Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(61,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.61 |
Dual form | 260.2.i.b.81.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 0.866025i | 0.0845154 | + | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50000 | + | 2.59808i | 0.400320 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | + | 2.59808i | −0.202260 | + | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | − | 9.52628i | −0.704203 | − | 1.21972i | −0.966978 | − | 0.254858i | \(-0.917971\pi\) |
0.262776 | − | 0.964857i | \(-0.415362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | + | 1.73205i | −0.125988 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | − | 3.46410i | 0.124035 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | + | 2.59808i | 0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | + | 2.59808i | 0.178017 | + | 0.308335i | 0.941201 | − | 0.337846i | \(-0.109698\pi\) |
−0.763184 | + | 0.646181i | \(0.776365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | + | 2.59808i | 0.162698 | + | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.50000 | + | 6.06218i | 0.359092 | + | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.50000 | + | 6.06218i | 0.355371 | + | 0.615521i | 0.987181 | − | 0.159602i | \(-0.0510211\pi\) |
−0.631810 | + | 0.775123i | \(0.717688\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | − | 7.79423i | 0.447767 | − | 0.775555i | −0.550474 | − | 0.834853i | \(-0.685553\pi\) |
0.998240 | + | 0.0592978i | \(0.0188862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.50000 | + | 7.79423i | −0.435031 | + | 0.753497i | −0.997298 | − | 0.0734594i | \(-0.976596\pi\) |
0.562267 | + | 0.826956i | \(0.309929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.50000 | − | 7.79423i | −0.423324 | − | 0.733219i | 0.572938 | − | 0.819599i | \(-0.305804\pi\) |
−0.996262 | + | 0.0863794i | \(0.972470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.00000 | − | 1.73205i | 0.647150 | − | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | + | 2.59808i | −0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.50000 | + | 7.79423i | 0.405751 | + | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.50000 | − | 16.4545i | 0.842989 | − | 1.46010i | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) |
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0000 | 0.968496 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50000 | + | 6.06218i | −0.303488 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.50000 | + | 12.9904i | 0.640768 | + | 1.10984i | 0.985262 | + | 0.171054i | \(0.0547174\pi\) |
−0.344493 | + | 0.938789i | \(0.611949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | − | 4.33013i | −0.212047 | − | 0.367277i | 0.740308 | − | 0.672268i | \(-0.234680\pi\) |
−0.952355 | + | 0.304991i | \(0.901346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.50000 | + | 7.79423i | 0.627182 | + | 0.651786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.50000 | + | 2.59808i | −0.124568 | + | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | + | 5.19615i | 0.247436 | + | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5000 | + | 18.1865i | 0.860194 | + | 1.48990i | 0.871742 | + | 0.489966i | \(0.162991\pi\) |
−0.0115483 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | + | 5.19615i | −0.242536 | + | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.00000 | + | 12.1244i | −0.535303 | + | 0.927173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | −0.225494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5000 | − | 18.1865i | 0.784807 | − | 1.35933i | −0.144308 | − | 0.989533i | \(-0.546095\pi\) |
0.929114 | − | 0.369792i | \(-0.120571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.50000 | − | 6.06218i | 0.257325 | − | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | −0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | − | 4.33013i | −0.181848 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | + | 2.59808i | 0.108536 | + | 0.187990i | 0.915177 | − | 0.403051i | \(-0.132050\pi\) |
−0.806641 | + | 0.591041i | \(0.798717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | + | 4.33013i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.50000 | + | 2.59808i | 0.179029 | + | 0.186052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5000 | + | 18.1865i | −0.748094 | + | 1.29574i | 0.200641 | + | 0.979665i | \(0.435697\pi\) |
−0.948735 | + | 0.316072i | \(0.897636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.50000 | − | 14.7224i | −0.602549 | − | 1.04365i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | + | 6.06218i | 0.246871 | + | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00000 | −0.210559 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0000 | −1.45260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.50000 | + | 9.52628i | −0.378636 | + | 0.655816i | −0.990864 | − | 0.134865i | \(-0.956940\pi\) |
0.612228 | + | 0.790681i | \(0.290273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | −0.205557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.50000 | − | 9.52628i | −0.375097 | − | 0.649687i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | − | 3.46410i | −0.135769 | − | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.5000 | − | 2.59808i | 0.706306 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 1.73205i | 0.0666667 | + | 0.115470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.5000 | − | 23.3827i | −0.896026 | − | 1.55196i | −0.832529 | − | 0.553981i | \(-0.813108\pi\) |
−0.0634974 | − | 0.997982i | \(-0.520225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | − | 5.19615i | 0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.5000 | − | 6.06218i | 1.55890 | − | 0.385727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5000 | − | 18.1865i | −0.662754 | − | 1.14792i | −0.979889 | − | 0.199543i | \(-0.936054\pi\) |
0.317135 | − | 0.948380i | \(-0.397279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.50000 | + | 7.79423i | 0.282913 | + | 0.490019i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | −0.187867 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.50000 | + | 7.79423i | −0.280702 | + | 0.486191i | −0.971558 | − | 0.236802i | \(-0.923901\pi\) |
0.690856 | + | 0.722993i | \(0.257234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.00000 | 0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.50000 | − | 2.59808i | 0.0924940 | − | 0.160204i | −0.816066 | − | 0.577959i | \(-0.803849\pi\) |
0.908560 | + | 0.417755i | \(0.137183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.50000 | − | 12.9904i | −0.458993 | − | 0.794998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5000 | − | 23.3827i | −0.823110 | − | 1.42567i | −0.903356 | − | 0.428892i | \(-0.858904\pi\) |
0.0802460 | − | 0.996775i | \(-0.474429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5000 | + | 19.9186i | −0.698575 | + | 1.20997i | 0.270385 | + | 0.962752i | \(0.412849\pi\) |
−0.968960 | + | 0.247216i | \(0.920484\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.00000 | + | 3.46410i | −0.0605228 | + | 0.209657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | − | 6.92820i | −0.239474 | − | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.50000 | + | 4.33013i | −0.148610 | + | 0.257399i | −0.930714 | − | 0.365748i | \(-0.880813\pi\) |
0.782104 | + | 0.623148i | \(0.214146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.00000 | −0.414644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.00000 | 0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5000 | + | 23.3827i | 0.788678 | + | 1.36603i | 0.926777 | + | 0.375613i | \(0.122568\pi\) |
−0.138098 | + | 0.990419i | \(0.544099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50000 | + | 2.59808i | 0.0873334 | + | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.50000 | − | 12.9904i | 0.435194 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.50000 | − | 7.79423i | −0.433736 | − | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.50000 | − | 9.52628i | 0.317015 | − | 0.549086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.50000 | + | 7.79423i | 0.258518 | + | 0.447767i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.50000 | − | 9.52628i | −0.314929 | − | 0.545473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | + | 6.92820i | −0.227552 | + | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | + | 1.73205i | −0.0563436 | + | 0.0975900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | − | 7.79423i | −0.251166 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.5000 | + | 18.1865i | −0.584236 | + | 1.01193i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | − | 3.46410i | 0.0554700 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00000 | + | 1.73205i | −0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | + | 16.4545i | 0.522167 | + | 0.904420i | 0.999667 | + | 0.0257885i | \(0.00820965\pi\) |
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0000 | 0.767195 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.50000 | − | 6.06218i | 0.191225 | − | 0.331212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.0000 | −1.85210 | −0.926049 | − | 0.377403i | \(-0.876817\pi\) | ||||
−0.926049 | + | 0.377403i | \(0.876817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | 0.488813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | + | 2.59808i | 0.0807573 | + | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.5000 | + | 28.5788i | 0.885766 | + | 1.53419i | 0.844833 | + | 0.535031i | \(0.179700\pi\) |
0.0409337 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.500000 | − | 0.866025i | 0.0267644 | − | 0.0463573i | −0.852333 | − | 0.523000i | \(-0.824813\pi\) |
0.879097 | + | 0.476642i | \(0.158146\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | + | 7.79423i | −0.239511 | + | 0.414845i | −0.960574 | − | 0.278024i | \(-0.910320\pi\) |
0.721063 | + | 0.692869i | \(0.243654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | + | 2.59808i | 0.0796117 | + | 0.137892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.50000 | − | 2.59808i | −0.0793884 | − | 0.137505i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50000 | + | 4.33013i | −0.130499 | + | 0.226031i | −0.923869 | − | 0.382709i | \(-0.874991\pi\) |
0.793370 | + | 0.608740i | \(0.208325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5000 | + | 26.8468i | 0.802560 | + | 1.39007i | 0.917926 | + | 0.396751i | \(0.129862\pi\) |
−0.115367 | + | 0.993323i | \(0.536804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.50000 | + | 7.79423i | 0.386270 | + | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.500000 | − | 0.866025i | 0.0256833 | − | 0.0444847i | −0.852898 | − | 0.522077i | \(-0.825157\pi\) |
0.878581 | + | 0.477593i | \(0.158491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.50000 | + | 16.4545i | 0.486700 | + | 0.842989i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.50000 | + | 7.79423i | 0.229939 | + | 0.398266i | 0.957790 | − | 0.287469i | \(-0.0928139\pi\) |
−0.727851 | + | 0.685736i | \(0.759481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0000 | − | 19.0526i | 0.559161 | − | 0.968496i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | 0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | − | 10.3923i | 0.302660 | − | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.50000 | − | 4.33013i | −0.125471 | − | 0.217323i | 0.796446 | − | 0.604710i | \(-0.206711\pi\) |
−0.921917 | + | 0.387387i | \(0.873378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.50000 | − | 6.06218i | −0.175219 | − | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 28.5788i | 0.823971 | − | 1.42716i | −0.0787327 | − | 0.996896i | \(-0.525087\pi\) |
0.902703 | − | 0.430263i | \(-0.141579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | + | 13.8564i | −0.199254 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5000 | + | 18.1865i | 0.520466 | + | 0.901473i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5000 | + | 21.6506i | 0.618085 | + | 1.07056i | 0.989835 | + | 0.142222i | \(0.0454247\pi\) |
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0000 | −0.739895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.50000 | + | 2.59808i | −0.0738102 | + | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00000 | 0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50000 | + | 2.59808i | 0.0727607 | + | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.50000 | − | 9.52628i | 0.266164 | − | 0.461009i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5000 | + | 2.59808i | −0.506945 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.50000 | − | 7.79423i | 0.216757 | − | 0.375435i | −0.737057 | − | 0.675830i | \(-0.763785\pi\) |
0.953815 | + | 0.300395i | \(0.0971186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.5000 | − | 25.1147i | −0.696826 | − | 1.20694i | −0.969561 | − | 0.244848i | \(-0.921262\pi\) |
0.272736 | − | 0.962089i | \(-0.412071\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.50000 | − | 2.59808i | −0.0719195 | − | 0.124568i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.0000 | 1.00457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.50000 | + | 9.52628i | −0.262501 | + | 0.454665i | −0.966906 | − | 0.255134i | \(-0.917881\pi\) |
0.704405 | + | 0.709798i | \(0.251214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.50000 | + | 12.9904i | −0.355534 | + | 0.615803i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.0000 | −0.993266 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.50000 | − | 2.59808i | −0.0707894 | − | 0.122611i | 0.828458 | − | 0.560051i | \(-0.189218\pi\) |
−0.899247 | + | 0.437440i | \(0.855885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5000 | + | 23.3827i | 0.635690 | + | 1.10105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | + | 6.92820i | −0.187936 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.50000 | − | 0.866025i | 0.164083 | − | 0.0405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | + | 4.33013i | −0.116945 | + | 0.202555i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) |
0.801611 | + | 0.597847i | \(0.203977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.50000 | − | 12.9904i | −0.350070 | − | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5000 | − | 23.3827i | −0.628758 | − | 1.08904i | −0.987801 | − | 0.155719i | \(-0.950230\pi\) |
0.359044 | − | 0.933321i | \(-0.383103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | − | 3.46410i | 0.0927478 | − | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.0000 | 1.51734 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | + | 6.06218i | 0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | − | 10.3923i | −0.274721 | − | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5000 | + | 33.7750i | −0.890978 | + | 1.54322i | −0.0522726 | + | 0.998633i | \(0.516646\pi\) |
−0.838705 | + | 0.544586i | \(0.816687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | − | 18.1865i | −0.797931 | − | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.50000 | + | 2.59808i | −0.0682524 | + | 0.118217i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.50000 | + | 6.06218i | 0.158927 | + | 0.275269i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.50000 | − | 9.52628i | −0.249229 | − | 0.431677i | 0.714083 | − | 0.700061i | \(-0.246844\pi\) |
−0.963312 | + | 0.268384i | \(0.913510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | − | 7.79423i | 0.203082 | − | 0.351749i | −0.746438 | − | 0.665455i | \(-0.768237\pi\) |
0.949520 | + | 0.313707i | \(0.101571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | −0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.50000 | + | 2.59808i | −0.0672842 | + | 0.116540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.50000 | − | 12.9904i | −0.334408 | − | 0.579212i | 0.648963 | − | 0.760820i | \(-0.275203\pi\) |
−0.983371 | + | 0.181608i | \(0.941870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.50000 | − | 7.79423i | 0.200247 | − | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5000 | − | 6.06218i | 0.510733 | − | 0.269231i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 0.0442374 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.5000 | − | 30.3109i | −0.772644 | − | 1.33826i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.00000 | −0.131685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5000 | + | 25.1147i | −0.634041 | + | 1.09819i | 0.352677 | + | 0.935745i | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | + | 5.19615i | −0.130189 | + | 0.225494i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.5000 | − | 23.3827i | −0.974583 | − | 1.01282i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | + | 7.79423i | −0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.5000 | + | 18.1865i | 0.453108 | + | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.00000 | + | 15.5885i | 0.387657 | + | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0000 | − | 19.0526i | 0.469469 | − | 0.813143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0000 | −0.894630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 6.92820i | 0.170097 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.50000 | + | 6.06218i | 0.148567 | + | 0.257325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.5000 | − | 33.7750i | 0.826242 | − | 1.43109i | −0.0747252 | − | 0.997204i | \(-0.523808\pi\) |
0.900967 | − | 0.433888i | \(-0.142859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.5000 | + | 9.52628i | −1.62838 | + | 0.402919i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.50000 | − | 7.79423i | 0.189990 | − | 0.329073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5000 | − | 33.7750i | −0.821827 | − | 1.42345i | −0.904320 | − | 0.426855i | \(-0.859622\pi\) |
0.0824933 | − | 0.996592i | \(-0.473712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | − | 7.79423i | −0.189316 | − | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5000 | + | 23.3827i | −0.565949 | + | 0.980253i | 0.431011 | + | 0.902347i | \(0.358157\pi\) |
−0.996961 | + | 0.0779066i | \(0.975176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.00000 | −0.125327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.50000 | − | 2.59808i | 0.0625543 | − | 0.108347i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.50000 | − | 4.33013i | −0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | − | 15.5885i | 0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.00000 | − | 1.73205i | 0.289414 | − | 0.0716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.5000 | + | 28.5788i | −0.681028 | + | 1.17957i | 0.293640 | + | 0.955916i | \(0.405133\pi\) |
−0.974668 | + | 0.223659i | \(0.928200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0000 | − | 24.2487i | −0.576860 | − | 0.999151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5000 | − | 18.1865i | −0.431912 | − | 0.748094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.50000 | + | 2.59808i | −0.0614940 | + | 0.106511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.0000 | 0.695764 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | + | 1.73205i | 0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.50000 | − | 2.59808i | 0.0607831 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5000 | − | 37.2391i | 0.868377 | − | 1.50407i | 0.00472215 | − | 0.999989i | \(-0.498497\pi\) |
0.863655 | − | 0.504084i | \(-0.168170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.50000 | + | 7.79423i | 0.181458 | + | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.5000 | − | 28.5788i | −0.664265 | − | 1.15054i | −0.979484 | − | 0.201522i | \(-0.935411\pi\) |
0.315219 | − | 0.949019i | \(-0.397922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.0000 | 1.76851 | 0.884255 | − | 0.467005i | \(-0.154667\pi\) | ||||
0.884255 | + | 0.467005i | \(0.154667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | + | 12.9904i | −0.300965 | + | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.0000 | −0.600962 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5000 | − | 18.1865i | 0.419330 | − | 0.726300i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0000 | 0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.50000 | − | 14.7224i | −0.338380 | − | 0.586091i | 0.645748 | − | 0.763550i | \(-0.276545\pi\) |
−0.984128 | + | 0.177459i | \(0.943212\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.50000 | − | 9.52628i | −0.218605 | − | 0.378636i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.50000 | − | 16.4545i | 0.376996 | − | 0.652976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | − | 15.5885i | −0.594322 | − | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 23.3827i | −0.533218 | − | 0.923561i | −0.999247 | − | 0.0387913i | \(-0.987649\pi\) |
0.466029 | − | 0.884769i | \(-0.345684\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.50000 | − | 9.52628i | −0.216899 | − | 0.375680i | 0.736959 | − | 0.675937i | \(-0.236261\pi\) |
−0.953858 | + | 0.300257i | \(0.902928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0000 | 0.433125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5000 | + | 38.9711i | −0.884566 | + | 1.53211i | −0.0383563 | + | 0.999264i | \(0.512212\pi\) |
−0.846210 | + | 0.532850i | \(0.821121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.5000 | − | 33.7750i | 0.763094 | − | 1.32172i | −0.178154 | − | 0.984003i | \(-0.557013\pi\) |
0.941248 | − | 0.337715i | \(-0.109654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | + | 3.46410i | 0.0780274 | + | 0.135147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.5000 | + | 33.7750i | 0.759612 | + | 1.31569i | 0.943049 | + | 0.332655i | \(0.107945\pi\) |
−0.183436 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | − | 0.866025i | 0.0194477 | − | 0.0336845i | −0.856138 | − | 0.516748i | \(-0.827143\pi\) |
0.875585 | + | 0.483063i | \(0.160476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.00000 | + | 10.3923i | −0.116510 | + | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.50000 | + | 6.06218i | −0.135724 | + | 0.235081i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50000 | + | 7.79423i | 0.174241 | + | 0.301794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.50000 | + | 16.4545i | 0.367291 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.0000 | 1.27395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.50000 | + | 14.7224i | −0.327651 | + | 0.567508i | −0.982045 | − | 0.188645i | \(-0.939590\pi\) |
0.654394 | + | 0.756153i | \(0.272924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.50000 | + | 6.06218i | −0.134318 | + | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.0000 | 1.03464 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.5000 | − | 44.1673i | −0.975730 | − | 1.69001i | −0.677503 | − | 0.735520i | \(-0.736938\pi\) |
−0.298227 | − | 0.954495i | \(-0.596395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.50000 | + | 12.9904i | 0.286560 | + | 0.496337i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0000 | − | 19.0526i | 0.419676 | − | 0.726900i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | + | 20.7846i | −0.228582 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5000 | + | 19.9186i | −0.437481 | + | 0.757739i | −0.997494 | − | 0.0707446i | \(-0.977462\pi\) |
0.560014 | + | 0.828483i | \(0.310796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.00000 | − | 5.19615i | −0.113961 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.50000 | − | 4.33013i | −0.0948304 | − | 0.164251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0000 | 1.02270 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.0000 | 1.84807 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.00000 | 0.338480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5000 | + | 32.0429i | 0.694782 | + | 1.20340i | 0.970254 | + | 0.242089i | \(0.0778325\pi\) |
−0.275472 | + | 0.961309i | \(0.588834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | + | 10.3923i | −0.224702 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.50000 | + | 7.79423i | 0.280484 | + | 0.291488i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.50000 | − | 7.79423i | −0.167822 | − | 0.290676i | 0.769832 | − | 0.638247i | \(-0.220340\pi\) |
−0.937654 | + | 0.347571i | \(0.887007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | + | 6.92820i | 0.148968 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00000 | −0.0371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | + | 2.59808i | −0.0557086 | + | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.0000 | −1.92857 | −0.964287 | − | 0.264861i | \(-0.914674\pi\) | ||||
−0.964287 | + | 0.264861i | \(0.914674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5000 | − | 28.5788i | 0.610275 | − | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.00000 | + | 5.19615i | 0.110657 | + | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5000 | + | 18.1865i | 0.386772 | + | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.5000 | + | 40.7032i | −0.864461 | + | 1.49729i | 0.00311943 | + | 0.999995i | \(0.499007\pi\) |
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | + | 24.2487i | −0.257151 | + | 0.890799i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5000 | + | 18.1865i | −0.385208 | + | 0.667199i | −0.991798 | − | 0.127815i | \(-0.959204\pi\) |
0.606590 | + | 0.795015i | \(0.292537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5000 | + | 18.1865i | 0.384690 | + | 0.666303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | − | 20.7846i | −0.439057 | − | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | −0.328853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.0000 | 0.765283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5000 | + | 25.1147i | −0.527011 | + | 0.912811i | 0.472493 | + | 0.881334i | \(0.343354\pi\) |
−0.999505 | + | 0.0314762i | \(0.989979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | −0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | − | 2.59808i | −0.0543750 | − | 0.0941802i | 0.837557 | − | 0.546350i | \(-0.183983\pi\) |
−0.891932 | + | 0.452170i | \(0.850650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | + | 1.73205i | 0.0362024 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | + | 5.19615i | −0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5000 | − | 2.59808i | 0.379133 | − | 0.0938111i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.50000 | − | 11.2583i | 0.234396 | − | 0.405986i | −0.724701 | − | 0.689063i | \(-0.758022\pi\) |
0.959097 | + | 0.283078i | \(0.0913554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | − | 7.79423i | −0.162064 | − | 0.280702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5000 | + | 23.3827i | 0.485561 | + | 0.841017i | 0.999862 | − | 0.0165929i | \(-0.00528194\pi\) |
−0.514301 | + | 0.857610i | \(0.671949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.50000 | + | 6.06218i | −0.125562 | + | 0.217479i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.0000 | 2.25721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.50000 | − | 12.9904i | 0.268028 | − | 0.464238i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | −0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5000 | + | 32.0429i | 0.659454 | + | 1.14221i | 0.980757 | + | 0.195231i | \(0.0625457\pi\) |
−0.321303 | + | 0.946976i | \(0.604121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.50000 | + | 2.59808i | 0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.50000 | − | 7.79423i | 0.160002 | − | 0.277131i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.5000 | + | 9.52628i | −1.36718 | + | 0.338288i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | − | 5.19615i | 0.106399 | − | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.5000 | + | 44.1673i | 0.903256 | + | 1.56449i | 0.823241 | + | 0.567692i | \(0.192164\pi\) |
0.0800155 | + | 0.996794i | \(0.474503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | + | 5.19615i | −0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | 0.105736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.0000 | 0.950445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.50000 | + | 12.9904i | −0.263686 | + | 0.456717i | −0.967219 | − | 0.253946i | \(-0.918272\pi\) |
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.5000 | − | 19.9186i | −0.403323 | − | 0.698575i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.500000 | + | 0.866025i | 0.0175142 | + | 0.0303355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.5000 | − | 66.6840i | 1.34694 | − | 2.33298i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00000 | + | 5.19615i | 0.174714 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.50000 | + | 12.9904i | −0.261752 | + | 0.453367i | −0.966708 | − | 0.255884i | \(-0.917634\pi\) |
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50000 | + | 11.2583i | 0.226576 | + | 0.392441i | 0.956791 | − | 0.290776i | \(-0.0939136\pi\) |
−0.730215 | + | 0.683217i | \(0.760580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | + | 9.52628i | −0.191023 | + | 0.330861i | −0.945589 | − | 0.325362i | \(-0.894514\pi\) |
0.754567 | + | 0.656223i | \(0.227847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0000 | −0.659103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000 | 0.691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5000 | − | 18.1865i | −0.362500 | − | 0.627869i | 0.625871 | − | 0.779926i | \(-0.284743\pi\) |
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | + | 5.19615i | −0.103325 | + | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0000 | − | 6.92820i | −0.378412 | − | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | + | 1.73205i | −0.0343604 | + | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.50000 | − | 4.33013i | −0.0857998 | − | 0.148610i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5000 | − | 18.1865i | −0.359935 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.00000 | + | 12.1244i | −0.239395 | + | 0.414644i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50000 | + | 7.79423i | −0.153360 | + | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.50000 | + | 2.59808i | 0.0510015 | + | 0.0883372i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | + | 20.7846i | −0.407072 | + | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5000 | − | 18.1865i | −0.592965 | − | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | + | 12.1244i | −0.236914 | + | 0.410347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5000 | − | 35.5070i | −0.692236 | − | 1.19899i | −0.971104 | − | 0.238658i | \(-0.923292\pi\) |
0.278868 | − | 0.960329i | \(-0.410041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.0000 | −0.910687 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.5000 | + | 23.3827i | −0.454827 | + | 0.787783i | −0.998678 | − | 0.0513987i | \(-0.983632\pi\) |
0.543852 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.00000 | −0.100844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.50000 | + | 7.79423i | −0.151095 | + | 0.261705i | −0.931630 | − | 0.363407i | \(-0.881613\pi\) |
0.780535 | + | 0.625112i | \(0.214947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0000 | 0.637240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5000 | − | 18.1865i | 0.350976 | − | 0.607909i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5000 | − | 2.59808i | 0.350585 | − | 0.0867472i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.00000 | − | 10.3923i | 0.200111 | − | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.50000 | + | 9.52628i | 0.183029 | + | 0.317015i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.00000 | 0.0664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.50000 | − | 16.4545i | 0.315442 | − | 0.546362i | −0.664089 | − | 0.747653i | \(-0.731180\pi\) |
0.979531 | + | 0.201291i | \(0.0645138\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.0000 | 0.363649 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | − | 10.3923i | −0.198137 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.5000 | − | 25.1147i | −0.478311 | − | 0.828459i | 0.521380 | − | 0.853325i | \(-0.325417\pi\) |
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.5000 | − | 2.59808i | 0.345612 | − | 0.0855167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50000 | − | 6.06218i | 0.115079 | − | 0.199323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | + | 13.8564i | 0.262754 | + | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.5000 | − | 44.1673i | −0.836628 | − | 1.44908i | −0.892698 | − | 0.450655i | \(-0.851190\pi\) |
0.0560703 | − | 0.998427i | \(-0.482143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.0000 | 1.37649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0000 | + | 20.7846i | −0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00000 | −0.294331 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0000 | − | 19.0526i | 0.358971 | − | 0.621757i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.5000 | − | 23.3827i | −0.439620 | − | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.50000 | − | 4.33013i | −0.0813250 | − | 0.140859i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.5000 | + | 18.1865i | −0.341204 | + | 0.590983i | −0.984657 | − | 0.174503i | \(-0.944168\pi\) |
0.643452 | + | 0.765486i | \(0.277501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | − | 6.92820i | 0.0649227 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00000 | − | 15.5885i | 0.291845 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.5000 | + | 44.1673i | 0.826026 | + | 1.43072i | 0.901133 | + | 0.433544i | \(0.142737\pi\) |
−0.0751066 | + | 0.997176i | \(0.523930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50000 | + | 2.59808i | 0.0485389 | + | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | 0.290929 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.50000 | + | 12.9904i | −0.242188 | + | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.50000 | + | 4.33013i | −0.0804778 | + | 0.139392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.5000 | − | 18.1865i | −0.337309 | − | 0.584236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5000 | − | 18.1865i | −0.336961 | − | 0.583634i | 0.646899 | − | 0.762576i | \(-0.276066\pi\) |
−0.983860 | + | 0.178942i | \(0.942732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 4.33013i | 0.0801463 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.50000 | + | 2.59808i | 0.0800641 | + | 0.0832050i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.50000 | + | 7.79423i | −0.143968 | + | 0.249359i | −0.928987 | − | 0.370111i | \(-0.879319\pi\) |
0.785020 | + | 0.619471i | \(0.212653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.5000 | − | 38.9711i | −0.719103 | − | 1.24552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | + | 3.46410i | 0.0638551 | + | 0.110600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.0000 | −1.14822 | −0.574111 | − | 0.818778i | \(-0.694652\pi\) | ||||
−0.574111 | + | 0.818778i | \(0.694652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.5000 | + | 18.1865i | −0.334558 | + | 0.579471i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.0000 | −1.04934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5000 | − | 52.8275i | 0.968864 | − | 1.67812i | 0.270011 | − | 0.962857i | \(-0.412973\pi\) |
0.698853 | − | 0.715265i | \(-0.253694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.0000 | −0.602947 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.50000 | − | 14.7224i | −0.269468 | − | 0.466732i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.5000 | + | 26.8468i | 0.490890 | + | 0.850246i | 0.999945 | − | 0.0104877i | \(-0.00333839\pi\) |
−0.509055 | + | 0.860734i | \(0.670005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.5000 | + | 30.3109i | −0.553675 | + | 0.958994i |
(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 | 260.2.i.b.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 2340.2.q.b.1621.1 | 2 | |||
4.3 | odd | 2 | 1040.2.q.j.321.1 | 2 | |||
5.2 | odd | 4 | 1300.2.bb.a.1049.2 | 4 | |||
5.3 | odd | 4 | 1300.2.bb.a.1049.1 | 4 | |||
5.4 | even | 2 | 1300.2.i.e.1101.1 | 2 | |||
13.3 | even | 3 | inner | 260.2.i.b.81.1 | yes | 2 | |
13.4 | even | 6 | 3380.2.a.g.1.1 | 1 | |||
13.6 | odd | 12 | 3380.2.f.e.3041.1 | 2 | |||
13.7 | odd | 12 | 3380.2.f.e.3041.2 | 2 | |||
13.9 | even | 3 | 3380.2.a.h.1.1 | 1 | |||
39.29 | odd | 6 | 2340.2.q.b.2161.1 | 2 | |||
52.3 | odd | 6 | 1040.2.q.j.81.1 | 2 | |||
65.3 | odd | 12 | 1300.2.bb.a.549.2 | 4 | |||
65.29 | even | 6 | 1300.2.i.e.601.1 | 2 | |||
65.42 | odd | 12 | 1300.2.bb.a.549.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.b.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
260.2.i.b.81.1 | yes | 2 | 13.3 | even | 3 | inner | |
1040.2.q.j.81.1 | 2 | 52.3 | odd | 6 | |||
1040.2.q.j.321.1 | 2 | 4.3 | odd | 2 | |||
1300.2.i.e.601.1 | 2 | 65.29 | even | 6 | |||
1300.2.i.e.1101.1 | 2 | 5.4 | even | 2 | |||
1300.2.bb.a.549.1 | 4 | 65.42 | odd | 12 | |||
1300.2.bb.a.549.2 | 4 | 65.3 | odd | 12 | |||
1300.2.bb.a.1049.1 | 4 | 5.3 | odd | 4 | |||
1300.2.bb.a.1049.2 | 4 | 5.2 | odd | 4 | |||
2340.2.q.b.1621.1 | 2 | 3.2 | odd | 2 | |||
2340.2.q.b.2161.1 | 2 | 39.29 | odd | 6 | |||
3380.2.a.g.1.1 | 1 | 13.4 | even | 6 | |||
3380.2.a.h.1.1 | 1 | 13.9 | even | 3 | |||
3380.2.f.e.3041.1 | 2 | 13.6 | odd | 12 | |||
3380.2.f.e.3041.2 | 2 | 13.7 | odd | 12 |