Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (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: | \(8.86339462436\) |
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 | 401.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.c.191.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 1.70711 | − | 0.292893i | 0.696923 | − | 0.119573i | ||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | −1.00000 | + | 1.41421i | −0.288675 | + | 0.408248i | ||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 2.82843 | − | 2.82843i | 0.755929 | − | 0.755929i | ||||
\(15\) | −0.292893 | − | 1.70711i | −0.0756247 | − | 0.440773i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.41421 | + | 1.41421i | 0.342997 | + | 0.342997i | 0.857493 | − | 0.514496i | \(-0.172021\pi\) |
−0.514496 | + | 0.857493i | \(0.672021\pi\) | |||||||
\(18\) | −2.70711 | − | 1.29289i | −0.638071 | − | 0.304738i | ||||
\(19\) | 4.00000 | − | 4.00000i | 0.917663 | − | 0.917663i | −0.0791961 | − | 0.996859i | \(-0.525235\pi\) |
0.996859 | + | 0.0791961i | \(0.0252353\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | 5.65685 | + | 4.00000i | 1.23443 | + | 0.872872i | ||||
\(22\) | −1.00000 | + | 1.00000i | −0.213201 | + | 0.213201i | ||||
\(23\) | 1.41421 | + | 1.41421i | 0.294884 | + | 0.294884i | 0.839006 | − | 0.544122i | \(-0.183137\pi\) |
−0.544122 | + | 0.839006i | \(0.683137\pi\) | |||||||
\(24\) | −0.292893 | − | 1.70711i | −0.0597866 | − | 0.348462i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | 2.82843 | − | 2.82843i | 0.525226 | − | 0.525226i | −0.393919 | − | 0.919145i | \(-0.628881\pi\) |
0.919145 | + | 0.393919i | \(0.128881\pi\) | |||||||
\(30\) | 1.41421 | + | 1.00000i | 0.258199 | + | 0.182574i | ||||
\(31\) | −3.00000 | − | 3.00000i | −0.538816 | − | 0.538816i | 0.384365 | − | 0.923181i | \(-0.374420\pi\) |
−0.923181 | + | 0.384365i | \(0.874420\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.00000 | − | 1.41421i | −0.348155 | − | 0.246183i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −2.82843 | − | 2.82843i | −0.478091 | − | 0.478091i | ||||
\(36\) | 2.82843 | − | 1.00000i | 0.471405 | − | 0.166667i | ||||
\(37\) | −6.00000 | − | 1.00000i | −0.986394 | − | 0.164399i | ||||
\(38\) | 5.65685i | 0.917663i | ||||||||
\(39\) | 7.24264 | − | 1.24264i | 1.15975 | − | 0.198982i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −5.65685 | −0.883452 | −0.441726 | − | 0.897150i | \(-0.645634\pi\) | ||||
−0.441726 | + | 0.897150i | \(0.645634\pi\) | |||||||
\(42\) | −6.82843 | + | 1.17157i | −1.05365 | + | 0.180778i | ||||
\(43\) | 3.00000 | − | 3.00000i | 0.457496 | − | 0.457496i | −0.440337 | − | 0.897833i | \(-0.645141\pi\) |
0.897833 | + | 0.440337i | \(0.145141\pi\) | |||||||
\(44\) | − | 1.41421i | − | 0.213201i | ||||||
\(45\) | −1.29289 | + | 2.70711i | −0.192733 | + | 0.403552i | ||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | − | 1.41421i | − | 0.206284i | −0.994667 | − | 0.103142i | \(-0.967110\pi\) | ||
0.994667 | − | 0.103142i | \(-0.0328896\pi\) | |||||||
\(48\) | 1.41421 | + | 1.00000i | 0.204124 | + | 0.144338i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.100000 | − | 0.100000i | ||||
\(51\) | −0.585786 | − | 3.41421i | −0.0820265 | − | 0.478086i | ||||
\(52\) | 3.00000 | + | 3.00000i | 0.416025 | + | 0.416025i | ||||
\(53\) | 2.82843i | 0.388514i | 0.980951 | + | 0.194257i | \(0.0622296\pi\) | ||||
−0.980951 | + | 0.194257i | \(0.937770\pi\) | |||||||
\(54\) | 2.53553 | + | 4.53553i | 0.345042 | + | 0.617208i | ||||
\(55\) | 1.00000 | + | 1.00000i | 0.134840 | + | 0.134840i | ||||
\(56\) | −2.82843 | − | 2.82843i | −0.377964 | − | 0.377964i | ||||
\(57\) | −9.65685 | + | 1.65685i | −1.27908 | + | 0.219456i | ||||
\(58\) | 4.00000i | 0.525226i | ||||||||
\(59\) | −8.48528 | − | 8.48528i | −1.10469 | − | 1.10469i | −0.993837 | − | 0.110853i | \(-0.964642\pi\) |
−0.110853 | − | 0.993837i | \(-0.535358\pi\) | |||||||
\(60\) | −1.70711 | + | 0.292893i | −0.220387 | + | 0.0378124i | ||||
\(61\) | −6.00000 | − | 6.00000i | −0.768221 | − | 0.768221i | 0.209572 | − | 0.977793i | \(-0.432793\pi\) |
−0.977793 | + | 0.209572i | \(0.932793\pi\) | |||||||
\(62\) | 4.24264 | 0.538816 | ||||||||
\(63\) | −4.00000 | − | 11.3137i | −0.503953 | − | 1.42539i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.24264 | −0.526235 | ||||||||
\(66\) | 2.41421 | − | 0.414214i | 0.297169 | − | 0.0509862i | ||||
\(67\) | − | 6.00000i | − | 0.733017i | −0.930415 | − | 0.366508i | \(-0.880553\pi\) | ||
0.930415 | − | 0.366508i | \(-0.119447\pi\) | |||||||
\(68\) | 1.41421 | − | 1.41421i | 0.171499 | − | 0.171499i | ||||
\(69\) | −0.585786 | − | 3.41421i | −0.0705204 | − | 0.411023i | ||||
\(70\) | 4.00000 | 0.478091 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | −1.29289 | + | 2.70711i | −0.152369 | + | 0.319036i | ||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 4.94975 | − | 3.53553i | 0.575396 | − | 0.410997i | ||||
\(75\) | 1.00000 | − | 1.41421i | 0.115470 | − | 0.163299i | ||||
\(76\) | −4.00000 | − | 4.00000i | −0.458831 | − | 0.458831i | ||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | −4.24264 | + | 6.00000i | −0.480384 | + | 0.679366i | ||||
\(79\) | 5.00000 | − | 5.00000i | 0.562544 | − | 0.562544i | −0.367485 | − | 0.930029i | \(-0.619781\pi\) |
0.930029 | + | 0.367485i | \(0.119781\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 4.00000 | − | 4.00000i | 0.441726 | − | 0.441726i | ||||
\(83\) | − | 2.82843i | − | 0.310460i | −0.987878 | − | 0.155230i | \(-0.950388\pi\) | ||
0.987878 | − | 0.155230i | \(-0.0496119\pi\) | |||||||
\(84\) | 4.00000 | − | 5.65685i | 0.436436 | − | 0.617213i | ||||
\(85\) | 2.00000i | 0.216930i | ||||||||
\(86\) | 4.24264i | 0.457496i | ||||||||
\(87\) | −6.82843 | + | 1.17157i | −0.732084 | + | 0.125606i | ||||
\(88\) | 1.00000 | + | 1.00000i | 0.106600 | + | 0.106600i | ||||
\(89\) | −1.41421 | + | 1.41421i | −0.149906 | + | 0.149906i | −0.778076 | − | 0.628170i | \(-0.783804\pi\) |
0.628170 | + | 0.778076i | \(0.283804\pi\) | |||||||
\(90\) | −1.00000 | − | 2.82843i | −0.105409 | − | 0.298142i | ||||
\(91\) | 12.0000 | − | 12.0000i | 1.25794 | − | 1.25794i | ||||
\(92\) | 1.41421 | − | 1.41421i | 0.147442 | − | 0.147442i | ||||
\(93\) | 1.24264 | + | 7.24264i | 0.128856 | + | 0.751027i | ||||
\(94\) | 1.00000 | + | 1.00000i | 0.103142 | + | 0.103142i | ||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | −1.70711 | + | 0.292893i | −0.174231 | + | 0.0298933i | ||||
\(97\) | 6.00000 | − | 6.00000i | 0.609208 | − | 0.609208i | −0.333531 | − | 0.942739i | \(-0.608240\pi\) |
0.942739 | + | 0.333531i | \(0.108240\pi\) | |||||||
\(98\) | −6.36396 | + | 6.36396i | −0.642857 | + | 0.642857i | ||||
\(99\) | 1.41421 | + | 4.00000i | 0.142134 | + | 0.402015i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.41421 | 0.140720 | 0.0703598 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703598 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(102\) | 2.82843 | + | 2.00000i | 0.280056 | + | 0.198030i | ||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 1.17157 | + | 6.82843i | 0.114334 | + | 0.666386i | ||||
\(106\) | −2.00000 | − | 2.00000i | −0.194257 | − | 0.194257i | ||||
\(107\) | − | 8.48528i | − | 0.820303i | −0.912017 | − | 0.410152i | \(-0.865476\pi\) | ||
0.912017 | − | 0.410152i | \(-0.134524\pi\) | |||||||
\(108\) | −5.00000 | − | 1.41421i | −0.481125 | − | 0.136083i | ||||
\(109\) | 14.0000 | − | 14.0000i | 1.34096 | − | 1.34096i | 0.445848 | − | 0.895109i | \(-0.352902\pi\) |
0.895109 | − | 0.445848i | \(-0.147098\pi\) | |||||||
\(110\) | −1.41421 | −0.134840 | ||||||||
\(111\) | 7.48528 | + | 7.41421i | 0.710471 | + | 0.703726i | ||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 1.41421 | − | 1.41421i | 0.133038 | − | 0.133038i | −0.637452 | − | 0.770490i | \(-0.720012\pi\) |
0.770490 | + | 0.637452i | \(0.220012\pi\) | |||||||
\(114\) | 5.65685 | − | 8.00000i | 0.529813 | − | 0.749269i | ||||
\(115\) | 2.00000i | 0.186501i | ||||||||
\(116\) | −2.82843 | − | 2.82843i | −0.262613 | − | 0.262613i | ||||
\(117\) | −11.4853 | − | 5.48528i | −1.06181 | − | 0.507114i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −5.65685 | − | 5.65685i | −0.518563 | − | 0.518563i | ||||
\(120\) | 1.00000 | − | 1.41421i | 0.0912871 | − | 0.129099i | ||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 8.48528 | 0.768221 | ||||||||
\(123\) | 8.00000 | + | 5.65685i | 0.721336 | + | 0.510061i | ||||
\(124\) | −3.00000 | + | 3.00000i | −0.269408 | + | 0.269408i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 10.8284 | + | 5.17157i | 0.964673 | + | 0.460720i | ||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −7.24264 | + | 1.24264i | −0.637679 | + | 0.109408i | ||||
\(130\) | 3.00000 | − | 3.00000i | 0.263117 | − | 0.263117i | ||||
\(131\) | −2.82843 | + | 2.82843i | −0.247121 | + | 0.247121i | −0.819788 | − | 0.572667i | \(-0.805909\pi\) |
0.572667 | + | 0.819788i | \(0.305909\pi\) | |||||||
\(132\) | −1.41421 | + | 2.00000i | −0.123091 | + | 0.174078i | ||||
\(133\) | −16.0000 | + | 16.0000i | −1.38738 | + | 1.38738i | ||||
\(134\) | 4.24264 | + | 4.24264i | 0.366508 | + | 0.366508i | ||||
\(135\) | 4.53553 | − | 2.53553i | 0.390357 | − | 0.218224i | ||||
\(136\) | 2.00000i | 0.171499i | ||||||||
\(137\) | − | 21.2132i | − | 1.81237i | −0.422885 | − | 0.906183i | \(-0.638983\pi\) | ||
0.422885 | − | 0.906183i | \(-0.361017\pi\) | |||||||
\(138\) | 2.82843 | + | 2.00000i | 0.240772 | + | 0.170251i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −2.82843 | + | 2.82843i | −0.239046 | + | 0.239046i | ||||
\(141\) | −1.41421 | + | 2.00000i | −0.119098 | + | 0.168430i | ||||
\(142\) | −2.00000 | − | 2.00000i | −0.167836 | − | 0.167836i | ||||
\(143\) | −4.24264 | + | 4.24264i | −0.354787 | + | 0.354787i | ||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | 7.07107 | + | 7.07107i | 0.585206 | + | 0.585206i | ||||
\(147\) | −12.7279 | − | 9.00000i | −1.04978 | − | 0.742307i | ||||
\(148\) | −1.00000 | + | 6.00000i | −0.0821995 | + | 0.493197i | ||||
\(149\) | 18.3848i | 1.50614i | 0.657941 | + | 0.753070i | \(0.271428\pi\) | ||||
−0.657941 | + | 0.753070i | \(0.728572\pi\) | |||||||
\(150\) | 0.292893 | + | 1.70711i | 0.0239146 | + | 0.139385i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 5.65685 | 0.458831 | ||||||||
\(153\) | −2.58579 | + | 5.41421i | −0.209048 | + | 0.437713i | ||||
\(154\) | 4.00000 | − | 4.00000i | 0.322329 | − | 0.322329i | ||||
\(155\) | − | 4.24264i | − | 0.340777i | ||||||
\(156\) | −1.24264 | − | 7.24264i | −0.0994909 | − | 0.579875i | ||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 7.07107i | 0.562544i | ||||||||
\(159\) | 2.82843 | − | 4.00000i | 0.224309 | − | 0.317221i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −5.65685 | − | 5.65685i | −0.445823 | − | 0.445823i | ||||
\(162\) | 0.949747 | − | 8.94975i | 0.0746192 | − | 0.703159i | ||||
\(163\) | −15.0000 | − | 15.0000i | −1.17489 | − | 1.17489i | −0.981029 | − | 0.193862i | \(-0.937899\pi\) |
−0.193862 | − | 0.981029i | \(-0.562101\pi\) | |||||||
\(164\) | 5.65685i | 0.441726i | ||||||||
\(165\) | −0.414214 | − | 2.41421i | −0.0322465 | − | 0.187946i | ||||
\(166\) | 2.00000 | + | 2.00000i | 0.155230 | + | 0.155230i | ||||
\(167\) | −1.41421 | − | 1.41421i | −0.109435 | − | 0.109435i | 0.650269 | − | 0.759704i | \(-0.274656\pi\) |
−0.759704 | + | 0.650269i | \(0.774656\pi\) | |||||||
\(168\) | 1.17157 | + | 6.82843i | 0.0903888 | + | 0.526825i | ||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | −1.41421 | − | 1.41421i | −0.108465 | − | 0.108465i | ||||
\(171\) | 15.3137 | + | 7.31371i | 1.17107 | + | 0.559293i | ||||
\(172\) | −3.00000 | − | 3.00000i | −0.228748 | − | 0.228748i | ||||
\(173\) | 19.7990 | 1.50529 | 0.752645 | − | 0.658427i | \(-0.228778\pi\) | ||||
0.752645 | + | 0.658427i | \(0.228778\pi\) | |||||||
\(174\) | 4.00000 | − | 5.65685i | 0.303239 | − | 0.428845i | ||||
\(175\) | − | 4.00000i | − | 0.302372i | ||||||
\(176\) | −1.41421 | −0.106600 | ||||||||
\(177\) | 3.51472 | + | 20.4853i | 0.264182 | + | 1.53977i | ||||
\(178\) | − | 2.00000i | − | 0.149906i | ||||||
\(179\) | 7.07107 | − | 7.07107i | 0.528516 | − | 0.528516i | −0.391613 | − | 0.920130i | \(-0.628083\pi\) |
0.920130 | + | 0.391613i | \(0.128083\pi\) | |||||||
\(180\) | 2.70711 | + | 1.29289i | 0.201776 | + | 0.0963666i | ||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 16.9706i | 1.25794i | ||||||||
\(183\) | 2.48528 | + | 14.4853i | 0.183717 | + | 1.07078i | ||||
\(184\) | 2.00000i | 0.147442i | ||||||||
\(185\) | −3.53553 | − | 4.94975i | −0.259938 | − | 0.363913i | ||||
\(186\) | −6.00000 | − | 4.24264i | −0.439941 | − | 0.311086i | ||||
\(187\) | 2.00000 | + | 2.00000i | 0.146254 | + | 0.146254i | ||||
\(188\) | −1.41421 | −0.103142 | ||||||||
\(189\) | −5.65685 | + | 20.0000i | −0.411476 | + | 1.45479i | ||||
\(190\) | −4.00000 | + | 4.00000i | −0.290191 | + | 0.290191i | ||||
\(191\) | 16.9706 | + | 16.9706i | 1.22795 | + | 1.22795i | 0.964739 | + | 0.263208i | \(0.0847804\pi\) |
0.263208 | + | 0.964739i | \(0.415220\pi\) | |||||||
\(192\) | 1.00000 | − | 1.41421i | 0.0721688 | − | 0.102062i | ||||
\(193\) | −12.0000 | + | 12.0000i | −0.863779 | + | 0.863779i | −0.991775 | − | 0.127996i | \(-0.959146\pi\) |
0.127996 | + | 0.991775i | \(0.459146\pi\) | |||||||
\(194\) | 8.48528i | 0.609208i | ||||||||
\(195\) | 6.00000 | + | 4.24264i | 0.429669 | + | 0.303822i | ||||
\(196\) | − | 9.00000i | − | 0.642857i | ||||||
\(197\) | 2.82843i | 0.201517i | 0.994911 | + | 0.100759i | \(0.0321270\pi\) | ||||
−0.994911 | + | 0.100759i | \(0.967873\pi\) | |||||||
\(198\) | −3.82843 | − | 1.82843i | −0.272074 | − | 0.129941i | ||||
\(199\) | 1.00000 | + | 1.00000i | 0.0708881 | + | 0.0708881i | 0.741662 | − | 0.670774i | \(-0.234038\pi\) |
−0.670774 | + | 0.741662i | \(0.734038\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.0500000 | + | 0.0500000i | ||||
\(201\) | −6.00000 | + | 8.48528i | −0.423207 | + | 0.598506i | ||||
\(202\) | −1.00000 | + | 1.00000i | −0.0703598 | + | 0.0703598i | ||||
\(203\) | −11.3137 | + | 11.3137i | −0.794067 | + | 0.794067i | ||||
\(204\) | −3.41421 | + | 0.585786i | −0.239043 | + | 0.0410133i | ||||
\(205\) | −4.00000 | − | 4.00000i | −0.279372 | − | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.58579 | + | 5.41421i | −0.179725 | + | 0.376314i | ||||
\(208\) | 3.00000 | − | 3.00000i | 0.208013 | − | 0.208013i | ||||
\(209\) | 5.65685 | − | 5.65685i | 0.391293 | − | 0.391293i | ||||
\(210\) | −5.65685 | − | 4.00000i | −0.390360 | − | 0.276026i | ||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 2.82843 | 0.194257 | ||||||||
\(213\) | 2.82843 | − | 4.00000i | 0.193801 | − | 0.274075i | ||||
\(214\) | 6.00000 | + | 6.00000i | 0.410152 | + | 0.410152i | ||||
\(215\) | 4.24264 | 0.289346 | ||||||||
\(216\) | 4.53553 | − | 2.53553i | 0.308604 | − | 0.172521i | ||||
\(217\) | 12.0000 | + | 12.0000i | 0.814613 | + | 0.814613i | ||||
\(218\) | 19.7990i | 1.34096i | ||||||||
\(219\) | −10.0000 | + | 14.1421i | −0.675737 | + | 0.955637i | ||||
\(220\) | 1.00000 | − | 1.00000i | 0.0674200 | − | 0.0674200i | ||||
\(221\) | −8.48528 | −0.570782 | ||||||||
\(222\) | −10.5355 | + | 0.0502525i | −0.707099 | + | 0.00337273i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | −2.82843 | + | 2.82843i | −0.188982 | + | 0.188982i | ||||
\(225\) | −2.82843 | + | 1.00000i | −0.188562 | + | 0.0666667i | ||||
\(226\) | 2.00000i | 0.133038i | ||||||||
\(227\) | −16.9706 | − | 16.9706i | −1.12638 | − | 1.12638i | −0.990762 | − | 0.135614i | \(-0.956699\pi\) |
−0.135614 | − | 0.990762i | \(-0.543301\pi\) | |||||||
\(228\) | 1.65685 | + | 9.65685i | 0.109728 | + | 0.639541i | ||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −1.41421 | − | 1.41421i | −0.0932505 | − | 0.0932505i | ||||
\(231\) | 8.00000 | + | 5.65685i | 0.526361 | + | 0.372194i | ||||
\(232\) | 4.00000 | 0.262613 | ||||||||
\(233\) | −12.7279 | −0.833834 | −0.416917 | − | 0.908945i | \(-0.636889\pi\) | ||||
−0.416917 | + | 0.908945i | \(0.636889\pi\) | |||||||
\(234\) | 12.0000 | − | 4.24264i | 0.784465 | − | 0.277350i | ||||
\(235\) | 1.00000 | − | 1.00000i | 0.0652328 | − | 0.0652328i | ||||
\(236\) | −8.48528 | + | 8.48528i | −0.552345 | + | 0.552345i | ||||
\(237\) | −12.0711 | + | 2.07107i | −0.784100 | + | 0.134530i | ||||
\(238\) | 8.00000 | 0.518563 | ||||||||
\(239\) | −14.1421 | − | 14.1421i | −0.914779 | − | 0.914779i | 0.0818647 | − | 0.996643i | \(-0.473912\pi\) |
−0.996643 | + | 0.0818647i | \(0.973912\pi\) | |||||||
\(240\) | 0.292893 | + | 1.70711i | 0.0189062 | + | 0.110193i | ||||
\(241\) | −13.0000 | + | 13.0000i | −0.837404 | + | 0.837404i | −0.988517 | − | 0.151113i | \(-0.951714\pi\) |
0.151113 | + | 0.988517i | \(0.451714\pi\) | |||||||
\(242\) | 6.36396 | − | 6.36396i | 0.409091 | − | 0.409091i | ||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | −6.00000 | + | 6.00000i | −0.384111 | + | 0.384111i | ||||
\(245\) | 6.36396 | + | 6.36396i | 0.406579 | + | 0.406579i | ||||
\(246\) | −9.65685 | + | 1.65685i | −0.615699 | + | 0.105637i | ||||
\(247\) | 24.0000i | 1.52708i | ||||||||
\(248\) | − | 4.24264i | − | 0.269408i | ||||||
\(249\) | −2.82843 | + | 4.00000i | −0.179244 | + | 0.253490i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −8.48528 | + | 8.48528i | −0.535586 | + | 0.535586i | −0.922229 | − | 0.386643i | \(-0.873635\pi\) |
0.386643 | + | 0.922229i | \(0.373635\pi\) | |||||||
\(252\) | −11.3137 | + | 4.00000i | −0.712697 | + | 0.251976i | ||||
\(253\) | 2.00000 | + | 2.00000i | 0.125739 | + | 0.125739i | ||||
\(254\) | −11.3137 | + | 11.3137i | −0.709885 | + | 0.709885i | ||||
\(255\) | 2.00000 | − | 2.82843i | 0.125245 | − | 0.177123i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9706 | + | 16.9706i | 1.05859 | + | 1.05859i | 0.998173 | + | 0.0604217i | \(0.0192445\pi\) |
0.0604217 | + | 0.998173i | \(0.480755\pi\) | |||||||
\(258\) | 4.24264 | − | 6.00000i | 0.264135 | − | 0.373544i | ||||
\(259\) | 24.0000 | + | 4.00000i | 1.49129 | + | 0.248548i | ||||
\(260\) | 4.24264i | 0.263117i | ||||||||
\(261\) | 10.8284 | + | 5.17157i | 0.670263 | + | 0.320112i | ||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | −26.8701 | −1.65688 | −0.828439 | − | 0.560079i | \(-0.810771\pi\) | ||||
−0.828439 | + | 0.560079i | \(0.810771\pi\) | |||||||
\(264\) | −0.414214 | − | 2.41421i | −0.0254931 | − | 0.148585i | ||||
\(265\) | −2.00000 | + | 2.00000i | −0.122859 | + | 0.122859i | ||||
\(266\) | − | 22.6274i | − | 1.38738i | ||||||
\(267\) | 3.41421 | − | 0.585786i | 0.208946 | − | 0.0358495i | ||||
\(268\) | −6.00000 | −0.366508 | ||||||||
\(269\) | 7.07107i | 0.431131i | 0.976489 | + | 0.215565i | \(0.0691594\pi\) | ||||
−0.976489 | + | 0.215565i | \(0.930841\pi\) | |||||||
\(270\) | −1.41421 | + | 5.00000i | −0.0860663 | + | 0.304290i | ||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | −1.41421 | − | 1.41421i | −0.0857493 | − | 0.0857493i | ||||
\(273\) | −28.9706 | + | 4.97056i | −1.75338 | + | 0.300832i | ||||
\(274\) | 15.0000 | + | 15.0000i | 0.906183 | + | 0.906183i | ||||
\(275\) | 1.41421i | 0.0852803i | ||||||||
\(276\) | −3.41421 | + | 0.585786i | −0.205512 | + | 0.0352602i | ||||
\(277\) | 15.0000 | + | 15.0000i | 0.901263 | + | 0.901263i | 0.995545 | − | 0.0942828i | \(-0.0300558\pi\) |
−0.0942828 | + | 0.995545i | \(0.530056\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.48528 | − | 11.4853i | 0.328395 | − | 0.687606i | ||||
\(280\) | − | 4.00000i | − | 0.239046i | ||||||
\(281\) | −4.24264 | − | 4.24264i | −0.253095 | − | 0.253095i | 0.569143 | − | 0.822238i | \(-0.307275\pi\) |
−0.822238 | + | 0.569143i | \(0.807275\pi\) | |||||||
\(282\) | −0.414214 | − | 2.41421i | −0.0246661 | − | 0.143764i | ||||
\(283\) | −21.0000 | − | 21.0000i | −1.24832 | − | 1.24832i | −0.956461 | − | 0.291859i | \(-0.905726\pi\) |
−0.291859 | − | 0.956461i | \(-0.594274\pi\) | |||||||
\(284\) | 2.82843 | 0.167836 | ||||||||
\(285\) | −8.00000 | − | 5.65685i | −0.473879 | − | 0.335083i | ||||
\(286\) | − | 6.00000i | − | 0.354787i | ||||||
\(287\) | 22.6274 | 1.33565 | ||||||||
\(288\) | 2.70711 | + | 1.29289i | 0.159518 | + | 0.0761845i | ||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | −2.82843 | + | 2.82843i | −0.166091 | + | 0.166091i | ||||
\(291\) | −14.4853 | + | 2.48528i | −0.849142 | + | 0.145690i | ||||
\(292\) | −10.0000 | −0.585206 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 15.3640 | − | 2.63604i | 0.896044 | − | 0.153737i | ||||
\(295\) | − | 12.0000i | − | 0.698667i | ||||||
\(296\) | −3.53553 | − | 4.94975i | −0.205499 | − | 0.287698i | ||||
\(297\) | 2.00000 | − | 7.07107i | 0.116052 | − | 0.410305i | ||||
\(298\) | −13.0000 | − | 13.0000i | −0.753070 | − | 0.753070i | ||||
\(299\) | −8.48528 | −0.490716 | ||||||||
\(300\) | −1.41421 | − | 1.00000i | −0.0816497 | − | 0.0577350i | ||||
\(301\) | −12.0000 | + | 12.0000i | −0.691669 | + | 0.691669i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.00000 | − | 1.41421i | −0.114897 | − | 0.0812444i | ||||
\(304\) | −4.00000 | + | 4.00000i | −0.229416 | + | 0.229416i | ||||
\(305\) | − | 8.48528i | − | 0.485866i | ||||||
\(306\) | −2.00000 | − | 5.65685i | −0.114332 | − | 0.323381i | ||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 5.65685i | 0.322329i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.00000 | + | 3.00000i | 0.170389 | + | 0.170389i | ||||
\(311\) | −14.1421 | + | 14.1421i | −0.801927 | + | 0.801927i | −0.983397 | − | 0.181470i | \(-0.941915\pi\) |
0.181470 | + | 0.983397i | \(0.441915\pi\) | |||||||
\(312\) | 6.00000 | + | 4.24264i | 0.339683 | + | 0.240192i | ||||
\(313\) | 24.0000 | − | 24.0000i | 1.35656 | − | 1.35656i | 0.478440 | − | 0.878120i | \(-0.341202\pi\) |
0.878120 | − | 0.478440i | \(-0.158798\pi\) | |||||||
\(314\) | 9.89949 | − | 9.89949i | 0.558661 | − | 0.558661i | ||||
\(315\) | 5.17157 | − | 10.8284i | 0.291385 | − | 0.610113i | ||||
\(316\) | −5.00000 | − | 5.00000i | −0.281272 | − | 0.281272i | ||||
\(317\) | 25.4558 | 1.42974 | 0.714871 | − | 0.699256i | \(-0.246485\pi\) | ||||
0.714871 | + | 0.699256i | \(0.246485\pi\) | |||||||
\(318\) | 0.828427 | + | 4.82843i | 0.0464559 | + | 0.270765i | ||||
\(319\) | 4.00000 | − | 4.00000i | 0.223957 | − | 0.223957i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | −8.48528 | + | 12.0000i | −0.473602 | + | 0.669775i | ||||
\(322\) | 8.00000 | 0.445823 | ||||||||
\(323\) | 11.3137 | 0.629512 | ||||||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | −3.00000 | − | 3.00000i | −0.166410 | − | 0.166410i | ||||
\(326\) | 21.2132 | 1.17489 | ||||||||
\(327\) | −33.7990 | + | 5.79899i | −1.86909 | + | 0.320685i | ||||
\(328\) | −4.00000 | − | 4.00000i | −0.220863 | − | 0.220863i | ||||
\(329\) | 5.65685i | 0.311872i | ||||||||
\(330\) | 2.00000 | + | 1.41421i | 0.110096 | + | 0.0778499i | ||||
\(331\) | −2.00000 | + | 2.00000i | −0.109930 | + | 0.109930i | −0.759932 | − | 0.650002i | \(-0.774768\pi\) |
0.650002 | + | 0.759932i | \(0.274768\pi\) | |||||||
\(332\) | −2.82843 | −0.155230 | ||||||||
\(333\) | −3.17157 | − | 17.9706i | −0.173801 | − | 0.984781i | ||||
\(334\) | 2.00000 | 0.109435 | ||||||||
\(335\) | 4.24264 | − | 4.24264i | 0.231800 | − | 0.231800i | ||||
\(336\) | −5.65685 | − | 4.00000i | −0.308607 | − | 0.218218i | ||||
\(337\) | − | 26.0000i | − | 1.41631i | −0.706057 | − | 0.708155i | \(-0.749528\pi\) | ||
0.706057 | − | 0.708155i | \(-0.250472\pi\) | |||||||
\(338\) | 3.53553 | + | 3.53553i | 0.192308 | + | 0.192308i | ||||
\(339\) | −3.41421 | + | 0.585786i | −0.185435 | + | 0.0318156i | ||||
\(340\) | 2.00000 | 0.108465 | ||||||||
\(341\) | −4.24264 | − | 4.24264i | −0.229752 | − | 0.229752i | ||||
\(342\) | −16.0000 | + | 5.65685i | −0.865181 | + | 0.305888i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 4.24264 | 0.228748 | ||||||||
\(345\) | 2.00000 | − | 2.82843i | 0.107676 | − | 0.152277i | ||||
\(346\) | −14.0000 | + | 14.0000i | −0.752645 | + | 0.752645i | ||||
\(347\) | −22.6274 | + | 22.6274i | −1.21470 | + | 1.21470i | −0.245241 | + | 0.969462i | \(0.578867\pi\) |
−0.969462 | + | 0.245241i | \(0.921133\pi\) | |||||||
\(348\) | 1.17157 | + | 6.82843i | 0.0628029 | + | 0.366042i | ||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 2.82843 | + | 2.82843i | 0.151186 | + | 0.151186i | ||||
\(351\) | 10.7574 | + | 19.2426i | 0.574185 | + | 1.02710i | ||||
\(352\) | 1.00000 | − | 1.00000i | 0.0533002 | − | 0.0533002i | ||||
\(353\) | 18.3848 | − | 18.3848i | 0.978523 | − | 0.978523i | −0.0212513 | − | 0.999774i | \(-0.506765\pi\) |
0.999774 | + | 0.0212513i | \(0.00676499\pi\) | |||||||
\(354\) | −16.9706 | − | 12.0000i | −0.901975 | − | 0.637793i | ||||
\(355\) | −2.00000 | + | 2.00000i | −0.106149 | + | 0.106149i | ||||
\(356\) | 1.41421 | + | 1.41421i | 0.0749532 | + | 0.0749532i | ||||
\(357\) | 2.34315 | + | 13.6569i | 0.124012 | + | 0.722797i | ||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | − | 22.6274i | − | 1.19423i | −0.802156 | − | 0.597115i | \(-0.796314\pi\) | ||
0.802156 | − | 0.597115i | \(-0.203686\pi\) | |||||||
\(360\) | −2.82843 | + | 1.00000i | −0.149071 | + | 0.0527046i | ||||
\(361\) | − | 13.0000i | − | 0.684211i | ||||||
\(362\) | −7.07107 | + | 7.07107i | −0.371647 | + | 0.371647i | ||||
\(363\) | 12.7279 | + | 9.00000i | 0.668043 | + | 0.472377i | ||||
\(364\) | −12.0000 | − | 12.0000i | −0.628971 | − | 0.628971i | ||||
\(365\) | 7.07107 | − | 7.07107i | 0.370117 | − | 0.370117i | ||||
\(366\) | −12.0000 | − | 8.48528i | −0.627250 | − | 0.443533i | ||||
\(367\) | −12.0000 | −0.626395 | −0.313197 | − | 0.949688i | \(-0.601400\pi\) | ||||
−0.313197 | + | 0.949688i | \(0.601400\pi\) | |||||||
\(368\) | −1.41421 | − | 1.41421i | −0.0737210 | − | 0.0737210i | ||||
\(369\) | −5.65685 | − | 16.0000i | −0.294484 | − | 0.832927i | ||||
\(370\) | 6.00000 | + | 1.00000i | 0.311925 | + | 0.0519875i | ||||
\(371\) | − | 11.3137i | − | 0.587378i | ||||||
\(372\) | 7.24264 | − | 1.24264i | 0.375513 | − | 0.0644279i | ||||
\(373\) | 22.0000i | 1.13912i | 0.821951 | + | 0.569558i | \(0.192886\pi\) | ||||
−0.821951 | + | 0.569558i | \(0.807114\pi\) | |||||||
\(374\) | −2.82843 | −0.146254 | ||||||||
\(375\) | 1.70711 | − | 0.292893i | 0.0881546 | − | 0.0151249i | ||||
\(376\) | 1.00000 | − | 1.00000i | 0.0515711 | − | 0.0515711i | ||||
\(377\) | 16.9706i | 0.874028i | ||||||||
\(378\) | −10.1421 | − | 18.1421i | −0.521655 | − | 0.933131i | ||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | − | 5.65685i | − | 0.290191i | ||||||
\(381\) | −22.6274 | − | 16.0000i | −1.15924 | − | 0.819705i | ||||
\(382\) | −24.0000 | −1.22795 | ||||||||
\(383\) | −16.9706 | − | 16.9706i | −0.867155 | − | 0.867155i | 0.125001 | − | 0.992157i | \(-0.460106\pi\) |
−0.992157 | + | 0.125001i | \(0.960106\pi\) | |||||||
\(384\) | 0.292893 | + | 1.70711i | 0.0149466 | + | 0.0871154i | ||||
\(385\) | −4.00000 | − | 4.00000i | −0.203859 | − | 0.203859i | ||||
\(386\) | − | 16.9706i | − | 0.863779i | ||||||
\(387\) | 11.4853 | + | 5.48528i | 0.583830 | + | 0.278833i | ||||
\(388\) | −6.00000 | − | 6.00000i | −0.304604 | − | 0.304604i | ||||
\(389\) | −16.9706 | − | 16.9706i | −0.860442 | − | 0.860442i | 0.130948 | − | 0.991389i | \(-0.458198\pi\) |
−0.991389 | + | 0.130948i | \(0.958198\pi\) | |||||||
\(390\) | −7.24264 | + | 1.24264i | −0.366745 | + | 0.0629236i | ||||
\(391\) | 4.00000i | 0.202289i | ||||||||
\(392\) | 6.36396 | + | 6.36396i | 0.321429 | + | 0.321429i | ||||
\(393\) | 6.82843 | − | 1.17157i | 0.344449 | − | 0.0590980i | ||||
\(394\) | −2.00000 | − | 2.00000i | −0.100759 | − | 0.100759i | ||||
\(395\) | 7.07107 | 0.355784 | ||||||||
\(396\) | 4.00000 | − | 1.41421i | 0.201008 | − | 0.0710669i | ||||
\(397\) | − | 22.0000i | − | 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(398\) | −1.41421 | −0.0708881 | ||||||||
\(399\) | 38.6274 | − | 6.62742i | 1.93379 | − | 0.331786i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | 4.24264 | − | 4.24264i | 0.211867 | − | 0.211867i | −0.593193 | − | 0.805060i | \(-0.702133\pi\) |
0.805060 | + | 0.593193i | \(0.202133\pi\) | |||||||
\(402\) | −1.75736 | − | 10.2426i | −0.0876491 | − | 0.510856i | ||||
\(403\) | 18.0000 | 0.896644 | ||||||||
\(404\) | − | 1.41421i | − | 0.0703598i | ||||||
\(405\) | −8.94975 | − | 0.949747i | −0.444717 | − | 0.0471933i | ||||
\(406\) | − | 16.0000i | − | 0.794067i | ||||||
\(407\) | −8.48528 | − | 1.41421i | −0.420600 | − | 0.0701000i | ||||
\(408\) | 2.00000 | − | 2.82843i | 0.0990148 | − | 0.140028i | ||||
\(409\) | −3.00000 | − | 3.00000i | −0.148340 | − | 0.148340i | 0.629036 | − | 0.777376i | \(-0.283450\pi\) |
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(410\) | 5.65685 | 0.279372 | ||||||||
\(411\) | −21.2132 | + | 30.0000i | −1.04637 | + | 1.47979i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.9411 | + | 33.9411i | 1.67013 | + | 1.67013i | ||||
\(414\) | −2.00000 | − | 5.65685i | −0.0982946 | − | 0.278019i | ||||
\(415\) | 2.00000 | − | 2.00000i | 0.0981761 | − | 0.0981761i | ||||
\(416\) | 4.24264i | 0.208013i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000i | 0.391293i | ||||||||
\(419\) | − | 32.5269i | − | 1.58904i | −0.607236 | − | 0.794522i | \(-0.707722\pi\) | ||
0.607236 | − | 0.794522i | \(-0.292278\pi\) | |||||||
\(420\) | 6.82843 | − | 1.17157i | 0.333193 | − | 0.0571669i | ||||
\(421\) | 20.0000 | + | 20.0000i | 0.974740 | + | 0.974740i | 0.999689 | − | 0.0249484i | \(-0.00794214\pi\) |
−0.0249484 | + | 0.999689i | \(0.507942\pi\) | |||||||
\(422\) | −5.65685 | + | 5.65685i | −0.275371 | + | 0.275371i | ||||
\(423\) | 4.00000 | − | 1.41421i | 0.194487 | − | 0.0687614i | ||||
\(424\) | −2.00000 | + | 2.00000i | −0.0971286 | + | 0.0971286i | ||||
\(425\) | −1.41421 | + | 1.41421i | −0.0685994 | + | 0.0685994i | ||||
\(426\) | 0.828427 | + | 4.82843i | 0.0401374 | + | 0.233938i | ||||
\(427\) | 24.0000 | + | 24.0000i | 1.16144 | + | 1.16144i | ||||
\(428\) | −8.48528 | −0.410152 | ||||||||
\(429\) | 10.2426 | − | 1.75736i | 0.494519 | − | 0.0848461i | ||||
\(430\) | −3.00000 | + | 3.00000i | −0.144673 | + | 0.144673i | ||||
\(431\) | −8.48528 | + | 8.48528i | −0.408722 | + | 0.408722i | −0.881293 | − | 0.472571i | \(-0.843326\pi\) |
0.472571 | + | 0.881293i | \(0.343326\pi\) | |||||||
\(432\) | −1.41421 | + | 5.00000i | −0.0680414 | + | 0.240563i | ||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | −16.9706 | −0.814613 | ||||||||
\(435\) | −5.65685 | − | 4.00000i | −0.271225 | − | 0.191785i | ||||
\(436\) | −14.0000 | − | 14.0000i | −0.670478 | − | 0.670478i | ||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | −2.92893 | − | 17.0711i | −0.139950 | − | 0.815687i | ||||
\(439\) | 9.00000 | + | 9.00000i | 0.429547 | + | 0.429547i | 0.888474 | − | 0.458927i | \(-0.151766\pi\) |
−0.458927 | + | 0.888474i | \(0.651766\pi\) | |||||||
\(440\) | 1.41421i | 0.0674200i | ||||||||
\(441\) | 9.00000 | + | 25.4558i | 0.428571 | + | 1.21218i | ||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | 14.1421 | 0.671913 | 0.335957 | − | 0.941877i | \(-0.390940\pi\) | ||||
0.335957 | + | 0.941877i | \(0.390940\pi\) | |||||||
\(444\) | 7.41421 | − | 7.48528i | 0.351863 | − | 0.355236i | ||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | −5.65685 | + | 5.65685i | −0.267860 | + | 0.267860i | ||||
\(447\) | 18.3848 | − | 26.0000i | 0.869570 | − | 1.22976i | ||||
\(448\) | − | 4.00000i | − | 0.188982i | ||||||
\(449\) | 15.5563 | + | 15.5563i | 0.734150 | + | 0.734150i | 0.971439 | − | 0.237289i | \(-0.0762590\pi\) |
−0.237289 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(450\) | 1.29289 | − | 2.70711i | 0.0609476 | − | 0.127614i | ||||
\(451\) | −8.00000 | −0.376705 | ||||||||
\(452\) | −1.41421 | − | 1.41421i | −0.0665190 | − | 0.0665190i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 16.9706 | 0.795592 | ||||||||
\(456\) | −8.00000 | − | 5.65685i | −0.374634 | − | 0.264906i | ||||
\(457\) | −30.0000 | + | 30.0000i | −1.40334 | + | 1.40334i | −0.614157 | + | 0.789184i | \(0.710504\pi\) |
−0.789184 | + | 0.614157i | \(0.789496\pi\) | |||||||
\(458\) | −7.07107 | + | 7.07107i | −0.330409 | + | 0.330409i | ||||
\(459\) | 9.07107 | − | 5.07107i | 0.423401 | − | 0.236697i | ||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 4.24264 | + | 4.24264i | 0.197599 | + | 0.197599i | 0.798970 | − | 0.601371i | \(-0.205378\pi\) |
−0.601371 | + | 0.798970i | \(0.705378\pi\) | |||||||
\(462\) | −9.65685 | + | 1.65685i | −0.449278 | + | 0.0770838i | ||||
\(463\) | −4.00000 | + | 4.00000i | −0.185896 | + | 0.185896i | −0.793919 | − | 0.608023i | \(-0.791963\pi\) |
0.608023 | + | 0.793919i | \(0.291963\pi\) | |||||||
\(464\) | −2.82843 | + | 2.82843i | −0.131306 | + | 0.131306i | ||||
\(465\) | −4.24264 | + | 6.00000i | −0.196748 | + | 0.278243i | ||||
\(466\) | 9.00000 | − | 9.00000i | 0.416917 | − | 0.416917i | ||||
\(467\) | 22.6274 | + | 22.6274i | 1.04707 | + | 1.04707i | 0.998836 | + | 0.0482360i | \(0.0153600\pi\) |
0.0482360 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(468\) | −5.48528 | + | 11.4853i | −0.253557 | + | 0.530907i | ||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 1.41421i | 0.0652328i | ||||||||
\(471\) | 19.7990 | + | 14.0000i | 0.912289 | + | 0.645086i | ||||
\(472\) | − | 12.0000i | − | 0.552345i | ||||||
\(473\) | 4.24264 | − | 4.24264i | 0.195077 | − | 0.195077i | ||||
\(474\) | 7.07107 | − | 10.0000i | 0.324785 | − | 0.459315i | ||||
\(475\) | 4.00000 | + | 4.00000i | 0.183533 | + | 0.183533i | ||||
\(476\) | −5.65685 | + | 5.65685i | −0.259281 | + | 0.259281i | ||||
\(477\) | −8.00000 | + | 2.82843i | −0.366295 | + | 0.129505i | ||||
\(478\) | 20.0000 | 0.914779 | ||||||||
\(479\) | −11.3137 | − | 11.3137i | −0.516937 | − | 0.516937i | 0.399707 | − | 0.916643i | \(-0.369112\pi\) |
−0.916643 | + | 0.399707i | \(0.869112\pi\) | |||||||
\(480\) | −1.41421 | − | 1.00000i | −0.0645497 | − | 0.0456435i | ||||
\(481\) | 21.0000 | − | 15.0000i | 0.957518 | − | 0.683941i | ||||
\(482\) | − | 18.3848i | − | 0.837404i | ||||||
\(483\) | 2.34315 | + | 13.6569i | 0.106617 | + | 0.621408i | ||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | 8.48528 | 0.385297 | ||||||||
\(486\) | −10.2929 | + | 11.7071i | −0.466895 | + | 0.531045i | ||||
\(487\) | 8.00000 | − | 8.00000i | 0.362515 | − | 0.362515i | −0.502223 | − | 0.864738i | \(-0.667484\pi\) |
0.864738 | + | 0.502223i | \(0.167484\pi\) | |||||||
\(488\) | − | 8.48528i | − | 0.384111i | ||||||
\(489\) | 6.21320 | + | 36.2132i | 0.280971 | + | 1.63762i | ||||
\(490\) | −9.00000 | −0.406579 | ||||||||
\(491\) | − | 12.7279i | − | 0.574403i | −0.957870 | − | 0.287202i | \(-0.907275\pi\) | ||
0.957870 | − | 0.287202i | \(-0.0927249\pi\) | |||||||
\(492\) | 5.65685 | − | 8.00000i | 0.255031 | − | 0.360668i | ||||
\(493\) | 8.00000 | 0.360302 | ||||||||
\(494\) | −16.9706 | − | 16.9706i | −0.763542 | − | 0.763542i | ||||
\(495\) | −1.82843 | + | 3.82843i | −0.0821817 | + | 0.172075i | ||||
\(496\) | 3.00000 | + | 3.00000i | 0.134704 | + | 0.134704i | ||||
\(497\) | − | 11.3137i | − | 0.507489i | ||||||
\(498\) | −0.828427 | − | 4.82843i | −0.0371227 | − | 0.216367i | ||||
\(499\) | 6.00000 | + | 6.00000i | 0.268597 | + | 0.268597i | 0.828535 | − | 0.559938i | \(-0.189175\pi\) |
−0.559938 | + | 0.828535i | \(0.689175\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | 0.585786 | + | 3.41421i | 0.0261710 | + | 0.152536i | ||||
\(502\) | − | 12.0000i | − | 0.535586i | ||||||
\(503\) | 7.07107 | + | 7.07107i | 0.315283 | + | 0.315283i | 0.846952 | − | 0.531669i | \(-0.178435\pi\) |
−0.531669 | + | 0.846952i | \(0.678435\pi\) | |||||||
\(504\) | 5.17157 | − | 10.8284i | 0.230360 | − | 0.482336i | ||||
\(505\) | 1.00000 | + | 1.00000i | 0.0444994 | + | 0.0444994i | ||||
\(506\) | −2.82843 | −0.125739 | ||||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | − | 16.0000i | − | 0.709885i | ||||||
\(509\) | 1.41421 | 0.0626839 | 0.0313420 | − | 0.999509i | \(-0.490022\pi\) | ||||
0.0313420 | + | 0.999509i | \(0.490022\pi\) | |||||||
\(510\) | 0.585786 | + | 3.41421i | 0.0259391 | + | 0.151184i | ||||
\(511\) | 40.0000i | 1.76950i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −14.3431 | − | 25.6569i | −0.633265 | − | 1.13278i | ||||
\(514\) | −24.0000 | −1.05859 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.24264 | + | 7.24264i | 0.0547042 | + | 0.318839i | ||||
\(517\) | − | 2.00000i | − | 0.0879599i | ||||||
\(518\) | −19.7990 | + | 14.1421i | −0.869918 | + | 0.621370i | ||||
\(519\) | −28.0000 | − | 19.7990i | −1.22906 | − | 0.869079i | ||||
\(520\) | −3.00000 | − | 3.00000i | −0.131559 | − | 0.131559i | ||||
\(521\) | 31.1127 | 1.36307 | 0.681536 | − | 0.731785i | \(-0.261312\pi\) | ||||
0.681536 | + | 0.731785i | \(0.261312\pi\) | |||||||
\(522\) | −11.3137 | + | 4.00000i | −0.495188 | + | 0.175075i | ||||
\(523\) | 21.0000 | − | 21.0000i | 0.918266 | − | 0.918266i | −0.0786374 | − | 0.996903i | \(-0.525057\pi\) |
0.996903 | + | 0.0786374i | \(0.0250569\pi\) | |||||||
\(524\) | 2.82843 | + | 2.82843i | 0.123560 | + | 0.123560i | ||||
\(525\) | −4.00000 | + | 5.65685i | −0.174574 | + | 0.246885i | ||||
\(526\) | 19.0000 | − | 19.0000i | 0.828439 | − | 0.828439i | ||||
\(527\) | − | 8.48528i | − | 0.369625i | ||||||
\(528\) | 2.00000 | + | 1.41421i | 0.0870388 | + | 0.0615457i | ||||
\(529\) | − | 19.0000i | − | 0.826087i | ||||||
\(530\) | − | 2.82843i | − | 0.122859i | ||||||
\(531\) | 15.5147 | − | 32.4853i | 0.673281 | − | 1.40974i | ||||
\(532\) | 16.0000 | + | 16.0000i | 0.693688 | + | 0.693688i | ||||
\(533\) | 16.9706 | − | 16.9706i | 0.735077 | − | 0.735077i | ||||
\(534\) | −2.00000 | + | 2.82843i | −0.0865485 | + | 0.122398i | ||||
\(535\) | 6.00000 | − | 6.00000i | 0.259403 | − | 0.259403i | ||||
\(536\) | 4.24264 | − | 4.24264i | 0.183254 | − | 0.183254i | ||||
\(537\) | −17.0711 | + | 2.92893i | −0.736671 | + | 0.126393i | ||||
\(538\) | −5.00000 | − | 5.00000i | −0.215565 | − | 0.215565i | ||||
\(539\) | 12.7279 | 0.548230 | ||||||||
\(540\) | −2.53553 | − | 4.53553i | −0.109112 | − | 0.195178i | ||||
\(541\) | −12.0000 | + | 12.0000i | −0.515920 | + | 0.515920i | −0.916334 | − | 0.400414i | \(-0.868866\pi\) |
0.400414 | + | 0.916334i | \(0.368866\pi\) | |||||||
\(542\) | 11.3137 | − | 11.3137i | 0.485965 | − | 0.485965i | ||||
\(543\) | −14.1421 | − | 10.0000i | −0.606897 | − | 0.429141i | ||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 19.7990 | 0.848096 | ||||||||
\(546\) | 16.9706 | − | 24.0000i | 0.726273 | − | 1.02711i | ||||
\(547\) | −3.00000 | − | 3.00000i | −0.128271 | − | 0.128271i | 0.640057 | − | 0.768328i | \(-0.278911\pi\) |
−0.768328 | + | 0.640057i | \(0.778911\pi\) | |||||||
\(548\) | −21.2132 | −0.906183 | ||||||||
\(549\) | 10.9706 | − | 22.9706i | 0.468212 | − | 0.980360i | ||||
\(550\) | −1.00000 | − | 1.00000i | −0.0426401 | − | 0.0426401i | ||||
\(551\) | − | 22.6274i | − | 0.963960i | ||||||
\(552\) | 2.00000 | − | 2.82843i | 0.0851257 | − | 0.120386i | ||||
\(553\) | −20.0000 | + | 20.0000i | −0.850487 | + | 0.850487i | ||||
\(554\) | −21.2132 | −0.901263 | ||||||||
\(555\) | 0.0502525 | + | 10.5355i | 0.00213310 | + | 0.447209i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421 | − | 1.41421i | 0.0599222 | − | 0.0599222i | −0.676511 | − | 0.736433i | \(-0.736509\pi\) |
0.736433 | + | 0.676511i | \(0.236509\pi\) | |||||||
\(558\) | 4.24264 | + | 12.0000i | 0.179605 | + | 0.508001i | ||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | 2.82843 | + | 2.82843i | 0.119523 | + | 0.119523i | ||||
\(561\) | −0.828427 | − | 4.82843i | −0.0349762 | − | 0.203856i | ||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 2.00000 | + | 1.41421i | 0.0842152 | + | 0.0595491i | ||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 29.6985 | 1.24832 | ||||||||
\(567\) | 28.0000 | − | 22.6274i | 1.17589 | − | 0.950262i | ||||
\(568\) | −2.00000 | + | 2.00000i | −0.0839181 | + | 0.0839181i | ||||
\(569\) | −29.6985 | + | 29.6985i | −1.24503 | + | 1.24503i | −0.287135 | + | 0.957890i | \(0.592703\pi\) |
−0.957890 | + | 0.287135i | \(0.907297\pi\) | |||||||
\(570\) | 9.65685 | − | 1.65685i | 0.404481 | − | 0.0693980i | ||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 4.24264 | + | 4.24264i | 0.177394 | + | 0.177394i | ||||
\(573\) | −7.02944 | − | 40.9706i | −0.293659 | − | 1.71157i | ||||
\(574\) | −16.0000 | + | 16.0000i | −0.667827 | + | 0.667827i | ||||
\(575\) | −1.41421 | + | 1.41421i | −0.0589768 | + | 0.0589768i | ||||
\(576\) | −2.82843 | + | 1.00000i | −0.117851 | + | 0.0416667i | ||||
\(577\) | 10.0000 | − | 10.0000i | 0.416305 | − | 0.416305i | −0.467623 | − | 0.883928i | \(-0.654889\pi\) |
0.883928 | + | 0.467623i | \(0.154889\pi\) | |||||||
\(578\) | 9.19239 | + | 9.19239i | 0.382353 | + | 0.382353i | ||||
\(579\) | 28.9706 | − | 4.97056i | 1.20398 | − | 0.206570i | ||||
\(580\) | − | 4.00000i | − | 0.166091i | ||||||
\(581\) | 11.3137i | 0.469372i | ||||||||
\(582\) | 8.48528 | − | 12.0000i | 0.351726 | − | 0.497416i | ||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 7.07107 | − | 7.07107i | 0.292603 | − | 0.292603i | ||||
\(585\) | −4.24264 | − | 12.0000i | −0.175412 | − | 0.496139i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.2843 | − | 28.2843i | 1.16742 | − | 1.16742i | 0.184604 | − | 0.982813i | \(-0.440900\pi\) |
0.982813 | − | 0.184604i | \(-0.0591002\pi\) | |||||||
\(588\) | −9.00000 | + | 12.7279i | −0.371154 | + | 0.524891i | ||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 8.48528 | + | 8.48528i | 0.349334 | + | 0.349334i | ||||
\(591\) | 2.82843 | − | 4.00000i | 0.116346 | − | 0.164538i | ||||
\(592\) | 6.00000 | + | 1.00000i | 0.246598 | + | 0.0410997i | ||||
\(593\) | − | 24.0416i | − | 0.987271i | −0.869669 | − | 0.493636i | \(-0.835668\pi\) | ||
0.869669 | − | 0.493636i | \(-0.164332\pi\) | |||||||
\(594\) | 3.58579 | + | 6.41421i | 0.147127 | + | 0.263178i | ||||
\(595\) | − | 8.00000i | − | 0.327968i | ||||||
\(596\) | 18.3848 | 0.753070 | ||||||||
\(597\) | −0.414214 | − | 2.41421i | −0.0169526 | − | 0.0988072i | ||||
\(598\) | 6.00000 | − | 6.00000i | 0.245358 | − | 0.245358i | ||||
\(599\) | − | 22.6274i | − | 0.924531i | −0.886742 | − | 0.462266i | \(-0.847037\pi\) | ||
0.886742 | − | 0.462266i | \(-0.152963\pi\) | |||||||
\(600\) | 1.70711 | − | 0.292893i | 0.0696923 | − | 0.0119573i | ||||
\(601\) | −42.0000 | −1.71322 | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | − | 16.9706i | − | 0.691669i | ||||||
\(603\) | 16.9706 | − | 6.00000i | 0.691095 | − | 0.244339i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.36396 | − | 6.36396i | −0.258732 | − | 0.258732i | ||||
\(606\) | 2.41421 | − | 0.414214i | 0.0980707 | − | 0.0168263i | ||||
\(607\) | −8.00000 | − | 8.00000i | −0.324710 | − | 0.324710i | 0.525861 | − | 0.850571i | \(-0.323743\pi\) |
−0.850571 | + | 0.525861i | \(0.823743\pi\) | |||||||
\(608\) | − | 5.65685i | − | 0.229416i | ||||||
\(609\) | 27.3137 | − | 4.68629i | 1.10681 | − | 0.189898i | ||||
\(610\) | 6.00000 | + | 6.00000i | 0.242933 | + | 0.242933i | ||||
\(611\) | 4.24264 | + | 4.24264i | 0.171639 | + | 0.171639i | ||||
\(612\) | 5.41421 | + | 2.58579i | 0.218857 | + | 0.104524i | ||||
\(613\) | − | 16.0000i | − | 0.646234i | −0.946359 | − | 0.323117i | \(-0.895269\pi\) | ||
0.946359 | − | 0.323117i | \(-0.104731\pi\) | |||||||
\(614\) | −19.7990 | − | 19.7990i | −0.799022 | − | 0.799022i | ||||
\(615\) | 1.65685 | + | 9.65685i | 0.0668108 | + | 0.389402i | ||||
\(616\) | −4.00000 | − | 4.00000i | −0.161165 | − | 0.161165i | ||||
\(617\) | 35.3553 | 1.42335 | 0.711676 | − | 0.702508i | \(-0.247936\pi\) | ||||
0.711676 | + | 0.702508i | \(0.247936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0000i | 0.803868i | 0.915669 | + | 0.401934i | \(0.131662\pi\) | ||||
−0.915669 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(620\) | −4.24264 | −0.170389 | ||||||||
\(621\) | 9.07107 | − | 5.07107i | 0.364009 | − | 0.203495i | ||||
\(622\) | − | 20.0000i | − | 0.801927i | ||||||
\(623\) | 5.65685 | − | 5.65685i | 0.226637 | − | 0.226637i | ||||
\(624\) | −7.24264 | + | 1.24264i | −0.289938 | + | 0.0497454i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 33.9411i | 1.35656i | ||||||||
\(627\) | −13.6569 | + | 2.34315i | −0.545402 | + | 0.0935762i | ||||
\(628\) | 14.0000i | 0.558661i | ||||||||
\(629\) | −7.07107 | − | 9.89949i | −0.281942 | − | 0.394719i | ||||
\(630\) | 4.00000 | + | 11.3137i | 0.159364 | + | 0.450749i | ||||
\(631\) | −11.0000 | − | 11.0000i | −0.437903 | − | 0.437903i | 0.453403 | − | 0.891306i | \(-0.350210\pi\) |
−0.891306 | + | 0.453403i | \(0.850210\pi\) | |||||||
\(632\) | 7.07107 | 0.281272 | ||||||||
\(633\) | −11.3137 | − | 8.00000i | −0.449680 | − | 0.317971i | ||||
\(634\) | −18.0000 | + | 18.0000i | −0.714871 | + | 0.714871i | ||||
\(635\) | 11.3137 | + | 11.3137i | 0.448971 | + | 0.448971i | ||||
\(636\) | −4.00000 | − | 2.82843i | −0.158610 | − | 0.112154i | ||||
\(637\) | −27.0000 | + | 27.0000i | −1.06978 | + | 1.06978i | ||||
\(638\) | 5.65685i | 0.223957i | ||||||||
\(639\) | −8.00000 | + | 2.82843i | −0.316475 | + | 0.111891i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 11.3137i | 0.446865i | 0.974719 | + | 0.223432i | \(0.0717262\pi\) | ||||
−0.974719 | + | 0.223432i | \(0.928274\pi\) | |||||||
\(642\) | −2.48528 | − | 14.4853i | −0.0980862 | − | 0.571688i | ||||
\(643\) | −25.0000 | − | 25.0000i | −0.985904 | − | 0.985904i | 0.0139983 | − | 0.999902i | \(-0.495544\pi\) |
−0.999902 | + | 0.0139983i | \(0.995544\pi\) | |||||||
\(644\) | −5.65685 | + | 5.65685i | −0.222911 | + | 0.222911i | ||||
\(645\) | −6.00000 | − | 4.24264i | −0.236250 | − | 0.167054i | ||||
\(646\) | −8.00000 | + | 8.00000i | −0.314756 | + | 0.314756i | ||||
\(647\) | −5.65685 | + | 5.65685i | −0.222394 | + | 0.222394i | −0.809506 | − | 0.587112i | \(-0.800265\pi\) |
0.587112 | + | 0.809506i | \(0.300265\pi\) | |||||||
\(648\) | −8.94975 | − | 0.949747i | −0.351579 | − | 0.0373096i | ||||
\(649\) | −12.0000 | − | 12.0000i | −0.471041 | − | 0.471041i | ||||
\(650\) | 4.24264 | 0.166410 | ||||||||
\(651\) | −4.97056 | − | 28.9706i | −0.194812 | − | 1.13545i | ||||
\(652\) | −15.0000 | + | 15.0000i | −0.587445 | + | 0.587445i | ||||
\(653\) | −12.7279 | + | 12.7279i | −0.498082 | + | 0.498082i | −0.910841 | − | 0.412758i | \(-0.864565\pi\) |
0.412758 | + | 0.910841i | \(0.364565\pi\) | |||||||
\(654\) | 19.7990 | − | 28.0000i | 0.774202 | − | 1.09489i | ||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 5.65685 | 0.220863 | ||||||||
\(657\) | 28.2843 | − | 10.0000i | 1.10347 | − | 0.390137i | ||||
\(658\) | −4.00000 | − | 4.00000i | −0.155936 | − | 0.155936i | ||||
\(659\) | −26.8701 | −1.04671 | −0.523354 | − | 0.852115i | \(-0.675320\pi\) | ||||
−0.523354 | + | 0.852115i | \(0.675320\pi\) | |||||||
\(660\) | −2.41421 | + | 0.414214i | −0.0939731 | + | 0.0161232i | ||||
\(661\) | −28.0000 | − | 28.0000i | −1.08907 | − | 1.08907i | −0.995624 | − | 0.0934498i | \(-0.970211\pi\) |
−0.0934498 | − | 0.995624i | \(-0.529789\pi\) | |||||||
\(662\) | − | 2.82843i | − | 0.109930i | ||||||
\(663\) | 12.0000 | + | 8.48528i | 0.466041 | + | 0.329541i | ||||
\(664\) | 2.00000 | − | 2.00000i | 0.0776151 | − | 0.0776151i | ||||
\(665\) | −22.6274 | −0.877454 | ||||||||
\(666\) | 14.9497 | + | 10.4645i | 0.579291 | + | 0.405490i | ||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | −1.41421 | + | 1.41421i | −0.0547176 | + | 0.0547176i | ||||
\(669\) | −11.3137 | − | 8.00000i | −0.437413 | − | 0.309298i | ||||
\(670\) | 6.00000i | 0.231800i | ||||||||
\(671\) | −8.48528 | − | 8.48528i | −0.327571 | − | 0.327571i | ||||
\(672\) | 6.82843 | − | 1.17157i | 0.263412 | − | 0.0451944i | ||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 18.3848 | + | 18.3848i | 0.708155 | + | 0.708155i | ||||
\(675\) | 5.00000 | + | 1.41421i | 0.192450 | + | 0.0544331i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −45.2548 | −1.73928 | −0.869642 | − | 0.493682i | \(-0.835651\pi\) | ||||
−0.869642 | + | 0.493682i | \(0.835651\pi\) | |||||||
\(678\) | 2.00000 | − | 2.82843i | 0.0768095 | − | 0.108625i | ||||
\(679\) | −24.0000 | + | 24.0000i | −0.921035 | + | 0.921035i | ||||
\(680\) | −1.41421 | + | 1.41421i | −0.0542326 | + | 0.0542326i | ||||
\(681\) | 7.02944 | + | 40.9706i | 0.269369 | + | 1.57000i | ||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | −33.9411 | − | 33.9411i | −1.29872 | − | 1.29872i | −0.929237 | − | 0.369484i | \(-0.879534\pi\) |
−0.369484 | − | 0.929237i | \(-0.620466\pi\) | |||||||
\(684\) | 7.31371 | − | 15.3137i | 0.279647 | − | 0.585534i | ||||
\(685\) | 15.0000 | − | 15.0000i | 0.573121 | − | 0.573121i | ||||
\(686\) | 5.65685 | − | 5.65685i | 0.215980 | − | 0.215980i | ||||
\(687\) | −14.1421 | − | 10.0000i | −0.539556 | − | 0.381524i | ||||
\(688\) | −3.00000 | + | 3.00000i | −0.114374 | + | 0.114374i | ||||
\(689\) | −8.48528 | − | 8.48528i | −0.323263 | − | 0.323263i | ||||
\(690\) | 0.585786 | + | 3.41421i | 0.0223005 | + | 0.129977i | ||||
\(691\) | 12.0000i | 0.456502i | 0.973602 | + | 0.228251i | \(0.0733006\pi\) | ||||
−0.973602 | + | 0.228251i | \(0.926699\pi\) | |||||||
\(692\) | − | 19.7990i | − | 0.752645i | ||||||
\(693\) | −5.65685 | − | 16.0000i | −0.214886 | − | 0.607790i | ||||
\(694\) | − | 32.0000i | − | 1.21470i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.65685 | − | 4.00000i | −0.214423 | − | 0.151620i | ||||
\(697\) | −8.00000 | − | 8.00000i | −0.303022 | − | 0.303022i | ||||
\(698\) | −4.24264 | + | 4.24264i | −0.160586 | + | 0.160586i | ||||
\(699\) | 18.0000 | + | 12.7279i | 0.680823 | + | 0.481414i | ||||
\(700\) | −4.00000 | −0.151186 | ||||||||
\(701\) | 21.2132 | + | 21.2132i | 0.801212 | + | 0.801212i | 0.983285 | − | 0.182073i | \(-0.0582808\pi\) |
−0.182073 | + | 0.983285i | \(0.558281\pi\) | |||||||
\(702\) | −21.2132 | − | 6.00000i | −0.800641 | − | 0.226455i | ||||
\(703\) | −28.0000 | + | 20.0000i | −1.05604 | + | 0.754314i | ||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | −2.41421 | + | 0.414214i | −0.0909245 | + | 0.0156002i | ||||
\(706\) | 26.0000i | 0.978523i | ||||||||
\(707\) | −5.65685 | −0.212748 | ||||||||
\(708\) | 20.4853 | − | 3.51472i | 0.769884 | − | 0.132091i | ||||
\(709\) | −14.0000 | + | 14.0000i | −0.525781 | + | 0.525781i | −0.919312 | − | 0.393531i | \(-0.871254\pi\) |
0.393531 | + | 0.919312i | \(0.371254\pi\) | |||||||
\(710\) | − | 2.82843i | − | 0.106149i | ||||||
\(711\) | 19.1421 | + | 9.14214i | 0.717886 | + | 0.342857i | ||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | − | 8.48528i | − | 0.317776i | ||||||
\(714\) | −11.3137 | − | 8.00000i | −0.423405 | − | 0.299392i | ||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | −7.07107 | − | 7.07107i | −0.264258 | − | 0.264258i | ||||
\(717\) | 5.85786 | + | 34.1421i | 0.218766 | + | 1.27506i | ||||
\(718\) | 16.0000 | + | 16.0000i | 0.597115 | + | 0.597115i | ||||
\(719\) | 14.1421i | 0.527413i | 0.964603 | + | 0.263706i | \(0.0849450\pi\) | ||||
−0.964603 | + | 0.263706i | \(0.915055\pi\) | |||||||
\(720\) | 1.29289 | − | 2.70711i | 0.0481833 | − | 0.100888i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.19239 | + | 9.19239i | 0.342105 | + | 0.342105i | ||||
\(723\) | 31.3848 | − | 5.38478i | 1.16721 | − | 0.200262i | ||||
\(724\) | − | 10.0000i | − | 0.371647i | ||||||
\(725\) | 2.82843 | + | 2.82843i | 0.105045 | + | 0.105045i | ||||
\(726\) | −15.3640 | + | 2.63604i | −0.570210 | + | 0.0978326i | ||||
\(727\) | −22.0000 | − | 22.0000i | −0.815935 | − | 0.815935i | 0.169581 | − | 0.985516i | \(-0.445758\pi\) |
−0.985516 | + | 0.169581i | \(0.945758\pi\) | |||||||
\(728\) | 16.9706 | 0.628971 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 10.0000i | 0.370117i | ||||||||
\(731\) | 8.48528 | 0.313839 | ||||||||
\(732\) | 14.4853 | − | 2.48528i | 0.535391 | − | 0.0918586i | ||||
\(733\) | 40.0000i | 1.47743i | 0.674016 | + | 0.738717i | \(0.264568\pi\) | ||||
−0.674016 | + | 0.738717i | \(0.735432\pi\) | |||||||
\(734\) | 8.48528 | − | 8.48528i | 0.313197 | − | 0.313197i | ||||
\(735\) | −2.63604 | − | 15.3640i | −0.0972318 | − | 0.566708i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | − | 8.48528i | − | 0.312559i | ||||||
\(738\) | 15.3137 | + | 7.31371i | 0.563705 | + | 0.269221i | ||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | −4.94975 | + | 3.53553i | −0.181956 | + | 0.129969i | ||||
\(741\) | 24.0000 | − | 33.9411i | 0.881662 | − | 1.24686i | ||||
\(742\) | 8.00000 | + | 8.00000i | 0.293689 | + | 0.293689i | ||||
\(743\) | −41.0122 | −1.50459 | −0.752296 | − | 0.658826i | \(-0.771054\pi\) | ||||
−0.752296 | + | 0.658826i | \(0.771054\pi\) | |||||||
\(744\) | −4.24264 | + | 6.00000i | −0.155543 | + | 0.219971i | ||||
\(745\) | −13.0000 | + | 13.0000i | −0.476283 | + | 0.476283i | ||||
\(746\) | −15.5563 | − | 15.5563i | −0.569558 | − | 0.569558i | ||||
\(747\) | 8.00000 | − | 2.82843i | 0.292705 | − | 0.103487i | ||||
\(748\) | 2.00000 | − | 2.00000i | 0.0731272 | − | 0.0731272i | ||||
\(749\) | 33.9411i | 1.24018i | ||||||||
\(750\) | −1.00000 | + | 1.41421i | −0.0365148 | + | 0.0516398i | ||||
\(751\) | 2.00000i | 0.0729810i | 0.999334 | + | 0.0364905i | \(0.0116179\pi\) | ||||
−0.999334 | + | 0.0364905i | \(0.988382\pi\) | |||||||
\(752\) | 1.41421i | 0.0515711i | ||||||||
\(753\) | 20.4853 | − | 3.51472i | 0.746525 | − | 0.128083i | ||||
\(754\) | −12.0000 | − | 12.0000i | −0.437014 | − | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.0000 | + | 5.65685i | 0.727393 | + | 0.205738i | ||||
\(757\) | 5.00000 | − | 5.00000i | 0.181728 | − | 0.181728i | −0.610380 | − | 0.792108i | \(-0.708983\pi\) |
0.792108 | + | 0.610380i | \(0.208983\pi\) | |||||||
\(758\) | −19.7990 | + | 19.7990i | −0.719132 | + | 0.719132i | ||||
\(759\) | −0.828427 | − | 4.82843i | −0.0300700 | − | 0.175261i | ||||
\(760\) | 4.00000 | + | 4.00000i | 0.145095 | + | 0.145095i | ||||
\(761\) | −5.65685 | −0.205061 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(762\) | 27.3137 | − | 4.68629i | 0.989471 | − | 0.169766i | ||||
\(763\) | −56.0000 | + | 56.0000i | −2.02734 | + | 2.02734i | ||||
\(764\) | 16.9706 | − | 16.9706i | 0.613973 | − | 0.613973i | ||||
\(765\) | −5.65685 | + | 2.00000i | −0.204524 | + | 0.0723102i | ||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 50.9117 | 1.83831 | ||||||||
\(768\) | −1.41421 | − | 1.00000i | −0.0510310 | − | 0.0360844i | ||||
\(769\) | −5.00000 | − | 5.00000i | −0.180305 | − | 0.180305i | 0.611184 | − | 0.791489i | \(-0.290694\pi\) |
−0.791489 | + | 0.611184i | \(0.790694\pi\) | |||||||
\(770\) | 5.65685 | 0.203859 | ||||||||
\(771\) | −7.02944 | − | 40.9706i | −0.253159 | − | 1.47552i | ||||
\(772\) | 12.0000 | + | 12.0000i | 0.431889 | + | 0.431889i | ||||
\(773\) | − | 28.2843i | − | 1.01731i | −0.860969 | − | 0.508657i | \(-0.830142\pi\) | ||
0.860969 | − | 0.508657i | \(-0.169858\pi\) | |||||||
\(774\) | −12.0000 | + | 4.24264i | −0.431331 | + | 0.152499i | ||||
\(775\) | 3.00000 | − | 3.00000i | 0.107763 | − | 0.107763i | ||||
\(776\) | 8.48528 | 0.304604 | ||||||||
\(777\) | −29.9411 | − | 29.6569i | −1.07413 | − | 1.06393i | ||||
\(778\) | 24.0000 | 0.860442 | ||||||||
\(779\) | −22.6274 | + | 22.6274i | −0.810711 | + | 0.810711i | ||||
\(780\) | 4.24264 | − | 6.00000i | 0.151911 | − | 0.214834i | ||||
\(781\) | 4.00000i | 0.143131i | ||||||||
\(782\) | −2.82843 | − | 2.82843i | −0.101144 | − | 0.101144i | ||||
\(783\) | −10.1421 | − | 18.1421i | −0.362450 | − | 0.648347i | ||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | −9.89949 | − | 9.89949i | −0.353328 | − | 0.353328i | ||||
\(786\) | −4.00000 | + | 5.65685i | −0.142675 | + | 0.201773i | ||||
\(787\) | 50.0000 | 1.78231 | 0.891154 | − | 0.453701i | \(-0.149897\pi\) | ||||
0.891154 | + | 0.453701i | \(0.149897\pi\) | |||||||
\(788\) | 2.82843 | 0.100759 | ||||||||
\(789\) | 38.0000 | + | 26.8701i | 1.35284 | + | 0.956599i | ||||
\(790\) | −5.00000 | + | 5.00000i | −0.177892 | + | 0.177892i | ||||
\(791\) | −5.65685 | + | 5.65685i | −0.201135 | + | 0.201135i | ||||
\(792\) | −1.82843 | + | 3.82843i | −0.0649703 | + | 0.136037i | ||||
\(793\) | 36.0000 | 1.27840 | ||||||||
\(794\) | 15.5563 | + | 15.5563i | 0.552074 | + | 0.552074i | ||||
\(795\) | 4.82843 | − | 0.828427i | 0.171247 | − | 0.0293813i | ||||
\(796\) | 1.00000 | − | 1.00000i | 0.0354441 | − | 0.0354441i | ||||
\(797\) | −29.6985 | + | 29.6985i | −1.05197 | + | 1.05197i | −0.0534012 | + | 0.998573i | \(0.517006\pi\) |
−0.998573 | + | 0.0534012i | \(0.982994\pi\) | |||||||
\(798\) | −22.6274 | + | 32.0000i | −0.801002 | + | 1.13279i | ||||
\(799\) | 2.00000 | − | 2.00000i | 0.0707549 | − | 0.0707549i | ||||
\(800\) | 0.707107 | + | 0.707107i | 0.0250000 | + | 0.0250000i | ||||
\(801\) | −5.41421 | − | 2.58579i | −0.191302 | − | 0.0913643i | ||||
\(802\) | 6.00000i | 0.211867i | ||||||||
\(803\) | − | 14.1421i | − | 0.499065i | ||||||
\(804\) | 8.48528 | + | 6.00000i | 0.299253 | + | 0.211604i | ||||
\(805\) | − | 8.00000i | − | 0.281963i | ||||||
\(806\) | −12.7279 | + | 12.7279i | −0.448322 | + | 0.448322i | ||||
\(807\) | 7.07107 | − | 10.0000i | 0.248913 | − | 0.352017i | ||||
\(808\) | 1.00000 | + | 1.00000i | 0.0351799 | + | 0.0351799i | ||||
\(809\) | −7.07107 | + | 7.07107i | −0.248606 | + | 0.248606i | −0.820398 | − | 0.571793i | \(-0.806248\pi\) |
0.571793 | + | 0.820398i | \(0.306248\pi\) | |||||||
\(810\) | 7.00000 | − | 5.65685i | 0.245955 | − | 0.198762i | ||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 11.3137 | + | 11.3137i | 0.397033 | + | 0.397033i | ||||
\(813\) | 22.6274 | + | 16.0000i | 0.793578 | + | 0.561144i | ||||
\(814\) | 7.00000 | − | 5.00000i | 0.245350 | − | 0.175250i | ||||
\(815\) | − | 21.2132i | − | 0.743066i | ||||||
\(816\) | 0.585786 | + | 3.41421i | 0.0205066 | + | 0.119521i | ||||
\(817\) | − | 24.0000i | − | 0.839654i | ||||||
\(818\) | 4.24264 | 0.148340 | ||||||||
\(819\) | 45.9411 | + | 21.9411i | 1.60531 | + | 0.766685i | ||||
\(820\) | −4.00000 | + | 4.00000i | −0.139686 | + | 0.139686i | ||||
\(821\) | 7.07107i | 0.246782i | 0.992358 | + | 0.123391i | \(0.0393769\pi\) | ||||
−0.992358 | + | 0.123391i | \(0.960623\pi\) | |||||||
\(822\) | −6.21320 | − | 36.2132i | −0.216710 | − | 1.26308i | ||||
\(823\) | −24.0000 | −0.836587 | −0.418294 | − | 0.908312i | \(-0.637372\pi\) | ||||
−0.418294 | + | 0.908312i | \(0.637372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.41421 | − | 2.00000i | 0.0492366 | − | 0.0696311i | ||||
\(826\) | −48.0000 | −1.67013 | ||||||||
\(827\) | 36.7696 | + | 36.7696i | 1.27860 | + | 1.27860i | 0.941450 | + | 0.337153i | \(0.109464\pi\) |
0.337153 | + | 0.941450i | \(0.390536\pi\) | |||||||
\(828\) | 5.41421 | + | 2.58579i | 0.188157 | + | 0.0898623i | ||||
\(829\) | −30.0000 | − | 30.0000i | −1.04194 | − | 1.04194i | −0.999081 | − | 0.0428621i | \(-0.986352\pi\) |
−0.0428621 | − | 0.999081i | \(-0.513648\pi\) | |||||||
\(830\) | 2.82843i | 0.0981761i | ||||||||
\(831\) | −6.21320 | − | 36.2132i | −0.215534 | − | 1.25622i | ||||
\(832\) | −3.00000 | − | 3.00000i | −0.104006 | − | 0.104006i | ||||
\(833\) | 12.7279 | + | 12.7279i | 0.440996 | + | 0.440996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.00000i | − | 0.0692129i | ||||||
\(836\) | −5.65685 | − | 5.65685i | −0.195646 | − | 0.195646i | ||||
\(837\) | −19.2426 | + | 10.7574i | −0.665123 | + | 0.371829i | ||||
\(838\) | 23.0000 | + | 23.0000i | 0.794522 | + | 0.794522i | ||||
\(839\) | −25.4558 | −0.878833 | −0.439417 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439417 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(840\) | −4.00000 | + | 5.65685i | −0.138013 | + | 0.195180i | ||||
\(841\) | 13.0000i | 0.448276i | ||||||||
\(842\) | −28.2843 | −0.974740 | ||||||||
\(843\) | 1.75736 | + | 10.2426i | 0.0605267 | + | 0.352775i | ||||
\(844\) | − | 8.00000i | − | 0.275371i | ||||||
\(845\) | 3.53553 | − | 3.53553i | 0.121626 | − | 0.121626i | ||||
\(846\) | −1.82843 | + | 3.82843i | −0.0628626 | + | 0.131624i | ||||
\(847\) | 36.0000 | 1.23697 | ||||||||
\(848\) | − | 2.82843i | − | 0.0971286i | ||||||
\(849\) | 8.69848 | + | 50.6985i | 0.298531 | + | 1.73997i | ||||
\(850\) | − | 2.00000i | − | 0.0685994i | ||||||
\(851\) | −7.07107 | − | 9.89949i | −0.242393 | − | 0.339350i | ||||
\(852\) | −4.00000 | − | 2.82843i | −0.137038 | − | 0.0969003i | ||||
\(853\) | 11.0000 | + | 11.0000i | 0.376633 | + | 0.376633i | 0.869886 | − | 0.493253i | \(-0.164192\pi\) |
−0.493253 | + | 0.869886i | \(0.664192\pi\) | |||||||
\(854\) | −33.9411 | −1.16144 | ||||||||
\(855\) | 5.65685 | + | 16.0000i | 0.193460 | + | 0.547188i | ||||
\(856\) | 6.00000 | − | 6.00000i | 0.205076 | − | 0.205076i | ||||
\(857\) | 15.5563 | + | 15.5563i | 0.531395 | + | 0.531395i | 0.920987 | − | 0.389593i | \(-0.127384\pi\) |
−0.389593 | + | 0.920987i | \(0.627384\pi\) | |||||||
\(858\) | −6.00000 | + | 8.48528i | −0.204837 | + | 0.289683i | ||||
\(859\) | −16.0000 | + | 16.0000i | −0.545913 | + | 0.545913i | −0.925256 | − | 0.379343i | \(-0.876150\pi\) |
0.379343 | + | 0.925256i | \(0.376150\pi\) | |||||||
\(860\) | − | 4.24264i | − | 0.144673i | ||||||
\(861\) | −32.0000 | − | 22.6274i | −1.09056 | − | 0.771140i | ||||
\(862\) | − | 12.0000i | − | 0.408722i | ||||||
\(863\) | 21.2132i | 0.722106i | 0.932545 | + | 0.361053i | \(0.117583\pi\) | ||||
−0.932545 | + | 0.361053i | \(0.882417\pi\) | |||||||
\(864\) | −2.53553 | − | 4.53553i | −0.0862606 | − | 0.154302i | ||||
\(865\) | 14.0000 | + | 14.0000i | 0.476014 | + | 0.476014i | ||||
\(866\) | 24.0416 | − | 24.0416i | 0.816968 | − | 0.816968i | ||||
\(867\) | −13.0000 | + | 18.3848i | −0.441503 | + | 0.624380i | ||||
\(868\) | 12.0000 | − | 12.0000i | 0.407307 | − | 0.407307i | ||||
\(869\) | 7.07107 | − | 7.07107i | 0.239870 | − | 0.239870i | ||||
\(870\) | 6.82843 | − | 1.17157i | 0.231505 | − | 0.0397200i | ||||
\(871\) | 18.0000 | + | 18.0000i | 0.609907 | + | 0.609907i | ||||
\(872\) | 19.7990 | 0.670478 | ||||||||
\(873\) | 22.9706 | + | 10.9706i | 0.777436 | + | 0.371297i | ||||
\(874\) | −8.00000 | + | 8.00000i | −0.270604 | + | 0.270604i | ||||
\(875\) | 2.82843 | − | 2.82843i | 0.0956183 | − | 0.0956183i | ||||
\(876\) | 14.1421 | + | 10.0000i | 0.477818 | + | 0.337869i | ||||
\(877\) | −36.0000 | −1.21563 | −0.607817 | − | 0.794077i | \(-0.707955\pi\) | ||||
−0.607817 | + | 0.794077i | \(0.707955\pi\) | |||||||
\(878\) | −12.7279 | −0.429547 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | − | 1.00000i | −0.0337100 | − | 0.0337100i | ||||
\(881\) | −33.9411 | −1.14351 | −0.571753 | − | 0.820426i | \(-0.693736\pi\) | ||||
−0.571753 | + | 0.820426i | \(0.693736\pi\) | |||||||
\(882\) | −24.3640 | − | 11.6360i | −0.820377 | − | 0.391806i | ||||
\(883\) | 21.0000 | + | 21.0000i | 0.706706 | + | 0.706706i | 0.965841 | − | 0.259135i | \(-0.0834374\pi\) |
−0.259135 | + | 0.965841i | \(0.583437\pi\) | |||||||
\(884\) | 8.48528i | 0.285391i | ||||||||
\(885\) | −12.0000 | + | 16.9706i | −0.403376 | + | 0.570459i | ||||
\(886\) | −10.0000 | + | 10.0000i | −0.335957 | + | 0.335957i | ||||
\(887\) | −49.4975 | −1.66196 | −0.830981 | − | 0.556300i | \(-0.812220\pi\) | ||||
−0.830981 | + | 0.556300i | \(0.812220\pi\) | |||||||
\(888\) | 0.0502525 | + | 10.5355i | 0.00168636 | + | 0.353549i | ||||
\(889\) | −64.0000 | −2.14649 | ||||||||
\(890\) | 1.41421 | − | 1.41421i | 0.0474045 | − | 0.0474045i | ||||
\(891\) | −9.89949 | + | 8.00000i | −0.331646 | + | 0.268010i | ||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | −5.65685 | − | 5.65685i | −0.189299 | − | 0.189299i | ||||
\(894\) | 5.38478 | + | 31.3848i | 0.180094 | + | 1.04966i | ||||
\(895\) | 10.0000 | 0.334263 | ||||||||
\(896\) | 2.82843 | + | 2.82843i | 0.0944911 | + | 0.0944911i | ||||
\(897\) | 12.0000 | + | 8.48528i | 0.400668 | + | 0.283315i | ||||
\(898\) | −22.0000 | −0.734150 | ||||||||
\(899\) | −16.9706 | −0.566000 | ||||||||
\(900\) | 1.00000 | + | 2.82843i | 0.0333333 | + | 0.0942809i | ||||
\(901\) | −4.00000 | + | 4.00000i | −0.133259 | + | 0.133259i | ||||
\(902\) | 5.65685 | − | 5.65685i | 0.188353 | − | 0.188353i | ||||
\(903\) | 28.9706 | − | 4.97056i | 0.964080 | − | 0.165410i | ||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | 7.07107 | + | 7.07107i | 0.235050 | + | 0.235050i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.0000 | − | 39.0000i | 1.29497 | − | 1.29497i | 0.363303 | − | 0.931671i | \(-0.381649\pi\) |
0.931671 | − | 0.363303i | \(-0.118351\pi\) | |||||||
\(908\) | −16.9706 | + | 16.9706i | −0.563188 | + | 0.563188i | ||||
\(909\) | 1.41421 | + | 4.00000i | 0.0469065 | + | 0.132672i | ||||
\(910\) | −12.0000 | + | 12.0000i | −0.397796 | + | 0.397796i | ||||
\(911\) | 8.48528 | + | 8.48528i | 0.281130 | + | 0.281130i | 0.833560 | − | 0.552430i | \(-0.186299\pi\) |
−0.552430 | + | 0.833560i | \(0.686299\pi\) | |||||||
\(912\) | 9.65685 | − | 1.65685i | 0.319770 | − | 0.0548639i | ||||
\(913\) | − | 4.00000i | − | 0.132381i | ||||||
\(914\) | − | 42.4264i | − | 1.40334i | ||||||
\(915\) | −8.48528 | + | 12.0000i | −0.280515 | + | 0.396708i | ||||
\(916\) | − | 10.0000i | − | 0.330409i | ||||||
\(917\) | 11.3137 | − | 11.3137i | 0.373612 | − | 0.373612i | ||||
\(918\) | −2.82843 | + | 10.0000i | −0.0933520 | + | 0.330049i | ||||
\(919\) | −33.0000 | − | 33.0000i | −1.08857 | − | 1.08857i | −0.995676 | − | 0.0928935i | \(-0.970388\pi\) |
−0.0928935 | − | 0.995676i | \(-0.529612\pi\) | |||||||
\(920\) | −1.41421 | + | 1.41421i | −0.0466252 | + | 0.0466252i | ||||
\(921\) | 28.0000 | − | 39.5980i | 0.922631 | − | 1.30480i | ||||
\(922\) | −6.00000 | −0.197599 | ||||||||
\(923\) | −8.48528 | − | 8.48528i | −0.279296 | − | 0.279296i | ||||
\(924\) | 5.65685 | − | 8.00000i | 0.186097 | − | 0.263181i | ||||
\(925\) | 1.00000 | − | 6.00000i | 0.0328798 | − | 0.197279i | ||||
\(926\) | − | 5.65685i | − | 0.185896i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 4.00000i | − | 0.131306i | ||||||
\(929\) | −59.3970 | −1.94875 | −0.974376 | − | 0.224927i | \(-0.927786\pi\) | ||||
−0.974376 | + | 0.224927i | \(0.927786\pi\) | |||||||
\(930\) | −1.24264 | − | 7.24264i | −0.0407478 | − | 0.237496i | ||||
\(931\) | 36.0000 | − | 36.0000i | 1.17985 | − | 1.17985i | ||||
\(932\) | 12.7279i | 0.416917i | ||||||||
\(933\) | 34.1421 | − | 5.85786i | 1.11776 | − | 0.191778i | ||||
\(934\) | −32.0000 | −1.04707 | ||||||||
\(935\) | 2.82843i | 0.0924995i | ||||||||
\(936\) | −4.24264 | − | 12.0000i | −0.138675 | − | 0.392232i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | −16.9706 | − | 16.9706i | −0.554109 | − | 0.554109i | ||||
\(939\) | −57.9411 | + | 9.94113i | −1.89084 | + | 0.324416i | ||||
\(940\) | −1.00000 | − | 1.00000i | −0.0326164 | − | 0.0326164i | ||||
\(941\) | − | 21.2132i | − | 0.691531i | −0.938321 | − | 0.345765i | \(-0.887619\pi\) | ||
0.938321 | − | 0.345765i | \(-0.112381\pi\) | |||||||
\(942\) | −23.8995 | + | 4.10051i | −0.778688 | + | 0.133602i | ||||
\(943\) | −8.00000 | − | 8.00000i | −0.260516 | − | 0.260516i | ||||
\(944\) | 8.48528 | + | 8.48528i | 0.276172 | + | 0.276172i | ||||
\(945\) | −18.1421 | + | 10.1421i | −0.590164 | + | 0.329924i | ||||
\(946\) | 6.00000i | 0.195077i | ||||||||
\(947\) | 36.7696 | + | 36.7696i | 1.19485 | + | 1.19485i | 0.975689 | + | 0.219161i | \(0.0703321\pi\) |
0.219161 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(948\) | 2.07107 | + | 12.0711i | 0.0672652 | + | 0.392050i | ||||
\(949\) | 30.0000 | + | 30.0000i | 0.973841 | + | 0.973841i | ||||
\(950\) | −5.65685 | −0.183533 | ||||||||
\(951\) | −36.0000 | − | 25.4558i | −1.16738 | − | 0.825462i | ||||
\(952\) | − | 8.00000i | − | 0.259281i | ||||||
\(953\) | −35.3553 | −1.14527 | −0.572636 | − | 0.819810i | \(-0.694079\pi\) | ||||
−0.572636 | + | 0.819810i | \(0.694079\pi\) | |||||||
\(954\) | 3.65685 | − | 7.65685i | 0.118395 | − | 0.247900i | ||||
\(955\) | 24.0000i | 0.776622i | ||||||||
\(956\) | −14.1421 | + | 14.1421i | −0.457389 | + | 0.457389i | ||||
\(957\) | −9.65685 | + | 1.65685i | −0.312162 | + | 0.0535585i | ||||
\(958\) | 16.0000 | 0.516937 | ||||||||
\(959\) | 84.8528i | 2.74004i | ||||||||
\(960\) | 1.70711 | − | 0.292893i | 0.0550966 | − | 0.00945309i | ||||
\(961\) | − | 13.0000i | − | 0.419355i | ||||||
\(962\) | −4.24264 | + | 25.4558i | −0.136788 | + | 0.820729i | ||||
\(963\) | 24.0000 | − | 8.48528i | 0.773389 | − | 0.273434i | ||||
\(964\) | 13.0000 | + | 13.0000i | 0.418702 | + | 0.418702i | ||||
\(965\) | −16.9706 | −0.546302 | ||||||||
\(966\) | −11.3137 | − | 8.00000i | −0.364013 | − | 0.257396i | ||||
\(967\) | 10.0000 | − | 10.0000i | 0.321578 | − | 0.321578i | −0.527794 | − | 0.849372i | \(-0.676981\pi\) |
0.849372 | + | 0.527794i | \(0.176981\pi\) | |||||||
\(968\) | −6.36396 | − | 6.36396i | −0.204545 | − | 0.204545i | ||||
\(969\) | −16.0000 | − | 11.3137i | −0.513994 | − | 0.363449i | ||||
\(970\) | −6.00000 | + | 6.00000i | −0.192648 | + | 0.192648i | ||||
\(971\) | − | 29.6985i | − | 0.953070i | −0.879156 | − | 0.476535i | \(-0.841893\pi\) | ||
0.879156 | − | 0.476535i | \(-0.158107\pi\) | |||||||
\(972\) | −1.00000 | − | 15.5563i | −0.0320750 | − | 0.498970i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.3137i | 0.362515i | ||||||||
\(975\) | 1.24264 | + | 7.24264i | 0.0397964 | + | 0.231950i | ||||
\(976\) | 6.00000 | + | 6.00000i | 0.192055 | + | 0.192055i | ||||
\(977\) | 42.4264 | − | 42.4264i | 1.35734 | − | 1.35734i | 0.480160 | − | 0.877181i | \(-0.340579\pi\) |
0.877181 | − | 0.480160i | \(-0.159421\pi\) | |||||||
\(978\) | −30.0000 | − | 21.2132i | −0.959294 | − | 0.678323i | ||||
\(979\) | −2.00000 | + | 2.00000i | −0.0639203 | + | 0.0639203i | ||||
\(980\) | 6.36396 | − | 6.36396i | 0.203289 | − | 0.203289i | ||||
\(981\) | 53.5980 | + | 25.5980i | 1.71125 | + | 0.817281i | ||||
\(982\) | 9.00000 | + | 9.00000i | 0.287202 | + | 0.287202i | ||||
\(983\) | 43.8406 | 1.39830 | 0.699149 | − | 0.714976i | \(-0.253562\pi\) | ||||
0.699149 | + | 0.714976i | \(0.253562\pi\) | |||||||
\(984\) | 1.65685 | + | 9.65685i | 0.0528186 | + | 0.307849i | ||||
\(985\) | −2.00000 | + | 2.00000i | −0.0637253 | + | 0.0637253i | ||||
\(986\) | −5.65685 | + | 5.65685i | −0.180151 | + | 0.180151i | ||||
\(987\) | 5.65685 | − | 8.00000i | 0.180060 | − | 0.254643i | ||||
\(988\) | 24.0000 | 0.763542 | ||||||||
\(989\) | 8.48528 | 0.269816 | ||||||||
\(990\) | −1.41421 | − | 4.00000i | −0.0449467 | − | 0.127128i | ||||
\(991\) | −21.0000 | − | 21.0000i | −0.667087 | − | 0.667087i | 0.289954 | − | 0.957041i | \(-0.406360\pi\) |
−0.957041 | + | 0.289954i | \(0.906360\pi\) | |||||||
\(992\) | −4.24264 | −0.134704 | ||||||||
\(993\) | 4.82843 | − | 0.828427i | 0.153226 | − | 0.0262893i | ||||
\(994\) | 8.00000 | + | 8.00000i | 0.253745 | + | 0.253745i | ||||
\(995\) | 1.41421i | 0.0448336i | ||||||||
\(996\) | 4.00000 | + | 2.82843i | 0.126745 | + | 0.0896221i | ||||
\(997\) | −23.0000 | + | 23.0000i | −0.728417 | + | 0.728417i | −0.970304 | − | 0.241887i | \(-0.922234\pi\) |
0.241887 | + | 0.970304i | \(0.422234\pi\) | |||||||
\(998\) | −8.48528 | −0.268597 | ||||||||
\(999\) | −13.4853 | + | 28.5858i | −0.426655 | + | 0.904414i |
(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 | 1110.2.u.c.401.1 | yes | 4 | |
3.2 | odd | 2 | inner | 1110.2.u.c.401.2 | yes | 4 | |
37.6 | odd | 4 | inner | 1110.2.u.c.191.2 | yes | 4 | |
111.80 | even | 4 | inner | 1110.2.u.c.191.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.c.191.1 | ✓ | 4 | 111.80 | even | 4 | inner | |
1110.2.u.c.191.2 | yes | 4 | 37.6 | odd | 4 | inner | |
1110.2.u.c.401.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1110.2.u.c.401.2 | yes | 4 | 3.2 | odd | 2 | inner |