Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(81,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.bo (of order \(5\), degree \(4\), 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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 220) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 641.2 | ||
Root | \(1.40799 + 0.132563i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.641 |
Dual form | 880.2.bo.f.81.2 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.346820 | + | 1.06740i | 0.200237 | + | 0.616265i | 0.999875 | + | 0.0157838i | \(0.00502435\pi\) |
−0.799639 | + | 0.600481i | \(0.794976\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.714347 | + | 2.19853i | −0.269998 | + | 0.830967i | 0.720502 | + | 0.693453i | \(0.243911\pi\) |
−0.990500 | + | 0.137515i | \(0.956089\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.40799 | − | 1.02296i | 0.469329 | − | 0.340987i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.14835 | − | 1.04301i | 0.949265 | − | 0.314479i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18616 | − | 3.04142i | 1.16103 | − | 0.843539i | 0.171123 | − | 0.985250i | \(-0.445260\pi\) |
0.989908 | + | 0.141711i | \(0.0452604\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.346820 | + | 1.06740i | −0.0895486 | + | 0.275602i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.339863 | − | 0.246925i | −0.0824290 | − | 0.0598882i | 0.545808 | − | 0.837911i | \(-0.316223\pi\) |
−0.628237 | + | 0.778022i | \(0.716223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.537803 | + | 1.65519i | 0.123381 | + | 0.379726i | 0.993603 | − | 0.112934i | \(-0.0360247\pi\) |
−0.870222 | + | 0.492660i | \(0.836025\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.59447 | −0.566160 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.90614 | −1.02300 | −0.511501 | − | 0.859283i | \(-0.670910\pi\) | ||||
−0.511501 | + | 0.859283i | \(0.670910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.30419 | + | 3.12718i | 0.828342 | + | 0.601826i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.849477 | + | 2.61442i | −0.157744 | + | 0.485486i | −0.998429 | − | 0.0560390i | \(-0.982153\pi\) |
0.840685 | + | 0.541525i | \(0.182153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.30849 | − | 3.85684i | 0.953433 | − | 0.692710i | 0.00181677 | − | 0.999998i | \(-0.499422\pi\) |
0.951616 | + | 0.307289i | \(0.0994217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.20522 | + | 2.99883i | 0.383880 | + | 0.522029i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.87018 | + | 1.35877i | −0.316119 | + | 0.229674i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.22859 | + | 9.93656i | −0.530776 | + | 1.63356i | 0.221827 | + | 0.975086i | \(0.428798\pi\) |
−0.752603 | + | 0.658475i | \(0.771202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.69826 | + | 3.41349i | 0.752324 | + | 0.546596i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.61055 | + | 8.03445i | 0.407700 | + | 1.25477i | 0.918620 | + | 0.395142i | \(0.129305\pi\) |
−0.510920 | + | 0.859628i | \(0.670695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.16578 | −0.940272 | −0.470136 | − | 0.882594i | \(-0.655795\pi\) | ||||
−0.470136 | + | 0.882594i | \(0.655795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.74037 | 0.259439 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.320799 | + | 0.987319i | 0.0467934 | + | 0.144015i | 0.971723 | − | 0.236122i | \(-0.0758766\pi\) |
−0.924930 | + | 0.380138i | \(0.875877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.33986 | + | 0.973468i | 0.191409 | + | 0.139067i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.145697 | − | 0.448410i | 0.0204017 | − | 0.0627899i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.38495 | + | 3.18585i | −0.602319 | + | 0.437610i | −0.846701 | − | 0.532069i | \(-0.821415\pi\) |
0.244382 | + | 0.969679i | \(0.421415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.16014 | + | 1.00675i | 0.426113 | + | 0.135750i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.58023 | + | 1.14810i | −0.209307 | + | 0.152070i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.45471 | − | 13.7102i | 0.579954 | − | 1.78492i | −0.0386977 | − | 0.999251i | \(-0.512321\pi\) |
0.618652 | − | 0.785665i | \(-0.287679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2838 | − | 7.47163i | −1.31671 | − | 0.956644i | −0.999967 | − | 0.00813122i | \(-0.997412\pi\) |
−0.316740 | − | 0.948512i | \(-0.602588\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.24323 | + | 3.82626i | 0.156632 | + | 0.482063i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.17438 | 0.641802 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.559626 | 0.0683692 | 0.0341846 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341846 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.70155 | − | 5.23683i | −0.204842 | − | 0.630440i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17060 | + | 3.03012i | 0.494959 | + | 0.359609i | 0.807088 | − | 0.590431i | \(-0.201042\pi\) |
−0.312129 | + | 0.950040i | \(0.601042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.83770 | − | 11.8112i | 0.449168 | − | 1.38240i | −0.428679 | − | 0.903457i | \(-0.641021\pi\) |
0.877847 | − | 0.478941i | \(-0.158979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.907987 | + | 0.659691i | −0.104845 | + | 0.0761746i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0440700 | + | 7.66683i | 0.00502224 | + | 0.873716i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.91229 | + | 2.84244i | −0.440167 | + | 0.319800i | −0.785701 | − | 0.618606i | \(-0.787698\pi\) |
0.345535 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.231768 | + | 0.713310i | −0.0257521 | + | 0.0792567i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.83021 | − | 4.23590i | −0.639949 | − | 0.464950i | 0.219884 | − | 0.975526i | \(-0.429432\pi\) |
−0.859833 | + | 0.510576i | \(0.829432\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.129816 | − | 0.399533i | −0.0140805 | − | 0.0433355i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.08526 | −0.330774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.95287 | 0.949002 | 0.474501 | − | 0.880255i | \(-0.342628\pi\) | ||||
0.474501 | + | 0.880255i | \(0.342628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.69630 | + | 11.3760i | 0.387477 | + | 1.19253i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.95790 | + | 4.32867i | 0.617805 | + | 0.448862i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.537803 | + | 1.65519i | −0.0551774 | + | 0.169819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.633590 | − | 0.460330i | 0.0643313 | − | 0.0467394i | −0.555155 | − | 0.831747i | \(-0.687341\pi\) |
0.619486 | + | 0.785008i | \(0.287341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.36588 | − | 4.68919i | 0.338284 | − | 0.471281i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.95520 | + | 6.50634i | −0.891076 | + | 0.647405i | −0.936158 | − | 0.351579i | \(-0.885645\pi\) |
0.0450823 | + | 0.998983i | \(0.485645\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.24201 | + | 3.82251i | −0.122379 | + | 0.376643i | −0.993414 | − | 0.114577i | \(-0.963449\pi\) |
0.871036 | + | 0.491220i | \(0.163449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.09897 | − | 1.52499i | −0.204838 | − | 0.148824i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.206864 | + | 0.636662i | 0.0199983 | + | 0.0615484i | 0.960558 | − | 0.278081i | \(-0.0896984\pi\) |
−0.940559 | + | 0.339629i | \(0.889698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.43834 | 0.616682 | 0.308341 | − | 0.951276i | \(-0.400226\pi\) | ||||
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.7261 | −1.11299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.48658 | − | 4.57521i | −0.139845 | − | 0.430399i | 0.856467 | − | 0.516202i | \(-0.172655\pi\) |
−0.996312 | + | 0.0858025i | \(0.972655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.96915 | − | 2.88376i | −0.370125 | − | 0.268912i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.78280 | − | 8.56456i | 0.257270 | − | 0.791794i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.785653 | − | 0.570811i | 0.0720207 | − | 0.0523261i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.82427 | − | 6.56751i | 0.802206 | − | 0.597047i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.67060 | + | 5.57302i | −0.691635 | + | 0.502502i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7385 | + | 8.52854i | 1.04163 | + | 0.756785i | 0.970602 | − | 0.240689i | \(-0.0773735\pi\) |
0.0710234 | + | 0.997475i | \(0.477374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.13842 | − | 6.58137i | −0.188277 | − | 0.579457i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2108 | −1.24160 | −0.620802 | − | 0.783968i | \(-0.713193\pi\) | ||||
−0.620802 | + | 0.783968i | \(0.713193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.02316 | −0.348852 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.64405 | + | 5.05988i | 0.141498 | + | 0.435485i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.18186 | + | 1.58521i | 0.186409 | + | 0.135434i | 0.677076 | − | 0.735913i | \(-0.263247\pi\) |
−0.490667 | + | 0.871347i | \(0.663247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.11219 | + | 6.50066i | −0.179154 | + | 0.551379i | −0.999799 | − | 0.0200595i | \(-0.993614\pi\) |
0.820645 | + | 0.571439i | \(0.193614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.942607 | + | 0.684844i | −0.0793818 | + | 0.0576743i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.0073 | − | 13.9417i | 0.836851 | − | 1.16586i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.22396 | + | 1.61580i | −0.184690 | + | 0.134185i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.574390 | + | 1.76779i | −0.0473749 | + | 0.145805i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0588 | − | 11.6674i | −1.31559 | − | 0.955831i | −0.999976 | − | 0.00694229i | \(-0.997790\pi\) |
−0.315612 | − | 0.948888i | \(-0.602210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.22714 | − | 16.0875i | −0.425379 | − | 1.30918i | −0.902631 | − | 0.430415i | \(-0.858367\pi\) |
0.477252 | − | 0.878766i | \(-0.341633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.731118 | −0.0591074 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.56166 | 0.527045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58072 | + | 11.0203i | 0.285773 | + | 0.879517i | 0.986166 | + | 0.165761i | \(0.0530079\pi\) |
−0.700393 | + | 0.713757i | \(0.746992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.92137 | − | 3.57559i | −0.390290 | − | 0.283563i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.50469 | − | 10.7863i | 0.276208 | − | 0.850081i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3592 | − | 13.3388i | 1.43800 | − | 1.04477i | 0.449550 | − | 0.893255i | \(-0.351584\pi\) |
0.988455 | − | 0.151516i | \(-0.0484156\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0213963 | + | 3.72230i | 0.00166570 | + | 0.289780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.3632 | + | 9.70893i | −1.03407 | + | 0.751299i | −0.969120 | − | 0.246589i | \(-0.920690\pi\) |
−0.0649545 | + | 0.997888i | \(0.520690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.25645 | − | 13.1000i | 0.327419 | − | 1.00769i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.45041 | + | 1.78033i | 0.187388 | + | 0.136145i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.44674 | − | 13.6857i | −0.338080 | − | 1.04050i | −0.965185 | − | 0.261568i | \(-0.915761\pi\) |
0.627106 | − | 0.778934i | \(-0.284239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.31167 | −0.174746 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.1793 | 1.21611 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.03442 | − | 18.5720i | −0.451034 | − | 1.38814i | −0.875729 | − | 0.482803i | \(-0.839619\pi\) |
0.424696 | − | 0.905336i | \(-0.360381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.05851 | − | 0.769052i | −0.0786784 | − | 0.0571632i | 0.547751 | − | 0.836642i | \(-0.315484\pi\) |
−0.626429 | + | 0.779478i | \(0.715484\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.40860 | − | 13.5683i | 0.325893 | − | 1.00300i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.45255 | + | 6.14113i | −0.621444 | + | 0.451505i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.32756 | − | 0.422928i | −0.0970804 | − | 0.0309276i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.94989 | + | 7.22902i | −0.723748 | + | 0.525834i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.47398 | − | 16.8472i | 0.396083 | − | 1.21902i | −0.532032 | − | 0.846725i | \(-0.678571\pi\) |
0.928115 | − | 0.372294i | \(-0.121429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8441 | − | 8.60526i | −0.852559 | − | 0.619420i | 0.0732915 | − | 0.997311i | \(-0.476650\pi\) |
−0.925850 | + | 0.377890i | \(0.876650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.79458 | + | 5.52314i | 0.128512 | + | 0.395520i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.4114 | −1.66799 | −0.833997 | − | 0.551768i | \(-0.813953\pi\) | ||||
−0.833997 | + | 0.551768i | \(0.813953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.478502 | −0.0339201 | −0.0169601 | − | 0.999856i | \(-0.505399\pi\) | ||||
−0.0169601 | + | 0.999856i | \(0.505399\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.194089 | + | 0.597346i | 0.0136900 | + | 0.0421335i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.14107 | − | 3.73521i | −0.360833 | − | 0.262160i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.61055 | + | 8.03445i | −0.182329 | + | 0.561150i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.90779 | + | 5.01880i | −0.480124 | + | 0.348831i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.41957 | + | 4.65019i | 0.236536 | + | 0.321660i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.50479 | − | 5.45255i | 0.516651 | − | 0.375369i | −0.298690 | − | 0.954350i | \(-0.596550\pi\) |
0.815341 | + | 0.578981i | \(0.196550\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.78791 | + | 5.50262i | −0.122505 | + | 0.377033i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.98822 | − | 3.62415i | −0.340194 | − | 0.247165i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.68730 | + | 14.4260i | 0.318194 | + | 0.979302i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.9383 | 0.941864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.17373 | −0.146221 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.18338 | − | 6.71974i | −0.146210 | − | 0.449987i | 0.850955 | − | 0.525239i | \(-0.176024\pi\) |
−0.997165 | + | 0.0752516i | \(0.976024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.40799 | + | 1.02296i | 0.0938658 | + | 0.0681975i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.16342 | + | 3.58064i | −0.0772190 | + | 0.237656i | −0.982213 | − | 0.187768i | \(-0.939875\pi\) |
0.904994 | + | 0.425423i | \(0.139875\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.27282 | − | 6.73710i | 0.612765 | − | 0.445200i | −0.237622 | − | 0.971358i | \(-0.576368\pi\) |
0.850387 | + | 0.526158i | \(0.176368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.16831 | + | 2.70605i | −0.537435 | + | 0.178045i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.02034 | + | 3.64749i | −0.328894 | + | 0.238955i | −0.739961 | − | 0.672650i | \(-0.765156\pi\) |
0.411067 | + | 0.911605i | \(0.365156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.320799 | + | 0.987319i | −0.0209266 | + | 0.0644056i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.39089 | − | 3.19017i | −0.285219 | − | 0.207224i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.21504 | − | 16.0502i | −0.337333 | − | 1.03820i | −0.965562 | − | 0.260175i | \(-0.916220\pi\) |
0.628229 | − | 0.778029i | \(-0.283780\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.7757 | 1.78919 | 0.894596 | − | 0.446875i | \(-0.147463\pi\) | ||||
0.894596 | + | 0.446875i | \(0.147463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1190 | 0.969887 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.511782 | + | 1.57510i | 0.0326966 | + | 0.100630i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.28545 | + | 5.29319i | 0.463562 | + | 0.336798i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.49937 | − | 7.69228i | 0.158391 | − | 0.487478i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.4086 | + | 14.8277i | −1.28818 | + | 0.935917i | −0.999767 | − | 0.0215891i | \(-0.993127\pi\) |
−0.288412 | + | 0.957506i | \(0.593127\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.4463 | + | 5.11714i | −0.971099 | + | 0.321712i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.381440 | − | 0.277132i | 0.0238867 | − | 0.0173547i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.22694 | − | 6.85383i | 0.138913 | − | 0.427530i | −0.857265 | − | 0.514875i | \(-0.827838\pi\) |
0.996178 | + | 0.0873452i | \(0.0278383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.5395 | − | 14.1963i | −1.21413 | − | 0.882115i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.47840 | + | 4.55006i | 0.0915108 | + | 0.281641i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1830 | 0.689572 | 0.344786 | − | 0.938681i | \(-0.387952\pi\) | ||||
0.344786 | + | 0.938681i | \(0.387952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.42009 | −0.332954 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.10504 | + | 9.55632i | 0.190025 | + | 0.584837i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4968 | − | 9.80598i | −0.822913 | − | 0.597881i | 0.0946323 | − | 0.995512i | \(-0.469832\pi\) |
−0.917545 | + | 0.397631i | \(0.869832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.354916 | + | 1.09232i | −0.0215596 | + | 0.0663537i | −0.961257 | − | 0.275652i | \(-0.911106\pi\) |
0.939698 | + | 0.342006i | \(0.111106\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.8609 | + | 7.89088i | −0.657329 | + | 0.477577i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.96485 | + | 2.67196i | 0.118485 | + | 0.161125i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.5666 | + | 14.2160i | −1.17564 | + | 0.854155i | −0.991674 | − | 0.128777i | \(-0.958895\pi\) |
−0.183970 | + | 0.982932i | \(0.558895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.52888 | − | 10.8608i | 0.211268 | − | 0.650217i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.08607 | − | 0.789077i | −0.0647896 | − | 0.0470724i | 0.554919 | − | 0.831904i | \(-0.312749\pi\) |
−0.619709 | + | 0.784832i | \(0.712749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.13341 | + | 28.1098i | 0.542925 | + | 1.67095i | 0.725873 | + | 0.687829i | \(0.241436\pi\) |
−0.182948 | + | 0.983123i | \(0.558564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.95327 | −0.115702 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.5288 | −1.15275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.19875 | − | 16.0001i | −0.305809 | − | 0.941183i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.711099 | + | 0.516644i | 0.0416854 | + | 0.0302862i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.67950 | − | 8.24666i | 0.156538 | − | 0.481775i | −0.841775 | − | 0.539828i | \(-0.818489\pi\) |
0.998314 | + | 0.0580530i | \(0.0184892\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6626 | − | 8.47337i | 0.679022 | − | 0.493339i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.8128 | + | 5.35616i | 0.975577 | + | 0.310796i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.5379 | + | 14.9217i | −1.18774 | + | 0.862941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.40450 | − | 13.5557i | 0.253871 | − | 0.781335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0507 | − | 7.30228i | −0.577399 | − | 0.419505i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.92807 | − | 12.0893i | −0.224920 | − | 0.692234i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.11110 | −0.177560 | −0.0887799 | − | 0.996051i | \(-0.528297\pi\) | ||||
−0.0887799 | + | 0.996051i | \(0.528297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.51091 | −0.256617 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.10193 | + | 21.8575i | 0.402713 | + | 1.23942i | 0.922789 | + | 0.385305i | \(0.125904\pi\) |
−0.520076 | + | 0.854120i | \(0.674096\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6517 | + | 12.0981i | 0.941208 | + | 0.683827i | 0.948711 | − | 0.316145i | \(-0.102388\pi\) |
−0.00750347 | + | 0.999972i | \(0.502388\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.24323 | + | 3.82626i | −0.0700478 | + | 0.215585i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.4316 | − | 19.2037i | 1.48455 | − | 1.07859i | 0.508493 | − | 0.861066i | \(-0.330203\pi\) |
0.976055 | − | 0.217522i | \(-0.0697973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0524066 | + | 9.11714i | 0.00293421 | + | 0.510462i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.607830 | + | 0.441614i | −0.0339257 | + | 0.0246485i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.225928 | − | 0.695335i | 0.0125710 | − | 0.0386895i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.18616 | + | 3.04142i | 0.232206 | + | 0.168708i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.23295 | + | 6.87231i | 0.123482 | + | 0.380039i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.39981 | −0.132306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5065 | −0.907281 | −0.453641 | − | 0.891185i | \(-0.649875\pi\) | ||||
−0.453641 | + | 0.891185i | \(0.649875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.61892 | + | 17.2933i | 0.307915 | + | 0.947665i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.452747 | + | 0.328940i | 0.0247362 | + | 0.0179719i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.77683 | + | 14.7016i | −0.260211 | + | 0.800846i | 0.732548 | + | 0.680716i | \(0.238331\pi\) |
−0.992758 | + | 0.120130i | \(0.961669\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.36802 | − | 3.17355i | 0.237238 | − | 0.172364i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6903 | − | 17.6795i | 0.687218 | − | 0.957399i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1886 | + | 11.7617i | −0.874103 | + | 0.635073i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.70155 | − | 5.23683i | 0.0916083 | − | 0.281941i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.16099 | − | 5.20276i | −0.384422 | − | 0.279299i | 0.378744 | − | 0.925501i | \(-0.376356\pi\) |
−0.763166 | + | 0.646203i | \(0.776356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.82441 | + | 5.61495i | 0.0976584 | + | 0.300562i | 0.987937 | − | 0.154854i | \(-0.0494907\pi\) |
−0.890279 | + | 0.455416i | \(0.849491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.5291 | 1.46939 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.4813 | −1.88848 | −0.944240 | − | 0.329258i | \(-0.893201\pi\) | ||||
−0.944240 | + | 0.329258i | \(0.893201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.59303 | + | 4.90284i | 0.0845492 | + | 0.260216i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.881765 | + | 0.640640i | 0.0466680 | + | 0.0339063i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.723147 | + | 2.22562i | −0.0381662 | + | 0.117464i | −0.968324 | − | 0.249695i | \(-0.919669\pi\) |
0.930158 | + | 0.367159i | \(0.119669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9209 | − | 9.38759i | 0.680048 | − | 0.494084i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0706 | + | 7.14130i | 0.528570 | + | 0.374821i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0472 | − | 7.29973i | 0.525895 | − | 0.382085i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.40910 | − | 19.7252i | 0.334552 | − | 1.02965i | −0.632390 | − | 0.774650i | \(-0.717926\pi\) |
0.966942 | − | 0.254996i | \(-0.0820742\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.8946 | + | 8.64191i | 0.619206 | + | 0.449880i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.87183 | − | 11.9163i | −0.201015 | − | 0.618661i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.2190 | 1.82357 | 0.911786 | − | 0.410665i | \(-0.134703\pi\) | ||||
0.911786 | + | 0.410665i | \(0.134703\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.12233 | −0.0579571 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.39551 | + | 13.5280i | 0.226381 | + | 0.696728i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.2585 | + | 12.5391i | 0.886512 | + | 0.644089i | 0.934966 | − | 0.354737i | \(-0.115430\pi\) |
−0.0484543 | + | 0.998825i | \(0.515430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.03223 | + | 15.4876i | −0.257809 | + | 0.793454i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.52120 | + | 4.73793i | −0.333218 | + | 0.242097i | −0.741795 | − | 0.670627i | \(-0.766025\pi\) |
0.408577 | + | 0.912724i | \(0.366025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.47080 | + | 6.22850i | −0.227853 | + | 0.317434i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.68133 | + | 6.30736i | −0.441297 | + | 0.320621i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.33258 | − | 10.2566i | 0.168969 | − | 0.520032i | −0.830338 | − | 0.557260i | \(-0.811853\pi\) |
0.999307 | + | 0.0372279i | \(0.0118528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.66742 | + | 1.21145i | 0.0843250 | + | 0.0612657i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.92859 | − | 15.1686i | −0.248615 | − | 0.765157i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.83585 | −0.243318 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4389 | −1.02580 | −0.512900 | − | 0.858448i | \(-0.671429\pi\) | ||||
−0.512900 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.39531 | − | 4.29433i | −0.0698531 | − | 0.214986i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2079 | − | 9.59609i | −0.659570 | − | 0.479206i | 0.206948 | − | 0.978352i | \(-0.433647\pi\) |
−0.866518 | + | 0.499146i | \(0.833647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4919 | − | 32.2907i | 0.522638 | − | 1.60852i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.606778 | + | 0.440850i | −0.0301510 | + | 0.0219060i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.199180 | + | 34.6513i | 0.00987300 | + | 1.71760i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.6595 | + | 11.3773i | −0.774311 | + | 0.562570i | −0.903266 | − | 0.429081i | \(-0.858838\pi\) |
0.128955 | + | 0.991650i | \(0.458838\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.935348 | + | 2.87870i | −0.0461373 | + | 0.141996i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.9601 | + | 19.5877i | 1.32662 | + | 0.963846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.22694 | − | 6.85383i | −0.109316 | − | 0.336441i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.67138 | −0.375669 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0672 | 0.540669 | 0.270334 | − | 0.962767i | \(-0.412866\pi\) | ||||
0.270334 | + | 0.962767i | \(0.412866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.68747 | + | 20.5819i | 0.325928 | + | 1.00310i | 0.971020 | + | 0.238998i | \(0.0768188\pi\) |
−0.645093 | + | 0.764104i | \(0.723181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.46167 | + | 1.06197i | 0.0710689 | + | 0.0516346i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.129816 | − | 0.399533i | 0.00629701 | − | 0.0193802i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.7728 | − | 17.2720i | 1.15045 | − | 0.835849i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.3521 | + | 5.84655i | 0.886048 | + | 0.282274i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.9413 | − | 11.5820i | 0.767865 | − | 0.557887i | −0.133448 | − | 0.991056i | \(-0.542605\pi\) |
0.901313 | + | 0.433169i | \(0.142605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1300 | − | 37.3323i | 0.582931 | − | 1.79408i | −0.0244951 | − | 0.999700i | \(-0.507798\pi\) |
0.607426 | − | 0.794376i | \(-0.292202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.49603 | − | 1.81347i | −0.119675 | − | 0.0869492i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.63854 | − | 8.12059i | −0.126218 | − | 0.388460i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.40014 | −0.400917 | −0.200458 | − | 0.979702i | \(-0.564243\pi\) | ||||
−0.200458 | + | 0.979702i | \(0.564243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.88233 | 0.137254 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.62643 | + | 5.00564i | 0.0772741 | + | 0.237825i | 0.982230 | − | 0.187679i | \(-0.0600966\pi\) |
−0.904956 | + | 0.425505i | \(0.860097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.24302 | + | 5.26237i | 0.343352 | + | 0.249460i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.88430 | − | 21.1877i | 0.325616 | − | 1.00214i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.2573 | + | 16.1709i | −1.05039 | + | 0.763152i | −0.972286 | − | 0.233794i | \(-0.924886\pi\) |
−0.0781020 | + | 0.996945i | \(0.524886\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5989 | + | 22.5725i | 0.781613 | + | 1.06290i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.3590 | − | 11.1589i | 0.721627 | − | 0.524292i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.69630 | + | 11.3760i | −0.173285 | + | 0.533317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0241 | + | 10.9157i | 0.702799 | + | 0.510613i | 0.880842 | − | 0.473409i | \(-0.156977\pi\) |
−0.178044 | + | 0.984023i | \(0.556977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.690658 | − | 2.12563i | −0.0322372 | − | 0.0992158i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.4696 | −1.55884 | −0.779418 | − | 0.626504i | \(-0.784485\pi\) | ||||
−0.779418 | + | 0.626504i | \(0.784485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.19202 | 0.334242 | 0.167121 | − | 0.985936i | \(-0.446553\pi\) | ||||
0.167121 | + | 0.985936i | \(0.446553\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.27571 | + | 7.00393i | 0.105534 | + | 0.324799i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3010 | + | 10.3903i | 0.661772 | + | 0.480805i | 0.867261 | − | 0.497854i | \(-0.165878\pi\) |
−0.205489 | + | 0.978659i | \(0.565878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.399767 | + | 1.23036i | −0.0184595 | + | 0.0568125i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5213 | + | 7.64414i | −0.484794 | + | 0.352223i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.4120 | + | 6.43095i | −0.892567 | + | 0.295695i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.40799 | + | 1.02296i | −0.0646029 | + | 0.0469367i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.91494 | + | 8.97127i | −0.133466 | + | 0.410766i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.90215 | − | 2.83508i | −0.178294 | − | 0.129538i | 0.495059 | − | 0.868859i | \(-0.335146\pi\) |
−0.673353 | + | 0.739321i | \(0.735146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7059 | + | 51.4155i | 0.761724 | + | 2.34435i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7288 | 0.579182 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.783160 | 0.0355615 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.87203 | + | 21.1499i | 0.311401 | + | 0.958395i | 0.977211 | + | 0.212273i | \(0.0680865\pi\) |
−0.665809 | + | 0.746122i | \(0.731914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.6052 | + | 14.9705i | 0.931798 | + | 0.676991i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.49346 | − | 19.9848i | 0.293046 | − | 0.901901i | −0.690825 | − | 0.723022i | \(-0.742753\pi\) |
0.983871 | − | 0.178880i | \(-0.0572473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.934273 | − | 0.678789i | 0.0420775 | − | 0.0305711i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.47929 | − | 1.81522i | 0.246276 | − | 0.0815879i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.64107 | + | 7.00465i | −0.432461 | + | 0.314201i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.12469 | + | 12.6945i | −0.184646 | + | 0.568283i | −0.999942 | − | 0.0107616i | \(-0.996574\pi\) |
0.815296 | + | 0.579045i | \(0.196574\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.9980 | − | 10.8967i | −0.670059 | − | 0.486827i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.59700 | + | 26.4589i | 0.383321 | + | 1.17974i | 0.937691 | + | 0.347471i | \(0.112960\pi\) |
−0.554369 | + | 0.832271i | \(0.687040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0692 | −0.492575 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.4592 | 0.686567 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.64140 | + | 8.12939i | 0.117078 | + | 0.360329i | 0.992375 | − | 0.123257i | \(-0.0393340\pi\) |
−0.875297 | + | 0.483586i | \(0.839334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.2259 | + | 16.8746i | 1.02745 | + | 0.746488i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.86126 | + | 8.80605i | −0.126328 | + | 0.388797i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.25162 | + | 2.36244i | −0.143284 | + | 0.104102i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.03977 | + | 2.77383i | 0.0897090 | + | 0.121993i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0659 | − | 9.49293i | 0.573529 | − | 0.416693i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.90594 | + | 8.94357i | −0.127312 | + | 0.391825i | −0.994315 | − | 0.106477i | \(-0.966043\pi\) |
0.867003 | + | 0.498302i | \(0.166043\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.0969 | − | 24.0463i | −1.44723 | − | 1.05147i | −0.986469 | − | 0.163948i | \(-0.947577\pi\) |
−0.460760 | − | 0.887525i | \(-0.652423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.801735 | − | 2.46749i | −0.0349906 | − | 0.107690i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.75651 | −0.120076 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.07025 | 0.0465324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.75284 | − | 23.8608i | −0.336445 | − | 1.03547i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.3643 | + | 25.6937i | 1.53180 | + | 1.11292i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.206864 | + | 0.636662i | −0.00894351 | + | 0.0275253i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7310 | − | 12.8823i | 0.765148 | − | 0.555913i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.23370 | + | 1.66733i | 0.225431 | + | 0.0718171i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.6654 | + | 18.6470i | −1.10344 | + | 0.801697i | −0.981618 | − | 0.190855i | \(-0.938874\pi\) |
−0.121822 | + | 0.992552i | \(0.538874\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.453776 | − | 1.39658i | 0.0194734 | − | 0.0599329i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.20873 | + | 3.78436i | 0.223117 | + | 0.162104i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7089 | − | 36.0362i | −0.500635 | − | 1.54080i | −0.807987 | − | 0.589201i | \(-0.799443\pi\) |
0.307352 | − | 0.951596i | \(-0.400557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.1227 | −0.944172 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.78421 | −0.203814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.45447 | − | 10.6318i | −0.146899 | − | 0.452109i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.48658 | − | 6.89240i | −0.402683 | − | 0.292566i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.52612 | − | 20.0853i | 0.276521 | − | 0.851043i | −0.712292 | − | 0.701883i | \(-0.752343\pi\) |
0.988813 | − | 0.149160i | \(-0.0476570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.8109 | + | 18.7527i | −1.09169 | + | 0.793156i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.00898845 | − | 1.56372i | −0.000379493 | − | 0.0660201i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4806 | + | 21.4189i | −1.24246 | + | 0.902698i | −0.997760 | − | 0.0669013i | \(-0.978689\pi\) |
−0.244698 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.48658 | − | 4.57521i | 0.0625407 | − | 0.192480i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.40267 | − | 1.01910i | −0.0589067 | − | 0.0427982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.54762 | − | 10.9184i | −0.148724 | − | 0.457725i | 0.848747 | − | 0.528799i | \(-0.177357\pi\) |
−0.997471 | + | 0.0710738i | \(0.977357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4382 | 1.39934 | 0.699672 | − | 0.714464i | \(-0.253329\pi\) | ||||
0.699672 | + | 0.714464i | \(0.253329\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.8812 | 0.830549 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.51608 | − | 4.66602i | −0.0632250 | − | 0.194586i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.57859 | − | 3.32654i | −0.190609 | − | 0.138486i | 0.488388 | − | 0.872627i | \(-0.337585\pi\) |
−0.678997 | + | 0.734141i | \(0.737585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.07750 | − | 15.6269i | 0.211014 | − | 0.649433i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.4776 | − | 9.79201i | 0.559143 | − | 0.406241i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.4825 | + | 14.6037i | −0.434141 | + | 0.604824i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.28545 | − | 5.29319i | 0.301216 | − | 0.218847i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.4907 | + | 32.2870i | −0.432996 | + | 1.33263i | 0.462129 | + | 0.886813i | \(0.347086\pi\) |
−0.895126 | + | 0.445814i | \(0.852914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.23873 | + | 6.71233i | 0.380675 | + | 0.276577i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.11955 | − | 24.9894i | −0.333994 | − | 1.02793i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.42927 | 0.346149 | 0.173074 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173074 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.971121 | 0.0398121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.165954 | − | 0.510755i | −0.00679206 | − | 0.0209038i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0192 | + | 23.2633i | 1.30827 | + | 0.950512i | 1.00000 | 0.000788105i | \(-0.000250862\pi\) | |
0.308267 | + | 0.951300i | \(0.400251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.357186 | − | 1.09930i | 0.0145699 | − | 0.0448416i | −0.943507 | − | 0.331352i | \(-0.892495\pi\) |
0.958077 | + | 0.286510i | \(0.0924953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.787946 | − | 0.572476i | 0.0320876 | − | 0.0233130i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9993 | − | 0.126455i | 0.447184 | − | 0.00514112i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.2814 | − | 25.6334i | 1.43203 | − | 1.04043i | 0.442393 | − | 0.896821i | \(-0.354130\pi\) |
0.989635 | − | 0.143608i | \(-0.0458705\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.20394 | − | 6.78304i | 0.0893083 | − | 0.274863i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.34577 | + | 3.15739i | 0.175811 | + | 0.127734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.46362 | − | 22.9706i | −0.301453 | − | 0.927776i | −0.980977 | − | 0.194123i | \(-0.937814\pi\) |
0.679525 | − | 0.733653i | \(-0.262186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.48139 | −0.382326 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2901 | −1.21943 | −0.609716 | − | 0.792620i | \(-0.708717\pi\) | ||||
−0.609716 | + | 0.792620i | \(0.708717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.74826 | + | 23.8467i | 0.311429 | + | 0.958480i | 0.977199 | + | 0.212323i | \(0.0681030\pi\) |
−0.665771 | + | 0.746157i | \(0.731897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.1170 | − | 15.3424i | −0.847395 | − | 0.615669i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.39545 | + | 19.6832i | −0.256228 | + | 0.788590i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.77764 | + | 5.26283i | −0.150865 | + | 0.210177i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.55087 | − | 2.57985i | 0.141582 | − | 0.102866i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.854729 | + | 2.63059i | −0.0340262 | + | 0.104722i | −0.966627 | − | 0.256187i | \(-0.917534\pi\) |
0.932601 | + | 0.360909i | \(0.117534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.42288 | + | 6.11958i | 0.334779 | + | 0.243231i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.48372 | + | 13.7995i | 0.177931 | + | 0.547615i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56960 | 0.339540 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.97185 | 0.354921 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.10346 | + | 15.7068i | 0.201574 | + | 0.620382i | 0.999837 | + | 0.0180722i | \(0.00575288\pi\) |
−0.798262 | + | 0.602310i | \(0.794247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.5405 | − | 24.3686i | −1.32271 | − | 0.961005i | −0.999894 | − | 0.0145433i | \(-0.995371\pi\) |
−0.322816 | − | 0.946462i | \(-0.604629\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.13842 | − | 6.58137i | 0.0842000 | − | 0.259141i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7768 | + | 15.0952i | −0.816821 | + | 0.593455i | −0.915800 | − | 0.401634i | \(-0.868442\pi\) |
0.0989792 | + | 0.995090i | \(0.468442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.274823 | − | 47.8109i | −0.0107878 | − | 1.87674i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.7727 | + | 10.0065i | −0.539795 | + | 0.392184i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.1771 | − | 31.3220i | 0.398262 | − | 1.22572i | −0.528130 | − | 0.849164i | \(-0.677107\pi\) |
0.926392 | − | 0.376561i | \(-0.122893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.4968 | − | 8.35290i | −0.449216 | − | 0.326375i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.67900 | − | 20.5558i | −0.260573 | − | 0.801960i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.58757 | 0.178706 | 0.0893532 | − | 0.996000i | \(-0.471520\pi\) | ||||
0.0893532 | + | 0.996000i | \(0.471520\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6825 | −0.843353 | −0.421676 | − | 0.906746i | \(-0.638558\pi\) | ||||
−0.421676 | + | 0.906746i | \(0.638558\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.753892 | − | 2.32024i | −0.0292787 | − | 0.0901106i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.25481 | − | 2.36476i | −0.126216 | − | 0.0917013i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.16766 | − | 12.8267i | 0.161372 | − | 0.496653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.41543 | − | 4.66108i | 0.248035 | − | 0.180208i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.1700 | − | 12.7972i | −1.55075 | − | 0.494032i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4381 | + | 10.4899i | −0.556547 | + | 0.404355i | −0.830193 | − | 0.557475i | \(-0.811770\pi\) |
0.273647 | + | 0.961830i | \(0.411770\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.64405 | + | 5.05988i | −0.0632797 | + | 0.194755i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.04338 | − | 5.84386i | −0.309132 | − | 0.224598i | 0.422392 | − | 0.906413i | \(-0.361191\pi\) |
−0.731524 | + | 0.681816i | \(0.761191\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.559448 | + | 1.72180i | 0.0214696 | + | 0.0660767i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.22548 | −0.161921 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.6508 | −0.407541 | −0.203770 | − | 0.979019i | \(-0.565320\pi\) | ||||
−0.203770 | + | 0.979019i | \(0.565320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.833396 | + | 2.56493i | 0.0318424 | + | 0.0980009i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.4072 | + | 7.56127i | 0.397059 | + | 0.288480i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.66657 | + | 26.6730i | −0.330170 | + | 1.01616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95202 | + | 6.50402i | −0.340551 | + | 0.247425i | −0.744894 | − | 0.667183i | \(-0.767500\pi\) |
0.404343 | + | 0.914607i | \(0.367500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.90493 | + | 10.7497i | 0.300283 | + | 0.408348i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.52979 | + | 4.01763i | −0.209757 | + | 0.152397i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.09668 | − | 3.37523i | 0.0415396 | − | 0.127846i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.63450 | − | 4.09370i | −0.213116 | − | 0.154838i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1808 | − | 40.5663i | −0.497832 | − | 1.53217i | −0.812496 | − | 0.582967i | \(-0.801892\pi\) |
0.314664 | − | 0.949203i | \(-0.398108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.1832 | −0.685793 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.16513 | −0.0438812 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.90727 | − | 24.3361i | −0.297384 | − | 0.915253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.6989 | + | 31.0226i | 1.60359 | + | 1.16508i | 0.880156 | + | 0.474685i | \(0.157438\pi\) |
0.723435 | + | 0.690392i | \(0.242562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.60074 | + | 8.00424i | −0.0975352 | + | 0.300183i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.0442 | + | 18.9222i | −0.975364 | + | 0.708643i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2908 | − | 5.39691i | 0.609240 | − | 0.201833i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.3234 | − | 11.1331i | 0.572262 | − | 0.415773i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.14399 | − | 12.7539i | 0.154545 | − | 0.475640i | −0.843570 | − | 0.537020i | \(-0.819550\pi\) |
0.998114 | + | 0.0613797i | \(0.0195500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.51669 | − | 5.46120i | −0.279936 | − | 0.203386i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.63319 | + | 29.6479i | 0.358262 | + | 1.10262i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.74897 | −0.102094 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.7639 | −0.436300 | −0.218150 | − | 0.975915i | \(-0.570002\pi\) | ||||
−0.218150 | + | 0.975915i | \(0.570002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.93890 | + | 18.2780i | 0.219959 | + | 0.676965i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.09552 | + | 1.52249i | 0.0775057 | + | 0.0563112i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.90057 | − | 12.0047i | 0.144071 | − | 0.443404i | −0.852820 | − | 0.522206i | \(-0.825109\pi\) |
0.996890 | + | 0.0788016i | \(0.0251093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50377 | + | 1.09256i | −0.0554675 | + | 0.0402995i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.76190 | − | 0.583694i | 0.0649004 | − | 0.0215006i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.57009 | + | 1.14074i | −0.0577567 | + | 0.0419627i | −0.616289 | − | 0.787520i | \(-0.711365\pi\) |
0.558532 | + | 0.829483i | \(0.311365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.12322 | + | 9.61230i | −0.114735 | + | 0.353117i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.56920 | + | 6.95243i | 0.351060 | + | 0.255060i | 0.749314 | − | 0.662215i | \(-0.230384\pi\) |
−0.398254 | + | 0.917275i | \(0.630384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.13391 | − | 18.8782i | −0.224729 | − | 0.691646i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.5420 | −0.458889 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.54749 | −0.0565442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.42808 | + | 19.7836i | 0.234564 | + | 0.721914i | 0.997179 | + | 0.0750610i | \(0.0239151\pi\) |
−0.762615 | + | 0.646853i | \(0.776085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9053 | − | 16.6416i | −0.834714 | − | 0.606455i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.22714 | − | 16.0875i | 0.190235 | − | 0.585484i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.9704 | + | 13.7828i | −0.689491 | + | 0.500944i | −0.876493 | − | 0.481415i | \(-0.840123\pi\) |
0.187002 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8191 | − | 14.7127i | −0.392710 | − | 0.534036i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.8441 | + | 15.1441i | −0.755599 | + | 0.548975i | −0.897557 | − | 0.440898i | \(-0.854660\pi\) |
0.141958 | + | 0.989873i | \(0.454660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.59921 | + | 14.1549i | −0.166503 | + | 0.512442i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.591487 | − | 0.429741i | −0.0213853 | − | 0.0155373i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.0504 | − | 70.9417i | −0.832300 | − | 2.56156i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.4583 | 0.593500 | 0.296750 | − | 0.954955i | \(-0.404097\pi\) | ||||
0.296750 | + | 0.954955i | \(0.404097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.08814 | 0.291287 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.8797 | + | 36.5620i | 0.427283 | + | 1.31504i | 0.900791 | + | 0.434253i | \(0.142987\pi\) |
−0.473508 | + | 0.880789i | \(0.657013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.30849 | + | 3.85684i | 0.190687 | + | 0.138542i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.37647 | − | 25.7801i | 0.300504 | − | 0.924856i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.8946 | + | 8.64191i | −0.426167 | + | 0.309628i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2910 | + | 5.18992i | 0.582937 | + | 0.185710i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.8321 | + | 8.59651i | −0.422844 | + | 0.307214i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.58072 | + | 11.0203i | −0.127801 | + | 0.393332i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | + | 1.08981i | 0.0534692 | + | 0.0388477i | 0.614199 | − | 0.789151i | \(-0.289479\pi\) |
−0.560730 | + | 0.827999i | \(0.689479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.87848 | + | 11.9367i | 0.138078 | + | 0.424959i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1207 | 0.395406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.7740 | −2.33570 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.87980 | − | 5.78542i | −0.0666696 | − | 0.205188i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.15265 | − | 6.64979i | −0.324204 | − | 0.235548i | 0.413763 | − | 0.910384i | \(-0.364214\pi\) |
−0.737967 | + | 0.674837i | \(0.764214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.134766 | − | 0.414767i | 0.00476768 | − | 0.0146734i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.6055 | − | 9.15845i | 0.445394 | − | 0.323598i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.236758 | − | 41.1886i | −0.00835500 | − | 1.45351i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.17539 | − | 6.66631i | 0.323390 | − | 0.234957i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.78598 | − | 17.8074i | 0.203676 | − | 0.626851i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.2679 | − | 15.4520i | −0.747739 | − | 0.543264i | 0.147386 | − | 0.989079i | \(-0.452914\pi\) |
−0.895125 | + | 0.445815i | \(0.852914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.68613 | + | 20.5778i | 0.234782 | + | 0.722585i | 0.997150 | + | 0.0754411i | \(0.0240365\pi\) |
−0.762368 | + | 0.647143i | \(0.775964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.28904 | −0.0452085 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.6932 | 0.794909 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31597 | − | 10.2055i | −0.116011 | − | 0.357046i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.8416 | + | 12.2361i | 0.588493 | + | 0.427565i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.6314 | − | 32.7200i | 0.371037 | − | 1.14194i | −0.575076 | − | 0.818100i | \(-0.695028\pi\) |
0.946113 | − | 0.323835i | \(-0.104972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.2211 | − | 16.8711i | 0.809435 | − | 0.588089i | −0.104231 | − | 0.994553i | \(-0.533238\pi\) |
0.913667 | + | 0.406464i | \(0.133238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.17060 | + | 3.02398i | −0.0755707 | + | 0.105281i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.4541 | − | 21.3997i | 1.02422 | − | 0.744139i | 0.0570762 | − | 0.998370i | \(-0.481822\pi\) |
0.967144 | + | 0.254231i | \(0.0818222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.499497 | − | 1.53729i | 0.0173482 | − | 0.0533924i | −0.942008 | − | 0.335591i | \(-0.891064\pi\) |
0.959356 | + | 0.282199i | \(0.0910639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.9603 | − | 15.9551i | −0.761793 | − | 0.553475i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.214997 | − | 0.661692i | −0.00744920 | − | 0.0229263i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.5178 | −0.571622 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.9098 | 1.20666 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.60378 | − | 26.4797i | −0.297036 | − | 0.914181i | −0.982530 | − | 0.186104i | \(-0.940414\pi\) |
0.685495 | − | 0.728078i | \(-0.259586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3479 | + | 12.6040i | 0.598203 | + | 0.434620i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.465591 | − | 1.43294i | 0.0160358 | − | 0.0493532i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1435 | − | 8.09625i | 0.383349 | − | 0.278519i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.13531 | + | 24.0919i | 0.279533 | + | 0.827809i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.8368 | + | 19.4981i | −0.921036 | + | 0.669172i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8399 | − | 48.7502i | 0.542985 | − | 1.67114i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7239 | + | 15.7834i | 0.743813 | + | 0.540412i | 0.893903 | − | 0.448261i | \(-0.147956\pi\) |
−0.150090 | + | 0.988672i | \(0.547956\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.935975 | + | 2.88064i | 0.0320097 | + | 0.0985156i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.8384 | −1.19006 | −0.595029 | − | 0.803704i | \(-0.702859\pi\) | ||||
−0.595029 | + | 0.803704i | \(0.702859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1475 | −0.721543 | −0.360771 | − | 0.932654i | \(-0.617487\pi\) | ||||
−0.360771 | + | 0.932654i | \(0.617487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.77300 | − | 20.8451i | −0.230823 | − | 0.710400i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.02412 | − | 3.65024i | −0.171023 | − | 0.124255i | 0.498981 | − | 0.866613i | \(-0.333708\pi\) |
−0.670004 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.44674 | − | 13.6857i | 0.151194 | − | 0.465327i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.2755 | − | 11.0983i | 0.518784 | − | 0.376919i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.35258 | + | 13.0296i | −0.317264 | + | 0.441998i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.34268 | − | 1.70206i | 0.0793787 | − | 0.0576720i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.421186 | − | 1.29628i | 0.0142550 | − | 0.0438723i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.87018 | − | 1.35877i | −0.0632238 | − | 0.0459347i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.180719 | − | 0.556195i | −0.00610244 | − | 0.0187814i | 0.947959 | − | 0.318393i | \(-0.103143\pi\) |
−0.954061 | + | 0.299611i | \(0.903143\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.73181 | 0.328246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.6436 | 0.830262 | 0.415131 | − | 0.909762i | \(-0.363736\pi\) | ||||
0.415131 | + | 0.909762i | \(0.363736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.44571 | + | 22.9155i | 0.250568 | + | 0.771170i | 0.994671 | + | 0.103104i | \(0.0328775\pi\) |
−0.744102 | + | 0.668066i | \(0.767123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0893 | + | 9.50995i | 0.439993 | + | 0.319673i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.3441 | − | 31.8360i | 0.347322 | − | 1.06895i | −0.613007 | − | 0.790078i | \(-0.710040\pi\) |
0.960329 | − | 0.278870i | \(-0.0899599\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.1356 | + | 19.7152i | −0.910100 | + | 0.661227i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0142984 | + | 2.48749i | 0.000479015 | + | 0.0833340i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.46167 | + | 1.06197i | −0.0489130 | + | 0.0355373i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.03442 | − | 18.5720i | 0.201708 | − | 0.620795i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.0504 | − | 16.7471i | −0.769629 | − | 0.559168i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.57398 | + | 17.1549i | 0.185903 | + | 0.572149i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.27695 | 0.0758562 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.9969 | 0.532344 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.404315 | − | 1.24435i | −0.0134399 | − | 0.0413637i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.7221 | − | 32.4925i | −1.48497 | − | 1.07890i | −0.975911 | − | 0.218168i | \(-0.929992\pi\) |
−0.509063 | − | 0.860729i | \(-0.670008\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.95307 | + | 18.3217i | −0.197451 | + | 0.607691i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.7635 | + | 11.4529i | −0.522269 | + | 0.379451i | −0.817458 | − | 0.575988i | \(-0.804617\pi\) |
0.295189 | + | 0.955439i | \(0.404617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.7736 | − | 7.25515i | −0.753698 | − | 0.240110i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.5419 | − | 8.38566i | 0.381562 | − | 0.277221i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.1514 | − | 31.2429i | 0.335230 | − | 1.03173i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.2356 | + | 29.2329i | 1.32725 | + | 0.964303i | 0.999811 | + | 0.0194309i | \(0.00618543\pi\) |
0.327439 | + | 0.944872i | \(0.393815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.07899 | − | 3.32080i | −0.0355540 | − | 0.109424i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.6747 | 0.878007 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4479 | −0.343526 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.16155 | + | 6.65258i | 0.0709947 | + | 0.218499i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.9997 | + | 26.8819i | 1.21392 | + | 0.881966i | 0.995581 | − | 0.0939069i | \(-0.0299356\pi\) |
0.218341 | + | 0.975873i | \(0.429936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.890689 | + | 2.74126i | −0.0291912 | + | 0.0898412i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.8677 | + | 15.1612i | −0.683176 | + | 0.496357i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.825424 | − | 1.12247i | −0.0269942 | − | 0.0367088i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.70092 | − | 7.04813i | 0.316915 | − | 0.230252i | −0.417943 | − | 0.908473i | \(-0.637249\pi\) |
0.734858 | + | 0.678221i | \(0.237249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.13846 | + | 21.9699i | −0.232955 | + | 0.716961i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3860 | + | 14.8113i | 0.664564 | + | 0.482834i | 0.868201 | − | 0.496212i | \(-0.165276\pi\) |
−0.203637 | + | 0.979046i | \(0.565276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.8077 | − | 39.4182i | −0.417077 | − | 1.28363i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.2987 | −0.400078 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.65426 | −0.313721 | −0.156861 | − | 0.987621i | \(-0.550137\pi\) | ||||
−0.156861 | + | 0.987621i | \(0.550137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.8577 | − | 61.1156i | −0.644607 | − | 1.98390i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.6651 | + | 21.5530i | 0.961957 | + | 0.698903i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.93492 | + | 30.5765i | −0.321824 | + | 0.990472i | 0.651030 | + | 0.759052i | \(0.274337\pi\) |
−0.972854 | + | 0.231420i | \(0.925663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3311 | − | 10.4121i | 0.463742 | − | 0.336929i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.71348 | + | 3.21795i | −0.313992 | + | 0.104021i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.04374 | + | 3.66450i | −0.162871 | + | 0.118333i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.72530 | − | 11.4653i | 0.120171 | − | 0.369848i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.942542 | + | 0.684797i | 0.0303730 | + | 0.0220673i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.52405 | − | 13.9236i | −0.145634 | − | 0.448217i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.4330 | −1.49318 | −0.746592 | − | 0.665283i | \(-0.768311\pi\) | ||||
−0.746592 | + | 0.665283i | \(0.768311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.820559 | 0.0263601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.66699 | − | 17.4412i | −0.181862 | − | 0.559715i | 0.818018 | − | 0.575193i | \(-0.195073\pi\) |
−0.999880 | + | 0.0154779i | \(0.995073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7831 | − | 9.28745i | −0.409807 | − | 0.297742i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.79458 | + | 5.52314i | −0.0574725 | + | 0.176882i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.3866 | − | 18.4444i | 0.812189 | − | 0.590090i | −0.102276 | − | 0.994756i | \(-0.532612\pi\) |
0.914464 | + | 0.404667i | \(0.132612\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.1868 | − | 9.33791i | 0.900854 | − | 0.298441i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.06510 | − | 6.58618i | 0.289427 | − | 0.210281i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.32332 | − | 19.4612i | 0.201683 | − | 0.620715i | −0.798151 | − | 0.602458i | \(-0.794188\pi\) |
0.999833 | − | 0.0182573i | \(-0.00581179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.9402 | − | 13.7609i | −0.603486 | − | 0.438458i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.832304 | − | 2.56157i | −0.0264925 | − | 0.0815356i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.2502 | 0.961900 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.5692 | −1.41579 | −0.707894 | − | 0.706318i | \(-0.750355\pi\) | ||||
−0.707894 | + | 0.706318i | \(0.750355\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.72480 | − | 17.6191i | −0.181671 | − | 0.559126i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.387117 | − | 0.281257i | −0.0122724 | − | 0.00891644i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.52704 | − | 20.0882i | 0.206713 | − | 0.636198i | −0.792925 | − | 0.609319i | \(-0.791443\pi\) |
0.999639 | − | 0.0268794i | \(-0.00855700\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.9699 | + | 32.6725i | −1.42278 | + | 1.03371i |
(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 | 880.2.bo.f.641.2 | 8 | ||
4.3 | odd | 2 | 220.2.m.a.201.1 | yes | 8 | ||
11.2 | odd | 10 | 9680.2.a.cl.1.3 | 4 | |||
11.4 | even | 5 | inner | 880.2.bo.f.81.2 | 8 | ||
11.9 | even | 5 | 9680.2.a.ck.1.3 | 4 | |||
12.11 | even | 2 | 1980.2.z.c.1081.2 | 8 | |||
20.3 | even | 4 | 1100.2.cb.c.949.3 | 16 | |||
20.7 | even | 4 | 1100.2.cb.c.949.2 | 16 | |||
20.19 | odd | 2 | 1100.2.n.c.201.2 | 8 | |||
44.15 | odd | 10 | 220.2.m.a.81.1 | ✓ | 8 | ||
44.31 | odd | 10 | 2420.2.a.n.1.2 | 4 | |||
44.35 | even | 10 | 2420.2.a.m.1.2 | 4 | |||
132.59 | even | 10 | 1980.2.z.c.1621.2 | 8 | |||
220.59 | odd | 10 | 1100.2.n.c.301.2 | 8 | |||
220.103 | even | 20 | 1100.2.cb.c.1049.2 | 16 | |||
220.147 | even | 20 | 1100.2.cb.c.1049.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.2.m.a.81.1 | ✓ | 8 | 44.15 | odd | 10 | ||
220.2.m.a.201.1 | yes | 8 | 4.3 | odd | 2 | ||
880.2.bo.f.81.2 | 8 | 11.4 | even | 5 | inner | ||
880.2.bo.f.641.2 | 8 | 1.1 | even | 1 | trivial | ||
1100.2.n.c.201.2 | 8 | 20.19 | odd | 2 | |||
1100.2.n.c.301.2 | 8 | 220.59 | odd | 10 | |||
1100.2.cb.c.949.2 | 16 | 20.7 | even | 4 | |||
1100.2.cb.c.949.3 | 16 | 20.3 | even | 4 | |||
1100.2.cb.c.1049.2 | 16 | 220.103 | even | 20 | |||
1100.2.cb.c.1049.3 | 16 | 220.147 | even | 20 | |||
1980.2.z.c.1081.2 | 8 | 12.11 | even | 2 | |||
1980.2.z.c.1621.2 | 8 | 132.59 | even | 10 | |||
2420.2.a.m.1.2 | 4 | 44.35 | even | 10 | |||
2420.2.a.n.1.2 | 4 | 44.31 | odd | 10 | |||
9680.2.a.ck.1.3 | 4 | 11.9 | even | 5 | |||
9680.2.a.cl.1.3 | 4 | 11.2 | odd | 10 |