Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), 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: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 481.1 | ||
Root | \(-1.17072 - 3.60310i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.481 |
Dual form | 930.2.n.g.901.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.17072 | + | 3.60310i | −0.442490 | + | 1.36184i | 0.442724 | + | 0.896658i | \(0.354012\pi\) |
−0.885213 | + | 0.465185i | \(0.845988\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −0.809017 | + | 0.587785i | −0.255834 | + | 0.185874i | ||||
\(11\) | −1.62721 | + | 5.00804i | −0.490622 | + | 1.50998i | 0.333047 | + | 0.942910i | \(0.391923\pi\) |
−0.823669 | + | 0.567070i | \(0.808077\pi\) | |||||||
\(12\) | −0.809017 | + | 0.587785i | −0.233543 | + | 0.169679i | ||||
\(13\) | −1.08783 | − | 0.790358i | −0.301711 | − | 0.219206i | 0.426621 | − | 0.904431i | \(-0.359704\pi\) |
−0.728332 | + | 0.685225i | \(0.759704\pi\) | |||||||
\(14\) | −1.17072 | − | 3.60310i | −0.312887 | − | 0.962969i | ||||
\(15\) | −0.809017 | − | 0.587785i | −0.208887 | − | 0.151765i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.54433 | − | 4.75295i | −0.374554 | − | 1.15276i | −0.943779 | − | 0.330578i | \(-0.892756\pi\) |
0.569224 | − | 0.822182i | \(-0.307244\pi\) | |||||||
\(18\) | −0.809017 | − | 0.587785i | −0.190687 | − | 0.138542i | ||||
\(19\) | 0.668127 | − | 0.485423i | 0.153279 | − | 0.111364i | −0.508502 | − | 0.861061i | \(-0.669801\pi\) |
0.661781 | + | 0.749697i | \(0.269801\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | 3.06498 | − | 2.22684i | 0.668833 | − | 0.485936i | ||||
\(22\) | −1.62721 | − | 5.00804i | −0.346922 | − | 1.06772i | ||||
\(23\) | −2.04174 | − | 6.28382i | −0.425732 | − | 1.31027i | −0.902292 | − | 0.431125i | \(-0.858117\pi\) |
0.476560 | − | 0.879142i | \(-0.341883\pi\) | |||||||
\(24\) | 0.309017 | − | 0.951057i | 0.0630778 | − | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.34464 | 0.263705 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 3.06498 | + | 2.22684i | 0.579227 | + | 0.420833i | ||||
\(29\) | 3.45527 | − | 2.51040i | 0.641627 | − | 0.466169i | −0.218782 | − | 0.975774i | \(-0.570208\pi\) |
0.860409 | + | 0.509605i | \(0.170208\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −3.69478 | + | 4.16517i | −0.663602 | + | 0.748086i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.26009 | − | 3.09514i | 0.741587 | − | 0.538794i | ||||
\(34\) | 4.04310 | + | 2.93749i | 0.693386 | + | 0.503775i | ||||
\(35\) | −1.17072 | + | 3.60310i | −0.197887 | + | 0.609035i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.77473 | −1.11376 | −0.556879 | − | 0.830594i | \(-0.688001\pi\) | ||||
−0.556879 | + | 0.830594i | \(0.688001\pi\) | |||||||
\(38\) | −0.255202 | + | 0.785431i | −0.0413992 | + | 0.127414i | ||||
\(39\) | 0.415516 | + | 1.27883i | 0.0665358 | + | 0.204776i | ||||
\(40\) | 0.309017 | + | 0.951057i | 0.0488599 | + | 0.150375i | ||||
\(41\) | −8.05861 | + | 5.85492i | −1.25854 | + | 0.914385i | −0.998685 | − | 0.0512616i | \(-0.983676\pi\) |
−0.259858 | + | 0.965647i | \(0.583676\pi\) | |||||||
\(42\) | −1.17072 | + | 3.60310i | −0.180646 | + | 0.555970i | ||||
\(43\) | −4.41583 | + | 3.20829i | −0.673408 | + | 0.489259i | −0.871164 | − | 0.490992i | \(-0.836635\pi\) |
0.197756 | + | 0.980251i | \(0.436635\pi\) | |||||||
\(44\) | 4.26009 | + | 3.09514i | 0.642233 | + | 0.466610i | ||||
\(45\) | 0.309017 | + | 0.951057i | 0.0460655 | + | 0.141775i | ||||
\(46\) | 5.34534 | + | 3.88361i | 0.788127 | + | 0.572608i | ||||
\(47\) | −5.45663 | − | 3.96447i | −0.795931 | − | 0.578278i | 0.113786 | − | 0.993505i | \(-0.463702\pi\) |
−0.909718 | + | 0.415227i | \(0.863702\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −5.94862 | − | 4.32193i | −0.849803 | − | 0.617418i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.114412 | + | 0.0831254i | ||||
\(51\) | −1.54433 | + | 4.75295i | −0.216249 | + | 0.665546i | ||||
\(52\) | −1.08783 | + | 0.790358i | −0.150855 | + | 0.109603i | ||||
\(53\) | −1.17898 | − | 3.62853i | −0.161945 | − | 0.498416i | 0.836853 | − | 0.547428i | \(-0.184393\pi\) |
−0.998798 | + | 0.0490114i | \(0.984393\pi\) | |||||||
\(54\) | 0.309017 | + | 0.951057i | 0.0420519 | + | 0.129422i | ||||
\(55\) | −1.62721 | + | 5.00804i | −0.219413 | + | 0.675284i | ||||
\(56\) | −3.78852 | −0.506263 | ||||||||
\(57\) | −0.825851 | −0.109387 | ||||||||
\(58\) | −1.31979 | + | 4.06191i | −0.173298 | + | 0.533355i | ||||
\(59\) | −6.81009 | − | 4.94782i | −0.886598 | − | 0.644151i | 0.0483905 | − | 0.998828i | \(-0.484591\pi\) |
−0.934989 | + | 0.354677i | \(0.884591\pi\) | |||||||
\(60\) | −0.809017 | + | 0.587785i | −0.104444 | + | 0.0758827i | ||||
\(61\) | 7.30290 | 0.935040 | 0.467520 | − | 0.883982i | \(-0.345148\pi\) | ||||
0.467520 | + | 0.883982i | \(0.345148\pi\) | |||||||
\(62\) | 0.540917 | − | 5.54143i | 0.0686965 | − | 0.703762i | ||||
\(63\) | −3.78852 | −0.477309 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −1.08783 | − | 0.790358i | −0.134929 | − | 0.0980318i | ||||
\(66\) | −1.62721 | + | 5.00804i | −0.200296 | + | 0.616447i | ||||
\(67\) | 3.63183 | 0.443699 | 0.221849 | − | 0.975081i | \(-0.428791\pi\) | ||||
0.221849 | + | 0.975081i | \(0.428791\pi\) | |||||||
\(68\) | −4.99755 | −0.606042 | ||||||||
\(69\) | −2.04174 | + | 6.28382i | −0.245796 | + | 0.756483i | ||||
\(70\) | −1.17072 | − | 3.60310i | −0.139928 | − | 0.430653i | ||||
\(71\) | 1.40173 | + | 4.31407i | 0.166354 | + | 0.511986i | 0.999134 | − | 0.0416194i | \(-0.0132517\pi\) |
−0.832779 | + | 0.553605i | \(0.813252\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | −0.630797 | + | 1.94139i | −0.0738292 | + | 0.227223i | −0.981161 | − | 0.193193i | \(-0.938116\pi\) |
0.907332 | + | 0.420416i | \(0.138116\pi\) | |||||||
\(74\) | 5.48087 | − | 3.98208i | 0.637138 | − | 0.462908i | ||||
\(75\) | −0.809017 | − | 0.587785i | −0.0934172 | − | 0.0678716i | ||||
\(76\) | −0.255202 | − | 0.785431i | −0.0292737 | − | 0.0900951i | ||||
\(77\) | −16.1395 | − | 11.7260i | −1.83926 | − | 1.33630i | ||||
\(78\) | −1.08783 | − | 0.790358i | −0.123173 | − | 0.0894904i | ||||
\(79\) | 2.10192 | + | 6.46905i | 0.236485 | + | 0.727825i | 0.996921 | + | 0.0784127i | \(0.0249852\pi\) |
−0.760436 | + | 0.649413i | \(0.775015\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 3.07811 | − | 9.47346i | 0.339921 | − | 1.04617i | ||||
\(83\) | 0.379511 | − | 0.275731i | 0.0416567 | − | 0.0302654i | −0.566762 | − | 0.823882i | \(-0.691804\pi\) |
0.608419 | + | 0.793616i | \(0.291804\pi\) | |||||||
\(84\) | −1.17072 | − | 3.60310i | −0.127736 | − | 0.393130i | ||||
\(85\) | −1.54433 | − | 4.75295i | −0.167506 | − | 0.515530i | ||||
\(86\) | 1.68670 | − | 5.19112i | 0.181881 | − | 0.559773i | ||||
\(87\) | −4.27094 | −0.457893 | ||||||||
\(88\) | −5.26576 | −0.561332 | ||||||||
\(89\) | 0.991032 | − | 3.05008i | 0.105049 | − | 0.323308i | −0.884693 | − | 0.466174i | \(-0.845632\pi\) |
0.989742 | + | 0.142866i | \(0.0456319\pi\) | |||||||
\(90\) | −0.809017 | − | 0.587785i | −0.0852779 | − | 0.0619580i | ||||
\(91\) | 4.12128 | − | 2.99429i | 0.432028 | − | 0.313887i | ||||
\(92\) | −6.60720 | −0.688848 | ||||||||
\(93\) | 5.43736 | − | 1.19795i | 0.563828 | − | 0.124222i | ||||
\(94\) | 6.74477 | 0.695670 | ||||||||
\(95\) | 0.668127 | − | 0.485423i | 0.0685484 | − | 0.0498033i | ||||
\(96\) | −0.809017 | − | 0.587785i | −0.0825700 | − | 0.0599906i | ||||
\(97\) | −5.38066 | + | 16.5600i | −0.546323 | + | 1.68141i | 0.171501 | + | 0.985184i | \(0.445138\pi\) |
−0.717824 | + | 0.696225i | \(0.754862\pi\) | |||||||
\(98\) | 7.35290 | 0.742755 | ||||||||
\(99\) | −5.26576 | −0.529229 | ||||||||
\(100\) | 0.309017 | − | 0.951057i | 0.0309017 | − | 0.0951057i | ||||
\(101\) | −4.95681 | − | 15.2555i | −0.493221 | − | 1.51798i | −0.819711 | − | 0.572777i | \(-0.805866\pi\) |
0.326490 | − | 0.945200i | \(-0.394134\pi\) | |||||||
\(102\) | −1.54433 | − | 4.75295i | −0.152911 | − | 0.470612i | ||||
\(103\) | −13.2793 | + | 9.64795i | −1.30844 | + | 0.950641i | −1.00000 | 0.000601277i | \(-0.999809\pi\) | |
−0.308445 | + | 0.951242i | \(0.599809\pi\) | |||||||
\(104\) | 0.415516 | − | 1.27883i | 0.0407447 | − | 0.125399i | ||||
\(105\) | 3.06498 | − | 2.22684i | 0.299111 | − | 0.217317i | ||||
\(106\) | 3.08661 | + | 2.24255i | 0.299798 | + | 0.217816i | ||||
\(107\) | −1.44283 | − | 4.44057i | −0.139484 | − | 0.429287i | 0.856777 | − | 0.515687i | \(-0.172463\pi\) |
−0.996260 | + | 0.0864009i | \(0.972463\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 5.35543 | + | 3.89095i | 0.512957 | + | 0.372685i | 0.813944 | − | 0.580943i | \(-0.197316\pi\) |
−0.300987 | + | 0.953628i | \(0.597316\pi\) | |||||||
\(110\) | −1.62721 | − | 5.00804i | −0.155148 | − | 0.477498i | ||||
\(111\) | 5.48087 | + | 3.98208i | 0.520221 | + | 0.377963i | ||||
\(112\) | 3.06498 | − | 2.22684i | 0.289613 | − | 0.210416i | ||||
\(113\) | 1.48844 | − | 4.58095i | 0.140021 | − | 0.430940i | −0.856316 | − | 0.516452i | \(-0.827253\pi\) |
0.996337 | + | 0.0855119i | \(0.0272526\pi\) | |||||||
\(114\) | 0.668127 | − | 0.485423i | 0.0625759 | − | 0.0454640i | ||||
\(115\) | −2.04174 | − | 6.28382i | −0.190393 | − | 0.585969i | ||||
\(116\) | −1.31979 | − | 4.06191i | −0.122540 | − | 0.377139i | ||||
\(117\) | 0.415516 | − | 1.27883i | 0.0384144 | − | 0.118228i | ||||
\(118\) | 8.41774 | 0.774915 | ||||||||
\(119\) | 18.9333 | 1.73561 | ||||||||
\(120\) | 0.309017 | − | 0.951057i | 0.0282093 | − | 0.0868192i | ||||
\(121\) | −13.5335 | − | 9.83263i | −1.23031 | − | 0.893876i | ||||
\(122\) | −5.90817 | + | 4.29254i | −0.534900 | + | 0.388628i | ||||
\(123\) | 9.96099 | 0.898152 | ||||||||
\(124\) | 2.81956 | + | 4.80105i | 0.253204 | + | 0.431147i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.06498 | − | 2.22684i | 0.273050 | − | 0.198382i | ||||
\(127\) | 4.84152 | + | 3.51757i | 0.429615 | + | 0.312134i | 0.781495 | − | 0.623911i | \(-0.214457\pi\) |
−0.351880 | + | 0.936045i | \(0.614457\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 5.45827 | 0.480574 | ||||||||
\(130\) | 1.34464 | 0.117932 | ||||||||
\(131\) | −5.15122 | + | 15.8538i | −0.450064 | + | 1.38516i | 0.426769 | + | 0.904361i | \(0.359652\pi\) |
−0.876833 | + | 0.480795i | \(0.840348\pi\) | |||||||
\(132\) | −1.62721 | − | 5.00804i | −0.141631 | − | 0.435894i | ||||
\(133\) | 0.966838 | + | 2.97562i | 0.0838355 | + | 0.258019i | ||||
\(134\) | −2.93821 | + | 2.13474i | −0.253823 | + | 0.184413i | ||||
\(135\) | 0.309017 | − | 0.951057i | 0.0265959 | − | 0.0818539i | ||||
\(136\) | 4.04310 | − | 2.93749i | 0.346693 | − | 0.251887i | ||||
\(137\) | −12.8558 | − | 9.34029i | −1.09835 | − | 0.797995i | −0.117556 | − | 0.993066i | \(-0.537506\pi\) |
−0.980789 | + | 0.195071i | \(0.937506\pi\) | |||||||
\(138\) | −2.04174 | − | 6.28382i | −0.173804 | − | 0.534914i | ||||
\(139\) | 5.46466 | + | 3.97031i | 0.463506 | + | 0.336757i | 0.794905 | − | 0.606734i | \(-0.207521\pi\) |
−0.331399 | + | 0.943491i | \(0.607521\pi\) | |||||||
\(140\) | 3.06498 | + | 2.22684i | 0.259038 | + | 0.188202i | ||||
\(141\) | 2.08425 | + | 6.41465i | 0.175525 | + | 0.540211i | ||||
\(142\) | −3.66977 | − | 2.66624i | −0.307960 | − | 0.223746i | ||||
\(143\) | 5.72828 | − | 4.16184i | 0.479023 | − | 0.348030i | ||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | 3.45527 | − | 2.51040i | 0.286944 | − | 0.208477i | ||||
\(146\) | −0.630797 | − | 1.94139i | −0.0522052 | − | 0.160671i | ||||
\(147\) | 2.27217 | + | 6.99302i | 0.187405 | + | 0.576775i | ||||
\(148\) | −2.09351 | + | 6.44315i | −0.172085 | + | 0.529624i | ||||
\(149\) | −16.0548 | −1.31526 | −0.657630 | − | 0.753341i | \(-0.728441\pi\) | ||||
−0.657630 | + | 0.753341i | \(0.728441\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 3.06420 | − | 9.43063i | 0.249361 | − | 0.767453i | −0.745528 | − | 0.666474i | \(-0.767803\pi\) |
0.994889 | − | 0.100979i | \(-0.0321975\pi\) | |||||||
\(152\) | 0.668127 | + | 0.485423i | 0.0541923 | + | 0.0393730i | ||||
\(153\) | 4.04310 | − | 2.93749i | 0.326865 | − | 0.237482i | ||||
\(154\) | 19.9495 | 1.60757 | ||||||||
\(155\) | −3.69478 | + | 4.16517i | −0.296772 | + | 0.334554i | ||||
\(156\) | 1.34464 | 0.107657 | ||||||||
\(157\) | −16.5406 | + | 12.0175i | −1.32009 | + | 0.959099i | −0.320156 | + | 0.947365i | \(0.603735\pi\) |
−0.999931 | + | 0.0117346i | \(0.996265\pi\) | |||||||
\(158\) | −5.50291 | − | 3.99809i | −0.437788 | − | 0.318071i | ||||
\(159\) | −1.17898 | + | 3.62853i | −0.0934992 | + | 0.287761i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 25.0315 | 1.97276 | ||||||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | 2.98547 | + | 9.18833i | 0.233840 | + | 0.719685i | 0.997273 | + | 0.0737985i | \(0.0235122\pi\) |
−0.763433 | + | 0.645887i | \(0.776488\pi\) | |||||||
\(164\) | 3.07811 | + | 9.47346i | 0.240360 | + | 0.739753i | ||||
\(165\) | 4.26009 | − | 3.09514i | 0.331648 | − | 0.240956i | ||||
\(166\) | −0.144960 | + | 0.446142i | −0.0112511 | + | 0.0346273i | ||||
\(167\) | 3.82856 | − | 2.78161i | 0.296263 | − | 0.215248i | −0.429717 | − | 0.902964i | \(-0.641387\pi\) |
0.725980 | + | 0.687716i | \(0.241387\pi\) | |||||||
\(168\) | 3.06498 | + | 2.22684i | 0.236468 | + | 0.171804i | ||||
\(169\) | −3.45850 | − | 10.6442i | −0.266039 | − | 0.818783i | ||||
\(170\) | 4.04310 | + | 2.93749i | 0.310092 | + | 0.225295i | ||||
\(171\) | 0.668127 | + | 0.485423i | 0.0510930 | + | 0.0371212i | ||||
\(172\) | 1.68670 | + | 5.19112i | 0.128609 | + | 0.395819i | ||||
\(173\) | 9.45979 | + | 6.87294i | 0.719214 | + | 0.522540i | 0.886133 | − | 0.463431i | \(-0.153382\pi\) |
−0.166919 | + | 0.985971i | \(0.553382\pi\) | |||||||
\(174\) | 3.45527 | − | 2.51040i | 0.261943 | − | 0.190313i | ||||
\(175\) | −1.17072 | + | 3.60310i | −0.0884979 | + | 0.272369i | ||||
\(176\) | 4.26009 | − | 3.09514i | 0.321117 | − | 0.233305i | ||||
\(177\) | 2.60122 | + | 8.00574i | 0.195520 | + | 0.601748i | ||||
\(178\) | 0.991032 | + | 3.05008i | 0.0742810 | + | 0.228613i | ||||
\(179\) | 0.278926 | − | 0.858447i | 0.0208479 | − | 0.0641633i | −0.940091 | − | 0.340923i | \(-0.889261\pi\) |
0.960939 | + | 0.276759i | \(0.0892605\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 0.992901 | 0.0738018 | 0.0369009 | − | 0.999319i | \(-0.488251\pi\) | ||||
0.0369009 | + | 0.999319i | \(0.488251\pi\) | |||||||
\(182\) | −1.57419 | + | 4.84486i | −0.116687 | + | 0.359125i | ||||
\(183\) | −5.90817 | − | 4.29254i | −0.436744 | − | 0.317313i | ||||
\(184\) | 5.34534 | − | 3.88361i | 0.394063 | − | 0.286304i | ||||
\(185\) | −6.77473 | −0.498088 | ||||||||
\(186\) | −3.69478 | + | 4.16517i | −0.270914 | + | 0.305405i | ||||
\(187\) | 26.3159 | 1.92441 | ||||||||
\(188\) | −5.45663 | + | 3.96447i | −0.397966 | + | 0.289139i | ||||
\(189\) | 3.06498 | + | 2.22684i | 0.222944 | + | 0.161979i | ||||
\(190\) | −0.255202 | + | 0.785431i | −0.0185143 | + | 0.0569811i | ||||
\(191\) | 20.7711 | 1.50294 | 0.751471 | − | 0.659766i | \(-0.229345\pi\) | ||||
0.751471 | + | 0.659766i | \(0.229345\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 8.10942 | − | 24.9582i | 0.583729 | − | 1.79653i | −0.0205885 | − | 0.999788i | \(-0.506554\pi\) |
0.604317 | − | 0.796744i | \(-0.293446\pi\) | |||||||
\(194\) | −5.38066 | − | 16.5600i | −0.386309 | − | 1.18894i | ||||
\(195\) | 0.415516 | + | 1.27883i | 0.0297557 | + | 0.0915786i | ||||
\(196\) | −5.94862 | + | 4.32193i | −0.424901 | + | 0.308709i | ||||
\(197\) | −1.86113 | + | 5.72798i | −0.132600 | + | 0.408102i | −0.995209 | − | 0.0977700i | \(-0.968829\pi\) |
0.862609 | + | 0.505872i | \(0.168829\pi\) | |||||||
\(198\) | 4.26009 | − | 3.09514i | 0.302752 | − | 0.219962i | ||||
\(199\) | 3.39114 | + | 2.46381i | 0.240392 | + | 0.174655i | 0.701458 | − | 0.712711i | \(-0.252533\pi\) |
−0.461066 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(200\) | 0.309017 | + | 0.951057i | 0.0218508 | + | 0.0672499i | ||||
\(201\) | −2.93821 | − | 2.13474i | −0.207245 | − | 0.150573i | ||||
\(202\) | 12.9771 | + | 9.42841i | 0.913065 | + | 0.663380i | ||||
\(203\) | 5.00007 | + | 15.3886i | 0.350936 | + | 1.08007i | ||||
\(204\) | 4.04310 | + | 2.93749i | 0.283074 | + | 0.205665i | ||||
\(205\) | −8.05861 | + | 5.85492i | −0.562838 | + | 0.408926i | ||||
\(206\) | 5.07223 | − | 15.6107i | 0.353399 | − | 1.08765i | ||||
\(207\) | 5.34534 | − | 3.88361i | 0.371527 | − | 0.269930i | ||||
\(208\) | 0.415516 | + | 1.27883i | 0.0288108 | + | 0.0886706i | ||||
\(209\) | 1.34383 | + | 4.13589i | 0.0929549 | + | 0.286086i | ||||
\(210\) | −1.17072 | + | 3.60310i | −0.0807872 | + | 0.248637i | ||||
\(211\) | −3.28602 | −0.226219 | −0.113109 | − | 0.993583i | \(-0.536081\pi\) | ||||
−0.113109 | + | 0.993583i | \(0.536081\pi\) | |||||||
\(212\) | −3.81526 | −0.262033 | ||||||||
\(213\) | 1.40173 | − | 4.31407i | 0.0960447 | − | 0.295595i | ||||
\(214\) | 3.77738 | + | 2.74443i | 0.258216 | + | 0.187605i | ||||
\(215\) | −4.41583 | + | 3.20829i | −0.301157 | + | 0.218803i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.6820 | − | 18.1889i | −0.725139 | − | 1.23474i | ||||
\(218\) | −6.61967 | −0.448341 | ||||||||
\(219\) | 1.65145 | − | 1.19985i | 0.111595 | − | 0.0810782i | ||||
\(220\) | 4.26009 | + | 3.09514i | 0.287215 | + | 0.208674i | ||||
\(221\) | −2.07656 | + | 6.39099i | −0.139685 | + | 0.429905i | ||||
\(222\) | −6.77473 | −0.454690 | ||||||||
\(223\) | 20.9568 | 1.40337 | 0.701686 | − | 0.712486i | \(-0.252431\pi\) | ||||
0.701686 | + | 0.712486i | \(0.252431\pi\) | |||||||
\(224\) | −1.17072 | + | 3.60310i | −0.0782219 | + | 0.240742i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | 1.48844 | + | 4.58095i | 0.0990097 | + | 0.304720i | ||||
\(227\) | −16.3479 | + | 11.8775i | −1.08505 | + | 0.788335i | −0.978557 | − | 0.205978i | \(-0.933962\pi\) |
−0.106493 | + | 0.994313i | \(0.533962\pi\) | |||||||
\(228\) | −0.255202 | + | 0.785431i | −0.0169012 | + | 0.0520164i | ||||
\(229\) | −4.15148 | + | 3.01623i | −0.274337 | + | 0.199318i | −0.716444 | − | 0.697645i | \(-0.754231\pi\) |
0.442106 | + | 0.896963i | \(0.354231\pi\) | |||||||
\(230\) | 5.34534 | + | 3.88361i | 0.352461 | + | 0.256078i | ||||
\(231\) | 6.16472 | + | 18.9731i | 0.405609 | + | 1.24834i | ||||
\(232\) | 3.45527 | + | 2.51040i | 0.226849 | + | 0.164816i | ||||
\(233\) | 19.8233 | + | 14.4025i | 1.29867 | + | 0.943537i | 0.999942 | − | 0.0108025i | \(-0.00343862\pi\) |
0.298725 | + | 0.954339i | \(0.403439\pi\) | |||||||
\(234\) | 0.415516 | + | 1.27883i | 0.0271631 | + | 0.0835995i | ||||
\(235\) | −5.45663 | − | 3.96447i | −0.355951 | − | 0.258614i | ||||
\(236\) | −6.81009 | + | 4.94782i | −0.443299 | + | 0.322076i | ||||
\(237\) | 2.10192 | − | 6.46905i | 0.136535 | − | 0.420210i | ||||
\(238\) | −15.3174 | + | 11.1287i | −0.992878 | + | 0.721368i | ||||
\(239\) | 4.73751 | + | 14.5805i | 0.306444 | + | 0.943137i | 0.979135 | + | 0.203213i | \(0.0651385\pi\) |
−0.672691 | + | 0.739924i | \(0.734862\pi\) | |||||||
\(240\) | 0.309017 | + | 0.951057i | 0.0199470 | + | 0.0613904i | ||||
\(241\) | −3.70554 | + | 11.4045i | −0.238695 | + | 0.734627i | 0.757915 | + | 0.652353i | \(0.226218\pi\) |
−0.996610 | + | 0.0822735i | \(0.973782\pi\) | |||||||
\(242\) | 16.7283 | 1.07533 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.25672 | − | 6.94547i | 0.144472 | − | 0.444638i | ||||
\(245\) | −5.94862 | − | 4.32193i | −0.380043 | − | 0.276118i | ||||
\(246\) | −8.05861 | + | 5.85492i | −0.513798 | + | 0.373296i | ||||
\(247\) | −1.11047 | −0.0706575 | ||||||||
\(248\) | −5.10306 | − | 2.22684i | −0.324044 | − | 0.141404i | ||||
\(249\) | −0.469101 | −0.0297281 | ||||||||
\(250\) | −0.809017 | + | 0.587785i | −0.0511667 | + | 0.0371748i | ||||
\(251\) | −6.46003 | − | 4.69349i | −0.407753 | − | 0.296250i | 0.364938 | − | 0.931032i | \(-0.381090\pi\) |
−0.772692 | + | 0.634782i | \(0.781090\pi\) | |||||||
\(252\) | −1.17072 | + | 3.60310i | −0.0737483 | + | 0.226974i | ||||
\(253\) | 34.7920 | 2.18735 | ||||||||
\(254\) | −5.98445 | −0.375498 | ||||||||
\(255\) | −1.54433 | + | 4.75295i | −0.0967095 | + | 0.297641i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 6.34512 | + | 19.5283i | 0.395798 | + | 1.21814i | 0.928339 | + | 0.371736i | \(0.121237\pi\) |
−0.532541 | + | 0.846404i | \(0.678763\pi\) | |||||||
\(258\) | −4.41583 | + | 3.20829i | −0.274918 | + | 0.199739i | ||||
\(259\) | 7.93129 | − | 24.4100i | 0.492827 | − | 1.51676i | ||||
\(260\) | −1.08783 | + | 0.790358i | −0.0674646 | + | 0.0490159i | ||||
\(261\) | 3.45527 | + | 2.51040i | 0.213876 | + | 0.155390i | ||||
\(262\) | −5.15122 | − | 15.8538i | −0.318244 | − | 0.979453i | ||||
\(263\) | −4.00331 | − | 2.90857i | −0.246854 | − | 0.179350i | 0.457477 | − | 0.889221i | \(-0.348753\pi\) |
−0.704332 | + | 0.709871i | \(0.748753\pi\) | |||||||
\(264\) | 4.26009 | + | 3.09514i | 0.262191 | + | 0.190493i | ||||
\(265\) | −1.17898 | − | 3.62853i | −0.0724241 | − | 0.222899i | ||||
\(266\) | −2.53122 | − | 1.83904i | −0.155199 | − | 0.112758i | ||||
\(267\) | −2.59456 | + | 1.88506i | −0.158784 | + | 0.115363i | ||||
\(268\) | 1.12230 | − | 3.45407i | 0.0685552 | − | 0.210991i | ||||
\(269\) | −15.5666 | + | 11.3098i | −0.949112 | + | 0.689570i | −0.950597 | − | 0.310429i | \(-0.899527\pi\) |
0.00148452 | + | 0.999999i | \(0.499527\pi\) | |||||||
\(270\) | 0.309017 | + | 0.951057i | 0.0188062 | + | 0.0578795i | ||||
\(271\) | −1.31649 | − | 4.05173i | −0.0799710 | − | 0.246125i | 0.903076 | − | 0.429482i | \(-0.141304\pi\) |
−0.983046 | + | 0.183356i | \(0.941304\pi\) | |||||||
\(272\) | −1.54433 | + | 4.75295i | −0.0936386 | + | 0.288190i | ||||
\(273\) | −5.09419 | −0.308314 | ||||||||
\(274\) | 15.8906 | 0.959989 | ||||||||
\(275\) | −1.62721 | + | 5.00804i | −0.0981245 | + | 0.301996i | ||||
\(276\) | 5.34534 | + | 3.88361i | 0.321751 | + | 0.233766i | ||||
\(277\) | −13.6649 | + | 9.92813i | −0.821044 | + | 0.596524i | −0.917011 | − | 0.398861i | \(-0.869406\pi\) |
0.0959671 | + | 0.995385i | \(0.469406\pi\) | |||||||
\(278\) | −6.75469 | −0.405119 | ||||||||
\(279\) | −5.10306 | − | 2.22684i | −0.305512 | − | 0.133317i | ||||
\(280\) | −3.78852 | −0.226407 | ||||||||
\(281\) | 17.3972 | − | 12.6398i | 1.03783 | − | 0.754027i | 0.0679687 | − | 0.997687i | \(-0.478348\pi\) |
0.969861 | + | 0.243660i | \(0.0783482\pi\) | |||||||
\(282\) | −5.45663 | − | 3.96447i | −0.324938 | − | 0.236081i | ||||
\(283\) | 5.78102 | − | 17.7922i | 0.343646 | − | 1.05763i | −0.618658 | − | 0.785660i | \(-0.712324\pi\) |
0.962305 | − | 0.271974i | \(-0.0876765\pi\) | |||||||
\(284\) | 4.53608 | 0.269167 | ||||||||
\(285\) | −0.825851 | −0.0489192 | ||||||||
\(286\) | −2.18801 | + | 6.73400i | −0.129380 | + | 0.398190i | ||||
\(287\) | −11.6615 | − | 35.8904i | −0.688357 | − | 2.11854i | ||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | −6.45230 | + | 4.68787i | −0.379547 | + | 0.275757i | ||||
\(290\) | −1.31979 | + | 4.06191i | −0.0775010 | + | 0.238524i | ||||
\(291\) | 14.0867 | − | 10.2346i | 0.825779 | − | 0.599964i | ||||
\(292\) | 1.65145 | + | 1.19985i | 0.0966437 | + | 0.0702158i | ||||
\(293\) | 7.28905 | + | 22.4334i | 0.425831 | + | 1.31057i | 0.902196 | + | 0.431326i | \(0.141954\pi\) |
−0.476365 | + | 0.879247i | \(0.658046\pi\) | |||||||
\(294\) | −5.94862 | − | 4.32193i | −0.346931 | − | 0.252060i | ||||
\(295\) | −6.81009 | − | 4.94782i | −0.396499 | − | 0.288073i | ||||
\(296\) | −2.09351 | − | 6.44315i | −0.121683 | − | 0.374500i | ||||
\(297\) | 4.26009 | + | 3.09514i | 0.247196 | + | 0.179598i | ||||
\(298\) | 12.9886 | − | 9.43677i | 0.752409 | − | 0.546657i | ||||
\(299\) | −2.74540 | + | 8.44946i | −0.158770 | + | 0.488645i | ||||
\(300\) | −0.809017 | + | 0.587785i | −0.0467086 | + | 0.0339358i | ||||
\(301\) | −6.39009 | − | 19.6667i | −0.368319 | − | 1.13357i | ||||
\(302\) | 3.06420 | + | 9.43063i | 0.176325 | + | 0.542672i | ||||
\(303\) | −4.95681 | + | 15.2555i | −0.284761 | + | 0.876405i | ||||
\(304\) | −0.825851 | −0.0473658 | ||||||||
\(305\) | 7.30290 | 0.418163 | ||||||||
\(306\) | −1.54433 | + | 4.75295i | −0.0882833 | + | 0.271708i | ||||
\(307\) | −16.7585 | − | 12.1757i | −0.956456 | − | 0.694906i | −0.00413119 | − | 0.999991i | \(-0.501315\pi\) |
−0.952325 | + | 0.305085i | \(0.901315\pi\) | |||||||
\(308\) | −16.1395 | + | 11.7260i | −0.919631 | + | 0.668151i | ||||
\(309\) | 16.4141 | 0.933764 | ||||||||
\(310\) | 0.540917 | − | 5.54143i | 0.0307220 | − | 0.314732i | ||||
\(311\) | 15.3352 | 0.869579 | 0.434790 | − | 0.900532i | \(-0.356823\pi\) | ||||
0.434790 | + | 0.900532i | \(0.356823\pi\) | |||||||
\(312\) | −1.08783 | + | 0.790358i | −0.0615865 | + | 0.0447452i | ||||
\(313\) | −7.24716 | − | 5.26537i | −0.409634 | − | 0.297616i | 0.363820 | − | 0.931469i | \(-0.381472\pi\) |
−0.773453 | + | 0.633853i | \(0.781472\pi\) | |||||||
\(314\) | 6.31796 | − | 19.4447i | 0.356543 | − | 1.09733i | ||||
\(315\) | −3.78852 | −0.213459 | ||||||||
\(316\) | 6.80196 | 0.382640 | ||||||||
\(317\) | 9.80482 | − | 30.1761i | 0.550693 | − | 1.69486i | −0.156360 | − | 0.987700i | \(-0.549976\pi\) |
0.707054 | − | 0.707160i | \(-0.250024\pi\) | |||||||
\(318\) | −1.17898 | − | 3.62853i | −0.0661139 | − | 0.203478i | ||||
\(319\) | 6.94973 | + | 21.3891i | 0.389110 | + | 1.19756i | ||||
\(320\) | −0.809017 | + | 0.587785i | −0.0452254 | + | 0.0328582i | ||||
\(321\) | −1.44283 | + | 4.44057i | −0.0805309 | + | 0.247849i | ||||
\(322\) | −20.2509 | + | 14.7132i | −1.12854 | + | 0.819932i | ||||
\(323\) | −3.33900 | − | 2.42592i | −0.185787 | − | 0.134982i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | −1.08783 | − | 0.790358i | −0.0603422 | − | 0.0438412i | ||||
\(326\) | −7.81606 | − | 5.67870i | −0.432891 | − | 0.314514i | ||||
\(327\) | −2.04559 | − | 6.29568i | −0.113121 | − | 0.348152i | ||||
\(328\) | −8.05861 | − | 5.85492i | −0.444962 | − | 0.323284i | ||||
\(329\) | 20.6726 | − | 15.0195i | 1.13972 | − | 0.828052i | ||||
\(330\) | −1.62721 | + | 5.00804i | −0.0895750 | + | 0.275683i | ||||
\(331\) | −1.95247 | + | 1.41856i | −0.107318 | + | 0.0779709i | −0.640150 | − | 0.768250i | \(-0.721128\pi\) |
0.532832 | + | 0.846221i | \(0.321128\pi\) | |||||||
\(332\) | −0.144960 | − | 0.446142i | −0.00795572 | − | 0.0244852i | ||||
\(333\) | −2.09351 | − | 6.44315i | −0.114723 | − | 0.353082i | ||||
\(334\) | −1.46238 | + | 4.50074i | −0.0800179 | + | 0.246270i | ||||
\(335\) | 3.63183 | 0.198428 | ||||||||
\(336\) | −3.78852 | −0.206681 | ||||||||
\(337\) | 9.46082 | − | 29.1174i | 0.515364 | − | 1.58613i | −0.267256 | − | 0.963626i | \(-0.586117\pi\) |
0.782619 | − | 0.622501i | \(-0.213883\pi\) | |||||||
\(338\) | 9.05448 | + | 6.57846i | 0.492499 | + | 0.357821i | ||||
\(339\) | −3.89679 | + | 2.83118i | −0.211645 | + | 0.153769i | ||||
\(340\) | −4.99755 | −0.271030 | ||||||||
\(341\) | −14.8471 | − | 25.2812i | −0.804017 | − | 1.36905i | ||||
\(342\) | −0.825851 | −0.0446569 | ||||||||
\(343\) | 1.08163 | − | 0.785849i | 0.0584025 | − | 0.0424319i | ||||
\(344\) | −4.41583 | − | 3.20829i | −0.238086 | − | 0.172979i | ||||
\(345\) | −2.04174 | + | 6.28382i | −0.109923 | + | 0.338310i | ||||
\(346\) | −11.6929 | −0.628617 | ||||||||
\(347\) | −5.98647 | −0.321371 | −0.160685 | − | 0.987006i | \(-0.551370\pi\) | ||||
−0.160685 | + | 0.987006i | \(0.551370\pi\) | |||||||
\(348\) | −1.31979 | + | 4.06191i | −0.0707484 | + | 0.217741i | ||||
\(349\) | 6.77990 | + | 20.8664i | 0.362920 | + | 1.11695i | 0.951274 | + | 0.308348i | \(0.0997762\pi\) |
−0.588354 | + | 0.808603i | \(0.700224\pi\) | |||||||
\(350\) | −1.17072 | − | 3.60310i | −0.0625775 | − | 0.192594i | ||||
\(351\) | −1.08783 | + | 0.790358i | −0.0580643 | + | 0.0421862i | ||||
\(352\) | −1.62721 | + | 5.00804i | −0.0867306 | + | 0.266929i | ||||
\(353\) | 21.8706 | − | 15.8899i | 1.16405 | − | 0.845734i | 0.173768 | − | 0.984787i | \(-0.444406\pi\) |
0.990285 | + | 0.139053i | \(0.0444057\pi\) | |||||||
\(354\) | −6.81009 | − | 4.94782i | −0.361952 | − | 0.262974i | ||||
\(355\) | 1.40173 | + | 4.31407i | 0.0743959 | + | 0.228967i | ||||
\(356\) | −2.59456 | − | 1.88506i | −0.137511 | − | 0.0999077i | ||||
\(357\) | −15.3174 | − | 11.1287i | −0.810682 | − | 0.588995i | ||||
\(358\) | 0.278926 | + | 0.858447i | 0.0147417 | + | 0.0453703i | ||||
\(359\) | 0.895277 | + | 0.650457i | 0.0472509 | + | 0.0343298i | 0.611160 | − | 0.791507i | \(-0.290703\pi\) |
−0.563909 | + | 0.825837i | \(0.690703\pi\) | |||||||
\(360\) | −0.809017 | + | 0.587785i | −0.0426389 | + | 0.0309790i | ||||
\(361\) | −5.66056 | + | 17.4214i | −0.297924 | + | 0.916917i | ||||
\(362\) | −0.803274 | + | 0.583613i | −0.0422191 | + | 0.0306740i | ||||
\(363\) | 5.16932 | + | 15.9095i | 0.271319 | + | 0.835034i | ||||
\(364\) | −1.57419 | − | 4.84486i | −0.0825100 | − | 0.253940i | ||||
\(365\) | −0.630797 | + | 1.94139i | −0.0330174 | + | 0.101617i | ||||
\(366\) | 7.30290 | 0.381729 | ||||||||
\(367\) | 1.57945 | 0.0824467 | 0.0412233 | − | 0.999150i | \(-0.486874\pi\) | ||||
0.0412233 | + | 0.999150i | \(0.486874\pi\) | |||||||
\(368\) | −2.04174 | + | 6.28382i | −0.106433 | + | 0.327567i | ||||
\(369\) | −8.05861 | − | 5.85492i | −0.419514 | − | 0.304795i | ||||
\(370\) | 5.48087 | − | 3.98208i | 0.284937 | − | 0.207019i | ||||
\(371\) | 14.4542 | 0.750424 | ||||||||
\(372\) | 0.540917 | − | 5.54143i | 0.0280452 | − | 0.287310i | ||||
\(373\) | −31.0660 | −1.60854 | −0.804269 | − | 0.594265i | \(-0.797443\pi\) | ||||
−0.804269 | + | 0.594265i | \(0.797443\pi\) | |||||||
\(374\) | −21.2900 | + | 15.4681i | −1.10088 | + | 0.799837i | ||||
\(375\) | −0.809017 | − | 0.587785i | −0.0417775 | − | 0.0303531i | ||||
\(376\) | 2.08425 | − | 6.41465i | 0.107487 | − | 0.330811i | ||||
\(377\) | −5.74287 | −0.295773 | ||||||||
\(378\) | −3.78852 | −0.194861 | ||||||||
\(379\) | −3.22507 | + | 9.92576i | −0.165661 | + | 0.509852i | −0.999084 | − | 0.0427830i | \(-0.986378\pi\) |
0.833423 | + | 0.552635i | \(0.186378\pi\) | |||||||
\(380\) | −0.255202 | − | 0.785431i | −0.0130916 | − | 0.0402917i | ||||
\(381\) | −1.84930 | − | 5.69155i | −0.0947423 | − | 0.291587i | ||||
\(382\) | −16.8041 | + | 12.2089i | −0.859775 | + | 0.624663i | ||||
\(383\) | −7.18366 | + | 22.1090i | −0.367068 | + | 1.12972i | 0.581608 | + | 0.813469i | \(0.302424\pi\) |
−0.948676 | + | 0.316249i | \(0.897576\pi\) | |||||||
\(384\) | −0.809017 | + | 0.587785i | −0.0412850 | + | 0.0299953i | ||||
\(385\) | −16.1395 | − | 11.7260i | −0.822543 | − | 0.597612i | ||||
\(386\) | 8.10942 | + | 24.9582i | 0.412758 | + | 1.27034i | ||||
\(387\) | −4.41583 | − | 3.20829i | −0.224469 | − | 0.163086i | ||||
\(388\) | 14.0867 | + | 10.2346i | 0.715146 | + | 0.519584i | ||||
\(389\) | 9.95958 | + | 30.6524i | 0.504971 | + | 1.55414i | 0.800820 | + | 0.598906i | \(0.204398\pi\) |
−0.295849 | + | 0.955235i | \(0.595602\pi\) | |||||||
\(390\) | −1.08783 | − | 0.790358i | −0.0550846 | − | 0.0400213i | ||||
\(391\) | −26.7136 | + | 19.4086i | −1.35096 | + | 0.981533i | ||||
\(392\) | 2.27217 | − | 6.99302i | 0.114762 | − | 0.353201i | ||||
\(393\) | 13.4861 | − | 9.79821i | 0.680282 | − | 0.494254i | ||||
\(394\) | −1.86113 | − | 5.72798i | −0.0937625 | − | 0.288571i | ||||
\(395\) | 2.10192 | + | 6.46905i | 0.105759 | + | 0.325493i | ||||
\(396\) | −1.62721 | + | 5.00804i | −0.0817704 | + | 0.251663i | ||||
\(397\) | 24.1365 | 1.21138 | 0.605688 | − | 0.795702i | \(-0.292898\pi\) | ||||
0.605688 | + | 0.795702i | \(0.292898\pi\) | |||||||
\(398\) | −4.19168 | −0.210110 | ||||||||
\(399\) | 0.966838 | − | 2.97562i | 0.0484024 | − | 0.148967i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | 31.7702 | − | 23.0824i | 1.58653 | − | 1.15268i | 0.677837 | − | 0.735212i | \(-0.262918\pi\) |
0.908692 | − | 0.417468i | \(-0.137082\pi\) | |||||||
\(402\) | 3.63183 | 0.181139 | ||||||||
\(403\) | 7.31128 | − | 1.61081i | 0.364201 | − | 0.0802402i | ||||
\(404\) | −16.0406 | −0.798048 | ||||||||
\(405\) | −0.809017 | + | 0.587785i | −0.0402004 | + | 0.0292073i | ||||
\(406\) | −13.0904 | − | 9.51070i | −0.649663 | − | 0.472008i | ||||
\(407\) | 11.0239 | − | 33.9281i | 0.546435 | − | 1.68175i | ||||
\(408\) | −4.99755 | −0.247415 | ||||||||
\(409\) | 4.52654 | 0.223823 | 0.111911 | − | 0.993718i | \(-0.464303\pi\) | ||||
0.111911 | + | 0.993718i | \(0.464303\pi\) | |||||||
\(410\) | 3.07811 | − | 9.47346i | 0.152017 | − | 0.467861i | ||||
\(411\) | 4.91048 | + | 15.1129i | 0.242216 | + | 0.745465i | ||||
\(412\) | 5.07223 | + | 15.6107i | 0.249891 | + | 0.769085i | ||||
\(413\) | 25.8002 | − | 18.7449i | 1.26954 | − | 0.922378i | ||||
\(414\) | −2.04174 | + | 6.28382i | −0.100346 | + | 0.308833i | ||||
\(415\) | 0.379511 | − | 0.275731i | 0.0186294 | − | 0.0135351i | ||||
\(416\) | −1.08783 | − | 0.790358i | −0.0533355 | − | 0.0387505i | ||||
\(417\) | −2.08731 | − | 6.42409i | −0.102216 | − | 0.314589i | ||||
\(418\) | −3.51820 | − | 2.55612i | −0.172081 | − | 0.125024i | ||||
\(419\) | 4.51349 | + | 3.27924i | 0.220498 | + | 0.160201i | 0.692551 | − | 0.721369i | \(-0.256487\pi\) |
−0.472053 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(420\) | −1.17072 | − | 3.60310i | −0.0571252 | − | 0.175813i | ||||
\(421\) | −11.8782 | − | 8.62999i | −0.578906 | − | 0.420600i | 0.259423 | − | 0.965764i | \(-0.416467\pi\) |
−0.838330 | + | 0.545164i | \(0.816467\pi\) | |||||||
\(422\) | 2.65844 | − | 1.93147i | 0.129411 | − | 0.0940226i | ||||
\(423\) | 2.08425 | − | 6.41465i | 0.101340 | − | 0.311891i | ||||
\(424\) | 3.08661 | − | 2.24255i | 0.149899 | − | 0.108908i | ||||
\(425\) | −1.54433 | − | 4.75295i | −0.0749109 | − | 0.230552i | ||||
\(426\) | 1.40173 | + | 4.31407i | 0.0679138 | + | 0.209017i | ||||
\(427\) | −8.54963 | + | 26.3131i | −0.413746 | + | 1.27338i | ||||
\(428\) | −4.66910 | −0.225689 | ||||||||
\(429\) | −7.08054 | −0.341852 | ||||||||
\(430\) | 1.68670 | − | 5.19112i | 0.0813398 | − | 0.250338i | ||||
\(431\) | 5.23962 | + | 3.80681i | 0.252384 | + | 0.183367i | 0.706783 | − | 0.707431i | \(-0.250146\pi\) |
−0.454399 | + | 0.890798i | \(0.650146\pi\) | |||||||
\(432\) | −0.809017 | + | 0.587785i | −0.0389238 | + | 0.0282798i | ||||
\(433\) | −5.79073 | −0.278285 | −0.139142 | − | 0.990272i | \(-0.544435\pi\) | ||||
−0.139142 | + | 0.990272i | \(0.544435\pi\) | |||||||
\(434\) | 19.3330 | + | 8.43642i | 0.928016 | + | 0.404961i | ||||
\(435\) | −4.27094 | −0.204776 | ||||||||
\(436\) | 5.35543 | − | 3.89095i | 0.256479 | − | 0.186343i | ||||
\(437\) | −4.41445 | − | 3.20729i | −0.211172 | − | 0.153425i | ||||
\(438\) | −0.630797 | + | 1.94139i | −0.0301407 | + | 0.0927634i | ||||
\(439\) | −27.5147 | −1.31320 | −0.656601 | − | 0.754238i | \(-0.728007\pi\) | ||||
−0.656601 | + | 0.754238i | \(0.728007\pi\) | |||||||
\(440\) | −5.26576 | −0.251035 | ||||||||
\(441\) | 2.27217 | − | 6.99302i | 0.108199 | − | 0.333001i | ||||
\(442\) | −2.07656 | − | 6.39099i | −0.0987719 | − | 0.303989i | ||||
\(443\) | 3.71016 | + | 11.4187i | 0.176275 | + | 0.542519i | 0.999689 | − | 0.0249216i | \(-0.00793362\pi\) |
−0.823414 | + | 0.567441i | \(0.807934\pi\) | |||||||
\(444\) | 5.48087 | − | 3.98208i | 0.260111 | − | 0.188981i | ||||
\(445\) | 0.991032 | − | 3.05008i | 0.0469794 | − | 0.144588i | ||||
\(446\) | −16.9544 | + | 12.3181i | −0.802815 | + | 0.583280i | ||||
\(447\) | 12.9886 | + | 9.43677i | 0.614340 | + | 0.446344i | ||||
\(448\) | −1.17072 | − | 3.60310i | −0.0553112 | − | 0.170230i | ||||
\(449\) | −13.3487 | − | 9.69843i | −0.629966 | − | 0.457697i | 0.226422 | − | 0.974029i | \(-0.427297\pi\) |
−0.856388 | + | 0.516332i | \(0.827297\pi\) | |||||||
\(450\) | −0.809017 | − | 0.587785i | −0.0381374 | − | 0.0277085i | ||||
\(451\) | −16.2086 | − | 49.8850i | −0.763234 | − | 2.34899i | ||||
\(452\) | −3.89679 | − | 2.83118i | −0.183290 | − | 0.133168i | ||||
\(453\) | −8.02217 | + | 5.82845i | −0.376914 | + | 0.273844i | ||||
\(454\) | 6.24435 | − | 19.2181i | 0.293062 | − | 0.901952i | ||||
\(455\) | 4.12128 | − | 2.99429i | 0.193209 | − | 0.140374i | ||||
\(456\) | −0.255202 | − | 0.785431i | −0.0119509 | − | 0.0367812i | ||||
\(457\) | 10.5262 | + | 32.3962i | 0.492393 | + | 1.51543i | 0.820980 | + | 0.570957i | \(0.193428\pi\) |
−0.328586 | + | 0.944474i | \(0.606572\pi\) | |||||||
\(458\) | 1.58572 | − | 4.88036i | 0.0740960 | − | 0.228044i | ||||
\(459\) | −4.99755 | −0.233266 | ||||||||
\(460\) | −6.60720 | −0.308062 | ||||||||
\(461\) | −8.42830 | + | 25.9396i | −0.392545 | + | 1.20813i | 0.538312 | + | 0.842745i | \(0.319062\pi\) |
−0.930857 | + | 0.365383i | \(0.880938\pi\) | |||||||
\(462\) | −16.1395 | − | 11.7260i | −0.750875 | − | 0.545543i | ||||
\(463\) | 27.1575 | − | 19.7311i | 1.26212 | − | 0.916981i | 0.263256 | − | 0.964726i | \(-0.415204\pi\) |
0.998860 | + | 0.0477452i | \(0.0152036\pi\) | |||||||
\(464\) | −4.27094 | −0.198274 | ||||||||
\(465\) | 5.43736 | − | 1.19795i | 0.252152 | − | 0.0555537i | ||||
\(466\) | −24.5029 | −1.13508 | ||||||||
\(467\) | −31.0181 | + | 22.5359i | −1.43534 | + | 1.04284i | −0.446355 | + | 0.894856i | \(0.647278\pi\) |
−0.988990 | + | 0.147983i | \(0.952722\pi\) | |||||||
\(468\) | −1.08783 | − | 0.790358i | −0.0502852 | − | 0.0365343i | ||||
\(469\) | −4.25185 | + | 13.0858i | −0.196332 | + | 0.604248i | ||||
\(470\) | 6.74477 | 0.311113 | ||||||||
\(471\) | 20.4454 | 0.942073 | ||||||||
\(472\) | 2.60122 | − | 8.00574i | 0.119731 | − | 0.368494i | ||||
\(473\) | −8.88175 | − | 27.3352i | −0.408383 | − | 1.25687i | ||||
\(474\) | 2.10192 | + | 6.46905i | 0.0965445 | + | 0.297133i | ||||
\(475\) | 0.668127 | − | 0.485423i | 0.0306558 | − | 0.0222727i | ||||
\(476\) | 5.85072 | − | 18.0067i | 0.268167 | − | 0.825334i | ||||
\(477\) | 3.08661 | − | 2.24255i | 0.141326 | − | 0.102679i | ||||
\(478\) | −12.4030 | − | 9.01127i | −0.567298 | − | 0.412166i | ||||
\(479\) | −3.39046 | − | 10.4348i | −0.154914 | − | 0.476777i | 0.843238 | − | 0.537540i | \(-0.180646\pi\) |
−0.998152 | + | 0.0607637i | \(0.980646\pi\) | |||||||
\(480\) | −0.809017 | − | 0.587785i | −0.0369264 | − | 0.0268286i | ||||
\(481\) | 7.36978 | + | 5.35446i | 0.336033 | + | 0.244142i | ||||
\(482\) | −3.70554 | − | 11.4045i | −0.168783 | − | 0.519459i | ||||
\(483\) | −20.2509 | − | 14.7132i | −0.921449 | − | 0.669472i | ||||
\(484\) | −13.5335 | + | 9.83263i | −0.615157 | + | 0.446938i | ||||
\(485\) | −5.38066 | + | 16.5600i | −0.244323 | + | 0.751949i | ||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 4.43976 | + | 13.6642i | 0.201185 | + | 0.619183i | 0.999849 | + | 0.0174053i | \(0.00554056\pi\) |
−0.798664 | + | 0.601777i | \(0.794459\pi\) | |||||||
\(488\) | 2.25672 | + | 6.94547i | 0.102157 | + | 0.314407i | ||||
\(489\) | 2.98547 | − | 9.18833i | 0.135008 | − | 0.415510i | ||||
\(490\) | 7.35290 | 0.332170 | ||||||||
\(491\) | −24.1830 | −1.09136 | −0.545682 | − | 0.837992i | \(-0.683730\pi\) | ||||
−0.545682 | + | 0.837992i | \(0.683730\pi\) | |||||||
\(492\) | 3.07811 | − | 9.47346i | 0.138772 | − | 0.427097i | ||||
\(493\) | −17.2679 | − | 12.5458i | −0.777705 | − | 0.565036i | ||||
\(494\) | 0.898389 | − | 0.652718i | 0.0404204 | − | 0.0293672i | ||||
\(495\) | −5.26576 | −0.236678 | ||||||||
\(496\) | 5.43736 | − | 1.19795i | 0.244145 | − | 0.0537897i | ||||
\(497\) | −17.1850 | −0.770854 | ||||||||
\(498\) | 0.379511 | − | 0.275731i | 0.0170063 | − | 0.0123558i | ||||
\(499\) | 7.15226 | + | 5.19642i | 0.320179 | + | 0.232624i | 0.736252 | − | 0.676707i | \(-0.236594\pi\) |
−0.416073 | + | 0.909331i | \(0.636594\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | −4.73236 | −0.211426 | ||||||||
\(502\) | 7.98503 | 0.356390 | ||||||||
\(503\) | 1.22358 | − | 3.76579i | 0.0545567 | − | 0.167908i | −0.920065 | − | 0.391765i | \(-0.871865\pi\) |
0.974622 | + | 0.223857i | \(0.0718647\pi\) | |||||||
\(504\) | −1.17072 | − | 3.60310i | −0.0521479 | − | 0.160495i | ||||
\(505\) | −4.95681 | − | 15.2555i | −0.220575 | − | 0.678860i | ||||
\(506\) | −28.1473 | + | 20.4502i | −1.25130 | + | 0.909122i | ||||
\(507\) | −3.45850 | + | 10.6442i | −0.153598 | + | 0.472725i | ||||
\(508\) | 4.84152 | − | 3.51757i | 0.214808 | − | 0.156067i | ||||
\(509\) | −4.31087 | − | 3.13203i | −0.191076 | − | 0.138825i | 0.488134 | − | 0.872768i | \(-0.337678\pi\) |
−0.679210 | + | 0.733944i | \(0.737678\pi\) | |||||||
\(510\) | −1.54433 | − | 4.75295i | −0.0683840 | − | 0.210464i | ||||
\(511\) | −6.25655 | − | 4.54565i | −0.276773 | − | 0.201088i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −0.255202 | − | 0.785431i | −0.0112674 | − | 0.0346776i | ||||
\(514\) | −16.6117 | − | 12.0691i | −0.732712 | − | 0.532347i | ||||
\(515\) | −13.2793 | + | 9.64795i | −0.585154 | + | 0.425140i | ||||
\(516\) | 1.68670 | − | 5.19112i | 0.0742527 | − | 0.228526i | ||||
\(517\) | 28.7333 | − | 20.8760i | 1.26369 | − | 0.918125i | ||||
\(518\) | 7.93129 | + | 24.4100i | 0.348481 | + | 1.07251i | ||||
\(519\) | −3.61332 | − | 11.1206i | −0.158607 | − | 0.488142i | ||||
\(520\) | 0.415516 | − | 1.27883i | 0.0182216 | − | 0.0560802i | ||||
\(521\) | −26.3009 | −1.15227 | −0.576133 | − | 0.817356i | \(-0.695439\pi\) | ||||
−0.576133 | + | 0.817356i | \(0.695439\pi\) | |||||||
\(522\) | −4.27094 | −0.186934 | ||||||||
\(523\) | 10.2516 | − | 31.5511i | 0.448270 | − | 1.37963i | −0.430587 | − | 0.902549i | \(-0.641694\pi\) |
0.878857 | − | 0.477085i | \(-0.158306\pi\) | |||||||
\(524\) | 13.4861 | + | 9.79821i | 0.589142 | + | 0.428037i | ||||
\(525\) | 3.06498 | − | 2.22684i | 0.133767 | − | 0.0971872i | ||||
\(526\) | 4.94836 | 0.215759 | ||||||||
\(527\) | 25.5028 | + | 11.1287i | 1.11092 | + | 0.484775i | ||||
\(528\) | −5.26576 | −0.229163 | ||||||||
\(529\) | −16.7103 | + | 12.1408i | −0.726535 | + | 0.527859i | ||||
\(530\) | 3.08661 | + | 2.24255i | 0.134074 | + | 0.0974102i | ||||
\(531\) | 2.60122 | − | 8.00574i | 0.112883 | − | 0.347420i | ||||
\(532\) | 3.12875 | 0.135649 | ||||||||
\(533\) | 13.3939 | 0.580155 | ||||||||
\(534\) | 0.991032 | − | 3.05008i | 0.0428862 | − | 0.131990i | ||||
\(535\) | −1.44283 | − | 4.44057i | −0.0623790 | − | 0.191983i | ||||
\(536\) | 1.12230 | + | 3.45407i | 0.0484758 | + | 0.149193i | ||||
\(537\) | −0.730238 | + | 0.530549i | −0.0315121 | + | 0.0228949i | ||||
\(538\) | 5.94591 | − | 18.2996i | 0.256346 | − | 0.788953i | ||||
\(539\) | 31.3240 | − | 22.7582i | 1.34922 | − | 0.980267i | ||||
\(540\) | −0.809017 | − | 0.587785i | −0.0348145 | − | 0.0252942i | ||||
\(541\) | 3.00708 | + | 9.25484i | 0.129284 | + | 0.397897i | 0.994657 | − | 0.103232i | \(-0.0329184\pi\) |
−0.865373 | + | 0.501128i | \(0.832918\pi\) | |||||||
\(542\) | 3.44661 | + | 2.50411i | 0.148045 | + | 0.107561i | ||||
\(543\) | −0.803274 | − | 0.583613i | −0.0344718 | − | 0.0250452i | ||||
\(544\) | −1.54433 | − | 4.75295i | −0.0662125 | − | 0.203781i | ||||
\(545\) | 5.35543 | + | 3.89095i | 0.229401 | + | 0.166670i | ||||
\(546\) | 4.12128 | − | 2.99429i | 0.176375 | − | 0.128144i | ||||
\(547\) | −1.84811 | + | 5.68791i | −0.0790197 | + | 0.243198i | −0.982761 | − | 0.184882i | \(-0.940810\pi\) |
0.903741 | + | 0.428080i | \(0.140810\pi\) | |||||||
\(548\) | −12.8558 | + | 9.34029i | −0.549173 | + | 0.398997i | ||||
\(549\) | 2.25672 | + | 6.94547i | 0.0963144 | + | 0.296425i | ||||
\(550\) | −1.62721 | − | 5.00804i | −0.0693845 | − | 0.213544i | ||||
\(551\) | 1.08995 | − | 3.35453i | 0.0464336 | − | 0.142908i | ||||
\(552\) | −6.60720 | −0.281221 | ||||||||
\(553\) | −25.7694 | −1.09583 | ||||||||
\(554\) | 5.21953 | − | 16.0641i | 0.221756 | − | 0.682496i | ||||
\(555\) | 5.48087 | + | 3.98208i | 0.232650 | + | 0.169030i | ||||
\(556\) | 5.46466 | − | 3.97031i | 0.231753 | − | 0.168379i | ||||
\(557\) | 11.5650 | 0.490025 | 0.245013 | − | 0.969520i | \(-0.421208\pi\) | ||||
0.245013 | + | 0.969520i | \(0.421208\pi\) | |||||||
\(558\) | 5.43736 | − | 1.19795i | 0.230182 | − | 0.0507134i | ||||
\(559\) | 7.33939 | 0.310423 | ||||||||
\(560\) | 3.06498 | − | 2.22684i | 0.129519 | − | 0.0941011i | ||||
\(561\) | −21.2900 | − | 15.4681i | −0.898865 | − | 0.653064i | ||||
\(562\) | −6.64513 | + | 20.4516i | −0.280308 | + | 0.862700i | ||||
\(563\) | −18.7514 | −0.790275 | −0.395138 | − | 0.918622i | \(-0.629303\pi\) | ||||
−0.395138 | + | 0.918622i | \(0.629303\pi\) | |||||||
\(564\) | 6.74477 | 0.284006 | ||||||||
\(565\) | 1.48844 | − | 4.58095i | 0.0626192 | − | 0.192722i | ||||
\(566\) | 5.78102 | + | 17.7922i | 0.242995 | + | 0.747860i | ||||
\(567\) | −1.17072 | − | 3.60310i | −0.0491655 | − | 0.151316i | ||||
\(568\) | −3.66977 | + | 2.66624i | −0.153980 | + | 0.111873i | ||||
\(569\) | 11.6125 | − | 35.7396i | 0.486822 | − | 1.49828i | −0.342503 | − | 0.939517i | \(-0.611275\pi\) |
0.829325 | − | 0.558767i | \(-0.188725\pi\) | |||||||
\(570\) | 0.668127 | − | 0.485423i | 0.0279848 | − | 0.0203321i | ||||
\(571\) | −20.0455 | − | 14.5639i | −0.838876 | − | 0.609479i | 0.0831802 | − | 0.996535i | \(-0.473492\pi\) |
−0.922057 | + | 0.387055i | \(0.873492\pi\) | |||||||
\(572\) | −2.18801 | − | 6.73400i | −0.0914852 | − | 0.281563i | ||||
\(573\) | −16.8041 | − | 12.2089i | −0.702003 | − | 0.510035i | ||||
\(574\) | 30.5302 | + | 22.1815i | 1.27431 | + | 0.925838i | ||||
\(575\) | −2.04174 | − | 6.28382i | −0.0851463 | − | 0.262053i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | −9.41110 | + | 6.83757i | −0.391789 | + | 0.284652i | −0.766188 | − | 0.642616i | \(-0.777849\pi\) |
0.374399 | + | 0.927268i | \(0.377849\pi\) | |||||||
\(578\) | 2.46456 | − | 7.58514i | 0.102512 | − | 0.315500i | ||||
\(579\) | −21.2307 | + | 15.4250i | −0.882319 | + | 0.641042i | ||||
\(580\) | −1.31979 | − | 4.06191i | −0.0548015 | − | 0.168662i | ||||
\(581\) | 0.549185 | + | 1.69022i | 0.0227840 | + | 0.0701220i | ||||
\(582\) | −5.38066 | + | 16.5600i | −0.223035 | + | 0.686432i | ||||
\(583\) | 20.0902 | 0.832053 | ||||||||
\(584\) | −2.04130 | −0.0844697 | ||||||||
\(585\) | 0.415516 | − | 1.27883i | 0.0171795 | − | 0.0528729i | ||||
\(586\) | −19.0830 | − | 13.8646i | −0.788311 | − | 0.572741i | ||||
\(587\) | −33.8100 | + | 24.5644i | −1.39549 | + | 1.01388i | −0.400251 | + | 0.916406i | \(0.631077\pi\) |
−0.995238 | + | 0.0974765i | \(0.968923\pi\) | |||||||
\(588\) | 7.35290 | 0.303228 | ||||||||
\(589\) | −0.446717 | + | 4.57639i | −0.0184066 | + | 0.188567i | ||||
\(590\) | 8.41774 | 0.346553 | ||||||||
\(591\) | 4.87251 | − | 3.54009i | 0.200428 | − | 0.145620i | ||||
\(592\) | 5.48087 | + | 3.98208i | 0.225262 | + | 0.163663i | ||||
\(593\) | −11.4595 | + | 35.2688i | −0.470586 | + | 1.44832i | 0.381233 | + | 0.924479i | \(0.375500\pi\) |
−0.851819 | + | 0.523836i | \(0.824500\pi\) | |||||||
\(594\) | −5.26576 | −0.216057 | ||||||||
\(595\) | 18.9333 | 0.776190 | ||||||||
\(596\) | −4.96120 | + | 15.2690i | −0.203219 | + | 0.625443i | ||||
\(597\) | −1.29530 | − | 3.98653i | −0.0530132 | − | 0.163158i | ||||
\(598\) | −2.74540 | − | 8.44946i | −0.112268 | − | 0.345524i | ||||
\(599\) | −34.1753 | + | 24.8298i | −1.39637 | + | 1.01452i | −0.401233 | + | 0.915976i | \(0.631418\pi\) |
−0.995133 | + | 0.0985428i | \(0.968582\pi\) | |||||||
\(600\) | 0.309017 | − | 0.951057i | 0.0126156 | − | 0.0388267i | ||||
\(601\) | 7.75507 | − | 5.63439i | 0.316336 | − | 0.229832i | −0.418274 | − | 0.908321i | \(-0.637365\pi\) |
0.734610 | + | 0.678489i | \(0.237365\pi\) | |||||||
\(602\) | 16.7295 | + | 12.1547i | 0.681842 | + | 0.495387i | ||||
\(603\) | 1.12230 | + | 3.45407i | 0.0457035 | + | 0.140661i | ||||
\(604\) | −8.02217 | − | 5.82845i | −0.326417 | − | 0.237156i | ||||
\(605\) | −13.5335 | − | 9.83263i | −0.550213 | − | 0.399753i | ||||
\(606\) | −4.95681 | − | 15.2555i | −0.201357 | − | 0.619712i | ||||
\(607\) | 27.7332 | + | 20.1493i | 1.12565 | + | 0.817836i | 0.985057 | − | 0.172231i | \(-0.0550976\pi\) |
0.140598 | + | 0.990067i | \(0.455098\pi\) | |||||||
\(608\) | 0.668127 | − | 0.485423i | 0.0270961 | − | 0.0196865i | ||||
\(609\) | 5.00007 | − | 15.3886i | 0.202613 | − | 0.623579i | ||||
\(610\) | −5.90817 | + | 4.29254i | −0.239215 | + | 0.173800i | ||||
\(611\) | 2.80256 | + | 8.62538i | 0.113379 | + | 0.348946i | ||||
\(612\) | −1.54433 | − | 4.75295i | −0.0624257 | − | 0.192127i | ||||
\(613\) | −5.36247 | + | 16.5040i | −0.216588 | + | 0.666589i | 0.782449 | + | 0.622715i | \(0.213970\pi\) |
−0.999037 | + | 0.0438748i | \(0.986030\pi\) | |||||||
\(614\) | 20.7146 | 0.835973 | ||||||||
\(615\) | 9.96099 | 0.401666 | ||||||||
\(616\) | 6.16472 | − | 18.9731i | 0.248384 | − | 0.764447i | ||||
\(617\) | 32.5282 | + | 23.6332i | 1.30954 | + | 0.951435i | 1.00000 | 0.000547791i | \(0.000174367\pi\) | |
0.309538 | + | 0.950887i | \(0.399826\pi\) | |||||||
\(618\) | −13.2793 | + | 9.64795i | −0.534170 | + | 0.388098i | ||||
\(619\) | −40.3836 | −1.62315 | −0.811577 | − | 0.584245i | \(-0.801391\pi\) | ||||
−0.811577 | + | 0.584245i | \(0.801391\pi\) | |||||||
\(620\) | 2.81956 | + | 4.80105i | 0.113236 | + | 0.192815i | ||||
\(621\) | −6.60720 | −0.265138 | ||||||||
\(622\) | −12.4064 | + | 9.01380i | −0.497453 | + | 0.361421i | ||||
\(623\) | 9.82953 | + | 7.14157i | 0.393812 | + | 0.286121i | ||||
\(624\) | 0.415516 | − | 1.27883i | 0.0166339 | − | 0.0511940i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.95798 | 0.358033 | ||||||||
\(627\) | 1.34383 | − | 4.13589i | 0.0536675 | − | 0.165172i | ||||
\(628\) | 6.31796 | + | 19.4447i | 0.252114 | + | 0.775928i | ||||
\(629\) | 10.4624 | + | 32.1999i | 0.417163 | + | 1.28390i | ||||
\(630\) | 3.06498 | − | 2.22684i | 0.122112 | − | 0.0887193i | ||||
\(631\) | 1.40371 | − | 4.32019i | 0.0558810 | − | 0.171984i | −0.919220 | − | 0.393743i | \(-0.871180\pi\) |
0.975101 | + | 0.221759i | \(0.0711799\pi\) | |||||||
\(632\) | −5.50291 | + | 3.99809i | −0.218894 | + | 0.159036i | ||||
\(633\) | 2.65844 | + | 1.93147i | 0.105664 | + | 0.0767691i | ||||
\(634\) | 9.80482 | + | 30.1761i | 0.389399 | + | 1.19845i | ||||
\(635\) | 4.84152 | + | 3.51757i | 0.192130 | + | 0.139591i | ||||
\(636\) | 3.08661 | + | 2.24255i | 0.122392 | + | 0.0889230i | ||||
\(637\) | 3.05525 | + | 9.40308i | 0.121053 | + | 0.372564i | ||||
\(638\) | −18.1946 | − | 13.2192i | −0.720332 | − | 0.523352i | ||||
\(639\) | −3.66977 | + | 2.66624i | −0.145174 | + | 0.105475i | ||||
\(640\) | 0.309017 | − | 0.951057i | 0.0122150 | − | 0.0375938i | ||||
\(641\) | −5.51114 | + | 4.00408i | −0.217677 | + | 0.158152i | −0.691280 | − | 0.722587i | \(-0.742953\pi\) |
0.473603 | + | 0.880738i | \(0.342953\pi\) | |||||||
\(642\) | −1.44283 | − | 4.44057i | −0.0569440 | − | 0.175255i | ||||
\(643\) | −2.64268 | − | 8.13332i | −0.104217 | − | 0.320747i | 0.885329 | − | 0.464965i | \(-0.153933\pi\) |
−0.989546 | + | 0.144218i | \(0.953933\pi\) | |||||||
\(644\) | 7.73517 | − | 23.8064i | 0.304808 | − | 0.938103i | ||||
\(645\) | 5.45827 | 0.214919 | ||||||||
\(646\) | 4.12723 | 0.162384 | ||||||||
\(647\) | −10.8394 | + | 33.3602i | −0.426141 | + | 1.31153i | 0.475757 | + | 0.879577i | \(0.342174\pi\) |
−0.901898 | + | 0.431950i | \(0.857826\pi\) | |||||||
\(648\) | −0.809017 | − | 0.587785i | −0.0317812 | − | 0.0230904i | ||||
\(649\) | 35.8603 | − | 26.0541i | 1.40764 | − | 1.02271i | ||||
\(650\) | 1.34464 | 0.0527410 | ||||||||
\(651\) | −2.04927 | + | 20.9938i | −0.0803174 | + | 0.822813i | ||||
\(652\) | 9.66118 | 0.378361 | ||||||||
\(653\) | −26.4093 | + | 19.1875i | −1.03348 | + | 0.750865i | −0.969002 | − | 0.247054i | \(-0.920537\pi\) |
−0.0644752 | + | 0.997919i | \(0.520537\pi\) | |||||||
\(654\) | 5.35543 | + | 3.89095i | 0.209414 | + | 0.152148i | ||||
\(655\) | −5.15122 | + | 15.8538i | −0.201275 | + | 0.619460i | ||||
\(656\) | 9.96099 | 0.388911 | ||||||||
\(657\) | −2.04130 | −0.0796388 | ||||||||
\(658\) | −7.89622 | + | 24.3021i | −0.307827 | + | 0.947393i | ||||
\(659\) | −8.25007 | − | 25.3911i | −0.321377 | − | 0.989097i | −0.973050 | − | 0.230596i | \(-0.925932\pi\) |
0.651672 | − | 0.758500i | \(-0.274068\pi\) | |||||||
\(660\) | −1.62721 | − | 5.00804i | −0.0633391 | − | 0.194938i | ||||
\(661\) | 14.6635 | − | 10.6536i | 0.570343 | − | 0.414379i | −0.264887 | − | 0.964280i | \(-0.585335\pi\) |
0.835230 | + | 0.549901i | \(0.185335\pi\) | |||||||
\(662\) | 0.745779 | − | 2.29527i | 0.0289855 | − | 0.0892083i | ||||
\(663\) | 5.43650 | − | 3.94985i | 0.211136 | − | 0.153400i | ||||
\(664\) | 0.379511 | + | 0.275731i | 0.0147279 | + | 0.0107004i | ||||
\(665\) | 0.966838 | + | 2.97562i | 0.0374924 | + | 0.115390i | ||||
\(666\) | 5.48087 | + | 3.98208i | 0.212379 | + | 0.154303i | ||||
\(667\) | −22.8296 | − | 16.5867i | −0.883967 | − | 0.642240i | ||||
\(668\) | −1.46238 | − | 4.50074i | −0.0565812 | − | 0.174139i | ||||
\(669\) | −16.9544 | − | 12.3181i | −0.655496 | − | 0.476246i | ||||
\(670\) | −2.93821 | + | 2.13474i | −0.113513 | + | 0.0824720i | ||||
\(671\) | −11.8834 | + | 36.5732i | −0.458752 | + | 1.41189i | ||||
\(672\) | 3.06498 | − | 2.22684i | 0.118234 | − | 0.0859021i | ||||
\(673\) | 14.5236 | + | 44.6990i | 0.559843 | + | 1.72302i | 0.682797 | + | 0.730608i | \(0.260763\pi\) |
−0.122953 | + | 0.992412i | \(0.539237\pi\) | |||||||
\(674\) | 9.46082 | + | 29.1174i | 0.364417 | + | 1.12156i | ||||
\(675\) | 0.309017 | − | 0.951057i | 0.0118941 | − | 0.0366062i | ||||
\(676\) | −11.1920 | −0.430460 | ||||||||
\(677\) | −6.31126 | −0.242561 | −0.121281 | − | 0.992618i | \(-0.538700\pi\) | ||||
−0.121281 | + | 0.992618i | \(0.538700\pi\) | |||||||
\(678\) | 1.48844 | − | 4.58095i | 0.0571633 | − | 0.175930i | ||||
\(679\) | −53.3679 | − | 38.7741i | −2.04807 | − | 1.48801i | ||||
\(680\) | 4.04310 | − | 2.93749i | 0.155046 | − | 0.112647i | ||||
\(681\) | 20.2071 | 0.774340 | ||||||||
\(682\) | 26.8715 | + | 11.7260i | 1.02896 | + | 0.449012i | ||||
\(683\) | −15.5095 | −0.593455 | −0.296727 | − | 0.954962i | \(-0.595895\pi\) | ||||
−0.296727 | + | 0.954962i | \(0.595895\pi\) | |||||||
\(684\) | 0.668127 | − | 0.485423i | 0.0255465 | − | 0.0185606i | ||||
\(685\) | −12.8558 | − | 9.34029i | −0.491195 | − | 0.356874i | ||||
\(686\) | −0.413145 | + | 1.27153i | −0.0157740 | + | 0.0485473i | ||||
\(687\) | 5.13151 | 0.195779 | ||||||||
\(688\) | 5.45827 | 0.208094 | ||||||||
\(689\) | −1.58530 | + | 4.87905i | −0.0603951 | + | 0.185877i | ||||
\(690\) | −2.04174 | − | 6.28382i | −0.0777276 | − | 0.239221i | ||||
\(691\) | 3.33819 | + | 10.2739i | 0.126991 | + | 0.390837i | 0.994259 | − | 0.107005i | \(-0.0341260\pi\) |
−0.867268 | + | 0.497842i | \(0.834126\pi\) | |||||||
\(692\) | 9.45979 | − | 6.87294i | 0.359607 | − | 0.261270i | ||||
\(693\) | 6.16472 | − | 18.9731i | 0.234178 | − | 0.720727i | ||||
\(694\) | 4.84316 | − | 3.51876i | 0.183844 | − | 0.133570i | ||||
\(695\) | 5.46466 | + | 3.97031i | 0.207286 | + | 0.150602i | ||||
\(696\) | −1.31979 | − | 4.06191i | −0.0500267 | − | 0.153966i | ||||
\(697\) | 40.2733 | + | 29.2603i | 1.52546 | + | 1.10831i | ||||
\(698\) | −17.7500 | − | 12.8961i | −0.671847 | − | 0.488126i | ||||
\(699\) | −7.57182 | − | 23.3037i | −0.286393 | − | 0.881426i | ||||
\(700\) | 3.06498 | + | 2.22684i | 0.115845 | + | 0.0841665i | ||||
\(701\) | 37.4065 | − | 27.1774i | 1.41282 | − | 1.02648i | 0.419920 | − | 0.907561i | \(-0.362058\pi\) |
0.992904 | − | 0.118916i | \(-0.0379420\pi\) | |||||||
\(702\) | 0.415516 | − | 1.27883i | 0.0156826 | − | 0.0482662i | ||||
\(703\) | −4.52638 | + | 3.28861i | −0.170716 | + | 0.124032i | ||||
\(704\) | −1.62721 | − | 5.00804i | −0.0613278 | − | 0.188748i | ||||
\(705\) | 2.08425 | + | 6.41465i | 0.0784973 | + | 0.241590i | ||||
\(706\) | −8.35381 | + | 25.7104i | −0.314400 | + | 0.967623i | ||||
\(707\) | 60.7700 | 2.28549 | ||||||||
\(708\) | 8.41774 | 0.316358 | ||||||||
\(709\) | −12.5491 | + | 38.6222i | −0.471292 | + | 1.45049i | 0.379601 | + | 0.925150i | \(0.376061\pi\) |
−0.850893 | + | 0.525339i | \(0.823939\pi\) | |||||||
\(710\) | −3.66977 | − | 2.66624i | −0.137724 | − | 0.100062i | ||||
\(711\) | −5.50291 | + | 3.99809i | −0.206375 | + | 0.149940i | ||||
\(712\) | 3.20705 | 0.120189 | ||||||||
\(713\) | 33.7169 | + | 14.7132i | 1.26271 | + | 0.551012i | ||||
\(714\) | 18.9333 | 0.708562 | ||||||||
\(715\) | 5.72828 | − | 4.16184i | 0.214225 | − | 0.155644i | ||||
\(716\) | −0.730238 | − | 0.530549i | −0.0272903 | − | 0.0198276i | ||||
\(717\) | 4.73751 | − | 14.5805i | 0.176925 | − | 0.544520i | ||||
\(718\) | −1.10662 | −0.0412988 | ||||||||
\(719\) | 30.6326 | 1.14240 | 0.571202 | − | 0.820809i | \(-0.306477\pi\) | ||||
0.571202 | + | 0.820809i | \(0.306477\pi\) | |||||||
\(720\) | 0.309017 | − | 0.951057i | 0.0115164 | − | 0.0354438i | ||||
\(721\) | −19.2162 | − | 59.1415i | −0.715650 | − | 2.20255i | ||||
\(722\) | −5.66056 | − | 17.4214i | −0.210664 | − | 0.648358i | ||||
\(723\) | 9.70122 | − | 7.04835i | 0.360792 | − | 0.262131i | ||||
\(724\) | 0.306823 | − | 0.944305i | 0.0114030 | − | 0.0350948i | ||||
\(725\) | 3.45527 | − | 2.51040i | 0.128325 | − | 0.0932339i | ||||
\(726\) | −13.5335 | − | 9.83263i | −0.502274 | − | 0.364923i | ||||
\(727\) | 2.91016 | + | 8.95655i | 0.107932 | + | 0.332180i | 0.990407 | − | 0.138178i | \(-0.0441247\pi\) |
−0.882476 | + | 0.470358i | \(0.844125\pi\) | |||||||
\(728\) | 4.12128 | + | 2.99429i | 0.152745 | + | 0.110976i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −0.630797 | − | 1.94139i | −0.0233469 | − | 0.0718542i | ||||
\(731\) | 22.0683 | + | 16.0336i | 0.816226 | + | 0.593023i | ||||
\(732\) | −5.90817 | + | 4.29254i | −0.218372 | + | 0.158657i | ||||
\(733\) | 1.07655 | − | 3.31327i | 0.0397631 | − | 0.122378i | −0.929205 | − | 0.369566i | \(-0.879506\pi\) |
0.968968 | + | 0.247188i | \(0.0795064\pi\) | |||||||
\(734\) | −1.27780 | + | 0.928378i | −0.0471646 | + | 0.0342671i | ||||
\(735\) | 2.27217 | + | 6.99302i | 0.0838103 | + | 0.257942i | ||||
\(736\) | −2.04174 | − | 6.28382i | −0.0752594 | − | 0.231625i | ||||
\(737\) | −5.90975 | + | 18.1883i | −0.217688 | + | 0.669976i | ||||
\(738\) | 9.96099 | 0.366669 | ||||||||
\(739\) | −1.56186 | −0.0574541 | −0.0287270 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287270 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(740\) | −2.09351 | + | 6.44315i | −0.0769588 | + | 0.236855i | ||||
\(741\) | 0.898389 | + | 0.652718i | 0.0330031 | + | 0.0239782i | ||||
\(742\) | −11.6937 | + | 8.49596i | −0.429289 | + | 0.311896i | ||||
\(743\) | −47.6516 | −1.74817 | −0.874084 | − | 0.485774i | \(-0.838538\pi\) | ||||
−0.874084 | + | 0.485774i | \(0.838538\pi\) | |||||||
\(744\) | 2.81956 | + | 4.80105i | 0.103370 | + | 0.176015i | ||||
\(745\) | −16.0548 | −0.588202 | ||||||||
\(746\) | 25.1330 | − | 18.2602i | 0.920183 | − | 0.668552i | ||||
\(747\) | 0.379511 | + | 0.275731i | 0.0138856 | + | 0.0100885i | ||||
\(748\) | 8.13206 | − | 25.0279i | 0.297338 | − | 0.915111i | ||||
\(749\) | 17.6890 | 0.646341 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 2.18989 | − | 6.73978i | 0.0799102 | − | 0.245938i | −0.903118 | − | 0.429392i | \(-0.858728\pi\) |
0.983028 | + | 0.183454i | \(0.0587278\pi\) | |||||||
\(752\) | 2.08425 | + | 6.41465i | 0.0760047 | + | 0.233918i | ||||
\(753\) | 2.46751 | + | 7.59422i | 0.0899211 | + | 0.276749i | ||||
\(754\) | 4.64608 | − | 3.37558i | 0.169200 | − | 0.122931i | ||||
\(755\) | 3.06420 | − | 9.43063i | 0.111518 | − | 0.343216i | ||||
\(756\) | 3.06498 | − | 2.22684i | 0.111472 | − | 0.0809893i | ||||
\(757\) | 28.1371 | + | 20.4428i | 1.02266 | + | 0.743007i | 0.966827 | − | 0.255433i | \(-0.0822181\pi\) |
0.0558344 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(758\) | −3.22507 | − | 9.92576i | −0.117140 | − | 0.360520i | ||||
\(759\) | −28.1473 | − | 20.4502i | −1.02168 | − | 0.742295i | ||||
\(760\) | 0.668127 | + | 0.485423i | 0.0242355 | + | 0.0176081i | ||||
\(761\) | −14.1548 | − | 43.5640i | −0.513111 | − | 1.57919i | −0.786693 | − | 0.617345i | \(-0.788208\pi\) |
0.273582 | − | 0.961849i | \(-0.411792\pi\) | |||||||
\(762\) | 4.84152 | + | 3.51757i | 0.175390 | + | 0.127428i | ||||
\(763\) | −20.2892 | + | 14.7409i | −0.734517 | + | 0.533658i | ||||
\(764\) | 6.41861 | − | 19.7545i | 0.232217 | − | 0.714691i | ||||
\(765\) | 4.04310 | − | 2.93749i | 0.146179 | − | 0.106205i | ||||
\(766\) | −7.18366 | − | 22.1090i | −0.259556 | − | 0.798831i | ||||
\(767\) | 3.49770 | + | 10.7648i | 0.126295 | + | 0.388695i | ||||
\(768\) | 0.309017 | − | 0.951057i | 0.0111507 | − | 0.0343183i | ||||
\(769\) | 25.5495 | 0.921340 | 0.460670 | − | 0.887571i | \(-0.347609\pi\) | ||||
0.460670 | + | 0.887571i | \(0.347609\pi\) | |||||||
\(770\) | 19.9495 | 0.718929 | ||||||||
\(771\) | 6.34512 | − | 19.5283i | 0.228514 | − | 0.703293i | ||||
\(772\) | −21.2307 | − | 15.4250i | −0.764111 | − | 0.555159i | ||||
\(773\) | 38.9216 | − | 28.2782i | 1.39991 | − | 1.01710i | 0.405220 | − | 0.914219i | \(-0.367195\pi\) |
0.994694 | − | 0.102878i | \(-0.0328052\pi\) | |||||||
\(774\) | 5.45827 | 0.196193 | ||||||||
\(775\) | −3.69478 | + | 4.16517i | −0.132720 | + | 0.149617i | ||||
\(776\) | −17.4122 | −0.625060 | ||||||||
\(777\) | −20.7644 | + | 15.0862i | −0.744919 | + | 0.541215i | ||||
\(778\) | −26.0745 | − | 18.9443i | −0.934817 | − | 0.679184i | ||||
\(779\) | −2.54206 | + | 7.82367i | −0.0910789 | + | 0.280312i | ||||
\(780\) | 1.34464 | 0.0481457 | ||||||||
\(781\) | −23.8859 | −0.854706 | ||||||||
\(782\) | 10.2037 | − | 31.4037i | 0.364883 | − | 1.12299i | ||||
\(783\) | −1.31979 | − | 4.06191i | −0.0471656 | − | 0.145161i | ||||
\(784\) | 2.27217 | + | 6.99302i | 0.0811490 | + | 0.249751i | ||||
\(785\) | −16.5406 | + | 12.0175i | −0.590361 | + | 0.428922i | ||||
\(786\) | −5.15122 | + | 15.8538i | −0.183738 | + | 0.565487i | ||||
\(787\) | 25.7742 | − | 18.7261i | 0.918751 | − | 0.667512i | −0.0244615 | − | 0.999701i | \(-0.507787\pi\) |
0.943213 | + | 0.332189i | \(0.107787\pi\) | |||||||
\(788\) | 4.87251 | + | 3.54009i | 0.173576 | + | 0.126110i | ||||
\(789\) | 1.52913 | + | 4.70617i | 0.0544384 | + | 0.167544i | ||||
\(790\) | −5.50291 | − | 3.99809i | −0.195785 | − | 0.142246i | ||||
\(791\) | 14.7631 | + | 10.7260i | 0.524915 | + | 0.381373i | ||||
\(792\) | −1.62721 | − | 5.00804i | −0.0578204 | − | 0.177953i | ||||
\(793\) | −7.94434 | − | 5.77190i | −0.282112 | − | 0.204966i | ||||
\(794\) | −19.5268 | + | 14.1871i | −0.692982 | + | 0.503481i | ||||
\(795\) | −1.17898 | + | 3.62853i | −0.0418141 | + | 0.128691i | ||||
\(796\) | 3.39114 | − | 2.46381i | 0.120196 | − | 0.0873274i | ||||
\(797\) | 3.26114 | + | 10.0368i | 0.115516 | + | 0.355520i | 0.992054 | − | 0.125811i | \(-0.0401533\pi\) |
−0.876539 | + | 0.481331i | \(0.840153\pi\) | |||||||
\(798\) | 0.966838 | + | 2.97562i | 0.0342257 | + | 0.105336i | ||||
\(799\) | −10.4161 | + | 32.0575i | −0.368496 | + | 1.13411i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 3.20705 | 0.113315 | ||||||||
\(802\) | −12.1351 | + | 37.3481i | −0.428507 | + | 1.31881i | ||||
\(803\) | −8.69614 | − | 6.31812i | −0.306880 | − | 0.222961i | ||||
\(804\) | −2.93821 | + | 2.13474i | −0.103623 | + | 0.0752863i | ||||
\(805\) | 25.0315 | 0.882245 | ||||||||
\(806\) | −4.96814 | + | 5.60064i | −0.174995 | + | 0.197274i | ||||
\(807\) | 19.2414 | 0.677328 | ||||||||
\(808\) | 12.9771 | − | 9.42841i | 0.456532 | − | 0.331690i | ||||
\(809\) | −23.5134 | − | 17.0835i | −0.826688 | − | 0.600624i | 0.0919324 | − | 0.995765i | \(-0.470696\pi\) |
−0.918620 | + | 0.395141i | \(0.870696\pi\) | |||||||
\(810\) | 0.309017 | − | 0.951057i | 0.0108578 | − | 0.0334167i | ||||
\(811\) | 46.9718 | 1.64940 | 0.824701 | − | 0.565569i | \(-0.191343\pi\) | ||||
0.824701 | + | 0.565569i | \(0.191343\pi\) | |||||||
\(812\) | 16.1806 | 0.567827 | ||||||||
\(813\) | −1.31649 | + | 4.05173i | −0.0461713 | + | 0.142100i | ||||
\(814\) | 11.0239 | + | 33.9281i | 0.386388 | + | 1.18918i | ||||
\(815\) | 2.98547 | + | 9.18833i | 0.104576 | + | 0.321853i | ||||
\(816\) | 4.04310 | − | 2.93749i | 0.141537 | − | 0.102833i | ||||
\(817\) | −1.39296 | + | 4.28709i | −0.0487335 | + | 0.149986i | ||||
\(818\) | −3.66205 | + | 2.66063i | −0.128040 | + | 0.0930268i | ||||
\(819\) | 4.12128 | + | 2.99429i | 0.144009 | + | 0.104629i | ||||
\(820\) | 3.07811 | + | 9.47346i | 0.107492 | + | 0.330828i | ||||
\(821\) | −22.0501 | − | 16.0203i | −0.769552 | − | 0.559112i | 0.132273 | − | 0.991213i | \(-0.457772\pi\) |
−0.901825 | + | 0.432101i | \(0.857772\pi\) | |||||||
\(822\) | −12.8558 | − | 9.34029i | −0.448398 | − | 0.325780i | ||||
\(823\) | 1.71347 | + | 5.27353i | 0.0597280 | + | 0.183824i | 0.976469 | − | 0.215659i | \(-0.0691898\pi\) |
−0.916741 | + | 0.399482i | \(0.869190\pi\) | |||||||
\(824\) | −13.2793 | − | 9.64795i | −0.462605 | − | 0.336102i | ||||
\(825\) | 4.26009 | − | 3.09514i | 0.148317 | − | 0.107759i | ||||
\(826\) | −9.85479 | + | 30.3299i | −0.342892 | + | 1.05531i | ||||
\(827\) | 36.1959 | − | 26.2978i | 1.25865 | − | 0.914465i | 0.259962 | − | 0.965619i | \(-0.416290\pi\) |
0.998691 | + | 0.0511537i | \(0.0162898\pi\) | |||||||
\(828\) | −2.04174 | − | 6.28382i | −0.0709553 | − | 0.218378i | ||||
\(829\) | 0.122146 | + | 0.375927i | 0.00424231 | + | 0.0130565i | 0.953155 | − | 0.302481i | \(-0.0978150\pi\) |
−0.948913 | + | 0.315538i | \(0.897815\pi\) | |||||||
\(830\) | −0.144960 | + | 0.446142i | −0.00503164 | + | 0.0154858i | ||||
\(831\) | 16.8907 | 0.585934 | ||||||||
\(832\) | 1.34464 | 0.0466169 | ||||||||
\(833\) | −11.3553 | + | 34.9480i | −0.393437 | + | 1.21088i | ||||
\(834\) | 5.46466 | + | 3.97031i | 0.189226 | + | 0.137481i | ||||
\(835\) | 3.82856 | − | 2.78161i | 0.132493 | − | 0.0962616i | ||||
\(836\) | 4.34874 | 0.150404 | ||||||||
\(837\) | 2.81956 | + | 4.80105i | 0.0974582 | + | 0.165949i | ||||
\(838\) | −5.57898 | −0.192723 | ||||||||
\(839\) | −32.8788 | + | 23.8878i | −1.13510 | + | 0.824699i | −0.986429 | − | 0.164187i | \(-0.947500\pi\) |
−0.148672 | + | 0.988887i | \(0.547500\pi\) | |||||||
\(840\) | 3.06498 | + | 2.22684i | 0.105752 | + | 0.0768332i | ||||
\(841\) | −3.32472 | + | 10.2324i | −0.114646 | + | 0.352843i | ||||
\(842\) | 14.6822 | 0.505983 | ||||||||
\(843\) | −21.5041 | −0.740641 | ||||||||
\(844\) | −1.01544 | + | 3.12519i | −0.0349527 | + | 0.107573i | ||||
\(845\) | −3.45850 | − | 10.6442i | −0.118976 | − | 0.366171i | ||||
\(846\) | 2.08425 | + | 6.41465i | 0.0716579 | + | 0.220540i | ||||
\(847\) | 51.2718 | − | 37.2511i | 1.76172 | − | 1.27996i | ||||
\(848\) | −1.17898 | + | 3.62853i | −0.0404863 | + | 0.124604i | ||||
\(849\) | −15.1349 | + | 10.9962i | −0.519429 | + | 0.377387i | ||||
\(850\) | 4.04310 | + | 2.93749i | 0.138677 | + | 0.100755i | ||||
\(851\) | 13.8322 | + | 42.5712i | 0.474162 | + | 1.45932i | ||||
\(852\) | −3.66977 | − | 2.66624i | −0.125724 | − | 0.0913439i | ||||
\(853\) | 1.67671 | + | 1.21820i | 0.0574093 | + | 0.0417103i | 0.616120 | − | 0.787652i | \(-0.288704\pi\) |
−0.558711 | + | 0.829363i | \(0.688704\pi\) | |||||||
\(854\) | −8.54963 | − | 26.3131i | −0.292562 | − | 0.900414i | ||||
\(855\) | 0.668127 | + | 0.485423i | 0.0228495 | + | 0.0166011i | ||||
\(856\) | 3.77738 | − | 2.74443i | 0.129108 | − | 0.0938025i | ||||
\(857\) | 12.2504 | − | 37.7027i | 0.418464 | − | 1.28790i | −0.490652 | − | 0.871356i | \(-0.663241\pi\) |
0.909116 | − | 0.416544i | \(-0.136759\pi\) | |||||||
\(858\) | 5.72828 | − | 4.16184i | 0.195560 | − | 0.142083i | ||||
\(859\) | 10.3730 | + | 31.9248i | 0.353922 | + | 1.08926i | 0.956632 | + | 0.291300i | \(0.0940877\pi\) |
−0.602710 | + | 0.797961i | \(0.705912\pi\) | |||||||
\(860\) | 1.68670 | + | 5.19112i | 0.0575159 | + | 0.177016i | ||||
\(861\) | −11.6615 | + | 35.8904i | −0.397423 | + | 1.22314i | ||||
\(862\) | −6.47653 | −0.220591 | ||||||||
\(863\) | 53.2834 | 1.81379 | 0.906894 | − | 0.421359i | \(-0.138447\pi\) | ||||
0.906894 | + | 0.421359i | \(0.138447\pi\) | |||||||
\(864\) | 0.309017 | − | 0.951057i | 0.0105130 | − | 0.0323556i | ||||
\(865\) | 9.45979 | + | 6.87294i | 0.321642 | + | 0.233687i | ||||
\(866\) | 4.68480 | − | 3.40371i | 0.159196 | − | 0.115663i | ||||
\(867\) | 7.97549 | 0.270862 | ||||||||
\(868\) | −20.5996 | + | 4.53847i | −0.699195 | + | 0.154046i | ||||
\(869\) | −35.8175 | −1.21503 | ||||||||
\(870\) | 3.45527 | − | 2.51040i | 0.117145 | − | 0.0851105i | ||||
\(871\) | −3.95083 | − | 2.87044i | −0.133869 | − | 0.0972613i | ||||
\(872\) | −2.04559 | + | 6.29568i | −0.0692725 | + | 0.213199i | ||||
\(873\) | −17.4122 | −0.589313 | ||||||||
\(874\) | 5.45656 | 0.184571 | ||||||||
\(875\) | −1.17072 | + | 3.60310i | −0.0395775 | + | 0.121807i | ||||
\(876\) | −0.630797 | − | 1.94139i | −0.0213127 | − | 0.0655936i | ||||
\(877\) | 9.24825 | + | 28.4632i | 0.312291 | + | 0.961134i | 0.976855 | + | 0.213902i | \(0.0686174\pi\) |
−0.664564 | + | 0.747232i | \(0.731383\pi\) | |||||||
\(878\) | 22.2598 | − | 16.1727i | 0.751233 | − | 0.545803i | ||||
\(879\) | 7.28905 | − | 22.4334i | 0.245854 | − | 0.756660i | ||||
\(880\) | 4.26009 | − | 3.09514i | 0.143608 | − | 0.104337i | ||||
\(881\) | 42.7814 | + | 31.0825i | 1.44134 | + | 1.04720i | 0.987760 | + | 0.155980i | \(0.0498537\pi\) |
0.453581 | + | 0.891215i | \(0.350146\pi\) | |||||||
\(882\) | 2.27217 | + | 6.99302i | 0.0765080 | + | 0.235467i | ||||
\(883\) | −30.6483 | − | 22.2673i | −1.03140 | − | 0.749354i | −0.0628095 | − | 0.998026i | \(-0.520006\pi\) |
−0.968588 | + | 0.248671i | \(0.920006\pi\) | |||||||
\(884\) | 5.43650 | + | 3.94985i | 0.182849 | + | 0.132848i | ||||
\(885\) | 2.60122 | + | 8.00574i | 0.0874392 | + | 0.269110i | ||||
\(886\) | −9.71333 | − | 7.05715i | −0.326326 | − | 0.237090i | ||||
\(887\) | 13.8509 | − | 10.0632i | 0.465067 | − | 0.337891i | −0.330449 | − | 0.943824i | \(-0.607200\pi\) |
0.795516 | + | 0.605933i | \(0.207200\pi\) | |||||||
\(888\) | −2.09351 | + | 6.44315i | −0.0702535 | + | 0.216218i | ||||
\(889\) | −18.3422 | + | 13.3264i | −0.615178 | + | 0.446953i | ||||
\(890\) | 0.991032 | + | 3.05008i | 0.0332195 | + | 0.102239i | ||||
\(891\) | −1.62721 | − | 5.00804i | −0.0545136 | − | 0.167776i | ||||
\(892\) | 6.47602 | − | 19.9311i | 0.216833 | − | 0.667343i | ||||
\(893\) | −5.57017 | −0.186399 | ||||||||
\(894\) | −16.0548 | −0.536953 | ||||||||
\(895\) | 0.278926 | − | 0.858447i | 0.00932347 | − | 0.0286947i | ||||
\(896\) | 3.06498 | + | 2.22684i | 0.102394 | + | 0.0743934i | ||||
\(897\) | 7.18754 | − | 5.22205i | 0.239985 | − | 0.174359i | ||||
\(898\) | 16.5000 | 0.550610 | ||||||||
\(899\) | −2.31023 | + | 23.6671i | −0.0770503 | + | 0.789343i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −15.4255 | + | 11.2073i | −0.513897 | + | 0.373368i | ||||
\(902\) | 42.4347 | + | 30.8306i | 1.41292 | + | 1.02655i | ||||
\(903\) | −6.39009 | + | 19.6667i | −0.212649 | + | 0.654466i | ||||
\(904\) | 4.81670 | 0.160201 | ||||||||
\(905\) | 0.992901 | 0.0330052 | ||||||||
\(906\) | 3.06420 | − | 9.43063i | 0.101801 | − | 0.313312i | ||||
\(907\) | −13.7904 | − | 42.4426i | −0.457904 | − | 1.40928i | −0.867692 | − | 0.497102i | \(-0.834397\pi\) |
0.409788 | − | 0.912181i | \(-0.365603\pi\) | |||||||
\(908\) | 6.24435 | + | 19.2181i | 0.207226 | + | 0.637776i | ||||
\(909\) | 12.9771 | − | 9.42841i | 0.430423 | − | 0.312721i | ||||
\(910\) | −1.57419 | + | 4.84486i | −0.0521839 | + | 0.160606i | ||||
\(911\) | −3.15123 | + | 2.28950i | −0.104405 | + | 0.0758546i | −0.638763 | − | 0.769404i | \(-0.720553\pi\) |
0.534358 | + | 0.845258i | \(0.320553\pi\) | |||||||
\(912\) | 0.668127 | + | 0.485423i | 0.0221239 | + | 0.0160740i | ||||
\(913\) | 0.763326 | + | 2.34928i | 0.0252624 | + | 0.0777497i | ||||
\(914\) | −27.5579 | − | 20.0220i | −0.911533 | − | 0.662268i | ||||
\(915\) | −5.90817 | − | 4.29254i | −0.195318 | − | 0.141907i | ||||
\(916\) | 1.58572 | + | 4.88036i | 0.0523938 | + | 0.161251i | ||||
\(917\) | −51.0923 | − | 37.1207i | −1.68722 | − | 1.22583i | ||||
\(918\) | 4.04310 | − | 2.93749i | 0.133442 | − | 0.0969515i | ||||
\(919\) | 18.2454 | − | 56.1535i | 0.601860 | − | 1.85233i | 0.0847751 | − | 0.996400i | \(-0.472983\pi\) |
0.517085 | − | 0.855934i | \(-0.327017\pi\) | |||||||
\(920\) | 5.34534 | − | 3.88361i | 0.176231 | − | 0.128039i | ||||
\(921\) | 6.40116 | + | 19.7008i | 0.210926 | + | 0.649162i | ||||
\(922\) | −8.42830 | − | 25.9396i | −0.277571 | − | 0.854276i | ||||
\(923\) | 1.88481 | − | 5.80086i | 0.0620394 | − | 0.190938i | ||||
\(924\) | 19.9495 | 0.656289 | ||||||||
\(925\) | −6.77473 | −0.222752 | ||||||||
\(926\) | −10.3732 | + | 31.9255i | −0.340886 | + | 1.04914i | ||||
\(927\) | −13.2793 | − | 9.64795i | −0.436148 | − | 0.316880i | ||||
\(928\) | 3.45527 | − | 2.51040i | 0.113425 | − | 0.0824079i | ||||
\(929\) | −8.65042 | −0.283811 | −0.141906 | − | 0.989880i | \(-0.545323\pi\) | ||||
−0.141906 | + | 0.989880i | \(0.545323\pi\) | |||||||
\(930\) | −3.69478 | + | 4.16517i | −0.121157 | + | 0.136581i | ||||
\(931\) | −6.07240 | −0.199015 | ||||||||
\(932\) | 19.8233 | − | 14.4025i | 0.649333 | − | 0.471768i | ||||
\(933\) | −12.4064 | − | 9.01380i | −0.406169 | − | 0.295099i | ||||
\(934\) | 11.8478 | − | 36.4639i | 0.387673 | − | 1.19314i | ||||
\(935\) | 26.3159 | 0.860622 | ||||||||
\(936\) | 1.34464 | 0.0439508 | ||||||||
\(937\) | −11.5572 | + | 35.5695i | −0.377558 | + | 1.16200i | 0.564179 | + | 0.825653i | \(0.309193\pi\) |
−0.941737 | + | 0.336351i | \(0.890807\pi\) | |||||||
\(938\) | −4.25185 | − | 13.0858i | −0.138828 | − | 0.427268i | ||||
\(939\) | 2.76817 | + | 8.51954i | 0.0903357 | + | 0.278025i | ||||
\(940\) | −5.45663 | + | 3.96447i | −0.177976 | + | 0.129307i | ||||
\(941\) | 16.8956 | − | 51.9992i | 0.550780 | − | 1.69513i | −0.156055 | − | 0.987748i | \(-0.549878\pi\) |
0.706835 | − | 0.707378i | \(-0.250122\pi\) | |||||||
\(942\) | −16.5406 | + | 12.0175i | −0.538923 | + | 0.391551i | ||||
\(943\) | 53.2448 | + | 38.6846i | 1.73389 | + | 1.25975i | ||||
\(944\) | 2.60122 | + | 8.00574i | 0.0846626 | + | 0.260565i | ||||
\(945\) | 3.06498 | + | 2.22684i | 0.0997038 | + | 0.0724390i | ||||
\(946\) | 23.2527 | + | 16.8941i | 0.756011 | + | 0.549274i | ||||
\(947\) | 2.36308 | + | 7.27280i | 0.0767896 | + | 0.236334i | 0.982082 | − | 0.188455i | \(-0.0603481\pi\) |
−0.905292 | + | 0.424790i | \(0.860348\pi\) | |||||||
\(948\) | −5.50291 | − | 3.99809i | −0.178726 | − | 0.129852i | ||||
\(949\) | 2.22060 | − | 1.61336i | 0.0720837 | − | 0.0523719i | ||||
\(950\) | −0.255202 | + | 0.785431i | −0.00827984 | + | 0.0254827i | ||||
\(951\) | −25.6693 | + | 18.6499i | −0.832386 | + | 0.604764i | ||||
\(952\) | 5.85072 | + | 18.0067i | 0.189623 | + | 0.583599i | ||||
\(953\) | 2.86117 | + | 8.80578i | 0.0926824 | + | 0.285247i | 0.986643 | − | 0.162899i | \(-0.0520845\pi\) |
−0.893960 | + | 0.448146i | \(0.852084\pi\) | |||||||
\(954\) | −1.17898 | + | 3.62853i | −0.0381709 | + | 0.117478i | ||||
\(955\) | 20.7711 | 0.672136 | ||||||||
\(956\) | 15.3309 | 0.495836 | ||||||||
\(957\) | 6.94973 | − | 21.3891i | 0.224653 | − | 0.691410i | ||||
\(958\) | 8.87634 | + | 6.44904i | 0.286782 | + | 0.208359i | ||||
\(959\) | 48.7045 | − | 35.3859i | 1.57275 | − | 1.14267i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −3.69721 | − | 30.7787i | −0.119265 | − | 0.992862i | ||||
\(962\) | −9.10955 | −0.293704 | ||||||||
\(963\) | 3.77738 | − | 2.74443i | 0.121724 | − | 0.0884379i | ||||
\(964\) | 9.70122 | + | 7.04835i | 0.312455 | + | 0.227012i | ||||
\(965\) | 8.10942 | − | 24.9582i | 0.261051 | − | 0.803434i | ||||
\(966\) | 25.0315 | 0.805376 | ||||||||
\(967\) | 4.32819 | 0.139185 | 0.0695927 | − | 0.997575i | \(-0.477830\pi\) | ||||
0.0695927 | + | 0.997575i | \(0.477830\pi\) | |||||||
\(968\) | 5.16932 | − | 15.9095i | 0.166148 | − | 0.511352i | ||||
\(969\) | 1.27538 | + | 3.92523i | 0.0409712 | + | 0.126096i | ||||
\(970\) | −5.38066 | − | 16.5600i | −0.172762 | − | 0.531708i | ||||
\(971\) | −41.3441 | + | 30.0383i | −1.32680 | + | 0.963974i | −0.326976 | + | 0.945033i | \(0.606030\pi\) |
−0.999821 | + | 0.0189412i | \(0.993970\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | −20.7030 | + | 15.0416i | −0.663707 | + | 0.482212i | ||||
\(974\) | −11.6234 | − | 8.44492i | −0.372439 | − | 0.270593i | ||||
\(975\) | 0.415516 | + | 1.27883i | 0.0133072 | + | 0.0409552i | ||||
\(976\) | −5.90817 | − | 4.29254i | −0.189116 | − | 0.137401i | ||||
\(977\) | −0.686416 | − | 0.498711i | −0.0219604 | − | 0.0159552i | 0.576751 | − | 0.816920i | \(-0.304320\pi\) |
−0.598711 | + | 0.800965i | \(0.704320\pi\) | |||||||
\(978\) | 2.98547 | + | 9.18833i | 0.0954647 | + | 0.293810i | ||||
\(979\) | 13.6623 | + | 9.92626i | 0.436650 | + | 0.317244i | ||||
\(980\) | −5.94862 | + | 4.32193i | −0.190022 | + | 0.138059i | ||||
\(981\) | −2.04559 | + | 6.29568i | −0.0653107 | + | 0.201006i | ||||
\(982\) | 19.5645 | − | 14.2144i | 0.624328 | − | 0.453601i | ||||
\(983\) | −6.70062 | − | 20.6224i | −0.213717 | − | 0.657752i | −0.999242 | − | 0.0389228i | \(-0.987607\pi\) |
0.785526 | − | 0.618829i | \(-0.212393\pi\) | |||||||
\(984\) | 3.07811 | + | 9.47346i | 0.0981267 | + | 0.302003i | ||||
\(985\) | −1.86113 | + | 5.72798i | −0.0593006 | + | 0.182509i | ||||
\(986\) | 21.3443 | 0.679739 | ||||||||
\(987\) | −25.5527 | −0.813351 | ||||||||
\(988\) | −0.343154 | + | 1.05612i | −0.0109172 | + | 0.0335996i | ||||
\(989\) | 29.1763 | + | 21.1978i | 0.927752 | + | 0.674051i | ||||
\(990\) | 4.26009 | − | 3.09514i | 0.135395 | − | 0.0983700i | ||||
\(991\) | −27.2001 | −0.864041 | −0.432020 | − | 0.901864i | \(-0.642199\pi\) | ||||
−0.432020 | + | 0.901864i | \(0.642199\pi\) | |||||||
\(992\) | −3.69478 | + | 4.16517i | −0.117309 | + | 0.132244i | ||||
\(993\) | 2.41339 | 0.0765867 | ||||||||
\(994\) | 13.9030 | − | 10.1011i | 0.440976 | − | 0.320388i | ||||
\(995\) | 3.39114 | + | 2.46381i | 0.107506 | + | 0.0781080i | ||||
\(996\) | −0.144960 | + | 0.446142i | −0.00459324 | + | 0.0141365i | ||||
\(997\) | 0.429809 | 0.0136122 | 0.00680610 | − | 0.999977i | \(-0.497834\pi\) | ||||
0.00680610 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(998\) | −8.84069 | −0.279847 | ||||||||
\(999\) | −2.09351 | + | 6.44315i | −0.0662356 | + | 0.203852i |
(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.n.g.481.1 | ✓ | 16 | |
31.2 | even | 5 | inner | 930.2.n.g.901.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.g.481.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
930.2.n.g.901.1 | yes | 16 | 31.2 | even | 5 | inner |