Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not 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: | \(2.79476407074\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.b.149.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | 0.228714 | − | 0.973494i | \(-0.426548\pi\) |
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.59808 | + | 0.500000i | −0.981981 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | − | 1.73205i | −0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | −1.73205 | − | 1.00000i | −0.408248 | − | 0.235702i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | −2.59808 | + | 1.50000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | \(-0.767924\pi\) |
0.204046 | + | 0.978961i | \(0.434591\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | − | 3.46410i | −0.392232 | − | 0.679366i | ||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | −0.866025 | + | 2.50000i | −0.163663 | + | 0.472456i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −5.19615 | + | 3.00000i | −0.904534 | + | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 3.46410 | − | 2.00000i | 0.569495 | − | 0.328798i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) |
0.756948 | + | 0.653476i | \(0.226690\pi\) | |||||||
\(38\) | 1.73205 | + | 1.00000i | 0.280976 | + | 0.162221i | ||||
\(39\) | −2.00000 | + | 3.46410i | −0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 2.59808 | − | 0.500000i | 0.400892 | − | 0.0771517i | ||||
\(43\) | − | 7.00000i | − | 1.06749i | −0.845645 | − | 0.533745i | \(-0.820784\pi\) | ||
0.845645 | − | 0.533745i | \(-0.179216\pi\) | |||||||
\(44\) | −3.00000 | − | 5.19615i | −0.452267 | − | 0.783349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46410 | − | 2.00000i | −0.480384 | − | 0.277350i | ||||
\(53\) | 5.19615 | + | 3.00000i | 0.713746 | + | 0.412082i | 0.812447 | − | 0.583036i | \(-0.198135\pi\) |
−0.0987002 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(54\) | 2.50000 | + | 4.33013i | 0.340207 | + | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | + | 2.59808i | 0.0668153 | + | 0.347183i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 2.59808 | − | 1.50000i | 0.341144 | − | 0.196960i | ||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | − | 4.33013i | −0.320092 | − | 0.554416i | 0.660415 | − | 0.750901i | \(-0.270381\pi\) |
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | 3.46410 | + | 4.00000i | 0.436436 | + | 0.503953i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | 4.33013 | + | 2.50000i | 0.529009 | + | 0.305424i | 0.740613 | − | 0.671932i | \(-0.234535\pi\) |
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −1.73205 | + | 1.00000i | −0.204124 | + | 0.117851i | ||||
\(73\) | 13.8564 | + | 8.00000i | 1.62177 | + | 0.936329i | 0.986447 | + | 0.164083i | \(0.0524664\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −5.19615 | + | 15.0000i | −0.592157 | + | 1.70941i | ||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 7.79423 | − | 4.50000i | 0.860729 | − | 0.496942i | ||||
\(83\) | 3.00000i | 0.329293i | 0.986353 | + | 0.164646i | \(0.0526483\pi\) | ||||
−0.986353 | + | 0.164646i | \(0.947352\pi\) | |||||||
\(84\) | 2.00000 | − | 1.73205i | 0.218218 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.50000 | − | 6.06218i | −0.377415 | − | 0.653701i | ||||
\(87\) | −2.59808 | − | 1.50000i | −0.278543 | − | 0.160817i | ||||
\(88\) | −5.19615 | − | 3.00000i | −0.553912 | − | 0.319801i | ||||
\(89\) | −7.50000 | − | 12.9904i | −0.794998 | − | 1.37698i | −0.922840 | − | 0.385183i | \(-0.874138\pi\) |
0.127842 | − | 0.991795i | \(-0.459195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 10.3923i | 0.209657 | + | 1.08941i | ||||
\(92\) | 3.00000i | 0.312772i | ||||||||
\(93\) | 6.92820 | − | 4.00000i | 0.718421 | − | 0.414781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 14.0000i | − | 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | 4.33013 | − | 5.50000i | 0.437409 | − | 0.555584i | ||||
\(99\) | −12.0000 | −1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.866025 | + | 0.500000i | −0.0853320 | + | 0.0492665i | −0.542059 | − | 0.840341i | \(-0.682355\pi\) |
0.456727 | + | 0.889607i | \(0.349022\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 12.9904 | − | 7.50000i | 1.25583 | − | 0.725052i | 0.283567 | − | 0.958952i | \(-0.408482\pi\) |
0.972261 | + | 0.233900i | \(0.0751489\pi\) | |||||||
\(108\) | 4.33013 | + | 2.50000i | 0.416667 | + | 0.240563i | ||||
\(109\) | 5.50000 | − | 9.52628i | 0.526804 | − | 0.912452i | −0.472708 | − | 0.881219i | \(-0.656723\pi\) |
0.999512 | − | 0.0312328i | \(-0.00994332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 1.73205 | + | 2.00000i | 0.163663 | + | 0.188982i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | −6.92820 | + | 4.00000i | −0.640513 | + | 0.369800i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −4.33013 | − | 2.50000i | −0.392031 | − | 0.226339i | ||||
\(123\) | −7.79423 | − | 4.50000i | −0.702782 | − | 0.405751i | ||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.00000 | + | 1.73205i | 0.445435 | + | 0.154303i | ||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −3.50000 | + | 6.06218i | −0.308158 | + | 0.533745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | −3.46410 | − | 4.00000i | −0.300376 | − | 0.346844i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | 2.59808 | − | 1.50000i | 0.221163 | − | 0.127688i | ||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | −20.7846 | − | 12.0000i | −1.73810 | − | 1.00349i | ||||
\(144\) | −1.00000 | + | 1.73205i | −0.0833333 | + | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | −6.92820 | − | 1.00000i | −0.571429 | − | 0.0824786i | ||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | 7.50000 | + | 12.9904i | 0.614424 | + | 1.06421i | 0.990485 | + | 0.137619i | \(0.0439449\pi\) |
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | 1.73205 | − | 1.00000i | 0.140488 | − | 0.0811107i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | + | 15.5885i | 0.241747 | + | 1.25615i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | −19.0526 | − | 11.0000i | −1.52056 | − | 0.877896i | −0.999706 | − | 0.0242497i | \(-0.992280\pi\) |
−0.520854 | − | 0.853646i | \(-0.674386\pi\) | |||||||
\(158\) | 1.73205 | + | 1.00000i | 0.137795 | + | 0.0795557i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 5.19615i | 0.472866 | − | 0.409514i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −3.46410 | + | 2.00000i | −0.271329 | + | 0.156652i | −0.629492 | − | 0.777007i | \(-0.716737\pi\) |
0.358162 | + | 0.933659i | \(0.383403\pi\) | |||||||
\(164\) | 4.50000 | − | 7.79423i | 0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | + | 2.59808i | 0.116423 | + | 0.201650i | ||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | 0.866025 | − | 2.50000i | 0.0668153 | − | 0.192879i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | −6.06218 | − | 3.50000i | −0.462237 | − | 0.266872i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 5.19615 | − | 3.00000i | 0.390567 | − | 0.225494i | ||||
\(178\) | −12.9904 | − | 7.50000i | −0.973670 | − | 0.562149i | ||||
\(179\) | −12.0000 | + | 20.7846i | −0.896922 | + | 1.55351i | −0.0655145 | + | 0.997852i | \(0.520869\pi\) |
−0.831408 | + | 0.555663i | \(0.812464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | 6.92820 | + | 8.00000i | 0.513553 | + | 0.592999i | ||||
\(183\) | 5.00000i | 0.369611i | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | − | 6.92820i | 0.293294 | − | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | − | 12.9904i | −0.181848 | − | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −1.73205 | − | 1.00000i | −0.124676 | − | 0.0719816i | 0.436365 | − | 0.899770i | \(-0.356266\pi\) |
−0.561041 | + | 0.827788i | \(0.689599\pi\) | |||||||
\(194\) | −7.00000 | − | 12.1244i | −0.502571 | − | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | −10.3923 | + | 6.00000i | −0.738549 | + | 0.426401i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | − | 4.33013i | −0.176336 | − | 0.305424i | ||||
\(202\) | 15.0000i | 1.05540i | ||||||||
\(203\) | −7.79423 | + | 1.50000i | −0.547048 | + | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 5.19615 | + | 3.00000i | 0.361158 | + | 0.208514i | ||||
\(208\) | −3.46410 | + | 2.00000i | −0.240192 | + | 0.138675i | ||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | 5.19615 | + | 3.00000i | 0.356034 | + | 0.205557i | ||||
\(214\) | 7.50000 | − | 12.9904i | 0.512689 | − | 0.888004i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 6.92820 | − | 20.0000i | 0.470317 | − | 1.35769i | ||||
\(218\) | − | 11.0000i | − | 0.745014i | ||||||
\(219\) | −8.00000 | − | 13.8564i | −0.540590 | − | 0.936329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.46410 | + | 2.00000i | −0.232495 | + | 0.134231i | ||||
\(223\) | − | 28.0000i | − | 1.87502i | −0.347960 | − | 0.937509i | \(-0.613126\pi\) | ||
0.347960 | − | 0.937509i | \(-0.386874\pi\) | |||||||
\(224\) | 2.50000 | + | 0.866025i | 0.167038 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | −10.3923 | − | 6.00000i | −0.689761 | − | 0.398234i | 0.113761 | − | 0.993508i | \(-0.463710\pi\) |
−0.803523 | + | 0.595274i | \(0.797043\pi\) | |||||||
\(228\) | −1.73205 | − | 1.00000i | −0.114708 | − | 0.0662266i | ||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 10.3923i | 0.789542 | − | 0.683763i | ||||
\(232\) | − | 3.00000i | − | 0.196960i | ||||||
\(233\) | −10.3923 | + | 6.00000i | −0.680823 | + | 0.393073i | −0.800165 | − | 0.599780i | \(-0.795255\pi\) |
0.119342 | + | 0.992853i | \(0.461921\pi\) | |||||||
\(234\) | −4.00000 | + | 6.92820i | −0.261488 | + | 0.452911i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | − | 2.00000i | − | 0.129914i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | + | 1.73205i | −0.0644157 | + | 0.111571i | −0.896435 | − | 0.443176i | \(-0.853852\pi\) |
0.832019 | + | 0.554747i | \(0.187185\pi\) | |||||||
\(242\) | −21.6506 | − | 12.5000i | −1.39176 | − | 0.803530i | ||||
\(243\) | 13.8564 | − | 8.00000i | 0.888889 | − | 0.513200i | ||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 6.92820 | − | 4.00000i | 0.440831 | − | 0.254514i | ||||
\(248\) | 6.92820 | + | 4.00000i | 0.439941 | + | 0.254000i | ||||
\(249\) | 1.50000 | − | 2.59808i | 0.0950586 | − | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 5.19615 | − | 1.00000i | 0.327327 | − | 0.0629941i | ||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | −4.00000 | − | 6.92820i | −0.250982 | − | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 7.00000i | 0.435801i | ||||||||
\(259\) | −8.00000 | + | 6.92820i | −0.497096 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1865 | + | 10.5000i | 1.12143 | + | 0.647458i | 0.941766 | − | 0.336270i | \(-0.109166\pi\) |
0.179664 | + | 0.983728i | \(0.442499\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.00000 | − | 1.73205i | −0.306570 | − | 0.106199i | ||||
\(267\) | 15.0000i | 0.917985i | ||||||||
\(268\) | 4.33013 | − | 2.50000i | 0.264505 | − | 0.152712i | ||||
\(269\) | 7.50000 | − | 12.9904i | 0.457283 | − | 0.792038i | −0.541533 | − | 0.840679i | \(-0.682156\pi\) |
0.998816 | + | 0.0486418i | \(0.0154893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.46410 | − | 10.0000i | 0.209657 | − | 0.605228i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.50000 | − | 2.59808i | 0.0902894 | − | 0.156386i | ||||
\(277\) | 6.92820 | + | 4.00000i | 0.416275 | + | 0.240337i | 0.693482 | − | 0.720473i | \(-0.256075\pi\) |
−0.277207 | + | 0.960810i | \(0.589409\pi\) | |||||||
\(278\) | 8.66025 | − | 5.00000i | 0.519408 | − | 0.299880i | ||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.46410 | + | 2.00000i | 0.205919 | + | 0.118888i | 0.599414 | − | 0.800439i | \(-0.295400\pi\) |
−0.393494 | + | 0.919327i | \(0.628734\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | −23.3827 | + | 4.50000i | −1.38024 | + | 0.265627i | ||||
\(288\) | 2.00000i | 0.117851i | ||||||||
\(289\) | −8.50000 | − | 14.7224i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | + | 12.1244i | −0.410347 | + | 0.710742i | ||||
\(292\) | 13.8564 | − | 8.00000i | 0.810885 | − | 0.468165i | ||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | −6.50000 | + | 2.59808i | −0.379088 | + | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | − | 3.46410i | −0.116248 | − | 0.201347i | ||||
\(297\) | 25.9808 | + | 15.0000i | 1.50756 | + | 0.870388i | ||||
\(298\) | 12.9904 | + | 7.50000i | 0.752513 | + | 0.434463i | ||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.50000 | + | 18.1865i | 0.201737 | + | 1.04825i | ||||
\(302\) | − | 4.00000i | − | 0.230174i | ||||||
\(303\) | 12.9904 | − | 7.50000i | 0.746278 | − | 0.430864i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.00000i | − | 0.285365i | −0.989769 | − | 0.142683i | \(-0.954427\pi\) | ||
0.989769 | − | 0.142683i | \(-0.0455728\pi\) | |||||||
\(308\) | 10.3923 | + | 12.0000i | 0.592157 | + | 0.683763i | ||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | 3.46410 | + | 2.00000i | 0.196116 | + | 0.113228i | ||||
\(313\) | 6.92820 | − | 4.00000i | 0.391605 | − | 0.226093i | −0.291250 | − | 0.956647i | \(-0.594071\pi\) |
0.682855 | + | 0.730554i | \(0.260738\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −10.3923 | + | 6.00000i | −0.583690 | + | 0.336994i | −0.762598 | − | 0.646872i | \(-0.776077\pi\) |
0.178908 | + | 0.983866i | \(0.442743\pi\) | |||||||
\(318\) | −5.19615 | − | 3.00000i | −0.291386 | − | 0.168232i | ||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0000 | −0.837218 | ||||||||
\(322\) | 2.59808 | − | 7.50000i | 0.144785 | − | 0.417959i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00000 | + | 3.46410i | −0.110770 | + | 0.191859i | ||||
\(327\) | −9.52628 | + | 5.50000i | −0.526804 | + | 0.304151i | ||||
\(328\) | − | 9.00000i | − | 0.496942i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | 2.59808 | + | 1.50000i | 0.142588 | + | 0.0823232i | ||||
\(333\) | −6.92820 | − | 4.00000i | −0.379663 | − | 0.219199i | ||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 2.59808i | −0.0272772 | − | 0.141737i | ||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | −2.59808 | + | 1.50000i | −0.141317 | + | 0.0815892i | ||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | + | 41.5692i | 1.29967 | + | 2.25110i | ||||
\(342\) | − | 4.00000i | − | 0.216295i | ||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −7.00000 | −0.377415 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.79423 | + | 4.50000i | 0.418416 | + | 0.241573i | 0.694399 | − | 0.719590i | \(-0.255670\pi\) |
−0.275983 | + | 0.961162i | \(0.589003\pi\) | |||||||
\(348\) | −2.59808 | + | 1.50000i | −0.139272 | + | 0.0804084i | ||||
\(349\) | −17.0000 | −0.909989 | −0.454995 | − | 0.890494i | \(-0.650359\pi\) | ||||
−0.454995 | + | 0.890494i | \(0.650359\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | −5.19615 | + | 3.00000i | −0.276956 | + | 0.159901i | ||||
\(353\) | 5.19615 | + | 3.00000i | 0.276563 | + | 0.159674i | 0.631867 | − | 0.775077i | \(-0.282289\pi\) |
−0.355303 | + | 0.934751i | \(0.615622\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0000 | −0.794998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000i | 1.26844i | ||||||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 9.52628 | − | 5.50000i | 0.500690 | − | 0.289074i | ||||
\(363\) | 25.0000i | 1.31216i | ||||||||
\(364\) | 10.0000 | + | 3.46410i | 0.524142 | + | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.50000 | + | 4.33013i | 0.130677 | + | 0.226339i | ||||
\(367\) | 30.3109 | + | 17.5000i | 1.58222 | + | 0.913493i | 0.994535 | + | 0.104399i | \(0.0332919\pi\) |
0.587680 | + | 0.809093i | \(0.300041\pi\) | |||||||
\(368\) | 2.59808 | + | 1.50000i | 0.135434 | + | 0.0781929i | ||||
\(369\) | −9.00000 | − | 15.5885i | −0.468521 | − | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.0000 | − | 5.19615i | −0.778761 | − | 0.269771i | ||||
\(372\) | − | 8.00000i | − | 0.414781i | ||||||
\(373\) | −3.46410 | + | 2.00000i | −0.179364 | + | 0.103556i | −0.586994 | − | 0.809591i | \(-0.699689\pi\) |
0.407630 | + | 0.913147i | \(0.366355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | −8.66025 | − | 10.0000i | −0.445435 | − | 0.514344i | ||||
\(379\) | 34.0000 | 1.74646 | 0.873231 | − | 0.487306i | \(-0.162020\pi\) | ||||
0.873231 | + | 0.487306i | \(0.162020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | 5.19615 | + | 3.00000i | 0.265858 | + | 0.153493i | ||||
\(383\) | −12.9904 | + | 7.50000i | −0.663777 | + | 0.383232i | −0.793715 | − | 0.608290i | \(-0.791856\pi\) |
0.129937 | + | 0.991522i | \(0.458522\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | −12.1244 | + | 7.00000i | −0.616316 | + | 0.355830i | ||||
\(388\) | −12.1244 | − | 7.00000i | −0.615521 | − | 0.355371i | ||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.59808 | − | 6.50000i | −0.131223 | − | 0.328300i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | + | 10.3923i | −0.301511 | + | 0.522233i | ||||
\(397\) | −12.1244 | + | 7.00000i | −0.608504 | + | 0.351320i | −0.772380 | − | 0.635161i | \(-0.780934\pi\) |
0.163876 | + | 0.986481i | \(0.447600\pi\) | |||||||
\(398\) | 4.00000i | 0.200502i | ||||||||
\(399\) | 1.00000 | + | 5.19615i | 0.0500626 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | −4.33013 | − | 2.50000i | −0.215967 | − | 0.124689i | ||||
\(403\) | 27.7128 | + | 16.0000i | 1.38047 | + | 0.797017i | ||||
\(404\) | 7.50000 | + | 12.9904i | 0.373139 | + | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | + | 5.19615i | −0.297775 | + | 0.257881i | ||||
\(407\) | − | 24.0000i | − | 1.18964i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | + | 11.2583i | −0.321404 | + | 0.556689i | −0.980778 | − | 0.195127i | \(-0.937488\pi\) |
0.659374 | + | 0.751815i | \(0.270822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | − | 10.3923i | −0.295958 | − | 0.512615i | ||||
\(412\) | 1.00000i | 0.0492665i | ||||||||
\(413\) | 5.19615 | − | 15.0000i | 0.255686 | − | 0.738102i | ||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | + | 3.46410i | −0.0980581 | + | 0.169842i | ||||
\(417\) | −8.66025 | − | 5.00000i | −0.424094 | − | 0.244851i | ||||
\(418\) | 10.3923 | − | 6.00000i | 0.508304 | − | 0.293470i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | −8.66025 | + | 5.00000i | −0.421575 | + | 0.243396i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 8.66025 | + | 10.0000i | 0.419099 | + | 0.483934i | ||||
\(428\) | − | 15.0000i | − | 0.725052i | ||||||
\(429\) | 12.0000 | + | 20.7846i | 0.579365 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | + | 25.9808i | −0.722525 | + | 1.25145i | 0.237460 | + | 0.971397i | \(0.423685\pi\) |
−0.959985 | + | 0.280052i | \(0.909648\pi\) | |||||||
\(432\) | 4.33013 | − | 2.50000i | 0.208333 | − | 0.120281i | ||||
\(433\) | − | 22.0000i | − | 1.05725i | −0.848855 | − | 0.528626i | \(-0.822707\pi\) | ||
0.848855 | − | 0.528626i | \(-0.177293\pi\) | |||||||
\(434\) | −4.00000 | − | 20.7846i | −0.192006 | − | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.50000 | − | 9.52628i | −0.263402 | − | 0.456226i | ||||
\(437\) | −5.19615 | − | 3.00000i | −0.248566 | − | 0.143509i | ||||
\(438\) | −13.8564 | − | 8.00000i | −0.662085 | − | 0.382255i | ||||
\(439\) | −14.0000 | − | 24.2487i | −0.668184 | − | 1.15733i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
0.310228 | − | 0.950662i | \(-0.399595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.1865 | − | 10.5000i | 0.864068 | − | 0.498870i | −0.00130426 | − | 0.999999i | \(-0.500415\pi\) |
0.865373 | + | 0.501129i | \(0.167082\pi\) | |||||||
\(444\) | −2.00000 | + | 3.46410i | −0.0949158 | + | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | − | 24.2487i | −0.662919 | − | 1.14821i | ||||
\(447\) | − | 15.0000i | − | 0.709476i | ||||||
\(448\) | 2.59808 | − | 0.500000i | 0.122748 | − | 0.0236228i | ||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | − | 46.7654i | 1.27138 | − | 2.20210i | ||||
\(452\) | 5.19615 | + | 3.00000i | 0.244406 | + | 0.141108i | ||||
\(453\) | −3.46410 | + | 2.00000i | −0.162758 | + | 0.0939682i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −27.7128 | + | 16.0000i | −1.29635 | + | 0.748448i | −0.979772 | − | 0.200118i | \(-0.935868\pi\) |
−0.316579 | + | 0.948566i | \(0.602534\pi\) | |||||||
\(458\) | 12.1244 | + | 7.00000i | 0.566534 | + | 0.327089i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 5.19615 | − | 15.0000i | 0.241747 | − | 0.697863i | ||||
\(463\) | − | 13.0000i | − | 0.604161i | −0.953282 | − | 0.302081i | \(-0.902319\pi\) | ||
0.953282 | − | 0.302081i | \(-0.0976812\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | + | 10.3923i | −0.277945 | + | 0.481414i | ||||
\(467\) | 12.9904 | − | 7.50000i | 0.601123 | − | 0.347059i | −0.168360 | − | 0.985726i | \(-0.553847\pi\) |
0.769483 | + | 0.638667i | \(0.220514\pi\) | |||||||
\(468\) | 8.00000i | 0.369800i | ||||||||
\(469\) | −12.5000 | − | 4.33013i | −0.577196 | − | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0000 | + | 19.0526i | 0.506853 | + | 0.877896i | ||||
\(472\) | 5.19615 | + | 3.00000i | 0.239172 | + | 0.138086i | ||||
\(473\) | −36.3731 | − | 21.0000i | −1.67244 | − | 0.965581i | ||||
\(474\) | −1.00000 | − | 1.73205i | −0.0459315 | − | 0.0795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.0000i | − | 0.549442i | ||||||
\(478\) | −10.3923 | + | 6.00000i | −0.475333 | + | 0.274434i | ||||
\(479\) | 6.00000 | − | 10.3923i | 0.274147 | − | 0.474837i | −0.695773 | − | 0.718262i | \(-0.744938\pi\) |
0.969920 | + | 0.243426i | \(0.0782712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | −7.79423 | + | 1.50000i | −0.354650 | + | 0.0682524i | ||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.00000 | − | 13.8564i | 0.362887 | − | 0.628539i | ||||
\(487\) | −13.8564 | − | 8.00000i | −0.627894 | − | 0.362515i | 0.152042 | − | 0.988374i | \(-0.451415\pi\) |
−0.779936 | + | 0.625859i | \(0.784748\pi\) | |||||||
\(488\) | −4.33013 | + | 2.50000i | −0.196016 | + | 0.113170i | ||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −7.79423 | + | 4.50000i | −0.351391 | + | 0.202876i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.00000 | − | 6.92820i | 0.179969 | − | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 15.5885 | − | 3.00000i | 0.699238 | − | 0.134568i | ||||
\(498\) | − | 3.00000i | − | 0.134433i | ||||||
\(499\) | −11.0000 | − | 19.0526i | −0.492428 | − | 0.852910i | 0.507534 | − | 0.861632i | \(-0.330557\pi\) |
−0.999962 | + | 0.00872186i | \(0.997224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | −10.3923 | + | 6.00000i | −0.463831 | + | 0.267793i | ||||
\(503\) | 21.0000i | 0.936344i | 0.883637 | + | 0.468172i | \(0.155087\pi\) | ||||
−0.883637 | + | 0.468172i | \(0.844913\pi\) | |||||||
\(504\) | 4.00000 | − | 3.46410i | 0.178174 | − | 0.154303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 2.59808 | + | 1.50000i | 0.115385 | + | 0.0666173i | ||||
\(508\) | −6.92820 | − | 4.00000i | −0.307389 | − | 0.177471i | ||||
\(509\) | 10.5000 | + | 18.1865i | 0.465404 | + | 0.806104i | 0.999220 | − | 0.0394971i | \(-0.0125756\pi\) |
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.0000 | − | 13.8564i | −1.76950 | − | 0.612971i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −8.66025 | + | 5.00000i | −0.382360 | + | 0.220755i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.50000 | + | 6.06218i | 0.154079 | + | 0.266872i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.46410 | + | 10.0000i | −0.152204 | + | 0.439375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | −24.2487 | + | 14.0000i | −1.06032 | + | 0.612177i | −0.925521 | − | 0.378695i | \(-0.876373\pi\) |
−0.134801 | + | 0.990873i | \(0.543039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | 0.915644 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.19615 | + | 3.00000i | 0.226134 | + | 0.130558i | ||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −5.19615 | + | 1.00000i | −0.225282 | + | 0.0433555i | ||||
\(533\) | − | 36.0000i | − | 1.55933i | ||||||
\(534\) | 7.50000 | + | 12.9904i | 0.324557 | + | 0.562149i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.50000 | − | 4.33013i | 0.107984 | − | 0.187033i | ||||
\(537\) | 20.7846 | − | 12.0000i | 0.896922 | − | 0.517838i | ||||
\(538\) | − | 15.0000i | − | 0.646696i | ||||||
\(539\) | 6.00000 | − | 41.5692i | 0.258438 | − | 1.79051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | −1.73205 | − | 1.00000i | −0.0743980 | − | 0.0429537i | ||||
\(543\) | −9.52628 | − | 5.50000i | −0.408812 | − | 0.236028i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | − | 10.3923i | −0.0855921 | − | 0.444750i | ||||
\(547\) | 19.0000i | 0.812381i | 0.913788 | + | 0.406191i | \(0.133143\pi\) | ||||
−0.913788 | + | 0.406191i | \(0.866857\pi\) | |||||||
\(548\) | 10.3923 | − | 6.00000i | 0.443937 | − | 0.256307i | ||||
\(549\) | −5.00000 | + | 8.66025i | −0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | − | 3.00000i | − | 0.127688i | ||||||
\(553\) | −3.46410 | − | 4.00000i | −0.147309 | − | 0.170097i | ||||
\(554\) | 8.00000 | 0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00000 | − | 8.66025i | 0.212047 | − | 0.367277i | ||||
\(557\) | −15.5885 | − | 9.00000i | −0.660504 | − | 0.381342i | 0.131965 | − | 0.991254i | \(-0.457871\pi\) |
−0.792469 | + | 0.609912i | \(0.791205\pi\) | |||||||
\(558\) | 13.8564 | − | 8.00000i | 0.586588 | − | 0.338667i | ||||
\(559\) | −28.0000 | −1.18427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.19615 | + | 3.00000i | −0.219186 | + | 0.126547i | ||||
\(563\) | −23.3827 | − | 13.5000i | −0.985463 | − | 0.568957i | −0.0815478 | − | 0.996669i | \(-0.525986\pi\) |
−0.903915 | + | 0.427712i | \(0.859320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0.866025 | − | 2.50000i | 0.0363696 | − | 0.104990i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | −20.7846 | + | 12.0000i | −0.869048 | + | 0.501745i | ||||
\(573\) | − | 6.00000i | − | 0.250654i | ||||||
\(574\) | −18.0000 | + | 15.5885i | −0.751305 | + | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | 22.5167 | + | 13.0000i | 0.937381 | + | 0.541197i | 0.889138 | − | 0.457639i | \(-0.151305\pi\) |
0.0482425 | + | 0.998836i | \(0.484638\pi\) | |||||||
\(578\) | −14.7224 | − | 8.50000i | −0.612372 | − | 0.353553i | ||||
\(579\) | 1.00000 | + | 1.73205i | 0.0415586 | + | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.50000 | − | 7.79423i | −0.0622305 | − | 0.323359i | ||||
\(582\) | 14.0000i | 0.580319i | ||||||||
\(583\) | 31.1769 | − | 18.0000i | 1.29122 | − | 0.745484i | ||||
\(584\) | 8.00000 | − | 13.8564i | 0.331042 | − | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 10.3923i | 0.247858 | + | 0.429302i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | −4.33013 | + | 5.50000i | −0.178571 | + | 0.226816i | ||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | − | 5.19615i | 0.123404 | − | 0.213741i | ||||
\(592\) | −3.46410 | − | 2.00000i | −0.142374 | − | 0.0821995i | ||||
\(593\) | 5.19615 | − | 3.00000i | 0.213380 | − | 0.123195i | −0.389501 | − | 0.921026i | \(-0.627353\pi\) |
0.602881 | + | 0.797831i | \(0.294019\pi\) | |||||||
\(594\) | 30.0000 | 1.23091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.0000 | 0.614424 | ||||||||
\(597\) | 3.46410 | − | 2.00000i | 0.141776 | − | 0.0818546i | ||||
\(598\) | 10.3923 | + | 6.00000i | 0.424973 | + | 0.245358i | ||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.0000 | −1.87638 | −0.938190 | − | 0.346122i | \(-0.887498\pi\) | ||||
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 12.1244 | + | 14.0000i | 0.494152 | + | 0.570597i | ||||
\(603\) | − | 10.0000i | − | 0.407231i | ||||||
\(604\) | −2.00000 | − | 3.46410i | −0.0813788 | − | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.50000 | − | 12.9904i | 0.304667 | − | 0.527698i | ||||
\(607\) | −19.9186 | + | 11.5000i | −0.808470 | + | 0.466771i | −0.846424 | − | 0.532509i | \(-0.821249\pi\) |
0.0379540 | + | 0.999279i | \(0.487916\pi\) | |||||||
\(608\) | − | 2.00000i | − | 0.0811107i | ||||||
\(609\) | 7.50000 | + | 2.59808i | 0.303915 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8564 | + | 8.00000i | 0.559655 | + | 0.323117i | 0.753007 | − | 0.658012i | \(-0.228603\pi\) |
−0.193352 | + | 0.981129i | \(0.561936\pi\) | |||||||
\(614\) | −2.50000 | − | 4.33013i | −0.100892 | − | 0.174750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.0000 | + | 5.19615i | 0.604367 | + | 0.209359i | ||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | 0.866025 | − | 0.500000i | 0.0348367 | − | 0.0201129i | ||||
\(619\) | 7.00000 | − | 12.1244i | 0.281354 | − | 0.487319i | −0.690365 | − | 0.723462i | \(-0.742550\pi\) |
0.971718 | + | 0.236143i | \(0.0758832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | − | 12.9904i | −0.300965 | − | 0.521286i | ||||
\(622\) | − | 18.0000i | − | 0.721734i | ||||||
\(623\) | 25.9808 | + | 30.0000i | 1.04090 | + | 1.20192i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.00000 | − | 6.92820i | 0.159872 | − | 0.276907i | ||||
\(627\) | −10.3923 | − | 6.00000i | −0.415029 | − | 0.239617i | ||||
\(628\) | −19.0526 | + | 11.0000i | −0.760280 | + | 0.438948i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 1.73205 | − | 1.00000i | 0.0688973 | − | 0.0397779i | ||||
\(633\) | 8.66025 | + | 5.00000i | 0.344214 | + | 0.198732i | ||||
\(634\) | −6.00000 | + | 10.3923i | −0.238290 | + | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −10.3923 | − | 26.0000i | −0.411758 | − | 1.03016i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | − | 2.59808i | 0.0592464 | − | 0.102618i | −0.834881 | − | 0.550431i | \(-0.814464\pi\) |
0.894127 | + | 0.447813i | \(0.147797\pi\) | |||||||
\(642\) | −12.9904 | + | 7.50000i | −0.512689 | + | 0.296001i | ||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | −1.50000 | − | 7.79423i | −0.0591083 | − | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.59808 | + | 1.50000i | 0.102141 | + | 0.0589711i | 0.550200 | − | 0.835033i | \(-0.314551\pi\) |
−0.448059 | + | 0.894004i | \(0.647885\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 18.0000 | + | 31.1769i | 0.706562 | + | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0000 | + | 13.8564i | −0.627089 | + | 0.543075i | ||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | −41.5692 | + | 24.0000i | −1.62673 | + | 0.939193i | −0.641669 | + | 0.766982i | \(0.721758\pi\) |
−0.985060 | + | 0.172211i | \(0.944909\pi\) | |||||||
\(654\) | −5.50000 | + | 9.52628i | −0.215067 | + | 0.372507i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | − | 7.79423i | −0.175695 | − | 0.304314i | ||||
\(657\) | − | 32.0000i | − | 1.24844i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5000 | + | 35.5070i | −0.797358 | + | 1.38106i | 0.123974 | + | 0.992286i | \(0.460436\pi\) |
−0.921331 | + | 0.388778i | \(0.872897\pi\) | |||||||
\(662\) | 24.2487 | + | 14.0000i | 0.942453 | + | 0.544125i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.00000 | 0.116423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | −7.79423 | + | 4.50000i | −0.301794 | + | 0.174241i | ||||
\(668\) | 2.59808 | + | 1.50000i | 0.100523 | + | 0.0580367i | ||||
\(669\) | −14.0000 | + | 24.2487i | −0.541271 | + | 0.937509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | −1.73205 | − | 2.00000i | −0.0668153 | − | 0.0771517i | ||||
\(673\) | 8.00000i | 0.308377i | 0.988041 | + | 0.154189i | \(0.0492764\pi\) | ||||
−0.988041 | + | 0.154189i | \(0.950724\pi\) | |||||||
\(674\) | 11.0000 | + | 19.0526i | 0.423704 | + | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | −10.3923 | + | 6.00000i | −0.399409 | + | 0.230599i | −0.686229 | − | 0.727386i | \(-0.740735\pi\) |
0.286820 | + | 0.957984i | \(0.407402\pi\) | |||||||
\(678\) | − | 6.00000i | − | 0.230429i | ||||||
\(679\) | 7.00000 | + | 36.3731i | 0.268635 | + | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 41.5692 | + | 24.0000i | 1.59177 | + | 0.919007i | ||||
\(683\) | −7.79423 | − | 4.50000i | −0.298238 | − | 0.172188i | 0.343413 | − | 0.939184i | \(-0.388417\pi\) |
−0.641651 | + | 0.766997i | \(0.721750\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 14.0000i | − | 0.534133i | ||||||
\(688\) | −6.06218 | + | 3.50000i | −0.231118 | + | 0.133436i | ||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | + | 19.0526i | 0.418460 | + | 0.724793i | 0.995785 | − | 0.0917209i | \(-0.0292368\pi\) |
−0.577325 | + | 0.816514i | \(0.695903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.1769 | − | 6.00000i | 1.18431 | − | 0.227921i | ||||
\(694\) | 9.00000 | 0.341635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14.7224 | + | 8.50000i | −0.557252 | + | 0.321730i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | 17.3205 | − | 10.0000i | 0.653720 | − | 0.377426i | ||||
\(703\) | 6.92820 | + | 4.00000i | 0.261302 | + | 0.150863i | ||||
\(704\) | −3.00000 | + | 5.19615i | −0.113067 | + | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | 12.9904 | − | 37.5000i | 0.488554 | − | 1.41033i | ||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −15.5000 | − | 26.8468i | −0.582115 | − | 1.00825i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.413114 | − | 0.910679i | \(-0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | −12.9904 | + | 7.50000i | −0.486835 | + | 0.281074i | ||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | + | 20.7846i | 0.448461 | + | 0.776757i | ||||
\(717\) | 10.3923 | + | 6.00000i | 0.388108 | + | 0.224074i | ||||
\(718\) | 20.7846 | + | 12.0000i | 0.775675 | + | 0.447836i | ||||
\(719\) | −9.00000 | − | 15.5885i | −0.335643 | − | 0.581351i | 0.647965 | − | 0.761670i | \(-0.275620\pi\) |
−0.983608 | + | 0.180319i | \(0.942287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | − | 1.73205i | 0.0744839 | − | 0.0645049i | ||||
\(722\) | − | 15.0000i | − | 0.558242i | ||||||
\(723\) | 1.73205 | − | 1.00000i | 0.0644157 | − | 0.0371904i | ||||
\(724\) | 5.50000 | − | 9.52628i | 0.204406 | − | 0.354041i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.5000 | + | 21.6506i | 0.463919 | + | 0.803530i | ||||
\(727\) | 19.0000i | 0.704671i | 0.935874 | + | 0.352335i | \(0.114612\pi\) | ||||
−0.935874 | + | 0.352335i | \(0.885388\pi\) | |||||||
\(728\) | 10.3923 | − | 2.00000i | 0.385164 | − | 0.0741249i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.33013 | + | 2.50000i | 0.160046 | + | 0.0924027i | ||||
\(733\) | −29.4449 | + | 17.0000i | −1.08757 | + | 0.627909i | −0.932929 | − | 0.360061i | \(-0.882756\pi\) |
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(734\) | 35.0000 | 1.29187 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 25.9808 | − | 15.0000i | 0.957014 | − | 0.552532i | ||||
\(738\) | −15.5885 | − | 9.00000i | −0.573819 | − | 0.331295i | ||||
\(739\) | 13.0000 | − | 22.5167i | 0.478213 | − | 0.828289i | −0.521475 | − | 0.853266i | \(-0.674618\pi\) |
0.999688 | + | 0.0249776i | \(0.00795146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | −15.5885 | + | 3.00000i | −0.572270 | + | 0.110133i | ||||
\(743\) | 39.0000i | 1.43077i | 0.698730 | + | 0.715386i | \(0.253749\pi\) | ||||
−0.698730 | + | 0.715386i | \(0.746251\pi\) | |||||||
\(744\) | −4.00000 | − | 6.92820i | −0.146647 | − | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.00000 | + | 3.46410i | −0.0732252 | + | 0.126830i | ||||
\(747\) | 5.19615 | − | 3.00000i | 0.190117 | − | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.0000 | + | 25.9808i | −1.09618 | + | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | + | 3.46410i | 0.0729810 | + | 0.126407i | 0.900207 | − | 0.435463i | \(-0.143415\pi\) |
−0.827225 | + | 0.561870i | \(0.810082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.3923 | + | 6.00000i | 0.378717 | + | 0.218652i | ||||
\(754\) | −6.00000 | − | 10.3923i | −0.218507 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.5000 | − | 4.33013i | −0.454621 | − | 0.157485i | ||||
\(757\) | 28.0000i | 1.01768i | 0.860862 | + | 0.508839i | \(0.169925\pi\) | ||||
−0.860862 | + | 0.508839i | \(0.830075\pi\) | |||||||
\(758\) | 29.4449 | − | 17.0000i | 1.06949 | − | 0.617468i | ||||
\(759\) | 9.00000 | − | 15.5885i | 0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.0000 | − | 36.3731i | −0.761249 | − | 1.31852i | −0.942207 | − | 0.335032i | \(-0.891253\pi\) |
0.180957 | − | 0.983491i | \(-0.442080\pi\) | |||||||
\(762\) | 8.00000i | 0.289809i | ||||||||
\(763\) | −9.52628 | + | 27.5000i | −0.344874 | + | 0.995567i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | ||||
\(767\) | 20.7846 | + | 12.0000i | 0.750489 | + | 0.433295i | ||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.73205 | + | 1.00000i | −0.0623379 | + | 0.0359908i | ||||
\(773\) | 10.3923 | + | 6.00000i | 0.373785 | + | 0.215805i | 0.675111 | − | 0.737716i | \(-0.264096\pi\) |
−0.301326 | + | 0.953521i | \(0.597429\pi\) | |||||||
\(774\) | −7.00000 | + | 12.1244i | −0.251610 | + | 0.435801i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.0000 | −0.502571 | ||||||||
\(777\) | 10.3923 | − | 2.00000i | 0.372822 | − | 0.0717496i | ||||
\(778\) | 30.0000i | 1.07555i | ||||||||
\(779\) | 9.00000 | + | 15.5885i | 0.322458 | + | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000i | 0.536056i | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.2391 | − | 21.5000i | −1.32743 | − | 0.766392i | −0.342529 | − | 0.939507i | \(-0.611283\pi\) |
−0.984902 | + | 0.173115i | \(0.944617\pi\) | |||||||
\(788\) | 5.19615 | + | 3.00000i | 0.185105 | + | 0.106871i | ||||
\(789\) | −10.5000 | − | 18.1865i | −0.373810 | − | 0.647458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.00000 | − | 15.5885i | −0.106668 | − | 0.554262i | ||||
\(792\) | 12.0000i | 0.426401i | ||||||||
\(793\) | −17.3205 | + | 10.0000i | −0.615069 | + | 0.355110i | ||||
\(794\) | −7.00000 | + | 12.1244i | −0.248421 | + | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 48.0000i | 1.70025i | 0.526583 | + | 0.850124i | \(0.323473\pi\) | ||||
−0.526583 | + | 0.850124i | \(0.676527\pi\) | |||||||
\(798\) | 3.46410 | + | 4.00000i | 0.122628 | + | 0.141598i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | + | 25.9808i | −0.529999 | + | 0.917985i | ||||
\(802\) | −12.9904 | − | 7.50000i | −0.458706 | − | 0.264834i | ||||
\(803\) | 83.1384 | − | 48.0000i | 2.93389 | − | 1.69388i | ||||
\(804\) | −5.00000 | −0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | −12.9904 | + | 7.50000i | −0.457283 | + | 0.264013i | ||||
\(808\) | 12.9904 | + | 7.50000i | 0.457000 | + | 0.263849i | ||||
\(809\) | 10.5000 | − | 18.1865i | 0.369160 | − | 0.639404i | −0.620274 | − | 0.784385i | \(-0.712979\pi\) |
0.989434 | + | 0.144981i | \(0.0463120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −2.59808 | + | 7.50000i | −0.0911746 | + | 0.263198i | ||||
\(813\) | 2.00000i | 0.0701431i | ||||||||
\(814\) | −12.0000 | − | 20.7846i | −0.420600 | − | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.1244 | − | 7.00000i | 0.424178 | − | 0.244899i | ||||
\(818\) | 13.0000i | 0.454534i | ||||||||
\(819\) | 16.0000 | − | 13.8564i | 0.559085 | − | 0.484182i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | −10.3923 | − | 6.00000i | −0.362473 | − | 0.209274i | ||||
\(823\) | 16.4545 | + | 9.50000i | 0.573567 | + | 0.331149i | 0.758573 | − | 0.651588i | \(-0.225897\pi\) |
−0.185006 | + | 0.982737i | \(0.559230\pi\) | |||||||
\(824\) | 0.500000 | + | 0.866025i | 0.0174183 | + | 0.0301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 15.5885i | −0.104383 | − | 0.542392i | ||||
\(827\) | − | 15.0000i | − | 0.521601i | −0.965393 | − | 0.260801i | \(-0.916014\pi\) | ||
0.965393 | − | 0.260801i | \(-0.0839865\pi\) | |||||||
\(828\) | 5.19615 | − | 3.00000i | 0.180579 | − | 0.104257i | ||||
\(829\) | 1.00000 | − | 1.73205i | 0.0347314 | − | 0.0601566i | −0.848137 | − | 0.529777i | \(-0.822276\pi\) |
0.882869 | + | 0.469620i | \(0.155609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.0000 | −0.346272 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | − | 10.3923i | 0.207514 | − | 0.359425i | ||||
\(837\) | −34.6410 | − | 20.0000i | −1.19737 | − | 0.691301i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 14.7224 | − | 8.50000i | 0.507369 | − | 0.292929i | ||||
\(843\) | 5.19615 | + | 3.00000i | 0.178965 | + | 0.103325i | ||||
\(844\) | −5.00000 | + | 8.66025i | −0.172107 | + | 0.298098i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.3013 | + | 50.0000i | 1.48785 | + | 1.71802i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −2.00000 | − | 3.46410i | −0.0686398 | − | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | 5.19615 | − | 3.00000i | 0.178017 | − | 0.102778i | ||||
\(853\) | − | 46.0000i | − | 1.57501i | −0.616308 | − | 0.787505i | \(-0.711372\pi\) | ||
0.616308 | − | 0.787505i | \(-0.288628\pi\) | |||||||
\(854\) | 12.5000 | + | 4.33013i | 0.427741 | + | 0.148174i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.50000 | − | 12.9904i | −0.256345 | − | 0.444002i | ||||
\(857\) | 5.19615 | + | 3.00000i | 0.177497 | + | 0.102478i | 0.586116 | − | 0.810227i | \(-0.300656\pi\) |
−0.408619 | + | 0.912705i | \(0.633990\pi\) | |||||||
\(858\) | 20.7846 | + | 12.0000i | 0.709575 | + | 0.409673i | ||||
\(859\) | 16.0000 | + | 27.7128i | 0.545913 | + | 0.945549i | 0.998549 | + | 0.0538535i | \(0.0171504\pi\) |
−0.452636 | + | 0.891695i | \(0.649516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.5000 | + | 7.79423i | 0.766798 | + | 0.265627i | ||||
\(862\) | 30.0000i | 1.02180i | ||||||||
\(863\) | 23.3827 | − | 13.5000i | 0.795956 | − | 0.459545i | −0.0460992 | − | 0.998937i | \(-0.514679\pi\) |
0.842055 | + | 0.539392i | \(0.181346\pi\) | |||||||
\(864\) | 2.50000 | − | 4.33013i | 0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0000 | − | 19.0526i | −0.373795 | − | 0.647432i | ||||
\(867\) | 17.0000i | 0.577350i | ||||||||
\(868\) | −13.8564 | − | 16.0000i | −0.470317 | − | 0.543075i | ||||
\(869\) | 12.0000 | 0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | − | 17.3205i | 0.338837 | − | 0.586883i | ||||
\(872\) | −9.52628 | − | 5.50000i | −0.322601 | − | 0.186254i | ||||
\(873\) | −24.2487 | + | 14.0000i | −0.820695 | + | 0.473828i | ||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | −1.73205 | + | 1.00000i | −0.0584872 | + | 0.0337676i | −0.528958 | − | 0.848648i | \(-0.677417\pi\) |
0.470471 | + | 0.882415i | \(0.344084\pi\) | |||||||
\(878\) | −24.2487 | − | 14.0000i | −0.818354 | − | 0.472477i | ||||
\(879\) | 6.00000 | − | 10.3923i | 0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.0000 | 1.92038 | 0.960189 | − | 0.279350i | \(-0.0901189\pi\) | ||||
0.960189 | + | 0.279350i | \(0.0901189\pi\) | |||||||
\(882\) | −13.8564 | − | 2.00000i | −0.466569 | − | 0.0673435i | ||||
\(883\) | − | 52.0000i | − | 1.74994i | −0.484178 | − | 0.874970i | \(-0.660881\pi\) | ||
0.484178 | − | 0.874970i | \(-0.339119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5000 | − | 18.1865i | 0.352754 | − | 0.610989i | ||||
\(887\) | 18.1865 | − | 10.5000i | 0.610644 | − | 0.352555i | −0.162573 | − | 0.986696i | \(-0.551979\pi\) |
0.773217 | + | 0.634141i | \(0.218646\pi\) | |||||||
\(888\) | 4.00000i | 0.134231i | ||||||||
\(889\) | 4.00000 | + | 20.7846i | 0.134156 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | + | 5.19615i | 0.100504 | + | 0.174078i | ||||
\(892\) | −24.2487 | − | 14.0000i | −0.811907 | − | 0.468755i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.50000 | − | 12.9904i | −0.250838 | − | 0.434463i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | − | 12.0000i | − | 0.400668i | ||||||
\(898\) | 7.79423 | − | 4.50000i | 0.260097 | − | 0.150167i | ||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 54.0000i | − | 1.79800i | ||||||
\(903\) | 6.06218 | − | 17.5000i | 0.201737 | − | 0.582364i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00000 | + | 3.46410i | −0.0664455 | + | 0.115087i | ||||
\(907\) | −21.6506 | − | 12.5000i | −0.718898 | − | 0.415056i | 0.0954492 | − | 0.995434i | \(-0.469571\pi\) |
−0.814347 | + | 0.580379i | \(0.802905\pi\) | |||||||
\(908\) | −10.3923 | + | 6.00000i | −0.344881 | + | 0.199117i | ||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0000 | 0.596367 | 0.298183 | − | 0.954509i | \(-0.403619\pi\) | ||||
0.298183 | + | 0.954509i | \(0.403619\pi\) | |||||||
\(912\) | −1.73205 | + | 1.00000i | −0.0573539 | + | 0.0331133i | ||||
\(913\) | 15.5885 | + | 9.00000i | 0.515903 | + | 0.297857i | ||||
\(914\) | −16.0000 | + | 27.7128i | −0.529233 | + | 0.916658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.00000 | + | 12.1244i | 0.230909 | + | 0.399946i | 0.958076 | − | 0.286515i | \(-0.0924968\pi\) |
−0.727167 | + | 0.686461i | \(0.759163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.50000 | + | 4.33013i | −0.0823778 | + | 0.142683i | ||||
\(922\) | 15.5885 | − | 9.00000i | 0.513378 | − | 0.296399i | ||||
\(923\) | 24.0000i | 0.789970i | ||||||||
\(924\) | −3.00000 | − | 15.5885i | −0.0986928 | − | 0.512823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.50000 | − | 11.2583i | −0.213603 | − | 0.369972i | ||||
\(927\) | 1.73205 | + | 1.00000i | 0.0568880 | + | 0.0328443i | ||||
\(928\) | −2.59808 | − | 1.50000i | −0.0852860 | − | 0.0492399i | ||||
\(929\) | −10.5000 | − | 18.1865i | −0.344494 | − | 0.596681i | 0.640768 | − | 0.767735i | \(-0.278616\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0000 | + | 8.66025i | 0.360510 | + | 0.283828i | ||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | −15.5885 | + | 9.00000i | −0.510343 | + | 0.294647i | ||||
\(934\) | 7.50000 | − | 12.9904i | 0.245407 | − | 0.425058i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.00000 | + | 6.92820i | 0.130744 | + | 0.226455i | ||||
\(937\) | 28.0000i | 0.914720i | 0.889282 | + | 0.457360i | \(0.151205\pi\) | ||||
−0.889282 | + | 0.457360i | \(0.848795\pi\) | |||||||
\(938\) | −12.9904 | + | 2.50000i | −0.424151 | + | 0.0816279i | ||||
\(939\) | −8.00000 | −0.261070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | − | 5.19615i | 0.0977972 | − | 0.169390i | −0.812975 | − | 0.582298i | \(-0.802154\pi\) |
0.910773 | + | 0.412908i | \(0.135487\pi\) | |||||||
\(942\) | 19.0526 | + | 11.0000i | 0.620766 | + | 0.358399i | ||||
\(943\) | −23.3827 | + | 13.5000i | −0.761445 | + | 0.439620i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.0000 | −1.36554 | ||||||||
\(947\) | 2.59808 | − | 1.50000i | 0.0844261 | − | 0.0487435i | −0.457193 | − | 0.889368i | \(-0.651145\pi\) |
0.541619 | + | 0.840624i | \(0.317812\pi\) | |||||||
\(948\) | −1.73205 | − | 1.00000i | −0.0562544 | − | 0.0324785i | ||||
\(949\) | 32.0000 | − | 55.4256i | 1.03876 | − | 1.79919i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0000i | 1.94359i | 0.235826 | + | 0.971795i | \(0.424220\pi\) | ||||
−0.235826 | + | 0.971795i | \(0.575780\pi\) | |||||||
\(954\) | −6.00000 | − | 10.3923i | −0.194257 | − | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | −15.5885 | + | 9.00000i | −0.503903 | + | 0.290929i | ||||
\(958\) | − | 12.0000i | − | 0.387702i | ||||||
\(959\) | −30.0000 | − | 10.3923i | −0.968751 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −13.8564 | − | 8.00000i | −0.446748 | − | 0.257930i | ||||
\(963\) | −25.9808 | − | 15.0000i | −0.837218 | − | 0.483368i | ||||
\(964\) | 1.00000 | + | 1.73205i | 0.0322078 | + | 0.0557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.00000 | + | 5.19615i | −0.193047 | + | 0.167183i | ||||
\(967\) | − | 35.0000i | − | 1.12552i | −0.826619 | − | 0.562762i | \(-0.809739\pi\) | ||
0.826619 | − | 0.562762i | \(-0.190261\pi\) | |||||||
\(968\) | −21.6506 | + | 12.5000i | −0.695878 | + | 0.401765i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | − | 16.0000i | − | 0.513200i | ||||||
\(973\) | −25.9808 | + | 5.00000i | −0.832905 | + | 0.160293i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.50000 | + | 4.33013i | −0.0800230 | + | 0.138604i | ||||
\(977\) | −5.19615 | − | 3.00000i | −0.166240 | − | 0.0959785i | 0.414572 | − | 0.910017i | \(-0.363931\pi\) |
−0.580812 | + | 0.814038i | \(0.697265\pi\) | |||||||
\(978\) | 3.46410 | − | 2.00000i | 0.110770 | − | 0.0639529i | ||||
\(979\) | −90.0000 | −2.87641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.0000 | −0.702406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7750 | − | 19.5000i | −1.07725 | − | 0.621953i | −0.147100 | − | 0.989122i | \(-0.546994\pi\) |
−0.930155 | + | 0.367168i | \(0.880327\pi\) | |||||||
\(984\) | −4.50000 | + | 7.79423i | −0.143455 | + | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.00000i | − | 0.254514i | ||||||
\(989\) | 10.5000 | + | 18.1865i | 0.333881 | + | 0.578298i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0000 | − | 24.2487i | 0.444725 | − | 0.770286i | −0.553308 | − | 0.832977i | \(-0.686635\pi\) |
0.998033 | + | 0.0626908i | \(0.0199682\pi\) | |||||||
\(992\) | 6.92820 | − | 4.00000i | 0.219971 | − | 0.127000i | ||||
\(993\) | − | 28.0000i | − | 0.888553i | ||||||
\(994\) | 12.0000 | − | 10.3923i | 0.380617 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.50000 | − | 2.59808i | −0.0475293 | − | 0.0823232i | ||||
\(997\) | 12.1244 | + | 7.00000i | 0.383982 | + | 0.221692i | 0.679549 | − | 0.733630i | \(-0.262175\pi\) |
−0.295567 | + | 0.955322i | \(0.595509\pi\) | |||||||
\(998\) | −19.0526 | − | 11.0000i | −0.603098 | − | 0.348199i | ||||
\(999\) | 10.0000 | + | 17.3205i | 0.316386 | + | 0.547997i |
(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 | 350.2.j.b.249.2 | 4 | ||
5.2 | odd | 4 | 70.2.e.c.11.1 | ✓ | 2 | ||
5.3 | odd | 4 | 350.2.e.e.151.1 | 2 | |||
5.4 | even | 2 | inner | 350.2.j.b.249.1 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.b.149.1 | 4 | ||
7.3 | odd | 6 | 2450.2.c.l.99.2 | 2 | |||
7.4 | even | 3 | 2450.2.c.g.99.2 | 2 | |||
15.2 | even | 4 | 630.2.k.b.361.1 | 2 | |||
20.7 | even | 4 | 560.2.q.g.81.1 | 2 | |||
35.2 | odd | 12 | 70.2.e.c.51.1 | yes | 2 | ||
35.3 | even | 12 | 2450.2.a.bc.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.g.99.1 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.b.149.2 | 4 | ||
35.12 | even | 12 | 490.2.e.h.471.1 | 2 | |||
35.17 | even | 12 | 490.2.a.b.1.1 | 1 | |||
35.18 | odd | 12 | 2450.2.a.w.1.1 | 1 | |||
35.23 | odd | 12 | 350.2.e.e.51.1 | 2 | |||
35.24 | odd | 6 | 2450.2.c.l.99.1 | 2 | |||
35.27 | even | 4 | 490.2.e.h.361.1 | 2 | |||
35.32 | odd | 12 | 490.2.a.c.1.1 | 1 | |||
105.2 | even | 12 | 630.2.k.b.541.1 | 2 | |||
105.17 | odd | 12 | 4410.2.a.bd.1.1 | 1 | |||
105.32 | even | 12 | 4410.2.a.bm.1.1 | 1 | |||
140.67 | even | 12 | 3920.2.a.p.1.1 | 1 | |||
140.87 | odd | 12 | 3920.2.a.bc.1.1 | 1 | |||
140.107 | even | 12 | 560.2.q.g.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.c.11.1 | ✓ | 2 | 5.2 | odd | 4 | ||
70.2.e.c.51.1 | yes | 2 | 35.2 | odd | 12 | ||
350.2.e.e.51.1 | 2 | 35.23 | odd | 12 | |||
350.2.e.e.151.1 | 2 | 5.3 | odd | 4 | |||
350.2.j.b.149.1 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.b.149.2 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.b.249.1 | 4 | 5.4 | even | 2 | inner | ||
350.2.j.b.249.2 | 4 | 1.1 | even | 1 | trivial | ||
490.2.a.b.1.1 | 1 | 35.17 | even | 12 | |||
490.2.a.c.1.1 | 1 | 35.32 | odd | 12 | |||
490.2.e.h.361.1 | 2 | 35.27 | even | 4 | |||
490.2.e.h.471.1 | 2 | 35.12 | even | 12 | |||
560.2.q.g.81.1 | 2 | 20.7 | even | 4 | |||
560.2.q.g.401.1 | 2 | 140.107 | even | 12 | |||
630.2.k.b.361.1 | 2 | 15.2 | even | 4 | |||
630.2.k.b.541.1 | 2 | 105.2 | even | 12 | |||
2450.2.a.w.1.1 | 1 | 35.18 | odd | 12 | |||
2450.2.a.bc.1.1 | 1 | 35.3 | even | 12 | |||
2450.2.c.g.99.1 | 2 | 35.4 | even | 6 | |||
2450.2.c.g.99.2 | 2 | 7.4 | even | 3 | |||
2450.2.c.l.99.1 | 2 | 35.24 | odd | 6 | |||
2450.2.c.l.99.2 | 2 | 7.3 | odd | 6 | |||
3920.2.a.p.1.1 | 1 | 140.67 | even | 12 | |||
3920.2.a.bc.1.1 | 1 | 140.87 | odd | 12 | |||
4410.2.a.bd.1.1 | 1 | 105.17 | odd | 12 | |||
4410.2.a.bm.1.1 | 1 | 105.32 | even | 12 |