Properties

Label 6012.2.a.h.1.4
Level $6012$
Weight $2$
Character 6012.1
Self dual yes
Analytic conductor $48.006$
Analytic rank $1$
Dimension $9$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6012,2,Mod(1,6012)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6012.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

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: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.907808\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.90781 q^{5} +2.81337 q^{7} +O(q^{10})\) \(q-1.90781 q^{5} +2.81337 q^{7} -0.318882 q^{11} +5.12583 q^{13} -3.73184 q^{17} -0.725453 q^{19} -0.612463 q^{23} -1.36027 q^{25} +3.87979 q^{29} -6.65817 q^{31} -5.36737 q^{35} -9.04643 q^{37} -9.55805 q^{41} -10.9328 q^{43} -8.76460 q^{47} +0.915046 q^{49} +2.46673 q^{53} +0.608366 q^{55} +11.0871 q^{59} +12.5460 q^{61} -9.77910 q^{65} +5.21723 q^{67} +11.3217 q^{71} +2.88490 q^{73} -0.897133 q^{77} +8.98655 q^{79} -4.04802 q^{83} +7.11963 q^{85} +9.15294 q^{89} +14.4208 q^{91} +1.38402 q^{95} -9.62101 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 9 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 9 q^{5} + 2 q^{7} - 7 q^{11} + 6 q^{13} - 7 q^{17} + 2 q^{19} - 19 q^{23} + 22 q^{25} - 13 q^{29} + 12 q^{31} - 4 q^{35} + 15 q^{37} - 18 q^{41} - 6 q^{43} - 25 q^{47} + 19 q^{49} - 17 q^{53} - 3 q^{55} - 3 q^{59} + 14 q^{61} - 14 q^{65} - 4 q^{67} - 17 q^{71} - 20 q^{73} - 14 q^{77} - 8 q^{79} + q^{83} + 5 q^{85} - 36 q^{89} - 41 q^{91} - 5 q^{95} + 31 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −1.90781 −0.853198 −0.426599 0.904441i \(-0.640288\pi\)
−0.426599 + 0.904441i \(0.640288\pi\)
\(6\) 0 0
\(7\) 2.81337 1.06335 0.531677 0.846947i \(-0.321562\pi\)
0.531677 + 0.846947i \(0.321562\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.318882 −0.0961466 −0.0480733 0.998844i \(-0.515308\pi\)
−0.0480733 + 0.998844i \(0.515308\pi\)
\(12\) 0 0
\(13\) 5.12583 1.42165 0.710824 0.703370i \(-0.248322\pi\)
0.710824 + 0.703370i \(0.248322\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.73184 −0.905104 −0.452552 0.891738i \(-0.649486\pi\)
−0.452552 + 0.891738i \(0.649486\pi\)
\(18\) 0 0
\(19\) −0.725453 −0.166430 −0.0832151 0.996532i \(-0.526519\pi\)
−0.0832151 + 0.996532i \(0.526519\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.612463 −0.127707 −0.0638537 0.997959i \(-0.520339\pi\)
−0.0638537 + 0.997959i \(0.520339\pi\)
\(24\) 0 0
\(25\) −1.36027 −0.272053
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.87979 0.720459 0.360229 0.932864i \(-0.382698\pi\)
0.360229 + 0.932864i \(0.382698\pi\)
\(30\) 0 0
\(31\) −6.65817 −1.19584 −0.597922 0.801554i \(-0.704007\pi\)
−0.597922 + 0.801554i \(0.704007\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5.36737 −0.907251
\(36\) 0 0
\(37\) −9.04643 −1.48722 −0.743612 0.668612i \(-0.766889\pi\)
−0.743612 + 0.668612i \(0.766889\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.55805 −1.49272 −0.746358 0.665545i \(-0.768199\pi\)
−0.746358 + 0.665545i \(0.768199\pi\)
\(42\) 0 0
\(43\) −10.9328 −1.66724 −0.833620 0.552338i \(-0.813736\pi\)
−0.833620 + 0.552338i \(0.813736\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.76460 −1.27845 −0.639224 0.769020i \(-0.720744\pi\)
−0.639224 + 0.769020i \(0.720744\pi\)
\(48\) 0 0
\(49\) 0.915046 0.130721
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.46673 0.338831 0.169416 0.985545i \(-0.445812\pi\)
0.169416 + 0.985545i \(0.445812\pi\)
\(54\) 0 0
\(55\) 0.608366 0.0820321
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.0871 1.44341 0.721706 0.692200i \(-0.243358\pi\)
0.721706 + 0.692200i \(0.243358\pi\)
\(60\) 0 0
\(61\) 12.5460 1.60636 0.803178 0.595739i \(-0.203141\pi\)
0.803178 + 0.595739i \(0.203141\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.77910 −1.21295
\(66\) 0 0
\(67\) 5.21723 0.637387 0.318693 0.947858i \(-0.396756\pi\)
0.318693 + 0.947858i \(0.396756\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.3217 1.34363 0.671816 0.740718i \(-0.265514\pi\)
0.671816 + 0.740718i \(0.265514\pi\)
\(72\) 0 0
\(73\) 2.88490 0.337652 0.168826 0.985646i \(-0.446002\pi\)
0.168826 + 0.985646i \(0.446002\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.897133 −0.102238
\(78\) 0 0
\(79\) 8.98655 1.01107 0.505533 0.862807i \(-0.331296\pi\)
0.505533 + 0.862807i \(0.331296\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.04802 −0.444327 −0.222164 0.975009i \(-0.571312\pi\)
−0.222164 + 0.975009i \(0.571312\pi\)
\(84\) 0 0
\(85\) 7.11963 0.772233
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.15294 0.970210 0.485105 0.874456i \(-0.338781\pi\)
0.485105 + 0.874456i \(0.338781\pi\)
\(90\) 0 0
\(91\) 14.4208 1.51172
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.38402 0.141998
\(96\) 0 0
\(97\) −9.62101 −0.976866 −0.488433 0.872601i \(-0.662431\pi\)
−0.488433 + 0.872601i \(0.662431\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.2834 1.32175 0.660875 0.750496i \(-0.270185\pi\)
0.660875 + 0.750496i \(0.270185\pi\)
\(102\) 0 0
\(103\) −18.4226 −1.81523 −0.907616 0.419802i \(-0.862099\pi\)
−0.907616 + 0.419802i \(0.862099\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.8365 −1.14428 −0.572139 0.820157i \(-0.693886\pi\)
−0.572139 + 0.820157i \(0.693886\pi\)
\(108\) 0 0
\(109\) −2.94111 −0.281708 −0.140854 0.990030i \(-0.544985\pi\)
−0.140854 + 0.990030i \(0.544985\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.9782 −1.59718 −0.798588 0.601878i \(-0.794419\pi\)
−0.798588 + 0.601878i \(0.794419\pi\)
\(114\) 0 0
\(115\) 1.16846 0.108960
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.4990 −0.962445
\(120\) 0 0
\(121\) −10.8983 −0.990756
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1342 1.08531
\(126\) 0 0
\(127\) 16.7091 1.48269 0.741345 0.671124i \(-0.234188\pi\)
0.741345 + 0.671124i \(0.234188\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.146536 0.0128029 0.00640144 0.999980i \(-0.497962\pi\)
0.00640144 + 0.999980i \(0.497962\pi\)
\(132\) 0 0
\(133\) −2.04097 −0.176974
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.7309 −1.00224 −0.501120 0.865378i \(-0.667078\pi\)
−0.501120 + 0.865378i \(0.667078\pi\)
\(138\) 0 0
\(139\) −9.09999 −0.771851 −0.385926 0.922530i \(-0.626118\pi\)
−0.385926 + 0.922530i \(0.626118\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.63454 −0.136687
\(144\) 0 0
\(145\) −7.40189 −0.614694
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −23.3492 −1.91284 −0.956422 0.291988i \(-0.905683\pi\)
−0.956422 + 0.291988i \(0.905683\pi\)
\(150\) 0 0
\(151\) −0.859951 −0.0699818 −0.0349909 0.999388i \(-0.511140\pi\)
−0.0349909 + 0.999388i \(0.511140\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 12.7025 1.02029
\(156\) 0 0
\(157\) −6.36080 −0.507647 −0.253824 0.967251i \(-0.581688\pi\)
−0.253824 + 0.967251i \(0.581688\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.72309 −0.135798
\(162\) 0 0
\(163\) −0.722678 −0.0566045 −0.0283023 0.999599i \(-0.509010\pi\)
−0.0283023 + 0.999599i \(0.509010\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 13.2741 1.02109
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −16.1210 −1.22566 −0.612829 0.790216i \(-0.709968\pi\)
−0.612829 + 0.790216i \(0.709968\pi\)
\(174\) 0 0
\(175\) −3.82693 −0.289289
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −11.5480 −0.863137 −0.431569 0.902080i \(-0.642040\pi\)
−0.431569 + 0.902080i \(0.642040\pi\)
\(180\) 0 0
\(181\) −3.91786 −0.291212 −0.145606 0.989343i \(-0.546513\pi\)
−0.145606 + 0.989343i \(0.546513\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 17.2588 1.26890
\(186\) 0 0
\(187\) 1.19002 0.0870226
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 19.5571 1.41510 0.707549 0.706664i \(-0.249801\pi\)
0.707549 + 0.706664i \(0.249801\pi\)
\(192\) 0 0
\(193\) 22.0005 1.58363 0.791814 0.610762i \(-0.209137\pi\)
0.791814 + 0.610762i \(0.209137\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.3862 −0.739989 −0.369995 0.929034i \(-0.620640\pi\)
−0.369995 + 0.929034i \(0.620640\pi\)
\(198\) 0 0
\(199\) −17.3380 −1.22906 −0.614528 0.788895i \(-0.710653\pi\)
−0.614528 + 0.788895i \(0.710653\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.9153 0.766102
\(204\) 0 0
\(205\) 18.2349 1.27358
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.231334 0.0160017
\(210\) 0 0
\(211\) −20.2222 −1.39216 −0.696078 0.717966i \(-0.745073\pi\)
−0.696078 + 0.717966i \(0.745073\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 20.8577 1.42249
\(216\) 0 0
\(217\) −18.7319 −1.27160
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −19.1288 −1.28674
\(222\) 0 0
\(223\) 9.60888 0.643458 0.321729 0.946832i \(-0.395736\pi\)
0.321729 + 0.946832i \(0.395736\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.3573 −1.55028 −0.775140 0.631790i \(-0.782321\pi\)
−0.775140 + 0.631790i \(0.782321\pi\)
\(228\) 0 0
\(229\) −14.5969 −0.964591 −0.482296 0.876008i \(-0.660197\pi\)
−0.482296 + 0.876008i \(0.660197\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0225 −1.18069 −0.590345 0.807151i \(-0.701008\pi\)
−0.590345 + 0.807151i \(0.701008\pi\)
\(234\) 0 0
\(235\) 16.7212 1.09077
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.44595 0.611007 0.305504 0.952191i \(-0.401175\pi\)
0.305504 + 0.952191i \(0.401175\pi\)
\(240\) 0 0
\(241\) 5.88509 0.379092 0.189546 0.981872i \(-0.439298\pi\)
0.189546 + 0.981872i \(0.439298\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.74573 −0.111531
\(246\) 0 0
\(247\) −3.71854 −0.236605
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.14251 −0.198353 −0.0991767 0.995070i \(-0.531621\pi\)
−0.0991767 + 0.995070i \(0.531621\pi\)
\(252\) 0 0
\(253\) 0.195304 0.0122786
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.52800 −0.0953142 −0.0476571 0.998864i \(-0.515175\pi\)
−0.0476571 + 0.998864i \(0.515175\pi\)
\(258\) 0 0
\(259\) −25.4509 −1.58144
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.3283 1.50015 0.750075 0.661353i \(-0.230017\pi\)
0.750075 + 0.661353i \(0.230017\pi\)
\(264\) 0 0
\(265\) −4.70604 −0.289090
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.163618 −0.00997594 −0.00498797 0.999988i \(-0.501588\pi\)
−0.00498797 + 0.999988i \(0.501588\pi\)
\(270\) 0 0
\(271\) −8.88391 −0.539659 −0.269829 0.962908i \(-0.586967\pi\)
−0.269829 + 0.962908i \(0.586967\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.433765 0.0261570
\(276\) 0 0
\(277\) −5.45934 −0.328020 −0.164010 0.986459i \(-0.552443\pi\)
−0.164010 + 0.986459i \(0.552443\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.18240 0.488121 0.244061 0.969760i \(-0.421520\pi\)
0.244061 + 0.969760i \(0.421520\pi\)
\(282\) 0 0
\(283\) 9.17416 0.545347 0.272674 0.962107i \(-0.412092\pi\)
0.272674 + 0.962107i \(0.412092\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −26.8903 −1.58728
\(288\) 0 0
\(289\) −3.07338 −0.180787
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 30.6446 1.79027 0.895137 0.445790i \(-0.147077\pi\)
0.895137 + 0.445790i \(0.147077\pi\)
\(294\) 0 0
\(295\) −21.1520 −1.23152
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.13938 −0.181555
\(300\) 0 0
\(301\) −30.7581 −1.77287
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −23.9354 −1.37054
\(306\) 0 0
\(307\) −25.0225 −1.42811 −0.714055 0.700090i \(-0.753143\pi\)
−0.714055 + 0.700090i \(0.753143\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −26.4473 −1.49969 −0.749845 0.661613i \(-0.769872\pi\)
−0.749845 + 0.661613i \(0.769872\pi\)
\(312\) 0 0
\(313\) 22.3927 1.26571 0.632854 0.774271i \(-0.281883\pi\)
0.632854 + 0.774271i \(0.281883\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.1684 −1.35743 −0.678717 0.734400i \(-0.737464\pi\)
−0.678717 + 0.734400i \(0.737464\pi\)
\(318\) 0 0
\(319\) −1.23720 −0.0692697
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.70727 0.150637
\(324\) 0 0
\(325\) −6.97249 −0.386764
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −24.6581 −1.35944
\(330\) 0 0
\(331\) −28.8009 −1.58304 −0.791521 0.611142i \(-0.790710\pi\)
−0.791521 + 0.611142i \(0.790710\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −9.95348 −0.543817
\(336\) 0 0
\(337\) −2.40083 −0.130782 −0.0653909 0.997860i \(-0.520829\pi\)
−0.0653909 + 0.997860i \(0.520829\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.12317 0.114976
\(342\) 0 0
\(343\) −17.1192 −0.924351
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.3977 1.04132 0.520662 0.853763i \(-0.325685\pi\)
0.520662 + 0.853763i \(0.325685\pi\)
\(348\) 0 0
\(349\) −36.7633 −1.96789 −0.983947 0.178462i \(-0.942888\pi\)
−0.983947 + 0.178462i \(0.942888\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.4854 1.35645 0.678226 0.734853i \(-0.262749\pi\)
0.678226 + 0.734853i \(0.262749\pi\)
\(354\) 0 0
\(355\) −21.5995 −1.14638
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.51148 0.396441 0.198220 0.980157i \(-0.436484\pi\)
0.198220 + 0.980157i \(0.436484\pi\)
\(360\) 0 0
\(361\) −18.4737 −0.972301
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.50384 −0.288084
\(366\) 0 0
\(367\) 15.8402 0.826853 0.413426 0.910537i \(-0.364332\pi\)
0.413426 + 0.910537i \(0.364332\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.93981 0.360297
\(372\) 0 0
\(373\) 34.3907 1.78068 0.890340 0.455296i \(-0.150466\pi\)
0.890340 + 0.455296i \(0.150466\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 19.8871 1.02424
\(378\) 0 0
\(379\) −13.6557 −0.701448 −0.350724 0.936479i \(-0.614064\pi\)
−0.350724 + 0.936479i \(0.614064\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.8238 −0.655263 −0.327632 0.944806i \(-0.606250\pi\)
−0.327632 + 0.944806i \(0.606250\pi\)
\(384\) 0 0
\(385\) 1.71156 0.0872291
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.34694 0.0682925 0.0341462 0.999417i \(-0.489129\pi\)
0.0341462 + 0.999417i \(0.489129\pi\)
\(390\) 0 0
\(391\) 2.28561 0.115588
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −17.1446 −0.862639
\(396\) 0 0
\(397\) 9.21493 0.462484 0.231242 0.972896i \(-0.425721\pi\)
0.231242 + 0.972896i \(0.425721\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.28032 −0.263686 −0.131843 0.991271i \(-0.542090\pi\)
−0.131843 + 0.991271i \(0.542090\pi\)
\(402\) 0 0
\(403\) −34.1287 −1.70007
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.88474 0.142991
\(408\) 0 0
\(409\) 36.9707 1.82808 0.914042 0.405619i \(-0.132944\pi\)
0.914042 + 0.405619i \(0.132944\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 31.1920 1.53486
\(414\) 0 0
\(415\) 7.72284 0.379099
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.2542 0.598655 0.299328 0.954150i \(-0.403238\pi\)
0.299328 + 0.954150i \(0.403238\pi\)
\(420\) 0 0
\(421\) 33.4130 1.62845 0.814225 0.580550i \(-0.197162\pi\)
0.814225 + 0.580550i \(0.197162\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.07630 0.246237
\(426\) 0 0
\(427\) 35.2966 1.70812
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.5835 0.750632 0.375316 0.926897i \(-0.377534\pi\)
0.375316 + 0.926897i \(0.377534\pi\)
\(432\) 0 0
\(433\) −14.5888 −0.701095 −0.350547 0.936545i \(-0.614004\pi\)
−0.350547 + 0.936545i \(0.614004\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.444313 0.0212544
\(438\) 0 0
\(439\) 0.127708 0.00609515 0.00304758 0.999995i \(-0.499030\pi\)
0.00304758 + 0.999995i \(0.499030\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.30938 −0.0622103 −0.0311052 0.999516i \(-0.509903\pi\)
−0.0311052 + 0.999516i \(0.509903\pi\)
\(444\) 0 0
\(445\) −17.4621 −0.827781
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.999933 0.0471898 0.0235949 0.999722i \(-0.492489\pi\)
0.0235949 + 0.999722i \(0.492489\pi\)
\(450\) 0 0
\(451\) 3.04789 0.143520
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −27.5122 −1.28979
\(456\) 0 0
\(457\) −22.5930 −1.05686 −0.528429 0.848977i \(-0.677219\pi\)
−0.528429 + 0.848977i \(0.677219\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.4897 −0.768002 −0.384001 0.923333i \(-0.625454\pi\)
−0.384001 + 0.923333i \(0.625454\pi\)
\(462\) 0 0
\(463\) 11.7668 0.546850 0.273425 0.961893i \(-0.411843\pi\)
0.273425 + 0.961893i \(0.411843\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 24.6075 1.13870 0.569349 0.822096i \(-0.307195\pi\)
0.569349 + 0.822096i \(0.307195\pi\)
\(468\) 0 0
\(469\) 14.6780 0.677767
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.48629 0.160300
\(474\) 0 0
\(475\) 0.986809 0.0452779
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.30934 0.0598252 0.0299126 0.999553i \(-0.490477\pi\)
0.0299126 + 0.999553i \(0.490477\pi\)
\(480\) 0 0
\(481\) −46.3704 −2.11431
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18.3550 0.833460
\(486\) 0 0
\(487\) 2.87718 0.130377 0.0651886 0.997873i \(-0.479235\pi\)
0.0651886 + 0.997873i \(0.479235\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.52068 0.113757 0.0568783 0.998381i \(-0.481885\pi\)
0.0568783 + 0.998381i \(0.481885\pi\)
\(492\) 0 0
\(493\) −14.4787 −0.652090
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 31.8520 1.42876
\(498\) 0 0
\(499\) −10.9276 −0.489185 −0.244592 0.969626i \(-0.578654\pi\)
−0.244592 + 0.969626i \(0.578654\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.15303 −0.185175 −0.0925873 0.995705i \(-0.529514\pi\)
−0.0925873 + 0.995705i \(0.529514\pi\)
\(504\) 0 0
\(505\) −25.3422 −1.12771
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.73062 −0.386978 −0.193489 0.981102i \(-0.561980\pi\)
−0.193489 + 0.981102i \(0.561980\pi\)
\(510\) 0 0
\(511\) 8.11629 0.359044
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 35.1468 1.54875
\(516\) 0 0
\(517\) 2.79488 0.122918
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −23.9413 −1.04889 −0.524444 0.851445i \(-0.675727\pi\)
−0.524444 + 0.851445i \(0.675727\pi\)
\(522\) 0 0
\(523\) −37.1193 −1.62311 −0.811557 0.584273i \(-0.801380\pi\)
−0.811557 + 0.584273i \(0.801380\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.8472 1.08236
\(528\) 0 0
\(529\) −22.6249 −0.983691
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −48.9929 −2.12212
\(534\) 0 0
\(535\) 22.5818 0.976295
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.291792 −0.0125684
\(540\) 0 0
\(541\) 33.9215 1.45840 0.729199 0.684302i \(-0.239893\pi\)
0.729199 + 0.684302i \(0.239893\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.61108 0.240352
\(546\) 0 0
\(547\) −16.6850 −0.713397 −0.356699 0.934219i \(-0.616098\pi\)
−0.356699 + 0.934219i \(0.616098\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.81460 −0.119906
\(552\) 0 0
\(553\) 25.2825 1.07512
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.4280 −1.28928 −0.644638 0.764488i \(-0.722992\pi\)
−0.644638 + 0.764488i \(0.722992\pi\)
\(558\) 0 0
\(559\) −56.0398 −2.37023
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 32.0419 1.35041 0.675203 0.737632i \(-0.264056\pi\)
0.675203 + 0.737632i \(0.264056\pi\)
\(564\) 0 0
\(565\) 32.3912 1.36271
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.2824 1.14374 0.571869 0.820345i \(-0.306218\pi\)
0.571869 + 0.820345i \(0.306218\pi\)
\(570\) 0 0
\(571\) −12.3064 −0.515007 −0.257503 0.966277i \(-0.582900\pi\)
−0.257503 + 0.966277i \(0.582900\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.833113 0.0347432
\(576\) 0 0
\(577\) 4.05674 0.168884 0.0844422 0.996428i \(-0.473089\pi\)
0.0844422 + 0.996428i \(0.473089\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.3886 −0.472477
\(582\) 0 0
\(583\) −0.786596 −0.0325775
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.5748 0.890489 0.445244 0.895409i \(-0.353117\pi\)
0.445244 + 0.895409i \(0.353117\pi\)
\(588\) 0 0
\(589\) 4.83019 0.199025
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.81937 0.238973 0.119486 0.992836i \(-0.461875\pi\)
0.119486 + 0.992836i \(0.461875\pi\)
\(594\) 0 0
\(595\) 20.0302 0.821156
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 14.0478 0.573978 0.286989 0.957934i \(-0.407346\pi\)
0.286989 + 0.957934i \(0.407346\pi\)
\(600\) 0 0
\(601\) 26.3024 1.07290 0.536448 0.843933i \(-0.319766\pi\)
0.536448 + 0.843933i \(0.319766\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.7919 0.845311
\(606\) 0 0
\(607\) 16.2583 0.659906 0.329953 0.943997i \(-0.392967\pi\)
0.329953 + 0.943997i \(0.392967\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −44.9258 −1.81750
\(612\) 0 0
\(613\) −10.3724 −0.418936 −0.209468 0.977816i \(-0.567173\pi\)
−0.209468 + 0.977816i \(0.567173\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 33.0424 1.33024 0.665118 0.746738i \(-0.268381\pi\)
0.665118 + 0.746738i \(0.268381\pi\)
\(618\) 0 0
\(619\) −5.92967 −0.238334 −0.119167 0.992874i \(-0.538022\pi\)
−0.119167 + 0.992874i \(0.538022\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 25.7506 1.03168
\(624\) 0 0
\(625\) −16.3483 −0.653934
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 33.7598 1.34609
\(630\) 0 0
\(631\) −35.5703 −1.41603 −0.708016 0.706196i \(-0.750410\pi\)
−0.708016 + 0.706196i \(0.750410\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −31.8777 −1.26503
\(636\) 0 0
\(637\) 4.69037 0.185839
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.75263 0.0692248 0.0346124 0.999401i \(-0.488980\pi\)
0.0346124 + 0.999401i \(0.488980\pi\)
\(642\) 0 0
\(643\) −44.6647 −1.76140 −0.880701 0.473672i \(-0.842928\pi\)
−0.880701 + 0.473672i \(0.842928\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.7568 −0.658776 −0.329388 0.944195i \(-0.606842\pi\)
−0.329388 + 0.944195i \(0.606842\pi\)
\(648\) 0 0
\(649\) −3.53547 −0.138779
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 29.8135 1.16669 0.583346 0.812224i \(-0.301743\pi\)
0.583346 + 0.812224i \(0.301743\pi\)
\(654\) 0 0
\(655\) −0.279562 −0.0109234
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −40.4834 −1.57701 −0.788504 0.615030i \(-0.789144\pi\)
−0.788504 + 0.615030i \(0.789144\pi\)
\(660\) 0 0
\(661\) 16.4694 0.640586 0.320293 0.947319i \(-0.396219\pi\)
0.320293 + 0.947319i \(0.396219\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.89377 0.150994
\(666\) 0 0
\(667\) −2.37623 −0.0920079
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00071 −0.154446
\(672\) 0 0
\(673\) 7.04173 0.271439 0.135719 0.990747i \(-0.456665\pi\)
0.135719 + 0.990747i \(0.456665\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.0327 −0.500888 −0.250444 0.968131i \(-0.580577\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(678\) 0 0
\(679\) −27.0675 −1.03875
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −44.8287 −1.71532 −0.857661 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(684\) 0 0
\(685\) 22.3803 0.855109
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12.6440 0.481699
\(690\) 0 0
\(691\) −10.2680 −0.390611 −0.195306 0.980742i \(-0.562570\pi\)
−0.195306 + 0.980742i \(0.562570\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17.3610 0.658542
\(696\) 0 0
\(697\) 35.6691 1.35106
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −29.6121 −1.11843 −0.559217 0.829021i \(-0.688898\pi\)
−0.559217 + 0.829021i \(0.688898\pi\)
\(702\) 0 0
\(703\) 6.56275 0.247519
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 37.3712 1.40549
\(708\) 0 0
\(709\) 29.7383 1.11685 0.558423 0.829556i \(-0.311406\pi\)
0.558423 + 0.829556i \(0.311406\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.07789 0.152718
\(714\) 0 0
\(715\) 3.11838 0.116621
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.84535 −0.0688200 −0.0344100 0.999408i \(-0.510955\pi\)
−0.0344100 + 0.999408i \(0.510955\pi\)
\(720\) 0 0
\(721\) −51.8295 −1.93023
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.27755 −0.196003
\(726\) 0 0
\(727\) 34.6845 1.28638 0.643189 0.765708i \(-0.277611\pi\)
0.643189 + 0.765708i \(0.277611\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 40.7996 1.50903
\(732\) 0 0
\(733\) −27.7444 −1.02476 −0.512381 0.858758i \(-0.671236\pi\)
−0.512381 + 0.858758i \(0.671236\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.66368 −0.0612826
\(738\) 0 0
\(739\) 3.98690 0.146660 0.0733302 0.997308i \(-0.476637\pi\)
0.0733302 + 0.997308i \(0.476637\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29.3305 −1.07603 −0.538016 0.842935i \(-0.680826\pi\)
−0.538016 + 0.842935i \(0.680826\pi\)
\(744\) 0 0
\(745\) 44.5459 1.63203
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −33.3004 −1.21677
\(750\) 0 0
\(751\) 17.0963 0.623851 0.311926 0.950107i \(-0.399026\pi\)
0.311926 + 0.950107i \(0.399026\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.64062 0.0597083
\(756\) 0 0
\(757\) −16.8059 −0.610819 −0.305410 0.952221i \(-0.598793\pi\)
−0.305410 + 0.952221i \(0.598793\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.1343 1.20112 0.600559 0.799580i \(-0.294945\pi\)
0.600559 + 0.799580i \(0.294945\pi\)
\(762\) 0 0
\(763\) −8.27444 −0.299555
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 56.8303 2.05202
\(768\) 0 0
\(769\) 46.8068 1.68790 0.843949 0.536424i \(-0.180225\pi\)
0.843949 + 0.536424i \(0.180225\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.5866 1.31593 0.657963 0.753050i \(-0.271418\pi\)
0.657963 + 0.753050i \(0.271418\pi\)
\(774\) 0 0
\(775\) 9.05690 0.325333
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.93391 0.248433
\(780\) 0 0
\(781\) −3.61027 −0.129186
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 12.1352 0.433124
\(786\) 0 0
\(787\) −47.3781 −1.68885 −0.844423 0.535677i \(-0.820057\pi\)
−0.844423 + 0.535677i \(0.820057\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −47.7660 −1.69836
\(792\) 0 0
\(793\) 64.3088 2.28367
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.4164 −1.64415 −0.822077 0.569376i \(-0.807185\pi\)
−0.822077 + 0.569376i \(0.807185\pi\)
\(798\) 0 0
\(799\) 32.7081 1.15713
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.919944 −0.0324641
\(804\) 0 0
\(805\) 3.28732 0.115863
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 36.9134 1.29781 0.648903 0.760871i \(-0.275228\pi\)
0.648903 + 0.760871i \(0.275228\pi\)
\(810\) 0 0
\(811\) 7.35245 0.258179 0.129090 0.991633i \(-0.458794\pi\)
0.129090 + 0.991633i \(0.458794\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.37873 0.0482948
\(816\) 0 0
\(817\) 7.93125 0.277479
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0419 −1.04847 −0.524235 0.851574i \(-0.675649\pi\)
−0.524235 + 0.851574i \(0.675649\pi\)
\(822\) 0 0
\(823\) −27.5122 −0.959016 −0.479508 0.877538i \(-0.659185\pi\)
−0.479508 + 0.877538i \(0.659185\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −49.1971 −1.71075 −0.855375 0.518009i \(-0.826674\pi\)
−0.855375 + 0.518009i \(0.826674\pi\)
\(828\) 0 0
\(829\) 41.9008 1.45527 0.727637 0.685963i \(-0.240619\pi\)
0.727637 + 0.685963i \(0.240619\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.41480 −0.118316
\(834\) 0 0
\(835\) 1.90781 0.0660224
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −34.5508 −1.19283 −0.596413 0.802678i \(-0.703408\pi\)
−0.596413 + 0.802678i \(0.703408\pi\)
\(840\) 0 0
\(841\) −13.9472 −0.480939
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −25.3245 −0.871188
\(846\) 0 0
\(847\) −30.6610 −1.05352
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5.54060 0.189929
\(852\) 0 0
\(853\) −27.6838 −0.947874 −0.473937 0.880559i \(-0.657168\pi\)
−0.473937 + 0.880559i \(0.657168\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15.1732 0.518307 0.259154 0.965836i \(-0.416556\pi\)
0.259154 + 0.965836i \(0.416556\pi\)
\(858\) 0 0
\(859\) 0.561134 0.0191456 0.00957281 0.999954i \(-0.496953\pi\)
0.00957281 + 0.999954i \(0.496953\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −21.7750 −0.741230 −0.370615 0.928786i \(-0.620853\pi\)
−0.370615 + 0.928786i \(0.620853\pi\)
\(864\) 0 0
\(865\) 30.7558 1.04573
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.86565 −0.0972105
\(870\) 0 0
\(871\) 26.7426 0.906140
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 34.1379 1.15407
\(876\) 0 0
\(877\) 20.0002 0.675358 0.337679 0.941261i \(-0.390358\pi\)
0.337679 + 0.941261i \(0.390358\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −5.92933 −0.199764 −0.0998821 0.994999i \(-0.531847\pi\)
−0.0998821 + 0.994999i \(0.531847\pi\)
\(882\) 0 0
\(883\) 6.56436 0.220908 0.110454 0.993881i \(-0.464769\pi\)
0.110454 + 0.993881i \(0.464769\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.74021 0.0584306 0.0292153 0.999573i \(-0.490699\pi\)
0.0292153 + 0.999573i \(0.490699\pi\)
\(888\) 0 0
\(889\) 47.0088 1.57662
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6.35830 0.212773
\(894\) 0 0
\(895\) 22.0314 0.736427
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −25.8323 −0.861556
\(900\) 0 0
\(901\) −9.20543 −0.306677
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.47452 0.248461
\(906\) 0 0
\(907\) 28.3718 0.942071 0.471036 0.882114i \(-0.343880\pi\)
0.471036 + 0.882114i \(0.343880\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.700571 0.0232110 0.0116055 0.999933i \(-0.496306\pi\)
0.0116055 + 0.999933i \(0.496306\pi\)
\(912\) 0 0
\(913\) 1.29084 0.0427206
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.412259 0.0136140
\(918\) 0 0
\(919\) 17.8304 0.588170 0.294085 0.955779i \(-0.404985\pi\)
0.294085 + 0.955779i \(0.404985\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 58.0328 1.91017
\(924\) 0 0
\(925\) 12.3056 0.404604
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 42.4672 1.39330 0.696652 0.717410i \(-0.254672\pi\)
0.696652 + 0.717410i \(0.254672\pi\)
\(930\) 0 0
\(931\) −0.663822 −0.0217559
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.27032 −0.0742475
\(936\) 0 0
\(937\) 44.9342 1.46794 0.733968 0.679184i \(-0.237666\pi\)
0.733968 + 0.679184i \(0.237666\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 39.9153 1.30120 0.650600 0.759420i \(-0.274517\pi\)
0.650600 + 0.759420i \(0.274517\pi\)
\(942\) 0 0
\(943\) 5.85395 0.190631
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.83044 −0.0594812 −0.0297406 0.999558i \(-0.509468\pi\)
−0.0297406 + 0.999558i \(0.509468\pi\)
\(948\) 0 0
\(949\) 14.7875 0.480023
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21.0500 −0.681877 −0.340938 0.940086i \(-0.610745\pi\)
−0.340938 + 0.940086i \(0.610745\pi\)
\(954\) 0 0
\(955\) −37.3111 −1.20736
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −33.0034 −1.06573
\(960\) 0 0
\(961\) 13.3313 0.430042
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −41.9727 −1.35115
\(966\) 0 0
\(967\) −49.7457 −1.59972 −0.799858 0.600190i \(-0.795092\pi\)
−0.799858 + 0.600190i \(0.795092\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 34.2216 1.09822 0.549112 0.835749i \(-0.314966\pi\)
0.549112 + 0.835749i \(0.314966\pi\)
\(972\) 0 0
\(973\) −25.6016 −0.820751
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −11.2596 −0.360227 −0.180113 0.983646i \(-0.557646\pi\)
−0.180113 + 0.983646i \(0.557646\pi\)
\(978\) 0 0
\(979\) −2.91871 −0.0932824
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −6.69693 −0.213599 −0.106799 0.994281i \(-0.534060\pi\)
−0.106799 + 0.994281i \(0.534060\pi\)
\(984\) 0 0
\(985\) 19.8150 0.631357
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.69596 0.212919
\(990\) 0 0
\(991\) 53.4452 1.69774 0.848872 0.528599i \(-0.177282\pi\)
0.848872 + 0.528599i \(0.177282\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 33.0775 1.04863
\(996\) 0 0
\(997\) 52.2893 1.65602 0.828009 0.560714i \(-0.189473\pi\)
0.828009 + 0.560714i \(0.189473\pi\)
\(998\) 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 6012.2.a.h.1.4 9
3.2 odd 2 2004.2.a.d.1.6 9
12.11 even 2 8016.2.a.bb.1.6 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.6 9 3.2 odd 2
6012.2.a.h.1.4 9 1.1 even 1 trivial
8016.2.a.bb.1.6 9 12.11 even 2