Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.3636603.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(0.715814 + 1.86751i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.n.811.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −2.25941 | − | 3.91341i | −0.853976 | − | 1.47913i | −0.877592 | − | 0.479409i | \(-0.840851\pi\) |
0.0236156 | − | 0.999721i | \(-0.492482\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 1.93163 | − | 3.34568i | 0.582407 | − | 1.00876i | −0.412786 | − | 0.910828i | \(-0.635444\pi\) |
0.995193 | − | 0.0979312i | \(-0.0312225\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −3.51882 | + | 6.09477i | −0.975944 | + | 1.69038i | −0.299161 | + | 0.954203i | \(0.596707\pi\) |
−0.676784 | + | 0.736182i | \(0.736627\pi\) | |||||||
\(14\) | 2.25941 | + | 3.91341i | 0.603852 | + | 1.04590i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.240592 | − | 0.416717i | −0.0583520 | − | 0.101069i | 0.835374 | − | 0.549682i | \(-0.185251\pi\) |
−0.893726 | + | 0.448614i | \(0.851918\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 3.95044 | + | 6.84237i | 0.906294 | + | 1.56975i | 0.819171 | + | 0.573550i | \(0.194434\pi\) |
0.0871232 | + | 0.996198i | \(0.472233\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 2.25941 | − | 3.91341i | 0.493043 | − | 0.853976i | ||||
\(22\) | −1.93163 | + | 3.34568i | −0.411824 | + | 0.713301i | ||||
\(23\) | 5.51882 | 1.15075 | 0.575376 | − | 0.817889i | \(-0.304856\pi\) | ||||
0.575376 | + | 0.817889i | \(0.304856\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 3.51882 | − | 6.09477i | 0.690097 | − | 1.19528i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.25941 | − | 3.91341i | −0.426988 | − | 0.739565i | ||||
\(29\) | 9.38207 | 1.74221 | 0.871103 | − | 0.491100i | \(-0.163405\pi\) | ||||
0.871103 | + | 0.491100i | \(0.163405\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 5.12266 | − | 2.18136i | 0.920057 | − | 0.391784i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.86325 | 0.672506 | ||||||||
\(34\) | 0.240592 | + | 0.416717i | 0.0412611 | + | 0.0714664i | ||||
\(35\) | 4.51882 | 0.763819 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 1.24059 | + | 2.14877i | 0.203952 | + | 0.353255i | 0.949798 | − | 0.312863i | \(-0.101288\pi\) |
−0.745846 | + | 0.666118i | \(0.767955\pi\) | |||||||
\(38\) | −3.95044 | − | 6.84237i | −0.640847 | − | 1.10998i | ||||
\(39\) | −7.03763 | −1.12692 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −4.08719 | + | 7.07922i | −0.638312 | + | 1.10559i | 0.347491 | + | 0.937683i | \(0.387034\pi\) |
−0.985803 | + | 0.167905i | \(0.946300\pi\) | |||||||
\(42\) | −2.25941 | + | 3.91341i | −0.348634 | + | 0.603852i | ||||
\(43\) | 2.19104 | + | 3.79498i | 0.334130 | + | 0.578730i | 0.983317 | − | 0.181899i | \(-0.0582243\pi\) |
−0.649188 | + | 0.760628i | \(0.724891\pi\) | |||||||
\(44\) | 1.93163 | − | 3.34568i | 0.291204 | − | 0.504380i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | −5.51882 | −0.813705 | ||||||||
\(47\) | 10.5565 | 1.53982 | 0.769908 | − | 0.638155i | \(-0.220302\pi\) | ||||
0.769908 | + | 0.638155i | \(0.220302\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −6.70985 | + | 11.6218i | −0.958550 | + | 1.66026i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | 0.240592 | − | 0.416717i | 0.0336896 | − | 0.0583520i | ||||
\(52\) | −3.51882 | + | 6.09477i | −0.487972 | + | 0.845192i | ||||
\(53\) | 0.827781 | − | 1.43376i | 0.113704 | − | 0.196942i | −0.803557 | − | 0.595228i | \(-0.797062\pi\) |
0.917261 | + | 0.398286i | \(0.130395\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.93163 | + | 3.34568i | 0.260461 | + | 0.451131i | ||||
\(56\) | 2.25941 | + | 3.91341i | 0.301926 | + | 0.522951i | ||||
\(57\) | −3.95044 | + | 6.84237i | −0.523249 | + | 0.906294i | ||||
\(58\) | −9.38207 | −1.23193 | ||||||||
\(59\) | −6.77823 | − | 11.7402i | −0.882450 | − | 1.52845i | −0.848609 | − | 0.529021i | \(-0.822559\pi\) |
−0.0338407 | − | 0.999427i | \(-0.510774\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.90089 | 0.755531 | 0.377766 | − | 0.925901i | \(-0.376693\pi\) | ||||
0.377766 | + | 0.925901i | \(0.376693\pi\) | |||||||
\(62\) | −5.12266 | + | 2.18136i | −0.650579 | + | 0.277033i | ||||
\(63\) | 4.51882 | 0.569317 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.51882 | − | 6.09477i | −0.436455 | − | 0.755963i | ||||
\(66\) | −3.86325 | −0.475534 | ||||||||
\(67\) | −1.24059 | + | 2.14877i | −0.151562 | + | 0.262514i | −0.931802 | − | 0.362967i | \(-0.881764\pi\) |
0.780240 | + | 0.625481i | \(0.215097\pi\) | |||||||
\(68\) | −0.240592 | − | 0.416717i | −0.0291760 | − | 0.0505344i | ||||
\(69\) | 2.75941 | + | 4.77944i | 0.332194 | + | 0.575376i | ||||
\(70\) | −4.51882 | −0.540102 | ||||||||
\(71\) | −1.51882 | + | 2.63067i | −0.180250 | + | 0.312203i | −0.941966 | − | 0.335709i | \(-0.891024\pi\) |
0.761715 | + | 0.647912i | \(0.224357\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | −1.24059 | − | 2.14877i | −0.144216 | − | 0.249789i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 3.95044 | + | 6.84237i | 0.453147 | + | 0.784874i | ||||
\(77\) | −17.4573 | −1.98945 | ||||||||
\(78\) | 7.03763 | 0.796855 | ||||||||
\(79\) | 2.19104 | + | 3.79498i | 0.246511 | + | 0.426969i | 0.962555 | − | 0.271085i | \(-0.0873826\pi\) |
−0.716045 | + | 0.698055i | \(0.754049\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.08719 | − | 7.07922i | 0.451355 | − | 0.781769i | ||||
\(83\) | 0.603846 | − | 1.04589i | 0.0662807 | − | 0.114802i | −0.830981 | − | 0.556301i | \(-0.812220\pi\) |
0.897261 | + | 0.441500i | \(0.145553\pi\) | |||||||
\(84\) | 2.25941 | − | 3.91341i | 0.246522 | − | 0.426988i | ||||
\(85\) | 0.481183 | 0.0521917 | ||||||||
\(86\) | −2.19104 | − | 3.79498i | −0.236265 | − | 0.409224i | ||||
\(87\) | 4.69104 | + | 8.12511i | 0.502932 | + | 0.871103i | ||||
\(88\) | −1.93163 | + | 3.34568i | −0.205912 | + | 0.356650i | ||||
\(89\) | −2.96237 | −0.314010 | −0.157005 | − | 0.987598i | \(-0.550184\pi\) | ||||
−0.157005 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 31.8018 | 3.33373 | ||||||||
\(92\) | 5.51882 | 0.575376 | ||||||||
\(93\) | 4.45044 | + | 3.34568i | 0.461490 | + | 0.346930i | ||||
\(94\) | −10.5565 | −1.08881 | ||||||||
\(95\) | −7.90089 | −0.810614 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −11.4573 | −1.16332 | −0.581658 | − | 0.813433i | \(-0.697596\pi\) | ||||
−0.581658 | + | 0.813433i | \(0.697596\pi\) | |||||||
\(98\) | 6.70985 | − | 11.6218i | 0.677797 | − | 1.17398i | ||||
\(99\) | 1.93163 | + | 3.34568i | 0.194136 | + | 0.336253i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 9.76414 | 0.971568 | 0.485784 | − | 0.874079i | \(-0.338534\pi\) | ||||
0.485784 | + | 0.874079i | \(0.338534\pi\) | |||||||
\(102\) | −0.240592 | + | 0.416717i | −0.0238221 | + | 0.0412611i | ||||
\(103\) | −7.77823 | + | 13.4723i | −0.766411 | + | 1.32746i | 0.173086 | + | 0.984907i | \(0.444626\pi\) |
−0.939497 | + | 0.342557i | \(0.888707\pi\) | |||||||
\(104\) | 3.51882 | − | 6.09477i | 0.345048 | − | 0.597641i | ||||
\(105\) | 2.25941 | + | 3.91341i | 0.220496 | + | 0.381910i | ||||
\(106\) | −0.827781 | + | 1.43376i | −0.0804012 | + | 0.139259i | ||||
\(107\) | −2.25941 | − | 3.91341i | −0.218425 | − | 0.378324i | 0.735901 | − | 0.677089i | \(-0.236759\pi\) |
−0.954327 | + | 0.298765i | \(0.903425\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.90089 | 0.756768 | 0.378384 | − | 0.925649i | \(-0.376480\pi\) | ||||
0.378384 | + | 0.925649i | \(0.376480\pi\) | |||||||
\(110\) | −1.93163 | − | 3.34568i | −0.184173 | − | 0.318998i | ||||
\(111\) | −1.24059 | + | 2.14877i | −0.117752 | + | 0.203952i | ||||
\(112\) | −2.25941 | − | 3.91341i | −0.213494 | − | 0.369782i | ||||
\(113\) | 3.70985 | − | 6.42565i | 0.348994 | − | 0.604475i | −0.637077 | − | 0.770800i | \(-0.719857\pi\) |
0.986071 | + | 0.166325i | \(0.0531902\pi\) | |||||||
\(114\) | 3.95044 | − | 6.84237i | 0.369993 | − | 0.640847i | ||||
\(115\) | −2.75941 | + | 4.77944i | −0.257316 | + | 0.445685i | ||||
\(116\) | 9.38207 | 0.871103 | ||||||||
\(117\) | −3.51882 | − | 6.09477i | −0.325315 | − | 0.563462i | ||||
\(118\) | 6.77823 | + | 11.7402i | 0.623986 | + | 1.08078i | ||||
\(119\) | −1.08719 | + | 1.88307i | −0.0996625 | + | 0.172621i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −1.96237 | − | 3.39892i | −0.178397 | − | 0.308993i | ||||
\(122\) | −5.90089 | −0.534241 | ||||||||
\(123\) | −8.17438 | −0.737059 | ||||||||
\(124\) | 5.12266 | − | 2.18136i | 0.460029 | − | 0.195892i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.51882 | −0.402568 | ||||||||
\(127\) | 1.60385 | + | 2.77794i | 0.142318 | + | 0.246503i | 0.928369 | − | 0.371659i | \(-0.121211\pi\) |
−0.786051 | + | 0.618162i | \(0.787878\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.19104 | + | 3.79498i | −0.192910 | + | 0.334130i | ||||
\(130\) | 3.51882 | + | 6.09477i | 0.308621 | + | 0.534547i | ||||
\(131\) | 3.32778 | + | 5.76389i | 0.290750 | + | 0.503593i | 0.973987 | − | 0.226603i | \(-0.0727620\pi\) |
−0.683238 | + | 0.730196i | \(0.739429\pi\) | |||||||
\(132\) | 3.86325 | 0.336253 | ||||||||
\(133\) | 17.8513 | − | 30.9194i | 1.54791 | − | 2.68105i | ||||
\(134\) | 1.24059 | − | 2.14877i | 0.107171 | − | 0.185625i | ||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0.240592 | + | 0.416717i | 0.0206306 | + | 0.0357332i | ||||
\(137\) | 2.41497 | − | 4.18285i | 0.206325 | − | 0.357365i | −0.744229 | − | 0.667924i | \(-0.767183\pi\) |
0.950554 | + | 0.310559i | \(0.100516\pi\) | |||||||
\(138\) | −2.75941 | − | 4.77944i | −0.234896 | − | 0.406853i | ||||
\(139\) | 8.86325 | 0.751771 | 0.375886 | − | 0.926666i | \(-0.377339\pi\) | ||||
0.375886 | + | 0.926666i | \(0.377339\pi\) | |||||||
\(140\) | 4.51882 | 0.381910 | ||||||||
\(141\) | 5.27823 | + | 9.14215i | 0.444507 | + | 0.769908i | ||||
\(142\) | 1.51882 | − | 2.63067i | 0.127456 | − | 0.220761i | ||||
\(143\) | 13.5941 | + | 23.5456i | 1.13679 | + | 1.96899i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −4.69104 | + | 8.12511i | −0.389569 | + | 0.674754i | ||||
\(146\) | −1.00000 | + | 1.73205i | −0.0827606 | + | 0.143346i | ||||
\(147\) | −13.4197 | −1.10684 | ||||||||
\(148\) | 1.24059 | + | 2.14877i | 0.101976 | + | 0.176628i | ||||
\(149\) | 7.82778 | + | 13.5581i | 0.641277 | + | 1.11072i | 0.985148 | + | 0.171707i | \(0.0549283\pi\) |
−0.343871 | + | 0.939017i | \(0.611738\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −14.9009 | −1.21262 | −0.606309 | − | 0.795230i | \(-0.707350\pi\) | ||||
−0.606309 | + | 0.795230i | \(0.707350\pi\) | |||||||
\(152\) | −3.95044 | − | 6.84237i | −0.320423 | − | 0.554989i | ||||
\(153\) | 0.481183 | 0.0389014 | ||||||||
\(154\) | 17.4573 | 1.40675 | ||||||||
\(155\) | −0.672219 | + | 5.52704i | −0.0539939 | + | 0.443942i | ||||
\(156\) | −7.03763 | −0.563462 | ||||||||
\(157\) | 2.44787 | 0.195361 | 0.0976807 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976807 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(158\) | −2.19104 | − | 3.79498i | −0.174309 | − | 0.301913i | ||||
\(159\) | 1.65556 | 0.131295 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −12.4693 | − | 21.5974i | −0.982715 | − | 1.70211i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −21.3206 | −1.66996 | −0.834979 | − | 0.550282i | \(-0.814520\pi\) | ||||
−0.834979 | + | 0.550282i | \(0.814520\pi\) | |||||||
\(164\) | −4.08719 | + | 7.07922i | −0.319156 | + | 0.552794i | ||||
\(165\) | −1.93163 | + | 3.34568i | −0.150377 | + | 0.260461i | ||||
\(166\) | −0.603846 | + | 1.04589i | −0.0468675 | + | 0.0811769i | ||||
\(167\) | 4.29488 | + | 7.43895i | 0.332348 | + | 0.575643i | 0.982972 | − | 0.183757i | \(-0.0588259\pi\) |
−0.650624 | + | 0.759400i | \(0.725493\pi\) | |||||||
\(168\) | −2.25941 | + | 3.91341i | −0.174317 | + | 0.301926i | ||||
\(169\) | −18.2641 | − | 31.6344i | −1.40493 | − | 2.43342i | ||||
\(170\) | −0.481183 | −0.0369051 | ||||||||
\(171\) | −7.90089 | −0.604196 | ||||||||
\(172\) | 2.19104 | + | 3.79498i | 0.167065 | + | 0.289365i | ||||
\(173\) | 2.69104 | − | 4.66101i | 0.204596 | − | 0.354370i | −0.745408 | − | 0.666608i | \(-0.767745\pi\) |
0.950004 | + | 0.312238i | \(0.101079\pi\) | |||||||
\(174\) | −4.69104 | − | 8.12511i | −0.355626 | − | 0.615963i | ||||
\(175\) | −2.25941 | + | 3.91341i | −0.170795 | + | 0.295826i | ||||
\(176\) | 1.93163 | − | 3.34568i | 0.145602 | − | 0.252190i | ||||
\(177\) | 6.77823 | − | 11.7402i | 0.509483 | − | 0.882450i | ||||
\(178\) | 2.96237 | 0.222039 | ||||||||
\(179\) | −6.10601 | − | 10.5759i | −0.456384 | − | 0.790481i | 0.542382 | − | 0.840132i | \(-0.317522\pi\) |
−0.998767 | + | 0.0496509i | \(0.984189\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 5.38207 | − | 9.32202i | 0.400046 | − | 0.692900i | −0.593685 | − | 0.804698i | \(-0.702327\pi\) |
0.993731 | + | 0.111797i | \(0.0356607\pi\) | |||||||
\(182\) | −31.8018 | −2.35730 | ||||||||
\(183\) | 2.95044 | + | 5.11032i | 0.218103 | + | 0.377766i | ||||
\(184\) | −5.51882 | −0.406853 | ||||||||
\(185\) | −2.48118 | −0.182420 | ||||||||
\(186\) | −4.45044 | − | 3.34568i | −0.326322 | − | 0.245317i | ||||
\(187\) | −1.85893 | −0.135939 | ||||||||
\(188\) | 10.5565 | 0.769908 | ||||||||
\(189\) | 2.25941 | + | 3.91341i | 0.164348 | + | 0.284659i | ||||
\(190\) | 7.90089 | 0.573191 | ||||||||
\(191\) | −4.95044 | + | 8.57442i | −0.358202 | + | 0.620423i | −0.987660 | − | 0.156611i | \(-0.949943\pi\) |
0.629459 | + | 0.777034i | \(0.283277\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −10.6910 | − | 18.5174i | −0.769558 | − | 1.33291i | −0.937803 | − | 0.347168i | \(-0.887143\pi\) |
0.168245 | − | 0.985745i | \(-0.446190\pi\) | |||||||
\(194\) | 11.4573 | 0.822589 | ||||||||
\(195\) | 3.51882 | − | 6.09477i | 0.251988 | − | 0.436455i | ||||
\(196\) | −6.70985 | + | 11.6218i | −0.479275 | + | 0.830129i | ||||
\(197\) | −3.65556 | + | 6.33162i | −0.260448 | + | 0.451109i | −0.966361 | − | 0.257189i | \(-0.917204\pi\) |
0.705913 | + | 0.708299i | \(0.250537\pi\) | |||||||
\(198\) | −1.93163 | − | 3.34568i | −0.137275 | − | 0.237767i | ||||
\(199\) | −1.39615 | + | 2.41821i | −0.0989707 | + | 0.171422i | −0.911259 | − | 0.411834i | \(-0.864888\pi\) |
0.812288 | + | 0.583256i | \(0.198222\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −2.48118 | −0.175009 | ||||||||
\(202\) | −9.76414 | −0.687003 | ||||||||
\(203\) | −21.1979 | − | 36.7159i | −1.48780 | − | 2.57695i | ||||
\(204\) | 0.240592 | − | 0.416717i | 0.0168448 | − | 0.0291760i | ||||
\(205\) | −4.08719 | − | 7.07922i | −0.285462 | − | 0.494434i | ||||
\(206\) | 7.77823 | − | 13.4723i | 0.541935 | − | 0.938658i | ||||
\(207\) | −2.75941 | + | 4.77944i | −0.191792 | + | 0.332194i | ||||
\(208\) | −3.51882 | + | 6.09477i | −0.243986 | + | 0.422596i | ||||
\(209\) | 30.5231 | 2.11133 | ||||||||
\(210\) | −2.25941 | − | 3.91341i | −0.155914 | − | 0.270051i | ||||
\(211\) | 0.0495562 | + | 0.0858338i | 0.00341159 | + | 0.00590905i | 0.867726 | − | 0.497043i | \(-0.165581\pi\) |
−0.864315 | + | 0.502952i | \(0.832247\pi\) | |||||||
\(212\) | 0.827781 | − | 1.43376i | 0.0568522 | − | 0.0984710i | ||||
\(213\) | −3.03763 | −0.208135 | ||||||||
\(214\) | 2.25941 | + | 3.91341i | 0.154450 | + | 0.267515i | ||||
\(215\) | −4.38207 | −0.298855 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −20.1107 | − | 15.1185i | −1.36521 | − | 1.02631i | ||||
\(218\) | −7.90089 | −0.535116 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 1.93163 | + | 3.34568i | 0.130230 | + | 0.225565i | ||||
\(221\) | 3.38639 | 0.227793 | ||||||||
\(222\) | 1.24059 | − | 2.14877i | 0.0832631 | − | 0.144216i | ||||
\(223\) | 8.12266 | + | 14.0689i | 0.543934 | + | 0.942121i | 0.998673 | + | 0.0514963i | \(0.0163990\pi\) |
−0.454739 | + | 0.890625i | \(0.650268\pi\) | |||||||
\(224\) | 2.25941 | + | 3.91341i | 0.150963 | + | 0.261476i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.70985 | + | 6.42565i | −0.246776 | + | 0.427428i | ||||
\(227\) | 5.64148 | − | 9.77133i | 0.374438 | − | 0.648546i | −0.615805 | − | 0.787899i | \(-0.711169\pi\) |
0.990243 | + | 0.139353i | \(0.0445023\pi\) | |||||||
\(228\) | −3.95044 | + | 6.84237i | −0.261625 | + | 0.453147i | ||||
\(229\) | −5.33251 | − | 9.23619i | −0.352382 | − | 0.610344i | 0.634284 | − | 0.773100i | \(-0.281295\pi\) |
−0.986666 | + | 0.162756i | \(0.947962\pi\) | |||||||
\(230\) | 2.75941 | − | 4.77944i | 0.181950 | − | 0.315147i | ||||
\(231\) | −8.72867 | − | 15.1185i | −0.574304 | − | 0.994724i | ||||
\(232\) | −9.38207 | −0.615963 | ||||||||
\(233\) | 6.48118 | 0.424596 | 0.212298 | − | 0.977205i | \(-0.431905\pi\) | ||||
0.212298 | + | 0.977205i | \(0.431905\pi\) | |||||||
\(234\) | 3.51882 | + | 6.09477i | 0.230032 | + | 0.398428i | ||||
\(235\) | −5.27823 | + | 9.14215i | −0.344313 | + | 0.596368i | ||||
\(236\) | −6.77823 | − | 11.7402i | −0.441225 | − | 0.764224i | ||||
\(237\) | −2.19104 | + | 3.79498i | −0.142323 | + | 0.246511i | ||||
\(238\) | 1.08719 | − | 1.88307i | 0.0704720 | − | 0.122061i | ||||
\(239\) | 10.3821 | − | 17.9823i | 0.671560 | − | 1.16318i | −0.305901 | − | 0.952063i | \(-0.598958\pi\) |
0.977462 | − | 0.211113i | \(-0.0677089\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 9.82778 | + | 17.0222i | 0.633063 | + | 1.09650i | 0.986922 | + | 0.161199i | \(0.0515360\pi\) |
−0.353859 | + | 0.935299i | \(0.615131\pi\) | |||||||
\(242\) | 1.96237 | + | 3.39892i | 0.126146 | + | 0.218491i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 5.90089 | 0.377766 | ||||||||
\(245\) | −6.70985 | − | 11.6218i | −0.428677 | − | 0.742490i | ||||
\(246\) | 8.17438 | 0.521179 | ||||||||
\(247\) | −55.6036 | −3.53797 | ||||||||
\(248\) | −5.12266 | + | 2.18136i | −0.325289 | + | 0.138516i | ||||
\(249\) | 1.20769 | 0.0765344 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0.191035 | + | 0.330883i | 0.0120581 | + | 0.0208852i | 0.871991 | − | 0.489521i | \(-0.162828\pi\) |
−0.859933 | + | 0.510406i | \(0.829495\pi\) | |||||||
\(252\) | 4.51882 | 0.284659 | ||||||||
\(253\) | 10.6603 | − | 18.4642i | 0.670207 | − | 1.16083i | ||||
\(254\) | −1.60385 | − | 2.77794i | −0.100634 | − | 0.174304i | ||||
\(255\) | 0.240592 | + | 0.416717i | 0.0150664 | + | 0.0260958i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.4859 | + | 18.1621i | −0.654094 | + | 1.13292i | 0.328027 | + | 0.944668i | \(0.393616\pi\) |
−0.982120 | + | 0.188255i | \(0.939717\pi\) | |||||||
\(258\) | 2.19104 | − | 3.79498i | 0.136408 | − | 0.236265i | ||||
\(259\) | 5.60601 | − | 9.70989i | 0.348340 | − | 0.603343i | ||||
\(260\) | −3.51882 | − | 6.09477i | −0.218228 | − | 0.377982i | ||||
\(261\) | −4.69104 | + | 8.12511i | −0.290368 | + | 0.502932i | ||||
\(262\) | −3.32778 | − | 5.76389i | −0.205591 | − | 0.356094i | ||||
\(263\) | 2.38207 | 0.146885 | 0.0734424 | − | 0.997299i | \(-0.476601\pi\) | ||||
0.0734424 | + | 0.997299i | \(0.476601\pi\) | |||||||
\(264\) | −3.86325 | −0.237767 | ||||||||
\(265\) | 0.827781 | + | 1.43376i | 0.0508502 | + | 0.0880751i | ||||
\(266\) | −17.8513 | + | 30.9194i | −1.09454 | + | 1.89579i | ||||
\(267\) | −1.48118 | − | 2.56548i | −0.0906469 | − | 0.157005i | ||||
\(268\) | −1.24059 | + | 2.14877i | −0.0757812 | + | 0.131257i | ||||
\(269\) | −9.36541 | + | 16.2214i | −0.571019 | + | 0.989035i | 0.425442 | + | 0.904986i | \(0.360119\pi\) |
−0.996462 | + | 0.0840490i | \(0.973215\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −7.82994 | −0.475635 | −0.237818 | − | 0.971310i | \(-0.576432\pi\) | ||||
−0.237818 | + | 0.971310i | \(0.576432\pi\) | |||||||
\(272\) | −0.240592 | − | 0.416717i | −0.0145880 | − | 0.0252672i | ||||
\(273\) | 15.9009 | + | 27.5411i | 0.962365 | + | 1.66687i | ||||
\(274\) | −2.41497 | + | 4.18285i | −0.145894 | + | 0.252695i | ||||
\(275\) | −3.86325 | −0.232963 | ||||||||
\(276\) | 2.75941 | + | 4.77944i | 0.166097 | + | 0.287688i | ||||
\(277\) | −14.2077 | −0.853657 | −0.426829 | − | 0.904332i | \(-0.640369\pi\) | ||||
−0.426829 | + | 0.904332i | \(0.640369\pi\) | |||||||
\(278\) | −8.86325 | −0.531583 | ||||||||
\(279\) | −0.672219 | + | 5.52704i | −0.0402447 | + | 0.330895i | ||||
\(280\) | −4.51882 | −0.270051 | ||||||||
\(281\) | 4.62225 | 0.275740 | 0.137870 | − | 0.990450i | \(-0.455974\pi\) | ||||
0.137870 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(282\) | −5.27823 | − | 9.14215i | −0.314314 | − | 0.544407i | ||||
\(283\) | 25.4950 | 1.51552 | 0.757759 | − | 0.652534i | \(-0.226294\pi\) | ||||
0.757759 | + | 0.652534i | \(0.226294\pi\) | |||||||
\(284\) | −1.51882 | + | 2.63067i | −0.0901252 | + | 0.156101i | ||||
\(285\) | −3.95044 | − | 6.84237i | −0.234004 | − | 0.405307i | ||||
\(286\) | −13.5941 | − | 23.5456i | −0.803835 | − | 1.39228i | ||||
\(287\) | 36.9385 | 2.18041 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.38423 | − | 14.5219i | 0.493190 | − | 0.854230i | ||||
\(290\) | 4.69104 | − | 8.12511i | 0.275467 | − | 0.477123i | ||||
\(291\) | −5.72867 | − | 9.92235i | −0.335821 | − | 0.581658i | ||||
\(292\) | 1.00000 | − | 1.73205i | 0.0585206 | − | 0.101361i | ||||
\(293\) | 3.86541 | + | 6.69509i | 0.225820 | + | 0.391132i | 0.956565 | − | 0.291519i | \(-0.0941606\pi\) |
−0.730745 | + | 0.682650i | \(0.760827\pi\) | |||||||
\(294\) | 13.4197 | 0.782653 | ||||||||
\(295\) | 13.5565 | 0.789287 | ||||||||
\(296\) | −1.24059 | − | 2.14877i | −0.0721079 | − | 0.124895i | ||||
\(297\) | −1.93163 | + | 3.34568i | −0.112084 | + | 0.194136i | ||||
\(298\) | −7.82778 | − | 13.5581i | −0.453451 | − | 0.785401i | ||||
\(299\) | −19.4197 | + | 33.6359i | −1.12307 | + | 1.94522i | ||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | 9.90089 | − | 17.1488i | 0.570678 | − | 0.988443i | ||||
\(302\) | 14.9009 | 0.857450 | ||||||||
\(303\) | 4.88207 | + | 8.45599i | 0.280468 | + | 0.485784i | ||||
\(304\) | 3.95044 | + | 6.84237i | 0.226573 | + | 0.392437i | ||||
\(305\) | −2.95044 | + | 5.11032i | −0.168942 | + | 0.292616i | ||||
\(306\) | −0.481183 | −0.0275074 | ||||||||
\(307\) | 0.223935 | + | 0.387867i | 0.0127807 | + | 0.0221368i | 0.872345 | − | 0.488891i | \(-0.162598\pi\) |
−0.859564 | + | 0.511028i | \(0.829265\pi\) | |||||||
\(308\) | −17.4573 | −0.994724 | ||||||||
\(309\) | −15.5565 | −0.884976 | ||||||||
\(310\) | 0.672219 | − | 5.52704i | 0.0381795 | − | 0.313915i | ||||
\(311\) | 6.68888 | 0.379291 | 0.189646 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189646 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(312\) | 7.03763 | 0.398428 | ||||||||
\(313\) | 1.48334 | + | 2.56923i | 0.0838435 | + | 0.145221i | 0.904898 | − | 0.425629i | \(-0.139947\pi\) |
−0.821054 | + | 0.570850i | \(0.806614\pi\) | |||||||
\(314\) | −2.44787 | −0.138141 | ||||||||
\(315\) | −2.25941 | + | 3.91341i | −0.127303 | + | 0.220496i | ||||
\(316\) | 2.19104 | + | 3.79498i | 0.123255 | + | 0.213485i | ||||
\(317\) | −3.34660 | − | 5.79648i | −0.187964 | − | 0.325563i | 0.756608 | − | 0.653869i | \(-0.226855\pi\) |
−0.944571 | + | 0.328307i | \(0.893522\pi\) | |||||||
\(318\) | −1.65556 | −0.0928393 | ||||||||
\(319\) | 18.1227 | − | 31.3894i | 1.01467 | − | 1.75747i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 2.25941 | − | 3.91341i | 0.126108 | − | 0.218425i | ||||
\(322\) | 12.4693 | + | 21.5974i | 0.694885 | + | 1.20358i | ||||
\(323\) | 1.90089 | − | 3.29243i | 0.105768 | − | 0.183196i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 7.03763 | 0.390378 | ||||||||
\(326\) | 21.3206 | 1.18084 | ||||||||
\(327\) | 3.95044 | + | 6.84237i | 0.218460 | + | 0.378384i | ||||
\(328\) | 4.08719 | − | 7.07922i | 0.225677 | − | 0.390885i | ||||
\(329\) | −23.8513 | − | 41.3117i | −1.31497 | − | 2.27759i | ||||
\(330\) | 1.93163 | − | 3.34568i | 0.106333 | − | 0.184173i | ||||
\(331\) | 3.70512 | − | 6.41745i | 0.203652 | − | 0.352735i | −0.746051 | − | 0.665889i | \(-0.768052\pi\) |
0.949702 | + | 0.313154i | \(0.101386\pi\) | |||||||
\(332\) | 0.603846 | − | 1.04589i | 0.0331403 | − | 0.0574008i | ||||
\(333\) | −2.48118 | −0.135968 | ||||||||
\(334\) | −4.29488 | − | 7.43895i | −0.235005 | − | 0.407041i | ||||
\(335\) | −1.24059 | − | 2.14877i | −0.0677808 | − | 0.117400i | ||||
\(336\) | 2.25941 | − | 3.91341i | 0.123261 | − | 0.213494i | ||||
\(337\) | −15.3821 | −0.837915 | −0.418957 | − | 0.908006i | \(-0.637604\pi\) | ||||
−0.418957 | + | 0.908006i | \(0.637604\pi\) | |||||||
\(338\) | 18.2641 | + | 31.6344i | 0.993438 | + | 1.72069i | ||||
\(339\) | 7.41970 | 0.402983 | ||||||||
\(340\) | 0.481183 | 0.0260958 | ||||||||
\(341\) | 2.59695 | − | 21.3523i | 0.140633 | − | 1.15629i | ||||
\(342\) | 7.90089 | 0.427231 | ||||||||
\(343\) | 29.0095 | 1.56636 | ||||||||
\(344\) | −2.19104 | − | 3.79498i | −0.118133 | − | 0.204612i | ||||
\(345\) | −5.51882 | −0.297123 | ||||||||
\(346\) | −2.69104 | + | 4.66101i | −0.144671 | + | 0.250577i | ||||
\(347\) | 4.64148 | + | 8.03928i | 0.249168 | + | 0.431571i | 0.963295 | − | 0.268445i | \(-0.0865096\pi\) |
−0.714127 | + | 0.700016i | \(0.753176\pi\) | |||||||
\(348\) | 4.69104 | + | 8.12511i | 0.251466 | + | 0.435552i | ||||
\(349\) | −18.5898 | −0.995087 | −0.497544 | − | 0.867439i | \(-0.665765\pi\) | ||||
−0.497544 | + | 0.867439i | \(0.665765\pi\) | |||||||
\(350\) | 2.25941 | − | 3.91341i | 0.120770 | − | 0.209181i | ||||
\(351\) | 3.51882 | − | 6.09477i | 0.187821 | − | 0.325315i | ||||
\(352\) | −1.93163 | + | 3.34568i | −0.102956 | + | 0.178325i | ||||
\(353\) | −13.2663 | − | 22.9779i | −0.706094 | − | 1.22299i | −0.966295 | − | 0.257436i | \(-0.917122\pi\) |
0.260201 | − | 0.965554i | \(-0.416211\pi\) | |||||||
\(354\) | −6.77823 | + | 11.7402i | −0.360259 | + | 0.623986i | ||||
\(355\) | −1.51882 | − | 2.63067i | −0.0806104 | − | 0.139621i | ||||
\(356\) | −2.96237 | −0.157005 | ||||||||
\(357\) | −2.17438 | −0.115080 | ||||||||
\(358\) | 6.10601 | + | 10.5759i | 0.322712 | + | 0.558954i | ||||
\(359\) | −4.56837 | + | 7.91265i | −0.241109 | + | 0.417614i | −0.961031 | − | 0.276442i | \(-0.910845\pi\) |
0.719921 | + | 0.694056i | \(0.244178\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | −21.7120 | + | 37.6063i | −1.14274 | + | 1.97928i | ||||
\(362\) | −5.38207 | + | 9.32202i | −0.282875 | + | 0.489955i | ||||
\(363\) | 1.96237 | − | 3.39892i | 0.102998 | − | 0.178397i | ||||
\(364\) | 31.8018 | 1.66687 | ||||||||
\(365\) | 1.00000 | + | 1.73205i | 0.0523424 | + | 0.0906597i | ||||
\(366\) | −2.95044 | − | 5.11032i | −0.154222 | − | 0.267121i | ||||
\(367\) | 12.0000 | − | 20.7846i | 0.626395 | − | 1.08495i | −0.361874 | − | 0.932227i | \(-0.617863\pi\) |
0.988269 | − | 0.152721i | \(-0.0488036\pi\) | |||||||
\(368\) | 5.51882 | 0.287688 | ||||||||
\(369\) | −4.08719 | − | 7.07922i | −0.212771 | − | 0.368529i | ||||
\(370\) | 2.48118 | 0.128991 | ||||||||
\(371\) | −7.48118 | −0.388404 | ||||||||
\(372\) | 4.45044 | + | 3.34568i | 0.230745 | + | 0.173465i | ||||
\(373\) | 25.3959 | 1.31495 | 0.657474 | − | 0.753477i | \(-0.271625\pi\) | ||||
0.657474 | + | 0.753477i | \(0.271625\pi\) | |||||||
\(374\) | 1.85893 | 0.0961232 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −10.5565 | −0.544407 | ||||||||
\(377\) | −33.0138 | + | 57.1816i | −1.70030 | + | 2.94500i | ||||
\(378\) | −2.25941 | − | 3.91341i | −0.116211 | − | 0.201284i | ||||
\(379\) | 13.9385 | + | 24.1422i | 0.715974 | + | 1.24010i | 0.962583 | + | 0.270988i | \(0.0873503\pi\) |
−0.246609 | + | 0.969115i | \(0.579316\pi\) | |||||||
\(380\) | −7.90089 | −0.405307 | ||||||||
\(381\) | −1.60385 | + | 2.77794i | −0.0821675 | + | 0.142318i | ||||
\(382\) | 4.95044 | − | 8.57442i | 0.253287 | − | 0.438706i | ||||
\(383\) | 8.27823 | − | 14.3383i | 0.422998 | − | 0.732653i | −0.573234 | − | 0.819392i | \(-0.694311\pi\) |
0.996231 | + | 0.0867388i | \(0.0276446\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 8.72867 | − | 15.1185i | 0.444854 | − | 0.770510i | ||||
\(386\) | 10.6910 | + | 18.5174i | 0.544159 | + | 0.942512i | ||||
\(387\) | −4.38207 | −0.222753 | ||||||||
\(388\) | −11.4573 | −0.581658 | ||||||||
\(389\) | −14.8842 | − | 25.7802i | −0.754660 | − | 1.30711i | −0.945543 | − | 0.325497i | \(-0.894468\pi\) |
0.190882 | − | 0.981613i | \(-0.438865\pi\) | |||||||
\(390\) | −3.51882 | + | 6.09477i | −0.178182 | + | 0.308621i | ||||
\(391\) | −1.32778 | − | 2.29978i | −0.0671488 | − | 0.116305i | ||||
\(392\) | 6.70985 | − | 11.6218i | 0.338899 | − | 0.586990i | ||||
\(393\) | −3.32778 | + | 5.76389i | −0.167864 | + | 0.290750i | ||||
\(394\) | 3.65556 | − | 6.33162i | 0.184165 | − | 0.318982i | ||||
\(395\) | −4.38207 | −0.220486 | ||||||||
\(396\) | 1.93163 | + | 3.34568i | 0.0970679 | + | 0.168127i | ||||
\(397\) | 10.3278 | + | 17.8882i | 0.518336 | + | 0.897785i | 0.999773 | + | 0.0213042i | \(0.00678184\pi\) |
−0.481437 | + | 0.876481i | \(0.659885\pi\) | |||||||
\(398\) | 1.39615 | − | 2.41821i | 0.0699829 | − | 0.121214i | ||||
\(399\) | 35.7027 | 1.78737 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −18.8394 | −0.940795 | −0.470398 | − | 0.882455i | \(-0.655889\pi\) | ||||
−0.470398 | + | 0.882455i | \(0.655889\pi\) | |||||||
\(402\) | 2.48118 | 0.123750 | ||||||||
\(403\) | −4.73083 | + | 38.8972i | −0.235659 | + | 1.93761i | ||||
\(404\) | 9.76414 | 0.485784 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 21.1979 | + | 36.7159i | 1.05204 | + | 1.82218i | ||||
\(407\) | 9.58544 | 0.475133 | ||||||||
\(408\) | −0.240592 | + | 0.416717i | −0.0119111 | + | 0.0206306i | ||||
\(409\) | −3.67438 | − | 6.36421i | −0.181686 | − | 0.314690i | 0.760769 | − | 0.649023i | \(-0.224822\pi\) |
−0.942455 | + | 0.334333i | \(0.891489\pi\) | |||||||
\(410\) | 4.08719 | + | 7.07922i | 0.201852 | + | 0.349618i | ||||
\(411\) | 4.82994 | 0.238243 | ||||||||
\(412\) | −7.77823 | + | 13.4723i | −0.383206 | + | 0.663732i | ||||
\(413\) | −30.6296 | + | 53.0519i | −1.50718 | + | 2.61052i | ||||
\(414\) | 2.75941 | − | 4.77944i | 0.135618 | − | 0.234896i | ||||
\(415\) | 0.603846 | + | 1.04589i | 0.0296416 | + | 0.0513408i | ||||
\(416\) | 3.51882 | − | 6.09477i | 0.172524 | − | 0.298821i | ||||
\(417\) | 4.43163 | + | 7.67580i | 0.217018 | + | 0.375886i | ||||
\(418\) | −30.5231 | −1.49294 | ||||||||
\(419\) | −11.8633 | −0.579558 | −0.289779 | − | 0.957094i | \(-0.593582\pi\) | ||||
−0.289779 | + | 0.957094i | \(0.593582\pi\) | |||||||
\(420\) | 2.25941 | + | 3.91341i | 0.110248 | + | 0.190955i | ||||
\(421\) | 9.81370 | − | 16.9978i | 0.478290 | − | 0.828423i | −0.521400 | − | 0.853312i | \(-0.674590\pi\) |
0.999690 | + | 0.0248893i | \(0.00792332\pi\) | |||||||
\(422\) | −0.0495562 | − | 0.0858338i | −0.00241236 | − | 0.00417833i | ||||
\(423\) | −5.27823 | + | 9.14215i | −0.256636 | + | 0.444507i | ||||
\(424\) | −0.827781 | + | 1.43376i | −0.0402006 | + | 0.0696295i | ||||
\(425\) | −0.240592 | + | 0.416717i | −0.0116704 | + | 0.0202137i | ||||
\(426\) | 3.03763 | 0.147174 | ||||||||
\(427\) | −13.3325 | − | 23.0926i | −0.645206 | − | 1.11753i | ||||
\(428\) | −2.25941 | − | 3.91341i | −0.109213 | − | 0.189162i | ||||
\(429\) | −13.5941 | + | 23.5456i | −0.656329 | + | 1.13679i | ||||
\(430\) | 4.38207 | 0.211322 | ||||||||
\(431\) | −15.6436 | − | 27.0956i | −0.753528 | − | 1.30515i | −0.946103 | − | 0.323866i | \(-0.895017\pi\) |
0.192575 | − | 0.981282i | \(-0.438316\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 8.68888 | 0.417561 | 0.208780 | − | 0.977963i | \(-0.433051\pi\) | ||||
0.208780 | + | 0.977963i | \(0.433051\pi\) | |||||||
\(434\) | 20.1107 | + | 15.1185i | 0.965346 | + | 0.725711i | ||||
\(435\) | −9.38207 | −0.449836 | ||||||||
\(436\) | 7.90089 | 0.378384 | ||||||||
\(437\) | 21.8018 | + | 37.7618i | 1.04292 | + | 1.80639i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | −16.6248 | + | 28.7950i | −0.793460 | + | 1.37431i | 0.130353 | + | 0.991468i | \(0.458389\pi\) |
−0.923813 | + | 0.382845i | \(0.874944\pi\) | |||||||
\(440\) | −1.93163 | − | 3.34568i | −0.0920867 | − | 0.159499i | ||||
\(441\) | −6.70985 | − | 11.6218i | −0.319517 | − | 0.553419i | ||||
\(442\) | −3.38639 | −0.161074 | ||||||||
\(443\) | −7.41970 | + | 12.8513i | −0.352521 | + | 0.610584i | −0.986690 | − | 0.162610i | \(-0.948009\pi\) |
0.634170 | + | 0.773194i | \(0.281342\pi\) | |||||||
\(444\) | −1.24059 | + | 2.14877i | −0.0588759 | + | 0.101976i | ||||
\(445\) | 1.48118 | − | 2.56548i | 0.0702148 | − | 0.121616i | ||||
\(446\) | −8.12266 | − | 14.0689i | −0.384619 | − | 0.666180i | ||||
\(447\) | −7.82778 | + | 13.5581i | −0.370241 | + | 0.641277i | ||||
\(448\) | −2.25941 | − | 3.91341i | −0.106747 | − | 0.184891i | ||||
\(449\) | 5.80178 | 0.273803 | 0.136901 | − | 0.990585i | \(-0.456286\pi\) | ||||
0.136901 | + | 0.990585i | \(0.456286\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 15.7899 | + | 27.3488i | 0.743515 | + | 1.28781i | ||||
\(452\) | 3.70985 | − | 6.42565i | 0.174497 | − | 0.302237i | ||||
\(453\) | −7.45044 | − | 12.9045i | −0.350052 | − | 0.606309i | ||||
\(454\) | −5.64148 | + | 9.77133i | −0.264768 | + | 0.458591i | ||||
\(455\) | −15.9009 | + | 27.5411i | −0.745445 | + | 1.29115i | ||||
\(456\) | 3.95044 | − | 6.84237i | 0.184996 | − | 0.320423i | ||||
\(457\) | 29.3864 | 1.37464 | 0.687319 | − | 0.726356i | \(-0.258788\pi\) | ||||
0.687319 | + | 0.726356i | \(0.258788\pi\) | |||||||
\(458\) | 5.33251 | + | 9.23619i | 0.249172 | + | 0.431579i | ||||
\(459\) | 0.240592 | + | 0.416717i | 0.0112299 | + | 0.0194507i | ||||
\(460\) | −2.75941 | + | 4.77944i | −0.128658 | + | 0.222842i | ||||
\(461\) | 25.4907 | 1.18722 | 0.593609 | − | 0.804754i | \(-0.297703\pi\) | ||||
0.593609 | + | 0.804754i | \(0.297703\pi\) | |||||||
\(462\) | 8.72867 | + | 15.1185i | 0.406094 | + | 0.703376i | ||||
\(463\) | 17.3582 | 0.806705 | 0.403353 | − | 0.915045i | \(-0.367845\pi\) | ||||
0.403353 | + | 0.915045i | \(0.367845\pi\) | |||||||
\(464\) | 9.38207 | 0.435552 | ||||||||
\(465\) | −5.12266 | + | 2.18136i | −0.237558 | + | 0.101158i | ||||
\(466\) | −6.48118 | −0.300235 | ||||||||
\(467\) | 31.9718 | 1.47948 | 0.739740 | − | 0.672893i | \(-0.234948\pi\) | ||||
0.739740 | + | 0.672893i | \(0.234948\pi\) | |||||||
\(468\) | −3.51882 | − | 6.09477i | −0.162657 | − | 0.281731i | ||||
\(469\) | 11.2120 | 0.517723 | ||||||||
\(470\) | 5.27823 | − | 9.14215i | 0.243466 | − | 0.421696i | ||||
\(471\) | 1.22394 | + | 2.11992i | 0.0563960 | + | 0.0976807i | ||||
\(472\) | 6.77823 | + | 11.7402i | 0.311993 | + | 0.540388i | ||||
\(473\) | 16.9291 | 0.778399 | ||||||||
\(474\) | 2.19104 | − | 3.79498i | 0.100638 | − | 0.174309i | ||||
\(475\) | 3.95044 | − | 6.84237i | 0.181259 | − | 0.313949i | ||||
\(476\) | −1.08719 | + | 1.88307i | −0.0498313 | + | 0.0863103i | ||||
\(477\) | 0.827781 | + | 1.43376i | 0.0379015 | + | 0.0656473i | ||||
\(478\) | −10.3821 | + | 17.9823i | −0.474865 | + | 0.822490i | ||||
\(479\) | 10.3325 | + | 17.8964i | 0.472105 | + | 0.817709i | 0.999491 | − | 0.0319166i | \(-0.0101611\pi\) |
−0.527386 | + | 0.849626i | \(0.676828\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −17.4617 | −0.796183 | ||||||||
\(482\) | −9.82778 | − | 17.0222i | −0.447643 | − | 0.775341i | ||||
\(483\) | 12.4693 | − | 21.5974i | 0.567371 | − | 0.982715i | ||||
\(484\) | −1.96237 | − | 3.39892i | −0.0891985 | − | 0.154496i | ||||
\(485\) | 5.72867 | − | 9.92235i | 0.260125 | − | 0.450551i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 11.6415 | − | 20.1636i | 0.527526 | − | 0.913701i | −0.471959 | − | 0.881620i | \(-0.656453\pi\) |
0.999485 | − | 0.0320812i | \(-0.0102135\pi\) | |||||||
\(488\) | −5.90089 | −0.267121 | ||||||||
\(489\) | −10.6603 | − | 18.4642i | −0.482075 | − | 0.834979i | ||||
\(490\) | 6.70985 | + | 11.6218i | 0.303120 | + | 0.525020i | ||||
\(491\) | 12.8701 | − | 22.2918i | 0.580822 | − | 1.00601i | −0.414561 | − | 0.910022i | \(-0.636065\pi\) |
0.995382 | − | 0.0959909i | \(-0.0306020\pi\) | |||||||
\(492\) | −8.17438 | −0.368529 | ||||||||
\(493\) | −2.25725 | − | 3.90967i | −0.101661 | − | 0.176083i | ||||
\(494\) | 55.6036 | 2.50172 | ||||||||
\(495\) | −3.86325 | −0.173640 | ||||||||
\(496\) | 5.12266 | − | 2.18136i | 0.230014 | − | 0.0979459i | ||||
\(497\) | 13.7265 | 0.615718 | ||||||||
\(498\) | −1.20769 | −0.0541180 | ||||||||
\(499\) | −6.37015 | − | 11.0334i | −0.285167 | − | 0.493924i | 0.687483 | − | 0.726201i | \(-0.258716\pi\) |
−0.972650 | + | 0.232277i | \(0.925382\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −4.29488 | + | 7.43895i | −0.191881 | + | 0.332348i | ||||
\(502\) | −0.191035 | − | 0.330883i | −0.00852633 | − | 0.0147680i | ||||
\(503\) | 7.15814 | + | 12.3983i | 0.319165 | + | 0.552811i | 0.980314 | − | 0.197444i | \(-0.0632641\pi\) |
−0.661149 | + | 0.750255i | \(0.729931\pi\) | |||||||
\(504\) | −4.51882 | −0.201284 | ||||||||
\(505\) | −4.88207 | + | 8.45599i | −0.217249 | + | 0.376287i | ||||
\(506\) | −10.6603 | + | 18.4642i | −0.473908 | + | 0.820833i | ||||
\(507\) | 18.2641 | − | 31.6344i | 0.811139 | − | 1.40493i | ||||
\(508\) | 1.60385 | + | 2.77794i | 0.0711592 | + | 0.123251i | ||||
\(509\) | 11.8488 | − | 20.5227i | 0.525187 | − | 0.909651i | −0.474383 | − | 0.880319i | \(-0.657329\pi\) |
0.999570 | − | 0.0293318i | \(-0.00933795\pi\) | |||||||
\(510\) | −0.240592 | − | 0.416717i | −0.0106536 | − | 0.0184525i | ||||
\(511\) | −9.03763 | −0.399801 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.95044 | − | 6.84237i | −0.174416 | − | 0.302098i | ||||
\(514\) | 10.4859 | − | 18.1621i | 0.462514 | − | 0.801098i | ||||
\(515\) | −7.77823 | − | 13.4723i | −0.342750 | − | 0.593660i | ||||
\(516\) | −2.19104 | + | 3.79498i | −0.0964550 | + | 0.167065i | ||||
\(517\) | 20.3911 | − | 35.3185i | 0.896801 | − | 1.55330i | ||||
\(518\) | −5.60601 | + | 9.70989i | −0.246314 | + | 0.426628i | ||||
\(519\) | 5.38207 | 0.236247 | ||||||||
\(520\) | 3.51882 | + | 6.09477i | 0.154310 | + | 0.267273i | ||||
\(521\) | 3.82562 | + | 6.62617i | 0.167603 | + | 0.290298i | 0.937577 | − | 0.347778i | \(-0.113064\pi\) |
−0.769973 | + | 0.638076i | \(0.779730\pi\) | |||||||
\(522\) | 4.69104 | − | 8.12511i | 0.205321 | − | 0.355626i | ||||
\(523\) | 3.07095 | 0.134283 | 0.0671415 | − | 0.997743i | \(-0.478612\pi\) | ||||
0.0671415 | + | 0.997743i | \(0.478612\pi\) | |||||||
\(524\) | 3.32778 | + | 5.76389i | 0.145375 | + | 0.251797i | ||||
\(525\) | −4.51882 | −0.197217 | ||||||||
\(526\) | −2.38207 | −0.103863 | ||||||||
\(527\) | −2.14148 | − | 1.60988i | −0.0932843 | − | 0.0701276i | ||||
\(528\) | 3.86325 | 0.168127 | ||||||||
\(529\) | 7.45734 | 0.324232 | ||||||||
\(530\) | −0.827781 | − | 1.43376i | −0.0359565 | − | 0.0622785i | ||||
\(531\) | 13.5565 | 0.588300 | ||||||||
\(532\) | 17.8513 | − | 30.9194i | 0.773953 | − | 1.34053i | ||||
\(533\) | −28.7641 | − | 49.8210i | −1.24591 | − | 2.15799i | ||||
\(534\) | 1.48118 | + | 2.56548i | 0.0640971 | + | 0.111019i | ||||
\(535\) | 4.51882 | 0.195365 | ||||||||
\(536\) | 1.24059 | − | 2.14877i | 0.0535854 | − | 0.0928126i | ||||
\(537\) | 6.10601 | − | 10.5759i | 0.263494 | − | 0.456384i | ||||
\(538\) | 9.36541 | − | 16.2214i | 0.403772 | − | 0.699353i | ||||
\(539\) | 25.9219 | + | 44.8980i | 1.11653 | + | 1.93389i | ||||
\(540\) | 0.500000 | − | 0.866025i | 0.0215166 | − | 0.0372678i | ||||
\(541\) | −7.22394 | − | 12.5122i | −0.310581 | − | 0.537942i | 0.667907 | − | 0.744245i | \(-0.267190\pi\) |
−0.978488 | + | 0.206302i | \(0.933857\pi\) | |||||||
\(542\) | 7.82994 | 0.336325 | ||||||||
\(543\) | 10.7641 | 0.461934 | ||||||||
\(544\) | 0.240592 | + | 0.416717i | 0.0103153 | + | 0.0178666i | ||||
\(545\) | −3.95044 | + | 6.84237i | −0.169218 | + | 0.293095i | ||||
\(546\) | −15.9009 | − | 27.5411i | −0.680495 | − | 1.17865i | ||||
\(547\) | −8.98334 | + | 15.5596i | −0.384100 | + | 0.665281i | −0.991644 | − | 0.129005i | \(-0.958822\pi\) |
0.607544 | + | 0.794286i | \(0.292155\pi\) | |||||||
\(548\) | 2.41497 | − | 4.18285i | 0.103162 | − | 0.178683i | ||||
\(549\) | −2.95044 | + | 5.11032i | −0.125922 | + | 0.218103i | ||||
\(550\) | 3.86325 | 0.164730 | ||||||||
\(551\) | 37.0633 | + | 64.1956i | 1.57895 | + | 2.73482i | ||||
\(552\) | −2.75941 | − | 4.77944i | −0.117448 | − | 0.203426i | ||||
\(553\) | 9.90089 | − | 17.1488i | 0.421029 | − | 0.729243i | ||||
\(554\) | 14.2077 | 0.603627 | ||||||||
\(555\) | −1.24059 | − | 2.14877i | −0.0526602 | − | 0.0912101i | ||||
\(556\) | 8.86325 | 0.375886 | ||||||||
\(557\) | 15.1838 | 0.643360 | 0.321680 | − | 0.946848i | \(-0.395752\pi\) | ||||
0.321680 | + | 0.946848i | \(0.395752\pi\) | |||||||
\(558\) | 0.672219 | − | 5.52704i | 0.0284573 | − | 0.233978i | ||||
\(559\) | −30.8394 | −1.30437 | ||||||||
\(560\) | 4.51882 | 0.190955 | ||||||||
\(561\) | −0.929467 | − | 1.60988i | −0.0392421 | − | 0.0679693i | ||||
\(562\) | −4.62225 | −0.194978 | ||||||||
\(563\) | 15.8535 | − | 27.4591i | 0.668145 | − | 1.15726i | −0.310277 | − | 0.950646i | \(-0.600422\pi\) |
0.978422 | − | 0.206615i | \(-0.0662448\pi\) | |||||||
\(564\) | 5.27823 | + | 9.14215i | 0.222253 | + | 0.384954i | ||||
\(565\) | 3.70985 | + | 6.42565i | 0.156075 | + | 0.270329i | ||||
\(566\) | −25.4950 | −1.07163 | ||||||||
\(567\) | −2.25941 | + | 3.91341i | −0.0948862 | + | 0.164348i | ||||
\(568\) | 1.51882 | − | 2.63067i | 0.0637281 | − | 0.110380i | ||||
\(569\) | −18.9718 | + | 32.8602i | −0.795341 | + | 1.37757i | 0.127282 | + | 0.991867i | \(0.459375\pi\) |
−0.922623 | + | 0.385704i | \(0.873959\pi\) | |||||||
\(570\) | 3.95044 | + | 6.84237i | 0.165466 | + | 0.286595i | ||||
\(571\) | −9.38207 | + | 16.2502i | −0.392627 | + | 0.680051i | −0.992795 | − | 0.119823i | \(-0.961767\pi\) |
0.600168 | + | 0.799874i | \(0.295100\pi\) | |||||||
\(572\) | 13.5941 | + | 23.5456i | 0.568397 | + | 0.984493i | ||||
\(573\) | −9.90089 | −0.413616 | ||||||||
\(574\) | −36.9385 | −1.54178 | ||||||||
\(575\) | −2.75941 | − | 4.77944i | −0.115075 | − | 0.199316i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −11.6556 | − | 20.1880i | −0.485227 | − | 0.840439i | 0.514629 | − | 0.857413i | \(-0.327930\pi\) |
−0.999856 | + | 0.0169747i | \(0.994597\pi\) | |||||||
\(578\) | −8.38423 | + | 14.5219i | −0.348738 | + | 0.604032i | ||||
\(579\) | 10.6910 | − | 18.5174i | 0.444304 | − | 0.769558i | ||||
\(580\) | −4.69104 | + | 8.12511i | −0.194785 | + | 0.337377i | ||||
\(581\) | −5.45734 | −0.226409 | ||||||||
\(582\) | 5.72867 | + | 9.92235i | 0.237461 | + | 0.411294i | ||||
\(583\) | −3.19793 | − | 5.53898i | −0.132445 | − | 0.229401i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | 7.03763 | 0.290970 | ||||||||
\(586\) | −3.86541 | − | 6.69509i | −0.159679 | − | 0.276572i | ||||
\(587\) | −33.4812 | −1.38192 | −0.690958 | − | 0.722895i | \(-0.742811\pi\) | ||||
−0.690958 | + | 0.722895i | \(0.742811\pi\) | |||||||
\(588\) | −13.4197 | −0.553419 | ||||||||
\(589\) | 35.1625 | + | 26.4338i | 1.44884 | + | 1.08919i | ||||
\(590\) | −13.5565 | −0.558110 | ||||||||
\(591\) | −7.31112 | −0.300739 | ||||||||
\(592\) | 1.24059 | + | 2.14877i | 0.0509880 | + | 0.0883138i | ||||
\(593\) | −31.0891 | −1.27667 | −0.638337 | − | 0.769757i | \(-0.720377\pi\) | ||||
−0.638337 | + | 0.769757i | \(0.720377\pi\) | |||||||
\(594\) | 1.93163 | − | 3.34568i | 0.0792556 | − | 0.137275i | ||||
\(595\) | −1.08719 | − | 1.88307i | −0.0445704 | − | 0.0771982i | ||||
\(596\) | 7.82778 | + | 13.5581i | 0.320638 | + | 0.555362i | ||||
\(597\) | −2.79231 | −0.114282 | ||||||||
\(598\) | 19.4197 | − | 33.6359i | 0.794131 | − | 1.37547i | ||||
\(599\) | 2.65556 | − | 4.59957i | 0.108503 | − | 0.187933i | −0.806661 | − | 0.591015i | \(-0.798728\pi\) |
0.915164 | + | 0.403081i | \(0.132061\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 16.2287 | + | 28.1089i | 0.661981 | + | 1.14659i | 0.980094 | + | 0.198532i | \(0.0636175\pi\) |
−0.318113 | + | 0.948053i | \(0.603049\pi\) | |||||||
\(602\) | −9.90089 | + | 17.1488i | −0.403530 | + | 0.698935i | ||||
\(603\) | −1.24059 | − | 2.14877i | −0.0505208 | − | 0.0875046i | ||||
\(604\) | −14.9009 | −0.606309 | ||||||||
\(605\) | 3.92473 | 0.159563 | ||||||||
\(606\) | −4.88207 | − | 8.45599i | −0.198321 | − | 0.343501i | ||||
\(607\) | 12.7641 | − | 22.1081i | 0.518081 | − | 0.897342i | −0.481699 | − | 0.876337i | \(-0.659980\pi\) |
0.999779 | − | 0.0210050i | \(-0.00668659\pi\) | |||||||
\(608\) | −3.95044 | − | 6.84237i | −0.160212 | − | 0.277495i | ||||
\(609\) | 21.1979 | − | 36.7159i | 0.858983 | − | 1.48780i | ||||
\(610\) | 2.95044 | − | 5.11032i | 0.119460 | − | 0.206911i | ||||
\(611\) | −37.1462 | + | 64.3391i | −1.50277 | + | 2.60288i | ||||
\(612\) | 0.481183 | 0.0194507 | ||||||||
\(613\) | 4.82994 | + | 8.36570i | 0.195080 | + | 0.337888i | 0.946927 | − | 0.321450i | \(-0.104170\pi\) |
−0.751847 | + | 0.659338i | \(0.770837\pi\) | |||||||
\(614\) | −0.223935 | − | 0.387867i | −0.00903730 | − | 0.0156531i | ||||
\(615\) | 4.08719 | − | 7.07922i | 0.164811 | − | 0.285462i | ||||
\(616\) | 17.4573 | 0.703376 | ||||||||
\(617\) | −2.20296 | − | 3.81564i | −0.0886878 | − | 0.153612i | 0.818269 | − | 0.574836i | \(-0.194934\pi\) |
−0.906957 | + | 0.421224i | \(0.861601\pi\) | |||||||
\(618\) | 15.5565 | 0.625772 | ||||||||
\(619\) | −48.4907 | −1.94900 | −0.974502 | − | 0.224379i | \(-0.927965\pi\) | ||||
−0.974502 | + | 0.224379i | \(0.927965\pi\) | |||||||
\(620\) | −0.672219 | + | 5.52704i | −0.0269970 | + | 0.221971i | ||||
\(621\) | −5.51882 | −0.221462 | ||||||||
\(622\) | −6.68888 | −0.268199 | ||||||||
\(623\) | 6.69320 | + | 11.5930i | 0.268157 | + | 0.464462i | ||||
\(624\) | −7.03763 | −0.281731 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −1.48334 | − | 2.56923i | −0.0592863 | − | 0.102687i | ||||
\(627\) | 15.2616 | + | 26.4338i | 0.609488 | + | 1.05566i | ||||
\(628\) | 2.44787 | 0.0976807 | ||||||||
\(629\) | 0.596952 | − | 1.03395i | 0.0238020 | − | 0.0412263i | ||||
\(630\) | 2.25941 | − | 3.91341i | 0.0900170 | − | 0.155914i | ||||
\(631\) | −6.35133 | + | 11.0008i | −0.252843 | + | 0.437936i | −0.964307 | − | 0.264786i | \(-0.914699\pi\) |
0.711465 | + | 0.702722i | \(0.248032\pi\) | |||||||
\(632\) | −2.19104 | − | 3.79498i | −0.0871547 | − | 0.150956i | ||||
\(633\) | −0.0495562 | + | 0.0858338i | −0.00196968 | + | 0.00341159i | ||||
\(634\) | 3.34660 | + | 5.79648i | 0.132910 | + | 0.230208i | ||||
\(635\) | −3.20769 | −0.127293 | ||||||||
\(636\) | 1.65556 | 0.0656473 | ||||||||
\(637\) | −47.2215 | − | 81.7900i | −1.87098 | − | 3.24064i | ||||
\(638\) | −18.1227 | + | 31.3894i | −0.717483 | + | 1.24272i | ||||
\(639\) | −1.51882 | − | 2.63067i | −0.0600835 | − | 0.104068i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −18.4693 | + | 31.9897i | −0.729492 | + | 1.26352i | 0.227606 | + | 0.973753i | \(0.426910\pi\) |
−0.957098 | + | 0.289764i | \(0.906423\pi\) | |||||||
\(642\) | −2.25941 | + | 3.91341i | −0.0891717 | + | 0.154450i | ||||
\(643\) | −13.2873 | −0.523999 | −0.262000 | − | 0.965068i | \(-0.584382\pi\) | ||||
−0.262000 | + | 0.965068i | \(0.584382\pi\) | |||||||
\(644\) | −12.4693 | − | 21.5974i | −0.491358 | − | 0.851056i | ||||
\(645\) | −2.19104 | − | 3.79498i | −0.0862719 | − | 0.149427i | ||||
\(646\) | −1.90089 | + | 3.29243i | −0.0747894 | + | 0.129539i | ||||
\(647\) | 5.27864 | 0.207525 | 0.103762 | − | 0.994602i | \(-0.466912\pi\) | ||||
0.103762 | + | 0.994602i | \(0.466912\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −52.3720 | −2.05578 | ||||||||
\(650\) | −7.03763 | −0.276039 | ||||||||
\(651\) | 3.03763 | − | 24.9757i | 0.119054 | − | 0.978873i | ||||
\(652\) | −21.3206 | −0.834979 | ||||||||
\(653\) | −32.4197 | −1.26868 | −0.634341 | − | 0.773054i | \(-0.718728\pi\) | ||||
−0.634341 | + | 0.773054i | \(0.718728\pi\) | |||||||
\(654\) | −3.95044 | − | 6.84237i | −0.154475 | − | 0.267558i | ||||
\(655\) | −6.65556 | −0.260054 | ||||||||
\(656\) | −4.08719 | + | 7.07922i | −0.159578 | + | 0.276397i | ||||
\(657\) | 1.00000 | + | 1.73205i | 0.0390137 | + | 0.0675737i | ||||
\(658\) | 23.8513 | + | 41.3117i | 0.929822 | + | 1.61050i | ||||
\(659\) | −13.2496 | −0.516133 | −0.258066 | − | 0.966127i | \(-0.583085\pi\) | ||||
−0.258066 | + | 0.966127i | \(0.583085\pi\) | |||||||
\(660\) | −1.93163 | + | 3.34568i | −0.0751885 | + | 0.130230i | ||||
\(661\) | −17.9881 | + | 31.1563i | −0.699655 | + | 1.21184i | 0.268931 | + | 0.963159i | \(0.413330\pi\) |
−0.968586 | + | 0.248679i | \(0.920004\pi\) | |||||||
\(662\) | −3.70512 | + | 6.41745i | −0.144004 | + | 0.249421i | ||||
\(663\) | 1.69320 | + | 2.93270i | 0.0657583 | + | 0.113897i | ||||
\(664\) | −0.603846 | + | 1.04589i | −0.0234338 | + | 0.0405885i | ||||
\(665\) | 17.8513 | + | 30.9194i | 0.692245 | + | 1.19900i | ||||
\(666\) | 2.48118 | 0.0961439 | ||||||||
\(667\) | 51.7779 | 2.00485 | ||||||||
\(668\) | 4.29488 | + | 7.43895i | 0.166174 | + | 0.287822i | ||||
\(669\) | −8.12266 | + | 14.0689i | −0.314040 | + | 0.543934i | ||||
\(670\) | 1.24059 | + | 2.14877i | 0.0479282 | + | 0.0830141i | ||||
\(671\) | 11.3983 | − | 19.7425i | 0.440027 | − | 0.762149i | ||||
\(672\) | −2.25941 | + | 3.91341i | −0.0871586 | + | 0.150963i | ||||
\(673\) | −6.69104 | + | 11.5892i | −0.257920 | + | 0.446731i | −0.965685 | − | 0.259717i | \(-0.916371\pi\) |
0.707764 | + | 0.706449i | \(0.249704\pi\) | |||||||
\(674\) | 15.3821 | 0.592495 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −18.2641 | − | 31.6344i | −0.702467 | − | 1.21671i | ||||
\(677\) | 2.10127 | − | 3.63951i | 0.0807585 | − | 0.139878i | −0.822817 | − | 0.568306i | \(-0.807599\pi\) |
0.903576 | + | 0.428428i | \(0.140932\pi\) | |||||||
\(678\) | −7.41970 | −0.284952 | ||||||||
\(679\) | 25.8868 | + | 44.8373i | 0.993444 | + | 1.72070i | ||||
\(680\) | −0.481183 | −0.0184525 | ||||||||
\(681\) | 11.2830 | 0.432364 | ||||||||
\(682\) | −2.59695 | + | 21.3523i | −0.0994424 | + | 0.817623i | ||||
\(683\) | 35.8299 | 1.37099 | 0.685497 | − | 0.728075i | \(-0.259585\pi\) | ||||
0.685497 | + | 0.728075i | \(0.259585\pi\) | |||||||
\(684\) | −7.90089 | −0.302098 | ||||||||
\(685\) | 2.41497 | + | 4.18285i | 0.0922713 | + | 0.159819i | ||||
\(686\) | −29.0095 | −1.10759 | ||||||||
\(687\) | 5.33251 | − | 9.23619i | 0.203448 | − | 0.352382i | ||||
\(688\) | 2.19104 | + | 3.79498i | 0.0835324 | + | 0.144682i | ||||
\(689\) | 5.82562 | + | 10.0903i | 0.221938 | + | 0.384409i | ||||
\(690\) | 5.51882 | 0.210098 | ||||||||
\(691\) | 17.4693 | − | 30.2576i | 0.664562 | − | 1.15106i | −0.314842 | − | 0.949144i | \(-0.601951\pi\) |
0.979404 | − | 0.201911i | \(-0.0647152\pi\) | |||||||
\(692\) | 2.69104 | − | 4.66101i | 0.102298 | − | 0.177185i | ||||
\(693\) | 8.72867 | − | 15.1185i | 0.331575 | − | 0.574304i | ||||
\(694\) | −4.64148 | − | 8.03928i | −0.176188 | − | 0.305167i | ||||
\(695\) | −4.43163 | + | 7.67580i | −0.168101 | + | 0.291160i | ||||
\(696\) | −4.69104 | − | 8.12511i | −0.177813 | − | 0.307982i | ||||
\(697\) | 3.93337 | 0.148987 | ||||||||
\(698\) | 18.5898 | 0.703633 | ||||||||
\(699\) | 3.24059 | + | 5.61287i | 0.122570 | + | 0.212298i | ||||
\(700\) | −2.25941 | + | 3.91341i | −0.0853976 | + | 0.147913i | ||||
\(701\) | −19.5376 | − | 33.8402i | −0.737926 | − | 1.27813i | −0.953428 | − | 0.301622i | \(-0.902472\pi\) |
0.215501 | − | 0.976504i | \(-0.430861\pi\) | |||||||
\(702\) | −3.51882 | + | 6.09477i | −0.132809 | + | 0.230032i | ||||
\(703\) | −9.80178 | + | 16.9772i | −0.369681 | + | 0.640306i | ||||
\(704\) | 1.93163 | − | 3.34568i | 0.0728009 | − | 0.126095i | ||||
\(705\) | −10.5565 | −0.397579 | ||||||||
\(706\) | 13.2663 | + | 22.9779i | 0.499284 | + | 0.864785i | ||||
\(707\) | −22.0612 | − | 38.2111i | −0.829696 | − | 1.43708i | ||||
\(708\) | 6.77823 | − | 11.7402i | 0.254741 | − | 0.441225i | ||||
\(709\) | −45.1557 | −1.69586 | −0.847929 | − | 0.530110i | \(-0.822150\pi\) | ||||
−0.847929 | + | 0.530110i | \(0.822150\pi\) | |||||||
\(710\) | 1.51882 | + | 2.63067i | 0.0570002 | + | 0.0987272i | ||||
\(711\) | −4.38207 | −0.164340 | ||||||||
\(712\) | 2.96237 | 0.111019 | ||||||||
\(713\) | 28.2710 | − | 12.0385i | 1.05876 | − | 0.450846i | ||||
\(714\) | 2.17438 | 0.0813741 | ||||||||
\(715\) | −27.1882 | −1.01678 | ||||||||
\(716\) | −6.10601 | − | 10.5759i | −0.228192 | − | 0.395240i | ||||
\(717\) | 20.7641 | 0.775451 | ||||||||
\(718\) | 4.56837 | − | 7.91265i | 0.170490 | − | 0.295298i | ||||
\(719\) | −3.18630 | − | 5.51884i | −0.118829 | − | 0.205818i | 0.800475 | − | 0.599366i | \(-0.204581\pi\) |
−0.919304 | + | 0.393548i | \(0.871247\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.0186339 | − | 0.0322749i | ||||
\(721\) | 70.2967 | 2.61799 | ||||||||
\(722\) | 21.7120 | − | 37.6063i | 0.808037 | − | 1.39956i | ||||
\(723\) | −9.82778 | + | 17.0222i | −0.365499 | + | 0.633063i | ||||
\(724\) | 5.38207 | − | 9.32202i | 0.200023 | − | 0.346450i | ||||
\(725\) | −4.69104 | − | 8.12511i | −0.174221 | − | 0.301759i | ||||
\(726\) | −1.96237 | + | 3.39892i | −0.0728303 | + | 0.126146i | ||||
\(727\) | −25.9902 | − | 45.0164i | −0.963925 | − | 1.66957i | −0.712477 | − | 0.701695i | \(-0.752427\pi\) |
−0.251447 | − | 0.967871i | \(-0.580907\pi\) | |||||||
\(728\) | −31.8018 | −1.17865 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | − | 1.73205i | −0.0370117 | − | 0.0641061i | ||||
\(731\) | 1.05429 | − | 1.82608i | 0.0389943 | − | 0.0675401i | ||||
\(732\) | 2.95044 | + | 5.11032i | 0.109052 | + | 0.188883i | ||||
\(733\) | 15.0586 | − | 26.0823i | 0.556202 | − | 0.963371i | −0.441606 | − | 0.897209i | \(-0.645591\pi\) |
0.997809 | − | 0.0661621i | \(-0.0210754\pi\) | |||||||
\(734\) | −12.0000 | + | 20.7846i | −0.442928 | + | 0.767174i | ||||
\(735\) | 6.70985 | − | 11.6218i | 0.247497 | − | 0.428677i | ||||
\(736\) | −5.51882 | −0.203426 | ||||||||
\(737\) | 4.79272 | + | 8.30124i | 0.176542 | + | 0.305780i | ||||
\(738\) | 4.08719 | + | 7.07922i | 0.150452 | + | 0.260590i | ||||
\(739\) | 16.6060 | − | 28.7624i | 0.610862 | − | 1.05804i | −0.380234 | − | 0.924890i | \(-0.624156\pi\) |
0.991095 | − | 0.133153i | \(-0.0425102\pi\) | |||||||
\(740\) | −2.48118 | −0.0912101 | ||||||||
\(741\) | −27.8018 | − | 48.1541i | −1.02132 | − | 1.76898i | ||||
\(742\) | 7.48118 | 0.274643 | ||||||||
\(743\) | −19.3444 | −0.709679 | −0.354839 | − | 0.934927i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934927i | \(0.615464\pi\) | |||||||
\(744\) | −4.45044 | − | 3.34568i | −0.163161 | − | 0.122658i | ||||
\(745\) | −15.6556 | −0.573575 | ||||||||
\(746\) | −25.3959 | −0.929808 | ||||||||
\(747\) | 0.603846 | + | 1.04589i | 0.0220936 | + | 0.0382672i | ||||
\(748\) | −1.85893 | −0.0679693 | ||||||||
\(749\) | −10.2099 | + | 17.6840i | −0.373060 | + | 0.646159i | ||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | 11.8325 | + | 20.4945i | 0.431775 | + | 0.747856i | 0.997026 | − | 0.0770630i | \(-0.0245543\pi\) |
−0.565252 | + | 0.824919i | \(0.691221\pi\) | |||||||
\(752\) | 10.5565 | 0.384954 | ||||||||
\(753\) | −0.191035 | + | 0.330883i | −0.00696172 | + | 0.0120581i | ||||
\(754\) | 33.0138 | − | 57.1816i | 1.20229 | − | 2.08243i | ||||
\(755\) | 7.45044 | − | 12.9045i | 0.271149 | − | 0.469645i | ||||
\(756\) | 2.25941 | + | 3.91341i | 0.0821739 | + | 0.142329i | ||||
\(757\) | −17.6107 | + | 30.5027i | −0.640073 | + | 1.10864i | 0.345343 | + | 0.938477i | \(0.387763\pi\) |
−0.985416 | + | 0.170163i | \(0.945571\pi\) | |||||||
\(758\) | −13.9385 | − | 24.1422i | −0.506270 | − | 0.876885i | ||||
\(759\) | 21.3206 | 0.773888 | ||||||||
\(760\) | 7.90089 | 0.286595 | ||||||||
\(761\) | −1.77606 | − | 3.07623i | −0.0643823 | − | 0.111513i | 0.832038 | − | 0.554719i | \(-0.187174\pi\) |
−0.896420 | + | 0.443206i | \(0.853841\pi\) | |||||||
\(762\) | 1.60385 | − | 2.77794i | 0.0581012 | − | 0.100634i | ||||
\(763\) | −17.8513 | − | 30.9194i | −0.646262 | − | 1.11936i | ||||
\(764\) | −4.95044 | + | 8.57442i | −0.179101 | + | 0.310212i | ||||
\(765\) | −0.240592 | + | 0.416717i | −0.00869861 | + | 0.0150664i | ||||
\(766\) | −8.27823 | + | 14.3383i | −0.299104 | + | 0.518064i | ||||
\(767\) | 95.4053 | 3.44489 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −8.69104 | − | 15.0533i | −0.313407 | − | 0.542836i | 0.665691 | − | 0.746228i | \(-0.268137\pi\) |
−0.979098 | + | 0.203391i | \(0.934804\pi\) | |||||||
\(770\) | −8.72867 | + | 15.1185i | −0.314559 | + | 0.544833i | ||||
\(771\) | −20.9718 | −0.755282 | ||||||||
\(772\) | −10.6910 | − | 18.5174i | −0.384779 | − | 0.666456i | ||||
\(773\) | −28.0753 | −1.00980 | −0.504899 | − | 0.863179i | \(-0.668470\pi\) | ||||
−0.504899 | + | 0.863179i | \(0.668470\pi\) | |||||||
\(774\) | 4.38207 | 0.157510 | ||||||||
\(775\) | −4.45044 | − | 3.34568i | −0.159865 | − | 0.120180i | ||||
\(776\) | 11.4573 | 0.411294 | ||||||||
\(777\) | 11.2120 | 0.402229 | ||||||||
\(778\) | 14.8842 | + | 25.7802i | 0.533626 | + | 0.924267i | ||||
\(779\) | −64.5849 | −2.31399 | ||||||||
\(780\) | 3.51882 | − | 6.09477i | 0.125994 | − | 0.218228i | ||||
\(781\) | 5.86758 | + | 10.1629i | 0.209958 | + | 0.363659i | ||||
\(782\) | 1.32778 | + | 2.29978i | 0.0474814 | + | 0.0822401i | ||||
\(783\) | −9.38207 | −0.335288 | ||||||||
\(784\) | −6.70985 | + | 11.6218i | −0.239638 | + | 0.415064i | ||||
\(785\) | −1.22394 | + | 2.11992i | −0.0436841 | + | 0.0756631i | ||||
\(786\) | 3.32778 | − | 5.76389i | 0.118698 | − | 0.205591i | ||||
\(787\) | 24.1791 | + | 41.8795i | 0.861892 | + | 1.49284i | 0.870100 | + | 0.492875i | \(0.164054\pi\) |
−0.00820790 | + | 0.999966i | \(0.502613\pi\) | |||||||
\(788\) | −3.65556 | + | 6.33162i | −0.130224 | + | 0.225555i | ||||
\(789\) | 1.19104 | + | 2.06293i | 0.0424020 | + | 0.0734424i | ||||
\(790\) | 4.38207 | 0.155907 | ||||||||
\(791\) | −33.5283 | −1.19213 | ||||||||
\(792\) | −1.93163 | − | 3.34568i | −0.0686374 | − | 0.118883i | ||||
\(793\) | −20.7641 | + | 35.9645i | −0.737356 | + | 1.27714i | ||||
\(794\) | −10.3278 | − | 17.8882i | −0.366519 | − | 0.634830i | ||||
\(795\) | −0.827781 | + | 1.43376i | −0.0293584 | + | 0.0508502i | ||||
\(796\) | −1.39615 | + | 2.41821i | −0.0494854 | + | 0.0857112i | ||||
\(797\) | −10.7287 | + | 18.5826i | −0.380029 | + | 0.658229i | −0.991066 | − | 0.133373i | \(-0.957419\pi\) |
0.611037 | + | 0.791602i | \(0.290753\pi\) | |||||||
\(798\) | −35.7027 | −1.26386 | ||||||||
\(799\) | −2.53979 | − | 4.39905i | −0.0898514 | − | 0.155627i | ||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 1.48118 | − | 2.56548i | 0.0523350 | − | 0.0906469i | ||||
\(802\) | 18.8394 | 0.665243 | ||||||||
\(803\) | −3.86325 | − | 6.69135i | −0.136331 | − | 0.236133i | ||||
\(804\) | −2.48118 | −0.0875046 | ||||||||
\(805\) | 24.9385 | 0.878967 | ||||||||
\(806\) | 4.73083 | − | 38.8972i | 0.166636 | − | 1.37010i | ||||
\(807\) | −18.7308 | −0.659356 | ||||||||
\(808\) | −9.76414 | −0.343501 | ||||||||
\(809\) | −17.7522 | − | 30.7477i | −0.624135 | − | 1.08103i | −0.988707 | − | 0.149858i | \(-0.952118\pi\) |
0.364573 | − | 0.931175i | \(-0.381215\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −10.3444 | + | 17.9171i | −0.363242 | + | 0.629154i | −0.988492 | − | 0.151270i | \(-0.951664\pi\) |
0.625250 | + | 0.780424i | \(0.284997\pi\) | |||||||
\(812\) | −21.1979 | − | 36.7159i | −0.743901 | − | 1.28848i | ||||
\(813\) | −3.91497 | − | 6.78093i | −0.137304 | − | 0.237818i | ||||
\(814\) | −9.58544 | −0.335970 | ||||||||
\(815\) | 10.6603 | − | 18.4642i | 0.373414 | − | 0.646772i | ||||
\(816\) | 0.240592 | − | 0.416717i | 0.00842239 | − | 0.0145880i | ||||
\(817\) | −17.3111 | + | 29.9837i | −0.605640 | + | 1.04900i | ||||
\(818\) | 3.67438 | + | 6.36421i | 0.128472 | + | 0.222519i | ||||
\(819\) | −15.9009 | + | 27.5411i | −0.555622 | + | 0.962365i | ||||
\(820\) | −4.08719 | − | 7.07922i | −0.142731 | − | 0.247217i | ||||
\(821\) | 1.34876 | 0.0470720 | 0.0235360 | − | 0.999723i | \(-0.492508\pi\) | ||||
0.0235360 | + | 0.999723i | \(0.492508\pi\) | |||||||
\(822\) | −4.82994 | −0.168464 | ||||||||
\(823\) | −9.33468 | − | 16.1681i | −0.325386 | − | 0.563586i | 0.656204 | − | 0.754583i | \(-0.272161\pi\) |
−0.981590 | + | 0.190998i | \(0.938828\pi\) | |||||||
\(824\) | 7.77823 | − | 13.4723i | 0.270967 | − | 0.469329i | ||||
\(825\) | −1.93163 | − | 3.34568i | −0.0672506 | − | 0.116481i | ||||
\(826\) | 30.6296 | − | 53.0519i | 1.06574 | − | 1.84591i | ||||
\(827\) | 13.0376 | − | 22.5818i | 0.453363 | − | 0.785248i | −0.545229 | − | 0.838287i | \(-0.683557\pi\) |
0.998592 | + | 0.0530392i | \(0.0168908\pi\) | |||||||
\(828\) | −2.75941 | + | 4.77944i | −0.0958961 | + | 0.166097i | ||||
\(829\) | −21.5608 | −0.748837 | −0.374418 | − | 0.927260i | \(-0.622158\pi\) | ||||
−0.374418 | + | 0.927260i | \(0.622158\pi\) | |||||||
\(830\) | −0.603846 | − | 1.04589i | −0.0209598 | − | 0.0363034i | ||||
\(831\) | −7.10385 | − | 12.3042i | −0.246430 | − | 0.426829i | ||||
\(832\) | −3.51882 | + | 6.09477i | −0.121993 | + | 0.211298i | ||||
\(833\) | 6.45734 | 0.223733 | ||||||||
\(834\) | −4.43163 | − | 7.67580i | −0.153455 | − | 0.265791i | ||||
\(835\) | −8.58976 | −0.297261 | ||||||||
\(836\) | 30.5231 | 1.05566 | ||||||||
\(837\) | −5.12266 | + | 2.18136i | −0.177065 | + | 0.0753988i | ||||
\(838\) | 11.8633 | 0.409809 | ||||||||
\(839\) | −9.56077 | −0.330074 | −0.165037 | − | 0.986287i | \(-0.552774\pi\) | ||||
−0.165037 | + | 0.986287i | \(0.552774\pi\) | |||||||
\(840\) | −2.25941 | − | 3.91341i | −0.0779570 | − | 0.135025i | ||||
\(841\) | 59.0233 | 2.03528 | ||||||||
\(842\) | −9.81370 | + | 16.9978i | −0.338202 | + | 0.585784i | ||||
\(843\) | 2.31112 | + | 4.00299i | 0.0795994 | + | 0.137870i | ||||
\(844\) | 0.0495562 | + | 0.0858338i | 0.00170579 | + | 0.00295452i | ||||
\(845\) | 36.5283 | 1.25661 | ||||||||
\(846\) | 5.27823 | − | 9.14215i | 0.181469 | − | 0.314314i | ||||
\(847\) | −8.86758 | + | 15.3591i | −0.304693 | + | 0.527745i | ||||
\(848\) | 0.827781 | − | 1.43376i | 0.0284261 | − | 0.0492355i | ||||
\(849\) | 12.7475 | + | 22.0793i | 0.437493 | + | 0.757759i | ||||
\(850\) | 0.240592 | − | 0.416717i | 0.00825223 | − | 0.0142933i | ||||
\(851\) | 6.84660 | + | 11.8587i | 0.234698 | + | 0.406509i | ||||
\(852\) | −3.03763 | −0.104068 | ||||||||
\(853\) | −42.6412 | −1.46001 | −0.730003 | − | 0.683444i | \(-0.760481\pi\) | ||||
−0.730003 | + | 0.683444i | \(0.760481\pi\) | |||||||
\(854\) | 13.3325 | + | 23.0926i | 0.456229 | + | 0.790212i | ||||
\(855\) | 3.95044 | − | 6.84237i | 0.135102 | − | 0.234004i | ||||
\(856\) | 2.25941 | + | 3.91341i | 0.0772250 | + | 0.133758i | ||||
\(857\) | −11.6765 | + | 20.2244i | −0.398863 | + | 0.690851i | −0.993586 | − | 0.113080i | \(-0.963928\pi\) |
0.594723 | + | 0.803931i | \(0.297262\pi\) | |||||||
\(858\) | 13.5941 | − | 23.5456i | 0.464094 | − | 0.803835i | ||||
\(859\) | 2.56837 | − | 4.44855i | 0.0876318 | − | 0.151783i | −0.818878 | − | 0.573968i | \(-0.805403\pi\) |
0.906510 | + | 0.422185i | \(0.138737\pi\) | |||||||
\(860\) | −4.38207 | −0.149427 | ||||||||
\(861\) | 18.4693 | + | 31.9897i | 0.629431 | + | 1.09021i | ||||
\(862\) | 15.6436 | + | 27.0956i | 0.532824 | + | 0.922879i | ||||
\(863\) | 22.1672 | − | 38.3947i | 0.754580 | − | 1.30697i | −0.191003 | − | 0.981589i | \(-0.561174\pi\) |
0.945583 | − | 0.325381i | \(-0.105493\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 2.69104 | + | 4.66101i | 0.0914980 | + | 0.158479i | ||||
\(866\) | −8.68888 | −0.295260 | ||||||||
\(867\) | 16.7685 | 0.569487 | ||||||||
\(868\) | −20.1107 | − | 15.1185i | −0.682603 | − | 0.513155i | ||||
\(869\) | 16.9291 | 0.574279 | ||||||||
\(870\) | 9.38207 | 0.318082 | ||||||||
\(871\) | −8.73083 | − | 15.1222i | −0.295833 | − | 0.512398i | ||||
\(872\) | −7.90089 | −0.267558 | ||||||||
\(873\) | 5.72867 | − | 9.92235i | 0.193886 | − | 0.335821i | ||||
\(874\) | −21.8018 | − | 37.7618i | −0.737456 | − | 1.27731i | ||||
\(875\) | −2.25941 | − | 3.91341i | −0.0763819 | − | 0.132297i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −4.17911 | + | 7.23844i | −0.141119 | + | 0.244425i | −0.927918 | − | 0.372784i | \(-0.878403\pi\) |
0.786800 | + | 0.617209i | \(0.211737\pi\) | |||||||
\(878\) | 16.6248 | − | 28.7950i | 0.561061 | − | 0.971785i | ||||
\(879\) | −3.86541 | + | 6.69509i | −0.130377 | + | 0.225820i | ||||
\(880\) | 1.93163 | + | 3.34568i | 0.0651151 | + | 0.112783i | ||||
\(881\) | −2.49311 | + | 4.31819i | −0.0839949 | + | 0.145483i | −0.904962 | − | 0.425491i | \(-0.860101\pi\) |
0.820968 | + | 0.570975i | \(0.193435\pi\) | |||||||
\(882\) | 6.70985 | + | 11.6218i | 0.225932 | + | 0.391327i | ||||
\(883\) | 16.1600 | 0.543827 | 0.271914 | − | 0.962322i | \(-0.412343\pi\) | ||||
0.271914 | + | 0.962322i | \(0.412343\pi\) | |||||||
\(884\) | 3.38639 | 0.113897 | ||||||||
\(885\) | 6.77823 | + | 11.7402i | 0.227848 | + | 0.394644i | ||||
\(886\) | 7.41970 | − | 12.8513i | 0.249270 | − | 0.431748i | ||||
\(887\) | 23.0586 | + | 39.9387i | 0.774232 | + | 1.34101i | 0.935225 | + | 0.354054i | \(0.115197\pi\) |
−0.160993 | + | 0.986956i | \(0.551470\pi\) | |||||||
\(888\) | 1.24059 | − | 2.14877i | 0.0416315 | − | 0.0721079i | ||||
\(889\) | 7.24749 | − | 12.5530i | 0.243073 | − | 0.421015i | ||||
\(890\) | −1.48118 | + | 2.56548i | −0.0496494 | + | 0.0859952i | ||||
\(891\) | −3.86325 | −0.129424 | ||||||||
\(892\) | 8.12266 | + | 14.0689i | 0.271967 | + | 0.471060i | ||||
\(893\) | 41.7027 | + | 72.2311i | 1.39553 | + | 2.41712i | ||||
\(894\) | 7.82778 | − | 13.5581i | 0.261800 | − | 0.453451i | ||||
\(895\) | 12.2120 | 0.408203 | ||||||||
\(896\) | 2.25941 | + | 3.91341i | 0.0754815 | + | 0.130738i | ||||
\(897\) | −38.8394 | −1.29681 | ||||||||
\(898\) | −5.80178 | −0.193608 | ||||||||
\(899\) | 48.0612 | − | 20.4657i | 1.60293 | − | 0.682568i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −0.796629 | −0.0265396 | ||||||||
\(902\) | −15.7899 | − | 27.3488i | −0.525745 | − | 0.910616i | ||||
\(903\) | 19.8018 | 0.658962 | ||||||||
\(904\) | −3.70985 | + | 6.42565i | −0.123388 | + | 0.213714i | ||||
\(905\) | 5.38207 | + | 9.32202i | 0.178906 | + | 0.309874i | ||||
\(906\) | 7.45044 | + | 12.9045i | 0.247524 | + | 0.428725i | ||||
\(907\) | 50.0753 | 1.66272 | 0.831361 | − | 0.555733i | \(-0.187562\pi\) | ||||
0.831361 | + | 0.555733i | \(0.187562\pi\) | |||||||
\(908\) | 5.64148 | − | 9.77133i | 0.187219 | − | 0.324273i | ||||
\(909\) | −4.88207 | + | 8.45599i | −0.161928 | + | 0.280468i | ||||
\(910\) | 15.9009 | − | 27.5411i | 0.527109 | − | 0.912980i | ||||
\(911\) | −24.7146 | − | 42.8069i | −0.818831 | − | 1.41826i | −0.906544 | − | 0.422111i | \(-0.861289\pi\) |
0.0877135 | − | 0.996146i | \(-0.472044\pi\) | |||||||
\(912\) | −3.95044 | + | 6.84237i | −0.130812 | + | 0.226573i | ||||
\(913\) | −2.33281 | − | 4.04055i | −0.0772047 | − | 0.133723i | ||||
\(914\) | −29.3864 | −0.972015 | ||||||||
\(915\) | −5.90089 | −0.195077 | ||||||||
\(916\) | −5.33251 | − | 9.23619i | −0.176191 | − | 0.305172i | ||||
\(917\) | 15.0376 | − | 26.0459i | 0.496586 | − | 0.860113i | ||||
\(918\) | −0.240592 | − | 0.416717i | −0.00794071 | − | 0.0137537i | ||||
\(919\) | −10.6958 | + | 18.5256i | −0.352821 | + | 0.611104i | −0.986743 | − | 0.162294i | \(-0.948111\pi\) |
0.633922 | + | 0.773397i | \(0.281444\pi\) | |||||||
\(920\) | 2.75941 | − | 4.77944i | 0.0909750 | − | 0.157573i | ||||
\(921\) | −0.223935 | + | 0.387867i | −0.00737892 | + | 0.0127807i | ||||
\(922\) | −25.4907 | −0.839490 | ||||||||
\(923\) | −10.6889 | − | 18.5137i | −0.351829 | − | 0.609385i | ||||
\(924\) | −8.72867 | − | 15.1185i | −0.287152 | − | 0.497362i | ||||
\(925\) | 1.24059 | − | 2.14877i | 0.0407904 | − | 0.0706510i | ||||
\(926\) | −17.3582 | −0.570427 | ||||||||
\(927\) | −7.77823 | − | 13.4723i | −0.255470 | − | 0.442488i | ||||
\(928\) | −9.38207 | −0.307982 | ||||||||
\(929\) | −50.1744 | −1.64617 | −0.823084 | − | 0.567920i | \(-0.807748\pi\) | ||||
−0.823084 | + | 0.567920i | \(0.807748\pi\) | |||||||
\(930\) | 5.12266 | − | 2.18136i | 0.167979 | − | 0.0715296i | ||||
\(931\) | −106.028 | −3.47491 | ||||||||
\(932\) | 6.48118 | 0.212298 | ||||||||
\(933\) | 3.34444 | + | 5.79274i | 0.109492 | + | 0.189646i | ||||
\(934\) | −31.9718 | −1.04615 | ||||||||
\(935\) | 0.929467 | − | 1.60988i | 0.0303968 | − | 0.0526488i | ||||
\(936\) | 3.51882 | + | 6.09477i | 0.115016 | + | 0.199214i | ||||
\(937\) | −8.80178 | − | 15.2451i | −0.287541 | − | 0.498036i | 0.685681 | − | 0.727902i | \(-0.259505\pi\) |
−0.973222 | + | 0.229866i | \(0.926171\pi\) | |||||||
\(938\) | −11.2120 | −0.366085 | ||||||||
\(939\) | −1.48334 | + | 2.56923i | −0.0484071 | + | 0.0838435i | ||||
\(940\) | −5.27823 | + | 9.14215i | −0.172157 | + | 0.298184i | ||||
\(941\) | −13.0188 | + | 22.5493i | −0.424401 | + | 0.735085i | −0.996364 | − | 0.0851948i | \(-0.972849\pi\) |
0.571963 | + | 0.820279i | \(0.306182\pi\) | |||||||
\(942\) | −1.22394 | − | 2.11992i | −0.0398780 | − | 0.0690707i | ||||
\(943\) | −22.5565 | + | 39.0689i | −0.734539 | + | 1.27226i | ||||
\(944\) | −6.77823 | − | 11.7402i | −0.220612 | − | 0.382112i | ||||
\(945\) | −4.51882 | −0.146997 | ||||||||
\(946\) | −16.9291 | −0.550411 | ||||||||
\(947\) | −5.44355 | − | 9.42851i | −0.176892 | − | 0.306385i | 0.763923 | − | 0.645308i | \(-0.223271\pi\) |
−0.940814 | + | 0.338923i | \(0.889938\pi\) | |||||||
\(948\) | −2.19104 | + | 3.79498i | −0.0711615 | + | 0.123255i | ||||
\(949\) | 7.03763 | + | 12.1895i | 0.228451 | + | 0.395689i | ||||
\(950\) | −3.95044 | + | 6.84237i | −0.128169 | + | 0.221996i | ||||
\(951\) | 3.34660 | − | 5.79648i | 0.108521 | − | 0.187964i | ||||
\(952\) | 1.08719 | − | 1.88307i | 0.0352360 | − | 0.0610306i | ||||
\(953\) | 26.0991 | 0.845433 | 0.422717 | − | 0.906262i | \(-0.361077\pi\) | ||||
0.422717 | + | 0.906262i | \(0.361077\pi\) | |||||||
\(954\) | −0.827781 | − | 1.43376i | −0.0268004 | − | 0.0464197i | ||||
\(955\) | −4.95044 | − | 8.57442i | −0.160193 | − | 0.277462i | ||||
\(956\) | 10.3821 | − | 17.9823i | 0.335780 | − | 0.581588i | ||||
\(957\) | 36.2453 | 1.17164 | ||||||||
\(958\) | −10.3325 | − | 17.8964i | −0.333828 | − | 0.578208i | ||||
\(959\) | −21.8256 | −0.704786 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 21.4833 | − | 22.3487i | 0.693011 | − | 0.720927i | ||||
\(962\) | 17.4617 | 0.562986 | ||||||||
\(963\) | 4.51882 | 0.145617 | ||||||||
\(964\) | 9.82778 | + | 17.0222i | 0.316532 | + | 0.548249i | ||||
\(965\) | 21.3821 | 0.688313 | ||||||||
\(966\) | −12.4693 | + | 21.5974i | −0.401192 | + | 0.694885i | ||||
\(967\) | 22.1505 | + | 38.3658i | 0.712313 | + | 1.23376i | 0.963987 | + | 0.265950i | \(0.0856857\pi\) |
−0.251674 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(968\) | 1.96237 | + | 3.39892i | 0.0630729 | + | 0.109245i | ||||
\(969\) | 3.80178 | 0.122131 | ||||||||
\(970\) | −5.72867 | + | 9.92235i | −0.183936 | + | 0.318587i | ||||
\(971\) | 9.41281 | − | 16.3035i | 0.302071 | − | 0.523203i | −0.674534 | − | 0.738244i | \(-0.735655\pi\) |
0.976605 | + | 0.215041i | \(0.0689885\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −20.0257 | − | 34.6855i | −0.641995 | − | 1.11197i | ||||
\(974\) | −11.6415 | + | 20.1636i | −0.373017 | + | 0.646084i | ||||
\(975\) | 3.51882 | + | 6.09477i | 0.112692 | + | 0.195189i | ||||
\(976\) | 5.90089 | 0.188883 | ||||||||
\(977\) | −35.0376 | −1.12095 | −0.560477 | − | 0.828170i | \(-0.689382\pi\) | ||||
−0.560477 | + | 0.828170i | \(0.689382\pi\) | |||||||
\(978\) | 10.6603 | + | 18.4642i | 0.340879 | + | 0.590419i | ||||
\(979\) | −5.72219 | + | 9.91112i | −0.182882 | + | 0.316761i | ||||
\(980\) | −6.70985 | − | 11.6218i | −0.214338 | − | 0.371245i | ||||
\(981\) | −3.95044 | + | 6.84237i | −0.126128 | + | 0.218460i | ||||
\(982\) | −12.8701 | + | 22.2918i | −0.410703 | + | 0.711358i | ||||
\(983\) | 0.617929 | − | 1.07028i | 0.0197089 | − | 0.0341368i | −0.856003 | − | 0.516971i | \(-0.827059\pi\) |
0.875712 | + | 0.482834i | \(0.160393\pi\) | |||||||
\(984\) | 8.17438 | 0.260590 | ||||||||
\(985\) | −3.65556 | − | 6.33162i | −0.116476 | − | 0.201742i | ||||
\(986\) | 2.25725 | + | 3.90967i | 0.0718854 | + | 0.124509i | ||||
\(987\) | 23.8513 | − | 41.3117i | 0.759196 | − | 1.31497i | ||||
\(988\) | −55.6036 | −1.76898 | ||||||||
\(989\) | 12.0919 | + | 20.9438i | 0.384501 | + | 0.665975i | ||||
\(990\) | 3.86325 | 0.122782 | ||||||||
\(991\) | 3.65124 | 0.115986 | 0.0579928 | − | 0.998317i | \(-0.481530\pi\) | ||||
0.0579928 | + | 0.998317i | \(0.481530\pi\) | |||||||
\(992\) | −5.12266 | + | 2.18136i | −0.162645 | + | 0.0692582i | ||||
\(993\) | 7.41024 | 0.235157 | ||||||||
\(994\) | −13.7265 | −0.435378 | ||||||||
\(995\) | −1.39615 | − | 2.41821i | −0.0442611 | − | 0.0766624i | ||||
\(996\) | 1.20769 | 0.0382672 | ||||||||
\(997\) | 21.7899 | − | 37.7411i | 0.690092 | − | 1.19527i | −0.281716 | − | 0.959498i | \(-0.590904\pi\) |
0.971807 | − | 0.235776i | \(-0.0757631\pi\) | |||||||
\(998\) | 6.37015 | + | 11.0334i | 0.201644 | + | 0.349257i | ||||
\(999\) | −1.24059 | − | 2.14877i | −0.0392506 | − | 0.0679840i |
(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 | 930.2.i.n.211.1 | ✓ | 6 | |
31.5 | even | 3 | inner | 930.2.i.n.811.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.n.211.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
930.2.i.n.811.1 | yes | 6 | 31.5 | even | 3 | inner |