Properties

Label 799.2.a.g.1.10
Level $799$
Weight $2$
Character 799.1
Self dual yes
Analytic conductor $6.380$
Analytic rank $0$
Dimension $20$
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] = [799,2,Mod(1,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, 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("799.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 799.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: \(6.38004712150\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + 1280 x^{12} - 24559 x^{11} + 3411 x^{10} + 49829 x^{9} - 15132 x^{8} - 58070 x^{7} + \cdots + 63 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.0537041\) of defining polynomial
Character \(\chi\) \(=\) 799.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.0537041 q^{2} -1.20296 q^{3} -1.99712 q^{4} +1.78333 q^{5} +0.0646037 q^{6} +2.05218 q^{7} +0.214661 q^{8} -1.55290 q^{9} +O(q^{10})\) \(q-0.0537041 q^{2} -1.20296 q^{3} -1.99712 q^{4} +1.78333 q^{5} +0.0646037 q^{6} +2.05218 q^{7} +0.214661 q^{8} -1.55290 q^{9} -0.0957722 q^{10} +1.15863 q^{11} +2.40244 q^{12} -1.26010 q^{13} -0.110210 q^{14} -2.14527 q^{15} +3.98270 q^{16} -1.00000 q^{17} +0.0833969 q^{18} -0.107776 q^{19} -3.56152 q^{20} -2.46868 q^{21} -0.0622233 q^{22} -1.11863 q^{23} -0.258228 q^{24} -1.81973 q^{25} +0.0676728 q^{26} +5.47694 q^{27} -4.09844 q^{28} +7.49117 q^{29} +0.115210 q^{30} +7.10636 q^{31} -0.643210 q^{32} -1.39378 q^{33} +0.0537041 q^{34} +3.65972 q^{35} +3.10131 q^{36} +1.62483 q^{37} +0.00578799 q^{38} +1.51585 q^{39} +0.382812 q^{40} +4.79805 q^{41} +0.132578 q^{42} +9.71471 q^{43} -2.31392 q^{44} -2.76933 q^{45} +0.0600748 q^{46} +1.00000 q^{47} -4.79102 q^{48} -2.78855 q^{49} +0.0977269 q^{50} +1.20296 q^{51} +2.51658 q^{52} +8.88526 q^{53} -0.294134 q^{54} +2.06622 q^{55} +0.440524 q^{56} +0.129649 q^{57} -0.402307 q^{58} -7.34515 q^{59} +4.28435 q^{60} +14.3783 q^{61} -0.381641 q^{62} -3.18682 q^{63} -7.93086 q^{64} -2.24718 q^{65} +0.0748519 q^{66} -4.99602 q^{67} +1.99712 q^{68} +1.34566 q^{69} -0.196542 q^{70} +7.36114 q^{71} -0.333347 q^{72} +16.7209 q^{73} -0.0872599 q^{74} +2.18905 q^{75} +0.215240 q^{76} +2.37772 q^{77} -0.0814074 q^{78} -3.88664 q^{79} +7.10248 q^{80} -1.92983 q^{81} -0.257675 q^{82} +0.850462 q^{83} +4.93025 q^{84} -1.78333 q^{85} -0.521720 q^{86} -9.01156 q^{87} +0.248714 q^{88} -8.65991 q^{89} +0.148724 q^{90} -2.58596 q^{91} +2.23403 q^{92} -8.54864 q^{93} -0.0537041 q^{94} -0.192200 q^{95} +0.773754 q^{96} +6.75261 q^{97} +0.149757 q^{98} -1.79924 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0537041 −0.0379745 −0.0189873 0.999820i \(-0.506044\pi\)
−0.0189873 + 0.999820i \(0.506044\pi\)
\(3\) −1.20296 −0.694527 −0.347264 0.937768i \(-0.612889\pi\)
−0.347264 + 0.937768i \(0.612889\pi\)
\(4\) −1.99712 −0.998558
\(5\) 1.78333 0.797530 0.398765 0.917053i \(-0.369439\pi\)
0.398765 + 0.917053i \(0.369439\pi\)
\(6\) 0.0646037 0.0263743
\(7\) 2.05218 0.775652 0.387826 0.921733i \(-0.373226\pi\)
0.387826 + 0.921733i \(0.373226\pi\)
\(8\) 0.214661 0.0758943
\(9\) −1.55290 −0.517632
\(10\) −0.0957722 −0.0302858
\(11\) 1.15863 0.349341 0.174670 0.984627i \(-0.444114\pi\)
0.174670 + 0.984627i \(0.444114\pi\)
\(12\) 2.40244 0.693526
\(13\) −1.26010 −0.349490 −0.174745 0.984614i \(-0.555910\pi\)
−0.174745 + 0.984614i \(0.555910\pi\)
\(14\) −0.110210 −0.0294550
\(15\) −2.14527 −0.553906
\(16\) 3.98270 0.995676
\(17\) −1.00000 −0.242536
\(18\) 0.0833969 0.0196568
\(19\) −0.107776 −0.0247254 −0.0123627 0.999924i \(-0.503935\pi\)
−0.0123627 + 0.999924i \(0.503935\pi\)
\(20\) −3.56152 −0.796380
\(21\) −2.46868 −0.538711
\(22\) −0.0622233 −0.0132660
\(23\) −1.11863 −0.233250 −0.116625 0.993176i \(-0.537208\pi\)
−0.116625 + 0.993176i \(0.537208\pi\)
\(24\) −0.258228 −0.0527106
\(25\) −1.81973 −0.363946
\(26\) 0.0676728 0.0132717
\(27\) 5.47694 1.05404
\(28\) −4.09844 −0.774533
\(29\) 7.49117 1.39108 0.695538 0.718489i \(-0.255166\pi\)
0.695538 + 0.718489i \(0.255166\pi\)
\(30\) 0.115210 0.0210343
\(31\) 7.10636 1.27634 0.638170 0.769895i \(-0.279692\pi\)
0.638170 + 0.769895i \(0.279692\pi\)
\(32\) −0.643210 −0.113705
\(33\) −1.39378 −0.242627
\(34\) 0.0537041 0.00921017
\(35\) 3.65972 0.618605
\(36\) 3.10131 0.516886
\(37\) 1.62483 0.267120 0.133560 0.991041i \(-0.457359\pi\)
0.133560 + 0.991041i \(0.457359\pi\)
\(38\) 0.00578799 0.000938935 0
\(39\) 1.51585 0.242730
\(40\) 0.382812 0.0605280
\(41\) 4.79805 0.749330 0.374665 0.927160i \(-0.377758\pi\)
0.374665 + 0.927160i \(0.377758\pi\)
\(42\) 0.132578 0.0204573
\(43\) 9.71471 1.48148 0.740740 0.671792i \(-0.234475\pi\)
0.740740 + 0.671792i \(0.234475\pi\)
\(44\) −2.31392 −0.348837
\(45\) −2.76933 −0.412827
\(46\) 0.0600748 0.00885754
\(47\) 1.00000 0.145865
\(48\) −4.79102 −0.691524
\(49\) −2.78855 −0.398365
\(50\) 0.0977269 0.0138207
\(51\) 1.20296 0.168448
\(52\) 2.51658 0.348986
\(53\) 8.88526 1.22048 0.610242 0.792215i \(-0.291072\pi\)
0.610242 + 0.792215i \(0.291072\pi\)
\(54\) −0.294134 −0.0400265
\(55\) 2.06622 0.278610
\(56\) 0.440524 0.0588675
\(57\) 0.129649 0.0171725
\(58\) −0.402307 −0.0528255
\(59\) −7.34515 −0.956257 −0.478129 0.878290i \(-0.658685\pi\)
−0.478129 + 0.878290i \(0.658685\pi\)
\(60\) 4.28435 0.553108
\(61\) 14.3783 1.84095 0.920477 0.390797i \(-0.127801\pi\)
0.920477 + 0.390797i \(0.127801\pi\)
\(62\) −0.381641 −0.0484684
\(63\) −3.18682 −0.401502
\(64\) −7.93086 −0.991358
\(65\) −2.24718 −0.278729
\(66\) 0.0748519 0.00921363
\(67\) −4.99602 −0.610362 −0.305181 0.952294i \(-0.598717\pi\)
−0.305181 + 0.952294i \(0.598717\pi\)
\(68\) 1.99712 0.242186
\(69\) 1.34566 0.161998
\(70\) −0.196542 −0.0234912
\(71\) 7.36114 0.873607 0.436803 0.899557i \(-0.356111\pi\)
0.436803 + 0.899557i \(0.356111\pi\)
\(72\) −0.333347 −0.0392853
\(73\) 16.7209 1.95704 0.978518 0.206163i \(-0.0660978\pi\)
0.978518 + 0.206163i \(0.0660978\pi\)
\(74\) −0.0872599 −0.0101438
\(75\) 2.18905 0.252770
\(76\) 0.215240 0.0246898
\(77\) 2.37772 0.270967
\(78\) −0.0814074 −0.00921757
\(79\) −3.88664 −0.437281 −0.218641 0.975805i \(-0.570162\pi\)
−0.218641 + 0.975805i \(0.570162\pi\)
\(80\) 7.10248 0.794081
\(81\) −1.92983 −0.214425
\(82\) −0.257675 −0.0284554
\(83\) 0.850462 0.0933503 0.0466752 0.998910i \(-0.485137\pi\)
0.0466752 + 0.998910i \(0.485137\pi\)
\(84\) 4.93025 0.537934
\(85\) −1.78333 −0.193429
\(86\) −0.521720 −0.0562585
\(87\) −9.01156 −0.966140
\(88\) 0.248714 0.0265130
\(89\) −8.65991 −0.917949 −0.458974 0.888450i \(-0.651783\pi\)
−0.458974 + 0.888450i \(0.651783\pi\)
\(90\) 0.148724 0.0156769
\(91\) −2.58596 −0.271083
\(92\) 2.23403 0.232913
\(93\) −8.54864 −0.886453
\(94\) −0.0537041 −0.00553915
\(95\) −0.192200 −0.0197193
\(96\) 0.773754 0.0789709
\(97\) 6.75261 0.685623 0.342812 0.939404i \(-0.388621\pi\)
0.342812 + 0.939404i \(0.388621\pi\)
\(98\) 0.149757 0.0151277
\(99\) −1.79924 −0.180830
\(100\) 3.63421 0.363421
\(101\) 1.70454 0.169608 0.0848040 0.996398i \(-0.472974\pi\)
0.0848040 + 0.996398i \(0.472974\pi\)
\(102\) −0.0646037 −0.00639672
\(103\) −18.8444 −1.85680 −0.928399 0.371584i \(-0.878815\pi\)
−0.928399 + 0.371584i \(0.878815\pi\)
\(104\) −0.270496 −0.0265243
\(105\) −4.40248 −0.429638
\(106\) −0.477175 −0.0463473
\(107\) −13.7971 −1.33382 −0.666909 0.745140i \(-0.732383\pi\)
−0.666909 + 0.745140i \(0.732383\pi\)
\(108\) −10.9381 −1.05252
\(109\) 9.87378 0.945736 0.472868 0.881133i \(-0.343219\pi\)
0.472868 + 0.881133i \(0.343219\pi\)
\(110\) −0.110965 −0.0105801
\(111\) −1.95460 −0.185522
\(112\) 8.17323 0.772298
\(113\) 7.67911 0.722390 0.361195 0.932490i \(-0.382369\pi\)
0.361195 + 0.932490i \(0.382369\pi\)
\(114\) −0.00696270 −0.000652116 0
\(115\) −1.99488 −0.186024
\(116\) −14.9607 −1.38907
\(117\) 1.95681 0.180907
\(118\) 0.394465 0.0363134
\(119\) −2.05218 −0.188123
\(120\) −0.460507 −0.0420383
\(121\) −9.65757 −0.877961
\(122\) −0.772174 −0.0699093
\(123\) −5.77185 −0.520430
\(124\) −14.1922 −1.27450
\(125\) −12.1618 −1.08779
\(126\) 0.171145 0.0152468
\(127\) −1.80978 −0.160592 −0.0802961 0.996771i \(-0.525587\pi\)
−0.0802961 + 0.996771i \(0.525587\pi\)
\(128\) 1.71234 0.151351
\(129\) −11.6864 −1.02893
\(130\) 0.120683 0.0105846
\(131\) −0.145721 −0.0127317 −0.00636587 0.999980i \(-0.502026\pi\)
−0.00636587 + 0.999980i \(0.502026\pi\)
\(132\) 2.78355 0.242277
\(133\) −0.221175 −0.0191783
\(134\) 0.268307 0.0231782
\(135\) 9.76719 0.840626
\(136\) −0.214661 −0.0184071
\(137\) 3.85798 0.329609 0.164805 0.986326i \(-0.447301\pi\)
0.164805 + 0.986326i \(0.447301\pi\)
\(138\) −0.0722673 −0.00615181
\(139\) −8.55663 −0.725764 −0.362882 0.931835i \(-0.618207\pi\)
−0.362882 + 0.931835i \(0.618207\pi\)
\(140\) −7.30888 −0.617713
\(141\) −1.20296 −0.101307
\(142\) −0.395323 −0.0331748
\(143\) −1.46000 −0.122091
\(144\) −6.18472 −0.515394
\(145\) 13.3592 1.10943
\(146\) −0.897981 −0.0743175
\(147\) 3.35451 0.276675
\(148\) −3.24497 −0.266735
\(149\) −0.389262 −0.0318896 −0.0159448 0.999873i \(-0.505076\pi\)
−0.0159448 + 0.999873i \(0.505076\pi\)
\(150\) −0.117561 −0.00959883
\(151\) 3.62728 0.295184 0.147592 0.989048i \(-0.452848\pi\)
0.147592 + 0.989048i \(0.452848\pi\)
\(152\) −0.0231353 −0.00187652
\(153\) 1.55290 0.125544
\(154\) −0.127693 −0.0102898
\(155\) 12.6730 1.01792
\(156\) −3.02733 −0.242380
\(157\) 10.9728 0.875724 0.437862 0.899042i \(-0.355736\pi\)
0.437862 + 0.899042i \(0.355736\pi\)
\(158\) 0.208729 0.0166055
\(159\) −10.6886 −0.847660
\(160\) −1.14706 −0.0906828
\(161\) −2.29562 −0.180920
\(162\) 0.103640 0.00814269
\(163\) −21.3056 −1.66879 −0.834393 0.551170i \(-0.814182\pi\)
−0.834393 + 0.551170i \(0.814182\pi\)
\(164\) −9.58227 −0.748249
\(165\) −2.48558 −0.193502
\(166\) −0.0456733 −0.00354493
\(167\) 11.4622 0.886971 0.443486 0.896282i \(-0.353742\pi\)
0.443486 + 0.896282i \(0.353742\pi\)
\(168\) −0.529931 −0.0408851
\(169\) −11.4121 −0.877857
\(170\) 0.0957722 0.00734539
\(171\) 0.167364 0.0127987
\(172\) −19.4014 −1.47934
\(173\) −19.1260 −1.45412 −0.727061 0.686573i \(-0.759114\pi\)
−0.727061 + 0.686573i \(0.759114\pi\)
\(174\) 0.483957 0.0366887
\(175\) −3.73441 −0.282295
\(176\) 4.61449 0.347830
\(177\) 8.83590 0.664147
\(178\) 0.465073 0.0348587
\(179\) 16.0162 1.19710 0.598552 0.801084i \(-0.295743\pi\)
0.598552 + 0.801084i \(0.295743\pi\)
\(180\) 5.53067 0.412232
\(181\) 3.82937 0.284635 0.142317 0.989821i \(-0.454545\pi\)
0.142317 + 0.989821i \(0.454545\pi\)
\(182\) 0.138877 0.0102942
\(183\) −17.2965 −1.27859
\(184\) −0.240126 −0.0177023
\(185\) 2.89761 0.213036
\(186\) 0.459097 0.0336626
\(187\) −1.15863 −0.0847276
\(188\) −1.99712 −0.145655
\(189\) 11.2397 0.817565
\(190\) 0.0103219 0.000748829 0
\(191\) −3.92689 −0.284140 −0.142070 0.989857i \(-0.545376\pi\)
−0.142070 + 0.989857i \(0.545376\pi\)
\(192\) 9.54048 0.688525
\(193\) −4.46618 −0.321482 −0.160741 0.986997i \(-0.551388\pi\)
−0.160741 + 0.986997i \(0.551388\pi\)
\(194\) −0.362643 −0.0260362
\(195\) 2.70326 0.193585
\(196\) 5.56906 0.397790
\(197\) 24.7118 1.76064 0.880322 0.474377i \(-0.157327\pi\)
0.880322 + 0.474377i \(0.157327\pi\)
\(198\) 0.0966263 0.00686693
\(199\) −1.93889 −0.137444 −0.0687221 0.997636i \(-0.521892\pi\)
−0.0687221 + 0.997636i \(0.521892\pi\)
\(200\) −0.390626 −0.0276214
\(201\) 6.01000 0.423913
\(202\) −0.0915407 −0.00644078
\(203\) 15.3732 1.07899
\(204\) −2.40244 −0.168205
\(205\) 8.55652 0.597613
\(206\) 1.01202 0.0705110
\(207\) 1.73711 0.120737
\(208\) −5.01862 −0.347979
\(209\) −0.124872 −0.00863759
\(210\) 0.236431 0.0163153
\(211\) −10.5427 −0.725791 −0.362895 0.931830i \(-0.618212\pi\)
−0.362895 + 0.931830i \(0.618212\pi\)
\(212\) −17.7449 −1.21872
\(213\) −8.85513 −0.606744
\(214\) 0.740961 0.0506511
\(215\) 17.3246 1.18152
\(216\) 1.17569 0.0799954
\(217\) 14.5835 0.989995
\(218\) −0.530262 −0.0359139
\(219\) −20.1145 −1.35921
\(220\) −4.12649 −0.278208
\(221\) 1.26010 0.0847638
\(222\) 0.104970 0.00704512
\(223\) 2.83758 0.190018 0.0950091 0.995476i \(-0.469712\pi\)
0.0950091 + 0.995476i \(0.469712\pi\)
\(224\) −1.31998 −0.0881951
\(225\) 2.82585 0.188390
\(226\) −0.412400 −0.0274324
\(227\) 7.87506 0.522686 0.261343 0.965246i \(-0.415835\pi\)
0.261343 + 0.965246i \(0.415835\pi\)
\(228\) −0.258925 −0.0171477
\(229\) −5.68520 −0.375689 −0.187844 0.982199i \(-0.560150\pi\)
−0.187844 + 0.982199i \(0.560150\pi\)
\(230\) 0.107133 0.00706416
\(231\) −2.86030 −0.188194
\(232\) 1.60807 0.105575
\(233\) 28.6251 1.87529 0.937647 0.347589i \(-0.113000\pi\)
0.937647 + 0.347589i \(0.113000\pi\)
\(234\) −0.105089 −0.00686987
\(235\) 1.78333 0.116332
\(236\) 14.6691 0.954878
\(237\) 4.67546 0.303704
\(238\) 0.110210 0.00714389
\(239\) 12.9200 0.835727 0.417863 0.908510i \(-0.362779\pi\)
0.417863 + 0.908510i \(0.362779\pi\)
\(240\) −8.54397 −0.551511
\(241\) −14.8446 −0.956222 −0.478111 0.878299i \(-0.658678\pi\)
−0.478111 + 0.878299i \(0.658678\pi\)
\(242\) 0.518651 0.0333402
\(243\) −14.1093 −0.905113
\(244\) −28.7151 −1.83830
\(245\) −4.97291 −0.317708
\(246\) 0.309972 0.0197631
\(247\) 0.135808 0.00864129
\(248\) 1.52546 0.0968669
\(249\) −1.02307 −0.0648343
\(250\) 0.653140 0.0413082
\(251\) −13.2109 −0.833862 −0.416931 0.908938i \(-0.636894\pi\)
−0.416931 + 0.908938i \(0.636894\pi\)
\(252\) 6.36446 0.400923
\(253\) −1.29608 −0.0814836
\(254\) 0.0971927 0.00609841
\(255\) 2.14527 0.134342
\(256\) 15.7698 0.985611
\(257\) −25.3870 −1.58360 −0.791798 0.610783i \(-0.790855\pi\)
−0.791798 + 0.610783i \(0.790855\pi\)
\(258\) 0.627606 0.0390731
\(259\) 3.33444 0.207192
\(260\) 4.48789 0.278327
\(261\) −11.6330 −0.720066
\(262\) 0.00782583 0.000483482 0
\(263\) −5.69051 −0.350892 −0.175446 0.984489i \(-0.556137\pi\)
−0.175446 + 0.984489i \(0.556137\pi\)
\(264\) −0.299192 −0.0184140
\(265\) 15.8454 0.973373
\(266\) 0.0118780 0.000728287 0
\(267\) 10.4175 0.637540
\(268\) 9.97764 0.609481
\(269\) 22.7426 1.38664 0.693322 0.720628i \(-0.256146\pi\)
0.693322 + 0.720628i \(0.256146\pi\)
\(270\) −0.524538 −0.0319224
\(271\) −2.26702 −0.137712 −0.0688559 0.997627i \(-0.521935\pi\)
−0.0688559 + 0.997627i \(0.521935\pi\)
\(272\) −3.98270 −0.241487
\(273\) 3.11080 0.188274
\(274\) −0.207189 −0.0125168
\(275\) −2.10840 −0.127141
\(276\) −2.68744 −0.161765
\(277\) −15.2541 −0.916533 −0.458266 0.888815i \(-0.651529\pi\)
−0.458266 + 0.888815i \(0.651529\pi\)
\(278\) 0.459526 0.0275605
\(279\) −11.0354 −0.660674
\(280\) 0.785601 0.0469486
\(281\) 17.3868 1.03721 0.518606 0.855014i \(-0.326451\pi\)
0.518606 + 0.855014i \(0.326451\pi\)
\(282\) 0.0646037 0.00384709
\(283\) −15.6798 −0.932069 −0.466034 0.884767i \(-0.654318\pi\)
−0.466034 + 0.884767i \(0.654318\pi\)
\(284\) −14.7011 −0.872347
\(285\) 0.231208 0.0136956
\(286\) 0.0784078 0.00463635
\(287\) 9.84647 0.581219
\(288\) 0.998839 0.0588571
\(289\) 1.00000 0.0588235
\(290\) −0.717446 −0.0421299
\(291\) −8.12309 −0.476184
\(292\) −33.3936 −1.95421
\(293\) −8.35007 −0.487817 −0.243908 0.969798i \(-0.578430\pi\)
−0.243908 + 0.969798i \(0.578430\pi\)
\(294\) −0.180151 −0.0105066
\(295\) −13.0988 −0.762644
\(296\) 0.348788 0.0202729
\(297\) 6.34575 0.368218
\(298\) 0.0209050 0.00121099
\(299\) 1.40959 0.0815185
\(300\) −4.37180 −0.252406
\(301\) 19.9364 1.14911
\(302\) −0.194800 −0.0112095
\(303\) −2.05049 −0.117797
\(304\) −0.429238 −0.0246185
\(305\) 25.6413 1.46822
\(306\) −0.0833969 −0.00476748
\(307\) −34.3115 −1.95826 −0.979130 0.203234i \(-0.934855\pi\)
−0.979130 + 0.203234i \(0.934855\pi\)
\(308\) −4.74859 −0.270576
\(309\) 22.6690 1.28960
\(310\) −0.680592 −0.0386550
\(311\) 23.3976 1.32676 0.663379 0.748284i \(-0.269122\pi\)
0.663379 + 0.748284i \(0.269122\pi\)
\(312\) 0.325395 0.0184219
\(313\) 4.09805 0.231636 0.115818 0.993270i \(-0.463051\pi\)
0.115818 + 0.993270i \(0.463051\pi\)
\(314\) −0.589283 −0.0332552
\(315\) −5.68316 −0.320210
\(316\) 7.76207 0.436651
\(317\) −11.7024 −0.657270 −0.328635 0.944457i \(-0.606589\pi\)
−0.328635 + 0.944457i \(0.606589\pi\)
\(318\) 0.574021 0.0321895
\(319\) 8.67952 0.485960
\(320\) −14.1434 −0.790638
\(321\) 16.5973 0.926372
\(322\) 0.123284 0.00687037
\(323\) 0.107776 0.00599679
\(324\) 3.85409 0.214116
\(325\) 2.29305 0.127195
\(326\) 1.14420 0.0633714
\(327\) −11.8777 −0.656840
\(328\) 1.02996 0.0568699
\(329\) 2.05218 0.113140
\(330\) 0.133486 0.00734815
\(331\) 17.6210 0.968540 0.484270 0.874919i \(-0.339085\pi\)
0.484270 + 0.874919i \(0.339085\pi\)
\(332\) −1.69847 −0.0932157
\(333\) −2.52319 −0.138270
\(334\) −0.615566 −0.0336823
\(335\) −8.90957 −0.486782
\(336\) −9.83204 −0.536382
\(337\) 14.9955 0.816855 0.408427 0.912791i \(-0.366077\pi\)
0.408427 + 0.912791i \(0.366077\pi\)
\(338\) 0.612878 0.0333362
\(339\) −9.23764 −0.501720
\(340\) 3.56152 0.193151
\(341\) 8.23366 0.445878
\(342\) −0.00898814 −0.000486023 0
\(343\) −20.0879 −1.08464
\(344\) 2.08537 0.112436
\(345\) 2.39975 0.129198
\(346\) 1.02714 0.0552196
\(347\) −8.87025 −0.476180 −0.238090 0.971243i \(-0.576521\pi\)
−0.238090 + 0.971243i \(0.576521\pi\)
\(348\) 17.9971 0.964747
\(349\) 27.6937 1.48241 0.741205 0.671278i \(-0.234254\pi\)
0.741205 + 0.671278i \(0.234254\pi\)
\(350\) 0.200553 0.0107200
\(351\) −6.90151 −0.368375
\(352\) −0.745244 −0.0397216
\(353\) 3.56917 0.189968 0.0949839 0.995479i \(-0.469720\pi\)
0.0949839 + 0.995479i \(0.469720\pi\)
\(354\) −0.474524 −0.0252206
\(355\) 13.1274 0.696728
\(356\) 17.2948 0.916625
\(357\) 2.46868 0.130657
\(358\) −0.860133 −0.0454594
\(359\) 11.6002 0.612235 0.306117 0.951994i \(-0.400970\pi\)
0.306117 + 0.951994i \(0.400970\pi\)
\(360\) −0.594468 −0.0313312
\(361\) −18.9884 −0.999389
\(362\) −0.205653 −0.0108089
\(363\) 11.6176 0.609768
\(364\) 5.16447 0.270692
\(365\) 29.8189 1.56079
\(366\) 0.928891 0.0485539
\(367\) 4.06335 0.212105 0.106053 0.994361i \(-0.466179\pi\)
0.106053 + 0.994361i \(0.466179\pi\)
\(368\) −4.45516 −0.232241
\(369\) −7.45088 −0.387877
\(370\) −0.155613 −0.00808996
\(371\) 18.2342 0.946671
\(372\) 17.0726 0.885175
\(373\) −23.2574 −1.20423 −0.602113 0.798411i \(-0.705674\pi\)
−0.602113 + 0.798411i \(0.705674\pi\)
\(374\) 0.0622233 0.00321749
\(375\) 14.6302 0.755498
\(376\) 0.214661 0.0110703
\(377\) −9.43967 −0.486167
\(378\) −0.603616 −0.0310466
\(379\) −25.5834 −1.31413 −0.657065 0.753834i \(-0.728202\pi\)
−0.657065 + 0.753834i \(0.728202\pi\)
\(380\) 0.383845 0.0196908
\(381\) 2.17709 0.111536
\(382\) 0.210890 0.0107901
\(383\) 13.1760 0.673263 0.336632 0.941636i \(-0.390712\pi\)
0.336632 + 0.941636i \(0.390712\pi\)
\(384\) −2.05987 −0.105117
\(385\) 4.24027 0.216104
\(386\) 0.239852 0.0122081
\(387\) −15.0859 −0.766861
\(388\) −13.4857 −0.684635
\(389\) 11.8538 0.601010 0.300505 0.953780i \(-0.402845\pi\)
0.300505 + 0.953780i \(0.402845\pi\)
\(390\) −0.145176 −0.00735129
\(391\) 1.11863 0.0565714
\(392\) −0.598595 −0.0302336
\(393\) 0.175296 0.00884254
\(394\) −1.32713 −0.0668596
\(395\) −6.93117 −0.348745
\(396\) 3.59328 0.180569
\(397\) −13.2441 −0.664705 −0.332352 0.943155i \(-0.607842\pi\)
−0.332352 + 0.943155i \(0.607842\pi\)
\(398\) 0.104126 0.00521938
\(399\) 0.266064 0.0133199
\(400\) −7.24744 −0.362372
\(401\) −11.3475 −0.566667 −0.283333 0.959021i \(-0.591440\pi\)
−0.283333 + 0.959021i \(0.591440\pi\)
\(402\) −0.322762 −0.0160979
\(403\) −8.95476 −0.446068
\(404\) −3.40416 −0.169363
\(405\) −3.44152 −0.171010
\(406\) −0.825606 −0.0409741
\(407\) 1.88258 0.0933160
\(408\) 0.258228 0.0127842
\(409\) 14.6735 0.725557 0.362778 0.931875i \(-0.381828\pi\)
0.362778 + 0.931875i \(0.381828\pi\)
\(410\) −0.459520 −0.0226941
\(411\) −4.64098 −0.228923
\(412\) 37.6345 1.85412
\(413\) −15.0736 −0.741722
\(414\) −0.0932899 −0.00458495
\(415\) 1.51666 0.0744497
\(416\) 0.810512 0.0397386
\(417\) 10.2933 0.504063
\(418\) 0.00670615 0.000328008 0
\(419\) −27.1956 −1.32859 −0.664296 0.747470i \(-0.731268\pi\)
−0.664296 + 0.747470i \(0.731268\pi\)
\(420\) 8.79227 0.429019
\(421\) 31.1619 1.51874 0.759368 0.650661i \(-0.225508\pi\)
0.759368 + 0.650661i \(0.225508\pi\)
\(422\) 0.566187 0.0275616
\(423\) −1.55290 −0.0755044
\(424\) 1.90732 0.0926278
\(425\) 1.81973 0.0882698
\(426\) 0.475557 0.0230408
\(427\) 29.5069 1.42794
\(428\) 27.5544 1.33189
\(429\) 1.75631 0.0847956
\(430\) −0.930399 −0.0448678
\(431\) −25.8000 −1.24274 −0.621371 0.783517i \(-0.713424\pi\)
−0.621371 + 0.783517i \(0.713424\pi\)
\(432\) 21.8130 1.04948
\(433\) −17.6242 −0.846966 −0.423483 0.905904i \(-0.639193\pi\)
−0.423483 + 0.905904i \(0.639193\pi\)
\(434\) −0.783196 −0.0375946
\(435\) −16.0706 −0.770526
\(436\) −19.7191 −0.944373
\(437\) 0.120561 0.00576719
\(438\) 1.08023 0.0516155
\(439\) 22.6146 1.07934 0.539668 0.841878i \(-0.318550\pi\)
0.539668 + 0.841878i \(0.318550\pi\)
\(440\) 0.443539 0.0211449
\(441\) 4.33033 0.206206
\(442\) −0.0676728 −0.00321887
\(443\) −1.75864 −0.0835554 −0.0417777 0.999127i \(-0.513302\pi\)
−0.0417777 + 0.999127i \(0.513302\pi\)
\(444\) 3.90356 0.185255
\(445\) −15.4435 −0.732092
\(446\) −0.152389 −0.00721585
\(447\) 0.468265 0.0221482
\(448\) −16.2756 −0.768948
\(449\) 3.14730 0.148530 0.0742650 0.997239i \(-0.476339\pi\)
0.0742650 + 0.997239i \(0.476339\pi\)
\(450\) −0.151760 −0.00715402
\(451\) 5.55918 0.261771
\(452\) −15.3361 −0.721348
\(453\) −4.36346 −0.205013
\(454\) −0.422923 −0.0198487
\(455\) −4.61163 −0.216197
\(456\) 0.0278307 0.00130329
\(457\) −22.5430 −1.05452 −0.527258 0.849706i \(-0.676780\pi\)
−0.527258 + 0.849706i \(0.676780\pi\)
\(458\) 0.305319 0.0142666
\(459\) −5.47694 −0.255641
\(460\) 3.98401 0.185755
\(461\) 4.94533 0.230327 0.115163 0.993347i \(-0.463261\pi\)
0.115163 + 0.993347i \(0.463261\pi\)
\(462\) 0.153610 0.00714657
\(463\) 8.12748 0.377716 0.188858 0.982004i \(-0.439521\pi\)
0.188858 + 0.982004i \(0.439521\pi\)
\(464\) 29.8351 1.38506
\(465\) −15.2451 −0.706973
\(466\) −1.53729 −0.0712134
\(467\) 38.0876 1.76248 0.881242 0.472665i \(-0.156708\pi\)
0.881242 + 0.472665i \(0.156708\pi\)
\(468\) −3.90798 −0.180646
\(469\) −10.2527 −0.473428
\(470\) −0.0957722 −0.00441764
\(471\) −13.1998 −0.608214
\(472\) −1.57672 −0.0725744
\(473\) 11.2558 0.517541
\(474\) −0.251091 −0.0115330
\(475\) 0.196122 0.00899871
\(476\) 4.09844 0.187852
\(477\) −13.7979 −0.631762
\(478\) −0.693858 −0.0317363
\(479\) 11.8897 0.543256 0.271628 0.962402i \(-0.412438\pi\)
0.271628 + 0.962402i \(0.412438\pi\)
\(480\) 1.37986 0.0629817
\(481\) −2.04745 −0.0933559
\(482\) 0.797213 0.0363121
\(483\) 2.76153 0.125654
\(484\) 19.2873 0.876695
\(485\) 12.0421 0.546805
\(486\) 0.757727 0.0343712
\(487\) −4.00978 −0.181700 −0.0908502 0.995865i \(-0.528958\pi\)
−0.0908502 + 0.995865i \(0.528958\pi\)
\(488\) 3.08647 0.139718
\(489\) 25.6298 1.15902
\(490\) 0.267066 0.0120648
\(491\) 30.9954 1.39880 0.699402 0.714729i \(-0.253450\pi\)
0.699402 + 0.714729i \(0.253450\pi\)
\(492\) 11.5271 0.519680
\(493\) −7.49117 −0.337386
\(494\) −0.00729347 −0.000328149 0
\(495\) −3.20863 −0.144217
\(496\) 28.3025 1.27082
\(497\) 15.1064 0.677614
\(498\) 0.0549430 0.00246205
\(499\) −36.6978 −1.64282 −0.821410 0.570338i \(-0.806812\pi\)
−0.821410 + 0.570338i \(0.806812\pi\)
\(500\) 24.2886 1.08622
\(501\) −13.7885 −0.616025
\(502\) 0.709477 0.0316655
\(503\) 35.8560 1.59874 0.799369 0.600840i \(-0.205167\pi\)
0.799369 + 0.600840i \(0.205167\pi\)
\(504\) −0.684088 −0.0304717
\(505\) 3.03976 0.135267
\(506\) 0.0696046 0.00309430
\(507\) 13.7283 0.609695
\(508\) 3.61435 0.160361
\(509\) 30.6393 1.35806 0.679031 0.734109i \(-0.262400\pi\)
0.679031 + 0.734109i \(0.262400\pi\)
\(510\) −0.115210 −0.00510157
\(511\) 34.3143 1.51798
\(512\) −4.27158 −0.188779
\(513\) −0.590280 −0.0260615
\(514\) 1.36338 0.0601363
\(515\) −33.6059 −1.48085
\(516\) 23.3390 1.02744
\(517\) 1.15863 0.0509566
\(518\) −0.179073 −0.00786803
\(519\) 23.0077 1.00993
\(520\) −0.482384 −0.0211539
\(521\) −17.4727 −0.765491 −0.382745 0.923854i \(-0.625021\pi\)
−0.382745 + 0.923854i \(0.625021\pi\)
\(522\) 0.624740 0.0273441
\(523\) −27.0469 −1.18268 −0.591339 0.806423i \(-0.701401\pi\)
−0.591339 + 0.806423i \(0.701401\pi\)
\(524\) 0.291022 0.0127134
\(525\) 4.49234 0.196062
\(526\) 0.305604 0.0133250
\(527\) −7.10636 −0.309558
\(528\) −5.55103 −0.241577
\(529\) −21.7487 −0.945595
\(530\) −0.850961 −0.0369634
\(531\) 11.4063 0.494989
\(532\) 0.441712 0.0191506
\(533\) −6.04605 −0.261883
\(534\) −0.559462 −0.0242103
\(535\) −24.6048 −1.06376
\(536\) −1.07245 −0.0463230
\(537\) −19.2667 −0.831421
\(538\) −1.22137 −0.0526571
\(539\) −3.23091 −0.139165
\(540\) −19.5062 −0.839414
\(541\) 22.4061 0.963314 0.481657 0.876360i \(-0.340035\pi\)
0.481657 + 0.876360i \(0.340035\pi\)
\(542\) 0.121748 0.00522954
\(543\) −4.60657 −0.197687
\(544\) 0.643210 0.0275774
\(545\) 17.6082 0.754253
\(546\) −0.167063 −0.00714962
\(547\) 9.91293 0.423846 0.211923 0.977286i \(-0.432027\pi\)
0.211923 + 0.977286i \(0.432027\pi\)
\(548\) −7.70483 −0.329134
\(549\) −22.3280 −0.952937
\(550\) 0.113229 0.00482812
\(551\) −0.807365 −0.0343949
\(552\) 0.288861 0.0122947
\(553\) −7.97609 −0.339178
\(554\) 0.819210 0.0348049
\(555\) −3.48570 −0.147960
\(556\) 17.0886 0.724717
\(557\) −14.2121 −0.602184 −0.301092 0.953595i \(-0.597351\pi\)
−0.301092 + 0.953595i \(0.597351\pi\)
\(558\) 0.592648 0.0250888
\(559\) −12.2416 −0.517763
\(560\) 14.5756 0.615930
\(561\) 1.39378 0.0588456
\(562\) −0.933744 −0.0393876
\(563\) −25.1266 −1.05896 −0.529480 0.848322i \(-0.677613\pi\)
−0.529480 + 0.848322i \(0.677613\pi\)
\(564\) 2.40244 0.101161
\(565\) 13.6944 0.576128
\(566\) 0.842070 0.0353949
\(567\) −3.96035 −0.166319
\(568\) 1.58015 0.0663018
\(569\) 36.4735 1.52905 0.764524 0.644596i \(-0.222974\pi\)
0.764524 + 0.644596i \(0.222974\pi\)
\(570\) −0.0124168 −0.000520082 0
\(571\) −34.6876 −1.45163 −0.725815 0.687889i \(-0.758537\pi\)
−0.725815 + 0.687889i \(0.758537\pi\)
\(572\) 2.91578 0.121915
\(573\) 4.72388 0.197343
\(574\) −0.528796 −0.0220715
\(575\) 2.03560 0.0848902
\(576\) 12.3158 0.513159
\(577\) −37.2637 −1.55131 −0.775655 0.631157i \(-0.782580\pi\)
−0.775655 + 0.631157i \(0.782580\pi\)
\(578\) −0.0537041 −0.00223380
\(579\) 5.37262 0.223278
\(580\) −26.6800 −1.10783
\(581\) 1.74530 0.0724073
\(582\) 0.436243 0.0180829
\(583\) 10.2948 0.426365
\(584\) 3.58934 0.148528
\(585\) 3.48964 0.144279
\(586\) 0.448433 0.0185246
\(587\) −23.6599 −0.976548 −0.488274 0.872690i \(-0.662373\pi\)
−0.488274 + 0.872690i \(0.662373\pi\)
\(588\) −6.69934 −0.276276
\(589\) −0.765892 −0.0315580
\(590\) 0.703461 0.0289610
\(591\) −29.7272 −1.22282
\(592\) 6.47121 0.265965
\(593\) 21.5070 0.883187 0.441593 0.897215i \(-0.354413\pi\)
0.441593 + 0.897215i \(0.354413\pi\)
\(594\) −0.340793 −0.0139829
\(595\) −3.65972 −0.150034
\(596\) 0.777401 0.0318436
\(597\) 2.33240 0.0954588
\(598\) −0.0757005 −0.00309562
\(599\) 37.8168 1.54515 0.772576 0.634923i \(-0.218968\pi\)
0.772576 + 0.634923i \(0.218968\pi\)
\(600\) 0.469906 0.0191838
\(601\) 28.8899 1.17844 0.589222 0.807971i \(-0.299434\pi\)
0.589222 + 0.807971i \(0.299434\pi\)
\(602\) −1.07066 −0.0436370
\(603\) 7.75831 0.315943
\(604\) −7.24410 −0.294758
\(605\) −17.2227 −0.700200
\(606\) 0.110119 0.00447330
\(607\) 17.6846 0.717794 0.358897 0.933377i \(-0.383153\pi\)
0.358897 + 0.933377i \(0.383153\pi\)
\(608\) 0.0693223 0.00281139
\(609\) −18.4933 −0.749388
\(610\) −1.37704 −0.0557548
\(611\) −1.26010 −0.0509784
\(612\) −3.10131 −0.125363
\(613\) −12.9620 −0.523529 −0.261764 0.965132i \(-0.584304\pi\)
−0.261764 + 0.965132i \(0.584304\pi\)
\(614\) 1.84267 0.0743640
\(615\) −10.2931 −0.415059
\(616\) 0.510405 0.0205648
\(617\) 14.5493 0.585732 0.292866 0.956153i \(-0.405391\pi\)
0.292866 + 0.956153i \(0.405391\pi\)
\(618\) −1.21742 −0.0489718
\(619\) −32.4564 −1.30453 −0.652267 0.757989i \(-0.726182\pi\)
−0.652267 + 0.757989i \(0.726182\pi\)
\(620\) −25.3094 −1.01645
\(621\) −6.12664 −0.245854
\(622\) −1.25655 −0.0503830
\(623\) −17.7717 −0.712008
\(624\) 6.03719 0.241681
\(625\) −12.5899 −0.503598
\(626\) −0.220082 −0.00879626
\(627\) 0.150216 0.00599904
\(628\) −21.9139 −0.874461
\(629\) −1.62483 −0.0647862
\(630\) 0.305209 0.0121598
\(631\) −33.3426 −1.32735 −0.663674 0.748022i \(-0.731004\pi\)
−0.663674 + 0.748022i \(0.731004\pi\)
\(632\) −0.834312 −0.0331872
\(633\) 12.6824 0.504081
\(634\) 0.628464 0.0249595
\(635\) −3.22744 −0.128077
\(636\) 21.3463 0.846438
\(637\) 3.51387 0.139225
\(638\) −0.466125 −0.0184541
\(639\) −11.4311 −0.452207
\(640\) 3.05367 0.120707
\(641\) −4.01316 −0.158510 −0.0792551 0.996854i \(-0.525254\pi\)
−0.0792551 + 0.996854i \(0.525254\pi\)
\(642\) −0.891344 −0.0351785
\(643\) 10.8029 0.426024 0.213012 0.977050i \(-0.431673\pi\)
0.213012 + 0.977050i \(0.431673\pi\)
\(644\) 4.58463 0.180660
\(645\) −20.8407 −0.820601
\(646\) −0.00578799 −0.000227725 0
\(647\) −38.7589 −1.52377 −0.761885 0.647712i \(-0.775726\pi\)
−0.761885 + 0.647712i \(0.775726\pi\)
\(648\) −0.414259 −0.0162736
\(649\) −8.51033 −0.334060
\(650\) −0.123146 −0.00483019
\(651\) −17.5434 −0.687579
\(652\) 42.5498 1.66638
\(653\) −30.5560 −1.19575 −0.597874 0.801590i \(-0.703988\pi\)
−0.597874 + 0.801590i \(0.703988\pi\)
\(654\) 0.637882 0.0249432
\(655\) −0.259869 −0.0101539
\(656\) 19.1092 0.746090
\(657\) −25.9658 −1.01302
\(658\) −0.110210 −0.00429645
\(659\) −0.720343 −0.0280606 −0.0140303 0.999902i \(-0.504466\pi\)
−0.0140303 + 0.999902i \(0.504466\pi\)
\(660\) 4.96399 0.193223
\(661\) −21.2213 −0.825412 −0.412706 0.910864i \(-0.635416\pi\)
−0.412706 + 0.910864i \(0.635416\pi\)
\(662\) −0.946322 −0.0367798
\(663\) −1.51585 −0.0588708
\(664\) 0.182561 0.00708476
\(665\) −0.394428 −0.0152953
\(666\) 0.135506 0.00525074
\(667\) −8.37982 −0.324468
\(668\) −22.8913 −0.885692
\(669\) −3.41348 −0.131973
\(670\) 0.478480 0.0184853
\(671\) 16.6592 0.643120
\(672\) 1.58788 0.0612539
\(673\) −44.1209 −1.70074 −0.850368 0.526188i \(-0.823621\pi\)
−0.850368 + 0.526188i \(0.823621\pi\)
\(674\) −0.805318 −0.0310197
\(675\) −9.96654 −0.383612
\(676\) 22.7914 0.876591
\(677\) 49.1546 1.88916 0.944582 0.328276i \(-0.106468\pi\)
0.944582 + 0.328276i \(0.106468\pi\)
\(678\) 0.496099 0.0190526
\(679\) 13.8576 0.531805
\(680\) −0.382812 −0.0146802
\(681\) −9.47335 −0.363020
\(682\) −0.442181 −0.0169320
\(683\) −46.7356 −1.78829 −0.894144 0.447779i \(-0.852215\pi\)
−0.894144 + 0.447779i \(0.852215\pi\)
\(684\) −0.334246 −0.0127802
\(685\) 6.88006 0.262873
\(686\) 1.07880 0.0411888
\(687\) 6.83905 0.260926
\(688\) 38.6908 1.47507
\(689\) −11.1964 −0.426547
\(690\) −0.128877 −0.00490625
\(691\) 29.7904 1.13328 0.566640 0.823965i \(-0.308243\pi\)
0.566640 + 0.823965i \(0.308243\pi\)
\(692\) 38.1968 1.45203
\(693\) −3.69236 −0.140261
\(694\) 0.476368 0.0180827
\(695\) −15.2593 −0.578818
\(696\) −1.93443 −0.0733245
\(697\) −4.79805 −0.181739
\(698\) −1.48727 −0.0562938
\(699\) −34.4348 −1.30244
\(700\) 7.45806 0.281888
\(701\) −9.77679 −0.369264 −0.184632 0.982808i \(-0.559109\pi\)
−0.184632 + 0.982808i \(0.559109\pi\)
\(702\) 0.370639 0.0139889
\(703\) −0.175117 −0.00660466
\(704\) −9.18895 −0.346322
\(705\) −2.14527 −0.0807955
\(706\) −0.191679 −0.00721394
\(707\) 3.49802 0.131557
\(708\) −17.6463 −0.663189
\(709\) 14.3071 0.537313 0.268656 0.963236i \(-0.413420\pi\)
0.268656 + 0.963236i \(0.413420\pi\)
\(710\) −0.704993 −0.0264579
\(711\) 6.03555 0.226351
\(712\) −1.85895 −0.0696671
\(713\) −7.94936 −0.297706
\(714\) −0.132578 −0.00496162
\(715\) −2.60366 −0.0973714
\(716\) −31.9861 −1.19538
\(717\) −15.5422 −0.580435
\(718\) −0.622978 −0.0232493
\(719\) 33.7718 1.25947 0.629737 0.776808i \(-0.283162\pi\)
0.629737 + 0.776808i \(0.283162\pi\)
\(720\) −11.0294 −0.411042
\(721\) −38.6722 −1.44023
\(722\) 1.01975 0.0379513
\(723\) 17.8574 0.664122
\(724\) −7.64770 −0.284224
\(725\) −13.6319 −0.506276
\(726\) −0.623915 −0.0231556
\(727\) −10.1616 −0.376871 −0.188436 0.982086i \(-0.560342\pi\)
−0.188436 + 0.982086i \(0.560342\pi\)
\(728\) −0.555107 −0.0205736
\(729\) 22.7624 0.843050
\(730\) −1.60140 −0.0592704
\(731\) −9.71471 −0.359312
\(732\) 34.5431 1.27675
\(733\) −2.70369 −0.0998630 −0.0499315 0.998753i \(-0.515900\pi\)
−0.0499315 + 0.998753i \(0.515900\pi\)
\(734\) −0.218219 −0.00805460
\(735\) 5.98220 0.220657
\(736\) 0.719512 0.0265216
\(737\) −5.78855 −0.213224
\(738\) 0.400143 0.0147294
\(739\) 52.3725 1.92655 0.963277 0.268510i \(-0.0865312\pi\)
0.963277 + 0.268510i \(0.0865312\pi\)
\(740\) −5.78686 −0.212729
\(741\) −0.163372 −0.00600161
\(742\) −0.979249 −0.0359494
\(743\) −7.72560 −0.283425 −0.141712 0.989908i \(-0.545261\pi\)
−0.141712 + 0.989908i \(0.545261\pi\)
\(744\) −1.83506 −0.0672767
\(745\) −0.694183 −0.0254329
\(746\) 1.24902 0.0457299
\(747\) −1.32068 −0.0483211
\(748\) 2.31392 0.0846054
\(749\) −28.3142 −1.03458
\(750\) −0.785699 −0.0286897
\(751\) 8.62146 0.314601 0.157301 0.987551i \(-0.449721\pi\)
0.157301 + 0.987551i \(0.449721\pi\)
\(752\) 3.98270 0.145234
\(753\) 15.8921 0.579140
\(754\) 0.506949 0.0184620
\(755\) 6.46864 0.235418
\(756\) −22.4469 −0.816386
\(757\) −10.8630 −0.394823 −0.197411 0.980321i \(-0.563254\pi\)
−0.197411 + 0.980321i \(0.563254\pi\)
\(758\) 1.37393 0.0499035
\(759\) 1.55912 0.0565926
\(760\) −0.0412578 −0.00149658
\(761\) −42.8962 −1.55499 −0.777493 0.628892i \(-0.783509\pi\)
−0.777493 + 0.628892i \(0.783509\pi\)
\(762\) −0.116919 −0.00423551
\(763\) 20.2628 0.733562
\(764\) 7.84245 0.283730
\(765\) 2.76933 0.100125
\(766\) −0.707606 −0.0255669
\(767\) 9.25566 0.334202
\(768\) −18.9703 −0.684533
\(769\) 33.4014 1.20448 0.602242 0.798314i \(-0.294274\pi\)
0.602242 + 0.798314i \(0.294274\pi\)
\(770\) −0.227720 −0.00820645
\(771\) 30.5394 1.09985
\(772\) 8.91947 0.321019
\(773\) −26.4878 −0.952701 −0.476350 0.879256i \(-0.658041\pi\)
−0.476350 + 0.879256i \(0.658041\pi\)
\(774\) 0.810177 0.0291212
\(775\) −12.9317 −0.464519
\(776\) 1.44952 0.0520349
\(777\) −4.01119 −0.143901
\(778\) −0.636596 −0.0228231
\(779\) −0.517113 −0.0185275
\(780\) −5.39873 −0.193306
\(781\) 8.52885 0.305186
\(782\) −0.0600748 −0.00214827
\(783\) 41.0287 1.46625
\(784\) −11.1060 −0.396642
\(785\) 19.5681 0.698416
\(786\) −0.00941413 −0.000335791 0
\(787\) 6.28921 0.224186 0.112093 0.993698i \(-0.464245\pi\)
0.112093 + 0.993698i \(0.464245\pi\)
\(788\) −49.3524 −1.75810
\(789\) 6.84544 0.243704
\(790\) 0.372232 0.0132434
\(791\) 15.7589 0.560323
\(792\) −0.386226 −0.0137240
\(793\) −18.1182 −0.643395
\(794\) 0.711265 0.0252418
\(795\) −19.0613 −0.676034
\(796\) 3.87219 0.137246
\(797\) −25.5794 −0.906067 −0.453034 0.891493i \(-0.649658\pi\)
−0.453034 + 0.891493i \(0.649658\pi\)
\(798\) −0.0142887 −0.000505815 0
\(799\) −1.00000 −0.0353775
\(800\) 1.17047 0.0413823
\(801\) 13.4479 0.475160
\(802\) 0.609407 0.0215189
\(803\) 19.3734 0.683672
\(804\) −12.0027 −0.423301
\(805\) −4.09386 −0.144290
\(806\) 0.480907 0.0169392
\(807\) −27.3584 −0.963062
\(808\) 0.365899 0.0128723
\(809\) 1.79712 0.0631834 0.0315917 0.999501i \(-0.489942\pi\)
0.0315917 + 0.999501i \(0.489942\pi\)
\(810\) 0.184824 0.00649404
\(811\) 20.1649 0.708085 0.354042 0.935229i \(-0.384807\pi\)
0.354042 + 0.935229i \(0.384807\pi\)
\(812\) −30.7022 −1.07743
\(813\) 2.72713 0.0956446
\(814\) −0.101102 −0.00354363
\(815\) −37.9950 −1.33091
\(816\) 4.79102 0.167719
\(817\) −1.04701 −0.0366302
\(818\) −0.788026 −0.0275527
\(819\) 4.01573 0.140321
\(820\) −17.0884 −0.596751
\(821\) −17.1159 −0.597347 −0.298674 0.954355i \(-0.596544\pi\)
−0.298674 + 0.954355i \(0.596544\pi\)
\(822\) 0.249240 0.00869323
\(823\) −0.855836 −0.0298326 −0.0149163 0.999889i \(-0.504748\pi\)
−0.0149163 + 0.999889i \(0.504748\pi\)
\(824\) −4.04518 −0.140920
\(825\) 2.53631 0.0883029
\(826\) 0.809513 0.0281665
\(827\) 14.6203 0.508398 0.254199 0.967152i \(-0.418188\pi\)
0.254199 + 0.967152i \(0.418188\pi\)
\(828\) −3.46921 −0.120563
\(829\) 39.2278 1.36244 0.681219 0.732080i \(-0.261450\pi\)
0.681219 + 0.732080i \(0.261450\pi\)
\(830\) −0.0814506 −0.00282719
\(831\) 18.3501 0.636557
\(832\) 9.99372 0.346470
\(833\) 2.78855 0.0966176
\(834\) −0.552790 −0.0191415
\(835\) 20.4409 0.707386
\(836\) 0.249384 0.00862513
\(837\) 38.9211 1.34531
\(838\) 1.46051 0.0504526
\(839\) −24.1087 −0.832324 −0.416162 0.909290i \(-0.636625\pi\)
−0.416162 + 0.909290i \(0.636625\pi\)
\(840\) −0.945043 −0.0326071
\(841\) 27.1177 0.935093
\(842\) −1.67352 −0.0576733
\(843\) −20.9156 −0.720372
\(844\) 21.0550 0.724744
\(845\) −20.3516 −0.700117
\(846\) 0.0833969 0.00286724
\(847\) −19.8191 −0.680992
\(848\) 35.3874 1.21521
\(849\) 18.8621 0.647347
\(850\) −0.0977269 −0.00335200
\(851\) −1.81758 −0.0623057
\(852\) 17.6847 0.605869
\(853\) −19.2066 −0.657622 −0.328811 0.944396i \(-0.606648\pi\)
−0.328811 + 0.944396i \(0.606648\pi\)
\(854\) −1.58464 −0.0542253
\(855\) 0.298466 0.0102073
\(856\) −2.96171 −0.101229
\(857\) 2.55045 0.0871218 0.0435609 0.999051i \(-0.486130\pi\)
0.0435609 + 0.999051i \(0.486130\pi\)
\(858\) −0.0943212 −0.00322007
\(859\) −14.5411 −0.496136 −0.248068 0.968743i \(-0.579796\pi\)
−0.248068 + 0.968743i \(0.579796\pi\)
\(860\) −34.5991 −1.17982
\(861\) −11.8449 −0.403672
\(862\) 1.38556 0.0471925
\(863\) −29.2219 −0.994726 −0.497363 0.867543i \(-0.665698\pi\)
−0.497363 + 0.867543i \(0.665698\pi\)
\(864\) −3.52282 −0.119849
\(865\) −34.1080 −1.15971
\(866\) 0.946493 0.0321631
\(867\) −1.20296 −0.0408545
\(868\) −29.1250 −0.988568
\(869\) −4.50319 −0.152760
\(870\) 0.863056 0.0292604
\(871\) 6.29551 0.213315
\(872\) 2.11952 0.0717760
\(873\) −10.4861 −0.354901
\(874\) −0.00647459 −0.000219006 0
\(875\) −24.9583 −0.843744
\(876\) 40.1711 1.35725
\(877\) −20.9049 −0.705909 −0.352955 0.935640i \(-0.614823\pi\)
−0.352955 + 0.935640i \(0.614823\pi\)
\(878\) −1.21450 −0.0409873
\(879\) 10.0448 0.338802
\(880\) 8.22916 0.277405
\(881\) 37.6761 1.26934 0.634670 0.772783i \(-0.281136\pi\)
0.634670 + 0.772783i \(0.281136\pi\)
\(882\) −0.232557 −0.00783059
\(883\) 28.2157 0.949532 0.474766 0.880112i \(-0.342533\pi\)
0.474766 + 0.880112i \(0.342533\pi\)
\(884\) −2.51658 −0.0846416
\(885\) 15.7573 0.529677
\(886\) 0.0944460 0.00317298
\(887\) 22.1836 0.744851 0.372426 0.928062i \(-0.378526\pi\)
0.372426 + 0.928062i \(0.378526\pi\)
\(888\) −0.419577 −0.0140801
\(889\) −3.71400 −0.124564
\(890\) 0.829379 0.0278008
\(891\) −2.23596 −0.0749074
\(892\) −5.66697 −0.189744
\(893\) −0.107776 −0.00360657
\(894\) −0.0251477 −0.000841066 0
\(895\) 28.5621 0.954726
\(896\) 3.51403 0.117396
\(897\) −1.69567 −0.0566168
\(898\) −0.169023 −0.00564036
\(899\) 53.2350 1.77549
\(900\) −5.64355 −0.188118
\(901\) −8.88526 −0.296011
\(902\) −0.298551 −0.00994065
\(903\) −23.9826 −0.798090
\(904\) 1.64841 0.0548253
\(905\) 6.82904 0.227005
\(906\) 0.234336 0.00778528
\(907\) −8.38001 −0.278254 −0.139127 0.990275i \(-0.544430\pi\)
−0.139127 + 0.990275i \(0.544430\pi\)
\(908\) −15.7274 −0.521932
\(909\) −2.64697 −0.0877945
\(910\) 0.247663 0.00820996
\(911\) −33.6818 −1.11593 −0.557964 0.829865i \(-0.688417\pi\)
−0.557964 + 0.829865i \(0.688417\pi\)
\(912\) 0.516355 0.0170982
\(913\) 0.985373 0.0326111
\(914\) 1.21065 0.0400447
\(915\) −30.8453 −1.01972
\(916\) 11.3540 0.375147
\(917\) −0.299047 −0.00987539
\(918\) 0.294134 0.00970786
\(919\) −38.7034 −1.27671 −0.638353 0.769744i \(-0.720384\pi\)
−0.638353 + 0.769744i \(0.720384\pi\)
\(920\) −0.428224 −0.0141181
\(921\) 41.2752 1.36007
\(922\) −0.265584 −0.00874655
\(923\) −9.27581 −0.305317
\(924\) 5.71234 0.187922
\(925\) −2.95675 −0.0972173
\(926\) −0.436479 −0.0143436
\(927\) 29.2635 0.961138
\(928\) −4.81840 −0.158172
\(929\) −3.15067 −0.103370 −0.0516851 0.998663i \(-0.516459\pi\)
−0.0516851 + 0.998663i \(0.516459\pi\)
\(930\) 0.818722 0.0268470
\(931\) 0.300538 0.00984973
\(932\) −57.1677 −1.87259
\(933\) −28.1463 −0.921469
\(934\) −2.04546 −0.0669295
\(935\) −2.06622 −0.0675728
\(936\) 0.420052 0.0137298
\(937\) −9.19856 −0.300504 −0.150252 0.988648i \(-0.548008\pi\)
−0.150252 + 0.988648i \(0.548008\pi\)
\(938\) 0.550614 0.0179782
\(939\) −4.92978 −0.160877
\(940\) −3.56152 −0.116164
\(941\) 16.6310 0.542154 0.271077 0.962558i \(-0.412620\pi\)
0.271077 + 0.962558i \(0.412620\pi\)
\(942\) 0.708882 0.0230966
\(943\) −5.36723 −0.174781
\(944\) −29.2536 −0.952122
\(945\) 20.0440 0.652033
\(946\) −0.604481 −0.0196534
\(947\) −48.6626 −1.58132 −0.790660 0.612255i \(-0.790263\pi\)
−0.790660 + 0.612255i \(0.790263\pi\)
\(948\) −9.33744 −0.303266
\(949\) −21.0701 −0.683965
\(950\) −0.0105326 −0.000341722 0
\(951\) 14.0774 0.456492
\(952\) −0.440524 −0.0142775
\(953\) −17.4665 −0.565796 −0.282898 0.959150i \(-0.591296\pi\)
−0.282898 + 0.959150i \(0.591296\pi\)
\(954\) 0.741003 0.0239909
\(955\) −7.00295 −0.226610
\(956\) −25.8028 −0.834521
\(957\) −10.4411 −0.337512
\(958\) −0.638527 −0.0206299
\(959\) 7.91727 0.255662
\(960\) 17.0138 0.549119
\(961\) 19.5004 0.629044
\(962\) 0.109957 0.00354515
\(963\) 21.4255 0.690426
\(964\) 29.6463 0.954843
\(965\) −7.96467 −0.256392
\(966\) −0.148306 −0.00477166
\(967\) 25.9162 0.833407 0.416704 0.909042i \(-0.363185\pi\)
0.416704 + 0.909042i \(0.363185\pi\)
\(968\) −2.07311 −0.0666322
\(969\) −0.129649 −0.00416493
\(970\) −0.646712 −0.0207647
\(971\) −29.2187 −0.937674 −0.468837 0.883285i \(-0.655327\pi\)
−0.468837 + 0.883285i \(0.655327\pi\)
\(972\) 28.1779 0.903807
\(973\) −17.5598 −0.562940
\(974\) 0.215341 0.00689998
\(975\) −2.75844 −0.0883407
\(976\) 57.2645 1.83299
\(977\) −11.7352 −0.375443 −0.187721 0.982222i \(-0.560110\pi\)
−0.187721 + 0.982222i \(0.560110\pi\)
\(978\) −1.37642 −0.0440131
\(979\) −10.0337 −0.320677
\(980\) 9.93149 0.317250
\(981\) −15.3329 −0.489543
\(982\) −1.66458 −0.0531189
\(983\) −24.2313 −0.772860 −0.386430 0.922319i \(-0.626292\pi\)
−0.386430 + 0.922319i \(0.626292\pi\)
\(984\) −1.23899 −0.0394977
\(985\) 44.0694 1.40417
\(986\) 0.402307 0.0128121
\(987\) −2.46868 −0.0785791
\(988\) −0.271225 −0.00862883
\(989\) −10.8671 −0.345555
\(990\) 0.172317 0.00547658
\(991\) 28.2402 0.897080 0.448540 0.893763i \(-0.351944\pi\)
0.448540 + 0.893763i \(0.351944\pi\)
\(992\) −4.57088 −0.145126
\(993\) −21.1973 −0.672677
\(994\) −0.811275 −0.0257321
\(995\) −3.45768 −0.109616
\(996\) 2.04319 0.0647408
\(997\) 6.34163 0.200842 0.100421 0.994945i \(-0.467981\pi\)
0.100421 + 0.994945i \(0.467981\pi\)
\(998\) 1.97082 0.0623853
\(999\) 8.89908 0.281555
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 799.2.a.g.1.10 20
3.2 odd 2 7191.2.a.bb.1.11 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.2.a.g.1.10 20 1.1 even 1 trivial
7191.2.a.bb.1.11 20 3.2 odd 2