Properties

Label 5290.2.a.bk.1.8
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $15$
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] = [5290,2,Mod(1,5290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.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: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.0566801\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.0566801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.0566801 q^{6} +5.00659 q^{7} +1.00000 q^{8} -2.99679 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.0566801 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.0566801 q^{6} +5.00659 q^{7} +1.00000 q^{8} -2.99679 q^{9} -1.00000 q^{10} +2.22584 q^{11} -0.0566801 q^{12} -2.99679 q^{13} +5.00659 q^{14} +0.0566801 q^{15} +1.00000 q^{16} +1.17205 q^{17} -2.99679 q^{18} -7.27464 q^{19} -1.00000 q^{20} -0.283774 q^{21} +2.22584 q^{22} -0.0566801 q^{24} +1.00000 q^{25} -2.99679 q^{26} +0.339899 q^{27} +5.00659 q^{28} +2.78953 q^{29} +0.0566801 q^{30} +7.90982 q^{31} +1.00000 q^{32} -0.126161 q^{33} +1.17205 q^{34} -5.00659 q^{35} -2.99679 q^{36} +0.498984 q^{37} -7.27464 q^{38} +0.169858 q^{39} -1.00000 q^{40} +5.54398 q^{41} -0.283774 q^{42} +10.3763 q^{43} +2.22584 q^{44} +2.99679 q^{45} +4.15586 q^{47} -0.0566801 q^{48} +18.0660 q^{49} +1.00000 q^{50} -0.0664321 q^{51} -2.99679 q^{52} +2.72827 q^{53} +0.339899 q^{54} -2.22584 q^{55} +5.00659 q^{56} +0.412328 q^{57} +2.78953 q^{58} -1.61972 q^{59} +0.0566801 q^{60} -5.58655 q^{61} +7.90982 q^{62} -15.0037 q^{63} +1.00000 q^{64} +2.99679 q^{65} -0.126161 q^{66} +6.27410 q^{67} +1.17205 q^{68} -5.00659 q^{70} +9.80578 q^{71} -2.99679 q^{72} +1.68505 q^{73} +0.498984 q^{74} -0.0566801 q^{75} -7.27464 q^{76} +11.1439 q^{77} +0.169858 q^{78} +11.0622 q^{79} -1.00000 q^{80} +8.97110 q^{81} +5.54398 q^{82} -1.37389 q^{83} -0.283774 q^{84} -1.17205 q^{85} +10.3763 q^{86} -0.158111 q^{87} +2.22584 q^{88} -16.2240 q^{89} +2.99679 q^{90} -15.0037 q^{91} -0.448330 q^{93} +4.15586 q^{94} +7.27464 q^{95} -0.0566801 q^{96} -4.93548 q^{97} +18.0660 q^{98} -6.67037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.0566801 −0.0327243 −0.0163621 0.999866i \(-0.505208\pi\)
−0.0163621 + 0.999866i \(0.505208\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.0566801 −0.0231396
\(7\) 5.00659 1.89231 0.946157 0.323708i \(-0.104930\pi\)
0.946157 + 0.323708i \(0.104930\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.99679 −0.998929
\(10\) −1.00000 −0.316228
\(11\) 2.22584 0.671116 0.335558 0.942019i \(-0.391075\pi\)
0.335558 + 0.942019i \(0.391075\pi\)
\(12\) −0.0566801 −0.0163621
\(13\) −2.99679 −0.831160 −0.415580 0.909557i \(-0.636421\pi\)
−0.415580 + 0.909557i \(0.636421\pi\)
\(14\) 5.00659 1.33807
\(15\) 0.0566801 0.0146347
\(16\) 1.00000 0.250000
\(17\) 1.17205 0.284265 0.142132 0.989848i \(-0.454604\pi\)
0.142132 + 0.989848i \(0.454604\pi\)
\(18\) −2.99679 −0.706350
\(19\) −7.27464 −1.66892 −0.834459 0.551071i \(-0.814220\pi\)
−0.834459 + 0.551071i \(0.814220\pi\)
\(20\) −1.00000 −0.223607
\(21\) −0.283774 −0.0619246
\(22\) 2.22584 0.474551
\(23\) 0 0
\(24\) −0.0566801 −0.0115698
\(25\) 1.00000 0.200000
\(26\) −2.99679 −0.587719
\(27\) 0.339899 0.0654135
\(28\) 5.00659 0.946157
\(29\) 2.78953 0.518002 0.259001 0.965877i \(-0.416607\pi\)
0.259001 + 0.965877i \(0.416607\pi\)
\(30\) 0.0566801 0.0103483
\(31\) 7.90982 1.42065 0.710323 0.703876i \(-0.248549\pi\)
0.710323 + 0.703876i \(0.248549\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.126161 −0.0219618
\(34\) 1.17205 0.201005
\(35\) −5.00659 −0.846269
\(36\) −2.99679 −0.499465
\(37\) 0.498984 0.0820324 0.0410162 0.999158i \(-0.486940\pi\)
0.0410162 + 0.999158i \(0.486940\pi\)
\(38\) −7.27464 −1.18010
\(39\) 0.169858 0.0271991
\(40\) −1.00000 −0.158114
\(41\) 5.54398 0.865824 0.432912 0.901436i \(-0.357486\pi\)
0.432912 + 0.901436i \(0.357486\pi\)
\(42\) −0.283774 −0.0437873
\(43\) 10.3763 1.58236 0.791182 0.611580i \(-0.209466\pi\)
0.791182 + 0.611580i \(0.209466\pi\)
\(44\) 2.22584 0.335558
\(45\) 2.99679 0.446735
\(46\) 0 0
\(47\) 4.15586 0.606194 0.303097 0.952960i \(-0.401979\pi\)
0.303097 + 0.952960i \(0.401979\pi\)
\(48\) −0.0566801 −0.00818107
\(49\) 18.0660 2.58085
\(50\) 1.00000 0.141421
\(51\) −0.0664321 −0.00930236
\(52\) −2.99679 −0.415580
\(53\) 2.72827 0.374757 0.187379 0.982288i \(-0.440001\pi\)
0.187379 + 0.982288i \(0.440001\pi\)
\(54\) 0.339899 0.0462543
\(55\) −2.22584 −0.300132
\(56\) 5.00659 0.669034
\(57\) 0.412328 0.0546141
\(58\) 2.78953 0.366283
\(59\) −1.61972 −0.210870 −0.105435 0.994426i \(-0.533624\pi\)
−0.105435 + 0.994426i \(0.533624\pi\)
\(60\) 0.0566801 0.00731737
\(61\) −5.58655 −0.715285 −0.357642 0.933859i \(-0.616419\pi\)
−0.357642 + 0.933859i \(0.616419\pi\)
\(62\) 7.90982 1.00455
\(63\) −15.0037 −1.89029
\(64\) 1.00000 0.125000
\(65\) 2.99679 0.371706
\(66\) −0.126161 −0.0155293
\(67\) 6.27410 0.766504 0.383252 0.923644i \(-0.374804\pi\)
0.383252 + 0.923644i \(0.374804\pi\)
\(68\) 1.17205 0.142132
\(69\) 0 0
\(70\) −5.00659 −0.598402
\(71\) 9.80578 1.16373 0.581866 0.813285i \(-0.302323\pi\)
0.581866 + 0.813285i \(0.302323\pi\)
\(72\) −2.99679 −0.353175
\(73\) 1.68505 0.197220 0.0986102 0.995126i \(-0.468560\pi\)
0.0986102 + 0.995126i \(0.468560\pi\)
\(74\) 0.498984 0.0580057
\(75\) −0.0566801 −0.00654486
\(76\) −7.27464 −0.834459
\(77\) 11.1439 1.26996
\(78\) 0.169858 0.0192327
\(79\) 11.0622 1.24459 0.622296 0.782782i \(-0.286200\pi\)
0.622296 + 0.782782i \(0.286200\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.97110 0.996789
\(82\) 5.54398 0.612230
\(83\) −1.37389 −0.150804 −0.0754021 0.997153i \(-0.524024\pi\)
−0.0754021 + 0.997153i \(0.524024\pi\)
\(84\) −0.283774 −0.0309623
\(85\) −1.17205 −0.127127
\(86\) 10.3763 1.11890
\(87\) −0.158111 −0.0169512
\(88\) 2.22584 0.237275
\(89\) −16.2240 −1.71974 −0.859871 0.510512i \(-0.829456\pi\)
−0.859871 + 0.510512i \(0.829456\pi\)
\(90\) 2.99679 0.315889
\(91\) −15.0037 −1.57282
\(92\) 0 0
\(93\) −0.448330 −0.0464896
\(94\) 4.15586 0.428644
\(95\) 7.27464 0.746363
\(96\) −0.0566801 −0.00578489
\(97\) −4.93548 −0.501122 −0.250561 0.968101i \(-0.580615\pi\)
−0.250561 + 0.968101i \(0.580615\pi\)
\(98\) 18.0660 1.82494
\(99\) −6.67037 −0.670398
\(100\) 1.00000 0.100000
\(101\) −2.55146 −0.253879 −0.126940 0.991910i \(-0.540515\pi\)
−0.126940 + 0.991910i \(0.540515\pi\)
\(102\) −0.0664321 −0.00657776
\(103\) −16.4581 −1.62166 −0.810831 0.585281i \(-0.800984\pi\)
−0.810831 + 0.585281i \(0.800984\pi\)
\(104\) −2.99679 −0.293860
\(105\) 0.283774 0.0276935
\(106\) 2.72827 0.264993
\(107\) 19.4802 1.88322 0.941612 0.336699i \(-0.109310\pi\)
0.941612 + 0.336699i \(0.109310\pi\)
\(108\) 0.339899 0.0327068
\(109\) −2.83881 −0.271909 −0.135954 0.990715i \(-0.543410\pi\)
−0.135954 + 0.990715i \(0.543410\pi\)
\(110\) −2.22584 −0.212226
\(111\) −0.0282824 −0.00268445
\(112\) 5.00659 0.473079
\(113\) −8.88945 −0.836249 −0.418125 0.908390i \(-0.637313\pi\)
−0.418125 + 0.908390i \(0.637313\pi\)
\(114\) 0.412328 0.0386180
\(115\) 0 0
\(116\) 2.78953 0.259001
\(117\) 8.98075 0.830270
\(118\) −1.61972 −0.149108
\(119\) 5.86799 0.537918
\(120\) 0.0566801 0.00517416
\(121\) −6.04563 −0.549603
\(122\) −5.58655 −0.505783
\(123\) −0.314233 −0.0283335
\(124\) 7.90982 0.710323
\(125\) −1.00000 −0.0894427
\(126\) −15.0037 −1.33664
\(127\) 3.43426 0.304741 0.152371 0.988323i \(-0.451309\pi\)
0.152371 + 0.988323i \(0.451309\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.588128 −0.0517817
\(130\) 2.99679 0.262836
\(131\) 19.1282 1.67124 0.835618 0.549311i \(-0.185110\pi\)
0.835618 + 0.549311i \(0.185110\pi\)
\(132\) −0.126161 −0.0109809
\(133\) −36.4212 −3.15812
\(134\) 6.27410 0.542000
\(135\) −0.339899 −0.0292538
\(136\) 1.17205 0.100503
\(137\) −17.0162 −1.45379 −0.726897 0.686747i \(-0.759038\pi\)
−0.726897 + 0.686747i \(0.759038\pi\)
\(138\) 0 0
\(139\) 3.94931 0.334976 0.167488 0.985874i \(-0.446434\pi\)
0.167488 + 0.985874i \(0.446434\pi\)
\(140\) −5.00659 −0.423134
\(141\) −0.235554 −0.0198373
\(142\) 9.80578 0.822883
\(143\) −6.67038 −0.557805
\(144\) −2.99679 −0.249732
\(145\) −2.78953 −0.231657
\(146\) 1.68505 0.139456
\(147\) −1.02398 −0.0844565
\(148\) 0.498984 0.0410162
\(149\) 18.6998 1.53195 0.765975 0.642871i \(-0.222257\pi\)
0.765975 + 0.642871i \(0.222257\pi\)
\(150\) −0.0566801 −0.00462791
\(151\) 18.3668 1.49467 0.747336 0.664447i \(-0.231333\pi\)
0.747336 + 0.664447i \(0.231333\pi\)
\(152\) −7.27464 −0.590051
\(153\) −3.51239 −0.283960
\(154\) 11.1439 0.897999
\(155\) −7.90982 −0.635332
\(156\) 0.169858 0.0135996
\(157\) −12.4944 −0.997162 −0.498581 0.866843i \(-0.666145\pi\)
−0.498581 + 0.866843i \(0.666145\pi\)
\(158\) 11.0622 0.880059
\(159\) −0.154639 −0.0122637
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 8.97110 0.704836
\(163\) 3.37214 0.264127 0.132063 0.991241i \(-0.457840\pi\)
0.132063 + 0.991241i \(0.457840\pi\)
\(164\) 5.54398 0.432912
\(165\) 0.126161 0.00982162
\(166\) −1.37389 −0.106635
\(167\) 19.9217 1.54159 0.770793 0.637086i \(-0.219860\pi\)
0.770793 + 0.637086i \(0.219860\pi\)
\(168\) −0.283774 −0.0218937
\(169\) −4.01924 −0.309173
\(170\) −1.17205 −0.0898924
\(171\) 21.8006 1.66713
\(172\) 10.3763 0.791182
\(173\) −17.0776 −1.29839 −0.649194 0.760623i \(-0.724894\pi\)
−0.649194 + 0.760623i \(0.724894\pi\)
\(174\) −0.158111 −0.0119863
\(175\) 5.00659 0.378463
\(176\) 2.22584 0.167779
\(177\) 0.0918062 0.00690058
\(178\) −16.2240 −1.21604
\(179\) −13.0442 −0.974967 −0.487483 0.873132i \(-0.662085\pi\)
−0.487483 + 0.873132i \(0.662085\pi\)
\(180\) 2.99679 0.223367
\(181\) −6.10807 −0.454009 −0.227005 0.973894i \(-0.572893\pi\)
−0.227005 + 0.973894i \(0.572893\pi\)
\(182\) −15.0037 −1.11215
\(183\) 0.316646 0.0234072
\(184\) 0 0
\(185\) −0.498984 −0.0366860
\(186\) −0.448330 −0.0328731
\(187\) 2.60880 0.190775
\(188\) 4.15586 0.303097
\(189\) 1.70173 0.123783
\(190\) 7.27464 0.527758
\(191\) −2.56505 −0.185600 −0.0928001 0.995685i \(-0.529582\pi\)
−0.0928001 + 0.995685i \(0.529582\pi\)
\(192\) −0.0566801 −0.00409054
\(193\) 11.1506 0.802637 0.401318 0.915939i \(-0.368552\pi\)
0.401318 + 0.915939i \(0.368552\pi\)
\(194\) −4.93548 −0.354347
\(195\) −0.169858 −0.0121638
\(196\) 18.0660 1.29043
\(197\) −7.61900 −0.542831 −0.271416 0.962462i \(-0.587492\pi\)
−0.271416 + 0.962462i \(0.587492\pi\)
\(198\) −6.67037 −0.474043
\(199\) 15.8779 1.12555 0.562777 0.826609i \(-0.309733\pi\)
0.562777 + 0.826609i \(0.309733\pi\)
\(200\) 1.00000 0.0707107
\(201\) −0.355617 −0.0250833
\(202\) −2.55146 −0.179520
\(203\) 13.9660 0.980222
\(204\) −0.0664321 −0.00465118
\(205\) −5.54398 −0.387208
\(206\) −16.4581 −1.14669
\(207\) 0 0
\(208\) −2.99679 −0.207790
\(209\) −16.1922 −1.12004
\(210\) 0.283774 0.0195823
\(211\) −1.50006 −0.103268 −0.0516341 0.998666i \(-0.516443\pi\)
−0.0516341 + 0.998666i \(0.516443\pi\)
\(212\) 2.72827 0.187379
\(213\) −0.555793 −0.0380823
\(214\) 19.4802 1.33164
\(215\) −10.3763 −0.707655
\(216\) 0.339899 0.0231272
\(217\) 39.6013 2.68831
\(218\) −2.83881 −0.192269
\(219\) −0.0955089 −0.00645389
\(220\) −2.22584 −0.150066
\(221\) −3.51240 −0.236270
\(222\) −0.0282824 −0.00189819
\(223\) −8.90770 −0.596504 −0.298252 0.954487i \(-0.596404\pi\)
−0.298252 + 0.954487i \(0.596404\pi\)
\(224\) 5.00659 0.334517
\(225\) −2.99679 −0.199786
\(226\) −8.88945 −0.591318
\(227\) −4.29484 −0.285059 −0.142529 0.989791i \(-0.545524\pi\)
−0.142529 + 0.989791i \(0.545524\pi\)
\(228\) 0.412328 0.0273071
\(229\) −17.8967 −1.18265 −0.591324 0.806434i \(-0.701395\pi\)
−0.591324 + 0.806434i \(0.701395\pi\)
\(230\) 0 0
\(231\) −0.631636 −0.0415586
\(232\) 2.78953 0.183141
\(233\) 27.2662 1.78627 0.893134 0.449790i \(-0.148501\pi\)
0.893134 + 0.449790i \(0.148501\pi\)
\(234\) 8.98075 0.587090
\(235\) −4.15586 −0.271098
\(236\) −1.61972 −0.105435
\(237\) −0.627005 −0.0407284
\(238\) 5.86799 0.380366
\(239\) −13.8416 −0.895341 −0.447671 0.894198i \(-0.647746\pi\)
−0.447671 + 0.894198i \(0.647746\pi\)
\(240\) 0.0566801 0.00365869
\(241\) 15.1156 0.973680 0.486840 0.873491i \(-0.338149\pi\)
0.486840 + 0.873491i \(0.338149\pi\)
\(242\) −6.04563 −0.388628
\(243\) −1.52818 −0.0980327
\(244\) −5.58655 −0.357642
\(245\) −18.0660 −1.15419
\(246\) −0.314233 −0.0200348
\(247\) 21.8006 1.38714
\(248\) 7.90982 0.502274
\(249\) 0.0778723 0.00493496
\(250\) −1.00000 −0.0632456
\(251\) 19.6466 1.24008 0.620040 0.784570i \(-0.287116\pi\)
0.620040 + 0.784570i \(0.287116\pi\)
\(252\) −15.0037 −0.945144
\(253\) 0 0
\(254\) 3.43426 0.215484
\(255\) 0.0664321 0.00416014
\(256\) 1.00000 0.0625000
\(257\) 1.35642 0.0846110 0.0423055 0.999105i \(-0.486530\pi\)
0.0423055 + 0.999105i \(0.486530\pi\)
\(258\) −0.588128 −0.0366152
\(259\) 2.49821 0.155231
\(260\) 2.99679 0.185853
\(261\) −8.35961 −0.517447
\(262\) 19.1282 1.18174
\(263\) 9.35101 0.576608 0.288304 0.957539i \(-0.406909\pi\)
0.288304 + 0.957539i \(0.406909\pi\)
\(264\) −0.126161 −0.00776467
\(265\) −2.72827 −0.167597
\(266\) −36.4212 −2.23313
\(267\) 0.919579 0.0562773
\(268\) 6.27410 0.383252
\(269\) 19.9733 1.21779 0.608897 0.793250i \(-0.291612\pi\)
0.608897 + 0.793250i \(0.291612\pi\)
\(270\) −0.339899 −0.0206856
\(271\) 22.3390 1.35700 0.678499 0.734602i \(-0.262631\pi\)
0.678499 + 0.734602i \(0.262631\pi\)
\(272\) 1.17205 0.0710662
\(273\) 0.850412 0.0514693
\(274\) −17.0162 −1.02799
\(275\) 2.22584 0.134223
\(276\) 0 0
\(277\) −18.2078 −1.09400 −0.547000 0.837132i \(-0.684230\pi\)
−0.547000 + 0.837132i \(0.684230\pi\)
\(278\) 3.94931 0.236864
\(279\) −23.7041 −1.41912
\(280\) −5.00659 −0.299201
\(281\) 10.7438 0.640919 0.320459 0.947262i \(-0.396163\pi\)
0.320459 + 0.947262i \(0.396163\pi\)
\(282\) −0.235554 −0.0140271
\(283\) −10.7171 −0.637067 −0.318533 0.947912i \(-0.603190\pi\)
−0.318533 + 0.947912i \(0.603190\pi\)
\(284\) 9.80578 0.581866
\(285\) −0.412328 −0.0244242
\(286\) −6.67038 −0.394428
\(287\) 27.7564 1.63841
\(288\) −2.99679 −0.176587
\(289\) −15.6263 −0.919194
\(290\) −2.78953 −0.163807
\(291\) 0.279744 0.0163989
\(292\) 1.68505 0.0986102
\(293\) −17.1056 −0.999320 −0.499660 0.866222i \(-0.666542\pi\)
−0.499660 + 0.866222i \(0.666542\pi\)
\(294\) −1.02398 −0.0597198
\(295\) 1.61972 0.0943040
\(296\) 0.498984 0.0290028
\(297\) 0.756560 0.0439001
\(298\) 18.6998 1.08325
\(299\) 0 0
\(300\) −0.0566801 −0.00327243
\(301\) 51.9497 2.99433
\(302\) 18.3668 1.05689
\(303\) 0.144617 0.00830802
\(304\) −7.27464 −0.417229
\(305\) 5.58655 0.319885
\(306\) −3.51239 −0.200790
\(307\) 5.94744 0.339438 0.169719 0.985492i \(-0.445714\pi\)
0.169719 + 0.985492i \(0.445714\pi\)
\(308\) 11.1439 0.634982
\(309\) 0.932845 0.0530677
\(310\) −7.90982 −0.449248
\(311\) −20.0565 −1.13730 −0.568650 0.822580i \(-0.692534\pi\)
−0.568650 + 0.822580i \(0.692534\pi\)
\(312\) 0.169858 0.00961634
\(313\) 20.8169 1.17664 0.588320 0.808628i \(-0.299790\pi\)
0.588320 + 0.808628i \(0.299790\pi\)
\(314\) −12.4944 −0.705100
\(315\) 15.0037 0.845362
\(316\) 11.0622 0.622296
\(317\) −13.5804 −0.762750 −0.381375 0.924420i \(-0.624549\pi\)
−0.381375 + 0.924420i \(0.624549\pi\)
\(318\) −0.154639 −0.00867172
\(319\) 6.20904 0.347640
\(320\) −1.00000 −0.0559017
\(321\) −1.10414 −0.0616272
\(322\) 0 0
\(323\) −8.52627 −0.474414
\(324\) 8.97110 0.498394
\(325\) −2.99679 −0.166232
\(326\) 3.37214 0.186766
\(327\) 0.160904 0.00889802
\(328\) 5.54398 0.306115
\(329\) 20.8067 1.14711
\(330\) 0.126161 0.00694493
\(331\) −18.1061 −0.995200 −0.497600 0.867407i \(-0.665785\pi\)
−0.497600 + 0.867407i \(0.665785\pi\)
\(332\) −1.37389 −0.0754021
\(333\) −1.49535 −0.0819445
\(334\) 19.9217 1.09007
\(335\) −6.27410 −0.342791
\(336\) −0.283774 −0.0154812
\(337\) −19.2644 −1.04940 −0.524699 0.851288i \(-0.675822\pi\)
−0.524699 + 0.851288i \(0.675822\pi\)
\(338\) −4.01924 −0.218618
\(339\) 0.503855 0.0273657
\(340\) −1.17205 −0.0635635
\(341\) 17.6060 0.953419
\(342\) 21.8006 1.17884
\(343\) 55.4028 2.99147
\(344\) 10.3763 0.559450
\(345\) 0 0
\(346\) −17.0776 −0.918099
\(347\) −3.92813 −0.210873 −0.105436 0.994426i \(-0.533624\pi\)
−0.105436 + 0.994426i \(0.533624\pi\)
\(348\) −0.158111 −0.00847562
\(349\) 13.6354 0.729884 0.364942 0.931030i \(-0.381089\pi\)
0.364942 + 0.931030i \(0.381089\pi\)
\(350\) 5.00659 0.267614
\(351\) −1.01861 −0.0543691
\(352\) 2.22584 0.118638
\(353\) 0.968813 0.0515647 0.0257823 0.999668i \(-0.491792\pi\)
0.0257823 + 0.999668i \(0.491792\pi\)
\(354\) 0.0918062 0.00487944
\(355\) −9.80578 −0.520437
\(356\) −16.2240 −0.859871
\(357\) −0.332599 −0.0176030
\(358\) −13.0442 −0.689406
\(359\) 14.2017 0.749536 0.374768 0.927119i \(-0.377722\pi\)
0.374768 + 0.927119i \(0.377722\pi\)
\(360\) 2.99679 0.157945
\(361\) 33.9204 1.78528
\(362\) −6.10807 −0.321033
\(363\) 0.342667 0.0179854
\(364\) −15.0037 −0.786408
\(365\) −1.68505 −0.0881996
\(366\) 0.316646 0.0165514
\(367\) 12.9049 0.673633 0.336816 0.941570i \(-0.390650\pi\)
0.336816 + 0.941570i \(0.390650\pi\)
\(368\) 0 0
\(369\) −16.6141 −0.864897
\(370\) −0.498984 −0.0259409
\(371\) 13.6594 0.709158
\(372\) −0.448330 −0.0232448
\(373\) −30.5092 −1.57970 −0.789852 0.613297i \(-0.789843\pi\)
−0.789852 + 0.613297i \(0.789843\pi\)
\(374\) 2.60880 0.134898
\(375\) 0.0566801 0.00292695
\(376\) 4.15586 0.214322
\(377\) −8.35962 −0.430543
\(378\) 1.70173 0.0875277
\(379\) −6.87704 −0.353250 −0.176625 0.984278i \(-0.556518\pi\)
−0.176625 + 0.984278i \(0.556518\pi\)
\(380\) 7.27464 0.373181
\(381\) −0.194654 −0.00997243
\(382\) −2.56505 −0.131239
\(383\) −14.0395 −0.717383 −0.358692 0.933456i \(-0.616777\pi\)
−0.358692 + 0.933456i \(0.616777\pi\)
\(384\) −0.0566801 −0.00289245
\(385\) −11.1439 −0.567945
\(386\) 11.1506 0.567550
\(387\) −31.0954 −1.58067
\(388\) −4.93548 −0.250561
\(389\) 7.36683 0.373513 0.186756 0.982406i \(-0.440202\pi\)
0.186756 + 0.982406i \(0.440202\pi\)
\(390\) −0.169858 −0.00860112
\(391\) 0 0
\(392\) 18.0660 0.912469
\(393\) −1.08419 −0.0546900
\(394\) −7.61900 −0.383840
\(395\) −11.0622 −0.556598
\(396\) −6.67037 −0.335199
\(397\) −25.4128 −1.27543 −0.637715 0.770273i \(-0.720120\pi\)
−0.637715 + 0.770273i \(0.720120\pi\)
\(398\) 15.8779 0.795886
\(399\) 2.06436 0.103347
\(400\) 1.00000 0.0500000
\(401\) −15.3171 −0.764898 −0.382449 0.923977i \(-0.624919\pi\)
−0.382449 + 0.923977i \(0.624919\pi\)
\(402\) −0.355617 −0.0177366
\(403\) −23.7041 −1.18078
\(404\) −2.55146 −0.126940
\(405\) −8.97110 −0.445777
\(406\) 13.9660 0.693122
\(407\) 1.11066 0.0550533
\(408\) −0.0664321 −0.00328888
\(409\) −0.156293 −0.00772821 −0.00386410 0.999993i \(-0.501230\pi\)
−0.00386410 + 0.999993i \(0.501230\pi\)
\(410\) −5.54398 −0.273798
\(411\) 0.964481 0.0475743
\(412\) −16.4581 −0.810831
\(413\) −8.10930 −0.399033
\(414\) 0 0
\(415\) 1.37389 0.0674416
\(416\) −2.99679 −0.146930
\(417\) −0.223848 −0.0109619
\(418\) −16.1922 −0.791986
\(419\) −22.0543 −1.07743 −0.538713 0.842490i \(-0.681089\pi\)
−0.538713 + 0.842490i \(0.681089\pi\)
\(420\) 0.283774 0.0138468
\(421\) −30.1447 −1.46916 −0.734581 0.678521i \(-0.762621\pi\)
−0.734581 + 0.678521i \(0.762621\pi\)
\(422\) −1.50006 −0.0730217
\(423\) −12.4542 −0.605545
\(424\) 2.72827 0.132497
\(425\) 1.17205 0.0568529
\(426\) −0.555793 −0.0269282
\(427\) −27.9696 −1.35354
\(428\) 19.4802 0.941612
\(429\) 0.378078 0.0182538
\(430\) −10.3763 −0.500388
\(431\) −2.39601 −0.115412 −0.0577058 0.998334i \(-0.518379\pi\)
−0.0577058 + 0.998334i \(0.518379\pi\)
\(432\) 0.339899 0.0163534
\(433\) −30.5472 −1.46801 −0.734003 0.679146i \(-0.762350\pi\)
−0.734003 + 0.679146i \(0.762350\pi\)
\(434\) 39.6013 1.90092
\(435\) 0.158111 0.00758082
\(436\) −2.83881 −0.135954
\(437\) 0 0
\(438\) −0.0955089 −0.00456359
\(439\) 5.72872 0.273417 0.136709 0.990611i \(-0.456348\pi\)
0.136709 + 0.990611i \(0.456348\pi\)
\(440\) −2.22584 −0.106113
\(441\) −54.1399 −2.57809
\(442\) −3.51240 −0.167068
\(443\) 26.3379 1.25135 0.625677 0.780082i \(-0.284823\pi\)
0.625677 + 0.780082i \(0.284823\pi\)
\(444\) −0.0282824 −0.00134223
\(445\) 16.2240 0.769092
\(446\) −8.90770 −0.421792
\(447\) −1.05991 −0.0501320
\(448\) 5.00659 0.236539
\(449\) 10.8553 0.512293 0.256147 0.966638i \(-0.417547\pi\)
0.256147 + 0.966638i \(0.417547\pi\)
\(450\) −2.99679 −0.141270
\(451\) 12.3400 0.581069
\(452\) −8.88945 −0.418125
\(453\) −1.04103 −0.0489121
\(454\) −4.29484 −0.201567
\(455\) 15.0037 0.703385
\(456\) 0.412328 0.0193090
\(457\) −1.74876 −0.0818035 −0.0409018 0.999163i \(-0.513023\pi\)
−0.0409018 + 0.999163i \(0.513023\pi\)
\(458\) −17.8967 −0.836259
\(459\) 0.398379 0.0185948
\(460\) 0 0
\(461\) −8.58259 −0.399731 −0.199865 0.979823i \(-0.564051\pi\)
−0.199865 + 0.979823i \(0.564051\pi\)
\(462\) −0.631636 −0.0293864
\(463\) 2.90364 0.134944 0.0674718 0.997721i \(-0.478507\pi\)
0.0674718 + 0.997721i \(0.478507\pi\)
\(464\) 2.78953 0.129500
\(465\) 0.448330 0.0207908
\(466\) 27.2662 1.26308
\(467\) 20.5715 0.951935 0.475967 0.879463i \(-0.342098\pi\)
0.475967 + 0.879463i \(0.342098\pi\)
\(468\) 8.98075 0.415135
\(469\) 31.4119 1.45047
\(470\) −4.15586 −0.191695
\(471\) 0.708184 0.0326314
\(472\) −1.61972 −0.0745539
\(473\) 23.0959 1.06195
\(474\) −0.627005 −0.0287993
\(475\) −7.27464 −0.333783
\(476\) 5.86799 0.268959
\(477\) −8.17606 −0.374356
\(478\) −13.8416 −0.633102
\(479\) 3.72487 0.170194 0.0850969 0.996373i \(-0.472880\pi\)
0.0850969 + 0.996373i \(0.472880\pi\)
\(480\) 0.0566801 0.00258708
\(481\) −1.49535 −0.0681821
\(482\) 15.1156 0.688496
\(483\) 0 0
\(484\) −6.04563 −0.274801
\(485\) 4.93548 0.224109
\(486\) −1.52818 −0.0693196
\(487\) 24.8257 1.12496 0.562481 0.826810i \(-0.309847\pi\)
0.562481 + 0.826810i \(0.309847\pi\)
\(488\) −5.58655 −0.252891
\(489\) −0.191133 −0.00864335
\(490\) −18.0660 −0.816137
\(491\) −34.9034 −1.57517 −0.787585 0.616206i \(-0.788669\pi\)
−0.787585 + 0.616206i \(0.788669\pi\)
\(492\) −0.314233 −0.0141667
\(493\) 3.26947 0.147250
\(494\) 21.8006 0.980855
\(495\) 6.67037 0.299811
\(496\) 7.90982 0.355162
\(497\) 49.0935 2.20215
\(498\) 0.0778723 0.00348954
\(499\) −13.3137 −0.596002 −0.298001 0.954566i \(-0.596320\pi\)
−0.298001 + 0.954566i \(0.596320\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −1.12916 −0.0504473
\(502\) 19.6466 0.876870
\(503\) −7.23280 −0.322495 −0.161247 0.986914i \(-0.551552\pi\)
−0.161247 + 0.986914i \(0.551552\pi\)
\(504\) −15.0037 −0.668318
\(505\) 2.55146 0.113538
\(506\) 0 0
\(507\) 0.227811 0.0101174
\(508\) 3.43426 0.152371
\(509\) −1.67195 −0.0741080 −0.0370540 0.999313i \(-0.511797\pi\)
−0.0370540 + 0.999313i \(0.511797\pi\)
\(510\) 0.0664321 0.00294166
\(511\) 8.43637 0.373203
\(512\) 1.00000 0.0441942
\(513\) −2.47264 −0.109170
\(514\) 1.35642 0.0598290
\(515\) 16.4581 0.725229
\(516\) −0.588128 −0.0258909
\(517\) 9.25028 0.406827
\(518\) 2.49821 0.109765
\(519\) 0.967962 0.0424888
\(520\) 2.99679 0.131418
\(521\) −11.4822 −0.503043 −0.251522 0.967852i \(-0.580931\pi\)
−0.251522 + 0.967852i \(0.580931\pi\)
\(522\) −8.35961 −0.365890
\(523\) 5.27033 0.230455 0.115228 0.993339i \(-0.463240\pi\)
0.115228 + 0.993339i \(0.463240\pi\)
\(524\) 19.1282 0.835618
\(525\) −0.283774 −0.0123849
\(526\) 9.35101 0.407723
\(527\) 9.27074 0.403840
\(528\) −0.126161 −0.00549045
\(529\) 0 0
\(530\) −2.72827 −0.118509
\(531\) 4.85397 0.210644
\(532\) −36.4212 −1.57906
\(533\) −16.6141 −0.719639
\(534\) 0.919579 0.0397941
\(535\) −19.4802 −0.842204
\(536\) 6.27410 0.271000
\(537\) 0.739345 0.0319051
\(538\) 19.9733 0.861110
\(539\) 40.2120 1.73205
\(540\) −0.339899 −0.0146269
\(541\) 9.53162 0.409796 0.204898 0.978783i \(-0.434314\pi\)
0.204898 + 0.978783i \(0.434314\pi\)
\(542\) 22.3390 0.959542
\(543\) 0.346206 0.0148571
\(544\) 1.17205 0.0502514
\(545\) 2.83881 0.121601
\(546\) 0.850412 0.0363943
\(547\) −31.5192 −1.34766 −0.673832 0.738884i \(-0.735353\pi\)
−0.673832 + 0.738884i \(0.735353\pi\)
\(548\) −17.0162 −0.726897
\(549\) 16.7417 0.714519
\(550\) 2.22584 0.0949102
\(551\) −20.2928 −0.864502
\(552\) 0 0
\(553\) 55.3838 2.35516
\(554\) −18.2078 −0.773575
\(555\) 0.0282824 0.00120052
\(556\) 3.94931 0.167488
\(557\) −7.13889 −0.302485 −0.151242 0.988497i \(-0.548327\pi\)
−0.151242 + 0.988497i \(0.548327\pi\)
\(558\) −23.7041 −1.00347
\(559\) −31.0955 −1.31520
\(560\) −5.00659 −0.211567
\(561\) −0.147867 −0.00624296
\(562\) 10.7438 0.453198
\(563\) 44.8946 1.89208 0.946040 0.324049i \(-0.105044\pi\)
0.946040 + 0.324049i \(0.105044\pi\)
\(564\) −0.235554 −0.00991863
\(565\) 8.88945 0.373982
\(566\) −10.7171 −0.450474
\(567\) 44.9146 1.88624
\(568\) 9.80578 0.411441
\(569\) −19.4266 −0.814405 −0.407203 0.913338i \(-0.633496\pi\)
−0.407203 + 0.913338i \(0.633496\pi\)
\(570\) −0.412328 −0.0172705
\(571\) 31.8075 1.33110 0.665551 0.746353i \(-0.268197\pi\)
0.665551 + 0.746353i \(0.268197\pi\)
\(572\) −6.67038 −0.278903
\(573\) 0.145387 0.00607363
\(574\) 27.7564 1.15853
\(575\) 0 0
\(576\) −2.99679 −0.124866
\(577\) −18.4918 −0.769822 −0.384911 0.922954i \(-0.625768\pi\)
−0.384911 + 0.922954i \(0.625768\pi\)
\(578\) −15.6263 −0.649968
\(579\) −0.632017 −0.0262657
\(580\) −2.78953 −0.115829
\(581\) −6.87851 −0.285369
\(582\) 0.279744 0.0115957
\(583\) 6.07271 0.251506
\(584\) 1.68505 0.0697279
\(585\) −8.98075 −0.371308
\(586\) −17.1056 −0.706626
\(587\) 34.7498 1.43428 0.717138 0.696931i \(-0.245452\pi\)
0.717138 + 0.696931i \(0.245452\pi\)
\(588\) −1.02398 −0.0422283
\(589\) −57.5411 −2.37094
\(590\) 1.61972 0.0666830
\(591\) 0.431846 0.0177638
\(592\) 0.498984 0.0205081
\(593\) 36.9329 1.51665 0.758326 0.651875i \(-0.226017\pi\)
0.758326 + 0.651875i \(0.226017\pi\)
\(594\) 0.756560 0.0310420
\(595\) −5.86799 −0.240564
\(596\) 18.6998 0.765975
\(597\) −0.899960 −0.0368329
\(598\) 0 0
\(599\) −12.4422 −0.508376 −0.254188 0.967155i \(-0.581808\pi\)
−0.254188 + 0.967155i \(0.581808\pi\)
\(600\) −0.0566801 −0.00231396
\(601\) 35.8127 1.46083 0.730416 0.683003i \(-0.239326\pi\)
0.730416 + 0.683003i \(0.239326\pi\)
\(602\) 51.9497 2.11731
\(603\) −18.8022 −0.765683
\(604\) 18.3668 0.747336
\(605\) 6.04563 0.245790
\(606\) 0.144617 0.00587466
\(607\) −23.6933 −0.961683 −0.480841 0.876808i \(-0.659669\pi\)
−0.480841 + 0.876808i \(0.659669\pi\)
\(608\) −7.27464 −0.295026
\(609\) −0.791595 −0.0320771
\(610\) 5.58655 0.226193
\(611\) −12.4542 −0.503844
\(612\) −3.51239 −0.141980
\(613\) 10.8013 0.436261 0.218131 0.975920i \(-0.430004\pi\)
0.218131 + 0.975920i \(0.430004\pi\)
\(614\) 5.94744 0.240019
\(615\) 0.314233 0.0126711
\(616\) 11.1439 0.449000
\(617\) 31.3128 1.26060 0.630302 0.776350i \(-0.282931\pi\)
0.630302 + 0.776350i \(0.282931\pi\)
\(618\) 0.932845 0.0375245
\(619\) −20.9694 −0.842830 −0.421415 0.906868i \(-0.638466\pi\)
−0.421415 + 0.906868i \(0.638466\pi\)
\(620\) −7.90982 −0.317666
\(621\) 0 0
\(622\) −20.0565 −0.804193
\(623\) −81.2270 −3.25429
\(624\) 0.169858 0.00679978
\(625\) 1.00000 0.0400000
\(626\) 20.8169 0.832010
\(627\) 0.917776 0.0366524
\(628\) −12.4944 −0.498581
\(629\) 0.584835 0.0233189
\(630\) 15.0037 0.597761
\(631\) −42.5823 −1.69518 −0.847588 0.530655i \(-0.821946\pi\)
−0.847588 + 0.530655i \(0.821946\pi\)
\(632\) 11.0622 0.440030
\(633\) 0.0850235 0.00337938
\(634\) −13.5804 −0.539346
\(635\) −3.43426 −0.136284
\(636\) −0.154639 −0.00613183
\(637\) −54.1399 −2.14510
\(638\) 6.20904 0.245818
\(639\) −29.3858 −1.16249
\(640\) −1.00000 −0.0395285
\(641\) 2.40551 0.0950120 0.0475060 0.998871i \(-0.484873\pi\)
0.0475060 + 0.998871i \(0.484873\pi\)
\(642\) −1.10414 −0.0435770
\(643\) −38.7743 −1.52911 −0.764555 0.644558i \(-0.777041\pi\)
−0.764555 + 0.644558i \(0.777041\pi\)
\(644\) 0 0
\(645\) 0.588128 0.0231575
\(646\) −8.52627 −0.335462
\(647\) −0.0464447 −0.00182593 −0.000912964 1.00000i \(-0.500291\pi\)
−0.000912964 1.00000i \(0.500291\pi\)
\(648\) 8.97110 0.352418
\(649\) −3.60525 −0.141518
\(650\) −2.99679 −0.117544
\(651\) −2.24460 −0.0879730
\(652\) 3.37214 0.132063
\(653\) 5.95455 0.233020 0.116510 0.993190i \(-0.462829\pi\)
0.116510 + 0.993190i \(0.462829\pi\)
\(654\) 0.160904 0.00629185
\(655\) −19.1282 −0.747400
\(656\) 5.54398 0.216456
\(657\) −5.04974 −0.197009
\(658\) 20.8067 0.811129
\(659\) 29.7390 1.15847 0.579234 0.815161i \(-0.303352\pi\)
0.579234 + 0.815161i \(0.303352\pi\)
\(660\) 0.126161 0.00491081
\(661\) −48.1510 −1.87286 −0.936428 0.350860i \(-0.885889\pi\)
−0.936428 + 0.350860i \(0.885889\pi\)
\(662\) −18.1061 −0.703713
\(663\) 0.199083 0.00773175
\(664\) −1.37389 −0.0533173
\(665\) 36.4212 1.41235
\(666\) −1.49535 −0.0579435
\(667\) 0 0
\(668\) 19.9217 0.770793
\(669\) 0.504890 0.0195202
\(670\) −6.27410 −0.242390
\(671\) −12.4348 −0.480039
\(672\) −0.283774 −0.0109468
\(673\) −24.3926 −0.940266 −0.470133 0.882596i \(-0.655794\pi\)
−0.470133 + 0.882596i \(0.655794\pi\)
\(674\) −19.2644 −0.742036
\(675\) 0.339899 0.0130827
\(676\) −4.01924 −0.154586
\(677\) −15.1521 −0.582344 −0.291172 0.956671i \(-0.594045\pi\)
−0.291172 + 0.956671i \(0.594045\pi\)
\(678\) 0.503855 0.0193504
\(679\) −24.7099 −0.948280
\(680\) −1.17205 −0.0449462
\(681\) 0.243432 0.00932834
\(682\) 17.6060 0.674169
\(683\) −27.8748 −1.06660 −0.533300 0.845926i \(-0.679048\pi\)
−0.533300 + 0.845926i \(0.679048\pi\)
\(684\) 21.8006 0.833565
\(685\) 17.0162 0.650156
\(686\) 55.4028 2.11529
\(687\) 1.01439 0.0387013
\(688\) 10.3763 0.395591
\(689\) −8.17607 −0.311483
\(690\) 0 0
\(691\) −23.9305 −0.910361 −0.455180 0.890399i \(-0.650425\pi\)
−0.455180 + 0.890399i \(0.650425\pi\)
\(692\) −17.0776 −0.649194
\(693\) −33.3958 −1.26860
\(694\) −3.92813 −0.149110
\(695\) −3.94931 −0.149806
\(696\) −0.158111 −0.00599317
\(697\) 6.49784 0.246123
\(698\) 13.6354 0.516106
\(699\) −1.54545 −0.0584544
\(700\) 5.00659 0.189231
\(701\) −8.03004 −0.303291 −0.151645 0.988435i \(-0.548457\pi\)
−0.151645 + 0.988435i \(0.548457\pi\)
\(702\) −1.01861 −0.0384448
\(703\) −3.62993 −0.136905
\(704\) 2.22584 0.0838896
\(705\) 0.235554 0.00887150
\(706\) 0.968813 0.0364617
\(707\) −12.7741 −0.480420
\(708\) 0.0918062 0.00345029
\(709\) −42.3583 −1.59080 −0.795400 0.606085i \(-0.792739\pi\)
−0.795400 + 0.606085i \(0.792739\pi\)
\(710\) −9.80578 −0.368004
\(711\) −33.1510 −1.24326
\(712\) −16.2240 −0.608020
\(713\) 0 0
\(714\) −0.332599 −0.0124472
\(715\) 6.67038 0.249458
\(716\) −13.0442 −0.487483
\(717\) 0.784546 0.0292994
\(718\) 14.2017 0.530002
\(719\) −11.2710 −0.420336 −0.210168 0.977665i \(-0.567401\pi\)
−0.210168 + 0.977665i \(0.567401\pi\)
\(720\) 2.99679 0.111684
\(721\) −82.3988 −3.06869
\(722\) 33.9204 1.26239
\(723\) −0.856753 −0.0318630
\(724\) −6.10807 −0.227005
\(725\) 2.78953 0.103600
\(726\) 0.342667 0.0127176
\(727\) −8.89695 −0.329970 −0.164985 0.986296i \(-0.552758\pi\)
−0.164985 + 0.986296i \(0.552758\pi\)
\(728\) −15.0037 −0.556075
\(729\) −26.8267 −0.993580
\(730\) −1.68505 −0.0623665
\(731\) 12.1615 0.449810
\(732\) 0.316646 0.0117036
\(733\) −30.8068 −1.13787 −0.568937 0.822381i \(-0.692645\pi\)
−0.568937 + 0.822381i \(0.692645\pi\)
\(734\) 12.9049 0.476330
\(735\) 1.02398 0.0377701
\(736\) 0 0
\(737\) 13.9652 0.514413
\(738\) −16.6141 −0.611575
\(739\) 0.588418 0.0216453 0.0108227 0.999941i \(-0.496555\pi\)
0.0108227 + 0.999941i \(0.496555\pi\)
\(740\) −0.498984 −0.0183430
\(741\) −1.23566 −0.0453931
\(742\) 13.6594 0.501451
\(743\) −7.13026 −0.261584 −0.130792 0.991410i \(-0.541752\pi\)
−0.130792 + 0.991410i \(0.541752\pi\)
\(744\) −0.448330 −0.0164366
\(745\) −18.6998 −0.685109
\(746\) −30.5092 −1.11702
\(747\) 4.11726 0.150643
\(748\) 2.60880 0.0953873
\(749\) 97.5296 3.56365
\(750\) 0.0566801 0.00206967
\(751\) −5.32474 −0.194303 −0.0971513 0.995270i \(-0.530973\pi\)
−0.0971513 + 0.995270i \(0.530973\pi\)
\(752\) 4.15586 0.151549
\(753\) −1.11357 −0.0405808
\(754\) −8.35962 −0.304440
\(755\) −18.3668 −0.668437
\(756\) 1.70173 0.0618915
\(757\) −37.1495 −1.35022 −0.675111 0.737716i \(-0.735904\pi\)
−0.675111 + 0.737716i \(0.735904\pi\)
\(758\) −6.87704 −0.249785
\(759\) 0 0
\(760\) 7.27464 0.263879
\(761\) 25.8794 0.938128 0.469064 0.883164i \(-0.344591\pi\)
0.469064 + 0.883164i \(0.344591\pi\)
\(762\) −0.194654 −0.00705157
\(763\) −14.2128 −0.514537
\(764\) −2.56505 −0.0928001
\(765\) 3.51239 0.126991
\(766\) −14.0395 −0.507266
\(767\) 4.85398 0.175267
\(768\) −0.0566801 −0.00204527
\(769\) −39.2207 −1.41434 −0.707168 0.707045i \(-0.750028\pi\)
−0.707168 + 0.707045i \(0.750028\pi\)
\(770\) −11.1439 −0.401598
\(771\) −0.0768819 −0.00276883
\(772\) 11.1506 0.401318
\(773\) −31.1305 −1.11969 −0.559843 0.828598i \(-0.689139\pi\)
−0.559843 + 0.828598i \(0.689139\pi\)
\(774\) −31.0954 −1.11770
\(775\) 7.90982 0.284129
\(776\) −4.93548 −0.177173
\(777\) −0.141599 −0.00507982
\(778\) 7.36683 0.264114
\(779\) −40.3305 −1.44499
\(780\) −0.169858 −0.00608191
\(781\) 21.8261 0.781000
\(782\) 0 0
\(783\) 0.948156 0.0338843
\(784\) 18.0660 0.645213
\(785\) 12.4944 0.445944
\(786\) −1.08419 −0.0386717
\(787\) −10.4888 −0.373886 −0.186943 0.982371i \(-0.559858\pi\)
−0.186943 + 0.982371i \(0.559858\pi\)
\(788\) −7.61900 −0.271416
\(789\) −0.530016 −0.0188691
\(790\) −11.0622 −0.393574
\(791\) −44.5059 −1.58245
\(792\) −6.67037 −0.237021
\(793\) 16.7417 0.594516
\(794\) −25.4128 −0.901865
\(795\) 0.154639 0.00548448
\(796\) 15.8779 0.562777
\(797\) 24.9934 0.885311 0.442656 0.896692i \(-0.354036\pi\)
0.442656 + 0.896692i \(0.354036\pi\)
\(798\) 2.06436 0.0730774
\(799\) 4.87089 0.172320
\(800\) 1.00000 0.0353553
\(801\) 48.6199 1.71790
\(802\) −15.3171 −0.540865
\(803\) 3.75066 0.132358
\(804\) −0.355617 −0.0125416
\(805\) 0 0
\(806\) −23.7041 −0.834941
\(807\) −1.13209 −0.0398514
\(808\) −2.55146 −0.0897599
\(809\) 40.3779 1.41961 0.709805 0.704398i \(-0.248783\pi\)
0.709805 + 0.704398i \(0.248783\pi\)
\(810\) −8.97110 −0.315212
\(811\) −4.58935 −0.161154 −0.0805770 0.996748i \(-0.525676\pi\)
−0.0805770 + 0.996748i \(0.525676\pi\)
\(812\) 13.9660 0.490111
\(813\) −1.26618 −0.0444068
\(814\) 1.11066 0.0389285
\(815\) −3.37214 −0.118121
\(816\) −0.0664321 −0.00232559
\(817\) −75.4836 −2.64084
\(818\) −0.156293 −0.00546467
\(819\) 44.9629 1.57113
\(820\) −5.54398 −0.193604
\(821\) −11.6467 −0.406471 −0.203236 0.979130i \(-0.565146\pi\)
−0.203236 + 0.979130i \(0.565146\pi\)
\(822\) 0.964481 0.0336401
\(823\) 54.5971 1.90313 0.951567 0.307440i \(-0.0994725\pi\)
0.951567 + 0.307440i \(0.0994725\pi\)
\(824\) −16.4581 −0.573344
\(825\) −0.126161 −0.00439236
\(826\) −8.10930 −0.282159
\(827\) 20.8693 0.725695 0.362848 0.931849i \(-0.381805\pi\)
0.362848 + 0.931849i \(0.381805\pi\)
\(828\) 0 0
\(829\) 11.1291 0.386529 0.193265 0.981147i \(-0.438092\pi\)
0.193265 + 0.981147i \(0.438092\pi\)
\(830\) 1.37389 0.0476884
\(831\) 1.03202 0.0358004
\(832\) −2.99679 −0.103895
\(833\) 21.1743 0.733645
\(834\) −0.223848 −0.00775121
\(835\) −19.9217 −0.689418
\(836\) −16.1922 −0.560019
\(837\) 2.68854 0.0929295
\(838\) −22.0543 −0.761855
\(839\) −9.25317 −0.319455 −0.159727 0.987161i \(-0.551062\pi\)
−0.159727 + 0.987161i \(0.551062\pi\)
\(840\) 0.283774 0.00979114
\(841\) −21.2185 −0.731674
\(842\) −30.1447 −1.03886
\(843\) −0.608957 −0.0209736
\(844\) −1.50006 −0.0516341
\(845\) 4.01924 0.138266
\(846\) −12.4542 −0.428185
\(847\) −30.2680 −1.04002
\(848\) 2.72827 0.0936893
\(849\) 0.607448 0.0208475
\(850\) 1.17205 0.0402011
\(851\) 0 0
\(852\) −0.555793 −0.0190411
\(853\) 17.8530 0.611276 0.305638 0.952148i \(-0.401130\pi\)
0.305638 + 0.952148i \(0.401130\pi\)
\(854\) −27.9696 −0.957100
\(855\) −21.8006 −0.745563
\(856\) 19.4802 0.665821
\(857\) −4.09253 −0.139798 −0.0698992 0.997554i \(-0.522268\pi\)
−0.0698992 + 0.997554i \(0.522268\pi\)
\(858\) 0.378078 0.0129074
\(859\) −46.0901 −1.57257 −0.786287 0.617862i \(-0.787999\pi\)
−0.786287 + 0.617862i \(0.787999\pi\)
\(860\) −10.3763 −0.353827
\(861\) −1.57324 −0.0536158
\(862\) −2.39601 −0.0816084
\(863\) 48.8355 1.66238 0.831189 0.555990i \(-0.187661\pi\)
0.831189 + 0.555990i \(0.187661\pi\)
\(864\) 0.339899 0.0115636
\(865\) 17.0776 0.580657
\(866\) −30.5472 −1.03804
\(867\) 0.885700 0.0300799
\(868\) 39.6013 1.34415
\(869\) 24.6226 0.835266
\(870\) 0.158111 0.00536045
\(871\) −18.8022 −0.637088
\(872\) −2.83881 −0.0961343
\(873\) 14.7906 0.500585
\(874\) 0 0
\(875\) −5.00659 −0.169254
\(876\) −0.0955089 −0.00322695
\(877\) 3.55596 0.120076 0.0600381 0.998196i \(-0.480878\pi\)
0.0600381 + 0.998196i \(0.480878\pi\)
\(878\) 5.72872 0.193335
\(879\) 0.969548 0.0327020
\(880\) −2.22584 −0.0750331
\(881\) −3.70062 −0.124677 −0.0623386 0.998055i \(-0.519856\pi\)
−0.0623386 + 0.998055i \(0.519856\pi\)
\(882\) −54.1399 −1.82298
\(883\) 48.9080 1.64588 0.822942 0.568125i \(-0.192331\pi\)
0.822942 + 0.568125i \(0.192331\pi\)
\(884\) −3.51240 −0.118135
\(885\) −0.0918062 −0.00308603
\(886\) 26.3379 0.884841
\(887\) 14.2490 0.478436 0.239218 0.970966i \(-0.423109\pi\)
0.239218 + 0.970966i \(0.423109\pi\)
\(888\) −0.0282824 −0.000949097 0
\(889\) 17.1939 0.576666
\(890\) 16.2240 0.543830
\(891\) 19.9682 0.668961
\(892\) −8.90770 −0.298252
\(893\) −30.2324 −1.01169
\(894\) −1.05991 −0.0354486
\(895\) 13.0442 0.436018
\(896\) 5.00659 0.167259
\(897\) 0 0
\(898\) 10.8553 0.362246
\(899\) 22.0647 0.735897
\(900\) −2.99679 −0.0998929
\(901\) 3.19768 0.106530
\(902\) 12.3400 0.410878
\(903\) −2.94451 −0.0979873
\(904\) −8.88945 −0.295659
\(905\) 6.10807 0.203039
\(906\) −1.04103 −0.0345860
\(907\) 41.9716 1.39364 0.696822 0.717244i \(-0.254597\pi\)
0.696822 + 0.717244i \(0.254597\pi\)
\(908\) −4.29484 −0.142529
\(909\) 7.64617 0.253608
\(910\) 15.0037 0.497368
\(911\) −44.2206 −1.46509 −0.732546 0.680717i \(-0.761668\pi\)
−0.732546 + 0.680717i \(0.761668\pi\)
\(912\) 0.412328 0.0136535
\(913\) −3.05806 −0.101207
\(914\) −1.74876 −0.0578438
\(915\) −0.316646 −0.0104680
\(916\) −17.8967 −0.591324
\(917\) 95.7670 3.16250
\(918\) 0.398379 0.0131485
\(919\) 1.40847 0.0464612 0.0232306 0.999730i \(-0.492605\pi\)
0.0232306 + 0.999730i \(0.492605\pi\)
\(920\) 0 0
\(921\) −0.337102 −0.0111079
\(922\) −8.58259 −0.282652
\(923\) −29.3859 −0.967248
\(924\) −0.631636 −0.0207793
\(925\) 0.498984 0.0164065
\(926\) 2.90364 0.0954196
\(927\) 49.3213 1.61993
\(928\) 2.78953 0.0915707
\(929\) −27.9060 −0.915565 −0.457783 0.889064i \(-0.651356\pi\)
−0.457783 + 0.889064i \(0.651356\pi\)
\(930\) 0.448330 0.0147013
\(931\) −131.423 −4.30723
\(932\) 27.2662 0.893134
\(933\) 1.13681 0.0372173
\(934\) 20.5715 0.673119
\(935\) −2.60880 −0.0853170
\(936\) 8.98075 0.293545
\(937\) 58.6731 1.91677 0.958384 0.285483i \(-0.0921541\pi\)
0.958384 + 0.285483i \(0.0921541\pi\)
\(938\) 31.4119 1.02563
\(939\) −1.17990 −0.0385047
\(940\) −4.15586 −0.135549
\(941\) 4.60998 0.150281 0.0751406 0.997173i \(-0.476059\pi\)
0.0751406 + 0.997173i \(0.476059\pi\)
\(942\) 0.708184 0.0230739
\(943\) 0 0
\(944\) −1.61972 −0.0527176
\(945\) −1.70173 −0.0553574
\(946\) 23.0959 0.750913
\(947\) −11.0202 −0.358107 −0.179054 0.983839i \(-0.557304\pi\)
−0.179054 + 0.983839i \(0.557304\pi\)
\(948\) −0.627005 −0.0203642
\(949\) −5.04975 −0.163922
\(950\) −7.27464 −0.236021
\(951\) 0.769737 0.0249604
\(952\) 5.86799 0.190183
\(953\) −16.1839 −0.524249 −0.262124 0.965034i \(-0.584423\pi\)
−0.262124 + 0.965034i \(0.584423\pi\)
\(954\) −8.17606 −0.264710
\(955\) 2.56505 0.0830029
\(956\) −13.8416 −0.447671
\(957\) −0.351929 −0.0113763
\(958\) 3.72487 0.120345
\(959\) −85.1932 −2.75103
\(960\) 0.0566801 0.00182934
\(961\) 31.5653 1.01824
\(962\) −1.49535 −0.0482120
\(963\) −58.3781 −1.88121
\(964\) 15.1156 0.486840
\(965\) −11.1506 −0.358950
\(966\) 0 0
\(967\) −47.3630 −1.52309 −0.761546 0.648111i \(-0.775559\pi\)
−0.761546 + 0.648111i \(0.775559\pi\)
\(968\) −6.04563 −0.194314
\(969\) 0.483270 0.0155249
\(970\) 4.93548 0.158469
\(971\) 26.7348 0.857960 0.428980 0.903314i \(-0.358873\pi\)
0.428980 + 0.903314i \(0.358873\pi\)
\(972\) −1.52818 −0.0490164
\(973\) 19.7726 0.633881
\(974\) 24.8257 0.795468
\(975\) 0.169858 0.00543982
\(976\) −5.58655 −0.178821
\(977\) 57.5025 1.83967 0.919835 0.392306i \(-0.128323\pi\)
0.919835 + 0.392306i \(0.128323\pi\)
\(978\) −0.191133 −0.00611177
\(979\) −36.1121 −1.15415
\(980\) −18.0660 −0.577096
\(981\) 8.50731 0.271618
\(982\) −34.9034 −1.11381
\(983\) 7.20561 0.229823 0.114912 0.993376i \(-0.463342\pi\)
0.114912 + 0.993376i \(0.463342\pi\)
\(984\) −0.314233 −0.0100174
\(985\) 7.61900 0.242762
\(986\) 3.26947 0.104121
\(987\) −1.17933 −0.0375383
\(988\) 21.8006 0.693569
\(989\) 0 0
\(990\) 6.67037 0.211998
\(991\) −18.9210 −0.601046 −0.300523 0.953775i \(-0.597161\pi\)
−0.300523 + 0.953775i \(0.597161\pi\)
\(992\) 7.90982 0.251137
\(993\) 1.02625 0.0325672
\(994\) 49.0935 1.55715
\(995\) −15.8779 −0.503363
\(996\) 0.0778723 0.00246748
\(997\) 31.2523 0.989771 0.494885 0.868958i \(-0.335210\pi\)
0.494885 + 0.868958i \(0.335210\pi\)
\(998\) −13.3137 −0.421437
\(999\) 0.169604 0.00536603
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 5290.2.a.bk.1.8 15
23.9 even 11 230.2.g.d.81.2 yes 30
23.18 even 11 230.2.g.d.71.2 30
23.22 odd 2 5290.2.a.bl.1.8 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.g.d.71.2 30 23.18 even 11
230.2.g.d.81.2 yes 30 23.9 even 11
5290.2.a.bk.1.8 15 1.1 even 1 trivial
5290.2.a.bl.1.8 15 23.22 odd 2