Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.12 | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.g.683.12 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.55395 | − | 0.765006i | −0.897174 | − | 0.441676i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.73301 | − | 1.41304i | −0.775024 | − | 0.631931i | ||||
\(6\) | −1.63975 | + | 0.557869i | −0.669425 | + | 0.227749i | ||||
\(7\) | 1.07773 | + | 1.07773i | 0.407342 | + | 0.407342i | 0.880811 | − | 0.473469i | \(-0.156998\pi\) |
−0.473469 | + | 0.880811i | \(0.656998\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.82953 | + | 2.37756i | 0.609844 | + | 0.792522i | ||||
\(10\) | −2.22459 | + | 0.226250i | −0.703478 | + | 0.0715466i | ||||
\(11\) | 5.88520i | 1.77445i | 0.461333 | + | 0.887227i | \(0.347371\pi\) | ||||
−0.461333 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(12\) | −0.765006 | + | 1.55395i | −0.220838 | + | 0.448587i | ||||
\(13\) | −2.66190 | + | 2.66190i | −0.738277 | + | 0.738277i | −0.972244 | − | 0.233967i | \(-0.924829\pi\) |
0.233967 | + | 0.972244i | \(0.424829\pi\) | |||||||
\(14\) | 1.52413 | 0.407342 | ||||||||
\(15\) | 1.61202 | + | 3.52156i | 0.416223 | + | 0.909263i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.04386 | − | 4.04386i | 0.980780 | − | 0.980780i | −0.0190383 | − | 0.999819i | \(-0.506060\pi\) |
0.999819 | + | 0.0190383i | \(0.00606045\pi\) | |||||||
\(18\) | 2.97487 | + | 0.387518i | 0.701183 | + | 0.0913388i | ||||
\(19\) | 3.95873i | 0.908194i | 0.890952 | + | 0.454097i | \(0.150038\pi\) | ||||
−0.890952 | + | 0.454097i | \(0.849962\pi\) | |||||||
\(20\) | −1.41304 | + | 1.73301i | −0.315966 | + | 0.387512i | ||||
\(21\) | −0.850267 | − | 2.49920i | −0.185543 | − | 0.545370i | ||||
\(22\) | 4.16146 | + | 4.16146i | 0.887227 | + | 0.887227i | ||||
\(23\) | −1.71748 | − | 1.71748i | −0.358120 | − | 0.358120i | 0.505000 | − | 0.863120i | \(-0.331493\pi\) |
−0.863120 | + | 0.505000i | \(0.831493\pi\) | |||||||
\(24\) | 0.557869 | + | 1.63975i | 0.113875 | + | 0.334713i | ||||
\(25\) | 1.00663 | + | 4.89762i | 0.201326 | + | 0.979524i | ||||
\(26\) | 3.76449i | 0.738277i | ||||||||
\(27\) | −1.02415 | − | 5.09422i | −0.197098 | − | 0.980384i | ||||
\(28\) | 1.07773 | − | 1.07773i | 0.203671 | − | 0.203671i | ||||
\(29\) | 1.71299 | 0.318094 | 0.159047 | − | 0.987271i | \(-0.449158\pi\) | ||||
0.159047 | + | 0.987271i | \(0.449158\pi\) | |||||||
\(30\) | 3.62999 | + | 1.35024i | 0.662743 | + | 0.246520i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 4.50221 | − | 9.14531i | 0.783734 | − | 1.59199i | ||||
\(34\) | − | 5.71888i | − | 0.980780i | ||||||
\(35\) | −0.344835 | − | 3.39058i | −0.0582878 | − | 0.573112i | ||||
\(36\) | 2.37756 | − | 1.82953i | 0.396261 | − | 0.304922i | ||||
\(37\) | 6.38692 | + | 6.38692i | 1.05000 | + | 1.05000i | 0.998682 | + | 0.0513204i | \(0.0163430\pi\) |
0.0513204 | + | 0.998682i | \(0.483657\pi\) | |||||||
\(38\) | 2.79924 | + | 2.79924i | 0.454097 | + | 0.454097i | ||||
\(39\) | 6.17283 | − | 2.10009i | 0.988443 | − | 0.336284i | ||||
\(40\) | 0.226250 | + | 2.22459i | 0.0357733 | + | 0.351739i | ||||
\(41\) | 2.84590i | 0.444455i | 0.974995 | + | 0.222228i | \(0.0713328\pi\) | ||||
−0.974995 | + | 0.222228i | \(0.928667\pi\) | |||||||
\(42\) | −2.36843 | − | 1.16597i | −0.365457 | − | 0.179913i | ||||
\(43\) | −0.535397 | + | 0.535397i | −0.0816473 | + | 0.0816473i | −0.746751 | − | 0.665104i | \(-0.768387\pi\) |
0.665104 | + | 0.746751i | \(0.268387\pi\) | |||||||
\(44\) | 5.88520 | 0.887227 | ||||||||
\(45\) | 0.189005 | − | 6.70554i | 0.0281752 | − | 0.999603i | ||||
\(46\) | −2.42889 | −0.358120 | ||||||||
\(47\) | 1.30867 | − | 1.30867i | 0.190888 | − | 0.190888i | −0.605191 | − | 0.796080i | \(-0.706903\pi\) |
0.796080 | + | 0.605191i | \(0.206903\pi\) | |||||||
\(48\) | 1.55395 | + | 0.765006i | 0.224294 | + | 0.110419i | ||||
\(49\) | − | 4.67702i | − | 0.668145i | ||||||
\(50\) | 4.17494 | + | 2.75135i | 0.590425 | + | 0.389099i | ||||
\(51\) | −9.37754 | + | 3.19039i | −1.31312 | + | 0.446744i | ||||
\(52\) | 2.66190 | + | 2.66190i | 0.369139 | + | 0.369139i | ||||
\(53\) | −1.86090 | − | 1.86090i | −0.255614 | − | 0.255614i | 0.567653 | − | 0.823268i | \(-0.307851\pi\) |
−0.823268 | + | 0.567653i | \(0.807851\pi\) | |||||||
\(54\) | −4.32635 | − | 2.87797i | −0.588741 | − | 0.391643i | ||||
\(55\) | 8.31603 | − | 10.1991i | 1.12133 | − | 1.37525i | ||||
\(56\) | − | 1.52413i | − | 0.203671i | ||||||
\(57\) | 3.02845 | − | 6.15167i | 0.401128 | − | 0.814808i | ||||
\(58\) | 1.21127 | − | 1.21127i | 0.159047 | − | 0.159047i | ||||
\(59\) | −6.57921 | −0.856541 | −0.428270 | − | 0.903651i | \(-0.640877\pi\) | ||||
−0.428270 | + | 0.903651i | \(0.640877\pi\) | |||||||
\(60\) | 3.52156 | − | 1.61202i | 0.454631 | − | 0.208111i | ||||
\(61\) | 3.80070 | 0.486630 | 0.243315 | − | 0.969947i | \(-0.421765\pi\) | ||||
0.243315 | + | 0.969947i | \(0.421765\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | −0.590629 | + | 4.53409i | −0.0744122 | + | 0.571242i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 8.37446 | − | 0.851716i | 1.03872 | − | 0.105642i | ||||
\(66\) | −3.28317 | − | 9.65026i | −0.404130 | − | 1.18786i | ||||
\(67\) | 8.88129 | + | 8.88129i | 1.08502 | + | 1.08502i | 0.996033 | + | 0.0889895i | \(0.0283637\pi\) |
0.0889895 | + | 0.996033i | \(0.471636\pi\) | |||||||
\(68\) | −4.04386 | − | 4.04386i | −0.490390 | − | 0.490390i | ||||
\(69\) | 1.35500 | + | 3.98277i | 0.163123 | + | 0.479469i | ||||
\(70\) | −2.64133 | − | 2.15366i | −0.315700 | − | 0.257412i | ||||
\(71\) | 5.12798i | 0.608579i | 0.952580 | + | 0.304290i | \(0.0984191\pi\) | ||||
−0.952580 | + | 0.304290i | \(0.901581\pi\) | |||||||
\(72\) | 0.387518 | − | 2.97487i | 0.0456694 | − | 0.350591i | ||||
\(73\) | −5.41812 | + | 5.41812i | −0.634143 | + | 0.634143i | −0.949104 | − | 0.314962i | \(-0.898008\pi\) |
0.314962 | + | 0.949104i | \(0.398008\pi\) | |||||||
\(74\) | 9.03246 | 1.05000 | ||||||||
\(75\) | 2.18246 | − | 8.38074i | 0.252009 | − | 0.967725i | ||||
\(76\) | 3.95873 | 0.454097 | ||||||||
\(77\) | −6.34263 | + | 6.34263i | −0.722809 | + | 0.722809i | ||||
\(78\) | 2.87986 | − | 5.84984i | 0.326080 | − | 0.662364i | ||||
\(79\) | 16.1838i | 1.82082i | 0.413706 | + | 0.910411i | \(0.364234\pi\) | ||||
−0.413706 | + | 0.910411i | \(0.635766\pi\) | |||||||
\(80\) | 1.73301 | + | 1.41304i | 0.193756 | + | 0.157983i | ||||
\(81\) | −2.30563 | + | 8.69966i | −0.256181 | + | 0.966629i | ||||
\(82\) | 2.01236 | + | 2.01236i | 0.222228 | + | 0.222228i | ||||
\(83\) | 11.7132 | + | 11.7132i | 1.28569 | + | 1.28569i | 0.937381 | + | 0.348305i | \(0.113242\pi\) |
0.348305 | + | 0.937381i | \(0.386758\pi\) | |||||||
\(84\) | −2.49920 | + | 0.850267i | −0.272685 | + | 0.0927717i | ||||
\(85\) | −12.7222 | + | 1.29390i | −1.37991 | + | 0.140343i | ||||
\(86\) | 0.757166i | 0.0816473i | ||||||||
\(87\) | −2.66190 | − | 1.31045i | −0.285386 | − | 0.140495i | ||||
\(88\) | 4.16146 | − | 4.16146i | 0.443613 | − | 0.443613i | ||||
\(89\) | −1.16940 | −0.123956 | −0.0619779 | − | 0.998078i | \(-0.519741\pi\) | ||||
−0.0619779 | + | 0.998078i | \(0.519741\pi\) | |||||||
\(90\) | −4.60789 | − | 4.87518i | −0.485714 | − | 0.513889i | ||||
\(91\) | −5.73759 | −0.601462 | ||||||||
\(92\) | −1.71748 | + | 1.71748i | −0.179060 | + | 0.179060i | ||||
\(93\) | −1.55395 | − | 0.765006i | −0.161137 | − | 0.0793274i | ||||
\(94\) | − | 1.85073i | − | 0.190888i | ||||||
\(95\) | 5.59384 | − | 6.86050i | 0.573916 | − | 0.703873i | ||||
\(96\) | 1.63975 | − | 0.557869i | 0.167356 | − | 0.0569373i | ||||
\(97\) | −9.95765 | − | 9.95765i | −1.01105 | − | 1.01105i | −0.999938 | − | 0.0111079i | \(-0.996464\pi\) |
−0.0111079 | − | 0.999938i | \(-0.503536\pi\) | |||||||
\(98\) | −3.30715 | − | 3.30715i | −0.334073 | − | 0.334073i | ||||
\(99\) | −13.9924 | + | 10.7672i | −1.40629 | + | 1.08214i | ||||
\(100\) | 4.89762 | − | 1.00663i | 0.489762 | − | 0.100663i | ||||
\(101\) | 10.1399i | 1.00895i | 0.863425 | + | 0.504477i | \(0.168315\pi\) | ||||
−0.863425 | + | 0.504477i | \(0.831685\pi\) | |||||||
\(102\) | −4.37498 | + | 8.88687i | −0.433188 | + | 0.879931i | ||||
\(103\) | 12.1481 | − | 12.1481i | 1.19699 | − | 1.19699i | 0.221924 | − | 0.975064i | \(-0.428766\pi\) |
0.975064 | − | 0.221924i | \(-0.0712336\pi\) | |||||||
\(104\) | 3.76449 | 0.369139 | ||||||||
\(105\) | −2.05795 | + | 5.53259i | −0.200836 | + | 0.539926i | ||||
\(106\) | −2.63171 | −0.255614 | ||||||||
\(107\) | −6.82642 | + | 6.82642i | −0.659935 | + | 0.659935i | −0.955364 | − | 0.295430i | \(-0.904537\pi\) |
0.295430 | + | 0.955364i | \(0.404537\pi\) | |||||||
\(108\) | −5.09422 | + | 1.02415i | −0.490192 | + | 0.0985492i | ||||
\(109\) | − | 14.5314i | − | 1.39185i | −0.718112 | − | 0.695927i | \(-0.754994\pi\) | ||
0.718112 | − | 0.695927i | \(-0.245006\pi\) | |||||||
\(110\) | −1.33153 | − | 13.0922i | −0.126956 | − | 1.24829i | ||||
\(111\) | −5.03893 | − | 14.8110i | −0.478274 | − | 1.40580i | ||||
\(112\) | −1.07773 | − | 1.07773i | −0.101835 | − | 0.101835i | ||||
\(113\) | 1.20082 | + | 1.20082i | 0.112963 | + | 0.112963i | 0.761329 | − | 0.648366i | \(-0.224547\pi\) |
−0.648366 | + | 0.761329i | \(0.724547\pi\) | |||||||
\(114\) | −2.20845 | − | 6.49132i | −0.206840 | − | 0.607968i | ||||
\(115\) | 0.549536 | + | 5.40328i | 0.0512445 | + | 0.503859i | ||||
\(116\) | − | 1.71299i | − | 0.159047i | ||||||
\(117\) | −11.1989 | − | 1.45881i | −1.03533 | − | 0.134867i | ||||
\(118\) | −4.65221 | + | 4.65221i | −0.428270 | + | 0.428270i | ||||
\(119\) | 8.71634 | 0.799026 | ||||||||
\(120\) | 1.35024 | − | 3.62999i | 0.123260 | − | 0.331371i | ||||
\(121\) | −23.6355 | −2.14869 | ||||||||
\(122\) | 2.68750 | − | 2.68750i | 0.243315 | − | 0.243315i | ||||
\(123\) | 2.17713 | − | 4.42239i | 0.196305 | − | 0.398754i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 5.17605 | − | 9.91002i | 0.462960 | − | 0.886379i | ||||
\(126\) | 2.78845 | + | 3.62373i | 0.248415 | + | 0.322827i | ||||
\(127\) | 3.09845 | + | 3.09845i | 0.274943 | + | 0.274943i | 0.831086 | − | 0.556143i | \(-0.187720\pi\) |
−0.556143 | + | 0.831086i | \(0.687720\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.24156 | − | 0.422399i | 0.109314 | − | 0.0371902i | ||||
\(130\) | 5.31938 | − | 6.52389i | 0.466541 | − | 0.572183i | ||||
\(131\) | − | 5.24622i | − | 0.458365i | −0.973384 | − | 0.229182i | \(-0.926395\pi\) | ||
0.973384 | − | 0.229182i | \(-0.0736052\pi\) | |||||||
\(132\) | −9.14531 | − | 4.50221i | −0.795997 | − | 0.391867i | ||||
\(133\) | −4.26642 | + | 4.26642i | −0.369945 | + | 0.369945i | ||||
\(134\) | 12.5600 | 1.08502 | ||||||||
\(135\) | −5.42348 | + | 10.2755i | −0.466779 | + | 0.884374i | ||||
\(136\) | −5.71888 | −0.490390 | ||||||||
\(137\) | −13.6538 | + | 13.6538i | −1.16652 | + | 1.16652i | −0.183505 | + | 0.983019i | \(0.558745\pi\) |
−0.983019 | + | 0.183505i | \(0.941255\pi\) | |||||||
\(138\) | 3.77437 | + | 1.85811i | 0.321296 | + | 0.158173i | ||||
\(139\) | 23.1290i | 1.96177i | 0.194577 | + | 0.980887i | \(0.437666\pi\) | ||||
−0.194577 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(140\) | −3.39058 | + | 0.344835i | −0.286556 | + | 0.0291439i | ||||
\(141\) | −3.03474 | + | 1.03247i | −0.255571 | + | 0.0869493i | ||||
\(142\) | 3.62603 | + | 3.62603i | 0.304290 | + | 0.304290i | ||||
\(143\) | −15.6658 | − | 15.6658i | −1.31004 | − | 1.31004i | ||||
\(144\) | −1.82953 | − | 2.37756i | −0.152461 | − | 0.198130i | ||||
\(145\) | −2.96863 | − | 2.42053i | −0.246531 | − | 0.201014i | ||||
\(146\) | 7.66238i | 0.634143i | ||||||||
\(147\) | −3.57795 | + | 7.26786i | −0.295104 | + | 0.599443i | ||||
\(148\) | 6.38692 | − | 6.38692i | 0.525001 | − | 0.525001i | ||||
\(149\) | −17.1237 | −1.40283 | −0.701414 | − | 0.712754i | \(-0.747447\pi\) | ||||
−0.701414 | + | 0.712754i | \(0.747447\pi\) | |||||||
\(150\) | −4.38285 | − | 7.46931i | −0.357858 | − | 0.609867i | ||||
\(151\) | 8.82338 | 0.718036 | 0.359018 | − | 0.933331i | \(-0.383112\pi\) | ||||
0.359018 | + | 0.933331i | \(0.383112\pi\) | |||||||
\(152\) | 2.79924 | − | 2.79924i | 0.227048 | − | 0.227048i | ||||
\(153\) | 17.0129 | + | 2.21617i | 1.37541 | + | 0.179167i | ||||
\(154\) | 8.96983i | 0.722809i | ||||||||
\(155\) | −1.73301 | − | 1.41304i | −0.139198 | − | 0.113498i | ||||
\(156\) | −2.10009 | − | 6.17283i | −0.168142 | − | 0.494222i | ||||
\(157\) | −3.93949 | − | 3.93949i | −0.314406 | − | 0.314406i | 0.532208 | − | 0.846614i | \(-0.321362\pi\) |
−0.846614 | + | 0.532208i | \(0.821362\pi\) | |||||||
\(158\) | 11.4437 | + | 11.4437i | 0.910411 | + | 0.910411i | ||||
\(159\) | 1.46815 | + | 4.31535i | 0.116432 | + | 0.342230i | ||||
\(160\) | 2.22459 | − | 0.226250i | 0.175869 | − | 0.0178866i | ||||
\(161\) | − | 3.70195i | − | 0.291754i | ||||||
\(162\) | 4.52126 | + | 7.78191i | 0.355224 | + | 0.611405i | ||||
\(163\) | 14.1999 | − | 14.1999i | 1.11222 | − | 1.11222i | 0.119369 | − | 0.992850i | \(-0.461913\pi\) |
0.992850 | − | 0.119369i | \(-0.0380871\pi\) | |||||||
\(164\) | 2.84590 | 0.222228 | ||||||||
\(165\) | −20.7251 | + | 9.48708i | −1.61344 | + | 0.738568i | ||||
\(166\) | 16.5649 | 1.28569 | ||||||||
\(167\) | 9.34843 | − | 9.34843i | 0.723403 | − | 0.723403i | −0.245893 | − | 0.969297i | \(-0.579081\pi\) |
0.969297 | + | 0.245893i | \(0.0790813\pi\) | |||||||
\(168\) | −1.16597 | + | 2.36843i | −0.0899566 | + | 0.182728i | ||||
\(169\) | − | 1.17139i | − | 0.0901067i | ||||||
\(170\) | −8.08102 | + | 9.91087i | −0.619786 | + | 0.760129i | ||||
\(171\) | −9.41213 | + | 7.24261i | −0.719763 | + | 0.553857i | ||||
\(172\) | 0.535397 | + | 0.535397i | 0.0408236 | + | 0.0408236i | ||||
\(173\) | −9.23238 | − | 9.23238i | −0.701925 | − | 0.701925i | 0.262898 | − | 0.964824i | \(-0.415322\pi\) |
−0.964824 | + | 0.262898i | \(0.915322\pi\) | |||||||
\(174\) | −2.80888 | + | 0.955624i | −0.212940 | + | 0.0724457i | ||||
\(175\) | −4.19342 | + | 6.36316i | −0.316993 | + | 0.481010i | ||||
\(176\) | − | 5.88520i | − | 0.443613i | ||||||
\(177\) | 10.2238 | + | 5.03314i | 0.768466 | + | 0.378314i | ||||
\(178\) | −0.826888 | + | 0.826888i | −0.0619779 | + | 0.0619779i | ||||
\(179\) | −10.6481 | −0.795880 | −0.397940 | − | 0.917412i | \(-0.630275\pi\) | ||||
−0.397940 | + | 0.917412i | \(0.630275\pi\) | |||||||
\(180\) | −6.70554 | − | 0.189005i | −0.499802 | − | 0.0140876i | ||||
\(181\) | 2.85916 | 0.212520 | 0.106260 | − | 0.994338i | \(-0.466112\pi\) | ||||
0.106260 | + | 0.994338i | \(0.466112\pi\) | |||||||
\(182\) | −4.05709 | + | 4.05709i | −0.300731 | + | 0.300731i | ||||
\(183\) | −5.90611 | − | 2.90756i | −0.436592 | − | 0.214933i | ||||
\(184\) | 2.42889i | 0.179060i | ||||||||
\(185\) | −2.04360 | − | 20.0935i | −0.150248 | − | 1.47731i | ||||
\(186\) | −1.63975 | + | 0.557869i | −0.120232 | + | 0.0409049i | ||||
\(187\) | 23.7989 | + | 23.7989i | 1.74035 | + | 1.74035i | ||||
\(188\) | −1.30867 | − | 1.30867i | −0.0954442 | − | 0.0954442i | ||||
\(189\) | 4.38642 | − | 6.59393i | 0.319065 | − | 0.479638i | ||||
\(190\) | −0.895662 | − | 8.80655i | −0.0649782 | − | 0.638894i | ||||
\(191\) | 12.5060i | 0.904905i | 0.891789 | + | 0.452452i | \(0.149451\pi\) | ||||
−0.891789 | + | 0.452452i | \(0.850549\pi\) | |||||||
\(192\) | 0.765006 | − | 1.55395i | 0.0552095 | − | 0.112147i | ||||
\(193\) | 15.0464 | − | 15.0464i | 1.08306 | − | 1.08306i | 0.0868411 | − | 0.996222i | \(-0.472323\pi\) |
0.996222 | − | 0.0868411i | \(-0.0276773\pi\) | |||||||
\(194\) | −14.0822 | −1.01105 | ||||||||
\(195\) | −13.6651 | − | 5.08298i | −0.978576 | − | 0.364000i | ||||
\(196\) | −4.67702 | −0.334073 | ||||||||
\(197\) | 3.75213 | − | 3.75213i | 0.267328 | − | 0.267328i | −0.560694 | − | 0.828023i | \(-0.689466\pi\) |
0.828023 | + | 0.560694i | \(0.189466\pi\) | |||||||
\(198\) | −2.28062 | + | 17.5077i | −0.162076 | + | 1.24422i | ||||
\(199\) | 11.3351i | 0.803526i | 0.915744 | + | 0.401763i | \(0.131602\pi\) | ||||
−0.915744 | + | 0.401763i | \(0.868398\pi\) | |||||||
\(200\) | 2.75135 | − | 4.17494i | 0.194550 | − | 0.295213i | ||||
\(201\) | −7.00685 | − | 20.5953i | −0.494225 | − | 1.45268i | ||||
\(202\) | 7.16996 | + | 7.16996i | 0.504477 | + | 0.504477i | ||||
\(203\) | 1.84613 | + | 1.84613i | 0.129573 | + | 0.129573i | ||||
\(204\) | 3.19039 | + | 9.37754i | 0.223372 | + | 0.656559i | ||||
\(205\) | 4.02138 | − | 4.93197i | 0.280865 | − | 0.344463i | ||||
\(206\) | − | 17.1800i | − | 1.19699i | ||||||
\(207\) | 0.941237 | − | 7.22562i | 0.0654205 | − | 0.502215i | ||||
\(208\) | 2.66190 | − | 2.66190i | 0.184569 | − | 0.184569i | ||||
\(209\) | −23.2979 | −1.61155 | ||||||||
\(210\) | 2.45694 | + | 5.36733i | 0.169545 | + | 0.370381i | ||||
\(211\) | −13.5196 | −0.930725 | −0.465363 | − | 0.885120i | \(-0.654076\pi\) | ||||
−0.465363 | + | 0.885120i | \(0.654076\pi\) | |||||||
\(212\) | −1.86090 | + | 1.86090i | −0.127807 | + | 0.127807i | ||||
\(213\) | 3.92294 | − | 7.96863i | 0.268795 | − | 0.546002i | ||||
\(214\) | 9.65401i | 0.659935i | ||||||||
\(215\) | 1.68438 | − | 0.171309i | 0.114874 | − | 0.0116832i | ||||
\(216\) | −2.87797 | + | 4.32635i | −0.195821 | + | 0.294371i | ||||
\(217\) | 1.07773 | + | 1.07773i | 0.0731608 | + | 0.0731608i | ||||
\(218\) | −10.2752 | − | 10.2752i | −0.695927 | − | 0.695927i | ||||
\(219\) | 12.5644 | − | 4.27460i | 0.849022 | − | 0.288851i | ||||
\(220\) | −10.1991 | − | 8.31603i | −0.687623 | − | 0.560666i | ||||
\(221\) | 21.5287i | 1.44818i | ||||||||
\(222\) | −14.0360 | − | 6.90989i | −0.942035 | − | 0.463761i | ||||
\(223\) | 6.00939 | − | 6.00939i | 0.402419 | − | 0.402419i | −0.476666 | − | 0.879084i | \(-0.658155\pi\) |
0.879084 | + | 0.476666i | \(0.158155\pi\) | |||||||
\(224\) | −1.52413 | −0.101835 | ||||||||
\(225\) | −9.80275 | + | 11.3537i | −0.653517 | + | 0.756912i | ||||
\(226\) | 1.69821 | 0.112963 | ||||||||
\(227\) | −16.1748 | + | 16.1748i | −1.07356 | + | 1.07356i | −0.0764914 | + | 0.997070i | \(0.524372\pi\) |
−0.997070 | + | 0.0764914i | \(0.975628\pi\) | |||||||
\(228\) | −6.15167 | − | 3.02845i | −0.407404 | − | 0.200564i | ||||
\(229\) | 5.34021i | 0.352891i | 0.984310 | + | 0.176446i | \(0.0564600\pi\) | ||||
−0.984310 | + | 0.176446i | \(0.943540\pi\) | |||||||
\(230\) | 4.20928 | + | 3.43212i | 0.277552 | + | 0.226307i | ||||
\(231\) | 14.7083 | − | 5.00399i | 0.967734 | − | 0.329238i | ||||
\(232\) | −1.21127 | − | 1.21127i | −0.0795236 | − | 0.0795236i | ||||
\(233\) | 3.40443 | + | 3.40443i | 0.223032 | + | 0.223032i | 0.809774 | − | 0.586742i | \(-0.199590\pi\) |
−0.586742 | + | 0.809774i | \(0.699590\pi\) | |||||||
\(234\) | −8.95032 | + | 6.88725i | −0.585101 | + | 0.450234i | ||||
\(235\) | −4.11712 | + | 0.418728i | −0.268572 | + | 0.0273148i | ||||
\(236\) | 6.57921i | 0.428270i | ||||||||
\(237\) | 12.3807 | − | 25.1489i | 0.804214 | − | 1.63359i | ||||
\(238\) | 6.16338 | − | 6.16338i | 0.399513 | − | 0.399513i | ||||
\(239\) | 2.52085 | 0.163061 | 0.0815303 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815303 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(240\) | −1.61202 | − | 3.52156i | −0.104056 | − | 0.227316i | ||||
\(241\) | 1.79206 | 0.115437 | 0.0577183 | − | 0.998333i | \(-0.481617\pi\) | ||||
0.0577183 | + | 0.998333i | \(0.481617\pi\) | |||||||
\(242\) | −16.7129 | + | 16.7129i | −1.07434 | + | 1.07434i | ||||
\(243\) | 10.2381 | − | 11.7550i | 0.656776 | − | 0.754086i | ||||
\(244\) | − | 3.80070i | − | 0.243315i | ||||||
\(245\) | −6.60882 | + | 8.10530i | −0.422222 | + | 0.517829i | ||||
\(246\) | −1.58764 | − | 4.66657i | −0.101224 | − | 0.297529i | ||||
\(247\) | −10.5377 | − | 10.5377i | −0.670499 | − | 0.670499i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | −9.24105 | − | 27.1623i | −0.585627 | − | 1.72134i | ||||
\(250\) | −3.34743 | − | 10.6675i | −0.211710 | − | 0.674670i | ||||
\(251\) | − | 6.83182i | − | 0.431221i | −0.976479 | − | 0.215610i | \(-0.930826\pi\) | ||
0.976479 | − | 0.215610i | \(-0.0691741\pi\) | |||||||
\(252\) | 4.53409 | + | 0.590629i | 0.285621 | + | 0.0372061i | ||||
\(253\) | 10.1077 | − | 10.1077i | 0.635467 | − | 0.635467i | ||||
\(254\) | 4.38187 | 0.274943 | ||||||||
\(255\) | 20.7595 | + | 7.72189i | 1.30001 | + | 0.483564i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.63537 | − | 7.63537i | 0.476281 | − | 0.476281i | −0.427659 | − | 0.903940i | \(-0.640662\pi\) |
0.903940 | + | 0.427659i | \(0.140662\pi\) | |||||||
\(258\) | 0.579236 | − | 1.17660i | 0.0360617 | − | 0.0732518i | ||||
\(259\) | 13.7667i | 0.855420i | ||||||||
\(260\) | −0.851716 | − | 8.37446i | −0.0528212 | − | 0.519362i | ||||
\(261\) | 3.13397 | + | 4.07275i | 0.193988 | + | 0.252097i | ||||
\(262\) | −3.70964 | − | 3.70964i | −0.229182 | − | 0.229182i | ||||
\(263\) | −18.0739 | − | 18.0739i | −1.11449 | − | 1.11449i | −0.992536 | − | 0.121950i | \(-0.961085\pi\) |
−0.121950 | − | 0.992536i | \(-0.538915\pi\) | |||||||
\(264\) | −9.65026 | + | 3.28317i | −0.593932 | + | 0.202065i | ||||
\(265\) | 0.595425 | + | 5.85448i | 0.0365767 | + | 0.359638i | ||||
\(266\) | 6.03363i | 0.369945i | ||||||||
\(267\) | 1.81719 | + | 0.894595i | 0.111210 | + | 0.0547483i | ||||
\(268\) | 8.88129 | − | 8.88129i | 0.542511 | − | 0.542511i | ||||
\(269\) | 7.67463 | 0.467930 | 0.233965 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233965 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(270\) | 3.43089 | + | 11.1009i | 0.208797 | + | 0.675577i | ||||
\(271\) | 18.7691 | 1.14014 | 0.570072 | − | 0.821595i | \(-0.306915\pi\) | ||||
0.570072 | + | 0.821595i | \(0.306915\pi\) | |||||||
\(272\) | −4.04386 | + | 4.04386i | −0.245195 | + | 0.245195i | ||||
\(273\) | 8.91593 | + | 4.38929i | 0.539617 | + | 0.265652i | ||||
\(274\) | 19.3094i | 1.16652i | ||||||||
\(275\) | −28.8235 | + | 5.92421i | −1.73812 | + | 0.357243i | ||||
\(276\) | 3.98277 | − | 1.35500i | 0.239735 | − | 0.0815615i | ||||
\(277\) | 3.61928 | + | 3.61928i | 0.217462 | + | 0.217462i | 0.807428 | − | 0.589966i | \(-0.200859\pi\) |
−0.589966 | + | 0.807428i | \(0.700859\pi\) | |||||||
\(278\) | 16.3547 | + | 16.3547i | 0.980887 | + | 0.980887i | ||||
\(279\) | 1.82953 | + | 2.37756i | 0.109531 | + | 0.142341i | ||||
\(280\) | −2.15366 | + | 2.64133i | −0.128706 | + | 0.157850i | ||||
\(281\) | 12.1681i | 0.725885i | 0.931812 | + | 0.362943i | \(0.118228\pi\) | ||||
−0.931812 | + | 0.362943i | \(0.881772\pi\) | |||||||
\(282\) | −1.41582 | + | 2.87595i | −0.0843109 | + | 0.171260i | ||||
\(283\) | −15.9927 | + | 15.9927i | −0.950666 | + | 0.950666i | −0.998839 | − | 0.0481726i | \(-0.984660\pi\) |
0.0481726 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(284\) | 5.12798 | 0.304290 | ||||||||
\(285\) | −13.9409 | + | 6.38156i | −0.825787 | + | 0.378011i | ||||
\(286\) | −22.1548 | −1.31004 | ||||||||
\(287\) | −3.06710 | + | 3.06710i | −0.181045 | + | 0.181045i | ||||
\(288\) | −2.97487 | − | 0.387518i | −0.175296 | − | 0.0228347i | ||||
\(289\) | − | 15.7056i | − | 0.923861i | ||||||
\(290\) | −3.81071 | + | 0.387564i | −0.223772 | + | 0.0227586i | ||||
\(291\) | 7.85605 | + | 23.0914i | 0.460530 | + | 1.35364i | ||||
\(292\) | 5.41812 | + | 5.41812i | 0.317071 | + | 0.317071i | ||||
\(293\) | 6.25670 | + | 6.25670i | 0.365520 | + | 0.365520i | 0.865841 | − | 0.500320i | \(-0.166784\pi\) |
−0.500320 | + | 0.865841i | \(0.666784\pi\) | |||||||
\(294\) | 2.60916 | + | 7.66914i | 0.152169 | + | 0.447273i | ||||
\(295\) | 11.4018 | + | 9.29670i | 0.663840 | + | 0.541275i | ||||
\(296\) | − | 9.03246i | − | 0.525001i | ||||||
\(297\) | 29.9805 | − | 6.02734i | 1.73965 | − | 0.349742i | ||||
\(298\) | −12.1083 | + | 12.1083i | −0.701414 | + | 0.701414i | ||||
\(299\) | 9.14352 | 0.528784 | ||||||||
\(300\) | −8.38074 | − | 2.18246i | −0.483863 | − | 0.126004i | ||||
\(301\) | −1.15402 | −0.0665167 | ||||||||
\(302\) | 6.23907 | − | 6.23907i | 0.359018 | − | 0.359018i | ||||
\(303\) | 7.75705 | − | 15.7568i | 0.445631 | − | 0.905207i | ||||
\(304\) | − | 3.95873i | − | 0.227048i | ||||||
\(305\) | −6.58664 | − | 5.37055i | −0.377150 | − | 0.307517i | ||||
\(306\) | 13.5970 | − | 10.4629i | 0.777290 | − | 0.598123i | ||||
\(307\) | −10.7489 | − | 10.7489i | −0.613469 | − | 0.613469i | 0.330379 | − | 0.943848i | \(-0.392823\pi\) |
−0.943848 | + | 0.330379i | \(0.892823\pi\) | |||||||
\(308\) | 6.34263 | + | 6.34263i | 0.361405 | + | 0.361405i | ||||
\(309\) | −28.1709 | + | 9.58419i | −1.60259 | + | 0.545226i | ||||
\(310\) | −2.22459 | + | 0.226250i | −0.126348 | + | 0.0128501i | ||||
\(311\) | − | 5.04541i | − | 0.286099i | −0.989716 | − | 0.143049i | \(-0.954309\pi\) | ||
0.989716 | − | 0.143049i | \(-0.0456908\pi\) | |||||||
\(312\) | −5.84984 | − | 2.87986i | −0.331182 | − | 0.163040i | ||||
\(313\) | −0.666018 | + | 0.666018i | −0.0376456 | + | 0.0376456i | −0.725679 | − | 0.688033i | \(-0.758474\pi\) |
0.688033 | + | 0.725679i | \(0.258474\pi\) | |||||||
\(314\) | −5.57128 | −0.314406 | ||||||||
\(315\) | 7.43043 | − | 7.02303i | 0.418657 | − | 0.395703i | ||||
\(316\) | 16.1838 | 0.910411 | ||||||||
\(317\) | 0.0859022 | − | 0.0859022i | 0.00482475 | − | 0.00482475i | −0.704690 | − | 0.709515i | \(-0.748914\pi\) |
0.709515 | + | 0.704690i | \(0.248914\pi\) | |||||||
\(318\) | 4.08955 | + | 2.01327i | 0.229331 | + | 0.112899i | ||||
\(319\) | 10.0813i | 0.564444i | ||||||||
\(320\) | 1.41304 | − | 1.73301i | 0.0789914 | − | 0.0968781i | ||||
\(321\) | 15.8302 | − | 5.38567i | 0.883554 | − | 0.300599i | ||||
\(322\) | −2.61767 | − | 2.61767i | −0.145877 | − | 0.145877i | ||||
\(323\) | 16.0085 | + | 16.0085i | 0.890739 | + | 0.890739i | ||||
\(324\) | 8.69966 | + | 2.30563i | 0.483314 | + | 0.128090i | ||||
\(325\) | −15.7165 | − | 10.3574i | −0.871795 | − | 0.574526i | ||||
\(326\) | − | 20.0816i | − | 1.11222i | ||||||
\(327\) | −11.1166 | + | 22.5811i | −0.614749 | + | 1.24874i | ||||
\(328\) | 2.01236 | − | 2.01236i | 0.111114 | − | 0.111114i | ||||
\(329\) | 2.82076 | 0.155514 | ||||||||
\(330\) | −7.94646 | + | 21.3632i | −0.437438 | + | 1.17601i | ||||
\(331\) | 14.5931 | 0.802107 | 0.401053 | − | 0.916055i | \(-0.368644\pi\) | ||||
0.401053 | + | 0.916055i | \(0.368644\pi\) | |||||||
\(332\) | 11.7132 | − | 11.7132i | 0.642843 | − | 0.642843i | ||||
\(333\) | −3.50024 | + | 26.8704i | −0.191812 | + | 1.47249i | ||||
\(334\) | − | 13.2207i | − | 0.723403i | ||||||
\(335\) | −2.84171 | − | 27.9410i | −0.155259 | − | 1.52658i | ||||
\(336\) | 0.850267 | + | 2.49920i | 0.0463859 | + | 0.136342i | ||||
\(337\) | 11.9367 | + | 11.9367i | 0.650236 | + | 0.650236i | 0.953050 | − | 0.302814i | \(-0.0979261\pi\) |
−0.302814 | + | 0.953050i | \(0.597926\pi\) | |||||||
\(338\) | −0.828296 | − | 0.828296i | −0.0450534 | − | 0.0450534i | ||||
\(339\) | −0.947380 | − | 2.78465i | −0.0514546 | − | 0.151241i | ||||
\(340\) | 1.29390 | + | 12.7222i | 0.0701715 | + | 0.689957i | ||||
\(341\) | 5.88520i | 0.318701i | ||||||||
\(342\) | −1.53408 | + | 11.7767i | −0.0829533 | + | 0.636810i | ||||
\(343\) | 12.5846 | − | 12.5846i | 0.679505 | − | 0.679505i | ||||
\(344\) | 0.757166 | 0.0408236 | ||||||||
\(345\) | 3.27959 | − | 8.81684i | 0.176567 | − | 0.474683i | ||||
\(346\) | −13.0566 | −0.701925 | ||||||||
\(347\) | 10.9974 | − | 10.9974i | 0.590371 | − | 0.590371i | −0.347361 | − | 0.937732i | \(-0.612922\pi\) |
0.937732 | + | 0.347361i | \(0.112922\pi\) | |||||||
\(348\) | −1.31045 | + | 2.66190i | −0.0702474 | + | 0.142693i | ||||
\(349\) | − | 21.9906i | − | 1.17713i | −0.808449 | − | 0.588566i | \(-0.799693\pi\) | ||
0.808449 | − | 0.588566i | \(-0.200307\pi\) | |||||||
\(350\) | 1.53424 | + | 7.46463i | 0.0820084 | + | 0.399001i | ||||
\(351\) | 16.2865 | + | 10.8341i | 0.869308 | + | 0.578282i | ||||
\(352\) | −4.16146 | − | 4.16146i | −0.221807 | − | 0.221807i | ||||
\(353\) | −22.1302 | − | 22.1302i | −1.17787 | − | 1.17787i | −0.980285 | − | 0.197587i | \(-0.936690\pi\) |
−0.197587 | − | 0.980285i | \(-0.563310\pi\) | |||||||
\(354\) | 10.7883 | − | 3.67034i | 0.573390 | − | 0.195076i | ||||
\(355\) | 7.24605 | − | 8.88683i | 0.384580 | − | 0.471664i | ||||
\(356\) | 1.16940i | 0.0619779i | ||||||||
\(357\) | −13.5448 | − | 6.66805i | −0.716866 | − | 0.352911i | ||||
\(358\) | −7.52937 | + | 7.52937i | −0.397940 | + | 0.397940i | ||||
\(359\) | −14.8084 | −0.781558 | −0.390779 | − | 0.920485i | \(-0.627794\pi\) | ||||
−0.390779 | + | 0.920485i | \(0.627794\pi\) | |||||||
\(360\) | −4.87518 | + | 4.60789i | −0.256945 | + | 0.242857i | ||||
\(361\) | 3.32849 | 0.175184 | ||||||||
\(362\) | 2.02173 | − | 2.02173i | 0.106260 | − | 0.106260i | ||||
\(363\) | 36.7285 | + | 18.0813i | 1.92775 | + | 0.949024i | ||||
\(364\) | 5.73759i | 0.300731i | ||||||||
\(365\) | 17.0457 | − | 1.73361i | 0.892211 | − | 0.0907415i | ||||
\(366\) | −6.23220 | + | 2.12029i | −0.325763 | + | 0.110830i | ||||
\(367\) | 0.143077 | + | 0.143077i | 0.00746858 | + | 0.00746858i | 0.710831 | − | 0.703363i | \(-0.248319\pi\) |
−0.703363 | + | 0.710831i | \(0.748319\pi\) | |||||||
\(368\) | 1.71748 | + | 1.71748i | 0.0895300 | + | 0.0895300i | ||||
\(369\) | −6.76631 | + | 5.20667i | −0.352240 | + | 0.271048i | ||||
\(370\) | −15.6533 | − | 12.7632i | −0.813778 | − | 0.663529i | ||||
\(371\) | − | 4.01108i | − | 0.208245i | ||||||
\(372\) | −0.765006 | + | 1.55395i | −0.0396637 | + | 0.0805686i | ||||
\(373\) | −22.4080 | + | 22.4080i | −1.16024 | + | 1.16024i | −0.175819 | + | 0.984423i | \(0.556257\pi\) |
−0.984423 | + | 0.175819i | \(0.943743\pi\) | |||||||
\(374\) | 33.6568 | 1.74035 | ||||||||
\(375\) | −15.6246 | + | 11.4400i | −0.806848 | + | 0.590758i | ||||
\(376\) | −1.85073 | −0.0954442 | ||||||||
\(377\) | −4.55980 | + | 4.55980i | −0.234842 | + | 0.234842i | ||||
\(378\) | −1.56095 | − | 7.76428i | −0.0802864 | − | 0.399351i | ||||
\(379\) | 23.1791i | 1.19063i | 0.803492 | + | 0.595316i | \(0.202973\pi\) | ||||
−0.803492 | + | 0.595316i | \(0.797027\pi\) | |||||||
\(380\) | −6.86050 | − | 5.59384i | −0.351936 | − | 0.286958i | ||||
\(381\) | −2.44451 | − | 7.18517i | −0.125236 | − | 0.368107i | ||||
\(382\) | 8.84310 | + | 8.84310i | 0.452452 | + | 0.452452i | ||||
\(383\) | 22.9626 | + | 22.9626i | 1.17333 | + | 1.17333i | 0.981410 | + | 0.191925i | \(0.0614729\pi\) |
0.191925 | + | 0.981410i | \(0.438527\pi\) | |||||||
\(384\) | −0.557869 | − | 1.63975i | −0.0284686 | − | 0.0836782i | ||||
\(385\) | 19.9542 | − | 2.02942i | 1.01696 | − | 0.103429i | ||||
\(386\) | − | 21.2788i | − | 1.08306i | ||||||
\(387\) | −2.25247 | − | 0.293415i | −0.114499 | − | 0.0149151i | ||||
\(388\) | −9.95765 | + | 9.95765i | −0.505523 | + | 0.505523i | ||||
\(389\) | 12.6552 | 0.641643 | 0.320822 | − | 0.947140i | \(-0.396041\pi\) | ||||
0.320822 | + | 0.947140i | \(0.396041\pi\) | |||||||
\(390\) | −13.2569 | + | 6.06845i | −0.671288 | + | 0.307288i | ||||
\(391\) | −13.8905 | −0.702474 | ||||||||
\(392\) | −3.30715 | + | 3.30715i | −0.167036 | + | 0.167036i | ||||
\(393\) | −4.01339 | + | 8.15238i | −0.202449 | + | 0.411233i | ||||
\(394\) | − | 5.30632i | − | 0.267328i | ||||||
\(395\) | 22.8684 | − | 28.0467i | 1.15063 | − | 1.41118i | ||||
\(396\) | 10.7672 | + | 13.9924i | 0.541070 | + | 0.703146i | ||||
\(397\) | −19.5158 | − | 19.5158i | −0.979468 | − | 0.979468i | 0.0203254 | − | 0.999793i | \(-0.493530\pi\) |
−0.999793 | + | 0.0203254i | \(0.993530\pi\) | |||||||
\(398\) | 8.01515 | + | 8.01515i | 0.401763 | + | 0.401763i | ||||
\(399\) | 9.89364 | − | 3.36597i | 0.495302 | − | 0.168509i | ||||
\(400\) | −1.00663 | − | 4.89762i | −0.0503314 | − | 0.244881i | ||||
\(401\) | − | 19.1422i | − | 0.955914i | −0.878383 | − | 0.477957i | \(-0.841378\pi\) | ||
0.878383 | − | 0.477957i | \(-0.158622\pi\) | |||||||
\(402\) | −19.5177 | − | 9.60850i | −0.973454 | − | 0.479229i | ||||
\(403\) | −2.66190 | + | 2.66190i | −0.132599 | + | 0.132599i | ||||
\(404\) | 10.1399 | 0.504477 | ||||||||
\(405\) | 16.2886 | − | 11.8186i | 0.809389 | − | 0.587272i | ||||
\(406\) | 2.61083 | 0.129573 | ||||||||
\(407\) | −37.5883 | + | 37.5883i | −1.86318 | + | 1.86318i | ||||
\(408\) | 8.88687 | + | 4.37498i | 0.439966 | + | 0.216594i | ||||
\(409\) | − | 24.1706i | − | 1.19516i | −0.801810 | − | 0.597579i | \(-0.796129\pi\) | ||
0.801810 | − | 0.597579i | \(-0.203871\pi\) | |||||||
\(410\) | −0.643885 | − | 6.33097i | −0.0317992 | − | 0.312664i | ||||
\(411\) | 31.6626 | − | 10.7721i | 1.56180 | − | 0.531349i | ||||
\(412\) | −12.1481 | − | 12.1481i | −0.598494 | − | 0.598494i | ||||
\(413\) | −7.09058 | − | 7.09058i | −0.348905 | − | 0.348905i | ||||
\(414\) | −4.44373 | − | 5.77484i | −0.218397 | − | 0.283818i | ||||
\(415\) | −3.74781 | − | 36.8502i | −0.183973 | − | 1.80890i | ||||
\(416\) | − | 3.76449i | − | 0.184569i | ||||||
\(417\) | 17.6938 | − | 35.9413i | 0.866469 | − | 1.76005i | ||||
\(418\) | −16.4741 | + | 16.4741i | −0.805774 | + | 0.805774i | ||||
\(419\) | 17.7582 | 0.867547 | 0.433774 | − | 0.901022i | \(-0.357182\pi\) | ||||
0.433774 | + | 0.901022i | \(0.357182\pi\) | |||||||
\(420\) | 5.53259 | + | 2.05795i | 0.269963 | + | 0.100418i | ||||
\(421\) | −2.93628 | −0.143105 | −0.0715527 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715527 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(422\) | −9.55977 | + | 9.55977i | −0.465363 | + | 0.465363i | ||||
\(423\) | 5.50568 | + | 0.717191i | 0.267695 | + | 0.0348710i | ||||
\(424\) | 2.63171i | 0.127807i | ||||||||
\(425\) | 23.8760 | + | 15.7346i | 1.15815 | + | 0.763242i | ||||
\(426\) | −2.86074 | − | 8.40861i | −0.138603 | − | 0.407398i | ||||
\(427\) | 4.09611 | + | 4.09611i | 0.198225 | + | 0.198225i | ||||
\(428\) | 6.82642 | + | 6.82642i | 0.329967 | + | 0.329967i | ||||
\(429\) | 12.3595 | + | 36.3283i | 0.596720 | + | 1.75395i | ||||
\(430\) | 1.06991 | − | 1.31217i | 0.0515955 | − | 0.0632786i | ||||
\(431\) | − | 15.7850i | − | 0.760336i | −0.924917 | − | 0.380168i | \(-0.875866\pi\) | ||
0.924917 | − | 0.380168i | \(-0.124134\pi\) | |||||||
\(432\) | 1.02415 | + | 5.09422i | 0.0492746 | + | 0.245096i | ||||
\(433\) | −13.1137 | + | 13.1137i | −0.630205 | + | 0.630205i | −0.948119 | − | 0.317915i | \(-0.897017\pi\) |
0.317915 | + | 0.948119i | \(0.397017\pi\) | |||||||
\(434\) | 1.52413 | 0.0731608 | ||||||||
\(435\) | 2.76138 | + | 6.03240i | 0.132398 | + | 0.289231i | ||||
\(436\) | −14.5314 | −0.695927 | ||||||||
\(437\) | 6.79904 | − | 6.79904i | 0.325242 | − | 0.325242i | ||||
\(438\) | 5.86176 | − | 11.9070i | 0.280086 | − | 0.568937i | ||||
\(439\) | − | 39.0288i | − | 1.86275i | −0.364068 | − | 0.931373i | \(-0.618612\pi\) | ||
0.364068 | − | 0.931373i | \(-0.381388\pi\) | |||||||
\(440\) | −13.0922 | + | 1.33153i | −0.624144 | + | 0.0634780i | ||||
\(441\) | 11.1199 | − | 8.55675i | 0.529520 | − | 0.407464i | ||||
\(442\) | 15.2231 | + | 15.2231i | 0.724088 | + | 0.724088i | ||||
\(443\) | −19.8465 | − | 19.8465i | −0.942936 | − | 0.942936i | 0.0555220 | − | 0.998457i | \(-0.482318\pi\) |
−0.998457 | + | 0.0555220i | \(0.982318\pi\) | |||||||
\(444\) | −14.8110 | + | 5.03893i | −0.702898 | + | 0.239137i | ||||
\(445\) | 2.02657 | + | 1.65241i | 0.0960688 | + | 0.0783315i | ||||
\(446\) | − | 8.49856i | − | 0.402419i | ||||||
\(447\) | 26.6094 | + | 13.0997i | 1.25858 | + | 0.619596i | ||||
\(448\) | −1.07773 | + | 1.07773i | −0.0509177 | + | 0.0509177i | ||||
\(449\) | 11.8070 | 0.557205 | 0.278603 | − | 0.960406i | \(-0.410129\pi\) | ||||
0.278603 | + | 0.960406i | \(0.410129\pi\) | |||||||
\(450\) | 1.09667 | + | 14.9599i | 0.0516975 | + | 0.705214i | ||||
\(451\) | −16.7487 | −0.788665 | ||||||||
\(452\) | 1.20082 | − | 1.20082i | 0.0564817 | − | 0.0564817i | ||||
\(453\) | −13.7111 | − | 6.74994i | −0.644204 | − | 0.317140i | ||||
\(454\) | 22.8747i | 1.07356i | ||||||||
\(455\) | 9.94328 | + | 8.10745i | 0.466148 | + | 0.380083i | ||||
\(456\) | −6.49132 | + | 2.20845i | −0.303984 | + | 0.103420i | ||||
\(457\) | −4.52375 | − | 4.52375i | −0.211612 | − | 0.211612i | 0.593340 | − | 0.804952i | \(-0.297809\pi\) |
−0.804952 | + | 0.593340i | \(0.797809\pi\) | |||||||
\(458\) | 3.77610 | + | 3.77610i | 0.176446 | + | 0.176446i | ||||
\(459\) | −24.7419 | − | 16.4588i | −1.15485 | − | 0.768231i | ||||
\(460\) | 5.40328 | − | 0.549536i | 0.251929 | − | 0.0256223i | ||||
\(461\) | 16.0944i | 0.749592i | 0.927107 | + | 0.374796i | \(0.122287\pi\) | ||||
−0.927107 | + | 0.374796i | \(0.877713\pi\) | |||||||
\(462\) | 6.86197 | − | 13.9387i | 0.319248 | − | 0.648486i | ||||
\(463\) | 5.96565 | − | 5.96565i | 0.277247 | − | 0.277247i | −0.554762 | − | 0.832009i | \(-0.687191\pi\) |
0.832009 | + | 0.554762i | \(0.187191\pi\) | |||||||
\(464\) | −1.71299 | −0.0795236 | ||||||||
\(465\) | 1.61202 | + | 3.52156i | 0.0747559 | + | 0.163308i | ||||
\(466\) | 4.81459 | 0.223032 | ||||||||
\(467\) | 25.3293 | − | 25.3293i | 1.17210 | − | 1.17210i | 0.190390 | − | 0.981709i | \(-0.439025\pi\) |
0.981709 | − | 0.190390i | \(-0.0609751\pi\) | |||||||
\(468\) | −1.45881 | + | 11.1989i | −0.0674334 | + | 0.517667i | ||||
\(469\) | 19.1432i | 0.883950i | ||||||||
\(470\) | −2.61516 | + | 3.20733i | −0.120628 | + | 0.147943i | ||||
\(471\) | 3.10804 | + | 9.13551i | 0.143211 | + | 0.420942i | ||||
\(472\) | 4.65221 | + | 4.65221i | 0.214135 | + | 0.214135i | ||||
\(473\) | −3.15092 | − | 3.15092i | −0.144879 | − | 0.144879i | ||||
\(474\) | −9.02845 | − | 26.5374i | −0.414690 | − | 1.21890i | ||||
\(475\) | −19.3883 | + | 3.98497i | −0.889598 | + | 0.182843i | ||||
\(476\) | − | 8.71634i | − | 0.399513i | ||||||
\(477\) | 1.01983 | − | 7.82899i | 0.0466950 | − | 0.358465i | ||||
\(478\) | 1.78251 | − | 1.78251i | 0.0815303 | − | 0.0815303i | ||||
\(479\) | 4.28019 | 0.195567 | 0.0977835 | − | 0.995208i | \(-0.468825\pi\) | ||||
0.0977835 | + | 0.995208i | \(0.468825\pi\) | |||||||
\(480\) | −3.62999 | − | 1.35024i | −0.165686 | − | 0.0616300i | ||||
\(481\) | −34.0026 | −1.55039 | ||||||||
\(482\) | 1.26718 | − | 1.26718i | 0.0577183 | − | 0.0577183i | ||||
\(483\) | −2.83201 | + | 5.75265i | −0.128861 | + | 0.261755i | ||||
\(484\) | 23.6355i | 1.07434i | ||||||||
\(485\) | 3.18611 | + | 31.3273i | 0.144674 | + | 1.42250i | ||||
\(486\) | −1.07262 | − | 15.5515i | −0.0486549 | − | 0.705431i | ||||
\(487\) | −10.4442 | − | 10.4442i | −0.473273 | − | 0.473273i | 0.429699 | − | 0.902972i | \(-0.358620\pi\) |
−0.902972 | + | 0.429699i | \(0.858620\pi\) | |||||||
\(488\) | −2.68750 | − | 2.68750i | −0.121658 | − | 0.121658i | ||||
\(489\) | −32.9289 | + | 11.2029i | −1.48909 | + | 0.506613i | ||||
\(490\) | 1.05818 | + | 10.4045i | 0.0478035 | + | 0.470025i | ||||
\(491\) | 15.1907i | 0.685546i | 0.939418 | + | 0.342773i | \(0.111366\pi\) | ||||
−0.939418 | + | 0.342773i | \(0.888634\pi\) | |||||||
\(492\) | −4.42239 | − | 2.17713i | −0.199377 | − | 0.0981526i | ||||
\(493\) | 6.92710 | − | 6.92710i | 0.311981 | − | 0.311981i | ||||
\(494\) | −14.9026 | −0.670499 | ||||||||
\(495\) | 39.4634 | + | 1.11233i | 1.77375 | + | 0.0499956i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −5.52655 | + | 5.52655i | −0.247900 | + | 0.247900i | ||||
\(498\) | −25.7411 | − | 12.6723i | −1.15348 | − | 0.567857i | ||||
\(499\) | − | 12.0062i | − | 0.537472i | −0.963214 | − | 0.268736i | \(-0.913394\pi\) | ||
0.963214 | − | 0.268736i | \(-0.0866060\pi\) | |||||||
\(500\) | −9.91002 | − | 5.17605i | −0.443190 | − | 0.231480i | ||||
\(501\) | −21.6786 | + | 7.37541i | −0.968529 | + | 0.329509i | ||||
\(502\) | −4.83083 | − | 4.83083i | −0.215610 | − | 0.215610i | ||||
\(503\) | −7.46239 | − | 7.46239i | −0.332731 | − | 0.332731i | 0.520891 | − | 0.853623i | \(-0.325600\pi\) |
−0.853623 | + | 0.520891i | \(0.825600\pi\) | |||||||
\(504\) | 3.62373 | − | 2.78845i | 0.161414 | − | 0.124207i | ||||
\(505\) | 14.3280 | − | 17.5724i | 0.637589 | − | 0.781963i | ||||
\(506\) | − | 14.2945i | − | 0.635467i | ||||||
\(507\) | −0.896118 | + | 1.82028i | −0.0397980 | + | 0.0808415i | ||||
\(508\) | 3.09845 | − | 3.09845i | 0.137471 | − | 0.137471i | ||||
\(509\) | 29.9286 | 1.32656 | 0.663280 | − | 0.748371i | \(-0.269164\pi\) | ||||
0.663280 | + | 0.748371i | \(0.269164\pi\) | |||||||
\(510\) | 20.1394 | − | 9.21898i | 0.891787 | − | 0.408223i | ||||
\(511\) | −11.6785 | −0.516626 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 20.1666 | − | 4.05434i | 0.890379 | − | 0.179004i | ||||
\(514\) | − | 10.7980i | − | 0.476281i | ||||||
\(515\) | −38.2185 | + | 3.88698i | −1.68411 | + | 0.171281i | ||||
\(516\) | −0.422399 | − | 1.24156i | −0.0185951 | − | 0.0546568i | ||||
\(517\) | 7.70175 | + | 7.70175i | 0.338723 | + | 0.338723i | ||||
\(518\) | 9.73451 | + | 9.73451i | 0.427710 | + | 0.427710i | ||||
\(519\) | 7.28385 | + | 21.4095i | 0.319726 | + | 0.939773i | ||||
\(520\) | −6.52389 | − | 5.31938i | −0.286091 | − | 0.233270i | ||||
\(521\) | − | 18.8758i | − | 0.826966i | −0.910512 | − | 0.413483i | \(-0.864312\pi\) | ||
0.910512 | − | 0.413483i | \(-0.135688\pi\) | |||||||
\(522\) | 5.09592 | + | 0.663814i | 0.223042 | + | 0.0290544i | ||||
\(523\) | −17.7678 | + | 17.7678i | −0.776932 | + | 0.776932i | −0.979308 | − | 0.202376i | \(-0.935134\pi\) |
0.202376 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(524\) | −5.24622 | −0.229182 | ||||||||
\(525\) | 11.3842 | − | 6.68005i | 0.496848 | − | 0.291541i | ||||
\(526\) | −25.5604 | −1.11449 | ||||||||
\(527\) | 4.04386 | − | 4.04386i | 0.176153 | − | 0.176153i | ||||
\(528\) | −4.50221 | + | 9.14531i | −0.195934 | + | 0.397999i | ||||
\(529\) | − | 17.1005i | − | 0.743500i | ||||||
\(530\) | 4.56077 | + | 3.71872i | 0.198107 | + | 0.161531i | ||||
\(531\) | −12.0369 | − | 15.6425i | −0.522356 | − | 0.678827i | ||||
\(532\) | 4.26642 | + | 4.26642i | 0.184973 | + | 0.184973i | ||||
\(533\) | −7.57549 | − | 7.57549i | −0.328131 | − | 0.328131i | ||||
\(534\) | 1.91752 | − | 0.652370i | 0.0829792 | − | 0.0282308i | ||||
\(535\) | 21.4762 | − | 2.18422i | 0.928499 | − | 0.0944321i | ||||
\(536\) | − | 12.5600i | − | 0.542511i | ||||||
\(537\) | 16.5467 | + | 8.14589i | 0.714043 | + | 0.351521i | ||||
\(538\) | 5.42678 | − | 5.42678i | 0.233965 | − | 0.233965i | ||||
\(539\) | 27.5252 | 1.18559 | ||||||||
\(540\) | 10.2755 | + | 5.42348i | 0.442187 | + | 0.233390i | ||||
\(541\) | 15.1735 | 0.652361 | 0.326181 | − | 0.945307i | \(-0.394238\pi\) | ||||
0.326181 | + | 0.945307i | \(0.394238\pi\) | |||||||
\(542\) | 13.2718 | − | 13.2718i | 0.570072 | − | 0.570072i | ||||
\(543\) | −4.44300 | − | 2.18728i | −0.190667 | − | 0.0938650i | ||||
\(544\) | 5.71888i | 0.245195i | ||||||||
\(545\) | −20.5335 | + | 25.1830i | −0.879557 | + | 1.07872i | ||||
\(546\) | 9.40821 | − | 3.20082i | 0.402634 | − | 0.136982i | ||||
\(547\) | 29.2556 | + | 29.2556i | 1.25088 | + | 1.25088i | 0.955327 | + | 0.295551i | \(0.0955033\pi\) |
0.295551 | + | 0.955327i | \(0.404497\pi\) | |||||||
\(548\) | 13.6538 | + | 13.6538i | 0.583262 | + | 0.583262i | ||||
\(549\) | 6.95351 | + | 9.03641i | 0.296768 | + | 0.385665i | ||||
\(550\) | −16.1922 | + | 24.5703i | −0.690439 | + | 1.04768i | ||||
\(551\) | 6.78126i | 0.288891i | ||||||||
\(552\) | 1.85811 | − | 3.77437i | 0.0790866 | − | 0.160648i | ||||
\(553\) | −17.4417 | + | 17.4417i | −0.741697 | + | 0.741697i | ||||
\(554\) | 5.11844 | 0.217462 | ||||||||
\(555\) | −12.1960 | + | 32.7878i | −0.517693 | + | 1.39176i | ||||
\(556\) | 23.1290 | 0.980887 | ||||||||
\(557\) | 19.8179 | − | 19.8179i | 0.839712 | − | 0.839712i | −0.149109 | − | 0.988821i | \(-0.547641\pi\) |
0.988821 | + | 0.149109i | \(0.0476405\pi\) | |||||||
\(558\) | 2.97487 | + | 0.387518i | 0.125936 | + | 0.0164049i | ||||
\(559\) | − | 2.85034i | − | 0.120557i | ||||||
\(560\) | 0.344835 | + | 3.39058i | 0.0145720 | + | 0.143278i | ||||
\(561\) | −18.7761 | − | 55.1887i | −0.792726 | − | 2.33007i | ||||
\(562\) | 8.60411 | + | 8.60411i | 0.362943 | + | 0.362943i | ||||
\(563\) | 15.4555 | + | 15.4555i | 0.651371 | + | 0.651371i | 0.953323 | − | 0.301952i | \(-0.0976383\pi\) |
−0.301952 | + | 0.953323i | \(0.597638\pi\) | |||||||
\(564\) | 1.03247 | + | 3.03474i | 0.0434747 | + | 0.127786i | ||||
\(565\) | −0.384221 | − | 3.77783i | −0.0161643 | − | 0.158935i | ||||
\(566\) | 22.6171i | 0.950666i | ||||||||
\(567\) | −11.8607 | + | 6.89101i | −0.498102 | + | 0.289395i | ||||
\(568\) | 3.62603 | − | 3.62603i | 0.152145 | − | 0.152145i | ||||
\(569\) | −16.1031 | −0.675076 | −0.337538 | − | 0.941312i | \(-0.609594\pi\) | ||||
−0.337538 | + | 0.941312i | \(0.609594\pi\) | |||||||
\(570\) | −5.34525 | + | 14.3701i | −0.223888 | + | 0.601899i | ||||
\(571\) | −13.0021 | −0.544119 | −0.272060 | − | 0.962280i | \(-0.587705\pi\) | ||||
−0.272060 | + | 0.962280i | \(0.587705\pi\) | |||||||
\(572\) | −15.6658 | + | 15.6658i | −0.655019 | + | 0.655019i | ||||
\(573\) | 9.56719 | − | 19.4338i | 0.399675 | − | 0.811857i | ||||
\(574\) | 4.33753i | 0.181045i | ||||||||
\(575\) | 6.68271 | − | 10.1404i | 0.278688 | − | 0.422886i | ||||
\(576\) | −2.37756 | + | 1.82953i | −0.0990652 | + | 0.0762305i | ||||
\(577\) | 16.5054 | + | 16.5054i | 0.687130 | + | 0.687130i | 0.961597 | − | 0.274467i | \(-0.0885014\pi\) |
−0.274467 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(578\) | −11.1056 | − | 11.1056i | −0.461930 | − | 0.461930i | ||||
\(579\) | −34.8920 | + | 11.8708i | −1.45006 | + | 0.493333i | ||||
\(580\) | −2.42053 | + | 2.96863i | −0.100507 | + | 0.123265i | ||||
\(581\) | 25.2471i | 1.04743i | ||||||||
\(582\) | 21.8831 | + | 10.7730i | 0.907085 | + | 0.446555i | ||||
\(583\) | 10.9518 | − | 10.9518i | 0.453576 | − | 0.453576i | ||||
\(584\) | 7.66238 | 0.317071 | ||||||||
\(585\) | 17.3463 | + | 18.3526i | 0.717183 | + | 0.758785i | ||||
\(586\) | 8.84831 | 0.365520 | ||||||||
\(587\) | 7.99099 | − | 7.99099i | 0.329823 | − | 0.329823i | −0.522696 | − | 0.852519i | \(-0.675074\pi\) |
0.852519 | + | 0.522696i | \(0.175074\pi\) | |||||||
\(588\) | 7.26786 | + | 3.57795i | 0.299721 | + | 0.147552i | ||||
\(589\) | 3.95873i | 0.163116i | ||||||||
\(590\) | 14.6361 | − | 1.48855i | 0.602557 | − | 0.0612825i | ||||
\(591\) | −8.70103 | + | 2.96023i | −0.357913 | + | 0.121768i | ||||
\(592\) | −6.38692 | − | 6.38692i | −0.262501 | − | 0.262501i | ||||
\(593\) | −18.8701 | − | 18.8701i | −0.774901 | − | 0.774901i | 0.204058 | − | 0.978959i | \(-0.434587\pi\) |
−0.978959 | + | 0.204058i | \(0.934587\pi\) | |||||||
\(594\) | 16.9374 | − | 25.4614i | 0.694952 | − | 1.04469i | ||||
\(595\) | −15.1055 | − | 12.3166i | −0.619264 | − | 0.504929i | ||||
\(596\) | 17.1237i | 0.701414i | ||||||||
\(597\) | 8.67144 | − | 17.6142i | 0.354898 | − | 0.720903i | ||||
\(598\) | 6.46545 | − | 6.46545i | 0.264392 | − | 0.264392i | ||||
\(599\) | 10.2519 | 0.418880 | 0.209440 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209440 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(600\) | −7.46931 | + | 4.38285i | −0.304933 | + | 0.178929i | ||||
\(601\) | −30.1688 | −1.23061 | −0.615306 | − | 0.788288i | \(-0.710968\pi\) | ||||
−0.615306 | + | 0.788288i | \(0.710968\pi\) | |||||||
\(602\) | −0.816016 | + | 0.816016i | −0.0332583 | + | 0.0332583i | ||||
\(603\) | −4.86724 | + | 37.3644i | −0.198209 | + | 1.52160i | ||||
\(604\) | − | 8.82338i | − | 0.359018i | ||||||
\(605\) | 40.9606 | + | 33.3980i | 1.66528 | + | 1.35782i | ||||
\(606\) | −5.65671 | − | 16.6268i | −0.229788 | − | 0.675419i | ||||
\(607\) | −15.5467 | − | 15.5467i | −0.631021 | − | 0.631021i | 0.317303 | − | 0.948324i | \(-0.397223\pi\) |
−0.948324 | + | 0.317303i | \(0.897223\pi\) | |||||||
\(608\) | −2.79924 | − | 2.79924i | −0.113524 | − | 0.113524i | ||||
\(609\) | −1.45650 | − | 4.28110i | −0.0590203 | − | 0.173479i | ||||
\(610\) | −8.45501 | + | 0.859909i | −0.342333 | + | 0.0348167i | ||||
\(611\) | 6.96706i | 0.281857i | ||||||||
\(612\) | 2.21617 | − | 17.0129i | 0.0895833 | − | 0.687706i | ||||
\(613\) | −4.00722 | + | 4.00722i | −0.161850 | + | 0.161850i | −0.783386 | − | 0.621536i | \(-0.786509\pi\) |
0.621536 | + | 0.783386i | \(0.286509\pi\) | |||||||
\(614\) | −15.2012 | −0.613469 | ||||||||
\(615\) | −10.0220 | + | 4.58766i | −0.404126 | + | 0.184992i | ||||
\(616\) | 8.96983 | 0.361405 | ||||||||
\(617\) | −5.30562 | + | 5.30562i | −0.213596 | + | 0.213596i | −0.805793 | − | 0.592197i | \(-0.798261\pi\) |
0.592197 | + | 0.805793i | \(0.298261\pi\) | |||||||
\(618\) | −13.1428 | + | 26.6969i | −0.528681 | + | 1.07391i | ||||
\(619\) | − | 29.5505i | − | 1.18774i | −0.804562 | − | 0.593868i | \(-0.797600\pi\) | ||
0.804562 | − | 0.593868i | \(-0.202400\pi\) | |||||||
\(620\) | −1.41304 | + | 1.73301i | −0.0567491 | + | 0.0695992i | ||||
\(621\) | −6.99028 | + | 10.5082i | −0.280510 | + | 0.421680i | ||||
\(622\) | −3.56764 | − | 3.56764i | −0.143049 | − | 0.143049i | ||||
\(623\) | −1.26029 | − | 1.26029i | −0.0504924 | − | 0.0504924i | ||||
\(624\) | −6.17283 | + | 2.10009i | −0.247111 | + | 0.0840710i | ||||
\(625\) | −22.9734 | + | 9.86017i | −0.918936 | + | 0.394407i | ||||
\(626\) | 0.941892i | 0.0376456i | ||||||||
\(627\) | 36.2038 | + | 17.8230i | 1.44584 | + | 0.711783i | ||||
\(628\) | −3.93949 | + | 3.93949i | −0.157203 | + | 0.157203i | ||||
\(629\) | 51.6556 | 2.05964 | ||||||||
\(630\) | 0.288069 | − | 10.2201i | 0.0114769 | − | 0.407180i | ||||
\(631\) | 20.0250 | 0.797182 | 0.398591 | − | 0.917129i | \(-0.369499\pi\) | ||||
0.398591 | + | 0.917129i | \(0.369499\pi\) | |||||||
\(632\) | 11.4437 | − | 11.4437i | 0.455205 | − | 0.455205i | ||||
\(633\) | 21.0087 | + | 10.3425i | 0.835023 | + | 0.411079i | ||||
\(634\) | − | 0.121484i | − | 0.00482475i | ||||||
\(635\) | −0.991398 | − | 9.74787i | −0.0393424 | − | 0.386832i | ||||
\(636\) | 4.31535 | − | 1.46815i | 0.171115 | − | 0.0582159i | ||||
\(637\) | 12.4497 | + | 12.4497i | 0.493276 | + | 0.493276i | ||||
\(638\) | 7.12855 | + | 7.12855i | 0.282222 | + | 0.282222i | ||||
\(639\) | −12.1921 | + | 9.38180i | −0.482312 | + | 0.371138i | ||||
\(640\) | −0.226250 | − | 2.22459i | −0.00894332 | − | 0.0879347i | ||||
\(641\) | 11.9695i | 0.472766i | 0.971660 | + | 0.236383i | \(0.0759620\pi\) | ||||
−0.971660 | + | 0.236383i | \(0.924038\pi\) | |||||||
\(642\) | 7.38538 | − | 15.0019i | 0.291478 | − | 0.592077i | ||||
\(643\) | 5.02495 | − | 5.02495i | 0.198165 | − | 0.198165i | −0.601048 | − | 0.799213i | \(-0.705250\pi\) |
0.799213 | + | 0.601048i | \(0.205250\pi\) | |||||||
\(644\) | −3.70195 | −0.145877 | ||||||||
\(645\) | −2.74850 | − | 1.02236i | −0.108222 | − | 0.0402553i | ||||
\(646\) | 22.6395 | 0.890739 | ||||||||
\(647\) | −29.4564 | + | 29.4564i | −1.15805 | + | 1.15805i | −0.173155 | + | 0.984895i | \(0.555396\pi\) |
−0.984895 | + | 0.173155i | \(0.944604\pi\) | |||||||
\(648\) | 7.78191 | − | 4.52126i | 0.305702 | − | 0.177612i | ||||
\(649\) | − | 38.7200i | − | 1.51989i | ||||||
\(650\) | −18.4370 | + | 3.78944i | −0.723161 | + | 0.148634i | ||||
\(651\) | −0.850267 | − | 2.49920i | −0.0333246 | − | 0.0979513i | ||||
\(652\) | −14.1999 | − | 14.1999i | −0.556109 | − | 0.556109i | ||||
\(653\) | 12.7404 | + | 12.7404i | 0.498570 | + | 0.498570i | 0.910993 | − | 0.412423i | \(-0.135317\pi\) |
−0.412423 | + | 0.910993i | \(0.635317\pi\) | |||||||
\(654\) | 8.10661 | + | 23.8279i | 0.316994 | + | 0.931743i | ||||
\(655\) | −7.41313 | + | 9.09174i | −0.289655 | + | 0.355244i | ||||
\(656\) | − | 2.84590i | − | 0.111114i | ||||||
\(657\) | −22.7945 | − | 2.96931i | −0.889300 | − | 0.115844i | ||||
\(658\) | 1.99458 | − | 1.99458i | 0.0777568 | − | 0.0777568i | ||||
\(659\) | −38.2781 | −1.49110 | −0.745551 | − | 0.666448i | \(-0.767814\pi\) | ||||
−0.745551 | + | 0.666448i | \(0.767814\pi\) | |||||||
\(660\) | 9.48708 | + | 20.7251i | 0.369284 | + | 0.806722i | ||||
\(661\) | 10.2605 | 0.399087 | 0.199544 | − | 0.979889i | \(-0.436054\pi\) | ||||
0.199544 | + | 0.979889i | \(0.436054\pi\) | |||||||
\(662\) | 10.3188 | − | 10.3188i | 0.401053 | − | 0.401053i | ||||
\(663\) | 16.4696 | − | 33.4545i | 0.639625 | − | 1.29927i | ||||
\(664\) | − | 16.5649i | − | 0.642843i | ||||||
\(665\) | 13.4224 | − | 1.36511i | 0.520497 | − | 0.0529366i | ||||
\(666\) | 16.5252 | + | 21.4753i | 0.640338 | + | 0.832150i | ||||
\(667\) | −2.94203 | − | 2.94203i | −0.113916 | − | 0.113916i | ||||
\(668\) | −9.34843 | − | 9.34843i | −0.361702 | − | 0.361702i | ||||
\(669\) | −13.9355 | + | 4.74108i | −0.538778 | + | 0.183301i | ||||
\(670\) | −21.7666 | − | 17.7479i | −0.840919 | − | 0.685659i | ||||
\(671\) | 22.3679i | 0.863503i | ||||||||
\(672\) | 2.36843 | + | 1.16597i | 0.0913642 | + | 0.0449783i | ||||
\(673\) | 30.9343 | − | 30.9343i | 1.19243 | − | 1.19243i | 0.216046 | − | 0.976383i | \(-0.430684\pi\) |
0.976383 | − | 0.216046i | \(-0.0693160\pi\) | |||||||
\(674\) | 16.8811 | 0.650236 | ||||||||
\(675\) | 23.9186 | − | 10.1439i | 0.920629 | − | 0.390439i | ||||
\(676\) | −1.17139 | −0.0450534 | ||||||||
\(677\) | 23.6196 | − | 23.6196i | 0.907776 | − | 0.907776i | −0.0883164 | − | 0.996092i | \(-0.528149\pi\) |
0.996092 | + | 0.0883164i | \(0.0281487\pi\) | |||||||
\(678\) | −2.63894 | − | 1.29914i | −0.101348 | − | 0.0498933i | ||||
\(679\) | − | 21.4632i | − | 0.823683i | ||||||
\(680\) | 9.91087 | + | 8.08102i | 0.380064 | + | 0.309893i | ||||
\(681\) | 37.5088 | − | 12.7611i | 1.43734 | − | 0.489005i | ||||
\(682\) | 4.16146 | + | 4.16146i | 0.159351 | + | 0.159351i | ||||
\(683\) | −30.8937 | − | 30.8937i | −1.18211 | − | 1.18211i | −0.979196 | − | 0.202917i | \(-0.934958\pi\) |
−0.202917 | − | 0.979196i | \(-0.565042\pi\) | |||||||
\(684\) | 7.24261 | + | 9.41213i | 0.276928 | + | 0.359882i | ||||
\(685\) | 42.9556 | − | 4.36876i | 1.64125 | − | 0.166922i | ||||
\(686\) | − | 17.7973i | − | 0.679505i | ||||||
\(687\) | 4.08529 | − | 8.29843i | 0.155864 | − | 0.316605i | ||||
\(688\) | 0.535397 | − | 0.535397i | 0.0204118 | − | 0.0204118i | ||||
\(689\) | 9.90705 | 0.377429 | ||||||||
\(690\) | −3.91543 | − | 8.55347i | −0.149058 | − | 0.325625i | ||||
\(691\) | 28.5957 | 1.08783 | 0.543915 | − | 0.839140i | \(-0.316941\pi\) | ||||
0.543915 | + | 0.839140i | \(0.316941\pi\) | |||||||
\(692\) | −9.23238 | + | 9.23238i | −0.350963 | + | 0.350963i | ||||
\(693\) | −26.6840 | − | 3.47597i | −1.01364 | − | 0.132041i | ||||
\(694\) | − | 15.5527i | − | 0.590371i | ||||||
\(695\) | 32.6822 | − | 40.0827i | 1.23971 | − | 1.52042i | ||||
\(696\) | 0.955624 | + | 2.80888i | 0.0362228 | + | 0.106470i | ||||
\(697\) | 11.5084 | + | 11.5084i | 0.435913 | + | 0.435913i | ||||
\(698\) | −15.5497 | − | 15.5497i | −0.588566 | − | 0.588566i | ||||
\(699\) | −2.68591 | − | 7.89473i | −0.101590 | − | 0.298606i | ||||
\(700\) | 6.36316 | + | 4.19342i | 0.240505 | + | 0.158496i | ||||
\(701\) | 28.2214i | 1.06591i | 0.846145 | + | 0.532953i | \(0.178918\pi\) | ||||
−0.846145 | + | 0.532953i | \(0.821082\pi\) | |||||||
\(702\) | 19.1772 | − | 3.85541i | 0.723795 | − | 0.145513i | ||||
\(703\) | −25.2841 | + | 25.2841i | −0.953606 | + | 0.953606i | ||||
\(704\) | −5.88520 | −0.221807 | ||||||||
\(705\) | 6.71814 | + | 2.49894i | 0.253020 | + | 0.0941156i | ||||
\(706\) | −31.2968 | −1.17787 | ||||||||
\(707\) | −10.9280 | + | 10.9280i | −0.410989 | + | 0.410989i | ||||
\(708\) | 5.03314 | − | 10.2238i | 0.189157 | − | 0.384233i | ||||
\(709\) | − | 48.6154i | − | 1.82579i | −0.408194 | − | 0.912895i | \(-0.633841\pi\) | ||
0.408194 | − | 0.912895i | \(-0.366159\pi\) | |||||||
\(710\) | −1.16021 | − | 11.4077i | −0.0435418 | − | 0.428122i | ||||
\(711\) | −38.4781 | + | 29.6088i | −1.44304 | + | 1.11042i | ||||
\(712\) | 0.826888 | + | 0.826888i | 0.0309889 | + | 0.0309889i | ||||
\(713\) | −1.71748 | − | 1.71748i | −0.0643202 | − | 0.0643202i | ||||
\(714\) | −14.2926 | + | 4.86258i | −0.534888 | + | 0.181977i | ||||
\(715\) | 5.01252 | + | 49.2853i | 0.187458 | + | 1.84317i | ||||
\(716\) | 10.6481i | 0.397940i | ||||||||
\(717\) | −3.91729 | − | 1.92847i | −0.146294 | − | 0.0720200i | ||||
\(718\) | −10.4711 | + | 10.4711i | −0.390779 | + | 0.390779i | ||||
\(719\) | −23.9331 | −0.892553 | −0.446276 | − | 0.894895i | \(-0.647250\pi\) | ||||
−0.446276 | + | 0.894895i | \(0.647250\pi\) | |||||||
\(720\) | −0.189005 | + | 6.70554i | −0.00704380 | + | 0.249901i | ||||
\(721\) | 26.1846 | 0.975166 | ||||||||
\(722\) | 2.35360 | − | 2.35360i | 0.0875918 | − | 0.0875918i | ||||
\(723\) | −2.78477 | − | 1.37094i | −0.103567 | − | 0.0509857i | ||||
\(724\) | − | 2.85916i | − | 0.106260i | ||||||
\(725\) | 1.72435 | + | 8.38958i | 0.0640406 | + | 0.311581i | ||||
\(726\) | 38.7564 | − | 13.1855i | 1.43839 | − | 0.489361i | ||||
\(727\) | −2.96197 | − | 2.96197i | −0.109854 | − | 0.109854i | 0.650043 | − | 0.759897i | \(-0.274751\pi\) |
−0.759897 | + | 0.650043i | \(0.774751\pi\) | |||||||
\(728\) | 4.05709 | + | 4.05709i | 0.150366 | + | 0.150366i | ||||
\(729\) | −24.9022 | + | 10.4345i | −0.922304 | + | 0.386464i | ||||
\(730\) | 10.8273 | − | 13.2790i | 0.400735 | − | 0.491476i | ||||
\(731\) | 4.33014i | 0.160156i | ||||||||
\(732\) | −2.90756 | + | 5.90611i | −0.107466 | + | 0.218296i | ||||
\(733\) | −16.0878 | + | 16.0878i | −0.594217 | + | 0.594217i | −0.938768 | − | 0.344551i | \(-0.888031\pi\) |
0.344551 | + | 0.938768i | \(0.388031\pi\) | |||||||
\(734\) | 0.202342 | 0.00746858 | ||||||||
\(735\) | 16.4704 | − | 7.53947i | 0.607520 | − | 0.278097i | ||||
\(736\) | 2.42889 | 0.0895300 | ||||||||
\(737\) | −52.2681 | + | 52.2681i | −1.92532 | + | 1.92532i | ||||
\(738\) | −1.10284 | + | 8.46617i | −0.0405960 | + | 0.311644i | ||||
\(739\) | 12.7994i | 0.470833i | 0.971895 | + | 0.235416i | \(0.0756454\pi\) | ||||
−0.971895 | + | 0.235416i | \(0.924355\pi\) | |||||||
\(740\) | −20.0935 | + | 2.04360i | −0.738654 | + | 0.0751241i | ||||
\(741\) | 8.31369 | + | 24.4365i | 0.305411 | + | 0.897698i | ||||
\(742\) | −2.83626 | − | 2.83626i | −0.104122 | − | 0.104122i | ||||
\(743\) | 20.7857 | + | 20.7857i | 0.762553 | + | 0.762553i | 0.976783 | − | 0.214230i | \(-0.0687243\pi\) |
−0.214230 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(744\) | 0.557869 | + | 1.63975i | 0.0204525 | + | 0.0601162i | ||||
\(745\) | 29.6755 | + | 24.1965i | 1.08723 | + | 0.886491i | ||||
\(746\) | 31.6897i | 1.16024i | ||||||||
\(747\) | −6.41919 | + | 49.2784i | −0.234866 | + | 1.80300i | ||||
\(748\) | 23.7989 | − | 23.7989i | 0.870175 | − | 0.870175i | ||||
\(749\) | −14.7140 | −0.537638 | ||||||||
\(750\) | −2.95893 | + | 19.1375i | −0.108045 | + | 0.698803i | ||||
\(751\) | 24.8859 | 0.908099 | 0.454049 | − | 0.890977i | \(-0.349979\pi\) | ||||
0.454049 | + | 0.890977i | \(0.349979\pi\) | |||||||
\(752\) | −1.30867 | + | 1.30867i | −0.0477221 | + | 0.0477221i | ||||
\(753\) | −5.22638 | + | 10.6163i | −0.190460 | + | 0.386880i | ||||
\(754\) | 6.44854i | 0.234842i | ||||||||
\(755\) | −15.2910 | − | 12.4678i | −0.556496 | − | 0.453750i | ||||
\(756\) | −6.59393 | − | 4.38642i | −0.239819 | − | 0.159532i | ||||
\(757\) | −24.2813 | − | 24.2813i | −0.882520 | − | 0.882520i | 0.111270 | − | 0.993790i | \(-0.464508\pi\) |
−0.993790 | + | 0.111270i | \(0.964508\pi\) | |||||||
\(758\) | 16.3901 | + | 16.3901i | 0.595316 | + | 0.595316i | ||||
\(759\) | −23.4394 | + | 7.97445i | −0.850796 | + | 0.289454i | ||||
\(760\) | −8.80655 | + | 0.895662i | −0.319447 | + | 0.0324891i | ||||
\(761\) | − | 30.1048i | − | 1.09130i | −0.838013 | − | 0.545650i | \(-0.816283\pi\) | ||
0.838013 | − | 0.545650i | \(-0.183717\pi\) | |||||||
\(762\) | −6.80921 | − | 3.35215i | −0.246672 | − | 0.121436i | ||||
\(763\) | 15.6608 | − | 15.6608i | 0.566961 | − | 0.566961i | ||||
\(764\) | 12.5060 | 0.452452 | ||||||||
\(765\) | −26.3520 | − | 27.8806i | −0.952757 | − | 1.00802i | ||||
\(766\) | 32.4740 | 1.17333 | ||||||||
\(767\) | 17.5132 | − | 17.5132i | 0.632364 | − | 0.632364i | ||||
\(768\) | −1.55395 | − | 0.765006i | −0.0560734 | − | 0.0276048i | ||||
\(769\) | 34.5113i | 1.24451i | 0.782814 | + | 0.622255i | \(0.213783\pi\) | ||||
−0.782814 | + | 0.622255i | \(0.786217\pi\) | |||||||
\(770\) | 12.6747 | − | 15.5448i | 0.456766 | − | 0.560195i | ||||
\(771\) | −17.7061 | + | 6.02389i | −0.637670 | + | 0.216945i | ||||
\(772\) | −15.0464 | − | 15.0464i | −0.541532 | − | 0.541532i | ||||
\(773\) | 25.5174 | + | 25.5174i | 0.917796 | + | 0.917796i | 0.996869 | − | 0.0790733i | \(-0.0251961\pi\) |
−0.0790733 | + | 0.996869i | \(0.525196\pi\) | |||||||
\(774\) | −1.80021 | + | 1.38526i | −0.0647072 | + | 0.0497921i | ||||
\(775\) | 1.00663 | + | 4.89762i | 0.0361592 | + | 0.175928i | ||||
\(776\) | 14.0822i | 0.505523i | ||||||||
\(777\) | 10.5316 | − | 21.3928i | 0.377819 | − | 0.767461i | ||||
\(778\) | 8.94856 | − | 8.94856i | 0.320822 | − | 0.320822i | ||||
\(779\) | −11.2661 | −0.403651 | ||||||||
\(780\) | −5.08298 | + | 13.6651i | −0.182000 | + | 0.489288i | ||||
\(781\) | −30.1792 | −1.07990 | ||||||||
\(782\) | −9.82208 | + | 9.82208i | −0.351237 | + | 0.351237i | ||||
\(783\) | −1.75436 | − | 8.72636i | −0.0626959 | − | 0.311855i | ||||
\(784\) | 4.67702i | 0.167036i | ||||||||
\(785\) | 1.26050 | + | 12.3938i | 0.0449893 | + | 0.442355i | ||||
\(786\) | 2.92670 | + | 8.60250i | 0.104392 | + | 0.306841i | ||||
\(787\) | −29.5518 | − | 29.5518i | −1.05341 | − | 1.05341i | −0.998491 | − | 0.0549181i | \(-0.982510\pi\) |
−0.0549181 | − | 0.998491i | \(-0.517490\pi\) | |||||||
\(788\) | −3.75213 | − | 3.75213i | −0.133664 | − | 0.133664i | ||||
\(789\) | 14.2593 | + | 41.9127i | 0.507646 | + | 1.49213i | ||||
\(790\) | −3.66159 | − | 36.0024i | −0.130274 | − | 1.28091i | ||||
\(791\) | 2.58830i | 0.0920295i | ||||||||
\(792\) | 17.5077 | + | 2.28062i | 0.622108 | + | 0.0810382i | ||||
\(793\) | −10.1171 | + | 10.1171i | −0.359268 | + | 0.359268i | ||||
\(794\) | −27.5995 | −0.979468 | ||||||||
\(795\) | 3.55345 | − | 9.55309i | 0.126028 | − | 0.338813i | ||||
\(796\) | 11.3351 | 0.401763 | ||||||||
\(797\) | −11.3248 | + | 11.3248i | −0.401145 | + | 0.401145i | −0.878636 | − | 0.477491i | \(-0.841546\pi\) |
0.477491 | + | 0.878636i | \(0.341546\pi\) | |||||||
\(798\) | 4.61576 | − | 9.37596i | 0.163396 | − | 0.331906i | ||||
\(799\) | − | 10.5841i | − | 0.374439i | ||||||
\(800\) | −4.17494 | − | 2.75135i | −0.147606 | − | 0.0972748i | ||||
\(801\) | −2.13945 | − | 2.78032i | −0.0755937 | − | 0.0982376i | ||||
\(802\) | −13.5355 | − | 13.5355i | −0.477957 | − | 0.477957i | ||||
\(803\) | −31.8867 | − | 31.8867i | −1.12526 | − | 1.12526i | ||||
\(804\) | −20.5953 | + | 7.00685i | −0.726341 | + | 0.247113i | ||||
\(805\) | −5.23101 | + | 6.41550i | −0.184369 | + | 0.226117i | ||||
\(806\) | 3.76449i | 0.132599i | ||||||||
\(807\) | −11.9260 | − | 5.87114i | −0.419815 | − | 0.206674i | ||||
\(808\) | 7.16996 | − | 7.16996i | 0.252238 | − | 0.252238i | ||||
\(809\) | 29.3613 | 1.03229 | 0.516143 | − | 0.856502i | \(-0.327367\pi\) | ||||
0.516143 | + | 0.856502i | \(0.327367\pi\) | |||||||
\(810\) | 3.16078 | − | 19.8748i | 0.111059 | − | 0.698331i | ||||
\(811\) | −5.16605 | −0.181405 | −0.0907023 | − | 0.995878i | \(-0.528911\pi\) | ||||
−0.0907023 | + | 0.995878i | \(0.528911\pi\) | |||||||
\(812\) | 1.84613 | − | 1.84613i | 0.0647866 | − | 0.0647866i | ||||
\(813\) | −29.1663 | − | 14.3585i | −1.02291 | − | 0.503574i | ||||
\(814\) | 53.1578i | 1.86318i | ||||||||
\(815\) | −44.6734 | + | 4.54347i | −1.56484 | + | 0.159151i | ||||
\(816\) | 9.37754 | − | 3.19039i | 0.328280 | − | 0.111686i | ||||
\(817\) | −2.11949 | − | 2.11949i | −0.0741516 | − | 0.0741516i | ||||
\(818\) | −17.0912 | − | 17.0912i | −0.597579 | − | 0.597579i | ||||
\(819\) | −10.4971 | − | 13.6415i | −0.366798 | − | 0.476672i | ||||
\(820\) | −4.93197 | − | 4.02138i | −0.172232 | − | 0.140433i | ||||
\(821\) | − | 0.234824i | − | 0.00819543i | −0.999992 | − | 0.00409771i | \(-0.998696\pi\) | ||
0.999992 | − | 0.00409771i | \(-0.00130435\pi\) | |||||||
\(822\) | 14.7718 | − | 30.0059i | 0.515226 | − | 1.04658i | ||||
\(823\) | 1.63126 | − | 1.63126i | 0.0568623 | − | 0.0568623i | −0.678104 | − | 0.734966i | \(-0.737198\pi\) |
0.734966 | + | 0.678104i | \(0.237198\pi\) | |||||||
\(824\) | −17.1800 | −0.598494 | ||||||||
\(825\) | 49.3223 | + | 12.8442i | 1.71718 | + | 0.447177i | ||||
\(826\) | −10.0276 | −0.348905 | ||||||||
\(827\) | −0.735311 | + | 0.735311i | −0.0255693 | + | 0.0255693i | −0.719776 | − | 0.694207i | \(-0.755755\pi\) |
0.694207 | + | 0.719776i | \(0.255755\pi\) | |||||||
\(828\) | −7.22562 | − | 0.941237i | −0.251108 | − | 0.0327102i | ||||
\(829\) | − | 20.7527i | − | 0.720771i | −0.932803 | − | 0.360386i | \(-0.882645\pi\) | ||
0.932803 | − | 0.360386i | \(-0.117355\pi\) | |||||||
\(830\) | −28.7071 | − | 23.4069i | −0.996438 | − | 0.812465i | ||||
\(831\) | −2.85542 | − | 8.39297i | −0.0990534 | − | 0.291149i | ||||
\(832\) | −2.66190 | − | 2.66190i | −0.0922847 | − | 0.0922847i | ||||
\(833\) | −18.9132 | − | 18.9132i | −0.655304 | − | 0.655304i | ||||
\(834\) | −12.9029 | − | 37.9258i | −0.446792 | − | 1.31326i | ||||
\(835\) | −29.4106 | + | 2.99118i | −1.01780 | + | 0.103514i | ||||
\(836\) | 23.2979i | 0.805774i | ||||||||
\(837\) | −1.02415 | − | 5.09422i | −0.0353999 | − | 0.176082i | ||||
\(838\) | 12.5570 | − | 12.5570i | 0.433774 | − | 0.433774i | ||||
\(839\) | 46.9394 | 1.62053 | 0.810264 | − | 0.586065i | \(-0.199323\pi\) | ||||
0.810264 | + | 0.586065i | \(0.199323\pi\) | |||||||
\(840\) | 5.36733 | − | 2.45694i | 0.185190 | − | 0.0847725i | ||||
\(841\) | −26.0657 | −0.898816 | ||||||||
\(842\) | −2.07626 | + | 2.07626i | −0.0715527 | + | 0.0715527i | ||||
\(843\) | 9.30863 | − | 18.9086i | 0.320606 | − | 0.651246i | ||||
\(844\) | 13.5196i | 0.465363i | ||||||||
\(845\) | −1.65522 | + | 2.03002i | −0.0569413 | + | 0.0698349i | ||||
\(846\) | 4.40023 | − | 3.38597i | 0.151283 | − | 0.116412i | ||||
\(847\) | −25.4726 | − | 25.4726i | −0.875250 | − | 0.875250i | ||||
\(848\) | 1.86090 | + | 1.86090i | 0.0639036 | + | 0.0639036i | ||||
\(849\) | 37.0864 | − | 12.6174i | 1.27280 | − | 0.433027i | ||||
\(850\) | 28.0089 | − | 5.75679i | 0.960698 | − | 0.197456i | ||||
\(851\) | − | 21.9388i | − | 0.752054i | ||||||
\(852\) | −7.96863 | − | 3.92294i | −0.273001 | − | 0.134398i | ||||
\(853\) | −19.2000 | + | 19.2000i | −0.657397 | + | 0.657397i | −0.954763 | − | 0.297367i | \(-0.903892\pi\) |
0.297367 | + | 0.954763i | \(0.403892\pi\) | |||||||
\(854\) | 5.79278 | 0.198225 | ||||||||
\(855\) | 26.5454 | + | 0.748219i | 0.907833 | + | 0.0255886i | ||||
\(856\) | 9.65401 | 0.329967 | ||||||||
\(857\) | 22.1292 | − | 22.1292i | 0.755919 | − | 0.755919i | −0.219658 | − | 0.975577i | \(-0.570494\pi\) |
0.975577 | + | 0.219658i | \(0.0704941\pi\) | |||||||
\(858\) | 34.4274 | + | 16.9485i | 1.17533 | + | 0.578613i | ||||
\(859\) | 19.2083i | 0.655377i | 0.944786 | + | 0.327689i | \(0.106270\pi\) | ||||
−0.944786 | + | 0.327689i | \(0.893730\pi\) | |||||||
\(860\) | −0.171309 | − | 1.68438i | −0.00584158 | − | 0.0574370i | ||||
\(861\) | 7.11247 | − | 2.41977i | 0.242392 | − | 0.0824657i | ||||
\(862\) | −11.1617 | − | 11.1617i | −0.380168 | − | 0.380168i | ||||
\(863\) | −4.98167 | − | 4.98167i | −0.169578 | − | 0.169578i | 0.617216 | − | 0.786794i | \(-0.288261\pi\) |
−0.786794 | + | 0.617216i | \(0.788261\pi\) | |||||||
\(864\) | 4.32635 | + | 2.87797i | 0.147185 | + | 0.0979107i | ||||
\(865\) | 2.95405 | + | 29.0455i | 0.100441 | + | 0.987577i | ||||
\(866\) | 18.5456i | 0.630205i | ||||||||
\(867\) | −12.0149 | + | 24.4058i | −0.408047 | + | 0.828864i | ||||
\(868\) | 1.07773 | − | 1.07773i | 0.0365804 | − | 0.0365804i | ||||
\(869\) | −95.2449 | −3.23096 | ||||||||
\(870\) | 6.21814 | + | 2.31296i | 0.210815 | + | 0.0784166i | ||||
\(871\) | −47.2821 | −1.60209 | ||||||||
\(872\) | −10.2752 | + | 10.2752i | −0.347964 | + | 0.347964i | ||||
\(873\) | 5.45712 | − | 41.8928i | 0.184695 | − | 1.41786i | ||||
\(874\) | − | 9.61530i | − | 0.325242i | ||||||
\(875\) | 16.2586 | − | 5.10192i | 0.549642 | − | 0.172476i | ||||
\(876\) | −4.27460 | − | 12.5644i | −0.144425 | − | 0.424511i | ||||
\(877\) | −15.3604 | − | 15.3604i | −0.518683 | − | 0.518683i | 0.398490 | − | 0.917173i | \(-0.369534\pi\) |
−0.917173 | + | 0.398490i | \(0.869534\pi\) | |||||||
\(878\) | −27.5976 | − | 27.5976i | −0.931373 | − | 0.931373i | ||||
\(879\) | −4.93620 | − | 14.5090i | −0.166494 | − | 0.489377i | ||||
\(880\) | −8.31603 | + | 10.1991i | −0.280333 | + | 0.343811i | ||||
\(881\) | 32.6789i | 1.10098i | 0.834842 | + | 0.550490i | \(0.185559\pi\) | ||||
−0.834842 | + | 0.550490i | \(0.814441\pi\) | |||||||
\(882\) | 1.81243 | − | 13.9135i | 0.0610276 | − | 0.468492i | ||||
\(883\) | −22.0645 | + | 22.0645i | −0.742530 | + | 0.742530i | −0.973064 | − | 0.230534i | \(-0.925953\pi\) |
0.230534 | + | 0.973064i | \(0.425953\pi\) | |||||||
\(884\) | 21.5287 | 0.724088 | ||||||||
\(885\) | −10.6059 | − | 23.1691i | −0.356512 | − | 0.778820i | ||||
\(886\) | −28.0672 | −0.942936 | ||||||||
\(887\) | −10.9781 | + | 10.9781i | −0.368607 | + | 0.368607i | −0.866969 | − | 0.498362i | \(-0.833935\pi\) |
0.498362 | + | 0.866969i | \(0.333935\pi\) | |||||||
\(888\) | −6.90989 | + | 14.0360i | −0.231881 | + | 0.471018i | ||||
\(889\) | 6.67855i | 0.223991i | ||||||||
\(890\) | 2.60143 | − | 0.264576i | 0.0872002 | − | 0.00886861i | ||||
\(891\) | −51.1992 | − | 13.5691i | −1.71524 | − | 0.454581i | ||||
\(892\) | −6.00939 | − | 6.00939i | −0.201209 | − | 0.201209i | ||||
\(893\) | 5.18065 | + | 5.18065i | 0.173364 | + | 0.173364i | ||||
\(894\) | 28.0786 | − | 9.55278i | 0.939089 | − | 0.319493i | ||||
\(895\) | 18.4533 | + | 15.0463i | 0.616826 | + | 0.502941i | ||||
\(896\) | 1.52413i | 0.0509177i | ||||||||
\(897\) | −14.2086 | − | 6.99485i | −0.474411 | − | 0.233551i | ||||
\(898\) | 8.34879 | − | 8.34879i | 0.278603 | − | 0.278603i | ||||
\(899\) | 1.71299 | 0.0571314 | ||||||||
\(900\) | 11.3537 | + | 9.80275i | 0.378456 | + | 0.326758i | ||||
\(901\) | −15.0505 | −0.501403 | ||||||||
\(902\) | −11.8431 | + | 11.8431i | −0.394332 | + | 0.394332i | ||||
\(903\) | 1.79329 | + | 0.882833i | 0.0596771 | + | 0.0293789i | ||||
\(904\) | − | 1.69821i | − | 0.0564817i | ||||||
\(905\) | −4.95495 | − | 4.04011i | −0.164708 | − | 0.134298i | ||||
\(906\) | −14.4681 | + | 4.92229i | −0.480672 | + | 0.163532i | ||||
\(907\) | −13.5200 | − | 13.5200i | −0.448924 | − | 0.448924i | 0.446073 | − | 0.894997i | \(-0.352822\pi\) |
−0.894997 | + | 0.446073i | \(0.852822\pi\) | |||||||
\(908\) | 16.1748 | + | 16.1748i | 0.536781 | + | 0.536781i | ||||
\(909\) | −24.1082 | + | 18.5512i | −0.799617 | + | 0.615304i | ||||
\(910\) | 12.7638 | − | 1.29813i | 0.423116 | − | 0.0430326i | ||||
\(911\) | 48.3234i | 1.60103i | 0.599315 | + | 0.800513i | \(0.295440\pi\) | ||||
−0.599315 | + | 0.800513i | \(0.704560\pi\) | |||||||
\(912\) | −3.02845 | + | 6.15167i | −0.100282 | + | 0.203702i | ||||
\(913\) | −68.9342 | + | 68.9342i | −2.28139 | + | 2.28139i | ||||
\(914\) | −6.39755 | −0.211612 | ||||||||
\(915\) | 6.12683 | + | 13.3844i | 0.202547 | + | 0.442474i | ||||
\(916\) | 5.34021 | 0.176446 | ||||||||
\(917\) | 5.65399 | − | 5.65399i | 0.186711 | − | 0.186711i | ||||
\(918\) | −29.1333 | + | 5.85701i | −0.961541 | + | 0.193310i | ||||
\(919\) | − | 48.5166i | − | 1.60041i | −0.599724 | − | 0.800207i | \(-0.704723\pi\) | ||
0.599724 | − | 0.800207i | \(-0.295277\pi\) | |||||||
\(920\) | 3.43212 | − | 4.20928i | 0.113154 | − | 0.138776i | ||||
\(921\) | 8.48026 | + | 24.9261i | 0.279434 | + | 0.821344i | ||||
\(922\) | 11.3805 | + | 11.3805i | 0.374796 | + | 0.374796i | ||||
\(923\) | −13.6502 | − | 13.6502i | −0.449300 | − | 0.449300i | ||||
\(924\) | −5.00399 | − | 14.7083i | −0.164619 | − | 0.483867i | ||||
\(925\) | −24.8514 | + | 37.7100i | −0.817111 | + | 1.23990i | ||||
\(926\) | − | 8.43671i | − | 0.277247i | ||||||
\(927\) | 51.1082 | + | 6.65756i | 1.67861 | + | 0.218663i | ||||
\(928\) | −1.21127 | + | 1.21127i | −0.0397618 | + | 0.0397618i | ||||
\(929\) | 19.1173 | 0.627219 | 0.313610 | − | 0.949552i | \(-0.398462\pi\) | ||||
0.313610 | + | 0.949552i | \(0.398462\pi\) | |||||||
\(930\) | 3.62999 | + | 1.35024i | 0.119032 | + | 0.0442763i | ||||
\(931\) | 18.5150 | 0.606806 | ||||||||
\(932\) | 3.40443 | − | 3.40443i | 0.111516 | − | 0.111516i | ||||
\(933\) | −3.85977 | + | 7.84032i | −0.126363 | + | 0.256681i | ||||
\(934\) | − | 35.8210i | − | 1.17210i | ||||||
\(935\) | −7.61485 | − | 74.8726i | −0.249032 | − | 2.44859i | ||||
\(936\) | 6.88725 | + | 8.95032i | 0.225117 | + | 0.292550i | ||||
\(937\) | 37.6734 | + | 37.6734i | 1.23074 | + | 1.23074i | 0.963682 | + | 0.267054i | \(0.0860501\pi\) |
0.267054 | + | 0.963682i | \(0.413950\pi\) | |||||||
\(938\) | 13.5363 | + | 13.5363i | 0.441975 | + | 0.441975i | ||||
\(939\) | 1.54447 | − | 0.525452i | 0.0504018 | − | 0.0171475i | ||||
\(940\) | 0.418728 | + | 4.11712i | 0.0136574 | + | 0.134286i | ||||
\(941\) | − | 27.8989i | − | 0.909477i | −0.890625 | − | 0.454738i | \(-0.849733\pi\) | ||
0.890625 | − | 0.454738i | \(-0.150267\pi\) | |||||||
\(942\) | 8.65750 | + | 4.26206i | 0.282077 | + | 0.138866i | ||||
\(943\) | 4.88779 | − | 4.88779i | 0.159168 | − | 0.159168i | ||||
\(944\) | 6.57921 | 0.214135 | ||||||||
\(945\) | −16.9192 | + | 5.22914i | −0.550381 | + | 0.170104i | ||||
\(946\) | −4.45607 | −0.144879 | ||||||||
\(947\) | −41.7393 | + | 41.7393i | −1.35635 | + | 1.35635i | −0.477971 | + | 0.878376i | \(0.658627\pi\) |
−0.878376 | + | 0.477971i | \(0.841373\pi\) | |||||||
\(948\) | −25.1489 | − | 12.3807i | −0.816797 | − | 0.402107i | ||||
\(949\) | − | 28.8449i | − | 0.936346i | ||||||
\(950\) | −10.8918 | + | 16.5274i | −0.353378 | + | 0.536220i | ||||
\(951\) | −0.199204 | + | 0.0677722i | −0.00645962 | + | 0.00219766i | ||||
\(952\) | −6.16338 | − | 6.16338i | −0.199756 | − | 0.199756i | ||||
\(953\) | 18.8803 | + | 18.8803i | 0.611594 | + | 0.611594i | 0.943361 | − | 0.331767i | \(-0.107645\pi\) |
−0.331767 | + | 0.943361i | \(0.607645\pi\) | |||||||
\(954\) | −4.81480 | − | 6.25706i | −0.155885 | − | 0.202580i | ||||
\(955\) | 17.6715 | − | 21.6730i | 0.571837 | − | 0.701323i | ||||
\(956\) | − | 2.52085i | − | 0.0815303i | ||||||
\(957\) | 7.71224 | − | 15.6658i | 0.249301 | − | 0.506404i | ||||
\(958\) | 3.02655 | − | 3.02655i | 0.0977835 | − | 0.0977835i | ||||
\(959\) | −29.4301 | −0.950348 | ||||||||
\(960\) | −3.52156 | + | 1.61202i | −0.113658 | + | 0.0520279i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −24.0435 | + | 24.0435i | −0.775193 | + | 0.775193i | ||||
\(963\) | −28.7194 | − | 3.74110i | −0.925470 | − | 0.120555i | ||||
\(964\) | − | 1.79206i | − | 0.0577183i | ||||||
\(965\) | −47.3367 | + | 4.81433i | −1.52382 | + | 0.154979i | ||||
\(966\) | 2.06520 | + | 6.07027i | 0.0664468 | + | 0.195308i | ||||
\(967\) | 43.1363 | + | 43.1363i | 1.38717 | + | 1.38717i | 0.831205 | + | 0.555967i | \(0.187652\pi\) |
0.555967 | + | 0.831205i | \(0.312348\pi\) | |||||||
\(968\) | 16.7129 | + | 16.7129i | 0.537172 | + | 0.537172i | ||||
\(969\) | −12.6299 | − | 37.1231i | −0.405730 | − | 1.19257i | ||||
\(970\) | 24.4046 | + | 19.8988i | 0.783585 | + | 0.638912i | ||||
\(971\) | − | 3.26395i | − | 0.104745i | −0.998628 | − | 0.0523725i | \(-0.983322\pi\) | ||
0.998628 | − | 0.0523725i | \(-0.0166783\pi\) | |||||||
\(972\) | −11.7550 | − | 10.2381i | −0.377043 | − | 0.328388i | ||||
\(973\) | −24.9267 | + | 24.9267i | −0.799113 | + | 0.799113i | ||||
\(974\) | −14.7704 | −0.473273 | ||||||||
\(975\) | 16.4992 | + | 28.1182i | 0.528397 | + | 0.900502i | ||||
\(976\) | −3.80070 | −0.121658 | ||||||||
\(977\) | 5.20121 | − | 5.20121i | 0.166401 | − | 0.166401i | −0.618994 | − | 0.785396i | \(-0.712460\pi\) |
0.785396 | + | 0.618994i | \(0.212460\pi\) | |||||||
\(978\) | −15.3626 | + | 31.2059i | −0.491241 | + | 0.997854i | ||||
\(979\) | − | 6.88213i | − | 0.219954i | ||||||
\(980\) | 8.10530 | + | 6.60882i | 0.258914 | + | 0.211111i | ||||
\(981\) | 34.5493 | − | 26.5856i | 1.10307 | − | 0.848814i | ||||
\(982\) | 10.7414 | + | 10.7414i | 0.342773 | + | 0.342773i | ||||
\(983\) | −36.7462 | − | 36.7462i | −1.17202 | − | 1.17202i | −0.981727 | − | 0.190295i | \(-0.939056\pi\) |
−0.190295 | − | 0.981727i | \(-0.560944\pi\) | |||||||
\(984\) | −4.66657 | + | 1.58764i | −0.148765 | + | 0.0506121i | ||||
\(985\) | −11.8044 | + | 1.20055i | −0.376119 | + | 0.0382528i | ||||
\(986\) | − | 9.79639i | − | 0.311981i | ||||||
\(987\) | −4.38333 | − | 2.15790i | −0.139523 | − | 0.0686867i | ||||
\(988\) | −10.5377 | + | 10.5377i | −0.335250 | + | 0.335250i | ||||
\(989\) | 1.83907 | 0.0584790 | ||||||||
\(990\) | 28.6914 | − | 27.1183i | 0.911872 | − | 0.861877i | ||||
\(991\) | 57.5096 | 1.82685 | 0.913426 | − | 0.407006i | \(-0.133427\pi\) | ||||
0.913426 | + | 0.407006i | \(0.133427\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | −22.6769 | − | 11.1638i | −0.719630 | − | 0.354272i | ||||
\(994\) | 7.81573i | 0.247900i | ||||||||
\(995\) | 16.0170 | − | 19.6439i | 0.507773 | − | 0.622752i | ||||
\(996\) | −27.1623 | + | 9.24105i | −0.860671 | + | 0.292814i | ||||
\(997\) | −17.7135 | − | 17.7135i | −0.560993 | − | 0.560993i | 0.368596 | − | 0.929590i | \(-0.379839\pi\) |
−0.929590 | + | 0.368596i | \(0.879839\pi\) | |||||||
\(998\) | −8.48968 | − | 8.48968i | −0.268736 | − | 0.268736i | ||||
\(999\) | 25.9952 | − | 39.0776i | 0.822452 | − | 1.23636i |
(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.j.g.497.12 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.j.g.497.7 | ✓ | 40 | |
5.3 | odd | 4 | inner | 930.2.j.g.683.7 | yes | 40 | |
15.8 | even | 4 | inner | 930.2.j.g.683.12 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.g.497.7 | ✓ | 40 | 3.2 | odd | 2 | inner | |
930.2.j.g.497.12 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.j.g.683.7 | yes | 40 | 5.3 | odd | 4 | inner | |
930.2.j.g.683.12 | yes | 40 | 15.8 | even | 4 | inner |