Properties

Label 3584.2.a.p.1.7
Level $3584$
Weight $2$
Character 3584.1
Self dual yes
Analytic conductor $28.618$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3584,2,Mod(1,3584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3584, 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("3584.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.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: \(28.6183840844\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 19x^{8} + 44x^{7} + 86x^{6} - 236x^{5} - 58x^{4} + 368x^{3} - 194x^{2} - 12x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(2.97399\) of defining polynomial
Character \(\chi\) \(=\) 3584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.783186 q^{3} +3.56843 q^{5} +1.00000 q^{7} -2.38662 q^{9} +O(q^{10})\) \(q+0.783186 q^{3} +3.56843 q^{5} +1.00000 q^{7} -2.38662 q^{9} +2.51888 q^{11} +6.52509 q^{13} +2.79474 q^{15} -1.93892 q^{17} +6.56828 q^{19} +0.783186 q^{21} +2.76749 q^{23} +7.73367 q^{25} -4.21872 q^{27} +2.34745 q^{29} -7.50115 q^{31} +1.97275 q^{33} +3.56843 q^{35} +6.05146 q^{37} +5.11036 q^{39} -7.71634 q^{41} -10.9178 q^{43} -8.51648 q^{45} -8.18136 q^{47} +1.00000 q^{49} -1.51854 q^{51} -2.04735 q^{53} +8.98842 q^{55} +5.14418 q^{57} +0.911427 q^{59} +2.08843 q^{61} -2.38662 q^{63} +23.2843 q^{65} +1.87592 q^{67} +2.16746 q^{69} -12.3355 q^{71} +14.1203 q^{73} +6.05690 q^{75} +2.51888 q^{77} -8.33547 q^{79} +3.85582 q^{81} +6.44004 q^{83} -6.91891 q^{85} +1.83849 q^{87} -1.56223 q^{89} +6.52509 q^{91} -5.87480 q^{93} +23.4384 q^{95} +18.9273 q^{97} -6.01160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{7} + 22 q^{9} + 16 q^{15} + 16 q^{17} + 8 q^{23} + 30 q^{25} - 8 q^{31} + 12 q^{33} + 20 q^{41} - 24 q^{47} + 10 q^{49} - 32 q^{55} + 28 q^{57} + 22 q^{63} + 32 q^{65} + 48 q^{73} + 40 q^{79} + 62 q^{81} - 8 q^{87} + 16 q^{89} - 32 q^{95} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.783186 0.452173 0.226086 0.974107i \(-0.427407\pi\)
0.226086 + 0.974107i \(0.427407\pi\)
\(4\) 0 0
\(5\) 3.56843 1.59585 0.797924 0.602758i \(-0.205931\pi\)
0.797924 + 0.602758i \(0.205931\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.38662 −0.795540
\(10\) 0 0
\(11\) 2.51888 0.759470 0.379735 0.925095i \(-0.376015\pi\)
0.379735 + 0.925095i \(0.376015\pi\)
\(12\) 0 0
\(13\) 6.52509 1.80974 0.904868 0.425693i \(-0.139970\pi\)
0.904868 + 0.425693i \(0.139970\pi\)
\(14\) 0 0
\(15\) 2.79474 0.721599
\(16\) 0 0
\(17\) −1.93892 −0.470258 −0.235129 0.971964i \(-0.575551\pi\)
−0.235129 + 0.971964i \(0.575551\pi\)
\(18\) 0 0
\(19\) 6.56828 1.50687 0.753434 0.657524i \(-0.228396\pi\)
0.753434 + 0.657524i \(0.228396\pi\)
\(20\) 0 0
\(21\) 0.783186 0.170905
\(22\) 0 0
\(23\) 2.76749 0.577061 0.288531 0.957471i \(-0.406833\pi\)
0.288531 + 0.957471i \(0.406833\pi\)
\(24\) 0 0
\(25\) 7.73367 1.54673
\(26\) 0 0
\(27\) −4.21872 −0.811894
\(28\) 0 0
\(29\) 2.34745 0.435910 0.217955 0.975959i \(-0.430061\pi\)
0.217955 + 0.975959i \(0.430061\pi\)
\(30\) 0 0
\(31\) −7.50115 −1.34725 −0.673623 0.739075i \(-0.735263\pi\)
−0.673623 + 0.739075i \(0.735263\pi\)
\(32\) 0 0
\(33\) 1.97275 0.343411
\(34\) 0 0
\(35\) 3.56843 0.603174
\(36\) 0 0
\(37\) 6.05146 0.994854 0.497427 0.867506i \(-0.334278\pi\)
0.497427 + 0.867506i \(0.334278\pi\)
\(38\) 0 0
\(39\) 5.11036 0.818313
\(40\) 0 0
\(41\) −7.71634 −1.20509 −0.602545 0.798085i \(-0.705846\pi\)
−0.602545 + 0.798085i \(0.705846\pi\)
\(42\) 0 0
\(43\) −10.9178 −1.66495 −0.832473 0.554065i \(-0.813076\pi\)
−0.832473 + 0.554065i \(0.813076\pi\)
\(44\) 0 0
\(45\) −8.51648 −1.26956
\(46\) 0 0
\(47\) −8.18136 −1.19337 −0.596687 0.802474i \(-0.703517\pi\)
−0.596687 + 0.802474i \(0.703517\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.51854 −0.212638
\(52\) 0 0
\(53\) −2.04735 −0.281225 −0.140613 0.990065i \(-0.544907\pi\)
−0.140613 + 0.990065i \(0.544907\pi\)
\(54\) 0 0
\(55\) 8.98842 1.21200
\(56\) 0 0
\(57\) 5.14418 0.681364
\(58\) 0 0
\(59\) 0.911427 0.118658 0.0593288 0.998238i \(-0.481104\pi\)
0.0593288 + 0.998238i \(0.481104\pi\)
\(60\) 0 0
\(61\) 2.08843 0.267396 0.133698 0.991022i \(-0.457315\pi\)
0.133698 + 0.991022i \(0.457315\pi\)
\(62\) 0 0
\(63\) −2.38662 −0.300686
\(64\) 0 0
\(65\) 23.2843 2.88806
\(66\) 0 0
\(67\) 1.87592 0.229180 0.114590 0.993413i \(-0.463445\pi\)
0.114590 + 0.993413i \(0.463445\pi\)
\(68\) 0 0
\(69\) 2.16746 0.260931
\(70\) 0 0
\(71\) −12.3355 −1.46395 −0.731975 0.681331i \(-0.761401\pi\)
−0.731975 + 0.681331i \(0.761401\pi\)
\(72\) 0 0
\(73\) 14.1203 1.65265 0.826327 0.563190i \(-0.190426\pi\)
0.826327 + 0.563190i \(0.190426\pi\)
\(74\) 0 0
\(75\) 6.05690 0.699390
\(76\) 0 0
\(77\) 2.51888 0.287053
\(78\) 0 0
\(79\) −8.33547 −0.937814 −0.468907 0.883248i \(-0.655352\pi\)
−0.468907 + 0.883248i \(0.655352\pi\)
\(80\) 0 0
\(81\) 3.85582 0.428424
\(82\) 0 0
\(83\) 6.44004 0.706886 0.353443 0.935456i \(-0.385011\pi\)
0.353443 + 0.935456i \(0.385011\pi\)
\(84\) 0 0
\(85\) −6.91891 −0.750461
\(86\) 0 0
\(87\) 1.83849 0.197107
\(88\) 0 0
\(89\) −1.56223 −0.165596 −0.0827980 0.996566i \(-0.526386\pi\)
−0.0827980 + 0.996566i \(0.526386\pi\)
\(90\) 0 0
\(91\) 6.52509 0.684016
\(92\) 0 0
\(93\) −5.87480 −0.609188
\(94\) 0 0
\(95\) 23.4384 2.40473
\(96\) 0 0
\(97\) 18.9273 1.92178 0.960891 0.276928i \(-0.0893165\pi\)
0.960891 + 0.276928i \(0.0893165\pi\)
\(98\) 0 0
\(99\) −6.01160 −0.604189
\(100\) 0 0
\(101\) −4.33962 −0.431808 −0.215904 0.976415i \(-0.569270\pi\)
−0.215904 + 0.976415i \(0.569270\pi\)
\(102\) 0 0
\(103\) 1.28597 0.126710 0.0633552 0.997991i \(-0.479820\pi\)
0.0633552 + 0.997991i \(0.479820\pi\)
\(104\) 0 0
\(105\) 2.79474 0.272739
\(106\) 0 0
\(107\) −16.1882 −1.56497 −0.782485 0.622670i \(-0.786048\pi\)
−0.782485 + 0.622670i \(0.786048\pi\)
\(108\) 0 0
\(109\) −3.27087 −0.313292 −0.156646 0.987655i \(-0.550068\pi\)
−0.156646 + 0.987655i \(0.550068\pi\)
\(110\) 0 0
\(111\) 4.73942 0.449846
\(112\) 0 0
\(113\) −10.6115 −0.998247 −0.499124 0.866531i \(-0.666345\pi\)
−0.499124 + 0.866531i \(0.666345\pi\)
\(114\) 0 0
\(115\) 9.87558 0.920902
\(116\) 0 0
\(117\) −15.5729 −1.43972
\(118\) 0 0
\(119\) −1.93892 −0.177741
\(120\) 0 0
\(121\) −4.65526 −0.423206
\(122\) 0 0
\(123\) −6.04333 −0.544908
\(124\) 0 0
\(125\) 9.75488 0.872503
\(126\) 0 0
\(127\) −4.00575 −0.355453 −0.177726 0.984080i \(-0.556874\pi\)
−0.177726 + 0.984080i \(0.556874\pi\)
\(128\) 0 0
\(129\) −8.55065 −0.752843
\(130\) 0 0
\(131\) 22.6188 1.97621 0.988105 0.153782i \(-0.0491452\pi\)
0.988105 + 0.153782i \(0.0491452\pi\)
\(132\) 0 0
\(133\) 6.56828 0.569542
\(134\) 0 0
\(135\) −15.0542 −1.29566
\(136\) 0 0
\(137\) 2.65295 0.226657 0.113329 0.993558i \(-0.463849\pi\)
0.113329 + 0.993558i \(0.463849\pi\)
\(138\) 0 0
\(139\) 12.0524 1.02227 0.511135 0.859500i \(-0.329225\pi\)
0.511135 + 0.859500i \(0.329225\pi\)
\(140\) 0 0
\(141\) −6.40752 −0.539611
\(142\) 0 0
\(143\) 16.4359 1.37444
\(144\) 0 0
\(145\) 8.37670 0.695647
\(146\) 0 0
\(147\) 0.783186 0.0645961
\(148\) 0 0
\(149\) −0.867450 −0.0710643 −0.0355321 0.999369i \(-0.511313\pi\)
−0.0355321 + 0.999369i \(0.511313\pi\)
\(150\) 0 0
\(151\) −16.6652 −1.35619 −0.678097 0.734973i \(-0.737195\pi\)
−0.678097 + 0.734973i \(0.737195\pi\)
\(152\) 0 0
\(153\) 4.62748 0.374109
\(154\) 0 0
\(155\) −26.7673 −2.15000
\(156\) 0 0
\(157\) 10.9584 0.874578 0.437289 0.899321i \(-0.355939\pi\)
0.437289 + 0.899321i \(0.355939\pi\)
\(158\) 0 0
\(159\) −1.60346 −0.127162
\(160\) 0 0
\(161\) 2.76749 0.218109
\(162\) 0 0
\(163\) 3.05160 0.239020 0.119510 0.992833i \(-0.461868\pi\)
0.119510 + 0.992833i \(0.461868\pi\)
\(164\) 0 0
\(165\) 7.03961 0.548033
\(166\) 0 0
\(167\) −14.8209 −1.14688 −0.573440 0.819248i \(-0.694391\pi\)
−0.573440 + 0.819248i \(0.694391\pi\)
\(168\) 0 0
\(169\) 29.5769 2.27514
\(170\) 0 0
\(171\) −15.6760 −1.19877
\(172\) 0 0
\(173\) −4.00098 −0.304189 −0.152095 0.988366i \(-0.548602\pi\)
−0.152095 + 0.988366i \(0.548602\pi\)
\(174\) 0 0
\(175\) 7.73367 0.584610
\(176\) 0 0
\(177\) 0.713817 0.0536537
\(178\) 0 0
\(179\) 3.78093 0.282600 0.141300 0.989967i \(-0.454872\pi\)
0.141300 + 0.989967i \(0.454872\pi\)
\(180\) 0 0
\(181\) −21.3282 −1.58531 −0.792656 0.609669i \(-0.791302\pi\)
−0.792656 + 0.609669i \(0.791302\pi\)
\(182\) 0 0
\(183\) 1.63563 0.120909
\(184\) 0 0
\(185\) 21.5942 1.58764
\(186\) 0 0
\(187\) −4.88391 −0.357147
\(188\) 0 0
\(189\) −4.21872 −0.306867
\(190\) 0 0
\(191\) 20.3082 1.46945 0.734726 0.678365i \(-0.237311\pi\)
0.734726 + 0.678365i \(0.237311\pi\)
\(192\) 0 0
\(193\) −11.2843 −0.812263 −0.406132 0.913815i \(-0.633123\pi\)
−0.406132 + 0.913815i \(0.633123\pi\)
\(194\) 0 0
\(195\) 18.2359 1.30590
\(196\) 0 0
\(197\) 21.4452 1.52791 0.763953 0.645272i \(-0.223256\pi\)
0.763953 + 0.645272i \(0.223256\pi\)
\(198\) 0 0
\(199\) 23.8094 1.68780 0.843901 0.536499i \(-0.180254\pi\)
0.843901 + 0.536499i \(0.180254\pi\)
\(200\) 0 0
\(201\) 1.46920 0.103629
\(202\) 0 0
\(203\) 2.34745 0.164759
\(204\) 0 0
\(205\) −27.5352 −1.92314
\(206\) 0 0
\(207\) −6.60494 −0.459075
\(208\) 0 0
\(209\) 16.5447 1.14442
\(210\) 0 0
\(211\) −21.2738 −1.46455 −0.732273 0.681011i \(-0.761540\pi\)
−0.732273 + 0.681011i \(0.761540\pi\)
\(212\) 0 0
\(213\) −9.66096 −0.661958
\(214\) 0 0
\(215\) −38.9593 −2.65700
\(216\) 0 0
\(217\) −7.50115 −0.509211
\(218\) 0 0
\(219\) 11.0588 0.747285
\(220\) 0 0
\(221\) −12.6517 −0.851043
\(222\) 0 0
\(223\) −11.8047 −0.790499 −0.395249 0.918574i \(-0.629342\pi\)
−0.395249 + 0.918574i \(0.629342\pi\)
\(224\) 0 0
\(225\) −18.4573 −1.23049
\(226\) 0 0
\(227\) −18.4000 −1.22125 −0.610626 0.791919i \(-0.709082\pi\)
−0.610626 + 0.791919i \(0.709082\pi\)
\(228\) 0 0
\(229\) −9.65784 −0.638208 −0.319104 0.947720i \(-0.603382\pi\)
−0.319104 + 0.947720i \(0.603382\pi\)
\(230\) 0 0
\(231\) 1.97275 0.129797
\(232\) 0 0
\(233\) −4.53080 −0.296823 −0.148411 0.988926i \(-0.547416\pi\)
−0.148411 + 0.988926i \(0.547416\pi\)
\(234\) 0 0
\(235\) −29.1946 −1.90444
\(236\) 0 0
\(237\) −6.52822 −0.424053
\(238\) 0 0
\(239\) −19.2524 −1.24533 −0.622666 0.782488i \(-0.713950\pi\)
−0.622666 + 0.782488i \(0.713950\pi\)
\(240\) 0 0
\(241\) 19.9588 1.28566 0.642829 0.766010i \(-0.277761\pi\)
0.642829 + 0.766010i \(0.277761\pi\)
\(242\) 0 0
\(243\) 15.6760 1.00562
\(244\) 0 0
\(245\) 3.56843 0.227978
\(246\) 0 0
\(247\) 42.8587 2.72703
\(248\) 0 0
\(249\) 5.04375 0.319635
\(250\) 0 0
\(251\) −9.57278 −0.604229 −0.302114 0.953272i \(-0.597692\pi\)
−0.302114 + 0.953272i \(0.597692\pi\)
\(252\) 0 0
\(253\) 6.97096 0.438261
\(254\) 0 0
\(255\) −5.41879 −0.339338
\(256\) 0 0
\(257\) 12.5779 0.784588 0.392294 0.919840i \(-0.371682\pi\)
0.392294 + 0.919840i \(0.371682\pi\)
\(258\) 0 0
\(259\) 6.05146 0.376019
\(260\) 0 0
\(261\) −5.60247 −0.346784
\(262\) 0 0
\(263\) 15.9051 0.980751 0.490375 0.871511i \(-0.336860\pi\)
0.490375 + 0.871511i \(0.336860\pi\)
\(264\) 0 0
\(265\) −7.30582 −0.448793
\(266\) 0 0
\(267\) −1.22352 −0.0748779
\(268\) 0 0
\(269\) 4.00098 0.243944 0.121972 0.992534i \(-0.461078\pi\)
0.121972 + 0.992534i \(0.461078\pi\)
\(270\) 0 0
\(271\) 3.80466 0.231117 0.115558 0.993301i \(-0.463134\pi\)
0.115558 + 0.993301i \(0.463134\pi\)
\(272\) 0 0
\(273\) 5.11036 0.309293
\(274\) 0 0
\(275\) 19.4801 1.17470
\(276\) 0 0
\(277\) −12.6170 −0.758085 −0.379042 0.925379i \(-0.623747\pi\)
−0.379042 + 0.925379i \(0.623747\pi\)
\(278\) 0 0
\(279\) 17.9024 1.07179
\(280\) 0 0
\(281\) 13.1161 0.782442 0.391221 0.920297i \(-0.372053\pi\)
0.391221 + 0.920297i \(0.372053\pi\)
\(282\) 0 0
\(283\) −12.4251 −0.738593 −0.369297 0.929312i \(-0.620401\pi\)
−0.369297 + 0.929312i \(0.620401\pi\)
\(284\) 0 0
\(285\) 18.3566 1.08735
\(286\) 0 0
\(287\) −7.71634 −0.455481
\(288\) 0 0
\(289\) −13.2406 −0.778857
\(290\) 0 0
\(291\) 14.8236 0.868977
\(292\) 0 0
\(293\) 19.8515 1.15974 0.579869 0.814709i \(-0.303104\pi\)
0.579869 + 0.814709i \(0.303104\pi\)
\(294\) 0 0
\(295\) 3.25236 0.189360
\(296\) 0 0
\(297\) −10.6264 −0.616609
\(298\) 0 0
\(299\) 18.0581 1.04433
\(300\) 0 0
\(301\) −10.9178 −0.629291
\(302\) 0 0
\(303\) −3.39873 −0.195252
\(304\) 0 0
\(305\) 7.45240 0.426723
\(306\) 0 0
\(307\) 2.17681 0.124237 0.0621186 0.998069i \(-0.480214\pi\)
0.0621186 + 0.998069i \(0.480214\pi\)
\(308\) 0 0
\(309\) 1.00715 0.0572950
\(310\) 0 0
\(311\) 3.14523 0.178350 0.0891748 0.996016i \(-0.471577\pi\)
0.0891748 + 0.996016i \(0.471577\pi\)
\(312\) 0 0
\(313\) −12.3476 −0.697926 −0.348963 0.937136i \(-0.613466\pi\)
−0.348963 + 0.937136i \(0.613466\pi\)
\(314\) 0 0
\(315\) −8.51648 −0.479849
\(316\) 0 0
\(317\) 17.6070 0.988906 0.494453 0.869204i \(-0.335368\pi\)
0.494453 + 0.869204i \(0.335368\pi\)
\(318\) 0 0
\(319\) 5.91293 0.331061
\(320\) 0 0
\(321\) −12.6783 −0.707636
\(322\) 0 0
\(323\) −12.7354 −0.708617
\(324\) 0 0
\(325\) 50.4629 2.79918
\(326\) 0 0
\(327\) −2.56170 −0.141662
\(328\) 0 0
\(329\) −8.18136 −0.451053
\(330\) 0 0
\(331\) 22.0587 1.21246 0.606229 0.795290i \(-0.292681\pi\)
0.606229 + 0.795290i \(0.292681\pi\)
\(332\) 0 0
\(333\) −14.4425 −0.791446
\(334\) 0 0
\(335\) 6.69409 0.365737
\(336\) 0 0
\(337\) 14.0594 0.765866 0.382933 0.923776i \(-0.374914\pi\)
0.382933 + 0.923776i \(0.374914\pi\)
\(338\) 0 0
\(339\) −8.31079 −0.451380
\(340\) 0 0
\(341\) −18.8945 −1.02319
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 7.73441 0.416407
\(346\) 0 0
\(347\) 8.30730 0.445959 0.222980 0.974823i \(-0.428422\pi\)
0.222980 + 0.974823i \(0.428422\pi\)
\(348\) 0 0
\(349\) 5.30333 0.283881 0.141940 0.989875i \(-0.454666\pi\)
0.141940 + 0.989875i \(0.454666\pi\)
\(350\) 0 0
\(351\) −27.5276 −1.46931
\(352\) 0 0
\(353\) −21.6280 −1.15114 −0.575571 0.817752i \(-0.695220\pi\)
−0.575571 + 0.817752i \(0.695220\pi\)
\(354\) 0 0
\(355\) −44.0182 −2.33624
\(356\) 0 0
\(357\) −1.51854 −0.0803696
\(358\) 0 0
\(359\) −26.8859 −1.41898 −0.709492 0.704713i \(-0.751076\pi\)
−0.709492 + 0.704713i \(0.751076\pi\)
\(360\) 0 0
\(361\) 24.1423 1.27065
\(362\) 0 0
\(363\) −3.64594 −0.191362
\(364\) 0 0
\(365\) 50.3872 2.63739
\(366\) 0 0
\(367\) −2.41052 −0.125828 −0.0629140 0.998019i \(-0.520039\pi\)
−0.0629140 + 0.998019i \(0.520039\pi\)
\(368\) 0 0
\(369\) 18.4160 0.958697
\(370\) 0 0
\(371\) −2.04735 −0.106293
\(372\) 0 0
\(373\) −11.0549 −0.572401 −0.286200 0.958170i \(-0.592392\pi\)
−0.286200 + 0.958170i \(0.592392\pi\)
\(374\) 0 0
\(375\) 7.63989 0.394522
\(376\) 0 0
\(377\) 15.3173 0.788882
\(378\) 0 0
\(379\) −7.96444 −0.409106 −0.204553 0.978855i \(-0.565574\pi\)
−0.204553 + 0.978855i \(0.565574\pi\)
\(380\) 0 0
\(381\) −3.13725 −0.160726
\(382\) 0 0
\(383\) −21.8440 −1.11618 −0.558089 0.829781i \(-0.688465\pi\)
−0.558089 + 0.829781i \(0.688465\pi\)
\(384\) 0 0
\(385\) 8.98842 0.458093
\(386\) 0 0
\(387\) 26.0566 1.32453
\(388\) 0 0
\(389\) 26.6875 1.35311 0.676555 0.736392i \(-0.263472\pi\)
0.676555 + 0.736392i \(0.263472\pi\)
\(390\) 0 0
\(391\) −5.36595 −0.271368
\(392\) 0 0
\(393\) 17.7147 0.893588
\(394\) 0 0
\(395\) −29.7445 −1.49661
\(396\) 0 0
\(397\) 22.8082 1.14471 0.572355 0.820006i \(-0.306030\pi\)
0.572355 + 0.820006i \(0.306030\pi\)
\(398\) 0 0
\(399\) 5.14418 0.257531
\(400\) 0 0
\(401\) −0.202861 −0.0101304 −0.00506520 0.999987i \(-0.501612\pi\)
−0.00506520 + 0.999987i \(0.501612\pi\)
\(402\) 0 0
\(403\) −48.9457 −2.43816
\(404\) 0 0
\(405\) 13.7592 0.683700
\(406\) 0 0
\(407\) 15.2429 0.755561
\(408\) 0 0
\(409\) −20.5826 −1.01774 −0.508872 0.860842i \(-0.669937\pi\)
−0.508872 + 0.860842i \(0.669937\pi\)
\(410\) 0 0
\(411\) 2.07776 0.102488
\(412\) 0 0
\(413\) 0.911427 0.0448484
\(414\) 0 0
\(415\) 22.9808 1.12808
\(416\) 0 0
\(417\) 9.43926 0.462243
\(418\) 0 0
\(419\) 11.4778 0.560727 0.280363 0.959894i \(-0.409545\pi\)
0.280363 + 0.959894i \(0.409545\pi\)
\(420\) 0 0
\(421\) −12.6170 −0.614917 −0.307459 0.951561i \(-0.599479\pi\)
−0.307459 + 0.951561i \(0.599479\pi\)
\(422\) 0 0
\(423\) 19.5258 0.949377
\(424\) 0 0
\(425\) −14.9950 −0.727364
\(426\) 0 0
\(427\) 2.08843 0.101066
\(428\) 0 0
\(429\) 12.8724 0.621484
\(430\) 0 0
\(431\) 16.7873 0.808618 0.404309 0.914623i \(-0.367512\pi\)
0.404309 + 0.914623i \(0.367512\pi\)
\(432\) 0 0
\(433\) −2.91585 −0.140127 −0.0700633 0.997543i \(-0.522320\pi\)
−0.0700633 + 0.997543i \(0.522320\pi\)
\(434\) 0 0
\(435\) 6.56051 0.314552
\(436\) 0 0
\(437\) 18.1776 0.869555
\(438\) 0 0
\(439\) −34.3281 −1.63839 −0.819195 0.573516i \(-0.805579\pi\)
−0.819195 + 0.573516i \(0.805579\pi\)
\(440\) 0 0
\(441\) −2.38662 −0.113649
\(442\) 0 0
\(443\) 7.70289 0.365975 0.182988 0.983115i \(-0.441423\pi\)
0.182988 + 0.983115i \(0.441423\pi\)
\(444\) 0 0
\(445\) −5.57470 −0.264266
\(446\) 0 0
\(447\) −0.679375 −0.0321333
\(448\) 0 0
\(449\) −32.5705 −1.53710 −0.768549 0.639792i \(-0.779021\pi\)
−0.768549 + 0.639792i \(0.779021\pi\)
\(450\) 0 0
\(451\) −19.4365 −0.915229
\(452\) 0 0
\(453\) −13.0519 −0.613233
\(454\) 0 0
\(455\) 23.2843 1.09159
\(456\) 0 0
\(457\) 35.2825 1.65044 0.825222 0.564809i \(-0.191050\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(458\) 0 0
\(459\) 8.17979 0.381800
\(460\) 0 0
\(461\) −1.63944 −0.0763561 −0.0381781 0.999271i \(-0.512155\pi\)
−0.0381781 + 0.999271i \(0.512155\pi\)
\(462\) 0 0
\(463\) 4.05450 0.188429 0.0942144 0.995552i \(-0.469966\pi\)
0.0942144 + 0.995552i \(0.469966\pi\)
\(464\) 0 0
\(465\) −20.9638 −0.972172
\(466\) 0 0
\(467\) 5.80041 0.268411 0.134206 0.990954i \(-0.457152\pi\)
0.134206 + 0.990954i \(0.457152\pi\)
\(468\) 0 0
\(469\) 1.87592 0.0866220
\(470\) 0 0
\(471\) 8.58249 0.395460
\(472\) 0 0
\(473\) −27.5005 −1.26448
\(474\) 0 0
\(475\) 50.7969 2.33072
\(476\) 0 0
\(477\) 4.88625 0.223726
\(478\) 0 0
\(479\) −7.83014 −0.357768 −0.178884 0.983870i \(-0.557249\pi\)
−0.178884 + 0.983870i \(0.557249\pi\)
\(480\) 0 0
\(481\) 39.4863 1.80042
\(482\) 0 0
\(483\) 2.16746 0.0986227
\(484\) 0 0
\(485\) 67.5408 3.06687
\(486\) 0 0
\(487\) 11.8721 0.537976 0.268988 0.963144i \(-0.413311\pi\)
0.268988 + 0.963144i \(0.413311\pi\)
\(488\) 0 0
\(489\) 2.38997 0.108078
\(490\) 0 0
\(491\) 10.3134 0.465436 0.232718 0.972544i \(-0.425238\pi\)
0.232718 + 0.972544i \(0.425238\pi\)
\(492\) 0 0
\(493\) −4.55153 −0.204990
\(494\) 0 0
\(495\) −21.4520 −0.964194
\(496\) 0 0
\(497\) −12.3355 −0.553321
\(498\) 0 0
\(499\) 18.2726 0.817993 0.408996 0.912536i \(-0.365879\pi\)
0.408996 + 0.912536i \(0.365879\pi\)
\(500\) 0 0
\(501\) −11.6076 −0.518587
\(502\) 0 0
\(503\) −3.13596 −0.139826 −0.0699128 0.997553i \(-0.522272\pi\)
−0.0699128 + 0.997553i \(0.522272\pi\)
\(504\) 0 0
\(505\) −15.4856 −0.689101
\(506\) 0 0
\(507\) 23.1642 1.02876
\(508\) 0 0
\(509\) 18.9768 0.841133 0.420567 0.907262i \(-0.361831\pi\)
0.420567 + 0.907262i \(0.361831\pi\)
\(510\) 0 0
\(511\) 14.1203 0.624645
\(512\) 0 0
\(513\) −27.7098 −1.22342
\(514\) 0 0
\(515\) 4.58889 0.202211
\(516\) 0 0
\(517\) −20.6078 −0.906332
\(518\) 0 0
\(519\) −3.13351 −0.137546
\(520\) 0 0
\(521\) −3.60942 −0.158132 −0.0790658 0.996869i \(-0.525194\pi\)
−0.0790658 + 0.996869i \(0.525194\pi\)
\(522\) 0 0
\(523\) −3.26279 −0.142672 −0.0713360 0.997452i \(-0.522726\pi\)
−0.0713360 + 0.997452i \(0.522726\pi\)
\(524\) 0 0
\(525\) 6.05690 0.264345
\(526\) 0 0
\(527\) 14.5442 0.633554
\(528\) 0 0
\(529\) −15.3410 −0.667000
\(530\) 0 0
\(531\) −2.17523 −0.0943969
\(532\) 0 0
\(533\) −50.3498 −2.18089
\(534\) 0 0
\(535\) −57.7663 −2.49745
\(536\) 0 0
\(537\) 2.96117 0.127784
\(538\) 0 0
\(539\) 2.51888 0.108496
\(540\) 0 0
\(541\) −40.8816 −1.75764 −0.878818 0.477158i \(-0.841667\pi\)
−0.878818 + 0.477158i \(0.841667\pi\)
\(542\) 0 0
\(543\) −16.7039 −0.716835
\(544\) 0 0
\(545\) −11.6718 −0.499967
\(546\) 0 0
\(547\) 39.4933 1.68861 0.844305 0.535863i \(-0.180014\pi\)
0.844305 + 0.535863i \(0.180014\pi\)
\(548\) 0 0
\(549\) −4.98428 −0.212724
\(550\) 0 0
\(551\) 15.4187 0.656859
\(552\) 0 0
\(553\) −8.33547 −0.354460
\(554\) 0 0
\(555\) 16.9123 0.717885
\(556\) 0 0
\(557\) −38.9287 −1.64946 −0.824731 0.565525i \(-0.808674\pi\)
−0.824731 + 0.565525i \(0.808674\pi\)
\(558\) 0 0
\(559\) −71.2396 −3.01311
\(560\) 0 0
\(561\) −3.82501 −0.161492
\(562\) 0 0
\(563\) 34.1618 1.43975 0.719873 0.694105i \(-0.244200\pi\)
0.719873 + 0.694105i \(0.244200\pi\)
\(564\) 0 0
\(565\) −37.8664 −1.59305
\(566\) 0 0
\(567\) 3.85582 0.161929
\(568\) 0 0
\(569\) −21.5861 −0.904935 −0.452467 0.891781i \(-0.649456\pi\)
−0.452467 + 0.891781i \(0.649456\pi\)
\(570\) 0 0
\(571\) −8.03105 −0.336089 −0.168045 0.985779i \(-0.553745\pi\)
−0.168045 + 0.985779i \(0.553745\pi\)
\(572\) 0 0
\(573\) 15.9051 0.664445
\(574\) 0 0
\(575\) 21.4028 0.892560
\(576\) 0 0
\(577\) 45.8009 1.90672 0.953359 0.301839i \(-0.0976005\pi\)
0.953359 + 0.301839i \(0.0976005\pi\)
\(578\) 0 0
\(579\) −8.83772 −0.367283
\(580\) 0 0
\(581\) 6.44004 0.267178
\(582\) 0 0
\(583\) −5.15702 −0.213582
\(584\) 0 0
\(585\) −55.5708 −2.29757
\(586\) 0 0
\(587\) −3.87142 −0.159791 −0.0798954 0.996803i \(-0.525459\pi\)
−0.0798954 + 0.996803i \(0.525459\pi\)
\(588\) 0 0
\(589\) −49.2697 −2.03012
\(590\) 0 0
\(591\) 16.7956 0.690877
\(592\) 0 0
\(593\) −40.4013 −1.65908 −0.829540 0.558447i \(-0.811397\pi\)
−0.829540 + 0.558447i \(0.811397\pi\)
\(594\) 0 0
\(595\) −6.91891 −0.283648
\(596\) 0 0
\(597\) 18.6472 0.763177
\(598\) 0 0
\(599\) −16.8607 −0.688911 −0.344455 0.938803i \(-0.611936\pi\)
−0.344455 + 0.938803i \(0.611936\pi\)
\(600\) 0 0
\(601\) −31.7796 −1.29632 −0.648159 0.761505i \(-0.724461\pi\)
−0.648159 + 0.761505i \(0.724461\pi\)
\(602\) 0 0
\(603\) −4.47711 −0.182322
\(604\) 0 0
\(605\) −16.6120 −0.675372
\(606\) 0 0
\(607\) −35.3989 −1.43680 −0.718399 0.695631i \(-0.755125\pi\)
−0.718399 + 0.695631i \(0.755125\pi\)
\(608\) 0 0
\(609\) 1.83849 0.0744993
\(610\) 0 0
\(611\) −53.3842 −2.15969
\(612\) 0 0
\(613\) −13.6414 −0.550971 −0.275485 0.961305i \(-0.588839\pi\)
−0.275485 + 0.961305i \(0.588839\pi\)
\(614\) 0 0
\(615\) −21.5652 −0.869591
\(616\) 0 0
\(617\) −40.2668 −1.62108 −0.810540 0.585684i \(-0.800826\pi\)
−0.810540 + 0.585684i \(0.800826\pi\)
\(618\) 0 0
\(619\) 16.1769 0.650205 0.325102 0.945679i \(-0.394601\pi\)
0.325102 + 0.945679i \(0.394601\pi\)
\(620\) 0 0
\(621\) −11.6753 −0.468512
\(622\) 0 0
\(623\) −1.56223 −0.0625894
\(624\) 0 0
\(625\) −3.85875 −0.154350
\(626\) 0 0
\(627\) 12.9576 0.517475
\(628\) 0 0
\(629\) −11.7333 −0.467838
\(630\) 0 0
\(631\) −4.79309 −0.190810 −0.0954049 0.995439i \(-0.530415\pi\)
−0.0954049 + 0.995439i \(0.530415\pi\)
\(632\) 0 0
\(633\) −16.6613 −0.662227
\(634\) 0 0
\(635\) −14.2942 −0.567249
\(636\) 0 0
\(637\) 6.52509 0.258534
\(638\) 0 0
\(639\) 29.4401 1.16463
\(640\) 0 0
\(641\) 4.63323 0.183002 0.0915008 0.995805i \(-0.470834\pi\)
0.0915008 + 0.995805i \(0.470834\pi\)
\(642\) 0 0
\(643\) −5.95425 −0.234813 −0.117406 0.993084i \(-0.537458\pi\)
−0.117406 + 0.993084i \(0.537458\pi\)
\(644\) 0 0
\(645\) −30.5124 −1.20142
\(646\) 0 0
\(647\) 16.8071 0.660754 0.330377 0.943849i \(-0.392824\pi\)
0.330377 + 0.943849i \(0.392824\pi\)
\(648\) 0 0
\(649\) 2.29577 0.0901169
\(650\) 0 0
\(651\) −5.87480 −0.230251
\(652\) 0 0
\(653\) −6.80213 −0.266188 −0.133094 0.991103i \(-0.542491\pi\)
−0.133094 + 0.991103i \(0.542491\pi\)
\(654\) 0 0
\(655\) 80.7134 3.15373
\(656\) 0 0
\(657\) −33.6998 −1.31475
\(658\) 0 0
\(659\) −45.8568 −1.78633 −0.893163 0.449733i \(-0.851519\pi\)
−0.893163 + 0.449733i \(0.851519\pi\)
\(660\) 0 0
\(661\) 3.22646 0.125495 0.0627474 0.998029i \(-0.480014\pi\)
0.0627474 + 0.998029i \(0.480014\pi\)
\(662\) 0 0
\(663\) −9.90861 −0.384818
\(664\) 0 0
\(665\) 23.4384 0.908903
\(666\) 0 0
\(667\) 6.49654 0.251547
\(668\) 0 0
\(669\) −9.24525 −0.357442
\(670\) 0 0
\(671\) 5.26049 0.203079
\(672\) 0 0
\(673\) 10.0871 0.388828 0.194414 0.980920i \(-0.437719\pi\)
0.194414 + 0.980920i \(0.437719\pi\)
\(674\) 0 0
\(675\) −32.6262 −1.25578
\(676\) 0 0
\(677\) −32.3792 −1.24443 −0.622216 0.782845i \(-0.713768\pi\)
−0.622216 + 0.782845i \(0.713768\pi\)
\(678\) 0 0
\(679\) 18.9273 0.726365
\(680\) 0 0
\(681\) −14.4106 −0.552217
\(682\) 0 0
\(683\) 35.7666 1.36857 0.684285 0.729215i \(-0.260114\pi\)
0.684285 + 0.729215i \(0.260114\pi\)
\(684\) 0 0
\(685\) 9.46687 0.361711
\(686\) 0 0
\(687\) −7.56388 −0.288580
\(688\) 0 0
\(689\) −13.3592 −0.508943
\(690\) 0 0
\(691\) −20.9942 −0.798657 −0.399329 0.916808i \(-0.630757\pi\)
−0.399329 + 0.916808i \(0.630757\pi\)
\(692\) 0 0
\(693\) −6.01160 −0.228362
\(694\) 0 0
\(695\) 43.0081 1.63139
\(696\) 0 0
\(697\) 14.9614 0.566703
\(698\) 0 0
\(699\) −3.54846 −0.134215
\(700\) 0 0
\(701\) 25.0388 0.945704 0.472852 0.881142i \(-0.343225\pi\)
0.472852 + 0.881142i \(0.343225\pi\)
\(702\) 0 0
\(703\) 39.7477 1.49911
\(704\) 0 0
\(705\) −22.8648 −0.861137
\(706\) 0 0
\(707\) −4.33962 −0.163208
\(708\) 0 0
\(709\) −32.5877 −1.22386 −0.611929 0.790913i \(-0.709606\pi\)
−0.611929 + 0.790913i \(0.709606\pi\)
\(710\) 0 0
\(711\) 19.8936 0.746068
\(712\) 0 0
\(713\) −20.7594 −0.777444
\(714\) 0 0
\(715\) 58.6503 2.19340
\(716\) 0 0
\(717\) −15.0782 −0.563105
\(718\) 0 0
\(719\) 9.02299 0.336501 0.168250 0.985744i \(-0.446188\pi\)
0.168250 + 0.985744i \(0.446188\pi\)
\(720\) 0 0
\(721\) 1.28597 0.0478920
\(722\) 0 0
\(723\) 15.6314 0.581339
\(724\) 0 0
\(725\) 18.1544 0.674237
\(726\) 0 0
\(727\) −16.8802 −0.626054 −0.313027 0.949744i \(-0.601343\pi\)
−0.313027 + 0.949744i \(0.601343\pi\)
\(728\) 0 0
\(729\) 0.709766 0.0262876
\(730\) 0 0
\(731\) 21.1688 0.782955
\(732\) 0 0
\(733\) 27.9470 1.03225 0.516123 0.856514i \(-0.327375\pi\)
0.516123 + 0.856514i \(0.327375\pi\)
\(734\) 0 0
\(735\) 2.79474 0.103086
\(736\) 0 0
\(737\) 4.72522 0.174056
\(738\) 0 0
\(739\) −10.6219 −0.390733 −0.195367 0.980730i \(-0.562590\pi\)
−0.195367 + 0.980730i \(0.562590\pi\)
\(740\) 0 0
\(741\) 33.5663 1.23309
\(742\) 0 0
\(743\) −43.1417 −1.58272 −0.791358 0.611353i \(-0.790626\pi\)
−0.791358 + 0.611353i \(0.790626\pi\)
\(744\) 0 0
\(745\) −3.09543 −0.113408
\(746\) 0 0
\(747\) −15.3699 −0.562356
\(748\) 0 0
\(749\) −16.1882 −0.591503
\(750\) 0 0
\(751\) 4.11267 0.150073 0.0750367 0.997181i \(-0.476093\pi\)
0.0750367 + 0.997181i \(0.476093\pi\)
\(752\) 0 0
\(753\) −7.49727 −0.273216
\(754\) 0 0
\(755\) −59.4685 −2.16428
\(756\) 0 0
\(757\) 4.08900 0.148617 0.0743087 0.997235i \(-0.476325\pi\)
0.0743087 + 0.997235i \(0.476325\pi\)
\(758\) 0 0
\(759\) 5.45956 0.198169
\(760\) 0 0
\(761\) 1.32450 0.0480131 0.0240065 0.999712i \(-0.492358\pi\)
0.0240065 + 0.999712i \(0.492358\pi\)
\(762\) 0 0
\(763\) −3.27087 −0.118413
\(764\) 0 0
\(765\) 16.5128 0.597022
\(766\) 0 0
\(767\) 5.94715 0.214739
\(768\) 0 0
\(769\) 17.8450 0.643506 0.321753 0.946824i \(-0.395728\pi\)
0.321753 + 0.946824i \(0.395728\pi\)
\(770\) 0 0
\(771\) 9.85084 0.354769
\(772\) 0 0
\(773\) 13.2378 0.476131 0.238066 0.971249i \(-0.423487\pi\)
0.238066 + 0.971249i \(0.423487\pi\)
\(774\) 0 0
\(775\) −58.0114 −2.08383
\(776\) 0 0
\(777\) 4.73942 0.170026
\(778\) 0 0
\(779\) −50.6831 −1.81591
\(780\) 0 0
\(781\) −31.0715 −1.11183
\(782\) 0 0
\(783\) −9.90324 −0.353913
\(784\) 0 0
\(785\) 39.1044 1.39569
\(786\) 0 0
\(787\) 25.2795 0.901118 0.450559 0.892747i \(-0.351225\pi\)
0.450559 + 0.892747i \(0.351225\pi\)
\(788\) 0 0
\(789\) 12.4566 0.443468
\(790\) 0 0
\(791\) −10.6115 −0.377302
\(792\) 0 0
\(793\) 13.6272 0.483916
\(794\) 0 0
\(795\) −5.72181 −0.202932
\(796\) 0 0
\(797\) −36.5312 −1.29400 −0.647000 0.762490i \(-0.723977\pi\)
−0.647000 + 0.762490i \(0.723977\pi\)
\(798\) 0 0
\(799\) 15.8630 0.561194
\(800\) 0 0
\(801\) 3.72845 0.131738
\(802\) 0 0
\(803\) 35.5673 1.25514
\(804\) 0 0
\(805\) 9.87558 0.348068
\(806\) 0 0
\(807\) 3.13351 0.110305
\(808\) 0 0
\(809\) 8.75351 0.307757 0.153879 0.988090i \(-0.450824\pi\)
0.153879 + 0.988090i \(0.450824\pi\)
\(810\) 0 0
\(811\) 23.4106 0.822057 0.411029 0.911622i \(-0.365170\pi\)
0.411029 + 0.911622i \(0.365170\pi\)
\(812\) 0 0
\(813\) 2.97976 0.104505
\(814\) 0 0
\(815\) 10.8894 0.381440
\(816\) 0 0
\(817\) −71.7111 −2.50885
\(818\) 0 0
\(819\) −15.5729 −0.544162
\(820\) 0 0
\(821\) −23.1296 −0.807229 −0.403614 0.914929i \(-0.632246\pi\)
−0.403614 + 0.914929i \(0.632246\pi\)
\(822\) 0 0
\(823\) 40.2133 1.40175 0.700874 0.713285i \(-0.252793\pi\)
0.700874 + 0.713285i \(0.252793\pi\)
\(824\) 0 0
\(825\) 15.2566 0.531166
\(826\) 0 0
\(827\) 34.4702 1.19865 0.599323 0.800507i \(-0.295436\pi\)
0.599323 + 0.800507i \(0.295436\pi\)
\(828\) 0 0
\(829\) −23.4776 −0.815412 −0.407706 0.913113i \(-0.633671\pi\)
−0.407706 + 0.913113i \(0.633671\pi\)
\(830\) 0 0
\(831\) −9.88149 −0.342785
\(832\) 0 0
\(833\) −1.93892 −0.0671798
\(834\) 0 0
\(835\) −52.8875 −1.83025
\(836\) 0 0
\(837\) 31.6453 1.09382
\(838\) 0 0
\(839\) 2.16748 0.0748296 0.0374148 0.999300i \(-0.488088\pi\)
0.0374148 + 0.999300i \(0.488088\pi\)
\(840\) 0 0
\(841\) −23.4895 −0.809982
\(842\) 0 0
\(843\) 10.2724 0.353799
\(844\) 0 0
\(845\) 105.543 3.63078
\(846\) 0 0
\(847\) −4.65526 −0.159957
\(848\) 0 0
\(849\) −9.73113 −0.333972
\(850\) 0 0
\(851\) 16.7473 0.574092
\(852\) 0 0
\(853\) 19.1247 0.654818 0.327409 0.944883i \(-0.393825\pi\)
0.327409 + 0.944883i \(0.393825\pi\)
\(854\) 0 0
\(855\) −55.9386 −1.91306
\(856\) 0 0
\(857\) 9.73619 0.332582 0.166291 0.986077i \(-0.446821\pi\)
0.166291 + 0.986077i \(0.446821\pi\)
\(858\) 0 0
\(859\) 37.3577 1.27463 0.637314 0.770604i \(-0.280045\pi\)
0.637314 + 0.770604i \(0.280045\pi\)
\(860\) 0 0
\(861\) −6.04333 −0.205956
\(862\) 0 0
\(863\) −17.6964 −0.602392 −0.301196 0.953562i \(-0.597386\pi\)
−0.301196 + 0.953562i \(0.597386\pi\)
\(864\) 0 0
\(865\) −14.2772 −0.485440
\(866\) 0 0
\(867\) −10.3698 −0.352178
\(868\) 0 0
\(869\) −20.9960 −0.712241
\(870\) 0 0
\(871\) 12.2406 0.414756
\(872\) 0 0
\(873\) −45.1724 −1.52885
\(874\) 0 0
\(875\) 9.75488 0.329775
\(876\) 0 0
\(877\) −14.9379 −0.504417 −0.252209 0.967673i \(-0.581157\pi\)
−0.252209 + 0.967673i \(0.581157\pi\)
\(878\) 0 0
\(879\) 15.5474 0.524402
\(880\) 0 0
\(881\) −12.1360 −0.408873 −0.204437 0.978880i \(-0.565536\pi\)
−0.204437 + 0.978880i \(0.565536\pi\)
\(882\) 0 0
\(883\) −10.5340 −0.354496 −0.177248 0.984166i \(-0.556719\pi\)
−0.177248 + 0.984166i \(0.556719\pi\)
\(884\) 0 0
\(885\) 2.54720 0.0856233
\(886\) 0 0
\(887\) −15.9916 −0.536944 −0.268472 0.963287i \(-0.586519\pi\)
−0.268472 + 0.963287i \(0.586519\pi\)
\(888\) 0 0
\(889\) −4.00575 −0.134349
\(890\) 0 0
\(891\) 9.71232 0.325375
\(892\) 0 0
\(893\) −53.7375 −1.79826
\(894\) 0 0
\(895\) 13.4920 0.450987
\(896\) 0 0
\(897\) 14.1429 0.472217
\(898\) 0 0
\(899\) −17.6086 −0.587279
\(900\) 0 0
\(901\) 3.96966 0.132248
\(902\) 0 0
\(903\) −8.55065 −0.284548
\(904\) 0 0
\(905\) −76.1081 −2.52992
\(906\) 0 0
\(907\) 43.0247 1.42861 0.714306 0.699833i \(-0.246742\pi\)
0.714306 + 0.699833i \(0.246742\pi\)
\(908\) 0 0
\(909\) 10.3570 0.343521
\(910\) 0 0
\(911\) −35.3708 −1.17189 −0.585943 0.810352i \(-0.699276\pi\)
−0.585943 + 0.810352i \(0.699276\pi\)
\(912\) 0 0
\(913\) 16.2217 0.536859
\(914\) 0 0
\(915\) 5.83661 0.192953
\(916\) 0 0
\(917\) 22.6188 0.746937
\(918\) 0 0
\(919\) 44.0087 1.45171 0.725857 0.687846i \(-0.241444\pi\)
0.725857 + 0.687846i \(0.241444\pi\)
\(920\) 0 0
\(921\) 1.70485 0.0561766
\(922\) 0 0
\(923\) −80.4901 −2.64936
\(924\) 0 0
\(925\) 46.8000 1.53877
\(926\) 0 0
\(927\) −3.06912 −0.100803
\(928\) 0 0
\(929\) −46.4669 −1.52453 −0.762265 0.647265i \(-0.775913\pi\)
−0.762265 + 0.647265i \(0.775913\pi\)
\(930\) 0 0
\(931\) 6.56828 0.215267
\(932\) 0 0
\(933\) 2.46330 0.0806448
\(934\) 0 0
\(935\) −17.4279 −0.569953
\(936\) 0 0
\(937\) 46.4077 1.51607 0.758037 0.652211i \(-0.226159\pi\)
0.758037 + 0.652211i \(0.226159\pi\)
\(938\) 0 0
\(939\) −9.67045 −0.315583
\(940\) 0 0
\(941\) 21.9398 0.715216 0.357608 0.933872i \(-0.383592\pi\)
0.357608 + 0.933872i \(0.383592\pi\)
\(942\) 0 0
\(943\) −21.3549 −0.695410
\(944\) 0 0
\(945\) −15.0542 −0.489713
\(946\) 0 0
\(947\) −52.5392 −1.70730 −0.853648 0.520851i \(-0.825615\pi\)
−0.853648 + 0.520851i \(0.825615\pi\)
\(948\) 0 0
\(949\) 92.1362 2.99087
\(950\) 0 0
\(951\) 13.7895 0.447156
\(952\) 0 0
\(953\) −59.7325 −1.93493 −0.967463 0.253011i \(-0.918579\pi\)
−0.967463 + 0.253011i \(0.918579\pi\)
\(954\) 0 0
\(955\) 72.4684 2.34502
\(956\) 0 0
\(957\) 4.63092 0.149697
\(958\) 0 0
\(959\) 2.65295 0.0856684
\(960\) 0 0
\(961\) 25.2673 0.815074
\(962\) 0 0
\(963\) 38.6350 1.24500
\(964\) 0 0
\(965\) −40.2673 −1.29625
\(966\) 0 0
\(967\) 9.91826 0.318950 0.159475 0.987202i \(-0.449020\pi\)
0.159475 + 0.987202i \(0.449020\pi\)
\(968\) 0 0
\(969\) −9.97419 −0.320417
\(970\) 0 0
\(971\) −16.4899 −0.529188 −0.264594 0.964360i \(-0.585238\pi\)
−0.264594 + 0.964360i \(0.585238\pi\)
\(972\) 0 0
\(973\) 12.0524 0.386382
\(974\) 0 0
\(975\) 39.5218 1.26571
\(976\) 0 0
\(977\) −20.8390 −0.666699 −0.333350 0.942803i \(-0.608179\pi\)
−0.333350 + 0.942803i \(0.608179\pi\)
\(978\) 0 0
\(979\) −3.93506 −0.125765
\(980\) 0 0
\(981\) 7.80631 0.249236
\(982\) 0 0
\(983\) 43.8056 1.39718 0.698591 0.715521i \(-0.253811\pi\)
0.698591 + 0.715521i \(0.253811\pi\)
\(984\) 0 0
\(985\) 76.5255 2.43831
\(986\) 0 0
\(987\) −6.40752 −0.203954
\(988\) 0 0
\(989\) −30.2148 −0.960776
\(990\) 0 0
\(991\) −52.6400 −1.67216 −0.836082 0.548605i \(-0.815159\pi\)
−0.836082 + 0.548605i \(0.815159\pi\)
\(992\) 0 0
\(993\) 17.2761 0.548240
\(994\) 0 0
\(995\) 84.9620 2.69348
\(996\) 0 0
\(997\) −22.2608 −0.705006 −0.352503 0.935811i \(-0.614669\pi\)
−0.352503 + 0.935811i \(0.614669\pi\)
\(998\) 0 0
\(999\) −25.5294 −0.807716
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 3584.2.a.p.1.7 yes 10
4.3 odd 2 3584.2.a.o.1.4 10
8.3 odd 2 3584.2.a.o.1.7 yes 10
8.5 even 2 inner 3584.2.a.p.1.4 yes 10
16.3 odd 4 3584.2.b.h.1793.4 10
16.5 even 4 3584.2.b.g.1793.4 10
16.11 odd 4 3584.2.b.h.1793.7 10
16.13 even 4 3584.2.b.g.1793.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3584.2.a.o.1.4 10 4.3 odd 2
3584.2.a.o.1.7 yes 10 8.3 odd 2
3584.2.a.p.1.4 yes 10 8.5 even 2 inner
3584.2.a.p.1.7 yes 10 1.1 even 1 trivial
3584.2.b.g.1793.4 10 16.5 even 4
3584.2.b.g.1793.7 10 16.13 even 4
3584.2.b.h.1793.4 10 16.3 odd 4
3584.2.b.h.1793.7 10 16.11 odd 4