Properties

Label 9800.2.a.ck.1.1
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $4$
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] = [9800,2,Mod(1,9800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9800.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.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: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.43449.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 7x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1400)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.31553\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.31553 q^{3} +7.99276 q^{9} +O(q^{10})\) \(q-3.31553 q^{3} +7.99276 q^{9} -4.24536 q^{11} +5.10909 q^{13} -0.883667 q^{17} +6.54096 q^{19} -5.33547 q^{23} -16.5536 q^{27} +4.54096 q^{29} -0.677224 q^{31} +14.0756 q^{33} -1.52198 q^{37} -16.9394 q^{39} +5.92666 q^{41} +5.49796 q^{43} +7.26937 q^{47} +2.92983 q^{51} -2.56813 q^{53} -21.6868 q^{57} +7.94660 q^{59} +9.01993 q^{61} -3.04395 q^{67} +17.6899 q^{69} +5.39840 q^{71} +3.85965 q^{73} +0.704402 q^{79} +30.9059 q^{81} -10.8135 q^{83} -15.0557 q^{87} +8.40564 q^{89} +2.24536 q^{93} +0.614293 q^{97} -33.9321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{3} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{3} + 5 q^{9} + 4 q^{13} + 7 q^{17} + 10 q^{19} - 12 q^{27} + 2 q^{29} + 14 q^{31} - 2 q^{33} - 2 q^{37} - 10 q^{39} + 4 q^{41} + 15 q^{43} + 15 q^{47} + 5 q^{51} - 10 q^{53} - 19 q^{57} + q^{59} + 25 q^{61} - 4 q^{67} + 16 q^{69} - 20 q^{71} + 2 q^{73} + 2 q^{79} + 24 q^{81} - 26 q^{83} - 13 q^{87} + 19 q^{89} - 8 q^{93} + 6 q^{97} - 51 q^{99}+O(q^{100}) \) 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
\(3\) −3.31553 −1.91422 −0.957112 0.289719i \(-0.906438\pi\)
−0.957112 + 0.289719i \(0.906438\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.99276 2.66425
\(10\) 0 0
\(11\) −4.24536 −1.28002 −0.640012 0.768365i \(-0.721071\pi\)
−0.640012 + 0.768365i \(0.721071\pi\)
\(12\) 0 0
\(13\) 5.10909 1.41701 0.708503 0.705708i \(-0.249371\pi\)
0.708503 + 0.705708i \(0.249371\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.883667 −0.214321 −0.107160 0.994242i \(-0.534176\pi\)
−0.107160 + 0.994242i \(0.534176\pi\)
\(18\) 0 0
\(19\) 6.54096 1.50060 0.750299 0.661099i \(-0.229909\pi\)
0.750299 + 0.661099i \(0.229909\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.33547 −1.11252 −0.556261 0.831008i \(-0.687764\pi\)
−0.556261 + 0.831008i \(0.687764\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −16.5536 −3.18575
\(28\) 0 0
\(29\) 4.54096 0.843234 0.421617 0.906774i \(-0.361463\pi\)
0.421617 + 0.906774i \(0.361463\pi\)
\(30\) 0 0
\(31\) −0.677224 −0.121633 −0.0608165 0.998149i \(-0.519370\pi\)
−0.0608165 + 0.998149i \(0.519370\pi\)
\(32\) 0 0
\(33\) 14.0756 2.45025
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.52198 −0.250211 −0.125106 0.992143i \(-0.539927\pi\)
−0.125106 + 0.992143i \(0.539927\pi\)
\(38\) 0 0
\(39\) −16.9394 −2.71247
\(40\) 0 0
\(41\) 5.92666 0.925589 0.462795 0.886466i \(-0.346847\pi\)
0.462795 + 0.886466i \(0.346847\pi\)
\(42\) 0 0
\(43\) 5.49796 0.838431 0.419215 0.907887i \(-0.362305\pi\)
0.419215 + 0.907887i \(0.362305\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.26937 1.06035 0.530174 0.847889i \(-0.322127\pi\)
0.530174 + 0.847889i \(0.322127\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.92983 0.410258
\(52\) 0 0
\(53\) −2.56813 −0.352760 −0.176380 0.984322i \(-0.556439\pi\)
−0.176380 + 0.984322i \(0.556439\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −21.6868 −2.87248
\(58\) 0 0
\(59\) 7.94660 1.03456 0.517279 0.855817i \(-0.326945\pi\)
0.517279 + 0.855817i \(0.326945\pi\)
\(60\) 0 0
\(61\) 9.01993 1.15488 0.577442 0.816432i \(-0.304051\pi\)
0.577442 + 0.816432i \(0.304051\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.04395 −0.371878 −0.185939 0.982561i \(-0.559533\pi\)
−0.185939 + 0.982561i \(0.559533\pi\)
\(68\) 0 0
\(69\) 17.6899 2.12962
\(70\) 0 0
\(71\) 5.39840 0.640672 0.320336 0.947304i \(-0.396204\pi\)
0.320336 + 0.947304i \(0.396204\pi\)
\(72\) 0 0
\(73\) 3.85965 0.451738 0.225869 0.974158i \(-0.427478\pi\)
0.225869 + 0.974158i \(0.427478\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.704402 0.0792514 0.0396257 0.999215i \(-0.487383\pi\)
0.0396257 + 0.999215i \(0.487383\pi\)
\(80\) 0 0
\(81\) 30.9059 3.43399
\(82\) 0 0
\(83\) −10.8135 −1.18693 −0.593467 0.804858i \(-0.702241\pi\)
−0.593467 + 0.804858i \(0.702241\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −15.0557 −1.61414
\(88\) 0 0
\(89\) 8.40564 0.890996 0.445498 0.895283i \(-0.353027\pi\)
0.445498 + 0.895283i \(0.353027\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.24536 0.232833
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.614293 0.0623720 0.0311860 0.999514i \(-0.490072\pi\)
0.0311860 + 0.999514i \(0.490072\pi\)
\(98\) 0 0
\(99\) −33.9321 −3.41031
\(100\) 0 0
\(101\) −5.65100 −0.562295 −0.281148 0.959664i \(-0.590715\pi\)
−0.281148 + 0.959664i \(0.590715\pi\)
\(102\) 0 0
\(103\) −2.34176 −0.230740 −0.115370 0.993323i \(-0.536805\pi\)
−0.115370 + 0.993323i \(0.536805\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.992756 −0.0959734 −0.0479867 0.998848i \(-0.515281\pi\)
−0.0479867 + 0.998848i \(0.515281\pi\)
\(108\) 0 0
\(109\) −18.1386 −1.73736 −0.868679 0.495375i \(-0.835031\pi\)
−0.868679 + 0.495375i \(0.835031\pi\)
\(110\) 0 0
\(111\) 5.04616 0.478960
\(112\) 0 0
\(113\) 6.22638 0.585728 0.292864 0.956154i \(-0.405392\pi\)
0.292864 + 0.956154i \(0.405392\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 40.8357 3.77526
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 7.02306 0.638460
\(122\) 0 0
\(123\) −19.6500 −1.77178
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.62382 0.144091 0.0720454 0.997401i \(-0.477047\pi\)
0.0720454 + 0.997401i \(0.477047\pi\)
\(128\) 0 0
\(129\) −18.2287 −1.60494
\(130\) 0 0
\(131\) −6.28206 −0.548867 −0.274433 0.961606i \(-0.588490\pi\)
−0.274433 + 0.961606i \(0.588490\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.9122 −1.53034 −0.765170 0.643828i \(-0.777345\pi\)
−0.765170 + 0.643828i \(0.777345\pi\)
\(138\) 0 0
\(139\) −23.0023 −1.95103 −0.975514 0.219936i \(-0.929415\pi\)
−0.975514 + 0.219936i \(0.929415\pi\)
\(140\) 0 0
\(141\) −24.1018 −2.02974
\(142\) 0 0
\(143\) −21.6899 −1.81380
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −10.4006 −0.852051 −0.426025 0.904711i \(-0.640087\pi\)
−0.426025 + 0.904711i \(0.640087\pi\)
\(150\) 0 0
\(151\) 21.1720 1.72295 0.861477 0.507796i \(-0.169540\pi\)
0.861477 + 0.507796i \(0.169540\pi\)
\(152\) 0 0
\(153\) −7.06293 −0.571004
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 7.82074 0.624163 0.312081 0.950055i \(-0.398974\pi\)
0.312081 + 0.950055i \(0.398974\pi\)
\(158\) 0 0
\(159\) 8.51473 0.675262
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −22.2811 −1.74519 −0.872596 0.488443i \(-0.837565\pi\)
−0.872596 + 0.488443i \(0.837565\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.8180 1.84309 0.921546 0.388270i \(-0.126927\pi\)
0.921546 + 0.388270i \(0.126927\pi\)
\(168\) 0 0
\(169\) 13.1028 1.00791
\(170\) 0 0
\(171\) 52.2803 3.99797
\(172\) 0 0
\(173\) −7.29247 −0.554436 −0.277218 0.960807i \(-0.589412\pi\)
−0.277218 + 0.960807i \(0.589412\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −26.3472 −1.98038
\(178\) 0 0
\(179\) 17.8452 1.33381 0.666905 0.745143i \(-0.267619\pi\)
0.666905 + 0.745143i \(0.267619\pi\)
\(180\) 0 0
\(181\) 9.62478 0.715404 0.357702 0.933836i \(-0.383560\pi\)
0.357702 + 0.933836i \(0.383560\pi\)
\(182\) 0 0
\(183\) −29.9059 −2.21071
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.75148 0.274335
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.4364 −1.26165 −0.630825 0.775925i \(-0.717284\pi\)
−0.630825 + 0.775925i \(0.717284\pi\)
\(192\) 0 0
\(193\) −2.61208 −0.188022 −0.0940110 0.995571i \(-0.529969\pi\)
−0.0940110 + 0.995571i \(0.529969\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.4853 −1.31703 −0.658513 0.752569i \(-0.728814\pi\)
−0.658513 + 0.752569i \(0.728814\pi\)
\(198\) 0 0
\(199\) 21.5274 1.52604 0.763019 0.646376i \(-0.223716\pi\)
0.763019 + 0.646376i \(0.223716\pi\)
\(200\) 0 0
\(201\) 10.0923 0.711857
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −42.6451 −2.96404
\(208\) 0 0
\(209\) −27.7687 −1.92080
\(210\) 0 0
\(211\) 18.3200 1.26120 0.630601 0.776107i \(-0.282808\pi\)
0.630601 + 0.776107i \(0.282808\pi\)
\(212\) 0 0
\(213\) −17.8986 −1.22639
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −12.7968 −0.864727
\(220\) 0 0
\(221\) −4.51473 −0.303694
\(222\) 0 0
\(223\) 2.61429 0.175066 0.0875330 0.996162i \(-0.472102\pi\)
0.0875330 + 0.996162i \(0.472102\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.02402 −0.399828 −0.199914 0.979813i \(-0.564066\pi\)
−0.199914 + 0.979813i \(0.564066\pi\)
\(228\) 0 0
\(229\) 15.0430 0.994069 0.497035 0.867731i \(-0.334422\pi\)
0.497035 + 0.867731i \(0.334422\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.70124 0.111452 0.0557260 0.998446i \(-0.482253\pi\)
0.0557260 + 0.998446i \(0.482253\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.33547 −0.151705
\(238\) 0 0
\(239\) −25.8208 −1.67021 −0.835105 0.550091i \(-0.814593\pi\)
−0.835105 + 0.550091i \(0.814593\pi\)
\(240\) 0 0
\(241\) 11.0851 0.714052 0.357026 0.934094i \(-0.383791\pi\)
0.357026 + 0.934094i \(0.383791\pi\)
\(242\) 0 0
\(243\) −52.8085 −3.38767
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 33.4183 2.12636
\(248\) 0 0
\(249\) 35.8525 2.27206
\(250\) 0 0
\(251\) −6.96558 −0.439663 −0.219832 0.975538i \(-0.570551\pi\)
−0.219832 + 0.975538i \(0.570551\pi\)
\(252\) 0 0
\(253\) 22.6510 1.42405
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.02946 −0.188973 −0.0944864 0.995526i \(-0.530121\pi\)
−0.0944864 + 0.995526i \(0.530121\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 36.2948 2.24659
\(262\) 0 0
\(263\) 7.33768 0.452460 0.226230 0.974074i \(-0.427360\pi\)
0.226230 + 0.974074i \(0.427360\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −27.8692 −1.70557
\(268\) 0 0
\(269\) −15.4142 −0.939821 −0.469911 0.882714i \(-0.655714\pi\)
−0.469911 + 0.882714i \(0.655714\pi\)
\(270\) 0 0
\(271\) −6.60933 −0.401488 −0.200744 0.979644i \(-0.564336\pi\)
−0.200744 + 0.979644i \(0.564336\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.7579 −0.646378 −0.323189 0.946334i \(-0.604755\pi\)
−0.323189 + 0.946334i \(0.604755\pi\)
\(278\) 0 0
\(279\) −5.41289 −0.324061
\(280\) 0 0
\(281\) 25.3033 1.50947 0.754735 0.656030i \(-0.227765\pi\)
0.754735 + 0.656030i \(0.227765\pi\)
\(282\) 0 0
\(283\) 6.34500 0.377171 0.188585 0.982057i \(-0.439610\pi\)
0.188585 + 0.982057i \(0.439610\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.2191 −0.954067
\(290\) 0 0
\(291\) −2.03671 −0.119394
\(292\) 0 0
\(293\) −20.3589 −1.18938 −0.594691 0.803954i \(-0.702726\pi\)
−0.594691 + 0.803954i \(0.702726\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 70.2762 4.07784
\(298\) 0 0
\(299\) −27.2594 −1.57645
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 18.7361 1.07636
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −29.5695 −1.68762 −0.843809 0.536643i \(-0.819692\pi\)
−0.843809 + 0.536643i \(0.819692\pi\)
\(308\) 0 0
\(309\) 7.76417 0.441688
\(310\) 0 0
\(311\) 12.4831 0.707849 0.353925 0.935274i \(-0.384847\pi\)
0.353925 + 0.935274i \(0.384847\pi\)
\(312\) 0 0
\(313\) −1.05340 −0.0595418 −0.0297709 0.999557i \(-0.509478\pi\)
−0.0297709 + 0.999557i \(0.509478\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.61933 −0.147116 −0.0735581 0.997291i \(-0.523435\pi\)
−0.0735581 + 0.997291i \(0.523435\pi\)
\(318\) 0 0
\(319\) −19.2780 −1.07936
\(320\) 0 0
\(321\) 3.29152 0.183715
\(322\) 0 0
\(323\) −5.78002 −0.321609
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 60.1390 3.32569
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 19.2739 1.05939 0.529694 0.848189i \(-0.322307\pi\)
0.529694 + 0.848189i \(0.322307\pi\)
\(332\) 0 0
\(333\) −12.1648 −0.666626
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.2979 0.560961 0.280481 0.959860i \(-0.409506\pi\)
0.280481 + 0.959860i \(0.409506\pi\)
\(338\) 0 0
\(339\) −20.6438 −1.12121
\(340\) 0 0
\(341\) 2.87506 0.155693
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.3051 1.09004 0.545018 0.838424i \(-0.316523\pi\)
0.545018 + 0.838424i \(0.316523\pi\)
\(348\) 0 0
\(349\) 2.62249 0.140379 0.0701893 0.997534i \(-0.477640\pi\)
0.0701893 + 0.997534i \(0.477640\pi\)
\(350\) 0 0
\(351\) −84.5741 −4.51423
\(352\) 0 0
\(353\) −8.72526 −0.464399 −0.232199 0.972668i \(-0.574592\pi\)
−0.232199 + 0.972668i \(0.574592\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0494 −0.635943 −0.317971 0.948100i \(-0.603002\pi\)
−0.317971 + 0.948100i \(0.603002\pi\)
\(360\) 0 0
\(361\) 23.7841 1.25180
\(362\) 0 0
\(363\) −23.2852 −1.22216
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.48527 −0.181930 −0.0909648 0.995854i \(-0.528995\pi\)
−0.0909648 + 0.995854i \(0.528995\pi\)
\(368\) 0 0
\(369\) 47.3704 2.46600
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 37.5696 1.94528 0.972639 0.232320i \(-0.0746316\pi\)
0.972639 + 0.232320i \(0.0746316\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 23.2002 1.19487
\(378\) 0 0
\(379\) −2.48935 −0.127869 −0.0639347 0.997954i \(-0.520365\pi\)
−0.0639347 + 0.997954i \(0.520365\pi\)
\(380\) 0 0
\(381\) −5.38383 −0.275822
\(382\) 0 0
\(383\) 21.4753 1.09734 0.548668 0.836041i \(-0.315135\pi\)
0.548668 + 0.836041i \(0.315135\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 43.9438 2.23379
\(388\) 0 0
\(389\) 11.3576 0.575854 0.287927 0.957652i \(-0.407034\pi\)
0.287927 + 0.957652i \(0.407034\pi\)
\(390\) 0 0
\(391\) 4.71477 0.238436
\(392\) 0 0
\(393\) 20.8284 1.05065
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −24.9040 −1.24990 −0.624948 0.780666i \(-0.714880\pi\)
−0.624948 + 0.780666i \(0.714880\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.36989 0.467910 0.233955 0.972247i \(-0.424833\pi\)
0.233955 + 0.972247i \(0.424833\pi\)
\(402\) 0 0
\(403\) −3.46000 −0.172355
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.46133 0.320276
\(408\) 0 0
\(409\) 13.0145 0.643525 0.321762 0.946820i \(-0.395725\pi\)
0.321762 + 0.946820i \(0.395725\pi\)
\(410\) 0 0
\(411\) 59.3884 2.92941
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 76.2648 3.73470
\(418\) 0 0
\(419\) −9.76954 −0.477273 −0.238637 0.971109i \(-0.576700\pi\)
−0.238637 + 0.971109i \(0.576700\pi\)
\(420\) 0 0
\(421\) −21.5881 −1.05214 −0.526069 0.850442i \(-0.676335\pi\)
−0.526069 + 0.850442i \(0.676335\pi\)
\(422\) 0 0
\(423\) 58.1023 2.82503
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 71.9136 3.47202
\(430\) 0 0
\(431\) 17.9969 0.866879 0.433439 0.901183i \(-0.357300\pi\)
0.433439 + 0.901183i \(0.357300\pi\)
\(432\) 0 0
\(433\) 24.2236 1.16411 0.582057 0.813148i \(-0.302248\pi\)
0.582057 + 0.813148i \(0.302248\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −34.8991 −1.66945
\(438\) 0 0
\(439\) 1.01490 0.0484385 0.0242192 0.999707i \(-0.492290\pi\)
0.0242192 + 0.999707i \(0.492290\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.0095 0.665613 0.332806 0.942995i \(-0.392004\pi\)
0.332806 + 0.942995i \(0.392004\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 34.4835 1.63102
\(448\) 0 0
\(449\) −9.76134 −0.460666 −0.230333 0.973112i \(-0.573982\pi\)
−0.230333 + 0.973112i \(0.573982\pi\)
\(450\) 0 0
\(451\) −25.1608 −1.18478
\(452\) 0 0
\(453\) −70.1965 −3.29812
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.7298 1.20359 0.601794 0.798651i \(-0.294453\pi\)
0.601794 + 0.798651i \(0.294453\pi\)
\(458\) 0 0
\(459\) 14.6279 0.682772
\(460\) 0 0
\(461\) −25.3115 −1.17888 −0.589438 0.807814i \(-0.700651\pi\)
−0.589438 + 0.807814i \(0.700651\pi\)
\(462\) 0 0
\(463\) 35.8484 1.66602 0.833008 0.553261i \(-0.186617\pi\)
0.833008 + 0.553261i \(0.186617\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.65732 0.169241 0.0846204 0.996413i \(-0.473032\pi\)
0.0846204 + 0.996413i \(0.473032\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −25.9299 −1.19479
\(472\) 0 0
\(473\) −23.3408 −1.07321
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −20.5265 −0.939842
\(478\) 0 0
\(479\) −1.87101 −0.0854886 −0.0427443 0.999086i \(-0.513610\pi\)
−0.0427443 + 0.999086i \(0.513610\pi\)
\(480\) 0 0
\(481\) −7.77591 −0.354551
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 9.38255 0.425164 0.212582 0.977143i \(-0.431813\pi\)
0.212582 + 0.977143i \(0.431813\pi\)
\(488\) 0 0
\(489\) 73.8738 3.34069
\(490\) 0 0
\(491\) −38.6545 −1.74445 −0.872227 0.489100i \(-0.837325\pi\)
−0.872227 + 0.489100i \(0.837325\pi\)
\(492\) 0 0
\(493\) −4.01269 −0.180723
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.10596 0.183808 0.0919040 0.995768i \(-0.470705\pi\)
0.0919040 + 0.995768i \(0.470705\pi\)
\(500\) 0 0
\(501\) −78.9693 −3.52809
\(502\) 0 0
\(503\) 26.6922 1.19015 0.595073 0.803672i \(-0.297123\pi\)
0.595073 + 0.803672i \(0.297123\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −43.4428 −1.92936
\(508\) 0 0
\(509\) 12.8094 0.567766 0.283883 0.958859i \(-0.408377\pi\)
0.283883 + 0.958859i \(0.408377\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −108.277 −4.78053
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.8611 −1.35727
\(518\) 0 0
\(519\) 24.1784 1.06131
\(520\) 0 0
\(521\) −23.8211 −1.04362 −0.521811 0.853061i \(-0.674743\pi\)
−0.521811 + 0.853061i \(0.674743\pi\)
\(522\) 0 0
\(523\) 12.7687 0.558335 0.279167 0.960242i \(-0.409942\pi\)
0.279167 + 0.960242i \(0.409942\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.598440 0.0260685
\(528\) 0 0
\(529\) 5.46721 0.237705
\(530\) 0 0
\(531\) 63.5152 2.75633
\(532\) 0 0
\(533\) 30.2799 1.31157
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −59.1662 −2.55321
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.6836 −0.760277 −0.380138 0.924930i \(-0.624124\pi\)
−0.380138 + 0.924930i \(0.624124\pi\)
\(542\) 0 0
\(543\) −31.9113 −1.36944
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 24.0580 1.02864 0.514322 0.857597i \(-0.328044\pi\)
0.514322 + 0.857597i \(0.328044\pi\)
\(548\) 0 0
\(549\) 72.0941 3.07690
\(550\) 0 0
\(551\) 29.7022 1.26536
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.86248 0.206030 0.103015 0.994680i \(-0.467151\pi\)
0.103015 + 0.994680i \(0.467151\pi\)
\(558\) 0 0
\(559\) 28.0896 1.18806
\(560\) 0 0
\(561\) −12.4382 −0.525139
\(562\) 0 0
\(563\) −11.0847 −0.467163 −0.233581 0.972337i \(-0.575045\pi\)
−0.233581 + 0.972337i \(0.575045\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.9571 −0.710878 −0.355439 0.934700i \(-0.615669\pi\)
−0.355439 + 0.934700i \(0.615669\pi\)
\(570\) 0 0
\(571\) 20.3450 0.851412 0.425706 0.904862i \(-0.360026\pi\)
0.425706 + 0.904862i \(0.360026\pi\)
\(572\) 0 0
\(573\) 57.8108 2.41508
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 41.7643 1.73867 0.869335 0.494223i \(-0.164548\pi\)
0.869335 + 0.494223i \(0.164548\pi\)
\(578\) 0 0
\(579\) 8.66045 0.359916
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.9026 0.451542
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −38.6858 −1.59674 −0.798368 0.602170i \(-0.794303\pi\)
−0.798368 + 0.602170i \(0.794303\pi\)
\(588\) 0 0
\(589\) −4.42969 −0.182522
\(590\) 0 0
\(591\) 61.2888 2.52108
\(592\) 0 0
\(593\) 18.5963 0.763660 0.381830 0.924233i \(-0.375294\pi\)
0.381830 + 0.924233i \(0.375294\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −71.3749 −2.92118
\(598\) 0 0
\(599\) −22.0538 −0.901093 −0.450547 0.892753i \(-0.648771\pi\)
−0.450547 + 0.892753i \(0.648771\pi\)
\(600\) 0 0
\(601\) 20.6533 0.842465 0.421233 0.906953i \(-0.361598\pi\)
0.421233 + 0.906953i \(0.361598\pi\)
\(602\) 0 0
\(603\) −24.3296 −0.990776
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −24.1712 −0.981078 −0.490539 0.871419i \(-0.663200\pi\)
−0.490539 + 0.871419i \(0.663200\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 37.1399 1.50252
\(612\) 0 0
\(613\) 45.8765 1.85293 0.926467 0.376376i \(-0.122830\pi\)
0.926467 + 0.376376i \(0.122830\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 25.8072 1.03896 0.519479 0.854483i \(-0.326126\pi\)
0.519479 + 0.854483i \(0.326126\pi\)
\(618\) 0 0
\(619\) 43.0431 1.73005 0.865024 0.501730i \(-0.167303\pi\)
0.865024 + 0.501730i \(0.167303\pi\)
\(620\) 0 0
\(621\) 88.3214 3.54422
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 92.0680 3.67684
\(628\) 0 0
\(629\) 1.34492 0.0536254
\(630\) 0 0
\(631\) 20.8872 0.831508 0.415754 0.909477i \(-0.363518\pi\)
0.415754 + 0.909477i \(0.363518\pi\)
\(632\) 0 0
\(633\) −60.7406 −2.41422
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 43.1481 1.70691
\(640\) 0 0
\(641\) −31.8932 −1.25971 −0.629853 0.776714i \(-0.716885\pi\)
−0.629853 + 0.776714i \(0.716885\pi\)
\(642\) 0 0
\(643\) 0.850088 0.0335242 0.0167621 0.999860i \(-0.494664\pi\)
0.0167621 + 0.999860i \(0.494664\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 34.3589 1.35079 0.675395 0.737456i \(-0.263973\pi\)
0.675395 + 0.737456i \(0.263973\pi\)
\(648\) 0 0
\(649\) −33.7362 −1.32426
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 22.0484 0.862822 0.431411 0.902155i \(-0.358016\pi\)
0.431411 + 0.902155i \(0.358016\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 30.8492 1.20354
\(658\) 0 0
\(659\) −16.9046 −0.658508 −0.329254 0.944241i \(-0.606797\pi\)
−0.329254 + 0.944241i \(0.606797\pi\)
\(660\) 0 0
\(661\) −14.8973 −0.579437 −0.289718 0.957112i \(-0.593562\pi\)
−0.289718 + 0.957112i \(0.593562\pi\)
\(662\) 0 0
\(663\) 14.9687 0.581338
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −24.2281 −0.938117
\(668\) 0 0
\(669\) −8.66777 −0.335115
\(670\) 0 0
\(671\) −38.2928 −1.47828
\(672\) 0 0
\(673\) 26.1490 1.00797 0.503984 0.863713i \(-0.331867\pi\)
0.503984 + 0.863713i \(0.331867\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.4405 1.24679 0.623394 0.781908i \(-0.285753\pi\)
0.623394 + 0.781908i \(0.285753\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 19.9728 0.765360
\(682\) 0 0
\(683\) 44.2540 1.69333 0.846667 0.532123i \(-0.178606\pi\)
0.846667 + 0.532123i \(0.178606\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −49.8755 −1.90287
\(688\) 0 0
\(689\) −13.1208 −0.499864
\(690\) 0 0
\(691\) 38.3586 1.45923 0.729616 0.683857i \(-0.239699\pi\)
0.729616 + 0.683857i \(0.239699\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −5.23719 −0.198373
\(698\) 0 0
\(699\) −5.64052 −0.213344
\(700\) 0 0
\(701\) 13.0696 0.493633 0.246817 0.969062i \(-0.420615\pi\)
0.246817 + 0.969062i \(0.420615\pi\)
\(702\) 0 0
\(703\) −9.95517 −0.375466
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −9.95918 −0.374025 −0.187012 0.982358i \(-0.559880\pi\)
−0.187012 + 0.982358i \(0.559880\pi\)
\(710\) 0 0
\(711\) 5.63011 0.211146
\(712\) 0 0
\(713\) 3.61331 0.135319
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 85.6097 3.19715
\(718\) 0 0
\(719\) −47.4595 −1.76994 −0.884971 0.465646i \(-0.845822\pi\)
−0.884971 + 0.465646i \(0.845822\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −36.7529 −1.36686
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.84829 0.142725 0.0713626 0.997450i \(-0.477265\pi\)
0.0713626 + 0.997450i \(0.477265\pi\)
\(728\) 0 0
\(729\) 82.3708 3.05077
\(730\) 0 0
\(731\) −4.85836 −0.179693
\(732\) 0 0
\(733\) −3.26076 −0.120439 −0.0602196 0.998185i \(-0.519180\pi\)
−0.0602196 + 0.998185i \(0.519180\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.9227 0.476012
\(738\) 0 0
\(739\) −19.0013 −0.698975 −0.349488 0.936941i \(-0.613644\pi\)
−0.349488 + 0.936941i \(0.613644\pi\)
\(740\) 0 0
\(741\) −110.800 −4.07032
\(742\) 0 0
\(743\) −4.02310 −0.147593 −0.0737965 0.997273i \(-0.523512\pi\)
−0.0737965 + 0.997273i \(0.523512\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −86.4296 −3.16229
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.690791 −0.0252073 −0.0126037 0.999921i \(-0.504012\pi\)
−0.0126037 + 0.999921i \(0.504012\pi\)
\(752\) 0 0
\(753\) 23.0946 0.841614
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 23.5723 0.856751 0.428375 0.903601i \(-0.359086\pi\)
0.428375 + 0.903601i \(0.359086\pi\)
\(758\) 0 0
\(759\) −75.1000 −2.72596
\(760\) 0 0
\(761\) −5.72338 −0.207472 −0.103736 0.994605i \(-0.533080\pi\)
−0.103736 + 0.994605i \(0.533080\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 40.5999 1.46598
\(768\) 0 0
\(769\) 34.8252 1.25583 0.627915 0.778282i \(-0.283909\pi\)
0.627915 + 0.778282i \(0.283909\pi\)
\(770\) 0 0
\(771\) 10.0443 0.361736
\(772\) 0 0
\(773\) 6.50204 0.233862 0.116931 0.993140i \(-0.462694\pi\)
0.116931 + 0.993140i \(0.462694\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 38.7660 1.38894
\(780\) 0 0
\(781\) −22.9181 −0.820075
\(782\) 0 0
\(783\) −75.1694 −2.68633
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −25.7306 −0.917198 −0.458599 0.888643i \(-0.651649\pi\)
−0.458599 + 0.888643i \(0.651649\pi\)
\(788\) 0 0
\(789\) −24.3283 −0.866110
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 46.0837 1.63648
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 44.8212 1.58765 0.793825 0.608147i \(-0.208087\pi\)
0.793825 + 0.608147i \(0.208087\pi\)
\(798\) 0 0
\(799\) −6.42370 −0.227254
\(800\) 0 0
\(801\) 67.1842 2.37384
\(802\) 0 0
\(803\) −16.3856 −0.578235
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 51.1063 1.79903
\(808\) 0 0
\(809\) 25.3839 0.892450 0.446225 0.894921i \(-0.352768\pi\)
0.446225 + 0.894921i \(0.352768\pi\)
\(810\) 0 0
\(811\) 6.86499 0.241062 0.120531 0.992710i \(-0.461540\pi\)
0.120531 + 0.992710i \(0.461540\pi\)
\(812\) 0 0
\(813\) 21.9135 0.768539
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 35.9619 1.25815
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31.2507 1.09066 0.545328 0.838223i \(-0.316405\pi\)
0.545328 + 0.838223i \(0.316405\pi\)
\(822\) 0 0
\(823\) −12.4667 −0.434562 −0.217281 0.976109i \(-0.569719\pi\)
−0.217281 + 0.976109i \(0.569719\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 20.0893 0.698572 0.349286 0.937016i \(-0.386424\pi\)
0.349286 + 0.937016i \(0.386424\pi\)
\(828\) 0 0
\(829\) 48.2767 1.67672 0.838359 0.545118i \(-0.183515\pi\)
0.838359 + 0.545118i \(0.183515\pi\)
\(830\) 0 0
\(831\) 35.6681 1.23731
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 11.2105 0.387492
\(838\) 0 0
\(839\) 56.1020 1.93686 0.968429 0.249291i \(-0.0801975\pi\)
0.968429 + 0.249291i \(0.0801975\pi\)
\(840\) 0 0
\(841\) −8.37972 −0.288956
\(842\) 0 0
\(843\) −83.8940 −2.88946
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −21.0370 −0.721989
\(850\) 0 0
\(851\) 8.12045 0.278365
\(852\) 0 0
\(853\) −16.4092 −0.561840 −0.280920 0.959731i \(-0.590640\pi\)
−0.280920 + 0.959731i \(0.590640\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.47307 −0.152797 −0.0763985 0.997077i \(-0.524342\pi\)
−0.0763985 + 0.997077i \(0.524342\pi\)
\(858\) 0 0
\(859\) 14.5116 0.495128 0.247564 0.968871i \(-0.420370\pi\)
0.247564 + 0.968871i \(0.420370\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14.5859 0.496508 0.248254 0.968695i \(-0.420143\pi\)
0.248254 + 0.968695i \(0.420143\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 53.7751 1.82630
\(868\) 0 0
\(869\) −2.99044 −0.101444
\(870\) 0 0
\(871\) −15.5518 −0.526953
\(872\) 0 0
\(873\) 4.90989 0.166175
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.6586 −1.27164 −0.635821 0.771837i \(-0.719338\pi\)
−0.635821 + 0.771837i \(0.719338\pi\)
\(878\) 0 0
\(879\) 67.5007 2.27674
\(880\) 0 0
\(881\) 44.4007 1.49590 0.747949 0.663757i \(-0.231039\pi\)
0.747949 + 0.663757i \(0.231039\pi\)
\(882\) 0 0
\(883\) 51.7213 1.74056 0.870279 0.492558i \(-0.163938\pi\)
0.870279 + 0.492558i \(0.163938\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0.489461 0.0164345 0.00821725 0.999966i \(-0.497384\pi\)
0.00821725 + 0.999966i \(0.497384\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −131.207 −4.39558
\(892\) 0 0
\(893\) 47.5487 1.59116
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 90.3794 3.01768
\(898\) 0 0
\(899\) −3.07524 −0.102565
\(900\) 0 0
\(901\) 2.26937 0.0756038
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −43.4541 −1.44287 −0.721435 0.692483i \(-0.756517\pi\)
−0.721435 + 0.692483i \(0.756517\pi\)
\(908\) 0 0
\(909\) −45.1671 −1.49810
\(910\) 0 0
\(911\) −4.77049 −0.158054 −0.0790268 0.996872i \(-0.525181\pi\)
−0.0790268 + 0.996872i \(0.525181\pi\)
\(912\) 0 0
\(913\) 45.9071 1.51930
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −41.2350 −1.36022 −0.680109 0.733111i \(-0.738068\pi\)
−0.680109 + 0.733111i \(0.738068\pi\)
\(920\) 0 0
\(921\) 98.0385 3.23048
\(922\) 0 0
\(923\) 27.5809 0.907836
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −18.7171 −0.614750
\(928\) 0 0
\(929\) −31.8922 −1.04635 −0.523175 0.852225i \(-0.675253\pi\)
−0.523175 + 0.852225i \(0.675253\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −41.3880 −1.35498
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 23.2518 0.759602 0.379801 0.925068i \(-0.375992\pi\)
0.379801 + 0.925068i \(0.375992\pi\)
\(938\) 0 0
\(939\) 3.49259 0.113976
\(940\) 0 0
\(941\) −26.6519 −0.868828 −0.434414 0.900713i \(-0.643044\pi\)
−0.434414 + 0.900713i \(0.643044\pi\)
\(942\) 0 0
\(943\) −31.6215 −1.02974
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.21410 −0.169435 −0.0847177 0.996405i \(-0.526999\pi\)
−0.0847177 + 0.996405i \(0.526999\pi\)
\(948\) 0 0
\(949\) 19.7193 0.640116
\(950\) 0 0
\(951\) 8.68447 0.281613
\(952\) 0 0
\(953\) −37.8674 −1.22664 −0.613322 0.789833i \(-0.710167\pi\)
−0.613322 + 0.789833i \(0.710167\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 63.9168 2.06614
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.5414 −0.985205
\(962\) 0 0
\(963\) −7.93486 −0.255697
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 17.7266 0.570049 0.285024 0.958520i \(-0.407998\pi\)
0.285024 + 0.958520i \(0.407998\pi\)
\(968\) 0 0
\(969\) 19.1639 0.615632
\(970\) 0 0
\(971\) −10.7641 −0.345436 −0.172718 0.984971i \(-0.555255\pi\)
−0.172718 + 0.984971i \(0.555255\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 39.5777 1.26620 0.633101 0.774069i \(-0.281782\pi\)
0.633101 + 0.774069i \(0.281782\pi\)
\(978\) 0 0
\(979\) −35.6850 −1.14050
\(980\) 0 0
\(981\) −144.977 −4.62876
\(982\) 0 0
\(983\) −30.9761 −0.987983 −0.493991 0.869467i \(-0.664463\pi\)
−0.493991 + 0.869467i \(0.664463\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −29.3342 −0.932773
\(990\) 0 0
\(991\) −33.1892 −1.05429 −0.527145 0.849775i \(-0.676738\pi\)
−0.527145 + 0.849775i \(0.676738\pi\)
\(992\) 0 0
\(993\) −63.9031 −2.02790
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −8.83435 −0.279787 −0.139893 0.990167i \(-0.544676\pi\)
−0.139893 + 0.990167i \(0.544676\pi\)
\(998\) 0 0
\(999\) 25.1942 0.797111
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 9800.2.a.ck.1.1 4
5.4 even 2 9800.2.a.cu.1.4 4
7.3 odd 6 1400.2.q.l.401.1 8
7.5 odd 6 1400.2.q.l.1201.1 yes 8
7.6 odd 2 9800.2.a.ct.1.4 4
35.3 even 12 1400.2.bh.j.849.8 16
35.12 even 12 1400.2.bh.j.249.8 16
35.17 even 12 1400.2.bh.j.849.1 16
35.19 odd 6 1400.2.q.m.1201.4 yes 8
35.24 odd 6 1400.2.q.m.401.4 yes 8
35.33 even 12 1400.2.bh.j.249.1 16
35.34 odd 2 9800.2.a.cj.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1400.2.q.l.401.1 8 7.3 odd 6
1400.2.q.l.1201.1 yes 8 7.5 odd 6
1400.2.q.m.401.4 yes 8 35.24 odd 6
1400.2.q.m.1201.4 yes 8 35.19 odd 6
1400.2.bh.j.249.1 16 35.33 even 12
1400.2.bh.j.249.8 16 35.12 even 12
1400.2.bh.j.849.1 16 35.17 even 12
1400.2.bh.j.849.8 16 35.3 even 12
9800.2.a.cj.1.1 4 35.34 odd 2
9800.2.a.ck.1.1 4 1.1 even 1 trivial
9800.2.a.ct.1.4 4 7.6 odd 2
9800.2.a.cu.1.4 4 5.4 even 2