Properties

Label 6008.2.a.c.1.17
Level $6008$
Weight $2$
Character 6008.1
Self dual yes
Analytic conductor $47.974$
Analytic rank $1$
Dimension $44$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6008,2,Mod(1,6008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6008, 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("6008.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6008.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: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.16746 q^{3} +2.71362 q^{5} -1.33257 q^{7} -1.63703 q^{9} +O(q^{10})\) \(q-1.16746 q^{3} +2.71362 q^{5} -1.33257 q^{7} -1.63703 q^{9} +5.08555 q^{11} -0.388876 q^{13} -3.16805 q^{15} +0.121828 q^{17} -7.29355 q^{19} +1.55573 q^{21} +7.31839 q^{23} +2.36375 q^{25} +5.41356 q^{27} -8.97697 q^{29} -6.78388 q^{31} -5.93718 q^{33} -3.61610 q^{35} -0.924411 q^{37} +0.453997 q^{39} +2.63874 q^{41} +1.12279 q^{43} -4.44229 q^{45} -0.220348 q^{47} -5.22424 q^{49} -0.142229 q^{51} -7.43226 q^{53} +13.8003 q^{55} +8.51494 q^{57} +1.34714 q^{59} -8.43689 q^{61} +2.18147 q^{63} -1.05526 q^{65} +0.702187 q^{67} -8.54394 q^{69} -10.1923 q^{71} +7.50346 q^{73} -2.75958 q^{75} -6.77688 q^{77} +5.63081 q^{79} -1.40901 q^{81} +13.3504 q^{83} +0.330595 q^{85} +10.4803 q^{87} -15.3464 q^{89} +0.518206 q^{91} +7.91992 q^{93} -19.7919 q^{95} +1.99311 q^{97} -8.32523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9} + 11 q^{11} - 36 q^{13} - 5 q^{15} - 10 q^{17} - 7 q^{19} - 42 q^{21} - 5 q^{23} + 29 q^{25} - 16 q^{27} - 57 q^{29} - 21 q^{31} - 32 q^{33} + 17 q^{35} - 52 q^{37} + 8 q^{39} - 16 q^{41} - 9 q^{43} - 84 q^{45} - q^{47} + 28 q^{49} - q^{51} - 52 q^{53} - 39 q^{55} - 15 q^{57} + 7 q^{59} - 85 q^{61} - 25 q^{63} - 9 q^{65} - 36 q^{67} - 72 q^{69} + 12 q^{71} - 60 q^{73} - 5 q^{75} - 81 q^{77} - 13 q^{79} + 20 q^{81} + 5 q^{83} - 72 q^{85} + 9 q^{87} - 37 q^{89} - 23 q^{91} - 60 q^{93} + 24 q^{95} - 79 q^{97} + 42 q^{99}+O(q^{100}) \) 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
\(3\) −1.16746 −0.674034 −0.337017 0.941499i \(-0.609418\pi\)
−0.337017 + 0.941499i \(0.609418\pi\)
\(4\) 0 0
\(5\) 2.71362 1.21357 0.606784 0.794866i \(-0.292459\pi\)
0.606784 + 0.794866i \(0.292459\pi\)
\(6\) 0 0
\(7\) −1.33257 −0.503666 −0.251833 0.967771i \(-0.581033\pi\)
−0.251833 + 0.967771i \(0.581033\pi\)
\(8\) 0 0
\(9\) −1.63703 −0.545678
\(10\) 0 0
\(11\) 5.08555 1.53335 0.766676 0.642034i \(-0.221909\pi\)
0.766676 + 0.642034i \(0.221909\pi\)
\(12\) 0 0
\(13\) −0.388876 −0.107855 −0.0539274 0.998545i \(-0.517174\pi\)
−0.0539274 + 0.998545i \(0.517174\pi\)
\(14\) 0 0
\(15\) −3.16805 −0.817987
\(16\) 0 0
\(17\) 0.121828 0.0295476 0.0147738 0.999891i \(-0.495297\pi\)
0.0147738 + 0.999891i \(0.495297\pi\)
\(18\) 0 0
\(19\) −7.29355 −1.67326 −0.836628 0.547772i \(-0.815476\pi\)
−0.836628 + 0.547772i \(0.815476\pi\)
\(20\) 0 0
\(21\) 1.55573 0.339488
\(22\) 0 0
\(23\) 7.31839 1.52599 0.762995 0.646404i \(-0.223728\pi\)
0.762995 + 0.646404i \(0.223728\pi\)
\(24\) 0 0
\(25\) 2.36375 0.472749
\(26\) 0 0
\(27\) 5.41356 1.04184
\(28\) 0 0
\(29\) −8.97697 −1.66698 −0.833491 0.552533i \(-0.813661\pi\)
−0.833491 + 0.552533i \(0.813661\pi\)
\(30\) 0 0
\(31\) −6.78388 −1.21842 −0.609211 0.793008i \(-0.708514\pi\)
−0.609211 + 0.793008i \(0.708514\pi\)
\(32\) 0 0
\(33\) −5.93718 −1.03353
\(34\) 0 0
\(35\) −3.61610 −0.611233
\(36\) 0 0
\(37\) −0.924411 −0.151972 −0.0759861 0.997109i \(-0.524210\pi\)
−0.0759861 + 0.997109i \(0.524210\pi\)
\(38\) 0 0
\(39\) 0.453997 0.0726978
\(40\) 0 0
\(41\) 2.63874 0.412101 0.206051 0.978541i \(-0.433939\pi\)
0.206051 + 0.978541i \(0.433939\pi\)
\(42\) 0 0
\(43\) 1.12279 0.171225 0.0856123 0.996329i \(-0.472715\pi\)
0.0856123 + 0.996329i \(0.472715\pi\)
\(44\) 0 0
\(45\) −4.44229 −0.662218
\(46\) 0 0
\(47\) −0.220348 −0.0321410 −0.0160705 0.999871i \(-0.505116\pi\)
−0.0160705 + 0.999871i \(0.505116\pi\)
\(48\) 0 0
\(49\) −5.22424 −0.746321
\(50\) 0 0
\(51\) −0.142229 −0.0199161
\(52\) 0 0
\(53\) −7.43226 −1.02090 −0.510450 0.859908i \(-0.670521\pi\)
−0.510450 + 0.859908i \(0.670521\pi\)
\(54\) 0 0
\(55\) 13.8003 1.86083
\(56\) 0 0
\(57\) 8.51494 1.12783
\(58\) 0 0
\(59\) 1.34714 0.175382 0.0876911 0.996148i \(-0.472051\pi\)
0.0876911 + 0.996148i \(0.472051\pi\)
\(60\) 0 0
\(61\) −8.43689 −1.08023 −0.540116 0.841590i \(-0.681620\pi\)
−0.540116 + 0.841590i \(0.681620\pi\)
\(62\) 0 0
\(63\) 2.18147 0.274840
\(64\) 0 0
\(65\) −1.05526 −0.130889
\(66\) 0 0
\(67\) 0.702187 0.0857858 0.0428929 0.999080i \(-0.486343\pi\)
0.0428929 + 0.999080i \(0.486343\pi\)
\(68\) 0 0
\(69\) −8.54394 −1.02857
\(70\) 0 0
\(71\) −10.1923 −1.20960 −0.604801 0.796377i \(-0.706747\pi\)
−0.604801 + 0.796377i \(0.706747\pi\)
\(72\) 0 0
\(73\) 7.50346 0.878213 0.439107 0.898435i \(-0.355295\pi\)
0.439107 + 0.898435i \(0.355295\pi\)
\(74\) 0 0
\(75\) −2.75958 −0.318649
\(76\) 0 0
\(77\) −6.77688 −0.772297
\(78\) 0 0
\(79\) 5.63081 0.633516 0.316758 0.948506i \(-0.397406\pi\)
0.316758 + 0.948506i \(0.397406\pi\)
\(80\) 0 0
\(81\) −1.40901 −0.156557
\(82\) 0 0
\(83\) 13.3504 1.46540 0.732698 0.680554i \(-0.238261\pi\)
0.732698 + 0.680554i \(0.238261\pi\)
\(84\) 0 0
\(85\) 0.330595 0.0358581
\(86\) 0 0
\(87\) 10.4803 1.12360
\(88\) 0 0
\(89\) −15.3464 −1.62672 −0.813358 0.581763i \(-0.802363\pi\)
−0.813358 + 0.581763i \(0.802363\pi\)
\(90\) 0 0
\(91\) 0.518206 0.0543228
\(92\) 0 0
\(93\) 7.91992 0.821257
\(94\) 0 0
\(95\) −19.7919 −2.03061
\(96\) 0 0
\(97\) 1.99311 0.202370 0.101185 0.994868i \(-0.467737\pi\)
0.101185 + 0.994868i \(0.467737\pi\)
\(98\) 0 0
\(99\) −8.32523 −0.836717
\(100\) 0 0
\(101\) 5.89841 0.586914 0.293457 0.955972i \(-0.405194\pi\)
0.293457 + 0.955972i \(0.405194\pi\)
\(102\) 0 0
\(103\) 10.5548 1.04000 0.519999 0.854167i \(-0.325932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(104\) 0 0
\(105\) 4.22166 0.411992
\(106\) 0 0
\(107\) −11.5575 −1.11730 −0.558652 0.829402i \(-0.688681\pi\)
−0.558652 + 0.829402i \(0.688681\pi\)
\(108\) 0 0
\(109\) 6.87019 0.658044 0.329022 0.944322i \(-0.393281\pi\)
0.329022 + 0.944322i \(0.393281\pi\)
\(110\) 0 0
\(111\) 1.07921 0.102434
\(112\) 0 0
\(113\) −20.1734 −1.89776 −0.948879 0.315640i \(-0.897781\pi\)
−0.948879 + 0.315640i \(0.897781\pi\)
\(114\) 0 0
\(115\) 19.8593 1.85189
\(116\) 0 0
\(117\) 0.636603 0.0588540
\(118\) 0 0
\(119\) −0.162345 −0.0148821
\(120\) 0 0
\(121\) 14.8628 1.35117
\(122\) 0 0
\(123\) −3.08062 −0.277770
\(124\) 0 0
\(125\) −7.15380 −0.639855
\(126\) 0 0
\(127\) −11.6903 −1.03734 −0.518672 0.854974i \(-0.673573\pi\)
−0.518672 + 0.854974i \(0.673573\pi\)
\(128\) 0 0
\(129\) −1.31082 −0.115411
\(130\) 0 0
\(131\) −4.88778 −0.427048 −0.213524 0.976938i \(-0.568494\pi\)
−0.213524 + 0.976938i \(0.568494\pi\)
\(132\) 0 0
\(133\) 9.71920 0.842762
\(134\) 0 0
\(135\) 14.6903 1.26434
\(136\) 0 0
\(137\) −13.0170 −1.11212 −0.556058 0.831144i \(-0.687687\pi\)
−0.556058 + 0.831144i \(0.687687\pi\)
\(138\) 0 0
\(139\) 10.8290 0.918508 0.459254 0.888305i \(-0.348117\pi\)
0.459254 + 0.888305i \(0.348117\pi\)
\(140\) 0 0
\(141\) 0.257247 0.0216641
\(142\) 0 0
\(143\) −1.97765 −0.165379
\(144\) 0 0
\(145\) −24.3601 −2.02300
\(146\) 0 0
\(147\) 6.09910 0.503045
\(148\) 0 0
\(149\) −1.00950 −0.0827014 −0.0413507 0.999145i \(-0.513166\pi\)
−0.0413507 + 0.999145i \(0.513166\pi\)
\(150\) 0 0
\(151\) −23.8268 −1.93900 −0.969499 0.245096i \(-0.921181\pi\)
−0.969499 + 0.245096i \(0.921181\pi\)
\(152\) 0 0
\(153\) −0.199437 −0.0161235
\(154\) 0 0
\(155\) −18.4089 −1.47864
\(156\) 0 0
\(157\) 9.34943 0.746166 0.373083 0.927798i \(-0.378301\pi\)
0.373083 + 0.927798i \(0.378301\pi\)
\(158\) 0 0
\(159\) 8.67687 0.688121
\(160\) 0 0
\(161\) −9.75230 −0.768589
\(162\) 0 0
\(163\) 8.19941 0.642227 0.321114 0.947041i \(-0.395943\pi\)
0.321114 + 0.947041i \(0.395943\pi\)
\(164\) 0 0
\(165\) −16.1113 −1.25426
\(166\) 0 0
\(167\) −0.554966 −0.0429446 −0.0214723 0.999769i \(-0.506835\pi\)
−0.0214723 + 0.999769i \(0.506835\pi\)
\(168\) 0 0
\(169\) −12.8488 −0.988367
\(170\) 0 0
\(171\) 11.9398 0.913059
\(172\) 0 0
\(173\) −20.4573 −1.55534 −0.777669 0.628674i \(-0.783598\pi\)
−0.777669 + 0.628674i \(0.783598\pi\)
\(174\) 0 0
\(175\) −3.14987 −0.238108
\(176\) 0 0
\(177\) −1.57273 −0.118214
\(178\) 0 0
\(179\) 17.3716 1.29842 0.649208 0.760611i \(-0.275100\pi\)
0.649208 + 0.760611i \(0.275100\pi\)
\(180\) 0 0
\(181\) 1.98576 0.147601 0.0738003 0.997273i \(-0.476487\pi\)
0.0738003 + 0.997273i \(0.476487\pi\)
\(182\) 0 0
\(183\) 9.84973 0.728113
\(184\) 0 0
\(185\) −2.50850 −0.184429
\(186\) 0 0
\(187\) 0.619562 0.0453069
\(188\) 0 0
\(189\) −7.21397 −0.524739
\(190\) 0 0
\(191\) 13.1242 0.949632 0.474816 0.880085i \(-0.342515\pi\)
0.474816 + 0.880085i \(0.342515\pi\)
\(192\) 0 0
\(193\) 18.5078 1.33222 0.666109 0.745854i \(-0.267959\pi\)
0.666109 + 0.745854i \(0.267959\pi\)
\(194\) 0 0
\(195\) 1.23198 0.0882237
\(196\) 0 0
\(197\) 14.0169 0.998664 0.499332 0.866411i \(-0.333579\pi\)
0.499332 + 0.866411i \(0.333579\pi\)
\(198\) 0 0
\(199\) −14.4832 −1.02669 −0.513343 0.858184i \(-0.671593\pi\)
−0.513343 + 0.858184i \(0.671593\pi\)
\(200\) 0 0
\(201\) −0.819776 −0.0578226
\(202\) 0 0
\(203\) 11.9625 0.839602
\(204\) 0 0
\(205\) 7.16054 0.500113
\(206\) 0 0
\(207\) −11.9805 −0.832700
\(208\) 0 0
\(209\) −37.0917 −2.56569
\(210\) 0 0
\(211\) −1.38189 −0.0951330 −0.0475665 0.998868i \(-0.515147\pi\)
−0.0475665 + 0.998868i \(0.515147\pi\)
\(212\) 0 0
\(213\) 11.8991 0.815313
\(214\) 0 0
\(215\) 3.04684 0.207793
\(216\) 0 0
\(217\) 9.04003 0.613677
\(218\) 0 0
\(219\) −8.75999 −0.591946
\(220\) 0 0
\(221\) −0.0473759 −0.00318685
\(222\) 0 0
\(223\) −2.77343 −0.185723 −0.0928613 0.995679i \(-0.529601\pi\)
−0.0928613 + 0.995679i \(0.529601\pi\)
\(224\) 0 0
\(225\) −3.86953 −0.257969
\(226\) 0 0
\(227\) −12.6621 −0.840414 −0.420207 0.907428i \(-0.638043\pi\)
−0.420207 + 0.907428i \(0.638043\pi\)
\(228\) 0 0
\(229\) 11.8252 0.781428 0.390714 0.920512i \(-0.372228\pi\)
0.390714 + 0.920512i \(0.372228\pi\)
\(230\) 0 0
\(231\) 7.91174 0.520554
\(232\) 0 0
\(233\) 16.8656 1.10490 0.552452 0.833544i \(-0.313692\pi\)
0.552452 + 0.833544i \(0.313692\pi\)
\(234\) 0 0
\(235\) −0.597940 −0.0390053
\(236\) 0 0
\(237\) −6.57375 −0.427011
\(238\) 0 0
\(239\) 9.70053 0.627475 0.313737 0.949510i \(-0.398419\pi\)
0.313737 + 0.949510i \(0.398419\pi\)
\(240\) 0 0
\(241\) −24.3108 −1.56599 −0.782997 0.622026i \(-0.786310\pi\)
−0.782997 + 0.622026i \(0.786310\pi\)
\(242\) 0 0
\(243\) −14.5957 −0.936315
\(244\) 0 0
\(245\) −14.1766 −0.905711
\(246\) 0 0
\(247\) 2.83629 0.180469
\(248\) 0 0
\(249\) −15.5861 −0.987726
\(250\) 0 0
\(251\) 23.9062 1.50894 0.754472 0.656332i \(-0.227893\pi\)
0.754472 + 0.656332i \(0.227893\pi\)
\(252\) 0 0
\(253\) 37.2181 2.33988
\(254\) 0 0
\(255\) −0.385957 −0.0241696
\(256\) 0 0
\(257\) −12.4942 −0.779364 −0.389682 0.920949i \(-0.627415\pi\)
−0.389682 + 0.920949i \(0.627415\pi\)
\(258\) 0 0
\(259\) 1.23185 0.0765432
\(260\) 0 0
\(261\) 14.6956 0.909636
\(262\) 0 0
\(263\) −4.33772 −0.267475 −0.133738 0.991017i \(-0.542698\pi\)
−0.133738 + 0.991017i \(0.542698\pi\)
\(264\) 0 0
\(265\) −20.1683 −1.23893
\(266\) 0 0
\(267\) 17.9163 1.09646
\(268\) 0 0
\(269\) −16.7394 −1.02062 −0.510309 0.859991i \(-0.670469\pi\)
−0.510309 + 0.859991i \(0.670469\pi\)
\(270\) 0 0
\(271\) 15.4434 0.938121 0.469061 0.883166i \(-0.344593\pi\)
0.469061 + 0.883166i \(0.344593\pi\)
\(272\) 0 0
\(273\) −0.604985 −0.0366154
\(274\) 0 0
\(275\) 12.0210 0.724891
\(276\) 0 0
\(277\) −27.1626 −1.63205 −0.816023 0.578020i \(-0.803826\pi\)
−0.816023 + 0.578020i \(0.803826\pi\)
\(278\) 0 0
\(279\) 11.1055 0.664866
\(280\) 0 0
\(281\) 18.7885 1.12083 0.560413 0.828213i \(-0.310642\pi\)
0.560413 + 0.828213i \(0.310642\pi\)
\(282\) 0 0
\(283\) 3.37619 0.200694 0.100347 0.994953i \(-0.468005\pi\)
0.100347 + 0.994953i \(0.468005\pi\)
\(284\) 0 0
\(285\) 23.1063 1.36870
\(286\) 0 0
\(287\) −3.51631 −0.207561
\(288\) 0 0
\(289\) −16.9852 −0.999127
\(290\) 0 0
\(291\) −2.32688 −0.136404
\(292\) 0 0
\(293\) −19.0808 −1.11471 −0.557355 0.830274i \(-0.688184\pi\)
−0.557355 + 0.830274i \(0.688184\pi\)
\(294\) 0 0
\(295\) 3.65562 0.212838
\(296\) 0 0
\(297\) 27.5309 1.59751
\(298\) 0 0
\(299\) −2.84595 −0.164585
\(300\) 0 0
\(301\) −1.49621 −0.0862400
\(302\) 0 0
\(303\) −6.88617 −0.395600
\(304\) 0 0
\(305\) −22.8945 −1.31094
\(306\) 0 0
\(307\) −8.86952 −0.506210 −0.253105 0.967439i \(-0.581452\pi\)
−0.253105 + 0.967439i \(0.581452\pi\)
\(308\) 0 0
\(309\) −12.3224 −0.700994
\(310\) 0 0
\(311\) 2.06654 0.117183 0.0585913 0.998282i \(-0.481339\pi\)
0.0585913 + 0.998282i \(0.481339\pi\)
\(312\) 0 0
\(313\) 8.69218 0.491311 0.245656 0.969357i \(-0.420997\pi\)
0.245656 + 0.969357i \(0.420997\pi\)
\(314\) 0 0
\(315\) 5.91969 0.333537
\(316\) 0 0
\(317\) −7.52454 −0.422620 −0.211310 0.977419i \(-0.567773\pi\)
−0.211310 + 0.977419i \(0.567773\pi\)
\(318\) 0 0
\(319\) −45.6529 −2.55607
\(320\) 0 0
\(321\) 13.4929 0.753100
\(322\) 0 0
\(323\) −0.888558 −0.0494407
\(324\) 0 0
\(325\) −0.919204 −0.0509883
\(326\) 0 0
\(327\) −8.02067 −0.443544
\(328\) 0 0
\(329\) 0.293630 0.0161883
\(330\) 0 0
\(331\) −0.396297 −0.0217825 −0.0108912 0.999941i \(-0.503467\pi\)
−0.0108912 + 0.999941i \(0.503467\pi\)
\(332\) 0 0
\(333\) 1.51329 0.0829279
\(334\) 0 0
\(335\) 1.90547 0.104107
\(336\) 0 0
\(337\) −21.4203 −1.16684 −0.583418 0.812172i \(-0.698285\pi\)
−0.583418 + 0.812172i \(0.698285\pi\)
\(338\) 0 0
\(339\) 23.5517 1.27915
\(340\) 0 0
\(341\) −34.4998 −1.86827
\(342\) 0 0
\(343\) 16.2897 0.879562
\(344\) 0 0
\(345\) −23.1850 −1.24824
\(346\) 0 0
\(347\) −20.2531 −1.08725 −0.543623 0.839330i \(-0.682948\pi\)
−0.543623 + 0.839330i \(0.682948\pi\)
\(348\) 0 0
\(349\) −20.2589 −1.08444 −0.542218 0.840238i \(-0.682415\pi\)
−0.542218 + 0.840238i \(0.682415\pi\)
\(350\) 0 0
\(351\) −2.10520 −0.112367
\(352\) 0 0
\(353\) −28.7266 −1.52896 −0.764482 0.644645i \(-0.777005\pi\)
−0.764482 + 0.644645i \(0.777005\pi\)
\(354\) 0 0
\(355\) −27.6580 −1.46794
\(356\) 0 0
\(357\) 0.189531 0.0100311
\(358\) 0 0
\(359\) 19.4920 1.02875 0.514375 0.857565i \(-0.328024\pi\)
0.514375 + 0.857565i \(0.328024\pi\)
\(360\) 0 0
\(361\) 34.1959 1.79978
\(362\) 0 0
\(363\) −17.3518 −0.910733
\(364\) 0 0
\(365\) 20.3616 1.06577
\(366\) 0 0
\(367\) −19.2145 −1.00299 −0.501496 0.865160i \(-0.667217\pi\)
−0.501496 + 0.865160i \(0.667217\pi\)
\(368\) 0 0
\(369\) −4.31970 −0.224875
\(370\) 0 0
\(371\) 9.90404 0.514192
\(372\) 0 0
\(373\) −16.3774 −0.847992 −0.423996 0.905664i \(-0.639373\pi\)
−0.423996 + 0.905664i \(0.639373\pi\)
\(374\) 0 0
\(375\) 8.35178 0.431284
\(376\) 0 0
\(377\) 3.49093 0.179792
\(378\) 0 0
\(379\) −34.6952 −1.78217 −0.891087 0.453832i \(-0.850057\pi\)
−0.891087 + 0.453832i \(0.850057\pi\)
\(380\) 0 0
\(381\) 13.6479 0.699205
\(382\) 0 0
\(383\) 3.93157 0.200894 0.100447 0.994942i \(-0.467973\pi\)
0.100447 + 0.994942i \(0.467973\pi\)
\(384\) 0 0
\(385\) −18.3899 −0.937236
\(386\) 0 0
\(387\) −1.83805 −0.0934336
\(388\) 0 0
\(389\) −12.3137 −0.624327 −0.312163 0.950028i \(-0.601054\pi\)
−0.312163 + 0.950028i \(0.601054\pi\)
\(390\) 0 0
\(391\) 0.891584 0.0450894
\(392\) 0 0
\(393\) 5.70630 0.287845
\(394\) 0 0
\(395\) 15.2799 0.768815
\(396\) 0 0
\(397\) 7.01879 0.352263 0.176132 0.984367i \(-0.443642\pi\)
0.176132 + 0.984367i \(0.443642\pi\)
\(398\) 0 0
\(399\) −11.3468 −0.568050
\(400\) 0 0
\(401\) −37.7726 −1.88627 −0.943137 0.332404i \(-0.892140\pi\)
−0.943137 + 0.332404i \(0.892140\pi\)
\(402\) 0 0
\(403\) 2.63809 0.131413
\(404\) 0 0
\(405\) −3.82353 −0.189993
\(406\) 0 0
\(407\) −4.70114 −0.233027
\(408\) 0 0
\(409\) 16.5818 0.819917 0.409958 0.912104i \(-0.365543\pi\)
0.409958 + 0.912104i \(0.365543\pi\)
\(410\) 0 0
\(411\) 15.1968 0.749604
\(412\) 0 0
\(413\) −1.79516 −0.0883340
\(414\) 0 0
\(415\) 36.2279 1.77836
\(416\) 0 0
\(417\) −12.6425 −0.619105
\(418\) 0 0
\(419\) 20.1367 0.983741 0.491871 0.870668i \(-0.336313\pi\)
0.491871 + 0.870668i \(0.336313\pi\)
\(420\) 0 0
\(421\) −13.2091 −0.643774 −0.321887 0.946778i \(-0.604317\pi\)
−0.321887 + 0.946778i \(0.604317\pi\)
\(422\) 0 0
\(423\) 0.360717 0.0175386
\(424\) 0 0
\(425\) 0.287970 0.0139686
\(426\) 0 0
\(427\) 11.2428 0.544076
\(428\) 0 0
\(429\) 2.30883 0.111471
\(430\) 0 0
\(431\) −28.6942 −1.38215 −0.691076 0.722782i \(-0.742863\pi\)
−0.691076 + 0.722782i \(0.742863\pi\)
\(432\) 0 0
\(433\) 16.2483 0.780845 0.390422 0.920636i \(-0.372329\pi\)
0.390422 + 0.920636i \(0.372329\pi\)
\(434\) 0 0
\(435\) 28.4395 1.36357
\(436\) 0 0
\(437\) −53.3771 −2.55337
\(438\) 0 0
\(439\) −30.8121 −1.47058 −0.735291 0.677752i \(-0.762954\pi\)
−0.735291 + 0.677752i \(0.762954\pi\)
\(440\) 0 0
\(441\) 8.55227 0.407251
\(442\) 0 0
\(443\) −31.9987 −1.52031 −0.760153 0.649744i \(-0.774876\pi\)
−0.760153 + 0.649744i \(0.774876\pi\)
\(444\) 0 0
\(445\) −41.6444 −1.97413
\(446\) 0 0
\(447\) 1.17855 0.0557435
\(448\) 0 0
\(449\) 9.25216 0.436637 0.218318 0.975878i \(-0.429943\pi\)
0.218318 + 0.975878i \(0.429943\pi\)
\(450\) 0 0
\(451\) 13.4194 0.631897
\(452\) 0 0
\(453\) 27.8169 1.30695
\(454\) 0 0
\(455\) 1.40622 0.0659244
\(456\) 0 0
\(457\) 26.1559 1.22352 0.611761 0.791043i \(-0.290462\pi\)
0.611761 + 0.791043i \(0.290462\pi\)
\(458\) 0 0
\(459\) 0.659523 0.0307839
\(460\) 0 0
\(461\) 14.7843 0.688576 0.344288 0.938864i \(-0.388120\pi\)
0.344288 + 0.938864i \(0.388120\pi\)
\(462\) 0 0
\(463\) 37.2989 1.73343 0.866713 0.498807i \(-0.166228\pi\)
0.866713 + 0.498807i \(0.166228\pi\)
\(464\) 0 0
\(465\) 21.4917 0.996652
\(466\) 0 0
\(467\) −22.4504 −1.03888 −0.519440 0.854507i \(-0.673860\pi\)
−0.519440 + 0.854507i \(0.673860\pi\)
\(468\) 0 0
\(469\) −0.935717 −0.0432074
\(470\) 0 0
\(471\) −10.9151 −0.502941
\(472\) 0 0
\(473\) 5.71003 0.262548
\(474\) 0 0
\(475\) −17.2401 −0.791030
\(476\) 0 0
\(477\) 12.1669 0.557082
\(478\) 0 0
\(479\) 13.7391 0.627754 0.313877 0.949464i \(-0.398372\pi\)
0.313877 + 0.949464i \(0.398372\pi\)
\(480\) 0 0
\(481\) 0.359481 0.0163909
\(482\) 0 0
\(483\) 11.3854 0.518055
\(484\) 0 0
\(485\) 5.40856 0.245590
\(486\) 0 0
\(487\) −6.65353 −0.301500 −0.150750 0.988572i \(-0.548169\pi\)
−0.150750 + 0.988572i \(0.548169\pi\)
\(488\) 0 0
\(489\) −9.57249 −0.432883
\(490\) 0 0
\(491\) −28.2371 −1.27432 −0.637162 0.770730i \(-0.719892\pi\)
−0.637162 + 0.770730i \(0.719892\pi\)
\(492\) 0 0
\(493\) −1.09365 −0.0492553
\(494\) 0 0
\(495\) −22.5915 −1.01541
\(496\) 0 0
\(497\) 13.5820 0.609235
\(498\) 0 0
\(499\) 4.31213 0.193038 0.0965188 0.995331i \(-0.469229\pi\)
0.0965188 + 0.995331i \(0.469229\pi\)
\(500\) 0 0
\(501\) 0.647901 0.0289461
\(502\) 0 0
\(503\) −13.0344 −0.581176 −0.290588 0.956848i \(-0.593851\pi\)
−0.290588 + 0.956848i \(0.593851\pi\)
\(504\) 0 0
\(505\) 16.0061 0.712261
\(506\) 0 0
\(507\) 15.0004 0.666193
\(508\) 0 0
\(509\) −0.880835 −0.0390423 −0.0195212 0.999809i \(-0.506214\pi\)
−0.0195212 + 0.999809i \(0.506214\pi\)
\(510\) 0 0
\(511\) −9.99892 −0.442326
\(512\) 0 0
\(513\) −39.4841 −1.74326
\(514\) 0 0
\(515\) 28.6418 1.26211
\(516\) 0 0
\(517\) −1.12059 −0.0492834
\(518\) 0 0
\(519\) 23.8831 1.04835
\(520\) 0 0
\(521\) 17.3881 0.761787 0.380893 0.924619i \(-0.375616\pi\)
0.380893 + 0.924619i \(0.375616\pi\)
\(522\) 0 0
\(523\) −2.70828 −0.118425 −0.0592123 0.998245i \(-0.518859\pi\)
−0.0592123 + 0.998245i \(0.518859\pi\)
\(524\) 0 0
\(525\) 3.67735 0.160493
\(526\) 0 0
\(527\) −0.826466 −0.0360014
\(528\) 0 0
\(529\) 30.5588 1.32865
\(530\) 0 0
\(531\) −2.20531 −0.0957022
\(532\) 0 0
\(533\) −1.02614 −0.0444471
\(534\) 0 0
\(535\) −31.3626 −1.35592
\(536\) 0 0
\(537\) −20.2807 −0.875177
\(538\) 0 0
\(539\) −26.5682 −1.14437
\(540\) 0 0
\(541\) 42.9672 1.84730 0.923652 0.383233i \(-0.125189\pi\)
0.923652 + 0.383233i \(0.125189\pi\)
\(542\) 0 0
\(543\) −2.31830 −0.0994878
\(544\) 0 0
\(545\) 18.6431 0.798582
\(546\) 0 0
\(547\) 25.9413 1.10917 0.554585 0.832127i \(-0.312877\pi\)
0.554585 + 0.832127i \(0.312877\pi\)
\(548\) 0 0
\(549\) 13.8115 0.589459
\(550\) 0 0
\(551\) 65.4740 2.78929
\(552\) 0 0
\(553\) −7.50348 −0.319080
\(554\) 0 0
\(555\) 2.92858 0.124311
\(556\) 0 0
\(557\) 4.63049 0.196200 0.0981001 0.995177i \(-0.468723\pi\)
0.0981001 + 0.995177i \(0.468723\pi\)
\(558\) 0 0
\(559\) −0.436628 −0.0184674
\(560\) 0 0
\(561\) −0.723315 −0.0305384
\(562\) 0 0
\(563\) −42.9346 −1.80948 −0.904739 0.425967i \(-0.859934\pi\)
−0.904739 + 0.425967i \(0.859934\pi\)
\(564\) 0 0
\(565\) −54.7431 −2.30306
\(566\) 0 0
\(567\) 1.87761 0.0788524
\(568\) 0 0
\(569\) −13.5418 −0.567701 −0.283850 0.958869i \(-0.591612\pi\)
−0.283850 + 0.958869i \(0.591612\pi\)
\(570\) 0 0
\(571\) 46.0898 1.92880 0.964398 0.264454i \(-0.0851917\pi\)
0.964398 + 0.264454i \(0.0851917\pi\)
\(572\) 0 0
\(573\) −15.3220 −0.640084
\(574\) 0 0
\(575\) 17.2988 0.721411
\(576\) 0 0
\(577\) −36.3950 −1.51514 −0.757571 0.652753i \(-0.773614\pi\)
−0.757571 + 0.652753i \(0.773614\pi\)
\(578\) 0 0
\(579\) −21.6071 −0.897960
\(580\) 0 0
\(581\) −17.7904 −0.738070
\(582\) 0 0
\(583\) −37.7971 −1.56540
\(584\) 0 0
\(585\) 1.72750 0.0714234
\(586\) 0 0
\(587\) −8.36832 −0.345397 −0.172699 0.984975i \(-0.555249\pi\)
−0.172699 + 0.984975i \(0.555249\pi\)
\(588\) 0 0
\(589\) 49.4786 2.03873
\(590\) 0 0
\(591\) −16.3642 −0.673133
\(592\) 0 0
\(593\) 38.5531 1.58319 0.791594 0.611048i \(-0.209252\pi\)
0.791594 + 0.611048i \(0.209252\pi\)
\(594\) 0 0
\(595\) −0.440543 −0.0180605
\(596\) 0 0
\(597\) 16.9085 0.692021
\(598\) 0 0
\(599\) 29.7029 1.21363 0.606813 0.794845i \(-0.292448\pi\)
0.606813 + 0.794845i \(0.292448\pi\)
\(600\) 0 0
\(601\) −25.9283 −1.05764 −0.528818 0.848735i \(-0.677365\pi\)
−0.528818 + 0.848735i \(0.677365\pi\)
\(602\) 0 0
\(603\) −1.14951 −0.0468115
\(604\) 0 0
\(605\) 40.3322 1.63974
\(606\) 0 0
\(607\) 0.769395 0.0312288 0.0156144 0.999878i \(-0.495030\pi\)
0.0156144 + 0.999878i \(0.495030\pi\)
\(608\) 0 0
\(609\) −13.9657 −0.565920
\(610\) 0 0
\(611\) 0.0856878 0.00346656
\(612\) 0 0
\(613\) 20.4941 0.827747 0.413874 0.910334i \(-0.364176\pi\)
0.413874 + 0.910334i \(0.364176\pi\)
\(614\) 0 0
\(615\) −8.35965 −0.337093
\(616\) 0 0
\(617\) 10.8472 0.436691 0.218345 0.975872i \(-0.429934\pi\)
0.218345 + 0.975872i \(0.429934\pi\)
\(618\) 0 0
\(619\) −45.8663 −1.84352 −0.921761 0.387758i \(-0.873249\pi\)
−0.921761 + 0.387758i \(0.873249\pi\)
\(620\) 0 0
\(621\) 39.6185 1.58984
\(622\) 0 0
\(623\) 20.4502 0.819322
\(624\) 0 0
\(625\) −31.2314 −1.24926
\(626\) 0 0
\(627\) 43.3032 1.72936
\(628\) 0 0
\(629\) −0.112619 −0.00449042
\(630\) 0 0
\(631\) 11.0051 0.438107 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(632\) 0 0
\(633\) 1.61330 0.0641228
\(634\) 0 0
\(635\) −31.7230 −1.25889
\(636\) 0 0
\(637\) 2.03158 0.0804942
\(638\) 0 0
\(639\) 16.6851 0.660054
\(640\) 0 0
\(641\) 43.7224 1.72693 0.863465 0.504409i \(-0.168289\pi\)
0.863465 + 0.504409i \(0.168289\pi\)
\(642\) 0 0
\(643\) −16.8257 −0.663542 −0.331771 0.943360i \(-0.607646\pi\)
−0.331771 + 0.943360i \(0.607646\pi\)
\(644\) 0 0
\(645\) −3.55707 −0.140059
\(646\) 0 0
\(647\) −26.0181 −1.02288 −0.511439 0.859320i \(-0.670887\pi\)
−0.511439 + 0.859320i \(0.670887\pi\)
\(648\) 0 0
\(649\) 6.85093 0.268923
\(650\) 0 0
\(651\) −10.5539 −0.413639
\(652\) 0 0
\(653\) 7.29081 0.285312 0.142656 0.989772i \(-0.454436\pi\)
0.142656 + 0.989772i \(0.454436\pi\)
\(654\) 0 0
\(655\) −13.2636 −0.518252
\(656\) 0 0
\(657\) −12.2834 −0.479222
\(658\) 0 0
\(659\) −0.949968 −0.0370055 −0.0185027 0.999829i \(-0.505890\pi\)
−0.0185027 + 0.999829i \(0.505890\pi\)
\(660\) 0 0
\(661\) 42.5999 1.65694 0.828472 0.560030i \(-0.189210\pi\)
0.828472 + 0.560030i \(0.189210\pi\)
\(662\) 0 0
\(663\) 0.0553096 0.00214805
\(664\) 0 0
\(665\) 26.3742 1.02275
\(666\) 0 0
\(667\) −65.6970 −2.54380
\(668\) 0 0
\(669\) 3.23787 0.125183
\(670\) 0 0
\(671\) −42.9062 −1.65638
\(672\) 0 0
\(673\) −3.94684 −0.152140 −0.0760698 0.997102i \(-0.524237\pi\)
−0.0760698 + 0.997102i \(0.524237\pi\)
\(674\) 0 0
\(675\) 12.7963 0.492529
\(676\) 0 0
\(677\) −13.4304 −0.516174 −0.258087 0.966122i \(-0.583092\pi\)
−0.258087 + 0.966122i \(0.583092\pi\)
\(678\) 0 0
\(679\) −2.65597 −0.101927
\(680\) 0 0
\(681\) 14.7825 0.566468
\(682\) 0 0
\(683\) −26.4002 −1.01017 −0.505087 0.863068i \(-0.668540\pi\)
−0.505087 + 0.863068i \(0.668540\pi\)
\(684\) 0 0
\(685\) −35.3232 −1.34963
\(686\) 0 0
\(687\) −13.8054 −0.526709
\(688\) 0 0
\(689\) 2.89023 0.110109
\(690\) 0 0
\(691\) 2.53805 0.0965519 0.0482760 0.998834i \(-0.484627\pi\)
0.0482760 + 0.998834i \(0.484627\pi\)
\(692\) 0 0
\(693\) 11.0940 0.421426
\(694\) 0 0
\(695\) 29.3859 1.11467
\(696\) 0 0
\(697\) 0.321472 0.0121766
\(698\) 0 0
\(699\) −19.6900 −0.744743
\(700\) 0 0
\(701\) −8.13196 −0.307140 −0.153570 0.988138i \(-0.549077\pi\)
−0.153570 + 0.988138i \(0.549077\pi\)
\(702\) 0 0
\(703\) 6.74224 0.254288
\(704\) 0 0
\(705\) 0.698072 0.0262909
\(706\) 0 0
\(707\) −7.86008 −0.295609
\(708\) 0 0
\(709\) 0.635274 0.0238582 0.0119291 0.999929i \(-0.496203\pi\)
0.0119291 + 0.999929i \(0.496203\pi\)
\(710\) 0 0
\(711\) −9.21783 −0.345696
\(712\) 0 0
\(713\) −49.6471 −1.85930
\(714\) 0 0
\(715\) −5.36659 −0.200699
\(716\) 0 0
\(717\) −11.3250 −0.422939
\(718\) 0 0
\(719\) −51.4664 −1.91937 −0.959687 0.281072i \(-0.909310\pi\)
−0.959687 + 0.281072i \(0.909310\pi\)
\(720\) 0 0
\(721\) −14.0651 −0.523812
\(722\) 0 0
\(723\) 28.3819 1.05553
\(724\) 0 0
\(725\) −21.2193 −0.788064
\(726\) 0 0
\(727\) −22.2966 −0.826933 −0.413467 0.910519i \(-0.635682\pi\)
−0.413467 + 0.910519i \(0.635682\pi\)
\(728\) 0 0
\(729\) 21.2670 0.787665
\(730\) 0 0
\(731\) 0.136788 0.00505928
\(732\) 0 0
\(733\) −44.7564 −1.65311 −0.826557 0.562853i \(-0.809704\pi\)
−0.826557 + 0.562853i \(0.809704\pi\)
\(734\) 0 0
\(735\) 16.5507 0.610480
\(736\) 0 0
\(737\) 3.57101 0.131540
\(738\) 0 0
\(739\) −9.87352 −0.363203 −0.181602 0.983372i \(-0.558128\pi\)
−0.181602 + 0.983372i \(0.558128\pi\)
\(740\) 0 0
\(741\) −3.31125 −0.121642
\(742\) 0 0
\(743\) −26.0393 −0.955291 −0.477645 0.878553i \(-0.658510\pi\)
−0.477645 + 0.878553i \(0.658510\pi\)
\(744\) 0 0
\(745\) −2.73940 −0.100364
\(746\) 0 0
\(747\) −21.8550 −0.799634
\(748\) 0 0
\(749\) 15.4012 0.562748
\(750\) 0 0
\(751\) 1.00000 0.0364905
\(752\) 0 0
\(753\) −27.9095 −1.01708
\(754\) 0 0
\(755\) −64.6569 −2.35311
\(756\) 0 0
\(757\) −22.8717 −0.831286 −0.415643 0.909528i \(-0.636443\pi\)
−0.415643 + 0.909528i \(0.636443\pi\)
\(758\) 0 0
\(759\) −43.4506 −1.57716
\(760\) 0 0
\(761\) 14.3492 0.520158 0.260079 0.965587i \(-0.416251\pi\)
0.260079 + 0.965587i \(0.416251\pi\)
\(762\) 0 0
\(763\) −9.15504 −0.331435
\(764\) 0 0
\(765\) −0.541196 −0.0195670
\(766\) 0 0
\(767\) −0.523869 −0.0189158
\(768\) 0 0
\(769\) −9.30693 −0.335617 −0.167808 0.985820i \(-0.553669\pi\)
−0.167808 + 0.985820i \(0.553669\pi\)
\(770\) 0 0
\(771\) 14.5864 0.525318
\(772\) 0 0
\(773\) 40.5213 1.45745 0.728725 0.684807i \(-0.240113\pi\)
0.728725 + 0.684807i \(0.240113\pi\)
\(774\) 0 0
\(775\) −16.0354 −0.576008
\(776\) 0 0
\(777\) −1.43813 −0.0515927
\(778\) 0 0
\(779\) −19.2458 −0.689551
\(780\) 0 0
\(781\) −51.8334 −1.85475
\(782\) 0 0
\(783\) −48.5973 −1.73673
\(784\) 0 0
\(785\) 25.3708 0.905523
\(786\) 0 0
\(787\) −43.1951 −1.53974 −0.769870 0.638201i \(-0.779679\pi\)
−0.769870 + 0.638201i \(0.779679\pi\)
\(788\) 0 0
\(789\) 5.06411 0.180287
\(790\) 0 0
\(791\) 26.8826 0.955836
\(792\) 0 0
\(793\) 3.28090 0.116508
\(794\) 0 0
\(795\) 23.5458 0.835082
\(796\) 0 0
\(797\) −0.985432 −0.0349058 −0.0174529 0.999848i \(-0.505556\pi\)
−0.0174529 + 0.999848i \(0.505556\pi\)
\(798\) 0 0
\(799\) −0.0268445 −0.000949689 0
\(800\) 0 0
\(801\) 25.1226 0.887664
\(802\) 0 0
\(803\) 38.1592 1.34661
\(804\) 0 0
\(805\) −26.4641 −0.932736
\(806\) 0 0
\(807\) 19.5426 0.687931
\(808\) 0 0
\(809\) −19.2227 −0.675834 −0.337917 0.941176i \(-0.609722\pi\)
−0.337917 + 0.941176i \(0.609722\pi\)
\(810\) 0 0
\(811\) 30.6025 1.07460 0.537300 0.843391i \(-0.319444\pi\)
0.537300 + 0.843391i \(0.319444\pi\)
\(812\) 0 0
\(813\) −18.0296 −0.632325
\(814\) 0 0
\(815\) 22.2501 0.779387
\(816\) 0 0
\(817\) −8.18916 −0.286502
\(818\) 0 0
\(819\) −0.848322 −0.0296428
\(820\) 0 0
\(821\) −0.590203 −0.0205982 −0.0102991 0.999947i \(-0.503278\pi\)
−0.0102991 + 0.999947i \(0.503278\pi\)
\(822\) 0 0
\(823\) 4.00610 0.139644 0.0698220 0.997559i \(-0.477757\pi\)
0.0698220 + 0.997559i \(0.477757\pi\)
\(824\) 0 0
\(825\) −14.0340 −0.488601
\(826\) 0 0
\(827\) 52.0294 1.80924 0.904619 0.426221i \(-0.140155\pi\)
0.904619 + 0.426221i \(0.140155\pi\)
\(828\) 0 0
\(829\) −41.1834 −1.43036 −0.715179 0.698941i \(-0.753655\pi\)
−0.715179 + 0.698941i \(0.753655\pi\)
\(830\) 0 0
\(831\) 31.7113 1.10005
\(832\) 0 0
\(833\) −0.636459 −0.0220520
\(834\) 0 0
\(835\) −1.50597 −0.0521162
\(836\) 0 0
\(837\) −36.7249 −1.26940
\(838\) 0 0
\(839\) −10.2524 −0.353951 −0.176976 0.984215i \(-0.556631\pi\)
−0.176976 + 0.984215i \(0.556631\pi\)
\(840\) 0 0
\(841\) 51.5860 1.77883
\(842\) 0 0
\(843\) −21.9348 −0.755475
\(844\) 0 0
\(845\) −34.8667 −1.19945
\(846\) 0 0
\(847\) −19.8059 −0.680537
\(848\) 0 0
\(849\) −3.94157 −0.135274
\(850\) 0 0
\(851\) −6.76520 −0.231908
\(852\) 0 0
\(853\) 13.2705 0.454372 0.227186 0.973851i \(-0.427047\pi\)
0.227186 + 0.973851i \(0.427047\pi\)
\(854\) 0 0
\(855\) 32.4001 1.10806
\(856\) 0 0
\(857\) −29.5362 −1.00894 −0.504469 0.863430i \(-0.668312\pi\)
−0.504469 + 0.863430i \(0.668312\pi\)
\(858\) 0 0
\(859\) 38.8936 1.32703 0.663516 0.748162i \(-0.269063\pi\)
0.663516 + 0.748162i \(0.269063\pi\)
\(860\) 0 0
\(861\) 4.10516 0.139903
\(862\) 0 0
\(863\) 52.7129 1.79437 0.897184 0.441658i \(-0.145609\pi\)
0.897184 + 0.441658i \(0.145609\pi\)
\(864\) 0 0
\(865\) −55.5133 −1.88751
\(866\) 0 0
\(867\) 19.8295 0.673445
\(868\) 0 0
\(869\) 28.6358 0.971402
\(870\) 0 0
\(871\) −0.273064 −0.00925241
\(872\) 0 0
\(873\) −3.26280 −0.110429
\(874\) 0 0
\(875\) 9.53297 0.322273
\(876\) 0 0
\(877\) 25.8366 0.872441 0.436221 0.899840i \(-0.356317\pi\)
0.436221 + 0.899840i \(0.356317\pi\)
\(878\) 0 0
\(879\) 22.2761 0.751353
\(880\) 0 0
\(881\) 4.58855 0.154592 0.0772961 0.997008i \(-0.475371\pi\)
0.0772961 + 0.997008i \(0.475371\pi\)
\(882\) 0 0
\(883\) −25.6061 −0.861713 −0.430856 0.902421i \(-0.641788\pi\)
−0.430856 + 0.902421i \(0.641788\pi\)
\(884\) 0 0
\(885\) −4.26779 −0.143460
\(886\) 0 0
\(887\) 32.8061 1.10152 0.550761 0.834663i \(-0.314338\pi\)
0.550761 + 0.834663i \(0.314338\pi\)
\(888\) 0 0
\(889\) 15.5782 0.522475
\(890\) 0 0
\(891\) −7.16561 −0.240057
\(892\) 0 0
\(893\) 1.60712 0.0537801
\(894\) 0 0
\(895\) 47.1400 1.57572
\(896\) 0 0
\(897\) 3.32253 0.110936
\(898\) 0 0
\(899\) 60.8987 2.03109
\(900\) 0 0
\(901\) −0.905457 −0.0301651
\(902\) 0 0
\(903\) 1.74676 0.0581287
\(904\) 0 0
\(905\) 5.38861 0.179123
\(906\) 0 0
\(907\) 55.6029 1.84627 0.923133 0.384482i \(-0.125620\pi\)
0.923133 + 0.384482i \(0.125620\pi\)
\(908\) 0 0
\(909\) −9.65591 −0.320266
\(910\) 0 0
\(911\) 38.2271 1.26652 0.633261 0.773938i \(-0.281716\pi\)
0.633261 + 0.773938i \(0.281716\pi\)
\(912\) 0 0
\(913\) 67.8941 2.24697
\(914\) 0 0
\(915\) 26.7285 0.883616
\(916\) 0 0
\(917\) 6.51334 0.215089
\(918\) 0 0
\(919\) 30.5273 1.00700 0.503501 0.863995i \(-0.332045\pi\)
0.503501 + 0.863995i \(0.332045\pi\)
\(920\) 0 0
\(921\) 10.3548 0.341203
\(922\) 0 0
\(923\) 3.96353 0.130461
\(924\) 0 0
\(925\) −2.18507 −0.0718448
\(926\) 0 0
\(927\) −17.2786 −0.567504
\(928\) 0 0
\(929\) −6.80821 −0.223370 −0.111685 0.993744i \(-0.535625\pi\)
−0.111685 + 0.993744i \(0.535625\pi\)
\(930\) 0 0
\(931\) 38.1033 1.24878
\(932\) 0 0
\(933\) −2.41260 −0.0789850
\(934\) 0 0
\(935\) 1.68126 0.0549830
\(936\) 0 0
\(937\) −1.02547 −0.0335008 −0.0167504 0.999860i \(-0.505332\pi\)
−0.0167504 + 0.999860i \(0.505332\pi\)
\(938\) 0 0
\(939\) −10.1478 −0.331160
\(940\) 0 0
\(941\) 9.67038 0.315245 0.157623 0.987499i \(-0.449617\pi\)
0.157623 + 0.987499i \(0.449617\pi\)
\(942\) 0 0
\(943\) 19.3113 0.628863
\(944\) 0 0
\(945\) −19.5760 −0.636807
\(946\) 0 0
\(947\) 34.5575 1.12297 0.561485 0.827487i \(-0.310230\pi\)
0.561485 + 0.827487i \(0.310230\pi\)
\(948\) 0 0
\(949\) −2.91791 −0.0947195
\(950\) 0 0
\(951\) 8.78461 0.284860
\(952\) 0 0
\(953\) 7.16843 0.232208 0.116104 0.993237i \(-0.462959\pi\)
0.116104 + 0.993237i \(0.462959\pi\)
\(954\) 0 0
\(955\) 35.6140 1.15244
\(956\) 0 0
\(957\) 53.2979 1.72288
\(958\) 0 0
\(959\) 17.3461 0.560135
\(960\) 0 0
\(961\) 15.0211 0.484550
\(962\) 0 0
\(963\) 18.9200 0.609688
\(964\) 0 0
\(965\) 50.2231 1.61674
\(966\) 0 0
\(967\) −1.14216 −0.0367294 −0.0183647 0.999831i \(-0.505846\pi\)
−0.0183647 + 0.999831i \(0.505846\pi\)
\(968\) 0 0
\(969\) 1.03736 0.0333247
\(970\) 0 0
\(971\) −43.4721 −1.39509 −0.697543 0.716543i \(-0.745723\pi\)
−0.697543 + 0.716543i \(0.745723\pi\)
\(972\) 0 0
\(973\) −14.4305 −0.462621
\(974\) 0 0
\(975\) 1.07313 0.0343678
\(976\) 0 0
\(977\) −23.2697 −0.744464 −0.372232 0.928140i \(-0.621407\pi\)
−0.372232 + 0.928140i \(0.621407\pi\)
\(978\) 0 0
\(979\) −78.0450 −2.49433
\(980\) 0 0
\(981\) −11.2467 −0.359081
\(982\) 0 0
\(983\) 6.81080 0.217231 0.108615 0.994084i \(-0.465358\pi\)
0.108615 + 0.994084i \(0.465358\pi\)
\(984\) 0 0
\(985\) 38.0366 1.21195
\(986\) 0 0
\(987\) −0.342801 −0.0109115
\(988\) 0 0
\(989\) 8.21705 0.261287
\(990\) 0 0
\(991\) 61.5372 1.95479 0.977397 0.211411i \(-0.0678059\pi\)
0.977397 + 0.211411i \(0.0678059\pi\)
\(992\) 0 0
\(993\) 0.462662 0.0146821
\(994\) 0 0
\(995\) −39.3019 −1.24595
\(996\) 0 0
\(997\) 18.6985 0.592187 0.296093 0.955159i \(-0.404316\pi\)
0.296093 + 0.955159i \(0.404316\pi\)
\(998\) 0 0
\(999\) −5.00435 −0.158331
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 6008.2.a.c.1.17 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.c.1.17 44 1.1 even 1 trivial