Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(184,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.184");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.r (of order \(6\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 214.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.214 |
Dual form | 315.2.r.a.184.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | 0.935414 | + | 0.353553i | \(0.115027\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.23205 | + | 1.86603i | 0.550990 | + | 0.834512i | ||||
\(6\) | −1.50000 | + | 0.866025i | −0.612372 | + | 0.353553i | ||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.86603 | + | 1.23205i | −0.590089 | + | 0.389609i | ||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0.866025 | + | 1.50000i | 0.250000 | + | 0.433013i | ||||
\(13\) | 3.46410 | − | 2.00000i | 0.960769 | − | 0.554700i | 0.0643593 | − | 0.997927i | \(-0.479500\pi\) |
0.896410 | + | 0.443227i | \(0.146166\pi\) | |||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | −1.73205 | + | 3.46410i | −0.447214 | + | 0.894427i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.73205 | − | 1.00000i | −0.420084 | − | 0.242536i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | −2.59808 | − | 1.50000i | −0.612372 | − | 0.353553i | ||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | 1.23205 | + | 1.86603i | 0.275495 | + | 0.417256i | ||||
\(21\) | 4.50000 | + | 0.866025i | 0.981981 | + | 0.188982i | ||||
\(22\) | 5.19615 | − | 3.00000i | 1.10782 | − | 0.639602i | ||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | −4.50000 | + | 2.59808i | −0.918559 | + | 0.530330i | ||||
\(25\) | −1.96410 | + | 4.59808i | −0.392820 | + | 0.919615i | ||||
\(26\) | 2.00000 | + | 3.46410i | 0.392232 | + | 0.679366i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 1.73205 | − | 2.00000i | 0.327327 | − | 0.377964i | ||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | −3.46410 | − | 1.73205i | −0.632456 | − | 0.316228i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 5.00000i | 0.883883i | ||||||||
\(33\) | 5.19615 | − | 9.00000i | 0.904534 | − | 1.56670i | ||||
\(34\) | 1.00000 | − | 1.73205i | 0.171499 | − | 0.297044i | ||||
\(35\) | 5.86603 | + | 0.767949i | 0.991539 | + | 0.129807i | ||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −6.92820 | + | 4.00000i | −1.13899 | + | 0.657596i | −0.946180 | − | 0.323640i | \(-0.895093\pi\) |
−0.192809 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(38\) | 5.19615 | − | 3.00000i | 0.842927 | − | 0.486664i | ||||
\(39\) | 6.00000 | + | 3.46410i | 0.960769 | + | 0.554700i | ||||
\(40\) | −5.59808 | + | 3.69615i | −0.885134 | + | 0.584413i | ||||
\(41\) | −1.00000 | − | 1.73205i | −0.156174 | − | 0.270501i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
−0.933486 | + | 0.358614i | \(0.883249\pi\) | |||||||
\(42\) | −0.866025 | + | 4.50000i | −0.133631 | + | 0.694365i | ||||
\(43\) | 0.866025 | + | 0.500000i | 0.132068 | + | 0.0762493i | 0.564578 | − | 0.825380i | \(-0.309039\pi\) |
−0.432511 | + | 0.901629i | \(0.642372\pi\) | |||||||
\(44\) | −3.00000 | − | 5.19615i | −0.452267 | − | 0.783349i | ||||
\(45\) | −6.69615 | + | 0.401924i | −0.998203 | + | 0.0599153i | ||||
\(46\) | 1.50000 | − | 2.59808i | 0.221163 | − | 0.383065i | ||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | −0.866025 | − | 1.50000i | −0.125000 | − | 0.216506i | ||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | −4.59808 | − | 1.96410i | −0.650266 | − | 0.277766i | ||||
\(51\) | − | 3.46410i | − | 0.485071i | ||||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | 10.3923 | + | 6.00000i | 1.42749 | + | 0.824163i | 0.996922 | − | 0.0783936i | \(-0.0249791\pi\) |
0.430570 | + | 0.902557i | \(0.358312\pi\) | |||||||
\(54\) | − | 5.19615i | − | 0.707107i | ||||||
\(55\) | 6.00000 | − | 12.0000i | 0.809040 | − | 1.61808i | ||||
\(56\) | 6.00000 | + | 5.19615i | 0.801784 | + | 0.694365i | ||||
\(57\) | 5.19615 | − | 9.00000i | 0.688247 | − | 1.19208i | ||||
\(58\) | −1.73205 | − | 1.00000i | −0.227429 | − | 0.131306i | ||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | −1.73205 | + | 3.46410i | −0.223607 | + | 0.447214i | ||||
\(61\) | 7.00000 | 0.896258 | 0.448129 | − | 0.893969i | \(-0.352090\pi\) | ||||
0.448129 | + | 0.893969i | \(0.352090\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 2.59808 | + | 7.50000i | 0.327327 | + | 0.944911i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 8.00000 | + | 4.00000i | 0.992278 | + | 0.496139i | ||||
\(66\) | 9.00000 | + | 5.19615i | 1.10782 | + | 0.639602i | ||||
\(67\) | 7.00000i | 0.855186i | 0.903971 | + | 0.427593i | \(0.140638\pi\) | ||||
−0.903971 | + | 0.427593i | \(0.859362\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | − | 5.19615i | − | 0.625543i | ||||||
\(70\) | −0.767949 | + | 5.86603i | −0.0917875 | + | 0.701124i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | −7.79423 | − | 4.50000i | −0.918559 | − | 0.530330i | ||||
\(73\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | −8.59808 | + | 1.03590i | −0.992820 | + | 0.119615i | ||||
\(76\) | −3.00000 | − | 5.19615i | −0.344124 | − | 0.596040i | ||||
\(77\) | −15.5885 | − | 3.00000i | −1.77647 | − | 0.341882i | ||||
\(78\) | −3.46410 | + | 6.00000i | −0.392232 | + | 0.679366i | ||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | −1.23205 | − | 1.86603i | −0.137747 | − | 0.208628i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 1.73205 | − | 1.00000i | 0.191273 | − | 0.110432i | ||||
\(83\) | 3.46410 | + | 2.00000i | 0.380235 | + | 0.219529i | 0.677920 | − | 0.735135i | \(-0.262881\pi\) |
−0.297686 | + | 0.954664i | \(0.596215\pi\) | |||||||
\(84\) | 4.50000 | + | 0.866025i | 0.490990 | + | 0.0944911i | ||||
\(85\) | −0.267949 | − | 4.46410i | −0.0290632 | − | 0.484200i | ||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | −3.46410 | −0.371391 | ||||||||
\(88\) | 15.5885 | − | 9.00000i | 1.66174 | − | 0.959403i | ||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | −0.401924 | − | 6.69615i | −0.0423665 | − | 0.705836i | ||||
\(91\) | 2.00000 | − | 10.3923i | 0.209657 | − | 1.08941i | ||||
\(92\) | −2.59808 | − | 1.50000i | −0.270868 | − | 0.156386i | ||||
\(93\) | −3.46410 | − | 6.00000i | −0.359211 | − | 0.622171i | ||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | 6.00000 | − | 12.0000i | 0.615587 | − | 1.23117i | ||||
\(96\) | −7.50000 | + | 4.33013i | −0.765466 | + | 0.441942i | ||||
\(97\) | −1.73205 | − | 1.00000i | −0.175863 | − | 0.101535i | 0.409484 | − | 0.912317i | \(-0.365709\pi\) |
−0.585348 | + | 0.810782i | \(0.699042\pi\) | |||||||
\(98\) | 6.92820 | − | 1.00000i | 0.699854 | − | 0.101015i | ||||
\(99\) | 18.0000 | 1.80907 | ||||||||
\(100\) | −1.96410 | + | 4.59808i | −0.196410 | + | 0.459808i | ||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 3.46410 | 0.342997 | ||||||||
\(103\) | 0.866025 | + | 0.500000i | 0.0853320 | + | 0.0492665i | 0.542059 | − | 0.840341i | \(-0.317645\pi\) |
−0.456727 | + | 0.889607i | \(0.650978\pi\) | |||||||
\(104\) | 6.00000 | + | 10.3923i | 0.588348 | + | 1.01905i | ||||
\(105\) | 3.92820 | + | 9.46410i | 0.383353 | + | 0.923602i | ||||
\(106\) | −6.00000 | + | 10.3923i | −0.582772 | + | 1.00939i | ||||
\(107\) | −3.46410 | + | 2.00000i | −0.334887 | + | 0.193347i | −0.658009 | − | 0.753010i | \(-0.728601\pi\) |
0.323122 | + | 0.946357i | \(0.395268\pi\) | |||||||
\(108\) | −5.19615 | −0.500000 | ||||||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 12.0000 | + | 6.00000i | 1.14416 | + | 0.572078i | ||||
\(111\) | −12.0000 | − | 6.92820i | −1.13899 | − | 0.657596i | ||||
\(112\) | −1.73205 | + | 2.00000i | −0.163663 | + | 0.188982i | ||||
\(113\) | 15.5885 | − | 9.00000i | 1.46644 | − | 0.846649i | 0.467143 | − | 0.884182i | \(-0.345283\pi\) |
0.999295 | + | 0.0375328i | \(0.0119499\pi\) | |||||||
\(114\) | 9.00000 | + | 5.19615i | 0.842927 | + | 0.486664i | ||||
\(115\) | −0.401924 | − | 6.69615i | −0.0374796 | − | 0.624419i | ||||
\(116\) | −1.00000 | + | 1.73205i | −0.0928477 | + | 0.160817i | ||||
\(117\) | 12.0000i | 1.10940i | ||||||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | −5.00000 | + | 1.73205i | −0.458349 | + | 0.158777i | ||||
\(120\) | −10.3923 | − | 5.19615i | −0.948683 | − | 0.474342i | ||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 7.00000i | 0.633750i | ||||||||
\(123\) | 1.73205 | − | 3.00000i | 0.156174 | − | 0.270501i | ||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | −7.50000 | + | 2.59808i | −0.668153 | + | 0.231455i | ||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | 3.00000i | 0.265165i | ||||||||
\(129\) | 1.73205i | 0.152499i | ||||||||
\(130\) | −4.00000 | + | 8.00000i | −0.350823 | + | 0.701646i | ||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 5.19615 | − | 9.00000i | 0.452267 | − | 0.783349i | ||||
\(133\) | −15.5885 | − | 3.00000i | −1.35169 | − | 0.260133i | ||||
\(134\) | −7.00000 | −0.604708 | ||||||||
\(135\) | −6.40192 | − | 9.69615i | −0.550990 | − | 0.834512i | ||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | −5.19615 | + | 3.00000i | −0.443937 | + | 0.256307i | −0.705266 | − | 0.708942i | \(-0.749173\pi\) |
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(138\) | 5.19615 | 0.442326 | ||||||||
\(139\) | 1.00000 | + | 1.73205i | 0.0848189 | + | 0.146911i | 0.905314 | − | 0.424743i | \(-0.139635\pi\) |
−0.820495 | + | 0.571654i | \(0.806302\pi\) | |||||||
\(140\) | 5.86603 | + | 0.767949i | 0.495770 | + | 0.0649036i | ||||
\(141\) | −4.50000 | + | 2.59808i | −0.378968 | + | 0.218797i | ||||
\(142\) | 4.00000i | 0.335673i | ||||||||
\(143\) | −20.7846 | − | 12.0000i | −1.73810 | − | 1.00349i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | −4.46410 | + | 0.267949i | −0.370723 | + | 0.0222520i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.52628 | − | 7.50000i | 0.785714 | − | 0.618590i | ||||
\(148\) | −6.92820 | + | 4.00000i | −0.569495 | + | 0.328798i | ||||
\(149\) | −11.5000 | + | 19.9186i | −0.942117 | + | 1.63179i | −0.180693 | + | 0.983540i | \(0.557834\pi\) |
−0.761424 | + | 0.648254i | \(0.775499\pi\) | |||||||
\(150\) | −1.03590 | − | 8.59808i | −0.0845807 | − | 0.702030i | ||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 15.5885 | − | 9.00000i | 1.26439 | − | 0.729996i | ||||
\(153\) | 5.19615 | − | 3.00000i | 0.420084 | − | 0.242536i | ||||
\(154\) | 3.00000 | − | 15.5885i | 0.241747 | − | 1.25615i | ||||
\(155\) | −4.92820 | − | 7.46410i | −0.395843 | − | 0.599531i | ||||
\(156\) | 6.00000 | + | 3.46410i | 0.480384 | + | 0.277350i | ||||
\(157\) | 12.0000i | 0.957704i | 0.877896 | + | 0.478852i | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 14.0000i | 1.11378i | ||||||||
\(159\) | 20.7846i | 1.64833i | ||||||||
\(160\) | −9.33013 | + | 6.16025i | −0.737611 | + | 0.487011i | ||||
\(161\) | −7.50000 | + | 2.59808i | −0.591083 | + | 0.204757i | ||||
\(162\) | 7.79423 | − | 4.50000i | 0.612372 | − | 0.353553i | ||||
\(163\) | 3.46410 | − | 2.00000i | 0.271329 | − | 0.156652i | −0.358162 | − | 0.933659i | \(-0.616597\pi\) |
0.629492 | + | 0.777007i | \(0.283263\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | 23.1962 | − | 1.39230i | 1.80582 | − | 0.108391i | ||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | −2.59808 | + | 1.50000i | −0.201045 | + | 0.116073i | −0.597143 | − | 0.802135i | \(-0.703697\pi\) |
0.396098 | + | 0.918208i | \(0.370364\pi\) | |||||||
\(168\) | −2.59808 | + | 13.5000i | −0.200446 | + | 1.04155i | ||||
\(169\) | 1.50000 | − | 2.59808i | 0.115385 | − | 0.199852i | ||||
\(170\) | 4.46410 | − | 0.267949i | 0.342381 | − | 0.0205508i | ||||
\(171\) | 18.0000 | 1.37649 | ||||||||
\(172\) | 0.866025 | + | 0.500000i | 0.0660338 | + | 0.0381246i | ||||
\(173\) | − | 18.0000i | − | 1.36851i | −0.729241 | − | 0.684257i | \(-0.760127\pi\) | ||
0.729241 | − | 0.684257i | \(-0.239873\pi\) | |||||||
\(174\) | − | 3.46410i | − | 0.262613i | ||||||
\(175\) | 5.79423 | + | 11.8923i | 0.438003 | + | 0.898974i | ||||
\(176\) | 3.00000 | + | 5.19615i | 0.226134 | + | 0.391675i | ||||
\(177\) | −3.46410 | − | 6.00000i | −0.260378 | − | 0.450988i | ||||
\(178\) | 2.59808 | − | 1.50000i | 0.194734 | − | 0.112430i | ||||
\(179\) | −1.00000 | + | 1.73205i | −0.0747435 | + | 0.129460i | −0.900975 | − | 0.433872i | \(-0.857147\pi\) |
0.826231 | + | 0.563331i | \(0.190480\pi\) | |||||||
\(180\) | −6.69615 | + | 0.401924i | −0.499102 | + | 0.0299576i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 10.3923 | + | 2.00000i | 0.770329 | + | 0.148250i | ||||
\(183\) | 6.06218 | + | 10.5000i | 0.448129 | + | 0.776182i | ||||
\(184\) | 4.50000 | − | 7.79423i | 0.331744 | − | 0.574598i | ||||
\(185\) | −16.0000 | − | 8.00000i | −1.17634 | − | 0.588172i | ||||
\(186\) | 6.00000 | − | 3.46410i | 0.439941 | − | 0.254000i | ||||
\(187\) | 12.0000i | 0.877527i | ||||||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 12.0000 | + | 6.00000i | 0.870572 | + | 0.435286i | ||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | −6.06218 | − | 10.5000i | −0.437500 | − | 0.757772i | ||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | 0.928203 | + | 15.4641i | 0.0664700 | + | 1.10741i | ||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | − | 14.0000i | − | 0.997459i | −0.866758 | − | 0.498729i | \(-0.833800\pi\) | ||
0.866758 | − | 0.498729i | \(-0.166200\pi\) | |||||||
\(198\) | 18.0000i | 1.27920i | ||||||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | −13.7942 | − | 5.89230i | −0.975399 | − | 0.416649i | ||||
\(201\) | −10.5000 | + | 6.06218i | −0.740613 | + | 0.427593i | ||||
\(202\) | −2.59808 | + | 1.50000i | −0.182800 | + | 0.105540i | ||||
\(203\) | 1.73205 | + | 5.00000i | 0.121566 | + | 0.350931i | ||||
\(204\) | − | 3.46410i | − | 0.242536i | ||||||
\(205\) | 2.00000 | − | 4.00000i | 0.139686 | − | 0.279372i | ||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 7.79423 | − | 4.50000i | 0.541736 | − | 0.312772i | ||||
\(208\) | −3.46410 | + | 2.00000i | −0.240192 | + | 0.138675i | ||||
\(209\) | −18.0000 | + | 31.1769i | −1.24509 | + | 2.15655i | ||||
\(210\) | −9.46410 | + | 3.92820i | −0.653085 | + | 0.271072i | ||||
\(211\) | −1.00000 | − | 1.73205i | −0.0688428 | − | 0.119239i | 0.829549 | − | 0.558433i | \(-0.188597\pi\) |
−0.898392 | + | 0.439194i | \(0.855264\pi\) | |||||||
\(212\) | 10.3923 | + | 6.00000i | 0.713746 | + | 0.412082i | ||||
\(213\) | 3.46410 | + | 6.00000i | 0.237356 | + | 0.411113i | ||||
\(214\) | −2.00000 | − | 3.46410i | −0.136717 | − | 0.236801i | ||||
\(215\) | 0.133975 | + | 2.23205i | 0.00913699 | + | 0.152225i | ||||
\(216\) | − | 15.5885i | − | 1.06066i | ||||||
\(217\) | −6.92820 | + | 8.00000i | −0.470317 | + | 0.543075i | ||||
\(218\) | −8.66025 | − | 5.00000i | −0.586546 | − | 0.338643i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.00000 | − | 12.0000i | 0.404520 | − | 0.809040i | ||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 6.92820 | − | 12.0000i | 0.464991 | − | 0.805387i | ||||
\(223\) | −2.59808 | − | 1.50000i | −0.173980 | − | 0.100447i | 0.410481 | − | 0.911869i | \(-0.365361\pi\) |
−0.584461 | + | 0.811422i | \(0.698694\pi\) | |||||||
\(224\) | 10.0000 | + | 8.66025i | 0.668153 | + | 0.578638i | ||||
\(225\) | −9.00000 | − | 12.0000i | −0.600000 | − | 0.800000i | ||||
\(226\) | 9.00000 | + | 15.5885i | 0.598671 | + | 1.03693i | ||||
\(227\) | 3.46410 | − | 2.00000i | 0.229920 | − | 0.132745i | −0.380615 | − | 0.924734i | \(-0.624288\pi\) |
0.610535 | + | 0.791989i | \(0.290954\pi\) | |||||||
\(228\) | 5.19615 | − | 9.00000i | 0.344124 | − | 0.596040i | ||||
\(229\) | 11.5000 | − | 19.9186i | 0.759941 | − | 1.31626i | −0.182939 | − | 0.983124i | \(-0.558561\pi\) |
0.942880 | − | 0.333133i | \(-0.108106\pi\) | |||||||
\(230\) | 6.69615 | − | 0.401924i | 0.441531 | − | 0.0265021i | ||||
\(231\) | −9.00000 | − | 25.9808i | −0.592157 | − | 1.70941i | ||||
\(232\) | −5.19615 | − | 3.00000i | −0.341144 | − | 0.196960i | ||||
\(233\) | −12.1244 | + | 7.00000i | −0.794293 | + | 0.458585i | −0.841472 | − | 0.540301i | \(-0.818310\pi\) |
0.0471787 | + | 0.998886i | \(0.484977\pi\) | |||||||
\(234\) | −12.0000 | −0.784465 | ||||||||
\(235\) | −5.59808 | + | 3.69615i | −0.365178 | + | 0.241110i | ||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 12.1244 | + | 21.0000i | 0.787562 | + | 1.36410i | ||||
\(238\) | −1.73205 | − | 5.00000i | −0.112272 | − | 0.324102i | ||||
\(239\) | −12.0000 | − | 20.7846i | −0.776215 | − | 1.34444i | −0.934109 | − | 0.356988i | \(-0.883804\pi\) |
0.157893 | − | 0.987456i | \(-0.449530\pi\) | |||||||
\(240\) | 1.73205 | − | 3.46410i | 0.111803 | − | 0.223607i | ||||
\(241\) | 11.5000 | + | 19.9186i | 0.740780 | + | 1.28307i | 0.952141 | + | 0.305661i | \(0.0988773\pi\) |
−0.211360 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(242\) | −21.6506 | − | 12.5000i | −1.39176 | − | 0.803530i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 7.00000 | 0.448129 | ||||||||
\(245\) | 11.6962 | − | 10.4019i | 0.747240 | − | 0.664555i | ||||
\(246\) | 3.00000 | + | 1.73205i | 0.191273 | + | 0.110432i | ||||
\(247\) | −20.7846 | − | 12.0000i | −1.32249 | − | 0.763542i | ||||
\(248\) | − | 12.0000i | − | 0.762001i | ||||||
\(249\) | 6.92820i | 0.439057i | ||||||||
\(250\) | −2.00000 | − | 11.0000i | −0.126491 | − | 0.695701i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 2.59808 | + | 7.50000i | 0.163663 | + | 0.472456i | ||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | −7.00000 | −0.439219 | ||||||||
\(255\) | 6.46410 | − | 4.26795i | 0.404798 | − | 0.267269i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −6.92820 | − | 4.00000i | −0.432169 | − | 0.249513i | 0.268101 | − | 0.963391i | \(-0.413604\pi\) |
−0.700270 | + | 0.713878i | \(0.746937\pi\) | |||||||
\(258\) | −1.73205 | −0.107833 | ||||||||
\(259\) | −4.00000 | + | 20.7846i | −0.248548 | + | 1.29149i | ||||
\(260\) | 8.00000 | + | 4.00000i | 0.496139 | + | 0.248069i | ||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 12.1244 | + | 7.00000i | 0.749045 | + | 0.432461i | ||||
\(263\) | −18.1865 | + | 10.5000i | −1.12143 | + | 0.647458i | −0.941766 | − | 0.336270i | \(-0.890834\pi\) |
−0.179664 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(264\) | 27.0000 | + | 15.5885i | 1.66174 | + | 0.959403i | ||||
\(265\) | 1.60770 | + | 26.7846i | 0.0987599 | + | 1.64537i | ||||
\(266\) | 3.00000 | − | 15.5885i | 0.183942 | − | 0.955790i | ||||
\(267\) | 2.59808 | − | 4.50000i | 0.159000 | − | 0.275396i | ||||
\(268\) | 7.00000i | 0.427593i | ||||||||
\(269\) | 6.50000 | − | 11.2583i | 0.396312 | − | 0.686433i | −0.596956 | − | 0.802274i | \(-0.703623\pi\) |
0.993268 | + | 0.115842i | \(0.0369565\pi\) | |||||||
\(270\) | 9.69615 | − | 6.40192i | 0.590089 | − | 0.389609i | ||||
\(271\) | −14.0000 | − | 24.2487i | −0.850439 | − | 1.47300i | −0.880812 | − | 0.473466i | \(-0.843003\pi\) |
0.0303728 | − | 0.999539i | \(-0.490331\pi\) | |||||||
\(272\) | 1.73205 | + | 1.00000i | 0.105021 | + | 0.0606339i | ||||
\(273\) | 17.3205 | − | 6.00000i | 1.04828 | − | 0.363137i | ||||
\(274\) | −3.00000 | − | 5.19615i | −0.181237 | − | 0.313911i | ||||
\(275\) | 29.7846 | − | 3.58846i | 1.79608 | − | 0.216392i | ||||
\(276\) | − | 5.19615i | − | 0.312772i | ||||||
\(277\) | 19.0526 | − | 11.0000i | 1.14476 | − | 0.660926i | 0.197153 | − | 0.980373i | \(-0.436830\pi\) |
0.947604 | + | 0.319447i | \(0.103497\pi\) | |||||||
\(278\) | −1.73205 | + | 1.00000i | −0.103882 | + | 0.0599760i | ||||
\(279\) | 6.00000 | − | 10.3923i | 0.359211 | − | 0.622171i | ||||
\(280\) | −2.30385 | + | 17.5981i | −0.137681 | + | 1.05169i | ||||
\(281\) | 11.5000 | − | 19.9186i | 0.686032 | − | 1.18824i | −0.287079 | − | 0.957907i | \(-0.592684\pi\) |
0.973111 | − | 0.230336i | \(-0.0739826\pi\) | |||||||
\(282\) | −2.59808 | − | 4.50000i | −0.154713 | − | 0.267971i | ||||
\(283\) | 11.0000i | 0.653882i | 0.945045 | + | 0.326941i | \(0.106018\pi\) | ||||
−0.945045 | + | 0.326941i | \(0.893982\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 23.1962 | − | 1.39230i | 1.37402 | − | 0.0824730i | ||||
\(286\) | 12.0000 | − | 20.7846i | 0.709575 | − | 1.22902i | ||||
\(287\) | −5.19615 | − | 1.00000i | −0.306719 | − | 0.0590281i | ||||
\(288\) | −12.9904 | − | 7.50000i | −0.765466 | − | 0.441942i | ||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | −0.267949 | − | 4.46410i | −0.0157345 | − | 0.262141i | ||||
\(291\) | − | 3.46410i | − | 0.203069i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923 | − | 6.00000i | 0.607125 | − | 0.350524i | −0.164714 | − | 0.986341i | \(-0.552670\pi\) |
0.771839 | + | 0.635818i | \(0.219337\pi\) | |||||||
\(294\) | 7.50000 | + | 9.52628i | 0.437409 | + | 0.555584i | ||||
\(295\) | −4.92820 | − | 7.46410i | −0.286931 | − | 0.434577i | ||||
\(296\) | −12.0000 | − | 20.7846i | −0.697486 | − | 1.20808i | ||||
\(297\) | 15.5885 | + | 27.0000i | 0.904534 | + | 1.56670i | ||||
\(298\) | −19.9186 | − | 11.5000i | −1.15385 | − | 0.666177i | ||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | −8.59808 | + | 1.03590i | −0.496410 | + | 0.0598076i | ||||
\(301\) | 2.50000 | − | 0.866025i | 0.144098 | − | 0.0499169i | ||||
\(302\) | −13.8564 | + | 8.00000i | −0.797347 | + | 0.460348i | ||||
\(303\) | −2.59808 | + | 4.50000i | −0.149256 | + | 0.258518i | ||||
\(304\) | 3.00000 | + | 5.19615i | 0.172062 | + | 0.298020i | ||||
\(305\) | 8.62436 | + | 13.0622i | 0.493829 | + | 0.747938i | ||||
\(306\) | 3.00000 | + | 5.19615i | 0.171499 | + | 0.297044i | ||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | −15.5885 | − | 3.00000i | −0.888235 | − | 0.170941i | ||||
\(309\) | 1.73205i | 0.0985329i | ||||||||
\(310\) | 7.46410 | − | 4.92820i | 0.423932 | − | 0.279903i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | −10.3923 | + | 18.0000i | −0.588348 | + | 1.01905i | ||||
\(313\) | 18.0000i | 1.01742i | 0.860938 | + | 0.508710i | \(0.169877\pi\) | ||||
−0.860938 | + | 0.508710i | \(0.830123\pi\) | |||||||
\(314\) | −12.0000 | −0.677199 | ||||||||
\(315\) | −10.7942 | + | 14.0885i | −0.608186 | + | 0.793795i | ||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −20.7846 | −1.16554 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | −8.62436 | − | 13.0622i | −0.482116 | − | 0.730198i | ||||
\(321\) | −6.00000 | − | 3.46410i | −0.334887 | − | 0.193347i | ||||
\(322\) | −2.59808 | − | 7.50000i | −0.144785 | − | 0.417959i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 2.39230 | + | 19.8564i | 0.132701 | + | 1.10144i | ||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −17.3205 | −0.957826 | ||||||||
\(328\) | 5.19615 | − | 3.00000i | 0.286910 | − | 0.165647i | ||||
\(329\) | 6.00000 | + | 5.19615i | 0.330791 | + | 0.286473i | ||||
\(330\) | 1.39230 | + | 23.1962i | 0.0766439 | + | 1.27691i | ||||
\(331\) | −6.00000 | −0.329790 | −0.164895 | − | 0.986311i | \(-0.552728\pi\) | ||||
−0.164895 | + | 0.986311i | \(0.552728\pi\) | |||||||
\(332\) | 3.46410 | + | 2.00000i | 0.190117 | + | 0.109764i | ||||
\(333\) | − | 24.0000i | − | 1.31519i | ||||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | −13.0622 | + | 8.62436i | −0.713663 | + | 0.471199i | ||||
\(336\) | −4.50000 | − | 0.866025i | −0.245495 | − | 0.0472456i | ||||
\(337\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(338\) | 2.59808 | + | 1.50000i | 0.141317 | + | 0.0815892i | ||||
\(339\) | 27.0000 | + | 15.5885i | 1.46644 | + | 0.846649i | ||||
\(340\) | −0.267949 | − | 4.46410i | −0.0145316 | − | 0.242100i | ||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 18.0000i | 0.973329i | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | −1.50000 | + | 2.59808i | −0.0808746 | + | 0.140079i | ||||
\(345\) | 9.69615 | − | 6.40192i | 0.522023 | − | 0.344668i | ||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | − | 3.00000i | − | 0.161048i | −0.996753 | − | 0.0805242i | \(-0.974341\pi\) | ||
0.996753 | − | 0.0805242i | \(-0.0256594\pi\) | |||||||
\(348\) | −3.46410 | −0.185695 | ||||||||
\(349\) | 15.5000 | − | 26.8468i | 0.829696 | − | 1.43708i | −0.0685808 | − | 0.997646i | \(-0.521847\pi\) |
0.898277 | − | 0.439430i | \(-0.144820\pi\) | |||||||
\(350\) | −11.8923 | + | 5.79423i | −0.635670 | + | 0.309715i | ||||
\(351\) | −18.0000 | + | 10.3923i | −0.960769 | + | 0.554700i | ||||
\(352\) | 25.9808 | − | 15.0000i | 1.38478 | − | 0.799503i | ||||
\(353\) | −8.66025 | + | 5.00000i | −0.460939 | + | 0.266123i | −0.712439 | − | 0.701734i | \(-0.752409\pi\) |
0.251500 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(354\) | 6.00000 | − | 3.46410i | 0.318896 | − | 0.184115i | ||||
\(355\) | 4.92820 | + | 7.46410i | 0.261562 | + | 0.396153i | ||||
\(356\) | −1.50000 | − | 2.59808i | −0.0794998 | − | 0.137698i | ||||
\(357\) | −6.92820 | − | 6.00000i | −0.366679 | − | 0.317554i | ||||
\(358\) | −1.73205 | − | 1.00000i | −0.0915417 | − | 0.0528516i | ||||
\(359\) | −1.00000 | − | 1.73205i | −0.0527780 | − | 0.0914141i | 0.838429 | − | 0.545010i | \(-0.183474\pi\) |
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(360\) | −1.20577 | − | 20.0885i | −0.0635497 | − | 1.05875i | ||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 6.00000i | 0.315353i | ||||||||
\(363\) | −43.3013 | −2.27273 | ||||||||
\(364\) | 2.00000 | − | 10.3923i | 0.104828 | − | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5000 | + | 6.06218i | −0.548844 | + | 0.316875i | ||||
\(367\) | −2.59808 | + | 1.50000i | −0.135618 | + | 0.0782994i | −0.566274 | − | 0.824217i | \(-0.691616\pi\) |
0.430656 | + | 0.902516i | \(0.358282\pi\) | |||||||
\(368\) | 2.59808 | + | 1.50000i | 0.135434 | + | 0.0781929i | ||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 8.00000 | − | 16.0000i | 0.415900 | − | 0.831800i | ||||
\(371\) | 30.0000 | − | 10.3923i | 1.55752 | − | 0.539542i | ||||
\(372\) | −3.46410 | − | 6.00000i | −0.179605 | − | 0.311086i | ||||
\(373\) | 20.7846 | + | 12.0000i | 1.07619 | + | 0.621336i | 0.929865 | − | 0.367901i | \(-0.119923\pi\) |
0.146321 | + | 0.989237i | \(0.453257\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | −12.5263 | − | 14.7679i | −0.646854 | − | 0.762614i | ||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 8.00000i | 0.412021i | ||||||||
\(378\) | −10.3923 | − | 9.00000i | −0.534522 | − | 0.462910i | ||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 6.00000 | − | 12.0000i | 0.307794 | − | 0.615587i | ||||
\(381\) | −10.5000 | + | 6.06218i | −0.537931 | + | 0.310575i | ||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | −0.866025 | − | 0.500000i | −0.0442518 | − | 0.0255488i | 0.477711 | − | 0.878517i | \(-0.341467\pi\) |
−0.521963 | + | 0.852968i | \(0.674800\pi\) | |||||||
\(384\) | −4.50000 | + | 2.59808i | −0.229640 | + | 0.132583i | ||||
\(385\) | −13.6077 | − | 32.7846i | −0.693512 | − | 1.67086i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | −2.59808 | + | 1.50000i | −0.132068 | + | 0.0762493i | ||||
\(388\) | −1.73205 | − | 1.00000i | −0.0879316 | − | 0.0507673i | ||||
\(389\) | −9.50000 | − | 16.4545i | −0.481669 | − | 0.834275i | 0.518110 | − | 0.855314i | \(-0.326636\pi\) |
−0.999779 | + | 0.0210389i | \(0.993303\pi\) | |||||||
\(390\) | −15.4641 | + | 0.928203i | −0.783055 | + | 0.0470014i | ||||
\(391\) | 3.00000 | + | 5.19615i | 0.151717 | + | 0.262781i | ||||
\(392\) | 20.7846 | − | 3.00000i | 1.04978 | − | 0.151523i | ||||
\(393\) | 24.2487 | 1.22319 | ||||||||
\(394\) | 14.0000 | 0.705310 | ||||||||
\(395\) | 17.2487 | + | 26.1244i | 0.867877 | + | 1.31446i | ||||
\(396\) | 18.0000 | 0.904534 | ||||||||
\(397\) | −8.66025 | + | 5.00000i | −0.434646 | + | 0.250943i | −0.701324 | − | 0.712843i | \(-0.747407\pi\) |
0.266678 | + | 0.963786i | \(0.414074\pi\) | |||||||
\(398\) | 12.1244 | + | 7.00000i | 0.607739 | + | 0.350878i | ||||
\(399\) | −9.00000 | − | 25.9808i | −0.450564 | − | 1.30066i | ||||
\(400\) | 1.96410 | − | 4.59808i | 0.0982051 | − | 0.229904i | ||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | −6.06218 | − | 10.5000i | −0.302354 | − | 0.523692i | ||||
\(403\) | −13.8564 | + | 8.00000i | −0.690237 | + | 0.398508i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 9.00000 | − | 18.0000i | 0.447214 | − | 0.894427i | ||||
\(406\) | −5.00000 | + | 1.73205i | −0.248146 | + | 0.0859602i | ||||
\(407\) | 41.5692 | + | 24.0000i | 2.06051 | + | 1.18964i | ||||
\(408\) | 10.3923 | 0.514496 | ||||||||
\(409\) | −35.0000 | −1.73064 | −0.865319 | − | 0.501221i | \(-0.832884\pi\) | ||||
−0.865319 | + | 0.501221i | \(0.832884\pi\) | |||||||
\(410\) | 4.00000 | + | 2.00000i | 0.197546 | + | 0.0987730i | ||||
\(411\) | −9.00000 | − | 5.19615i | −0.443937 | − | 0.256307i | ||||
\(412\) | 0.866025 | + | 0.500000i | 0.0426660 | + | 0.0246332i | ||||
\(413\) | −6.92820 | + | 8.00000i | −0.340915 | + | 0.393654i | ||||
\(414\) | 4.50000 | + | 7.79423i | 0.221163 | + | 0.383065i | ||||
\(415\) | 0.535898 | + | 8.92820i | 0.0263062 | + | 0.438268i | ||||
\(416\) | 10.0000 | + | 17.3205i | 0.490290 | + | 0.849208i | ||||
\(417\) | −1.73205 | + | 3.00000i | −0.0848189 | + | 0.146911i | ||||
\(418\) | −31.1769 | − | 18.0000i | −1.52491 | − | 0.880409i | ||||
\(419\) | 9.00000 | + | 15.5885i | 0.439679 | + | 0.761546i | 0.997665 | − | 0.0683046i | \(-0.0217590\pi\) |
−0.557986 | + | 0.829851i | \(0.688426\pi\) | |||||||
\(420\) | 3.92820 | + | 9.46410i | 0.191677 | + | 0.461801i | ||||
\(421\) | −1.50000 | + | 2.59808i | −0.0731055 | + | 0.126622i | −0.900261 | − | 0.435351i | \(-0.856624\pi\) |
0.827155 | + | 0.561973i | \(0.189958\pi\) | |||||||
\(422\) | 1.73205 | − | 1.00000i | 0.0843149 | − | 0.0486792i | ||||
\(423\) | −7.79423 | − | 4.50000i | −0.378968 | − | 0.218797i | ||||
\(424\) | −18.0000 | + | 31.1769i | −0.874157 | + | 1.51408i | ||||
\(425\) | 8.00000 | − | 6.00000i | 0.388057 | − | 0.291043i | ||||
\(426\) | −6.00000 | + | 3.46410i | −0.290701 | + | 0.167836i | ||||
\(427\) | 12.1244 | − | 14.0000i | 0.586739 | − | 0.677507i | ||||
\(428\) | −3.46410 | + | 2.00000i | −0.167444 | + | 0.0966736i | ||||
\(429\) | − | 41.5692i | − | 2.00698i | ||||||
\(430\) | −2.23205 | + | 0.133975i | −0.107639 | + | 0.00646083i | ||||
\(431\) | 1.00000 | − | 1.73205i | 0.0481683 | − | 0.0834300i | −0.840936 | − | 0.541135i | \(-0.817995\pi\) |
0.889104 | + | 0.457705i | \(0.151328\pi\) | |||||||
\(432\) | 5.19615 | 0.250000 | ||||||||
\(433\) | 32.0000i | 1.53782i | 0.639356 | + | 0.768911i | \(0.279201\pi\) | ||||
−0.639356 | + | 0.768911i | \(0.720799\pi\) | |||||||
\(434\) | −8.00000 | − | 6.92820i | −0.384012 | − | 0.332564i | ||||
\(435\) | −4.26795 | − | 6.46410i | −0.204633 | − | 0.309930i | ||||
\(436\) | −5.00000 | + | 8.66025i | −0.239457 | + | 0.414751i | ||||
\(437\) | 18.0000i | 0.861057i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.0000 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(440\) | 36.0000 | + | 18.0000i | 1.71623 | + | 0.858116i | ||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | − | 8.00000i | − | 0.380521i | ||||||
\(443\) | − | 4.00000i | − | 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | −12.0000 | − | 6.92820i | −0.569495 | − | 0.328798i | ||||
\(445\) | 3.00000 | − | 6.00000i | 0.142214 | − | 0.284427i | ||||
\(446\) | 1.50000 | − | 2.59808i | 0.0710271 | − | 0.123022i | ||||
\(447\) | −39.8372 | −1.88423 | ||||||||
\(448\) | −12.1244 | + | 14.0000i | −0.572822 | + | 0.661438i | ||||
\(449\) | 5.00000 | 0.235965 | 0.117982 | − | 0.993016i | \(-0.462357\pi\) | ||||
0.117982 | + | 0.993016i | \(0.462357\pi\) | |||||||
\(450\) | 12.0000 | − | 9.00000i | 0.565685 | − | 0.424264i | ||||
\(451\) | −6.00000 | + | 10.3923i | −0.282529 | + | 0.489355i | ||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | −13.8564 | + | 24.0000i | −0.651031 | + | 1.12762i | ||||
\(454\) | 2.00000 | + | 3.46410i | 0.0938647 | + | 0.162578i | ||||
\(455\) | 21.8564 | − | 9.07180i | 1.02464 | − | 0.425292i | ||||
\(456\) | 27.0000 | + | 15.5885i | 1.26439 | + | 0.729996i | ||||
\(457\) | 20.0000i | 0.935561i | 0.883845 | + | 0.467780i | \(0.154946\pi\) | ||||
−0.883845 | + | 0.467780i | \(0.845054\pi\) | |||||||
\(458\) | 19.9186 | + | 11.5000i | 0.930734 | + | 0.537360i | ||||
\(459\) | 9.00000 | + | 5.19615i | 0.420084 | + | 0.242536i | ||||
\(460\) | −0.401924 | − | 6.69615i | −0.0187398 | − | 0.312210i | ||||
\(461\) | −10.5000 | + | 18.1865i | −0.489034 | + | 0.847031i | −0.999920 | − | 0.0126168i | \(-0.995984\pi\) |
0.510887 | + | 0.859648i | \(0.329317\pi\) | |||||||
\(462\) | 25.9808 | − | 9.00000i | 1.20873 | − | 0.418718i | ||||
\(463\) | 23.3827 | − | 13.5000i | 1.08669 | − | 0.627398i | 0.153993 | − | 0.988072i | \(-0.450787\pi\) |
0.932692 | + | 0.360674i | \(0.117453\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 6.92820 | − | 13.8564i | 0.321288 | − | 0.642575i | ||||
\(466\) | −7.00000 | − | 12.1244i | −0.324269 | − | 0.561650i | ||||
\(467\) | −2.59808 | + | 1.50000i | −0.120225 | + | 0.0694117i | −0.558906 | − | 0.829231i | \(-0.688779\pi\) |
0.438682 | + | 0.898642i | \(0.355446\pi\) | |||||||
\(468\) | 12.0000i | 0.554700i | ||||||||
\(469\) | 14.0000 | + | 12.1244i | 0.646460 | + | 0.559851i | ||||
\(470\) | −3.69615 | − | 5.59808i | −0.170491 | − | 0.258220i | ||||
\(471\) | −18.0000 | + | 10.3923i | −0.829396 | + | 0.478852i | ||||
\(472\) | − | 12.0000i | − | 0.552345i | ||||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | −21.0000 | + | 12.1244i | −0.964562 | + | 0.556890i | ||||
\(475\) | 29.7846 | − | 3.58846i | 1.36661 | − | 0.164650i | ||||
\(476\) | −5.00000 | + | 1.73205i | −0.229175 | + | 0.0793884i | ||||
\(477\) | −31.1769 | + | 18.0000i | −1.42749 | + | 0.824163i | ||||
\(478\) | 20.7846 | − | 12.0000i | 0.950666 | − | 0.548867i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | −17.3205 | − | 8.66025i | −0.790569 | − | 0.395285i | ||||
\(481\) | −16.0000 | + | 27.7128i | −0.729537 | + | 1.26360i | ||||
\(482\) | −19.9186 | + | 11.5000i | −0.907267 | + | 0.523811i | ||||
\(483\) | −10.3923 | − | 9.00000i | −0.472866 | − | 0.409514i | ||||
\(484\) | −12.5000 | + | 21.6506i | −0.568182 | + | 0.984120i | ||||
\(485\) | −0.267949 | − | 4.46410i | −0.0121669 | − | 0.202704i | ||||
\(486\) | 13.5000 | + | 7.79423i | 0.612372 | + | 0.353553i | ||||
\(487\) | 10.3923 | + | 6.00000i | 0.470920 | + | 0.271886i | 0.716625 | − | 0.697459i | \(-0.245686\pi\) |
−0.245705 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(488\) | 21.0000i | 0.950625i | ||||||||
\(489\) | 6.00000 | + | 3.46410i | 0.271329 | + | 0.156652i | ||||
\(490\) | 10.4019 | + | 11.6962i | 0.469911 | + | 0.528378i | ||||
\(491\) | 16.0000 | + | 27.7128i | 0.722070 | + | 1.25066i | 0.960169 | + | 0.279421i | \(0.0901424\pi\) |
−0.238099 | + | 0.971241i | \(0.576524\pi\) | |||||||
\(492\) | 1.73205 | − | 3.00000i | 0.0780869 | − | 0.135250i | ||||
\(493\) | 3.46410 | − | 2.00000i | 0.156015 | − | 0.0900755i | ||||
\(494\) | 12.0000 | − | 20.7846i | 0.539906 | − | 0.935144i | ||||
\(495\) | 22.1769 | + | 33.5885i | 0.996778 | + | 1.50969i | ||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 6.92820 | − | 8.00000i | 0.310772 | − | 0.358849i | ||||
\(498\) | −6.92820 | −0.310460 | ||||||||
\(499\) | 14.0000 | − | 24.2487i | 0.626726 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153141i | \(-0.0489388\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | −4.50000 | − | 2.59808i | −0.201045 | − | 0.116073i | ||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | −22.5000 | + | 7.79423i | −1.00223 | + | 0.347183i | ||||
\(505\) | −3.00000 | + | 6.00000i | −0.133498 | + | 0.266996i | ||||
\(506\) | −18.0000 | −0.800198 | ||||||||
\(507\) | 5.19615 | 0.230769 | ||||||||
\(508\) | 7.00000i | 0.310575i | ||||||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 4.26795 | + | 6.46410i | 0.188988 | + | 0.286235i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | 15.5885 | + | 27.0000i | 0.688247 | + | 1.19208i | ||||
\(514\) | 4.00000 | − | 6.92820i | 0.176432 | − | 0.305590i | ||||
\(515\) | 0.133975 | + | 2.23205i | 0.00590363 | + | 0.0983559i | ||||
\(516\) | 1.73205i | 0.0762493i | ||||||||
\(517\) | 15.5885 | − | 9.00000i | 0.685580 | − | 0.395820i | ||||
\(518\) | −20.7846 | − | 4.00000i | −0.913223 | − | 0.175750i | ||||
\(519\) | 27.0000 | − | 15.5885i | 1.18517 | − | 0.684257i | ||||
\(520\) | −12.0000 | + | 24.0000i | −0.526235 | + | 1.05247i | ||||
\(521\) | 18.5000 | − | 32.0429i | 0.810500 | − | 1.40383i | −0.102015 | − | 0.994783i | \(-0.532529\pi\) |
0.912515 | − | 0.409044i | \(-0.134138\pi\) | |||||||
\(522\) | 5.19615 | − | 3.00000i | 0.227429 | − | 0.131306i | ||||
\(523\) | 35.5070 | − | 20.5000i | 1.55261 | − | 0.896402i | 0.554687 | − | 0.832059i | \(-0.312838\pi\) |
0.997928 | − | 0.0643431i | \(-0.0204952\pi\) | |||||||
\(524\) | 7.00000 | − | 12.1244i | 0.305796 | − | 0.529655i | ||||
\(525\) | −12.8205 | + | 18.9904i | −0.559533 | + | 0.828808i | ||||
\(526\) | −10.5000 | − | 18.1865i | −0.457822 | − | 0.792971i | ||||
\(527\) | 6.92820 | + | 4.00000i | 0.301797 | + | 0.174243i | ||||
\(528\) | −5.19615 | + | 9.00000i | −0.226134 | + | 0.391675i | ||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | −26.7846 | + | 1.60770i | −1.16345 | + | 0.0698338i | ||||
\(531\) | 6.00000 | − | 10.3923i | 0.260378 | − | 0.450988i | ||||
\(532\) | −15.5885 | − | 3.00000i | −0.675845 | − | 0.130066i | ||||
\(533\) | −6.92820 | − | 4.00000i | −0.300094 | − | 0.173259i | ||||
\(534\) | 4.50000 | + | 2.59808i | 0.194734 | + | 0.112430i | ||||
\(535\) | −8.00000 | − | 4.00000i | −0.345870 | − | 0.172935i | ||||
\(536\) | −21.0000 | −0.907062 | ||||||||
\(537\) | −3.46410 | −0.149487 | ||||||||
\(538\) | 11.2583 | + | 6.50000i | 0.485381 | + | 0.280235i | ||||
\(539\) | −33.0000 | + | 25.9808i | −1.42141 | + | 1.11907i | ||||
\(540\) | −6.40192 | − | 9.69615i | −0.275495 | − | 0.417256i | ||||
\(541\) | −10.5000 | − | 18.1865i | −0.451430 | − | 0.781900i | 0.547045 | − | 0.837103i | \(-0.315753\pi\) |
−0.998475 | + | 0.0552031i | \(0.982419\pi\) | |||||||
\(542\) | 24.2487 | − | 14.0000i | 1.04157 | − | 0.601351i | ||||
\(543\) | 5.19615 | + | 9.00000i | 0.222988 | + | 0.386227i | ||||
\(544\) | 5.00000 | − | 8.66025i | 0.214373 | − | 0.371305i | ||||
\(545\) | −22.3205 | + | 1.33975i | −0.956106 | + | 0.0573884i | ||||
\(546\) | 6.00000 | + | 17.3205i | 0.256776 | + | 0.741249i | ||||
\(547\) | −24.2487 | − | 14.0000i | −1.03680 | − | 0.598597i | −0.117875 | − | 0.993028i | \(-0.537608\pi\) |
−0.918925 | + | 0.394432i | \(0.870941\pi\) | |||||||
\(548\) | −5.19615 | + | 3.00000i | −0.221969 | + | 0.128154i | ||||
\(549\) | −10.5000 | + | 18.1865i | −0.448129 | + | 0.776182i | ||||
\(550\) | 3.58846 | + | 29.7846i | 0.153012 | + | 1.27002i | ||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | 15.5885 | 0.663489 | ||||||||
\(553\) | 24.2487 | − | 28.0000i | 1.03116 | − | 1.19068i | ||||
\(554\) | 11.0000 | + | 19.0526i | 0.467345 | + | 0.809466i | ||||
\(555\) | −1.85641 | − | 30.9282i | −0.0788001 | − | 1.31283i | ||||
\(556\) | 1.00000 | + | 1.73205i | 0.0424094 | + | 0.0734553i | ||||
\(557\) | 1.73205 | + | 1.00000i | 0.0733893 | + | 0.0423714i | 0.536246 | − | 0.844062i | \(-0.319842\pi\) |
−0.462856 | + | 0.886433i | \(0.653175\pi\) | |||||||
\(558\) | 10.3923 | + | 6.00000i | 0.439941 | + | 0.254000i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −5.86603 | − | 0.767949i | −0.247885 | − | 0.0324518i | ||||
\(561\) | −18.0000 | + | 10.3923i | −0.759961 | + | 0.438763i | ||||
\(562\) | 19.9186 | + | 11.5000i | 0.840215 | + | 0.485098i | ||||
\(563\) | 27.0000i | 1.13791i | 0.822367 | + | 0.568957i | \(0.192653\pi\) | ||||
−0.822367 | + | 0.568957i | \(0.807347\pi\) | |||||||
\(564\) | −4.50000 | + | 2.59808i | −0.189484 | + | 0.109399i | ||||
\(565\) | 36.0000 | + | 18.0000i | 1.51453 | + | 0.757266i | ||||
\(566\) | −11.0000 | −0.462364 | ||||||||
\(567\) | −23.3827 | − | 4.50000i | −0.981981 | − | 0.188982i | ||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 1.39230 | + | 23.1962i | 0.0583172 | + | 0.971580i | ||||
\(571\) | 6.00000 | 0.251092 | 0.125546 | − | 0.992088i | \(-0.459932\pi\) | ||||
0.125546 | + | 0.992088i | \(0.459932\pi\) | |||||||
\(572\) | −20.7846 | − | 12.0000i | −0.869048 | − | 0.501745i | ||||
\(573\) | −5.19615 | − | 9.00000i | −0.217072 | − | 0.375980i | ||||
\(574\) | 1.00000 | − | 5.19615i | 0.0417392 | − | 0.216883i | ||||
\(575\) | 12.0000 | − | 9.00000i | 0.500435 | − | 0.375326i | ||||
\(576\) | 10.5000 | − | 18.1865i | 0.437500 | − | 0.757772i | ||||
\(577\) | −34.6410 | − | 20.0000i | −1.44212 | − | 0.832611i | −0.444133 | − | 0.895961i | \(-0.646488\pi\) |
−0.997991 | + | 0.0633500i | \(0.979822\pi\) | |||||||
\(578\) | 11.2583 | − | 6.50000i | 0.468285 | − | 0.270364i | ||||
\(579\) | −15.0000 | + | 8.66025i | −0.623379 | + | 0.359908i | ||||
\(580\) | −4.46410 | + | 0.267949i | −0.185362 | + | 0.0111260i | ||||
\(581\) | 10.0000 | − | 3.46410i | 0.414870 | − | 0.143715i | ||||
\(582\) | 3.46410 | 0.143592 | ||||||||
\(583\) | − | 72.0000i | − | 2.98194i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.3923 | + | 14.7846i | −0.925808 | + | 0.611268i | ||||
\(586\) | 6.00000 | + | 10.3923i | 0.247858 | + | 0.429302i | ||||
\(587\) | 38.9711 | + | 22.5000i | 1.60851 | + | 0.928674i | 0.989704 | + | 0.143132i | \(0.0457173\pi\) |
0.618808 | + | 0.785543i | \(0.287616\pi\) | |||||||
\(588\) | 9.52628 | − | 7.50000i | 0.392857 | − | 0.309295i | ||||
\(589\) | 12.0000 | + | 20.7846i | 0.494451 | + | 0.856415i | ||||
\(590\) | 7.46410 | − | 4.92820i | 0.307292 | − | 0.202891i | ||||
\(591\) | 21.0000 | − | 12.1244i | 0.863825 | − | 0.498729i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | 17.3205 | − | 10.0000i | 0.711268 | − | 0.410651i | −0.100262 | − | 0.994961i | \(-0.531968\pi\) |
0.811530 | + | 0.584310i | \(0.198635\pi\) | |||||||
\(594\) | −27.0000 | + | 15.5885i | −1.10782 | + | 0.639602i | ||||
\(595\) | −9.39230 | − | 7.19615i | −0.385047 | − | 0.295013i | ||||
\(596\) | −11.5000 | + | 19.9186i | −0.471058 | + | 0.815897i | ||||
\(597\) | 24.2487 | 0.992434 | ||||||||
\(598\) | − | 12.0000i | − | 0.490716i | ||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | −3.10770 | − | 25.7942i | −0.126871 | − | 1.05304i | ||||
\(601\) | −5.00000 | + | 8.66025i | −0.203954 | + | 0.353259i | −0.949799 | − | 0.312861i | \(-0.898713\pi\) |
0.745845 | + | 0.666120i | \(0.232046\pi\) | |||||||
\(602\) | 0.866025 | + | 2.50000i | 0.0352966 | + | 0.101892i | ||||
\(603\) | −18.1865 | − | 10.5000i | −0.740613 | − | 0.427593i | ||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | −55.8013 | + | 3.34936i | −2.26864 | + | 0.136171i | ||||
\(606\) | −4.50000 | − | 2.59808i | −0.182800 | − | 0.105540i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 25.9808 | − | 15.0000i | 1.05366 | − | 0.608330i | ||||
\(609\) | −6.00000 | + | 6.92820i | −0.243132 | + | 0.280745i | ||||
\(610\) | −13.0622 | + | 8.62436i | −0.528872 | + | 0.349190i | ||||
\(611\) | 6.00000 | + | 10.3923i | 0.242734 | + | 0.420428i | ||||
\(612\) | 5.19615 | − | 3.00000i | 0.210042 | − | 0.121268i | ||||
\(613\) | −29.4449 | − | 17.0000i | −1.18927 | − | 0.686624i | −0.231127 | − | 0.972924i | \(-0.574241\pi\) |
−0.958140 | + | 0.286300i | \(0.907575\pi\) | |||||||
\(614\) | 28.0000 | 1.12999 | ||||||||
\(615\) | 7.73205 | − | 0.464102i | 0.311786 | − | 0.0187144i | ||||
\(616\) | 9.00000 | − | 46.7654i | 0.362620 | − | 1.88423i | ||||
\(617\) | −24.2487 | + | 14.0000i | −0.976216 | + | 0.563619i | −0.901126 | − | 0.433558i | \(-0.857258\pi\) |
−0.0750907 | + | 0.997177i | \(0.523925\pi\) | |||||||
\(618\) | −1.73205 | −0.0696733 | ||||||||
\(619\) | −19.0000 | − | 32.9090i | −0.763674 | − | 1.32272i | −0.940945 | − | 0.338561i | \(-0.890060\pi\) |
0.177270 | − | 0.984162i | \(-0.443273\pi\) | |||||||
\(620\) | −4.92820 | − | 7.46410i | −0.197921 | − | 0.299766i | ||||
\(621\) | 13.5000 | + | 7.79423i | 0.541736 | + | 0.312772i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | −7.79423 | − | 1.50000i | −0.312269 | − | 0.0600962i | ||||
\(624\) | −6.00000 | − | 3.46410i | −0.240192 | − | 0.138675i | ||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | −18.0000 | −0.719425 | ||||||||
\(627\) | −62.3538 | −2.49017 | ||||||||
\(628\) | 12.0000i | 0.478852i | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | −14.0885 | − | 10.7942i | −0.561298 | − | 0.430052i | ||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 42.0000i | 1.67067i | ||||||||
\(633\) | 1.73205 | − | 3.00000i | 0.0688428 | − | 0.119239i | ||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | −13.0622 | + | 8.62436i | −0.518357 | + | 0.342247i | ||||
\(636\) | 20.7846i | 0.824163i | ||||||||
\(637\) | −17.3205 | − | 22.0000i | −0.686264 | − | 0.871672i | ||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | −5.59808 | + | 3.69615i | −0.221283 | + | 0.146103i | ||||
\(641\) | −18.5000 | − | 32.0429i | −0.730706 | − | 1.26562i | −0.956582 | − | 0.291464i | \(-0.905858\pi\) |
0.225876 | − | 0.974156i | \(-0.427476\pi\) | |||||||
\(642\) | 3.46410 | − | 6.00000i | 0.136717 | − | 0.236801i | ||||
\(643\) | −40.7032 | + | 23.5000i | −1.60518 | + | 0.926750i | −0.614749 | + | 0.788723i | \(0.710743\pi\) |
−0.990429 | + | 0.138027i | \(0.955924\pi\) | |||||||
\(644\) | −7.50000 | + | 2.59808i | −0.295541 | + | 0.102379i | ||||
\(645\) | −3.23205 | + | 2.13397i | −0.127262 | + | 0.0840252i | ||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −6.92820 | − | 4.00000i | −0.272376 | − | 0.157256i | 0.357591 | − | 0.933878i | \(-0.383598\pi\) |
−0.629967 | + | 0.776622i | \(0.716932\pi\) | |||||||
\(648\) | 23.3827 | − | 13.5000i | 0.918559 | − | 0.530330i | ||||
\(649\) | 12.0000 | + | 20.7846i | 0.471041 | + | 0.815867i | ||||
\(650\) | −19.8564 | + | 2.39230i | −0.778832 | + | 0.0938339i | ||||
\(651\) | −18.0000 | − | 3.46410i | −0.705476 | − | 0.135769i | ||||
\(652\) | 3.46410 | − | 2.00000i | 0.135665 | − | 0.0783260i | ||||
\(653\) | −32.9090 | − | 19.0000i | −1.28783 | − | 0.743527i | −0.309561 | − | 0.950880i | \(-0.600182\pi\) |
−0.978266 | + | 0.207352i | \(0.933515\pi\) | |||||||
\(654\) | − | 17.3205i | − | 0.677285i | ||||||
\(655\) | 31.2487 | − | 1.87564i | 1.22099 | − | 0.0732875i | ||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.19615 | + | 6.00000i | −0.202567 | + | 0.233904i | ||||
\(659\) | 15.0000 | − | 25.9808i | 0.584317 | − | 1.01207i | −0.410643 | − | 0.911796i | \(-0.634696\pi\) |
0.994960 | − | 0.100271i | \(-0.0319709\pi\) | |||||||
\(660\) | 23.1962 | − | 1.39230i | 0.902909 | − | 0.0541954i | ||||
\(661\) | 39.0000 | 1.51692 | 0.758462 | − | 0.651717i | \(-0.225951\pi\) | ||||
0.758462 | + | 0.651717i | \(0.225951\pi\) | |||||||
\(662\) | − | 6.00000i | − | 0.233197i | ||||||
\(663\) | −6.92820 | − | 12.0000i | −0.269069 | − | 0.466041i | ||||
\(664\) | −6.00000 | + | 10.3923i | −0.232845 | + | 0.403300i | ||||
\(665\) | −13.6077 | − | 32.7846i | −0.527684 | − | 1.27133i | ||||
\(666\) | 24.0000 | 0.929981 | ||||||||
\(667\) | 5.19615 | − | 3.00000i | 0.201196 | − | 0.116160i | ||||
\(668\) | −2.59808 | + | 1.50000i | −0.100523 | + | 0.0580367i | ||||
\(669\) | − | 5.19615i | − | 0.200895i | ||||||
\(670\) | −8.62436 | − | 13.0622i | −0.333188 | − | 0.504636i | ||||
\(671\) | −21.0000 | − | 36.3731i | −0.810696 | − | 1.40417i | ||||
\(672\) | −4.33013 | + | 22.5000i | −0.167038 | + | 0.867956i | ||||
\(673\) | 20.7846 | + | 12.0000i | 0.801188 | + | 0.462566i | 0.843886 | − | 0.536522i | \(-0.180262\pi\) |
−0.0426985 | + | 0.999088i | \(0.513595\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2058 | − | 23.8923i | 0.392820 | − | 0.919615i | ||||
\(676\) | 1.50000 | − | 2.59808i | 0.0576923 | − | 0.0999260i | ||||
\(677\) | − | 8.00000i | − | 0.307465i | −0.988113 | − | 0.153732i | \(-0.950871\pi\) | ||
0.988113 | − | 0.153732i | \(-0.0491294\pi\) | |||||||
\(678\) | −15.5885 | + | 27.0000i | −0.598671 | + | 1.03693i | ||||
\(679\) | −5.00000 | + | 1.73205i | −0.191882 | + | 0.0664700i | ||||
\(680\) | 13.3923 | − | 0.803848i | 0.513571 | − | 0.0308261i | ||||
\(681\) | 6.00000 | + | 3.46410i | 0.229920 | + | 0.132745i | ||||
\(682\) | −20.7846 | + | 12.0000i | −0.795884 | + | 0.459504i | ||||
\(683\) | −6.06218 | − | 3.50000i | −0.231963 | − | 0.133924i | 0.379514 | − | 0.925186i | \(-0.376091\pi\) |
−0.611477 | + | 0.791262i | \(0.709424\pi\) | |||||||
\(684\) | 18.0000 | 0.688247 | ||||||||
\(685\) | −12.0000 | − | 6.00000i | −0.458496 | − | 0.229248i | ||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | 39.8372 | 1.51988 | ||||||||
\(688\) | −0.866025 | − | 0.500000i | −0.0330169 | − | 0.0190623i | ||||
\(689\) | 48.0000 | 1.82865 | ||||||||
\(690\) | 6.40192 | + | 9.69615i | 0.243717 | + | 0.369126i | ||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 31.1769 | − | 36.0000i | 1.18431 | − | 1.36753i | ||||
\(694\) | 3.00000 | 0.113878 | ||||||||
\(695\) | −2.00000 | + | 4.00000i | −0.0758643 | + | 0.151729i | ||||
\(696\) | − | 10.3923i | − | 0.393919i | ||||||
\(697\) | 4.00000i | 0.151511i | ||||||||
\(698\) | 26.8468 | + | 15.5000i | 1.01617 | + | 0.586684i | ||||
\(699\) | −21.0000 | − | 12.1244i | −0.794293 | − | 0.458585i | ||||
\(700\) | 5.79423 | + | 11.8923i | 0.219001 | + | 0.449487i | ||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | −10.3923 | − | 18.0000i | −0.392232 | − | 0.679366i | ||||
\(703\) | 41.5692 | + | 24.0000i | 1.56781 | + | 0.905177i | ||||
\(704\) | 21.0000 | + | 36.3731i | 0.791467 | + | 1.37086i | ||||
\(705\) | −10.3923 | − | 5.19615i | −0.391397 | − | 0.195698i | ||||
\(706\) | −5.00000 | − | 8.66025i | −0.188177 | − | 0.325933i | ||||
\(707\) | 7.79423 | + | 1.50000i | 0.293132 | + | 0.0564133i | ||||
\(708\) | −3.46410 | − | 6.00000i | −0.130189 | − | 0.225494i | ||||
\(709\) | 13.0000 | 0.488225 | 0.244113 | − | 0.969747i | \(-0.421503\pi\) | ||||
0.244113 | + | 0.969747i | \(0.421503\pi\) | |||||||
\(710\) | −7.46410 | + | 4.92820i | −0.280123 | + | 0.184952i | ||||
\(711\) | −21.0000 | + | 36.3731i | −0.787562 | + | 1.36410i | ||||
\(712\) | 7.79423 | − | 4.50000i | 0.292101 | − | 0.168645i | ||||
\(713\) | 10.3923 | + | 6.00000i | 0.389195 | + | 0.224702i | ||||
\(714\) | 6.00000 | − | 6.92820i | 0.224544 | − | 0.259281i | ||||
\(715\) | −3.21539 | − | 53.5692i | −0.120249 | − | 2.00338i | ||||
\(716\) | −1.00000 | + | 1.73205i | −0.0373718 | + | 0.0647298i | ||||
\(717\) | 20.7846 | − | 36.0000i | 0.776215 | − | 1.34444i | ||||
\(718\) | 1.73205 | − | 1.00000i | 0.0646396 | − | 0.0373197i | ||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 6.69615 | − | 0.401924i | 0.249551 | − | 0.0149788i | ||||
\(721\) | 2.50000 | − | 0.866025i | 0.0931049 | − | 0.0322525i | ||||
\(722\) | −14.7224 | − | 8.50000i | −0.547912 | − | 0.316337i | ||||
\(723\) | −19.9186 | + | 34.5000i | −0.740780 | + | 1.28307i | ||||
\(724\) | 6.00000 | 0.222988 | ||||||||
\(725\) | −6.00000 | − | 8.00000i | −0.222834 | − | 0.297113i | ||||
\(726\) | − | 43.3013i | − | 1.60706i | ||||||
\(727\) | −11.2583 | − | 6.50000i | −0.417548 | − | 0.241072i | 0.276479 | − | 0.961020i | \(-0.410832\pi\) |
−0.694028 | + | 0.719948i | \(0.744166\pi\) | |||||||
\(728\) | 31.1769 | + | 6.00000i | 1.15549 | + | 0.222375i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00000 | − | 1.73205i | −0.0369863 | − | 0.0640622i | ||||
\(732\) | 6.06218 | + | 10.5000i | 0.224065 | + | 0.388091i | ||||
\(733\) | −34.6410 | − | 20.0000i | −1.27950 | − | 0.738717i | −0.302740 | − | 0.953073i | \(-0.597901\pi\) |
−0.976756 | + | 0.214356i | \(0.931235\pi\) | |||||||
\(734\) | −1.50000 | − | 2.59808i | −0.0553660 | − | 0.0958967i | ||||
\(735\) | 25.7321 | + | 8.53590i | 0.949141 | + | 0.314851i | ||||
\(736\) | 7.50000 | − | 12.9904i | 0.276454 | − | 0.478832i | ||||
\(737\) | 36.3731 | − | 21.0000i | 1.33982 | − | 0.773545i | ||||
\(738\) | 6.00000i | 0.220863i | ||||||||
\(739\) | 17.0000 | − | 29.4449i | 0.625355 | − | 1.08315i | −0.363117 | − | 0.931744i | \(-0.618287\pi\) |
0.988472 | − | 0.151403i | \(-0.0483792\pi\) | |||||||
\(740\) | −16.0000 | − | 8.00000i | −0.588172 | − | 0.294086i | ||||
\(741\) | − | 41.5692i | − | 1.52708i | ||||||
\(742\) | 10.3923 | + | 30.0000i | 0.381514 | + | 1.10133i | ||||
\(743\) | −6.92820 | + | 4.00000i | −0.254171 | + | 0.146746i | −0.621673 | − | 0.783277i | \(-0.713547\pi\) |
0.367502 | + | 0.930023i | \(0.380213\pi\) | |||||||
\(744\) | 18.0000 | − | 10.3923i | 0.659912 | − | 0.381000i | ||||
\(745\) | −51.3372 | + | 3.08142i | −1.88085 | + | 0.112894i | ||||
\(746\) | −12.0000 | + | 20.7846i | −0.439351 | + | 0.760979i | ||||
\(747\) | −10.3923 | + | 6.00000i | −0.380235 | + | 0.219529i | ||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | −2.00000 | + | 10.3923i | −0.0730784 | + | 0.379727i | ||||
\(750\) | 14.7679 | − | 12.5263i | 0.539249 | − | 0.457395i | ||||
\(751\) | 9.00000 | − | 15.5885i | 0.328415 | − | 0.568831i | −0.653783 | − | 0.756682i | \(-0.726819\pi\) |
0.982197 | + | 0.187851i | \(0.0601523\pi\) | |||||||
\(752\) | − | 3.00000i | − | 0.109399i | ||||||
\(753\) | 10.3923 | + | 18.0000i | 0.378717 | + | 0.655956i | ||||
\(754\) | −8.00000 | −0.291343 | ||||||||
\(755\) | −16.0000 | + | 32.0000i | −0.582300 | + | 1.16460i | ||||
\(756\) | −9.00000 | + | 10.3923i | −0.327327 | + | 0.377964i | ||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | − | 20.0000i | − | 0.726433i | ||||||
\(759\) | −27.0000 | + | 15.5885i | −0.980038 | + | 0.565825i | ||||
\(760\) | 36.0000 | + | 18.0000i | 1.30586 | + | 0.652929i | ||||
\(761\) | −17.5000 | + | 30.3109i | −0.634375 | + | 1.09877i | 0.352273 | + | 0.935897i | \(0.385409\pi\) |
−0.986647 | + | 0.162872i | \(0.947924\pi\) | |||||||
\(762\) | −6.06218 | − | 10.5000i | −0.219610 | − | 0.380375i | ||||
\(763\) | 8.66025 | + | 25.0000i | 0.313522 | + | 0.905061i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 12.0000 | + | 6.00000i | 0.433861 | + | 0.216930i | ||||
\(766\) | 0.500000 | − | 0.866025i | 0.0180657 | − | 0.0312908i | ||||
\(767\) | −13.8564 | + | 8.00000i | −0.500326 | + | 0.288863i | ||||
\(768\) | −14.7224 | − | 25.5000i | −0.531250 | − | 0.920152i | ||||
\(769\) | 16.5000 | + | 28.5788i | 0.595005 | + | 1.03058i | 0.993546 | + | 0.113429i | \(0.0361834\pi\) |
−0.398541 | + | 0.917151i | \(0.630483\pi\) | |||||||
\(770\) | 32.7846 | − | 13.6077i | 1.18148 | − | 0.490387i | ||||
\(771\) | − | 13.8564i | − | 0.499026i | ||||||
\(772\) | 10.0000i | 0.359908i | ||||||||
\(773\) | −5.19615 | − | 3.00000i | −0.186893 | − | 0.107903i | 0.403634 | − | 0.914920i | \(-0.367747\pi\) |
−0.590527 | + | 0.807018i | \(0.701080\pi\) | |||||||
\(774\) | −1.50000 | − | 2.59808i | −0.0539164 | − | 0.0933859i | ||||
\(775\) | 7.85641 | − | 18.3923i | 0.282210 | − | 0.660671i | ||||
\(776\) | 3.00000 | − | 5.19615i | 0.107694 | − | 0.186531i | ||||
\(777\) | −34.6410 | + | 12.0000i | −1.24274 | + | 0.430498i | ||||
\(778\) | 16.4545 | − | 9.50000i | 0.589922 | − | 0.340592i | ||||
\(779\) | −6.00000 | + | 10.3923i | −0.214972 | + | 0.372343i | ||||
\(780\) | 0.928203 | + | 15.4641i | 0.0332350 | + | 0.553704i | ||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | −5.19615 | + | 3.00000i | −0.185814 | + | 0.107280i | ||||
\(783\) | 5.19615 | − | 9.00000i | 0.185695 | − | 0.321634i | ||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −22.3923 | + | 14.7846i | −0.799216 | + | 0.527685i | ||||
\(786\) | 24.2487i | 0.864923i | ||||||||
\(787\) | − | 23.0000i | − | 0.819861i | −0.912117 | − | 0.409931i | \(-0.865553\pi\) | ||
0.912117 | − | 0.409931i | \(-0.134447\pi\) | |||||||
\(788\) | − | 14.0000i | − | 0.498729i | ||||||
\(789\) | −31.5000 | − | 18.1865i | −1.12143 | − | 0.647458i | ||||
\(790\) | −26.1244 | + | 17.2487i | −0.929463 | + | 0.613682i | ||||
\(791\) | 9.00000 | − | 46.7654i | 0.320003 | − | 1.66279i | ||||
\(792\) | 54.0000i | 1.91881i | ||||||||
\(793\) | 24.2487 | − | 14.0000i | 0.861097 | − | 0.497155i | ||||
\(794\) | −5.00000 | − | 8.66025i | −0.177443 | − | 0.307341i | ||||
\(795\) | −38.7846 | + | 25.6077i | −1.37555 | + | 0.908211i | ||||
\(796\) | 7.00000 | − | 12.1244i | 0.248108 | − | 0.429736i | ||||
\(797\) | −12.1244 | + | 7.00000i | −0.429467 | + | 0.247953i | −0.699119 | − | 0.715005i | \(-0.746424\pi\) |
0.269653 | + | 0.962958i | \(0.413091\pi\) | |||||||
\(798\) | 25.9808 | − | 9.00000i | 0.919709 | − | 0.318597i | ||||
\(799\) | 3.00000 | − | 5.19615i | 0.106132 | − | 0.183827i | ||||
\(800\) | −22.9904 | − | 9.82051i | −0.812833 | − | 0.347207i | ||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | −23.3827 | − | 13.5000i | −0.825671 | − | 0.476702i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −10.5000 | + | 6.06218i | −0.370306 | + | 0.213797i | ||||
\(805\) | −14.0885 | − | 10.7942i | −0.496553 | − | 0.380447i | ||||
\(806\) | −8.00000 | − | 13.8564i | −0.281788 | − | 0.488071i | ||||
\(807\) | 22.5167 | 0.792624 | ||||||||
\(808\) | −7.79423 | + | 4.50000i | −0.274200 | + | 0.158309i | ||||
\(809\) | −1.50000 | + | 2.59808i | −0.0527372 | + | 0.0913435i | −0.891189 | − | 0.453632i | \(-0.850128\pi\) |
0.838452 | + | 0.544976i | \(0.183461\pi\) | |||||||
\(810\) | 18.0000 | + | 9.00000i | 0.632456 | + | 0.316228i | ||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 1.73205 | + | 5.00000i | 0.0607831 | + | 0.175466i | ||||
\(813\) | 24.2487 | − | 42.0000i | 0.850439 | − | 1.47300i | ||||
\(814\) | −24.0000 | + | 41.5692i | −0.841200 | + | 1.45700i | ||||
\(815\) | 8.00000 | + | 4.00000i | 0.280228 | + | 0.140114i | ||||
\(816\) | 3.46410i | 0.121268i | ||||||||
\(817\) | − | 6.00000i | − | 0.209913i | ||||||
\(818\) | − | 35.0000i | − | 1.22375i | ||||||
\(819\) | 24.0000 | + | 20.7846i | 0.838628 | + | 0.726273i | ||||
\(820\) | 2.00000 | − | 4.00000i | 0.0698430 | − | 0.139686i | ||||
\(821\) | 31.0000 | 1.08191 | 0.540954 | − | 0.841052i | \(-0.318063\pi\) | ||||
0.540954 | + | 0.841052i | \(0.318063\pi\) | |||||||
\(822\) | 5.19615 | − | 9.00000i | 0.181237 | − | 0.313911i | ||||
\(823\) | 44.0000i | 1.53374i | 0.641800 | + | 0.766872i | \(0.278188\pi\) | ||||
−0.641800 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(824\) | −1.50000 | + | 2.59808i | −0.0522550 | + | 0.0905083i | ||||
\(825\) | 31.1769 | + | 41.5692i | 1.08544 | + | 1.44725i | ||||
\(826\) | −8.00000 | − | 6.92820i | −0.278356 | − | 0.241063i | ||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 7.79423 | − | 4.50000i | 0.270868 | − | 0.156386i | ||||
\(829\) | −25.5000 | + | 44.1673i | −0.885652 | + | 1.53399i | −0.0406866 | + | 0.999172i | \(0.512955\pi\) |
−0.844965 | + | 0.534822i | \(0.820379\pi\) | |||||||
\(830\) | −8.92820 | + | 0.535898i | −0.309902 | + | 0.0186013i | ||||
\(831\) | 33.0000 | + | 19.0526i | 1.14476 | + | 0.660926i | ||||
\(832\) | −24.2487 | + | 14.0000i | −0.840673 | + | 0.485363i | ||||
\(833\) | −5.19615 | + | 13.0000i | −0.180036 | + | 0.450423i | ||||
\(834\) | −3.00000 | − | 1.73205i | −0.103882 | − | 0.0599760i | ||||
\(835\) | −6.00000 | − | 3.00000i | −0.207639 | − | 0.103819i | ||||
\(836\) | −18.0000 | + | 31.1769i | −0.622543 | + | 1.07828i | ||||
\(837\) | 20.7846 | 0.718421 | ||||||||
\(838\) | −15.5885 | + | 9.00000i | −0.538494 | + | 0.310900i | ||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | −28.3923 | + | 11.7846i | −0.979628 | + | 0.406608i | ||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | −2.59808 | − | 1.50000i | −0.0895356 | − | 0.0516934i | ||||
\(843\) | 39.8372 | 1.37206 | ||||||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | 6.69615 | − | 0.401924i | 0.230355 | − | 0.0138266i | ||||
\(846\) | 4.50000 | − | 7.79423i | 0.154713 | − | 0.267971i | ||||
\(847\) | 21.6506 | + | 62.5000i | 0.743925 | + | 2.14753i | ||||
\(848\) | −10.3923 | − | 6.00000i | −0.356873 | − | 0.206041i | ||||
\(849\) | −16.5000 | + | 9.52628i | −0.566279 | + | 0.326941i | ||||
\(850\) | 6.00000 | + | 8.00000i | 0.205798 | + | 0.274398i | ||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 3.46410 | + | 6.00000i | 0.118678 | + | 0.205557i | ||||
\(853\) | 15.5885 | + | 9.00000i | 0.533739 | + | 0.308154i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.208799 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(854\) | 14.0000 | + | 12.1244i | 0.479070 | + | 0.414887i | ||||
\(855\) | 22.1769 | + | 33.5885i | 0.758434 | + | 1.14870i | ||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 41.5692 | 1.41915 | ||||||||
\(859\) | −19.0000 | + | 32.9090i | −0.648272 | + | 1.12284i | 0.335264 | + | 0.942124i | \(0.391175\pi\) |
−0.983535 | + | 0.180715i | \(0.942159\pi\) | |||||||
\(860\) | 0.133975 | + | 2.23205i | 0.00456850 | + | 0.0761123i | ||||
\(861\) | −3.00000 | − | 8.66025i | −0.102240 | − | 0.295141i | ||||
\(862\) | 1.73205 | + | 1.00000i | 0.0589939 | + | 0.0340601i | ||||
\(863\) | −12.9904 | + | 7.50000i | −0.442198 | + | 0.255303i | −0.704529 | − | 0.709675i | \(-0.748842\pi\) |
0.262332 | + | 0.964978i | \(0.415509\pi\) | |||||||
\(864\) | − | 25.9808i | − | 0.883883i | ||||||
\(865\) | 33.5885 | − | 22.1769i | 1.14204 | − | 0.754038i | ||||
\(866\) | −32.0000 | −1.08740 | ||||||||
\(867\) | 11.2583 | − | 19.5000i | 0.382353 | − | 0.662255i | ||||
\(868\) | −6.92820 | + | 8.00000i | −0.235159 | + | 0.271538i | ||||
\(869\) | −42.0000 | − | 72.7461i | −1.42475 | − | 2.46774i | ||||
\(870\) | 6.46410 | − | 4.26795i | 0.219154 | − | 0.144697i | ||||
\(871\) | 14.0000 | + | 24.2487i | 0.474372 | + | 0.821636i | ||||
\(872\) | −25.9808 | − | 15.0000i | −0.879820 | − | 0.507964i | ||||
\(873\) | 5.19615 | − | 3.00000i | 0.175863 | − | 0.101535i | ||||
\(874\) | −18.0000 | −0.608859 | ||||||||
\(875\) | −15.0526 | + | 25.4641i | −0.508869 | + | 0.860844i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.66025 | − | 5.00000i | −0.292436 | − | 0.168838i | 0.346604 | − | 0.938012i | \(-0.387335\pi\) |
−0.639040 | + | 0.769174i | \(0.720668\pi\) | |||||||
\(878\) | − | 30.0000i | − | 1.01245i | ||||||
\(879\) | 18.0000 | + | 10.3923i | 0.607125 | + | 0.350524i | ||||
\(880\) | −6.00000 | + | 12.0000i | −0.202260 | + | 0.404520i | ||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | −7.79423 | + | 19.5000i | −0.262445 | + | 0.656599i | ||||
\(883\) | − | 3.00000i | − | 0.100958i | −0.998725 | − | 0.0504790i | \(-0.983925\pi\) | ||
0.998725 | − | 0.0504790i | \(-0.0160748\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | 6.92820 | − | 13.8564i | 0.232889 | − | 0.465778i | ||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | 19.9186 | + | 11.5000i | 0.668801 | + | 0.386132i | 0.795622 | − | 0.605793i | \(-0.207144\pi\) |
−0.126821 | + | 0.991926i | \(0.540478\pi\) | |||||||
\(888\) | 20.7846 | − | 36.0000i | 0.697486 | − | 1.20808i | ||||
\(889\) | 14.0000 | + | 12.1244i | 0.469545 | + | 0.406638i | ||||
\(890\) | 6.00000 | + | 3.00000i | 0.201120 | + | 0.100560i | ||||
\(891\) | −27.0000 | + | 46.7654i | −0.904534 | + | 1.56670i | ||||
\(892\) | −2.59808 | − | 1.50000i | −0.0869900 | − | 0.0502237i | ||||
\(893\) | 15.5885 | − | 9.00000i | 0.521648 | − | 0.301174i | ||||
\(894\) | − | 39.8372i | − | 1.33235i | ||||||
\(895\) | −4.46410 | + | 0.267949i | −0.149218 | + | 0.00895655i | ||||
\(896\) | 6.00000 | + | 5.19615i | 0.200446 | + | 0.173591i | ||||
\(897\) | −10.3923 | − | 18.0000i | −0.346989 | − | 0.601003i | ||||
\(898\) | 5.00000i | 0.166852i | ||||||||
\(899\) | 4.00000 | − | 6.92820i | 0.133407 | − | 0.231069i | ||||
\(900\) | −9.00000 | − | 12.0000i | −0.300000 | − | 0.400000i | ||||
\(901\) | −12.0000 | − | 20.7846i | −0.399778 | − | 0.692436i | ||||
\(902\) | −10.3923 | − | 6.00000i | −0.346026 | − | 0.199778i | ||||
\(903\) | 3.46410 | + | 3.00000i | 0.115278 | + | 0.0998337i | ||||
\(904\) | 27.0000 | + | 46.7654i | 0.898007 | + | 1.55539i | ||||
\(905\) | 7.39230 | + | 11.1962i | 0.245729 | + | 0.372173i | ||||
\(906\) | −24.0000 | − | 13.8564i | −0.797347 | − | 0.460348i | ||||
\(907\) | 17.3205 | − | 10.0000i | 0.575118 | − | 0.332045i | −0.184073 | − | 0.982913i | \(-0.558928\pi\) |
0.759191 | + | 0.650868i | \(0.225595\pi\) | |||||||
\(908\) | 3.46410 | − | 2.00000i | 0.114960 | − | 0.0663723i | ||||
\(909\) | −9.00000 | −0.298511 | ||||||||
\(910\) | 9.07180 | + | 21.8564i | 0.300727 | + | 0.724533i | ||||
\(911\) | −24.0000 | + | 41.5692i | −0.795155 | + | 1.37725i | 0.127585 | + | 0.991828i | \(0.459277\pi\) |
−0.922740 | + | 0.385422i | \(0.874056\pi\) | |||||||
\(912\) | −5.19615 | + | 9.00000i | −0.172062 | + | 0.298020i | ||||
\(913\) | − | 24.0000i | − | 0.794284i | ||||||
\(914\) | −20.0000 | −0.661541 | ||||||||
\(915\) | −12.1244 | + | 24.2487i | −0.400819 | + | 0.801638i | ||||
\(916\) | 11.5000 | − | 19.9186i | 0.379971 | − | 0.658129i | ||||
\(917\) | −12.1244 | − | 35.0000i | −0.400381 | − | 1.15580i | ||||
\(918\) | −5.19615 | + | 9.00000i | −0.171499 | + | 0.297044i | ||||
\(919\) | 11.0000 | + | 19.0526i | 0.362857 | + | 0.628486i | 0.988430 | − | 0.151680i | \(-0.0484682\pi\) |
−0.625573 | + | 0.780165i | \(0.715135\pi\) | |||||||
\(920\) | 20.0885 | − | 1.20577i | 0.662297 | − | 0.0397531i | ||||
\(921\) | 42.0000 | − | 24.2487i | 1.38395 | − | 0.799022i | ||||
\(922\) | −18.1865 | − | 10.5000i | −0.598942 | − | 0.345799i | ||||
\(923\) | 13.8564 | − | 8.00000i | 0.456089 | − | 0.263323i | ||||
\(924\) | −9.00000 | − | 25.9808i | −0.296078 | − | 0.854704i | ||||
\(925\) | −4.78461 | − | 39.7128i | −0.157317 | − | 1.30575i | ||||
\(926\) | 13.5000 | + | 23.3827i | 0.443638 | + | 0.768403i | ||||
\(927\) | −2.59808 | + | 1.50000i | −0.0853320 | + | 0.0492665i | ||||
\(928\) | −8.66025 | − | 5.00000i | −0.284287 | − | 0.164133i | ||||
\(929\) | −7.00000 | −0.229663 | −0.114831 | − | 0.993385i | \(-0.536633\pi\) | ||||
−0.114831 | + | 0.993385i | \(0.536633\pi\) | |||||||
\(930\) | 13.8564 | + | 6.92820i | 0.454369 | + | 0.227185i | ||||
\(931\) | −33.0000 | + | 25.9808i | −1.08153 | + | 0.851485i | ||||
\(932\) | −12.1244 | + | 7.00000i | −0.397146 | + | 0.229293i | ||||
\(933\) | 10.3923 | + | 18.0000i | 0.340229 | + | 0.589294i | ||||
\(934\) | −1.50000 | − | 2.59808i | −0.0490815 | − | 0.0850117i | ||||
\(935\) | −22.3923 | + | 14.7846i | −0.732307 | + | 0.483508i | ||||
\(936\) | −36.0000 | −1.17670 | ||||||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | −12.1244 | + | 14.0000i | −0.395874 | + | 0.457116i | ||||
\(939\) | −27.0000 | + | 15.5885i | −0.881112 | + | 0.508710i | ||||
\(940\) | −5.59808 | + | 3.69615i | −0.182589 | + | 0.120555i | ||||
\(941\) | 45.0000 | 1.46696 | 0.733479 | − | 0.679712i | \(-0.237895\pi\) | ||||
0.733479 | + | 0.679712i | \(0.237895\pi\) | |||||||
\(942\) | −10.3923 | − | 18.0000i | −0.338600 | − | 0.586472i | ||||
\(943\) | 6.00000i | 0.195387i | ||||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | −30.4808 | − | 3.99038i | −0.991539 | − | 0.129807i | ||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 3.00000i | 0.0974869i | 0.998811 | + | 0.0487435i | \(0.0155217\pi\) | ||||
−0.998811 | + | 0.0487435i | \(0.984478\pi\) | |||||||
\(948\) | 12.1244 | + | 21.0000i | 0.393781 | + | 0.682048i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.58846 | + | 29.7846i | 0.116425 | + | 0.966340i | ||||
\(951\) | 27.0000 | − | 15.5885i | 0.875535 | − | 0.505490i | ||||
\(952\) | −5.19615 | − | 15.0000i | −0.168408 | − | 0.486153i | ||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | −18.0000 | − | 31.1769i | −0.582772 | − | 1.00939i | ||||
\(955\) | −7.39230 | − | 11.1962i | −0.239209 | − | 0.362299i | ||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 10.3923 | + | 18.0000i | 0.335936 | + | 0.581857i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | + | 15.5885i | −0.0968751 | + | 0.503378i | ||||
\(960\) | 12.1244 | − | 24.2487i | 0.391312 | − | 0.782624i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −27.7128 | − | 16.0000i | −0.893497 | − | 0.515861i | ||||
\(963\) | − | 12.0000i | − | 0.386695i | ||||||
\(964\) | 11.5000 | + | 19.9186i | 0.370390 | + | 0.641534i | ||||
\(965\) | −18.6603 | + | 12.3205i | −0.600695 | + | 0.396611i | ||||
\(966\) | 9.00000 | − | 10.3923i | 0.289570 | − | 0.334367i | ||||
\(967\) | −32.0429 | + | 18.5000i | −1.03043 | + | 0.594920i | −0.917108 | − | 0.398638i | \(-0.869483\pi\) |
−0.113323 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(968\) | −64.9519 | − | 37.5000i | −2.08763 | − | 1.20530i | ||||
\(969\) | −18.0000 | + | 10.3923i | −0.578243 | + | 0.333849i | ||||
\(970\) | 4.46410 | − | 0.267949i | 0.143334 | − | 0.00860333i | ||||
\(971\) | −14.0000 | − | 24.2487i | −0.449281 | − | 0.778178i | 0.549058 | − | 0.835784i | \(-0.314987\pi\) |
−0.998339 | + | 0.0576061i | \(0.981653\pi\) | |||||||
\(972\) | 7.79423 | − | 13.5000i | 0.250000 | − | 0.433013i | ||||
\(973\) | 5.19615 | + | 1.00000i | 0.166581 | + | 0.0320585i | ||||
\(974\) | −6.00000 | + | 10.3923i | −0.192252 | + | 0.332991i | ||||
\(975\) | −27.7128 | + | 20.7846i | −0.887520 | + | 0.665640i | ||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | 12.0000i | 0.383914i | 0.981403 | + | 0.191957i | \(0.0614834\pi\) | ||||
−0.981403 | + | 0.191957i | \(0.938517\pi\) | |||||||
\(978\) | −3.46410 | + | 6.00000i | −0.110770 | + | 0.191859i | ||||
\(979\) | −9.00000 | + | 15.5885i | −0.287641 | + | 0.498209i | ||||
\(980\) | 11.6962 | − | 10.4019i | 0.373620 | − | 0.332277i | ||||
\(981\) | −15.0000 | − | 25.9808i | −0.478913 | − | 0.829502i | ||||
\(982\) | −27.7128 | + | 16.0000i | −0.884351 | + | 0.510581i | ||||
\(983\) | 20.7846 | − | 12.0000i | 0.662926 | − | 0.382741i | −0.130465 | − | 0.991453i | \(-0.541647\pi\) |
0.793391 | + | 0.608712i | \(0.208314\pi\) | |||||||
\(984\) | 9.00000 | + | 5.19615i | 0.286910 | + | 0.165647i | ||||
\(985\) | 26.1244 | − | 17.2487i | 0.832391 | − | 0.549590i | ||||
\(986\) | 2.00000 | + | 3.46410i | 0.0636930 | + | 0.110319i | ||||
\(987\) | −2.59808 | + | 13.5000i | −0.0826977 | + | 0.429710i | ||||
\(988\) | −20.7846 | − | 12.0000i | −0.661247 | − | 0.381771i | ||||
\(989\) | −1.50000 | − | 2.59808i | −0.0476972 | − | 0.0826140i | ||||
\(990\) | −33.5885 | + | 22.1769i | −1.06751 | + | 0.704829i | ||||
\(991\) | −20.0000 | + | 34.6410i | −0.635321 | + | 1.10041i | 0.351126 | + | 0.936328i | \(0.385799\pi\) |
−0.986447 | + | 0.164080i | \(0.947534\pi\) | |||||||
\(992\) | − | 20.0000i | − | 0.635001i | ||||||
\(993\) | −5.19615 | − | 9.00000i | −0.164895 | − | 0.285606i | ||||
\(994\) | 8.00000 | + | 6.92820i | 0.253745 | + | 0.219749i | ||||
\(995\) | 31.2487 | − | 1.87564i | 0.990651 | − | 0.0594619i | ||||
\(996\) | 6.92820i | 0.219529i | ||||||||
\(997\) | 8.66025 | − | 5.00000i | 0.274273 | − | 0.158352i | −0.356555 | − | 0.934274i | \(-0.616049\pi\) |
0.630828 | + | 0.775923i | \(0.282715\pi\) | |||||||
\(998\) | 24.2487 | + | 14.0000i | 0.767580 | + | 0.443162i | ||||
\(999\) | 36.0000 | − | 20.7846i | 1.13899 | − | 0.657596i |
(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 | 315.2.r.a.214.2 | yes | 4 | |
3.2 | odd | 2 | 945.2.r.a.424.1 | 4 | |||
5.4 | even | 2 | inner | 315.2.r.a.214.1 | yes | 4 | |
7.2 | even | 3 | 315.2.bo.a.79.2 | yes | 4 | ||
9.4 | even | 3 | 315.2.bo.a.4.1 | yes | 4 | ||
9.5 | odd | 6 | 945.2.bo.a.739.2 | 4 | |||
15.14 | odd | 2 | 945.2.r.a.424.2 | 4 | |||
21.2 | odd | 6 | 945.2.bo.a.289.1 | 4 | |||
35.9 | even | 6 | 315.2.bo.a.79.1 | yes | 4 | ||
45.4 | even | 6 | 315.2.bo.a.4.2 | yes | 4 | ||
45.14 | odd | 6 | 945.2.bo.a.739.1 | 4 | |||
63.23 | odd | 6 | 945.2.r.a.604.1 | 4 | |||
63.58 | even | 3 | inner | 315.2.r.a.184.2 | yes | 4 | |
105.44 | odd | 6 | 945.2.bo.a.289.2 | 4 | |||
315.149 | odd | 6 | 945.2.r.a.604.2 | 4 | |||
315.184 | even | 6 | inner | 315.2.r.a.184.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.r.a.184.1 | ✓ | 4 | 315.184 | even | 6 | inner | |
315.2.r.a.184.2 | yes | 4 | 63.58 | even | 3 | inner | |
315.2.r.a.214.1 | yes | 4 | 5.4 | even | 2 | inner | |
315.2.r.a.214.2 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.bo.a.4.1 | yes | 4 | 9.4 | even | 3 | ||
315.2.bo.a.4.2 | yes | 4 | 45.4 | even | 6 | ||
315.2.bo.a.79.1 | yes | 4 | 35.9 | even | 6 | ||
315.2.bo.a.79.2 | yes | 4 | 7.2 | even | 3 | ||
945.2.r.a.424.1 | 4 | 3.2 | odd | 2 | |||
945.2.r.a.424.2 | 4 | 15.14 | odd | 2 | |||
945.2.r.a.604.1 | 4 | 63.23 | odd | 6 | |||
945.2.r.a.604.2 | 4 | 315.149 | odd | 6 | |||
945.2.bo.a.289.1 | 4 | 21.2 | odd | 6 | |||
945.2.bo.a.289.2 | 4 | 105.44 | odd | 6 | |||
945.2.bo.a.739.1 | 4 | 45.14 | odd | 6 | |||
945.2.bo.a.739.2 | 4 | 9.5 | odd | 6 |