Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(239,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Character | \(\chi\) | \(=\) | 1344.239 |
Dual form | 1344.2.s.d.911.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.71763 | − | 0.223071i | −0.991672 | − | 0.128790i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.27022 | − | 2.27022i | −1.01527 | − | 1.01527i | −0.999882 | − | 0.0153920i | \(-0.995100\pi\) |
−0.0153920 | − | 0.999882i | \(-0.504900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.90048 | + | 0.766304i | 0.966826 | + | 0.255435i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.53672 | + | 1.53672i | −0.463337 | + | 0.463337i | −0.899748 | − | 0.436411i | \(-0.856250\pi\) |
0.436411 | + | 0.899748i | \(0.356250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.63094 | − | 3.63094i | −1.00704 | − | 1.00704i | −0.999975 | − | 0.00706768i | \(-0.997750\pi\) |
−0.00706768 | − | 0.999975i | \(-0.502250\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.39297 | + | 4.40581i | 0.876061 | + | 1.13758i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.81890i | − | 0.441148i | −0.975370 | − | 0.220574i | \(-0.929207\pi\) | ||
0.975370 | − | 0.220574i | \(-0.0707931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.98250 | + | 4.98250i | −1.14306 | + | 1.14306i | −0.155177 | + | 0.987887i | \(0.549595\pi\) |
−0.987887 | + | 0.155177i | \(0.950405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.71763 | + | 0.223071i | 0.374817 | + | 0.0486780i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.21608i | − | 1.50466i | −0.658789 | − | 0.752328i | \(-0.728931\pi\) | ||
0.658789 | − | 0.752328i | \(-0.271069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.30780i | 1.06156i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.81100 | − | 1.96324i | −0.925877 | − | 0.377825i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.77187 | − | 2.77187i | 0.514724 | − | 0.514724i | −0.401246 | − | 0.915970i | \(-0.631423\pi\) |
0.915970 | + | 0.401246i | \(0.131423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.14621i | 0.744681i | 0.928096 | + | 0.372340i | \(0.121445\pi\) | ||||
−0.928096 | + | 0.372340i | \(0.878555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.98230 | − | 2.29671i | 0.519151 | − | 0.399805i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.27022 | + | 2.27022i | 0.383737 | + | 0.383737i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.77185 | + | 1.77185i | −0.291290 | + | 0.291290i | −0.837590 | − | 0.546300i | \(-0.816036\pi\) |
0.546300 | + | 0.837590i | \(0.316036\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.42665 | + | 7.04656i | 0.868959 | + | 1.12835i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.517924 | −0.0808862 | −0.0404431 | − | 0.999182i | \(-0.512877\pi\) | ||||
−0.0404431 | + | 0.999182i | \(0.512877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.67423 | + | 4.67423i | 0.712813 | + | 0.712813i | 0.967123 | − | 0.254310i | \(-0.0818483\pi\) |
−0.254310 | + | 0.967123i | \(0.581848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.84505 | − | 8.32441i | −0.722257 | − | 1.24093i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.19336 | 0.174069 | 0.0870346 | − | 0.996205i | \(-0.472261\pi\) | ||||
0.0870346 | + | 0.996205i | \(0.472261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.405744 | + | 3.12419i | −0.0568155 | + | 0.437474i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.94384 | + | 7.94384i | 1.09117 | + | 1.09117i | 0.995404 | + | 0.0957666i | \(0.0305302\pi\) |
0.0957666 | + | 0.995404i | \(0.469470\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.97737 | 0.940828 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.66952 | − | 7.44662i | 1.28076 | − | 0.986329i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.94904 | − | 1.94904i | 0.253744 | − | 0.253744i | −0.568760 | − | 0.822504i | \(-0.692577\pi\) |
0.822504 | + | 0.568760i | \(0.192577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.94791 | + | 2.94791i | 0.377441 | + | 0.377441i | 0.870178 | − | 0.492737i | \(-0.164004\pi\) |
−0.492737 | + | 0.870178i | \(0.664004\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.90048 | − | 0.766304i | −0.365426 | − | 0.0965453i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.4861i | 2.04485i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.85747 | − | 7.85747i | 0.959943 | − | 0.959943i | −0.0392854 | − | 0.999228i | \(-0.512508\pi\) |
0.999228 | + | 0.0392854i | \(0.0125082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60970 | + | 12.3945i | −0.193785 | + | 1.49212i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9009i | 1.29370i | 0.762619 | + | 0.646848i | \(0.223913\pi\) | ||||
−0.762619 | + | 0.646848i | \(0.776087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.7454i | 1.84286i | 0.388539 | + | 0.921432i | \(0.372980\pi\) | ||||
−0.388539 | + | 0.921432i | \(0.627020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.18402 | − | 9.11682i | 0.136718 | − | 1.05272i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.53672 | − | 1.53672i | 0.175125 | − | 0.175125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.40437i | − | 0.608039i | −0.952666 | − | 0.304019i | \(-0.901671\pi\) | ||
0.952666 | − | 0.304019i | \(-0.0983288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82556 | + | 4.44530i | 0.869506 | + | 0.493922i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.12290 | − | 7.12290i | −0.781840 | − | 0.781840i | 0.198301 | − | 0.980141i | \(-0.436458\pi\) |
−0.980141 | + | 0.198301i | \(0.936458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.12931 | + | 4.12931i | −0.447886 | + | 0.447886i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.37937 | + | 4.14272i | −0.576729 | + | 0.444146i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1745 | −1.18449 | −0.592246 | − | 0.805758i | \(-0.701758\pi\) | ||||
−0.592246 | + | 0.805758i | \(0.701758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63094 | + | 3.63094i | 0.380626 | + | 0.380626i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.924898 | − | 7.12163i | 0.0959074 | − | 0.738479i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.6227 | 2.32105 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3244 | 1.25136 | 0.625678 | − | 0.780081i | \(-0.284822\pi\) | ||||
0.625678 | + | 0.780081i | \(0.284822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.63480 | + | 3.27962i | −0.566319 | + | 0.329614i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.72339 | + | 8.72339i | 0.868009 | + | 0.868009i | 0.992252 | − | 0.124242i | \(-0.0396501\pi\) |
−0.124242 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.74109 | 0.171555 | 0.0857774 | − | 0.996314i | \(-0.472663\pi\) | ||||
0.0857774 | + | 0.996314i | \(0.472663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.39297 | − | 4.40581i | −0.331120 | − | 0.429963i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.640107 | − | 0.640107i | 0.0618814 | − | 0.0618814i | −0.675489 | − | 0.737370i | \(-0.736067\pi\) |
0.737370 | + | 0.675489i | \(0.236067\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.52892 | + | 4.52892i | 0.433791 | + | 0.433791i | 0.889916 | − | 0.456125i | \(-0.150763\pi\) |
−0.456125 | + | 0.889916i | \(0.650763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.43862 | − | 2.64812i | 0.326379 | − | 0.251349i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.86038i | 0.269082i | 0.990908 | + | 0.134541i | \(0.0429559\pi\) | ||||
−0.990908 | + | 0.134541i | \(0.957044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.3821 | + | 16.3821i | −1.52764 | + | 1.52764i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.74907 | − | 13.3139i | −0.716402 | − | 1.23087i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.81890i | 0.166738i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.27701i | 0.570638i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.889601 | + | 0.115534i | 0.0802126 | + | 0.0104173i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.698783 | − | 0.698783i | 0.0625011 | − | 0.0625011i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.44899i | − | 0.572256i | −0.958191 | − | 0.286128i | \(-0.907632\pi\) | ||
0.958191 | − | 0.286128i | \(-0.0923682\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.98589 | − | 9.07126i | −0.615073 | − | 0.798680i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.83186 | − | 2.83186i | −0.247421 | − | 0.247421i | 0.572491 | − | 0.819911i | \(-0.305977\pi\) |
−0.819911 | + | 0.572491i | \(0.805977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.98250 | − | 4.98250i | 0.432038 | − | 0.432038i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.46505 | + | 15.3790i | 0.556423 | + | 1.32361i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.1051 | −1.20508 | −0.602538 | − | 0.798090i | \(-0.705844\pi\) | ||||
−0.602538 | + | 0.798090i | \(0.705844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.16493 | + | 5.16493i | 0.438083 | + | 0.438083i | 0.891367 | − | 0.453283i | \(-0.149747\pi\) |
−0.453283 | + | 0.891367i | \(0.649747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.04974 | − | 0.266203i | −0.172619 | − | 0.0224184i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1595 | 0.933200 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.5855 | −1.04517 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.71763 | − | 0.223071i | −0.141667 | − | 0.0183986i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.3665 | − | 11.3665i | −0.931178 | − | 0.931178i | 0.0666019 | − | 0.997780i | \(-0.478784\pi\) |
−0.997780 | + | 0.0666019i | \(0.978784\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4171 | −1.66152 | −0.830758 | − | 0.556634i | \(-0.812093\pi\) | ||||
−0.830758 | + | 0.556634i | \(0.812093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.39383 | − | 5.27569i | 0.112685 | − | 0.426514i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.41281 | − | 9.41281i | 0.756055 | − | 0.756055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.20353 | − | 6.20353i | −0.495096 | − | 0.495096i | 0.414812 | − | 0.909907i | \(-0.363847\pi\) |
−0.909907 | + | 0.414812i | \(0.863847\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.8725 | − | 15.4166i | −0.941551 | − | 1.22261i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.21608i | 0.568706i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.87321 | + | 3.87321i | −0.303373 | + | 0.303373i | −0.842332 | − | 0.538959i | \(-0.818818\pi\) |
0.538959 | + | 0.842332i | \(0.318818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.9845 | − | 1.55645i | −0.932992 | − | 0.121169i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.25436i | − | 0.483977i | −0.970279 | − | 0.241989i | \(-0.922200\pi\) | ||
0.970279 | − | 0.241989i | \(-0.0777996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.3675i | 1.02827i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2697 | + | 10.6335i | −1.39712 | + | 0.813166i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.7186 | − | 14.7186i | 1.11903 | − | 1.11903i | 0.127148 | − | 0.991884i | \(-0.459418\pi\) |
0.991884 | − | 0.127148i | \(-0.0405823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.30780i | − | 0.401232i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.78251 | + | 2.91296i | −0.284310 | + | 0.218951i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.4907 | + | 12.4907i | 0.933596 | + | 0.933596i | 0.997929 | − | 0.0643321i | \(-0.0204917\pi\) |
−0.0643321 | + | 0.997929i | \(0.520492\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.06356 | − | 1.06356i | 0.0790541 | − | 0.0790541i | −0.666474 | − | 0.745528i | \(-0.732197\pi\) |
0.745528 | + | 0.666474i | \(0.232197\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.40581 | − | 5.72099i | −0.325687 | − | 0.422908i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.04497 | 0.591478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.79513 | + | 2.79513i | 0.204400 | + | 0.204400i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.81100 | + | 1.96324i | 0.349949 | + | 0.142804i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9350 | −1.37009 | −0.685044 | − | 0.728502i | \(-0.740217\pi\) | ||||
−0.685044 | + | 0.728502i | \(0.740217\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.39738 | −0.100585 | −0.0502927 | − | 0.998735i | \(-0.516015\pi\) | ||||
−0.0502927 | + | 0.998735i | \(0.516015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.67756 | − | 28.3169i | 0.263356 | − | 2.02782i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.87505 | + | 8.87505i | 0.632321 | + | 0.632321i | 0.948650 | − | 0.316328i | \(-0.102450\pi\) |
−0.316328 | + | 0.948650i | \(0.602450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.8865 | 1.55149 | 0.775747 | − | 0.631044i | \(-0.217373\pi\) | ||||
0.775747 | + | 0.631044i | \(0.217373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.2490 | + | 11.7434i | −1.07558 | + | 0.828317i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.77187 | + | 2.77187i | −0.194547 | + | 0.194547i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.17580 | + | 1.17580i | 0.0821216 | + | 0.0821216i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.52971 | − | 20.9301i | 0.384341 | − | 1.45474i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 15.3134i | − | 1.05925i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.14716 | + | 6.14716i | −0.423188 | + | 0.423188i | −0.886300 | − | 0.463112i | \(-0.846733\pi\) |
0.463112 | + | 0.886300i | \(0.346733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.43167 | − | 18.7236i | 0.166615 | − | 1.28292i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 21.2231i | − | 1.44740i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.14621i | − | 0.281463i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.51235 | − | 27.0448i | 0.237342 | − | 1.82752i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.60433 | + | 6.60433i | −0.444255 | + | 0.444255i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5496i | 1.51004i | 0.655704 | + | 0.755018i | \(0.272372\pi\) | ||||
−0.655704 | + | 0.755018i | \(0.727628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.06739 | + | 15.3952i | −0.271160 | + | 1.02634i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.88171 | + | 7.88171i | 0.523127 | + | 0.523127i | 0.918515 | − | 0.395387i | \(-0.129390\pi\) |
−0.395387 | + | 0.918515i | \(0.629390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.66460 | − | 9.66460i | 0.638654 | − | 0.638654i | −0.311569 | − | 0.950224i | \(-0.600855\pi\) |
0.950224 | + | 0.311569i | \(0.100855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.98230 | + | 2.29671i | −0.196221 | + | 0.151112i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.8685 | −1.36714 | −0.683571 | − | 0.729884i | \(-0.739574\pi\) | ||||
−0.683571 | + | 0.729884i | \(0.739574\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.70919 | − | 2.70919i | −0.176728 | − | 0.176728i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.20556 | + | 9.28268i | −0.0783093 | + | 0.602975i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.99752 | −0.646686 | −0.323343 | − | 0.946282i | \(-0.604807\pi\) | ||||
−0.323343 | + | 0.946282i | \(0.604807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.6499 | 1.07251 | 0.536256 | − | 0.844055i | \(-0.319838\pi\) | ||||
0.536256 | + | 0.844055i | \(0.319838\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.4498 | − | 9.38101i | −0.798653 | − | 0.601792i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.27022 | − | 2.27022i | −0.145039 | − | 0.145039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.1824 | 2.30223 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.6456 | + | 13.8234i | 0.674635 | + | 0.876021i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.9403 | + | 13.9403i | −0.879903 | + | 0.879903i | −0.993524 | − | 0.113621i | \(-0.963755\pi\) |
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0891 | + | 11.0891i | 0.697163 | + | 0.697163i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.01374 | − | 6.17148i | 0.501840 | − | 0.386473i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.37152i | − | 0.522201i | −0.965312 | − | 0.261100i | \(-0.915915\pi\) | ||
0.965312 | − | 0.261100i | \(-0.0840854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.77185 | − | 1.77185i | 0.110097 | − | 0.110097i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1639 | − | 5.91566i | 0.629127 | − | 0.366170i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3.62005i | − | 0.223222i | −0.993752 | − | 0.111611i | \(-0.964399\pi\) | ||
0.993752 | − | 0.111611i | \(-0.0356011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 36.0685i | − | 2.21567i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.1936 | + | 2.49270i | 1.17463 | + | 0.152551i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.136662 | + | 0.136662i | −0.00833240 | + | 0.00833240i | −0.711261 | − | 0.702928i | \(-0.751875\pi\) |
0.702928 | + | 0.711261i | \(0.251875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.1261i | − | 1.34406i | −0.740523 | − | 0.672031i | \(-0.765422\pi\) | ||
0.740523 | − | 0.672031i | \(-0.234578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.42665 | − | 7.04656i | −0.328436 | − | 0.426477i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.15658 | − | 8.15658i | −0.491860 | − | 0.491860i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.42315 | + | 7.42315i | −0.446014 | + | 0.446014i | −0.894027 | − | 0.448013i | \(-0.852132\pi\) |
0.448013 | + | 0.894027i | \(0.352132\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.17726 | + | 12.0260i | −0.190217 | + | 0.719977i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.16601 | 0.129213 | 0.0646067 | − | 0.997911i | \(-0.479421\pi\) | ||||
0.0646067 | + | 0.997911i | \(0.479421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6179 | + | 10.6179i | 0.631171 | + | 0.631171i | 0.948362 | − | 0.317190i | \(-0.102739\pi\) |
−0.317190 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −38.8574 | − | 5.04647i | −2.30172 | − | 0.298927i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.517924 | 0.0305721 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.6916 | 0.805388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.1688 | − | 2.74922i | −1.24094 | − | 0.161162i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.34724 | − | 6.34724i | −0.370810 | − | 0.370810i | 0.496962 | − | 0.867772i | \(-0.334449\pi\) |
−0.867772 | + | 0.496962i | \(0.834449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.84952 | −0.515239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.4101 | − | 4.37620i | 0.604053 | − | 0.253933i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.2012 | + | 26.2012i | −1.51525 | + | 1.51525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.67423 | − | 4.67423i | −0.269418 | − | 0.269418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.0376 | − | 16.9294i | −0.748990 | − | 0.972571i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13.3848i | − | 0.766411i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0463 | + | 12.0463i | −0.687521 | + | 0.687521i | −0.961683 | − | 0.274162i | \(-0.911599\pi\) |
0.274162 | + | 0.961683i | \(0.411599\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.99054 | − | 0.388386i | −0.170126 | − | 0.0220945i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.3544i | − | 1.04078i | −0.853928 | − | 0.520392i | \(-0.825786\pi\) | ||
0.853928 | − | 0.520392i | \(-0.174214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8602i | 0.670379i | 0.942151 | + | 0.335190i | \(0.108800\pi\) | ||||
−0.942151 | + | 0.335190i | \(0.891200\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.84505 | + | 8.32441i | 0.272988 | + | 0.469027i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.44587 | + | 7.44587i | −0.418201 | + | 0.418201i | −0.884583 | − | 0.466382i | \(-0.845557\pi\) |
0.466382 | + | 0.884583i | \(0.345557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.51916i | 0.476981i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.24225 | + | 0.956675i | −0.0693358 | + | 0.0533964i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.06268 | + | 9.06268i | 0.504261 | + | 0.504261i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2723 | − | 19.2723i | 1.06904 | − | 1.06904i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.76871 | − | 8.78925i | −0.374311 | − | 0.486047i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.19336 | −0.0657919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1210 | − | 18.1210i | −0.996018 | − | 0.996018i | 0.00397423 | − | 0.999992i | \(-0.498735\pi\) |
−0.999992 | + | 0.00397423i | \(0.998735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.49698 | + | 3.78143i | −0.356032 | + | 0.207221i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −35.6764 | −1.94921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.87814 | −0.538096 | −0.269048 | − | 0.963127i | \(-0.586709\pi\) | ||||
−0.269048 | + | 0.963127i | \(0.586709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.638066 | − | 4.91306i | 0.0346550 | − | 0.266841i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.37154 | − | 6.37154i | −0.345038 | − | 0.345038i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.7927 | − | 24.4839i | 1.71166 | − | 1.31817i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.05190 | − | 7.05190i | 0.378566 | − | 0.378566i | −0.492019 | − | 0.870585i | \(-0.663741\pi\) |
0.870585 | + | 0.492019i | \(0.163741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.5451 | − | 24.5451i | −1.31387 | − | 1.31387i | −0.918539 | − | 0.395331i | \(-0.870630\pi\) |
−0.395331 | − | 0.918539i | \(-0.629370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3401 | + | 24.5969i | 0.551912 | + | 1.31288i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0409i | 1.06667i | 0.845905 | + | 0.533334i | \(0.179061\pi\) | ||||
−0.845905 | + | 0.533334i | \(0.820939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7474 | − | 24.7474i | 1.31346 | − | 1.31346i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.405744 | − | 3.12419i | 0.0214742 | − | 0.165350i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.58285i | 0.505763i | 0.967497 | + | 0.252882i | \(0.0813784\pi\) | ||||
−0.967497 | + | 0.252882i | \(0.918622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 30.6506i | − | 1.61319i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.40022 | − | 10.7816i | 0.0734924 | − | 0.565885i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.7456 | − | 35.7456i | 1.87101 | − | 1.87101i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5432i | 0.706952i | 0.935444 | + | 0.353476i | \(0.115000\pi\) | ||||
−0.935444 | + | 0.353476i | \(0.885000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.50223 | − | 0.396888i | −0.0782029 | − | 0.0206611i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.94384 | − | 7.94384i | −0.412424 | − | 0.412424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3451 | + | 17.3451i | −0.898095 | + | 0.898095i | −0.995268 | − | 0.0971728i | \(-0.969020\pi\) |
0.0971728 | + | 0.995268i | \(0.469020\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.35613 | + | 1.04437i | −0.0700301 | + | 0.0539311i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.1290 | −1.03670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.61555 | − | 3.61555i | −0.185718 | − | 0.185718i | 0.608124 | − | 0.793842i | \(-0.291922\pi\) |
−0.793842 | + | 0.608124i | \(0.791922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.43858 | + | 11.0770i | −0.0737008 | + | 0.567490i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.95251 | −0.201964 | −0.100982 | − | 0.994888i | \(-0.532198\pi\) | ||||
−0.100982 | + | 0.994888i | \(0.532198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.97737 | −0.355599 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.97562 | + | 17.1394i | 0.507089 | + | 0.871243i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.65725 | + | 7.65725i | 0.388238 | + | 0.388238i | 0.874059 | − | 0.485821i | \(-0.161479\pi\) |
−0.485821 | + | 0.874059i | \(0.661479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.1253 | −0.663777 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.23237 | + | 5.49578i | 0.213495 | + | 0.277225i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.2691 | + | 12.2691i | −0.617326 | + | 0.617326i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5714 | + | 11.5714i | 0.580750 | + | 0.580750i | 0.935109 | − | 0.354359i | \(-0.115301\pi\) |
−0.354359 | + | 0.935109i | \(0.615301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.66952 | + | 7.44662i | −0.484082 | + | 0.372797i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.44074i | − | 0.221760i | −0.993834 | − | 0.110880i | \(-0.964633\pi\) | ||
0.993834 | − | 0.110880i | \(-0.0353670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0546 | − | 15.0546i | 0.749925 | − | 0.749925i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.67393 | − | 27.8575i | −0.381321 | − | 1.38425i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.44565i | − | 0.269931i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.0682i | 1.63512i | 0.575846 | + | 0.817558i | \(0.304673\pi\) | ||||
−0.575846 | + | 0.817558i | \(0.695327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.2272 | + | 3.14642i | 1.19504 | + | 0.155202i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.94904 | + | 1.94904i | −0.0959062 | + | 0.0959062i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.3411i | 1.58756i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.71927 | − | 10.0236i | −0.378014 | − | 0.490856i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.39061 | − | 4.39061i | −0.214495 | − | 0.214495i | 0.591679 | − | 0.806174i | \(-0.298465\pi\) |
−0.806174 | + | 0.591679i | \(0.798465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6244 | + | 28.6244i | −1.39507 | + | 1.39507i | −0.581581 | + | 0.813488i | \(0.697566\pi\) |
−0.813488 | + | 0.581581i | \(0.802434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.46131 | + | 0.914475i | 0.168295 | + | 0.0444633i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.65437 | 0.468306 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.94791 | − | 2.94791i | −0.142659 | − | 0.142659i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.1678 | − | 2.48935i | −0.925429 | − | 0.120187i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.8985 | −0.765805 | −0.382903 | − | 0.923789i | \(-0.625076\pi\) | ||||
−0.382903 | + | 0.923789i | \(0.625076\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.4239 | 1.17374 | 0.586870 | − | 0.809681i | \(-0.300360\pi\) | ||||
0.586870 | + | 0.809681i | \(0.300360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.6172 | + | 2.80746i | 1.03647 | + | 0.134608i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.9541 | + | 35.9541i | 1.71992 | + | 1.71992i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.55315 | −0.121855 | −0.0609277 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609277 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.90048 | + | 0.766304i | 0.138118 | + | 0.0364907i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.64628 | − | 6.64628i | 0.315774 | − | 0.315774i | −0.531367 | − | 0.847142i | \(-0.678322\pi\) |
0.847142 | + | 0.531367i | \(0.178322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.3685 | + | 25.3685i | 1.20258 | + | 1.20258i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9878 | + | 22.0589i | 0.803496 | + | 1.04335i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.463395i | − | 0.0218689i | −0.999940 | − | 0.0109345i | \(-0.996519\pi\) | ||
0.999940 | − | 0.0109345i | \(-0.00348062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.795902 | − | 0.795902i | 0.0374776 | − | 0.0374776i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.0689 | + | 4.55445i | 1.64768 | + | 0.213987i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16.4861i | − | 0.772880i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.8788i | − | 0.602445i | −0.953554 | − | 0.301222i | \(-0.902605\pi\) | ||
0.953554 | − | 0.301222i | \(-0.0973947\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.57093 | + | 8.75073i | −0.166677 | + | 0.408449i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.25658 | + | 9.25658i | −0.431122 | + | 0.431122i | −0.889010 | − | 0.457888i | \(-0.848606\pi\) |
0.457888 | + | 0.889010i | \(0.348606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2993i | 1.03634i | 0.855278 | + | 0.518169i | \(0.173386\pi\) | ||||
−0.855278 | + | 0.518169i | \(0.826614\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.2674 | + | 14.0680i | −0.847131 | + | 0.652386i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3536 | + | 14.3536i | 0.664205 | + | 0.664205i | 0.956368 | − | 0.292163i | \(-0.0943751\pi\) |
−0.292163 | + | 0.956368i | \(0.594375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.85747 | + | 7.85747i | −0.362824 | + | 0.362824i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.27152 | + | 12.0392i | 0.427209 | + | 0.554736i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.3659 | −0.660545 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.4461 | − | 26.4461i | −1.21343 | − | 1.21343i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9535 | + | 29.1283i | 0.776249 | + | 1.33370i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.08030 | 0.232125 | 0.116062 | − | 0.993242i | \(-0.462973\pi\) | ||||
0.116062 | + | 0.993242i | \(0.462973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8670 | 0.586683 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.60970 | − | 12.3945i | 0.0732437 | − | 0.563970i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.9792 | − | 27.9792i | −1.27047 | − | 1.27047i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3722 | −0.696582 | −0.348291 | − | 0.937386i | \(-0.613238\pi\) | ||||
−0.348291 | + | 0.937386i | \(0.613238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.51672 | − | 5.78873i | 0.339918 | − | 0.261775i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6352 | + | 17.6352i | −0.795867 | + | 0.795867i | −0.982441 | − | 0.186574i | \(-0.940262\pi\) |
0.186574 | + | 0.982441i | \(0.440262\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.04177 | − | 5.04177i | −0.227070 | − | 0.227070i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.2377 | + | 5.34678i | 0.909617 | + | 0.240320i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 10.9009i | − | 0.488971i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.5178 | − | 27.5178i | 1.23187 | − | 1.23187i | 0.268622 | − | 0.963246i | \(-0.413432\pi\) |
0.963246 | − | 0.268622i | \(-0.0865683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.39517 | + | 10.7427i | −0.0623314 | + | 0.479946i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.92907i | 0.398128i | 0.979987 | + | 0.199064i | \(0.0637901\pi\) | ||||
−0.979987 | + | 0.199064i | \(0.936210\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 39.6080i | − | 1.76253i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.98190 | − | 22.9604i | 0.132431 | − | 1.01971i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.3303 | + | 16.3303i | −0.723829 | + | 0.723829i | −0.969383 | − | 0.245554i | \(-0.921030\pi\) |
0.245554 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 15.7454i | − | 0.696537i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.7526 | − | 14.1890i | 1.49021 | − | 0.626459i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.95266 | − | 3.95266i | −0.174175 | − | 0.174175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.83385 | + | 1.83385i | −0.0806527 | + | 0.0806527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.5643 | + | 21.9977i | −1.25383 | + | 0.965592i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.4790 | −0.459093 | −0.229547 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229547 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.75338 | + | 1.75338i | 0.0766700 | + | 0.0766700i | 0.744402 | − | 0.667732i | \(-0.232735\pi\) |
−0.667732 | + | 0.744402i | \(0.732735\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.18402 | + | 9.11682i | −0.0516747 | + | 0.397891i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.54154 | 0.328515 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0718 | −1.26399 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.14672 | − | 4.15960i | 0.310141 | − | 0.180511i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88055 | + | 1.88055i | 0.0814559 | + | 0.0814559i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.90637 | −0.125653 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.6680 | − | 24.2406i | −0.805584 | − | 1.04606i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.53672 | + | 1.53672i | −0.0661910 | + | 0.0661910i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1268 | + | 21.1268i | 0.908311 | + | 0.908311i | 0.996136 | − | 0.0878251i | \(-0.0279917\pi\) |
−0.0878251 | + | 0.996136i | \(0.527992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.06405 | + | 1.58955i | −0.0885771 | + | 0.0682143i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 20.5633i | − | 0.880834i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0948 | + | 10.0948i | −0.431622 | + | 0.431622i | −0.889180 | − | 0.457558i | \(-0.848724\pi\) |
0.457558 | + | 0.889180i | \(0.348724\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.29135 | + | 10.8093i | 0.268508 | + | 0.461331i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.6217i | 1.17672i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.40437i | 0.229817i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.8182 | − | 1.79460i | −0.586552 | − | 0.0761764i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.89116 | − | 6.89116i | 0.291988 | − | 0.291988i | −0.545877 | − | 0.837865i | \(-0.683803\pi\) |
0.837865 | + | 0.545877i | \(0.183803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 33.9437i | − | 1.43567i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.17748 | − | 5.42451i | −0.176373 | − | 0.229023i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.3031 | + | 20.3031i | 0.855675 | + | 0.855675i | 0.990825 | − | 0.135150i | \(-0.0431517\pi\) |
−0.135150 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.49369 | − | 6.49369i | 0.273192 | − | 0.273192i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.82556 | − | 4.44530i | −0.328642 | − | 0.186685i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.5437 | 1.02893 | 0.514463 | − | 0.857512i | \(-0.327991\pi\) | ||||
0.514463 | + | 0.857512i | \(0.327991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.2789 | + | 24.2789i | 1.01604 | + | 1.01604i | 0.999869 | + | 0.0161720i | \(0.00514793\pi\) |
0.0161720 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.5232 | + | 4.22384i | 1.35868 | + | 0.176454i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.3015 | 1.59728 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2283 | −1.54983 | −0.774916 | − | 0.632064i | \(-0.782208\pi\) | ||||
−0.774916 | + | 0.632064i | \(0.782208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.40017 | + | 0.311714i | 0.0997478 | + | 0.0129544i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.12290 | + | 7.12290i | 0.295508 | + | 0.295508i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.4148 | −1.01116 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.6334 | + | 47.8176i | −0.522325 | + | 1.97701i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.9789 | − | 16.9789i | 0.700796 | − | 0.700796i | −0.263785 | − | 0.964581i | \(-0.584971\pi\) |
0.964581 | + | 0.263785i | \(0.0849710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.6585 | − | 20.6585i | −0.851218 | − | 0.851218i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2643 | − | 17.2238i | −0.545619 | − | 0.708492i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.6074i | − | 0.723050i | −0.932362 | − | 0.361525i | \(-0.882256\pi\) | ||
0.932362 | − | 0.361525i | \(-0.117744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.12931 | − | 4.12931i | 0.169285 | − | 0.169285i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.5929 | − | 4.88224i | −1.53857 | − | 0.199817i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.5694i | − | 1.12646i | −0.826302 | − | 0.563228i | \(-0.809559\pi\) | ||
0.826302 | − | 0.563228i | \(-0.190441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.35161i | 0.177506i | 0.996054 | + | 0.0887529i | \(0.0282881\pi\) | ||||
−0.996054 | + | 0.0887529i | \(0.971712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.8116 | − | 16.7692i | 1.17330 | − | 0.682895i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.2502 | − | 14.2502i | 0.579353 | − | 0.579353i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.85518i | 0.318832i | 0.987212 | + | 0.159416i | \(0.0509611\pi\) | ||||
−0.987212 | + | 0.159416i | \(0.949039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.37937 | − | 4.14272i | 0.217983 | − | 0.167871i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.33302 | − | 4.33302i | −0.175295 | − | 0.175295i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.45171 | − | 8.45171i | 0.341361 | − | 0.341361i | −0.515518 | − | 0.856879i | \(-0.672400\pi\) |
0.856879 | + | 0.515518i | \(0.172400\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.75730 | − | 2.28188i | −0.0708613 | − | 0.0920142i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.2865 | 1.17903 | 0.589515 | − | 0.807758i | \(-0.299319\pi\) | ||||
0.589515 | + | 0.807758i | \(0.299319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8403 | + | 26.8403i | 1.07880 | + | 1.07880i | 0.996617 | + | 0.0821872i | \(0.0261905\pi\) |
0.0821872 | + | 0.996617i | \(0.473809\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.1669 | + | 34.7165i | −0.568497 | + | 1.39313i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.1745 | 0.447696 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3662 | 0.934649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.41596 | + | 26.3026i | −0.136420 | + | 1.05043i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.22282 | + | 3.22282i | 0.128502 | + | 0.128502i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.489937 | −0.0195041 | −0.00975204 | − | 0.999952i | \(-0.503104\pi\) | ||||
−0.00975204 | + | 0.999952i | \(0.503104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.9298 | − | 9.18726i | 0.474166 | − | 0.365161i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6406 | + | 14.6406i | −0.580996 | + | 0.580996i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.63094 | − | 3.63094i | −0.143863 | − | 0.143863i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.35339 | + | 31.6178i | −0.330455 | + | 1.25078i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.0818i | 0.911676i | 0.890063 | + | 0.455838i | \(0.150660\pi\) | ||||
−0.890063 | + | 0.455838i | \(0.849340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.66945 | − | 4.66945i | 0.184145 | − | 0.184145i | −0.609014 | − | 0.793159i | \(-0.708435\pi\) |
0.793159 | + | 0.609014i | \(0.208435\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.73424 | + | 36.4533i | −0.186411 | + | 1.43535i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.56882i | − | 0.100991i | −0.998724 | − | 0.0504953i | \(-0.983920\pi\) | ||
0.998724 | − | 0.0504953i | \(-0.0160800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.99025i | 0.235138i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.924898 | + | 7.12163i | −0.0362496 | + | 0.279119i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.969829 | + | 0.969829i | −0.0379523 | + | 0.0379523i | −0.725828 | − | 0.687876i | \(-0.758543\pi\) |
0.687876 | + | 0.725828i | \(0.258543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8579i | 0.502399i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.0658 | + | 45.6693i | −0.470732 | + | 1.78173i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.8082 | + | 30.8082i | 1.20012 | + | 1.20012i | 0.974131 | + | 0.225985i | \(0.0725601\pi\) |
0.225985 | + | 0.974131i | \(0.427440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.86728 | + | 1.86728i | −0.0726286 | + | 0.0726286i | −0.742488 | − | 0.669859i | \(-0.766354\pi\) |
0.669859 | + | 0.742488i | \(0.266354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8170 | − | 9.87054i | 0.497771 | − | 0.383340i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.6227 | −0.877273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0021 | − | 20.0021i | −0.774482 | − | 0.774482i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.03017 | − | 38.7319i | 0.194477 | − | 1.49746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.06019 | −0.349765 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3158 | −0.397643 | −0.198822 | − | 0.980036i | \(-0.563711\pi\) | ||||
−0.198822 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.4205 | − | 25.5358i | 0.401084 | − | 0.982875i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.2802 | + | 26.2802i | 1.01003 | + | 1.01003i | 0.999949 | + | 0.0100808i | \(0.00320887\pi\) |
0.0100808 | + | 0.999949i | \(0.496791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.3244 | −0.472968 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.7797 | − | 15.2960i | −0.451397 | − | 0.586144i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.4251 | − | 23.4251i | 0.896335 | − | 0.896335i | −0.0987751 | − | 0.995110i | \(-0.531492\pi\) |
0.995110 | + | 0.0987751i | \(0.0314924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.0216 | + | 32.0216i | 1.22348 | + | 1.22348i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7561 | + | 14.4443i | −0.715588 | + | 0.551083i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 57.6873i | − | 2.19771i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.99950 | − | 9.99950i | 0.380399 | − | 0.380399i | −0.490847 | − | 0.871246i | \(-0.663313\pi\) |
0.871246 | + | 0.490847i | \(0.163313\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.63480 | − | 3.27962i | 0.214048 | − | 0.124582i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 23.4510i | − | 0.889549i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.942054i | 0.0356828i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.8443 | + | 4.65516i | 1.35576 | + | 0.176074i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.9895 | + | 28.9895i | −1.09492 | + | 1.09492i | −0.0999251 | + | 0.994995i | \(0.531860\pi\) |
−0.994995 | + | 0.0999251i | \(0.968140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17.6565i | − | 0.665926i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.04903 | + | 5.25771i | 0.152495 | + | 0.198017i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.72339 | − | 8.72339i | −0.328077 | − | 0.328077i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.235410 | − | 0.235410i | 0.00884102 | − | 0.00884102i | −0.702672 | − | 0.711513i | \(-0.748010\pi\) |
0.711513 | + | 0.702672i | \(0.248010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.14139 | − | 15.6753i | 0.155314 | − | 0.587868i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.9193 | 1.12049 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.3344 | − | 25.3344i | −0.947454 | − | 0.947454i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.1720 | + | 2.23016i | 0.641300 | + | 0.0832867i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.4145 | −0.574864 | −0.287432 | − | 0.957801i | \(-0.592802\pi\) | ||||
−0.287432 | + | 0.957801i | \(0.592802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.74109 | −0.0648416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.5983 | − | 3.71410i | −1.06358 | − | 0.138129i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.7126 | + | 14.7126i | 0.546411 | + | 0.546411i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3548 | 1.31124 | 0.655619 | − | 0.755092i | \(-0.272408\pi\) | ||||
0.655619 | + | 0.755092i | \(0.272408\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.2914 | + | 18.8903i | 0.714497 | + | 0.699639i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.50196 | − | 8.50196i | 0.314456 | − | 0.314456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.83561 | + | 8.83561i | 0.326351 | + | 0.326351i | 0.851197 | − | 0.524846i | \(-0.175877\pi\) |
−0.524846 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.39297 | + | 4.40581i | 0.125152 | + | 0.162511i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.1494i | 0.889554i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.37067 | − | 6.37067i | 0.234349 | − | 0.234349i | −0.580156 | − | 0.814505i | \(-0.697009\pi\) |
0.814505 | + | 0.580156i | \(0.197009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −62.1478 | − | 8.07123i | −2.28306 | − | 0.296504i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.69026i | − | 0.282128i | −0.990000 | − | 0.141064i | \(-0.954948\pi\) | ||
0.990000 | − | 0.141064i | \(-0.0450524\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.6088i | 1.89080i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.2015 | − | 26.1181i | −0.556194 | − | 0.955612i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.640107 | + | 0.640107i | −0.0233890 | + | 0.0233890i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7075i | 0.682646i | 0.939946 | + | 0.341323i | \(0.110875\pi\) | ||||
−0.939946 | + | 0.341323i | \(0.889125\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.0539 | − | 20.8345i | 0.985897 | − | 0.759252i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.3512 | + | 46.3512i | 1.68689 | + | 1.68689i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2403 | − | 11.2403i | 0.408537 | − | 0.408537i | −0.472691 | − | 0.881228i | \(-0.656717\pi\) |
0.881228 | + | 0.472691i | \(0.156717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.5732 | − | 21.5205i | −0.601569 | − | 0.781144i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.13022 | 0.222220 | 0.111110 | − | 0.993808i | \(-0.464559\pi\) | ||||
0.111110 | + | 0.993808i | \(0.464559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.52892 | − | 4.52892i | −0.163958 | − | 0.163958i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.1413 | + | 8.81266i | −0.547434 | + | 0.318623i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.1537 | −0.511062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.7274 | −1.75716 | −0.878578 | − | 0.477599i | \(-0.841507\pi\) | ||||
−0.878578 | + | 0.477599i | \(0.841507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.86744 | + | 14.3791i | −0.0672542 | + | 0.517852i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.8293 | − | 27.8293i | −1.00095 | − | 1.00095i | −1.00000 | 0.000951442i | \(-0.999697\pi\) | |
−0.000951442 | − | 1.00000i | \(-0.500303\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0073 | −0.790524 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.43862 | + | 2.64812i | −0.123360 | + | 0.0950009i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.58056 | − | 2.58056i | 0.0924581 | − | 0.0924581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.7515 | − | 16.7515i | −0.599417 | − | 0.599417i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.7773 | + | 7.89364i | −0.671047 | + | 0.282096i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.1668i | 1.00532i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.1930 | + | 27.1930i | −0.969327 | + | 0.969327i | −0.999543 | − | 0.0302163i | \(-0.990380\pi\) |
0.0302163 | + | 0.999543i | \(0.490380\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.807528 | + | 6.21790i | −0.0287488 | + | 0.221363i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.86038i | − | 0.101703i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 21.4074i | − | 0.760198i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.04584 | + | 61.9523i | −0.285356 | + | 2.19722i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.82223 | + | 4.82223i | −0.170812 | + | 0.170812i | −0.787336 | − | 0.616524i | \(-0.788540\pi\) |
0.616524 | + | 0.787336i | \(0.288540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.17060i | − | 0.0767903i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.4113 | − | 8.56304i | −1.14520 | − | 0.302560i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.1963 | − | 24.1963i | −0.853868 | − | 0.853868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3821 | − | 16.3821i | 0.577393 | − | 0.577393i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.265219 | − | 0.204248i | 0.00933614 | − | 0.00718988i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.7157 | 1.46665 | 0.733323 | − | 0.679880i | \(-0.237968\pi\) | ||||
0.733323 | + | 0.679880i | \(0.237968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.12966 | − | 2.12966i | −0.0747826 | − | 0.0747826i | 0.668726 | − | 0.743509i | \(-0.266840\pi\) |
−0.743509 | + | 0.668726i | \(0.766840\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.93568 | + | 38.0043i | −0.173102 | + | 1.33287i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5861 | 0.616013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.5787 | −1.62958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.74907 | + | 13.3139i | 0.270774 | + | 0.465225i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.6123 | − | 17.6123i | −0.614675 | − | 0.614675i | 0.329485 | − | 0.944161i | \(-0.393125\pi\) |
−0.944161 | + | 0.329485i | \(0.893125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8604 | −0.796864 | −0.398432 | − | 0.917198i | \(-0.630446\pi\) | ||||
−0.398432 | + | 0.917198i | \(0.630446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.1905 | + | 15.8295i | 0.424418 | + | 0.551111i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.8096 | + | 17.8096i | −0.619299 | + | 0.619299i | −0.945352 | − | 0.326052i | \(-0.894281\pi\) |
0.326052 | + | 0.945352i | \(0.394281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5707 | + | 18.5707i | 0.644986 | + | 0.644986i | 0.951777 | − | 0.306791i | \(-0.0992553\pi\) |
−0.306791 | + | 0.951777i | \(0.599255\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.4061 | − | 11.0943i | 0.499742 | − | 0.384857i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.81890i | − | 0.0630212i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1988 | + | 14.1988i | −0.491369 | + | 0.491369i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.13998 | − | 19.9474i | 0.281359 | − | 0.689483i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.12371i | 0.314986i | 0.987520 | + | 0.157493i | \(0.0503411\pi\) | ||||
−0.987520 | + | 0.157493i | \(0.949659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6334i | 0.470118i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.72040 | − | 0.483174i | −0.128137 | − | 0.0166414i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.3472 | − | 30.3472i | 1.04398 | − | 1.04398i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.27701i | − | 0.215681i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.8691 | − | 20.6062i | −0.544626 | − | 0.707204i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7858 | + | 12.7858i | 0.438291 | + | 0.438291i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.691738 | − | 0.691738i | 0.0236846 | − | 0.0236846i | −0.695165 | − | 0.718850i | \(-0.744669\pi\) |
0.718850 | + | 0.695165i | \(0.244669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 65.6168 | + | 17.3359i | 2.24405 | + | 0.592876i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5386 | −0.974860 | −0.487430 | − | 0.873162i | \(-0.662066\pi\) | ||||
−0.487430 | + | 0.873162i | \(0.662066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.6833 | + | 16.6833i | 0.569228 | + | 0.569228i | 0.931912 | − | 0.362684i | \(-0.118140\pi\) |
−0.362684 | + | 0.931912i | \(0.618140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.889601 | − | 0.115534i | −0.0303175 | − | 0.00393738i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7028 | 0.602610 | 0.301305 | − | 0.953528i | \(-0.402578\pi\) | ||||
0.301305 | + | 0.953528i | \(0.402578\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.8288 | −2.27225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.5170 | − | 3.05419i | −0.798681 | − | 0.103726i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.30497 | + | 8.30497i | 0.281727 | + | 0.281727i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.0601 | −1.93341 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.7468 | + | 9.44427i | 1.20984 | + | 0.319640i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.698783 | + | 0.698783i | −0.0236232 | + | 0.0236232i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5896 | − | 25.5896i | −0.864099 | − | 0.864099i | 0.127712 | − | 0.991811i | \(-0.459237\pi\) |
−0.991811 | + | 0.127712i | \(0.959237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.48631 | + | 12.3181i | 0.319965 | + | 0.415478i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.2911i | 1.76173i | 0.473367 | + | 0.880865i | \(0.343039\pi\) | ||||
−0.473367 | + | 0.880865i | \(0.656961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.05344 | + | 1.05344i | −0.0354512 | + | 0.0354512i | −0.724610 | − | 0.689159i | \(-0.757980\pi\) |
0.689159 | + | 0.724610i | \(0.257980\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.2002 | + | 1.97407i | 0.510948 | + | 0.0663576i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.92643i | 0.266143i | 0.991106 | + | 0.133072i | \(0.0424841\pi\) | ||||
−0.991106 | + | 0.133072i | \(0.957516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.44899i | 0.216292i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.8568 | + | 5.19449i | −0.631727 | + | 0.174022i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.94590 | + | 5.94590i | −0.198972 | + | 0.198972i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 56.7132i | − | 1.89571i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.8485 | − | 39.1591i | 1.69778 | − | 1.30748i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.4928 | + | 11.4928i | 0.383305 | + | 0.383305i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.4491 | − | 14.4491i | 0.481368 | − | 0.481368i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.98589 | + | 9.07126i | 0.232476 | + | 0.301873i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.82905 | −0.160523 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.6768 | − | 19.6768i | −0.653358 | − | 0.653358i | 0.300442 | − | 0.953800i | \(-0.402866\pi\) |
−0.953800 | + | 0.300442i | \(0.902866\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.6172 | + | 31.9868i | 0.617495 | + | 1.06093i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4338 | 1.07458 | 0.537291 | − | 0.843397i | \(-0.319448\pi\) | ||||
0.537291 | + | 0.843397i | \(0.319448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8917 | 0.724511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.98576 | + | 22.9901i | −0.0987061 | + | 0.760029i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.83186 | + | 2.83186i | 0.0935162 | + | 0.0935162i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6029 | 0.613653 | 0.306827 | − | 0.951765i | \(-0.400733\pi\) | ||||
0.306827 | + | 0.951765i | \(0.400733\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3783 | − | 18.0039i | 0.770341 | − | 0.593250i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.5805 | − | 39.5805i | 1.30281 | − | 1.30281i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.40462 | − | 9.40462i | −0.309222 | − | 0.309222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.05000 | + | 1.33421i | 0.165864 | + | 0.0438210i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.43671i | 0.276800i | 0.990376 | + | 0.138400i | \(0.0441959\pi\) | ||||
−0.990376 | + | 0.138400i | \(0.955804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.98250 | + | 4.98250i | −0.163295 | + | 0.163295i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.09433 | + | 31.5260i | −0.134042 | + | 1.03212i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.6911i | − | 0.415045i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.1378i | − | 0.625206i | −0.949884 | − | 0.312603i | \(-0.898799\pi\) | ||
0.949884 | − | 0.312603i | \(-0.101201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.64567 | − | 20.3714i | 0.0863381 | − | 0.664796i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.2568 | + | 29.2568i | −0.953745 | + | 0.953745i | −0.998977 | − | 0.0452313i | \(-0.985598\pi\) |
0.0452313 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.73738i | 0.121706i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.46505 | − | 15.3790i | −0.210308 | − | 0.500279i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.36713 | + | 5.36713i | 0.174408 | + | 0.174408i | 0.788913 | − | 0.614505i | \(-0.210644\pi\) |
−0.614505 | + | 0.788913i | \(0.710644\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.1708 | − | 57.1708i | 1.85584 | − | 1.85584i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.4502 | − | 11.1283i | 0.468579 | − | 0.360859i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.7962 | 1.19195 | 0.595973 | − | 0.803004i | \(-0.296766\pi\) | ||||
0.595973 | + | 0.803004i | \(0.296766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.9866 | + | 42.9866i | 1.39101 | + | 1.39101i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.90038 | − | 14.6327i | 0.0614304 | − | 0.473009i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.1051 | 0.455476 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8090 | 0.445450 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.34713 | − | 1.36610i | 0.0756353 | − | 0.0440219i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.17236 | + | 3.17236i | 0.102122 | + | 0.102122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6511 | 0.921358 | 0.460679 | − | 0.887567i | \(-0.347606\pi\) | ||||
0.460679 | + | 0.887567i | \(0.347606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.5447 | − | 17.5879i | −0.435118 | − | 0.565005i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5134 | + | 22.5134i | −0.722489 | + | 0.722489i | −0.969112 | − | 0.246623i | \(-0.920679\pi\) |
0.246623 | + | 0.969112i | \(0.420679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.16493 | − | 5.16493i | −0.165580 | − | 0.165580i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.4018 | + | 28.8036i | −1.19782 | + | 0.922453i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6244i | 0.339906i | 0.985452 | + | 0.169953i | \(0.0543616\pi\) | ||||
−0.985452 | + | 0.169953i | \(0.945638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1720 | − | 17.1720i | 0.548819 | − | 0.548819i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.66550 | + | 16.6066i | 0.308596 | + | 0.530206i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 45.6286i | − | 1.45533i | −0.685935 | − | 0.727663i | \(-0.740606\pi\) | ||
0.685935 | − | 0.727663i | \(-0.259394\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 40.2967i | − | 1.28396i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.04974 | + | 0.266203i | 0.0652440 | + | 0.00847334i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.7296 | − | 33.7296i | 1.07254 | − | 1.07254i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 39.6701i | − | 1.26016i | −0.776529 | − | 0.630082i | \(-0.783021\pi\) | ||
0.776529 | − | 0.630082i | \(-0.216979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.0828 | + | 35.1673i | 0.859446 | + | 1.11600i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.6872 | − | 49.6872i | −1.57519 | − | 1.57519i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7009 | + | 17.7009i | −0.560594 | + | 0.560594i | −0.929476 | − | 0.368883i | \(-0.879740\pi\) |
0.368883 | + | 0.929476i | \(0.379740\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0029 | − | 5.04580i | 0.379755 | − | 0.159642i |
(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 | 1344.2.s.d.239.1 | 48 | ||
3.2 | odd | 2 | inner | 1344.2.s.d.239.13 | 48 | ||
4.3 | odd | 2 | 336.2.s.d.323.4 | yes | 48 | ||
12.11 | even | 2 | 336.2.s.d.323.21 | yes | 48 | ||
16.5 | even | 4 | 336.2.s.d.155.21 | yes | 48 | ||
16.11 | odd | 4 | inner | 1344.2.s.d.911.13 | 48 | ||
48.5 | odd | 4 | 336.2.s.d.155.4 | ✓ | 48 | ||
48.11 | even | 4 | inner | 1344.2.s.d.911.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.d.155.4 | ✓ | 48 | 48.5 | odd | 4 | ||
336.2.s.d.155.21 | yes | 48 | 16.5 | even | 4 | ||
336.2.s.d.323.4 | yes | 48 | 4.3 | odd | 2 | ||
336.2.s.d.323.21 | yes | 48 | 12.11 | even | 2 | ||
1344.2.s.d.239.1 | 48 | 1.1 | even | 1 | trivial | ||
1344.2.s.d.239.13 | 48 | 3.2 | odd | 2 | inner | ||
1344.2.s.d.911.1 | 48 | 48.11 | even | 4 | inner | ||
1344.2.s.d.911.13 | 48 | 16.11 | odd | 4 | inner |