Properties

Label 585.2.j.a.406.1
Level $585$
Weight $2$
Character 585.406
Analytic conductor $4.671$
Analytic rank $0$
Dimension $2$
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] = [585,2,Mod(406,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.j (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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 585.406
Dual form 585.2.j.a.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +(2.50000 + 2.59808i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{19} +(1.00000 - 1.73205i) q^{20} +(-3.00000 - 5.19615i) q^{23} +1.00000 q^{25} +(-1.00000 - 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(-5.50000 + 9.52628i) q^{43} +12.0000 q^{44} -6.00000 q^{47} +(3.00000 + 5.19615i) q^{49} +(7.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{55} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{64} +(2.50000 + 2.59808i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{71} +5.00000 q^{73} +(-4.00000 - 6.92820i) q^{76} +6.00000 q^{77} +11.0000 q^{79} +(-2.00000 - 3.46410i) q^{80} -12.0000 q^{83} +(6.00000 + 10.3923i) q^{89} +(3.50000 - 0.866025i) q^{91} -12.0000 q^{92} +(2.00000 - 3.46410i) q^{95} +(-8.50000 + 14.7224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} + 2 q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} + 2 q^{5} + q^{7} + 6 q^{11} + 5 q^{13} - 4 q^{16} + 4 q^{19} + 2 q^{20} - 6 q^{23} + 2 q^{25} - 2 q^{28} - 6 q^{29} + 10 q^{31} + q^{35} - 2 q^{37} - 11 q^{43} + 24 q^{44} - 12 q^{47} + 6 q^{49} + 14 q^{52} + 6 q^{55} + 6 q^{59} + q^{61} - 16 q^{64} + 5 q^{65} - 11 q^{67} - 6 q^{71} + 10 q^{73} - 8 q^{76} + 12 q^{77} + 22 q^{79} - 4 q^{80} - 24 q^{83} + 12 q^{89} + 7 q^{91} - 24 q^{92} + 4 q^{95} - 17 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) 0 0
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.500000 0.866025i 0.0845154 0.146385i
\(36\) 0 0
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) 12.0000 1.80907
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) 0 0
\(51\) 0 0
\(52\) 7.00000 1.73205i 0.970725 0.240192i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 2.50000 + 2.59808i 0.310087 + 0.322252i
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) −2.00000 3.46410i −0.223607 0.387298i
\(81\) 0 0
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) 0 0
\(91\) 3.50000 0.866025i 0.366900 0.0907841i
\(92\) −12.0000 −1.25109
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) 0 0
\(97\) −8.50000 + 14.7224i −0.863044 + 1.49484i 0.00593185 + 0.999982i \(0.498112\pi\)
−0.868976 + 0.494854i \(0.835222\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) −12.0000 −1.11417
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 0 0
\(123\) 0 0
\(124\) 5.00000 8.66025i 0.449013 0.777714i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.500000 + 0.866025i 0.0443678 + 0.0768473i 0.887357 0.461084i \(-0.152539\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i \(-0.535080\pi\)
0.915764 0.401718i \(-0.131587\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 0 0
\(142\) 0 0
\(143\) −6.00000 + 20.7846i −0.501745 + 1.73810i
\(144\) 0 0
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 0 0
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 12.0000 20.7846i 0.983078 1.70274i 0.332896 0.942964i \(-0.391974\pi\)
0.650183 0.759778i \(-0.274692\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.00000 0.401610
\(156\) 0 0
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i \(-0.975100\pi\)
0.566149 + 0.824303i \(0.308433\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 0 0
\(172\) 11.0000 + 19.0526i 0.838742 + 1.45274i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 12.0000 20.7846i 0.904534 1.56670i
\(177\) 0 0
\(178\) 0 0
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 + 10.3923i −0.437595 + 0.757937i
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i \(-0.0116845\pi\)
−0.531446 + 0.847092i \(0.678351\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 12.0000 0.857143
\(197\) 6.00000 + 10.3923i 0.427482 + 0.740421i 0.996649 0.0818013i \(-0.0260673\pi\)
−0.569166 + 0.822222i \(0.692734\pi\)
\(198\) 0 0
\(199\) −8.50000 + 14.7224i −0.602549 + 1.04365i 0.389885 + 0.920864i \(0.372515\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 4.00000 13.8564i 0.277350 0.960769i
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.50000 + 9.52628i −0.375097 + 0.649687i
\(216\) 0 0
\(217\) 2.50000 4.33013i 0.169711 0.293948i
\(218\) 0 0
\(219\) 0 0
\(220\) 12.0000 0.809040
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) 3.00000 + 5.19615i 0.191663 + 0.331970i
\(246\) 0 0
\(247\) 14.0000 3.46410i 0.890799 0.220416i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 18.0000 31.1769i 1.13165 1.96008i
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 7.00000 1.73205i 0.434122 0.107417i
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −22.0000 −1.34386
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i \(-0.0984703\pi\)
−0.739921 + 0.672694i \(0.765137\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.00000 + 5.19615i 0.180907 + 0.313340i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −11.5000 19.9186i −0.683604 1.18404i −0.973873 0.227092i \(-0.927078\pi\)
0.290269 0.956945i \(-0.406255\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i \(-0.777256\pi\)
0.940252 + 0.340480i \(0.110589\pi\)
\(294\) 0 0
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.00000 20.7846i 0.346989 1.20201i
\(300\) 0 0
\(301\) 5.50000 + 9.52628i 0.317015 + 0.549086i
\(302\) 0 0
\(303\) 0 0
\(304\) −16.0000 −0.917663
\(305\) 0.500000 0.866025i 0.0286299 0.0495885i
\(306\) 0 0
\(307\) −25.0000 −1.42683 −0.713413 0.700744i \(-0.752851\pi\)
−0.713413 + 0.700744i \(0.752851\pi\)
\(308\) 6.00000 10.3923i 0.341882 0.592157i
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 23.0000 1.30004 0.650018 0.759918i \(-0.274761\pi\)
0.650018 + 0.759918i \(0.274761\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 11.0000 19.0526i 0.618798 1.07179i
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) −8.00000 −0.447214
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 2.50000 + 2.59808i 0.138675 + 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.00000 + 5.19615i −0.165395 + 0.286473i
\(330\) 0 0
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) −12.0000 + 20.7846i −0.658586 + 1.14070i
\(333\) 0 0
\(334\) 0 0
\(335\) −5.50000 9.52628i −0.300497 0.520476i
\(336\) 0 0
\(337\) −7.00000 −0.381314 −0.190657 0.981657i \(-0.561062\pi\)
−0.190657 + 0.981657i \(0.561062\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.0000 + 25.9808i 0.812296 + 1.40694i
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −5.50000 9.52628i −0.294408 0.509930i 0.680439 0.732805i \(-0.261789\pi\)
−0.974847 + 0.222875i \(0.928456\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 24.0000 1.27200
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 2.00000 6.92820i 0.104828 0.363137i
\(365\) 5.00000 0.261712
\(366\) 0 0
\(367\) −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i \(-0.208325\pi\)
−0.923869 + 0.382709i \(0.874991\pi\)
\(368\) −12.0000 + 20.7846i −0.625543 + 1.08347i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000 20.7846i 0.309016 1.07046i
\(378\) 0 0
\(379\) 0.500000 + 0.866025i 0.0256833 + 0.0444847i 0.878581 0.477593i \(-0.158491\pi\)
−0.852898 + 0.522077i \(0.825157\pi\)
\(380\) −4.00000 6.92820i −0.205196 0.355409i
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 0 0
\(387\) 0 0
\(388\) 17.0000 + 29.4449i 0.863044 + 1.49484i
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.0000 0.553470
\(396\) 0 0
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 0 0
\(403\) 12.5000 + 12.9904i 0.622669 + 0.647097i
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −13.0000 + 22.5167i −0.640464 + 1.10932i
\(413\) −3.00000 5.19615i −0.147620 0.255686i
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12.0000 20.7846i −0.586238 1.01539i −0.994720 0.102628i \(-0.967275\pi\)
0.408481 0.912767i \(-0.366058\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.500000 0.866025i −0.0241967 0.0419099i
\(428\) 36.0000 1.74013
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 0 0
\(433\) −5.50000 + 9.52628i −0.264313 + 0.457804i −0.967383 0.253317i \(-0.918479\pi\)
0.703070 + 0.711120i \(0.251812\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) −24.0000 −1.14808
\(438\) 0 0
\(439\) −5.50000 9.52628i −0.262501 0.454665i 0.704405 0.709798i \(-0.251214\pi\)
−0.966906 + 0.255134i \(0.917881\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) 0 0
\(447\) 0 0
\(448\) −4.00000 + 6.92820i −0.188982 + 0.327327i
\(449\) 3.00000 5.19615i 0.141579 0.245222i −0.786513 0.617574i \(-0.788115\pi\)
0.928091 + 0.372353i \(0.121449\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 0 0
\(454\) 0 0
\(455\) 3.50000 0.866025i 0.164083 0.0405999i
\(456\) 0 0
\(457\) 15.5000 + 26.8468i 0.725059 + 1.25584i 0.958950 + 0.283577i \(0.0915211\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −12.0000 −0.559503
\(461\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0 0
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) −12.0000 + 20.7846i −0.557086 + 0.964901i
\(465\) 0 0
\(466\) 0 0
\(467\) −42.0000 −1.94353 −0.971764 0.235954i \(-0.924178\pi\)
−0.971764 + 0.235954i \(0.924178\pi\)
\(468\) 0 0
\(469\) −11.0000 −0.507933
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −66.0000 −3.03468
\(474\) 0 0
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 2.00000 6.92820i 0.0911922 0.315899i
\(482\) 0 0
\(483\) 0 0
\(484\) 25.0000 + 43.3013i 1.13636 + 1.96824i
\(485\) −8.50000 + 14.7224i −0.385965 + 0.668511i
\(486\) 0 0
\(487\) 14.0000 24.2487i 0.634401 1.09881i −0.352241 0.935909i \(-0.614580\pi\)
0.986642 0.162905i \(-0.0520863\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15.0000 + 25.9808i 0.676941 + 1.17250i 0.975898 + 0.218229i \(0.0700279\pi\)
−0.298957 + 0.954267i \(0.596639\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −10.0000 17.3205i −0.449013 0.777714i
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) 0 0
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 0 0
\(502\) 0 0
\(503\) 21.0000 36.3731i 0.936344 1.62179i 0.164124 0.986440i \(-0.447520\pi\)
0.772220 0.635355i \(-0.219146\pi\)
\(504\) 0 0
\(505\) 3.00000 + 5.19615i 0.133498 + 0.231226i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) 2.50000 4.33013i 0.110593 0.191554i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13.0000 −0.572848
\(516\) 0 0
\(517\) −18.0000 31.1769i −0.791639 1.37116i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 36.0000 1.57719 0.788594 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) −18.0000 + 31.1769i −0.786334 + 1.36197i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 0 0
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −18.0000 + 31.1769i −0.775315 + 1.34288i
\(540\) 0 0
\(541\) −7.00000 −0.300954 −0.150477 0.988614i \(-0.548081\pi\)
−0.150477 + 0.988614i \(0.548081\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.00000 −0.299847
\(546\) 0 0
\(547\) −7.00000 −0.299298 −0.149649 0.988739i \(-0.547814\pi\)
−0.149649 + 0.988739i \(0.547814\pi\)
\(548\) −12.0000 20.7846i −0.512615 0.887875i
\(549\) 0 0
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 5.50000 9.52628i 0.233884 0.405099i
\(554\) 0 0
\(555\) 0 0
\(556\) −19.0000 32.9090i −0.805779 1.39565i
\(557\) −6.00000 10.3923i −0.254228 0.440336i 0.710457 0.703740i \(-0.248488\pi\)
−0.964686 + 0.263404i \(0.915155\pi\)
\(558\) 0 0
\(559\) −38.5000 + 9.52628i −1.62838 + 0.402919i
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 0 0
\(563\) 21.0000 36.3731i 0.885044 1.53294i 0.0393818 0.999224i \(-0.487461\pi\)
0.845663 0.533718i \(-0.179206\pi\)
\(564\) 0 0
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 30.0000 + 31.1769i 1.25436 + 1.30357i
\(573\) 0 0
\(574\) 0 0
\(575\) −3.00000 5.19615i −0.125109 0.216695i
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) −12.0000 −0.498273
\(581\) −6.00000 + 10.3923i −0.248922 + 0.431145i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.0000 + 36.3731i 0.866763 + 1.50128i 0.865286 + 0.501278i \(0.167137\pi\)
0.00147660 + 0.999999i \(0.499530\pi\)
\(588\) 0 0
\(589\) 10.0000 17.3205i 0.412043 0.713679i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −24.0000 41.5692i −0.983078 1.70274i
\(597\) 0 0
\(598\) 0 0
\(599\) −18.0000 −0.735460 −0.367730 0.929933i \(-0.619865\pi\)
−0.367730 + 0.929933i \(0.619865\pi\)
\(600\) 0 0
\(601\) −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i \(-0.988753\pi\)
0.469095 0.883148i \(-0.344580\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −16.0000 + 27.7128i −0.651031 + 1.12762i
\(605\) −12.5000 + 21.6506i −0.508197 + 0.880223i
\(606\) 0 0
\(607\) 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i \(-0.531835\pi\)
0.911621 0.411033i \(-0.134832\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 15.5885i −0.606835 0.630641i
\(612\) 0 0
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 0 0
\(619\) −19.0000 −0.763674 −0.381837 0.924230i \(-0.624709\pi\)
−0.381837 + 0.924230i \(0.624709\pi\)
\(620\) 5.00000 8.66025i 0.200805 0.347804i
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000 0.480770
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) 0 0
\(630\) 0 0
\(631\) 18.5000 32.0429i 0.736473 1.27561i −0.217601 0.976038i \(-0.569823\pi\)
0.954074 0.299571i \(-0.0968437\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.500000 + 0.866025i 0.0198419 + 0.0343672i
\(636\) 0 0
\(637\) −6.00000 + 20.7846i −0.237729 + 0.823516i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 0 0
\(643\) −5.50000 + 9.52628i −0.216899 + 0.375680i −0.953858 0.300257i \(-0.902928\pi\)
0.736959 + 0.675937i \(0.236261\pi\)
\(644\) −6.00000 + 10.3923i −0.236433 + 0.409514i
\(645\) 0 0
\(646\) 0 0
\(647\) −3.00000 5.19615i −0.117942 0.204282i 0.801010 0.598651i \(-0.204296\pi\)
−0.918952 + 0.394369i \(0.870963\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 11.0000 + 19.0526i 0.430793 + 0.746156i
\(653\) 24.0000 + 41.5692i 0.939193 + 1.62673i 0.766982 + 0.641669i \(0.221758\pi\)
0.172211 + 0.985060i \(0.444909\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) 24.5000 + 42.4352i 0.952940 + 1.65054i 0.739014 + 0.673690i \(0.235292\pi\)
0.213925 + 0.976850i \(0.431375\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.00000 3.46410i −0.0775567 0.134332i
\(666\) 0 0
\(667\) −18.0000 + 31.1769i −0.696963 + 1.20717i
\(668\) −24.0000 −0.928588
\(669\) 0 0
\(670\) 0 0
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) −5.50000 9.52628i −0.212009 0.367211i 0.740334 0.672239i \(-0.234667\pi\)
−0.952343 + 0.305028i \(0.901334\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 22.0000 + 13.8564i 0.846154 + 0.532939i
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 8.50000 + 14.7224i 0.326200 + 0.564995i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.00000 15.5885i 0.344375 0.596476i −0.640865 0.767654i \(-0.721424\pi\)
0.985240 + 0.171178i \(0.0547574\pi\)
\(684\) 0 0
\(685\) 6.00000 10.3923i 0.229248 0.397070i
\(686\) 0 0
\(687\) 0 0
\(688\) 44.0000 1.67748
\(689\) 0 0
\(690\) 0 0
\(691\) −2.50000 4.33013i −0.0951045 0.164726i 0.814548 0.580097i \(-0.196985\pi\)
−0.909652 + 0.415371i \(0.863652\pi\)
\(692\) 6.00000 + 10.3923i 0.228086 + 0.395056i
\(693\) 0 0
\(694\) 0 0
\(695\) 9.50000 16.4545i 0.360356 0.624154i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.00000 1.73205i −0.0377964 0.0654654i
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) −24.0000 41.5692i −0.904534 1.56670i
\(705\) 0 0
\(706\) 0 0
\(707\) 6.00000 0.225653
\(708\) 0 0
\(709\) 9.50000 16.4545i 0.356780 0.617961i −0.630641 0.776075i \(-0.717208\pi\)
0.987421 + 0.158114i \(0.0505412\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15.0000 25.9808i −0.561754 0.972987i
\(714\) 0 0
\(715\) −6.00000 + 20.7846i −0.224387 + 0.777300i
\(716\) −24.0000 −0.896922
\(717\) 0 0
\(718\) 0 0
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) −6.50000 + 11.2583i −0.242073 + 0.419282i
\(722\) 0 0
\(723\) 0 0
\(724\) −10.0000 + 17.3205i −0.371647 + 0.643712i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 0 0
\(727\) −25.0000 −0.927199 −0.463599 0.886045i \(-0.653442\pi\)
−0.463599 + 0.886045i \(0.653442\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 29.0000 1.07114 0.535570 0.844491i \(-0.320097\pi\)
0.535570 + 0.844491i \(0.320097\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 33.0000 57.1577i 1.21557 2.10543i
\(738\) 0 0
\(739\) −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) 0 0
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 18.0000 0.657706
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 12.0000 + 20.7846i 0.437595 + 0.757937i
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −7.00000 12.1244i −0.254419 0.440667i 0.710318 0.703881i \(-0.248551\pi\)
−0.964738 + 0.263213i \(0.915218\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) −3.50000 + 6.06218i −0.126709 + 0.219466i
\(764\) −6.00000 10.3923i −0.217072 0.375980i
\(765\) 0 0
\(766\) 0 0
\(767\) 21.0000 5.19615i 0.758266 0.187622i
\(768\) 0 0
\(769\) −19.0000 32.9090i −0.685158 1.18673i −0.973387 0.229166i \(-0.926400\pi\)
0.288230 0.957561i \(-0.406933\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 26.0000 0.935760
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 0 0
\(775\) 5.00000 0.179605
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 0 0
\(783\) 0 0
\(784\) 12.0000 20.7846i 0.428571 0.742307i
\(785\) −1.00000 −0.0356915
\(786\) 0 0
\(787\) 6.50000 11.2583i 0.231700 0.401316i −0.726609 0.687052i \(-0.758905\pi\)
0.958308 + 0.285736i \(0.0922379\pi\)
\(788\) 24.0000 0.854965
\(789\) 0 0
\(790\) 0 0
\(791\) 3.00000 + 5.19615i 0.106668 + 0.184754i
\(792\) 0 0
\(793\) 3.50000 0.866025i 0.124289 0.0307535i
\(794\) 0 0
\(795\) 0 0
\(796\) 17.0000 + 29.4449i 0.602549 + 1.04365i
\(797\) 6.00000 10.3923i 0.212531 0.368114i −0.739975 0.672634i \(-0.765163\pi\)
0.952506 + 0.304520i \(0.0984960\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.0000 + 25.9808i 0.529339 + 0.916841i
\(804\) 0 0
\(805\) −6.00000 −0.211472
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −12.0000 20.7846i −0.421898 0.730748i 0.574228 0.818696i \(-0.305302\pi\)
−0.996125 + 0.0879478i \(0.971969\pi\)
\(810\) 0 0
\(811\) 5.00000 0.175574 0.0877869 0.996139i \(-0.472021\pi\)
0.0877869 + 0.996139i \(0.472021\pi\)
\(812\) −6.00000 + 10.3923i −0.210559 + 0.364698i
\(813\) 0 0
\(814\) 0 0
\(815\) −5.50000 + 9.52628i −0.192657 + 0.333691i
\(816\) 0 0
\(817\) 22.0000 + 38.1051i 0.769683 + 1.33313i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.00000 5.19615i −0.104701 0.181347i 0.808915 0.587925i \(-0.200055\pi\)
−0.913616 + 0.406578i \(0.866722\pi\)
\(822\) 0 0
\(823\) 8.00000 13.8564i 0.278862 0.483004i −0.692240 0.721668i \(-0.743376\pi\)
0.971102 + 0.238664i \(0.0767093\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 15.5000 + 26.8468i 0.538337 + 0.932427i 0.998994 + 0.0448490i \(0.0142807\pi\)
−0.460657 + 0.887578i \(0.652386\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −20.0000 20.7846i −0.693375 0.720577i
\(833\) 0 0
\(834\) 0 0
\(835\) −6.00000 10.3923i −0.207639 0.359641i
\(836\) 24.0000 41.5692i 0.830057 1.43770i
\(837\) 0 0
\(838\) 0 0
\(839\) −9.00000 + 15.5885i −0.310715 + 0.538173i −0.978517 0.206165i \(-0.933902\pi\)
0.667803 + 0.744338i \(0.267235\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 0 0
\(843\) 0 0
\(844\) 26.0000 0.894957
\(845\) −0.500000 + 12.9904i −0.0172005 + 0.446883i
\(846\) 0 0
\(847\) 12.5000 + 21.6506i 0.429505 + 0.743925i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −6.00000 + 10.3923i −0.205677 + 0.356244i
\(852\) 0 0
\(853\) 35.0000 1.19838 0.599189 0.800608i \(-0.295490\pi\)
0.599189 + 0.800608i \(0.295490\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) −13.0000 −0.443554 −0.221777 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) 11.0000 + 19.0526i 0.375097 + 0.649687i
\(861\) 0 0
\(862\) 0 0
\(863\) 54.0000 1.83818 0.919091 0.394046i \(-0.128925\pi\)
0.919091 + 0.394046i \(0.128925\pi\)
\(864\) 0 0
\(865\) −3.00000 + 5.19615i −0.102003 + 0.176674i
\(866\) 0 0
\(867\) 0 0
\(868\) −5.00000 8.66025i −0.169711 0.293948i
\(869\) 33.0000 + 57.1577i 1.11945 + 1.93894i
\(870\) 0 0
\(871\) 11.0000 38.1051i 0.372721 1.29114i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.500000 0.866025i 0.0169031 0.0292770i
\(876\) 0 0
\(877\) 23.0000 39.8372i 0.776655 1.34521i −0.157205 0.987566i \(-0.550248\pi\)
0.933860 0.357640i \(-0.116418\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 12.0000 20.7846i 0.404520 0.700649i
\(881\) −24.0000 41.5692i −0.808581 1.40050i −0.913847 0.406059i \(-0.866903\pi\)
0.105267 0.994444i \(-0.466430\pi\)
\(882\) 0 0
\(883\) −7.00000 −0.235569 −0.117784 0.993039i \(-0.537579\pi\)
−0.117784 + 0.993039i \(0.537579\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21.0000 36.3731i −0.705111 1.22129i −0.966651 0.256096i \(-0.917564\pi\)
0.261540 0.965193i \(-0.415770\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 0 0
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) −12.0000 + 20.7846i −0.401565 + 0.695530i
\(894\) 0 0
\(895\) −6.00000 10.3923i −0.200558 0.347376i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15.0000 25.9808i −0.500278 0.866507i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.0000 −0.332411
\(906\) 0 0
\(907\) 14.0000 + 24.2487i 0.464862 + 0.805165i 0.999195 0.0401089i \(-0.0127705\pi\)
−0.534333 + 0.845274i \(0.679437\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 0 0
\(913\) −36.0000 62.3538i −1.19143 2.06361i
\(914\) 0 0
\(915\) 0 0
\(916\) 14.0000 24.2487i 0.462573 0.801200i
\(917\) −9.00000 + 15.5885i −0.297206 + 0.514776i
\(918\) 0 0
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −21.0000 + 5.19615i −0.691223 + 0.171033i
\(924\) 0 0
\(925\) −1.00000 1.73205i −0.0328798 0.0569495i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.00000 10.3923i 0.196854 0.340960i −0.750653 0.660697i \(-0.770261\pi\)
0.947507 + 0.319736i \(0.103594\pi\)
\(930\) 0 0
\(931\) 24.0000 0.786568
\(932\) 6.00000 10.3923i 0.196537 0.340411i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −6.00000 + 10.3923i −0.195698 + 0.338960i
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −24.0000 −0.781133
\(945\) 0 0
\(946\) 0 0
\(947\) −24.0000 41.5692i −0.779895 1.35082i −0.932002 0.362454i \(-0.881939\pi\)
0.152106 0.988364i \(-0.451394\pi\)
\(948\) 0 0
\(949\) 12.5000 + 12.9904i 0.405767 + 0.421686i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21.0000 + 36.3731i −0.680257 + 1.17824i 0.294646 + 0.955607i \(0.404798\pi\)
−0.974902 + 0.222633i \(0.928535\pi\)
\(954\) 0 0
\(955\) 3.00000 5.19615i 0.0970777 0.168144i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.00000 10.3923i −0.193750 0.335585i
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) 0 0
\(963\) 0 0
\(964\) −22.0000 38.1051i −0.708572 1.22728i
\(965\) 6.50000 + 11.2583i 0.209242 + 0.362418i
\(966\) 0 0
\(967\) −4.00000 −0.128631 −0.0643157 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6.00000 10.3923i 0.192549 0.333505i −0.753545 0.657396i \(-0.771658\pi\)
0.946094 + 0.323891i \(0.104991\pi\)
\(972\) 0 0
\(973\) −9.50000 16.4545i −0.304556 0.527506i
\(974\) 0 0
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) 24.0000 + 41.5692i 0.767828 + 1.32992i 0.938738 + 0.344631i \(0.111996\pi\)
−0.170910 + 0.985287i \(0.554671\pi\)
\(978\) 0 0
\(979\) −36.0000 + 62.3538i −1.15056 + 1.99284i
\(980\) 12.0000 0.383326
\(981\) 0 0
\(982\) 0 0
\(983\) 42.0000 1.33959 0.669796 0.742545i \(-0.266382\pi\)
0.669796 + 0.742545i \(0.266382\pi\)
\(984\) 0 0
\(985\) 6.00000 + 10.3923i 0.191176 + 0.331126i
\(986\) 0 0
\(987\) 0 0
\(988\) 8.00000 27.7128i 0.254514 0.881662i
\(989\) 66.0000 2.09868
\(990\) 0 0
\(991\) −16.0000 27.7128i −0.508257 0.880327i −0.999954 0.00956046i \(-0.996957\pi\)
0.491698 0.870766i \(-0.336377\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8.50000 + 14.7224i −0.269468 + 0.466732i
\(996\) 0 0
\(997\) 24.5000 42.4352i 0.775923 1.34394i −0.158352 0.987383i \(-0.550618\pi\)
0.934274 0.356555i \(-0.116049\pi\)
\(998\) 0 0
\(999\) 0 0
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 585.2.j.a.406.1 2
3.2 odd 2 195.2.i.b.16.1 2
13.3 even 3 7605.2.a.l.1.1 1
13.9 even 3 inner 585.2.j.a.451.1 2
13.10 even 6 7605.2.a.k.1.1 1
15.2 even 4 975.2.bb.b.874.1 4
15.8 even 4 975.2.bb.b.874.2 4
15.14 odd 2 975.2.i.d.601.1 2
39.23 odd 6 2535.2.a.i.1.1 1
39.29 odd 6 2535.2.a.h.1.1 1
39.35 odd 6 195.2.i.b.61.1 yes 2
195.74 odd 6 975.2.i.d.451.1 2
195.113 even 12 975.2.bb.b.724.1 4
195.152 even 12 975.2.bb.b.724.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.b.16.1 2 3.2 odd 2
195.2.i.b.61.1 yes 2 39.35 odd 6
585.2.j.a.406.1 2 1.1 even 1 trivial
585.2.j.a.451.1 2 13.9 even 3 inner
975.2.i.d.451.1 2 195.74 odd 6
975.2.i.d.601.1 2 15.14 odd 2
975.2.bb.b.724.1 4 195.113 even 12
975.2.bb.b.724.2 4 195.152 even 12
975.2.bb.b.874.1 4 15.2 even 4
975.2.bb.b.874.2 4 15.8 even 4
2535.2.a.h.1.1 1 39.29 odd 6
2535.2.a.i.1.1 1 39.23 odd 6
7605.2.a.k.1.1 1 13.10 even 6
7605.2.a.l.1.1 1 13.3 even 3