Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(51,350)]
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([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.151 |
Dual form | 350.2.e.e.51.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 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 | \(-0.193114\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 2.00000 | − | 1.73205i | 0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | − | 3.46410i | −0.392232 | − | 0.679366i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −2.50000 | − | 0.866025i | −0.472456 | − | 0.163663i | ||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −3.00000 | − | 5.19615i | −0.522233 | − | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | 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 | \(0.251941\pi\) | |||||||
\(42\) | −0.500000 | − | 2.59808i | −0.0771517 | − | 0.400892i | ||||
\(43\) | 7.00000 | 1.06749 | 0.533745 | − | 0.845645i | \(-0.320784\pi\) | ||||
0.533745 | + | 0.845645i | \(0.320784\pi\) | |||||||
\(44\) | 3.00000 | + | 5.19615i | 0.452267 | + | 0.783349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | + | 2.59808i | 0.0668153 | + | 0.347183i | ||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | − | 4.33013i | −0.320092 | − | 0.554416i | 0.660415 | − | 0.750901i | \(-0.270381\pi\) |
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | −4.00000 | + | 3.46410i | −0.503953 | + | 0.436436i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | 2.50000 | − | 4.33013i | 0.305424 | − | 0.529009i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | 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 | \(0.615871\pi\) | |||||||
\(72\) | 1.00000 | + | 1.73205i | 0.117851 | + | 0.204124i | ||||
\(73\) | −8.00000 | + | 13.8564i | −0.936329 | + | 1.62177i | −0.164083 | + | 0.986447i | \(0.552466\pi\) |
−0.772246 | + | 0.635323i | \(0.780867\pi\) | |||||||
\(74\) | −2.00000 | + | 3.46410i | −0.232495 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 15.0000 | + | 5.19615i | 1.70941 | + | 0.592157i | ||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −4.50000 | − | 7.79423i | −0.496942 | − | 0.860729i | ||||
\(83\) | −3.00000 | −0.329293 | −0.164646 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164646 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(84\) | −2.00000 | + | 1.73205i | −0.218218 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.50000 | − | 6.06218i | −0.377415 | − | 0.653701i | ||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | 7.50000 | + | 12.9904i | 0.794998 | + | 1.37698i | 0.922840 | + | 0.385183i | \(0.125862\pi\) |
−0.127842 | + | 0.991795i | \(0.540805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 10.3923i | 0.209657 | + | 1.08941i | ||||
\(92\) | 3.00000 | 0.312772 | ||||||||
\(93\) | 4.00000 | + | 6.92820i | 0.414781 | + | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 5.50000 | + | 4.33013i | 0.555584 | + | 0.437409i | ||||
\(99\) | 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 | ||||||||
\(103\) | −0.500000 | − | 0.866025i | −0.0492665 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −7.50000 | − | 12.9904i | −0.725052 | − | 1.25583i | −0.958952 | − | 0.283567i | \(-0.908482\pi\) |
0.233900 | − | 0.972261i | \(-0.424851\pi\) | |||||||
\(108\) | −2.50000 | + | 4.33013i | −0.240563 | + | 0.416667i | ||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | 4.00000 | + | 6.92820i | 0.369800 | + | 0.640513i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −2.50000 | + | 4.33013i | −0.226339 | + | 0.392031i | ||||
\(123\) | 4.50000 | − | 7.79423i | 0.405751 | − | 0.702782i | ||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.00000 | + | 1.73205i | 0.445435 | + | 0.154303i | ||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 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 | \(0.833333\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 4.00000 | − | 3.46410i | 0.346844 | − | 0.300376i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 1.50000 | + | 2.59808i | 0.127688 | + | 0.221163i | ||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | + | 5.19615i | 0.251754 | + | 0.436051i | ||||
\(143\) | 12.0000 | − | 20.7846i | 1.00349 | − | 1.73810i | ||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | −1.00000 | + | 6.92820i | −0.0824786 | + | 0.571429i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −7.50000 | − | 12.9904i | −0.614424 | − | 1.06421i | −0.990485 | − | 0.137619i | \(-0.956055\pi\) |
0.376061 | − | 0.926595i | \(-0.377278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | −1.00000 | − | 1.73205i | −0.0811107 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.00000 | − | 15.5885i | −0.241747 | − | 1.25615i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | −11.0000 | + | 19.0526i | −0.877896 | + | 1.52056i | −0.0242497 | + | 0.999706i | \(0.507720\pi\) |
−0.853646 | + | 0.520854i | \(0.825614\pi\) | |||||||
\(158\) | −1.00000 | + | 1.73205i | −0.0795557 | + | 0.137795i | ||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 5.19615i | 0.472866 | − | 0.409514i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | −4.50000 | + | 7.79423i | −0.351391 | + | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | + | 2.59808i | 0.116423 | + | 0.201650i | ||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | 2.50000 | + | 0.866025i | 0.192879 | + | 0.0668153i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | −3.50000 | + | 6.06218i | −0.266872 | + | 0.462237i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 7.50000 | − | 12.9904i | 0.562149 | − | 0.973670i | ||||
\(179\) | 12.0000 | − | 20.7846i | 0.896922 | − | 1.55351i | 0.0655145 | − | 0.997852i | \(-0.479131\pi\) |
0.831408 | − | 0.555663i | \(-0.187536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | 8.00000 | − | 6.92820i | 0.592999 | − | 0.513553i | ||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | −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 | \(0.763683\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 7.00000 | + | 12.1244i | 0.502571 | + | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | −6.00000 | − | 10.3923i | −0.426401 | − | 0.738549i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | − | 4.33013i | −0.176336 | − | 0.305424i | ||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | −1.50000 | − | 7.79423i | −0.105279 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.138675 | − | 0.240192i | ||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | −3.00000 | + | 5.19615i | −0.205557 | + | 0.356034i | ||||
\(214\) | −7.50000 | + | 12.9904i | −0.512689 | + | 0.888004i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | −20.0000 | − | 6.92820i | −1.35769 | − | 0.470317i | ||||
\(218\) | 11.0000 | 0.745014 | ||||||||
\(219\) | 8.00000 | + | 13.8564i | 0.540590 | + | 0.936329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.00000 | + | 3.46410i | 0.134231 | + | 0.232495i | ||||
\(223\) | 28.0000 | 1.87502 | 0.937509 | − | 0.347960i | \(-0.113126\pi\) | ||||
0.937509 | + | 0.347960i | \(0.113126\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 1.00000 | − | 1.73205i | 0.0662266 | − | 0.114708i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 10.3923i | 0.789542 | − | 0.683763i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | −6.00000 | − | 10.3923i | −0.393073 | − | 0.680823i | 0.599780 | − | 0.800165i | \(-0.295255\pi\) |
−0.992853 | + | 0.119342i | \(0.961921\pi\) | |||||||
\(234\) | 4.00000 | − | 6.92820i | 0.261488 | − | 0.452911i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | −2.00000 | −0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | + | 1.73205i | −0.0644157 | + | 0.111571i | −0.896435 | − | 0.443176i | \(-0.853852\pi\) |
0.832019 | + | 0.554747i | \(0.187185\pi\) | |||||||
\(242\) | −12.5000 | + | 21.6506i | −0.803530 | + | 1.39176i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 5.00000 | 0.320092 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −4.00000 | − | 6.92820i | −0.254514 | − | 0.440831i | ||||
\(248\) | −4.00000 | + | 6.92820i | −0.254000 | + | 0.439941i | ||||
\(249\) | −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 | \(0.623635\pi\) | |||||||
\(252\) | −1.00000 | − | 5.19615i | −0.0629941 | − | 0.327327i | ||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 4.00000 | + | 6.92820i | 0.250982 | + | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | −7.00000 | −0.435801 | ||||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5000 | + | 18.1865i | −0.647458 | + | 1.12143i | 0.336270 | + | 0.941766i | \(0.390834\pi\) |
−0.983728 | + | 0.179664i | \(0.942499\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.00000 | − | 1.73205i | −0.306570 | − | 0.106199i | ||||
\(267\) | 15.0000 | 0.917985 | ||||||||
\(268\) | 2.50000 | + | 4.33013i | 0.152712 | + | 0.264505i | ||||
\(269\) | −7.50000 | + | 12.9904i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486418i | \(-0.984511\pi\) |
0.541533 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 10.0000 | + | 3.46410i | 0.605228 | + | 0.209657i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.50000 | − | 2.59808i | 0.0902894 | − | 0.156386i | ||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | 5.00000 | + | 8.66025i | 0.299880 | + | 0.519408i | ||||
\(279\) | −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 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | 4.50000 | + | 23.3827i | 0.265627 | + | 1.38024i | ||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | + | 12.1244i | −0.410347 | + | 0.710742i | ||||
\(292\) | −8.00000 | − | 13.8564i | −0.468165 | − | 0.810885i | ||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | 6.50000 | − | 2.59808i | 0.379088 | − | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | − | 3.46410i | −0.116248 | − | 0.201347i | ||||
\(297\) | 15.0000 | − | 25.9808i | 0.870388 | − | 1.50756i | ||||
\(298\) | −7.50000 | + | 12.9904i | −0.434463 | + | 0.752513i | ||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.50000 | + | 18.1865i | 0.201737 | + | 1.04825i | ||||
\(302\) | −4.00000 | −0.230174 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | −0.285365 | −0.142683 | − | 0.989769i | \(-0.545573\pi\) | ||||
−0.142683 | + | 0.989769i | \(0.545573\pi\) | |||||||
\(308\) | −12.0000 | + | 10.3923i | −0.683763 | + | 0.592157i | ||||
\(309\) | −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 | \(-0.00381495\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 4.00000 | + | 6.92820i | 0.226093 | + | 0.391605i | 0.956647 | − | 0.291250i | \(-0.0940712\pi\) |
−0.730554 | + | 0.682855i | \(0.760738\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 3.00000 | − | 5.19615i | 0.168232 | − | 0.291386i | ||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0000 | −0.837218 | ||||||||
\(322\) | −7.50000 | − | 2.59808i | −0.417959 | − | 0.144785i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00000 | + | 3.46410i | −0.110770 | + | 0.191859i | ||||
\(327\) | 5.50000 | + | 9.52628i | 0.304151 | + | 0.526804i | ||||
\(328\) | 9.00000 | 0.496942 | ||||||||
\(329\) | 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 | \(0.553834\pi\) | |||||||
\(332\) | 1.50000 | − | 2.59808i | 0.0823232 | − | 0.142588i | ||||
\(333\) | 4.00000 | − | 6.92820i | 0.219199 | − | 0.379663i | ||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 2.59808i | −0.0272772 | − | 0.141737i | ||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | −1.50000 | − | 2.59808i | −0.0815892 | − | 0.141317i | ||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | + | 41.5692i | 1.29967 | + | 2.25110i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 7.00000 | 0.377415 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.50000 | − | 7.79423i | 0.241573 | − | 0.418416i | −0.719590 | − | 0.694399i | \(-0.755670\pi\) |
0.961162 | + | 0.275983i | \(0.0890035\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | 17.0000 | 0.909989 | 0.454995 | − | 0.890494i | \(-0.349641\pi\) | ||||
0.454995 | + | 0.890494i | \(0.349641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 3.00000 | + | 5.19615i | 0.159901 | + | 0.276956i | ||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0000 | −0.794998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.0000 | −1.26844 | ||||||||
\(359\) | −12.0000 | − | 20.7846i | −0.633336 | − | 1.09697i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.353529 | − | 0.935423i | \(-0.384981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −5.50000 | − | 9.52628i | −0.289074 | − | 0.500690i | ||||
\(363\) | −25.0000 | −1.31216 | ||||||||
\(364\) | −10.0000 | − | 3.46410i | −0.524142 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.50000 | + | 4.33013i | 0.130677 | + | 0.226339i | ||||
\(367\) | 17.5000 | − | 30.3109i | 0.913493 | − | 1.58222i | 0.104399 | − | 0.994535i | \(-0.466708\pi\) |
0.809093 | − | 0.587680i | \(-0.199959\pi\) | |||||||
\(368\) | −1.50000 | + | 2.59808i | −0.0781929 | + | 0.135434i | ||||
\(369\) | 9.00000 | + | 15.5885i | 0.468521 | + | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.0000 | − | 5.19615i | −0.778761 | − | 0.269771i | ||||
\(372\) | −8.00000 | −0.414781 | ||||||||
\(373\) | −2.00000 | − | 3.46410i | −0.103556 | − | 0.179364i | 0.809591 | − | 0.586994i | \(-0.199689\pi\) |
−0.913147 | + | 0.407630i | \(0.866355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 10.0000 | − | 8.66025i | 0.514344 | − | 0.445435i | ||||
\(379\) | −34.0000 | −1.74646 | −0.873231 | − | 0.487306i | \(-0.837980\pi\) | ||||
−0.873231 | + | 0.487306i | \(0.837980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | 3.00000 | − | 5.19615i | 0.153493 | − | 0.265858i | ||||
\(383\) | −7.50000 | − | 12.9904i | −0.383232 | − | 0.663777i | 0.608290 | − | 0.793715i | \(-0.291856\pi\) |
−0.991522 | + | 0.129937i | \(0.958522\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 7.00000 | + | 12.1244i | 0.355830 | + | 0.616316i | ||||
\(388\) | 7.00000 | − | 12.1244i | 0.355371 | − | 0.615521i | ||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.50000 | + | 2.59808i | −0.328300 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | − | 5.19615i | −0.151138 | − | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | + | 10.3923i | −0.301511 | + | 0.522233i | ||||
\(397\) | 7.00000 | + | 12.1244i | 0.351320 | + | 0.608504i | 0.986481 | − | 0.163876i | \(-0.0523996\pi\) |
−0.635161 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −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 | \(0.955530\pi\) | |||||||
\(402\) | −2.50000 | + | 4.33013i | −0.124689 | + | 0.215967i | ||||
\(403\) | −16.0000 | + | 27.7128i | −0.797017 | + | 1.38047i | ||||
\(404\) | −7.50000 | − | 12.9904i | −0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | + | 5.19615i | −0.297775 | + | 0.257881i | ||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | − | 11.2583i | 0.321404 | − | 0.556689i | −0.659374 | − | 0.751815i | \(-0.729178\pi\) |
0.980778 | + | 0.195127i | \(0.0625118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | − | 10.3923i | −0.295958 | − | 0.512615i | ||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 15.0000 | + | 5.19615i | 0.738102 | + | 0.255686i | ||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | + | 3.46410i | −0.0980581 | + | 0.169842i | ||||
\(417\) | −5.00000 | + | 8.66025i | −0.244851 | + | 0.424094i | ||||
\(418\) | 6.00000 | + | 10.3923i | 0.293470 | + | 0.508304i | ||||
\(419\) | 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 | \(0.364039\pi\) | |||||||
\(422\) | 5.00000 | + | 8.66025i | 0.243396 | + | 0.421575i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 10.0000 | − | 8.66025i | 0.483934 | − | 0.419099i | ||||
\(428\) | 15.0000 | 0.725052 | ||||||||
\(429\) | −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 | \(0.909648\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | 22.0000 | 1.05725 | 0.528626 | − | 0.848855i | \(-0.322707\pi\) | ||||
0.528626 | + | 0.848855i | \(0.322707\pi\) | |||||||
\(434\) | 4.00000 | + | 20.7846i | 0.192006 | + | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.50000 | − | 9.52628i | −0.263402 | − | 0.456226i | ||||
\(437\) | −3.00000 | + | 5.19615i | −0.143509 | + | 0.248566i | ||||
\(438\) | 8.00000 | − | 13.8564i | 0.382255 | − | 0.662085i | ||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5000 | + | 18.1865i | 0.498870 | + | 0.864068i | 0.999999 | − | 0.00130426i | \(-0.000415158\pi\) |
−0.501129 | + | 0.865373i | \(0.667082\pi\) | |||||||
\(444\) | 2.00000 | − | 3.46410i | 0.0949158 | − | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | − | 24.2487i | −0.662919 | − | 1.14821i | ||||
\(447\) | −15.0000 | −0.709476 | ||||||||
\(448\) | 0.500000 | + | 2.59808i | 0.0236228 | + | 0.122748i | ||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | − | 46.7654i | 1.27138 | − | 2.20210i | ||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | −2.00000 | − | 3.46410i | −0.0939682 | − | 0.162758i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 16.0000 | + | 27.7128i | 0.748448 | + | 1.29635i | 0.948566 | + | 0.316579i | \(0.102534\pi\) |
−0.200118 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(458\) | −7.00000 | + | 12.1244i | −0.327089 | + | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | −15.0000 | − | 5.19615i | −0.697863 | − | 0.241747i | ||||
\(463\) | 13.0000 | 0.604161 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | + | 10.3923i | −0.277945 | + | 0.481414i | ||||
\(467\) | −7.50000 | − | 12.9904i | −0.347059 | − | 0.601123i | 0.638667 | − | 0.769483i | \(-0.279486\pi\) |
−0.985726 | + | 0.168360i | \(0.946153\pi\) | |||||||
\(468\) | −8.00000 | −0.369800 | ||||||||
\(469\) | 12.5000 | + | 4.33013i | 0.577196 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0000 | + | 19.0526i | 0.506853 | + | 0.877896i | ||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 21.0000 | − | 36.3731i | 0.965581 | − | 1.67244i | ||||
\(474\) | 1.00000 | + | 1.73205i | 0.0459315 | + | 0.0795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | −1.50000 | − | 7.79423i | −0.0682524 | − | 0.354650i | ||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.00000 | − | 13.8564i | 0.362887 | − | 0.628539i | ||||
\(487\) | −8.00000 | + | 13.8564i | −0.362515 | + | 0.627894i | −0.988374 | − | 0.152042i | \(-0.951415\pi\) |
0.625859 | + | 0.779936i | \(0.284748\pi\) | |||||||
\(488\) | −2.50000 | − | 4.33013i | −0.113170 | − | 0.196016i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 4.50000 | + | 7.79423i | 0.202876 | + | 0.351391i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −4.00000 | + | 6.92820i | −0.179969 | + | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −3.00000 | − | 15.5885i | −0.134568 | − | 0.699238i | ||||
\(498\) | 3.00000 | 0.134433 | ||||||||
\(499\) | 11.0000 | + | 19.0526i | 0.492428 | + | 0.852910i | 0.999962 | − | 0.00872186i | \(-0.00277629\pi\) |
−0.507534 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −21.0000 | −0.936344 | −0.468172 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468172 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(504\) | −4.00000 | + | 3.46410i | −0.178174 | + | 0.154303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 1.50000 | − | 2.59808i | 0.0666173 | − | 0.115385i | ||||
\(508\) | 4.00000 | − | 6.92820i | 0.177471 | − | 0.307389i | ||||
\(509\) | −10.5000 | − | 18.1865i | −0.465404 | − | 0.806104i | 0.533815 | − | 0.845601i | \(-0.320758\pi\) |
−0.999220 | + | 0.0394971i | \(0.987424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.0000 | − | 13.8564i | −1.76950 | − | 0.612971i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.00000 | − | 8.66025i | −0.220755 | − | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.50000 | + | 6.06218i | 0.154079 | + | 0.266872i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.0000 | − | 3.46410i | −0.439375 | − | 0.152204i | ||||
\(519\) | 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 | \(0.0376547\pi\) | |||||||
\(522\) | −3.00000 | + | 5.19615i | −0.131306 | + | 0.227429i | ||||
\(523\) | −14.0000 | − | 24.2487i | −0.612177 | − | 1.06032i | −0.990873 | − | 0.134801i | \(-0.956961\pi\) |
0.378695 | − | 0.925521i | \(-0.376373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | 0.915644 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.00000 | + | 5.19615i | −0.130558 | + | 0.226134i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 1.00000 | + | 5.19615i | 0.0433555 | + | 0.225282i | ||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | −7.50000 | − | 12.9904i | −0.324557 | − | 0.562149i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.50000 | − | 4.33013i | 0.107984 | − | 0.187033i | ||||
\(537\) | −12.0000 | − | 20.7846i | −0.517838 | − | 0.896922i | ||||
\(538\) | 15.0000 | 0.646696 | ||||||||
\(539\) | −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 | \(0.652733\pi\) | |||||||
\(542\) | −1.00000 | + | 1.73205i | −0.0429537 | + | 0.0743980i | ||||
\(543\) | 5.50000 | − | 9.52628i | 0.236028 | − | 0.408812i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | − | 10.3923i | −0.0855921 | − | 0.444750i | ||||
\(547\) | 19.0000 | 0.812381 | 0.406191 | − | 0.913788i | \(-0.366857\pi\) | ||||
0.406191 | + | 0.913788i | \(0.366857\pi\) | |||||||
\(548\) | 6.00000 | + | 10.3923i | 0.256307 | + | 0.443937i | ||||
\(549\) | 5.00000 | − | 8.66025i | 0.213395 | − | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | −3.00000 | −0.127688 | ||||||||
\(553\) | 4.00000 | − | 3.46410i | 0.170097 | − | 0.147309i | ||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00000 | − | 8.66025i | 0.212047 | − | 0.367277i | ||||
\(557\) | −9.00000 | + | 15.5885i | −0.381342 | + | 0.660504i | −0.991254 | − | 0.131965i | \(-0.957871\pi\) |
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(558\) | 8.00000 | + | 13.8564i | 0.338667 | + | 0.586588i | ||||
\(559\) | 28.0000 | 1.18427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 13.5000 | − | 23.3827i | 0.568957 | − | 0.985463i | −0.427712 | − | 0.903915i | \(-0.640680\pi\) |
0.996669 | − | 0.0815478i | \(-0.0259863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | −2.50000 | − | 0.866025i | −0.104990 | − | 0.0363696i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | 12.0000 | + | 20.7846i | 0.501745 | + | 0.869048i | ||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 18.0000 | − | 15.5885i | 0.751305 | − | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | 13.0000 | − | 22.5167i | 0.541197 | − | 0.937381i | −0.457639 | − | 0.889138i | \(-0.651305\pi\) |
0.998836 | − | 0.0482425i | \(-0.0153620\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −1.00000 | − | 1.73205i | −0.0415586 | − | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.50000 | − | 7.79423i | −0.0622305 | − | 0.323359i | ||||
\(582\) | 14.0000 | 0.580319 | ||||||||
\(583\) | 18.0000 | + | 31.1769i | 0.745484 | + | 1.29122i | ||||
\(584\) | −8.00000 | + | 13.8564i | −0.331042 | + | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 10.3923i | 0.247858 | + | 0.429302i | ||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | −5.50000 | − | 4.33013i | −0.226816 | − | 0.178571i | ||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | − | 5.19615i | 0.123404 | − | 0.213741i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | −30.0000 | −1.23091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.0000 | 0.614424 | ||||||||
\(597\) | −2.00000 | − | 3.46410i | −0.0818546 | − | 0.141776i | ||||
\(598\) | −6.00000 | + | 10.3923i | −0.245358 | + | 0.424973i | ||||
\(599\) | −6.00000 | + | 10.3923i | −0.245153 | + | 0.424618i | −0.962175 | − | 0.272433i | \(-0.912172\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.0000 | −1.87638 | −0.938190 | − | 0.346122i | \(-0.887498\pi\) | ||||
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 14.0000 | − | 12.1244i | 0.570597 | − | 0.494152i | ||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | 2.00000 | + | 3.46410i | 0.0813788 | + | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.50000 | − | 12.9904i | 0.304667 | − | 0.527698i | ||||
\(607\) | 11.5000 | + | 19.9186i | 0.466771 | + | 0.808470i | 0.999279 | − | 0.0379540i | \(-0.0120840\pi\) |
−0.532509 | + | 0.846424i | \(0.678751\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −7.50000 | − | 2.59808i | −0.303915 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.00000 | + | 13.8564i | −0.323117 | + | 0.559655i | −0.981129 | − | 0.193352i | \(-0.938064\pi\) |
0.658012 | + | 0.753007i | \(0.271397\pi\) | |||||||
\(614\) | 2.50000 | + | 4.33013i | 0.100892 | + | 0.174750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.0000 | + | 5.19615i | 0.604367 | + | 0.209359i | ||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 0.500000 | + | 0.866025i | 0.0201129 | + | 0.0348367i | ||||
\(619\) | −7.00000 | + | 12.1244i | −0.281354 | + | 0.487319i | −0.971718 | − | 0.236143i | \(-0.924117\pi\) |
0.690365 | + | 0.723462i | \(0.257450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | − | 12.9904i | −0.300965 | − | 0.521286i | ||||
\(622\) | −18.0000 | −0.721734 | ||||||||
\(623\) | −30.0000 | + | 25.9808i | −1.20192 | + | 1.04090i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.00000 | − | 6.92820i | 0.159872 | − | 0.276907i | ||||
\(627\) | −6.00000 | + | 10.3923i | −0.239617 | + | 0.415029i | ||||
\(628\) | −11.0000 | − | 19.0526i | −0.438948 | − | 0.760280i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | −1.00000 | − | 1.73205i | −0.0397779 | − | 0.0688973i | ||||
\(633\) | −5.00000 | + | 8.66025i | −0.198732 | + | 0.344214i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −26.0000 | + | 10.3923i | −1.03016 | + | 0.411758i | ||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | −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 | \(0.147797\pi\) | |||||||
\(642\) | 7.50000 | + | 12.9904i | 0.296001 | + | 0.512689i | ||||
\(643\) | −20.0000 | −0.788723 | −0.394362 | − | 0.918955i | \(-0.629034\pi\) | ||||
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(644\) | 1.50000 | + | 7.79423i | 0.0591083 | + | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.50000 | − | 2.59808i | 0.0589711 | − | 0.102141i | −0.835033 | − | 0.550200i | \(-0.814551\pi\) |
0.894004 | + | 0.448059i | \(0.147885\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −18.0000 | − | 31.1769i | −0.706562 | − | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0000 | + | 13.8564i | −0.627089 | + | 0.543075i | ||||
\(652\) | 4.00000 | 0.156652 | ||||||||
\(653\) | −24.0000 | − | 41.5692i | −0.939193 | − | 1.62673i | −0.766982 | − | 0.641669i | \(-0.778242\pi\) |
−0.172211 | − | 0.985060i | \(-0.555091\pi\) | |||||||
\(654\) | 5.50000 | − | 9.52628i | 0.215067 | − | 0.372507i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | − | 7.79423i | −0.175695 | − | 0.304314i | ||||
\(657\) | −32.0000 | −1.24844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5000 | + | 35.5070i | −0.797358 | + | 1.38106i | 0.123974 | + | 0.992286i | \(0.460436\pi\) |
−0.921331 | + | 0.388778i | \(0.872897\pi\) | |||||||
\(662\) | 14.0000 | − | 24.2487i | 0.544125 | − | 0.942453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.00000 | −0.116423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | 4.50000 | + | 7.79423i | 0.174241 | + | 0.301794i | ||||
\(668\) | −1.50000 | + | 2.59808i | −0.0580367 | + | 0.100523i | ||||
\(669\) | 14.0000 | − | 24.2487i | 0.541271 | − | 0.937509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | −2.00000 | + | 1.73205i | −0.0771517 | + | 0.0668153i | ||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | −11.0000 | − | 19.0526i | −0.423704 | − | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | 6.00000 | + | 10.3923i | 0.230599 | + | 0.399409i | 0.957984 | − | 0.286820i | \(-0.0925982\pi\) |
−0.727386 | + | 0.686229i | \(0.759265\pi\) | |||||||
\(678\) | 6.00000 | 0.230429 | ||||||||
\(679\) | −7.00000 | − | 36.3731i | −0.268635 | − | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 24.0000 | − | 41.5692i | 0.919007 | − | 1.59177i | ||||
\(683\) | 4.50000 | − | 7.79423i | 0.172188 | − | 0.298238i | −0.766997 | − | 0.641651i | \(-0.778250\pi\) |
0.939184 | + | 0.343413i | \(0.111583\pi\) | |||||||
\(684\) | 2.00000 | + | 3.46410i | 0.0764719 | + | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | −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 | ||||||||
\(693\) | 6.00000 | + | 31.1769i | 0.227921 | + | 1.18431i | ||||
\(694\) | −9.00000 | −0.341635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8.50000 | − | 14.7224i | −0.321730 | − | 0.557252i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | −10.0000 | − | 17.3205i | −0.377426 | − | 0.653720i | ||||
\(703\) | −4.00000 | + | 6.92820i | −0.150863 | + | 0.261302i | ||||
\(704\) | 3.00000 | − | 5.19615i | 0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | −37.5000 | − | 12.9904i | −1.41033 | − | 0.488554i | ||||
\(708\) | 6.00000 | 0.225494 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | 7.50000 | + | 12.9904i | 0.281074 | + | 0.486835i | ||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | + | 20.7846i | 0.448461 | + | 0.776757i | ||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | 9.00000 | + | 15.5885i | 0.335643 | + | 0.581351i | 0.983608 | − | 0.180319i | \(-0.0577130\pi\) |
−0.647965 | + | 0.761670i | \(0.724380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | − | 1.73205i | 0.0744839 | − | 0.0645049i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 1.00000 | + | 1.73205i | 0.0371904 | + | 0.0644157i | ||||
\(724\) | −5.50000 | + | 9.52628i | −0.204406 | + | 0.354041i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.5000 | + | 21.6506i | 0.463919 | + | 0.803530i | ||||
\(727\) | 19.0000 | 0.704671 | 0.352335 | − | 0.935874i | \(-0.385388\pi\) | ||||
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(728\) | 2.00000 | + | 10.3923i | 0.0741249 | + | 0.385164i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.50000 | − | 4.33013i | 0.0924027 | − | 0.160046i | ||||
\(733\) | −17.0000 | − | 29.4449i | −0.627909 | − | 1.08757i | −0.987971 | − | 0.154642i | \(-0.950578\pi\) |
0.360061 | − | 0.932929i | \(-0.382756\pi\) | |||||||
\(734\) | −35.0000 | −1.29187 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | −15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | ||||
\(738\) | 9.00000 | − | 15.5885i | 0.331295 | − | 0.573819i | ||||
\(739\) | −13.0000 | + | 22.5167i | −0.478213 | + | 0.828289i | −0.999688 | − | 0.0249776i | \(-0.992049\pi\) |
0.521475 | + | 0.853266i | \(0.325382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 3.00000 | + | 15.5885i | 0.110133 | + | 0.572270i | ||||
\(743\) | −39.0000 | −1.43077 | −0.715386 | − | 0.698730i | \(-0.753749\pi\) | ||||
−0.715386 | + | 0.698730i | \(0.753749\pi\) | |||||||
\(744\) | 4.00000 | + | 6.92820i | 0.146647 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.00000 | + | 3.46410i | −0.0732252 | + | 0.126830i | ||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 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 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 6.00000 | + | 10.3923i | 0.218507 | + | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.5000 | − | 4.33013i | −0.454621 | − | 0.157485i | ||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | 17.0000 | + | 29.4449i | 0.617468 | + | 1.06949i | ||||
\(759\) | −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 | \(-0.442080\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | −27.5000 | − | 9.52628i | −0.995567 | − | 0.344874i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | ||||
\(767\) | 12.0000 | − | 20.7846i | 0.433295 | − | 0.750489i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.00000 | + | 1.73205i | 0.0359908 | + | 0.0623379i | ||||
\(773\) | −6.00000 | + | 10.3923i | −0.215805 | + | 0.373785i | −0.953521 | − | 0.301326i | \(-0.902571\pi\) |
0.737716 | + | 0.675111i | \(0.235904\pi\) | |||||||
\(774\) | 7.00000 | − | 12.1244i | 0.251610 | − | 0.435801i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.0000 | −0.502571 | ||||||||
\(777\) | −2.00000 | − | 10.3923i | −0.0717496 | − | 0.372822i | ||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | −9.00000 | − | 15.5885i | −0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.0000 | −0.536056 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5000 | + | 37.2391i | −0.766392 | + | 1.32743i | 0.173115 | + | 0.984902i | \(0.444617\pi\) |
−0.939507 | + | 0.342529i | \(0.888717\pi\) | |||||||
\(788\) | −3.00000 | + | 5.19615i | −0.106871 | + | 0.185105i | ||||
\(789\) | 10.5000 | + | 18.1865i | 0.373810 | + | 0.647458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.00000 | − | 15.5885i | −0.106668 | − | 0.554262i | ||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | −10.0000 | − | 17.3205i | −0.355110 | − | 0.615069i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 48.0000 | 1.70025 | 0.850124 | − | 0.526583i | \(-0.176527\pi\) | ||||
0.850124 | + | 0.526583i | \(0.176527\pi\) | |||||||
\(798\) | −4.00000 | + | 3.46410i | −0.141598 | + | 0.122628i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | + | 25.9808i | −0.529999 | + | 0.917985i | ||||
\(802\) | −7.50000 | + | 12.9904i | −0.264834 | + | 0.458706i | ||||
\(803\) | 48.0000 | + | 83.1384i | 1.69388 | + | 2.93389i | ||||
\(804\) | 5.00000 | 0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | 7.50000 | + | 12.9904i | 0.264013 | + | 0.457283i | ||||
\(808\) | −7.50000 | + | 12.9904i | −0.263849 | + | 0.457000i | ||||
\(809\) | −10.5000 | + | 18.1865i | −0.369160 | + | 0.639404i | −0.989434 | − | 0.144981i | \(-0.953688\pi\) |
0.620274 | + | 0.784385i | \(0.287021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 7.50000 | + | 2.59808i | 0.263198 | + | 0.0911746i | ||||
\(813\) | −2.00000 | −0.0701431 | ||||||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.00000 | − | 12.1244i | −0.244899 | − | 0.424178i | ||||
\(818\) | −13.0000 | −0.454534 | ||||||||
\(819\) | −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 | \(0.731630\pi\) | |||||||
\(822\) | −6.00000 | + | 10.3923i | −0.209274 | + | 0.362473i | ||||
\(823\) | −9.50000 | + | 16.4545i | −0.331149 | + | 0.573567i | −0.982737 | − | 0.185006i | \(-0.940770\pi\) |
0.651588 | + | 0.758573i | \(0.274103\pi\) | |||||||
\(824\) | −0.500000 | − | 0.866025i | −0.0174183 | − | 0.0301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 15.5885i | −0.104383 | − | 0.542392i | ||||
\(827\) | −15.0000 | −0.521601 | −0.260801 | − | 0.965393i | \(-0.583986\pi\) | ||||
−0.260801 | + | 0.965393i | \(0.583986\pi\) | |||||||
\(828\) | 3.00000 | + | 5.19615i | 0.104257 | + | 0.180579i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.0000 | 0.346272 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | − | 10.3923i | 0.207514 | − | 0.359425i | ||||
\(837\) | −20.0000 | + | 34.6410i | −0.691301 | + | 1.19737i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −8.50000 | − | 14.7224i | −0.292929 | − | 0.507369i | ||||
\(843\) | −3.00000 | + | 5.19615i | −0.103325 | + | 0.178965i | ||||
\(844\) | 5.00000 | − | 8.66025i | 0.172107 | − | 0.298098i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.0000 | − | 43.3013i | 1.71802 | − | 1.48785i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 2.00000 | + | 3.46410i | 0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | −3.00000 | − | 5.19615i | −0.102778 | − | 0.178017i | ||||
\(853\) | 46.0000 | 1.57501 | 0.787505 | − | 0.616308i | \(-0.211372\pi\) | ||||
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | −12.5000 | − | 4.33013i | −0.427741 | − | 0.148174i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.50000 | − | 12.9904i | −0.256345 | − | 0.444002i | ||||
\(857\) | 3.00000 | − | 5.19615i | 0.102478 | − | 0.177497i | −0.810227 | − | 0.586116i | \(-0.800656\pi\) |
0.912705 | + | 0.408619i | \(0.133990\pi\) | |||||||
\(858\) | −12.0000 | + | 20.7846i | −0.409673 | + | 0.709575i | ||||
\(859\) | −16.0000 | − | 27.7128i | −0.545913 | − | 0.945549i | −0.998549 | − | 0.0538535i | \(-0.982850\pi\) |
0.452636 | − | 0.891695i | \(-0.350484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.5000 | + | 7.79423i | 0.766798 | + | 0.265627i | ||||
\(862\) | 30.0000 | 1.02180 | ||||||||
\(863\) | 13.5000 | + | 23.3827i | 0.459545 | + | 0.795956i | 0.998937 | − | 0.0460992i | \(-0.0146790\pi\) |
−0.539392 | + | 0.842055i | \(0.681346\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0000 | − | 19.0526i | −0.373795 | − | 0.647432i | ||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 16.0000 | − | 13.8564i | 0.543075 | − | 0.470317i | ||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | − | 17.3205i | 0.338837 | − | 0.586883i | ||||
\(872\) | −5.50000 | + | 9.52628i | −0.186254 | + | 0.322601i | ||||
\(873\) | −14.0000 | − | 24.2487i | −0.473828 | − | 0.820695i | ||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | 1.00000 | + | 1.73205i | 0.0337676 | + | 0.0584872i | 0.882415 | − | 0.470471i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(878\) | 14.0000 | − | 24.2487i | 0.472477 | − | 0.818354i | ||||
\(879\) | −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 | \(0.0901189\pi\) | |||||||
\(882\) | −2.00000 | + | 13.8564i | −0.0673435 | + | 0.466569i | ||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5000 | − | 18.1865i | 0.352754 | − | 0.610989i | ||||
\(887\) | −10.5000 | − | 18.1865i | −0.352555 | − | 0.610644i | 0.634141 | − | 0.773217i | \(-0.281354\pi\) |
−0.986696 | + | 0.162573i | \(0.948021\pi\) | |||||||
\(888\) | −4.00000 | −0.134231 | ||||||||
\(889\) | −4.00000 | − | 20.7846i | −0.134156 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | + | 5.19615i | 0.100504 | + | 0.174078i | ||||
\(892\) | −14.0000 | + | 24.2487i | −0.468755 | + | 0.811907i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.50000 | + | 12.9904i | 0.250838 | + | 0.434463i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 4.50000 | + | 7.79423i | 0.150167 | + | 0.260097i | ||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −54.0000 | −1.79800 | ||||||||
\(903\) | 17.5000 | + | 6.06218i | 0.582364 | + | 0.201737i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00000 | + | 3.46410i | −0.0664455 | + | 0.115087i | ||||
\(907\) | −12.5000 | + | 21.6506i | −0.415056 | + | 0.718898i | −0.995434 | − | 0.0954492i | \(-0.969571\pi\) |
0.580379 | + | 0.814347i | \(0.302905\pi\) | |||||||
\(908\) | −6.00000 | − | 10.3923i | −0.199117 | − | 0.344881i | ||||
\(909\) | −30.0000 | −0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0000 | 0.596367 | 0.298183 | − | 0.954509i | \(-0.403619\pi\) | ||||
0.298183 | + | 0.954509i | \(0.403619\pi\) | |||||||
\(912\) | 1.00000 | + | 1.73205i | 0.0331133 | + | 0.0573539i | ||||
\(913\) | −9.00000 | + | 15.5885i | −0.297857 | + | 0.515903i | ||||
\(914\) | 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 | 0.727167 | − | 0.686461i | \(-0.240837\pi\) |
−0.958076 | + | 0.286515i | \(0.907503\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.50000 | + | 4.33013i | −0.0823778 | + | 0.142683i | ||||
\(922\) | −9.00000 | − | 15.5885i | −0.296399 | − | 0.513378i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | 3.00000 | + | 15.5885i | 0.0986928 | + | 0.512823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.50000 | − | 11.2583i | −0.213603 | − | 0.369972i | ||||
\(927\) | 1.00000 | − | 1.73205i | 0.0328443 | − | 0.0568880i | ||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0000 | + | 8.66025i | 0.360510 | + | 0.283828i | ||||
\(932\) | 12.0000 | 0.393073 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −7.50000 | + | 12.9904i | −0.245407 | + | 0.425058i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.00000 | + | 6.92820i | 0.130744 | + | 0.226455i | ||||
\(937\) | 28.0000 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(938\) | −2.50000 | − | 12.9904i | −0.0816279 | − | 0.424151i | ||||
\(939\) | 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 | \(0.135487\pi\) | |||||||
\(942\) | 11.0000 | − | 19.0526i | 0.358399 | − | 0.620766i | ||||
\(943\) | −13.5000 | − | 23.3827i | −0.439620 | − | 0.761445i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.0000 | −1.36554 | ||||||||
\(947\) | −1.50000 | − | 2.59808i | −0.0487435 | − | 0.0844261i | 0.840624 | − | 0.541619i | \(-0.182188\pi\) |
−0.889368 | + | 0.457193i | \(0.848855\pi\) | |||||||
\(948\) | 1.00000 | − | 1.73205i | 0.0324785 | − | 0.0562544i | ||||
\(949\) | −32.0000 | + | 55.4256i | −1.03876 | + | 1.79919i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −60.0000 | −1.94359 | −0.971795 | − | 0.235826i | \(-0.924220\pi\) | ||||
−0.971795 | + | 0.235826i | \(0.924220\pi\) | |||||||
\(954\) | 6.00000 | + | 10.3923i | 0.194257 | + | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | 9.00000 | + | 15.5885i | 0.290929 | + | 0.503903i | ||||
\(958\) | 12.0000 | 0.387702 | ||||||||
\(959\) | 30.0000 | + | 10.3923i | 0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −8.00000 | + | 13.8564i | −0.257930 | + | 0.446748i | ||||
\(963\) | 15.0000 | − | 25.9808i | 0.483368 | − | 0.837218i | ||||
\(964\) | −1.00000 | − | 1.73205i | −0.0322078 | − | 0.0557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.00000 | + | 5.19615i | −0.193047 | + | 0.167183i | ||||
\(967\) | −35.0000 | −1.12552 | −0.562762 | − | 0.826619i | \(-0.690261\pi\) | ||||
−0.562762 | + | 0.826619i | \(0.690261\pi\) | |||||||
\(968\) | −12.5000 | − | 21.6506i | −0.401765 | − | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | −5.00000 | − | 25.9808i | −0.160293 | − | 0.832905i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.50000 | + | 4.33013i | −0.0800230 | + | 0.138604i | ||||
\(977\) | −3.00000 | + | 5.19615i | −0.0959785 | + | 0.166240i | −0.910017 | − | 0.414572i | \(-0.863931\pi\) |
0.814038 | + | 0.580812i | \(0.197265\pi\) | |||||||
\(978\) | 2.00000 | + | 3.46410i | 0.0639529 | + | 0.110770i | ||||
\(979\) | 90.0000 | 2.87641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.0000 | −0.702406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.5000 | − | 33.7750i | 0.621953 | − | 1.07725i | −0.367168 | − | 0.930155i | \(-0.619673\pi\) |
0.989122 | − | 0.147100i | \(-0.0469940\pi\) | |||||||
\(984\) | 4.50000 | − | 7.79423i | 0.143455 | − | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | −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 | \(0.0199682\pi\) | |||||||
\(992\) | −4.00000 | − | 6.92820i | −0.127000 | − | 0.219971i | ||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | −12.0000 | + | 10.3923i | −0.380617 | + | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.50000 | − | 2.59808i | −0.0475293 | − | 0.0823232i | ||||
\(997\) | 7.00000 | − | 12.1244i | 0.221692 | − | 0.383982i | −0.733630 | − | 0.679549i | \(-0.762175\pi\) |
0.955322 | + | 0.295567i | \(0.0955086\pi\) | |||||||
\(998\) | 11.0000 | − | 19.0526i | 0.348199 | − | 0.603098i | ||||
\(999\) | −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.e.e.151.1 | 2 | ||
5.2 | odd | 4 | 350.2.j.b.249.2 | 4 | |||
5.3 | odd | 4 | 350.2.j.b.249.1 | 4 | |||
5.4 | even | 2 | 70.2.e.c.11.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 350.2.e.e.51.1 | 2 | ||
7.3 | odd | 6 | 2450.2.a.bc.1.1 | 1 | |||
7.4 | even | 3 | 2450.2.a.w.1.1 | 1 | |||
15.14 | odd | 2 | 630.2.k.b.361.1 | 2 | |||
20.19 | odd | 2 | 560.2.q.g.81.1 | 2 | |||
35.2 | odd | 12 | 350.2.j.b.149.1 | 4 | |||
35.3 | even | 12 | 2450.2.c.l.99.1 | 2 | |||
35.4 | even | 6 | 490.2.a.c.1.1 | 1 | |||
35.9 | even | 6 | 70.2.e.c.51.1 | yes | 2 | ||
35.17 | even | 12 | 2450.2.c.l.99.2 | 2 | |||
35.18 | odd | 12 | 2450.2.c.g.99.1 | 2 | |||
35.19 | odd | 6 | 490.2.e.h.471.1 | 2 | |||
35.23 | odd | 12 | 350.2.j.b.149.2 | 4 | |||
35.24 | odd | 6 | 490.2.a.b.1.1 | 1 | |||
35.32 | odd | 12 | 2450.2.c.g.99.2 | 2 | |||
35.34 | odd | 2 | 490.2.e.h.361.1 | 2 | |||
105.44 | odd | 6 | 630.2.k.b.541.1 | 2 | |||
105.59 | even | 6 | 4410.2.a.bd.1.1 | 1 | |||
105.74 | odd | 6 | 4410.2.a.bm.1.1 | 1 | |||
140.39 | odd | 6 | 3920.2.a.p.1.1 | 1 | |||
140.59 | even | 6 | 3920.2.a.bc.1.1 | 1 | |||
140.79 | odd | 6 | 560.2.q.g.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.c.11.1 | ✓ | 2 | 5.4 | even | 2 | ||
70.2.e.c.51.1 | yes | 2 | 35.9 | even | 6 | ||
350.2.e.e.51.1 | 2 | 7.2 | even | 3 | inner | ||
350.2.e.e.151.1 | 2 | 1.1 | even | 1 | trivial | ||
350.2.j.b.149.1 | 4 | 35.2 | odd | 12 | |||
350.2.j.b.149.2 | 4 | 35.23 | odd | 12 | |||
350.2.j.b.249.1 | 4 | 5.3 | odd | 4 | |||
350.2.j.b.249.2 | 4 | 5.2 | odd | 4 | |||
490.2.a.b.1.1 | 1 | 35.24 | odd | 6 | |||
490.2.a.c.1.1 | 1 | 35.4 | even | 6 | |||
490.2.e.h.361.1 | 2 | 35.34 | odd | 2 | |||
490.2.e.h.471.1 | 2 | 35.19 | odd | 6 | |||
560.2.q.g.81.1 | 2 | 20.19 | odd | 2 | |||
560.2.q.g.401.1 | 2 | 140.79 | odd | 6 | |||
630.2.k.b.361.1 | 2 | 15.14 | odd | 2 | |||
630.2.k.b.541.1 | 2 | 105.44 | odd | 6 | |||
2450.2.a.w.1.1 | 1 | 7.4 | even | 3 | |||
2450.2.a.bc.1.1 | 1 | 7.3 | odd | 6 | |||
2450.2.c.g.99.1 | 2 | 35.18 | odd | 12 | |||
2450.2.c.g.99.2 | 2 | 35.32 | odd | 12 | |||
2450.2.c.l.99.1 | 2 | 35.3 | even | 12 | |||
2450.2.c.l.99.2 | 2 | 35.17 | even | 12 | |||
3920.2.a.p.1.1 | 1 | 140.39 | odd | 6 | |||
3920.2.a.bc.1.1 | 1 | 140.59 | even | 6 | |||
4410.2.a.bd.1.1 | 1 | 105.59 | even | 6 | |||
4410.2.a.bm.1.1 | 1 | 105.74 | odd | 6 |