Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(549,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bb (of order \(6\), degree \(2\), not 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1049.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.1049 |
Dual form | 1300.2.bb.a.549.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | 0.728714 | − | 0.684819i | \(-0.240119\pi\) |
−0.228714 | + | 0.973494i | \(0.573452\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) |
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −3.46410 | − | 1.00000i | −0.960769 | − | 0.277350i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.59808 | + | 1.50000i | −0.630126 | + | 0.363803i | −0.780801 | − | 0.624780i | \(-0.785189\pi\) |
0.150675 | + | 0.988583i | \(0.451855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.59808 | + | 1.50000i | −0.452267 | + | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.06218 | + | 3.50000i | 0.996616 | + | 0.575396i | 0.907245 | − | 0.420602i | \(-0.138181\pi\) |
0.0893706 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −9.52628 | + | 5.50000i | −1.45274 | + | 0.838742i | −0.998636 | − | 0.0522047i | \(-0.983375\pi\) |
−0.454108 | + | 0.890947i | \(0.650042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 5.19615i | −0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.00000i | − | 0.927173i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 1.73205 | + | 1.00000i | 0.218218 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06218 | + | 3.50000i | 0.740613 | + | 0.427593i | 0.822292 | − | 0.569066i | \(-0.192695\pi\) |
−0.0816792 | + | 0.996659i | \(0.526028\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.00000i | − | 0.341882i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59808 | − | 1.50000i | 0.278543 | − | 0.160817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | − | 12.9904i | 0.794998 | − | 1.37698i | −0.127842 | − | 0.991795i | \(-0.540805\pi\) |
0.922840 | − | 0.385183i | \(-0.125862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.06218 | + | 3.50000i | −0.615521 | + | 0.355371i | −0.775123 | − | 0.631810i | \(-0.782312\pi\) |
0.159602 | + | 0.987181i | \(0.448979\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79423 | − | 4.50000i | −0.753497 | − | 0.435031i | 0.0734594 | − | 0.997298i | \(-0.476596\pi\) |
−0.826956 | + | 0.562267i | \(0.809929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.79423 | + | 4.50000i | −0.733219 | + | 0.423324i | −0.819599 | − | 0.572938i | \(-0.805804\pi\) |
0.0863794 | + | 0.996262i | \(0.472470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.73205 | + | 7.00000i | 0.160128 | + | 0.647150i | ||||
\(118\) | 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 | ||||||||
\(123\) | 7.79423 | − | 4.50000i | 0.702782 | − | 0.405751i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4545 | + | 9.50000i | 1.46010 | + | 0.842989i | 0.999015 | − | 0.0443678i | \(-0.0141274\pi\) |
0.461084 | + | 0.887357i | \(0.347461\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 6.06218 | + | 3.50000i | 0.525657 | + | 0.303488i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9904 | + | 7.50000i | −1.10984 | + | 0.640768i | −0.938789 | − | 0.344493i | \(-0.888051\pi\) |
−0.171054 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.79423 | − | 7.50000i | 0.651786 | − | 0.627182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.19615 | + | 3.00000i | −0.428571 | + | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5000 | − | 18.1865i | −0.860194 | − | 1.48990i | −0.871742 | − | 0.489966i | \(-0.837009\pi\) |
0.0115483 | − | 0.999933i | \(-0.496324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.19615 | + | 3.00000i | 0.420084 | + | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0000i | − | 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.866025 | − | 0.500000i | 0.0678323 | − | 0.0391630i | −0.465700 | − | 0.884943i | \(-0.654198\pi\) |
0.533533 | + | 0.845780i | \(0.320864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59808 | + | 1.50000i | 0.201045 | + | 0.116073i | 0.597143 | − | 0.802135i | \(-0.296303\pi\) |
−0.396098 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | 2.59808 | − | 1.50000i | 0.197528 | − | 0.114043i | −0.397974 | − | 0.917397i | \(-0.630287\pi\) |
0.595502 | + | 0.803354i | \(0.296953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.00000i | − | 0.225494i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | + | 18.1865i | −0.784807 | + | 1.35933i | 0.144308 | + | 0.989533i | \(0.453905\pi\) |
−0.929114 | + | 0.369792i | \(0.879429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.0000i | − | 0.813143i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.00000i | − | 0.658145i | ||||||
\(188\) | 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 | ||||||||
\(193\) | 4.33013 | + | 2.50000i | 0.311689 | + | 0.179954i | 0.647682 | − | 0.761911i | \(-0.275738\pi\) |
−0.335993 | + | 0.941865i | \(0.609072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1865 | − | 10.5000i | −1.29574 | − | 0.748094i | −0.316072 | − | 0.948735i | \(-0.602364\pi\) |
−0.979665 | + | 0.200641i | \(0.935697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.50000 | + | 14.7224i | 0.602549 | + | 1.04365i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | + | 6.06218i | 0.246871 | + | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000i | 0.210559i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 3.00000i | 0.205557i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.46410 | − | 2.00000i | 0.235159 | − | 0.135769i | ||||
\(218\) | 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 | ||||||||
\(223\) | −16.4545 | − | 9.50000i | −1.10187 | − | 0.636167i | −0.165161 | − | 0.986267i | \(-0.552814\pi\) |
−0.936713 | + | 0.350100i | \(0.886148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3827 | − | 13.5000i | 1.55196 | − | 0.896026i | 0.553981 | − | 0.832529i | \(-0.313108\pi\) |
0.997982 | − | 0.0634974i | \(-0.0202255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.92820 | − | 4.00000i | −0.450035 | − | 0.259828i | ||||
\(238\) | 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 | ||||||||
\(243\) | −13.8564 | + | 8.00000i | −0.888889 | + | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.06218 | + | 24.5000i | 0.385727 | + | 1.55890i | ||||
\(248\) | 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 | ||||||||
\(253\) | 7.79423 | − | 4.50000i | 0.490019 | − | 0.282913i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.79423 | − | 4.50000i | −0.486191 | − | 0.280702i | 0.236802 | − | 0.971558i | \(-0.423901\pi\) |
−0.722993 | + | 0.690856i | \(0.757234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.59808 | − | 1.50000i | −0.160204 | − | 0.0924940i | 0.417755 | − | 0.908560i | \(-0.362817\pi\) |
−0.577959 | + | 0.816066i | \(0.696151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9904 | − | 7.50000i | 0.794998 | − | 0.458993i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5000 | + | 23.3827i | 0.823110 | + | 1.42567i | 0.903356 | + | 0.428892i | \(0.141096\pi\) |
−0.0802460 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 3.46410 | + | 1.00000i | 0.209657 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.4545 | + | 9.50000i | −0.988654 | + | 0.570800i | −0.904872 | − | 0.425684i | \(-0.860033\pi\) |
−0.0837823 | + | 0.996484i | \(0.526700\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 4.33013 | + | 2.50000i | 0.257399 | + | 0.148610i | 0.623148 | − | 0.782104i | \(-0.285854\pi\) |
−0.365748 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.00000i | 0.531253i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.3827 | − | 13.5000i | 1.36603 | − | 0.788678i | 0.375613 | − | 0.926777i | \(-0.377432\pi\) |
0.990419 | + | 0.138098i | \(0.0440990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9904 | + | 7.50000i | 0.753778 | + | 0.435194i | ||||
\(298\) | 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 | ||||||||
\(303\) | 7.79423 | − | 4.50000i | 0.447767 | − | 0.258518i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 22.0000i | 1.24351i | 0.783210 | + | 0.621757i | \(0.213581\pi\) | ||||
−0.783210 | + | 0.621757i | \(0.786419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 18.1865 | + | 10.5000i | 1.01193 | + | 0.584236i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.73205 | − | 1.00000i | −0.0957826 | − | 0.0553001i | ||||
\(328\) | 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 | ||||||||
\(333\) | − | 14.0000i | − | 0.767195i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.0000i | − | 1.85210i | −0.377403 | − | 0.926049i | \(-0.623183\pi\) | ||
0.377403 | − | 0.926049i | \(-0.376817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.5788 | + | 16.5000i | −1.53419 | + | 0.885766i | −0.535031 | + | 0.844833i | \(0.679700\pi\) |
−0.999162 | + | 0.0409337i | \(0.986967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.500000 | + | 0.866025i | −0.0267644 | + | 0.0463573i | −0.879097 | − | 0.476642i | \(-0.841854\pi\) |
0.852333 | + | 0.523000i | \(0.175187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.79423 | + | 4.50000i | 0.414845 | + | 0.239511i | 0.692869 | − | 0.721063i | \(-0.256346\pi\) |
−0.278024 | + | 0.960574i | \(0.589680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.59808 | − | 1.50000i | 0.137505 | − | 0.0793884i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000i | 0.104973i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.33013 | − | 2.50000i | −0.226031 | − | 0.130499i | 0.382709 | − | 0.923869i | \(-0.374991\pi\) |
−0.608740 | + | 0.793370i | \(0.708325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.8468 | − | 15.5000i | 1.39007 | − | 0.802560i | 0.396751 | − | 0.917926i | \(-0.370138\pi\) |
0.993323 | + | 0.115367i | \(0.0368043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.79423 | + | 7.50000i | −0.401423 | + | 0.386270i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.500000 | + | 0.866025i | −0.0256833 | + | 0.0444847i | −0.878581 | − | 0.477593i | \(-0.841509\pi\) |
0.852898 | + | 0.522077i | \(0.174843\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.50000 | + | 16.4545i | 0.486700 | + | 0.842989i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.79423 | − | 4.50000i | 0.398266 | − | 0.229939i | −0.287469 | − | 0.957790i | \(-0.592814\pi\) |
0.685736 | + | 0.727851i | \(0.259481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.0526 | + | 11.0000i | 0.968496 | + | 0.559161i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | 0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3923 | − | 6.00000i | −0.524222 | − | 0.302660i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.33013 | − | 2.50000i | 0.217323 | − | 0.125471i | −0.387387 | − | 0.921917i | \(-0.626622\pi\) |
0.604710 | + | 0.796446i | \(0.293289\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 13.8564 | + | 4.00000i | 0.690237 | + | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.1865 | + | 10.5000i | −0.901473 | + | 0.520466i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | − | 21.6506i | −0.618085 | − | 1.07056i | −0.989835 | − | 0.142222i | \(-0.954575\pi\) |
0.371750 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0000 | −0.739895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.59808 | + | 1.50000i | 0.127843 | + | 0.0738102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00000i | 0.244851i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.50000 | + | 7.79423i | −0.219839 | + | 0.380773i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.52628 | + | 5.50000i | 0.461009 | + | 0.266164i | ||||
\(428\) | 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 | ||||||||
\(433\) | −25.1147 | + | 14.5000i | −1.20694 | + | 0.696826i | −0.962089 | − | 0.272736i | \(-0.912071\pi\) |
−0.244848 | + | 0.969561i | \(0.578738\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.0000i | 1.00457i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.50000 | − | 9.52628i | 0.262501 | − | 0.454665i | −0.704405 | − | 0.709798i | \(-0.748786\pi\) |
0.966906 | + | 0.255134i | \(0.0821195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 21.0000i | − | 0.993266i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.50000 | + | 2.59808i | 0.0707894 | + | 0.122611i | 0.899247 | − | 0.437440i | \(-0.144115\pi\) |
−0.828458 | + | 0.560051i | \(0.810782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5000 | + | 23.3827i | 0.635690 | + | 1.10105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820 | + | 4.00000i | 0.325515 | + | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.33013 | − | 2.50000i | −0.202555 | − | 0.116945i | 0.395292 | − | 0.918556i | \(-0.370643\pi\) |
−0.597847 | + | 0.801611i | \(0.703977\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 36.0000i | − | 1.66588i | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||
0.553362 | − | 0.832941i | \(-0.313345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.00000 | −0.323230 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33.0000i | − | 1.51734i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3923 | − | 6.00000i | 0.475831 | − | 0.274721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5000 | − | 33.7750i | 0.890978 | − | 1.54322i | 0.0522726 | − | 0.998633i | \(-0.483354\pi\) |
0.838705 | − | 0.544586i | \(-0.183313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | − | 18.1865i | −0.797931 | − | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.59808 | + | 1.50000i | 0.118217 | + | 0.0682524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.52628 | − | 5.50000i | 0.431677 | − | 0.249229i | −0.268384 | − | 0.963312i | \(-0.586490\pi\) |
0.700061 | + | 0.714083i | \(0.253156\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 9.00000i | 0.405340i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.59808 | − | 1.50000i | −0.116540 | − | 0.0672842i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9904 | + | 7.50000i | −0.579212 | + | 0.334408i | −0.760820 | − | 0.648963i | \(-0.775203\pi\) |
0.181608 | + | 0.983371i | \(0.441870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.06218 | + | 11.5000i | 0.269231 | + | 0.510733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.50000 | + | 7.79423i | −0.199459 | + | 0.345473i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 0.0442374 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.3109 | + | 17.5000i | −1.33826 | + | 0.772644i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | ||||||||
\(523\) | 25.1147 | + | 14.5000i | 1.09819 | + | 0.634041i | 0.935745 | − | 0.352677i | \(-0.114728\pi\) |
0.162446 | + | 0.986718i | \(0.448062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3923 | − | 6.00000i | 0.452696 | − | 0.261364i | ||||
\(528\) | 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 | ||||||||
\(533\) | −23.3827 | + | 22.5000i | −1.01282 | + | 0.974583i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.1865 | + | 10.5000i | −0.784807 | + | 0.453108i | ||||
\(538\) | 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 | ||||||||
\(543\) | 1.73205 | + | 1.00000i | 0.0743294 | + | 0.0429141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.0000 | + | 19.0526i | −0.469469 | + | 0.813143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0000 | −0.894630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92820 | − | 4.00000i | 0.294617 | − | 0.170097i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.7750 | + | 19.5000i | 1.43109 | + | 0.826242i | 0.997204 | − | 0.0747252i | \(-0.0238080\pi\) |
0.433888 | + | 0.900967i | \(0.357141\pi\) | |||||||
\(558\) | 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 | ||||||||
\(563\) | −33.7750 | + | 19.5000i | −1.42345 | + | 0.821827i | −0.996592 | − | 0.0824933i | \(-0.973712\pi\) |
−0.426855 | + | 0.904320i | \(0.640378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 23.3827i | 0.565949 | − | 0.980253i | −0.431011 | − | 0.902347i | \(-0.641843\pi\) |
0.996961 | − | 0.0779066i | \(-0.0248236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.00000i | 0.125327i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −15.5885 | − | 9.00000i | −0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.5788 | − | 16.5000i | −1.17957 | − | 0.681028i | −0.223659 | − | 0.974668i | \(-0.571800\pi\) |
−0.955916 | + | 0.293640i | \(0.905133\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 6.00000i | 0.246390i | 0.992382 | + | 0.123195i | \(0.0393141\pi\) | ||||
−0.992382 | + | 0.123195i | \(0.960686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.0000i | 0.695764i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | − | 14.0000i | − | 0.570124i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2583 | + | 6.50000i | −0.456962 | + | 0.263827i | −0.710766 | − | 0.703429i | \(-0.751651\pi\) |
0.253804 | + | 0.967256i | \(0.418318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.50000 | + | 2.59808i | −0.0607831 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2391 | − | 21.5000i | −1.50407 | − | 0.868377i | −0.999989 | − | 0.00472215i | \(-0.998497\pi\) |
−0.504084 | − | 0.863655i | \(-0.668170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5788 | − | 16.5000i | 1.15054 | − | 0.664265i | 0.201522 | − | 0.979484i | \(-0.435411\pi\) |
0.949019 | + | 0.315219i | \(0.102078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.0000 | −1.76851 | −0.884255 | − | 0.467005i | \(-0.845333\pi\) | ||||
−0.884255 | + | 0.467005i | \(0.845333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | + | 12.9904i | −0.300965 | + | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0000i | 0.600962i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.1865 | + | 10.5000i | 0.726300 | + | 0.419330i | ||||
\(628\) | 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 | ||||||||
\(633\) | −9.52628 | + | 5.50000i | −0.378636 | + | 0.218605i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5885 | − | 15.0000i | 0.617637 | − | 0.594322i | ||||
\(638\) | 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 | ||||||||
\(643\) | −9.52628 | + | 5.50000i | −0.375680 | + | 0.216899i | −0.675937 | − | 0.736959i | \(-0.736261\pi\) |
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.9711 | − | 22.5000i | −1.53211 | − | 0.884566i | −0.999264 | − | 0.0383563i | \(-0.987788\pi\) |
−0.532850 | − | 0.846210i | \(-0.678879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7750 | − | 19.5000i | −1.32172 | − | 0.763094i | −0.337715 | − | 0.941248i | \(-0.609654\pi\) |
−0.984003 | + | 0.178154i | \(0.942987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.46410 | + | 2.00000i | −0.135147 | + | 0.0780274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5000 | − | 33.7750i | −0.759612 | − | 1.31569i | −0.943049 | − | 0.332655i | \(-0.892055\pi\) |
0.183436 | − | 0.983032i | \(-0.441278\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 10.3923 | + | 3.00000i | 0.403604 | + | 0.116510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.79423 | + | 4.50000i | −0.301794 | + | 0.174241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.0000 | 1.27395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.7224 | + | 8.50000i | 0.567508 | + | 0.327651i | 0.756153 | − | 0.654394i | \(-0.227076\pi\) |
−0.188645 | + | 0.982045i | \(0.560410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 42.0000i | − | 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | − | 6.06218i | 0.134318 | − | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.0000 | 1.03464 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.1673 | + | 25.5000i | −1.69001 | + | 0.975730i | −0.735520 | + | 0.677503i | \(0.763062\pi\) |
−0.954495 | + | 0.298227i | \(0.903605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.0526 | + | 11.0000i | 0.726900 | + | 0.419676i | ||||
\(688\) | 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 | ||||||||
\(693\) | −5.19615 | + | 3.00000i | −0.197386 | + | 0.113961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0000i | 1.02270i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | − | 49.0000i | − | 1.84807i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.00000i | 0.338480i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.5000 | − | 32.0429i | −0.694782 | − | 1.20340i | −0.970254 | − | 0.242089i | \(-0.922167\pi\) |
0.275472 | − | 0.961309i | \(-0.411166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3923 | + | 6.00000i | 0.389195 | + | 0.224702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.50000 | + | 7.79423i | 0.167822 | + | 0.290676i | 0.937654 | − | 0.347571i | \(-0.112993\pi\) |
−0.769832 | + | 0.638247i | \(0.779660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | + | 6.92820i | 0.148968 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00000i | 0.0371904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 52.0000i | − | 1.92857i | −0.264861 | − | 0.964287i | \(-0.585326\pi\) | ||
0.264861 | − | 0.964287i | \(-0.414674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5000 | − | 28.5788i | 0.610275 | − | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0000i | 1.25582i | 0.778287 | + | 0.627909i | \(0.216089\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.1865 | + | 10.5000i | −0.669910 | + | 0.386772i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.5000 | − | 40.7032i | 0.864461 | − | 1.49729i | −0.00311943 | − | 0.999995i | \(-0.500993\pi\) |
0.867581 | − | 0.497296i | \(-0.165674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | + | 24.2487i | −0.257151 | + | 0.890799i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1865 | + | 10.5000i | 0.667199 | + | 0.385208i | 0.795015 | − | 0.606590i | \(-0.207463\pi\) |
−0.127815 | + | 0.991798i | \(0.540796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7846 | − | 12.0000i | 0.760469 | − | 0.439057i | ||||
\(748\) | 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 | ||||||||
\(753\) | − | 21.0000i | − | 0.765283i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1147 | − | 14.5000i | −0.912811 | − | 0.527011i | −0.0314762 | − | 0.999505i | \(-0.510021\pi\) |
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1.73205 | − | 1.00000i | 0.0627044 | − | 0.0362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.59808 | + | 10.5000i | 0.0938111 | + | 0.379133i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.50000 | + | 11.2583i | −0.234396 | + | 0.405986i | −0.959097 | − | 0.283078i | \(-0.908645\pi\) |
0.724701 | + | 0.689063i | \(0.241978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | − | 7.79423i | −0.162064 | − | 0.280702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3827 | − | 13.5000i | 0.841017 | − | 0.485561i | −0.0165929 | − | 0.999862i | \(-0.505282\pi\) |
0.857610 | + | 0.514301i | \(0.171949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.06218 | − | 3.50000i | −0.217479 | − | 0.125562i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.0000 | −2.25721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.9904 | − | 7.50000i | −0.464238 | − | 0.268028i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.0429 | + | 18.5000i | −1.14221 | + | 0.659454i | −0.946976 | − | 0.321303i | \(-0.895879\pi\) |
−0.195231 | + | 0.980757i | \(0.562546\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 9.52628 | + | 38.5000i | 0.338288 | + | 1.36718i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.1673 | + | 25.5000i | −1.56449 | + | 0.903256i | −0.567692 | + | 0.823241i | \(0.692164\pi\) |
−0.996794 | + | 0.0800155i | \(0.974503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.19615 | + | 3.00000i | 0.183368 | + | 0.105868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.0000i | 0.950445i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.50000 | − | 12.9904i | 0.263686 | − | 0.456717i | −0.703533 | − | 0.710663i | \(-0.748395\pi\) |
0.967219 | + | 0.253946i | \(0.0817284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9186 | + | 11.5000i | −0.698575 | + | 0.403323i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.6840 | + | 38.5000i | 2.33298 | + | 1.34694i | ||||
\(818\) | 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 | ||||||||
\(823\) | 11.2583 | − | 6.50000i | 0.392441 | − | 0.226576i | −0.290776 | − | 0.956791i | \(-0.593914\pi\) |
0.683217 | + | 0.730215i | \(0.260580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0000 | −0.659103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18.0000i | − | 0.623663i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000i | 0.691301i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5000 | + | 18.1865i | 0.362500 | + | 0.627869i | 0.988372 | − | 0.152057i | \(-0.0485899\pi\) |
−0.625871 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.19615 | + | 3.00000i | 0.178965 | + | 0.103325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73205 | − | 1.00000i | −0.0595140 | − | 0.0343604i | ||||
\(848\) | 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 | ||||||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.0000i | − | 1.02478i | −0.858753 | − | 0.512390i | \(-0.828760\pi\) | ||
0.858753 | − | 0.512390i | \(-0.171240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0000 | −1.50126 | −0.750630 | − | 0.660722i | \(-0.770250\pi\) | ||||
−0.750630 | + | 0.660722i | \(0.770250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50000 | + | 7.79423i | −0.153360 | + | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.92820 | + | 4.00000i | −0.235294 | + | 0.135847i | ||||
\(868\) | 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 | ||||||||
\(873\) | 12.1244 | + | 7.00000i | 0.410347 | + | 0.236914i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.5070 | − | 20.5000i | 1.19899 | − | 0.692236i | 0.238658 | − | 0.971104i | \(-0.423292\pi\) |
0.960329 | + | 0.278868i | \(0.0899591\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.79423 | − | 4.50000i | −0.261705 | − | 0.151095i | 0.363407 | − | 0.931630i | \(-0.381613\pi\) |
−0.625112 | + | 0.780535i | \(0.714947\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.59808 | + | 10.5000i | 0.0867472 | + | 0.350585i | ||||
\(898\) | 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 | ||||||||
\(903\) | 9.52628 | − | 5.50000i | 0.317015 | − | 0.183029i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4545 | + | 9.50000i | 0.546362 | + | 0.315442i | 0.747653 | − | 0.664089i | \(-0.231180\pi\) |
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −31.1769 | − | 18.0000i | −1.03181 | − | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.3923 | − | 6.00000i | 0.343184 | − | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5000 | + | 25.1147i | 0.478311 | + | 0.828459i | 0.999691 | − | 0.0248659i | \(-0.00791589\pi\) |
−0.521380 | + | 0.853325i | \(0.674583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.59808 | − | 10.5000i | −0.0855167 | − | 0.345612i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.8564 | + | 8.00000i | −0.455104 | + | 0.262754i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5000 | + | 44.1673i | 0.836628 | + | 1.44908i | 0.892698 | + | 0.450655i | \(0.148810\pi\) |
−0.0560703 | + | 0.998427i | \(0.517857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.0000 | 1.37649 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.7846 | + | 12.0000i | 0.680458 | + | 0.392862i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −23.3827 | + | 13.5000i | −0.761445 | + | 0.439620i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.1865 | − | 10.5000i | −0.590983 | − | 0.341204i | 0.174503 | − | 0.984657i | \(-0.444168\pi\) |
−0.765486 | + | 0.643452i | \(0.777501\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | 44.1673 | − | 25.5000i | 1.43072 | − | 0.826026i | 0.433544 | − | 0.901133i | \(-0.357263\pi\) |
0.997176 | + | 0.0751066i | \(0.0239297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000i | 0.290929i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.50000 | − | 12.9904i | 0.242188 | − | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000i | 0.580042i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0000i | − | 1.28631i | −0.765735 | − | 0.643157i | \(-0.777624\pi\) | ||
0.765735 | − | 0.643157i | \(-0.222376\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −4.33013 | − | 2.50000i | −0.138817 | − | 0.0801463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.79423 | − | 4.50000i | −0.249359 | − | 0.143968i | 0.370111 | − | 0.928987i | \(-0.379319\pi\) |
−0.619471 | + | 0.785020i | \(0.712653\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 36.0000i | 1.14822i | 0.818778 | + | 0.574111i | \(0.194652\pi\) | ||||
−0.818778 | + | 0.574111i | \(0.805348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||||
\(993\) | 19.0000i | 0.602947i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8468 | + | 15.5000i | −0.850246 | + | 0.490890i | −0.860734 | − | 0.509055i | \(-0.829995\pi\) |
0.0104877 | + | 0.999945i | \(0.496662\pi\) | |||||||
\(998\) | 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 | 1300.2.bb.a.1049.2 | 4 | ||
5.2 | odd | 4 | 1300.2.i.e.1101.1 | 2 | |||
5.3 | odd | 4 | 260.2.i.b.61.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1300.2.bb.a.1049.1 | 4 | ||
13.3 | even | 3 | inner | 1300.2.bb.a.549.1 | 4 | ||
15.8 | even | 4 | 2340.2.q.b.1621.1 | 2 | |||
20.3 | even | 4 | 1040.2.q.j.321.1 | 2 | |||
65.3 | odd | 12 | 260.2.i.b.81.1 | yes | 2 | ||
65.29 | even | 6 | inner | 1300.2.bb.a.549.2 | 4 | ||
65.33 | even | 12 | 3380.2.f.e.3041.2 | 2 | |||
65.42 | odd | 12 | 1300.2.i.e.601.1 | 2 | |||
65.43 | odd | 12 | 3380.2.a.g.1.1 | 1 | |||
65.48 | odd | 12 | 3380.2.a.h.1.1 | 1 | |||
65.58 | even | 12 | 3380.2.f.e.3041.1 | 2 | |||
195.68 | even | 12 | 2340.2.q.b.2161.1 | 2 | |||
260.3 | even | 12 | 1040.2.q.j.81.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.b.61.1 | ✓ | 2 | 5.3 | odd | 4 | ||
260.2.i.b.81.1 | yes | 2 | 65.3 | odd | 12 | ||
1040.2.q.j.81.1 | 2 | 260.3 | even | 12 | |||
1040.2.q.j.321.1 | 2 | 20.3 | even | 4 | |||
1300.2.i.e.601.1 | 2 | 65.42 | odd | 12 | |||
1300.2.i.e.1101.1 | 2 | 5.2 | odd | 4 | |||
1300.2.bb.a.549.1 | 4 | 13.3 | even | 3 | inner | ||
1300.2.bb.a.549.2 | 4 | 65.29 | even | 6 | inner | ||
1300.2.bb.a.1049.1 | 4 | 5.4 | even | 2 | inner | ||
1300.2.bb.a.1049.2 | 4 | 1.1 | even | 1 | trivial | ||
2340.2.q.b.1621.1 | 2 | 15.8 | even | 4 | |||
2340.2.q.b.2161.1 | 2 | 195.68 | even | 12 | |||
3380.2.a.g.1.1 | 1 | 65.43 | odd | 12 | |||
3380.2.a.h.1.1 | 1 | 65.48 | odd | 12 | |||
3380.2.f.e.3041.1 | 2 | 65.58 | even | 12 | |||
3380.2.f.e.3041.2 | 2 | 65.33 | even | 12 |