Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(385,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.385");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 769.4 | ||
Root | \(-1.28252 - 1.16410i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.769 |
Dual form | 1152.2.i.i.385.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.366879 | − | 1.69275i | −0.211818 | − | 0.977309i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.05471 | + | 1.82681i | −0.471681 | + | 0.816975i | −0.999475 | − | 0.0323971i | \(-0.989686\pi\) |
0.527794 | + | 0.849372i | \(0.323019\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.43914 | + | 2.49267i | 0.543944 | + | 0.942139i | 0.998673 | + | 0.0515089i | \(0.0164031\pi\) |
−0.454728 | + | 0.890630i | \(0.650264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.73080 | + | 1.24207i | −0.910267 | + | 0.414022i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.21325 | + | 2.10141i | 0.365808 | + | 0.633598i | 0.988905 | − | 0.148546i | \(-0.0474594\pi\) |
−0.623097 | + | 0.782144i | \(0.714126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.30008 | − | 5.71590i | 0.915277 | − | 1.58531i | 0.108781 | − | 0.994066i | \(-0.465305\pi\) |
0.806496 | − | 0.591240i | \(-0.201361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.47929 | + | 1.11514i | 0.898348 | + | 0.287928i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.56848 | −1.83563 | −0.917813 | − | 0.397013i | \(-0.870047\pi\) | ||||
−0.917813 | + | 0.397013i | \(0.870047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.25779 | −1.43563 | −0.717817 | − | 0.696231i | \(-0.754859\pi\) | ||||
−0.717817 | + | 0.696231i | \(0.754859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.69147 | − | 3.35061i | 0.805544 | − | 0.731163i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.63611 | + | 4.56587i | −0.549666 | + | 0.952050i | 0.448631 | + | 0.893717i | \(0.351912\pi\) |
−0.998297 | + | 0.0583329i | \(0.981422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.275172 | + | 0.476612i | 0.0550344 | + | 0.0953223i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.10438 | + | 4.16687i | 0.597438 | + | 0.801915i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.57821 | − | 2.73353i | −0.293065 | − | 0.507604i | 0.681468 | − | 0.731848i | \(-0.261342\pi\) |
−0.974533 | + | 0.224244i | \(0.928009\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.79039 | + | 3.10104i | −0.321563 | + | 0.556964i | −0.980811 | − | 0.194962i | \(-0.937542\pi\) |
0.659248 | + | 0.751926i | \(0.270875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.11204 | − | 2.82469i | 0.541737 | − | 0.491715i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.07151 | −1.02627 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.70957 | −1.10305 | −0.551524 | − | 0.834159i | \(-0.685953\pi\) | ||||
−0.551524 | + | 0.834159i | \(0.685953\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8863 | − | 3.48916i | −1.74321 | − | 0.558713i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.74537 | + | 3.02306i | −0.272580 | + | 0.472123i | −0.969522 | − | 0.245005i | \(-0.921210\pi\) |
0.696941 | + | 0.717128i | \(0.254544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12570 | − | 5.41388i | −0.476665 | − | 0.825608i | 0.522977 | − | 0.852347i | \(-0.324821\pi\) |
−0.999642 | + | 0.0267383i | \(0.991488\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.611180 | − | 6.29868i | 0.0911093 | − | 0.938952i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.32972 | + | 2.30314i | 0.193960 | + | 0.335948i | 0.946559 | − | 0.322531i | \(-0.104534\pi\) |
−0.752599 | + | 0.658479i | \(0.771200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.642255 | + | 1.11242i | −0.0917508 | + | 0.158917i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.77671 | + | 12.8115i | 0.388818 | + | 1.79397i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.953009 | 0.130906 | 0.0654529 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654529 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.11850 | −0.690178 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29585 | + | 10.5929i | 0.304093 | + | 1.40306i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.84757 | + | 8.39624i | −0.631100 | + | 1.09310i | 0.356227 | + | 0.934400i | \(0.384063\pi\) |
−0.987327 | + | 0.158698i | \(0.949270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.57821 | + | 4.46558i | 0.330105 | + | 0.571759i | 0.982532 | − | 0.186092i | \(-0.0595824\pi\) |
−0.652427 | + | 0.757852i | \(0.726249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.02607 | − | 5.01946i | −0.885201 | − | 0.632393i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.96125 | + | 12.0572i | 0.863437 | + | 1.49552i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.949546 | + | 1.64466i | −0.116005 | + | 0.200927i | −0.918181 | − | 0.396161i | \(-0.870342\pi\) |
0.802176 | + | 0.597088i | \(0.203676\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.69601 | + | 2.78715i | 1.04688 | + | 0.335533i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82491 | 0.691290 | 0.345645 | − | 0.938365i | \(-0.387660\pi\) | ||||
0.345645 | + | 0.938365i | \(0.387660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.01222 | −0.586636 | −0.293318 | − | 0.956015i | \(-0.594760\pi\) | ||||
−0.293318 | + | 0.956015i | \(0.594760\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.705829 | − | 0.640656i | 0.0815021 | − | 0.0739765i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.49207 | + | 6.04844i | −0.397958 | + | 0.689284i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.49996 | + | 11.2583i | 0.731303 | + | 1.26665i | 0.956327 | + | 0.292301i | \(0.0944207\pi\) |
−0.225024 | + | 0.974353i | \(0.572246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.91454 | − | 6.78368i | 0.657171 | − | 0.753742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.54502 | − | 2.67606i | −0.169588 | − | 0.293735i | 0.768687 | − | 0.639625i | \(-0.220910\pi\) |
−0.938275 | + | 0.345890i | \(0.887577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.98256 | − | 13.8262i | 0.865830 | − | 1.49966i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.04818 | + | 3.67438i | −0.434010 | + | 0.393935i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.95301 | −0.313018 | −0.156509 | − | 0.987677i | \(-0.550024\pi\) | ||||
−0.156509 | + | 0.987677i | \(0.550024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.9971 | 1.99144 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.90614 | + | 1.89297i | 0.612439 | + | 0.196292i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.60015 | − | 11.4318i | 0.677161 | − | 1.17288i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.51242 | − | 9.54779i | −0.559702 | − | 0.969432i | −0.997521 | − | 0.0703686i | \(-0.977582\pi\) |
0.437820 | − | 0.899063i | \(-0.355751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.92323 | − | 4.23159i | −0.595307 | − | 0.425290i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.82357 | + | 3.15852i | 0.181452 | + | 0.314284i | 0.942375 | − | 0.334558i | \(-0.108587\pi\) |
−0.760923 | + | 0.648842i | \(0.775254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.43914 | + | 9.42087i | −0.535935 | + | 0.928266i | 0.463183 | + | 0.886263i | \(0.346707\pi\) |
−0.999117 | + | 0.0420031i | \(0.986626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.22751 | + | 10.2775i | 0.217382 | + | 1.00299i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.94922 | 0.575133 | 0.287567 | − | 0.957761i | \(-0.407154\pi\) | ||||
0.287567 | + | 0.957761i | \(0.407154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.87113 | 0.945483 | 0.472741 | − | 0.881201i | \(-0.343265\pi\) | ||||
0.472741 | + | 0.881201i | \(0.343265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.46160 | + | 11.3576i | 0.233645 | + | 1.07802i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.51518 | + | 13.0167i | −0.706969 | + | 1.22451i | 0.259008 | + | 0.965875i | \(0.416604\pi\) |
−0.965976 | + | 0.258630i | \(0.916729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.56066 | − | 9.63134i | −0.518534 | − | 0.898128i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.91232 | + | 19.7079i | −0.176794 | + | 1.82200i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.8921 | − | 18.8657i | −0.998478 | − | 1.72942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55606 | − | 4.42722i | 0.232369 | − | 0.402475i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.75763 | + | 1.84537i | 0.519148 | + | 0.166391i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7080 | −1.04720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.07789 | 0.716797 | 0.358398 | − | 0.933569i | \(-0.383323\pi\) | ||||
0.358398 | + | 0.933569i | \(0.383323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.01758 | + | 7.27727i | −0.705909 | + | 0.640728i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1329 | + | 19.2827i | −0.972684 | + | 1.68474i | −0.285309 | + | 0.958435i | \(0.592096\pi\) |
−0.687375 | + | 0.726303i | \(0.741237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.00584 | − | 15.5986i | −0.780905 | − | 1.35257i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.8863 | + | 1.27628i | −0.936945 | + | 0.109844i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.62365 | − | 8.00839i | −0.395025 | − | 0.684203i | 0.598079 | − | 0.801437i | \(-0.295931\pi\) |
−0.993104 | + | 0.117234i | \(0.962597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.20256 | + | 7.27905i | −0.356456 | + | 0.617401i | −0.987366 | − | 0.158456i | \(-0.949349\pi\) |
0.630910 | + | 0.775856i | \(0.282682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.41080 | − | 3.09586i | 0.287241 | − | 0.260718i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0152 | 1.33926 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65820 | 0.552934 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.11868 | + | 0.679055i | 0.174745 | + | 0.0560075i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.17836 | − | 10.7012i | 0.506151 | − | 0.876679i | −0.493824 | − | 0.869562i | \(-0.664401\pi\) |
0.999975 | − | 0.00711709i | \(-0.00226546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.91424 | − | 8.51171i | −0.399915 | − | 0.692673i | 0.593800 | − | 0.804613i | \(-0.297627\pi\) |
−0.993715 | + | 0.111940i | \(0.964294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.6680 | − | 9.40056i | 1.67091 | − | 0.759990i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.77668 | − | 6.54141i | −0.303350 | − | 0.525418i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.108083 | + | 0.187206i | −0.00862598 | + | 0.0149406i | −0.870306 | − | 0.492511i | \(-0.836079\pi\) |
0.861680 | + | 0.507452i | \(0.169412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.349639 | − | 1.61321i | −0.0277282 | − | 0.127935i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.1749 | −1.19595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.78116 | 0.452815 | 0.226408 | − | 0.974033i | \(-0.427302\pi\) | ||||
0.226408 | + | 0.974033i | \(0.427302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.87787 | + | 8.66434i | 0.146192 | + | 0.674518i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.818646 | − | 1.41794i | 0.0633487 | − | 0.109723i | −0.832612 | − | 0.553857i | \(-0.813155\pi\) |
0.895960 | + | 0.444134i | \(0.146489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.2810 | − | 26.4675i | −1.17546 | − | 2.03596i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.0888 | − | 7.77259i | 1.30681 | − | 0.594385i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.99228 | − | 5.18278i | −0.227499 | − | 0.394040i | 0.729567 | − | 0.683909i | \(-0.239721\pi\) |
−0.957066 | + | 0.289869i | \(0.906388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.792022 | + | 1.37182i | −0.0598713 | + | 0.103700i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.9912 | + | 5.12532i | 1.20197 | + | 0.385243i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.51313 | −0.711045 | −0.355522 | − | 0.934668i | \(-0.615697\pi\) | ||||
−0.355522 | + | 0.934668i | \(0.615697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.7526 | −1.76551 | −0.882757 | − | 0.469830i | \(-0.844315\pi\) | ||||
−0.882757 | + | 0.469830i | \(0.844315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.61322 | − | 6.00258i | 0.488864 | − | 0.443724i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.07666 | − | 12.2571i | 0.520286 | − | 0.901162i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.18244 | − | 15.9045i | −0.671487 | − | 1.16305i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.91898 | + | 13.7349i | −0.430542 | + | 0.999067i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.14164 | + | 7.17352i | 0.299678 | + | 0.519058i | 0.976062 | − | 0.217491i | \(-0.0697873\pi\) |
−0.676384 | + | 0.736549i | \(0.736454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00315 | − | 8.66572i | 0.360135 | − | 0.623772i | −0.627848 | − | 0.778336i | \(-0.716064\pi\) |
0.987983 | + | 0.154564i | \(0.0493973\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.8559 | − | 16.2072i | 1.27869 | − | 1.16062i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.556259 | 0.0396318 | 0.0198159 | − | 0.999804i | \(-0.493692\pi\) | ||||
0.0198159 | + | 0.999804i | \(0.493692\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5526 | 1.52782 | 0.763912 | − | 0.645320i | \(-0.223276\pi\) | ||||
0.763912 | + | 0.645320i | \(0.223276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.13237 | + | 1.00395i | 0.220940 | + | 0.0708133i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.54252 | − | 7.86788i | 0.318823 | − | 0.552217i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.68171 | − | 6.37691i | −0.257142 | − | 0.445383i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.52756 | − | 15.7427i | 0.106173 | − | 1.09419i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.59225 | − | 13.1502i | −0.525167 | − | 0.909615i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.32984 | − | 14.4277i | 0.573450 | − | 0.993245i | −0.422758 | − | 0.906243i | \(-0.638938\pi\) |
0.996208 | − | 0.0870022i | \(-0.0277287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.13704 | − | 9.86011i | −0.146427 | − | 0.675604i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.1868 | 0.899335 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.3065 | −0.699650 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.83888 | + | 8.48443i | 0.124260 | + | 0.573325i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.9766 | + | 43.2607i | −1.68011 | + | 2.91003i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.49251 | − | 7.78126i | −0.300841 | − | 0.521072i | 0.675486 | − | 0.737373i | \(-0.263934\pi\) |
−0.976327 | + | 0.216301i | \(0.930601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.34342 | − | 0.959749i | −0.0895615 | − | 0.0639833i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.32448 | − | 9.22226i | −0.353398 | − | 0.612103i | 0.633445 | − | 0.773788i | \(-0.281640\pi\) |
−0.986842 | + | 0.161685i | \(0.948307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.50786 | + | 9.53988i | −0.363969 | + | 0.630413i | −0.988610 | − | 0.150499i | \(-0.951912\pi\) |
0.624641 | + | 0.780912i | \(0.285245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.5197 | + | 3.69215i | 0.757938 | + | 0.242926i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.2595 | 1.78583 | 0.892915 | − | 0.450225i | \(-0.148656\pi\) | ||||
0.892915 | + | 0.450225i | \(0.148656\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.60988 | −0.365948 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.6727 | − | 15.1332i | 1.08301 | − | 0.983009i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.82295 | − | 10.0856i | 0.376655 | − | 0.652386i | −0.613918 | − | 0.789370i | \(-0.710407\pi\) |
0.990573 | + | 0.136984i | \(0.0437407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.83554 | + | 17.0356i | 0.633563 | + | 1.09736i | 0.986818 | + | 0.161835i | \(0.0517414\pi\) |
−0.353255 | + | 0.935527i | \(0.614925\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.6530 | − | 7.52304i | −0.875839 | − | 0.482603i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.35479 | − | 2.34656i | −0.0865542 | − | 0.149916i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.6512 | + | 35.7689i | −1.31400 | + | 2.27592i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.96306 | + | 3.59712i | −0.251149 | + | 0.227958i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.3802 | −1.47575 | −0.737873 | − | 0.674940i | \(-0.764170\pi\) | ||||
−0.737873 | + | 0.674940i | \(0.764170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7930 | −0.804289 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.3329 | − | 8.43993i | −1.64903 | − | 0.528529i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.89037 | + | 3.27421i | −0.117918 | + | 0.204240i | −0.918942 | − | 0.394392i | \(-0.870955\pi\) |
0.801024 | + | 0.598632i | \(0.204289\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.65603 | − | 16.7247i | −0.599996 | − | 1.03922i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.70500 | + | 5.50449i | 0.476927 | + | 0.340720i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3638 | + | 17.9507i | 0.639060 | + | 1.10689i | 0.985639 | + | 0.168864i | \(0.0540100\pi\) |
−0.346579 | + | 0.938021i | \(0.612657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00515 | + | 1.74097i | −0.0617458 | + | 0.106947i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08340 | + | 4.99870i | 0.0663028 | + | 0.305916i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.965772 | 0.0588842 | 0.0294421 | − | 0.999566i | \(-0.490627\pi\) | ||||
0.0294421 | + | 0.999566i | \(0.490627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.28219 | 0.260124 | 0.130062 | − | 0.991506i | \(-0.458482\pi\) | ||||
0.130062 | + | 0.991506i | \(0.458482\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.96963 | − | 32.1573i | −0.421821 | − | 1.94625i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.667703 | + | 1.15650i | −0.0402640 | + | 0.0697393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.83619 | + | 8.37653i | 0.290579 | + | 0.503297i | 0.973947 | − | 0.226777i | \(-0.0728189\pi\) |
−0.683368 | + | 0.730074i | \(0.739486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.03749 | − | 10.6921i | 0.0621128 | − | 0.640120i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.34848 | + | 12.7279i | 0.438373 | + | 0.759285i | 0.997564 | − | 0.0697540i | \(-0.0222214\pi\) |
−0.559191 | + | 0.829039i | \(0.688888\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.90174 | − | 13.6862i | 0.469710 | − | 0.813561i | −0.529690 | − | 0.848191i | \(-0.677692\pi\) |
0.999400 | + | 0.0346299i | \(0.0110252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.7726 | − | 6.97832i | −1.28970 | − | 0.413360i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0473 | −0.593074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.2819 | 2.36952 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1396 | + | 12.8340i | −0.828880 | + | 0.752344i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.99866 | + | 5.19384i | −0.175184 | + | 0.303427i | −0.940225 | − | 0.340554i | \(-0.889385\pi\) |
0.765041 | + | 0.643981i | \(0.222719\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2256 | − | 17.7112i | −0.595356 | − | 1.03119i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.98991 | + | 11.5790i | −0.289544 | + | 0.671883i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.3987 | + | 30.1355i | 1.00619 | + | 1.74278i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.99666 | − | 15.5827i | 0.518559 | − | 0.898170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.67755 | − | 4.24564i | 0.268718 | − | 0.243906i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8770 | −0.622818 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7568 | 0.670994 | 0.335497 | − | 0.942041i | \(-0.391096\pi\) | ||||
0.335497 | + | 0.942041i | \(0.391096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9427 | + | 5.75079i | 1.02072 | + | 0.327151i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.1797 | − | 28.0240i | 0.917465 | − | 1.58910i | 0.114213 | − | 0.993456i | \(-0.463565\pi\) |
0.803252 | − | 0.595640i | \(-0.203101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6062 | − | 25.2987i | −0.825591 | − | 1.42997i | −0.901466 | − | 0.432849i | \(-0.857508\pi\) |
0.0758750 | − | 0.997117i | \(-0.475825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.5801 | − | 7.54122i | 0.934182 | − | 0.424900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7011 | + | 23.7310i | 0.769530 | + | 1.33286i | 0.937818 | + | 0.347127i | \(0.112843\pi\) |
−0.168288 | + | 0.985738i | \(0.553824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.82951 | − | 6.63291i | 0.214411 | − | 0.371371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.18264 | − | 10.0705i | −0.121823 | − | 0.562083i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.3619 | 2.63529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.63235 | 0.201487 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.62151 | − | 16.7093i | −0.200270 | − | 0.924029i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.82731 | + | 6.62910i | −0.211007 | + | 0.365474i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.08930 | + | 1.88673i | 0.0598735 | + | 0.103704i | 0.894408 | − | 0.447251i | \(-0.147597\pi\) |
−0.834535 | + | 0.550955i | \(0.814264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.3225 | − | 8.33374i | 1.00407 | − | 0.456686i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00299 | − | 3.46928i | −0.109435 | − | 0.189547i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.715700 | + | 1.23963i | −0.0389866 | + | 0.0675268i | −0.884860 | − | 0.465856i | \(-0.845746\pi\) |
0.845874 | + | 0.533383i | \(0.179080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.7911 | + | 7.94577i | 1.34647 | + | 0.431555i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.68874 | −0.470522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4508 | 0.888259 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.2634 | + | 12.9463i | −0.767914 | + | 0.697007i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1223 | − | 22.7285i | 0.704441 | − | 1.22013i | −0.262452 | − | 0.964945i | \(-0.584531\pi\) |
0.966893 | − | 0.255183i | \(-0.0821357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1673 | + | 29.7346i | 0.918944 | + | 1.59166i | 0.801022 | + | 0.598635i | \(0.204290\pi\) |
0.117923 | + | 0.993023i | \(0.462377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.0621 | − | 3.99334i | 1.81810 | − | 0.213149i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.28933 | − | 3.96523i | −0.121849 | − | 0.211048i | 0.798648 | − | 0.601798i | \(-0.205549\pi\) |
−0.920497 | + | 0.390750i | \(0.872216\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.14359 | + | 10.6410i | −0.326068 | + | 0.564766i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.9388 | + | 25.3590i | −1.47868 | + | 1.34214i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0591 | −0.689231 | −0.344616 | − | 0.938744i | \(-0.611991\pi\) | ||||
−0.344616 | + | 0.938744i | \(0.611991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.1599 | 1.06105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.43195 | − | 2.70251i | −0.442562 | − | 0.141845i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.28644 | − | 9.15639i | 0.276705 | − | 0.479267i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.70626 | − | 2.95533i | −0.0890660 | − | 0.154267i | 0.818051 | − | 0.575146i | \(-0.195055\pi\) |
−0.907117 | + | 0.420879i | \(0.861722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.01140 | − | 10.4232i | 0.0526513 | − | 0.542612i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.37151 | + | 2.37553i | 0.0712055 | + | 0.123332i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.42179 | − | 11.1229i | 0.332508 | − | 0.575921i | −0.650495 | − | 0.759511i | \(-0.725439\pi\) |
0.983003 | + | 0.183590i | \(0.0587719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.29542 | + | 19.8187i | 0.221815 | + | 1.02343i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.8328 | −1.07294 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1642 | −0.624833 | −0.312417 | − | 0.949945i | \(-0.601138\pi\) | ||||
−0.312417 | + | 0.949945i | \(0.601138\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.96361 | − | 13.6738i | −0.151830 | − | 0.700532i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.84072 | + | 15.3126i | −0.451740 | + | 0.782436i | −0.998494 | − | 0.0548568i | \(-0.982530\pi\) |
0.546755 | + | 0.837293i | \(0.315863\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.36625 | − | 12.7587i | −0.375419 | − | 0.650244i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.2601 | + | 10.9019i | 0.775713 | + | 0.554174i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.77658 | − | 6.54123i | −0.191480 | − | 0.331654i | 0.754261 | − | 0.656575i | \(-0.227995\pi\) |
−0.945741 | + | 0.324921i | \(0.894662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.9513 | − | 34.5567i | 1.00898 | − | 1.74761i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.7252 | + | 11.7708i | 1.85254 | + | 0.593756i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.4223 | −1.37977 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.97075 | 0.400040 | 0.200020 | − | 0.979792i | \(-0.435899\pi\) | ||||
0.200020 | + | 0.979792i | \(0.435899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.1004 | + | 20.9674i | −1.15647 | + | 1.04968i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.53771 | + | 6.12750i | −0.176665 | + | 0.305993i | −0.940736 | − | 0.339139i | \(-0.889864\pi\) |
0.764071 | + | 0.645132i | \(0.223198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8168 | + | 20.4674i | 0.588639 | + | 1.01955i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.15438 | + | 17.9596i | 0.305813 | + | 0.892418i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.14038 | − | 14.0995i | −0.403503 | − | 0.698889i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0499 | + | 27.7993i | −0.793619 | + | 1.37459i | 0.130094 | + | 0.991502i | \(0.458472\pi\) |
−0.923713 | + | 0.383086i | \(0.874861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8599 | + | 10.7648i | −0.585005 | + | 0.530988i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.9054 | −1.37313 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.51820 | 0.319966 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.8634 | + | 4.44335i | 0.678895 | + | 0.217592i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.63571 | − | 9.76133i | 0.275322 | − | 0.476872i | −0.694894 | − | 0.719112i | \(-0.744549\pi\) |
0.970216 | + | 0.242240i | \(0.0778821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.82872 | + | 8.36359i | 0.235337 | + | 0.407616i | 0.959371 | − | 0.282149i | \(-0.0910471\pi\) |
−0.724033 | + | 0.689765i | \(0.757714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.49186 | − | 4.63782i | −0.315645 | − | 0.225499i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.08263 | − | 3.60723i | −0.101023 | − | 0.174976i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.42081 | + | 12.8532i | −0.359118 | + | 0.622011i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.87565 | − | 27.1098i | −0.283679 | − | 1.30887i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.1842 | −1.93560 | −0.967802 | − | 0.251711i | \(-0.919007\pi\) | ||||
−0.967802 | + | 0.251711i | \(0.919007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1510 | 0.776168 | 0.388084 | − | 0.921624i | \(-0.373137\pi\) | ||||
0.388084 | + | 0.921624i | \(0.373137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.44275 | − | 11.2707i | −0.117121 | − | 0.540387i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4962 | − | 28.5723i | 0.789120 | − | 1.36680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.25383 | + | 16.0281i | 0.441661 | + | 0.764980i | 0.997813 | − | 0.0661011i | \(-0.0210560\pi\) |
−0.556152 | + | 0.831081i | \(0.687723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.372172 | − | 3.83552i | 0.0177225 | − | 0.182644i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.72586 | − | 2.98927i | −0.0819979 | − | 0.142025i | 0.822110 | − | 0.569329i | \(-0.192797\pi\) |
−0.904108 | + | 0.427304i | \(0.859463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.11457 | − | 5.39459i | 0.147645 | − | 0.255728i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.3812 | − | 6.53236i | −0.963998 | − | 0.308970i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.83790 | 0.464279 | 0.232140 | − | 0.972682i | \(-0.425427\pi\) | ||||
0.232140 | + | 0.972682i | \(0.425427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.47025 | −0.398848 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6053 | + | 11.4413i | −0.592247 | + | 0.537561i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.0364 | + | 34.7041i | −0.939323 | + | 1.62696i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0111990 | + | 0.0193973i | 0.000523869 | + | 0.000907367i | 0.866287 | − | 0.499546i | \(-0.166500\pi\) |
−0.865763 | + | 0.500454i | \(0.833167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.4954 | − | 31.5369i | −1.09667 | − | 1.47202i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.50986 | − | 13.0075i | −0.349769 | − | 0.605818i | 0.636439 | − | 0.771327i | \(-0.280407\pi\) |
−0.986208 | + | 0.165509i | \(0.947073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2691 | + | 28.1790i | −0.756091 | + | 1.30959i | 0.188738 | + | 0.982027i | \(0.439560\pi\) |
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.68738 | + | 8.79288i | −0.449241 | + | 0.407760i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.2983 | −0.476550 | −0.238275 | − | 0.971198i | \(-0.576582\pi\) | ||||
−0.238275 | + | 0.971198i | \(0.576582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.46612 | −0.252402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.356545 | + | 0.114276i | 0.0164287 | + | 0.00526556i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.58450 | − | 13.1367i | 0.348736 | − | 0.604028i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.72197 | − | 2.98253i | −0.0790093 | − | 0.136848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.60248 | + | 1.18370i | −0.119159 | + | 0.0541980i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.79020 | + | 6.56481i | 0.173178 | + | 0.299954i | 0.939529 | − | 0.342468i | \(-0.111263\pi\) |
−0.766351 | + | 0.642422i | \(0.777930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1421 | + | 38.3513i | −1.00959 | + | 1.74867i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.56736 | + | 25.6873i | 0.253323 | + | 1.16881i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.2560 | 1.05600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6214 | 0.934444 | 0.467222 | − | 0.884140i | \(-0.345255\pi\) | ||||
0.467222 | + | 0.884140i | \(0.345255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.12098 | − | 9.78605i | −0.0959142 | − | 0.442541i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.98229 | − | 6.89752i | 0.179718 | − | 0.311281i | −0.762066 | − | 0.647499i | \(-0.775815\pi\) |
0.941784 | + | 0.336219i | \(0.109148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.9446 | + | 20.6887i | 0.537959 | + | 0.931772i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.9776 | − | 6.35752i | 0.628246 | − | 0.285749i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.38287 | + | 14.5196i | 0.376023 | + | 0.651291i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5911 | + | 18.3444i | −0.474125 | + | 0.821208i | −0.999561 | − | 0.0296248i | \(-0.990569\pi\) |
0.525436 | + | 0.850833i | \(0.323902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.70055 | − | 0.865552i | −0.120652 | − | 0.0386700i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0876 | 0.851073 | 0.425536 | − | 0.904941i | \(-0.360085\pi\) | ||||
0.425536 | + | 0.904941i | \(0.360085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.69336 | −0.342350 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.1965 | + | 35.5773i | −1.74078 | + | 1.58004i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.3596 | − | 31.7998i | 0.813776 | − | 1.40950i | −0.0964283 | − | 0.995340i | \(-0.530742\pi\) |
0.910204 | − | 0.414161i | \(-0.135925\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.21330 | − | 12.4938i | −0.319097 | − | 0.552693i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.4266 | − | 26.0754i | −0.857703 | − | 1.15126i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4734 | − | 19.8726i | −0.505580 | − | 0.875690i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.22656 | + | 5.58857i | −0.141904 | + | 0.245785i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.67535 | + | 6.96663i | −0.336910 | + | 0.305801i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.5620 | 0.900839 | 0.450419 | − | 0.892817i | \(-0.351275\pi\) | ||||
0.450419 | + | 0.892817i | \(0.351275\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2754 | 0.711672 | 0.355836 | − | 0.934548i | \(-0.384196\pi\) | ||||
0.355836 | + | 0.934548i | \(0.384196\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.61273 | + | 0.837403i | 0.114029 | + | 0.0365472i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5505 | − | 23.4702i | 0.590270 | − | 1.02238i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.39812 | − | 4.15367i | −0.104266 | − | 0.180594i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.80905 | − | 28.9495i | 0.121903 | − | 1.25630i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.5197 | + | 19.9527i | 0.498973 | + | 0.864246i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.27471 | + | 10.8681i | −0.271279 | + | 0.469870i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.49017 | + | 16.1033i | 0.150612 | + | 0.694911i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.11686 | −0.134253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.19402 | −0.137322 | −0.0686609 | − | 0.997640i | \(-0.521873\pi\) | ||||
−0.0686609 | + | 0.997640i | \(0.521873\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.71431 | + | 40.2071i | 0.373967 | + | 1.72545i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.4112 | + | 18.0327i | −0.445966 | + | 0.772436i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.43936 | + | 12.8854i | 0.318084 | + | 0.550938i | 0.980088 | − | 0.198562i | \(-0.0636272\pi\) |
−0.662004 | + | 0.749500i | \(0.730294\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5871 | − | 8.99231i | −0.537205 | − | 0.383782i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.87608 | + | 17.1059i | 0.420735 | + | 0.728734i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.7087 | + | 32.4045i | −0.795576 | + | 1.37798i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.3445 | − | 7.48213i | −0.990920 | − | 0.317599i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.76686 | −0.244350 | −0.122175 | − | 0.992509i | \(-0.538987\pi\) | ||||
−0.122175 | + | 0.992509i | \(0.538987\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.2602 | −1.74512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.5534 | + | 21.3786i | −0.994426 | + | 0.902604i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.76738 | + | 8.25734i | −0.200921 | + | 0.348005i | −0.948825 | − | 0.315801i | \(-0.897727\pi\) |
0.747904 | + | 0.663806i | \(0.231060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.8527 | − | 27.4576i | −0.666927 | − | 1.15515i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.4213 | + | 4.98030i | 1.06759 | + | 0.209153i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.27200 | − | 7.39933i | −0.179092 | − | 0.310196i | 0.762478 | − | 0.647014i | \(-0.223983\pi\) |
−0.941570 | + | 0.336818i | \(0.890649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.1444 | + | 31.4270i | −0.759318 | + | 1.31518i | 0.183881 | + | 0.982949i | \(0.441134\pi\) |
−0.943199 | + | 0.332229i | \(0.892199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6235 | − | 9.64256i | 0.443803 | − | 0.402824i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.90153 | −0.121002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.11652 | −0.254634 | −0.127317 | − | 0.991862i | \(-0.540637\pi\) | ||||
−0.127317 | + | 0.991862i | \(0.540637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.5044 | − | 5.28982i | −0.685901 | − | 0.219837i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.44701 | − | 7.70245i | 0.184493 | − | 0.319551i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.15624 | + | 2.00266i | 0.0478864 | + | 0.0829417i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.9857 | − | 24.2796i | −1.40514 | − | 1.00384i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.92500 | − | 3.33419i | −0.0794532 | − | 0.137617i | 0.823561 | − | 0.567228i | \(-0.191984\pi\) |
−0.903014 | + | 0.429611i | \(0.858651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2039 | − | 19.4057i | 0.461647 | − | 0.799597i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.204079 | − | 0.941606i | −0.00839471 | − | 0.0387325i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6462 | 0.683579 | 0.341789 | − | 0.939777i | \(-0.388967\pi\) | ||||
0.341789 | + | 0.939777i | \(0.388967\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.9521 | 1.88385 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.90720 | − | 36.4832i | −0.323620 | − | 1.49316i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8791 | + | 30.9675i | −0.730520 | + | 1.26530i | 0.226141 | + | 0.974095i | \(0.427389\pi\) |
−0.956661 | + | 0.291203i | \(0.905944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.77202 | + | 11.7295i | 0.276236 | + | 0.478455i | 0.970446 | − | 0.241317i | \(-0.0775794\pi\) |
−0.694210 | + | 0.719773i | \(0.744246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.550239 | − | 5.67064i | 0.0224075 | − | 0.230926i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.39181 | + | 9.33888i | 0.219208 | + | 0.379679i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0131 | + | 24.2714i | −0.568775 | + | 0.985147i | 0.427913 | + | 0.903820i | \(0.359249\pi\) |
−0.996688 | + | 0.0813266i | \(0.974084\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.9849 | − | 4.80279i | −0.607219 | − | 0.194619i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.5527 | 0.710107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.6283 | −1.51979 | −0.759897 | − | 0.650043i | \(-0.774751\pi\) | ||||
−0.759897 | + | 0.650043i | \(0.774751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.44377 | + | 8.57177i | −0.380810 | + | 0.345647i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.57241 | − | 9.65169i | 0.224337 | − | 0.388562i | −0.731784 | − | 0.681537i | \(-0.761312\pi\) |
0.956120 | + | 0.292975i | \(0.0946451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.54119 | − | 16.5258i | −0.383493 | − | 0.664229i | 0.608066 | − | 0.793886i | \(-0.291946\pi\) |
−0.991559 | + | 0.129658i | \(0.958612\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.2089 | + | 3.18989i | −1.09185 | + | 0.128006i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.24980 | − | 7.36086i | −0.170265 | − | 0.294907i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.9727 | − | 19.0053i | 0.438908 | − | 0.760211i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.4745 | + | 17.6763i | −0.777736 | + | 0.705923i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.7813 | 2.02478 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.7049 | −1.18253 | −0.591267 | − | 0.806476i | \(-0.701372\pi\) | ||||
−0.591267 | + | 0.806476i | \(0.701372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.4785 | − | 8.80712i | −1.09217 | − | 0.350051i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.51984 | + | 14.7568i | −0.338099 | + | 0.585605i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.23898 | + | 7.34214i | 0.167955 | + | 0.290906i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9067 | + | 7.23493i | −0.629258 | + | 0.286209i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.60138 | − | 16.6301i | −0.379232 | − | 0.656848i | 0.611719 | − | 0.791075i | \(-0.290478\pi\) |
−0.990951 | + | 0.134227i | \(0.957145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.52181 | + | 6.09995i | −0.138887 | + | 0.240559i | −0.927075 | − | 0.374875i | \(-0.877686\pi\) |
0.788189 | + | 0.615434i | \(0.211019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.83797 | − | 22.3220i | −0.190495 | − | 0.878929i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8474 | 1.44862 | 0.724311 | − | 0.689473i | \(-0.242158\pi\) | ||||
0.724311 | + | 0.689473i | \(0.242158\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5252 | −0.923446 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.78123 | + | 17.4463i | 0.148198 | + | 0.683774i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.6354 | − | 35.7416i | 0.807526 | − | 1.39868i | −0.107046 | − | 0.994254i | \(-0.534139\pi\) |
0.914572 | − | 0.404422i | \(-0.132527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.4839 | − | 40.6754i | −0.917593 | − | 1.58932i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.6874 | − | 6.22552i | 0.533995 | − | 0.242881i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.79606 | + | 13.5032i | 0.303691 | + | 0.526009i | 0.976969 | − | 0.213381i | \(-0.0684475\pi\) |
−0.673278 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.273228 | + | 0.473246i | −0.0106274 | + | 0.0184071i | −0.871290 | − | 0.490768i | \(-0.836716\pi\) |
0.860663 | + | 0.509175i | \(0.170050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 82.3929 | + | 26.4076i | 3.19987 | + | 1.02559i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 37.9942 | 1.47335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.6413 | 0.644353 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.5235 | + | 10.4595i | −0.445525 | + | 0.404387i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.25601 | + | 10.8357i | −0.241510 | + | 0.418308i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.71994 | + | 13.3713i | 0.297582 | + | 0.515427i | 0.975582 | − | 0.219635i | \(-0.0704866\pi\) |
−0.678000 | + | 0.735061i | \(0.737153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.13174 | + | 2.62619i | −0.0435607 | + | 0.101082i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7394 | − | 35.9216i | −0.797079 | − | 1.38058i | −0.921511 | − | 0.388353i | \(-0.873044\pi\) |
0.124432 | − | 0.992228i | \(-0.460289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8663 | − | 27.4812i | 0.608893 | − | 1.05463i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6575 | + | 12.3965i | −0.523358 | + | 0.475033i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.83506 | −0.299800 | −0.149900 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149900 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.5064 | 0.745303 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.1693 | + | 5.82344i | 0.693204 | + | 0.222178i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.14500 | − | 5.44730i | 0.119815 | − | 0.207526i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8366 | − | 20.5016i | −0.450286 | − | 0.779918i | 0.548118 | − | 0.836401i | \(-0.315345\pi\) |
−0.998404 | + | 0.0564831i | \(0.982011\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.02357 | − | 20.8545i | 0.0768691 | − | 0.792196i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.86497 | − | 15.3546i | −0.336267 | − | 0.582432i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2098 | − | 22.8800i | 0.500356 | − | 0.866642i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0009 | − | 46.1435i | −0.378270 | − | 1.74531i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.14909 | −0.270017 | −0.135009 | − | 0.990844i | \(-0.543106\pi\) | ||||
−0.135009 | + | 0.990844i | \(0.543106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.9871 | 1.58357 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.05815 | + | 9.49612i | 0.0775143 | + | 0.357645i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.24876 | + | 9.09111i | −0.197400 | + | 0.341906i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3826 | + | 33.5716i | 0.727928 | + | 1.26081i | 0.957757 | + | 0.287577i | \(0.0928498\pi\) |
−0.229830 | + | 0.973231i | \(0.573817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.7336 | − | 22.6707i | −1.19010 | − | 0.850217i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.43931 | − | 16.3494i | −0.353505 | − | 0.612289i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.8914 | + | 29.2568i | −0.631704 | + | 1.09414i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.2088 | − | 6.15659i | −0.717365 | − | 0.229922i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.3429 | −1.42995 | −0.714975 | − | 0.699151i | \(-0.753562\pi\) | ||||
−0.714975 | + | 0.699151i | \(0.753562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.3108 | −1.16607 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.2286 | − | 22.8991i | 0.938263 | − | 0.851627i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.868556 | − | 1.50438i | 0.0322574 | − | 0.0558714i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.9734 | − | 38.0591i | −0.814950 | − | 1.41154i | −0.909364 | − | 0.416002i | \(-0.863431\pi\) |
0.0944136 | − | 0.995533i | \(-0.469902\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.72564 | + | 25.8711i | −0.286135 | + | 0.958189i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.6568 | + | 40.9748i | 0.874979 | + | 1.51551i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7222 | + | 42.8202i | −0.913137 | + | 1.58160i | −0.103531 | + | 0.994626i | \(0.533014\pi\) |
−0.809606 | + | 0.586973i | \(0.800319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.47510 | + | 3.15422i | −0.128181 | + | 0.116345i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.60814 | −0.169743 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.25073 | −0.340294 | −0.170147 | − | 0.985419i | \(-0.554424\pi\) | ||||
−0.170147 | + | 0.985419i | \(0.554424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 68.1242 | + | 21.8344i | 2.50261 | + | 0.802107i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6473 | + | 35.7621i | −0.757475 | + | 1.31198i | 0.186660 | + | 0.982425i | \(0.440234\pi\) |
−0.944135 | + | 0.329560i | \(0.893100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0328 | + | 22.5734i | 0.477483 | + | 0.827025i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.54299 | + | 5.38875i | 0.275984 | + | 0.197164i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.56178 | + | 14.8294i | 0.312840 | + | 0.541856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2101 | − | 17.6845i | 0.372573 | − | 0.645315i | −0.617388 | − | 0.786659i | \(-0.711809\pi\) |
0.989961 | + | 0.141344i | \(0.0451423\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.57770 | + | 39.5768i | 0.312589 | + | 1.44226i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.7324 | 0.754529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.74944 | 0.281658 | 0.140829 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140829 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.69348 | + | 21.6554i | 0.170363 | + | 0.786039i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3416 | − | 23.1084i | 0.483634 | − | 0.837679i | −0.516189 | − | 0.856475i | \(-0.672650\pi\) |
0.999823 | + | 0.0187955i | \(0.00598315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2059 | + | 24.6054i | 0.514290 | + | 0.890776i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.62570 | + | 47.6714i | −0.167243 | + | 1.72356i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.9947 | + | 55.4165i | 1.15526 | + | 2.00097i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.5226 | + | 42.4744i | −0.884307 | + | 1.53166i | −0.0378010 | + | 0.999285i | \(0.512035\pi\) |
−0.846506 | + | 0.532379i | \(0.821298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.23596 | + | 1.99868i | 0.224583 | + | 0.0719807i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1406 | 0.436665 | 0.218333 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218333 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.97066 | −0.0707881 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.7682 | + | 22.4812i | −0.888553 | + | 0.806508i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9221 | − | 18.9177i | 0.391326 | − | 0.677796i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.06706 | + | 12.2405i | 0.252879 | + | 0.438000i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.49093 | − | 15.0621i | 0.231967 | − | 0.538276i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.227993 | − | 0.394895i | −0.00813742 | − | 0.0140944i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2553 | + | 42.0114i | −0.864608 | + | 1.49754i | 0.00282812 | + | 0.999996i | \(0.499100\pi\) |
−0.867436 | + | 0.497549i | \(0.834234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.5837 | − | 24.1291i | 0.946405 | − | 0.859017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.2616 | −1.53821 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.0331 | 1.20855 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.31579 | + | 1.06274i | 0.117599 | + | 0.0376915i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.54989 | + | 4.41654i | −0.0903218 | + | 0.156442i | −0.907647 | − | 0.419735i | \(-0.862123\pi\) |
0.817325 | + | 0.576177i | \(0.195456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0640 | − | 17.4313i | −0.356037 | − | 0.616675i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.06408 | − | 3.66784i | 0.284930 | − | 0.129597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.08107 | − | 10.5327i | −0.214596 | − | 0.371692i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0051 | − | 27.7217i | 0.564107 | − | 0.977063i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.354321 | − | 1.63481i | −0.0124727 | − | 0.0575480i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.1416 | −1.34099 | −0.670494 | − | 0.741915i | \(-0.733918\pi\) | ||||
−0.670494 | + | 0.741915i | \(0.733918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.88343 | 0.101251 | 0.0506255 | − | 0.998718i | \(-0.483878\pi\) | ||||
0.0506255 | + | 0.998718i | \(0.483878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.57104 | − | 7.24867i | −0.0550989 | − | 0.254222i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.09745 | + | 10.5611i | −0.213584 | + | 0.369939i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.5600 | + | 33.8789i | 0.684317 | + | 1.18527i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −51.8773 | + | 23.5957i | −1.81274 | + | 0.824500i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.84327 | − | 10.1208i | −0.203931 | − | 0.353220i | 0.745860 | − | 0.666102i | \(-0.232039\pi\) |
−0.949792 | + | 0.312883i | \(0.898705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.91203 | + | 10.2399i | −0.206080 | + | 0.356942i | −0.950476 | − | 0.310797i | \(-0.899404\pi\) |
0.744396 | + | 0.667738i | \(0.232738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.20262 | + | 0.705961i | 0.0766855 | + | 0.0245784i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5265 | 0.957192 | 0.478596 | − | 0.878035i | \(-0.341146\pi\) | ||||
0.478596 | + | 0.878035i | \(0.341146\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.7398 | −0.963443 | −0.481721 | − | 0.876324i | \(-0.659988\pi\) | ||||
−0.481721 | + | 0.876324i | \(0.659988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.4051 | − | 11.2596i | 0.430327 | − | 0.390592i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.86090 | − | 8.41932i | 0.168420 | − | 0.291712i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.72687 | + | 2.99102i | 0.0597608 | + | 0.103509i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.4797 | + | 2.16650i | −0.638752 | + | 0.0748853i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.7349 | − | 22.0574i | −0.439656 | − | 0.761507i | 0.558007 | − | 0.829837i | \(-0.311566\pi\) |
−0.997663 | + | 0.0683295i | \(0.978233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.51853 | − | 16.4866i | 0.328225 | − | 0.568503i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.8492 | − | 17.1087i | 0.649201 | − | 0.589256i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.4682 | 2.21777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.7141 | 0.505583 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.0663 | − | 8.35448i | −0.894594 | − | 0.286725i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.6872 | − | 30.6351i | 0.606308 | − | 1.05016i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.2819 | + | 26.4690i | 0.523241 | + | 0.906280i | 0.999634 | + | 0.0270477i | \(0.00861061\pi\) |
−0.476393 | + | 0.879232i | \(0.658056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.82463 | + | 39.4158i | −0.130800 | + | 1.34799i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.69252 | + | 13.3238i | 0.262772 | + | 0.455134i | 0.966977 | − | 0.254862i | \(-0.0820301\pi\) |
−0.704206 | + | 0.709996i | \(0.748697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.19471 | + | 15.9257i | −0.313720 | + | 0.543378i | −0.979164 | − | 0.203069i | \(-0.934909\pi\) |
0.665445 | + | 0.746447i | \(0.268242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.68615 | + | 17.0076i | 0.125624 | + | 0.579617i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.5698 | −1.21081 | −0.605404 | − | 0.795918i | \(-0.706989\pi\) | ||||
−0.605404 | + | 0.795918i | \(0.706989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.6240 | 0.429227 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7786 | − | 68.1871i | −0.501907 | − | 2.31576i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.7721 | + | 27.3181i | −0.535033 | + | 0.926704i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.26715 | + | 10.8550i | 0.212354 | + | 0.367808i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.9123 | + | 19.2263i | 0.910844 | + | 0.650712i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.8495 | − | 29.1842i | −0.569616 | − | 0.986605i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1127 | − | 19.2477i | 0.375249 | − | 0.649950i | −0.615115 | − | 0.788437i | \(-0.710891\pi\) |
0.990364 | + | 0.138487i | \(0.0442239\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.89201 | + | 3.17048i | 0.333649 | + | 0.106937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.5586 | 1.29907 | 0.649536 | − | 0.760331i | \(-0.274963\pi\) | ||||
0.649536 | + | 0.760331i | \(0.274963\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.4984 | −0.353298 | −0.176649 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176649 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.2291 | + | 23.8072i | −0.881681 | + | 0.800270i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0186 | − | 39.8693i | 0.772888 | − | 1.33868i | −0.163087 | − | 0.986612i | \(-0.552145\pi\) |
0.935974 | − | 0.352069i | \(-0.114522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6252 | + | 20.1355i | 0.389898 | + | 0.675322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.4311 | + | 4.19857i | 0.717968 | + | 0.140657i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.32111 | − | 14.4126i | −0.278455 | − | 0.482299i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0336 | − | 17.3787i | 0.335386 | − | 0.580906i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.6285 | − | 40.5077i | 1.49010 | − | 1.35251i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3024 | 0.376956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.21283 | −0.240294 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.6782 | − | 9.51213i | −0.987630 | − | 0.316544i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.0521 | − | 43.3914i | 0.832759 | − | 1.44238i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.68354 | + | 15.0403i | 0.288332 | + | 0.499406i | 0.973412 | − | 0.229062i | \(-0.0735659\pi\) |
−0.685080 | + | 0.728468i | \(0.740233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.90291 | − | 6.36029i | −0.295291 | − | 0.210957i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.29095 | − | 2.23599i | −0.0427711 | − | 0.0740817i | 0.843847 | − | 0.536583i | \(-0.180285\pi\) |
−0.886618 | + | 0.462502i | \(0.846952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.74899 | − | 6.49344i | 0.124073 | − | 0.214902i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.99056 | + | 18.4121i | 0.131924 | + | 0.608685i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −64.0871 | −2.11634 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.8909 | −1.15095 | −0.575473 | − | 0.817821i | \(-0.695182\pi\) | ||||
−0.575473 | + | 0.817821i | \(0.695182\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.31330 | − | 19.9012i | −0.142128 | − | 0.655768i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.2226 | − | 33.2946i | 0.632721 | − | 1.09591i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.84629 | − | 3.19786i | −0.0607055 | − | 0.105145i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.15185 | − | 32.4823i | 0.103520 | − | 1.06686i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.38201 | + | 7.58986i | 0.143769 | + | 0.249015i | 0.928913 | − | 0.370298i | \(-0.120744\pi\) |
−0.785144 | + | 0.619313i | \(0.787411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.01910 | − | 6.96128i | 0.131721 | − | 0.228147i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −53.3736 | − | 17.1067i | −1.74737 | − | 0.560049i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.7393 | 1.26691 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.6212 | 1.29437 | 0.647184 | − | 0.762334i | \(-0.275946\pi\) | ||||
0.647184 | + | 0.762334i | \(0.275946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.4656 | + | 34.0062i | −1.22264 | + | 1.10975i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5675 | + | 23.4995i | −0.442287 | + | 0.766063i | −0.997859 | − | 0.0654053i | \(-0.979166\pi\) |
0.555572 | + | 0.831468i | \(0.312499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.20195 | − | 15.9382i | −0.299657 | − | 0.519020i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.8483 | − | 25.2992i | −0.613135 | − | 0.822983i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.06166 | + | 1.83886i | 0.0344995 | + | 0.0597548i | 0.882760 | − | 0.469825i | \(-0.155683\pi\) |
−0.848260 | + | 0.529580i | \(0.822350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.5407 | + | 28.6494i | −0.536934 | + | 0.929998i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.1440 | − | 31.8989i | 1.13962 | − | 1.03439i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.523434 | −0.0169557 | −0.00847784 | − | 0.999964i | \(-0.502699\pi\) | ||||
−0.00847784 | + | 0.999964i | \(0.502699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.4729 | −0.565410 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.6328 | − | 4.04893i | −0.408361 | − | 0.130883i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3082 | − | 23.0504i | 0.429743 | − | 0.744337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.08902 | + | 15.7426i | 0.293194 | + | 0.507827i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2461 | + | 7.38934i | −0.523525 | + | 0.238118i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.5538 | + | 18.2796i | 0.339737 | + | 0.588442i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.74196 | − | 4.74922i | 0.0881756 | − | 0.152725i | −0.818564 | − | 0.574415i | \(-0.805230\pi\) |
0.906740 | + | 0.421690i | \(0.138563\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.3761 | − | 80.1719i | −0.558200 | − | 2.57549i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.813501 | 0.0261065 | 0.0130532 | − | 0.999915i | \(-0.495845\pi\) | ||||
0.0130532 | + | 0.999915i | \(0.495845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.1923 | −0.775570 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.33263 | − | 6.14866i | −0.0426784 | − | 0.196915i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.85335 | − | 17.0665i | 0.315237 | − | 0.546006i | −0.664251 | − | 0.747509i | \(-0.731249\pi\) |
0.979488 | + | 0.201504i | \(0.0645828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.58273 | − | 6.20547i | −0.114505 | − | 0.198328i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.9561 | + | 12.2606i | −0.860641 | + | 0.391451i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9588 | − | 48.4261i | −0.891747 | − | 1.54455i | −0.837779 | − | 0.546009i | \(-0.816146\pi\) |
−0.0539681 | − | 0.998543i | \(-0.517187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.586692 | + | 1.01618i | −0.0186936 | + | 0.0323782i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.6256 | + | 4.04660i | 0.401876 | + | 0.128805i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.9588 | 1.04803 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.4053 | 0.711727 | 0.355863 | − | 0.934538i | \(-0.384187\pi\) | ||||
0.355863 | + | 0.934538i | \(0.384187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.79412 | − | 2.53612i | 0.0886686 | − | 0.0804813i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.7318 | + | 39.3726i | −0.720646 | + | 1.24819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.6132 | + | 28.7749i | 0.526146 | + | 0.911311i | 0.999536 | + | 0.0304585i | \(0.00969675\pi\) |
−0.473390 | + | 0.880853i | \(0.656970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.8291 | − | 27.9579i | −0.659003 | − | 0.884550i |
(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 | 1152.2.i.i.769.4 | yes | 12 | |
3.2 | odd | 2 | 3456.2.i.k.2305.4 | 12 | |||
4.3 | odd | 2 | 1152.2.i.k.769.3 | yes | 12 | ||
8.3 | odd | 2 | 1152.2.i.j.769.4 | yes | 12 | ||
8.5 | even | 2 | 1152.2.i.l.769.3 | yes | 12 | ||
9.2 | odd | 6 | 3456.2.i.k.1153.4 | 12 | |||
9.7 | even | 3 | inner | 1152.2.i.i.385.4 | ✓ | 12 | |
12.11 | even | 2 | 3456.2.i.l.2305.4 | 12 | |||
24.5 | odd | 2 | 3456.2.i.i.2305.3 | 12 | |||
24.11 | even | 2 | 3456.2.i.j.2305.3 | 12 | |||
36.7 | odd | 6 | 1152.2.i.k.385.3 | yes | 12 | ||
36.11 | even | 6 | 3456.2.i.l.1153.4 | 12 | |||
72.11 | even | 6 | 3456.2.i.j.1153.3 | 12 | |||
72.29 | odd | 6 | 3456.2.i.i.1153.3 | 12 | |||
72.43 | odd | 6 | 1152.2.i.j.385.4 | yes | 12 | ||
72.61 | even | 6 | 1152.2.i.l.385.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.i.385.4 | ✓ | 12 | 9.7 | even | 3 | inner | |
1152.2.i.i.769.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1152.2.i.j.385.4 | yes | 12 | 72.43 | odd | 6 | ||
1152.2.i.j.769.4 | yes | 12 | 8.3 | odd | 2 | ||
1152.2.i.k.385.3 | yes | 12 | 36.7 | odd | 6 | ||
1152.2.i.k.769.3 | yes | 12 | 4.3 | odd | 2 | ||
1152.2.i.l.385.3 | yes | 12 | 72.61 | even | 6 | ||
1152.2.i.l.769.3 | yes | 12 | 8.5 | even | 2 | ||
3456.2.i.i.1153.3 | 12 | 72.29 | odd | 6 | |||
3456.2.i.i.2305.3 | 12 | 24.5 | odd | 2 | |||
3456.2.i.j.1153.3 | 12 | 72.11 | even | 6 | |||
3456.2.i.j.2305.3 | 12 | 24.11 | even | 2 | |||
3456.2.i.k.1153.4 | 12 | 9.2 | odd | 6 | |||
3456.2.i.k.2305.4 | 12 | 3.2 | odd | 2 | |||
3456.2.i.l.1153.4 | 12 | 36.11 | even | 6 | |||
3456.2.i.l.2305.4 | 12 | 12.11 | even | 2 |