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 | 497.7 | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.g.683.7 |
$q$-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 | ||||
\(3\) | 0.765006 | + | 1.55395i | 0.441676 | + | 0.897174i | ||||
\(4\) | − | 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 | \(-0.652629\pi\) | ||
0.461333 | − | 0.887227i | \(-0.347371\pi\) | |||||||
\(12\) | 1.55395 | − | 0.765006i | 0.448587 | − | 0.220838i | ||||
\(13\) | −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 | ||||||||
\(15\) | −0.870037 | + | 3.77399i | −0.224643 | + | 0.974441i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.04386 | + | 4.04386i | −0.980780 | + | 0.980780i | −0.999819 | − | 0.0190383i | \(-0.993940\pi\) |
0.0190383 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(18\) | −0.387518 | − | 2.97487i | −0.0913388 | − | 0.701183i | ||||
\(19\) | 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 | 0.863120 | − | 0.505000i | \(-0.168507\pi\) |
−0.505000 | + | 0.863120i | \(0.668507\pi\) | |||||||
\(24\) | −0.557869 | + | 1.63975i | −0.113875 | + | 0.334713i | ||||
\(25\) | 1.00663 | + | 4.89762i | 0.201326 | + | 0.979524i | ||||
\(26\) | − | 3.76449i | − | 0.738277i | ||||||
\(27\) | −5.09422 | − | 1.02415i | −0.980384 | − | 0.197098i | ||||
\(28\) | 1.07773 | − | 1.07773i | 0.203671 | − | 0.203671i | ||||
\(29\) | −1.71299 | −0.318094 | −0.159047 | − | 0.987271i | \(-0.550842\pi\) | ||||
−0.159047 | + | 0.987271i | \(0.550842\pi\) | |||||||
\(30\) | −2.05341 | − | 3.28383i | −0.374899 | − | 0.599542i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 9.14531 | − | 4.50221i | 1.59199 | − | 0.783734i | ||||
\(34\) | − | 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 | \(-0.928667\pi\) | ||
0.974995 | − | 0.222228i | \(-0.0713328\pi\) | |||||||
\(42\) | −1.16597 | − | 2.36843i | −0.179913 | − | 0.365457i | ||||
\(43\) | −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 | ||||||||
\(45\) | −6.53019 | + | 1.53513i | −0.973463 | + | 0.228844i | ||||
\(46\) | −2.42889 | −0.358120 | ||||||||
\(47\) | −1.30867 | + | 1.30867i | −0.190888 | + | 0.190888i | −0.796080 | − | 0.605191i | \(-0.793097\pi\) |
0.605191 | + | 0.796080i | \(0.293097\pi\) | |||||||
\(48\) | −0.765006 | − | 1.55395i | −0.110419 | − | 0.224294i | ||||
\(49\) | − | 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 | 0.823268 | − | 0.567653i | \(-0.192149\pi\) |
−0.567653 | + | 0.823268i | \(0.692149\pi\) | |||||||
\(54\) | 4.32635 | − | 2.87797i | 0.588741 | − | 0.391643i | ||||
\(55\) | 8.31603 | − | 10.1991i | 1.12133 | − | 1.37525i | ||||
\(56\) | 1.52413i | 0.203671i | ||||||||
\(57\) | −6.15167 | + | 3.02845i | −0.814808 | + | 0.401128i | ||||
\(58\) | 1.21127 | − | 1.21127i | 0.159047 | − | 0.159047i | ||||
\(59\) | 6.57921 | 0.856541 | 0.428270 | − | 0.903651i | \(-0.359123\pi\) | ||||
0.428270 | + | 0.903651i | \(0.359123\pi\) | |||||||
\(60\) | 3.77399 | + | 0.870037i | 0.487221 | + | 0.112321i | ||||
\(61\) | 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 | ||||
\(63\) | −4.53409 | + | 0.590629i | −0.571242 | + | 0.0744122i | ||||
\(64\) | 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 | \(-0.901581\pi\) | ||
0.952580 | − | 0.304290i | \(-0.0984191\pi\) | |||||||
\(72\) | −2.97487 | + | 0.387518i | −0.350591 | + | 0.0456694i | ||||
\(73\) | −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 | ||||||||
\(75\) | −6.84059 | + | 5.31096i | −0.789883 | + | 0.613257i | ||||
\(76\) | 3.95873 | 0.454097 | ||||||||
\(77\) | 6.34263 | − | 6.34263i | 0.722809 | − | 0.722809i | ||||
\(78\) | 5.84984 | − | 2.87986i | 0.662364 | − | 0.326080i | ||||
\(79\) | 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 | \(-0.886758\pi\) |
−0.348305 | − | 0.937381i | \(-0.613242\pi\) | |||||||
\(84\) | 2.49920 | + | 0.850267i | 0.272685 | + | 0.0927717i | ||||
\(85\) | −12.7222 | + | 1.29390i | −1.37991 | + | 0.140343i | ||||
\(86\) | − | 0.757166i | − | 0.0816473i | ||||||
\(87\) | −1.31045 | − | 2.66190i | −0.140495 | − | 0.285386i | ||||
\(88\) | 4.16146 | − | 4.16146i | 0.443613 | − | 0.443613i | ||||
\(89\) | 1.16940 | 0.123956 | 0.0619779 | − | 0.998078i | \(-0.480259\pi\) | ||||
0.0619779 | + | 0.998078i | \(0.480259\pi\) | |||||||
\(90\) | 3.53204 | − | 5.70304i | 0.372310 | − | 0.601154i | ||||
\(91\) | −5.73759 | −0.601462 | ||||||||
\(92\) | 1.71748 | − | 1.71748i | 0.179060 | − | 0.179060i | ||||
\(93\) | 0.765006 | + | 1.55395i | 0.0793274 | + | 0.161137i | ||||
\(94\) | − | 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 | \(-0.831685\pi\) | ||
0.863425 | − | 0.504477i | \(-0.168315\pi\) | |||||||
\(102\) | 8.88687 | − | 4.37498i | 0.879931 | − | 0.433188i | ||||
\(103\) | 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 | ||||||||
\(105\) | −5.00499 | + | 3.12967i | −0.488437 | + | 0.305424i | ||||
\(106\) | −2.63171 | −0.255614 | ||||||||
\(107\) | 6.82642 | − | 6.82642i | 0.659935 | − | 0.659935i | −0.295430 | − | 0.955364i | \(-0.595463\pi\) |
0.955364 | + | 0.295430i | \(0.0954628\pi\) | |||||||
\(108\) | −1.02415 | + | 5.09422i | −0.0985492 | + | 0.490192i | ||||
\(109\) | − | 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 | 0.648366 | − | 0.761329i | \(-0.275453\pi\) |
−0.761329 | + | 0.648366i | \(0.775453\pi\) | |||||||
\(114\) | 2.20845 | − | 6.49132i | 0.206840 | − | 0.607968i | ||||
\(115\) | 0.549536 | + | 5.40328i | 0.0512445 | + | 0.503859i | ||||
\(116\) | 1.71299i | 0.159047i | ||||||||
\(117\) | −1.45881 | − | 11.1989i | −0.134867 | − | 1.03533i | ||||
\(118\) | −4.65221 | + | 4.65221i | −0.428270 | + | 0.428270i | ||||
\(119\) | −8.71634 | −0.799026 | ||||||||
\(120\) | −3.28383 | + | 2.05341i | −0.299771 | + | 0.187450i | ||||
\(121\) | −23.6355 | −2.14869 | ||||||||
\(122\) | −2.68750 | + | 2.68750i | −0.243315 | + | 0.243315i | ||||
\(123\) | 4.42239 | − | 2.17713i | 0.398754 | − | 0.196305i | ||||
\(124\) | − | 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 | \(0.0736052\pi\) | ||||
−0.973384 | + | 0.229182i | \(0.926395\pi\) | |||||||
\(132\) | −4.50221 | − | 9.14531i | −0.391867 | − | 0.795997i | ||||
\(133\) | −4.26642 | + | 4.26642i | −0.369945 | + | 0.369945i | ||||
\(134\) | −12.5600 | −1.08502 | ||||||||
\(135\) | −7.38116 | − | 8.97321i | −0.635269 | − | 0.772291i | ||||
\(136\) | −5.71888 | −0.490390 | ||||||||
\(137\) | 13.6538 | − | 13.6538i | 1.16652 | − | 1.16652i | 0.183505 | − | 0.983019i | \(-0.441255\pi\) |
0.983019 | − | 0.183505i | \(-0.0587445\pi\) | |||||||
\(138\) | −1.85811 | − | 3.77437i | −0.158173 | − | 0.321296i | ||||
\(139\) | 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 | ||||||
\(147\) | 7.26786 | − | 3.57795i | 0.599443 | − | 0.295104i | ||||
\(148\) | 6.38692 | − | 6.38692i | 0.525001 | − | 0.525001i | ||||
\(149\) | 17.1237 | 1.40283 | 0.701414 | − | 0.712754i | \(-0.252553\pi\) | ||||
0.701414 | + | 0.712754i | \(0.252553\pi\) | |||||||
\(150\) | 1.08161 | − | 8.59245i | 0.0883132 | − | 0.701570i | ||||
\(151\) | 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 | ||||
\(153\) | −2.21617 | − | 17.0129i | −0.179167 | − | 1.37541i | ||||
\(154\) | 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 | ||||||||
\(162\) | 7.78191 | + | 4.52126i | 0.611405 | + | 0.355224i | ||||
\(163\) | 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 | ||||||||
\(165\) | 22.2107 | + | 5.12034i | 1.72910 | + | 0.398618i | ||||
\(166\) | 16.5649 | 1.28569 | ||||||||
\(167\) | −9.34843 | + | 9.34843i | −0.723403 | + | 0.723403i | −0.969297 | − | 0.245893i | \(-0.920919\pi\) |
0.245893 | + | 0.969297i | \(0.420919\pi\) | |||||||
\(168\) | −2.36843 | + | 1.16597i | −0.182728 | + | 0.0899566i | ||||
\(169\) | − | 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 | 0.964824 | − | 0.262898i | \(-0.0846784\pi\) |
−0.262898 | + | 0.964824i | \(0.584678\pi\) | |||||||
\(174\) | 2.80888 | + | 0.955624i | 0.212940 | + | 0.0724457i | ||||
\(175\) | −4.19342 | + | 6.36316i | −0.316993 | + | 0.481010i | ||||
\(176\) | 5.88520i | 0.443613i | ||||||||
\(177\) | 5.03314 | + | 10.2238i | 0.378314 | + | 0.768466i | ||||
\(178\) | −0.826888 | + | 0.826888i | −0.0619779 | + | 0.0619779i | ||||
\(179\) | 10.6481 | 0.795880 | 0.397940 | − | 0.917412i | \(-0.369725\pi\) | ||||
0.397940 | + | 0.917412i | \(0.369725\pi\) | |||||||
\(180\) | 1.53513 | + | 6.53019i | 0.114422 | + | 0.486732i | ||||
\(181\) | 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 | ||||
\(183\) | 2.90756 | + | 5.90611i | 0.214933 | + | 0.436592i | ||||
\(184\) | 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 | \(-0.850549\pi\) | ||
0.891789 | − | 0.452452i | \(-0.149451\pi\) | |||||||
\(192\) | −1.55395 | + | 0.765006i | −0.112147 | + | 0.0552095i | ||||
\(193\) | 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 | ||||||||
\(195\) | −7.73003 | − | 12.3619i | −0.553559 | − | 0.885256i | ||||
\(196\) | −4.67702 | −0.334073 | ||||||||
\(197\) | −3.75213 | + | 3.75213i | −0.267328 | + | 0.267328i | −0.828023 | − | 0.560694i | \(-0.810534\pi\) |
0.560694 | + | 0.828023i | \(0.310534\pi\) | |||||||
\(198\) | −17.5077 | + | 2.28062i | −1.24422 | + | 0.162076i | ||||
\(199\) | 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 | ||||||||
\(207\) | −7.22562 | + | 0.941237i | −0.502215 | + | 0.0654205i | ||||
\(208\) | 2.66190 | − | 2.66190i | 0.184569 | − | 0.184569i | ||||
\(209\) | 23.2979 | 1.61155 | ||||||||
\(210\) | 1.32605 | − | 5.75207i | 0.0915063 | − | 0.396931i | ||||
\(211\) | −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 | ||||
\(213\) | 7.96863 | − | 3.92294i | 0.546002 | − | 0.268795i | ||||
\(214\) | 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 | ||||||
\(222\) | −6.90989 | − | 14.0360i | −0.463761 | − | 0.942035i | ||||
\(223\) | 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 | ||||||||
\(225\) | −13.4861 | − | 6.56703i | −0.899071 | − | 0.437802i | ||||
\(226\) | 1.69821 | 0.112963 | ||||||||
\(227\) | 16.1748 | − | 16.1748i | 1.07356 | − | 1.07356i | 0.0764914 | − | 0.997070i | \(-0.475628\pi\) |
0.997070 | − | 0.0764914i | \(-0.0243718\pi\) | |||||||
\(228\) | 3.02845 | + | 6.15167i | 0.200564 | + | 0.407404i | ||||
\(229\) | 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 | 0.586742 | − | 0.809774i | \(-0.300410\pi\) |
−0.809774 | + | 0.586742i | \(0.800410\pi\) | |||||||
\(234\) | 8.95032 | + | 6.88725i | 0.585101 | + | 0.450234i | ||||
\(235\) | −4.11712 | + | 0.418728i | −0.268572 | + | 0.0273148i | ||||
\(236\) | − | 6.57921i | − | 0.428270i | ||||||
\(237\) | −25.1489 | + | 12.3807i | −1.63359 | + | 0.804214i | ||||
\(238\) | 6.16338 | − | 6.16338i | 0.399513 | − | 0.399513i | ||||
\(239\) | −2.52085 | −0.163061 | −0.0815303 | − | 0.996671i | \(-0.525981\pi\) | ||||
−0.0815303 | + | 0.996671i | \(0.525981\pi\) | |||||||
\(240\) | 0.870037 | − | 3.77399i | 0.0561607 | − | 0.243610i | ||||
\(241\) | 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 | ||||
\(243\) | 11.7550 | − | 10.2381i | 0.754086 | − | 0.656776i | ||||
\(244\) | − | 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 | \(0.0691741\pi\) | ||||
−0.976479 | + | 0.215610i | \(0.930826\pi\) | |||||||
\(252\) | 0.590629 | + | 4.53409i | 0.0372061 | + | 0.285621i | ||||
\(253\) | 10.1077 | − | 10.1077i | 0.635467 | − | 0.635467i | ||||
\(254\) | −4.38187 | −0.274943 | ||||||||
\(255\) | −11.7432 | − | 18.7798i | −0.735388 | − | 1.17604i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.63537 | + | 7.63537i | −0.476281 | + | 0.476281i | −0.903940 | − | 0.427659i | \(-0.859338\pi\) |
0.427659 | + | 0.903940i | \(0.359338\pi\) | |||||||
\(258\) | 1.17660 | − | 0.579236i | 0.0732518 | − | 0.0360617i | ||||
\(259\) | 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 | \(0.0389147\pi\) |
0.121950 | + | 0.992536i | \(0.461085\pi\) | |||||||
\(264\) | 9.65026 | + | 3.28317i | 0.593932 | + | 0.202065i | ||||
\(265\) | 0.595425 | + | 5.85448i | 0.0365767 | + | 0.359638i | ||||
\(266\) | − | 6.03363i | − | 0.369945i | ||||||
\(267\) | 0.894595 | + | 1.81719i | 0.0547483 | + | 0.111210i | ||||
\(268\) | 8.88129 | − | 8.88129i | 0.542511 | − | 0.542511i | ||||
\(269\) | −7.67463 | −0.467930 | −0.233965 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233965 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(270\) | 11.5643 | + | 1.12575i | 0.703780 | + | 0.0685112i | ||||
\(271\) | 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 | ||||
\(273\) | −4.38929 | − | 8.91593i | −0.265652 | − | 0.539617i | ||||
\(274\) | 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 | \(-0.881772\pi\) | ||
0.931812 | − | 0.362943i | \(-0.118228\pi\) | |||||||
\(282\) | 2.87595 | − | 1.41582i | 0.171260 | − | 0.0843109i | ||||
\(283\) | −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 | ||||||||
\(285\) | −14.9402 | − | 3.44424i | −0.884982 | − | 0.204019i | ||||
\(286\) | −22.1548 | −1.31004 | ||||||||
\(287\) | 3.06710 | − | 3.06710i | 0.181045 | − | 0.181045i | ||||
\(288\) | 0.387518 | + | 2.97487i | 0.0228347 | + | 0.175296i | ||||
\(289\) | − | 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 | 0.500320 | − | 0.865841i | \(-0.333216\pi\) |
−0.865841 | + | 0.500320i | \(0.833216\pi\) | |||||||
\(294\) | −2.60916 | + | 7.66914i | −0.152169 | + | 0.447273i | ||||
\(295\) | 11.4018 | + | 9.29670i | 0.663840 | + | 0.541275i | ||||
\(296\) | 9.03246i | 0.525001i | ||||||||
\(297\) | −6.02734 | + | 29.9805i | −0.349742 | + | 1.73965i | ||||
\(298\) | −12.1083 | + | 12.1083i | −0.701414 | + | 0.701414i | ||||
\(299\) | −9.14352 | −0.528784 | ||||||||
\(300\) | 5.31096 | + | 6.84059i | 0.306629 | + | 0.394942i | ||||
\(301\) | −1.15402 | −0.0665167 | ||||||||
\(302\) | −6.23907 | + | 6.23907i | −0.359018 | + | 0.359018i | ||||
\(303\) | 15.7568 | − | 7.75705i | 0.905207 | − | 0.445631i | ||||
\(304\) | − | 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 | \(0.0456908\pi\) | ||||
−0.989716 | + | 0.143049i | \(0.954309\pi\) | |||||||
\(312\) | −2.87986 | − | 5.84984i | −0.163040 | − | 0.331182i | ||||
\(313\) | −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 | ||||||||
\(315\) | −8.69220 | − | 5.38330i | −0.489750 | − | 0.303314i | ||||
\(316\) | 16.1838 | 0.910411 | ||||||||
\(317\) | −0.0859022 | + | 0.0859022i | −0.00482475 | + | 0.00482475i | −0.709515 | − | 0.704690i | \(-0.751086\pi\) |
0.704690 | + | 0.709515i | \(0.251086\pi\) | |||||||
\(318\) | −2.01327 | − | 4.08955i | −0.112899 | − | 0.229331i | ||||
\(319\) | 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 | ||||||||
\(327\) | 22.5811 | − | 11.1166i | 1.24874 | − | 0.614749i | ||||
\(328\) | 2.01236 | − | 2.01236i | 0.111114 | − | 0.111114i | ||||
\(329\) | −2.82076 | −0.155514 | ||||||||
\(330\) | −19.3260 | + | 12.0847i | −1.06386 | + | 0.665241i | ||||
\(331\) | 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 | ||||
\(333\) | −26.8704 | + | 3.50024i | −1.47249 | + | 0.191812i | ||||
\(334\) | − | 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 | ||||||
\(342\) | 11.7767 | − | 1.53408i | 0.636810 | − | 0.0829533i | ||||
\(343\) | 12.5846 | − | 12.5846i | 0.679505 | − | 0.679505i | ||||
\(344\) | −0.757166 | −0.0408236 | ||||||||
\(345\) | −7.97604 | + | 4.98750i | −0.429416 | + | 0.268518i | ||||
\(346\) | −13.0566 | −0.701925 | ||||||||
\(347\) | −10.9974 | + | 10.9974i | −0.590371 | + | 0.590371i | −0.937732 | − | 0.347361i | \(-0.887078\pi\) |
0.347361 | + | 0.937732i | \(0.387078\pi\) | |||||||
\(348\) | −2.66190 | + | 1.31045i | −0.142693 | + | 0.0702474i | ||||
\(349\) | − | 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 | \(0.0633105\pi\) |
0.197587 | + | 0.980285i | \(0.436690\pi\) | |||||||
\(354\) | −10.7883 | − | 3.67034i | −0.573390 | − | 0.195076i | ||||
\(355\) | 7.24605 | − | 8.88683i | 0.384580 | − | 0.471664i | ||||
\(356\) | − | 1.16940i | − | 0.0619779i | ||||||
\(357\) | −6.66805 | − | 13.5448i | −0.352911 | − | 0.716866i | ||||
\(358\) | −7.52937 | + | 7.52937i | −0.397940 | + | 0.397940i | ||||
\(359\) | 14.8084 | 0.781558 | 0.390779 | − | 0.920485i | \(-0.372206\pi\) | ||||
0.390779 | + | 0.920485i | \(0.372206\pi\) | |||||||
\(360\) | −5.70304 | − | 3.53204i | −0.300577 | − | 0.186155i | ||||
\(361\) | 3.32849 | 0.175184 | ||||||||
\(362\) | −2.02173 | + | 2.02173i | −0.106260 | + | 0.106260i | ||||
\(363\) | −18.0813 | − | 36.7285i | −0.949024 | − | 1.92775i | ||||
\(364\) | 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 | ||||||||
\(372\) | 1.55395 | − | 0.765006i | 0.0805686 | − | 0.0396637i | ||||
\(373\) | −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 | ||||||||
\(375\) | −19.3594 | − | 0.462102i | −0.999715 | − | 0.0238628i | ||||
\(376\) | −1.85073 | −0.0954442 | ||||||||
\(377\) | 4.55980 | − | 4.55980i | 0.234842 | − | 0.234842i | ||||
\(378\) | 7.76428 | + | 1.56095i | 0.399351 | + | 0.0802864i | ||||
\(379\) | 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 | \(-0.938527\pi\) |
−0.191925 | − | 0.981410i | \(-0.561473\pi\) | |||||||
\(384\) | 0.557869 | − | 1.63975i | 0.0284686 | − | 0.0836782i | ||||
\(385\) | 19.9542 | − | 2.02942i | 1.01696 | − | 0.103429i | ||||
\(386\) | 21.2788i | 1.08306i | ||||||||
\(387\) | −0.293415 | − | 2.25247i | −0.0149151 | − | 0.114499i | ||||
\(388\) | −9.95765 | + | 9.95765i | −0.505523 | + | 0.505523i | ||||
\(389\) | −12.6552 | −0.641643 | −0.320822 | − | 0.947140i | \(-0.603959\pi\) | ||||
−0.320822 | + | 0.947140i | \(0.603959\pi\) | |||||||
\(390\) | 14.2072 | + | 3.27525i | 0.719408 | + | 0.165849i | ||||
\(391\) | −13.8905 | −0.702474 | ||||||||
\(392\) | 3.30715 | − | 3.30715i | 0.167036 | − | 0.167036i | ||||
\(393\) | −8.15238 | + | 4.01339i | −0.411233 | + | 0.202449i | ||||
\(394\) | − | 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 | \(0.158622\pi\) | ||||
−0.878383 | + | 0.477957i | \(0.841378\pi\) | |||||||
\(402\) | −9.60850 | − | 19.5177i | −0.479229 | − | 0.973454i | ||||
\(403\) | −2.66190 | + | 2.66190i | −0.132599 | + | 0.132599i | ||||
\(404\) | −10.1399 | −0.504477 | ||||||||
\(405\) | 8.29731 | − | 18.3345i | 0.412297 | − | 0.911050i | ||||
\(406\) | 2.61083 | 0.129573 | ||||||||
\(407\) | 37.5883 | − | 37.5883i | 1.86318 | − | 1.86318i | ||||
\(408\) | −4.37498 | − | 8.88687i | −0.216594 | − | 0.439966i | ||||
\(409\) | − | 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 | ||||||||
\(417\) | −35.9413 | + | 17.6938i | −1.76005 | + | 0.866469i | ||||
\(418\) | −16.4741 | + | 16.4741i | −0.805774 | + | 0.805774i | ||||
\(419\) | −17.7582 | −0.867547 | −0.433774 | − | 0.901022i | \(-0.642818\pi\) | ||||
−0.433774 | + | 0.901022i | \(0.642818\pi\) | |||||||
\(420\) | 3.12967 | + | 5.00499i | 0.152712 | + | 0.244218i | ||||
\(421\) | −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 | ||||
\(423\) | −0.717191 | − | 5.50568i | −0.0348710 | − | 0.267695i | ||||
\(424\) | 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 | \(0.124134\pi\) | ||||
−0.924917 | + | 0.380168i | \(0.875866\pi\) | |||||||
\(432\) | 5.09422 | + | 1.02415i | 0.245096 | + | 0.0492746i | ||||
\(433\) | −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 | ||||||||
\(435\) | 1.49037 | − | 6.46482i | 0.0714575 | − | 0.309964i | ||||
\(436\) | −14.5314 | −0.695927 | ||||||||
\(437\) | −6.79904 | + | 6.79904i | −0.325242 | + | 0.325242i | ||||
\(438\) | 11.9070 | − | 5.86176i | 0.568937 | − | 0.280086i | ||||
\(439\) | − | 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 | 0.998457 | − | 0.0555220i | \(-0.0176823\pi\) |
−0.0555220 | + | 0.998457i | \(0.517682\pi\) | |||||||
\(444\) | 14.8110 | + | 5.03893i | 0.702898 | + | 0.239137i | ||||
\(445\) | 2.02657 | + | 1.65241i | 0.0960688 | + | 0.0783315i | ||||
\(446\) | 8.49856i | 0.402419i | ||||||||
\(447\) | 13.0997 | + | 26.6094i | 0.619596 | + | 1.25858i | ||||
\(448\) | −1.07773 | + | 1.07773i | −0.0509177 | + | 0.0509177i | ||||
\(449\) | −11.8070 | −0.557205 | −0.278603 | − | 0.960406i | \(-0.589871\pi\) | ||||
−0.278603 | + | 0.960406i | \(0.589871\pi\) | |||||||
\(450\) | 14.1797 | − | 4.89250i | 0.668437 | − | 0.230635i | ||||
\(451\) | −16.7487 | −0.788665 | ||||||||
\(452\) | −1.20082 | + | 1.20082i | −0.0564817 | + | 0.0564817i | ||||
\(453\) | 6.74994 | + | 13.7111i | 0.317140 | + | 0.644204i | ||||
\(454\) | 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 | \(-0.877713\pi\) | ||
0.927107 | − | 0.374796i | \(-0.122287\pi\) | |||||||
\(462\) | −13.9387 | + | 6.86197i | −0.648486 | + | 0.319248i | ||||
\(463\) | 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 | ||||||||
\(465\) | −0.870037 | + | 3.77399i | −0.0403470 | + | 0.175015i | ||||
\(466\) | 4.81459 | 0.223032 | ||||||||
\(467\) | −25.3293 | + | 25.3293i | −1.17210 | + | 1.17210i | −0.190390 | + | 0.981709i | \(0.560975\pi\) |
−0.981709 | + | 0.190390i | \(0.939025\pi\) | |||||||
\(468\) | −11.1989 | + | 1.45881i | −0.517667 | + | 0.0674334i | ||||
\(469\) | 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 | ||||||||
\(477\) | −7.82899 | + | 1.01983i | −0.358465 | + | 0.0466950i | ||||
\(478\) | 1.78251 | − | 1.78251i | 0.0815303 | − | 0.0815303i | ||||
\(479\) | −4.28019 | −0.195567 | −0.0977835 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977835 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(480\) | 2.05341 | + | 3.28383i | 0.0937248 | + | 0.149885i | ||||
\(481\) | −34.0026 | −1.55039 | ||||||||
\(482\) | −1.26718 | + | 1.26718i | −0.0577183 | + | 0.0577183i | ||||
\(483\) | −5.75265 | + | 2.83201i | −0.261755 | + | 0.128861i | ||||
\(484\) | 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 | \(-0.888634\pi\) | ||
0.939418 | − | 0.342773i | \(-0.111366\pi\) | |||||||
\(492\) | −2.17713 | − | 4.42239i | −0.0981526 | − | 0.199377i | ||||
\(493\) | 6.92710 | − | 6.92710i | 0.311981 | − | 0.311981i | ||||
\(494\) | 14.9026 | 0.670499 | ||||||||
\(495\) | 9.03456 | + | 38.4315i | 0.406073 | + | 1.72737i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 5.52655 | − | 5.52655i | 0.247900 | − | 0.247900i | ||||
\(498\) | 12.6723 | + | 25.7411i | 0.567857 | + | 1.15348i | ||||
\(499\) | − | 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 | 0.853623 | − | 0.520891i | \(-0.174400\pi\) |
−0.520891 | + | 0.853623i | \(0.674400\pi\) | |||||||
\(504\) | −3.62373 | − | 2.78845i | −0.161414 | − | 0.124207i | ||||
\(505\) | 14.3280 | − | 17.5724i | 0.637589 | − | 0.781963i | ||||
\(506\) | 14.2945i | 0.635467i | ||||||||
\(507\) | 1.82028 | − | 0.896118i | 0.0808415 | − | 0.0397980i | ||||
\(508\) | 3.09845 | − | 3.09845i | 0.137471 | − | 0.137471i | ||||
\(509\) | −29.9286 | −1.32656 | −0.663280 | − | 0.748371i | \(-0.730836\pi\) | ||||
−0.663280 | + | 0.748371i | \(0.730836\pi\) | |||||||
\(510\) | 21.5830 | + | 4.97564i | 0.955713 | + | 0.220325i | ||||
\(511\) | −11.6785 | −0.516626 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.05434 | − | 20.1666i | 0.179004 | − | 0.890379i | ||||
\(514\) | − | 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 | \(0.135688\pi\) | ||||
−0.910512 | + | 0.413483i | \(0.864312\pi\) | |||||||
\(522\) | 0.663814 | + | 5.09592i | 0.0290544 | + | 0.223042i | ||||
\(523\) | −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 | ||||||||
\(525\) | −13.0960 | − | 1.64852i | −0.571558 | − | 0.0719473i | ||||
\(526\) | −25.5604 | −1.11449 | ||||||||
\(527\) | −4.04386 | + | 4.04386i | −0.176153 | + | 0.176153i | ||||
\(528\) | −9.14531 | + | 4.50221i | −0.397999 | + | 0.195934i | ||||
\(529\) | − | 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 | ||||||||
\(537\) | 8.14589 | + | 16.5467i | 0.351521 | + | 0.714043i | ||||
\(538\) | 5.42678 | − | 5.42678i | 0.233965 | − | 0.233965i | ||||
\(539\) | −27.5252 | −1.18559 | ||||||||
\(540\) | −8.97321 | + | 7.38116i | −0.386146 | + | 0.317634i | ||||
\(541\) | 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 | ||||
\(543\) | 2.18728 | + | 4.44300i | 0.0938650 | + | 0.190667i | ||||
\(544\) | 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 | ||||||
\(552\) | −3.77437 | + | 1.85811i | −0.160648 | + | 0.0790866i | ||||
\(553\) | −17.4417 | + | 17.4417i | −0.741697 | + | 0.741697i | ||||
\(554\) | −5.11844 | −0.217462 | ||||||||
\(555\) | −29.6610 | + | 18.5473i | −1.25904 | + | 0.787290i | ||||
\(556\) | 23.1290 | 0.980887 | ||||||||
\(557\) | −19.8179 | + | 19.8179i | −0.839712 | + | 0.839712i | −0.988821 | − | 0.149109i | \(-0.952359\pi\) |
0.149109 | + | 0.988821i | \(0.452359\pi\) | |||||||
\(558\) | −0.387518 | − | 2.97487i | −0.0164049 | − | 0.125936i | ||||
\(559\) | − | 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 | 0.301952 | − | 0.953323i | \(-0.402362\pi\) |
−0.953323 | + | 0.301952i | \(0.902362\pi\) | |||||||
\(564\) | −1.03247 | + | 3.03474i | −0.0434747 | + | 0.127786i | ||||
\(565\) | −0.384221 | − | 3.77783i | −0.0161643 | − | 0.158935i | ||||
\(566\) | − | 22.6171i | − | 0.950666i | ||||||
\(567\) | 6.89101 | − | 11.8607i | 0.289395 | − | 0.498102i | ||||
\(568\) | 3.62603 | − | 3.62603i | 0.152145 | − | 0.152145i | ||||
\(569\) | 16.1031 | 0.675076 | 0.337538 | − | 0.941312i | \(-0.390406\pi\) | ||||
0.337538 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(570\) | 12.9998 | − | 8.12888i | 0.544500 | − | 0.340481i | ||||
\(571\) | −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 | ||||
\(573\) | 19.4338 | − | 9.56719i | 0.811857 | − | 0.399675i | ||||
\(574\) | 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 | ||||||
\(582\) | 10.7730 | + | 21.8831i | 0.446555 | + | 0.907085i | ||||
\(583\) | 10.9518 | − | 10.9518i | 0.453576 | − | 0.453576i | ||||
\(584\) | −7.66238 | −0.317071 | ||||||||
\(585\) | 13.2963 | − | 21.4691i | 0.549735 | − | 0.887636i | ||||
\(586\) | 8.84831 | 0.365520 | ||||||||
\(587\) | −7.99099 | + | 7.99099i | −0.329823 | + | 0.329823i | −0.852519 | − | 0.522696i | \(-0.824926\pi\) |
0.522696 | + | 0.852519i | \(0.324926\pi\) | |||||||
\(588\) | −3.57795 | − | 7.26786i | −0.147552 | − | 0.299721i | ||||
\(589\) | 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 | 0.978959 | − | 0.204058i | \(-0.0654132\pi\) |
−0.204058 | + | 0.978959i | \(0.565413\pi\) | |||||||
\(594\) | −16.9374 | − | 25.4614i | −0.694952 | − | 1.04469i | ||||
\(595\) | −15.1055 | − | 12.3166i | −0.619264 | − | 0.504929i | ||||
\(596\) | − | 17.1237i | − | 0.701414i | ||||||
\(597\) | −17.6142 | + | 8.67144i | −0.720903 | + | 0.354898i | ||||
\(598\) | 6.46545 | − | 6.46545i | 0.264392 | − | 0.264392i | ||||
\(599\) | −10.2519 | −0.418880 | −0.209440 | − | 0.977822i | \(-0.567164\pi\) | ||||
−0.209440 | + | 0.977822i | \(0.567164\pi\) | |||||||
\(600\) | −8.59245 | − | 1.08161i | −0.350785 | − | 0.0441566i | ||||
\(601\) | −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 | ||||
\(603\) | −37.3644 | + | 4.86724i | −1.52160 | + | 0.198209i | ||||
\(604\) | − | 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 | ||||||
\(612\) | −17.0129 | + | 2.21617i | −0.687706 | + | 0.0895833i | ||||
\(613\) | −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 | ||||||||
\(615\) | 10.7404 | + | 2.47604i | 0.433095 | + | 0.0998435i | ||||
\(616\) | 8.96983 | 0.361405 | ||||||||
\(617\) | 5.30562 | − | 5.30562i | 0.213596 | − | 0.213596i | −0.592197 | − | 0.805793i | \(-0.701739\pi\) |
0.805793 | + | 0.592197i | \(0.201739\pi\) | |||||||
\(618\) | −26.6969 | + | 13.1428i | −1.07391 | + | 0.528681i | ||||
\(619\) | − | 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 | ||||||
\(627\) | 17.8230 | + | 36.2038i | 0.711783 | + | 1.44584i | ||||
\(628\) | −3.93949 | + | 3.93949i | −0.157203 | + | 0.157203i | ||||
\(629\) | −51.6556 | −2.05964 | ||||||||
\(630\) | 9.95288 | − | 2.33975i | 0.396532 | − | 0.0932178i | ||||
\(631\) | 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 | ||||
\(633\) | −10.3425 | − | 21.0087i | −0.411079 | − | 0.835023i | ||||
\(634\) | − | 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 | \(-0.924038\pi\) | ||
0.971660 | − | 0.236383i | \(-0.0759620\pi\) | |||||||
\(642\) | −15.0019 | + | 7.38538i | −0.592077 | + | 0.291478i | ||||
\(643\) | 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 | ||||||||
\(645\) | −1.55477 | − | 2.48640i | −0.0612190 | − | 0.0979019i | ||||
\(646\) | 22.6395 | 0.890739 | ||||||||
\(647\) | 29.4564 | − | 29.4564i | 1.15805 | − | 1.15805i | 0.173155 | − | 0.984895i | \(-0.444604\pi\) |
0.984895 | − | 0.173155i | \(-0.0553961\pi\) | |||||||
\(648\) | 4.52126 | − | 7.78191i | 0.177612 | − | 0.305702i | ||||
\(649\) | − | 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 | 0.412423 | − | 0.910993i | \(-0.364683\pi\) |
−0.910993 | + | 0.412423i | \(0.864683\pi\) | |||||||
\(654\) | −8.10661 | + | 23.8279i | −0.316994 | + | 0.931743i | ||||
\(655\) | −7.41313 | + | 9.09174i | −0.289655 | + | 0.355244i | ||||
\(656\) | 2.84590i | 0.111114i | ||||||||
\(657\) | −2.96931 | − | 22.7945i | −0.115844 | − | 0.889300i | ||||
\(658\) | 1.99458 | − | 1.99458i | 0.0777568 | − | 0.0777568i | ||||
\(659\) | 38.2781 | 1.49110 | 0.745551 | − | 0.666448i | \(-0.232186\pi\) | ||||
0.745551 | + | 0.666448i | \(0.232186\pi\) | |||||||
\(660\) | 5.12034 | − | 22.2107i | 0.199309 | − | 0.864550i | ||||
\(661\) | 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 | ||||
\(663\) | 33.4545 | − | 16.4696i | 1.29927 | − | 0.639625i | ||||
\(664\) | − | 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 | ||||||
\(672\) | 1.16597 | + | 2.36843i | 0.0449783 | + | 0.0913642i | ||||
\(673\) | 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 | ||||||||
\(675\) | −0.112076 | − | 25.9805i | −0.00431381 | − | 0.999991i | ||||
\(676\) | −1.17139 | −0.0450534 | ||||||||
\(677\) | −23.6196 | + | 23.6196i | −0.907776 | + | 0.907776i | −0.996092 | − | 0.0883164i | \(-0.971851\pi\) |
0.0883164 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(678\) | 1.29914 | + | 2.63894i | 0.0498933 | + | 0.101348i | ||||
\(679\) | − | 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 | \(0.0650422\pi\) |
0.202917 | + | 0.979196i | \(0.434958\pi\) | |||||||
\(684\) | −7.24261 | + | 9.41213i | −0.276928 | + | 0.359882i | ||||
\(685\) | 42.9556 | − | 4.36876i | 1.64125 | − | 0.166922i | ||||
\(686\) | 17.7973i | 0.679505i | ||||||||
\(687\) | −8.29843 | + | 4.08529i | −0.316605 | + | 0.155864i | ||||
\(688\) | 0.535397 | − | 0.535397i | 0.0204118 | − | 0.0204118i | ||||
\(689\) | −9.90705 | −0.377429 | ||||||||
\(690\) | 2.11322 | − | 9.16661i | 0.0804490 | − | 0.348967i | ||||
\(691\) | 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 | ||||
\(693\) | 3.47597 | + | 26.6840i | 0.132041 | + | 1.01364i | ||||
\(694\) | − | 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 | \(-0.821082\pi\) | ||
0.846145 | − | 0.532953i | \(-0.178918\pi\) | |||||||
\(702\) | −3.85541 | + | 19.1772i | −0.145513 | + | 0.723795i | ||||
\(703\) | −25.2841 | + | 25.2841i | −0.953606 | + | 0.953606i | ||||
\(704\) | 5.88520 | 0.221807 | ||||||||
\(705\) | −3.80031 | − | 6.07748i | −0.143128 | − | 0.228891i | ||||
\(706\) | −31.2968 | −1.17787 | ||||||||
\(707\) | 10.9280 | − | 10.9280i | 0.410989 | − | 0.410989i | ||||
\(708\) | 10.2238 | − | 5.03314i | 0.384233 | − | 0.189157i | ||||
\(709\) | − | 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 | ||||||
\(717\) | −1.92847 | − | 3.91729i | −0.0720200 | − | 0.146294i | ||||
\(718\) | −10.4711 | + | 10.4711i | −0.390779 | + | 0.390779i | ||||
\(719\) | 23.9331 | 0.892553 | 0.446276 | − | 0.894895i | \(-0.352750\pi\) | ||||
0.446276 | + | 0.894895i | \(0.352750\pi\) | |||||||
\(720\) | 6.53019 | − | 1.53513i | 0.243366 | − | 0.0572110i | ||||
\(721\) | 26.1846 | 0.975166 | ||||||||
\(722\) | −2.35360 | + | 2.35360i | −0.0875918 | + | 0.0875918i | ||||
\(723\) | 1.37094 | + | 2.78477i | 0.0509857 | + | 0.103567i | ||||
\(724\) | − | 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 | ||||||
\(732\) | 5.90611 | − | 2.90756i | 0.218296 | − | 0.107466i | ||||
\(733\) | −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 | ||||||||
\(735\) | 17.6510 | + | 4.06918i | 0.651068 | + | 0.150094i | ||||
\(736\) | 2.42889 | 0.0895300 | ||||||||
\(737\) | 52.2681 | − | 52.2681i | 1.92532 | − | 1.92532i | ||||
\(738\) | −8.46617 | + | 1.10284i | −0.311644 | + | 0.0405960i | ||||
\(739\) | 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 | 0.214230 | − | 0.976783i | \(-0.431276\pi\) |
−0.976783 | + | 0.214230i | \(0.931276\pi\) | |||||||
\(744\) | −0.557869 | + | 1.63975i | −0.0204525 | + | 0.0601162i | ||||
\(745\) | 29.6755 | + | 24.1965i | 1.08723 | + | 0.886491i | ||||
\(746\) | − | 31.6897i | − | 1.16024i | ||||||
\(747\) | 49.2784 | − | 6.41919i | 1.80300 | − | 0.234866i | ||||
\(748\) | 23.7989 | − | 23.7989i | 0.870175 | − | 0.870175i | ||||
\(749\) | 14.7140 | 0.537638 | ||||||||
\(750\) | 14.0159 | − | 13.3624i | 0.511789 | − | 0.487926i | ||||
\(751\) | 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 | ||||
\(753\) | −10.6163 | + | 5.22638i | −0.386880 | + | 0.190460i | ||||
\(754\) | 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 | \(0.183717\pi\) | ||||
−0.838013 | + | 0.545650i | \(0.816283\pi\) | |||||||
\(762\) | −3.35215 | − | 6.80921i | −0.121436 | − | 0.246672i | ||||
\(763\) | 15.6608 | − | 15.6608i | 0.566961 | − | 0.566961i | ||||
\(764\) | −12.5060 | −0.452452 | ||||||||
\(765\) | 20.1993 | − | 32.6150i | 0.730308 | − | 1.17920i | ||||
\(766\) | 32.4740 | 1.17333 | ||||||||
\(767\) | −17.5132 | + | 17.5132i | −0.632364 | + | 0.632364i | ||||
\(768\) | 0.765006 | + | 1.55395i | 0.0276048 | + | 0.0560734i | ||||
\(769\) | 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 | 0.0790733 | − | 0.996869i | \(-0.474804\pi\) |
−0.996869 | + | 0.0790733i | \(0.974804\pi\) | |||||||
\(774\) | 1.80021 | + | 1.38526i | 0.0647072 | + | 0.0497921i | ||||
\(775\) | 1.00663 | + | 4.89762i | 0.0361592 | + | 0.175928i | ||||
\(776\) | − | 14.0822i | − | 0.505523i | ||||||
\(777\) | −21.3928 | + | 10.5316i | −0.767461 | + | 0.377819i | ||||
\(778\) | 8.94856 | − | 8.94856i | 0.320822 | − | 0.320822i | ||||
\(779\) | 11.2661 | 0.403651 | ||||||||
\(780\) | −12.3619 | + | 7.73003i | −0.442628 | + | 0.276780i | ||||
\(781\) | −30.1792 | −1.07990 | ||||||||
\(782\) | 9.82208 | − | 9.82208i | 0.351237 | − | 0.351237i | ||||
\(783\) | 8.72636 | + | 1.75436i | 0.311855 | + | 0.0626959i | ||||
\(784\) | 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 | ||||||
\(792\) | 2.28062 | + | 17.5077i | 0.0810382 | + | 0.622108i | ||||
\(793\) | −10.1171 | + | 10.1171i | −0.359268 | + | 0.359268i | ||||
\(794\) | 27.5995 | 0.979468 | ||||||||
\(795\) | −8.64208 | + | 5.40398i | −0.306503 | + | 0.191659i | ||||
\(796\) | 11.3351 | 0.401763 | ||||||||
\(797\) | 11.3248 | − | 11.3248i | 0.401145 | − | 0.401145i | −0.477491 | − | 0.878636i | \(-0.658454\pi\) |
0.878636 | + | 0.477491i | \(0.158454\pi\) | |||||||
\(798\) | 9.37596 | − | 4.61576i | 0.331906 | − | 0.163396i | ||||
\(799\) | − | 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 | ||||||
\(807\) | −5.87114 | − | 11.9260i | −0.206674 | − | 0.419815i | ||||
\(808\) | 7.16996 | − | 7.16996i | 0.252238 | − | 0.252238i | ||||
\(809\) | −29.3613 | −1.03229 | −0.516143 | − | 0.856502i | \(-0.672633\pi\) | ||||
−0.516143 | + | 0.856502i | \(0.672633\pi\) | |||||||
\(810\) | 7.09738 | + | 18.8315i | 0.249376 | + | 0.661673i | ||||
\(811\) | −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 | ||||
\(813\) | 14.3585 | + | 29.1663i | 0.503574 | + | 1.02291i | ||||
\(814\) | 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 | \(0.00130435\pi\) | ||||
−0.999992 | + | 0.00409771i | \(0.998696\pi\) | |||||||
\(822\) | −30.0059 | + | 14.7718i | −1.04658 | + | 0.515226i | ||||
\(823\) | 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 | ||||||||
\(825\) | 31.2561 | + | 40.2582i | 1.08820 | + | 1.40161i | ||||
\(826\) | −10.0276 | −0.348905 | ||||||||
\(827\) | 0.735311 | − | 0.735311i | 0.0255693 | − | 0.0255693i | −0.694207 | − | 0.719776i | \(-0.744245\pi\) |
0.719776 | + | 0.694207i | \(0.244245\pi\) | |||||||
\(828\) | 0.941237 | + | 7.22562i | 0.0327102 | + | 0.251108i | ||||
\(829\) | − | 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 | ||||||
\(837\) | −5.09422 | − | 1.02415i | −0.176082 | − | 0.0353999i | ||||
\(838\) | 12.5570 | − | 12.5570i | 0.433774 | − | 0.433774i | ||||
\(839\) | −46.9394 | −1.62053 | −0.810264 | − | 0.586065i | \(-0.800677\pi\) | ||||
−0.810264 | + | 0.586065i | \(0.800677\pi\) | |||||||
\(840\) | −5.75207 | − | 1.32605i | −0.198465 | − | 0.0457532i | ||||
\(841\) | −26.0657 | −0.898816 | ||||||||
\(842\) | 2.07626 | − | 2.07626i | 0.0715527 | − | 0.0715527i | ||||
\(843\) | 18.9086 | − | 9.30863i | 0.651246 | − | 0.320606i | ||||
\(844\) | 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 | ||||||||
\(852\) | −3.92294 | − | 7.96863i | −0.134398 | − | 0.273001i | ||||
\(853\) | −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 | ||||||||
\(855\) | −6.07717 | − | 25.8512i | −0.207835 | − | 0.884093i | ||||
\(856\) | 9.65401 | 0.329967 | ||||||||
\(857\) | −22.1292 | + | 22.1292i | −0.755919 | + | 0.755919i | −0.975577 | − | 0.219658i | \(-0.929506\pi\) |
0.219658 | + | 0.975577i | \(0.429506\pi\) | |||||||
\(858\) | −16.9485 | − | 34.4274i | −0.578613 | − | 1.17533i | ||||
\(859\) | 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 | 0.786794 | − | 0.617216i | \(-0.211739\pi\) |
−0.617216 | + | 0.786794i | \(0.711739\pi\) | |||||||
\(864\) | −4.32635 | + | 2.87797i | −0.147185 | + | 0.0979107i | ||||
\(865\) | 2.95405 | + | 29.0455i | 0.100441 | + | 0.987577i | ||||
\(866\) | − | 18.5456i | − | 0.630205i | ||||||
\(867\) | 24.4058 | − | 12.0149i | 0.828864 | − | 0.408047i | ||||
\(868\) | 1.07773 | − | 1.07773i | 0.0365804 | − | 0.0365804i | ||||
\(869\) | 95.2449 | 3.23096 | ||||||||
\(870\) | 3.51747 | + | 5.62516i | 0.119253 | + | 0.190711i | ||||
\(871\) | −47.2821 | −1.60209 | ||||||||
\(872\) | 10.2752 | − | 10.2752i | 0.347964 | − | 0.347964i | ||||
\(873\) | 41.8928 | − | 5.45712i | 1.41786 | − | 0.184695i | ||||
\(874\) | − | 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 | \(-0.814441\pi\) | ||
0.834842 | − | 0.550490i | \(-0.185559\pi\) | |||||||
\(882\) | −13.9135 | + | 1.81243i | −0.468492 | + | 0.0610276i | ||||
\(883\) | −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 | ||||||||
\(885\) | −5.72416 | + | 24.8299i | −0.192416 | + | 0.834648i | ||||
\(886\) | −28.0672 | −0.942936 | ||||||||
\(887\) | 10.9781 | − | 10.9781i | 0.368607 | − | 0.368607i | −0.498362 | − | 0.866969i | \(-0.666065\pi\) |
0.866969 | + | 0.498362i | \(0.166065\pi\) | |||||||
\(888\) | −14.0360 | + | 6.90989i | −0.471018 | + | 0.231881i | ||||
\(889\) | 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 | ||||||
\(897\) | −6.99485 | − | 14.2086i | −0.233551 | − | 0.474411i | ||||
\(898\) | 8.34879 | − | 8.34879i | 0.278603 | − | 0.278603i | ||||
\(899\) | −1.71299 | −0.0571314 | ||||||||
\(900\) | −6.56703 | + | 13.4861i | −0.218901 | + | 0.449536i | ||||
\(901\) | −15.0505 | −0.501403 | ||||||||
\(902\) | 11.8431 | − | 11.8431i | 0.394332 | − | 0.394332i | ||||
\(903\) | −0.882833 | − | 1.79329i | −0.0293789 | − | 0.0596771i | ||||
\(904\) | − | 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 | \(-0.704560\pi\) | ||
0.599315 | − | 0.800513i | \(-0.295440\pi\) | |||||||
\(912\) | 6.15167 | − | 3.02845i | 0.203702 | − | 0.100282i | ||||
\(913\) | −68.9342 | + | 68.9342i | −2.28139 | + | 2.28139i | ||||
\(914\) | 6.39755 | 0.211612 | ||||||||
\(915\) | −3.30675 | + | 14.3438i | −0.109318 | + | 0.474192i | ||||
\(916\) | 5.34021 | 0.176446 | ||||||||
\(917\) | −5.65399 | + | 5.65399i | −0.186711 | + | 0.186711i | ||||
\(918\) | −5.85701 | + | 29.1333i | −0.193310 | + | 0.961541i | ||||
\(919\) | − | 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 | ||||||||
\(927\) | 6.65756 | + | 51.1082i | 0.218663 | + | 1.67861i | ||||
\(928\) | −1.21127 | + | 1.21127i | −0.0397618 | + | 0.0397618i | ||||
\(929\) | −19.1173 | −0.627219 | −0.313610 | − | 0.949552i | \(-0.601538\pi\) | ||||
−0.313610 | + | 0.949552i | \(0.601538\pi\) | |||||||
\(930\) | −2.05341 | − | 3.28383i | −0.0673339 | − | 0.107681i | ||||
\(931\) | 18.5150 | 0.606806 | ||||||||
\(932\) | −3.40443 | + | 3.40443i | −0.111516 | + | 0.111516i | ||||
\(933\) | −7.84032 | + | 3.85977i | −0.256681 | + | 0.126363i | ||||
\(934\) | − | 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 | \(0.150267\pi\) | ||||
−0.890625 | + | 0.454738i | \(0.849733\pi\) | |||||||
\(942\) | 4.26206 | + | 8.65750i | 0.138866 | + | 0.282077i | ||||
\(943\) | 4.88779 | − | 4.88779i | 0.159168 | − | 0.159168i | ||||
\(944\) | −6.57921 | −0.214135 | ||||||||
\(945\) | 1.71580 | − | 17.6255i | 0.0558150 | − | 0.573358i | ||||
\(946\) | −4.45607 | −0.144879 | ||||||||
\(947\) | 41.7393 | − | 41.7393i | 1.35635 | − | 1.35635i | 0.477971 | − | 0.878376i | \(-0.341373\pi\) |
0.878376 | − | 0.477971i | \(-0.158627\pi\) | |||||||
\(948\) | 12.3807 | + | 25.1489i | 0.402107 | + | 0.816797i | ||||
\(949\) | − | 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 | 0.331767 | − | 0.943361i | \(-0.392355\pi\) |
−0.943361 | + | 0.331767i | \(0.892355\pi\) | |||||||
\(954\) | 4.81480 | − | 6.25706i | 0.155885 | − | 0.202580i | ||||
\(955\) | 17.6715 | − | 21.6730i | 0.571837 | − | 0.701323i | ||||
\(956\) | 2.52085i | 0.0815303i | ||||||||
\(957\) | −15.6658 | + | 7.71224i | −0.506404 | + | 0.249301i | ||||
\(958\) | 3.02655 | − | 3.02655i | 0.0977835 | − | 0.0977835i | ||||
\(959\) | 29.4301 | 0.950348 | ||||||||
\(960\) | −3.77399 | − | 0.870037i | −0.121805 | − | 0.0280803i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 24.0435 | − | 24.0435i | 0.775193 | − | 0.775193i | ||||
\(963\) | 3.74110 | + | 28.7194i | 0.120555 | + | 0.925470i | ||||
\(964\) | − | 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 | \(0.0166783\pi\) | ||||
−0.998628 | + | 0.0523725i | \(0.983322\pi\) | |||||||
\(972\) | −10.2381 | − | 11.7550i | −0.328388 | − | 0.377043i | ||||
\(973\) | −24.9267 | + | 24.9267i | −0.799113 | + | 0.799113i | ||||
\(974\) | 14.7704 | 0.473273 | ||||||||
\(975\) | 4.07171 | − | 32.3462i | 0.130399 | − | 1.03591i | ||||
\(976\) | −3.80070 | −0.121658 | ||||||||
\(977\) | −5.20121 | + | 5.20121i | −0.166401 | + | 0.166401i | −0.785396 | − | 0.618994i | \(-0.787540\pi\) |
0.618994 | + | 0.785396i | \(0.287540\pi\) | |||||||
\(978\) | −31.2059 | + | 15.3626i | −0.997854 | + | 0.491241i | ||||
\(979\) | − | 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 | \(0.0609445\pi\) |
0.190295 | + | 0.981727i | \(0.439056\pi\) | |||||||
\(984\) | 4.66657 | + | 1.58764i | 0.148765 | + | 0.0506121i | ||||
\(985\) | −11.8044 | + | 1.20055i | −0.376119 | + | 0.0382528i | ||||
\(986\) | 9.79639i | 0.311981i | ||||||||
\(987\) | −2.15790 | − | 4.38333i | −0.0686867 | − | 0.139523i | ||||
\(988\) | −10.5377 | + | 10.5377i | −0.335250 | + | 0.335250i | ||||
\(989\) | −1.83907 | −0.0584790 | ||||||||
\(990\) | −33.5635 | − | 20.7867i | −1.06672 | − | 0.660646i | ||||
\(991\) | 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 | ||||
\(993\) | 11.1638 | + | 22.6769i | 0.354272 | + | 0.719630i | ||||
\(994\) | 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.497.7 | ✓ | 40 | |
3.2 | odd | 2 | inner | 930.2.j.g.497.12 | yes | 40 | |
5.3 | odd | 4 | inner | 930.2.j.g.683.12 | yes | 40 | |
15.8 | even | 4 | inner | 930.2.j.g.683.7 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.g.497.7 | ✓ | 40 | 1.1 | even | 1 | trivial | |
930.2.j.g.497.12 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.j.g.683.7 | yes | 40 | 15.8 | even | 4 | inner | |
930.2.j.g.683.12 | yes | 40 | 5.3 | odd | 4 | inner |