Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(197,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.m (of order \(4\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.197 |
Dual form | 630.2.m.a.323.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.707107 | + | 2.12132i | −0.223607 | + | 0.670820i | ||||
\(11\) | − | 3.41421i | − | 1.02942i | −0.857363 | − | 0.514712i | \(-0.827899\pi\) | ||
0.857363 | − | 0.514712i | \(-0.172101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | − | 4.00000i | 1.10940 | − | 1.10940i | 0.116171 | − | 0.993229i | \(-0.462938\pi\) |
0.993229 | − | 0.116171i | \(-0.0370621\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.41421 | − | 3.41421i | 0.828068 | − | 0.828068i | −0.159181 | − | 0.987249i | \(-0.550885\pi\) |
0.987249 | + | 0.159181i | \(0.0508853\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.41421 | − | 2.41421i | −0.514712 | − | 0.514712i | ||||
\(23\) | −0.828427 | − | 0.828427i | −0.172739 | − | 0.172739i | 0.615443 | − | 0.788182i | \(-0.288977\pi\) |
−0.788182 | + | 0.615443i | \(0.788977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | − | 5.65685i | − | 1.10940i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.707107 | − | 0.707107i | 0.133631 | − | 0.133631i | ||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2426 | 1.83963 | 0.919816 | − | 0.392349i | \(-0.128338\pi\) | ||||
0.919816 | + | 0.392349i | \(0.128338\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.82843i | − | 0.828068i | ||||||
\(35\) | −2.12132 | − | 0.707107i | −0.358569 | − | 0.119523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24264 | − | 2.24264i | −0.368688 | − | 0.368688i | 0.498311 | − | 0.866999i | \(-0.333954\pi\) |
−0.866999 | + | 0.498311i | \(0.833954\pi\) | |||||||
\(38\) | −2.00000 | − | 2.00000i | −0.324443 | − | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | + | 0.707107i | 0.335410 | + | 0.111803i | ||||
\(41\) | 8.82843i | 1.37877i | 0.724396 | + | 0.689384i | \(0.242119\pi\) | ||||
−0.724396 | + | 0.689384i | \(0.757881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.07107 | + | 8.07107i | −1.23083 | + | 1.23083i | −0.267180 | + | 0.963647i | \(0.586092\pi\) |
−0.963647 | + | 0.267180i | \(0.913908\pi\) | |||||||
\(44\) | −3.41421 | −0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17157 | −0.172739 | ||||||||
\(47\) | 0.757359 | − | 0.757359i | 0.110472 | − | 0.110472i | −0.649710 | − | 0.760182i | \(-0.725110\pi\) |
0.760182 | + | 0.649710i | \(0.225110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −0.707107 | − | 4.94975i | −0.100000 | − | 0.700000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 4.00000i | −0.554700 | − | 0.554700i | ||||
\(53\) | −5.41421 | − | 5.41421i | −0.743699 | − | 0.743699i | 0.229588 | − | 0.973288i | \(-0.426262\pi\) |
−0.973288 | + | 0.229588i | \(0.926262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41421 | + | 6.82843i | 0.460372 | + | 0.920745i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.41421 | + | 3.41421i | −0.448308 | + | 0.448308i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89949 | 1.26750 | 0.633750 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(62\) | 7.24264 | − | 7.24264i | 0.919816 | − | 0.919816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.00000 | + | 12.0000i | −0.496139 | + | 1.48842i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.58579 | + | 5.58579i | 0.682412 | + | 0.682412i | 0.960543 | − | 0.278131i | \(-0.0897149\pi\) |
−0.278131 | + | 0.960543i | \(0.589715\pi\) | |||||||
\(68\) | −3.41421 | − | 3.41421i | −0.414034 | − | 0.414034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | + | 1.00000i | −0.239046 | + | 0.119523i | ||||
\(71\) | − | 6.82843i | − | 0.810385i | −0.914231 | − | 0.405193i | \(-0.867204\pi\) | ||
0.914231 | − | 0.405193i | \(-0.132796\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.07107 | + | 7.07107i | −0.827606 | + | 0.827606i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
0.159579 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(74\) | −3.17157 | −0.368688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | 2.41421 | − | 2.41421i | 0.275125 | − | 0.275125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.65685i | − | 0.636446i | −0.948016 | − | 0.318223i | \(-0.896914\pi\) | ||
0.948016 | − | 0.318223i | \(-0.103086\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.24264 | + | 6.24264i | 0.689384 | + | 0.689384i | ||||
\(83\) | 4.82843 | + | 4.82843i | 0.529989 | + | 0.529989i | 0.920569 | − | 0.390580i | \(-0.127726\pi\) |
−0.390580 | + | 0.920569i | \(0.627726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.41421 | + | 10.2426i | −0.370323 | + | 1.11097i | ||||
\(86\) | 11.4142i | 1.23083i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.41421 | + | 2.41421i | −0.257356 | + | 0.257356i | ||||
\(89\) | 8.82843 | 0.935811 | 0.467906 | − | 0.883778i | \(-0.345009\pi\) | ||||
0.467906 | + | 0.883778i | \(0.345009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | 0.592999 | ||||||||
\(92\) | −0.828427 | + | 0.828427i | −0.0863695 | + | 0.0863695i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1.07107i | − | 0.110472i | ||||||
\(95\) | 2.82843 | + | 5.65685i | 0.290191 | + | 0.580381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.41421 | − | 7.41421i | −0.752799 | − | 0.752799i | 0.222201 | − | 0.975001i | \(-0.428676\pi\) |
−0.975001 | + | 0.222201i | \(0.928676\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.00000 | − | 3.00000i | −0.400000 | − | 0.300000i | ||||
\(101\) | − | 6.34315i | − | 0.631167i | −0.948898 | − | 0.315583i | \(-0.897800\pi\) | ||
0.948898 | − | 0.315583i | \(-0.102200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.58579 | + | 4.58579i | −0.451851 | + | 0.451851i | −0.895969 | − | 0.444118i | \(-0.853517\pi\) |
0.444118 | + | 0.895969i | \(0.353517\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.65685 | −0.743699 | ||||||||
\(107\) | −10.8284 | + | 10.8284i | −1.04682 | + | 1.04682i | −0.0479750 | + | 0.998849i | \(0.515277\pi\) |
−0.998849 | + | 0.0479750i | \(0.984723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.3137i | − | 1.27522i | −0.770358 | − | 0.637611i | \(-0.779923\pi\) | ||
0.770358 | − | 0.637611i | \(-0.220077\pi\) | |||||||
\(110\) | 7.24264 | + | 2.41421i | 0.690559 | + | 0.230186i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | 11.3137 | + | 11.3137i | 1.06430 | + | 1.06430i | 0.997785 | + | 0.0665190i | \(0.0211893\pi\) |
0.0665190 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.48528 | + | 0.828427i | 0.231754 | + | 0.0772512i | ||||
\(116\) | 4.82843i | 0.448308i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | + | 2.00000i | −0.184115 | + | 0.184115i | ||||
\(119\) | 4.82843 | 0.442621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.656854 | −0.0597140 | ||||||||
\(122\) | 7.00000 | − | 7.00000i | 0.633750 | − | 0.633750i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.2426i | − | 0.919816i | ||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.65685 | − | 3.65685i | −0.324493 | − | 0.324493i | 0.525995 | − | 0.850488i | \(-0.323693\pi\) |
−0.850488 | + | 0.525995i | \(0.823693\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.65685 | + | 11.3137i | 0.496139 | + | 0.992278i | ||||
\(131\) | 0.485281i | 0.0423992i | 0.999775 | + | 0.0211996i | \(0.00674855\pi\) | ||||
−0.999775 | + | 0.0211996i | \(0.993251\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | − | 2.00000i | 0.173422 | − | 0.173422i | ||||
\(134\) | 7.89949 | 0.682412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.82843 | −0.414034 | ||||||||
\(137\) | 12.0000 | − | 12.0000i | 1.02523 | − | 1.02523i | 0.0255558 | − | 0.999673i | \(-0.491864\pi\) |
0.999673 | − | 0.0255558i | \(-0.00813555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.34315i | 0.538019i | 0.963138 | + | 0.269009i | \(0.0866962\pi\) | ||||
−0.963138 | + | 0.269009i | \(0.913304\pi\) | |||||||
\(140\) | −0.707107 | + | 2.12132i | −0.0597614 | + | 0.179284i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.82843 | − | 4.82843i | −0.405193 | − | 0.405193i | ||||
\(143\) | −13.6569 | − | 13.6569i | −1.14204 | − | 1.14204i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.65685 | − | 4.82843i | 0.801958 | − | 0.400979i | ||||
\(146\) | 10.0000i | 0.827606i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.24264 | + | 2.24264i | −0.184344 | + | 0.184344i | ||||
\(149\) | 20.1421 | 1.65011 | 0.825054 | − | 0.565054i | \(-0.191145\pi\) | ||||
0.825054 | + | 0.565054i | \(0.191145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1716 | −1.07189 | −0.535944 | − | 0.844254i | \(-0.680044\pi\) | ||||
−0.535944 | + | 0.844254i | \(0.680044\pi\) | |||||||
\(152\) | −2.00000 | + | 2.00000i | −0.162221 | + | 0.162221i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.41421i | − | 0.275125i | ||||||
\(155\) | −20.4853 | + | 10.2426i | −1.64542 | + | 0.822709i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.65685 | + | 1.65685i | 0.132231 | + | 0.132231i | 0.770125 | − | 0.637893i | \(-0.220194\pi\) |
−0.637893 | + | 0.770125i | \(0.720194\pi\) | |||||||
\(158\) | −4.00000 | − | 4.00000i | −0.318223 | − | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.707107 | − | 2.12132i | 0.0559017 | − | 0.167705i | ||||
\(161\) | − | 1.17157i | − | 0.0923329i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.7279 | + | 13.7279i | −1.07525 | + | 1.07525i | −0.0783260 | + | 0.996928i | \(0.524958\pi\) |
−0.996928 | + | 0.0783260i | \(0.975042\pi\) | |||||||
\(164\) | 8.82843 | 0.689384 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.82843 | 0.529989 | ||||||||
\(167\) | −10.4142 | + | 10.4142i | −0.805876 | + | 0.805876i | −0.984007 | − | 0.178131i | \(-0.942995\pi\) |
0.178131 | + | 0.984007i | \(0.442995\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.0000i | − | 1.46154i | ||||||
\(170\) | 4.82843 | + | 9.65685i | 0.370323 | + | 0.740647i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.07107 | + | 8.07107i | 0.615413 | + | 0.615413i | ||||
\(173\) | 5.48528 | + | 5.48528i | 0.417038 | + | 0.417038i | 0.884182 | − | 0.467143i | \(-0.154717\pi\) |
−0.467143 | + | 0.884182i | \(0.654717\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.94975 | − | 0.707107i | 0.374166 | − | 0.0534522i | ||||
\(176\) | 3.41421i | 0.257356i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.24264 | − | 6.24264i | 0.467906 | − | 0.467906i | ||||
\(179\) | 19.4142 | 1.45109 | 0.725543 | − | 0.688177i | \(-0.241589\pi\) | ||||
0.725543 | + | 0.688177i | \(0.241589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.92893 | −0.366365 | −0.183182 | − | 0.983079i | \(-0.558640\pi\) | ||||
−0.183182 | + | 0.983079i | \(0.558640\pi\) | |||||||
\(182\) | 4.00000 | − | 4.00000i | 0.296500 | − | 0.296500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.17157i | 0.0863695i | ||||||||
\(185\) | 6.72792 | + | 2.24264i | 0.494647 | + | 0.164882i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6569 | − | 11.6569i | −0.852434 | − | 0.852434i | ||||
\(188\) | −0.757359 | − | 0.757359i | −0.0552361 | − | 0.0552361i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | + | 2.00000i | 0.435286 | + | 0.145095i | ||||
\(191\) | 25.6569i | 1.85646i | 0.372001 | + | 0.928232i | \(0.378672\pi\) | ||||
−0.372001 | + | 0.928232i | \(0.621328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.48528 | + | 3.48528i | −0.250876 | + | 0.250876i | −0.821330 | − | 0.570454i | \(-0.806767\pi\) |
0.570454 | + | 0.821330i | \(0.306767\pi\) | |||||||
\(194\) | −10.4853 | −0.752799 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −1.75736 | + | 1.75736i | −0.125207 | + | 0.125207i | −0.766933 | − | 0.641727i | \(-0.778218\pi\) |
0.641727 | + | 0.766933i | \(0.278218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.8995i | 1.69419i | 0.531441 | + | 0.847095i | \(0.321651\pi\) | ||||
−0.531441 | + | 0.847095i | \(0.678349\pi\) | |||||||
\(200\) | −4.94975 | + | 0.707107i | −0.350000 | + | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.48528 | − | 4.48528i | −0.315583 | − | 0.315583i | ||||
\(203\) | −3.41421 | − | 3.41421i | −0.239631 | − | 0.239631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.82843 | − | 17.6569i | −0.616604 | − | 1.23321i | ||||
\(206\) | 6.48528i | 0.451851i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | + | 4.00000i | −0.277350 | + | 0.277350i | ||||
\(209\) | −9.65685 | −0.667979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | −5.41421 | + | 5.41421i | −0.371850 | + | 0.371850i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.3137i | 1.04682i | ||||||||
\(215\) | 8.07107 | − | 24.2132i | 0.550442 | − | 1.65133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.24264 | + | 7.24264i | 0.491662 | + | 0.491662i | ||||
\(218\) | −9.41421 | − | 9.41421i | −0.637611 | − | 0.637611i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.82843 | − | 3.41421i | 0.460372 | − | 0.230186i | ||||
\(221\) | − | 27.3137i | − | 1.83732i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3137 | + | 15.3137i | −1.02548 | + | 1.02548i | −0.0258150 | + | 0.999667i | \(0.508218\pi\) |
−0.999667 | + | 0.0258150i | \(0.991782\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | 6.82843 | − | 6.82843i | 0.453219 | − | 0.453219i | −0.443203 | − | 0.896421i | \(-0.646158\pi\) |
0.896421 | + | 0.443203i | \(0.146158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.242641i | 0.0160341i | 0.999968 | + | 0.00801707i | \(0.00255194\pi\) | ||||
−0.999968 | + | 0.00801707i | \(0.997448\pi\) | |||||||
\(230\) | 2.34315 | − | 1.17157i | 0.154502 | − | 0.0772512i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.41421 | + | 3.41421i | 0.224154 | + | 0.224154i | ||||
\(233\) | 9.17157 | + | 9.17157i | 0.600850 | + | 0.600850i | 0.940538 | − | 0.339688i | \(-0.110322\pi\) |
−0.339688 | + | 0.940538i | \(0.610322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.757359 | + | 2.27208i | −0.0494047 | + | 0.148214i | ||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.41421 | − | 3.41421i | 0.221311 | − | 0.221311i | ||||
\(239\) | 2.34315 | 0.151565 | 0.0757827 | − | 0.997124i | \(-0.475854\pi\) | ||||
0.0757827 | + | 0.997124i | \(0.475854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1421 | 1.55513 | 0.777566 | − | 0.628802i | \(-0.216454\pi\) | ||||
0.777566 | + | 0.628802i | \(0.216454\pi\) | |||||||
\(242\) | −0.464466 | + | 0.464466i | −0.0298570 | + | 0.0298570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.89949i | − | 0.633750i | ||||||
\(245\) | −1.00000 | − | 2.00000i | −0.0638877 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3137 | − | 11.3137i | −0.719874 | − | 0.719874i | ||||
\(248\) | −7.24264 | − | 7.24264i | −0.459908 | − | 0.459908i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.36396 | + | 9.19239i | 0.402492 | + | 0.581378i | ||||
\(251\) | − | 18.6274i | − | 1.17575i | −0.808951 | − | 0.587876i | \(-0.799964\pi\) | ||
0.808951 | − | 0.587876i | \(-0.200036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | + | 2.82843i | −0.177822 | + | 0.177822i | ||||
\(254\) | −5.17157 | −0.324493 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.4142 | − | 11.4142i | 0.711999 | − | 0.711999i | −0.254954 | − | 0.966953i | \(-0.582060\pi\) |
0.966953 | + | 0.254954i | \(0.0820604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.17157i | − | 0.197072i | ||||||
\(260\) | 12.0000 | + | 4.00000i | 0.744208 | + | 0.248069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.343146 | + | 0.343146i | 0.0211996 | + | 0.0211996i | ||||
\(263\) | −3.65685 | − | 3.65685i | −0.225491 | − | 0.225491i | 0.585315 | − | 0.810806i | \(-0.300971\pi\) |
−0.810806 | + | 0.585315i | \(0.800971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2426 | + | 5.41421i | 0.997777 | + | 0.332592i | ||||
\(266\) | − | 2.82843i | − | 0.173422i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.58579 | − | 5.58579i | 0.341206 | − | 0.341206i | ||||
\(269\) | −5.65685 | −0.344904 | −0.172452 | − | 0.985018i | \(-0.555169\pi\) | ||||
−0.172452 | + | 0.985018i | \(0.555169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8995 | 1.45179 | 0.725895 | − | 0.687805i | \(-0.241426\pi\) | ||||
0.725895 | + | 0.687805i | \(0.241426\pi\) | |||||||
\(272\) | −3.41421 | + | 3.41421i | −0.207017 | + | 0.207017i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.9706i | − | 1.02523i | ||||||
\(275\) | −13.6569 | − | 10.2426i | −0.823539 | − | 0.617654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.8995 | − | 21.8995i | −1.31581 | − | 1.31581i | −0.917057 | − | 0.398756i | \(-0.869442\pi\) |
−0.398756 | − | 0.917057i | \(-0.630558\pi\) | |||||||
\(278\) | 4.48528 | + | 4.48528i | 0.269009 | + | 0.269009i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | + | 2.00000i | 0.0597614 | + | 0.119523i | ||||
\(281\) | 4.92893i | 0.294035i | 0.989134 | + | 0.147018i | \(0.0469674\pi\) | ||||
−0.989134 | + | 0.147018i | \(0.953033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31371 | − | 1.31371i | 0.0780919 | − | 0.0780919i | −0.666982 | − | 0.745074i | \(-0.732414\pi\) |
0.745074 | + | 0.666982i | \(0.232414\pi\) | |||||||
\(284\) | −6.82843 | −0.405193 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.3137 | −1.14204 | ||||||||
\(287\) | −6.24264 | + | 6.24264i | −0.368491 | + | 0.368491i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.31371i | − | 0.371395i | ||||||
\(290\) | 3.41421 | − | 10.2426i | 0.200490 | − | 0.601469i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.07107 | + | 7.07107i | 0.413803 | + | 0.413803i | ||||
\(293\) | −2.65685 | − | 2.65685i | −0.155215 | − | 0.155215i | 0.625227 | − | 0.780443i | \(-0.285006\pi\) |
−0.780443 | + | 0.625227i | \(0.785006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.65685 | − | 2.82843i | 0.329355 | − | 0.164677i | ||||
\(296\) | 3.17157i | 0.184344i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.2426 | − | 14.2426i | 0.825054 | − | 0.825054i | ||||
\(299\) | −6.62742 | −0.383273 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.4142 | −0.657904 | ||||||||
\(302\) | −9.31371 | + | 9.31371i | −0.535944 | + | 0.535944i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.82843i | 0.162221i | ||||||||
\(305\) | −19.7990 | + | 9.89949i | −1.13369 | + | 0.566843i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | −2.41421 | − | 2.41421i | −0.137563 | − | 0.137563i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.24264 | + | 21.7279i | −0.411354 | + | 1.23406i | ||||
\(311\) | − | 0.828427i | − | 0.0469758i | −0.999724 | − | 0.0234879i | \(-0.992523\pi\) | ||
0.999724 | − | 0.0234879i | \(-0.00747712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.24264 | + | 6.24264i | −0.352855 | + | 0.352855i | −0.861171 | − | 0.508316i | \(-0.830268\pi\) |
0.508316 | + | 0.861171i | \(0.330268\pi\) | |||||||
\(314\) | 2.34315 | 0.132231 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65685 | −0.318223 | ||||||||
\(317\) | 0.727922 | − | 0.727922i | 0.0408842 | − | 0.0408842i | −0.686369 | − | 0.727253i | \(-0.740797\pi\) |
0.727253 | + | 0.686369i | \(0.240797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4853i | 0.922999i | ||||||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.828427 | − | 0.828427i | −0.0461664 | − | 0.0461664i | ||||
\(323\) | −9.65685 | − | 9.65685i | −0.537322 | − | 0.537322i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | − | 28.0000i | −0.221880 | − | 1.55316i | ||||
\(326\) | 19.4142i | 1.07525i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.24264 | − | 6.24264i | 0.344692 | − | 0.344692i | ||||
\(329\) | 1.07107 | 0.0590499 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.6274 | −1.46358 | −0.731788 | − | 0.681533i | \(-0.761314\pi\) | ||||
−0.731788 | + | 0.681533i | \(0.761314\pi\) | |||||||
\(332\) | 4.82843 | − | 4.82843i | 0.264994 | − | 0.264994i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7279i | 0.805876i | ||||||||
\(335\) | −16.7574 | − | 5.58579i | −0.915552 | − | 0.305184i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8284 | + | 15.8284i | 0.862229 | + | 0.862229i | 0.991597 | − | 0.129367i | \(-0.0412946\pi\) |
−0.129367 | + | 0.991597i | \(0.541295\pi\) | |||||||
\(338\) | −13.4350 | − | 13.4350i | −0.730769 | − | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.2426 | + | 3.41421i | 0.555485 | + | 0.185162i | ||||
\(341\) | − | 34.9706i | − | 1.89376i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 11.4142 | 0.615413 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.75736 | 0.417038 | ||||||||
\(347\) | 8.48528 | − | 8.48528i | 0.455514 | − | 0.455514i | −0.441666 | − | 0.897180i | \(-0.645612\pi\) |
0.897180 | + | 0.441666i | \(0.145612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.27208i | − | 0.389265i | −0.980876 | − | 0.194633i | \(-0.937649\pi\) | ||
0.980876 | − | 0.194633i | \(-0.0623515\pi\) | |||||||
\(350\) | 3.00000 | − | 4.00000i | 0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.41421 | + | 2.41421i | 0.128678 | + | 0.128678i | ||||
\(353\) | −18.3848 | − | 18.3848i | −0.978523 | − | 0.978523i | 0.0212513 | − | 0.999774i | \(-0.493235\pi\) |
−0.999774 | + | 0.0212513i | \(0.993235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.82843 | + | 13.6569i | 0.362415 | + | 0.724831i | ||||
\(356\) | − | 8.82843i | − | 0.467906i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.7279 | − | 13.7279i | 0.725543 | − | 0.725543i | ||||
\(359\) | −15.7990 | −0.833839 | −0.416919 | − | 0.908943i | \(-0.636890\pi\) | ||||
−0.416919 | + | 0.908943i | \(0.636890\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | −3.48528 | + | 3.48528i | −0.183182 | + | 0.183182i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 5.65685i | − | 0.296500i | ||||||
\(365\) | 7.07107 | − | 21.2132i | 0.370117 | − | 1.11035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.75736 | − | 1.75736i | −0.0917334 | − | 0.0917334i | 0.659751 | − | 0.751484i | \(-0.270662\pi\) |
−0.751484 | + | 0.659751i | \(0.770662\pi\) | |||||||
\(368\) | 0.828427 | + | 0.828427i | 0.0431847 | + | 0.0431847i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.34315 | − | 3.17157i | 0.329764 | − | 0.164882i | ||||
\(371\) | − | 7.65685i | − | 0.397524i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.07107 | − | 3.07107i | 0.159014 | − | 0.159014i | −0.623116 | − | 0.782130i | \(-0.714133\pi\) |
0.782130 | + | 0.623116i | \(0.214133\pi\) | |||||||
\(374\) | −16.4853 | −0.852434 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.07107 | −0.0552361 | ||||||||
\(377\) | −19.3137 | + | 19.3137i | −0.994707 | + | 0.994707i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7990i | 0.708806i | 0.935093 | + | 0.354403i | \(0.115316\pi\) | ||||
−0.935093 | + | 0.354403i | \(0.884684\pi\) | |||||||
\(380\) | 5.65685 | − | 2.82843i | 0.290191 | − | 0.145095i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.1421 | + | 18.1421i | 0.928232 | + | 0.928232i | ||||
\(383\) | 1.58579 | + | 1.58579i | 0.0810299 | + | 0.0810299i | 0.746460 | − | 0.665430i | \(-0.231752\pi\) |
−0.665430 | + | 0.746460i | \(0.731752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.41421 | + | 7.24264i | −0.123040 | + | 0.369119i | ||||
\(386\) | 4.92893i | 0.250876i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.41421 | + | 7.41421i | −0.376400 | + | 0.376400i | ||||
\(389\) | 29.7990 | 1.51087 | 0.755434 | − | 0.655224i | \(-0.227426\pi\) | ||||
0.755434 | + | 0.655224i | \(0.227426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65685 | −0.286079 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.48528i | 0.125207i | ||||||||
\(395\) | 5.65685 | + | 11.3137i | 0.284627 | + | 0.569254i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0711 | − | 15.0711i | −0.756395 | − | 0.756395i | 0.219269 | − | 0.975664i | \(-0.429633\pi\) |
−0.975664 | + | 0.219269i | \(0.929633\pi\) | |||||||
\(398\) | 16.8995 | + | 16.8995i | 0.847095 | + | 0.847095i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.9706 | − | 40.9706i | 2.04089 | − | 2.04089i | ||||
\(404\) | −6.34315 | −0.315583 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.82843 | −0.239631 | ||||||||
\(407\) | −7.65685 | + | 7.65685i | −0.379536 | + | 0.379536i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | −18.7279 | − | 6.24264i | −0.924906 | − | 0.308302i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.58579 | + | 4.58579i | 0.225925 | + | 0.225925i | ||||
\(413\) | −2.00000 | − | 2.00000i | −0.0984136 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.4853 | − | 4.82843i | −0.711054 | − | 0.237018i | ||||
\(416\) | 5.65685i | 0.277350i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.82843 | + | 6.82843i | −0.333989 | + | 0.333989i | ||||
\(419\) | 26.6274 | 1.30083 | 0.650417 | − | 0.759577i | \(-0.274594\pi\) | ||||
0.650417 | + | 0.759577i | \(0.274594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.62742 | 0.225527 | 0.112763 | − | 0.993622i | \(-0.464030\pi\) | ||||
0.112763 | + | 0.993622i | \(0.464030\pi\) | |||||||
\(422\) | −2.82843 | + | 2.82843i | −0.137686 | + | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.65685i | 0.371850i | ||||||||
\(425\) | −3.41421 | − | 23.8995i | −0.165614 | − | 1.15930i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.00000 | + | 7.00000i | 0.338754 | + | 0.338754i | ||||
\(428\) | 10.8284 | + | 10.8284i | 0.523412 | + | 0.523412i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.4142 | − | 22.8284i | −0.550442 | − | 1.10088i | ||||
\(431\) | 2.14214i | 0.103183i | 0.998668 | + | 0.0515915i | \(0.0164294\pi\) | ||||
−0.998668 | + | 0.0515915i | \(0.983571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.75736 | − | 9.75736i | 0.468909 | − | 0.468909i | −0.432652 | − | 0.901561i | \(-0.642422\pi\) |
0.901561 | + | 0.432652i | \(0.142422\pi\) | |||||||
\(434\) | 10.2426 | 0.491662 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.3137 | −0.637611 | ||||||||
\(437\) | −2.34315 | + | 2.34315i | −0.112088 | + | 0.112088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.8995i | − | 0.758841i | −0.925224 | − | 0.379421i | \(-0.876123\pi\) | ||
0.925224 | − | 0.379421i | \(-0.123877\pi\) | |||||||
\(440\) | 2.41421 | − | 7.24264i | 0.115093 | − | 0.345279i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.3137 | − | 19.3137i | −0.918659 | − | 0.918659i | ||||
\(443\) | −20.4853 | − | 20.4853i | −0.973285 | − | 0.973285i | 0.0263672 | − | 0.999652i | \(-0.491606\pi\) |
−0.999652 | + | 0.0263672i | \(0.991606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.6569 | + | 8.82843i | −0.837015 | + | 0.418508i | ||||
\(446\) | 21.6569i | 1.02548i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.707107 | + | 0.707107i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 8.72792 | 0.411896 | 0.205948 | − | 0.978563i | \(-0.433972\pi\) | ||||
0.205948 | + | 0.978563i | \(0.433972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.1421 | 1.41934 | ||||||||
\(452\) | 11.3137 | − | 11.3137i | 0.532152 | − | 0.532152i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 9.65685i | − | 0.453219i | ||||||
\(455\) | −11.3137 | + | 5.65685i | −0.530395 | + | 0.265197i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.82843 | + | 7.82843i | 0.366198 | + | 0.366198i | 0.866089 | − | 0.499890i | \(-0.166626\pi\) |
−0.499890 | + | 0.866089i | \(0.666626\pi\) | |||||||
\(458\) | 0.171573 | + | 0.171573i | 0.00801707 | + | 0.00801707i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.828427 | − | 2.48528i | 0.0386256 | − | 0.115877i | ||||
\(461\) | − | 17.3137i | − | 0.806380i | −0.915116 | − | 0.403190i | \(-0.867901\pi\) | ||
0.915116 | − | 0.403190i | \(-0.132099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7990 | − | 19.7990i | 0.920137 | − | 0.920137i | −0.0769016 | − | 0.997039i | \(-0.524503\pi\) |
0.997039 | + | 0.0769016i | \(0.0245027\pi\) | |||||||
\(464\) | 4.82843 | 0.224154 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.9706 | 0.600850 | ||||||||
\(467\) | −14.0000 | + | 14.0000i | −0.647843 | + | 0.647843i | −0.952471 | − | 0.304629i | \(-0.901468\pi\) |
0.304629 | + | 0.952471i | \(0.401468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.89949i | 0.364765i | ||||||||
\(470\) | 1.07107 | + | 2.14214i | 0.0494047 | + | 0.0988093i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | + | 2.00000i | 0.0920575 | + | 0.0920575i | ||||
\(473\) | 27.5563 | + | 27.5563i | 1.26704 | + | 1.26704i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.3137 | − | 8.48528i | −0.519109 | − | 0.389331i | ||||
\(476\) | − | 4.82843i | − | 0.221311i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.65685 | − | 1.65685i | 0.0757827 | − | 0.0757827i | ||||
\(479\) | 24.8284 | 1.13444 | 0.567220 | − | 0.823566i | \(-0.308019\pi\) | ||||
0.567220 | + | 0.823566i | \(0.308019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.9411 | −0.818045 | ||||||||
\(482\) | 17.0711 | − | 17.0711i | 0.777566 | − | 0.777566i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.656854i | 0.0298570i | ||||||||
\(485\) | 22.2426 | + | 7.41421i | 1.00999 | + | 0.336662i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9706 | − | 14.9706i | −0.678381 | − | 0.678381i | 0.281253 | − | 0.959634i | \(-0.409250\pi\) |
−0.959634 | + | 0.281253i | \(0.909250\pi\) | |||||||
\(488\) | −7.00000 | − | 7.00000i | −0.316875 | − | 0.316875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.12132 | − | 0.707107i | −0.0958315 | − | 0.0319438i | ||||
\(491\) | 1.27208i | 0.0574081i | 0.999588 | + | 0.0287040i | \(0.00913803\pi\) | ||||
−0.999588 | + | 0.0287040i | \(0.990862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.4853 | + | 16.4853i | −0.742460 | + | 0.742460i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.2426 | −0.459908 | ||||||||
\(497\) | 4.82843 | − | 4.82843i | 0.216585 | − | 0.216585i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.4558i | 1.22909i | 0.788881 | + | 0.614546i | \(0.210661\pi\) | ||||
−0.788881 | + | 0.614546i | \(0.789339\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.1716 | − | 13.1716i | −0.587876 | − | 0.587876i | ||||
\(503\) | 14.5563 | + | 14.5563i | 0.649036 | + | 0.649036i | 0.952760 | − | 0.303724i | \(-0.0982302\pi\) |
−0.303724 | + | 0.952760i | \(0.598230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.34315 | + | 12.6863i | 0.282266 | + | 0.564533i | ||||
\(506\) | 4.00000i | 0.177822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.65685 | + | 3.65685i | −0.162247 | + | 0.162247i | ||||
\(509\) | −29.6569 | −1.31452 | −0.657258 | − | 0.753665i | \(-0.728284\pi\) | ||||
−0.657258 | + | 0.753665i | \(0.728284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.1421i | − | 0.711999i | ||||||
\(515\) | 4.58579 | − | 13.7574i | 0.202074 | − | 0.606222i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.58579 | − | 2.58579i | −0.113723 | − | 0.113723i | ||||
\(518\) | −2.24264 | − | 2.24264i | −0.0985360 | − | 0.0985360i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11.3137 | − | 5.65685i | 0.496139 | − | 0.248069i | ||||
\(521\) | 30.7696i | 1.34804i | 0.738714 | + | 0.674019i | \(0.235434\pi\) | ||||
−0.738714 | + | 0.674019i | \(0.764566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.68629 | + | 2.68629i | −0.117463 | + | 0.117463i | −0.763395 | − | 0.645932i | \(-0.776469\pi\) |
0.645932 | + | 0.763395i | \(0.276469\pi\) | |||||||
\(524\) | 0.485281 | 0.0211996 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.17157 | −0.225491 | ||||||||
\(527\) | 34.9706 | − | 34.9706i | 1.52334 | − | 1.52334i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.6274i | − | 0.940322i | ||||||
\(530\) | 15.3137 | − | 7.65685i | 0.665185 | − | 0.332592i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | − | 2.00000i | −0.0867110 | − | 0.0867110i | ||||
\(533\) | 35.3137 | + | 35.3137i | 1.52961 | + | 1.52961i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8284 | − | 32.4853i | 0.468154 | − | 1.40446i | ||||
\(536\) | − | 7.89949i | − | 0.341206i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.00000 | + | 4.00000i | −0.172452 | + | 0.172452i | ||||
\(539\) | 3.41421 | 0.147061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.1127 | 1.42363 | 0.711813 | − | 0.702369i | \(-0.247874\pi\) | ||||
0.711813 | + | 0.702369i | \(0.247874\pi\) | |||||||
\(542\) | 16.8995 | − | 16.8995i | 0.725895 | − | 0.725895i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.82843i | 0.207017i | ||||||||
\(545\) | 13.3137 | + | 26.6274i | 0.570297 | + | 1.14059i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5563 | + | 18.5563i | 0.793412 | + | 0.793412i | 0.982047 | − | 0.188635i | \(-0.0604063\pi\) |
−0.188635 | + | 0.982047i | \(0.560406\pi\) | |||||||
\(548\) | −12.0000 | − | 12.0000i | −0.512615 | − | 0.512615i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.8995 | + | 2.41421i | −0.720597 | + | 0.102942i | ||||
\(551\) | 13.6569i | 0.581802i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 4.00000i | 0.170097 | − | 0.170097i | ||||
\(554\) | −30.9706 | −1.31581 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.34315 | 0.269009 | ||||||||
\(557\) | −23.5563 | + | 23.5563i | −0.998115 | + | 0.998115i | −0.999998 | − | 0.00188368i | \(-0.999400\pi\) |
0.00188368 | + | 0.999998i | \(0.499400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 64.5685i | 2.73096i | ||||||||
\(560\) | 2.12132 | + | 0.707107i | 0.0896421 | + | 0.0298807i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.48528 | + | 3.48528i | 0.147018 | + | 0.147018i | ||||
\(563\) | 29.3137 | + | 29.3137i | 1.23543 | + | 1.23543i | 0.961851 | + | 0.273575i | \(0.0882061\pi\) |
0.273575 | + | 0.961851i | \(0.411794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.9411 | − | 11.3137i | −1.42791 | − | 0.475971i | ||||
\(566\) | − | 1.85786i | − | 0.0780919i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.82843 | + | 4.82843i | −0.202596 | + | 0.202596i | ||||
\(569\) | −33.8995 | −1.42114 | −0.710570 | − | 0.703626i | \(-0.751563\pi\) | ||||
−0.710570 | + | 0.703626i | \(0.751563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.9706 | −1.88196 | −0.940980 | − | 0.338463i | \(-0.890093\pi\) | ||||
−0.940980 | + | 0.338463i | \(0.890093\pi\) | |||||||
\(572\) | −13.6569 | + | 13.6569i | −0.571022 | + | 0.571022i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.82843i | 0.368491i | ||||||||
\(575\) | −5.79899 | + | 0.828427i | −0.241835 | + | 0.0345478i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7279 | + | 14.7279i | 0.613131 | + | 0.613131i | 0.943761 | − | 0.330629i | \(-0.107261\pi\) |
−0.330629 | + | 0.943761i | \(0.607261\pi\) | |||||||
\(578\) | −4.46447 | − | 4.46447i | −0.185697 | − | 0.185697i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.82843 | − | 9.65685i | −0.200490 | − | 0.400979i | ||||
\(581\) | 6.82843i | 0.283291i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.4853 | + | 18.4853i | −0.765582 | + | 0.765582i | ||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.75736 | −0.155215 | ||||||||
\(587\) | −21.7990 | + | 21.7990i | −0.899741 | + | 0.899741i | −0.995413 | − | 0.0956723i | \(-0.969500\pi\) |
0.0956723 | + | 0.995413i | \(0.469500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 28.9706i | − | 1.19371i | ||||||
\(590\) | 2.00000 | − | 6.00000i | 0.0823387 | − | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.24264 | + | 2.24264i | 0.0921720 | + | 0.0921720i | ||||
\(593\) | 20.3848 | + | 20.3848i | 0.837102 | + | 0.837102i | 0.988477 | − | 0.151374i | \(-0.0483698\pi\) |
−0.151374 | + | 0.988477i | \(0.548370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.65685 | + | 4.82843i | −0.395892 | + | 0.197946i | ||||
\(596\) | − | 20.1421i | − | 0.825054i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.68629 | + | 4.68629i | −0.191637 | + | 0.191637i | ||||
\(599\) | 7.31371 | 0.298830 | 0.149415 | − | 0.988775i | \(-0.452261\pi\) | ||||
0.149415 | + | 0.988775i | \(0.452261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1421 | 0.984778 | 0.492389 | − | 0.870375i | \(-0.336124\pi\) | ||||
0.492389 | + | 0.870375i | \(0.336124\pi\) | |||||||
\(602\) | −8.07107 | + | 8.07107i | −0.328952 | + | 0.328952i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.1716i | 0.535944i | ||||||||
\(605\) | 1.31371 | − | 0.656854i | 0.0534098 | − | 0.0267049i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3137 | + | 15.3137i | 0.621564 | + | 0.621564i | 0.945931 | − | 0.324367i | \(-0.105151\pi\) |
−0.324367 | + | 0.945931i | \(0.605151\pi\) | |||||||
\(608\) | 2.00000 | + | 2.00000i | 0.0811107 | + | 0.0811107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.00000 | + | 21.0000i | −0.283422 | + | 0.850265i | ||||
\(611\) | − | 6.05887i | − | 0.245116i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.07107 | − | 5.07107i | 0.204818 | − | 0.204818i | −0.597242 | − | 0.802061i | \(-0.703737\pi\) |
0.802061 | + | 0.597242i | \(0.203737\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.41421 | −0.137563 | ||||||||
\(617\) | −24.0416 | + | 24.0416i | −0.967880 | + | 0.967880i | −0.999500 | − | 0.0316203i | \(-0.989933\pi\) |
0.0316203 | + | 0.999500i | \(0.489933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.1421i | 1.85461i | 0.374308 | + | 0.927305i | \(0.377880\pi\) | ||||
−0.374308 | + | 0.927305i | \(0.622120\pi\) | |||||||
\(620\) | 10.2426 | + | 20.4853i | 0.411354 | + | 0.822709i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.585786 | − | 0.585786i | −0.0234879 | − | 0.0234879i | ||||
\(623\) | 6.24264 | + | 6.24264i | 0.250106 | + | 0.250106i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 8.82843i | 0.352855i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.65685 | − | 1.65685i | 0.0661157 | − | 0.0661157i | ||||
\(629\) | −15.3137 | −0.610598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.7990 | −1.58437 | −0.792186 | − | 0.610279i | \(-0.791057\pi\) | ||||
−0.792186 | + | 0.610279i | \(0.791057\pi\) | |||||||
\(632\) | −4.00000 | + | 4.00000i | −0.159111 | + | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.02944i | − | 0.0408842i | ||||||
\(635\) | 10.9706 | + | 3.65685i | 0.435354 | + | 0.145118i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | + | 4.00000i | 0.158486 | + | 0.158486i | ||||
\(638\) | 11.6569 | + | 11.6569i | 0.461499 | + | 0.461499i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.12132 | − | 0.707107i | −0.0838525 | − | 0.0279508i | ||||
\(641\) | − | 21.2132i | − | 0.837871i | −0.908016 | − | 0.418936i | \(-0.862403\pi\) | ||
0.908016 | − | 0.418936i | \(-0.137597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9706 | − | 22.9706i | 0.905871 | − | 0.905871i | −0.0900653 | − | 0.995936i | \(-0.528708\pi\) |
0.995936 | + | 0.0900653i | \(0.0287076\pi\) | |||||||
\(644\) | −1.17157 | −0.0461664 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6569 | −0.537322 | ||||||||
\(647\) | −24.7574 | + | 24.7574i | −0.973312 | + | 0.973312i | −0.999653 | − | 0.0263408i | \(-0.991614\pi\) |
0.0263408 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.65685i | 0.379065i | ||||||||
\(650\) | −22.6274 | − | 16.9706i | −0.887520 | − | 0.665640i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7279 | + | 13.7279i | 0.537627 | + | 0.537627i | ||||
\(653\) | 5.75736 | + | 5.75736i | 0.225303 | + | 0.225303i | 0.810727 | − | 0.585424i | \(-0.199072\pi\) |
−0.585424 | + | 0.810727i | \(0.699072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.485281 | − | 0.970563i | −0.0189615 | − | 0.0379230i | ||||
\(656\) | − | 8.82843i | − | 0.344692i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.757359 | − | 0.757359i | 0.0295249 | − | 0.0295249i | ||||
\(659\) | −1.27208 | −0.0495531 | −0.0247766 | − | 0.999693i | \(-0.507887\pi\) | ||||
−0.0247766 | + | 0.999693i | \(0.507887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.04163 | −0.312783 | −0.156392 | − | 0.987695i | \(-0.549986\pi\) | ||||
−0.156392 | + | 0.987695i | \(0.549986\pi\) | |||||||
\(662\) | −18.8284 | + | 18.8284i | −0.731788 | + | 0.731788i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.82843i | − | 0.264994i | ||||||
\(665\) | −2.00000 | + | 6.00000i | −0.0775567 | + | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | + | 4.00000i | 0.154881 | + | 0.154881i | ||||
\(668\) | 10.4142 | + | 10.4142i | 0.402938 | + | 0.402938i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15.7990 | + | 7.89949i | −0.610368 | + | 0.305184i | ||||
\(671\) | − | 33.7990i | − | 1.30480i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6569 | − | 14.6569i | 0.564980 | − | 0.564980i | −0.365738 | − | 0.930718i | \(-0.619183\pi\) |
0.930718 | + | 0.365738i | \(0.119183\pi\) | |||||||
\(674\) | 22.3848 | 0.862229 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | 10.1716 | − | 10.1716i | 0.390925 | − | 0.390925i | −0.484092 | − | 0.875017i | \(-0.660850\pi\) |
0.875017 | + | 0.484092i | \(0.160850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.4853i | − | 0.402388i | ||||||
\(680\) | 9.65685 | − | 4.82843i | 0.370323 | − | 0.185162i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.7279 | − | 24.7279i | −0.946881 | − | 0.946881i | ||||
\(683\) | −12.3848 | − | 12.3848i | −0.473890 | − | 0.473890i | 0.429281 | − | 0.903171i | \(-0.358767\pi\) |
−0.903171 | + | 0.429281i | \(0.858767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | + | 36.0000i | −0.458496 | + | 1.37549i | ||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.07107 | − | 8.07107i | 0.307707 | − | 0.307707i | ||||
\(689\) | −43.3137 | −1.65012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 5.48528 | − | 5.48528i | 0.208519 | − | 0.208519i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | −6.34315 | − | 12.6863i | −0.240609 | − | 0.481218i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1421 | + | 30.1421i | 1.14171 | + | 1.14171i | ||||
\(698\) | −5.14214 | − | 5.14214i | −0.194633 | − | 0.194633i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.707107 | − | 4.94975i | −0.0267261 | − | 0.187083i | ||||
\(701\) | − | 35.1716i | − | 1.32841i | −0.747550 | − | 0.664206i | \(-0.768770\pi\) | ||
0.747550 | − | 0.664206i | \(-0.231230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.34315 | + | 6.34315i | −0.239236 | + | 0.239236i | ||||
\(704\) | 3.41421 | 0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | 4.48528 | − | 4.48528i | 0.168686 | − | 0.168686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1716i | 1.32090i | 0.750872 | + | 0.660448i | \(0.229634\pi\) | ||||
−0.750872 | + | 0.660448i | \(0.770366\pi\) | |||||||
\(710\) | 14.4853 | + | 4.82843i | 0.543623 | + | 0.181208i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.24264 | − | 6.24264i | −0.233953 | − | 0.233953i | ||||
\(713\) | −8.48528 | − | 8.48528i | −0.317776 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.9706 | + | 13.6569i | 1.53221 | + | 0.510737i | ||||
\(716\) | − | 19.4142i | − | 0.725543i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.1716 | + | 11.1716i | −0.416919 | + | 0.416919i | ||||
\(719\) | −6.62742 | −0.247161 | −0.123580 | − | 0.992335i | \(-0.539438\pi\) | ||||
−0.123580 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.48528 | −0.241524 | ||||||||
\(722\) | 7.77817 | − | 7.77817i | 0.289474 | − | 0.289474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.92893i | 0.183182i | ||||||||
\(725\) | −14.4853 | + | 19.3137i | −0.537970 | + | 0.717293i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6274 | + | 22.6274i | 0.839204 | + | 0.839204i | 0.988754 | − | 0.149550i | \(-0.0477824\pi\) |
−0.149550 | + | 0.988754i | \(0.547782\pi\) | |||||||
\(728\) | −4.00000 | − | 4.00000i | −0.148250 | − | 0.148250i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.0000 | − | 20.0000i | −0.370117 | − | 0.740233i | ||||
\(731\) | 55.1127i | 2.03842i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5563 | + | 31.5563i | −1.16556 | + | 1.16556i | −0.182321 | + | 0.983239i | \(0.558361\pi\) |
−0.983239 | + | 0.182321i | \(0.941639\pi\) | |||||||
\(734\) | −2.48528 | −0.0917334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17157 | 0.0431847 | ||||||||
\(737\) | 19.0711 | − | 19.0711i | 0.702492 | − | 0.702492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 43.4558i | − | 1.59855i | −0.600966 | − | 0.799275i | \(-0.705217\pi\) | ||
0.600966 | − | 0.799275i | \(-0.294783\pi\) | |||||||
\(740\) | 2.24264 | − | 6.72792i | 0.0824411 | − | 0.247323i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.41421 | − | 5.41421i | −0.198762 | − | 0.198762i | ||||
\(743\) | 31.1127 | + | 31.1127i | 1.14141 | + | 1.14141i | 0.988192 | + | 0.153222i | \(0.0489651\pi\) |
0.153222 | + | 0.988192i | \(0.451035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.2843 | + | 20.1421i | −1.47590 | + | 0.737951i | ||||
\(746\) | − | 4.34315i | − | 0.159014i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.6569 | + | 11.6569i | −0.426217 | + | 0.426217i | ||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5147 | 1.14999 | 0.574994 | − | 0.818157i | \(-0.305004\pi\) | ||||
0.574994 | + | 0.818157i | \(0.305004\pi\) | |||||||
\(752\) | −0.757359 | + | 0.757359i | −0.0276181 | + | 0.0276181i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.3137i | 0.994707i | ||||||||
\(755\) | 26.3431 | − | 13.1716i | 0.958725 | − | 0.479363i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.55635 | + | 7.55635i | 0.274640 | + | 0.274640i | 0.830965 | − | 0.556325i | \(-0.187789\pi\) |
−0.556325 | + | 0.830965i | \(0.687789\pi\) | |||||||
\(758\) | 9.75736 | + | 9.75736i | 0.354403 | + | 0.354403i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | − | 6.00000i | 0.0725476 | − | 0.217643i | ||||
\(761\) | 14.9706i | 0.542682i | 0.962483 | + | 0.271341i | \(0.0874672\pi\) | ||||
−0.962483 | + | 0.271341i | \(0.912533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.41421 | − | 9.41421i | 0.340817 | − | 0.340817i | ||||
\(764\) | 25.6569 | 0.928232 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.24264 | 0.0810299 | ||||||||
\(767\) | −11.3137 | + | 11.3137i | −0.408514 | + | 0.408514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.5980i | − | 1.35582i | −0.735146 | − | 0.677909i | \(-0.762886\pi\) | ||
0.735146 | − | 0.677909i | \(-0.237114\pi\) | |||||||
\(770\) | 3.41421 | + | 6.82843i | 0.123040 | + | 0.246079i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.48528 | + | 3.48528i | 0.125438 | + | 0.125438i | ||||
\(773\) | −32.9411 | − | 32.9411i | −1.18481 | − | 1.18481i | −0.978483 | − | 0.206327i | \(-0.933849\pi\) |
−0.206327 | − | 0.978483i | \(-0.566151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.7279 | − | 40.9706i | 1.10378 | − | 1.47171i | ||||
\(776\) | 10.4853i | 0.376400i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.0711 | − | 21.0711i | 0.755434 | − | 0.755434i | ||||
\(779\) | 24.9706 | 0.894663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3137 | −0.834230 | ||||||||
\(782\) | −4.00000 | + | 4.00000i | −0.143040 | + | 0.143040i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −4.97056 | − | 1.65685i | −0.177407 | − | 0.0591357i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.4853 | − | 32.4853i | −1.15798 | − | 1.15798i | −0.984910 | − | 0.173065i | \(-0.944633\pi\) |
−0.173065 | − | 0.984910i | \(-0.555367\pi\) | |||||||
\(788\) | 1.75736 | + | 1.75736i | 0.0626033 | + | 0.0626033i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | + | 4.00000i | 0.426941 | + | 0.142314i | ||||
\(791\) | 16.0000i | 0.568895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.5980 | − | 39.5980i | 1.40617 | − | 1.40617i | ||||
\(794\) | −21.3137 | −0.756395 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.8995 | 0.847095 | ||||||||
\(797\) | 25.8284 | − | 25.8284i | 0.914890 | − | 0.914890i | −0.0817621 | − | 0.996652i | \(-0.526055\pi\) |
0.996652 | + | 0.0817621i | \(0.0260548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.17157i | − | 0.182957i | ||||||
\(800\) | 0.707107 | + | 4.94975i | 0.0250000 | + | 0.175000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.0000 | + | 19.0000i | 0.670913 | + | 0.670913i | ||||
\(803\) | 24.1421 | + | 24.1421i | 0.851957 | + | 0.851957i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.17157 | + | 2.34315i | 0.0412925 | + | 0.0825850i | ||||
\(806\) | − | 57.9411i | − | 2.04089i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.48528 | + | 4.48528i | −0.157792 | + | 0.157792i | ||||
\(809\) | −9.61522 | −0.338053 | −0.169027 | − | 0.985611i | \(-0.554062\pi\) | ||||
−0.169027 | + | 0.985611i | \(0.554062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.97056 | −0.174540 | −0.0872700 | − | 0.996185i | \(-0.527814\pi\) | ||||
−0.0872700 | + | 0.996185i | \(0.527814\pi\) | |||||||
\(812\) | −3.41421 | + | 3.41421i | −0.119815 | + | 0.119815i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8284i | 0.379536i | ||||||||
\(815\) | 13.7279 | − | 41.1838i | 0.480868 | − | 1.44260i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.8284 | + | 22.8284i | 0.798666 | + | 0.798666i | ||||
\(818\) | 7.07107 | + | 7.07107i | 0.247234 | + | 0.247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.6569 | + | 8.82843i | −0.616604 | + | 0.308302i | ||||
\(821\) | − | 29.7990i | − | 1.03999i | −0.854169 | − | 0.519996i | \(-0.825933\pi\) | ||
0.854169 | − | 0.519996i | \(-0.174067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5147 | − | 11.5147i | 0.401378 | − | 0.401378i | −0.477341 | − | 0.878718i | \(-0.658399\pi\) |
0.878718 | + | 0.477341i | \(0.158399\pi\) | |||||||
\(824\) | 6.48528 | 0.225925 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.82843 | −0.0984136 | ||||||||
\(827\) | −5.75736 | + | 5.75736i | −0.200203 | + | 0.200203i | −0.800087 | − | 0.599884i | \(-0.795213\pi\) |
0.599884 | + | 0.800087i | \(0.295213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2426i | 0.703056i | 0.936177 | + | 0.351528i | \(0.114338\pi\) | ||||
−0.936177 | + | 0.351528i | \(0.885662\pi\) | |||||||
\(830\) | −13.6569 | + | 6.82843i | −0.474036 | + | 0.237018i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000 | + | 4.00000i | 0.138675 | + | 0.138675i | ||||
\(833\) | 3.41421 | + | 3.41421i | 0.118295 | + | 0.118295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.4142 | − | 31.2426i | 0.360399 | − | 1.08120i | ||||
\(836\) | 9.65685i | 0.333989i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.8284 | − | 18.8284i | 0.650417 | − | 0.650417i | ||||
\(839\) | −13.5147 | −0.466580 | −0.233290 | − | 0.972407i | \(-0.574949\pi\) | ||||
−0.233290 | + | 0.972407i | \(0.574949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 3.27208 | − | 3.27208i | 0.112763 | − | 0.112763i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000i | 0.137686i | ||||||||
\(845\) | 19.0000 | + | 38.0000i | 0.653620 | + | 1.30724i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.464466 | − | 0.464466i | −0.0159592 | − | 0.0159592i | ||||
\(848\) | 5.41421 | + | 5.41421i | 0.185925 | + | 0.185925i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.3137 | − | 14.4853i | −0.662455 | − | 0.496841i | ||||
\(851\) | 3.71573i | 0.127374i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.928932 | + | 0.928932i | −0.0318060 | + | 0.0318060i | −0.722831 | − | 0.691025i | \(-0.757159\pi\) |
0.691025 | + | 0.722831i | \(0.257159\pi\) | |||||||
\(854\) | 9.89949 | 0.338754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.3137 | 0.523412 | ||||||||
\(857\) | 37.5563 | − | 37.5563i | 1.28290 | − | 1.28290i | 0.343891 | − | 0.939010i | \(-0.388255\pi\) |
0.939010 | − | 0.343891i | \(-0.111745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.0000i | − | 1.36478i | −0.730987 | − | 0.682391i | \(-0.760940\pi\) | ||
0.730987 | − | 0.682391i | \(-0.239060\pi\) | |||||||
\(860\) | −24.2132 | − | 8.07107i | −0.825663 | − | 0.275221i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.51472 | + | 1.51472i | 0.0515915 | + | 0.0515915i | ||||
\(863\) | −26.8284 | − | 26.8284i | −0.913250 | − | 0.913250i | 0.0832762 | − | 0.996527i | \(-0.473462\pi\) |
−0.996527 | + | 0.0832762i | \(0.973462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.4558 | − | 5.48528i | −0.559515 | − | 0.186505i | ||||
\(866\) | − | 13.7990i | − | 0.468909i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.24264 | − | 7.24264i | 0.245831 | − | 0.245831i | ||||
\(869\) | −19.3137 | −0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.6863 | 1.51414 | ||||||||
\(872\) | −9.41421 | + | 9.41421i | −0.318805 | + | 0.318805i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.31371i | 0.112088i | ||||||||
\(875\) | −9.19239 | + | 6.36396i | −0.310759 | + | 0.215141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6985 | + | 21.6985i | 0.732706 | + | 0.732706i | 0.971155 | − | 0.238449i | \(-0.0766391\pi\) |
−0.238449 | + | 0.971155i | \(0.576639\pi\) | |||||||
\(878\) | −11.2426 | − | 11.2426i | −0.379421 | − | 0.379421i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.41421 | − | 6.82843i | −0.115093 | − | 0.230186i | ||||
\(881\) | − | 36.6274i | − | 1.23401i | −0.786960 | − | 0.617005i | \(-0.788346\pi\) | ||
0.786960 | − | 0.617005i | \(-0.211654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.615224 | − | 0.615224i | 0.0207039 | − | 0.0207039i | −0.696679 | − | 0.717383i | \(-0.745340\pi\) |
0.717383 | + | 0.696679i | \(0.245340\pi\) | |||||||
\(884\) | −27.3137 | −0.918659 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9706 | −0.973285 | ||||||||
\(887\) | −14.2721 | + | 14.2721i | −0.479209 | + | 0.479209i | −0.904879 | − | 0.425669i | \(-0.860039\pi\) |
0.425669 | + | 0.904879i | \(0.360039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.17157i | − | 0.173449i | ||||||
\(890\) | −6.24264 | + | 18.7279i | −0.209254 | + | 0.627761i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.3137 | + | 15.3137i | 0.512741 | + | 0.512741i | ||||
\(893\) | −2.14214 | − | 2.14214i | −0.0716838 | − | 0.0716838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.8284 | + | 19.4142i | −1.29789 | + | 0.648946i | ||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.17157 | − | 6.17157i | 0.205948 | − | 0.205948i | ||||
\(899\) | −49.4558 | −1.64944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.9706 | −1.23167 | ||||||||
\(902\) | 21.3137 | − | 21.3137i | 0.709669 | − | 0.709669i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.0000i | − | 0.532152i | ||||||
\(905\) | 9.85786 | − | 4.92893i | 0.327686 | − | 0.163843i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.4142 | + | 22.4142i | 0.744252 | + | 0.744252i | 0.973393 | − | 0.229141i | \(-0.0735918\pi\) |
−0.229141 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(908\) | −6.82843 | − | 6.82843i | −0.226609 | − | 0.226609i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 12.0000i | −0.132599 | + | 0.397796i | ||||
\(911\) | − | 4.00000i | − | 0.132526i | −0.997802 | − | 0.0662630i | \(-0.978892\pi\) | ||
0.997802 | − | 0.0662630i | \(-0.0211076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.4853 | − | 16.4853i | 0.545583 | − | 0.545583i | ||||
\(914\) | 11.0711 | 0.366198 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.242641 | 0.00801707 | ||||||||
\(917\) | −0.343146 | + | 0.343146i | −0.0113317 | + | 0.0113317i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.2010i | − | 0.534422i | −0.963638 | − | 0.267211i | \(-0.913898\pi\) | ||
0.963638 | − | 0.267211i | \(-0.0861021\pi\) | |||||||
\(920\) | −1.17157 | − | 2.34315i | −0.0386256 | − | 0.0772512i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.2426 | − | 12.2426i | −0.403190 | − | 0.403190i | ||||
\(923\) | −27.3137 | − | 27.3137i | −0.899042 | − | 0.899042i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6985 | + | 2.24264i | −0.516163 | + | 0.0737376i | ||||
\(926\) | − | 28.0000i | − | 0.920137i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.41421 | − | 3.41421i | 0.112077 | − | 0.112077i | ||||
\(929\) | −46.9706 | −1.54105 | −0.770527 | − | 0.637407i | \(-0.780007\pi\) | ||||
−0.770527 | + | 0.637407i | \(0.780007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 9.17157 | − | 9.17157i | 0.300425 | − | 0.300425i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.7990i | 0.647843i | ||||||||
\(935\) | 34.9706 | + | 11.6569i | 1.14366 | + | 0.381220i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.2132 | + | 13.2132i | 0.431657 | + | 0.431657i | 0.889192 | − | 0.457535i | \(-0.151268\pi\) |
−0.457535 | + | 0.889192i | \(0.651268\pi\) | |||||||
\(938\) | 5.58579 | + | 5.58579i | 0.182382 | + | 0.182382i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.27208 | + | 0.757359i | 0.0741070 | + | 0.0247023i | ||||
\(941\) | 46.2843i | 1.50882i | 0.656401 | + | 0.754412i | \(0.272078\pi\) | ||||
−0.656401 | + | 0.754412i | \(0.727922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.31371 | − | 7.31371i | 0.238167 | − | 0.238167i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.9706 | 1.26704 | ||||||||
\(947\) | 18.2426 | − | 18.2426i | 0.592806 | − | 0.592806i | −0.345582 | − | 0.938388i | \(-0.612319\pi\) |
0.938388 | + | 0.345582i | \(0.112319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.5685i | 1.83629i | ||||||||
\(950\) | −14.0000 | + | 2.00000i | −0.454220 | + | 0.0648886i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.41421 | − | 3.41421i | −0.110655 | − | 0.110655i | ||||
\(953\) | −36.2426 | − | 36.2426i | −1.17401 | − | 1.17401i | −0.981244 | − | 0.192770i | \(-0.938253\pi\) |
−0.192770 | − | 0.981244i | \(-0.561747\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.6569 | − | 51.3137i | −0.830236 | − | 1.66047i | ||||
\(956\) | − | 2.34315i | − | 0.0757827i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.5563 | − | 17.5563i | 0.567220 | − | 0.567220i | ||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | −12.6863 | + | 12.6863i | −0.409022 | + | 0.409022i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 24.1421i | − | 0.777566i | ||||||
\(965\) | 3.48528 | − | 10.4558i | 0.112195 | − | 0.336586i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.2843 | − | 36.2843i | −1.16682 | − | 1.16682i | −0.982950 | − | 0.183874i | \(-0.941136\pi\) |
−0.183874 | − | 0.982950i | \(-0.558864\pi\) | |||||||
\(968\) | 0.464466 | + | 0.464466i | 0.0149285 | + | 0.0149285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.9706 | − | 10.4853i | 0.673324 | − | 0.336662i | ||||
\(971\) | 36.0000i | 1.15529i | 0.816286 | + | 0.577647i | \(0.196029\pi\) | ||||
−0.816286 | + | 0.577647i | \(0.803971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.48528 | + | 4.48528i | −0.143792 | + | 0.143792i | ||||
\(974\) | −21.1716 | −0.678381 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.89949 | −0.316875 | ||||||||
\(977\) | −0.970563 | + | 0.970563i | −0.0310511 | + | 0.0310511i | −0.722462 | − | 0.691411i | \(-0.756990\pi\) |
0.691411 | + | 0.722462i | \(0.256990\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.1421i | − | 0.963347i | ||||||
\(980\) | −2.00000 | + | 1.00000i | −0.0638877 | + | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.899495 | + | 0.899495i | 0.0287040 | + | 0.0287040i | ||||
\(983\) | 9.44365 | + | 9.44365i | 0.301206 | + | 0.301206i | 0.841485 | − | 0.540280i | \(-0.181682\pi\) |
−0.540280 | + | 0.841485i | \(0.681682\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.75736 | − | 5.27208i | 0.0559941 | − | 0.167982i | ||||
\(986\) | 23.3137i | 0.742460i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.3137 | + | 11.3137i | −0.359937 | + | 0.359937i | ||||
\(989\) | 13.3726 | 0.425223 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.85786 | −0.0590170 | −0.0295085 | − | 0.999565i | \(-0.509394\pi\) | ||||
−0.0295085 | + | 0.999565i | \(0.509394\pi\) | |||||||
\(992\) | −7.24264 | + | 7.24264i | −0.229954 | + | 0.229954i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 6.82843i | − | 0.216585i | ||||||
\(995\) | −23.8995 | − | 47.7990i | −0.757665 | − | 1.51533i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8995 | − | 17.8995i | −0.566883 | − | 0.566883i | 0.364371 | − | 0.931254i | \(-0.381284\pi\) |
−0.931254 | + | 0.364371i | \(0.881284\pi\) | |||||||
\(998\) | 19.4142 | + | 19.4142i | 0.614546 | + | 0.614546i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.m.a.197.2 | ✓ | 4 | |
3.2 | odd | 2 | 630.2.m.b.197.1 | yes | 4 | ||
5.2 | odd | 4 | 3150.2.m.a.2843.2 | 4 | |||
5.3 | odd | 4 | 630.2.m.b.323.1 | yes | 4 | ||
5.4 | even | 2 | 3150.2.m.b.1457.1 | 4 | |||
15.2 | even | 4 | 3150.2.m.b.2843.1 | 4 | |||
15.8 | even | 4 | inner | 630.2.m.a.323.2 | yes | 4 | |
15.14 | odd | 2 | 3150.2.m.a.1457.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.a.197.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
630.2.m.a.323.2 | yes | 4 | 15.8 | even | 4 | inner | |
630.2.m.b.197.1 | yes | 4 | 3.2 | odd | 2 | ||
630.2.m.b.323.1 | yes | 4 | 5.3 | odd | 4 | ||
3150.2.m.a.1457.2 | 4 | 15.14 | odd | 2 | |||
3150.2.m.a.2843.2 | 4 | 5.2 | odd | 4 | |||
3150.2.m.b.1457.1 | 4 | 5.4 | even | 2 | |||
3150.2.m.b.2843.1 | 4 | 15.2 | even | 4 |