Properties

Label 592.2.a.i.1.1
Level $592$
Weight $2$
Character 592.1
Self dual yes
Analytic conductor $4.727$
Analytic rank $1$
Dimension $3$
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] = [592,2,Mod(1,592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(592, 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("592.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.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: \(4.72714379966\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 4x - 1 \) 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 296)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.11491\) of defining polynomial
Character \(\chi\) \(=\) 592.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.47283 q^{3} +1.47283 q^{5} -2.64207 q^{7} +3.11491 q^{9} +O(q^{10})\) \(q-2.47283 q^{3} +1.47283 q^{5} -2.64207 q^{7} +3.11491 q^{9} +6.34472 q^{11} -5.34472 q^{13} -3.64207 q^{15} -0.715853 q^{17} -3.28415 q^{19} +6.53341 q^{21} -0.885092 q^{23} -2.83076 q^{25} -0.284147 q^{27} -0.885092 q^{29} -7.47283 q^{31} -15.6894 q^{33} -3.89134 q^{35} -1.00000 q^{37} +13.2166 q^{39} -7.75698 q^{41} -10.1212 q^{43} +4.58774 q^{45} -11.8176 q^{47} -0.0194469 q^{49} +1.77018 q^{51} +4.15604 q^{53} +9.34472 q^{55} +8.12115 q^{57} +12.1212 q^{59} +3.81131 q^{61} -8.22982 q^{63} -7.87189 q^{65} +5.32528 q^{67} +2.18869 q^{69} -2.87189 q^{71} -8.34472 q^{73} +7.00000 q^{75} -16.7632 q^{77} +1.83076 q^{79} -8.64207 q^{81} -2.15604 q^{83} -1.05433 q^{85} +2.18869 q^{87} -1.89134 q^{89} +14.1212 q^{91} +18.4791 q^{93} -4.83700 q^{95} +15.0668 q^{97} +19.7632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - q^{5} - 7 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - q^{5} - 7 q^{7} + 3 q^{9} + 3 q^{13} - 10 q^{15} - 4 q^{17} - 8 q^{19} - 3 q^{21} - 9 q^{23} - 4 q^{25} + q^{27} - 9 q^{29} - 17 q^{31} - 9 q^{33} + 10 q^{35} - 3 q^{37} + 7 q^{39} - 16 q^{41} + 4 q^{43} + 2 q^{45} - 11 q^{47} + 8 q^{49} + 18 q^{51} - 3 q^{53} + 9 q^{55} - 10 q^{57} + 2 q^{59} + 15 q^{61} - 12 q^{63} - 10 q^{65} + 5 q^{67} + 3 q^{69} + 5 q^{71} - 6 q^{73} + 21 q^{75} - 15 q^{77} + q^{79} - 25 q^{81} + 9 q^{83} - 14 q^{85} + 3 q^{87} + 16 q^{89} + 8 q^{91} + 22 q^{93} + 18 q^{95} + 24 q^{99}+O(q^{100}) \) 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
\(3\) −2.47283 −1.42769 −0.713846 0.700303i \(-0.753048\pi\)
−0.713846 + 0.700303i \(0.753048\pi\)
\(4\) 0 0
\(5\) 1.47283 0.658671 0.329336 0.944213i \(-0.393175\pi\)
0.329336 + 0.944213i \(0.393175\pi\)
\(6\) 0 0
\(7\) −2.64207 −0.998610 −0.499305 0.866426i \(-0.666411\pi\)
−0.499305 + 0.866426i \(0.666411\pi\)
\(8\) 0 0
\(9\) 3.11491 1.03830
\(10\) 0 0
\(11\) 6.34472 1.91301 0.956503 0.291723i \(-0.0942285\pi\)
0.956503 + 0.291723i \(0.0942285\pi\)
\(12\) 0 0
\(13\) −5.34472 −1.48236 −0.741180 0.671307i \(-0.765733\pi\)
−0.741180 + 0.671307i \(0.765733\pi\)
\(14\) 0 0
\(15\) −3.64207 −0.940379
\(16\) 0 0
\(17\) −0.715853 −0.173620 −0.0868099 0.996225i \(-0.527667\pi\)
−0.0868099 + 0.996225i \(0.527667\pi\)
\(18\) 0 0
\(19\) −3.28415 −0.753435 −0.376718 0.926328i \(-0.622947\pi\)
−0.376718 + 0.926328i \(0.622947\pi\)
\(20\) 0 0
\(21\) 6.53341 1.42571
\(22\) 0 0
\(23\) −0.885092 −0.184555 −0.0922773 0.995733i \(-0.529415\pi\)
−0.0922773 + 0.995733i \(0.529415\pi\)
\(24\) 0 0
\(25\) −2.83076 −0.566152
\(26\) 0 0
\(27\) −0.284147 −0.0546842
\(28\) 0 0
\(29\) −0.885092 −0.164358 −0.0821788 0.996618i \(-0.526188\pi\)
−0.0821788 + 0.996618i \(0.526188\pi\)
\(30\) 0 0
\(31\) −7.47283 −1.34216 −0.671080 0.741385i \(-0.734169\pi\)
−0.671080 + 0.741385i \(0.734169\pi\)
\(32\) 0 0
\(33\) −15.6894 −2.73118
\(34\) 0 0
\(35\) −3.89134 −0.657756
\(36\) 0 0
\(37\) −1.00000 −0.164399
\(38\) 0 0
\(39\) 13.2166 2.11635
\(40\) 0 0
\(41\) −7.75698 −1.21144 −0.605718 0.795679i \(-0.707114\pi\)
−0.605718 + 0.795679i \(0.707114\pi\)
\(42\) 0 0
\(43\) −10.1212 −1.54346 −0.771731 0.635950i \(-0.780609\pi\)
−0.771731 + 0.635950i \(0.780609\pi\)
\(44\) 0 0
\(45\) 4.58774 0.683900
\(46\) 0 0
\(47\) −11.8176 −1.72377 −0.861884 0.507106i \(-0.830715\pi\)
−0.861884 + 0.507106i \(0.830715\pi\)
\(48\) 0 0
\(49\) −0.0194469 −0.00277813
\(50\) 0 0
\(51\) 1.77018 0.247875
\(52\) 0 0
\(53\) 4.15604 0.570875 0.285438 0.958397i \(-0.407861\pi\)
0.285438 + 0.958397i \(0.407861\pi\)
\(54\) 0 0
\(55\) 9.34472 1.26004
\(56\) 0 0
\(57\) 8.12115 1.07567
\(58\) 0 0
\(59\) 12.1212 1.57804 0.789020 0.614368i \(-0.210589\pi\)
0.789020 + 0.614368i \(0.210589\pi\)
\(60\) 0 0
\(61\) 3.81131 0.487989 0.243994 0.969777i \(-0.421542\pi\)
0.243994 + 0.969777i \(0.421542\pi\)
\(62\) 0 0
\(63\) −8.22982 −1.03686
\(64\) 0 0
\(65\) −7.87189 −0.976388
\(66\) 0 0
\(67\) 5.32528 0.650586 0.325293 0.945613i \(-0.394537\pi\)
0.325293 + 0.945613i \(0.394537\pi\)
\(68\) 0 0
\(69\) 2.18869 0.263487
\(70\) 0 0
\(71\) −2.87189 −0.340830 −0.170415 0.985372i \(-0.554511\pi\)
−0.170415 + 0.985372i \(0.554511\pi\)
\(72\) 0 0
\(73\) −8.34472 −0.976676 −0.488338 0.872655i \(-0.662397\pi\)
−0.488338 + 0.872655i \(0.662397\pi\)
\(74\) 0 0
\(75\) 7.00000 0.808290
\(76\) 0 0
\(77\) −16.7632 −1.91035
\(78\) 0 0
\(79\) 1.83076 0.205977 0.102988 0.994683i \(-0.467160\pi\)
0.102988 + 0.994683i \(0.467160\pi\)
\(80\) 0 0
\(81\) −8.64207 −0.960230
\(82\) 0 0
\(83\) −2.15604 −0.236656 −0.118328 0.992975i \(-0.537753\pi\)
−0.118328 + 0.992975i \(0.537753\pi\)
\(84\) 0 0
\(85\) −1.05433 −0.114358
\(86\) 0 0
\(87\) 2.18869 0.234652
\(88\) 0 0
\(89\) −1.89134 −0.200481 −0.100241 0.994963i \(-0.531961\pi\)
−0.100241 + 0.994963i \(0.531961\pi\)
\(90\) 0 0
\(91\) 14.1212 1.48030
\(92\) 0 0
\(93\) 18.4791 1.91619
\(94\) 0 0
\(95\) −4.83700 −0.496266
\(96\) 0 0
\(97\) 15.0668 1.52980 0.764902 0.644147i \(-0.222787\pi\)
0.764902 + 0.644147i \(0.222787\pi\)
\(98\) 0 0
\(99\) 19.7632 1.98628
\(100\) 0 0
\(101\) −8.15604 −0.811556 −0.405778 0.913972i \(-0.632999\pi\)
−0.405778 + 0.913972i \(0.632999\pi\)
\(102\) 0 0
\(103\) −14.6483 −1.44334 −0.721671 0.692236i \(-0.756626\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(104\) 0 0
\(105\) 9.62263 0.939072
\(106\) 0 0
\(107\) 6.20813 0.600163 0.300081 0.953914i \(-0.402986\pi\)
0.300081 + 0.953914i \(0.402986\pi\)
\(108\) 0 0
\(109\) 6.82452 0.653670 0.326835 0.945081i \(-0.394018\pi\)
0.326835 + 0.945081i \(0.394018\pi\)
\(110\) 0 0
\(111\) 2.47283 0.234711
\(112\) 0 0
\(113\) 12.3510 1.16188 0.580941 0.813946i \(-0.302685\pi\)
0.580941 + 0.813946i \(0.302685\pi\)
\(114\) 0 0
\(115\) −1.30359 −0.121561
\(116\) 0 0
\(117\) −16.6483 −1.53914
\(118\) 0 0
\(119\) 1.89134 0.173378
\(120\) 0 0
\(121\) 29.2555 2.65959
\(122\) 0 0
\(123\) 19.1817 1.72956
\(124\) 0 0
\(125\) −11.5334 −1.03158
\(126\) 0 0
\(127\) 18.5070 1.64223 0.821115 0.570762i \(-0.193352\pi\)
0.821115 + 0.570762i \(0.193352\pi\)
\(128\) 0 0
\(129\) 25.0279 2.20359
\(130\) 0 0
\(131\) 14.6894 1.28342 0.641711 0.766946i \(-0.278225\pi\)
0.641711 + 0.766946i \(0.278225\pi\)
\(132\) 0 0
\(133\) 8.67696 0.752388
\(134\) 0 0
\(135\) −0.418502 −0.0360189
\(136\) 0 0
\(137\) −3.32528 −0.284097 −0.142049 0.989860i \(-0.545369\pi\)
−0.142049 + 0.989860i \(0.545369\pi\)
\(138\) 0 0
\(139\) −9.23606 −0.783392 −0.391696 0.920095i \(-0.628112\pi\)
−0.391696 + 0.920095i \(0.628112\pi\)
\(140\) 0 0
\(141\) 29.2229 2.46101
\(142\) 0 0
\(143\) −33.9108 −2.83576
\(144\) 0 0
\(145\) −1.30359 −0.108258
\(146\) 0 0
\(147\) 0.0480890 0.00396631
\(148\) 0 0
\(149\) −2.64207 −0.216447 −0.108224 0.994127i \(-0.534516\pi\)
−0.108224 + 0.994127i \(0.534516\pi\)
\(150\) 0 0
\(151\) −17.9736 −1.46267 −0.731335 0.682018i \(-0.761102\pi\)
−0.731335 + 0.682018i \(0.761102\pi\)
\(152\) 0 0
\(153\) −2.22982 −0.180270
\(154\) 0 0
\(155\) −11.0062 −0.884043
\(156\) 0 0
\(157\) −4.15604 −0.331688 −0.165844 0.986152i \(-0.553035\pi\)
−0.165844 + 0.986152i \(0.553035\pi\)
\(158\) 0 0
\(159\) −10.2772 −0.815034
\(160\) 0 0
\(161\) 2.33848 0.184298
\(162\) 0 0
\(163\) −15.8913 −1.24471 −0.622353 0.782737i \(-0.713823\pi\)
−0.622353 + 0.782737i \(0.713823\pi\)
\(164\) 0 0
\(165\) −23.1079 −1.79895
\(166\) 0 0
\(167\) 16.7695 1.29766 0.648830 0.760933i \(-0.275259\pi\)
0.648830 + 0.760933i \(0.275259\pi\)
\(168\) 0 0
\(169\) 15.5661 1.19739
\(170\) 0 0
\(171\) −10.2298 −0.782294
\(172\) 0 0
\(173\) −2.41226 −0.183401 −0.0917003 0.995787i \(-0.529230\pi\)
−0.0917003 + 0.995787i \(0.529230\pi\)
\(174\) 0 0
\(175\) 7.47908 0.565365
\(176\) 0 0
\(177\) −29.9736 −2.25295
\(178\) 0 0
\(179\) −24.0125 −1.79478 −0.897389 0.441241i \(-0.854538\pi\)
−0.897389 + 0.441241i \(0.854538\pi\)
\(180\) 0 0
\(181\) 17.3315 1.28824 0.644121 0.764924i \(-0.277223\pi\)
0.644121 + 0.764924i \(0.277223\pi\)
\(182\) 0 0
\(183\) −9.42474 −0.696697
\(184\) 0 0
\(185\) −1.47283 −0.108285
\(186\) 0 0
\(187\) −4.54189 −0.332136
\(188\) 0 0
\(189\) 0.750738 0.0546082
\(190\) 0 0
\(191\) 7.55509 0.546667 0.273334 0.961919i \(-0.411874\pi\)
0.273334 + 0.961919i \(0.411874\pi\)
\(192\) 0 0
\(193\) 5.74378 0.413446 0.206723 0.978399i \(-0.433720\pi\)
0.206723 + 0.978399i \(0.433720\pi\)
\(194\) 0 0
\(195\) 19.4659 1.39398
\(196\) 0 0
\(197\) −16.1560 −1.15107 −0.575535 0.817777i \(-0.695206\pi\)
−0.575535 + 0.817777i \(0.695206\pi\)
\(198\) 0 0
\(199\) 7.17548 0.508656 0.254328 0.967118i \(-0.418146\pi\)
0.254328 + 0.967118i \(0.418146\pi\)
\(200\) 0 0
\(201\) −13.1685 −0.928836
\(202\) 0 0
\(203\) 2.33848 0.164129
\(204\) 0 0
\(205\) −11.4247 −0.797939
\(206\) 0 0
\(207\) −2.75698 −0.191623
\(208\) 0 0
\(209\) −20.8370 −1.44133
\(210\) 0 0
\(211\) −15.1692 −1.04429 −0.522147 0.852856i \(-0.674869\pi\)
−0.522147 + 0.852856i \(0.674869\pi\)
\(212\) 0 0
\(213\) 7.10170 0.486601
\(214\) 0 0
\(215\) −14.9068 −1.01663
\(216\) 0 0
\(217\) 19.7438 1.34029
\(218\) 0 0
\(219\) 20.6351 1.39439
\(220\) 0 0
\(221\) 3.82603 0.257367
\(222\) 0 0
\(223\) −0.789632 −0.0528777 −0.0264388 0.999650i \(-0.508417\pi\)
−0.0264388 + 0.999650i \(0.508417\pi\)
\(224\) 0 0
\(225\) −8.81756 −0.587837
\(226\) 0 0
\(227\) 1.05433 0.0699785 0.0349892 0.999388i \(-0.488860\pi\)
0.0349892 + 0.999388i \(0.488860\pi\)
\(228\) 0 0
\(229\) −29.7089 −1.96322 −0.981609 0.190900i \(-0.938859\pi\)
−0.981609 + 0.190900i \(0.938859\pi\)
\(230\) 0 0
\(231\) 41.4527 2.72739
\(232\) 0 0
\(233\) 18.9798 1.24341 0.621705 0.783251i \(-0.286440\pi\)
0.621705 + 0.783251i \(0.286440\pi\)
\(234\) 0 0
\(235\) −17.4053 −1.13540
\(236\) 0 0
\(237\) −4.52717 −0.294071
\(238\) 0 0
\(239\) −0.756981 −0.0489650 −0.0244825 0.999700i \(-0.507794\pi\)
−0.0244825 + 0.999700i \(0.507794\pi\)
\(240\) 0 0
\(241\) 0.147558 0.00950506 0.00475253 0.999989i \(-0.498487\pi\)
0.00475253 + 0.999989i \(0.498487\pi\)
\(242\) 0 0
\(243\) 22.2229 1.42560
\(244\) 0 0
\(245\) −0.0286421 −0.00182988
\(246\) 0 0
\(247\) 17.5529 1.11686
\(248\) 0 0
\(249\) 5.33152 0.337871
\(250\) 0 0
\(251\) 15.1755 0.957868 0.478934 0.877851i \(-0.341023\pi\)
0.478934 + 0.877851i \(0.341023\pi\)
\(252\) 0 0
\(253\) −5.61567 −0.353054
\(254\) 0 0
\(255\) 2.60719 0.163268
\(256\) 0 0
\(257\) 23.5264 1.46754 0.733770 0.679398i \(-0.237759\pi\)
0.733770 + 0.679398i \(0.237759\pi\)
\(258\) 0 0
\(259\) 2.64207 0.164170
\(260\) 0 0
\(261\) −2.75698 −0.170653
\(262\) 0 0
\(263\) −24.7368 −1.52534 −0.762669 0.646789i \(-0.776111\pi\)
−0.762669 + 0.646789i \(0.776111\pi\)
\(264\) 0 0
\(265\) 6.12115 0.376019
\(266\) 0 0
\(267\) 4.67696 0.286225
\(268\) 0 0
\(269\) 14.0389 0.855966 0.427983 0.903787i \(-0.359224\pi\)
0.427983 + 0.903787i \(0.359224\pi\)
\(270\) 0 0
\(271\) −4.04737 −0.245860 −0.122930 0.992415i \(-0.539229\pi\)
−0.122930 + 0.992415i \(0.539229\pi\)
\(272\) 0 0
\(273\) −34.9193 −2.11341
\(274\) 0 0
\(275\) −17.9604 −1.08305
\(276\) 0 0
\(277\) −16.2709 −0.977626 −0.488813 0.872389i \(-0.662570\pi\)
−0.488813 + 0.872389i \(0.662570\pi\)
\(278\) 0 0
\(279\) −23.2772 −1.39357
\(280\) 0 0
\(281\) −12.9193 −0.770698 −0.385349 0.922771i \(-0.625919\pi\)
−0.385349 + 0.922771i \(0.625919\pi\)
\(282\) 0 0
\(283\) 1.97359 0.117318 0.0586589 0.998278i \(-0.481318\pi\)
0.0586589 + 0.998278i \(0.481318\pi\)
\(284\) 0 0
\(285\) 11.9611 0.708515
\(286\) 0 0
\(287\) 20.4945 1.20975
\(288\) 0 0
\(289\) −16.4876 −0.969856
\(290\) 0 0
\(291\) −37.2577 −2.18409
\(292\) 0 0
\(293\) −34.1212 −1.99338 −0.996689 0.0813027i \(-0.974092\pi\)
−0.996689 + 0.0813027i \(0.974092\pi\)
\(294\) 0 0
\(295\) 17.8524 1.03941
\(296\) 0 0
\(297\) −1.80284 −0.104611
\(298\) 0 0
\(299\) 4.73057 0.273576
\(300\) 0 0
\(301\) 26.7408 1.54132
\(302\) 0 0
\(303\) 20.1685 1.15865
\(304\) 0 0
\(305\) 5.61343 0.321424
\(306\) 0 0
\(307\) 20.3642 1.16224 0.581122 0.813816i \(-0.302614\pi\)
0.581122 + 0.813816i \(0.302614\pi\)
\(308\) 0 0
\(309\) 36.2229 2.06065
\(310\) 0 0
\(311\) −28.0606 −1.59117 −0.795585 0.605842i \(-0.792836\pi\)
−0.795585 + 0.605842i \(0.792836\pi\)
\(312\) 0 0
\(313\) −14.3774 −0.812657 −0.406329 0.913727i \(-0.633191\pi\)
−0.406329 + 0.913727i \(0.633191\pi\)
\(314\) 0 0
\(315\) −12.1212 −0.682949
\(316\) 0 0
\(317\) 20.3121 1.14084 0.570420 0.821353i \(-0.306781\pi\)
0.570420 + 0.821353i \(0.306781\pi\)
\(318\) 0 0
\(319\) −5.61567 −0.314417
\(320\) 0 0
\(321\) −15.3517 −0.856847
\(322\) 0 0
\(323\) 2.35097 0.130811
\(324\) 0 0
\(325\) 15.1296 0.839241
\(326\) 0 0
\(327\) −16.8759 −0.933239
\(328\) 0 0
\(329\) 31.2229 1.72137
\(330\) 0 0
\(331\) 13.7438 0.755426 0.377713 0.925923i \(-0.376711\pi\)
0.377713 + 0.925923i \(0.376711\pi\)
\(332\) 0 0
\(333\) −3.11491 −0.170696
\(334\) 0 0
\(335\) 7.84325 0.428522
\(336\) 0 0
\(337\) −24.3447 −1.32614 −0.663071 0.748557i \(-0.730747\pi\)
−0.663071 + 0.748557i \(0.730747\pi\)
\(338\) 0 0
\(339\) −30.5419 −1.65881
\(340\) 0 0
\(341\) −47.4131 −2.56756
\(342\) 0 0
\(343\) 18.5459 1.00138
\(344\) 0 0
\(345\) 3.22357 0.173551
\(346\) 0 0
\(347\) 23.7702 1.27605 0.638025 0.770015i \(-0.279752\pi\)
0.638025 + 0.770015i \(0.279752\pi\)
\(348\) 0 0
\(349\) 11.7702 0.630044 0.315022 0.949084i \(-0.397988\pi\)
0.315022 + 0.949084i \(0.397988\pi\)
\(350\) 0 0
\(351\) 1.51869 0.0810616
\(352\) 0 0
\(353\) 5.05433 0.269015 0.134507 0.990913i \(-0.457055\pi\)
0.134507 + 0.990913i \(0.457055\pi\)
\(354\) 0 0
\(355\) −4.22982 −0.224495
\(356\) 0 0
\(357\) −4.67696 −0.247531
\(358\) 0 0
\(359\) 3.93871 0.207877 0.103939 0.994584i \(-0.466855\pi\)
0.103939 + 0.994584i \(0.466855\pi\)
\(360\) 0 0
\(361\) −8.21438 −0.432336
\(362\) 0 0
\(363\) −72.3440 −3.79708
\(364\) 0 0
\(365\) −12.2904 −0.643308
\(366\) 0 0
\(367\) 2.90677 0.151732 0.0758662 0.997118i \(-0.475828\pi\)
0.0758662 + 0.997118i \(0.475828\pi\)
\(368\) 0 0
\(369\) −24.1623 −1.25784
\(370\) 0 0
\(371\) −10.9806 −0.570082
\(372\) 0 0
\(373\) 8.95415 0.463628 0.231814 0.972760i \(-0.425534\pi\)
0.231814 + 0.972760i \(0.425534\pi\)
\(374\) 0 0
\(375\) 28.5202 1.47278
\(376\) 0 0
\(377\) 4.73057 0.243637
\(378\) 0 0
\(379\) 34.9325 1.79436 0.897180 0.441665i \(-0.145612\pi\)
0.897180 + 0.441665i \(0.145612\pi\)
\(380\) 0 0
\(381\) −45.7647 −2.34460
\(382\) 0 0
\(383\) 19.4876 0.995768 0.497884 0.867244i \(-0.334111\pi\)
0.497884 + 0.867244i \(0.334111\pi\)
\(384\) 0 0
\(385\) −24.6894 −1.25829
\(386\) 0 0
\(387\) −31.5264 −1.60258
\(388\) 0 0
\(389\) 21.8308 1.10686 0.553432 0.832895i \(-0.313318\pi\)
0.553432 + 0.832895i \(0.313318\pi\)
\(390\) 0 0
\(391\) 0.633596 0.0320423
\(392\) 0 0
\(393\) −36.3246 −1.83233
\(394\) 0 0
\(395\) 2.69641 0.135671
\(396\) 0 0
\(397\) 17.5613 0.881378 0.440689 0.897660i \(-0.354734\pi\)
0.440689 + 0.897660i \(0.354734\pi\)
\(398\) 0 0
\(399\) −21.4567 −1.07418
\(400\) 0 0
\(401\) 5.62263 0.280781 0.140390 0.990096i \(-0.455164\pi\)
0.140390 + 0.990096i \(0.455164\pi\)
\(402\) 0 0
\(403\) 39.9402 1.98956
\(404\) 0 0
\(405\) −12.7283 −0.632476
\(406\) 0 0
\(407\) −6.34472 −0.314496
\(408\) 0 0
\(409\) −12.3246 −0.609410 −0.304705 0.952447i \(-0.598558\pi\)
−0.304705 + 0.952447i \(0.598558\pi\)
\(410\) 0 0
\(411\) 8.22285 0.405604
\(412\) 0 0
\(413\) −32.0250 −1.57585
\(414\) 0 0
\(415\) −3.17548 −0.155878
\(416\) 0 0
\(417\) 22.8392 1.11844
\(418\) 0 0
\(419\) −16.2166 −0.792233 −0.396117 0.918200i \(-0.629642\pi\)
−0.396117 + 0.918200i \(0.629642\pi\)
\(420\) 0 0
\(421\) 32.0078 1.55996 0.779981 0.625803i \(-0.215228\pi\)
0.779981 + 0.625803i \(0.215228\pi\)
\(422\) 0 0
\(423\) −36.8106 −1.78979
\(424\) 0 0
\(425\) 2.02641 0.0982952
\(426\) 0 0
\(427\) −10.0698 −0.487310
\(428\) 0 0
\(429\) 83.8557 4.04859
\(430\) 0 0
\(431\) −27.4178 −1.32067 −0.660334 0.750972i \(-0.729585\pi\)
−0.660334 + 0.750972i \(0.729585\pi\)
\(432\) 0 0
\(433\) 28.4589 1.36765 0.683824 0.729647i \(-0.260316\pi\)
0.683824 + 0.729647i \(0.260316\pi\)
\(434\) 0 0
\(435\) 3.22357 0.154558
\(436\) 0 0
\(437\) 2.90677 0.139050
\(438\) 0 0
\(439\) −13.4923 −0.643951 −0.321976 0.946748i \(-0.604347\pi\)
−0.321976 + 0.946748i \(0.604347\pi\)
\(440\) 0 0
\(441\) −0.0605754 −0.00288454
\(442\) 0 0
\(443\) 1.43795 0.0683190 0.0341595 0.999416i \(-0.489125\pi\)
0.0341595 + 0.999416i \(0.489125\pi\)
\(444\) 0 0
\(445\) −2.78562 −0.132051
\(446\) 0 0
\(447\) 6.53341 0.309020
\(448\) 0 0
\(449\) −12.4985 −0.589842 −0.294921 0.955522i \(-0.595293\pi\)
−0.294921 + 0.955522i \(0.595293\pi\)
\(450\) 0 0
\(451\) −49.2159 −2.31749
\(452\) 0 0
\(453\) 44.4457 2.08824
\(454\) 0 0
\(455\) 20.7981 0.975030
\(456\) 0 0
\(457\) 12.4860 0.584072 0.292036 0.956407i \(-0.405667\pi\)
0.292036 + 0.956407i \(0.405667\pi\)
\(458\) 0 0
\(459\) 0.203408 0.00949425
\(460\) 0 0
\(461\) 24.1336 1.12402 0.562008 0.827132i \(-0.310029\pi\)
0.562008 + 0.827132i \(0.310029\pi\)
\(462\) 0 0
\(463\) −10.2640 −0.477008 −0.238504 0.971142i \(-0.576657\pi\)
−0.238504 + 0.971142i \(0.576657\pi\)
\(464\) 0 0
\(465\) 27.2166 1.26214
\(466\) 0 0
\(467\) 28.5544 1.32134 0.660669 0.750677i \(-0.270273\pi\)
0.660669 + 0.750677i \(0.270273\pi\)
\(468\) 0 0
\(469\) −14.0698 −0.649682
\(470\) 0 0
\(471\) 10.2772 0.473548
\(472\) 0 0
\(473\) −64.2159 −2.95265
\(474\) 0 0
\(475\) 9.29663 0.426559
\(476\) 0 0
\(477\) 12.9457 0.592741
\(478\) 0 0
\(479\) −3.79187 −0.173255 −0.0866274 0.996241i \(-0.527609\pi\)
−0.0866274 + 0.996241i \(0.527609\pi\)
\(480\) 0 0
\(481\) 5.34472 0.243698
\(482\) 0 0
\(483\) −5.78267 −0.263121
\(484\) 0 0
\(485\) 22.1909 1.00764
\(486\) 0 0
\(487\) 6.10866 0.276810 0.138405 0.990376i \(-0.455802\pi\)
0.138405 + 0.990376i \(0.455802\pi\)
\(488\) 0 0
\(489\) 39.2966 1.77706
\(490\) 0 0
\(491\) −15.1274 −0.682690 −0.341345 0.939938i \(-0.610882\pi\)
−0.341345 + 0.939938i \(0.610882\pi\)
\(492\) 0 0
\(493\) 0.633596 0.0285357
\(494\) 0 0
\(495\) 29.1079 1.30830
\(496\) 0 0
\(497\) 7.58774 0.340357
\(498\) 0 0
\(499\) 10.6894 0.478525 0.239263 0.970955i \(-0.423094\pi\)
0.239263 + 0.970955i \(0.423094\pi\)
\(500\) 0 0
\(501\) −41.4681 −1.85266
\(502\) 0 0
\(503\) −0.0675359 −0.00301128 −0.00150564 0.999999i \(-0.500479\pi\)
−0.00150564 + 0.999999i \(0.500479\pi\)
\(504\) 0 0
\(505\) −12.0125 −0.534549
\(506\) 0 0
\(507\) −38.4923 −1.70950
\(508\) 0 0
\(509\) 7.39682 0.327858 0.163929 0.986472i \(-0.447583\pi\)
0.163929 + 0.986472i \(0.447583\pi\)
\(510\) 0 0
\(511\) 22.0474 0.975318
\(512\) 0 0
\(513\) 0.933181 0.0412010
\(514\) 0 0
\(515\) −21.5745 −0.950688
\(516\) 0 0
\(517\) −74.9791 −3.29758
\(518\) 0 0
\(519\) 5.96511 0.261839
\(520\) 0 0
\(521\) 20.9806 0.919175 0.459587 0.888133i \(-0.347997\pi\)
0.459587 + 0.888133i \(0.347997\pi\)
\(522\) 0 0
\(523\) −4.43322 −0.193851 −0.0969256 0.995292i \(-0.530901\pi\)
−0.0969256 + 0.995292i \(0.530901\pi\)
\(524\) 0 0
\(525\) −18.4945 −0.807167
\(526\) 0 0
\(527\) 5.34945 0.233026
\(528\) 0 0
\(529\) −22.2166 −0.965940
\(530\) 0 0
\(531\) 37.7563 1.63848
\(532\) 0 0
\(533\) 41.4589 1.79578
\(534\) 0 0
\(535\) 9.14355 0.395310
\(536\) 0 0
\(537\) 59.3789 2.56239
\(538\) 0 0
\(539\) −0.123385 −0.00531458
\(540\) 0 0
\(541\) 3.81131 0.163861 0.0819306 0.996638i \(-0.473891\pi\)
0.0819306 + 0.996638i \(0.473891\pi\)
\(542\) 0 0
\(543\) −42.8580 −1.83921
\(544\) 0 0
\(545\) 10.0514 0.430554
\(546\) 0 0
\(547\) 28.8370 1.23298 0.616491 0.787362i \(-0.288554\pi\)
0.616491 + 0.787362i \(0.288554\pi\)
\(548\) 0 0
\(549\) 11.8719 0.506680
\(550\) 0 0
\(551\) 2.90677 0.123833
\(552\) 0 0
\(553\) −4.83700 −0.205690
\(554\) 0 0
\(555\) 3.64207 0.154597
\(556\) 0 0
\(557\) −29.7151 −1.25907 −0.629535 0.776972i \(-0.716755\pi\)
−0.629535 + 0.776972i \(0.716755\pi\)
\(558\) 0 0
\(559\) 54.0947 2.28796
\(560\) 0 0
\(561\) 11.2313 0.474187
\(562\) 0 0
\(563\) −22.6241 −0.953494 −0.476747 0.879041i \(-0.658184\pi\)
−0.476747 + 0.879041i \(0.658184\pi\)
\(564\) 0 0
\(565\) 18.1909 0.765298
\(566\) 0 0
\(567\) 22.8330 0.958896
\(568\) 0 0
\(569\) 31.7827 1.33240 0.666199 0.745774i \(-0.267920\pi\)
0.666199 + 0.745774i \(0.267920\pi\)
\(570\) 0 0
\(571\) −23.2974 −0.974964 −0.487482 0.873133i \(-0.662084\pi\)
−0.487482 + 0.873133i \(0.662084\pi\)
\(572\) 0 0
\(573\) −18.6825 −0.780472
\(574\) 0 0
\(575\) 2.50548 0.104486
\(576\) 0 0
\(577\) 4.33848 0.180613 0.0903066 0.995914i \(-0.471215\pi\)
0.0903066 + 0.995914i \(0.471215\pi\)
\(578\) 0 0
\(579\) −14.2034 −0.590273
\(580\) 0 0
\(581\) 5.69641 0.236327
\(582\) 0 0
\(583\) 26.3689 1.09209
\(584\) 0 0
\(585\) −24.5202 −1.01379
\(586\) 0 0
\(587\) −1.68793 −0.0696682 −0.0348341 0.999393i \(-0.511090\pi\)
−0.0348341 + 0.999393i \(0.511090\pi\)
\(588\) 0 0
\(589\) 24.5419 1.01123
\(590\) 0 0
\(591\) 39.9512 1.64337
\(592\) 0 0
\(593\) −21.0217 −0.863257 −0.431628 0.902051i \(-0.642061\pi\)
−0.431628 + 0.902051i \(0.642061\pi\)
\(594\) 0 0
\(595\) 2.78562 0.114199
\(596\) 0 0
\(597\) −17.7438 −0.726204
\(598\) 0 0
\(599\) 13.2926 0.543122 0.271561 0.962421i \(-0.412460\pi\)
0.271561 + 0.962421i \(0.412460\pi\)
\(600\) 0 0
\(601\) −16.2974 −0.664783 −0.332391 0.943142i \(-0.607855\pi\)
−0.332391 + 0.943142i \(0.607855\pi\)
\(602\) 0 0
\(603\) 16.5877 0.675505
\(604\) 0 0
\(605\) 43.0885 1.75180
\(606\) 0 0
\(607\) −11.9394 −0.484606 −0.242303 0.970201i \(-0.577903\pi\)
−0.242303 + 0.970201i \(0.577903\pi\)
\(608\) 0 0
\(609\) −5.78267 −0.234326
\(610\) 0 0
\(611\) 63.1616 2.55524
\(612\) 0 0
\(613\) −44.5195 −1.79813 −0.899063 0.437820i \(-0.855751\pi\)
−0.899063 + 0.437820i \(0.855751\pi\)
\(614\) 0 0
\(615\) 28.2515 1.13921
\(616\) 0 0
\(617\) −43.3921 −1.74690 −0.873450 0.486914i \(-0.838123\pi\)
−0.873450 + 0.486914i \(0.838123\pi\)
\(618\) 0 0
\(619\) −34.3572 −1.38093 −0.690466 0.723364i \(-0.742595\pi\)
−0.690466 + 0.723364i \(0.742595\pi\)
\(620\) 0 0
\(621\) 0.251497 0.0100922
\(622\) 0 0
\(623\) 4.99705 0.200203
\(624\) 0 0
\(625\) −2.83299 −0.113320
\(626\) 0 0
\(627\) 51.5264 2.05777
\(628\) 0 0
\(629\) 0.715853 0.0285429
\(630\) 0 0
\(631\) 28.3991 1.13055 0.565274 0.824903i \(-0.308770\pi\)
0.565274 + 0.824903i \(0.308770\pi\)
\(632\) 0 0
\(633\) 37.5110 1.49093
\(634\) 0 0
\(635\) 27.2577 1.08169
\(636\) 0 0
\(637\) 0.103938 0.00411819
\(638\) 0 0
\(639\) −8.94567 −0.353885
\(640\) 0 0
\(641\) 18.5940 0.734418 0.367209 0.930138i \(-0.380313\pi\)
0.367209 + 0.930138i \(0.380313\pi\)
\(642\) 0 0
\(643\) 7.51396 0.296322 0.148161 0.988963i \(-0.452665\pi\)
0.148161 + 0.988963i \(0.452665\pi\)
\(644\) 0 0
\(645\) 36.8620 1.45144
\(646\) 0 0
\(647\) −18.2904 −0.719069 −0.359535 0.933132i \(-0.617065\pi\)
−0.359535 + 0.933132i \(0.617065\pi\)
\(648\) 0 0
\(649\) 76.9053 3.01880
\(650\) 0 0
\(651\) −48.8231 −1.91353
\(652\) 0 0
\(653\) −1.70961 −0.0669022 −0.0334511 0.999440i \(-0.510650\pi\)
−0.0334511 + 0.999440i \(0.510650\pi\)
\(654\) 0 0
\(655\) 21.6351 0.845354
\(656\) 0 0
\(657\) −25.9930 −1.01409
\(658\) 0 0
\(659\) 21.4310 0.834833 0.417416 0.908715i \(-0.362936\pi\)
0.417416 + 0.908715i \(0.362936\pi\)
\(660\) 0 0
\(661\) −45.5606 −1.77210 −0.886051 0.463587i \(-0.846562\pi\)
−0.886051 + 0.463587i \(0.846562\pi\)
\(662\) 0 0
\(663\) −9.46115 −0.367441
\(664\) 0 0
\(665\) 12.7797 0.495576
\(666\) 0 0
\(667\) 0.783389 0.0303329
\(668\) 0 0
\(669\) 1.95263 0.0754930
\(670\) 0 0
\(671\) 24.1817 0.933525
\(672\) 0 0
\(673\) −45.4310 −1.75124 −0.875618 0.483004i \(-0.839546\pi\)
−0.875618 + 0.483004i \(0.839546\pi\)
\(674\) 0 0
\(675\) 0.804353 0.0309596
\(676\) 0 0
\(677\) −13.4357 −0.516376 −0.258188 0.966095i \(-0.583125\pi\)
−0.258188 + 0.966095i \(0.583125\pi\)
\(678\) 0 0
\(679\) −39.8076 −1.52768
\(680\) 0 0
\(681\) −2.60719 −0.0999077
\(682\) 0 0
\(683\) −18.4985 −0.707826 −0.353913 0.935278i \(-0.615149\pi\)
−0.353913 + 0.935278i \(0.615149\pi\)
\(684\) 0 0
\(685\) −4.89758 −0.187127
\(686\) 0 0
\(687\) 73.4652 2.80287
\(688\) 0 0
\(689\) −22.2129 −0.846243
\(690\) 0 0
\(691\) 11.4876 0.437007 0.218504 0.975836i \(-0.429882\pi\)
0.218504 + 0.975836i \(0.429882\pi\)
\(692\) 0 0
\(693\) −52.2159 −1.98352
\(694\) 0 0
\(695\) −13.6032 −0.515998
\(696\) 0 0
\(697\) 5.55286 0.210329
\(698\) 0 0
\(699\) −46.9340 −1.77521
\(700\) 0 0
\(701\) 22.0800 0.833951 0.416975 0.908918i \(-0.363090\pi\)
0.416975 + 0.908918i \(0.363090\pi\)
\(702\) 0 0
\(703\) 3.28415 0.123864
\(704\) 0 0
\(705\) 43.0404 1.62100
\(706\) 0 0
\(707\) 21.5488 0.810428
\(708\) 0 0
\(709\) −18.7570 −0.704433 −0.352217 0.935919i \(-0.614572\pi\)
−0.352217 + 0.935919i \(0.614572\pi\)
\(710\) 0 0
\(711\) 5.70265 0.213866
\(712\) 0 0
\(713\) 6.61415 0.247702
\(714\) 0 0
\(715\) −49.9450 −1.86784
\(716\) 0 0
\(717\) 1.87189 0.0699070
\(718\) 0 0
\(719\) −31.9776 −1.19256 −0.596282 0.802775i \(-0.703356\pi\)
−0.596282 + 0.802775i \(0.703356\pi\)
\(720\) 0 0
\(721\) 38.7019 1.44134
\(722\) 0 0
\(723\) −0.364887 −0.0135703
\(724\) 0 0
\(725\) 2.50548 0.0930514
\(726\) 0 0
\(727\) −37.9061 −1.40586 −0.702929 0.711260i \(-0.748125\pi\)
−0.702929 + 0.711260i \(0.748125\pi\)
\(728\) 0 0
\(729\) −29.0272 −1.07508
\(730\) 0 0
\(731\) 7.24525 0.267975
\(732\) 0 0
\(733\) −17.8051 −0.657645 −0.328823 0.944392i \(-0.606652\pi\)
−0.328823 + 0.944392i \(0.606652\pi\)
\(734\) 0 0
\(735\) 0.0708271 0.00261250
\(736\) 0 0
\(737\) 33.7874 1.24457
\(738\) 0 0
\(739\) −29.3851 −1.08095 −0.540475 0.841360i \(-0.681755\pi\)
−0.540475 + 0.841360i \(0.681755\pi\)
\(740\) 0 0
\(741\) −43.4053 −1.59453
\(742\) 0 0
\(743\) −3.72281 −0.136577 −0.0682884 0.997666i \(-0.521754\pi\)
−0.0682884 + 0.997666i \(0.521754\pi\)
\(744\) 0 0
\(745\) −3.89134 −0.142568
\(746\) 0 0
\(747\) −6.71585 −0.245720
\(748\) 0 0
\(749\) −16.4023 −0.599329
\(750\) 0 0
\(751\) 7.47908 0.272915 0.136458 0.990646i \(-0.456428\pi\)
0.136458 + 0.990646i \(0.456428\pi\)
\(752\) 0 0
\(753\) −37.5264 −1.36754
\(754\) 0 0
\(755\) −26.4721 −0.963419
\(756\) 0 0
\(757\) −15.1513 −0.550684 −0.275342 0.961346i \(-0.588791\pi\)
−0.275342 + 0.961346i \(0.588791\pi\)
\(758\) 0 0
\(759\) 13.8866 0.504052
\(760\) 0 0
\(761\) −32.1902 −1.16689 −0.583447 0.812151i \(-0.698296\pi\)
−0.583447 + 0.812151i \(0.698296\pi\)
\(762\) 0 0
\(763\) −18.0309 −0.652762
\(764\) 0 0
\(765\) −3.28415 −0.118739
\(766\) 0 0
\(767\) −64.7842 −2.33922
\(768\) 0 0
\(769\) 6.91926 0.249515 0.124757 0.992187i \(-0.460185\pi\)
0.124757 + 0.992187i \(0.460185\pi\)
\(770\) 0 0
\(771\) −58.1770 −2.09519
\(772\) 0 0
\(773\) 45.2617 1.62795 0.813976 0.580899i \(-0.197299\pi\)
0.813976 + 0.580899i \(0.197299\pi\)
\(774\) 0 0
\(775\) 21.1538 0.759867
\(776\) 0 0
\(777\) −6.53341 −0.234385
\(778\) 0 0
\(779\) 25.4751 0.912739
\(780\) 0 0
\(781\) −18.2213 −0.652011
\(782\) 0 0
\(783\) 0.251497 0.00898776
\(784\) 0 0
\(785\) −6.12115 −0.218473
\(786\) 0 0
\(787\) 14.2338 0.507381 0.253691 0.967285i \(-0.418356\pi\)
0.253691 + 0.967285i \(0.418356\pi\)
\(788\) 0 0
\(789\) 61.1700 2.17771
\(790\) 0 0
\(791\) −32.6322 −1.16027
\(792\) 0 0
\(793\) −20.3704 −0.723375
\(794\) 0 0
\(795\) −15.1366 −0.536839
\(796\) 0 0
\(797\) −34.5077 −1.22233 −0.611163 0.791505i \(-0.709298\pi\)
−0.611163 + 0.791505i \(0.709298\pi\)
\(798\) 0 0
\(799\) 8.45963 0.299280
\(800\) 0 0
\(801\) −5.89134 −0.208160
\(802\) 0 0
\(803\) −52.9450 −1.86839
\(804\) 0 0
\(805\) 3.44419 0.121392
\(806\) 0 0
\(807\) −34.7159 −1.22206
\(808\) 0 0
\(809\) 4.65055 0.163505 0.0817523 0.996653i \(-0.473948\pi\)
0.0817523 + 0.996653i \(0.473948\pi\)
\(810\) 0 0
\(811\) −26.8697 −0.943521 −0.471761 0.881727i \(-0.656381\pi\)
−0.471761 + 0.881727i \(0.656381\pi\)
\(812\) 0 0
\(813\) 10.0085 0.351013
\(814\) 0 0
\(815\) −23.4053 −0.819852
\(816\) 0 0
\(817\) 33.2393 1.16290
\(818\) 0 0
\(819\) 43.9861 1.53700
\(820\) 0 0
\(821\) 7.86092 0.274348 0.137174 0.990547i \(-0.456198\pi\)
0.137174 + 0.990547i \(0.456198\pi\)
\(822\) 0 0
\(823\) 32.9193 1.14749 0.573747 0.819033i \(-0.305489\pi\)
0.573747 + 0.819033i \(0.305489\pi\)
\(824\) 0 0
\(825\) 44.4131 1.54626
\(826\) 0 0
\(827\) 20.2687 0.704812 0.352406 0.935847i \(-0.385364\pi\)
0.352406 + 0.935847i \(0.385364\pi\)
\(828\) 0 0
\(829\) −1.83076 −0.0635849 −0.0317925 0.999494i \(-0.510122\pi\)
−0.0317925 + 0.999494i \(0.510122\pi\)
\(830\) 0 0
\(831\) 40.2353 1.39575
\(832\) 0 0
\(833\) 0.0139211 0.000482339 0
\(834\) 0 0
\(835\) 24.6986 0.854732
\(836\) 0 0
\(837\) 2.12339 0.0733949
\(838\) 0 0
\(839\) 7.64760 0.264024 0.132012 0.991248i \(-0.457856\pi\)
0.132012 + 0.991248i \(0.457856\pi\)
\(840\) 0 0
\(841\) −28.2166 −0.972987
\(842\) 0 0
\(843\) 31.9472 1.10032
\(844\) 0 0
\(845\) 22.9262 0.788686
\(846\) 0 0
\(847\) −77.2952 −2.65589
\(848\) 0 0
\(849\) −4.88037 −0.167494
\(850\) 0 0
\(851\) 0.885092 0.0303406
\(852\) 0 0
\(853\) 16.7431 0.573271 0.286636 0.958040i \(-0.407463\pi\)
0.286636 + 0.958040i \(0.407463\pi\)
\(854\) 0 0
\(855\) −15.0668 −0.515274
\(856\) 0 0
\(857\) −15.4487 −0.527716 −0.263858 0.964562i \(-0.584995\pi\)
−0.263858 + 0.964562i \(0.584995\pi\)
\(858\) 0 0
\(859\) 38.4766 1.31280 0.656402 0.754411i \(-0.272078\pi\)
0.656402 + 0.754411i \(0.272078\pi\)
\(860\) 0 0
\(861\) −50.6795 −1.72715
\(862\) 0 0
\(863\) 17.5962 0.598982 0.299491 0.954099i \(-0.403183\pi\)
0.299491 + 0.954099i \(0.403183\pi\)
\(864\) 0 0
\(865\) −3.55286 −0.120801
\(866\) 0 0
\(867\) 40.7710 1.38466
\(868\) 0 0
\(869\) 11.6157 0.394034
\(870\) 0 0
\(871\) −28.4621 −0.964402
\(872\) 0 0
\(873\) 46.9317 1.58840
\(874\) 0 0
\(875\) 30.4721 1.03015
\(876\) 0 0
\(877\) −20.1336 −0.679865 −0.339932 0.940450i \(-0.610404\pi\)
−0.339932 + 0.940450i \(0.610404\pi\)
\(878\) 0 0
\(879\) 84.3759 2.84593
\(880\) 0 0
\(881\) −8.91703 −0.300422 −0.150211 0.988654i \(-0.547995\pi\)
−0.150211 + 0.988654i \(0.547995\pi\)
\(882\) 0 0
\(883\) 5.59622 0.188328 0.0941639 0.995557i \(-0.469982\pi\)
0.0941639 + 0.995557i \(0.469982\pi\)
\(884\) 0 0
\(885\) −44.1461 −1.48396
\(886\) 0 0
\(887\) −42.3594 −1.42229 −0.711145 0.703045i \(-0.751823\pi\)
−0.711145 + 0.703045i \(0.751823\pi\)
\(888\) 0 0
\(889\) −48.8969 −1.63995
\(890\) 0 0
\(891\) −54.8316 −1.83693
\(892\) 0 0
\(893\) 38.8106 1.29875
\(894\) 0 0
\(895\) −35.3664 −1.18217
\(896\) 0 0
\(897\) −11.6979 −0.390582
\(898\) 0 0
\(899\) 6.61415 0.220594
\(900\) 0 0
\(901\) −2.97511 −0.0991153
\(902\) 0 0
\(903\) −66.1256 −2.20052
\(904\) 0 0
\(905\) 25.5264 0.848528
\(906\) 0 0
\(907\) −22.3121 −0.740860 −0.370430 0.928860i \(-0.620790\pi\)
−0.370430 + 0.928860i \(0.620790\pi\)
\(908\) 0 0
\(909\) −25.4053 −0.842641
\(910\) 0 0
\(911\) −20.0947 −0.665769 −0.332884 0.942968i \(-0.608022\pi\)
−0.332884 + 0.942968i \(0.608022\pi\)
\(912\) 0 0
\(913\) −13.6795 −0.452724
\(914\) 0 0
\(915\) −13.8811 −0.458894
\(916\) 0 0
\(917\) −38.8106 −1.28164
\(918\) 0 0
\(919\) 3.47060 0.114485 0.0572423 0.998360i \(-0.481769\pi\)
0.0572423 + 0.998360i \(0.481769\pi\)
\(920\) 0 0
\(921\) −50.3572 −1.65933
\(922\) 0 0
\(923\) 15.3494 0.505233
\(924\) 0 0
\(925\) 2.83076 0.0930748
\(926\) 0 0
\(927\) −45.6282 −1.49863
\(928\) 0 0
\(929\) −1.59398 −0.0522969 −0.0261485 0.999658i \(-0.508324\pi\)
−0.0261485 + 0.999658i \(0.508324\pi\)
\(930\) 0 0
\(931\) 0.0638666 0.00209314
\(932\) 0 0
\(933\) 69.3891 2.27170
\(934\) 0 0
\(935\) −6.68945 −0.218768
\(936\) 0 0
\(937\) 13.0675 0.426898 0.213449 0.976954i \(-0.431530\pi\)
0.213449 + 0.976954i \(0.431530\pi\)
\(938\) 0 0
\(939\) 35.5529 1.16022
\(940\) 0 0
\(941\) −18.2857 −0.596096 −0.298048 0.954551i \(-0.596335\pi\)
−0.298048 + 0.954551i \(0.596335\pi\)
\(942\) 0 0
\(943\) 6.86565 0.223576
\(944\) 0 0
\(945\) 1.10571 0.0359688
\(946\) 0 0
\(947\) −6.86341 −0.223031 −0.111515 0.993763i \(-0.535570\pi\)
−0.111515 + 0.993763i \(0.535570\pi\)
\(948\) 0 0
\(949\) 44.6002 1.44778
\(950\) 0 0
\(951\) −50.2284 −1.62877
\(952\) 0 0
\(953\) 20.1319 0.652135 0.326068 0.945346i \(-0.394276\pi\)
0.326068 + 0.945346i \(0.394276\pi\)
\(954\) 0 0
\(955\) 11.1274 0.360074
\(956\) 0 0
\(957\) 13.8866 0.448890
\(958\) 0 0
\(959\) 8.78562 0.283703
\(960\) 0 0
\(961\) 24.8432 0.801395
\(962\) 0 0
\(963\) 19.3378 0.623151
\(964\) 0 0
\(965\) 8.45963 0.272325
\(966\) 0 0
\(967\) 36.6219 1.17768 0.588841 0.808249i \(-0.299585\pi\)
0.588841 + 0.808249i \(0.299585\pi\)
\(968\) 0 0
\(969\) −5.81355 −0.186758
\(970\) 0 0
\(971\) −49.3502 −1.58372 −0.791862 0.610700i \(-0.790888\pi\)
−0.791862 + 0.610700i \(0.790888\pi\)
\(972\) 0 0
\(973\) 24.4023 0.782303
\(974\) 0 0
\(975\) −37.4131 −1.19818
\(976\) 0 0
\(977\) −33.6351 −1.07608 −0.538041 0.842918i \(-0.680836\pi\)
−0.538041 + 0.842918i \(0.680836\pi\)
\(978\) 0 0
\(979\) −12.0000 −0.383522
\(980\) 0 0
\(981\) 21.2577 0.678707
\(982\) 0 0
\(983\) 4.35944 0.139045 0.0695223 0.997580i \(-0.477852\pi\)
0.0695223 + 0.997580i \(0.477852\pi\)
\(984\) 0 0
\(985\) −23.7952 −0.758177
\(986\) 0 0
\(987\) −77.2089 −2.45759
\(988\) 0 0
\(989\) 8.95815 0.284853
\(990\) 0 0
\(991\) 53.1957 1.68982 0.844909 0.534910i \(-0.179655\pi\)
0.844909 + 0.534910i \(0.179655\pi\)
\(992\) 0 0
\(993\) −33.9861 −1.07852
\(994\) 0 0
\(995\) 10.5683 0.335037
\(996\) 0 0
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) 0 0
\(999\) 0.284147 0.00899002
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 592.2.a.i.1.1 3
3.2 odd 2 5328.2.a.bn.1.1 3
4.3 odd 2 296.2.a.c.1.3 3
8.3 odd 2 2368.2.a.bb.1.1 3
8.5 even 2 2368.2.a.be.1.3 3
12.11 even 2 2664.2.a.p.1.1 3
20.19 odd 2 7400.2.a.k.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
296.2.a.c.1.3 3 4.3 odd 2
592.2.a.i.1.1 3 1.1 even 1 trivial
2368.2.a.bb.1.1 3 8.3 odd 2
2368.2.a.be.1.3 3 8.5 even 2
2664.2.a.p.1.1 3 12.11 even 2
5328.2.a.bn.1.1 3 3.2 odd 2
7400.2.a.k.1.1 3 20.19 odd 2