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Properties

Label 1334.2.a.c.1.1
Level $1334$
Weight $2$
Character 1334.1
Self dual yes
Analytic conductor $10.652$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1334,2,Mod(1,1334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.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: \(10.6520436296\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +2.00000 q^{18} -8.00000 q^{19} +1.00000 q^{20} +3.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} -5.00000 q^{27} -1.00000 q^{29} -1.00000 q^{30} +9.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} +2.00000 q^{34} -2.00000 q^{36} -10.0000 q^{37} +8.00000 q^{38} +1.00000 q^{39} -1.00000 q^{40} -11.0000 q^{43} -3.00000 q^{44} -2.00000 q^{45} +1.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} +4.00000 q^{50} -2.00000 q^{51} +1.00000 q^{52} +5.00000 q^{53} +5.00000 q^{54} -3.00000 q^{55} -8.00000 q^{57} +1.00000 q^{58} +8.00000 q^{59} +1.00000 q^{60} -6.00000 q^{61} -9.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} +3.00000 q^{66} +2.00000 q^{67} -2.00000 q^{68} -1.00000 q^{69} +6.00000 q^{71} +2.00000 q^{72} +6.00000 q^{73} +10.0000 q^{74} -4.00000 q^{75} -8.00000 q^{76} -1.00000 q^{78} +1.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -4.00000 q^{83} -2.00000 q^{85} +11.0000 q^{86} -1.00000 q^{87} +3.00000 q^{88} +2.00000 q^{90} -1.00000 q^{92} +9.00000 q^{93} -9.00000 q^{94} -8.00000 q^{95} -1.00000 q^{96} +6.00000 q^{97} +7.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) −1.00000 −0.316228
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350 0.138675 − 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 2.00000 0.471405
\(19\) −8.00000 −1.83533 −0.917663 − 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) −1.00000 −0.208514
\(24\) −1.00000 −0.204124
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) −1.00000 −0.182574
\(31\) 9.00000 1.61645 0.808224 − 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.00000 −0.522233
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 8.00000 1.29777
\(39\) 1.00000 0.160128
\(40\) −1.00000 −0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 − 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) −3.00000 −0.452267
\(45\) −2.00000 −0.298142
\(46\) 1.00000 0.147442
\(47\) 9.00000 1.31278 0.656392 − 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) 4.00000 0.565685
\(51\) −2.00000 −0.280056
\(52\) 1.00000 0.138675
\(53\) 5.00000 0.686803 0.343401 − 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) 5.00000 0.680414
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) 1.00000 0.131306
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 1.00000 0.129099
\(61\) −6.00000 −0.768221 −0.384111 − 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −9.00000 −1.14300
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 3.00000 0.369274
\(67\) 2.00000 0.244339 0.122169 − 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −2.00000 −0.242536
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 − 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 2.00000 0.235702
\(73\) 6.00000 0.702247 0.351123 − 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 10.0000 1.16248
\(75\) −4.00000 −0.461880
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) 1.00000 0.112509 0.0562544 − 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 11.0000 1.18616
\(87\) −1.00000 −0.107211
\(88\) 3.00000 0.319801
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −1.00000 −0.104257
\(93\) 9.00000 0.933257
\(94\) −9.00000 −0.928279
\(95\) −8.00000 −0.820783
\(96\) −1.00000 −0.102062
\(97\) 6.00000 0.609208 0.304604 − 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 7.00000 0.707107
\(99\) 6.00000 0.603023
\(100\) −4.00000 −0.400000
\(101\) −2.00000 −0.199007 −0.0995037 − 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 2.00000 0.198030
\(103\) 14.0000 1.37946 0.689730 − 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −5.00000 −0.485643
\(107\) −18.0000 −1.74013 −0.870063 − 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −5.00000 −0.481125
\(109\) 5.00000 0.478913 0.239457 − 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 3.00000 0.286039
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 − 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 8.00000 0.749269
\(115\) −1.00000 −0.0932505
\(116\) −1.00000 −0.0928477
\(117\) −2.00000 −0.184900
\(118\) −8.00000 −0.736460
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −2.00000 −0.181818
\(122\) 6.00000 0.543214
\(123\) 0 0
\(124\) 9.00000 0.808224
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.0000 −0.968496
\(130\) −1.00000 −0.0877058
\(131\) −4.00000 −0.349482 −0.174741 − 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) −5.00000 −0.430331
\(136\) 2.00000 0.171499
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 1.00000 0.0851257
\(139\) −10.0000 −0.848189 −0.424094 − 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) −6.00000 −0.503509
\(143\) −3.00000 −0.250873
\(144\) −2.00000 −0.166667
\(145\) −1.00000 −0.0830455
\(146\) −6.00000 −0.496564
\(147\) −7.00000 −0.577350
\(148\) −10.0000 −0.821995
\(149\) 3.00000 0.245770 0.122885 − 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 4.00000 0.326599
\(151\) 6.00000 0.488273 0.244137 − 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 8.00000 0.648886
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) 1.00000 0.0800641
\(157\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) −1.00000 −0.0795557
\(159\) 5.00000 0.396526
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −21.0000 −1.64485 −0.822423 − 0.568876i \(-0.807379\pi\)
−0.822423 + 0.568876i \(0.807379\pi\)
\(164\) 0 0
\(165\) −3.00000 −0.233550
\(166\) 4.00000 0.310460
\(167\) 14.0000 1.08335 0.541676 − 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 2.00000 0.153393
\(171\) 16.0000 1.22355
\(172\) −11.0000 −0.838742
\(173\) 18.0000 1.36851 0.684257 − 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 1.00000 0.0758098
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 8.00000 0.601317
\(178\) 0 0
\(179\) −20.0000 −1.49487 −0.747435 − 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) −2.00000 −0.149071
\(181\) 11.0000 0.817624 0.408812 − 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 1.00000 0.0737210
\(185\) −10.0000 −0.735215
\(186\) −9.00000 −0.659912
\(187\) 6.00000 0.438763
\(188\) 9.00000 0.656392
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 24.0000 1.73658 0.868290 − 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 1.00000 0.0721688
\(193\) −26.0000 −1.87152 −0.935760 − 0.352636i \(-0.885285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) −6.00000 −0.430775
\(195\) 1.00000 0.0716115
\(196\) −7.00000 −0.500000
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −6.00000 −0.426401
\(199\) −14.0000 −0.992434 −0.496217 − 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 4.00000 0.282843
\(201\) 2.00000 0.141069
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) −14.0000 −0.975426
\(207\) 2.00000 0.139010
\(208\) 1.00000 0.0693375
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 27.0000 1.85876 0.929378 − 0.369129i \(-0.120344\pi\)
0.929378 + 0.369129i \(0.120344\pi\)
\(212\) 5.00000 0.343401
\(213\) 6.00000 0.411113
\(214\) 18.0000 1.23045
\(215\) −11.0000 −0.750194
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) −5.00000 −0.338643
\(219\) 6.00000 0.405442
\(220\) −3.00000 −0.202260
\(221\) −2.00000 −0.134535
\(222\) 10.0000 0.671156
\(223\) −10.0000 −0.669650 −0.334825 − 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 10.0000 0.665190
\(227\) 24.0000 1.59294 0.796468 − 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) −8.00000 −0.529813
\(229\) −12.0000 −0.792982 −0.396491 − 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 1.00000 0.0659380
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) 19.0000 1.24473 0.622366 − 0.782727i \(-0.286172\pi\)
0.622366 + 0.782727i \(0.286172\pi\)
\(234\) 2.00000 0.130744
\(235\) 9.00000 0.587095
\(236\) 8.00000 0.520756
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 1.00000 0.0645497
\(241\) −17.0000 −1.09507 −0.547533 − 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 2.00000 0.128565
\(243\) 16.0000 1.02640
\(244\) −6.00000 −0.384111
\(245\) −7.00000 −0.447214
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) −9.00000 −0.571501
\(249\) −4.00000 −0.253490
\(250\) 9.00000 0.569210
\(251\) −13.0000 −0.820553 −0.410276 − 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 8.00000 0.501965
\(255\) −2.00000 −0.125245
\(256\) 1.00000 0.0625000
\(257\) 21.0000 1.30994 0.654972 − 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 11.0000 0.684830
\(259\) 0 0
\(260\) 1.00000 0.0620174
\(261\) 2.00000 0.123797
\(262\) 4.00000 0.247121
\(263\) −1.00000 −0.0616626 −0.0308313 − 0.999525i \(-0.509815\pi\)
−0.0308313 + 0.999525i \(0.509815\pi\)
\(264\) 3.00000 0.184637
\(265\) 5.00000 0.307148
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 5.00000 0.304290
\(271\) −25.0000 −1.51864 −0.759321 − 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 12.0000 0.723627
\(276\) −1.00000 −0.0601929
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 10.0000 0.599760
\(279\) −18.0000 −1.07763
\(280\) 0 0
\(281\) −3.00000 −0.178965 −0.0894825 − 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) −9.00000 −0.535942
\(283\) 22.0000 1.30776 0.653882 − 0.756596i \(-0.273139\pi\)
0.653882 + 0.756596i \(0.273139\pi\)
\(284\) 6.00000 0.356034
\(285\) −8.00000 −0.473879
\(286\) 3.00000 0.177394
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) −13.0000 −0.764706
\(290\) 1.00000 0.0587220
\(291\) 6.00000 0.351726
\(292\) 6.00000 0.351123
\(293\) −12.0000 −0.701047 −0.350524 − 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 7.00000 0.408248
\(295\) 8.00000 0.465778
\(296\) 10.0000 0.581238
\(297\) 15.0000 0.870388
\(298\) −3.00000 −0.173785
\(299\) −1.00000 −0.0578315
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) −6.00000 −0.345261
\(303\) −2.00000 −0.114897
\(304\) −8.00000 −0.458831
\(305\) −6.00000 −0.343559
\(306\) −4.00000 −0.228665
\(307\) 15.0000 0.856095 0.428048 − 0.903756i \(-0.359202\pi\)
0.428048 + 0.903756i \(0.359202\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) −9.00000 −0.511166
\(311\) 32.0000 1.81455 0.907277 − 0.420534i \(-0.138157\pi\)
0.907277 + 0.420534i \(0.138157\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −17.0000 −0.960897 −0.480448 − 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) 10.0000 0.561656 0.280828 − 0.959758i \(-0.409391\pi\)
0.280828 + 0.959758i \(0.409391\pi\)
\(318\) −5.00000 −0.280386
\(319\) 3.00000 0.167968
\(320\) 1.00000 0.0559017
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 21.0000 1.16308
\(327\) 5.00000 0.276501
\(328\) 0 0
\(329\) 0 0
\(330\) 3.00000 0.165145
\(331\) 19.0000 1.04433 0.522167 − 0.852843i \(-0.325124\pi\)
0.522167 + 0.852843i \(0.325124\pi\)
\(332\) −4.00000 −0.219529
\(333\) 20.0000 1.09599
\(334\) −14.0000 −0.766046
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 16.0000 0.871576 0.435788 − 0.900049i \(-0.356470\pi\)
0.435788 + 0.900049i \(0.356470\pi\)
\(338\) 12.0000 0.652714
\(339\) −10.0000 −0.543125
\(340\) −2.00000 −0.108465
\(341\) −27.0000 −1.46213
\(342\) −16.0000 −0.865181
\(343\) 0 0
\(344\) 11.0000 0.593080
\(345\) −1.00000 −0.0538382
\(346\) −18.0000 −0.967686
\(347\) 22.0000 1.18102 0.590511 − 0.807030i \(-0.298926\pi\)
0.590511 + 0.807030i \(0.298926\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 7.00000 0.374701 0.187351 − 0.982293i \(-0.440010\pi\)
0.187351 + 0.982293i \(0.440010\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 3.00000 0.159901
\(353\) −10.0000 −0.532246 −0.266123 − 0.963939i \(-0.585743\pi\)
−0.266123 + 0.963939i \(0.585743\pi\)
\(354\) −8.00000 −0.425195
\(355\) 6.00000 0.318447
\(356\) 0 0
\(357\) 0 0
\(358\) 20.0000 1.05703
\(359\) 13.0000 0.686114 0.343057 − 0.939315i \(-0.388538\pi\)
0.343057 + 0.939315i \(0.388538\pi\)
\(360\) 2.00000 0.105409
\(361\) 45.0000 2.36842
\(362\) −11.0000 −0.578147
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 6.00000 0.313625
\(367\) 32.0000 1.67039 0.835193 − 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) 10.0000 0.519875
\(371\) 0 0
\(372\) 9.00000 0.466628
\(373\) 27.0000 1.39801 0.699004 − 0.715118i \(-0.253627\pi\)
0.699004 + 0.715118i \(0.253627\pi\)
\(374\) −6.00000 −0.310253
\(375\) −9.00000 −0.464758
\(376\) −9.00000 −0.464140
\(377\) −1.00000 −0.0515026
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 − 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −8.00000 −0.410391
\(381\) −8.00000 −0.409852
\(382\) −24.0000 −1.22795
\(383\) 20.0000 1.02195 0.510976 − 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) 22.0000 1.11832
\(388\) 6.00000 0.304604
\(389\) −28.0000 −1.41966 −0.709828 − 0.704375i \(-0.751227\pi\)
−0.709828 + 0.704375i \(0.751227\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 2.00000 0.101144
\(392\) 7.00000 0.353553
\(393\) −4.00000 −0.201773
\(394\) 18.0000 0.906827
\(395\) 1.00000 0.0503155
\(396\) 6.00000 0.301511
\(397\) 25.0000 1.25471 0.627357 − 0.778732i \(-0.284137\pi\)
0.627357 + 0.778732i \(0.284137\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −7.00000 −0.349563 −0.174782 − 0.984607i \(-0.555922\pi\)
−0.174782 + 0.984607i \(0.555922\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 9.00000 0.448322
\(404\) −2.00000 −0.0995037
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 30.0000 1.48704
\(408\) 2.00000 0.0990148
\(409\) 4.00000 0.197787 0.0988936 − 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) −2.00000 −0.0982946
\(415\) −4.00000 −0.196352
\(416\) −1.00000 −0.0490290
\(417\) −10.0000 −0.489702
\(418\) −24.0000 −1.17388
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 − 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) −27.0000 −1.31434
\(423\) −18.0000 −0.875190
\(424\) −5.00000 −0.242821
\(425\) 8.00000 0.388057
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) −3.00000 −0.144841
\(430\) 11.0000 0.530467
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) −5.00000 −0.240563
\(433\) −22.0000 −1.05725 −0.528626 − 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 0 0
\(435\) −1.00000 −0.0479463
\(436\) 5.00000 0.239457
\(437\) 8.00000 0.382692
\(438\) −6.00000 −0.286691
\(439\) −6.00000 −0.286364 −0.143182 − 0.989696i \(-0.545733\pi\)
−0.143182 + 0.989696i \(0.545733\pi\)
\(440\) 3.00000 0.143019
\(441\) 14.0000 0.666667
\(442\) 2.00000 0.0951303
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) 10.0000 0.473514
\(447\) 3.00000 0.141895
\(448\) 0 0
\(449\) −4.00000 −0.188772 −0.0943858 − 0.995536i \(-0.530089\pi\)
−0.0943858 + 0.995536i \(0.530089\pi\)
\(450\) −8.00000 −0.377124
\(451\) 0 0
\(452\) −10.0000 −0.470360
\(453\) 6.00000 0.281905
\(454\) −24.0000 −1.12638
\(455\) 0 0
\(456\) 8.00000 0.374634
\(457\) −14.0000 −0.654892 −0.327446 − 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(458\) 12.0000 0.560723
\(459\) 10.0000 0.466760
\(460\) −1.00000 −0.0466252
\(461\) 8.00000 0.372597 0.186299 − 0.982493i \(-0.440351\pi\)
0.186299 + 0.982493i \(0.440351\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 − 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 9.00000 0.417365
\(466\) −19.0000 −0.880158
\(467\) −7.00000 −0.323921 −0.161961 − 0.986797i \(-0.551782\pi\)
−0.161961 + 0.986797i \(0.551782\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) −9.00000 −0.415139
\(471\) 0 0
\(472\) −8.00000 −0.368230
\(473\) 33.0000 1.51734
\(474\) −1.00000 −0.0459315
\(475\) 32.0000 1.46826
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) −6.00000 −0.274434
\(479\) −27.0000 −1.23366 −0.616831 − 0.787096i \(-0.711584\pi\)
−0.616831 + 0.787096i \(0.711584\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −10.0000 −0.455961
\(482\) 17.0000 0.774329
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 6.00000 0.272446
\(486\) −16.0000 −0.725775
\(487\) −24.0000 −1.08754 −0.543772 − 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 6.00000 0.271607
\(489\) −21.0000 −0.949653
\(490\) 7.00000 0.316228
\(491\) −31.0000 −1.39901 −0.699505 − 0.714628i \(-0.746596\pi\)
−0.699505 + 0.714628i \(0.746596\pi\)
\(492\) 0 0
\(493\) 2.00000 0.0900755
\(494\) 8.00000 0.359937
\(495\) 6.00000 0.269680
\(496\) 9.00000 0.404112
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) −24.0000 −1.07439 −0.537194 − 0.843459i \(-0.680516\pi\)
−0.537194 + 0.843459i \(0.680516\pi\)
\(500\) −9.00000 −0.402492
\(501\) 14.0000 0.625474
\(502\) 13.0000 0.580218
\(503\) 29.0000 1.29305 0.646523 − 0.762894i \(-0.276222\pi\)
0.646523 + 0.762894i \(0.276222\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) −3.00000 −0.133366
\(507\) −12.0000 −0.532939
\(508\) −8.00000 −0.354943
\(509\) −33.0000 −1.46270 −0.731350 − 0.682003i \(-0.761109\pi\)
−0.731350 + 0.682003i \(0.761109\pi\)
\(510\) 2.00000 0.0885615
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 40.0000 1.76604
\(514\) −21.0000 −0.926270
\(515\) 14.0000 0.616914
\(516\) −11.0000 −0.484248
\(517\) −27.0000 −1.18746
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) −1.00000 −0.0438529
\(521\) 21.0000 0.920027 0.460013 − 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 28.0000 1.22435 0.612177 − 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) 1.00000 0.0436021
\(527\) −18.0000 −0.784092
\(528\) −3.00000 −0.130558
\(529\) 1.00000 0.0434783
\(530\) −5.00000 −0.217186
\(531\) −16.0000 −0.694341
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 −0.778208
\(536\) −2.00000 −0.0863868
\(537\) −20.0000 −0.863064
\(538\) −6.00000 −0.258678
\(539\) 21.0000 0.904534
\(540\) −5.00000 −0.215166
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 25.0000 1.07384
\(543\) 11.0000 0.472055
\(544\) 2.00000 0.0857493
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) 40.0000 1.71028 0.855138 − 0.518400i \(-0.173472\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) −6.00000 −0.256307
\(549\) 12.0000 0.512148
\(550\) −12.0000 −0.511682
\(551\) 8.00000 0.340811
\(552\) 1.00000 0.0425628
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) −10.0000 −0.424476
\(556\) −10.0000 −0.424094
\(557\) −10.0000 −0.423714 −0.211857 − 0.977301i \(-0.567951\pi\)
−0.211857 + 0.977301i \(0.567951\pi\)
\(558\) 18.0000 0.762001
\(559\) −11.0000 −0.465250
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 3.00000 0.126547
\(563\) 33.0000 1.39078 0.695392 − 0.718631i \(-0.255231\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(564\) 9.00000 0.378968
\(565\) −10.0000 −0.420703
\(566\) −22.0000 −0.924729
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 30.0000 1.25767 0.628833 − 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 8.00000 0.335083
\(571\) −40.0000 −1.67395 −0.836974 − 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −3.00000 −0.125436
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) −2.00000 −0.0833333
\(577\) −2.00000 −0.0832611 −0.0416305 − 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 13.0000 0.540729
\(579\) −26.0000 −1.08052
\(580\) −1.00000 −0.0415227
\(581\) 0 0
\(582\) −6.00000 −0.248708
\(583\) −15.0000 −0.621237
\(584\) −6.00000 −0.248282
\(585\) −2.00000 −0.0826898
\(586\) 12.0000 0.495715
\(587\) −32.0000 −1.32078 −0.660391 − 0.750922i \(-0.729609\pi\)
−0.660391 + 0.750922i \(0.729609\pi\)
\(588\) −7.00000 −0.288675
\(589\) −72.0000 −2.96671
\(590\) −8.00000 −0.329355
\(591\) −18.0000 −0.740421
\(592\) −10.0000 −0.410997
\(593\) −17.0000 −0.698106 −0.349053 − 0.937103i \(-0.613497\pi\)
−0.349053 + 0.937103i \(0.613497\pi\)
\(594\) −15.0000 −0.615457
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) −14.0000 −0.572982
\(598\) 1.00000 0.0408930
\(599\) −9.00000 −0.367730 −0.183865 − 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) 4.00000 0.163299
\(601\) −42.0000 −1.71322 −0.856608 − 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 6.00000 0.244137
\(605\) −2.00000 −0.0813116
\(606\) 2.00000 0.0812444
\(607\) −13.0000 −0.527654 −0.263827 − 0.964570i \(-0.584985\pi\)
−0.263827 + 0.964570i \(0.584985\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 9.00000 0.364101
\(612\) 4.00000 0.161690
\(613\) −31.0000 −1.25208 −0.626039 − 0.779792i \(-0.715325\pi\)
−0.626039 + 0.779792i \(0.715325\pi\)
\(614\) −15.0000 −0.605351
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 − 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) −14.0000 −0.563163
\(619\) 9.00000 0.361741 0.180870 − 0.983507i \(-0.442109\pi\)
0.180870 + 0.983507i \(0.442109\pi\)
\(620\) 9.00000 0.361449
\(621\) 5.00000 0.200643
\(622\) −32.0000 −1.28308
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 11.0000 0.440000
\(626\) 17.0000 0.679457
\(627\) 24.0000 0.958468
\(628\) 0 0
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 22.0000 0.875806 0.437903 − 0.899022i \(-0.355721\pi\)
0.437903 + 0.899022i \(0.355721\pi\)
\(632\) −1.00000 −0.0397779
\(633\) 27.0000 1.07315
\(634\) −10.0000 −0.397151
\(635\) −8.00000 −0.317470
\(636\) 5.00000 0.198263
\(637\) −7.00000 −0.277350
\(638\) −3.00000 −0.118771
\(639\) −12.0000 −0.474713
\(640\) −1.00000 −0.0395285
\(641\) −24.0000 −0.947943 −0.473972 − 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) 18.0000 0.710403
\(643\) −20.0000 −0.788723 −0.394362 − 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) −11.0000 −0.433125
\(646\) −16.0000 −0.629512
\(647\) 14.0000 0.550397 0.275198 − 0.961387i \(-0.411256\pi\)
0.275198 + 0.961387i \(0.411256\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −24.0000 −0.942082
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) −21.0000 −0.822423
\(653\) −6.00000 −0.234798 −0.117399 − 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −5.00000 −0.195515
\(655\) −4.00000 −0.156293
\(656\) 0 0
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) −21.0000 −0.818044 −0.409022 − 0.912525i \(-0.634130\pi\)
−0.409022 + 0.912525i \(0.634130\pi\)
\(660\) −3.00000 −0.116775
\(661\) 38.0000 1.47803 0.739014 − 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −19.0000 −0.738456
\(663\) −2.00000 −0.0776736
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −20.0000 −0.774984
\(667\) 1.00000 0.0387202
\(668\) 14.0000 0.541676
\(669\) −10.0000 −0.386622
\(670\) −2.00000 −0.0772667
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 21.0000 0.809491 0.404745 − 0.914429i \(-0.367360\pi\)
0.404745 + 0.914429i \(0.367360\pi\)
\(674\) −16.0000 −0.616297
\(675\) 20.0000 0.769800
\(676\) −12.0000 −0.461538
\(677\) −40.0000 −1.53732 −0.768662 − 0.639655i \(-0.779077\pi\)
−0.768662 + 0.639655i \(0.779077\pi\)
\(678\) 10.0000 0.384048
\(679\) 0 0
\(680\) 2.00000 0.0766965
\(681\) 24.0000 0.919682
\(682\) 27.0000 1.03388
\(683\) 36.0000 1.37750 0.688751 − 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 16.0000 0.611775
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) −12.0000 −0.457829
\(688\) −11.0000 −0.419371
\(689\) 5.00000 0.190485
\(690\) 1.00000 0.0380693
\(691\) −10.0000 −0.380418 −0.190209 − 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) −22.0000 −0.835109
\(695\) −10.0000 −0.379322
\(696\) 1.00000 0.0379049
\(697\) 0 0
\(698\) −7.00000 −0.264954
\(699\) 19.0000 0.718646
\(700\) 0 0
\(701\) −25.0000 −0.944237 −0.472118 − 0.881535i \(-0.656511\pi\)
−0.472118 + 0.881535i \(0.656511\pi\)
\(702\) 5.00000 0.188713
\(703\) 80.0000 3.01726
\(704\) −3.00000 −0.113067
\(705\) 9.00000 0.338960
\(706\) 10.0000 0.376355
\(707\) 0 0
\(708\) 8.00000 0.300658
\(709\) −29.0000 −1.08912 −0.544559 − 0.838723i \(-0.683303\pi\)
−0.544559 + 0.838723i \(0.683303\pi\)
\(710\) −6.00000 −0.225176
\(711\) −2.00000 −0.0750059
\(712\) 0 0
\(713\) −9.00000 −0.337053
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) −20.0000 −0.747435
\(717\) 6.00000 0.224074
\(718\) −13.0000 −0.485156
\(719\) 46.0000 1.71551 0.857755 − 0.514058i \(-0.171858\pi\)
0.857755 + 0.514058i \(0.171858\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) −45.0000 −1.67473
\(723\) −17.0000 −0.632237
\(724\) 11.0000 0.408812
\(725\) 4.00000 0.148556
\(726\) 2.00000 0.0742270
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −6.00000 −0.222070
\(731\) 22.0000 0.813699
\(732\) −6.00000 −0.221766
\(733\) −2.00000 −0.0738717 −0.0369358 − 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) −32.0000 −1.18114
\(735\) −7.00000 −0.258199
\(736\) 1.00000 0.0368605
\(737\) −6.00000 −0.221013
\(738\) 0 0
\(739\) −27.0000 −0.993211 −0.496606 − 0.867976i \(-0.665420\pi\)
−0.496606 + 0.867976i \(0.665420\pi\)
\(740\) −10.0000 −0.367607
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −9.00000 −0.329956
\(745\) 3.00000 0.109911
\(746\) −27.0000 −0.988540
\(747\) 8.00000 0.292705
\(748\) 6.00000 0.219382
\(749\) 0 0
\(750\) 9.00000 0.328634
\(751\) −8.00000 −0.291924 −0.145962 − 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 9.00000 0.328196
\(753\) −13.0000 −0.473746
\(754\) 1.00000 0.0364179
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 28.0000 1.01768 0.508839 − 0.860862i \(-0.330075\pi\)
0.508839 + 0.860862i \(0.330075\pi\)
\(758\) 16.0000 0.581146
\(759\) 3.00000 0.108893
\(760\) 8.00000 0.290191
\(761\) −38.0000 −1.37750 −0.688749 − 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) 4.00000 0.144620
\(766\) −20.0000 −0.722629
\(767\) 8.00000 0.288863
\(768\) 1.00000 0.0360844
\(769\) −16.0000 −0.576975 −0.288487 − 0.957484i \(-0.593152\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(770\) 0 0
\(771\) 21.0000 0.756297
\(772\) −26.0000 −0.935760
\(773\) 36.0000 1.29483 0.647415 − 0.762138i \(-0.275850\pi\)
0.647415 + 0.762138i \(0.275850\pi\)
\(774\) −22.0000 −0.790774
\(775\) −36.0000 −1.29316
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 28.0000 1.00385
\(779\) 0 0
\(780\) 1.00000 0.0358057
\(781\) −18.0000 −0.644091
\(782\) −2.00000 −0.0715199
\(783\) 5.00000 0.178685
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) 4.00000 0.142675
\(787\) 40.0000 1.42585 0.712923 − 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) −18.0000 −0.641223
\(789\) −1.00000 −0.0356009
\(790\) −1.00000 −0.0355784
\(791\) 0 0
\(792\) −6.00000 −0.213201
\(793\) −6.00000 −0.213066
\(794\) −25.0000 −0.887217
\(795\) 5.00000 0.177332
\(796\) −14.0000 −0.496217
\(797\) −40.0000 −1.41687 −0.708436 − 0.705775i \(-0.750599\pi\)
−0.708436 + 0.705775i \(0.750599\pi\)
\(798\) 0 0
\(799\) −18.0000 −0.636794
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) 7.00000 0.247179
\(803\) −18.0000 −0.635206
\(804\) 2.00000 0.0705346
\(805\) 0 0
\(806\) −9.00000 −0.317011
\(807\) 6.00000 0.211210
\(808\) 2.00000 0.0703598
\(809\) −26.0000 −0.914111 −0.457056 − 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −22.0000 −0.772524 −0.386262 − 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(812\) 0 0
\(813\) −25.0000 −0.876788
\(814\) −30.0000 −1.05150
\(815\) −21.0000 −0.735598
\(816\) −2.00000 −0.0700140
\(817\) 88.0000 3.07873
\(818\) −4.00000 −0.139857
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 −0.523504 −0.261752 − 0.965135i \(-0.584300\pi\)
−0.261752 + 0.965135i \(0.584300\pi\)
\(822\) 6.00000 0.209274
\(823\) 32.0000 1.11545 0.557725 − 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) −14.0000 −0.487713
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) −27.0000 −0.938882 −0.469441 − 0.882964i \(-0.655545\pi\)
−0.469441 + 0.882964i \(0.655545\pi\)
\(828\) 2.00000 0.0695048
\(829\) 16.0000 0.555703 0.277851 − 0.960624i \(-0.410378\pi\)
0.277851 + 0.960624i \(0.410378\pi\)
\(830\) 4.00000 0.138842
\(831\) −22.0000 −0.763172
\(832\) 1.00000 0.0346688
\(833\) 14.0000 0.485071
\(834\) 10.0000 0.346272
\(835\) 14.0000 0.484490
\(836\) 24.0000 0.830057
\(837\) −45.0000 −1.55543
\(838\) −12.0000 −0.414533
\(839\) 35.0000 1.20833 0.604167 − 0.796858i \(-0.293506\pi\)
0.604167 + 0.796858i \(0.293506\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 8.00000 0.275698
\(843\) −3.00000 −0.103325
\(844\) 27.0000 0.929378
\(845\) −12.0000 −0.412813
\(846\) 18.0000 0.618853
\(847\) 0 0
\(848\) 5.00000 0.171701
\(849\) 22.0000 0.755038
\(850\) −8.00000 −0.274398
\(851\) 10.0000 0.342796
\(852\) 6.00000 0.205557
\(853\) −14.0000 −0.479351 −0.239675 − 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 0 0
\(855\) 16.0000 0.547188
\(856\) 18.0000 0.615227
\(857\) −23.0000 −0.785665 −0.392833 − 0.919610i \(-0.628505\pi\)
−0.392833 + 0.919610i \(0.628505\pi\)
\(858\) 3.00000 0.102418
\(859\) −31.0000 −1.05771 −0.528853 − 0.848713i \(-0.677378\pi\)
−0.528853 + 0.848713i \(0.677378\pi\)
\(860\) −11.0000 −0.375097
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) 40.0000 1.36162 0.680808 − 0.732462i \(-0.261629\pi\)
0.680808 + 0.732462i \(0.261629\pi\)
\(864\) 5.00000 0.170103
\(865\) 18.0000 0.612018
\(866\) 22.0000 0.747590
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) −3.00000 −0.101768
\(870\) 1.00000 0.0339032
\(871\) 2.00000 0.0677674
\(872\) −5.00000 −0.169321
\(873\) −12.0000 −0.406138
\(874\) −8.00000 −0.270604
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) −17.0000 −0.574049 −0.287025 − 0.957923i \(-0.592666\pi\)
−0.287025 + 0.957923i \(0.592666\pi\)
\(878\) 6.00000 0.202490
\(879\) −12.0000 −0.404750
\(880\) −3.00000 −0.101130
\(881\) 40.0000 1.34763 0.673817 − 0.738898i \(-0.264654\pi\)
0.673817 + 0.738898i \(0.264654\pi\)
\(882\) −14.0000 −0.471405
\(883\) 30.0000 1.00958 0.504790 − 0.863242i \(-0.331570\pi\)
0.504790 + 0.863242i \(0.331570\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 8.00000 0.268917
\(886\) 0 0
\(887\) −3.00000 −0.100730 −0.0503651 − 0.998731i \(-0.516038\pi\)
−0.0503651 + 0.998731i \(0.516038\pi\)
\(888\) 10.0000 0.335578
\(889\) 0 0
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) −10.0000 −0.334825
\(893\) −72.0000 −2.40939
\(894\) −3.00000 −0.100335
\(895\) −20.0000 −0.668526
\(896\) 0 0
\(897\) −1.00000 −0.0333890
\(898\) 4.00000 0.133482
\(899\) −9.00000 −0.300167
\(900\) 8.00000 0.266667
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 11.0000 0.365652
\(906\) −6.00000 −0.199337
\(907\) 4.00000 0.132818 0.0664089 − 0.997792i \(-0.478846\pi\)
0.0664089 + 0.997792i \(0.478846\pi\)
\(908\) 24.0000 0.796468
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) −55.0000 −1.82223 −0.911116 − 0.412151i \(-0.864778\pi\)
−0.911116 + 0.412151i \(0.864778\pi\)
\(912\) −8.00000 −0.264906
\(913\) 12.0000 0.397142
\(914\) 14.0000 0.463079
\(915\) −6.00000 −0.198354
\(916\) −12.0000 −0.396491
\(917\) 0 0
\(918\) −10.0000 −0.330049
\(919\) −32.0000 −1.05558 −0.527791 − 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) 1.00000 0.0329690
\(921\) 15.0000 0.494267
\(922\) −8.00000 −0.263466
\(923\) 6.00000 0.197492
\(924\) 0 0
\(925\) 40.0000 1.31519
\(926\) 24.0000 0.788689
\(927\) −28.0000 −0.919641
\(928\) 1.00000 0.0328266
\(929\) 42.0000 1.37798 0.688988 − 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) −9.00000 −0.295122
\(931\) 56.0000 1.83533
\(932\) 19.0000 0.622366
\(933\) 32.0000 1.04763
\(934\) 7.00000 0.229047
\(935\) 6.00000 0.196221
\(936\) 2.00000 0.0653720
\(937\) −54.0000 −1.76410 −0.882052 − 0.471153i \(-0.843838\pi\)
−0.882052 + 0.471153i \(0.843838\pi\)
\(938\) 0 0
\(939\) −17.0000 −0.554774
\(940\) 9.00000 0.293548
\(941\) 29.0000 0.945373 0.472686 − 0.881231i \(-0.343284\pi\)
0.472686 + 0.881231i \(0.343284\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) −33.0000 −1.07292
\(947\) −33.0000 −1.07236 −0.536178 − 0.844105i \(-0.680132\pi\)
−0.536178 + 0.844105i \(0.680132\pi\)
\(948\) 1.00000 0.0324785
\(949\) 6.00000 0.194768
\(950\) −32.0000 −1.03822
\(951\) 10.0000 0.324272
\(952\) 0 0
\(953\) −51.0000 −1.65205 −0.826026 − 0.563632i \(-0.809404\pi\)
−0.826026 + 0.563632i \(0.809404\pi\)
\(954\) 10.0000 0.323762
\(955\) 24.0000 0.776622
\(956\) 6.00000 0.194054
\(957\) 3.00000 0.0969762
\(958\) 27.0000 0.872330
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) 50.0000 1.61290
\(962\) 10.0000 0.322413
\(963\) 36.0000 1.16008
\(964\) −17.0000 −0.547533
\(965\) −26.0000 −0.836970
\(966\) 0 0
\(967\) 13.0000 0.418052 0.209026 − 0.977910i \(-0.432971\pi\)
0.209026 + 0.977910i \(0.432971\pi\)
\(968\) 2.00000 0.0642824
\(969\) 16.0000 0.513994
\(970\) −6.00000 −0.192648
\(971\) 56.0000 1.79713 0.898563 − 0.438845i \(-0.144612\pi\)
0.898563 + 0.438845i \(0.144612\pi\)
\(972\) 16.0000 0.513200
\(973\) 0 0
\(974\) 24.0000 0.769010
\(975\) −4.00000 −0.128103
\(976\) −6.00000 −0.192055
\(977\) −37.0000 −1.18373 −0.591867 − 0.806035i \(-0.701609\pi\)
−0.591867 + 0.806035i \(0.701609\pi\)
\(978\) 21.0000 0.671506
\(979\) 0 0
\(980\) −7.00000 −0.223607
\(981\) −10.0000 −0.319275
\(982\) 31.0000 0.989250
\(983\) −37.0000 −1.18012 −0.590058 − 0.807361i \(-0.700895\pi\)
−0.590058 + 0.807361i \(0.700895\pi\)
\(984\) 0 0
\(985\) −18.0000 −0.573528
\(986\) −2.00000 −0.0636930
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 11.0000 0.349780
\(990\) −6.00000 −0.190693
\(991\) 16.0000 0.508257 0.254128 − 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) −9.00000 −0.285750
\(993\) 19.0000 0.602947
\(994\) 0 0
\(995\) −14.0000 −0.443830
\(996\) −4.00000 −0.126745
\(997\) 6.00000 0.190022 0.0950110 − 0.995476i \(-0.469711\pi\)
0.0950110 + 0.995476i \(0.469711\pi\)
\(998\) 24.0000 0.759707
\(999\) 50.0000 1.58193
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 1334.2.a.c.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1334.2.a.c.1.1 ✓ 1 1.1 even 1 trivial