Properties

Label 460.2.m.a.441.2
Level $460$
Weight $2$
Character 460.441
Analytic conductor $3.673$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 441.2
Character \(\chi\) \(=\) 460.441
Dual form 460.2.m.a.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0447663 - 0.0131446i) q^{3} +(0.841254 + 0.540641i) q^{5} +(0.423834 + 2.94783i) q^{7} +(-2.52193 + 1.62075i) q^{9} +O(q^{10})\) \(q+(0.0447663 - 0.0131446i) q^{3} +(0.841254 + 0.540641i) q^{5} +(0.423834 + 2.94783i) q^{7} +(-2.52193 + 1.62075i) q^{9} +(0.116050 - 0.254114i) q^{11} +(-0.287174 + 1.99734i) q^{13} +(0.0447663 + 0.0131446i) q^{15} +(1.46880 + 1.69508i) q^{17} +(-2.64237 + 3.04946i) q^{19} +(0.0577214 + 0.126392i) q^{21} +(2.21614 - 4.25308i) q^{23} +(0.415415 + 0.909632i) q^{25} +(-0.183253 + 0.211486i) q^{27} +(4.42317 + 5.10461i) q^{29} +(-3.52347 - 1.03458i) q^{31} +(0.00185491 - 0.0129012i) q^{33} +(-1.23716 + 2.70901i) q^{35} +(5.26609 - 3.38431i) q^{37} +(0.0133984 + 0.0931882i) q^{39} +(7.90965 + 5.08323i) q^{41} +(1.04239 - 0.306072i) q^{43} -2.99782 q^{45} -4.44460 q^{47} +(-1.79360 + 0.526649i) q^{49} +(0.0880338 + 0.0565759i) q^{51} +(-0.0276399 - 0.192240i) q^{53} +(0.235012 - 0.151033i) q^{55} +(-0.0782053 + 0.171246i) q^{57} +(-1.27607 + 8.87523i) q^{59} +(-2.28267 - 0.670253i) q^{61} +(-5.84656 - 6.74729i) q^{63} +(-1.32143 + 1.52501i) q^{65} +(-4.17476 - 9.14146i) q^{67} +(0.0433035 - 0.219525i) q^{69} +(-5.39907 - 11.8223i) q^{71} +(8.19579 - 9.45844i) q^{73} +(0.0305533 + 0.0352604i) q^{75} +(0.798272 + 0.234394i) q^{77} +(-0.917054 + 6.37825i) q^{79} +(3.73060 - 8.16887i) q^{81} +(7.09216 - 4.55785i) q^{83} +(0.319200 + 2.22009i) q^{85} +(0.265107 + 0.170374i) q^{87} +(0.984393 - 0.289044i) q^{89} -6.00952 q^{91} -0.171332 q^{93} +(-3.87156 + 1.13679i) q^{95} +(-10.8010 - 6.94136i) q^{97} +(0.119185 + 0.828946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0447663 0.0131446i 0.0258458 0.00758902i −0.268784 0.963200i \(-0.586622\pi\)
0.294630 + 0.955611i \(0.404804\pi\)
\(4\) 0 0
\(5\) 0.841254 + 0.540641i 0.376220 + 0.241782i
\(6\) 0 0
\(7\) 0.423834 + 2.94783i 0.160194 + 1.11417i 0.898266 + 0.439452i \(0.144827\pi\)
−0.738072 + 0.674722i \(0.764264\pi\)
\(8\) 0 0
\(9\) −2.52193 + 1.62075i −0.840643 + 0.540249i
\(10\) 0 0
\(11\) 0.116050 0.254114i 0.0349904 0.0766184i −0.891330 0.453356i \(-0.850227\pi\)
0.926320 + 0.376737i \(0.122954\pi\)
\(12\) 0 0
\(13\) −0.287174 + 1.99734i −0.0796477 + 0.553962i 0.910454 + 0.413610i \(0.135732\pi\)
−0.990102 + 0.140352i \(0.955177\pi\)
\(14\) 0 0
\(15\) 0.0447663 + 0.0131446i 0.0115586 + 0.00339391i
\(16\) 0 0
\(17\) 1.46880 + 1.69508i 0.356236 + 0.411118i 0.905375 0.424613i \(-0.139590\pi\)
−0.549139 + 0.835731i \(0.685044\pi\)
\(18\) 0 0
\(19\) −2.64237 + 3.04946i −0.606201 + 0.699593i −0.973026 0.230697i \(-0.925899\pi\)
0.366825 + 0.930290i \(0.380445\pi\)
\(20\) 0 0
\(21\) 0.0577214 + 0.126392i 0.0125958 + 0.0275811i
\(22\) 0 0
\(23\) 2.21614 4.25308i 0.462097 0.886829i
\(24\) 0 0
\(25\) 0.415415 + 0.909632i 0.0830830 + 0.181926i
\(26\) 0 0
\(27\) −0.183253 + 0.211486i −0.0352671 + 0.0407005i
\(28\) 0 0
\(29\) 4.42317 + 5.10461i 0.821362 + 0.947903i 0.999347 0.0361307i \(-0.0115032\pi\)
−0.177985 + 0.984033i \(0.556958\pi\)
\(30\) 0 0
\(31\) −3.52347 1.03458i −0.632833 0.185817i −0.0504442 0.998727i \(-0.516064\pi\)
−0.582389 + 0.812910i \(0.697882\pi\)
\(32\) 0 0
\(33\) 0.00185491 0.0129012i 0.000322899 0.00224581i
\(34\) 0 0
\(35\) −1.23716 + 2.70901i −0.209119 + 0.457907i
\(36\) 0 0
\(37\) 5.26609 3.38431i 0.865739 0.556377i −0.0307073 0.999528i \(-0.509776\pi\)
0.896447 + 0.443151i \(0.146140\pi\)
\(38\) 0 0
\(39\) 0.0133984 + 0.0931882i 0.00214547 + 0.0149221i
\(40\) 0 0
\(41\) 7.90965 + 5.08323i 1.23528 + 0.793866i 0.984705 0.174231i \(-0.0557438\pi\)
0.250575 + 0.968097i \(0.419380\pi\)
\(42\) 0 0
\(43\) 1.04239 0.306072i 0.158962 0.0466756i −0.201283 0.979533i \(-0.564511\pi\)
0.360245 + 0.932858i \(0.382693\pi\)
\(44\) 0 0
\(45\) −2.99782 −0.446889
\(46\) 0 0
\(47\) −4.44460 −0.648312 −0.324156 0.946004i \(-0.605080\pi\)
−0.324156 + 0.946004i \(0.605080\pi\)
\(48\) 0 0
\(49\) −1.79360 + 0.526649i −0.256229 + 0.0752356i
\(50\) 0 0
\(51\) 0.0880338 + 0.0565759i 0.0123272 + 0.00792221i
\(52\) 0 0
\(53\) −0.0276399 0.192240i −0.00379663 0.0264062i 0.987835 0.155505i \(-0.0497006\pi\)
−0.991632 + 0.129099i \(0.958791\pi\)
\(54\) 0 0
\(55\) 0.235012 0.151033i 0.0316890 0.0203653i
\(56\) 0 0
\(57\) −0.0782053 + 0.171246i −0.0103585 + 0.0226821i
\(58\) 0 0
\(59\) −1.27607 + 8.87523i −0.166130 + 1.15546i 0.720662 + 0.693287i \(0.243838\pi\)
−0.886792 + 0.462170i \(0.847071\pi\)
\(60\) 0 0
\(61\) −2.28267 0.670253i −0.292266 0.0858171i 0.132313 0.991208i \(-0.457760\pi\)
−0.424579 + 0.905391i \(0.639578\pi\)
\(62\) 0 0
\(63\) −5.84656 6.74729i −0.736597 0.850078i
\(64\) 0 0
\(65\) −1.32143 + 1.52501i −0.163903 + 0.189154i
\(66\) 0 0
\(67\) −4.17476 9.14146i −0.510029 1.11681i −0.973078 0.230474i \(-0.925972\pi\)
0.463050 0.886332i \(-0.346755\pi\)
\(68\) 0 0
\(69\) 0.0433035 0.219525i 0.00521313 0.0264277i
\(70\) 0 0
\(71\) −5.39907 11.8223i −0.640752 1.40305i −0.899420 0.437085i \(-0.856011\pi\)
0.258668 0.965966i \(-0.416716\pi\)
\(72\) 0 0
\(73\) 8.19579 9.45844i 0.959244 1.10703i −0.0349459 0.999389i \(-0.511126\pi\)
0.994190 0.107638i \(-0.0343287\pi\)
\(74\) 0 0
\(75\) 0.0305533 + 0.0352604i 0.00352799 + 0.00407152i
\(76\) 0 0
\(77\) 0.798272 + 0.234394i 0.0909715 + 0.0267116i
\(78\) 0 0
\(79\) −0.917054 + 6.37825i −0.103177 + 0.717610i 0.870911 + 0.491440i \(0.163529\pi\)
−0.974088 + 0.226169i \(0.927380\pi\)
\(80\) 0 0
\(81\) 3.73060 8.16887i 0.414511 0.907652i
\(82\) 0 0
\(83\) 7.09216 4.55785i 0.778465 0.500289i −0.0900587 0.995936i \(-0.528705\pi\)
0.868524 + 0.495647i \(0.165069\pi\)
\(84\) 0 0
\(85\) 0.319200 + 2.22009i 0.0346221 + 0.240802i
\(86\) 0 0
\(87\) 0.265107 + 0.170374i 0.0284225 + 0.0182660i
\(88\) 0 0
\(89\) 0.984393 0.289044i 0.104345 0.0306386i −0.229143 0.973393i \(-0.573592\pi\)
0.333488 + 0.942754i \(0.391774\pi\)
\(90\) 0 0
\(91\) −6.00952 −0.629969
\(92\) 0 0
\(93\) −0.171332 −0.0177663
\(94\) 0 0
\(95\) −3.87156 + 1.13679i −0.397214 + 0.116633i
\(96\) 0 0
\(97\) −10.8010 6.94136i −1.09667 0.704788i −0.138322 0.990387i \(-0.544171\pi\)
−0.958349 + 0.285599i \(0.907807\pi\)
\(98\) 0 0
\(99\) 0.119185 + 0.828946i 0.0119785 + 0.0833123i
\(100\) 0 0
\(101\) 2.85238 1.83311i 0.283823 0.182402i −0.390982 0.920398i \(-0.627864\pi\)
0.674804 + 0.737997i \(0.264228\pi\)
\(102\) 0 0
\(103\) 5.77460 12.6446i 0.568988 1.24591i −0.378347 0.925664i \(-0.623507\pi\)
0.947335 0.320246i \(-0.103765\pi\)
\(104\) 0 0
\(105\) −0.0197745 + 0.137534i −0.00192979 + 0.0134220i
\(106\) 0 0
\(107\) 4.58015 + 1.34485i 0.442780 + 0.130012i 0.495520 0.868596i \(-0.334977\pi\)
−0.0527406 + 0.998608i \(0.516796\pi\)
\(108\) 0 0
\(109\) −2.32042 2.67790i −0.222256 0.256497i 0.633661 0.773611i \(-0.281552\pi\)
−0.855916 + 0.517115i \(0.827006\pi\)
\(110\) 0 0
\(111\) 0.191258 0.220724i 0.0181534 0.0209501i
\(112\) 0 0
\(113\) 1.30443 + 2.85631i 0.122711 + 0.268699i 0.961011 0.276510i \(-0.0891778\pi\)
−0.838301 + 0.545208i \(0.816451\pi\)
\(114\) 0 0
\(115\) 4.16373 2.37978i 0.388270 0.221916i
\(116\) 0 0
\(117\) −2.51294 5.50258i −0.232322 0.508714i
\(118\) 0 0
\(119\) −4.37429 + 5.04819i −0.400990 + 0.462767i
\(120\) 0 0
\(121\) 7.15236 + 8.25427i 0.650215 + 0.750388i
\(122\) 0 0
\(123\) 0.420903 + 0.123588i 0.0379515 + 0.0111436i
\(124\) 0 0
\(125\) −0.142315 + 0.989821i −0.0127290 + 0.0885323i
\(126\) 0 0
\(127\) −0.437510 + 0.958013i −0.0388227 + 0.0850099i −0.928050 0.372456i \(-0.878516\pi\)
0.889227 + 0.457466i \(0.151243\pi\)
\(128\) 0 0
\(129\) 0.0426406 0.0274034i 0.00375429 0.00241274i
\(130\) 0 0
\(131\) −1.78544 12.4180i −0.155995 1.08497i −0.905921 0.423447i \(-0.860820\pi\)
0.749926 0.661522i \(-0.230089\pi\)
\(132\) 0 0
\(133\) −10.1092 6.49679i −0.876579 0.563343i
\(134\) 0 0
\(135\) −0.268500 + 0.0788388i −0.0231088 + 0.00678537i
\(136\) 0 0
\(137\) 8.45078 0.721999 0.360999 0.932566i \(-0.382436\pi\)
0.360999 + 0.932566i \(0.382436\pi\)
\(138\) 0 0
\(139\) −13.6424 −1.15713 −0.578566 0.815636i \(-0.696387\pi\)
−0.578566 + 0.815636i \(0.696387\pi\)
\(140\) 0 0
\(141\) −0.198968 + 0.0584224i −0.0167562 + 0.00492005i
\(142\) 0 0
\(143\) 0.474226 + 0.304766i 0.0396568 + 0.0254858i
\(144\) 0 0
\(145\) 0.961247 + 6.68562i 0.0798272 + 0.555210i
\(146\) 0 0
\(147\) −0.0733704 + 0.0471523i −0.00605149 + 0.00388905i
\(148\) 0 0
\(149\) −7.61559 + 16.6758i −0.623893 + 1.36614i 0.288761 + 0.957401i \(0.406757\pi\)
−0.912654 + 0.408734i \(0.865970\pi\)
\(150\) 0 0
\(151\) 1.91145 13.2944i 0.155551 1.08188i −0.751157 0.660124i \(-0.770504\pi\)
0.906708 0.421759i \(-0.138587\pi\)
\(152\) 0 0
\(153\) −6.45150 1.89433i −0.521573 0.153148i
\(154\) 0 0
\(155\) −2.40479 2.77528i −0.193157 0.222916i
\(156\) 0 0
\(157\) −1.36233 + 1.57221i −0.108726 + 0.125476i −0.807504 0.589862i \(-0.799182\pi\)
0.698778 + 0.715338i \(0.253727\pi\)
\(158\) 0 0
\(159\) −0.00376425 0.00824255i −0.000298524 0.000653677i
\(160\) 0 0
\(161\) 13.4766 + 4.73020i 1.06211 + 0.372792i
\(162\) 0 0
\(163\) −4.10288 8.98406i −0.321363 0.703686i 0.678149 0.734924i \(-0.262782\pi\)
−0.999512 + 0.0312380i \(0.990055\pi\)
\(164\) 0 0
\(165\) 0.00853537 0.00985034i 0.000664477 0.000766848i
\(166\) 0 0
\(167\) 10.9281 + 12.6117i 0.845640 + 0.975921i 0.999927 0.0121052i \(-0.00385331\pi\)
−0.154286 + 0.988026i \(0.549308\pi\)
\(168\) 0 0
\(169\) 8.56652 + 2.51536i 0.658963 + 0.193489i
\(170\) 0 0
\(171\) 1.72147 11.9731i 0.131644 0.915607i
\(172\) 0 0
\(173\) 0.354550 0.776357i 0.0269560 0.0590253i −0.895675 0.444709i \(-0.853307\pi\)
0.922631 + 0.385684i \(0.126034\pi\)
\(174\) 0 0
\(175\) −2.50537 + 1.61010i −0.189388 + 0.121712i
\(176\) 0 0
\(177\) 0.0595364 + 0.414085i 0.00447503 + 0.0311245i
\(178\) 0 0
\(179\) 1.61378 + 1.03711i 0.120619 + 0.0775174i 0.599559 0.800330i \(-0.295342\pi\)
−0.478940 + 0.877848i \(0.658979\pi\)
\(180\) 0 0
\(181\) −6.01911 + 1.76737i −0.447397 + 0.131368i −0.497667 0.867368i \(-0.665810\pi\)
0.0502701 + 0.998736i \(0.483992\pi\)
\(182\) 0 0
\(183\) −0.110997 −0.00820514
\(184\) 0 0
\(185\) 6.25981 0.460230
\(186\) 0 0
\(187\) 0.601199 0.176528i 0.0439640 0.0129090i
\(188\) 0 0
\(189\) −0.701093 0.450565i −0.0509970 0.0327738i
\(190\) 0 0
\(191\) 2.52104 + 17.5342i 0.182416 + 1.26873i 0.851028 + 0.525121i \(0.175980\pi\)
−0.668611 + 0.743612i \(0.733111\pi\)
\(192\) 0 0
\(193\) 19.7149 12.6700i 1.41911 0.912005i 0.419115 0.907933i \(-0.362340\pi\)
0.999992 0.00407167i \(-0.00129606\pi\)
\(194\) 0 0
\(195\) −0.0391099 + 0.0856387i −0.00280072 + 0.00613271i
\(196\) 0 0
\(197\) −1.88432 + 13.1057i −0.134252 + 0.933744i 0.805672 + 0.592361i \(0.201804\pi\)
−0.939925 + 0.341382i \(0.889105\pi\)
\(198\) 0 0
\(199\) −6.21074 1.82364i −0.440268 0.129274i 0.0540838 0.998536i \(-0.482776\pi\)
−0.494351 + 0.869262i \(0.664594\pi\)
\(200\) 0 0
\(201\) −0.307049 0.354354i −0.0216576 0.0249942i
\(202\) 0 0
\(203\) −13.1728 + 15.2023i −0.924551 + 1.06699i
\(204\) 0 0
\(205\) 3.90582 + 8.55256i 0.272795 + 0.597337i
\(206\) 0 0
\(207\) 1.30421 + 14.3178i 0.0906491 + 0.995154i
\(208\) 0 0
\(209\) 0.468264 + 1.02535i 0.0323905 + 0.0709252i
\(210\) 0 0
\(211\) −6.23790 + 7.19892i −0.429435 + 0.495594i −0.928688 0.370862i \(-0.879062\pi\)
0.499253 + 0.866456i \(0.333608\pi\)
\(212\) 0 0
\(213\) −0.397096 0.458273i −0.0272086 0.0314004i
\(214\) 0 0
\(215\) 1.04239 + 0.306072i 0.0710901 + 0.0208739i
\(216\) 0 0
\(217\) 1.55641 10.8251i 0.105656 0.734853i
\(218\) 0 0
\(219\) 0.242568 0.531150i 0.0163912 0.0358918i
\(220\) 0 0
\(221\) −3.80745 + 2.44690i −0.256117 + 0.164596i
\(222\) 0 0
\(223\) 3.66703 + 25.5048i 0.245562 + 1.70792i 0.623276 + 0.782002i \(0.285801\pi\)
−0.377713 + 0.925923i \(0.623290\pi\)
\(224\) 0 0
\(225\) −2.52193 1.62075i −0.168129 0.108050i
\(226\) 0 0
\(227\) 8.56609 2.51523i 0.568551 0.166942i 0.0151924 0.999885i \(-0.495164\pi\)
0.553359 + 0.832943i \(0.313346\pi\)
\(228\) 0 0
\(229\) −16.1261 −1.06564 −0.532821 0.846228i \(-0.678868\pi\)
−0.532821 + 0.846228i \(0.678868\pi\)
\(230\) 0 0
\(231\) 0.0388167 0.00255395
\(232\) 0 0
\(233\) 10.6789 3.13561i 0.699599 0.205421i 0.0874569 0.996168i \(-0.472126\pi\)
0.612143 + 0.790747i \(0.290308\pi\)
\(234\) 0 0
\(235\) −3.73904 2.40293i −0.243908 0.156750i
\(236\) 0 0
\(237\) 0.0427863 + 0.297585i 0.00277927 + 0.0193302i
\(238\) 0 0
\(239\) 16.2462 10.4408i 1.05088 0.675359i 0.103225 0.994658i \(-0.467084\pi\)
0.947654 + 0.319299i \(0.103447\pi\)
\(240\) 0 0
\(241\) −9.55704 + 20.9270i −0.615623 + 1.34803i 0.303038 + 0.952979i \(0.401999\pi\)
−0.918661 + 0.395048i \(0.870728\pi\)
\(242\) 0 0
\(243\) 0.179103 1.24569i 0.0114895 0.0799110i
\(244\) 0 0
\(245\) −1.79360 0.526649i −0.114589 0.0336464i
\(246\) 0 0
\(247\) −5.33198 6.15343i −0.339265 0.391533i
\(248\) 0 0
\(249\) 0.257579 0.297262i 0.0163234 0.0188382i
\(250\) 0 0
\(251\) 3.15836 + 6.91583i 0.199354 + 0.436524i 0.982735 0.185017i \(-0.0592342\pi\)
−0.783382 + 0.621541i \(0.786507\pi\)
\(252\) 0 0
\(253\) −0.823586 1.05672i −0.0517784 0.0664357i
\(254\) 0 0
\(255\) 0.0434715 + 0.0951893i 0.00272229 + 0.00596099i
\(256\) 0 0
\(257\) 18.4932 21.3423i 1.15358 1.33130i 0.218920 0.975743i \(-0.429747\pi\)
0.934656 0.355555i \(-0.115708\pi\)
\(258\) 0 0
\(259\) 12.2083 + 14.0891i 0.758587 + 0.875456i
\(260\) 0 0
\(261\) −19.4282 5.70463i −1.20258 0.353108i
\(262\) 0 0
\(263\) −0.220540 + 1.53389i −0.0135991 + 0.0945835i −0.995491 0.0948605i \(-0.969759\pi\)
0.981892 + 0.189444i \(0.0606686\pi\)
\(264\) 0 0
\(265\) 0.0806805 0.176666i 0.00495617 0.0108525i
\(266\) 0 0
\(267\) 0.0402683 0.0258789i 0.00246438 0.00158376i
\(268\) 0 0
\(269\) 3.16608 + 22.0206i 0.193039 + 1.34262i 0.823906 + 0.566727i \(0.191790\pi\)
−0.630867 + 0.775891i \(0.717300\pi\)
\(270\) 0 0
\(271\) −4.20783 2.70421i −0.255607 0.164269i 0.406562 0.913623i \(-0.366728\pi\)
−0.662169 + 0.749354i \(0.730364\pi\)
\(272\) 0 0
\(273\) −0.269024 + 0.0789926i −0.0162821 + 0.00478085i
\(274\) 0 0
\(275\) 0.279360 0.0168460
\(276\) 0 0
\(277\) −24.2911 −1.45951 −0.729756 0.683708i \(-0.760366\pi\)
−0.729756 + 0.683708i \(0.760366\pi\)
\(278\) 0 0
\(279\) 10.5627 3.10150i 0.632374 0.185682i
\(280\) 0 0
\(281\) 16.4389 + 10.5647i 0.980665 + 0.630235i 0.929643 0.368462i \(-0.120116\pi\)
0.0510225 + 0.998698i \(0.483752\pi\)
\(282\) 0 0
\(283\) 1.50374 + 10.4587i 0.0893881 + 0.621708i 0.984437 + 0.175739i \(0.0562316\pi\)
−0.895049 + 0.445969i \(0.852859\pi\)
\(284\) 0 0
\(285\) −0.158373 + 0.101780i −0.00938120 + 0.00602893i
\(286\) 0 0
\(287\) −11.6321 + 25.4707i −0.686621 + 1.50349i
\(288\) 0 0
\(289\) 1.70341 11.8475i 0.100201 0.696912i
\(290\) 0 0
\(291\) −0.574760 0.168765i −0.0336931 0.00989317i
\(292\) 0 0
\(293\) 3.04354 + 3.51243i 0.177805 + 0.205198i 0.837656 0.546199i \(-0.183926\pi\)
−0.659850 + 0.751397i \(0.729380\pi\)
\(294\) 0 0
\(295\) −5.87180 + 6.77642i −0.341870 + 0.394539i
\(296\) 0 0
\(297\) 0.0324750 + 0.0711103i 0.00188439 + 0.00412624i
\(298\) 0 0
\(299\) 7.85843 + 5.64776i 0.454464 + 0.326618i
\(300\) 0 0
\(301\) 1.34405 + 2.94305i 0.0774695 + 0.169635i
\(302\) 0 0
\(303\) 0.103595 0.119555i 0.00595138 0.00686826i
\(304\) 0 0
\(305\) −1.55794 1.79796i −0.0892074 0.102951i
\(306\) 0 0
\(307\) 24.9718 + 7.33238i 1.42521 + 0.418481i 0.901265 0.433268i \(-0.142640\pi\)
0.523950 + 0.851749i \(0.324458\pi\)
\(308\) 0 0
\(309\) 0.0922995 0.641957i 0.00525073 0.0365196i
\(310\) 0 0
\(311\) 5.31445 11.6370i 0.301355 0.659876i −0.697008 0.717063i \(-0.745486\pi\)
0.998363 + 0.0571874i \(0.0182133\pi\)
\(312\) 0 0
\(313\) −0.493249 + 0.316992i −0.0278801 + 0.0179175i −0.554507 0.832179i \(-0.687093\pi\)
0.526627 + 0.850097i \(0.323457\pi\)
\(314\) 0 0
\(315\) −1.27058 8.83707i −0.0715890 0.497912i
\(316\) 0 0
\(317\) −12.8061 8.22995i −0.719260 0.462240i 0.129120 0.991629i \(-0.458785\pi\)
−0.848379 + 0.529389i \(0.822421\pi\)
\(318\) 0 0
\(319\) 1.81047 0.531601i 0.101367 0.0297639i
\(320\) 0 0
\(321\) 0.222714 0.0124307
\(322\) 0 0
\(323\) −9.05018 −0.503566
\(324\) 0 0
\(325\) −1.93614 + 0.568502i −0.107398 + 0.0315348i
\(326\) 0 0
\(327\) −0.139076 0.0893789i −0.00769094 0.00494267i
\(328\) 0 0
\(329\) −1.88377 13.1019i −0.103856 0.722332i
\(330\) 0 0
\(331\) 11.9894 7.70510i 0.658996 0.423511i −0.167948 0.985796i \(-0.553714\pi\)
0.826943 + 0.562285i \(0.190078\pi\)
\(332\) 0 0
\(333\) −7.79560 + 17.0700i −0.427196 + 0.935429i
\(334\) 0 0
\(335\) 1.43021 9.94733i 0.0781407 0.543481i
\(336\) 0 0
\(337\) −30.6673 9.00472i −1.67055 0.490518i −0.696635 0.717425i \(-0.745320\pi\)
−0.973916 + 0.226907i \(0.927139\pi\)
\(338\) 0 0
\(339\) 0.0959396 + 0.110720i 0.00521072 + 0.00601349i
\(340\) 0 0
\(341\) −0.671801 + 0.775300i −0.0363801 + 0.0419848i
\(342\) 0 0
\(343\) 6.34749 + 13.8991i 0.342732 + 0.750479i
\(344\) 0 0
\(345\) 0.155113 0.161265i 0.00835103 0.00868219i
\(346\) 0 0
\(347\) −2.48941 5.45105i −0.133639 0.292628i 0.830968 0.556320i \(-0.187787\pi\)
−0.964607 + 0.263692i \(0.915060\pi\)
\(348\) 0 0
\(349\) 19.1292 22.0763i 1.02396 1.18172i 0.0407670 0.999169i \(-0.487020\pi\)
0.983197 0.182549i \(-0.0584347\pi\)
\(350\) 0 0
\(351\) −0.369783 0.426752i −0.0197376 0.0227783i
\(352\) 0 0
\(353\) 20.6487 + 6.06300i 1.09902 + 0.322701i 0.780462 0.625203i \(-0.214984\pi\)
0.318556 + 0.947904i \(0.396802\pi\)
\(354\) 0 0
\(355\) 1.84964 12.8645i 0.0981687 0.682778i
\(356\) 0 0
\(357\) −0.129464 + 0.283487i −0.00685197 + 0.0150037i
\(358\) 0 0
\(359\) 7.81442 5.02203i 0.412430 0.265052i −0.317932 0.948114i \(-0.602988\pi\)
0.730361 + 0.683061i \(0.239352\pi\)
\(360\) 0 0
\(361\) 0.386912 + 2.69103i 0.0203638 + 0.141633i
\(362\) 0 0
\(363\) 0.428684 + 0.275498i 0.0225001 + 0.0144599i
\(364\) 0 0
\(365\) 12.0084 3.52597i 0.628546 0.184558i
\(366\) 0 0
\(367\) 16.9124 0.882821 0.441411 0.897305i \(-0.354478\pi\)
0.441411 + 0.897305i \(0.354478\pi\)
\(368\) 0 0
\(369\) −28.1862 −1.46732
\(370\) 0 0
\(371\) 0.554975 0.162955i 0.0288129 0.00846022i
\(372\) 0 0
\(373\) −25.3642 16.3006i −1.31331 0.844011i −0.318712 0.947852i \(-0.603250\pi\)
−0.994594 + 0.103841i \(0.966887\pi\)
\(374\) 0 0
\(375\) 0.00663987 + 0.0461813i 0.000342882 + 0.00238479i
\(376\) 0 0
\(377\) −11.4659 + 7.36866i −0.590521 + 0.379505i
\(378\) 0 0
\(379\) 4.57823 10.0249i 0.235168 0.514946i −0.754848 0.655899i \(-0.772290\pi\)
0.990016 + 0.140954i \(0.0450168\pi\)
\(380\) 0 0
\(381\) −0.00699303 + 0.0486376i −0.000358264 + 0.00249178i
\(382\) 0 0
\(383\) −13.5374 3.97493i −0.691727 0.203109i −0.0830709 0.996544i \(-0.526473\pi\)
−0.608656 + 0.793434i \(0.708291\pi\)
\(384\) 0 0
\(385\) 0.544826 + 0.628763i 0.0277669 + 0.0320447i
\(386\) 0 0
\(387\) −2.13276 + 2.46133i −0.108414 + 0.125117i
\(388\) 0 0
\(389\) −12.5461 27.4720i −0.636111 1.39289i −0.903202 0.429217i \(-0.858790\pi\)
0.267091 0.963671i \(-0.413938\pi\)
\(390\) 0 0
\(391\) 10.4644 2.49037i 0.529207 0.125944i
\(392\) 0 0
\(393\) −0.243157 0.532440i −0.0122657 0.0268581i
\(394\) 0 0
\(395\) −4.21982 + 4.86993i −0.212322 + 0.245033i
\(396\) 0 0
\(397\) −14.1431 16.3220i −0.709823 0.819179i 0.280221 0.959935i \(-0.409592\pi\)
−0.990044 + 0.140756i \(0.955047\pi\)
\(398\) 0 0
\(399\) −0.537949 0.157956i −0.0269311 0.00790769i
\(400\) 0 0
\(401\) 2.44544 17.0084i 0.122119 0.849358i −0.833029 0.553230i \(-0.813395\pi\)
0.955148 0.296129i \(-0.0956957\pi\)
\(402\) 0 0
\(403\) 3.07826 6.74045i 0.153339 0.335766i
\(404\) 0 0
\(405\) 7.55480 4.85518i 0.375401 0.241256i
\(406\) 0 0
\(407\) −0.248871 1.73094i −0.0123361 0.0857994i
\(408\) 0 0
\(409\) −14.6990 9.44646i −0.726818 0.467097i 0.124185 0.992259i \(-0.460368\pi\)
−0.851002 + 0.525162i \(0.824005\pi\)
\(410\) 0 0
\(411\) 0.378310 0.111082i 0.0186607 0.00547927i
\(412\) 0 0
\(413\) −26.7035 −1.31399
\(414\) 0 0
\(415\) 8.43046 0.413835
\(416\) 0 0
\(417\) −0.610719 + 0.179323i −0.0299070 + 0.00878150i
\(418\) 0 0
\(419\) 12.1199 + 7.78900i 0.592097 + 0.380518i 0.802106 0.597182i \(-0.203713\pi\)
−0.210009 + 0.977699i \(0.567349\pi\)
\(420\) 0 0
\(421\) 5.30471 + 36.8951i 0.258536 + 1.79816i 0.543279 + 0.839552i \(0.317183\pi\)
−0.284743 + 0.958604i \(0.591908\pi\)
\(422\) 0 0
\(423\) 11.2090 7.20357i 0.544999 0.350249i
\(424\) 0 0
\(425\) −0.931741 + 2.04023i −0.0451961 + 0.0989656i
\(426\) 0 0
\(427\) 1.00832 7.01300i 0.0487959 0.339383i
\(428\) 0 0
\(429\) 0.0252354 + 0.00740977i 0.00121837 + 0.000357747i
\(430\) 0 0
\(431\) −24.7585 28.5728i −1.19258 1.37631i −0.908703 0.417444i \(-0.862926\pi\)
−0.283873 0.958862i \(-0.591619\pi\)
\(432\) 0 0
\(433\) −13.0595 + 15.0714i −0.627598 + 0.724287i −0.977131 0.212637i \(-0.931795\pi\)
0.349533 + 0.936924i \(0.386340\pi\)
\(434\) 0 0
\(435\) 0.130911 + 0.286655i 0.00627671 + 0.0137441i
\(436\) 0 0
\(437\) 7.11373 + 17.9962i 0.340296 + 0.860877i
\(438\) 0 0
\(439\) −8.76405 19.1906i −0.418285 0.915917i −0.995084 0.0990311i \(-0.968426\pi\)
0.576799 0.816886i \(-0.304302\pi\)
\(440\) 0 0
\(441\) 3.66977 4.23514i 0.174751 0.201674i
\(442\) 0 0
\(443\) 11.7673 + 13.5802i 0.559081 + 0.645214i 0.962975 0.269592i \(-0.0868888\pi\)
−0.403893 + 0.914806i \(0.632343\pi\)
\(444\) 0 0
\(445\) 0.984393 + 0.289044i 0.0466647 + 0.0137020i
\(446\) 0 0
\(447\) −0.121725 + 0.846618i −0.00575741 + 0.0400437i
\(448\) 0 0
\(449\) 11.9826 26.2382i 0.565493 1.23826i −0.383669 0.923471i \(-0.625340\pi\)
0.949162 0.314787i \(-0.101933\pi\)
\(450\) 0 0
\(451\) 2.20964 1.42005i 0.104048 0.0668674i
\(452\) 0 0
\(453\) −0.0891809 0.620267i −0.00419008 0.0291427i
\(454\) 0 0
\(455\) −5.05553 3.24899i −0.237007 0.152315i
\(456\) 0 0
\(457\) 18.9640 5.56832i 0.887097 0.260475i 0.193726 0.981056i \(-0.437943\pi\)
0.693371 + 0.720580i \(0.256125\pi\)
\(458\) 0 0
\(459\) −0.627648 −0.0292961
\(460\) 0 0
\(461\) −28.7215 −1.33769 −0.668846 0.743401i \(-0.733212\pi\)
−0.668846 + 0.743401i \(0.733212\pi\)
\(462\) 0 0
\(463\) −9.45598 + 2.77653i −0.439457 + 0.129036i −0.493974 0.869477i \(-0.664456\pi\)
0.0545173 + 0.998513i \(0.482638\pi\)
\(464\) 0 0
\(465\) −0.144133 0.0926289i −0.00668403 0.00429556i
\(466\) 0 0
\(467\) 4.94738 + 34.4098i 0.228938 + 1.59230i 0.702597 + 0.711588i \(0.252024\pi\)
−0.473659 + 0.880708i \(0.657067\pi\)
\(468\) 0 0
\(469\) 25.1780 16.1809i 1.16261 0.747166i
\(470\) 0 0
\(471\) −0.0403204 + 0.0882893i −0.00185786 + 0.00406816i
\(472\) 0 0
\(473\) 0.0431917 0.300405i 0.00198596 0.0138126i
\(474\) 0 0
\(475\) −3.87156 1.13679i −0.177639 0.0521597i
\(476\) 0 0
\(477\) 0.381278 + 0.440018i 0.0174575 + 0.0201470i
\(478\) 0 0
\(479\) −3.07644 + 3.55040i −0.140566 + 0.162222i −0.821667 0.569967i \(-0.806956\pi\)
0.681101 + 0.732189i \(0.261501\pi\)
\(480\) 0 0
\(481\) 5.24733 + 11.4900i 0.239257 + 0.523901i
\(482\) 0 0
\(483\) 0.665476 + 0.0346092i 0.0302802 + 0.00157477i
\(484\) 0 0
\(485\) −5.33357 11.6789i −0.242185 0.530311i
\(486\) 0 0
\(487\) 10.5225 12.1436i 0.476820 0.550280i −0.465476 0.885060i \(-0.654117\pi\)
0.942296 + 0.334781i \(0.108662\pi\)
\(488\) 0 0
\(489\) −0.301763 0.348253i −0.0136462 0.0157485i
\(490\) 0 0
\(491\) −18.3137 5.37739i −0.826486 0.242678i −0.158979 0.987282i \(-0.550820\pi\)
−0.667507 + 0.744604i \(0.732639\pi\)
\(492\) 0 0
\(493\) −2.15600 + 14.9953i −0.0971012 + 0.675353i
\(494\) 0 0
\(495\) −0.347898 + 0.761790i −0.0156368 + 0.0342399i
\(496\) 0 0
\(497\) 32.5619 20.9262i 1.46060 0.938670i
\(498\) 0 0
\(499\) −3.64675 25.3637i −0.163251 1.13544i −0.892454 0.451139i \(-0.851018\pi\)
0.729203 0.684298i \(-0.239891\pi\)
\(500\) 0 0
\(501\) 0.654985 + 0.420933i 0.0292626 + 0.0188059i
\(502\) 0 0
\(503\) 8.34924 2.45156i 0.372274 0.109310i −0.0902432 0.995920i \(-0.528764\pi\)
0.462517 + 0.886610i \(0.346946\pi\)
\(504\) 0 0
\(505\) 3.39063 0.150881
\(506\) 0 0
\(507\) 0.416555 0.0184998
\(508\) 0 0
\(509\) 11.2681 3.30861i 0.499450 0.146652i −0.0222980 0.999751i \(-0.507098\pi\)
0.521748 + 0.853100i \(0.325280\pi\)
\(510\) 0 0
\(511\) 31.3555 + 20.1510i 1.38709 + 0.891426i
\(512\) 0 0
\(513\) −0.160693 1.11765i −0.00709478 0.0493453i
\(514\) 0 0
\(515\) 11.6941 7.51533i 0.515303 0.331165i
\(516\) 0 0
\(517\) −0.515797 + 1.12944i −0.0226847 + 0.0496726i
\(518\) 0 0
\(519\) 0.00566703 0.0394150i 0.000248755 0.00173013i
\(520\) 0 0
\(521\) 1.42515 + 0.418463i 0.0624371 + 0.0183332i 0.312802 0.949818i \(-0.398732\pi\)
−0.250365 + 0.968152i \(0.580551\pi\)
\(522\) 0 0
\(523\) 0.404488 + 0.466804i 0.0176870 + 0.0204119i 0.764524 0.644595i \(-0.222974\pi\)
−0.746837 + 0.665007i \(0.768429\pi\)
\(524\) 0 0
\(525\) −0.0909921 + 0.105010i −0.00397122 + 0.00458303i
\(526\) 0 0
\(527\) −3.42155 7.49216i −0.149045 0.326363i
\(528\) 0 0
\(529\) −13.1774 18.8509i −0.572932 0.819603i
\(530\) 0 0
\(531\) −11.1663 24.4509i −0.484578 1.06108i
\(532\) 0 0
\(533\) −12.4244 + 14.3385i −0.538159 + 0.621069i
\(534\) 0 0
\(535\) 3.12598 + 3.60758i 0.135148 + 0.155969i
\(536\) 0 0
\(537\) 0.0858753 + 0.0252153i 0.00370579 + 0.00108812i
\(538\) 0 0
\(539\) −0.0743187 + 0.516898i −0.00320113 + 0.0222644i
\(540\) 0 0
\(541\) −6.56383 + 14.3728i −0.282201 + 0.617934i −0.996653 0.0817507i \(-0.973949\pi\)
0.714452 + 0.699685i \(0.246676\pi\)
\(542\) 0 0
\(543\) −0.246222 + 0.158237i −0.0105664 + 0.00679062i
\(544\) 0 0
\(545\) −0.504275 3.50731i −0.0216007 0.150236i
\(546\) 0 0
\(547\) −2.40938 1.54842i −0.103018 0.0662055i 0.488118 0.872778i \(-0.337684\pi\)
−0.591135 + 0.806572i \(0.701320\pi\)
\(548\) 0 0
\(549\) 6.84305 2.00930i 0.292054 0.0857548i
\(550\) 0 0
\(551\) −27.2539 −1.16106
\(552\) 0 0
\(553\) −19.1907 −0.816070
\(554\) 0 0
\(555\) 0.280229 0.0822825i 0.0118950 0.00349270i
\(556\) 0 0
\(557\) −25.6497 16.4841i −1.08681 0.698453i −0.130692 0.991423i \(-0.541720\pi\)
−0.956122 + 0.292970i \(0.905356\pi\)
\(558\) 0 0
\(559\) 0.311983 + 2.16989i 0.0131955 + 0.0917767i
\(560\) 0 0
\(561\) 0.0245931 0.0158050i 0.00103832 0.000667288i
\(562\) 0 0
\(563\) −7.17373 + 15.7083i −0.302337 + 0.662025i −0.998435 0.0559214i \(-0.982190\pi\)
0.696099 + 0.717946i \(0.254918\pi\)
\(564\) 0 0
\(565\) −0.446878 + 3.10811i −0.0188003 + 0.130759i
\(566\) 0 0
\(567\) 25.6616 + 7.53492i 1.07768 + 0.316437i
\(568\) 0 0
\(569\) −20.5908 23.7630i −0.863211 0.996199i −0.999984 0.00559615i \(-0.998219\pi\)
0.136773 0.990602i \(-0.456327\pi\)
\(570\) 0 0
\(571\) −26.3971 + 30.4638i −1.10468 + 1.27487i −0.146345 + 0.989234i \(0.546751\pi\)
−0.958338 + 0.285638i \(0.907794\pi\)
\(572\) 0 0
\(573\) 0.343338 + 0.751805i 0.0143431 + 0.0314071i
\(574\) 0 0
\(575\) 4.78936 + 0.249079i 0.199730 + 0.0103873i
\(576\) 0 0
\(577\) −6.15706 13.4821i −0.256322 0.561267i 0.737099 0.675784i \(-0.236195\pi\)
−0.993421 + 0.114518i \(0.963468\pi\)
\(578\) 0 0
\(579\) 0.716020 0.826332i 0.0297568 0.0343412i
\(580\) 0 0
\(581\) 16.4417 + 18.9747i 0.682115 + 0.787202i
\(582\) 0 0
\(583\) −0.0520585 0.0152858i −0.00215604 0.000633072i
\(584\) 0 0
\(585\) 0.860896 5.98767i 0.0355937 0.247560i
\(586\) 0 0
\(587\) −15.8070 + 34.6125i −0.652424 + 1.42861i 0.236992 + 0.971512i \(0.423838\pi\)
−0.889416 + 0.457098i \(0.848889\pi\)
\(588\) 0 0
\(589\) 12.4652 8.01091i 0.513620 0.330084i
\(590\) 0 0
\(591\) 0.0879151 + 0.611463i 0.00361635 + 0.0251522i
\(592\) 0 0
\(593\) 23.0636 + 14.8221i 0.947110 + 0.608670i 0.920402 0.390973i \(-0.127861\pi\)
0.0267075 + 0.999643i \(0.491498\pi\)
\(594\) 0 0
\(595\) −6.40914 + 1.88189i −0.262749 + 0.0771501i
\(596\) 0 0
\(597\) −0.302003 −0.0123602
\(598\) 0 0
\(599\) −14.9351 −0.610232 −0.305116 0.952315i \(-0.598695\pi\)
−0.305116 + 0.952315i \(0.598695\pi\)
\(600\) 0 0
\(601\) 10.0034 2.93726i 0.408047 0.119813i −0.0712664 0.997457i \(-0.522704\pi\)
0.479313 + 0.877644i \(0.340886\pi\)
\(602\) 0 0
\(603\) 25.3444 + 16.2879i 1.03211 + 0.663294i
\(604\) 0 0
\(605\) 1.55436 + 10.8108i 0.0631936 + 0.439521i
\(606\) 0 0
\(607\) −3.51535 + 2.25918i −0.142684 + 0.0916971i −0.610035 0.792374i \(-0.708845\pi\)
0.467351 + 0.884072i \(0.345208\pi\)
\(608\) 0 0
\(609\) −0.389872 + 0.853700i −0.0157984 + 0.0345937i
\(610\) 0 0
\(611\) 1.27637 8.87737i 0.0516365 0.359140i
\(612\) 0 0
\(613\) −22.3386 6.55921i −0.902248 0.264924i −0.202474 0.979288i \(-0.564898\pi\)
−0.699775 + 0.714364i \(0.746716\pi\)
\(614\) 0 0
\(615\) 0.287269 + 0.331526i 0.0115838 + 0.0133684i
\(616\) 0 0
\(617\) 1.56566 1.80687i 0.0630310 0.0727417i −0.723358 0.690473i \(-0.757403\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(618\) 0 0
\(619\) 16.0811 + 35.2128i 0.646356 + 1.41532i 0.894708 + 0.446652i \(0.147384\pi\)
−0.248352 + 0.968670i \(0.579889\pi\)
\(620\) 0 0
\(621\) 0.493351 + 1.24807i 0.0197975 + 0.0500835i
\(622\) 0 0
\(623\) 1.26927 + 2.77931i 0.0508522 + 0.111351i
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.0261944 + 0.0302300i
\(626\) 0 0
\(627\) 0.0344403 + 0.0397462i 0.00137541 + 0.00158731i
\(628\) 0 0
\(629\) 13.4715 + 3.95559i 0.537144 + 0.157720i
\(630\) 0 0
\(631\) −3.76199 + 26.1652i −0.149763 + 1.04162i 0.766844 + 0.641833i \(0.221826\pi\)
−0.916607 + 0.399789i \(0.869083\pi\)
\(632\) 0 0
\(633\) −0.184621 + 0.404263i −0.00733802 + 0.0160680i
\(634\) 0 0
\(635\) −0.885998 + 0.569396i −0.0351597 + 0.0225958i
\(636\) 0 0
\(637\) −0.536821 3.73367i −0.0212696 0.147933i
\(638\) 0 0
\(639\) 32.7771 + 21.0645i 1.29664 + 0.833300i
\(640\) 0 0
\(641\) 6.23851 1.83179i 0.246406 0.0723514i −0.156197 0.987726i \(-0.549924\pi\)
0.402603 + 0.915374i \(0.368105\pi\)
\(642\) 0 0
\(643\) −11.0497 −0.435757 −0.217879 0.975976i \(-0.569914\pi\)
−0.217879 + 0.975976i \(0.569914\pi\)
\(644\) 0 0
\(645\) 0.0506870 0.00199580
\(646\) 0 0
\(647\) −39.4465 + 11.5825i −1.55080 + 0.455356i −0.941340 0.337459i \(-0.890432\pi\)
−0.609461 + 0.792816i \(0.708614\pi\)
\(648\) 0 0
\(649\) 2.10724 + 1.35424i 0.0827163 + 0.0531585i
\(650\) 0 0
\(651\) −0.0726161 0.505056i −0.00284605 0.0197947i
\(652\) 0 0
\(653\) 10.1759 6.53968i 0.398215 0.255918i −0.326172 0.945310i \(-0.605759\pi\)
0.724388 + 0.689393i \(0.242123\pi\)
\(654\) 0 0
\(655\) 5.21168 11.4120i 0.203637 0.445903i
\(656\) 0 0
\(657\) −5.33947 + 37.1368i −0.208312 + 1.44884i
\(658\) 0 0
\(659\) −20.0814 5.89644i −0.782262 0.229693i −0.133869 0.990999i \(-0.542740\pi\)
−0.648392 + 0.761306i \(0.724558\pi\)
\(660\) 0 0
\(661\) 14.1761 + 16.3601i 0.551387 + 0.636335i 0.961206 0.275832i \(-0.0889534\pi\)
−0.409818 + 0.912167i \(0.634408\pi\)
\(662\) 0 0
\(663\) −0.138282 + 0.159586i −0.00537043 + 0.00619781i
\(664\) 0 0
\(665\) −4.99197 10.9309i −0.193580 0.423882i
\(666\) 0 0
\(667\) 31.5127 7.49957i 1.22018 0.290385i
\(668\) 0 0
\(669\) 0.499409 + 1.09355i 0.0193083 + 0.0422792i
\(670\) 0 0
\(671\) −0.435226 + 0.502277i −0.0168017 + 0.0193902i
\(672\) 0 0
\(673\) 32.9869 + 38.0689i 1.27155 + 1.46745i 0.816899 + 0.576781i \(0.195691\pi\)
0.454653 + 0.890669i \(0.349763\pi\)
\(674\) 0 0
\(675\) −0.268500 0.0788388i −0.0103346 0.00303451i
\(676\) 0 0
\(677\) 1.11800 7.77585i 0.0429682 0.298850i −0.956994 0.290109i \(-0.906308\pi\)
0.999962 0.00874126i \(-0.00278246\pi\)
\(678\) 0 0
\(679\) 15.8841 34.7814i 0.609576 1.33479i
\(680\) 0 0
\(681\) 0.350411 0.225195i 0.0134278 0.00862950i
\(682\) 0 0
\(683\) −2.42284 16.8513i −0.0927076 0.644795i −0.982199 0.187843i \(-0.939850\pi\)
0.889491 0.456952i \(-0.151059\pi\)
\(684\) 0 0
\(685\) 7.10925 + 4.56884i 0.271630 + 0.174566i
\(686\) 0 0
\(687\) −0.721905 + 0.211971i −0.0275424 + 0.00808718i
\(688\) 0 0
\(689\) 0.391905 0.0149304
\(690\) 0 0
\(691\) 20.1063 0.764879 0.382439 0.923981i \(-0.375084\pi\)
0.382439 + 0.923981i \(0.375084\pi\)
\(692\) 0 0
\(693\) −2.39308 + 0.702671i −0.0909055 + 0.0266923i
\(694\) 0 0
\(695\) −11.4767 7.37563i −0.435336 0.279774i
\(696\) 0 0
\(697\) 3.00119 + 20.8737i 0.113678 + 0.790649i
\(698\) 0 0
\(699\) 0.436840 0.280740i 0.0165228 0.0106186i
\(700\) 0 0
\(701\) 1.77020 3.87619i 0.0668595 0.146402i −0.873252 0.487269i \(-0.837993\pi\)
0.940112 + 0.340867i \(0.110721\pi\)
\(702\) 0 0
\(703\) −3.59464 + 25.0013i −0.135575 + 0.942942i
\(704\) 0 0
\(705\) −0.198968 0.0584224i −0.00749358 0.00220031i
\(706\) 0 0
\(707\) 6.61264 + 7.63139i 0.248694 + 0.287008i
\(708\) 0 0
\(709\) −2.18654 + 2.52340i −0.0821172 + 0.0947683i −0.795321 0.606188i \(-0.792698\pi\)
0.713204 + 0.700956i \(0.247243\pi\)
\(710\) 0 0
\(711\) −8.02478 17.5718i −0.300953 0.658995i
\(712\) 0 0
\(713\) −12.2087 + 12.6928i −0.457218 + 0.475349i
\(714\) 0 0
\(715\) 0.234175 + 0.512772i 0.00875765 + 0.0191766i
\(716\) 0 0
\(717\) 0.590042 0.680945i 0.0220355 0.0254304i
\(718\) 0 0
\(719\) 9.53735 + 11.0067i 0.355683 + 0.410480i 0.905189 0.425010i \(-0.139729\pi\)
−0.549506 + 0.835490i \(0.685184\pi\)
\(720\) 0 0
\(721\) 39.7216 + 11.6633i 1.47931 + 0.434364i
\(722\) 0 0
\(723\) −0.152757 + 1.06245i −0.00568109 + 0.0395129i
\(724\) 0 0
\(725\) −2.80587 + 6.14399i −0.104207 + 0.228182i
\(726\) 0 0
\(727\) 20.9525 13.4654i 0.777087 0.499403i −0.0909789 0.995853i \(-0.529000\pi\)
0.868066 + 0.496449i \(0.165363\pi\)
\(728\) 0 0
\(729\) 3.82578 + 26.6089i 0.141696 + 0.985515i
\(730\) 0 0
\(731\) 2.04987 + 1.31737i 0.0758172 + 0.0487248i
\(732\) 0 0
\(733\) −32.2166 + 9.45965i −1.18995 + 0.349400i −0.816001 0.578050i \(-0.803814\pi\)
−0.373947 + 0.927450i \(0.621996\pi\)
\(734\) 0 0
\(735\) −0.0872155 −0.00321699
\(736\) 0 0
\(737\) −2.80746 −0.103414
\(738\) 0 0
\(739\) 30.0785 8.83184i 1.10645 0.324884i 0.323041 0.946385i \(-0.395295\pi\)
0.783414 + 0.621501i \(0.213477\pi\)
\(740\) 0 0
\(741\) −0.319577 0.205380i −0.0117400 0.00754481i
\(742\) 0 0
\(743\) 1.06080 + 7.37806i 0.0389171 + 0.270675i 0.999984 0.00564092i \(-0.00179557\pi\)
−0.961067 + 0.276316i \(0.910886\pi\)
\(744\) 0 0
\(745\) −15.4223 + 9.91128i −0.565028 + 0.363121i
\(746\) 0 0
\(747\) −10.4988 + 22.9892i −0.384131 + 0.841129i
\(748\) 0 0
\(749\) −2.02317 + 14.0715i −0.0739251 + 0.514161i
\(750\) 0 0
\(751\) −24.1440 7.08932i −0.881028 0.258693i −0.190229 0.981740i \(-0.560923\pi\)
−0.690799 + 0.723047i \(0.742741\pi\)
\(752\) 0 0
\(753\) 0.232294 + 0.268081i 0.00846525 + 0.00976942i
\(754\) 0 0
\(755\) 8.79551 10.1506i 0.320101 0.369417i
\(756\) 0 0
\(757\) −7.65858 16.7699i −0.278356 0.609514i 0.717883 0.696164i \(-0.245111\pi\)
−0.996239 + 0.0866495i \(0.972384\pi\)
\(758\) 0 0
\(759\) −0.0507591 0.0364800i −0.00184244 0.00132414i
\(760\) 0 0
\(761\) −1.42209 3.11394i −0.0515507 0.112880i 0.882104 0.471055i \(-0.156127\pi\)
−0.933655 + 0.358174i \(0.883399\pi\)
\(762\) 0 0
\(763\) 6.91052 7.97517i 0.250178 0.288721i
\(764\) 0 0
\(765\) −4.40319 5.08156i −0.159198 0.183724i
\(766\) 0 0
\(767\) −17.3604 5.09747i −0.626847 0.184059i
\(768\) 0 0
\(769\) −6.13693 + 42.6833i −0.221303 + 1.53920i 0.511815 + 0.859096i \(0.328973\pi\)
−0.733118 + 0.680102i \(0.761936\pi\)
\(770\) 0 0
\(771\) 0.547338 1.19850i 0.0197119 0.0431630i
\(772\) 0 0
\(773\) 23.3071 14.9786i 0.838297 0.538741i −0.0496071 0.998769i \(-0.515797\pi\)
0.887905 + 0.460028i \(0.152161\pi\)
\(774\) 0 0
\(775\) −0.522611 3.63484i −0.0187727 0.130567i
\(776\) 0 0
\(777\) 0.731716 + 0.470246i 0.0262502 + 0.0168700i
\(778\) 0 0
\(779\) −36.4013 + 10.6884i −1.30421 + 0.382951i
\(780\) 0 0
\(781\) −3.63079 −0.129920
\(782\) 0 0
\(783\) −1.89011 −0.0675472
\(784\) 0 0
\(785\) −1.99606 + 0.586097i −0.0712426 + 0.0209187i
\(786\) 0 0
\(787\) −40.1813 25.8229i −1.43231 0.920489i −0.999822 0.0188479i \(-0.994000\pi\)
−0.432486 0.901641i \(-0.642363\pi\)
\(788\) 0 0
\(789\) 0.0102895 + 0.0715654i 0.000366318 + 0.00254779i
\(790\) 0 0
\(791\) −7.86704 + 5.05584i −0.279720 + 0.179765i
\(792\) 0 0
\(793\) 1.99425 4.36679i 0.0708177 0.155069i
\(794\) 0 0
\(795\) 0.00128957 0.00896918i 4.57365e−5 0.000318104i
\(796\) 0 0
\(797\) 1.11687 + 0.327942i 0.0395615 + 0.0116163i 0.301453 0.953481i \(-0.402528\pi\)
−0.261892 + 0.965097i \(0.584346\pi\)
\(798\) 0 0
\(799\) −6.52822 7.53396i −0.230952 0.266533i
\(800\) 0 0
\(801\) −2.01410 + 2.32440i −0.0711648 + 0.0821286i
\(802\) 0 0
\(803\) −1.45240 3.18032i −0.0512542 0.112231i
\(804\) 0 0
\(805\) 8.77992 + 11.2653i 0.309452 + 0.397050i
\(806\) 0 0
\(807\) 0.431185 + 0.944163i 0.0151784 + 0.0332361i
\(808\) 0 0
\(809\) 13.8053 15.9322i 0.485370 0.560147i −0.459252 0.888306i \(-0.651883\pi\)
0.944623 + 0.328159i \(0.106428\pi\)
\(810\) 0 0
\(811\) 12.7377 + 14.7001i 0.447282 + 0.516191i 0.933954 0.357394i \(-0.116335\pi\)
−0.486672 + 0.873585i \(0.661789\pi\)
\(812\) 0 0
\(813\) −0.223914 0.0657472i −0.00785302 0.00230586i
\(814\) 0 0
\(815\) 1.40559 9.77606i 0.0492355 0.342441i
\(816\) 0 0
\(817\) −1.82101 + 3.98747i −0.0637092 + 0.139504i
\(818\) 0 0
\(819\) 15.1556 9.73991i 0.529579 0.340340i
\(820\) 0 0
\(821\) −0.389483 2.70892i −0.0135931 0.0945418i 0.981896 0.189423i \(-0.0606619\pi\)
−0.995489 + 0.0948816i \(0.969753\pi\)
\(822\) 0 0
\(823\) −18.7607 12.0568i −0.653956 0.420272i 0.171154 0.985244i \(-0.445251\pi\)
−0.825110 + 0.564972i \(0.808887\pi\)
\(824\) 0 0
\(825\) 0.0125059 0.00367206i 0.000435400 0.000127845i
\(826\) 0 0
\(827\) 8.80241 0.306090 0.153045 0.988219i \(-0.451092\pi\)
0.153045 + 0.988219i \(0.451092\pi\)
\(828\) 0 0
\(829\) −1.91551 −0.0665283 −0.0332642 0.999447i \(-0.510590\pi\)
−0.0332642 + 0.999447i \(0.510590\pi\)
\(830\) 0 0
\(831\) −1.08742 + 0.319296i −0.0377223 + 0.0110763i
\(832\) 0 0
\(833\) −3.52715 2.26676i −0.122209 0.0785387i
\(834\) 0 0
\(835\) 2.37490 + 16.5178i 0.0821868 + 0.571622i
\(836\) 0 0
\(837\) 0.864487 0.555572i 0.0298810 0.0192034i
\(838\) 0 0
\(839\) −8.33976 + 18.2615i −0.287920 + 0.630458i −0.997225 0.0744441i \(-0.976282\pi\)
0.709305 + 0.704902i \(0.249009\pi\)
\(840\) 0 0
\(841\) −2.36549 + 16.4523i −0.0815685 + 0.567321i
\(842\) 0 0
\(843\) 0.874779 + 0.256858i 0.0301290 + 0.00884667i
\(844\) 0 0
\(845\) 5.84671 + 6.74746i 0.201133 + 0.232120i
\(846\) 0 0
\(847\) −21.3007 + 24.5824i −0.731902 + 0.844660i
\(848\) 0 0
\(849\) 0.204793 + 0.448434i 0.00702847 + 0.0153902i
\(850\) 0 0
\(851\) −2.72335 29.8972i −0.0933553 1.02486i
\(852\) 0 0
\(853\) −5.07462 11.1119i −0.173752 0.380463i 0.802642 0.596461i \(-0.203427\pi\)
−0.976394 + 0.215998i \(0.930700\pi\)
\(854\) 0 0
\(855\) 7.92136 9.14173i 0.270905 0.312641i
\(856\) 0 0
\(857\) 6.38459 + 7.36821i 0.218094 + 0.251693i 0.854245 0.519871i \(-0.174020\pi\)
−0.636151 + 0.771564i \(0.719475\pi\)
\(858\) 0 0
\(859\) −26.9782 7.92152i −0.920485 0.270279i −0.213037 0.977044i \(-0.568335\pi\)
−0.707448 + 0.706765i \(0.750154\pi\)
\(860\) 0 0
\(861\) −0.185924 + 1.29313i −0.00633627 + 0.0440698i
\(862\) 0 0
\(863\) 2.90772 6.36703i 0.0989801 0.216736i −0.853664 0.520825i \(-0.825625\pi\)
0.952644 + 0.304088i \(0.0983518\pi\)
\(864\) 0 0
\(865\) 0.717997 0.461429i 0.0244126 0.0156890i
\(866\) 0 0
\(867\) −0.0794748 0.552760i −0.00269911 0.0187727i
\(868\) 0 0
\(869\) 1.51438 + 0.973234i 0.0513719 + 0.0330147i
\(870\) 0 0
\(871\) 19.4575 5.71323i 0.659291 0.193585i
\(872\) 0 0
\(873\) 38.4894 1.30267
\(874\) 0 0
\(875\) −2.97814 −0.100680
\(876\) 0 0
\(877\) −18.3125 + 5.37704i −0.618369 + 0.181570i −0.575889 0.817528i \(-0.695344\pi\)
−0.0424800 + 0.999097i \(0.513526\pi\)
\(878\) 0 0
\(879\) 0.182417 + 0.117233i 0.00615279 + 0.00395416i
\(880\) 0 0
\(881\) −4.37583 30.4346i −0.147426 1.02537i −0.920413 0.390946i \(-0.872148\pi\)
0.772988 0.634421i \(-0.218761\pi\)
\(882\) 0 0
\(883\) −3.64108 + 2.33998i −0.122532 + 0.0787466i −0.600471 0.799646i \(-0.705020\pi\)
0.477939 + 0.878393i \(0.341384\pi\)
\(884\) 0 0
\(885\) −0.173786 + 0.380538i −0.00584175 + 0.0127916i
\(886\) 0 0
\(887\) 6.04515 42.0449i 0.202976 1.41173i −0.592414 0.805634i \(-0.701825\pi\)
0.795390 0.606097i \(-0.207266\pi\)
\(888\) 0 0
\(889\) −3.00949 0.883666i −0.100935 0.0296372i
\(890\) 0 0
\(891\) −1.64289 1.89600i −0.0550389 0.0635183i
\(892\) 0 0
\(893\) 11.7443 13.5536i 0.393007 0.453554i
\(894\) 0 0
\(895\) 0.796892 + 1.74495i 0.0266372 + 0.0583272i
\(896\) 0 0
\(897\) 0.426030 + 0.149534i 0.0142247 + 0.00499278i
\(898\) 0 0
\(899\) −10.3037 22.5621i −0.343649 0.752487i
\(900\) 0 0
\(901\) 0.285265 0.329213i 0.00950355 0.0109677i
\(902\) 0 0
\(903\) 0.0988531 + 0.114083i 0.00328963 + 0.00379643i
\(904\) 0 0
\(905\) −6.01911 1.76737i −0.200082 0.0587494i
\(906\) 0 0
\(907\) 6.50131 45.2176i 0.215872 1.50143i −0.537181 0.843467i \(-0.680511\pi\)
0.753054 0.657959i \(-0.228580\pi\)
\(908\) 0 0
\(909\) −4.22249 + 9.24597i −0.140051 + 0.306669i
\(910\) 0 0
\(911\) −1.02386 + 0.657993i −0.0339219 + 0.0218003i −0.557492 0.830182i \(-0.688236\pi\)
0.523570 + 0.851983i \(0.324600\pi\)
\(912\) 0 0
\(913\) −0.335170 2.33116i −0.0110925 0.0771501i
\(914\) 0 0
\(915\) −0.0933766 0.0600095i −0.00308694 0.00198385i
\(916\) 0 0
\(917\) 35.8495 10.5264i 1.18385 0.347611i
\(918\) 0 0
\(919\) −44.0297 −1.45241 −0.726203 0.687480i \(-0.758717\pi\)
−0.726203 + 0.687480i \(0.758717\pi\)
\(920\) 0 0
\(921\) 1.21428 0.0400117
\(922\) 0 0
\(923\) 25.1636 7.38871i 0.828271 0.243202i
\(924\) 0 0
\(925\) 5.26609 + 3.38431i 0.173148 + 0.111275i
\(926\) 0 0
\(927\) 5.93056 + 41.2479i 0.194785 + 1.35476i
\(928\) 0 0
\(929\) 14.9269 9.59293i 0.489735 0.314734i −0.272363 0.962194i \(-0.587805\pi\)
0.762099 + 0.647461i \(0.224169\pi\)
\(930\) 0 0
\(931\) 3.13337 6.86111i 0.102692 0.224864i
\(932\) 0 0
\(933\) 0.0849447 0.590803i 0.00278096 0.0193420i
\(934\) 0 0
\(935\) 0.601199 + 0.176528i 0.0196613 + 0.00577308i
\(936\) 0 0
\(937\) −1.42968 1.64994i −0.0467057 0.0539013i 0.731916 0.681395i \(-0.238626\pi\)
−0.778622 + 0.627494i \(0.784081\pi\)
\(938\) 0 0
\(939\) −0.0179142 + 0.0206741i −0.000584609 + 0.000674674i
\(940\) 0 0
\(941\) −9.96049 21.8104i −0.324703 0.711000i 0.674936 0.737876i \(-0.264171\pi\)
−0.999639 + 0.0268765i \(0.991444\pi\)
\(942\) 0 0
\(943\) 39.1483 22.3753i 1.27484 0.728639i
\(944\) 0 0
\(945\) −0.346203 0.758078i −0.0112620 0.0246603i
\(946\) 0 0
\(947\) 3.23129 3.72910i 0.105003 0.121180i −0.700816 0.713343i \(-0.747180\pi\)
0.805818 + 0.592163i \(0.201726\pi\)
\(948\) 0 0
\(949\) 16.5381 + 19.0860i 0.536849 + 0.619557i
\(950\) 0 0
\(951\) −0.681459 0.200094i −0.0220978 0.00648851i
\(952\) 0 0
\(953\) 3.31975 23.0894i 0.107537 0.747938i −0.862688 0.505736i \(-0.831221\pi\)
0.970226 0.242203i \(-0.0778698\pi\)
\(954\) 0 0
\(955\) −7.35889 + 16.1137i −0.238128 + 0.521428i
\(956\) 0 0
\(957\) 0.0740602 0.0475956i 0.00239403 0.00153855i
\(958\) 0 0
\(959\) 3.58172 + 24.9114i 0.115660 + 0.804432i
\(960\) 0 0
\(961\) −14.7344 9.46923i −0.475304 0.305459i
\(962\) 0 0
\(963\) −13.7305 + 4.03163i −0.442458 + 0.129917i
\(964\) 0 0
\(965\) 23.4351 0.754403
\(966\) 0 0
\(967\) 56.8799 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(968\) 0 0
\(969\) −0.405143 + 0.118961i −0.0130151 + 0.00382157i
\(970\) 0 0
\(971\) −46.9482 30.1717i −1.50664 0.968257i −0.993968 0.109672i \(-0.965020\pi\)
−0.512670 0.858586i \(-0.671344\pi\)
\(972\) 0 0
\(973\) −5.78210 40.2154i −0.185366 1.28925i
\(974\) 0 0
\(975\) −0.0792011 + 0.0508994i −0.00253646 + 0.00163009i
\(976\) 0 0
\(977\) −1.36909 + 2.99790i −0.0438012 + 0.0959112i −0.930268 0.366882i \(-0.880425\pi\)
0.886466 + 0.462793i \(0.153153\pi\)
\(978\) 0 0
\(979\) 0.0407888 0.283692i 0.00130361 0.00906684i
\(980\) 0 0
\(981\) 10.1921 + 2.99268i 0.325409 + 0.0955488i
\(982\) 0 0
\(983\) −38.5232 44.4582i −1.22870 1.41800i −0.876035 0.482247i \(-0.839821\pi\)
−0.352665 0.935750i \(-0.614725\pi\)
\(984\) 0 0
\(985\) −8.67067 + 10.0065i −0.276271 + 0.318833i
\(986\) 0 0
\(987\) −0.256549 0.561763i −0.00816603 0.0178811i
\(988\) 0 0
\(989\) 1.00832 5.11165i 0.0320629 0.162541i
\(990\) 0 0
\(991\) −0.425967 0.932737i −0.0135313 0.0296294i 0.902746 0.430175i \(-0.141548\pi\)
−0.916277 + 0.400545i \(0.868821\pi\)
\(992\) 0 0
\(993\) 0.435440 0.502524i 0.0138183 0.0159471i
\(994\) 0 0
\(995\) −4.23887 4.89192i −0.134381 0.155084i
\(996\) 0 0
\(997\) 38.2928 + 11.2438i 1.21275 + 0.356094i 0.824713 0.565551i \(-0.191336\pi\)
0.388033 + 0.921645i \(0.373155\pi\)
\(998\) 0 0
\(999\) −0.249296 + 1.73389i −0.00788736 + 0.0548578i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 460.2.m.a.441.2 yes 30
23.6 even 11 inner 460.2.m.a.121.2 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.a.121.2 30 23.6 even 11 inner
460.2.m.a.441.2 yes 30 1.1 even 1 trivial