Properties

Label 2736.3.m.e.1711.9
Level $2736$
Weight $3$
Character 2736.1711
Analytic conductor $74.551$
Analytic rank $0$
Dimension $12$
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] = [2736,3,Mod(1711,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1711");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.m (of order \(2\), degree \(1\), 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: \(74.5506003290\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 2 x^{10} - 28 x^{9} - 400 x^{8} - 520 x^{7} + 17067 x^{6} - 3250 x^{5} - 195494 x^{4} + 302996 x^{3} + 602332 x^{2} - 2263536 x + 2052928 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: no (minimal twist has level 912)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1711.9
Root \(1.30395 + 1.41343i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1711
Dual form 2736.3.m.e.1711.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.08630 q^{5} -8.85163i q^{7} +O(q^{10})\) \(q+6.08630 q^{5} -8.85163i q^{7} +6.64046i q^{11} -2.95680 q^{13} -21.7835 q^{17} -4.35890i q^{19} -30.4779i q^{23} +12.0431 q^{25} +17.0059 q^{29} +58.0298i q^{31} -53.8737i q^{35} -44.3601 q^{37} +5.33039 q^{41} -50.1443i q^{43} -74.0431i q^{47} -29.3513 q^{49} -51.5148 q^{53} +40.4159i q^{55} -18.5370i q^{59} -100.168 q^{61} -17.9960 q^{65} -31.1882i q^{67} -74.3566i q^{71} -50.4741 q^{73} +58.7789 q^{77} +6.81405i q^{79} -25.6400i q^{83} -132.581 q^{85} -3.61427 q^{89} +26.1725i q^{91} -26.5296i q^{95} +140.421 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{5} + 36 q^{13} - 14 q^{17} + 10 q^{25} + 108 q^{29} - 16 q^{37} - 16 q^{41} - 118 q^{49} - 220 q^{53} + 366 q^{61} - 140 q^{65} - 158 q^{73} + 286 q^{77} + 98 q^{85} + 396 q^{89} + 224 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

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



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 0
\(4\) 0 0
\(5\) 6.08630 1.21726 0.608630 0.793454i \(-0.291719\pi\)
0.608630 + 0.793454i \(0.291719\pi\)
\(6\) 0 0
\(7\) − 8.85163i − 1.26452i −0.774757 0.632259i \(-0.782128\pi\)
0.774757 0.632259i \(-0.217872\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.64046i 0.603678i 0.953359 + 0.301839i \(0.0976005\pi\)
−0.953359 + 0.301839i \(0.902399\pi\)
\(12\) 0 0
\(13\) −2.95680 −0.227446 −0.113723 0.993512i \(-0.536278\pi\)
−0.113723 + 0.993512i \(0.536278\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −21.7835 −1.28138 −0.640691 0.767799i \(-0.721352\pi\)
−0.640691 + 0.767799i \(0.721352\pi\)
\(18\) 0 0
\(19\) − 4.35890i − 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 30.4779i − 1.32513i −0.749006 0.662563i \(-0.769469\pi\)
0.749006 0.662563i \(-0.230531\pi\)
\(24\) 0 0
\(25\) 12.0431 0.481724
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 17.0059 0.586410 0.293205 0.956050i \(-0.405278\pi\)
0.293205 + 0.956050i \(0.405278\pi\)
\(30\) 0 0
\(31\) 58.0298i 1.87193i 0.352094 + 0.935965i \(0.385470\pi\)
−0.352094 + 0.935965i \(0.614530\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 53.8737i − 1.53925i
\(36\) 0 0
\(37\) −44.3601 −1.19892 −0.599461 0.800404i \(-0.704618\pi\)
−0.599461 + 0.800404i \(0.704618\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.33039 0.130009 0.0650047 0.997885i \(-0.479294\pi\)
0.0650047 + 0.997885i \(0.479294\pi\)
\(42\) 0 0
\(43\) − 50.1443i − 1.16615i −0.812419 0.583074i \(-0.801850\pi\)
0.812419 0.583074i \(-0.198150\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 74.0431i − 1.57538i −0.616069 0.787692i \(-0.711276\pi\)
0.616069 0.787692i \(-0.288724\pi\)
\(48\) 0 0
\(49\) −29.3513 −0.599005
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −51.5148 −0.971977 −0.485988 0.873965i \(-0.661540\pi\)
−0.485988 + 0.873965i \(0.661540\pi\)
\(54\) 0 0
\(55\) 40.4159i 0.734834i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 18.5370i − 0.314187i −0.987584 0.157093i \(-0.949788\pi\)
0.987584 0.157093i \(-0.0502124\pi\)
\(60\) 0 0
\(61\) −100.168 −1.64210 −0.821048 0.570859i \(-0.806610\pi\)
−0.821048 + 0.570859i \(0.806610\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −17.9960 −0.276861
\(66\) 0 0
\(67\) − 31.1882i − 0.465495i −0.972537 0.232747i \(-0.925228\pi\)
0.972537 0.232747i \(-0.0747715\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 74.3566i − 1.04728i −0.851941 0.523638i \(-0.824574\pi\)
0.851941 0.523638i \(-0.175426\pi\)
\(72\) 0 0
\(73\) −50.4741 −0.691426 −0.345713 0.938340i \(-0.612363\pi\)
−0.345713 + 0.938340i \(0.612363\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 58.7789 0.763362
\(78\) 0 0
\(79\) 6.81405i 0.0862538i 0.999070 + 0.0431269i \(0.0137320\pi\)
−0.999070 + 0.0431269i \(0.986268\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 25.6400i − 0.308916i −0.987999 0.154458i \(-0.950637\pi\)
0.987999 0.154458i \(-0.0493632\pi\)
\(84\) 0 0
\(85\) −132.581 −1.55978
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.61427 −0.0406098 −0.0203049 0.999794i \(-0.506464\pi\)
−0.0203049 + 0.999794i \(0.506464\pi\)
\(90\) 0 0
\(91\) 26.1725i 0.287610i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) − 26.5296i − 0.279259i
\(96\) 0 0
\(97\) 140.421 1.44764 0.723819 0.689990i \(-0.242385\pi\)
0.723819 + 0.689990i \(0.242385\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −71.3972 −0.706903 −0.353451 0.935453i \(-0.614992\pi\)
−0.353451 + 0.935453i \(0.614992\pi\)
\(102\) 0 0
\(103\) 102.721i 0.997295i 0.866805 + 0.498647i \(0.166170\pi\)
−0.866805 + 0.498647i \(0.833830\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 64.9271i − 0.606796i −0.952864 0.303398i \(-0.901879\pi\)
0.952864 0.303398i \(-0.0981211\pi\)
\(108\) 0 0
\(109\) −115.572 −1.06029 −0.530145 0.847907i \(-0.677863\pi\)
−0.530145 + 0.847907i \(0.677863\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 217.263 1.92268 0.961339 0.275366i \(-0.0887991\pi\)
0.961339 + 0.275366i \(0.0887991\pi\)
\(114\) 0 0
\(115\) − 185.498i − 1.61302i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 192.819i 1.62033i
\(120\) 0 0
\(121\) 76.9043 0.635573
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −78.8596 −0.630877
\(126\) 0 0
\(127\) 17.3029i 0.136243i 0.997677 + 0.0681217i \(0.0217006\pi\)
−0.997677 + 0.0681217i \(0.978299\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 72.8478i − 0.556090i −0.960568 0.278045i \(-0.910314\pi\)
0.960568 0.278045i \(-0.0896864\pi\)
\(132\) 0 0
\(133\) −38.5833 −0.290100
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −166.375 −1.21441 −0.607207 0.794544i \(-0.707710\pi\)
−0.607207 + 0.794544i \(0.707710\pi\)
\(138\) 0 0
\(139\) 197.109i 1.41805i 0.705184 + 0.709024i \(0.250864\pi\)
−0.705184 + 0.709024i \(0.749136\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 19.6345i − 0.137304i
\(144\) 0 0
\(145\) 103.503 0.713814
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −240.667 −1.61522 −0.807608 0.589720i \(-0.799238\pi\)
−0.807608 + 0.589720i \(0.799238\pi\)
\(150\) 0 0
\(151\) 123.722i 0.819354i 0.912231 + 0.409677i \(0.134359\pi\)
−0.912231 + 0.409677i \(0.865641\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 353.187i 2.27863i
\(156\) 0 0
\(157\) 114.012 0.726194 0.363097 0.931751i \(-0.381719\pi\)
0.363097 + 0.931751i \(0.381719\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −269.779 −1.67565
\(162\) 0 0
\(163\) 227.685i 1.39684i 0.715689 + 0.698419i \(0.246113\pi\)
−0.715689 + 0.698419i \(0.753887\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 96.0499i − 0.575149i −0.957758 0.287575i \(-0.907151\pi\)
0.957758 0.287575i \(-0.0928489\pi\)
\(168\) 0 0
\(169\) −160.257 −0.948268
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 277.388 1.60340 0.801698 0.597729i \(-0.203930\pi\)
0.801698 + 0.597729i \(0.203930\pi\)
\(174\) 0 0
\(175\) − 106.601i − 0.609149i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 103.569i − 0.578600i −0.957239 0.289300i \(-0.906578\pi\)
0.957239 0.289300i \(-0.0934225\pi\)
\(180\) 0 0
\(181\) −126.631 −0.699621 −0.349810 0.936821i \(-0.613754\pi\)
−0.349810 + 0.936821i \(0.613754\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −269.989 −1.45940
\(186\) 0 0
\(187\) − 144.652i − 0.773542i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 118.419i − 0.619997i −0.950737 0.309998i \(-0.899672\pi\)
0.950737 0.309998i \(-0.100328\pi\)
\(192\) 0 0
\(193\) −179.569 −0.930412 −0.465206 0.885203i \(-0.654020\pi\)
−0.465206 + 0.885203i \(0.654020\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −185.985 −0.944088 −0.472044 0.881575i \(-0.656484\pi\)
−0.472044 + 0.881575i \(0.656484\pi\)
\(198\) 0 0
\(199\) − 11.9251i − 0.0599251i −0.999551 0.0299625i \(-0.990461\pi\)
0.999551 0.0299625i \(-0.00953880\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 150.530i − 0.741526i
\(204\) 0 0
\(205\) 32.4423 0.158255
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 28.9451 0.138493
\(210\) 0 0
\(211\) − 54.6535i − 0.259021i −0.991578 0.129511i \(-0.958659\pi\)
0.991578 0.129511i \(-0.0413406\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 305.194i − 1.41951i
\(216\) 0 0
\(217\) 513.658 2.36709
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 64.4094 0.291445
\(222\) 0 0
\(223\) − 125.844i − 0.564321i −0.959367 0.282161i \(-0.908949\pi\)
0.959367 0.282161i \(-0.0910511\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 372.784i − 1.64222i −0.570769 0.821110i \(-0.693355\pi\)
0.570769 0.821110i \(-0.306645\pi\)
\(228\) 0 0
\(229\) −14.2915 −0.0624082 −0.0312041 0.999513i \(-0.509934\pi\)
−0.0312041 + 0.999513i \(0.509934\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −19.2964 −0.0828170 −0.0414085 0.999142i \(-0.513184\pi\)
−0.0414085 + 0.999142i \(0.513184\pi\)
\(234\) 0 0
\(235\) − 450.649i − 1.91765i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 147.097i 0.615470i 0.951472 + 0.307735i \(0.0995710\pi\)
−0.951472 + 0.307735i \(0.900429\pi\)
\(240\) 0 0
\(241\) −210.083 −0.871713 −0.435857 0.900016i \(-0.643555\pi\)
−0.435857 + 0.900016i \(0.643555\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −178.641 −0.729146
\(246\) 0 0
\(247\) 12.8884i 0.0521797i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 53.6081i 0.213578i 0.994282 + 0.106789i \(0.0340570\pi\)
−0.994282 + 0.106789i \(0.965943\pi\)
\(252\) 0 0
\(253\) 202.387 0.799950
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 346.789 1.34937 0.674686 0.738105i \(-0.264279\pi\)
0.674686 + 0.738105i \(0.264279\pi\)
\(258\) 0 0
\(259\) 392.659i 1.51606i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 355.183i 1.35050i 0.737587 + 0.675252i \(0.235965\pi\)
−0.737587 + 0.675252i \(0.764035\pi\)
\(264\) 0 0
\(265\) −313.535 −1.18315
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 41.7600 0.155242 0.0776209 0.996983i \(-0.475268\pi\)
0.0776209 + 0.996983i \(0.475268\pi\)
\(270\) 0 0
\(271\) − 433.198i − 1.59852i −0.600987 0.799259i \(-0.705226\pi\)
0.600987 0.799259i \(-0.294774\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 79.9717i 0.290806i
\(276\) 0 0
\(277\) 380.398 1.37328 0.686640 0.726998i \(-0.259085\pi\)
0.686640 + 0.726998i \(0.259085\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −185.121 −0.658792 −0.329396 0.944192i \(-0.606845\pi\)
−0.329396 + 0.944192i \(0.606845\pi\)
\(282\) 0 0
\(283\) − 397.379i − 1.40417i −0.712096 0.702083i \(-0.752254\pi\)
0.712096 0.702083i \(-0.247746\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 47.1826i − 0.164399i
\(288\) 0 0
\(289\) 185.520 0.641939
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −489.006 −1.66896 −0.834480 0.551037i \(-0.814232\pi\)
−0.834480 + 0.551037i \(0.814232\pi\)
\(294\) 0 0
\(295\) − 112.822i − 0.382447i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 90.1170i 0.301395i
\(300\) 0 0
\(301\) −443.859 −1.47461
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −609.652 −1.99886
\(306\) 0 0
\(307\) 93.4725i 0.304471i 0.988344 + 0.152235i \(0.0486471\pi\)
−0.988344 + 0.152235i \(0.951353\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 214.371i − 0.689294i −0.938732 0.344647i \(-0.887999\pi\)
0.938732 0.344647i \(-0.112001\pi\)
\(312\) 0 0
\(313\) 148.994 0.476020 0.238010 0.971263i \(-0.423505\pi\)
0.238010 + 0.971263i \(0.423505\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 490.937 1.54870 0.774349 0.632759i \(-0.218077\pi\)
0.774349 + 0.632759i \(0.218077\pi\)
\(318\) 0 0
\(319\) 112.927i 0.354003i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 94.9520i 0.293969i
\(324\) 0 0
\(325\) −35.6090 −0.109566
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −655.401 −1.99210
\(330\) 0 0
\(331\) − 489.131i − 1.47774i −0.673850 0.738868i \(-0.735361\pi\)
0.673850 0.738868i \(-0.264639\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 189.821i − 0.566629i
\(336\) 0 0
\(337\) 3.82451 0.0113487 0.00567435 0.999984i \(-0.498194\pi\)
0.00567435 + 0.999984i \(0.498194\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −385.345 −1.13004
\(342\) 0 0
\(343\) − 173.923i − 0.507065i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 151.748i 0.437314i 0.975802 + 0.218657i \(0.0701676\pi\)
−0.975802 + 0.218657i \(0.929832\pi\)
\(348\) 0 0
\(349\) 12.2852 0.0352011 0.0176005 0.999845i \(-0.494397\pi\)
0.0176005 + 0.999845i \(0.494397\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.69743 0.0104743 0.00523716 0.999986i \(-0.498333\pi\)
0.00523716 + 0.999986i \(0.498333\pi\)
\(354\) 0 0
\(355\) − 452.557i − 1.27481i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 109.483i 0.304966i 0.988306 + 0.152483i \(0.0487270\pi\)
−0.988306 + 0.152483i \(0.951273\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −307.201 −0.841646
\(366\) 0 0
\(367\) − 611.742i − 1.66687i −0.552615 0.833436i \(-0.686370\pi\)
0.552615 0.833436i \(-0.313630\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 455.989i 1.22908i
\(372\) 0 0
\(373\) −670.407 −1.79734 −0.898669 0.438628i \(-0.855465\pi\)
−0.898669 + 0.438628i \(0.855465\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −50.2830 −0.133377
\(378\) 0 0
\(379\) − 187.724i − 0.495315i −0.968848 0.247658i \(-0.920339\pi\)
0.968848 0.247658i \(-0.0796608\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 190.583i − 0.497605i −0.968554 0.248803i \(-0.919963\pi\)
0.968554 0.248803i \(-0.0800370\pi\)
\(384\) 0 0
\(385\) 357.746 0.929211
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 584.136 1.50164 0.750818 0.660510i \(-0.229660\pi\)
0.750818 + 0.660510i \(0.229660\pi\)
\(390\) 0 0
\(391\) 663.915i 1.69799i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 41.4724i 0.104993i
\(396\) 0 0
\(397\) −571.136 −1.43863 −0.719315 0.694684i \(-0.755544\pi\)
−0.719315 + 0.694684i \(0.755544\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −56.0922 −0.139881 −0.0699404 0.997551i \(-0.522281\pi\)
−0.0699404 + 0.997551i \(0.522281\pi\)
\(402\) 0 0
\(403\) − 171.582i − 0.425763i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 294.572i − 0.723763i
\(408\) 0 0
\(409\) −136.122 −0.332816 −0.166408 0.986057i \(-0.553217\pi\)
−0.166408 + 0.986057i \(0.553217\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −164.083 −0.397295
\(414\) 0 0
\(415\) − 156.053i − 0.376032i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 235.462i 0.561962i 0.959713 + 0.280981i \(0.0906598\pi\)
−0.959713 + 0.280981i \(0.909340\pi\)
\(420\) 0 0
\(421\) −568.408 −1.35014 −0.675068 0.737755i \(-0.735886\pi\)
−0.675068 + 0.737755i \(0.735886\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −262.341 −0.617272
\(426\) 0 0
\(427\) 886.649i 2.07646i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 40.3202i − 0.0935504i −0.998905 0.0467752i \(-0.985106\pi\)
0.998905 0.0467752i \(-0.0148944\pi\)
\(432\) 0 0
\(433\) 122.057 0.281887 0.140943 0.990018i \(-0.454986\pi\)
0.140943 + 0.990018i \(0.454986\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −132.850 −0.304005
\(438\) 0 0
\(439\) − 701.020i − 1.59686i −0.602090 0.798428i \(-0.705665\pi\)
0.602090 0.798428i \(-0.294335\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 693.845i − 1.56624i −0.621870 0.783120i \(-0.713627\pi\)
0.621870 0.783120i \(-0.286373\pi\)
\(444\) 0 0
\(445\) −21.9976 −0.0494327
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −383.490 −0.854098 −0.427049 0.904228i \(-0.640447\pi\)
−0.427049 + 0.904228i \(0.640447\pi\)
\(450\) 0 0
\(451\) 35.3962i 0.0784838i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 159.294i 0.350096i
\(456\) 0 0
\(457\) −191.679 −0.419429 −0.209715 0.977763i \(-0.567253\pi\)
−0.209715 + 0.977763i \(0.567253\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 674.072 1.46220 0.731098 0.682272i \(-0.239008\pi\)
0.731098 + 0.682272i \(0.239008\pi\)
\(462\) 0 0
\(463\) 439.695i 0.949666i 0.880076 + 0.474833i \(0.157491\pi\)
−0.880076 + 0.474833i \(0.842509\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 221.787i 0.474920i 0.971397 + 0.237460i \(0.0763148\pi\)
−0.971397 + 0.237460i \(0.923685\pi\)
\(468\) 0 0
\(469\) −276.066 −0.588627
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 332.981 0.703978
\(474\) 0 0
\(475\) − 52.4947i − 0.110515i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 226.990i 0.473882i 0.971524 + 0.236941i \(0.0761449\pi\)
−0.971524 + 0.236941i \(0.923855\pi\)
\(480\) 0 0
\(481\) 131.164 0.272690
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 854.644 1.76215
\(486\) 0 0
\(487\) 801.415i 1.64562i 0.568319 + 0.822808i \(0.307594\pi\)
−0.568319 + 0.822808i \(0.692406\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 64.6780i − 0.131727i −0.997829 0.0658635i \(-0.979020\pi\)
0.997829 0.0658635i \(-0.0209802\pi\)
\(492\) 0 0
\(493\) −370.448 −0.751415
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −658.177 −1.32430
\(498\) 0 0
\(499\) 183.365i 0.367465i 0.982976 + 0.183732i \(0.0588180\pi\)
−0.982976 + 0.183732i \(0.941182\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 587.722i 1.16843i 0.811598 + 0.584217i \(0.198598\pi\)
−0.811598 + 0.584217i \(0.801402\pi\)
\(504\) 0 0
\(505\) −434.545 −0.860485
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 152.232 0.299080 0.149540 0.988756i \(-0.452221\pi\)
0.149540 + 0.988756i \(0.452221\pi\)
\(510\) 0 0
\(511\) 446.778i 0.874321i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 625.193i 1.21397i
\(516\) 0 0
\(517\) 491.680 0.951025
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −705.378 −1.35389 −0.676946 0.736032i \(-0.736697\pi\)
−0.676946 + 0.736032i \(0.736697\pi\)
\(522\) 0 0
\(523\) 579.461i 1.10796i 0.832531 + 0.553978i \(0.186891\pi\)
−0.832531 + 0.553978i \(0.813109\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 1264.09i − 2.39866i
\(528\) 0 0
\(529\) −399.902 −0.755959
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −15.7609 −0.0295701
\(534\) 0 0
\(535\) − 395.166i − 0.738629i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 194.906i − 0.361607i
\(540\) 0 0
\(541\) 275.470 0.509187 0.254593 0.967048i \(-0.418058\pi\)
0.254593 + 0.967048i \(0.418058\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −703.405 −1.29065
\(546\) 0 0
\(547\) 920.704i 1.68319i 0.540111 + 0.841594i \(0.318382\pi\)
−0.540111 + 0.841594i \(0.681618\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 74.1269i − 0.134532i
\(552\) 0 0
\(553\) 60.3154 0.109069
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 154.313 0.277043 0.138522 0.990359i \(-0.455765\pi\)
0.138522 + 0.990359i \(0.455765\pi\)
\(558\) 0 0
\(559\) 148.267i 0.265235i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 317.068i 0.563176i 0.959535 + 0.281588i \(0.0908611\pi\)
−0.959535 + 0.281588i \(0.909139\pi\)
\(564\) 0 0
\(565\) 1322.33 2.34040
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 420.374 0.738794 0.369397 0.929272i \(-0.379564\pi\)
0.369397 + 0.929272i \(0.379564\pi\)
\(570\) 0 0
\(571\) 426.174i 0.746364i 0.927758 + 0.373182i \(0.121733\pi\)
−0.927758 + 0.373182i \(0.878267\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 367.048i − 0.638345i
\(576\) 0 0
\(577\) 865.702 1.50035 0.750175 0.661239i \(-0.229969\pi\)
0.750175 + 0.661239i \(0.229969\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −226.956 −0.390630
\(582\) 0 0
\(583\) − 342.082i − 0.586761i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 327.570i − 0.558041i −0.960285 0.279021i \(-0.909990\pi\)
0.960285 0.279021i \(-0.0900098\pi\)
\(588\) 0 0
\(589\) 252.946 0.429450
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 250.431 0.422312 0.211156 0.977452i \(-0.432277\pi\)
0.211156 + 0.977452i \(0.432277\pi\)
\(594\) 0 0
\(595\) 1173.56i 1.97236i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 369.741i − 0.617264i −0.951182 0.308632i \(-0.900129\pi\)
0.951182 0.308632i \(-0.0998711\pi\)
\(600\) 0 0
\(601\) 1109.33 1.84581 0.922903 0.385034i \(-0.125810\pi\)
0.922903 + 0.385034i \(0.125810\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 468.063 0.773658
\(606\) 0 0
\(607\) − 1103.84i − 1.81852i −0.416228 0.909260i \(-0.636648\pi\)
0.416228 0.909260i \(-0.363352\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 218.930i 0.358315i
\(612\) 0 0
\(613\) 808.834 1.31947 0.659734 0.751499i \(-0.270669\pi\)
0.659734 + 0.751499i \(0.270669\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 681.933 1.10524 0.552620 0.833433i \(-0.313628\pi\)
0.552620 + 0.833433i \(0.313628\pi\)
\(618\) 0 0
\(619\) − 203.788i − 0.329222i −0.986359 0.164611i \(-0.947363\pi\)
0.986359 0.164611i \(-0.0526368\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 31.9922i 0.0513518i
\(624\) 0 0
\(625\) −781.041 −1.24967
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 966.318 1.53628
\(630\) 0 0
\(631\) − 51.4201i − 0.0814899i −0.999170 0.0407449i \(-0.987027\pi\)
0.999170 0.0407449i \(-0.0129731\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 105.311i 0.165844i
\(636\) 0 0
\(637\) 86.7858 0.136241
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 652.952 1.01865 0.509323 0.860576i \(-0.329896\pi\)
0.509323 + 0.860576i \(0.329896\pi\)
\(642\) 0 0
\(643\) 620.192i 0.964529i 0.876026 + 0.482264i \(0.160186\pi\)
−0.876026 + 0.482264i \(0.839814\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 510.756i − 0.789421i −0.918805 0.394711i \(-0.870845\pi\)
0.918805 0.394711i \(-0.129155\pi\)
\(648\) 0 0
\(649\) 123.094 0.189668
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1227.41 1.87964 0.939821 0.341666i \(-0.110991\pi\)
0.939821 + 0.341666i \(0.110991\pi\)
\(654\) 0 0
\(655\) − 443.374i − 0.676906i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 335.934i − 0.509763i −0.966972 0.254881i \(-0.917964\pi\)
0.966972 0.254881i \(-0.0820364\pi\)
\(660\) 0 0
\(661\) 170.169 0.257442 0.128721 0.991681i \(-0.458913\pi\)
0.128721 + 0.991681i \(0.458913\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −234.830 −0.353128
\(666\) 0 0
\(667\) − 518.304i − 0.777067i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) − 665.161i − 0.991298i
\(672\) 0 0
\(673\) −738.836 −1.09782 −0.548912 0.835880i \(-0.684958\pi\)
−0.548912 + 0.835880i \(0.684958\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −443.165 −0.654601 −0.327300 0.944920i \(-0.606139\pi\)
−0.327300 + 0.944920i \(0.606139\pi\)
\(678\) 0 0
\(679\) − 1242.95i − 1.83056i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 335.857i − 0.491738i −0.969303 0.245869i \(-0.920927\pi\)
0.969303 0.245869i \(-0.0790734\pi\)
\(684\) 0 0
\(685\) −1012.61 −1.47826
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 152.319 0.221072
\(690\) 0 0
\(691\) 818.494i 1.18451i 0.805752 + 0.592254i \(0.201762\pi\)
−0.805752 + 0.592254i \(0.798238\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1199.66i 1.72613i
\(696\) 0 0
\(697\) −116.114 −0.166592
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 601.994 0.858765 0.429383 0.903123i \(-0.358731\pi\)
0.429383 + 0.903123i \(0.358731\pi\)
\(702\) 0 0
\(703\) 193.361i 0.275052i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 631.981i 0.893891i
\(708\) 0 0
\(709\) 720.442 1.01614 0.508069 0.861316i \(-0.330359\pi\)
0.508069 + 0.861316i \(0.330359\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1768.63 2.48054
\(714\) 0 0
\(715\) − 119.502i − 0.167135i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 1106.86i − 1.53944i −0.638379 0.769722i \(-0.720395\pi\)
0.638379 0.769722i \(-0.279605\pi\)
\(720\) 0 0
\(721\) 909.251 1.26110
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 204.804 0.282488
\(726\) 0 0
\(727\) 108.860i 0.149739i 0.997193 + 0.0748696i \(0.0238541\pi\)
−0.997193 + 0.0748696i \(0.976146\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1092.32i 1.49428i
\(732\) 0 0
\(733\) −1251.06 −1.70677 −0.853385 0.521280i \(-0.825455\pi\)
−0.853385 + 0.521280i \(0.825455\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 207.104 0.281009
\(738\) 0 0
\(739\) − 246.376i − 0.333391i −0.986008 0.166696i \(-0.946690\pi\)
0.986008 0.166696i \(-0.0533098\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 160.506i − 0.216024i −0.994150 0.108012i \(-0.965551\pi\)
0.994150 0.108012i \(-0.0344486\pi\)
\(744\) 0 0
\(745\) −1464.77 −1.96614
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −574.711 −0.767304
\(750\) 0 0
\(751\) 774.408i 1.03117i 0.856839 + 0.515584i \(0.172425\pi\)
−0.856839 + 0.515584i \(0.827575\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 753.012i 0.997367i
\(756\) 0 0
\(757\) −159.858 −0.211174 −0.105587 0.994410i \(-0.533672\pi\)
−0.105587 + 0.994410i \(0.533672\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −66.4269 −0.0872889 −0.0436445 0.999047i \(-0.513897\pi\)
−0.0436445 + 0.999047i \(0.513897\pi\)
\(762\) 0 0
\(763\) 1023.00i 1.34076i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 54.8102i 0.0714605i
\(768\) 0 0
\(769\) 1469.57 1.91102 0.955509 0.294960i \(-0.0953064\pi\)
0.955509 + 0.294960i \(0.0953064\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −255.482 −0.330508 −0.165254 0.986251i \(-0.552844\pi\)
−0.165254 + 0.986251i \(0.552844\pi\)
\(774\) 0 0
\(775\) 698.859i 0.901754i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 23.2346i − 0.0298262i
\(780\) 0 0
\(781\) 493.762 0.632218
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 693.915 0.883968
\(786\) 0 0
\(787\) 640.558i 0.813923i 0.913445 + 0.406962i \(0.133412\pi\)
−0.913445 + 0.406962i \(0.866588\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 1923.13i − 2.43126i
\(792\) 0 0
\(793\) 296.176 0.373488
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 780.994 0.979917 0.489959 0.871746i \(-0.337012\pi\)
0.489959 + 0.871746i \(0.337012\pi\)
\(798\) 0 0
\(799\) 1612.92i 2.01867i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 335.171i − 0.417399i
\(804\) 0 0
\(805\) −1641.96 −2.03970
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1091.04 1.34862 0.674312 0.738446i \(-0.264440\pi\)
0.674312 + 0.738446i \(0.264440\pi\)
\(810\) 0 0
\(811\) 587.805i 0.724790i 0.932025 + 0.362395i \(0.118041\pi\)
−0.932025 + 0.362395i \(0.881959\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1385.76i 1.70032i
\(816\) 0 0
\(817\) −218.574 −0.267532
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −397.797 −0.484527 −0.242264 0.970210i \(-0.577890\pi\)
−0.242264 + 0.970210i \(0.577890\pi\)
\(822\) 0 0
\(823\) − 772.958i − 0.939195i −0.882880 0.469598i \(-0.844399\pi\)
0.882880 0.469598i \(-0.155601\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 604.655i 0.731143i 0.930783 + 0.365572i \(0.119126\pi\)
−0.930783 + 0.365572i \(0.880874\pi\)
\(828\) 0 0
\(829\) 391.614 0.472393 0.236197 0.971705i \(-0.424099\pi\)
0.236197 + 0.971705i \(0.424099\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 639.373 0.767555
\(834\) 0 0
\(835\) − 584.589i − 0.700106i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 1446.75i − 1.72437i −0.506590 0.862187i \(-0.669094\pi\)
0.506590 0.862187i \(-0.330906\pi\)
\(840\) 0 0
\(841\) −551.800 −0.656123
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −975.375 −1.15429
\(846\) 0 0
\(847\) − 680.728i − 0.803693i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1352.00i 1.58872i
\(852\) 0 0
\(853\) 77.7668 0.0911686 0.0455843 0.998960i \(-0.485485\pi\)
0.0455843 + 0.998960i \(0.485485\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1213.91 1.41646 0.708230 0.705981i \(-0.249494\pi\)
0.708230 + 0.705981i \(0.249494\pi\)
\(858\) 0 0
\(859\) − 1427.11i − 1.66136i −0.556751 0.830679i \(-0.687952\pi\)
0.556751 0.830679i \(-0.312048\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 1371.18i − 1.58885i −0.607362 0.794425i \(-0.707772\pi\)
0.607362 0.794425i \(-0.292228\pi\)
\(864\) 0 0
\(865\) 1688.27 1.95175
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −45.2484 −0.0520695
\(870\) 0 0
\(871\) 92.2171i 0.105875i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 698.036i 0.797755i
\(876\) 0 0
\(877\) 1329.39 1.51584 0.757920 0.652348i \(-0.226216\pi\)
0.757920 + 0.652348i \(0.226216\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 887.373 1.00723 0.503617 0.863927i \(-0.332002\pi\)
0.503617 + 0.863927i \(0.332002\pi\)
\(882\) 0 0
\(883\) 1238.75i 1.40288i 0.712726 + 0.701442i \(0.247460\pi\)
−0.712726 + 0.701442i \(0.752540\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 717.716i 0.809150i 0.914505 + 0.404575i \(0.132581\pi\)
−0.914505 + 0.404575i \(0.867419\pi\)
\(888\) 0 0
\(889\) 153.159 0.172282
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −322.746 −0.361418
\(894\) 0 0
\(895\) − 630.355i − 0.704307i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 986.848i 1.09772i
\(900\) 0 0
\(901\) 1122.17 1.24547
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −770.717 −0.851621
\(906\) 0 0
\(907\) − 484.018i − 0.533647i −0.963745 0.266824i \(-0.914026\pi\)
0.963745 0.266824i \(-0.0859741\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1391.42i 1.52736i 0.645595 + 0.763680i \(0.276609\pi\)
−0.645595 + 0.763680i \(0.723391\pi\)
\(912\) 0 0
\(913\) 170.262 0.186486
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −644.821 −0.703186
\(918\) 0 0
\(919\) − 50.4361i − 0.0548815i −0.999623 0.0274407i \(-0.991264\pi\)
0.999623 0.0274407i \(-0.00873576\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 219.857i 0.238199i
\(924\) 0 0
\(925\) −534.233 −0.577550
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −783.700 −0.843595 −0.421798 0.906690i \(-0.638601\pi\)
−0.421798 + 0.906690i \(0.638601\pi\)
\(930\) 0 0
\(931\) 127.939i 0.137421i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 880.398i − 0.941603i
\(936\) 0 0
\(937\) −50.8290 −0.0542465 −0.0271233 0.999632i \(-0.508635\pi\)
−0.0271233 + 0.999632i \(0.508635\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1572.18 −1.67076 −0.835380 0.549673i \(-0.814752\pi\)
−0.835380 + 0.549673i \(0.814752\pi\)
\(942\) 0 0
\(943\) − 162.459i − 0.172279i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 81.5277i 0.0860905i 0.999073 + 0.0430453i \(0.0137060\pi\)
−0.999073 + 0.0430453i \(0.986294\pi\)
\(948\) 0 0
\(949\) 149.242 0.157262
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1153.28 1.21016 0.605079 0.796165i \(-0.293141\pi\)
0.605079 + 0.796165i \(0.293141\pi\)
\(954\) 0 0
\(955\) − 720.736i − 0.754698i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1472.69i 1.53565i
\(960\) 0 0
\(961\) −2406.46 −2.50412
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1092.91 −1.13255
\(966\) 0 0
\(967\) − 889.643i − 0.920003i −0.887918 0.460001i \(-0.847849\pi\)
0.887918 0.460001i \(-0.152151\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1664.80i 1.71452i 0.514882 + 0.857261i \(0.327836\pi\)
−0.514882 + 0.857261i \(0.672164\pi\)
\(972\) 0 0
\(973\) 1744.73 1.79315
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1362.00 1.39406 0.697030 0.717042i \(-0.254504\pi\)
0.697030 + 0.717042i \(0.254504\pi\)
\(978\) 0 0
\(979\) − 24.0004i − 0.0245152i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 1173.24i − 1.19353i −0.802415 0.596766i \(-0.796452\pi\)
0.802415 0.596766i \(-0.203548\pi\)
\(984\) 0 0
\(985\) −1131.96 −1.14920
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1528.29 −1.54529
\(990\) 0 0
\(991\) 797.134i 0.804373i 0.915558 + 0.402186i \(0.131750\pi\)
−0.915558 + 0.402186i \(0.868250\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 72.5797i − 0.0729444i
\(996\) 0 0
\(997\) −1534.22 −1.53884 −0.769419 0.638744i \(-0.779454\pi\)
−0.769419 + 0.638744i \(0.779454\pi\)
\(998\) 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 2736.3.m.e.1711.9 12
3.2 odd 2 912.3.m.b.799.8 yes 12
4.3 odd 2 inner 2736.3.m.e.1711.10 12
12.11 even 2 912.3.m.b.799.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
912.3.m.b.799.2 12 12.11 even 2
912.3.m.b.799.8 yes 12 3.2 odd 2
2736.3.m.e.1711.9 12 1.1 even 1 trivial
2736.3.m.e.1711.10 12 4.3 odd 2 inner