Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, 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("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2843.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.2843 |
Dual form | 3150.2.m.h.1457.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 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 | 0 | ||||||||
\(11\) | 0.585786i | 0.176621i | 0.996093 | + | 0.0883106i | \(0.0281468\pi\) | ||||
−0.996093 | + | 0.0883106i | \(0.971853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.43916 | − | 3.43916i | −0.953851 | − | 0.953851i | 0.0451304 | − | 0.998981i | \(-0.485630\pi\) |
−0.998981 | + | 0.0451304i | \(0.985630\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.906908 | + | 0.906908i | 0.219957 | + | 0.219957i | 0.808480 | − | 0.588523i | \(-0.200290\pi\) |
−0.588523 | + | 0.808480i | \(0.700290\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.04989i | 0.470277i | 0.971962 | + | 0.235138i | \(0.0755543\pi\) | ||||
−0.971962 | + | 0.235138i | \(0.924446\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.414214 | − | 0.414214i | 0.0883106 | − | 0.0883106i | ||||
\(23\) | −0.257617 | + | 0.257617i | −0.0537169 | + | 0.0537169i | −0.733455 | − | 0.679738i | \(-0.762093\pi\) |
0.679738 | + | 0.733455i | \(0.262093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.86370i | 0.953851i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 1.75272 | 0.325471 | 0.162736 | − | 0.986670i | \(-0.447968\pi\) | ||||
0.162736 | + | 0.986670i | \(0.447968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.47531 | 0.264974 | 0.132487 | − | 0.991185i | \(-0.457704\pi\) | ||||
0.132487 | + | 0.991185i | \(0.457704\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.28256i | − | 0.219957i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.04989 | − | 4.04989i | 0.665797 | − | 0.665797i | −0.290943 | − | 0.956740i | \(-0.593969\pi\) |
0.956740 | + | 0.290943i | \(0.0939690\pi\) | |||||||
\(38\) | 1.44949 | − | 1.44949i | 0.235138 | − | 0.235138i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.84909i | 0.601127i | 0.953762 | + | 0.300564i | \(0.0971747\pi\) | ||||
−0.953762 | + | 0.300564i | \(0.902825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.10306 | − | 5.10306i | −0.778209 | − | 0.778209i | 0.201317 | − | 0.979526i | \(-0.435478\pi\) |
−0.979526 | + | 0.201317i | \(0.935478\pi\) | |||||||
\(44\) | −0.585786 | −0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.364326 | 0.0537169 | ||||||||
\(47\) | 5.49938 | + | 5.49938i | 0.802167 | + | 0.802167i | 0.983434 | − | 0.181267i | \(-0.0580199\pi\) |
−0.181267 | + | 0.983434i | \(0.558020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.43916 | − | 3.43916i | 0.476925 | − | 0.476925i | ||||
\(53\) | −5.02494 | + | 5.02494i | −0.690229 | + | 0.690229i | −0.962282 | − | 0.272053i | \(-0.912297\pi\) |
0.272053 | + | 0.962282i | \(0.412297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.23936 | − | 1.23936i | −0.162736 | − | 0.162736i | ||||
\(59\) | 11.1562 | 1.45242 | 0.726209 | − | 0.687474i | \(-0.241281\pi\) | ||||
0.726209 | + | 0.687474i | \(0.241281\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.78851 | 0.485069 | 0.242534 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242534 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(62\) | −1.04320 | − | 1.04320i | −0.132487 | − | 0.132487i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.74202 | − | 6.74202i | 0.823669 | − | 0.823669i | −0.162963 | − | 0.986632i | \(-0.552105\pi\) |
0.986632 | + | 0.162963i | \(0.0521053\pi\) | |||||||
\(68\) | −0.906908 | + | 0.906908i | −0.109979 | + | 0.109979i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9282i | 1.29694i | 0.761241 | + | 0.648470i | \(0.224591\pi\) | ||||
−0.761241 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.97469 | − | 5.97469i | −0.699285 | − | 0.699285i | 0.264971 | − | 0.964256i | \(-0.414637\pi\) |
−0.964256 | + | 0.264971i | \(0.914637\pi\) | |||||||
\(74\) | −5.72741 | −0.665797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.04989 | −0.235138 | ||||||||
\(77\) | −0.414214 | − | 0.414214i | −0.0472040 | − | 0.0472040i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.944060i | 0.106215i | 0.998589 | + | 0.0531075i | \(0.0169126\pi\) | ||||
−0.998589 | + | 0.0531075i | \(0.983087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.72172 | − | 2.72172i | 0.300564 | − | 0.300564i | ||||
\(83\) | 7.82050 | − | 7.82050i | 0.858411 | − | 0.858411i | −0.132740 | − | 0.991151i | \(-0.542377\pi\) |
0.991151 | + | 0.132740i | \(0.0423774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.21682i | 0.778209i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.414214 | + | 0.414214i | 0.0441553 | + | 0.0441553i | ||||
\(89\) | 0.0705524 | 0.00747854 | 0.00373927 | − | 0.999993i | \(-0.498810\pi\) | ||||
0.00373927 | + | 0.999993i | \(0.498810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.86370 | 0.509855 | ||||||||
\(92\) | −0.257617 | − | 0.257617i | −0.0268584 | − | 0.0268584i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 7.77729i | − | 0.802167i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.746663 | − | 0.746663i | 0.0758121 | − | 0.0758121i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.743996 | + | 0.668184i | \(0.232928\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.15696i | 0.413633i | 0.978380 | + | 0.206817i | \(0.0663103\pi\) | ||||
−0.978380 | + | 0.206817i | \(0.933690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.14198 | + | 3.14198i | 0.309589 | + | 0.309589i | 0.844750 | − | 0.535161i | \(-0.179749\pi\) |
−0.535161 | + | 0.844750i | \(0.679749\pi\) | |||||||
\(104\) | −4.86370 | −0.476925 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.10634 | 0.690229 | ||||||||
\(107\) | 6.84909 | + | 6.84909i | 0.662127 | + | 0.662127i | 0.955881 | − | 0.293754i | \(-0.0949047\pi\) |
−0.293754 | + | 0.955881i | \(0.594905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.9335i | 1.90929i | 0.297753 | + | 0.954643i | \(0.403763\pi\) | ||||
−0.297753 | + | 0.954643i | \(0.596237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −4.69677 | + | 4.69677i | −0.441835 | + | 0.441835i | −0.892628 | − | 0.450793i | \(-0.851141\pi\) |
0.450793 | + | 0.892628i | \(0.351141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.75272i | 0.162736i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.88865 | − | 7.88865i | −0.726209 | − | 0.726209i | ||||
\(119\) | −1.28256 | −0.117572 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6569 | 0.968805 | ||||||||
\(122\) | −2.67888 | − | 2.67888i | −0.242534 | − | 0.242534i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.47531i | 0.132487i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.17814 | + | 5.17814i | −0.459486 | + | 0.459486i | −0.898487 | − | 0.439001i | \(-0.855332\pi\) |
0.439001 | + | 0.898487i | \(0.355332\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.58630i | 0.837559i | 0.908088 | + | 0.418780i | \(0.137542\pi\) | ||||
−0.908088 | + | 0.418780i | \(0.862458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.44949 | − | 1.44949i | −0.125687 | − | 0.125687i | ||||
\(134\) | −9.53465 | −0.823669 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.28256 | 0.109979 | ||||||||
\(137\) | 2.47015 | + | 2.47015i | 0.211040 | + | 0.211040i | 0.804709 | − | 0.593669i | \(-0.202321\pi\) |
−0.593669 | + | 0.804709i | \(0.702321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.33386i | 0.706869i | 0.935459 | + | 0.353434i | \(0.114986\pi\) | ||||
−0.935459 | + | 0.353434i | \(0.885014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.72741 | − | 7.72741i | 0.648470 | − | 0.648470i | ||||
\(143\) | 2.01461 | − | 2.01461i | 0.168470 | − | 0.168470i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.44949i | 0.699285i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.04989 | + | 4.04989i | 0.332899 | + | 0.332899i | ||||
\(149\) | 13.5799 | 1.11251 | 0.556254 | − | 0.831012i | \(-0.312238\pi\) | ||||
0.556254 | + | 0.831012i | \(0.312238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1210 | 1.06777 | 0.533884 | − | 0.845558i | \(-0.320732\pi\) | ||||
0.533884 | + | 0.845558i | \(0.320732\pi\) | |||||||
\(152\) | 1.44949 | + | 1.44949i | 0.117569 | + | 0.117569i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.585786i | 0.0472040i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9988 | − | 16.9988i | 1.35665 | − | 1.35665i | 0.478634 | − | 0.878015i | \(-0.341132\pi\) |
0.878015 | − | 0.478634i | \(-0.158868\pi\) | |||||||
\(158\) | 0.667551 | − | 0.667551i | 0.0531075 | − | 0.0531075i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.364326i | − | 0.0287129i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0884482 | − | 0.0884482i | −0.00692780 | − | 0.00692780i | 0.703634 | − | 0.710562i | \(-0.251559\pi\) |
−0.710562 | + | 0.703634i | \(0.751559\pi\) | |||||||
\(164\) | −3.84909 | −0.300564 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.0599 | −0.858411 | ||||||||
\(167\) | 9.31319 | + | 9.31319i | 0.720677 | + | 0.720677i | 0.968743 | − | 0.248066i | \(-0.0797951\pi\) |
−0.248066 | + | 0.968743i | \(0.579795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6556i | 0.819662i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.10306 | − | 5.10306i | 0.389105 | − | 0.389105i | ||||
\(173\) | 5.81257 | − | 5.81257i | 0.441922 | − | 0.441922i | −0.450736 | − | 0.892657i | \(-0.648838\pi\) |
0.892657 | + | 0.450736i | \(0.148838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.585786i | − | 0.0441553i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.0498881 | − | 0.0498881i | −0.00373927 | − | 0.00373927i | ||||
\(179\) | −9.20080 | −0.687700 | −0.343850 | − | 0.939025i | \(-0.611731\pi\) | ||||
−0.343850 | + | 0.939025i | \(0.611731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.24316 | 0.389721 | 0.194860 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194860 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(182\) | −3.43916 | − | 3.43916i | −0.254927 | − | 0.254927i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.364326i | 0.0268584i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.531254 | + | 0.531254i | −0.0388492 | + | 0.0388492i | ||||
\(188\) | −5.49938 | + | 5.49938i | −0.401083 | + | 0.401083i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.1869i | − | 0.809453i | −0.914438 | − | 0.404727i | \(-0.867367\pi\) | ||
0.914438 | − | 0.404727i | \(-0.132633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9136 | − | 11.9136i | −0.857559 | − | 0.857559i | 0.133491 | − | 0.991050i | \(-0.457381\pi\) |
−0.991050 | + | 0.133491i | \(0.957381\pi\) | |||||||
\(194\) | −1.05594 | −0.0758121 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.7811 | + | 11.7811i | 0.839366 | + | 0.839366i | 0.988775 | − | 0.149410i | \(-0.0477373\pi\) |
−0.149410 | + | 0.988775i | \(0.547737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.11188i | − | 0.149707i | −0.997195 | − | 0.0748536i | \(-0.976151\pi\) | ||
0.997195 | − | 0.0748536i | \(-0.0238490\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.93942 | − | 2.93942i | 0.206817 | − | 0.206817i | ||||
\(203\) | −1.23936 | + | 1.23936i | −0.0869858 | + | 0.0869858i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4.44344i | − | 0.309589i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.43916 | + | 3.43916i | 0.238463 | + | 0.238463i | ||||
\(209\) | −1.20080 | −0.0830608 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1968 | 1.04619 | 0.523097 | − | 0.852273i | \(-0.324777\pi\) | ||||
0.523097 | + | 0.852273i | \(0.324777\pi\) | |||||||
\(212\) | −5.02494 | − | 5.02494i | −0.345115 | − | 0.345115i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 9.68608i | − | 0.662127i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.04320 | + | 1.04320i | −0.0708173 | + | 0.0708173i | ||||
\(218\) | 14.0951 | − | 14.0951i | 0.954643 | − | 0.954643i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.23800i | − | 0.419613i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.39391 | − | 1.39391i | −0.0933434 | − | 0.0933434i | 0.658893 | − | 0.752237i | \(-0.271025\pi\) |
−0.752237 | + | 0.658893i | \(0.771025\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.64224 | 0.441835 | ||||||||
\(227\) | 13.5638 | + | 13.5638i | 0.900258 | + | 0.900258i | 0.995458 | − | 0.0951997i | \(-0.0303490\pi\) |
−0.0951997 | + | 0.995458i | \(0.530349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.4336i | − | 0.689474i | −0.938699 | − | 0.344737i | \(-0.887968\pi\) | ||
0.938699 | − | 0.344737i | \(-0.112032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.23936 | − | 1.23936i | 0.0813678 | − | 0.0813678i | ||||
\(233\) | −11.3730 | + | 11.3730i | −0.745073 | + | 0.745073i | −0.973549 | − | 0.228476i | \(-0.926626\pi\) |
0.228476 | + | 0.973549i | \(0.426626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.1562i | 0.726209i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.906908 | + | 0.906908i | 0.0587861 | + | 0.0587861i | ||||
\(239\) | −0.485281 | −0.0313902 | −0.0156951 | − | 0.999877i | \(-0.504996\pi\) | ||||
−0.0156951 | + | 0.999877i | \(0.504996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8897 | −0.830298 | −0.415149 | − | 0.909753i | \(-0.636271\pi\) | ||||
−0.415149 | + | 0.909753i | \(0.636271\pi\) | |||||||
\(242\) | −7.53553 | − | 7.53553i | −0.484402 | − | 0.484402i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.78851i | 0.242534i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.04989 | − | 7.04989i | 0.448574 | − | 0.448574i | ||||
\(248\) | 1.04320 | − | 1.04320i | 0.0662435 | − | 0.0662435i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.3679i | − | 1.09625i | −0.836396 | − | 0.548126i | \(-0.815342\pi\) | ||
0.836396 | − | 0.548126i | \(-0.184658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.150909 | − | 0.150909i | −0.00948754 | − | 0.00948754i | ||||
\(254\) | 7.32300 | 0.459486 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.5212 | + | 21.5212i | 1.34245 | + | 1.34245i | 0.893609 | + | 0.448846i | \(0.148165\pi\) |
0.448846 | + | 0.893609i | \(0.351835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.72741i | 0.355884i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.77854 | − | 6.77854i | 0.418780 | − | 0.418780i | ||||
\(263\) | 12.5708 | − | 12.5708i | 0.775149 | − | 0.775149i | −0.203852 | − | 0.979002i | \(-0.565346\pi\) |
0.979002 | + | 0.203852i | \(0.0653462\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.04989i | 0.125687i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.74202 | + | 6.74202i | 0.411834 | + | 0.411834i | ||||
\(269\) | 10.1197 | 0.617010 | 0.308505 | − | 0.951223i | \(-0.400171\pi\) | ||||
0.308505 | + | 0.951223i | \(0.400171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.59310 | 0.0967740 | 0.0483870 | − | 0.998829i | \(-0.484592\pi\) | ||||
0.0483870 | + | 0.998829i | \(0.484592\pi\) | |||||||
\(272\) | −0.906908 | − | 0.906908i | −0.0549894 | − | 0.0549894i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.49333i | − | 0.211040i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4354 | + | 13.4354i | −0.807255 | + | 0.807255i | −0.984218 | − | 0.176963i | \(-0.943373\pi\) |
0.176963 | + | 0.984218i | \(0.443373\pi\) | |||||||
\(278\) | 5.89293 | − | 5.89293i | 0.353434 | − | 0.353434i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1421i | 1.32089i | 0.750875 | + | 0.660445i | \(0.229632\pi\) | ||||
−0.750875 | + | 0.660445i | \(0.770368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9959 | + | 10.9959i | 0.653637 | + | 0.653637i | 0.953867 | − | 0.300230i | \(-0.0970635\pi\) |
−0.300230 | + | 0.953867i | \(0.597063\pi\) | |||||||
\(284\) | −10.9282 | −0.648470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.84909 | −0.168470 | ||||||||
\(287\) | −2.72172 | − | 2.72172i | −0.160658 | − | 0.160658i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.3550i | − | 0.903237i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.97469 | − | 5.97469i | 0.349642 | − | 0.349642i | ||||
\(293\) | 13.4135 | − | 13.4135i | 0.783624 | − | 0.783624i | −0.196816 | − | 0.980440i | \(-0.563060\pi\) |
0.980440 | + | 0.196816i | \(0.0630602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 5.72741i | − | 0.332899i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.60244 | − | 9.60244i | −0.556254 | − | 0.556254i | ||||
\(299\) | 1.77197 | 0.102476 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.21682 | 0.415970 | ||||||||
\(302\) | −9.27792 | − | 9.27792i | −0.533884 | − | 0.533884i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.04989i | − | 0.117569i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.60091 | + | 6.60091i | −0.376734 | + | 0.376734i | −0.869922 | − | 0.493188i | \(-0.835831\pi\) |
0.493188 | + | 0.869922i | \(0.335831\pi\) | |||||||
\(308\) | 0.414214 | − | 0.414214i | 0.0236020 | − | 0.0236020i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.0892i | − | 1.87632i | −0.346204 | − | 0.938159i | \(-0.612529\pi\) | ||
0.346204 | − | 0.938159i | \(-0.387471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.803119 | − | 0.803119i | −0.0453949 | − | 0.0453949i | 0.684045 | − | 0.729440i | \(-0.260219\pi\) |
−0.729440 | + | 0.684045i | \(0.760219\pi\) | |||||||
\(314\) | −24.0399 | −1.35665 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.944060 | −0.0531075 | ||||||||
\(317\) | −0.832191 | − | 0.832191i | −0.0467405 | − | 0.0467405i | 0.683350 | − | 0.730091i | \(-0.260522\pi\) |
−0.730091 | + | 0.683350i | \(0.760522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.02672i | 0.0574851i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.257617 | + | 0.257617i | −0.0143564 | + | 0.0143564i | ||||
\(323\) | −1.85906 | + | 1.85906i | −0.103441 | + | 0.103441i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.125085i | 0.00692780i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.72172 | + | 2.72172i | 0.150282 | + | 0.150282i | ||||
\(329\) | −7.77729 | −0.428776 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5997 | 1.02233 | 0.511165 | − | 0.859483i | \(-0.329214\pi\) | ||||
0.511165 | + | 0.859483i | \(0.329214\pi\) | |||||||
\(332\) | 7.82050 | + | 7.82050i | 0.429206 | + | 0.429206i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 13.1708i | − | 0.720677i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0161 | + | 15.0161i | −0.817981 | + | 0.817981i | −0.985815 | − | 0.167834i | \(-0.946323\pi\) |
0.167834 | + | 0.985815i | \(0.446323\pi\) | |||||||
\(338\) | 7.53465 | − | 7.53465i | 0.409831 | − | 0.409831i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.864219i | 0.0468001i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −7.21682 | −0.389105 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.22022 | −0.441922 | ||||||||
\(347\) | −25.8218 | − | 25.8218i | −1.38619 | − | 1.38619i | −0.833169 | − | 0.553018i | \(-0.813476\pi\) |
−0.553018 | − | 0.833169i | \(-0.686524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.1584i | 1.61434i | 0.590318 | + | 0.807171i | \(0.299002\pi\) | ||||
−0.590318 | + | 0.807171i | \(0.700998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.414214 | + | 0.414214i | −0.0220777 | + | 0.0220777i | ||||
\(353\) | −8.78710 | + | 8.78710i | −0.467690 | + | 0.467690i | −0.901165 | − | 0.433475i | \(-0.857287\pi\) |
0.433475 | + | 0.901165i | \(0.357287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.0705524i | 0.00373927i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.50595 | + | 6.50595i | 0.343850 | + | 0.343850i | ||||
\(359\) | −7.67360 | −0.404997 | −0.202499 | − | 0.979283i | \(-0.564906\pi\) | ||||
−0.202499 | + | 0.979283i | \(0.564906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7980 | 0.778840 | ||||||||
\(362\) | −3.70747 | − | 3.70747i | −0.194860 | − | 0.194860i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.86370i | 0.254927i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4146 | − | 13.4146i | 0.700235 | − | 0.700235i | −0.264226 | − | 0.964461i | \(-0.585116\pi\) |
0.964461 | + | 0.264226i | \(0.0851164\pi\) | |||||||
\(368\) | 0.257617 | − | 0.257617i | 0.0134292 | − | 0.0134292i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.10634i | − | 0.368943i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.79796 | − | 2.79796i | −0.144873 | − | 0.144873i | 0.630950 | − | 0.775823i | \(-0.282665\pi\) |
−0.775823 | + | 0.630950i | \(0.782665\pi\) | |||||||
\(374\) | 0.751307 | 0.0388492 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.77729 | 0.401083 | ||||||||
\(377\) | −6.02786 | − | 6.02786i | −0.310451 | − | 0.310451i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.8539i | 0.711627i | 0.934557 | + | 0.355814i | \(0.115796\pi\) | ||||
−0.934557 | + | 0.355814i | \(0.884204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.91031 | + | 7.91031i | −0.404727 | + | 0.404727i | ||||
\(383\) | 15.6710 | − | 15.6710i | 0.800748 | − | 0.800748i | −0.182464 | − | 0.983212i | \(-0.558407\pi\) |
0.983212 | + | 0.182464i | \(0.0584074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.8484i | 0.857559i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.746663 | + | 0.746663i | 0.0379061 | + | 0.0379061i | ||||
\(389\) | 34.7194 | 1.76034 | 0.880171 | − | 0.474657i | \(-0.157428\pi\) | ||||
0.880171 | + | 0.474657i | \(0.157428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.467270 | −0.0236308 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 16.6609i | − | 0.839366i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9937 | + | 18.9937i | −0.953269 | + | 0.953269i | −0.998956 | − | 0.0456870i | \(-0.985452\pi\) |
0.0456870 | + | 0.998956i | \(0.485452\pi\) | |||||||
\(398\) | −1.49333 | + | 1.49333i | −0.0748536 | + | 0.0748536i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.88008i | − | 0.343575i | −0.985134 | − | 0.171787i | \(-0.945046\pi\) | ||
0.985134 | − | 0.171787i | \(-0.0549542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.07384 | − | 5.07384i | −0.252746 | − | 0.252746i | ||||
\(404\) | −4.15696 | −0.206817 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.75272 | 0.0869858 | ||||||||
\(407\) | 2.37237 | + | 2.37237i | 0.117594 | + | 0.117594i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.2722i | − | 1.29908i | −0.760329 | − | 0.649538i | \(-0.774962\pi\) | ||
0.760329 | − | 0.649538i | \(-0.225038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.14198 | + | 3.14198i | −0.154794 | + | 0.154794i | ||||
\(413\) | −7.88865 | + | 7.88865i | −0.388175 | + | 0.388175i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.86370i | − | 0.238463i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.849091 | + | 0.849091i | 0.0415304 | + | 0.0415304i | ||||
\(419\) | 2.85690 | 0.139569 | 0.0697844 | − | 0.997562i | \(-0.477769\pi\) | ||||
0.0697844 | + | 0.997562i | \(0.477769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.99446 | −0.194678 | −0.0973391 | − | 0.995251i | \(-0.531033\pi\) | ||||
−0.0973391 | + | 0.995251i | \(0.531033\pi\) | |||||||
\(422\) | −10.7458 | − | 10.7458i | −0.523097 | − | 0.523097i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.10634i | 0.345115i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.67888 | + | 2.67888i | −0.129640 | + | 0.129640i | ||||
\(428\) | −6.84909 | + | 6.84909i | −0.331063 | + | 0.331063i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.0871i | − | 0.726719i | −0.931649 | − | 0.363360i | \(-0.881630\pi\) | ||
0.931649 | − | 0.363360i | \(-0.118370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0406 | + | 12.0406i | 0.578634 | + | 0.578634i | 0.934527 | − | 0.355893i | \(-0.115823\pi\) |
−0.355893 | + | 0.934527i | \(0.615823\pi\) | |||||||
\(434\) | 1.47531 | 0.0708173 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.9335 | −0.954643 | ||||||||
\(437\) | −0.528086 | − | 0.528086i | −0.0252618 | − | 0.0252618i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.4660i | − | 1.21543i | −0.794156 | − | 0.607714i | \(-0.792087\pi\) | ||
0.794156 | − | 0.607714i | \(-0.207913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41093 | + | 4.41093i | −0.209807 | + | 0.209807i | ||||
\(443\) | −0.326397 | + | 0.326397i | −0.0155076 | + | 0.0155076i | −0.714818 | − | 0.699310i | \(-0.753491\pi\) |
0.699310 | + | 0.714818i | \(0.253491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.97129i | 0.0933434i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −32.0990 | −1.51485 | −0.757424 | − | 0.652924i | \(-0.773542\pi\) | ||||
−0.757424 | + | 0.652924i | \(0.773542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.25475 | −0.106172 | ||||||||
\(452\) | −4.69677 | − | 4.69677i | −0.220918 | − | 0.220918i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 19.1821i | − | 0.900258i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.63040 | − | 2.63040i | 0.123045 | − | 0.123045i | −0.642903 | − | 0.765948i | \(-0.722270\pi\) |
0.765948 | + | 0.642903i | \(0.222270\pi\) | |||||||
\(458\) | −7.37769 | + | 7.37769i | −0.344737 | + | 0.344737i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8005i | 0.968774i | 0.874854 | + | 0.484387i | \(0.160957\pi\) | ||||
−0.874854 | + | 0.484387i | \(0.839043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7214 | + | 12.7214i | 0.591211 | + | 0.591211i | 0.937959 | − | 0.346747i | \(-0.112714\pi\) |
−0.346747 | + | 0.937959i | \(0.612714\pi\) | |||||||
\(464\) | −1.75272 | −0.0813678 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.0839 | 0.745073 | ||||||||
\(467\) | 12.2128 | + | 12.2128i | 0.565141 | + | 0.565141i | 0.930763 | − | 0.365622i | \(-0.119144\pi\) |
−0.365622 | + | 0.930763i | \(0.619144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.53465i | 0.440269i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.88865 | − | 7.88865i | 0.363104 | − | 0.363104i | ||||
\(473\) | 2.98930 | − | 2.98930i | 0.137448 | − | 0.137448i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1.28256i | − | 0.0587861i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.343146 | + | 0.343146i | 0.0156951 | + | 0.0156951i | ||||
\(479\) | 32.5054 | 1.48521 | 0.742606 | − | 0.669729i | \(-0.233590\pi\) | ||||
0.742606 | + | 0.669729i | \(0.233590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8564 | −1.27014 | ||||||||
\(482\) | 9.11439 | + | 9.11439i | 0.415149 | + | 0.415149i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.6569i | 0.484402i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1806 | + | 11.1806i | −0.506644 | + | 0.506644i | −0.913495 | − | 0.406851i | \(-0.866627\pi\) |
0.406851 | + | 0.913495i | \(0.366627\pi\) | |||||||
\(488\) | 2.67888 | − | 2.67888i | 0.121267 | − | 0.121267i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 29.6889i | − | 1.33984i | −0.742433 | − | 0.669921i | \(-0.766328\pi\) | ||
0.742433 | − | 0.669921i | \(-0.233672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.58955 | + | 1.58955i | 0.0715898 | + | 0.0715898i | ||||
\(494\) | −9.97005 | −0.448574 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.47531 | −0.0662435 | ||||||||
\(497\) | −7.72741 | − | 7.72741i | −0.346622 | − | 0.346622i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.1119i | − | 1.70612i | −0.521810 | − | 0.853061i | \(-0.674743\pi\) | ||
0.521810 | − | 0.853061i | \(-0.325257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.2810 | + | 12.2810i | −0.548126 | + | 0.548126i | ||||
\(503\) | −0.0267167 | + | 0.0267167i | −0.00119124 | + | 0.00119124i | −0.707702 | − | 0.706511i | \(-0.750268\pi\) |
0.706511 | + | 0.707702i | \(0.250268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.213417i | 0.00948754i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.17814 | − | 5.17814i | −0.229743 | − | 0.229743i | ||||
\(509\) | 24.8899 | 1.10323 | 0.551613 | − | 0.834100i | \(-0.314012\pi\) | ||||
0.551613 | + | 0.834100i | \(0.314012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.44949 | 0.373783 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 30.4356i | − | 1.34245i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.22146 | + | 3.22146i | −0.141680 | + | 0.141680i | ||||
\(518\) | 4.04989 | − | 4.04989i | 0.177942 | − | 0.177942i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 32.1495i | − | 1.40849i | −0.709956 | − | 0.704247i | \(-0.751285\pi\) | ||
0.709956 | − | 0.704247i | \(-0.248715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3237 | + | 10.3237i | 0.451423 | + | 0.451423i | 0.895827 | − | 0.444404i | \(-0.146584\pi\) |
−0.444404 | + | 0.895827i | \(0.646584\pi\) | |||||||
\(524\) | −9.58630 | −0.418780 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.7778 | −0.775149 | ||||||||
\(527\) | 1.33797 | + | 1.33797i | 0.0582830 | + | 0.0582830i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8673i | 0.994229i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.44949 | − | 1.44949i | 0.0628434 | − | 0.0628434i | ||||
\(533\) | 13.2376 | − | 13.2376i | 0.573385 | − | 0.573385i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 9.53465i | − | 0.411834i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.15572 | − | 7.15572i | −0.308505 | − | 0.308505i | ||||
\(539\) | 0.585786 | 0.0252316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3694 | −1.09072 | −0.545359 | − | 0.838203i | \(-0.683607\pi\) | ||||
−0.545359 | + | 0.838203i | \(0.683607\pi\) | |||||||
\(542\) | −1.12649 | − | 1.12649i | −0.0483870 | − | 0.0483870i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.28256i | 0.0549894i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9461 | + | 28.9461i | −1.23765 | + | 1.23765i | −0.276685 | + | 0.960961i | \(0.589236\pi\) |
−0.960961 | + | 0.276685i | \(0.910764\pi\) | |||||||
\(548\) | −2.47015 | + | 2.47015i | −0.105520 | + | 0.105520i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.59287i | 0.153061i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.667551 | − | 0.667551i | −0.0283872 | − | 0.0283872i | ||||
\(554\) | 19.0005 | 0.807255 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.33386 | −0.353434 | ||||||||
\(557\) | −1.22073 | − | 1.22073i | −0.0517241 | − | 0.0517241i | 0.680772 | − | 0.732496i | \(-0.261645\pi\) |
−0.732496 | + | 0.680772i | \(0.761645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.1005i | 1.48459i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6569 | − | 15.6569i | 0.660445 | − | 0.660445i | ||||
\(563\) | −6.26999 | + | 6.26999i | −0.264249 | + | 0.264249i | −0.826778 | − | 0.562529i | \(-0.809828\pi\) |
0.562529 | + | 0.826778i | \(0.309828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 15.5505i | − | 0.653637i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.72741 | + | 7.72741i | 0.324235 | + | 0.324235i | ||||
\(569\) | 23.1192 | 0.969207 | 0.484604 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484604 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94303 | 0.0813132 | 0.0406566 | − | 0.999173i | \(-0.487055\pi\) | ||||
0.0406566 | + | 0.999173i | \(0.487055\pi\) | |||||||
\(572\) | 2.01461 | + | 2.01461i | 0.0842352 | + | 0.0842352i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.84909i | 0.160658i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6576 | − | 13.6576i | 0.568573 | − | 0.568573i | −0.363156 | − | 0.931728i | \(-0.618301\pi\) |
0.931728 | + | 0.363156i | \(0.118301\pi\) | |||||||
\(578\) | −10.8577 | + | 10.8577i | −0.451619 | + | 0.451619i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.0599i | 0.458840i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.94354 | − | 2.94354i | −0.121909 | − | 0.121909i | ||||
\(584\) | −8.44949 | −0.349642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.9695 | −0.783624 | ||||||||
\(587\) | −22.9322 | − | 22.9322i | −0.946512 | − | 0.946512i | 0.0521286 | − | 0.998640i | \(-0.483399\pi\) |
−0.998640 | + | 0.0521286i | \(0.983399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.02423i | 0.124611i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.04989 | + | 4.04989i | −0.166449 | + | 0.166449i | ||||
\(593\) | −31.8592 | + | 31.8592i | −1.30830 | + | 1.30830i | −0.385661 | + | 0.922641i | \(0.626027\pi\) |
−0.922641 | + | 0.385661i | \(0.873973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.5799i | 0.556254i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.25297 | − | 1.25297i | −0.0512379 | − | 0.0512379i | ||||
\(599\) | −22.1019 | −0.903060 | −0.451530 | − | 0.892256i | \(-0.649122\pi\) | ||||
−0.451530 | + | 0.892256i | \(0.649122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8874 | −1.46388 | −0.731939 | − | 0.681371i | \(-0.761384\pi\) | ||||
−0.731939 | + | 0.681371i | \(0.761384\pi\) | |||||||
\(602\) | −5.10306 | − | 5.10306i | −0.207985 | − | 0.207985i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.1210i | 0.533884i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7675 | + | 10.7675i | −0.437039 | + | 0.437039i | −0.891014 | − | 0.453975i | \(-0.850005\pi\) |
0.453975 | + | 0.891014i | \(0.350005\pi\) | |||||||
\(608\) | −1.44949 | + | 1.44949i | −0.0587846 | + | 0.0587846i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 37.8265i | − | 1.53029i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.86194 | + | 5.86194i | 0.236762 | + | 0.236762i | 0.815508 | − | 0.578746i | \(-0.196458\pi\) |
−0.578746 | + | 0.815508i | \(0.696458\pi\) | |||||||
\(614\) | 9.33510 | 0.376734 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.585786 | −0.0236020 | ||||||||
\(617\) | −31.6118 | − | 31.6118i | −1.27264 | − | 1.27264i | −0.944697 | − | 0.327945i | \(-0.893644\pi\) |
−0.327945 | − | 0.944697i | \(-0.606356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.4856i | − | 1.30571i | −0.757484 | − | 0.652853i | \(-0.773572\pi\) | ||
0.757484 | − | 0.652853i | \(-0.226428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.3976 | + | 23.3976i | −0.938159 | + | 0.938159i | ||||
\(623\) | −0.0498881 | + | 0.0498881i | −0.00199872 | + | 0.00199872i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.13578i | 0.0453949i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.9988 | + | 16.9988i | 0.678324 | + | 0.678324i | ||||
\(629\) | 7.34575 | 0.292894 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5826 | 0.978617 | 0.489308 | − | 0.872111i | \(-0.337249\pi\) | ||||
0.489308 | + | 0.872111i | \(0.337249\pi\) | |||||||
\(632\) | 0.667551 | + | 0.667551i | 0.0265537 | + | 0.0265537i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.17690i | 0.0467405i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.43916 | + | 3.43916i | −0.136264 | + | 0.136264i | ||||
\(638\) | 0.725998 | − | 0.725998i | 0.0287426 | − | 0.0287426i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.35255i | 0.290408i | 0.989402 | + | 0.145204i | \(0.0463839\pi\) | ||||
−0.989402 | + | 0.145204i | \(0.953616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.73081 | + | 8.73081i | 0.344309 | + | 0.344309i | 0.857985 | − | 0.513675i | \(-0.171716\pi\) |
−0.513675 | + | 0.857985i | \(0.671716\pi\) | |||||||
\(644\) | 0.364326 | 0.0143564 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.62911 | 0.103441 | ||||||||
\(647\) | 28.3694 | + | 28.3694i | 1.11532 | + | 1.11532i | 0.992419 | + | 0.122898i | \(0.0392189\pi\) |
0.122898 | + | 0.992419i | \(0.460781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.53517i | 0.256528i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.0884482 | − | 0.0884482i | 0.00346390 | − | 0.00346390i | ||||
\(653\) | −27.4634 | + | 27.4634i | −1.07472 | + | 1.07472i | −0.0777521 | + | 0.996973i | \(0.524774\pi\) |
−0.996973 | + | 0.0777521i | \(0.975226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3.84909i | − | 0.150282i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.49938 | + | 5.49938i | 0.214388 | + | 0.214388i | ||||
\(659\) | −26.5619 | −1.03470 | −0.517352 | − | 0.855772i | \(-0.673082\pi\) | ||||
−0.517352 | + | 0.855772i | \(0.673082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.3725 | −1.06467 | −0.532333 | − | 0.846535i | \(-0.678685\pi\) | ||||
−0.532333 | + | 0.846535i | \(0.678685\pi\) | |||||||
\(662\) | −13.1520 | − | 13.1520i | −0.511165 | − | 0.511165i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.0599i | − | 0.429206i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.451529 | + | 0.451529i | −0.0174833 | + | 0.0174833i | ||||
\(668\) | −9.31319 | + | 9.31319i | −0.360338 | + | 0.360338i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.21926i | 0.0856734i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4095 | − | 12.4095i | −0.478349 | − | 0.478349i | 0.426254 | − | 0.904603i | \(-0.359833\pi\) |
−0.904603 | + | 0.426254i | \(0.859833\pi\) | |||||||
\(674\) | 21.2360 | 0.817981 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.6556 | −0.409831 | ||||||||
\(677\) | 8.04384 | + | 8.04384i | 0.309150 | + | 0.309150i | 0.844580 | − | 0.535430i | \(-0.179850\pi\) |
−0.535430 | + | 0.844580i | \(0.679850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.05594i | 0.0405233i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.611095 | − | 0.611095i | 0.0234000 | − | 0.0234000i | ||||
\(683\) | −6.88312 | + | 6.88312i | −0.263375 | + | 0.263375i | −0.826424 | − | 0.563048i | \(-0.809628\pi\) |
0.563048 | + | 0.826424i | \(0.309628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.10306 | + | 5.10306i | 0.194552 | + | 0.194552i | ||||
\(689\) | 34.5631 | 1.31675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.4327 | −1.72834 | −0.864171 | − | 0.503199i | \(-0.832156\pi\) | ||||
−0.864171 | + | 0.503199i | \(0.832156\pi\) | |||||||
\(692\) | 5.81257 | + | 5.81257i | 0.220961 | + | 0.220961i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.5176i | 1.38619i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.49077 | + | 3.49077i | −0.132222 | + | 0.132222i | ||||
\(698\) | 21.3252 | − | 21.3252i | 0.807171 | − | 0.807171i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9123i | 0.903155i | 0.892232 | + | 0.451578i | \(0.149139\pi\) | ||||
−0.892232 | + | 0.451578i | \(0.850861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.30182 | + | 8.30182i | 0.313109 | + | 0.313109i | ||||
\(704\) | 0.585786 | 0.0220777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.4268 | 0.467690 | ||||||||
\(707\) | −2.93942 | − | 2.93942i | −0.110548 | − | 0.110548i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6939i | 1.11518i | 0.830117 | + | 0.557589i | \(0.188273\pi\) | ||||
−0.830117 | + | 0.557589i | \(0.811727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.0498881 | − | 0.0498881i | 0.00186963 | − | 0.00186963i | ||||
\(713\) | −0.380066 | + | 0.380066i | −0.0142336 | + | 0.0142336i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 9.20080i | − | 0.343850i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.42606 | + | 5.42606i | 0.202499 | + | 0.202499i | ||||
\(719\) | −44.7620 | −1.66934 | −0.834670 | − | 0.550751i | \(-0.814341\pi\) | ||||
−0.834670 | + | 0.550751i | \(0.814341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.44344 | −0.165482 | ||||||||
\(722\) | −10.4637 | − | 10.4637i | −0.389420 | − | 0.389420i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.24316i | 0.194860i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.1992 | + | 30.1992i | −1.12003 | + | 1.12003i | −0.128289 | + | 0.991737i | \(0.540949\pi\) |
−0.991737 | + | 0.128289i | \(0.959051\pi\) | |||||||
\(728\) | 3.43916 | − | 3.43916i | 0.127464 | − | 0.127464i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.25601i | − | 0.342346i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.22450 | + | 8.22450i | 0.303779 | + | 0.303779i | 0.842490 | − | 0.538712i | \(-0.181089\pi\) |
−0.538712 | + | 0.842490i | \(0.681089\pi\) | |||||||
\(734\) | −18.9711 | −0.700235 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.364326 | −0.0134292 | ||||||||
\(737\) | 3.94938 | + | 3.94938i | 0.145477 | + | 0.145477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6997i | 1.01895i | 0.860486 | + | 0.509474i | \(0.170160\pi\) | ||||
−0.860486 | + | 0.509474i | \(0.829840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.02494 | + | 5.02494i | −0.184471 | + | 0.184471i | ||||
\(743\) | −1.50830 | + | 1.50830i | −0.0553342 | + | 0.0553342i | −0.734232 | − | 0.678898i | \(-0.762458\pi\) |
0.678898 | + | 0.734232i | \(0.262458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.95691i | 0.144873i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.531254 | − | 0.531254i | −0.0194246 | − | 0.0194246i | ||||
\(749\) | −9.68608 | −0.353922 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.5599 | −1.26111 | −0.630555 | − | 0.776145i | \(-0.717172\pi\) | ||||
−0.630555 | + | 0.776145i | \(0.717172\pi\) | |||||||
\(752\) | −5.49938 | − | 5.49938i | −0.200542 | − | 0.200542i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.52469i | 0.310451i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3636 | + | 26.3636i | −0.958201 | + | 0.958201i | −0.999161 | − | 0.0409596i | \(-0.986959\pi\) |
0.0409596 | + | 0.999161i | \(0.486959\pi\) | |||||||
\(758\) | 9.79619 | − | 9.79619i | 0.355814 | − | 0.355814i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.6078i | 1.47203i | 0.676964 | + | 0.736016i | \(0.263295\pi\) | ||||
−0.676964 | + | 0.736016i | \(0.736705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0951 | − | 14.0951i | −0.510278 | − | 0.510278i | ||||
\(764\) | 11.1869 | 0.404727 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.1621 | −0.800748 | ||||||||
\(767\) | −38.3680 | − | 38.3680i | −1.38539 | − | 1.38539i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.37968i | − | 0.193996i | −0.995285 | − | 0.0969982i | \(-0.969076\pi\) | ||
0.995285 | − | 0.0969982i | \(-0.0309241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.9136 | − | 11.9136i | 0.428780 | − | 0.428780i | ||||
\(773\) | −25.8174 | + | 25.8174i | −0.928587 | + | 0.928587i | −0.997615 | − | 0.0690281i | \(-0.978010\pi\) |
0.0690281 | + | 0.997615i | \(0.478010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1.05594i | − | 0.0379061i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.5503 | − | 24.5503i | −0.880171 | − | 0.880171i | ||||
\(779\) | −7.89021 | −0.282696 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.40159 | −0.229067 | ||||||||
\(782\) | 0.330410 | + | 0.330410i | 0.0118154 | + | 0.0118154i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9421 | − | 18.9421i | 0.675212 | − | 0.675212i | −0.283701 | − | 0.958913i | \(-0.591562\pi\) |
0.958913 | + | 0.283701i | \(0.0915623\pi\) | |||||||
\(788\) | −11.7811 | + | 11.7811i | −0.419683 | + | 0.419683i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.64224i | − | 0.236171i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0293 | − | 13.0293i | −0.462683 | − | 0.462683i | ||||
\(794\) | 26.8612 | 0.953269 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.11188 | 0.0748536 | ||||||||
\(797\) | −19.5851 | − | 19.5851i | −0.693738 | − | 0.693738i | 0.269314 | − | 0.963052i | \(-0.413203\pi\) |
−0.963052 | + | 0.269314i | \(0.913203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.97486i | 0.352885i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.86495 | + | 4.86495i | −0.171787 | + | 0.171787i | ||||
\(803\) | 3.49989 | − | 3.49989i | 0.123509 | − | 0.123509i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.17549i | 0.252746i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.93942 | + | 2.93942i | 0.103408 | + | 0.103408i | ||||
\(809\) | −20.2933 | −0.713473 | −0.356736 | − | 0.934205i | \(-0.616111\pi\) | ||||
−0.356736 | + | 0.934205i | \(0.616111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8254 | 0.836624 | 0.418312 | − | 0.908303i | \(-0.362622\pi\) | ||||
0.418312 | + | 0.908303i | \(0.362622\pi\) | |||||||
\(812\) | −1.23936 | − | 1.23936i | −0.0434929 | − | 0.0434929i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 3.35504i | − | 0.117594i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4607 | − | 10.4607i | 0.365974 | − | 0.365974i | ||||
\(818\) | −18.5772 | + | 18.5772i | −0.649538 | + | 0.649538i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24.2298i | − | 0.845626i | −0.906217 | − | 0.422813i | \(-0.861043\pi\) | ||
0.906217 | − | 0.422813i | \(-0.138957\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.9552 | + | 30.9552i | 1.07903 | + | 1.07903i | 0.996596 | + | 0.0824347i | \(0.0262696\pi\) |
0.0824347 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(824\) | 4.44344 | 0.154794 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.1562 | 0.388175 | ||||||||
\(827\) | 7.83272 | + | 7.83272i | 0.272370 | + | 0.272370i | 0.830054 | − | 0.557683i | \(-0.188310\pi\) |
−0.557683 | + | 0.830054i | \(0.688310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 53.9816i | − | 1.87486i | −0.348176 | − | 0.937429i | \(-0.613199\pi\) | ||
0.348176 | − | 0.937429i | \(-0.386801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.43916 | + | 3.43916i | −0.119231 | + | 0.119231i | ||||
\(833\) | 0.906908 | − | 0.906908i | 0.0314225 | − | 0.0314225i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1.20080i | − | 0.0415304i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.02014 | − | 2.02014i | −0.0697844 | − | 0.0697844i | ||||
\(839\) | 47.5236 | 1.64070 | 0.820348 | − | 0.571864i | \(-0.193780\pi\) | ||||
0.820348 | + | 0.571864i | \(0.193780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9280 | −0.894069 | ||||||||
\(842\) | 2.82451 | + | 2.82451i | 0.0973391 | + | 0.0973391i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.1968i | 0.523097i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.53553 | + | 7.53553i | −0.258924 | + | 0.258924i | ||||
\(848\) | 5.02494 | − | 5.02494i | 0.172557 | − | 0.172557i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.08664i | 0.0715291i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.07711 | − | 1.07711i | −0.0368795 | − | 0.0368795i | 0.688427 | − | 0.725306i | \(-0.258302\pi\) |
−0.725306 | + | 0.688427i | \(0.758302\pi\) | |||||||
\(854\) | 3.78851 | 0.129640 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.68608 | 0.331063 | ||||||||
\(857\) | −21.5122 | − | 21.5122i | −0.734844 | − | 0.734844i | 0.236731 | − | 0.971575i | \(-0.423924\pi\) |
−0.971575 | + | 0.236731i | \(0.923924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.1691i | − | 0.654041i | −0.945017 | − | 0.327020i | \(-0.893955\pi\) | ||
0.945017 | − | 0.327020i | \(-0.106045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.6682 | + | 10.6682i | −0.363360 | + | 0.363360i | ||||
\(863\) | −33.4024 | + | 33.4024i | −1.13703 | + | 1.13703i | −0.148053 | + | 0.988979i | \(0.547301\pi\) |
−0.988979 | + | 0.148053i | \(0.952699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 17.0280i | − | 0.578634i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.04320 | − | 1.04320i | −0.0354087 | − | 0.0354087i | ||||
\(869\) | −0.553017 | −0.0187598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.3737 | −1.57131 | ||||||||
\(872\) | 14.0951 | + | 14.0951i | 0.477321 | + | 0.477321i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.746827i | 0.0252618i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.04257 | − | 5.04257i | 0.170276 | − | 0.170276i | −0.616825 | − | 0.787100i | \(-0.711581\pi\) |
0.787100 | + | 0.616825i | \(0.211581\pi\) | |||||||
\(878\) | −18.0072 | + | 18.0072i | −0.607714 | + | 0.607714i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.3415i | 1.69605i | 0.529958 | + | 0.848024i | \(0.322208\pi\) | ||||
−0.529958 | + | 0.848024i | \(0.677792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.32504 | + | 5.32504i | 0.179202 | + | 0.179202i | 0.791008 | − | 0.611806i | \(-0.209557\pi\) |
−0.611806 | + | 0.791008i | \(0.709557\pi\) | |||||||
\(884\) | 6.23800 | 0.209807 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.461595 | 0.0155076 | ||||||||
\(887\) | 15.1295 | + | 15.1295i | 0.507999 | + | 0.507999i | 0.913912 | − | 0.405913i | \(-0.133046\pi\) |
−0.405913 | + | 0.913912i | \(0.633046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.32300i | − | 0.245605i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.39391 | − | 1.39391i | 0.0466717 | − | 0.0466717i | ||||
\(893\) | −11.2731 | + | 11.2731i | −0.377240 | + | 0.377240i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6975 | + | 22.6975i | 0.757424 | + | 0.757424i | ||||
\(899\) | 2.58580 | 0.0862414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.11432 | −0.303642 | ||||||||
\(902\) | 1.59435 | + | 1.59435i | 0.0530859 | + | 0.0530859i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.64224i | 0.220918i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.50318 | − | 4.50318i | 0.149526 | − | 0.149526i | −0.628381 | − | 0.777906i | \(-0.716282\pi\) |
0.777906 | + | 0.628381i | \(0.216282\pi\) | |||||||
\(908\) | −13.5638 | + | 13.5638i | −0.450129 | + | 0.450129i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 13.7520i | − | 0.455624i | −0.973705 | − | 0.227812i | \(-0.926843\pi\) | ||
0.973705 | − | 0.227812i | \(-0.0731571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.58114 | + | 4.58114i | 0.151614 | + | 0.151614i | ||||
\(914\) | −3.71995 | −0.123045 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.4336 | 0.344737 | ||||||||
\(917\) | −6.77854 | − | 6.77854i | −0.223847 | − | 0.223847i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 43.8245i | − | 1.44564i | −0.691039 | − | 0.722818i | \(-0.742847\pi\) | ||
0.691039 | − | 0.722818i | \(-0.257153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.7082 | − | 14.7082i | 0.484387 | − | 0.484387i | ||||
\(923\) | 37.5838 | − | 37.5838i | 1.23709 | − | 1.23709i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 17.9907i | − | 0.591211i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.23936 | + | 1.23936i | 0.0406839 | + | 0.0406839i | ||||
\(929\) | 9.15215 | 0.300272 | 0.150136 | − | 0.988665i | \(-0.452029\pi\) | ||||
0.150136 | + | 0.988665i | \(0.452029\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.04989 | 0.0671824 | ||||||||
\(932\) | −11.3730 | − | 11.3730i | −0.372537 | − | 0.372537i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 17.2715i | − | 0.565141i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.96275 | − | 9.96275i | 0.325469 | − | 0.325469i | −0.525392 | − | 0.850861i | \(-0.676081\pi\) |
0.850861 | + | 0.525392i | \(0.176081\pi\) | |||||||
\(938\) | 6.74202 | − | 6.74202i | 0.220135 | − | 0.220135i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 19.9173i | − | 0.649287i | −0.945836 | − | 0.324643i | \(-0.894756\pi\) | ||
0.945836 | − | 0.324643i | \(-0.105244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.991592 | − | 0.991592i | −0.0322907 | − | 0.0322907i | ||||
\(944\) | −11.1562 | −0.363104 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.22751 | −0.137448 | ||||||||
\(947\) | 9.40403 | + | 9.40403i | 0.305590 | + | 0.305590i | 0.843196 | − | 0.537606i | \(-0.180671\pi\) |
−0.537606 | + | 0.843196i | \(0.680671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.0958i | 1.33403i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.906908 | + | 0.906908i | −0.0293930 | + | 0.0293930i | ||||
\(953\) | −13.5760 | + | 13.5760i | −0.439769 | + | 0.439769i | −0.891934 | − | 0.452165i | \(-0.850652\pi\) |
0.452165 | + | 0.891934i | \(0.350652\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 0.485281i | − | 0.0156951i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.9848 | − | 22.9848i | −0.742606 | − | 0.742606i | ||||
\(959\) | −3.49333 | −0.112805 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8234 | −0.929789 | ||||||||
\(962\) | 19.6975 | + | 19.6975i | 0.635071 | + | 0.635071i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 12.8897i | − | 0.415149i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4331 | + | 14.4331i | −0.464138 | + | 0.464138i | −0.900009 | − | 0.435871i | \(-0.856440\pi\) |
0.435871 | + | 0.900009i | \(0.356440\pi\) | |||||||
\(968\) | 7.53553 | − | 7.53553i | 0.242201 | − | 0.242201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 16.9403i | − | 0.543640i | −0.962348 | − | 0.271820i | \(-0.912374\pi\) | ||
0.962348 | − | 0.271820i | \(-0.0876256\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.89293 | − | 5.89293i | −0.188919 | − | 0.188919i | ||||
\(974\) | 15.8118 | 0.506644 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.78851 | −0.121267 | ||||||||
\(977\) | −19.9652 | − | 19.9652i | −0.638745 | − | 0.638745i | 0.311501 | − | 0.950246i | \(-0.399168\pi\) |
−0.950246 | + | 0.311501i | \(0.899168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0413286i | 0.00132087i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.9932 | + | 20.9932i | −0.669921 | + | 0.669921i | ||||
\(983\) | 40.4112 | − | 40.4112i | 1.28892 | − | 1.28892i | 0.353472 | − | 0.935445i | \(-0.385001\pi\) |
0.935445 | − | 0.353472i | \(-0.114999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2.24796i | − | 0.0715898i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.04989 | + | 7.04989i | 0.224287 | + | 0.224287i | ||||
\(989\) | 2.62927 | 0.0836059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.6002 | 0.527323 | 0.263662 | − | 0.964615i | \(-0.415070\pi\) | ||||
0.263662 | + | 0.964615i | \(0.415070\pi\) | |||||||
\(992\) | 1.04320 | + | 1.04320i | 0.0331218 | + | 0.0331218i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.9282i | 0.346622i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6264 | − | 38.6264i | 1.22331 | − | 1.22331i | 0.256862 | − | 0.966448i | \(-0.417311\pi\) |
0.966448 | − | 0.256862i | \(-0.0826885\pi\) | |||||||
\(998\) | −26.9492 | + | 26.9492i | −0.853061 | + | 0.853061i | ||||
\(999\) | 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 | 3150.2.m.h.2843.1 | yes | 8 | |
3.2 | odd | 2 | 3150.2.m.g.2843.3 | yes | 8 | ||
5.2 | odd | 4 | 3150.2.m.g.1457.3 | ✓ | 8 | ||
5.3 | odd | 4 | 3150.2.m.k.1457.2 | yes | 8 | ||
5.4 | even | 2 | 3150.2.m.l.2843.4 | yes | 8 | ||
15.2 | even | 4 | inner | 3150.2.m.h.1457.1 | yes | 8 | |
15.8 | even | 4 | 3150.2.m.l.1457.4 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.m.k.2843.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.g.1457.3 | ✓ | 8 | 5.2 | odd | 4 | ||
3150.2.m.g.2843.3 | yes | 8 | 3.2 | odd | 2 | ||
3150.2.m.h.1457.1 | yes | 8 | 15.2 | even | 4 | inner | |
3150.2.m.h.2843.1 | yes | 8 | 1.1 | even | 1 | trivial | |
3150.2.m.k.1457.2 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.m.k.2843.2 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.m.l.1457.4 | yes | 8 | 15.8 | even | 4 | ||
3150.2.m.l.2843.4 | yes | 8 | 5.4 | even | 2 |