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 | 81.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.81 |
Dual form | 260.2.i.b.61.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 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 | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | − | 6.06218i | 0.802955 | − | 1.39076i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 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 | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | 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 | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) |
−0.420602 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50000 | − | 2.59808i | 0.400320 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 7.79423i | 0.702782 | + | 1.21725i | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | + | 9.52628i | −0.838742 | + | 1.45274i | 0.0522047 | + | 0.998636i | \(0.483375\pi\) |
−0.890947 | + | 0.454108i | \(0.849958\pi\) | |||||||
\(44\) | 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 | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | + | 9.52628i | −0.704203 | + | 1.21972i | 0.262776 | + | 0.964857i | \(0.415362\pi\) |
−0.966978 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(62\) | 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 | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | − | 2.59808i | 0.180579 | − | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | − | 2.59808i | 0.178017 | − | 0.308335i | −0.763184 | − | 0.646181i | \(-0.776365\pi\) |
0.941201 | + | 0.337846i | \(0.109698\pi\) | |||||||
\(72\) | 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 | −0.922840 | − | 0.385183i | \(-0.874138\pi\) |
0.127842 | − | 0.991795i | \(-0.459195\pi\) | |||||||
\(90\) | 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 | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 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 | 0.562267 | − | 0.826956i | \(-0.309929\pi\) |
−0.997298 | + | 0.0734594i | \(0.976596\pi\) | |||||||
\(108\) | 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 | −0.996262 | − | 0.0863794i | \(-0.972470\pi\) |
0.572938 | + | 0.819599i | \(0.305804\pi\) | |||||||
\(114\) | 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 | 0.887357 | + | 0.461084i | \(0.152539\pi\) |
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 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 | −0.344493 | − | 0.938789i | \(-0.611949\pi\) |
0.985262 | − | 0.171054i | \(-0.0547174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 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 | −0.0115483 | − | 0.999933i | \(-0.503676\pi\) |
0.871742 | − | 0.489966i | \(-0.162991\pi\) | |||||||
\(150\) | 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 | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | + | 2.59808i | 0.116073 | + | 0.201045i | 0.918208 | − | 0.396098i | \(-0.129636\pi\) |
−0.802135 | + | 0.597143i | \(0.796303\pi\) | |||||||
\(168\) | 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 | −0.803354 | − | 0.595502i | \(-0.796953\pi\) |
0.917397 | + | 0.397974i | \(0.130287\pi\) | |||||||
\(174\) | 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 | 0.929114 | + | 0.369792i | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | 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 | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.50000 | − | 2.59808i | 0.179029 | − | 0.186052i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5000 | − | 18.1865i | −0.748094 | − | 1.29574i | −0.948735 | − | 0.316072i | \(-0.897636\pi\) |
0.200641 | − | 0.979665i | \(-0.435697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.50000 | + | 14.7224i | −0.602549 | + | 1.04365i | 0.389885 | + | 0.920864i | \(0.372515\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 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 | 0.612228 | − | 0.790681i | \(-0.290273\pi\) |
−0.990864 | + | 0.134865i | \(0.956940\pi\) | |||||||
\(212\) | 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 | 0.986267 | + | 0.165161i | \(0.0528144\pi\) |
−0.350100 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | − | 1.73205i | 0.0666667 | − | 0.115470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.5000 | + | 23.3827i | −0.896026 | + | 1.55196i | −0.0634974 | + | 0.997982i | \(0.520225\pi\) |
−0.832529 | + | 0.553981i | \(0.813108\pi\) | |||||||
\(228\) | 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 | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 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 | 0.317135 | + | 0.948380i | \(0.397279\pi\) |
−0.979889 | + | 0.199543i | \(0.936054\pi\) | |||||||
\(252\) | 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 | 0.690856 | − | 0.722993i | \(-0.257234\pi\) |
−0.971558 | + | 0.236802i | \(0.923901\pi\) | |||||||
\(258\) | 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 | 0.908560 | − | 0.417755i | \(-0.137183\pi\) |
−0.816066 | + | 0.577959i | \(0.803849\pi\) | |||||||
\(264\) | 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 | 0.0802460 | + | 0.996775i | \(0.474429\pi\) |
−0.903356 | + | 0.428892i | \(0.858904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5000 | − | 19.9186i | −0.698575 | − | 1.20997i | −0.968960 | − | 0.247216i | \(-0.920484\pi\) |
0.270385 | − | 0.962752i | \(-0.412849\pi\) | |||||||
\(272\) | 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 | −0.425684 | − | 0.904872i | \(-0.639967\pi\) |
0.996484 | − | 0.0837823i | \(-0.0267000\pi\) | |||||||
\(278\) | 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 | 0.782104 | − | 0.623148i | \(-0.214146\pi\) |
−0.930714 | + | 0.365748i | \(0.880813\pi\) | |||||||
\(284\) | 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 | −0.138098 | − | 0.990419i | \(-0.544099\pi\) |
0.926777 | − | 0.375613i | \(-0.122568\pi\) | |||||||
\(294\) | 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 | −0.477500 | − | 0.878632i | \(-0.658457\pi\) |
0.999667 | − | 0.0257885i | \(-0.00820965\pi\) | |||||||
\(332\) | 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 | 0.0409337 | − | 0.999162i | \(-0.486967\pi\) |
0.844833 | − | 0.535031i | \(-0.179700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.500000 | + | 0.866025i | 0.0267644 | + | 0.0463573i | 0.879097 | − | 0.476642i | \(-0.158146\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 17.3205i | −0.266880 | − | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | − | 7.79423i | −0.239511 | − | 0.414845i | 0.721063 | − | 0.692869i | \(-0.243654\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | 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 | 0.793370 | − | 0.608740i | \(-0.208325\pi\) |
−0.923869 | + | 0.382709i | \(0.874991\pi\) | |||||||
\(368\) | 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 | −0.115367 | − | 0.993323i | \(-0.536804\pi\) |
0.917926 | − | 0.396751i | \(-0.129862\pi\) | |||||||
\(374\) | 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 | 0.878581 | − | 0.477593i | \(-0.158491\pi\) |
−0.852898 | + | 0.522077i | \(0.825157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.50000 | − | 16.4545i | 0.486700 | − | 0.842989i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.50000 | − | 7.79423i | 0.229939 | − | 0.398266i | −0.727851 | − | 0.685736i | \(-0.759481\pi\) |
0.957790 | + | 0.287469i | \(0.0928139\pi\) | |||||||
\(384\) | 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 | −0.921917 | − | 0.387387i | \(-0.873378\pi\) |
0.796446 | + | 0.604710i | \(0.206711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.50000 | + | 6.06218i | −0.175219 | + | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | + | 28.5788i | 0.823971 | + | 1.42716i | 0.902703 | + | 0.430263i | \(0.141579\pi\) |
−0.0787327 | + | 0.996896i | \(0.525087\pi\) | |||||||
\(402\) | 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 | −0.371750 | − | 0.928333i | \(-0.621242\pi\) |
0.989835 | − | 0.142222i | \(-0.0454247\pi\) | |||||||
\(410\) | 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 | 0.954759 | − | 0.297382i | \(-0.0961133\pi\) |
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(420\) | 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 | 0.953815 | − | 0.300395i | \(-0.0971186\pi\) |
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.5000 | + | 25.1147i | −0.696826 | + | 1.20694i | 0.272736 | + | 0.962089i | \(0.412071\pi\) |
−0.969561 | + | 0.244848i | \(0.921262\pi\) | |||||||
\(434\) | 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 | 0.704405 | − | 0.709798i | \(-0.251214\pi\) |
−0.966906 | + | 0.255134i | \(0.917881\pi\) | |||||||
\(440\) | 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 | −0.899247 | − | 0.437440i | \(-0.855885\pi\) |
0.828458 | + | 0.560051i | \(0.189218\pi\) | |||||||
\(450\) | 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 | 0.801611 | − | 0.597847i | \(-0.203977\pi\) |
−0.918556 | + | 0.395292i | \(0.870643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.50000 | + | 12.9904i | −0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5000 | + | 23.3827i | −0.628758 | + | 1.08904i | 0.359044 | + | 0.933321i | \(0.383103\pi\) |
−0.987801 | + | 0.155719i | \(0.950230\pi\) | |||||||
\(462\) | 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 | −0.838705 | − | 0.544586i | \(-0.816687\pi\) |
−0.0522726 | − | 0.998633i | \(-0.516646\pi\) | |||||||
\(480\) | 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 | −0.963312 | − | 0.268384i | \(-0.913510\pi\) |
0.714083 | + | 0.700061i | \(0.246844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 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 | −0.983371 | − | 0.181608i | \(-0.941870\pi\) |
0.648963 | + | 0.760820i | \(0.275203\pi\) | |||||||
\(504\) | 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 | 0.948353 | − | 0.317217i | \(-0.102748\pi\) |
−0.748894 | + | 0.662690i | \(0.769415\pi\) | |||||||
\(510\) | 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 | −0.986718 | − | 0.162446i | \(-0.948062\pi\) |
0.352677 | − | 0.935745i | \(-0.385272\pi\) | |||||||
\(524\) | 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 | 0.900967 | + | 0.433888i | \(0.142859\pi\) |
−0.0747252 | + | 0.997204i | \(0.523808\pi\) | |||||||
\(558\) | 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 | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | 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 | −0.996961 | − | 0.0779066i | \(-0.975176\pi\) |
0.431011 | − | 0.902347i | \(-0.358157\pi\) | |||||||
\(570\) | 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 | −0.974668 | − | 0.223659i | \(-0.928200\pi\) |
0.293640 | − | 0.955916i | \(-0.405133\pi\) | |||||||
\(588\) | 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 | −0.963405 | − | 0.268049i | \(-0.913621\pi\) |
0.249565 | − | 0.968358i | \(-0.419712\pi\) | |||||||
\(602\) | 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 | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | 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 | 0.863655 | + | 0.504084i | \(0.168170\pi\) |
0.00472215 | + | 0.999989i | \(0.498497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.50000 | − | 7.79423i | 0.181458 | − | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.5000 | + | 28.5788i | −0.664265 | + | 1.15054i | 0.315219 | + | 0.949019i | \(0.397922\pi\) |
−0.979484 | + | 0.201522i | \(0.935411\pi\) | |||||||
\(618\) | 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 | −0.984128 | − | 0.177459i | \(-0.943212\pi\) |
0.645748 | + | 0.763550i | \(0.276545\pi\) | |||||||
\(632\) | 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 | 0.466029 | + | 0.884769i | \(0.345684\pi\) |
−0.999247 | + | 0.0387913i | \(0.987649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.50000 | + | 9.52628i | −0.216899 | + | 0.375680i | −0.953858 | − | 0.300257i | \(-0.902928\pi\) |
0.736959 | + | 0.675937i | \(0.236261\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0000 | 0.433125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5000 | − | 38.9711i | −0.884566 | − | 1.53211i | −0.846210 | − | 0.532850i | \(-0.821121\pi\) |
−0.0383563 | − | 0.999264i | \(-0.512212\pi\) | |||||||
\(648\) | 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 | 0.941248 | + | 0.337715i | \(0.109654\pi\) |
−0.178154 | + | 0.984003i | \(0.557013\pi\) | |||||||
\(654\) | 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 | −0.183436 | − | 0.983032i | \(-0.558722\pi\) |
0.943049 | − | 0.332655i | \(-0.107945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | + | 0.866025i | 0.0194477 | + | 0.0336845i | 0.875585 | − | 0.483063i | \(-0.160476\pi\) |
−0.856138 | + | 0.516748i | \(0.827143\pi\) | |||||||
\(662\) | 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 | 0.654394 | − | 0.756153i | \(-0.272924\pi\) |
−0.982045 | + | 0.188645i | \(0.939590\pi\) | |||||||
\(674\) | 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 | −0.298227 | + | 0.954495i | \(0.596395\pi\) |
−0.677503 | + | 0.735520i | \(0.736938\pi\) | |||||||
\(684\) | 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 | 0.560014 | − | 0.828483i | \(-0.310796\pi\) |
−0.997494 | + | 0.0707446i | \(0.977462\pi\) | |||||||
\(692\) | 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 | −0.275472 | − | 0.961309i | \(-0.588834\pi\) |
0.970254 | − | 0.242089i | \(-0.0778325\pi\) | |||||||
\(710\) | 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 | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 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 | −0.867581 | − | 0.497296i | \(-0.834326\pi\) |
0.00311943 | − | 0.999995i | \(-0.499007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | − | 24.2487i | −0.257151 | − | 0.890799i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5000 | − | 18.1865i | −0.385208 | − | 0.667199i | 0.606590 | − | 0.795015i | \(-0.292537\pi\) |
−0.991798 | + | 0.127815i | \(0.959204\pi\) | |||||||
\(744\) | 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 | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | 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 | −0.999505 | − | 0.0314762i | \(-0.989979\pi\) |
0.472493 | − | 0.881334i | \(-0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | −0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | + | 2.59808i | −0.0543750 | + | 0.0941802i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) |
0.837557 | + | 0.546350i | \(0.183983\pi\) | |||||||
\(762\) | 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 | 0.959097 | − | 0.283078i | \(-0.0913554\pi\) |
−0.724701 | + | 0.689063i | \(0.758022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | + | 7.79423i | −0.162064 | + | 0.280702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5000 | − | 23.3827i | 0.485561 | − | 0.841017i | −0.514301 | − | 0.857610i | \(-0.671949\pi\) |
0.999862 | + | 0.0165929i | \(0.00528194\pi\) | |||||||
\(774\) | 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 | −0.321303 | − | 0.946976i | \(-0.604121\pi\) |
0.980757 | − | 0.195231i | \(-0.0625457\pi\) | |||||||
\(788\) | 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 | 0.0800155 | − | 0.996794i | \(-0.474503\pi\) |
0.823241 | − | 0.567692i | \(-0.192164\pi\) | |||||||
\(798\) | 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 | 0.703533 | − | 0.710663i | \(-0.251605\pi\) |
−0.967219 | + | 0.253946i | \(0.918272\pi\) | |||||||
\(810\) | 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 | 0.704956 | − | 0.709251i | \(-0.250967\pi\) |
−0.966708 | + | 0.255884i | \(0.917634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50000 | − | 11.2583i | 0.226576 | − | 0.392441i | −0.730215 | − | 0.683217i | \(-0.760580\pi\) |
0.956791 | + | 0.290776i | \(0.0939136\pi\) | |||||||
\(824\) | 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 | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 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 | −0.988372 | − | 0.152057i | \(-0.951410\pi\) |
0.625871 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(840\) | 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 | 0.278868 | + | 0.960329i | \(0.410041\pi\) |
−0.971104 | + | 0.238658i | \(0.923292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.0000 | −0.910687 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.5000 | − | 23.3827i | −0.454827 | − | 0.787783i | 0.543852 | − | 0.839181i | \(-0.316965\pi\) |
−0.998678 | + | 0.0513987i | \(0.983632\pi\) | |||||||
\(882\) | 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 | 0.780535 | − | 0.625112i | \(-0.214947\pi\) |
−0.931630 | + | 0.363407i | \(0.881613\pi\) | |||||||
\(888\) | 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 | 0.979531 | − | 0.201291i | \(-0.0645138\pi\) |
−0.664089 | + | 0.747653i | \(0.731180\pi\) | |||||||
\(908\) | 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 | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 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 | 0.0560703 | + | 0.998427i | \(0.482143\pi\) |
−0.892698 | + | 0.450655i | \(0.851190\pi\) | |||||||
\(930\) | 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 | 0.643452 | − | 0.765486i | \(-0.277501\pi\) |
−0.984657 | + | 0.174503i | \(0.944168\pi\) | |||||||
\(948\) | 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 | −0.0751066 | − | 0.997176i | \(-0.523930\pi\) |
0.901133 | − | 0.433544i | \(-0.142737\pi\) | |||||||
\(954\) | 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 | −0.983860 | − | 0.178942i | \(-0.942732\pi\) |
0.646899 | + | 0.762576i | \(0.276066\pi\) | |||||||
\(972\) | 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 | 0.785020 | − | 0.619471i | \(-0.212653\pi\) |
−0.928987 | + | 0.370111i | \(0.879319\pi\) | |||||||
\(978\) | 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 | 0.698853 | + | 0.715265i | \(0.253694\pi\) |
0.270011 | + | 0.962857i | \(0.412973\pi\) | |||||||
\(992\) | 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 | −0.509055 | − | 0.860734i | \(-0.670005\pi\) |
0.999945 | + | 0.0104877i | \(0.00333839\pi\) | |||||||
\(998\) | 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.81.1 | yes | 2 | |
3.2 | odd | 2 | 2340.2.q.b.2161.1 | 2 | |||
4.3 | odd | 2 | 1040.2.q.j.81.1 | 2 | |||
5.2 | odd | 4 | 1300.2.bb.a.549.1 | 4 | |||
5.3 | odd | 4 | 1300.2.bb.a.549.2 | 4 | |||
5.4 | even | 2 | 1300.2.i.e.601.1 | 2 | |||
13.2 | odd | 12 | 3380.2.f.e.3041.1 | 2 | |||
13.3 | even | 3 | 3380.2.a.h.1.1 | 1 | |||
13.9 | even | 3 | inner | 260.2.i.b.61.1 | ✓ | 2 | |
13.10 | even | 6 | 3380.2.a.g.1.1 | 1 | |||
13.11 | odd | 12 | 3380.2.f.e.3041.2 | 2 | |||
39.35 | odd | 6 | 2340.2.q.b.1621.1 | 2 | |||
52.35 | odd | 6 | 1040.2.q.j.321.1 | 2 | |||
65.9 | even | 6 | 1300.2.i.e.1101.1 | 2 | |||
65.22 | odd | 12 | 1300.2.bb.a.1049.2 | 4 | |||
65.48 | odd | 12 | 1300.2.bb.a.1049.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.b.61.1 | ✓ | 2 | 13.9 | even | 3 | inner | |
260.2.i.b.81.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1040.2.q.j.81.1 | 2 | 4.3 | odd | 2 | |||
1040.2.q.j.321.1 | 2 | 52.35 | odd | 6 | |||
1300.2.i.e.601.1 | 2 | 5.4 | even | 2 | |||
1300.2.i.e.1101.1 | 2 | 65.9 | even | 6 | |||
1300.2.bb.a.549.1 | 4 | 5.2 | odd | 4 | |||
1300.2.bb.a.549.2 | 4 | 5.3 | odd | 4 | |||
1300.2.bb.a.1049.1 | 4 | 65.48 | odd | 12 | |||
1300.2.bb.a.1049.2 | 4 | 65.22 | odd | 12 | |||
2340.2.q.b.1621.1 | 2 | 39.35 | odd | 6 | |||
2340.2.q.b.2161.1 | 2 | 3.2 | odd | 2 | |||
3380.2.a.g.1.1 | 1 | 13.10 | even | 6 | |||
3380.2.a.h.1.1 | 1 | 13.3 | even | 3 | |||
3380.2.f.e.3041.1 | 2 | 13.2 | odd | 12 | |||
3380.2.f.e.3041.2 | 2 | 13.11 | odd | 12 |