Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(459,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.g (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 459.8 | ||
Root | \(-1.14412 + 1.98168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.459 |
Dual form | 460.2.g.b.459.6 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.500000 | + | 0.866025i | ||||
\(3\) | −2.82843 | −1.63299 | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | −2.00000 | − | 3.46410i | −0.816497 | − | 1.41421i | ||||
\(7\) | − | 3.87298i | − | 1.46385i | −0.681385 | − | 0.731925i | \(-0.738622\pi\) | ||
0.681385 | − | 0.731925i | \(-0.261378\pi\) | |||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 5.00000 | 1.66667 | ||||||||
\(10\) | 1.58114 | + | 2.73861i | 0.500000 | + | 0.866025i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 2.82843 | − | 4.89898i | 0.816497 | − | 1.41421i | ||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 4.74342 | − | 2.73861i | 1.26773 | − | 0.731925i | ||||
\(15\) | −6.32456 | −1.63299 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −2.23607 | −0.542326 | −0.271163 | − | 0.962533i | \(-0.587408\pi\) | ||||
−0.271163 | + | 0.962533i | \(0.587408\pi\) | |||||||
\(18\) | 3.53553 | + | 6.12372i | 0.833333 | + | 1.44338i | ||||
\(19\) | 6.32456 | 1.45095 | 0.725476 | − | 0.688247i | \(-0.241620\pi\) | ||||
0.725476 | + | 0.688247i | \(0.241620\pi\) | |||||||
\(20\) | −2.23607 | + | 3.87298i | −0.500000 | + | 0.866025i | ||||
\(21\) | 10.9545i | 2.39046i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | + | 3.87298i | 0.589768 | + | 0.807573i | ||||
\(24\) | 8.00000 | 1.63299 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 6.00000 | − | 3.46410i | 1.17670 | − | 0.679366i | ||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 6.70820 | + | 3.87298i | 1.26773 | + | 0.731925i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −4.47214 | − | 7.74597i | −0.816497 | − | 1.41421i | ||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.58114 | − | 2.73861i | −0.271163 | − | 0.469668i | ||||
\(35\) | − | 8.66025i | − | 1.46385i | ||||||
\(36\) | −5.00000 | + | 8.66025i | −0.833333 | + | 1.44338i | ||||
\(37\) | 6.70820 | 1.10282 | 0.551411 | − | 0.834234i | \(-0.314090\pi\) | ||||
0.551411 | + | 0.834234i | \(0.314090\pi\) | |||||||
\(38\) | 4.47214 | + | 7.74597i | 0.725476 | + | 1.25656i | ||||
\(39\) | 13.8564i | 2.21880i | ||||||||
\(40\) | −6.32456 | −1.00000 | ||||||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | −13.4164 | + | 7.74597i | −2.07020 | + | 1.19523i | ||||
\(43\) | − | 7.74597i | − | 1.18125i | −0.806947 | − | 0.590624i | \(-0.798881\pi\) | ||
0.806947 | − | 0.590624i | \(-0.201119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1803 | 1.66667 | ||||||||
\(46\) | −2.74342 | + | 6.20271i | −0.404495 | + | 0.914540i | ||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 5.65685 | + | 9.79796i | 0.816497 | + | 1.41421i | ||||
\(49\) | −8.00000 | −1.14286 | ||||||||
\(50\) | 3.53553 | + | 6.12372i | 0.500000 | + | 0.866025i | ||||
\(51\) | 6.32456 | 0.885615 | ||||||||
\(52\) | 8.48528 | + | 4.89898i | 1.17670 | + | 0.679366i | ||||
\(53\) | −2.23607 | −0.307148 | −0.153574 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153574 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(54\) | −4.00000 | − | 6.92820i | −0.544331 | − | 0.942809i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.9545i | 1.46385i | ||||||||
\(57\) | −17.8885 | −2.36940 | ||||||||
\(58\) | 2.12132 | + | 3.67423i | 0.278543 | + | 0.482451i | ||||
\(59\) | − | 8.66025i | − | 1.12747i | −0.825956 | − | 0.563735i | \(-0.809364\pi\) | ||
0.825956 | − | 0.563735i | \(-0.190636\pi\) | |||||||
\(60\) | 6.32456 | − | 10.9545i | 0.816497 | − | 1.41421i | ||||
\(61\) | − | 10.9545i | − | 1.40257i | −0.712879 | − | 0.701287i | \(-0.752609\pi\) | ||
0.712879 | − | 0.701287i | \(-0.247391\pi\) | |||||||
\(62\) | 2.12132 | − | 1.22474i | 0.269408 | − | 0.155543i | ||||
\(63\) | − | 19.3649i | − | 2.43975i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | − | 10.9545i | − | 1.35873i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6190i | 1.41948i | 0.704463 | + | 0.709740i | \(0.251188\pi\) | ||||
−0.704463 | + | 0.709740i | \(0.748812\pi\) | |||||||
\(68\) | 2.23607 | − | 3.87298i | 0.271163 | − | 0.469668i | ||||
\(69\) | −8.00000 | − | 10.9545i | −0.963087 | − | 1.31876i | ||||
\(70\) | 10.6066 | − | 6.12372i | 1.26773 | − | 0.731925i | ||||
\(71\) | − | 1.73205i | − | 0.205557i | −0.994704 | − | 0.102778i | \(-0.967227\pi\) | ||
0.994704 | − | 0.102778i | \(-0.0327732\pi\) | |||||||
\(72\) | −14.1421 | −1.66667 | ||||||||
\(73\) | − | 4.89898i | − | 0.573382i | −0.958023 | − | 0.286691i | \(-0.907445\pi\) | ||
0.958023 | − | 0.286691i | \(-0.0925553\pi\) | |||||||
\(74\) | 4.74342 | + | 8.21584i | 0.551411 | + | 0.955072i | ||||
\(75\) | −14.1421 | −1.63299 | ||||||||
\(76\) | −6.32456 | + | 10.9545i | −0.725476 | + | 1.25656i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −16.9706 | + | 9.79796i | −1.92154 | + | 1.10940i | ||||
\(79\) | 12.6491 | 1.42314 | 0.711568 | − | 0.702617i | \(-0.247985\pi\) | ||||
0.711568 | + | 0.702617i | \(0.247985\pi\) | |||||||
\(80\) | −4.47214 | − | 7.74597i | −0.500000 | − | 0.866025i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.36396 | − | 11.0227i | −0.702782 | − | 1.21725i | ||||
\(83\) | − | 3.87298i | − | 0.425115i | −0.977149 | − | 0.212558i | \(-0.931821\pi\) | ||
0.977149 | − | 0.212558i | \(-0.0681793\pi\) | |||||||
\(84\) | −18.9737 | − | 10.9545i | −2.07020 | − | 1.19523i | ||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 9.48683 | − | 5.47723i | 1.02299 | − | 0.590624i | ||||
\(87\) | −8.48528 | −0.909718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9545i | 1.16117i | 0.814200 | + | 0.580585i | \(0.197176\pi\) | ||||
−0.814200 | + | 0.580585i | \(0.802824\pi\) | |||||||
\(90\) | 7.90569 | + | 13.6931i | 0.833333 | + | 1.44338i | ||||
\(91\) | −18.9737 | −1.98898 | ||||||||
\(92\) | −9.53663 | + | 1.02600i | −0.994263 | + | 0.106967i | ||||
\(93\) | 4.89898i | 0.508001i | ||||||||
\(94\) | −4.00000 | − | 6.92820i | −0.412568 | − | 0.714590i | ||||
\(95\) | 14.1421 | 1.45095 | ||||||||
\(96\) | −8.00000 | + | 13.8564i | −0.816497 | + | 1.41421i | ||||
\(97\) | 13.4164 | 1.36223 | 0.681115 | − | 0.732177i | \(-0.261495\pi\) | ||||
0.681115 | + | 0.732177i | \(0.261495\pi\) | |||||||
\(98\) | −5.65685 | − | 9.79796i | −0.571429 | − | 0.989743i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | + | 8.66025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 3.00000 | 0.298511 | 0.149256 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149256 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(102\) | 4.47214 | + | 7.74597i | 0.442807 | + | 0.766965i | ||||
\(103\) | 7.74597i | 0.763233i | 0.924321 | + | 0.381616i | \(0.124632\pi\) | ||||
−0.924321 | + | 0.381616i | \(0.875368\pi\) | |||||||
\(104\) | 13.8564i | 1.35873i | ||||||||
\(105\) | 24.4949i | 2.39046i | ||||||||
\(106\) | −1.58114 | − | 2.73861i | −0.153574 | − | 0.265998i | ||||
\(107\) | 11.6190i | 1.12325i | 0.827393 | + | 0.561623i | \(0.189823\pi\) | ||||
−0.827393 | + | 0.561623i | \(0.810177\pi\) | |||||||
\(108\) | 5.65685 | − | 9.79796i | 0.544331 | − | 0.942809i | ||||
\(109\) | − | 10.9545i | − | 1.04925i | −0.851335 | − | 0.524623i | \(-0.824206\pi\) | ||
0.851335 | − | 0.524623i | \(-0.175794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.9737 | −1.80090 | ||||||||
\(112\) | −13.4164 | + | 7.74597i | −1.26773 | + | 0.731925i | ||||
\(113\) | −11.1803 | −1.05176 | −0.525879 | − | 0.850559i | \(-0.676264\pi\) | ||||
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(114\) | −12.6491 | − | 21.9089i | −1.18470 | − | 2.05196i | ||||
\(115\) | 6.32456 | + | 8.66025i | 0.589768 | + | 0.807573i | ||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | − | 24.4949i | − | 2.26455i | ||||||
\(118\) | 10.6066 | − | 6.12372i | 0.976417 | − | 0.563735i | ||||
\(119\) | 8.66025i | 0.793884i | ||||||||
\(120\) | 17.8885 | 1.63299 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 13.4164 | − | 7.74597i | 1.21466 | − | 0.701287i | ||||
\(123\) | 25.4558 | 2.29528 | ||||||||
\(124\) | 3.00000 | + | 1.73205i | 0.269408 | + | 0.155543i | ||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 23.7171 | − | 13.6931i | 2.11289 | − | 1.21988i | ||||
\(127\) | −8.48528 | −0.752947 | −0.376473 | − | 0.926427i | \(-0.622863\pi\) | ||||
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.500000 | + | 0.866025i | ||||
\(129\) | 21.9089i | 1.92897i | ||||||||
\(130\) | 13.4164 | − | 7.74597i | 1.17670 | − | 0.679366i | ||||
\(131\) | − | 10.3923i | − | 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 24.4949i | − | 2.12398i | ||||||
\(134\) | −14.2302 | + | 8.21584i | −1.22931 | + | 0.709740i | ||||
\(135\) | −12.6491 | −1.08866 | ||||||||
\(136\) | 6.32456 | 0.542326 | ||||||||
\(137\) | −4.47214 | −0.382080 | −0.191040 | − | 0.981582i | \(-0.561186\pi\) | ||||
−0.191040 | + | 0.981582i | \(0.561186\pi\) | |||||||
\(138\) | 7.75955 | − | 17.5439i | 0.660537 | − | 1.49344i | ||||
\(139\) | 5.19615i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 15.0000 | + | 8.66025i | 1.26773 | + | 0.731925i | ||||
\(141\) | 16.0000 | 1.34744 | ||||||||
\(142\) | 2.12132 | − | 1.22474i | 0.178017 | − | 0.102778i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.0000 | − | 17.3205i | −0.833333 | − | 1.44338i | ||||
\(145\) | 6.70820 | 0.557086 | ||||||||
\(146\) | 6.00000 | − | 3.46410i | 0.496564 | − | 0.286691i | ||||
\(147\) | 22.6274 | 1.86628 | ||||||||
\(148\) | −6.70820 | + | 11.6190i | −0.551411 | + | 0.955072i | ||||
\(149\) | 10.9545i | 0.897424i | 0.893677 | + | 0.448712i | \(0.148117\pi\) | ||||
−0.893677 | + | 0.448712i | \(0.851883\pi\) | |||||||
\(150\) | −10.0000 | − | 17.3205i | −0.816497 | − | 1.41421i | ||||
\(151\) | 10.3923i | 0.845714i | 0.906196 | + | 0.422857i | \(0.138973\pi\) | ||||
−0.906196 | + | 0.422857i | \(0.861027\pi\) | |||||||
\(152\) | −17.8885 | −1.45095 | ||||||||
\(153\) | −11.1803 | −0.903877 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.87298i | − | 0.311086i | ||||||
\(156\) | −24.0000 | − | 13.8564i | −1.92154 | − | 1.10940i | ||||
\(157\) | 6.70820 | 0.535373 | 0.267686 | − | 0.963506i | \(-0.413741\pi\) | ||||
0.267686 | + | 0.963506i | \(0.413741\pi\) | |||||||
\(158\) | 8.94427 | + | 15.4919i | 0.711568 | + | 1.23247i | ||||
\(159\) | 6.32456 | 0.501570 | ||||||||
\(160\) | 6.32456 | − | 10.9545i | 0.500000 | − | 0.866025i | ||||
\(161\) | 15.0000 | − | 10.9545i | 1.18217 | − | 0.863332i | ||||
\(162\) | 0.707107 | + | 1.22474i | 0.0555556 | + | 0.0962250i | ||||
\(163\) | −16.9706 | −1.32924 | −0.664619 | − | 0.747183i | \(-0.731406\pi\) | ||||
−0.664619 | + | 0.747183i | \(0.731406\pi\) | |||||||
\(164\) | 9.00000 | − | 15.5885i | 0.702782 | − | 1.21725i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.74342 | − | 2.73861i | 0.368161 | − | 0.212558i | ||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | − | 30.9839i | − | 2.39046i | ||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −3.53553 | − | 6.12372i | −0.271163 | − | 0.469668i | ||||
\(171\) | 31.6228 | 2.41825 | ||||||||
\(172\) | 13.4164 | + | 7.74597i | 1.02299 | + | 0.590624i | ||||
\(173\) | 24.4949i | 1.86231i | 0.364620 | + | 0.931156i | \(0.381199\pi\) | ||||
−0.364620 | + | 0.931156i | \(0.618801\pi\) | |||||||
\(174\) | −6.00000 | − | 10.3923i | −0.454859 | − | 0.787839i | ||||
\(175\) | − | 19.3649i | − | 1.46385i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.4949i | 1.84115i | ||||||||
\(178\) | −13.4164 | + | 7.74597i | −1.00560 | + | 0.580585i | ||||
\(179\) | 3.46410i | 0.258919i | 0.991585 | + | 0.129460i | \(0.0413242\pi\) | ||||
−0.991585 | + | 0.129460i | \(0.958676\pi\) | |||||||
\(180\) | −11.1803 | + | 19.3649i | −0.833333 | + | 1.44338i | ||||
\(181\) | 10.9545i | 0.814238i | 0.913375 | + | 0.407119i | \(0.133467\pi\) | ||||
−0.913375 | + | 0.407119i | \(0.866533\pi\) | |||||||
\(182\) | −13.4164 | − | 23.2379i | −0.994490 | − | 1.72251i | ||||
\(183\) | 30.9839i | 2.29039i | ||||||||
\(184\) | −8.00000 | − | 10.9545i | −0.589768 | − | 0.807573i | ||||
\(185\) | 15.0000 | 1.10282 | ||||||||
\(186\) | −6.00000 | + | 3.46410i | −0.439941 | + | 0.254000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.65685 | − | 9.79796i | 0.412568 | − | 0.714590i | ||||
\(189\) | 21.9089i | 1.59364i | ||||||||
\(190\) | 10.0000 | + | 17.3205i | 0.725476 | + | 1.25656i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −22.6274 | −1.63299 | ||||||||
\(193\) | 4.89898i | 0.352636i | 0.984333 | + | 0.176318i | \(0.0564187\pi\) | ||||
−0.984333 | + | 0.176318i | \(0.943581\pi\) | |||||||
\(194\) | 9.48683 | + | 16.4317i | 0.681115 | + | 1.17973i | ||||
\(195\) | 30.9839i | 2.21880i | ||||||||
\(196\) | 8.00000 | − | 13.8564i | 0.571429 | − | 0.989743i | ||||
\(197\) | − | 9.79796i | − | 0.698076i | −0.937109 | − | 0.349038i | \(-0.886508\pi\) | ||
0.937109 | − | 0.349038i | \(-0.113492\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.32456 | −0.448336 | −0.224168 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224168 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(200\) | −14.1421 | −1.00000 | ||||||||
\(201\) | − | 32.8634i | − | 2.31800i | ||||||
\(202\) | 2.12132 | + | 3.67423i | 0.149256 | + | 0.258518i | ||||
\(203\) | − | 11.6190i | − | 0.815490i | ||||||
\(204\) | −6.32456 | + | 10.9545i | −0.442807 | + | 0.766965i | ||||
\(205\) | −20.1246 | −1.40556 | ||||||||
\(206\) | −9.48683 | + | 5.47723i | −0.660979 | + | 0.381616i | ||||
\(207\) | 14.1421 | + | 19.3649i | 0.982946 | + | 1.34595i | ||||
\(208\) | −16.9706 | + | 9.79796i | −1.17670 | + | 0.679366i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −30.0000 | + | 17.3205i | −2.07020 | + | 1.19523i | ||||
\(211\) | − | 8.66025i | − | 0.596196i | −0.954535 | − | 0.298098i | \(-0.903648\pi\) | ||
0.954535 | − | 0.298098i | \(-0.0963523\pi\) | |||||||
\(212\) | 2.23607 | − | 3.87298i | 0.153574 | − | 0.265998i | ||||
\(213\) | 4.89898i | 0.335673i | ||||||||
\(214\) | −14.2302 | + | 8.21584i | −0.972760 | + | 0.561623i | ||||
\(215\) | − | 17.3205i | − | 1.18125i | ||||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | −6.70820 | −0.455383 | ||||||||
\(218\) | 13.4164 | − | 7.74597i | 0.908674 | − | 0.524623i | ||||
\(219\) | 13.8564i | 0.936329i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9545i | 0.736876i | ||||||||
\(222\) | −13.4164 | − | 23.2379i | −0.900450 | − | 1.55963i | ||||
\(223\) | −8.48528 | −0.568216 | −0.284108 | − | 0.958792i | \(-0.591698\pi\) | ||||
−0.284108 | + | 0.958792i | \(0.591698\pi\) | |||||||
\(224\) | −18.9737 | − | 10.9545i | −1.26773 | − | 0.731925i | ||||
\(225\) | 25.0000 | 1.66667 | ||||||||
\(226\) | −7.90569 | − | 13.6931i | −0.525879 | − | 0.910849i | ||||
\(227\) | − | 7.74597i | − | 0.514118i | −0.966396 | − | 0.257059i | \(-0.917247\pi\) | ||
0.966396 | − | 0.257059i | \(-0.0827534\pi\) | |||||||
\(228\) | 17.8885 | − | 30.9839i | 1.18470 | − | 2.05196i | ||||
\(229\) | − | 10.9545i | − | 0.723891i | −0.932199 | − | 0.361945i | \(-0.882113\pi\) | ||
0.932199 | − | 0.361945i | \(-0.117887\pi\) | |||||||
\(230\) | −6.13447 | + | 13.8697i | −0.404495 | + | 0.914540i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.48528 | −0.557086 | ||||||||
\(233\) | 29.3939i | 1.92566i | 0.270114 | + | 0.962828i | \(0.412939\pi\) | ||||
−0.270114 | + | 0.962828i | \(0.587061\pi\) | |||||||
\(234\) | 30.0000 | − | 17.3205i | 1.96116 | − | 1.13228i | ||||
\(235\) | −12.6491 | −0.825137 | ||||||||
\(236\) | 15.0000 | + | 8.66025i | 0.976417 | + | 0.563735i | ||||
\(237\) | −35.7771 | −2.32397 | ||||||||
\(238\) | −10.6066 | + | 6.12372i | −0.687524 | + | 0.396942i | ||||
\(239\) | 12.1244i | 0.784259i | 0.919910 | + | 0.392130i | \(0.128262\pi\) | ||||
−0.919910 | + | 0.392130i | \(0.871738\pi\) | |||||||
\(240\) | 12.6491 | + | 21.9089i | 0.816497 | + | 1.41421i | ||||
\(241\) | 10.9545i | 0.705638i | 0.935692 | + | 0.352819i | \(0.114777\pi\) | ||||
−0.935692 | + | 0.352819i | \(0.885223\pi\) | |||||||
\(242\) | −7.77817 | − | 13.4722i | −0.500000 | − | 0.866025i | ||||
\(243\) | 14.1421 | 0.907218 | ||||||||
\(244\) | 18.9737 | + | 10.9545i | 1.21466 | + | 0.701287i | ||||
\(245\) | −17.8885 | −1.14286 | ||||||||
\(246\) | 18.0000 | + | 31.1769i | 1.14764 | + | 1.98777i | ||||
\(247\) | − | 30.9839i | − | 1.97146i | ||||||
\(248\) | 4.89898i | 0.311086i | ||||||||
\(249\) | 10.9545i | 0.694210i | ||||||||
\(250\) | 7.90569 | + | 13.6931i | 0.500000 | + | 0.866025i | ||||
\(251\) | 18.9737 | 1.19761 | 0.598804 | − | 0.800896i | \(-0.295643\pi\) | ||||
0.598804 | + | 0.800896i | \(0.295643\pi\) | |||||||
\(252\) | 33.5410 | + | 19.3649i | 2.11289 | + | 1.21988i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.00000 | − | 10.3923i | −0.376473 | − | 0.652071i | ||||
\(255\) | 14.1421 | 0.885615 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | − | 9.79796i | − | 0.611180i | −0.952163 | − | 0.305590i | \(-0.901146\pi\) | ||
0.952163 | − | 0.305590i | \(-0.0988537\pi\) | |||||||
\(258\) | −26.8328 | + | 15.4919i | −1.67054 | + | 0.964486i | ||||
\(259\) | − | 25.9808i | − | 1.61437i | ||||||
\(260\) | 18.9737 | + | 10.9545i | 1.17670 | + | 0.679366i | ||||
\(261\) | 15.0000 | 0.928477 | ||||||||
\(262\) | 12.7279 | − | 7.34847i | 0.786334 | − | 0.453990i | ||||
\(263\) | 11.6190i | 0.716455i | 0.933634 | + | 0.358228i | \(0.116619\pi\) | ||||
−0.933634 | + | 0.358228i | \(0.883381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.00000 | −0.307148 | ||||||||
\(266\) | 30.0000 | − | 17.3205i | 1.83942 | − | 1.06199i | ||||
\(267\) | − | 30.9839i | − | 1.89618i | ||||||
\(268\) | −20.1246 | − | 11.6190i | −1.22931 | − | 0.709740i | ||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | −8.94427 | − | 15.4919i | −0.544331 | − | 0.942809i | ||||
\(271\) | − | 8.66025i | − | 0.526073i | −0.964786 | − | 0.263036i | \(-0.915276\pi\) | ||
0.964786 | − | 0.263036i | \(-0.0847240\pi\) | |||||||
\(272\) | 4.47214 | + | 7.74597i | 0.271163 | + | 0.469668i | ||||
\(273\) | 53.6656 | 3.24799 | ||||||||
\(274\) | −3.16228 | − | 5.47723i | −0.191040 | − | 0.330891i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 26.9737 | − | 2.90196i | 1.62362 | − | 0.174677i | ||||
\(277\) | 9.79796i | 0.588702i | 0.955697 | + | 0.294351i | \(0.0951035\pi\) | ||||
−0.955697 | + | 0.294351i | \(0.904896\pi\) | |||||||
\(278\) | −6.36396 | + | 3.67423i | −0.381685 | + | 0.220366i | ||||
\(279\) | − | 8.66025i | − | 0.518476i | ||||||
\(280\) | 24.4949i | 1.46385i | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 11.3137 | + | 19.5959i | 0.673722 | + | 1.16692i | ||||
\(283\) | 11.6190i | 0.690675i | 0.938479 | + | 0.345337i | \(0.112236\pi\) | ||||
−0.938479 | + | 0.345337i | \(0.887764\pi\) | |||||||
\(284\) | 3.00000 | + | 1.73205i | 0.178017 | + | 0.102778i | ||||
\(285\) | −40.0000 | −2.36940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.8569i | 2.05753i | ||||||||
\(288\) | 14.1421 | − | 24.4949i | 0.833333 | − | 1.44338i | ||||
\(289\) | −12.0000 | −0.705882 | ||||||||
\(290\) | 4.74342 | + | 8.21584i | 0.278543 | + | 0.482451i | ||||
\(291\) | −37.9473 | −2.22451 | ||||||||
\(292\) | 8.48528 | + | 4.89898i | 0.496564 | + | 0.286691i | ||||
\(293\) | 24.5967 | 1.43696 | 0.718479 | − | 0.695549i | \(-0.244839\pi\) | ||||
0.718479 | + | 0.695549i | \(0.244839\pi\) | |||||||
\(294\) | 16.0000 | + | 27.7128i | 0.933139 | + | 1.61624i | ||||
\(295\) | − | 19.3649i | − | 1.12747i | ||||||
\(296\) | −18.9737 | −1.10282 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.4164 | + | 7.74597i | −0.777192 | + | 0.448712i | ||||
\(299\) | 18.9737 | − | 13.8564i | 1.09728 | − | 0.801337i | ||||
\(300\) | 14.1421 | − | 24.4949i | 0.816497 | − | 1.41421i | ||||
\(301\) | −30.0000 | −1.72917 | ||||||||
\(302\) | −12.7279 | + | 7.34847i | −0.732410 | + | 0.422857i | ||||
\(303\) | −8.48528 | −0.487467 | ||||||||
\(304\) | −12.6491 | − | 21.9089i | −0.725476 | − | 1.25656i | ||||
\(305\) | − | 24.4949i | − | 1.40257i | ||||||
\(306\) | −7.90569 | − | 13.6931i | −0.451938 | − | 0.782780i | ||||
\(307\) | −16.9706 | −0.968561 | −0.484281 | − | 0.874913i | \(-0.660919\pi\) | ||||
−0.484281 | + | 0.874913i | \(0.660919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 21.9089i | − | 1.24635i | ||||||
\(310\) | 4.74342 | − | 2.73861i | 0.269408 | − | 0.155543i | ||||
\(311\) | 10.3923i | 0.589294i | 0.955606 | + | 0.294647i | \(0.0952020\pi\) | ||||
−0.955606 | + | 0.294647i | \(0.904798\pi\) | |||||||
\(312\) | − | 39.1918i | − | 2.21880i | ||||||
\(313\) | −20.1246 | −1.13751 | −0.568755 | − | 0.822507i | \(-0.692575\pi\) | ||||
−0.568755 | + | 0.822507i | \(0.692575\pi\) | |||||||
\(314\) | 4.74342 | + | 8.21584i | 0.267686 | + | 0.463647i | ||||
\(315\) | − | 43.3013i | − | 2.43975i | ||||||
\(316\) | −12.6491 | + | 21.9089i | −0.711568 | + | 1.23247i | ||||
\(317\) | 24.4949i | 1.37577i | 0.725819 | + | 0.687885i | \(0.241461\pi\) | ||||
−0.725819 | + | 0.687885i | \(0.758539\pi\) | |||||||
\(318\) | 4.47214 | + | 7.74597i | 0.250785 | + | 0.434372i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.8885 | 1.00000 | ||||||||
\(321\) | − | 32.8634i | − | 1.83425i | ||||||
\(322\) | 24.0230 | + | 10.6252i | 1.33875 | + | 0.592120i | ||||
\(323\) | −14.1421 | −0.786889 | ||||||||
\(324\) | −1.00000 | + | 1.73205i | −0.0555556 | + | 0.0962250i | ||||
\(325\) | − | 24.4949i | − | 1.35873i | ||||||
\(326\) | −12.0000 | − | 20.7846i | −0.664619 | − | 1.15115i | ||||
\(327\) | 30.9839i | 1.71341i | ||||||||
\(328\) | 25.4558 | 1.40556 | ||||||||
\(329\) | 21.9089i | 1.20788i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.5885i | − | 0.856819i | −0.903585 | − | 0.428410i | \(-0.859074\pi\) | ||
0.903585 | − | 0.428410i | \(-0.140926\pi\) | |||||||
\(332\) | 6.70820 | + | 3.87298i | 0.368161 | + | 0.212558i | ||||
\(333\) | 33.5410 | 1.83804 | ||||||||
\(334\) | 8.00000 | + | 13.8564i | 0.437741 | + | 0.758189i | ||||
\(335\) | 25.9808i | 1.41948i | ||||||||
\(336\) | 37.9473 | − | 21.9089i | 2.07020 | − | 1.19523i | ||||
\(337\) | 13.4164 | 0.730838 | 0.365419 | − | 0.930843i | \(-0.380926\pi\) | ||||
0.365419 | + | 0.930843i | \(0.380926\pi\) | |||||||
\(338\) | −7.77817 | − | 13.4722i | −0.423077 | − | 0.732791i | ||||
\(339\) | 31.6228 | 1.71751 | ||||||||
\(340\) | 5.00000 | − | 8.66025i | 0.271163 | − | 0.469668i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 22.3607 | + | 38.7298i | 1.20913 | + | 2.09427i | ||||
\(343\) | 3.87298i | 0.209121i | ||||||||
\(344\) | 21.9089i | 1.18125i | ||||||||
\(345\) | −17.8885 | − | 24.4949i | −0.963087 | − | 1.31876i | ||||
\(346\) | −30.0000 | + | 17.3205i | −1.61281 | + | 0.931156i | ||||
\(347\) | 2.82843 | 0.151838 | 0.0759190 | − | 0.997114i | \(-0.475811\pi\) | ||||
0.0759190 | + | 0.997114i | \(0.475811\pi\) | |||||||
\(348\) | 8.48528 | − | 14.6969i | 0.454859 | − | 0.787839i | ||||
\(349\) | 23.0000 | 1.23116 | 0.615581 | − | 0.788074i | \(-0.288921\pi\) | ||||
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 23.7171 | − | 13.6931i | 1.26773 | − | 0.731925i | ||||
\(351\) | 27.7128i | 1.47920i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.3939i | − | 1.56448i | −0.622978 | − | 0.782239i | \(-0.714078\pi\) | ||
0.622978 | − | 0.782239i | \(-0.285922\pi\) | |||||||
\(354\) | −30.0000 | + | 17.3205i | −1.59448 | + | 0.920575i | ||||
\(355\) | − | 3.87298i | − | 0.205557i | ||||||
\(356\) | −18.9737 | − | 10.9545i | −1.00560 | − | 0.580585i | ||||
\(357\) | − | 24.4949i | − | 1.29641i | ||||||
\(358\) | −4.24264 | + | 2.44949i | −0.224231 | + | 0.129460i | ||||
\(359\) | 18.9737 | 1.00139 | 0.500696 | − | 0.865623i | \(-0.333077\pi\) | ||||
0.500696 | + | 0.865623i | \(0.333077\pi\) | |||||||
\(360\) | −31.6228 | −1.66667 | ||||||||
\(361\) | 21.0000 | 1.10526 | ||||||||
\(362\) | −13.4164 | + | 7.74597i | −0.705151 | + | 0.407119i | ||||
\(363\) | 31.1127 | 1.63299 | ||||||||
\(364\) | 18.9737 | − | 32.8634i | 0.994490 | − | 1.72251i | ||||
\(365\) | − | 10.9545i | − | 0.573382i | ||||||
\(366\) | −37.9473 | + | 21.9089i | −1.98354 | + | 1.14520i | ||||
\(367\) | − | 3.87298i | − | 0.202168i | −0.994878 | − | 0.101084i | \(-0.967769\pi\) | ||
0.994878 | − | 0.101084i | \(-0.0322311\pi\) | |||||||
\(368\) | 7.75955 | − | 17.5439i | 0.404495 | − | 0.914540i | ||||
\(369\) | −45.0000 | −2.34261 | ||||||||
\(370\) | 10.6066 | + | 18.3712i | 0.551411 | + | 0.955072i | ||||
\(371\) | 8.66025i | 0.449618i | ||||||||
\(372\) | −8.48528 | − | 4.89898i | −0.439941 | − | 0.254000i | ||||
\(373\) | −13.4164 | −0.694675 | −0.347338 | − | 0.937740i | \(-0.612914\pi\) | ||||
−0.347338 | + | 0.937740i | \(0.612914\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.6228 | −1.63299 | ||||||||
\(376\) | 16.0000 | 0.825137 | ||||||||
\(377\) | − | 14.6969i | − | 0.756931i | ||||||
\(378\) | −26.8328 | + | 15.4919i | −1.38013 | + | 0.796819i | ||||
\(379\) | 6.32456 | 0.324871 | 0.162435 | − | 0.986719i | \(-0.448065\pi\) | ||||
0.162435 | + | 0.986719i | \(0.448065\pi\) | |||||||
\(380\) | −14.1421 | + | 24.4949i | −0.725476 | + | 1.25656i | ||||
\(381\) | 24.0000 | 1.22956 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.87298i | − | 0.197900i | −0.995092 | − | 0.0989501i | \(-0.968452\pi\) | ||
0.995092 | − | 0.0989501i | \(-0.0315484\pi\) | |||||||
\(384\) | −16.0000 | − | 27.7128i | −0.816497 | − | 1.41421i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | + | 3.46410i | −0.305392 | + | 0.176318i | ||||
\(387\) | − | 38.7298i | − | 1.96875i | ||||||
\(388\) | −13.4164 | + | 23.2379i | −0.681115 | + | 1.17973i | ||||
\(389\) | − | 21.9089i | − | 1.11083i | −0.831575 | − | 0.555413i | \(-0.812560\pi\) | ||
0.831575 | − | 0.555413i | \(-0.187440\pi\) | |||||||
\(390\) | −37.9473 | + | 21.9089i | −1.92154 | + | 1.10940i | ||||
\(391\) | −6.32456 | − | 8.66025i | −0.319847 | − | 0.437968i | ||||
\(392\) | 22.6274 | 1.14286 | ||||||||
\(393\) | 29.3939i | 1.48272i | ||||||||
\(394\) | 12.0000 | − | 6.92820i | 0.604551 | − | 0.349038i | ||||
\(395\) | 28.2843 | 1.42314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.2929i | 1.72111i | 0.509358 | + | 0.860555i | \(0.329883\pi\) | ||||
−0.509358 | + | 0.860555i | \(0.670117\pi\) | |||||||
\(398\) | −4.47214 | − | 7.74597i | −0.224168 | − | 0.388270i | ||||
\(399\) | 69.2820i | 3.46844i | ||||||||
\(400\) | −10.0000 | − | 17.3205i | −0.500000 | − | 0.866025i | ||||
\(401\) | 21.9089i | 1.09408i | 0.837107 | + | 0.547039i | \(0.184245\pi\) | ||||
−0.837107 | + | 0.547039i | \(0.815755\pi\) | |||||||
\(402\) | 40.2492 | − | 23.2379i | 2.00745 | − | 1.15900i | ||||
\(403\) | −8.48528 | −0.422682 | ||||||||
\(404\) | −3.00000 | + | 5.19615i | −0.149256 | + | 0.258518i | ||||
\(405\) | 2.23607 | 0.111111 | ||||||||
\(406\) | 14.2302 | − | 8.21584i | 0.706235 | − | 0.407745i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −17.8885 | −0.885615 | ||||||||
\(409\) | 7.00000 | 0.346128 | 0.173064 | − | 0.984911i | \(-0.444633\pi\) | ||||
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | −14.2302 | − | 24.6475i | −0.702782 | − | 1.21725i | ||||
\(411\) | 12.6491 | 0.623935 | ||||||||
\(412\) | −13.4164 | − | 7.74597i | −0.660979 | − | 0.381616i | ||||
\(413\) | −33.5410 | −1.65045 | ||||||||
\(414\) | −13.7171 | + | 31.0136i | −0.674158 | + | 1.52423i | ||||
\(415\) | − | 8.66025i | − | 0.425115i | ||||||
\(416\) | −24.0000 | − | 13.8564i | −1.17670 | − | 0.679366i | ||||
\(417\) | − | 14.6969i | − | 0.719712i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −42.4264 | − | 24.4949i | −2.07020 | − | 1.19523i | ||||
\(421\) | 21.9089i | 1.06777i | 0.845556 | + | 0.533887i | \(0.179269\pi\) | ||||
−0.845556 | + | 0.533887i | \(0.820731\pi\) | |||||||
\(422\) | 10.6066 | − | 6.12372i | 0.516321 | − | 0.298098i | ||||
\(423\) | −28.2843 | −1.37523 | ||||||||
\(424\) | 6.32456 | 0.307148 | ||||||||
\(425\) | −11.1803 | −0.542326 | ||||||||
\(426\) | −6.00000 | + | 3.46410i | −0.290701 | + | 0.167836i | ||||
\(427\) | −42.4264 | −2.05316 | ||||||||
\(428\) | −20.1246 | − | 11.6190i | −0.972760 | − | 0.561623i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.2132 | − | 12.2474i | 1.02299 | − | 0.590624i | ||||
\(431\) | −18.9737 | −0.913929 | −0.456965 | − | 0.889485i | \(-0.651063\pi\) | ||||
−0.456965 | + | 0.889485i | \(0.651063\pi\) | |||||||
\(432\) | 11.3137 | + | 19.5959i | 0.544331 | + | 0.942809i | ||||
\(433\) | 33.5410 | 1.61188 | 0.805939 | − | 0.591998i | \(-0.201661\pi\) | ||||
0.805939 | + | 0.591998i | \(0.201661\pi\) | |||||||
\(434\) | −4.74342 | − | 8.21584i | −0.227691 | − | 0.394373i | ||||
\(435\) | −18.9737 | −0.909718 | ||||||||
\(436\) | 18.9737 | + | 10.9545i | 0.908674 | + | 0.524623i | ||||
\(437\) | 17.8885 | + | 24.4949i | 0.855725 | + | 1.17175i | ||||
\(438\) | −16.9706 | + | 9.79796i | −0.810885 | + | 0.468165i | ||||
\(439\) | 38.1051i | 1.81866i | 0.416078 | + | 0.909329i | \(0.363404\pi\) | ||||
−0.416078 | + | 0.909329i | \(0.636596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.0000 | −1.90476 | ||||||||
\(442\) | −13.4164 | + | 7.74597i | −0.638153 | + | 0.368438i | ||||
\(443\) | −2.82843 | −0.134383 | −0.0671913 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671913 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(444\) | 18.9737 | − | 32.8634i | 0.900450 | − | 1.55963i | ||||
\(445\) | 24.4949i | 1.16117i | ||||||||
\(446\) | −6.00000 | − | 10.3923i | −0.284108 | − | 0.492090i | ||||
\(447\) | − | 30.9839i | − | 1.46549i | ||||||
\(448\) | − | 30.9839i | − | 1.46385i | ||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 17.6777 | + | 30.6186i | 0.833333 | + | 1.44338i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 11.1803 | − | 19.3649i | 0.525879 | − | 0.910849i | ||||
\(453\) | − | 29.3939i | − | 1.38104i | ||||||
\(454\) | 9.48683 | − | 5.47723i | 0.445239 | − | 0.257059i | ||||
\(455\) | −42.4264 | −1.98898 | ||||||||
\(456\) | 50.5964 | 2.36940 | ||||||||
\(457\) | 33.5410 | 1.56898 | 0.784491 | − | 0.620140i | \(-0.212924\pi\) | ||||
0.784491 | + | 0.620140i | \(0.212924\pi\) | |||||||
\(458\) | 13.4164 | − | 7.74597i | 0.626908 | − | 0.361945i | ||||
\(459\) | 12.6491 | 0.590410 | ||||||||
\(460\) | −21.3246 | + | 2.29420i | −0.994263 | + | 0.106967i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.48528 | −0.394344 | −0.197172 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197172 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(464\) | −6.00000 | − | 10.3923i | −0.278543 | − | 0.482451i | ||||
\(465\) | 10.9545i | 0.508001i | ||||||||
\(466\) | −36.0000 | + | 20.7846i | −1.66767 | + | 0.962828i | ||||
\(467\) | − | 19.3649i | − | 0.896101i | −0.894008 | − | 0.448051i | \(-0.852118\pi\) | ||
0.894008 | − | 0.448051i | \(-0.147882\pi\) | |||||||
\(468\) | 42.4264 | + | 24.4949i | 1.96116 | + | 1.13228i | ||||
\(469\) | 45.0000 | 2.07791 | ||||||||
\(470\) | −8.94427 | − | 15.4919i | −0.412568 | − | 0.714590i | ||||
\(471\) | −18.9737 | −0.874260 | ||||||||
\(472\) | 24.4949i | 1.12747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −25.2982 | − | 43.8178i | −1.16199 | − | 2.01262i | ||||
\(475\) | 31.6228 | 1.45095 | ||||||||
\(476\) | −15.0000 | − | 8.66025i | −0.687524 | − | 0.396942i | ||||
\(477\) | −11.1803 | −0.511913 | ||||||||
\(478\) | −14.8492 | + | 8.57321i | −0.679189 | + | 0.392130i | ||||
\(479\) | −37.9473 | −1.73386 | −0.866929 | − | 0.498432i | \(-0.833909\pi\) | ||||
−0.866929 | + | 0.498432i | \(0.833909\pi\) | |||||||
\(480\) | −17.8885 | + | 30.9839i | −0.816497 | + | 1.41421i | ||||
\(481\) | − | 32.8634i | − | 1.49844i | ||||||
\(482\) | −13.4164 | + | 7.74597i | −0.611101 | + | 0.352819i | ||||
\(483\) | −42.4264 | + | 30.9839i | −1.93047 | + | 1.40981i | ||||
\(484\) | 11.0000 | − | 19.0526i | 0.500000 | − | 0.866025i | ||||
\(485\) | 30.0000 | 1.36223 | ||||||||
\(486\) | 10.0000 | + | 17.3205i | 0.453609 | + | 0.785674i | ||||
\(487\) | −8.48528 | −0.384505 | −0.192252 | − | 0.981346i | \(-0.561579\pi\) | ||||
−0.192252 | + | 0.981346i | \(0.561579\pi\) | |||||||
\(488\) | 30.9839i | 1.40257i | ||||||||
\(489\) | 48.0000 | 2.17064 | ||||||||
\(490\) | −12.6491 | − | 21.9089i | −0.571429 | − | 0.989743i | ||||
\(491\) | − | 36.3731i | − | 1.64149i | −0.571292 | − | 0.820747i | \(-0.693558\pi\) | ||
0.571292 | − | 0.820747i | \(-0.306442\pi\) | |||||||
\(492\) | −25.4558 | + | 44.0908i | −1.14764 | + | 1.98777i | ||||
\(493\) | −6.70820 | −0.302122 | ||||||||
\(494\) | 37.9473 | − | 21.9089i | 1.70733 | − | 0.985728i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | + | 3.46410i | −0.269408 | + | 0.155543i | ||||
\(497\) | −6.70820 | −0.300904 | ||||||||
\(498\) | −13.4164 | + | 7.74597i | −0.601204 | + | 0.347105i | ||||
\(499\) | 39.8372i | 1.78336i | 0.452670 | + | 0.891678i | \(0.350472\pi\) | ||||
−0.452670 | + | 0.891678i | \(0.649528\pi\) | |||||||
\(500\) | −11.1803 | + | 19.3649i | −0.500000 | + | 0.866025i | ||||
\(501\) | −32.0000 | −1.42965 | ||||||||
\(502\) | 13.4164 | + | 23.2379i | 0.598804 | + | 1.03716i | ||||
\(503\) | − | 19.3649i | − | 0.863439i | −0.902008 | − | 0.431719i | \(-0.857907\pi\) | ||
0.902008 | − | 0.431719i | \(-0.142093\pi\) | |||||||
\(504\) | 54.7723i | 2.43975i | ||||||||
\(505\) | 6.70820 | 0.298511 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.1127 | 1.38176 | ||||||||
\(508\) | 8.48528 | − | 14.6969i | 0.376473 | − | 0.652071i | ||||
\(509\) | −42.0000 | −1.86162 | −0.930809 | − | 0.365507i | \(-0.880896\pi\) | ||||
−0.930809 | + | 0.365507i | \(0.880896\pi\) | |||||||
\(510\) | 10.0000 | + | 17.3205i | 0.442807 | + | 0.766965i | ||||
\(511\) | −18.9737 | −0.839346 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −35.7771 | −1.57960 | ||||||||
\(514\) | 12.0000 | − | 6.92820i | 0.529297 | − | 0.305590i | ||||
\(515\) | 17.3205i | 0.763233i | ||||||||
\(516\) | −37.9473 | − | 21.9089i | −1.67054 | − | 0.964486i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 31.8198 | − | 18.3712i | 1.39808 | − | 0.807183i | ||||
\(519\) | − | 69.2820i | − | 3.04114i | ||||||
\(520\) | 30.9839i | 1.35873i | ||||||||
\(521\) | 32.8634i | 1.43977i | 0.694094 | + | 0.719885i | \(0.255805\pi\) | ||||
−0.694094 | + | 0.719885i | \(0.744195\pi\) | |||||||
\(522\) | 10.6066 | + | 18.3712i | 0.464238 | + | 0.804084i | ||||
\(523\) | − | 38.7298i | − | 1.69354i | −0.531961 | − | 0.846769i | \(-0.678545\pi\) | ||
0.531961 | − | 0.846769i | \(-0.321455\pi\) | |||||||
\(524\) | 18.0000 | + | 10.3923i | 0.786334 | + | 0.453990i | ||||
\(525\) | 54.7723i | 2.39046i | ||||||||
\(526\) | −14.2302 | + | 8.21584i | −0.620468 | + | 0.358228i | ||||
\(527\) | 3.87298i | 0.168710i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | + | 21.9089i | −0.304348 | + | 0.952561i | ||||
\(530\) | −3.53553 | − | 6.12372i | −0.153574 | − | 0.265998i | ||||
\(531\) | − | 43.3013i | − | 1.87912i | ||||||
\(532\) | 42.4264 | + | 24.4949i | 1.83942 | + | 1.06199i | ||||
\(533\) | 44.0908i | 1.90979i | ||||||||
\(534\) | 37.9473 | − | 21.9089i | 1.64214 | − | 0.948091i | ||||
\(535\) | 25.9808i | 1.12325i | ||||||||
\(536\) | − | 32.8634i | − | 1.41948i | ||||||
\(537\) | − | 9.79796i | − | 0.422813i | ||||||
\(538\) | 2.12132 | + | 3.67423i | 0.0914566 | + | 0.158408i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.6491 | − | 21.9089i | 0.544331 | − | 0.942809i | ||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 10.6066 | − | 6.12372i | 0.455593 | − | 0.263036i | ||||
\(543\) | − | 30.9839i | − | 1.32964i | ||||||
\(544\) | −6.32456 | + | 10.9545i | −0.271163 | + | 0.469668i | ||||
\(545\) | − | 24.4949i | − | 1.04925i | ||||||
\(546\) | 37.9473 | + | 65.7267i | 1.62400 | + | 2.81284i | ||||
\(547\) | 33.9411 | 1.45122 | 0.725609 | − | 0.688107i | \(-0.241558\pi\) | ||||
0.725609 | + | 0.688107i | \(0.241558\pi\) | |||||||
\(548\) | 4.47214 | − | 7.74597i | 0.191040 | − | 0.330891i | ||||
\(549\) | − | 54.7723i | − | 2.33762i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9737 | 0.808305 | ||||||||
\(552\) | 22.6274 | + | 30.9839i | 0.963087 | + | 1.31876i | ||||
\(553\) | − | 48.9898i | − | 2.08326i | ||||||
\(554\) | −12.0000 | + | 6.92820i | −0.509831 | + | 0.294351i | ||||
\(555\) | −42.4264 | −1.80090 | ||||||||
\(556\) | −9.00000 | − | 5.19615i | −0.381685 | − | 0.220366i | ||||
\(557\) | 24.5967 | 1.04220 | 0.521099 | − | 0.853496i | \(-0.325522\pi\) | ||||
0.521099 | + | 0.853496i | \(0.325522\pi\) | |||||||
\(558\) | 10.6066 | − | 6.12372i | 0.449013 | − | 0.259238i | ||||
\(559\) | −37.9473 | −1.60500 | ||||||||
\(560\) | −30.0000 | + | 17.3205i | −1.26773 | + | 0.731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6190i | 0.489680i | 0.969563 | + | 0.244840i | \(0.0787355\pi\) | ||||
−0.969563 | + | 0.244840i | \(0.921265\pi\) | |||||||
\(564\) | −16.0000 | + | 27.7128i | −0.673722 | + | 1.16692i | ||||
\(565\) | −25.0000 | −1.05176 | ||||||||
\(566\) | −14.2302 | + | 8.21584i | −0.598142 | + | 0.345337i | ||||
\(567\) | − | 3.87298i | − | 0.162650i | ||||||
\(568\) | 4.89898i | 0.205557i | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | −28.2843 | − | 48.9898i | −1.18470 | − | 2.05196i | ||||
\(571\) | 6.32456 | 0.264674 | 0.132337 | − | 0.991205i | \(-0.457752\pi\) | ||||
0.132337 | + | 0.991205i | \(0.457752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −42.6907 | + | 24.6475i | −1.78188 | + | 1.02877i | ||||
\(575\) | 14.1421 | + | 19.3649i | 0.589768 | + | 0.807573i | ||||
\(576\) | 40.0000 | 1.66667 | ||||||||
\(577\) | − | 14.6969i | − | 0.611842i | −0.952057 | − | 0.305921i | \(-0.901036\pi\) | ||
0.952057 | − | 0.305921i | \(-0.0989643\pi\) | |||||||
\(578\) | −8.48528 | − | 14.6969i | −0.352941 | − | 0.611312i | ||||
\(579\) | − | 13.8564i | − | 0.575853i | ||||||
\(580\) | −6.70820 | + | 11.6190i | −0.278543 | + | 0.482451i | ||||
\(581\) | −15.0000 | −0.622305 | ||||||||
\(582\) | −26.8328 | − | 46.4758i | −1.11226 | − | 1.92648i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.8564i | 0.573382i | ||||||||
\(585\) | − | 54.7723i | − | 2.26455i | ||||||
\(586\) | 17.3925 | + | 30.1247i | 0.718479 | + | 1.24444i | ||||
\(587\) | 22.6274 | 0.933933 | 0.466967 | − | 0.884275i | \(-0.345347\pi\) | ||||
0.466967 | + | 0.884275i | \(0.345347\pi\) | |||||||
\(588\) | −22.6274 | + | 39.1918i | −0.933139 | + | 1.61624i | ||||
\(589\) | − | 10.9545i | − | 0.451370i | ||||||
\(590\) | 23.7171 | − | 13.6931i | 0.976417 | − | 0.563735i | ||||
\(591\) | 27.7128i | 1.13995i | ||||||||
\(592\) | −13.4164 | − | 23.2379i | −0.551411 | − | 0.955072i | ||||
\(593\) | − | 24.4949i | − | 1.00588i | −0.864320 | − | 0.502942i | \(-0.832251\pi\) | ||
0.864320 | − | 0.502942i | \(-0.167749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.3649i | 0.793884i | ||||||||
\(596\) | −18.9737 | − | 10.9545i | −0.777192 | − | 0.448712i | ||||
\(597\) | 17.8885 | 0.732129 | ||||||||
\(598\) | 30.3870 | + | 13.4399i | 1.24262 | + | 0.549600i | ||||
\(599\) | − | 17.3205i | − | 0.707697i | −0.935303 | − | 0.353848i | \(-0.884873\pi\) | ||
0.935303 | − | 0.353848i | \(-0.115127\pi\) | |||||||
\(600\) | 40.0000 | 1.63299 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | −21.2132 | − | 36.7423i | −0.864586 | − | 1.49751i | ||||
\(603\) | 58.0948i | 2.36580i | ||||||||
\(604\) | −18.0000 | − | 10.3923i | −0.732410 | − | 0.422857i | ||||
\(605\) | −24.5967 | −1.00000 | ||||||||
\(606\) | −6.00000 | − | 10.3923i | −0.243733 | − | 0.422159i | ||||
\(607\) | −25.4558 | −1.03322 | −0.516610 | − | 0.856221i | \(-0.672806\pi\) | ||||
−0.516610 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(608\) | 17.8885 | − | 30.9839i | 0.725476 | − | 1.25656i | ||||
\(609\) | 32.8634i | 1.33169i | ||||||||
\(610\) | 30.0000 | − | 17.3205i | 1.21466 | − | 0.701287i | ||||
\(611\) | 27.7128i | 1.12114i | ||||||||
\(612\) | 11.1803 | − | 19.3649i | 0.451938 | − | 0.782780i | ||||
\(613\) | −13.4164 | −0.541884 | −0.270942 | − | 0.962596i | \(-0.587335\pi\) | ||||
−0.270942 | + | 0.962596i | \(0.587335\pi\) | |||||||
\(614\) | −12.0000 | − | 20.7846i | −0.484281 | − | 0.838799i | ||||
\(615\) | 56.9210 | 2.29528 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.6525 | 0.630145 | 0.315072 | − | 0.949068i | \(-0.397971\pi\) | ||||
0.315072 | + | 0.949068i | \(0.397971\pi\) | |||||||
\(618\) | 26.8328 | − | 15.4919i | 1.07937 | − | 0.623177i | ||||
\(619\) | −6.32456 | −0.254205 | −0.127103 | − | 0.991890i | \(-0.540568\pi\) | ||||
−0.127103 | + | 0.991890i | \(0.540568\pi\) | |||||||
\(620\) | 6.70820 | + | 3.87298i | 0.269408 | + | 0.155543i | ||||
\(621\) | −16.0000 | − | 21.9089i | −0.642058 | − | 0.879174i | ||||
\(622\) | −12.7279 | + | 7.34847i | −0.510343 | + | 0.294647i | ||||
\(623\) | 42.4264 | 1.69978 | ||||||||
\(624\) | 48.0000 | − | 27.7128i | 1.92154 | − | 1.10940i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −14.2302 | − | 24.6475i | −0.568755 | − | 0.985113i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.70820 | + | 11.6190i | −0.267686 | + | 0.463647i | ||||
\(629\) | −15.0000 | −0.598089 | ||||||||
\(630\) | 53.0330 | − | 30.6186i | 2.11289 | − | 1.21988i | ||||
\(631\) | 6.32456 | 0.251777 | 0.125888 | − | 0.992044i | \(-0.459822\pi\) | ||||
0.125888 | + | 0.992044i | \(0.459822\pi\) | |||||||
\(632\) | −35.7771 | −1.42314 | ||||||||
\(633\) | 24.4949i | 0.973585i | ||||||||
\(634\) | −30.0000 | + | 17.3205i | −1.19145 | + | 0.687885i | ||||
\(635\) | −18.9737 | −0.752947 | ||||||||
\(636\) | −6.32456 | + | 10.9545i | −0.250785 | + | 0.434372i | ||||
\(637\) | 39.1918i | 1.55284i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8.66025i | − | 0.342594i | ||||||
\(640\) | 12.6491 | + | 21.9089i | 0.500000 | + | 0.866025i | ||||
\(641\) | − | 21.9089i | − | 0.865350i | −0.901550 | − | 0.432675i | \(-0.857570\pi\) | ||
0.901550 | − | 0.432675i | \(-0.142430\pi\) | |||||||
\(642\) | 40.2492 | − | 23.2379i | 1.58851 | − | 0.917127i | ||||
\(643\) | 11.6190i | 0.458207i | 0.973402 | + | 0.229103i | \(0.0735794\pi\) | ||||
−0.973402 | + | 0.229103i | \(0.926421\pi\) | |||||||
\(644\) | 3.97367 | + | 36.9352i | 0.156584 | + | 1.45545i | ||||
\(645\) | 48.9898i | 1.92897i | ||||||||
\(646\) | −10.0000 | − | 17.3205i | −0.393445 | − | 0.681466i | ||||
\(647\) | 19.7990 | 0.778379 | 0.389189 | − | 0.921158i | \(-0.372755\pi\) | ||||
0.389189 | + | 0.921158i | \(0.372755\pi\) | |||||||
\(648\) | −2.82843 | −0.111111 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 30.0000 | − | 17.3205i | 1.17670 | − | 0.679366i | ||||
\(651\) | 18.9737 | 0.743637 | ||||||||
\(652\) | 16.9706 | − | 29.3939i | 0.664619 | − | 1.15115i | ||||
\(653\) | − | 19.5959i | − | 0.766848i | −0.923573 | − | 0.383424i | \(-0.874745\pi\) | ||
0.923573 | − | 0.383424i | \(-0.125255\pi\) | |||||||
\(654\) | −37.9473 | + | 21.9089i | −1.48386 | + | 0.856706i | ||||
\(655\) | − | 23.2379i | − | 0.907980i | ||||||
\(656\) | 18.0000 | + | 31.1769i | 0.702782 | + | 1.21725i | ||||
\(657\) | − | 24.4949i | − | 0.955637i | ||||||
\(658\) | −26.8328 | + | 15.4919i | −1.04605 | + | 0.603938i | ||||
\(659\) | 18.9737 | 0.739109 | 0.369555 | − | 0.929209i | \(-0.379510\pi\) | ||||
0.369555 | + | 0.929209i | \(0.379510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 19.0919 | − | 11.0227i | 0.742027 | − | 0.428410i | ||||
\(663\) | − | 30.9839i | − | 1.20331i | ||||||
\(664\) | 10.9545i | 0.425115i | ||||||||
\(665\) | − | 54.7723i | − | 2.12398i | ||||||
\(666\) | 23.7171 | + | 41.0792i | 0.919018 | + | 1.59179i | ||||
\(667\) | 8.48528 | + | 11.6190i | 0.328551 | + | 0.449888i | ||||
\(668\) | −11.3137 | + | 19.5959i | −0.437741 | + | 0.758189i | ||||
\(669\) | 24.0000 | 0.927894 | ||||||||
\(670\) | −31.8198 | + | 18.3712i | −1.22931 | + | 0.709740i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 53.6656 | + | 30.9839i | 2.07020 | + | 1.19523i | ||||
\(673\) | − | 29.3939i | − | 1.13305i | −0.824044 | − | 0.566525i | \(-0.808287\pi\) | ||
0.824044 | − | 0.566525i | \(-0.191713\pi\) | |||||||
\(674\) | 9.48683 | + | 16.4317i | 0.365419 | + | 0.632925i | ||||
\(675\) | −28.2843 | −1.08866 | ||||||||
\(676\) | 11.0000 | − | 19.0526i | 0.423077 | − | 0.732791i | ||||
\(677\) | 42.4853 | 1.63284 | 0.816421 | − | 0.577457i | \(-0.195955\pi\) | ||||
0.816421 | + | 0.577457i | \(0.195955\pi\) | |||||||
\(678\) | 22.3607 | + | 38.7298i | 0.858757 | + | 1.48741i | ||||
\(679\) | − | 51.9615i | − | 1.99410i | ||||||
\(680\) | 14.1421 | 0.542326 | ||||||||
\(681\) | 21.9089i | 0.839551i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.82843 | 0.108227 | 0.0541134 | − | 0.998535i | \(-0.482767\pi\) | ||||
0.0541134 | + | 0.998535i | \(0.482767\pi\) | |||||||
\(684\) | −31.6228 | + | 54.7723i | −1.20913 | + | 2.09427i | ||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | −4.74342 | + | 2.73861i | −0.181104 | + | 0.104561i | ||||
\(687\) | 30.9839i | 1.18211i | ||||||||
\(688\) | −26.8328 | + | 15.4919i | −1.02299 | + | 0.590624i | ||||
\(689\) | 10.9545i | 0.417331i | ||||||||
\(690\) | 17.3509 | − | 39.2294i | 0.660537 | − | 1.49344i | ||||
\(691\) | 17.3205i | 0.658903i | 0.944172 | + | 0.329452i | \(0.106864\pi\) | ||||
−0.944172 | + | 0.329452i | \(0.893136\pi\) | |||||||
\(692\) | −42.4264 | − | 24.4949i | −1.61281 | − | 0.931156i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.00000 | + | 3.46410i | 0.0759190 | + | 0.131495i | ||||
\(695\) | 11.6190i | 0.440732i | ||||||||
\(696\) | 24.0000 | 0.909718 | ||||||||
\(697\) | 20.1246 | 0.762274 | ||||||||
\(698\) | 16.2635 | + | 28.1691i | 0.615581 | + | 1.06622i | ||||
\(699\) | − | 83.1384i | − | 3.14458i | ||||||
\(700\) | 33.5410 | + | 19.3649i | 1.26773 | + | 0.731925i | ||||
\(701\) | 21.9089i | 0.827488i | 0.910393 | + | 0.413744i | \(0.135779\pi\) | ||||
−0.910393 | + | 0.413744i | \(0.864221\pi\) | |||||||
\(702\) | −33.9411 | + | 19.5959i | −1.28103 | + | 0.739600i | ||||
\(703\) | 42.4264 | 1.60014 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35.7771 | 1.34744 | ||||||||
\(706\) | 36.0000 | − | 20.7846i | 1.35488 | − | 0.782239i | ||||
\(707\) | − | 11.6190i | − | 0.436976i | ||||||
\(708\) | −42.4264 | − | 24.4949i | −1.59448 | − | 0.920575i | ||||
\(709\) | 32.8634i | 1.23421i | 0.786881 | + | 0.617105i | \(0.211694\pi\) | ||||
−0.786881 | + | 0.617105i | \(0.788306\pi\) | |||||||
\(710\) | 4.74342 | − | 2.73861i | 0.178017 | − | 0.102778i | ||||
\(711\) | 63.2456 | 2.37189 | ||||||||
\(712\) | − | 30.9839i | − | 1.16117i | ||||||
\(713\) | 6.70820 | − | 4.89898i | 0.251224 | − | 0.183468i | ||||
\(714\) | 30.0000 | − | 17.3205i | 1.12272 | − | 0.648204i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | − | 3.46410i | −0.224231 | − | 0.129460i | ||||
\(717\) | − | 34.2929i | − | 1.28069i | ||||||
\(718\) | 13.4164 | + | 23.2379i | 0.500696 | + | 0.867231i | ||||
\(719\) | − | 8.66025i | − | 0.322973i | −0.986875 | − | 0.161486i | \(-0.948371\pi\) | ||
0.986875 | − | 0.161486i | \(-0.0516288\pi\) | |||||||
\(720\) | −22.3607 | − | 38.7298i | −0.833333 | − | 1.44338i | ||||
\(721\) | 30.0000 | 1.11726 | ||||||||
\(722\) | 14.8492 | + | 25.7196i | 0.552632 | + | 0.957186i | ||||
\(723\) | − | 30.9839i | − | 1.15230i | ||||||
\(724\) | −18.9737 | − | 10.9545i | −0.705151 | − | 0.407119i | ||||
\(725\) | 15.0000 | 0.557086 | ||||||||
\(726\) | 22.0000 | + | 38.1051i | 0.816497 | + | 1.41421i | ||||
\(727\) | 11.6190i | 0.430923i | 0.976512 | + | 0.215462i | \(0.0691256\pi\) | ||||
−0.976512 | + | 0.215462i | \(0.930874\pi\) | |||||||
\(728\) | 53.6656 | 1.98898 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 13.4164 | − | 7.74597i | 0.496564 | − | 0.286691i | ||||
\(731\) | 17.3205i | 0.640622i | ||||||||
\(732\) | −53.6656 | − | 30.9839i | −1.98354 | − | 1.14520i | ||||
\(733\) | −46.9574 | −1.73441 | −0.867206 | − | 0.497949i | \(-0.834087\pi\) | ||||
−0.867206 | + | 0.497949i | \(0.834087\pi\) | |||||||
\(734\) | 4.74342 | − | 2.73861i | 0.175083 | − | 0.101084i | ||||
\(735\) | 50.5964 | 1.86628 | ||||||||
\(736\) | 26.9737 | − | 2.90196i | 0.994263 | − | 0.106967i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −31.8198 | − | 55.1135i | −1.17130 | − | 2.02876i | ||||
\(739\) | 39.8372i | 1.46543i | 0.680534 | + | 0.732717i | \(0.261748\pi\) | ||||
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | −15.0000 | + | 25.9808i | −0.551411 | + | 0.955072i | ||||
\(741\) | 87.6356i | 3.21937i | ||||||||
\(742\) | −10.6066 | + | 6.12372i | −0.389381 | + | 0.224809i | ||||
\(743\) | − | 23.2379i | − | 0.852516i | −0.904602 | − | 0.426258i | \(-0.859832\pi\) | ||
0.904602 | − | 0.426258i | \(-0.140168\pi\) | |||||||
\(744\) | − | 13.8564i | − | 0.508001i | ||||||
\(745\) | 24.4949i | 0.897424i | ||||||||
\(746\) | −9.48683 | − | 16.4317i | −0.347338 | − | 0.601606i | ||||
\(747\) | − | 19.3649i | − | 0.708525i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.0000 | 1.64426 | ||||||||
\(750\) | −22.3607 | − | 38.7298i | −0.816497 | − | 1.41421i | ||||
\(751\) | −6.32456 | −0.230786 | −0.115393 | − | 0.993320i | \(-0.536813\pi\) | ||||
−0.115393 | + | 0.993320i | \(0.536813\pi\) | |||||||
\(752\) | 11.3137 | + | 19.5959i | 0.412568 | + | 0.714590i | ||||
\(753\) | −53.6656 | −1.95568 | ||||||||
\(754\) | 18.0000 | − | 10.3923i | 0.655521 | − | 0.378465i | ||||
\(755\) | 23.2379i | 0.845714i | ||||||||
\(756\) | −37.9473 | − | 21.9089i | −1.38013 | − | 0.796819i | ||||
\(757\) | −20.1246 | −0.731441 | −0.365721 | − | 0.930725i | \(-0.619177\pi\) | ||||
−0.365721 | + | 0.930725i | \(0.619177\pi\) | |||||||
\(758\) | 4.47214 | + | 7.74597i | 0.162435 | + | 0.281346i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −40.0000 | −1.45095 | ||||||||
\(761\) | −21.0000 | −0.761249 | −0.380625 | − | 0.924730i | \(-0.624291\pi\) | ||||
−0.380625 | + | 0.924730i | \(0.624291\pi\) | |||||||
\(762\) | 16.9706 | + | 29.3939i | 0.614779 | + | 1.06483i | ||||
\(763\) | −42.4264 | −1.53594 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.0000 | −0.903877 | ||||||||
\(766\) | 4.74342 | − | 2.73861i | 0.171387 | − | 0.0989501i | ||||
\(767\) | −42.4264 | −1.53193 | ||||||||
\(768\) | 22.6274 | − | 39.1918i | 0.816497 | − | 1.41421i | ||||
\(769\) | − | 43.8178i | − | 1.58011i | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||
0.613036 | − | 0.790055i | \(-0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.7128i | 0.998053i | ||||||||
\(772\) | −8.48528 | − | 4.89898i | −0.305392 | − | 0.176318i | ||||
\(773\) | 22.3607 | 0.804258 | 0.402129 | − | 0.915583i | \(-0.368270\pi\) | ||||
0.402129 | + | 0.915583i | \(0.368270\pi\) | |||||||
\(774\) | 47.4342 | − | 27.3861i | 1.70499 | − | 0.984374i | ||||
\(775\) | − | 8.66025i | − | 0.311086i | ||||||
\(776\) | −37.9473 | −1.36223 | ||||||||
\(777\) | 73.4847i | 2.63625i | ||||||||
\(778\) | 26.8328 | − | 15.4919i | 0.962003 | − | 0.555413i | ||||
\(779\) | −56.9210 | −2.03941 | ||||||||
\(780\) | −53.6656 | − | 30.9839i | −1.92154 | − | 1.10940i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.13447 | − | 13.8697i | 0.219368 | − | 0.495979i | ||||
\(783\) | −16.9706 | −0.606478 | ||||||||
\(784\) | 16.0000 | + | 27.7128i | 0.571429 | + | 0.989743i | ||||
\(785\) | 15.0000 | 0.535373 | ||||||||
\(786\) | −36.0000 | + | 20.7846i | −1.28408 | + | 0.741362i | ||||
\(787\) | − | 19.3649i | − | 0.690285i | −0.938550 | − | 0.345142i | \(-0.887831\pi\) | ||
0.938550 | − | 0.345142i | \(-0.112169\pi\) | |||||||
\(788\) | 16.9706 | + | 9.79796i | 0.604551 | + | 0.349038i | ||||
\(789\) | − | 32.8634i | − | 1.16997i | ||||||
\(790\) | 20.0000 | + | 34.6410i | 0.711568 | + | 1.23247i | ||||
\(791\) | 43.3013i | 1.53962i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.6656 | −1.90572 | ||||||||
\(794\) | −42.0000 | + | 24.2487i | −1.49052 | + | 0.860555i | ||||
\(795\) | 14.1421 | 0.501570 | ||||||||
\(796\) | 6.32456 | − | 10.9545i | 0.224168 | − | 0.388270i | ||||
\(797\) | −38.0132 | −1.34650 | −0.673248 | − | 0.739417i | \(-0.735101\pi\) | ||||
−0.673248 | + | 0.739417i | \(0.735101\pi\) | |||||||
\(798\) | −84.8528 | + | 48.9898i | −3.00376 | + | 1.73422i | ||||
\(799\) | 12.6491 | 0.447493 | ||||||||
\(800\) | 14.1421 | − | 24.4949i | 0.500000 | − | 0.866025i | ||||
\(801\) | 54.7723i | 1.93528i | ||||||||
\(802\) | −26.8328 | + | 15.4919i | −0.947500 | + | 0.547039i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 56.9210 | + | 32.8634i | 2.00745 | + | 1.15900i | ||||
\(805\) | 33.5410 | − | 24.4949i | 1.18217 | − | 0.863332i | ||||
\(806\) | −6.00000 | − | 10.3923i | −0.211341 | − | 0.366053i | ||||
\(807\) | −8.48528 | −0.298696 | ||||||||
\(808\) | −8.48528 | −0.298511 | ||||||||
\(809\) | −21.0000 | −0.738321 | −0.369160 | − | 0.929366i | \(-0.620355\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(810\) | 1.58114 | + | 2.73861i | 0.0555556 | + | 0.0962250i | ||||
\(811\) | − | 15.5885i | − | 0.547385i | −0.961817 | − | 0.273692i | \(-0.911755\pi\) | ||
0.961817 | − | 0.273692i | \(-0.0882450\pi\) | |||||||
\(812\) | 20.1246 | + | 11.6190i | 0.706235 | + | 0.407745i | ||||
\(813\) | 24.4949i | 0.859074i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.9473 | −1.32924 | ||||||||
\(816\) | −12.6491 | − | 21.9089i | −0.442807 | − | 0.766965i | ||||
\(817\) | − | 48.9898i | − | 1.71394i | ||||||
\(818\) | 4.94975 | + | 8.57321i | 0.173064 | + | 0.299755i | ||||
\(819\) | −94.8683 | −3.31497 | ||||||||
\(820\) | 20.1246 | − | 34.8569i | 0.702782 | − | 1.21725i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 8.94427 | + | 15.4919i | 0.311967 | + | 0.540343i | ||||
\(823\) | 25.4558 | 0.887335 | 0.443667 | − | 0.896191i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896191i | \(0.353677\pi\) | |||||||
\(824\) | − | 21.9089i | − | 0.763233i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.7171 | − | 41.0792i | −0.825223 | − | 1.42933i | ||||
\(827\) | 42.6028i | 1.48145i | 0.671811 | + | 0.740723i | \(0.265517\pi\) | ||||
−0.671811 | + | 0.740723i | \(0.734483\pi\) | |||||||
\(828\) | −47.6832 | + | 5.12998i | −1.65710 | + | 0.178279i | ||||
\(829\) | 31.0000 | 1.07667 | 0.538337 | − | 0.842729i | \(-0.319053\pi\) | ||||
0.538337 | + | 0.842729i | \(0.319053\pi\) | |||||||
\(830\) | 10.6066 | − | 6.12372i | 0.368161 | − | 0.212558i | ||||
\(831\) | − | 27.7128i | − | 0.961347i | ||||||
\(832\) | − | 39.1918i | − | 1.35873i | ||||||
\(833\) | 17.8885 | 0.619801 | ||||||||
\(834\) | 18.0000 | − | 10.3923i | 0.623289 | − | 0.359856i | ||||
\(835\) | 25.2982 | 0.875481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.79796i | 0.338667i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.9737 | −0.655044 | −0.327522 | − | 0.944844i | \(-0.606214\pi\) | ||||
−0.327522 | + | 0.944844i | \(0.606214\pi\) | |||||||
\(840\) | − | 69.2820i | − | 2.39046i | ||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −26.8328 | + | 15.4919i | −0.924720 | + | 0.533887i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.0000 | + | 8.66025i | 0.516321 | + | 0.298098i | ||||
\(845\) | −24.5967 | −0.846154 | ||||||||
\(846\) | −20.0000 | − | 34.6410i | −0.687614 | − | 1.19098i | ||||
\(847\) | 42.6028i | 1.46385i | ||||||||
\(848\) | 4.47214 | + | 7.74597i | 0.153574 | + | 0.265998i | ||||
\(849\) | − | 32.8634i | − | 1.12787i | ||||||
\(850\) | −7.90569 | − | 13.6931i | −0.271163 | − | 0.469668i | ||||
\(851\) | 18.9737 | + | 25.9808i | 0.650409 | + | 0.890609i | ||||
\(852\) | −8.48528 | − | 4.89898i | −0.290701 | − | 0.167836i | ||||
\(853\) | 24.4949i | 0.838689i | 0.907827 | + | 0.419345i | \(0.137740\pi\) | ||||
−0.907827 | + | 0.419345i | \(0.862260\pi\) | |||||||
\(854\) | −30.0000 | − | 51.9615i | −1.02658 | − | 1.77809i | ||||
\(855\) | 70.7107 | 2.41825 | ||||||||
\(856\) | − | 32.8634i | − | 1.12325i | ||||||
\(857\) | 39.1918i | 1.33877i | 0.742917 | + | 0.669384i | \(0.233442\pi\) | ||||
−0.742917 | + | 0.669384i | \(0.766558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1244i | 0.413678i | 0.978375 | + | 0.206839i | \(0.0663176\pi\) | ||||
−0.978375 | + | 0.206839i | \(0.933682\pi\) | |||||||
\(860\) | 30.0000 | + | 17.3205i | 1.02299 | + | 0.590624i | ||||
\(861\) | − | 98.5901i | − | 3.35994i | ||||||
\(862\) | −13.4164 | − | 23.2379i | −0.456965 | − | 0.791486i | ||||
\(863\) | 45.2548 | 1.54049 | 0.770246 | − | 0.637747i | \(-0.220133\pi\) | ||||
0.770246 | + | 0.637747i | \(0.220133\pi\) | |||||||
\(864\) | −16.0000 | + | 27.7128i | −0.544331 | + | 0.942809i | ||||
\(865\) | 54.7723i | 1.86231i | ||||||||
\(866\) | 23.7171 | + | 41.0792i | 0.805939 | + | 1.39593i | ||||
\(867\) | 33.9411 | 1.15270 | ||||||||
\(868\) | 6.70820 | − | 11.6190i | 0.227691 | − | 0.394373i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −13.4164 | − | 23.2379i | −0.454859 | − | 0.787839i | ||||
\(871\) | 56.9210 | 1.92869 | ||||||||
\(872\) | 30.9839i | 1.04925i | ||||||||
\(873\) | 67.0820 | 2.27038 | ||||||||
\(874\) | −17.3509 | + | 39.2294i | −0.586903 | + | 1.32695i | ||||
\(875\) | − | 43.3013i | − | 1.46385i | ||||||
\(876\) | −24.0000 | − | 13.8564i | −0.810885 | − | 0.468165i | ||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | −46.6690 | + | 26.9444i | −1.57500 | + | 0.909329i | ||||
\(879\) | −69.5701 | −2.34654 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.9545i | − | 0.369065i | −0.982826 | − | 0.184532i | \(-0.940923\pi\) | ||
0.982826 | − | 0.184532i | \(-0.0590771\pi\) | |||||||
\(882\) | −28.2843 | − | 48.9898i | −0.952381 | − | 1.64957i | ||||
\(883\) | 8.48528 | 0.285552 | 0.142776 | − | 0.989755i | \(-0.454397\pi\) | ||||
0.142776 | + | 0.989755i | \(0.454397\pi\) | |||||||
\(884\) | −18.9737 | − | 10.9545i | −0.638153 | − | 0.368438i | ||||
\(885\) | 54.7723i | 1.84115i | ||||||||
\(886\) | −2.00000 | − | 3.46410i | −0.0671913 | − | 0.116379i | ||||
\(887\) | −36.7696 | −1.23460 | −0.617300 | − | 0.786728i | \(-0.711774\pi\) | ||||
−0.617300 | + | 0.786728i | \(0.711774\pi\) | |||||||
\(888\) | 53.6656 | 1.80090 | ||||||||
\(889\) | 32.8634i | 1.10220i | ||||||||
\(890\) | −30.0000 | + | 17.3205i | −1.00560 | + | 0.580585i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.48528 | − | 14.6969i | 0.284108 | − | 0.492090i | ||||
\(893\) | −35.7771 | −1.19723 | ||||||||
\(894\) | 37.9473 | − | 21.9089i | 1.26915 | − | 0.732743i | ||||
\(895\) | 7.74597i | 0.258919i | ||||||||
\(896\) | 37.9473 | − | 21.9089i | 1.26773 | − | 0.731925i | ||||
\(897\) | −53.6656 | + | 39.1918i | −1.79184 | + | 1.30858i | ||||
\(898\) | −6.36396 | − | 11.0227i | −0.212368 | − | 0.367832i | ||||
\(899\) | − | 5.19615i | − | 0.173301i | ||||||
\(900\) | −25.0000 | + | 43.3013i | −0.833333 | + | 1.44338i | ||||
\(901\) | 5.00000 | 0.166574 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 84.8528 | 2.82372 | ||||||||
\(904\) | 31.6228 | 1.05176 | ||||||||
\(905\) | 24.4949i | 0.814238i | ||||||||
\(906\) | 36.0000 | − | 20.7846i | 1.19602 | − | 0.690522i | ||||
\(907\) | 58.0948i | 1.92900i | 0.264075 | + | 0.964502i | \(0.414933\pi\) | ||||
−0.264075 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(908\) | 13.4164 | + | 7.74597i | 0.445239 | + | 0.257059i | ||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | −30.0000 | − | 51.9615i | −0.994490 | − | 1.72251i | ||||
\(911\) | −18.9737 | −0.628626 | −0.314313 | − | 0.949319i | \(-0.601774\pi\) | ||||
−0.314313 | + | 0.949319i | \(0.601774\pi\) | |||||||
\(912\) | 35.7771 | + | 61.9677i | 1.18470 | + | 2.05196i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.7171 | + | 41.0792i | 0.784491 | + | 1.35878i | ||||
\(915\) | 69.2820i | 2.29039i | ||||||||
\(916\) | 18.9737 | + | 10.9545i | 0.626908 | + | 0.361945i | ||||
\(917\) | −40.2492 | −1.32915 | ||||||||
\(918\) | 8.94427 | + | 15.4919i | 0.295205 | + | 0.511310i | ||||
\(919\) | 44.2719 | 1.46039 | 0.730197 | − | 0.683236i | \(-0.239428\pi\) | ||||
0.730197 | + | 0.683236i | \(0.239428\pi\) | |||||||
\(920\) | −17.8885 | − | 24.4949i | −0.589768 | − | 0.807573i | ||||
\(921\) | 48.0000 | 1.58165 | ||||||||
\(922\) | 4.24264 | + | 7.34847i | 0.139724 | + | 0.242009i | ||||
\(923\) | −8.48528 | −0.279296 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.5410 | 1.10282 | ||||||||
\(926\) | −6.00000 | − | 10.3923i | −0.197172 | − | 0.341512i | ||||
\(927\) | 38.7298i | 1.27205i | ||||||||
\(928\) | 8.48528 | − | 14.6969i | 0.278543 | − | 0.482451i | ||||
\(929\) | 3.00000 | 0.0984268 | 0.0492134 | − | 0.998788i | \(-0.484329\pi\) | ||||
0.0492134 | + | 0.998788i | \(0.484329\pi\) | |||||||
\(930\) | −13.4164 | + | 7.74597i | −0.439941 | + | 0.254000i | ||||
\(931\) | −50.5964 | −1.65823 | ||||||||
\(932\) | −50.9117 | − | 29.3939i | −1.66767 | − | 0.962828i | ||||
\(933\) | − | 29.3939i | − | 0.962312i | ||||||
\(934\) | 23.7171 | − | 13.6931i | 0.776047 | − | 0.448051i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 69.2820i | 2.26455i | ||||||||
\(937\) | 13.4164 | 0.438295 | 0.219147 | − | 0.975692i | \(-0.429672\pi\) | ||||
0.219147 | + | 0.975692i | \(0.429672\pi\) | |||||||
\(938\) | 31.8198 | + | 55.1135i | 1.03895 | + | 1.79952i | ||||
\(939\) | 56.9210 | 1.85755 | ||||||||
\(940\) | 12.6491 | − | 21.9089i | 0.412568 | − | 0.714590i | ||||
\(941\) | − | 10.9545i | − | 0.357105i | −0.983930 | − | 0.178552i | \(-0.942859\pi\) | ||
0.983930 | − | 0.178552i | \(-0.0571414\pi\) | |||||||
\(942\) | −13.4164 | − | 23.2379i | −0.437130 | − | 0.757132i | ||||
\(943\) | −25.4558 | − | 34.8569i | −0.828956 | − | 1.13510i | ||||
\(944\) | −30.0000 | + | 17.3205i | −0.976417 | + | 0.563735i | ||||
\(945\) | 48.9898i | 1.59364i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6274 | 0.735292 | 0.367646 | − | 0.929966i | \(-0.380164\pi\) | ||||
0.367646 | + | 0.929966i | \(0.380164\pi\) | |||||||
\(948\) | 35.7771 | − | 61.9677i | 1.16199 | − | 2.01262i | ||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 22.3607 | + | 38.7298i | 0.725476 | + | 1.25656i | ||||
\(951\) | − | 69.2820i | − | 2.24662i | ||||||
\(952\) | − | 24.4949i | − | 0.793884i | ||||||
\(953\) | −4.47214 | −0.144867 | −0.0724333 | − | 0.997373i | \(-0.523076\pi\) | ||||
−0.0724333 | + | 0.997373i | \(0.523076\pi\) | |||||||
\(954\) | −7.90569 | − | 13.6931i | −0.255956 | − | 0.443329i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.0000 | − | 12.1244i | −0.679189 | − | 0.392130i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.8328 | − | 46.4758i | −0.866929 | − | 1.50156i | ||||
\(959\) | 17.3205i | 0.559308i | ||||||||
\(960\) | −50.5964 | −1.63299 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 40.2492 | − | 23.2379i | 1.29769 | − | 0.749220i | ||||
\(963\) | 58.0948i | 1.87208i | ||||||||
\(964\) | −18.9737 | − | 10.9545i | −0.611101 | − | 0.352819i | ||||
\(965\) | 10.9545i | 0.352636i | ||||||||
\(966\) | −67.9473 | − | 30.0526i | −2.18617 | − | 0.966927i | ||||
\(967\) | 50.9117 | 1.63721 | 0.818605 | − | 0.574357i | \(-0.194748\pi\) | ||||
0.818605 | + | 0.574357i | \(0.194748\pi\) | |||||||
\(968\) | 31.1127 | 1.00000 | ||||||||
\(969\) | 40.0000 | 1.28499 | ||||||||
\(970\) | 21.2132 | + | 36.7423i | 0.681115 | + | 1.17973i | ||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −14.1421 | + | 24.4949i | −0.453609 | + | 0.785674i | ||||
\(973\) | 20.1246 | 0.645165 | ||||||||
\(974\) | −6.00000 | − | 10.3923i | −0.192252 | − | 0.332991i | ||||
\(975\) | 69.2820i | 2.21880i | ||||||||
\(976\) | −37.9473 | + | 21.9089i | −1.21466 | + | 0.701287i | ||||
\(977\) | 24.5967 | 0.786920 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(978\) | 33.9411 | + | 58.7878i | 1.08532 | + | 1.87983i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 17.8885 | − | 30.9839i | 0.571429 | − | 0.989743i | ||||
\(981\) | − | 54.7723i | − | 1.74874i | ||||||
\(982\) | 44.5477 | − | 25.7196i | 1.42158 | − | 0.820747i | ||||
\(983\) | 42.6028i | 1.35882i | 0.733759 | + | 0.679409i | \(0.237764\pi\) | ||||
−0.733759 | + | 0.679409i | \(0.762236\pi\) | |||||||
\(984\) | −72.0000 | −2.29528 | ||||||||
\(985\) | − | 21.9089i | − | 0.698076i | ||||||
\(986\) | −4.74342 | − | 8.21584i | −0.151061 | − | 0.261646i | ||||
\(987\) | − | 61.9677i | − | 1.97245i | ||||||
\(988\) | 53.6656 | + | 30.9839i | 1.70733 | + | 0.985728i | ||||
\(989\) | 30.0000 | − | 21.9089i | 0.953945 | − | 0.696663i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 8.66025i | − | 0.275102i | −0.990495 | − | 0.137551i | \(-0.956077\pi\) | ||
0.990495 | − | 0.137551i | \(-0.0439231\pi\) | |||||||
\(992\) | −8.48528 | − | 4.89898i | −0.269408 | − | 0.155543i | ||||
\(993\) | 44.0908i | 1.39918i | ||||||||
\(994\) | −4.74342 | − | 8.21584i | −0.150452 | − | 0.260591i | ||||
\(995\) | −14.1421 | −0.448336 | ||||||||
\(996\) | −18.9737 | − | 10.9545i | −0.601204 | − | 0.347105i | ||||
\(997\) | − | 48.9898i | − | 1.55152i | −0.631027 | − | 0.775761i | \(-0.717366\pi\) | ||
0.631027 | − | 0.775761i | \(-0.282634\pi\) | |||||||
\(998\) | −48.7904 | + | 28.1691i | −1.54443 | + | 0.891678i | ||||
\(999\) | −37.9473 | −1.20060 |
(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 | 460.2.g.b.459.8 | yes | 8 | |
4.3 | odd | 2 | inner | 460.2.g.b.459.4 | yes | 8 | |
5.4 | even | 2 | inner | 460.2.g.b.459.1 | ✓ | 8 | |
20.19 | odd | 2 | inner | 460.2.g.b.459.5 | yes | 8 | |
23.22 | odd | 2 | inner | 460.2.g.b.459.7 | yes | 8 | |
92.91 | even | 2 | inner | 460.2.g.b.459.3 | yes | 8 | |
115.114 | odd | 2 | inner | 460.2.g.b.459.2 | yes | 8 | |
460.459 | even | 2 | inner | 460.2.g.b.459.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.g.b.459.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
460.2.g.b.459.2 | yes | 8 | 115.114 | odd | 2 | inner | |
460.2.g.b.459.3 | yes | 8 | 92.91 | even | 2 | inner | |
460.2.g.b.459.4 | yes | 8 | 4.3 | odd | 2 | inner | |
460.2.g.b.459.5 | yes | 8 | 20.19 | odd | 2 | inner | |
460.2.g.b.459.6 | yes | 8 | 460.459 | even | 2 | inner | |
460.2.g.b.459.7 | yes | 8 | 23.22 | odd | 2 | inner | |
460.2.g.b.459.8 | yes | 8 | 1.1 | even | 1 | trivial |