.6334i | 1.65906i | ||||||||
\(896\) | 6.45127 | + | 6.28959i | 0.215522 | + | 0.210120i | ||||
\(897\) | −11.0072 | − | 3.63234i | −0.367521 | − | 0.121280i | ||||
\(898\) | −29.6733 | + | 10.4436i | −0.990211 | + | 0.348506i | ||||
\(899\) | −14.6666 | −0.489159 | ||||||||
\(900\) | 3.10037 | − | 0.122024i | 0.103346 | − | 0.00406746i | ||||
\(901\) | 7.66158 | 0.255244 | ||||||||
\(902\) | 32.7558 | − | 11.5285i | 1.09065 | − | 0.383856i | ||||
\(903\) | −14.5040 | − | 4.78624i | −0.482662 | − | 0.159276i | ||||
\(904\) | −17.5016 | + | 28.1929i | −0.582095 | + | 0.937681i | ||||
\(905\) | − | 30.0543i | − | 0.999039i | ||||||
\(906\) | 1.60859 | − | 0.0316431i | 0.0534419 | − | 0.00105127i | ||||
\(907\) | 1.21466i | 0.0403321i | 0.999797 | + | 0.0201661i | \(0.00641949\pi\) | ||||
−0.999797 | + | 0.0201661i | \(0.993581\pi\) | |||||||
\(908\) | 9.64946 | − | 7.75259i | 0.320228 | − | 0.257279i | ||||
\(909\) | 12.9558 | − | 17.4925i | 0.429715 | − | 0.580191i | ||||
\(910\) | −5.87724 | − | 16.6990i | −0.194829 | − | 0.553567i | ||||
\(911\) | 27.8311 | 0.922085 | 0.461042 | − | 0.887378i | \(-0.347476\pi\) | ||||
0.461042 | + | 0.887378i | \(0.347476\pi\) | |||||||
\(912\) | −4.28930 | − | 2.54724i | −0.142033 | − | 0.0843474i | ||||
\(913\) | 27.1400 | 0.898203 | ||||||||
\(914\) | 5.74768 | + | 16.3309i | 0.190116 | + | 0.540178i | ||||
\(915\) | 8.56180 | − | 25.9452i | 0.283044 | − | 0.857723i | ||||
\(916\) | −8.23613 | + | 6.61709i | −0.272129 | + | 0.218635i | ||||
\(917\) | − | 4.59156i | − | 0.151627i | ||||||
\(918\) | 4.04670 | + | 2.87567i | 0.133561 | + | 0.0949112i | ||||
\(919\) | − | 33.8802i | − | 1.11760i | −0.829301 | − | 0.558802i | \(-0.811261\pi\) | ||
0.829301 | − | 0.558802i | \(-0.188739\pi\) | |||||||
\(920\) | −3.50395 | + | 5.64441i | −0.115522 | + | 0.186091i | ||||
\(921\) | −2.27799 | + | 6.90308i | −0.0750622 | + | 0.227464i | ||||
\(922\) | 33.5268 | − | 11.7998i | 1.10415 | − | 0.388606i | ||||
\(923\) | 63.1906 | 2.07994 | ||||||||
\(924\) | 3.10809 | + | 8.30566i | 0.102249 | + | 0.273236i | ||||
\(925\) | −0.981552 | −0.0322732 | ||||||||
\(926\) | −29.6970 | + | 10.4519i | −0.975902 | + | 0.343470i | ||||
\(927\) | −20.7324 | + | 27.9924i | −0.680942 | + | 0.919392i | ||||
\(928\) | 1.31782 | + | 10.8141i | 0.0432597 | + | 0.354989i | ||||
\(929\) | 38.5389i | 1.26442i | 0.774798 | + | 0.632209i | \(0.217852\pi\) | ||||
−0.774798 | + | 0.632209i | \(0.782148\pi\) | |||||||
\(930\) | 0.861778 | + | 43.8089i | 0.0282588 | + | 1.43655i | ||||
\(931\) | 4.58368i | 0.150224i | ||||||||
\(932\) | 12.5866 | + | 15.6663i | 0.412289 | + | 0.513166i | ||||
\(933\) | −2.59518 | − | 0.856396i | −0.0849623 | − | 0.0280372i | ||||
\(934\) | 4.86931 | + | 13.8352i | 0.159329 | + | 0.452701i | ||||
\(935\) | 5.10100 | 0.166821 | ||||||||
\(936\) | 20.9438 | + | 52.7810i | 0.684570 | + | 1.72520i | ||||
\(937\) | 31.1633 | 1.01806 | 0.509031 | − | 0.860748i | \(-0.330004\pi\) | ||||
0.509031 | + | 0.860748i | \(0.330004\pi\) | |||||||
\(938\) | 3.50241 | + | 9.95140i | 0.114358 | + | 0.324925i | ||||
\(939\) | −11.5548 | − | 3.81304i | −0.377078 | − | 0.124434i | ||||
\(940\) | 3.60732 | + | 4.48994i | 0.117658 | + | 0.146446i | ||||
\(941\) | − | 39.0601i | − | 1.27332i | −0.771143 | − | 0.636662i | \(-0.780315\pi\) | ||
0.771143 | − | 0.636662i | \(-0.219685\pi\) | |||||||
\(942\) | 0.655724 | + | 33.3340i | 0.0213646 | + | 1.08608i | ||||
\(943\) | − | 7.63841i | − | 0.248741i | ||||||
\(944\) | 0.152509 | − | 0.691253i | 0.00496374 | − | 0.0224984i | ||||
\(945\) | −5.60441 | − | 7.94121i | −0.182312 | − | 0.258328i | ||||
\(946\) | 47.4837 | − | 16.7119i | 1.54383 | − | 0.543352i | ||||
\(947\) | 51.7977 | 1.68320 | 0.841599 | − | 0.540103i | \(-0.181615\pi\) | ||||
0.841599 | + | 0.540103i | \(0.181615\pi\) | |||||||
\(948\) | −12.2930 | − | 32.8502i | −0.399258 | − | 1.06693i | ||||
\(949\) | −2.82478 | −0.0916963 | ||||||||
\(950\) | 0.496725 | − | 0.174823i | 0.0161159 | − | 0.00567201i | ||||
\(951\) | −0.0433297 | + | 0.131304i | −0.00140506 | + | 0.00425782i | ||||
\(952\) | −1.29284 | − | 0.802573i | −0.0419013 | − | 0.0260116i | ||||
\(953\) | 33.0339i | 1.07007i | 0.844829 | + | 0.535036i | \(0.179702\pi\) | ||||
−0.844829 | + | 0.535036i | \(0.820298\pi\) | |||||||
\(954\) | 45.9796 | + | 14.1765i | 1.48864 | + | 0.458983i | ||||
\(955\) | 18.9642i | 0.613666i | ||||||||
\(956\) | −21.4188 | + | 17.2083i | −0.692733 | + | 0.556557i | ||||
\(957\) | −3.36021 | + | 10.1826i | −0.108620 | + | 0.329157i | ||||
\(958\) | 6.99159 | + | 19.8652i | 0.225888 | + | 0.641816i | ||||
\(959\) | −11.4784 | −0.370657 | ||||||||
\(960\) | 32.2240 | − | 4.57173i | 1.04003 | − | 0.147552i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −5.96373 | − | 16.9448i | −0.192278 | − | 0.546321i | ||||
\(963\) | 48.1389 | + | 35.6538i | 1.55125 | + | 1.14893i | ||||
\(964\) | 22.8459 | − | 18.3549i | 0.735817 | − | 0.591172i | ||||
\(965\) | 12.5456i | 0.403859i | ||||||||
\(966\) | 1.95032 | − | 0.0383653i | 0.0627504 | − | 0.00123438i | ||||
\(967\) | 1.66263i | 0.0534665i | 0.999643 | + | 0.0267332i | \(0.00851047\pi\) | ||||
−0.999643 | + | 0.0267332i | \(0.991490\pi\) | |||||||
\(968\) | 1.60105 | + | 0.993902i | 0.0514597 | + | 0.0319452i | ||||
\(969\) | 0.800104 | + | 0.264030i | 0.0257030 | + | 0.00848188i | ||||
\(970\) | 22.7818 | − | 8.01807i | 0.731479 | − | 0.257445i | ||||
\(971\) | −48.4858 | −1.55598 | −0.777991 | − | 0.628275i | \(-0.783761\pi\) | ||||
−0.777991 | + | 0.628275i | \(0.783761\pi\) | |||||||
\(972\) | 18.9646 | + | 24.7456i | 0.608290 | + | 0.793715i | ||||
\(973\) | −9.29797 | −0.298079 | ||||||||
\(974\) | 17.4528 | − | 6.14254i | 0.559224 | − | 0.196820i | ||||
\(975\) | −5.69216 | − | 1.87838i | −0.182295 | − | 0.0601564i | ||||
\(976\) | 5.78740 | − | 26.2316i | 0.185250 | − | 0.839654i | ||||
\(977\) | 39.7689i | 1.27232i | 0.771557 | + | 0.636160i | \(0.219478\pi\) | ||||
−0.771557 | + | 0.636160i | \(0.780522\pi\) | |||||||
\(978\) | 7.52987 | − | 0.148122i | 0.240779 | − | 0.00473643i | ||||
\(979\) | − | 36.2589i | − | 1.15884i | ||||||
\(980\) | −18.7299 | − | 23.3127i | −0.598305 | − | 0.744696i | ||||
\(981\) | −35.8338 | − | 26.5401i | −1.14408 | − | 0.847360i | ||||
\(982\) | 15.5586 | + | 44.2068i | 0.496496 | + | 1.41069i | ||||
\(983\) | 11.2968 | 0.360313 | 0.180156 | − | 0.983638i | \(-0.442340\pi\) | ||||
0.180156 | + | 0.983638i | \(0.442340\pi\) | |||||||
\(984\) | −28.7051 | + | 24.0064i | −0.915085 | + | 0.765295i | ||||
\(985\) | 2.79958 | 0.0892019 | ||||||||
\(986\) | −0.610836 | − | 1.73557i | −0.0194530 | − | 0.0552719i | ||||
\(987\) | 0.529954 | − | 1.60594i | 0.0168686 | − | 0.0511178i | ||||
\(988\) | 6.03603 | + | 7.51290i | 0.192032 | + | 0.239017i | ||||
\(989\) | − | 11.0728i | − | 0.352095i | ||||||
\(990\) | 30.6127 | + | 9.43859i | 0.972936 | + | 0.299978i | ||||
\(991\) | 9.26312i | 0.294253i | 0.989118 | + | 0.147126i | \(0.0470024\pi\) | ||||
−0.989118 | + | 0.147126i | \(0.952998\pi\) | |||||||
\(992\) | 5.21141 | + | 42.7650i | 0.165463 | + | 1.35779i | ||||
\(993\) | −15.9952 | + | 48.4711i | −0.507593 | + | 1.53818i | ||||
\(994\) | −10.0313 | + | 3.53055i | −0.318175 | + | 0.111982i | ||||
\(995\) | −56.9722 | −1.80614 | ||||||||
\(996\) | −27.3913 | + | 10.2502i | −0.867926 | + | 0.324790i | ||||
\(997\) | −6.05016 | −0.191610 | −0.0958052 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958052 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(998\) | −54.7557 | + | 19.2713i | −1.73326 | + | 0.610024i | ||||
\(999\) | −5.68689 | − | 8.05808i | −0.179925 | − | 0.254946i |
(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 | 276.2.c.b.47.14 | yes | 22 | |
3.2 | odd | 2 | 276.2.c.a.47.9 | ✓ | 22 | ||
4.3 | odd | 2 | 276.2.c.a.47.10 | yes | 22 | ||
12.11 | even | 2 | inner | 276.2.c.b.47.13 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.c.a.47.9 | ✓ | 22 | 3.2 | odd | 2 | ||
276.2.c.a.47.10 | yes | 22 | 4.3 | odd | 2 | ||
276.2.c.b.47.13 | yes | 22 | 12.11 | even | 2 | inner | |
276.2.c.b.47.14 | yes | 22 | 1.1 | even | 1 | trivial |