Properties

Label 2001.2.a.n.1.6
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $0$
Dimension $16$
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] = [2001,2,Mod(1,2001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, 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("2001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.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: \(15.9780654445\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + 5778 x^{8} - 5124 x^{7} - 9405 x^{6} + 8288 x^{5} + 6405 x^{4} - 6032 x^{3} + \cdots - 192 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.40306\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.40306 q^{2} +1.00000 q^{3} -0.0314276 q^{4} +1.13298 q^{5} -1.40306 q^{6} -1.90949 q^{7} +2.85021 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.40306 q^{2} +1.00000 q^{3} -0.0314276 q^{4} +1.13298 q^{5} -1.40306 q^{6} -1.90949 q^{7} +2.85021 q^{8} +1.00000 q^{9} -1.58963 q^{10} +5.04448 q^{11} -0.0314276 q^{12} +3.78403 q^{13} +2.67912 q^{14} +1.13298 q^{15} -3.93616 q^{16} +7.36033 q^{17} -1.40306 q^{18} -0.713891 q^{19} -0.0356067 q^{20} -1.90949 q^{21} -7.07770 q^{22} -1.00000 q^{23} +2.85021 q^{24} -3.71636 q^{25} -5.30922 q^{26} +1.00000 q^{27} +0.0600106 q^{28} -1.00000 q^{29} -1.58963 q^{30} +4.34024 q^{31} -0.177765 q^{32} +5.04448 q^{33} -10.3270 q^{34} -2.16340 q^{35} -0.0314276 q^{36} +7.55271 q^{37} +1.00163 q^{38} +3.78403 q^{39} +3.22922 q^{40} -10.0365 q^{41} +2.67912 q^{42} -12.7870 q^{43} -0.158536 q^{44} +1.13298 q^{45} +1.40306 q^{46} -1.16858 q^{47} -3.93616 q^{48} -3.35386 q^{49} +5.21428 q^{50} +7.36033 q^{51} -0.118923 q^{52} -4.59897 q^{53} -1.40306 q^{54} +5.71528 q^{55} -5.44244 q^{56} -0.713891 q^{57} +1.40306 q^{58} +4.46982 q^{59} -0.0356067 q^{60} -1.01012 q^{61} -6.08960 q^{62} -1.90949 q^{63} +8.12173 q^{64} +4.28722 q^{65} -7.07770 q^{66} +16.2568 q^{67} -0.231317 q^{68} -1.00000 q^{69} +3.03538 q^{70} +13.7025 q^{71} +2.85021 q^{72} +14.2596 q^{73} -10.5969 q^{74} -3.71636 q^{75} +0.0224359 q^{76} -9.63238 q^{77} -5.30922 q^{78} -0.947565 q^{79} -4.45957 q^{80} +1.00000 q^{81} +14.0818 q^{82} +11.2596 q^{83} +0.0600106 q^{84} +8.33908 q^{85} +17.9409 q^{86} -1.00000 q^{87} +14.3778 q^{88} -9.66768 q^{89} -1.58963 q^{90} -7.22556 q^{91} +0.0314276 q^{92} +4.34024 q^{93} +1.63959 q^{94} -0.808822 q^{95} -0.177765 q^{96} -3.19378 q^{97} +4.70566 q^{98} +5.04448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40306 −0.992112 −0.496056 0.868291i \(-0.665219\pi\)
−0.496056 + 0.868291i \(0.665219\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.0314276 −0.0157138
\(5\) 1.13298 0.506683 0.253341 0.967377i \(-0.418470\pi\)
0.253341 + 0.967377i \(0.418470\pi\)
\(6\) −1.40306 −0.572796
\(7\) −1.90949 −0.721718 −0.360859 0.932620i \(-0.617517\pi\)
−0.360859 + 0.932620i \(0.617517\pi\)
\(8\) 2.85021 1.00770
\(9\) 1.00000 0.333333
\(10\) −1.58963 −0.502686
\(11\) 5.04448 1.52097 0.760484 0.649356i \(-0.224962\pi\)
0.760484 + 0.649356i \(0.224962\pi\)
\(12\) −0.0314276 −0.00907236
\(13\) 3.78403 1.04950 0.524751 0.851256i \(-0.324159\pi\)
0.524751 + 0.851256i \(0.324159\pi\)
\(14\) 2.67912 0.716025
\(15\) 1.13298 0.292533
\(16\) −3.93616 −0.984039
\(17\) 7.36033 1.78514 0.892571 0.450907i \(-0.148899\pi\)
0.892571 + 0.450907i \(0.148899\pi\)
\(18\) −1.40306 −0.330704
\(19\) −0.713891 −0.163778 −0.0818889 0.996641i \(-0.526095\pi\)
−0.0818889 + 0.996641i \(0.526095\pi\)
\(20\) −0.0356067 −0.00796190
\(21\) −1.90949 −0.416684
\(22\) −7.07770 −1.50897
\(23\) −1.00000 −0.208514
\(24\) 2.85021 0.581797
\(25\) −3.71636 −0.743273
\(26\) −5.30922 −1.04122
\(27\) 1.00000 0.192450
\(28\) 0.0600106 0.0113409
\(29\) −1.00000 −0.185695
\(30\) −1.58963 −0.290226
\(31\) 4.34024 0.779529 0.389765 0.920914i \(-0.372556\pi\)
0.389765 + 0.920914i \(0.372556\pi\)
\(32\) −0.177765 −0.0314247
\(33\) 5.04448 0.878132
\(34\) −10.3270 −1.77106
\(35\) −2.16340 −0.365682
\(36\) −0.0314276 −0.00523793
\(37\) 7.55271 1.24166 0.620829 0.783946i \(-0.286796\pi\)
0.620829 + 0.783946i \(0.286796\pi\)
\(38\) 1.00163 0.162486
\(39\) 3.78403 0.605930
\(40\) 3.22922 0.510585
\(41\) −10.0365 −1.56743 −0.783717 0.621118i \(-0.786679\pi\)
−0.783717 + 0.621118i \(0.786679\pi\)
\(42\) 2.67912 0.413397
\(43\) −12.7870 −1.95000 −0.974998 0.222215i \(-0.928671\pi\)
−0.974998 + 0.222215i \(0.928671\pi\)
\(44\) −0.158536 −0.0239002
\(45\) 1.13298 0.168894
\(46\) 1.40306 0.206870
\(47\) −1.16858 −0.170455 −0.0852277 0.996362i \(-0.527162\pi\)
−0.0852277 + 0.996362i \(0.527162\pi\)
\(48\) −3.93616 −0.568135
\(49\) −3.35386 −0.479123
\(50\) 5.21428 0.737410
\(51\) 7.36033 1.03065
\(52\) −0.118923 −0.0164916
\(53\) −4.59897 −0.631717 −0.315859 0.948806i \(-0.602292\pi\)
−0.315859 + 0.948806i \(0.602292\pi\)
\(54\) −1.40306 −0.190932
\(55\) 5.71528 0.770648
\(56\) −5.44244 −0.727277
\(57\) −0.713891 −0.0945572
\(58\) 1.40306 0.184231
\(59\) 4.46982 0.581921 0.290960 0.956735i \(-0.406025\pi\)
0.290960 + 0.956735i \(0.406025\pi\)
\(60\) −0.0356067 −0.00459681
\(61\) −1.01012 −0.129332 −0.0646662 0.997907i \(-0.520598\pi\)
−0.0646662 + 0.997907i \(0.520598\pi\)
\(62\) −6.08960 −0.773380
\(63\) −1.90949 −0.240573
\(64\) 8.12173 1.01522
\(65\) 4.28722 0.531764
\(66\) −7.07770 −0.871205
\(67\) 16.2568 1.98608 0.993041 0.117771i \(-0.0375749\pi\)
0.993041 + 0.117771i \(0.0375749\pi\)
\(68\) −0.231317 −0.0280513
\(69\) −1.00000 −0.120386
\(70\) 3.03538 0.362798
\(71\) 13.7025 1.62619 0.813096 0.582129i \(-0.197780\pi\)
0.813096 + 0.582129i \(0.197780\pi\)
\(72\) 2.85021 0.335901
\(73\) 14.2596 1.66896 0.834481 0.551037i \(-0.185768\pi\)
0.834481 + 0.551037i \(0.185768\pi\)
\(74\) −10.5969 −1.23186
\(75\) −3.71636 −0.429129
\(76\) 0.0224359 0.00257357
\(77\) −9.63238 −1.09771
\(78\) −5.30922 −0.601150
\(79\) −0.947565 −0.106609 −0.0533047 0.998578i \(-0.516975\pi\)
−0.0533047 + 0.998578i \(0.516975\pi\)
\(80\) −4.45957 −0.498596
\(81\) 1.00000 0.111111
\(82\) 14.0818 1.55507
\(83\) 11.2596 1.23591 0.617953 0.786215i \(-0.287962\pi\)
0.617953 + 0.786215i \(0.287962\pi\)
\(84\) 0.0600106 0.00654769
\(85\) 8.33908 0.904500
\(86\) 17.9409 1.93461
\(87\) −1.00000 −0.107211
\(88\) 14.3778 1.53268
\(89\) −9.66768 −1.02477 −0.512386 0.858755i \(-0.671238\pi\)
−0.512386 + 0.858755i \(0.671238\pi\)
\(90\) −1.58963 −0.167562
\(91\) −7.22556 −0.757444
\(92\) 0.0314276 0.00327655
\(93\) 4.34024 0.450062
\(94\) 1.63959 0.169111
\(95\) −0.808822 −0.0829834
\(96\) −0.177765 −0.0181430
\(97\) −3.19378 −0.324279 −0.162139 0.986768i \(-0.551839\pi\)
−0.162139 + 0.986768i \(0.551839\pi\)
\(98\) 4.70566 0.475343
\(99\) 5.04448 0.506990
\(100\) 0.116796 0.0116796
\(101\) −1.42381 −0.141674 −0.0708372 0.997488i \(-0.522567\pi\)
−0.0708372 + 0.997488i \(0.522567\pi\)
\(102\) −10.3270 −1.02252
\(103\) −4.14252 −0.408175 −0.204087 0.978953i \(-0.565423\pi\)
−0.204087 + 0.978953i \(0.565423\pi\)
\(104\) 10.7853 1.05758
\(105\) −2.16340 −0.211127
\(106\) 6.45262 0.626734
\(107\) 0.700112 0.0676823 0.0338412 0.999427i \(-0.489226\pi\)
0.0338412 + 0.999427i \(0.489226\pi\)
\(108\) −0.0314276 −0.00302412
\(109\) 9.22855 0.883935 0.441968 0.897031i \(-0.354281\pi\)
0.441968 + 0.897031i \(0.354281\pi\)
\(110\) −8.01887 −0.764569
\(111\) 7.55271 0.716872
\(112\) 7.51604 0.710199
\(113\) −20.1001 −1.89086 −0.945429 0.325829i \(-0.894357\pi\)
−0.945429 + 0.325829i \(0.894357\pi\)
\(114\) 1.00163 0.0938113
\(115\) −1.13298 −0.105651
\(116\) 0.0314276 0.00291798
\(117\) 3.78403 0.349834
\(118\) −6.27141 −0.577330
\(119\) −14.0545 −1.28837
\(120\) 3.22922 0.294786
\(121\) 14.4468 1.31335
\(122\) 1.41725 0.128312
\(123\) −10.0365 −0.904958
\(124\) −0.136403 −0.0122494
\(125\) −9.87544 −0.883286
\(126\) 2.67912 0.238675
\(127\) 2.50338 0.222139 0.111069 0.993813i \(-0.464572\pi\)
0.111069 + 0.993813i \(0.464572\pi\)
\(128\) −11.0397 −0.975783
\(129\) −12.7870 −1.12583
\(130\) −6.01522 −0.527569
\(131\) −5.46381 −0.477375 −0.238688 0.971096i \(-0.576717\pi\)
−0.238688 + 0.971096i \(0.576717\pi\)
\(132\) −0.158536 −0.0137988
\(133\) 1.36317 0.118202
\(134\) −22.8092 −1.97042
\(135\) 1.13298 0.0975111
\(136\) 20.9785 1.79889
\(137\) 11.6644 0.996560 0.498280 0.867016i \(-0.333965\pi\)
0.498280 + 0.867016i \(0.333965\pi\)
\(138\) 1.40306 0.119436
\(139\) 10.1861 0.863970 0.431985 0.901881i \(-0.357813\pi\)
0.431985 + 0.901881i \(0.357813\pi\)
\(140\) 0.0679906 0.00574625
\(141\) −1.16858 −0.0984125
\(142\) −19.2255 −1.61337
\(143\) 19.0885 1.59626
\(144\) −3.93616 −0.328013
\(145\) −1.13298 −0.0940886
\(146\) −20.0071 −1.65580
\(147\) −3.35386 −0.276622
\(148\) −0.237363 −0.0195112
\(149\) −3.54639 −0.290532 −0.145266 0.989393i \(-0.546404\pi\)
−0.145266 + 0.989393i \(0.546404\pi\)
\(150\) 5.21428 0.425744
\(151\) 9.02885 0.734758 0.367379 0.930071i \(-0.380255\pi\)
0.367379 + 0.930071i \(0.380255\pi\)
\(152\) −2.03474 −0.165039
\(153\) 7.36033 0.595047
\(154\) 13.5148 1.08905
\(155\) 4.91739 0.394974
\(156\) −0.118923 −0.00952146
\(157\) −16.9807 −1.35521 −0.677605 0.735426i \(-0.736982\pi\)
−0.677605 + 0.735426i \(0.736982\pi\)
\(158\) 1.32949 0.105768
\(159\) −4.59897 −0.364722
\(160\) −0.201403 −0.0159223
\(161\) 1.90949 0.150489
\(162\) −1.40306 −0.110235
\(163\) 7.63708 0.598182 0.299091 0.954225i \(-0.403317\pi\)
0.299091 + 0.954225i \(0.403317\pi\)
\(164\) 0.315422 0.0246303
\(165\) 5.71528 0.444934
\(166\) −15.7979 −1.22616
\(167\) 9.37125 0.725169 0.362585 0.931951i \(-0.381894\pi\)
0.362585 + 0.931951i \(0.381894\pi\)
\(168\) −5.44244 −0.419894
\(169\) 1.31889 0.101453
\(170\) −11.7002 −0.897366
\(171\) −0.713891 −0.0545926
\(172\) 0.401864 0.0306418
\(173\) 14.5789 1.10841 0.554205 0.832380i \(-0.313022\pi\)
0.554205 + 0.832380i \(0.313022\pi\)
\(174\) 1.40306 0.106366
\(175\) 7.09635 0.536434
\(176\) −19.8559 −1.49669
\(177\) 4.46982 0.335972
\(178\) 13.5643 1.01669
\(179\) 1.72578 0.128991 0.0644954 0.997918i \(-0.479456\pi\)
0.0644954 + 0.997918i \(0.479456\pi\)
\(180\) −0.0356067 −0.00265397
\(181\) −12.1091 −0.900066 −0.450033 0.893012i \(-0.648588\pi\)
−0.450033 + 0.893012i \(0.648588\pi\)
\(182\) 10.1379 0.751470
\(183\) −1.01012 −0.0746701
\(184\) −2.85021 −0.210120
\(185\) 8.55704 0.629126
\(186\) −6.08960 −0.446511
\(187\) 37.1291 2.71515
\(188\) 0.0367257 0.00267850
\(189\) −1.90949 −0.138895
\(190\) 1.13482 0.0823288
\(191\) 18.1357 1.31225 0.656126 0.754651i \(-0.272194\pi\)
0.656126 + 0.754651i \(0.272194\pi\)
\(192\) 8.12173 0.586135
\(193\) −4.56459 −0.328566 −0.164283 0.986413i \(-0.552531\pi\)
−0.164283 + 0.986413i \(0.552531\pi\)
\(194\) 4.48106 0.321721
\(195\) 4.28722 0.307014
\(196\) 0.105404 0.00752883
\(197\) −2.63724 −0.187896 −0.0939479 0.995577i \(-0.529949\pi\)
−0.0939479 + 0.995577i \(0.529949\pi\)
\(198\) −7.07770 −0.502991
\(199\) −21.7181 −1.53955 −0.769777 0.638313i \(-0.779633\pi\)
−0.769777 + 0.638313i \(0.779633\pi\)
\(200\) −10.5924 −0.748997
\(201\) 16.2568 1.14666
\(202\) 1.99769 0.140557
\(203\) 1.90949 0.134020
\(204\) −0.231317 −0.0161955
\(205\) −11.3711 −0.794191
\(206\) 5.81220 0.404955
\(207\) −1.00000 −0.0695048
\(208\) −14.8945 −1.03275
\(209\) −3.60121 −0.249101
\(210\) 3.03538 0.209461
\(211\) 13.5636 0.933758 0.466879 0.884321i \(-0.345378\pi\)
0.466879 + 0.884321i \(0.345378\pi\)
\(212\) 0.144534 0.00992667
\(213\) 13.7025 0.938883
\(214\) −0.982297 −0.0671485
\(215\) −14.4873 −0.988029
\(216\) 2.85021 0.193932
\(217\) −8.28763 −0.562601
\(218\) −12.9482 −0.876963
\(219\) 14.2596 0.963576
\(220\) −0.179617 −0.0121098
\(221\) 27.8517 1.87351
\(222\) −10.5969 −0.711217
\(223\) 9.70226 0.649711 0.324856 0.945764i \(-0.394684\pi\)
0.324856 + 0.945764i \(0.394684\pi\)
\(224\) 0.339439 0.0226798
\(225\) −3.71636 −0.247758
\(226\) 28.2016 1.87594
\(227\) −20.8423 −1.38335 −0.691676 0.722208i \(-0.743127\pi\)
−0.691676 + 0.722208i \(0.743127\pi\)
\(228\) 0.0224359 0.00148585
\(229\) 11.7579 0.776984 0.388492 0.921452i \(-0.372996\pi\)
0.388492 + 0.921452i \(0.372996\pi\)
\(230\) 1.58963 0.104817
\(231\) −9.63238 −0.633764
\(232\) −2.85021 −0.187126
\(233\) −0.963016 −0.0630893 −0.0315446 0.999502i \(-0.510043\pi\)
−0.0315446 + 0.999502i \(0.510043\pi\)
\(234\) −5.30922 −0.347074
\(235\) −1.32398 −0.0863668
\(236\) −0.140476 −0.00914418
\(237\) −0.947565 −0.0615510
\(238\) 19.7192 1.27821
\(239\) −28.8074 −1.86339 −0.931697 0.363237i \(-0.881672\pi\)
−0.931697 + 0.363237i \(0.881672\pi\)
\(240\) −4.45957 −0.287864
\(241\) 11.7498 0.756869 0.378435 0.925628i \(-0.376462\pi\)
0.378435 + 0.925628i \(0.376462\pi\)
\(242\) −20.2697 −1.30299
\(243\) 1.00000 0.0641500
\(244\) 0.0317456 0.00203230
\(245\) −3.79984 −0.242763
\(246\) 14.0818 0.897820
\(247\) −2.70139 −0.171885
\(248\) 12.3706 0.785533
\(249\) 11.2596 0.713551
\(250\) 13.8558 0.876319
\(251\) 15.1439 0.955872 0.477936 0.878395i \(-0.341385\pi\)
0.477936 + 0.878395i \(0.341385\pi\)
\(252\) 0.0600106 0.00378031
\(253\) −5.04448 −0.317144
\(254\) −3.51238 −0.220387
\(255\) 8.33908 0.522213
\(256\) −0.754075 −0.0471297
\(257\) −7.48604 −0.466966 −0.233483 0.972361i \(-0.575012\pi\)
−0.233483 + 0.972361i \(0.575012\pi\)
\(258\) 17.9409 1.11695
\(259\) −14.4218 −0.896127
\(260\) −0.134737 −0.00835603
\(261\) −1.00000 −0.0618984
\(262\) 7.66604 0.473609
\(263\) −0.748198 −0.0461359 −0.0230679 0.999734i \(-0.507343\pi\)
−0.0230679 + 0.999734i \(0.507343\pi\)
\(264\) 14.3778 0.884895
\(265\) −5.21052 −0.320080
\(266\) −1.91260 −0.117269
\(267\) −9.66768 −0.591653
\(268\) −0.510911 −0.0312089
\(269\) 5.29003 0.322539 0.161269 0.986910i \(-0.448441\pi\)
0.161269 + 0.986910i \(0.448441\pi\)
\(270\) −1.58963 −0.0967419
\(271\) 25.5087 1.54954 0.774771 0.632242i \(-0.217865\pi\)
0.774771 + 0.632242i \(0.217865\pi\)
\(272\) −28.9714 −1.75665
\(273\) −7.22556 −0.437311
\(274\) −16.3659 −0.988699
\(275\) −18.7471 −1.13049
\(276\) 0.0314276 0.00189172
\(277\) −11.7482 −0.705884 −0.352942 0.935645i \(-0.614819\pi\)
−0.352942 + 0.935645i \(0.614819\pi\)
\(278\) −14.2916 −0.857155
\(279\) 4.34024 0.259843
\(280\) −6.16616 −0.368498
\(281\) −12.3525 −0.736890 −0.368445 0.929650i \(-0.620110\pi\)
−0.368445 + 0.929650i \(0.620110\pi\)
\(282\) 1.63959 0.0976362
\(283\) 7.72479 0.459191 0.229596 0.973286i \(-0.426260\pi\)
0.229596 + 0.973286i \(0.426260\pi\)
\(284\) −0.430638 −0.0255537
\(285\) −0.808822 −0.0479105
\(286\) −26.7822 −1.58367
\(287\) 19.1645 1.13125
\(288\) −0.177765 −0.0104749
\(289\) 37.1744 2.18673
\(290\) 1.58963 0.0933464
\(291\) −3.19378 −0.187223
\(292\) −0.448145 −0.0262257
\(293\) 19.8822 1.16153 0.580765 0.814071i \(-0.302754\pi\)
0.580765 + 0.814071i \(0.302754\pi\)
\(294\) 4.70566 0.274440
\(295\) 5.06420 0.294849
\(296\) 21.5268 1.25122
\(297\) 5.04448 0.292711
\(298\) 4.97579 0.288240
\(299\) −3.78403 −0.218836
\(300\) 0.116796 0.00674324
\(301\) 24.4166 1.40735
\(302\) −12.6680 −0.728962
\(303\) −1.42381 −0.0817957
\(304\) 2.80999 0.161164
\(305\) −1.14444 −0.0655304
\(306\) −10.3270 −0.590354
\(307\) −23.7258 −1.35410 −0.677050 0.735937i \(-0.736742\pi\)
−0.677050 + 0.735937i \(0.736742\pi\)
\(308\) 0.302722 0.0172492
\(309\) −4.14252 −0.235660
\(310\) −6.89938 −0.391858
\(311\) 18.1409 1.02868 0.514338 0.857587i \(-0.328038\pi\)
0.514338 + 0.857587i \(0.328038\pi\)
\(312\) 10.7853 0.610597
\(313\) 9.20479 0.520285 0.260143 0.965570i \(-0.416230\pi\)
0.260143 + 0.965570i \(0.416230\pi\)
\(314\) 23.8249 1.34452
\(315\) −2.16340 −0.121894
\(316\) 0.0297797 0.00167524
\(317\) −17.6458 −0.991087 −0.495544 0.868583i \(-0.665031\pi\)
−0.495544 + 0.868583i \(0.665031\pi\)
\(318\) 6.45262 0.361845
\(319\) −5.04448 −0.282437
\(320\) 9.20173 0.514392
\(321\) 0.700112 0.0390764
\(322\) −2.67912 −0.149302
\(323\) −5.25447 −0.292367
\(324\) −0.0314276 −0.00174598
\(325\) −14.0628 −0.780066
\(326\) −10.7153 −0.593464
\(327\) 9.22855 0.510340
\(328\) −28.6061 −1.57951
\(329\) 2.23139 0.123021
\(330\) −8.01887 −0.441424
\(331\) 9.43619 0.518660 0.259330 0.965789i \(-0.416498\pi\)
0.259330 + 0.965789i \(0.416498\pi\)
\(332\) −0.353863 −0.0194208
\(333\) 7.55271 0.413886
\(334\) −13.1484 −0.719449
\(335\) 18.4185 1.00631
\(336\) 7.51604 0.410034
\(337\) 2.46272 0.134153 0.0670765 0.997748i \(-0.478633\pi\)
0.0670765 + 0.997748i \(0.478633\pi\)
\(338\) −1.85048 −0.100653
\(339\) −20.1001 −1.09169
\(340\) −0.262077 −0.0142131
\(341\) 21.8942 1.18564
\(342\) 1.00163 0.0541620
\(343\) 19.7706 1.06751
\(344\) −36.4456 −1.96501
\(345\) −1.13298 −0.0609974
\(346\) −20.4550 −1.09967
\(347\) −13.6465 −0.732581 −0.366291 0.930501i \(-0.619372\pi\)
−0.366291 + 0.930501i \(0.619372\pi\)
\(348\) 0.0314276 0.00168470
\(349\) 35.4897 1.89972 0.949860 0.312677i \(-0.101226\pi\)
0.949860 + 0.312677i \(0.101226\pi\)
\(350\) −9.95659 −0.532202
\(351\) 3.78403 0.201977
\(352\) −0.896731 −0.0477959
\(353\) −24.3193 −1.29439 −0.647194 0.762326i \(-0.724057\pi\)
−0.647194 + 0.762326i \(0.724057\pi\)
\(354\) −6.27141 −0.333322
\(355\) 15.5247 0.823964
\(356\) 0.303832 0.0161031
\(357\) −14.0545 −0.743841
\(358\) −2.42137 −0.127973
\(359\) −25.0671 −1.32299 −0.661496 0.749948i \(-0.730078\pi\)
−0.661496 + 0.749948i \(0.730078\pi\)
\(360\) 3.22922 0.170195
\(361\) −18.4904 −0.973177
\(362\) 16.9898 0.892966
\(363\) 14.4468 0.758261
\(364\) 0.227082 0.0119023
\(365\) 16.1558 0.845634
\(366\) 1.41725 0.0740811
\(367\) 4.93174 0.257435 0.128717 0.991681i \(-0.458914\pi\)
0.128717 + 0.991681i \(0.458914\pi\)
\(368\) 3.93616 0.205186
\(369\) −10.0365 −0.522478
\(370\) −12.0060 −0.624164
\(371\) 8.78167 0.455922
\(372\) −0.136403 −0.00707217
\(373\) −11.4296 −0.591801 −0.295901 0.955219i \(-0.595620\pi\)
−0.295901 + 0.955219i \(0.595620\pi\)
\(374\) −52.0942 −2.69373
\(375\) −9.87544 −0.509965
\(376\) −3.33071 −0.171768
\(377\) −3.78403 −0.194888
\(378\) 2.67912 0.137799
\(379\) 11.1586 0.573181 0.286590 0.958053i \(-0.407478\pi\)
0.286590 + 0.958053i \(0.407478\pi\)
\(380\) 0.0254193 0.00130398
\(381\) 2.50338 0.128252
\(382\) −25.4454 −1.30190
\(383\) −1.36723 −0.0698624 −0.0349312 0.999390i \(-0.511121\pi\)
−0.0349312 + 0.999390i \(0.511121\pi\)
\(384\) −11.0397 −0.563369
\(385\) −10.9133 −0.556191
\(386\) 6.40439 0.325975
\(387\) −12.7870 −0.649999
\(388\) 0.100373 0.00509565
\(389\) 11.2965 0.572755 0.286378 0.958117i \(-0.407549\pi\)
0.286378 + 0.958117i \(0.407549\pi\)
\(390\) −6.01522 −0.304592
\(391\) −7.36033 −0.372228
\(392\) −9.55920 −0.482813
\(393\) −5.46381 −0.275613
\(394\) 3.70021 0.186414
\(395\) −1.07357 −0.0540171
\(396\) −0.158536 −0.00796673
\(397\) 22.7967 1.14413 0.572067 0.820207i \(-0.306142\pi\)
0.572067 + 0.820207i \(0.306142\pi\)
\(398\) 30.4717 1.52741
\(399\) 1.36317 0.0682437
\(400\) 14.6282 0.731410
\(401\) 14.6666 0.732415 0.366207 0.930533i \(-0.380656\pi\)
0.366207 + 0.930533i \(0.380656\pi\)
\(402\) −22.8092 −1.13762
\(403\) 16.4236 0.818117
\(404\) 0.0447469 0.00222624
\(405\) 1.13298 0.0562981
\(406\) −2.67912 −0.132963
\(407\) 38.0995 1.88852
\(408\) 20.9785 1.03859
\(409\) −28.2408 −1.39642 −0.698210 0.715893i \(-0.746020\pi\)
−0.698210 + 0.715893i \(0.746020\pi\)
\(410\) 15.9543 0.787927
\(411\) 11.6644 0.575364
\(412\) 0.130189 0.00641397
\(413\) −8.53506 −0.419983
\(414\) 1.40306 0.0689566
\(415\) 12.7569 0.626212
\(416\) −0.672667 −0.0329802
\(417\) 10.1861 0.498813
\(418\) 5.05271 0.247136
\(419\) 4.68128 0.228696 0.114348 0.993441i \(-0.463522\pi\)
0.114348 + 0.993441i \(0.463522\pi\)
\(420\) 0.0679906 0.00331760
\(421\) −22.7427 −1.10841 −0.554205 0.832380i \(-0.686978\pi\)
−0.554205 + 0.832380i \(0.686978\pi\)
\(422\) −19.0305 −0.926392
\(423\) −1.16858 −0.0568185
\(424\) −13.1080 −0.636582
\(425\) −27.3537 −1.32685
\(426\) −19.2255 −0.931477
\(427\) 1.92881 0.0933415
\(428\) −0.0220028 −0.00106355
\(429\) 19.0885 0.921600
\(430\) 20.3266 0.980235
\(431\) 1.39056 0.0669808 0.0334904 0.999439i \(-0.489338\pi\)
0.0334904 + 0.999439i \(0.489338\pi\)
\(432\) −3.93616 −0.189378
\(433\) −22.3475 −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(434\) 11.6280 0.558163
\(435\) −1.13298 −0.0543221
\(436\) −0.290031 −0.0138900
\(437\) 0.713891 0.0341500
\(438\) −20.0071 −0.955975
\(439\) −30.6009 −1.46050 −0.730251 0.683179i \(-0.760597\pi\)
−0.730251 + 0.683179i \(0.760597\pi\)
\(440\) 16.2898 0.776584
\(441\) −3.35386 −0.159708
\(442\) −39.0776 −1.85873
\(443\) −10.0083 −0.475506 −0.237753 0.971326i \(-0.576411\pi\)
−0.237753 + 0.971326i \(0.576411\pi\)
\(444\) −0.237363 −0.0112648
\(445\) −10.9533 −0.519234
\(446\) −13.6128 −0.644586
\(447\) −3.54639 −0.167739
\(448\) −15.5083 −0.732700
\(449\) −26.4391 −1.24774 −0.623869 0.781529i \(-0.714440\pi\)
−0.623869 + 0.781529i \(0.714440\pi\)
\(450\) 5.21428 0.245803
\(451\) −50.6288 −2.38402
\(452\) 0.631697 0.0297125
\(453\) 9.02885 0.424213
\(454\) 29.2430 1.37244
\(455\) −8.18639 −0.383784
\(456\) −2.03474 −0.0952855
\(457\) −13.9533 −0.652709 −0.326354 0.945248i \(-0.605820\pi\)
−0.326354 + 0.945248i \(0.605820\pi\)
\(458\) −16.4970 −0.770855
\(459\) 7.36033 0.343551
\(460\) 0.0356067 0.00166017
\(461\) −11.7230 −0.545996 −0.272998 0.962015i \(-0.588015\pi\)
−0.272998 + 0.962015i \(0.588015\pi\)
\(462\) 13.5148 0.628765
\(463\) −14.6877 −0.682595 −0.341298 0.939955i \(-0.610866\pi\)
−0.341298 + 0.939955i \(0.610866\pi\)
\(464\) 3.93616 0.182732
\(465\) 4.91739 0.228038
\(466\) 1.35117 0.0625916
\(467\) 25.1197 1.16240 0.581200 0.813761i \(-0.302583\pi\)
0.581200 + 0.813761i \(0.302583\pi\)
\(468\) −0.118923 −0.00549722
\(469\) −31.0421 −1.43339
\(470\) 1.85762 0.0856855
\(471\) −16.9807 −0.782431
\(472\) 12.7399 0.586402
\(473\) −64.5037 −2.96588
\(474\) 1.32949 0.0610654
\(475\) 2.65308 0.121732
\(476\) 0.441698 0.0202452
\(477\) −4.59897 −0.210572
\(478\) 40.4184 1.84870
\(479\) −11.1186 −0.508022 −0.254011 0.967201i \(-0.581750\pi\)
−0.254011 + 0.967201i \(0.581750\pi\)
\(480\) −0.201403 −0.00919276
\(481\) 28.5797 1.30312
\(482\) −16.4856 −0.750899
\(483\) 1.90949 0.0868847
\(484\) −0.454028 −0.0206377
\(485\) −3.61847 −0.164306
\(486\) −1.40306 −0.0636440
\(487\) −31.6400 −1.43374 −0.716872 0.697204i \(-0.754427\pi\)
−0.716872 + 0.697204i \(0.754427\pi\)
\(488\) −2.87905 −0.130328
\(489\) 7.63708 0.345361
\(490\) 5.33140 0.240848
\(491\) 4.47521 0.201963 0.100982 0.994888i \(-0.467802\pi\)
0.100982 + 0.994888i \(0.467802\pi\)
\(492\) 0.315422 0.0142203
\(493\) −7.36033 −0.331493
\(494\) 3.79020 0.170529
\(495\) 5.71528 0.256883
\(496\) −17.0839 −0.767088
\(497\) −26.1648 −1.17365
\(498\) −15.7979 −0.707922
\(499\) −24.9535 −1.11707 −0.558537 0.829480i \(-0.688637\pi\)
−0.558537 + 0.829480i \(0.688637\pi\)
\(500\) 0.310361 0.0138798
\(501\) 9.37125 0.418677
\(502\) −21.2477 −0.948332
\(503\) 27.4289 1.22299 0.611496 0.791247i \(-0.290568\pi\)
0.611496 + 0.791247i \(0.290568\pi\)
\(504\) −5.44244 −0.242426
\(505\) −1.61314 −0.0717839
\(506\) 7.07770 0.314642
\(507\) 1.31889 0.0585739
\(508\) −0.0786751 −0.00349064
\(509\) 7.90743 0.350491 0.175245 0.984525i \(-0.443928\pi\)
0.175245 + 0.984525i \(0.443928\pi\)
\(510\) −11.7002 −0.518094
\(511\) −27.2286 −1.20452
\(512\) 23.1375 1.02254
\(513\) −0.713891 −0.0315191
\(514\) 10.5034 0.463283
\(515\) −4.69338 −0.206815
\(516\) 0.401864 0.0176911
\(517\) −5.89490 −0.259257
\(518\) 20.2346 0.889059
\(519\) 14.5789 0.639941
\(520\) 12.2195 0.535860
\(521\) 24.6282 1.07898 0.539491 0.841992i \(-0.318617\pi\)
0.539491 + 0.841992i \(0.318617\pi\)
\(522\) 1.40306 0.0614102
\(523\) 13.5197 0.591174 0.295587 0.955316i \(-0.404485\pi\)
0.295587 + 0.955316i \(0.404485\pi\)
\(524\) 0.171714 0.00750137
\(525\) 7.09635 0.309710
\(526\) 1.04977 0.0457720
\(527\) 31.9456 1.39157
\(528\) −19.8559 −0.864116
\(529\) 1.00000 0.0434783
\(530\) 7.31067 0.317555
\(531\) 4.46982 0.193974
\(532\) −0.0428410 −0.00185739
\(533\) −37.9783 −1.64502
\(534\) 13.5643 0.586986
\(535\) 0.793210 0.0342935
\(536\) 46.3353 2.00138
\(537\) 1.72578 0.0744728
\(538\) −7.42222 −0.319995
\(539\) −16.9185 −0.728731
\(540\) −0.0356067 −0.00153227
\(541\) 9.32195 0.400782 0.200391 0.979716i \(-0.435779\pi\)
0.200391 + 0.979716i \(0.435779\pi\)
\(542\) −35.7901 −1.53732
\(543\) −12.1091 −0.519653
\(544\) −1.30841 −0.0560975
\(545\) 10.4557 0.447875
\(546\) 10.1379 0.433861
\(547\) −19.8523 −0.848825 −0.424413 0.905469i \(-0.639519\pi\)
−0.424413 + 0.905469i \(0.639519\pi\)
\(548\) −0.366585 −0.0156597
\(549\) −1.01012 −0.0431108
\(550\) 26.3033 1.12158
\(551\) 0.713891 0.0304128
\(552\) −2.85021 −0.121313
\(553\) 1.80936 0.0769420
\(554\) 16.4835 0.700316
\(555\) 8.55704 0.363226
\(556\) −0.320123 −0.0135762
\(557\) −41.2989 −1.74989 −0.874946 0.484221i \(-0.839103\pi\)
−0.874946 + 0.484221i \(0.839103\pi\)
\(558\) −6.08960 −0.257793
\(559\) −48.3863 −2.04652
\(560\) 8.51550 0.359846
\(561\) 37.1291 1.56759
\(562\) 17.3313 0.731078
\(563\) −37.1011 −1.56363 −0.781813 0.623513i \(-0.785705\pi\)
−0.781813 + 0.623513i \(0.785705\pi\)
\(564\) 0.0367257 0.00154643
\(565\) −22.7729 −0.958064
\(566\) −10.8383 −0.455569
\(567\) −1.90949 −0.0801909
\(568\) 39.0551 1.63872
\(569\) −20.3186 −0.851800 −0.425900 0.904770i \(-0.640043\pi\)
−0.425900 + 0.904770i \(0.640043\pi\)
\(570\) 1.13482 0.0475326
\(571\) 18.4758 0.773190 0.386595 0.922250i \(-0.373651\pi\)
0.386595 + 0.922250i \(0.373651\pi\)
\(572\) −0.599905 −0.0250833
\(573\) 18.1357 0.757629
\(574\) −26.8889 −1.12232
\(575\) 3.71636 0.154983
\(576\) 8.12173 0.338405
\(577\) 34.6426 1.44219 0.721095 0.692837i \(-0.243639\pi\)
0.721095 + 0.692837i \(0.243639\pi\)
\(578\) −52.1579 −2.16948
\(579\) −4.56459 −0.189698
\(580\) 0.0356067 0.00147849
\(581\) −21.5001 −0.891976
\(582\) 4.48106 0.185746
\(583\) −23.1994 −0.960822
\(584\) 40.6429 1.68182
\(585\) 4.28722 0.177255
\(586\) −27.8959 −1.15237
\(587\) 20.5344 0.847544 0.423772 0.905769i \(-0.360706\pi\)
0.423772 + 0.905769i \(0.360706\pi\)
\(588\) 0.105404 0.00434677
\(589\) −3.09846 −0.127670
\(590\) −7.10536 −0.292523
\(591\) −2.63724 −0.108482
\(592\) −29.7287 −1.22184
\(593\) −33.0577 −1.35752 −0.678759 0.734361i \(-0.737482\pi\)
−0.678759 + 0.734361i \(0.737482\pi\)
\(594\) −7.07770 −0.290402
\(595\) −15.9234 −0.652794
\(596\) 0.111454 0.00456535
\(597\) −21.7181 −0.888862
\(598\) 5.30922 0.217110
\(599\) 16.6667 0.680984 0.340492 0.940247i \(-0.389406\pi\)
0.340492 + 0.940247i \(0.389406\pi\)
\(600\) −10.5924 −0.432434
\(601\) −29.9855 −1.22313 −0.611566 0.791193i \(-0.709460\pi\)
−0.611566 + 0.791193i \(0.709460\pi\)
\(602\) −34.2579 −1.39625
\(603\) 16.2568 0.662027
\(604\) −0.283755 −0.0115458
\(605\) 16.3679 0.665450
\(606\) 1.99769 0.0811505
\(607\) −7.14403 −0.289967 −0.144984 0.989434i \(-0.546313\pi\)
−0.144984 + 0.989434i \(0.546313\pi\)
\(608\) 0.126905 0.00514666
\(609\) 1.90949 0.0773763
\(610\) 1.60572 0.0650135
\(611\) −4.42196 −0.178893
\(612\) −0.231317 −0.00935045
\(613\) 30.1935 1.21951 0.609753 0.792592i \(-0.291269\pi\)
0.609753 + 0.792592i \(0.291269\pi\)
\(614\) 33.2886 1.34342
\(615\) −11.3711 −0.458527
\(616\) −27.4543 −1.10617
\(617\) −18.0943 −0.728449 −0.364225 0.931311i \(-0.618666\pi\)
−0.364225 + 0.931311i \(0.618666\pi\)
\(618\) 5.81220 0.233801
\(619\) −19.8935 −0.799588 −0.399794 0.916605i \(-0.630918\pi\)
−0.399794 + 0.916605i \(0.630918\pi\)
\(620\) −0.154542 −0.00620654
\(621\) −1.00000 −0.0401286
\(622\) −25.4527 −1.02056
\(623\) 18.4603 0.739597
\(624\) −14.8945 −0.596259
\(625\) 7.39318 0.295727
\(626\) −12.9149 −0.516181
\(627\) −3.60121 −0.143819
\(628\) 0.533663 0.0212955
\(629\) 55.5904 2.21654
\(630\) 3.03538 0.120933
\(631\) 24.6952 0.983100 0.491550 0.870849i \(-0.336430\pi\)
0.491550 + 0.870849i \(0.336430\pi\)
\(632\) −2.70076 −0.107430
\(633\) 13.5636 0.539105
\(634\) 24.7581 0.983270
\(635\) 2.83627 0.112554
\(636\) 0.144534 0.00573117
\(637\) −12.6911 −0.502840
\(638\) 7.07770 0.280209
\(639\) 13.7025 0.542064
\(640\) −12.5078 −0.494412
\(641\) −7.28526 −0.287750 −0.143875 0.989596i \(-0.545956\pi\)
−0.143875 + 0.989596i \(0.545956\pi\)
\(642\) −0.982297 −0.0387682
\(643\) 9.67614 0.381590 0.190795 0.981630i \(-0.438893\pi\)
0.190795 + 0.981630i \(0.438893\pi\)
\(644\) −0.0600106 −0.00236475
\(645\) −14.4873 −0.570439
\(646\) 7.37233 0.290061
\(647\) −48.4492 −1.90474 −0.952368 0.304951i \(-0.901360\pi\)
−0.952368 + 0.304951i \(0.901360\pi\)
\(648\) 2.85021 0.111967
\(649\) 22.5479 0.885083
\(650\) 19.7310 0.773913
\(651\) −8.28763 −0.324818
\(652\) −0.240015 −0.00939971
\(653\) 2.44513 0.0956854 0.0478427 0.998855i \(-0.484765\pi\)
0.0478427 + 0.998855i \(0.484765\pi\)
\(654\) −12.9482 −0.506315
\(655\) −6.19037 −0.241878
\(656\) 39.5051 1.54242
\(657\) 14.2596 0.556321
\(658\) −3.13078 −0.122050
\(659\) −0.362884 −0.0141360 −0.00706798 0.999975i \(-0.502250\pi\)
−0.00706798 + 0.999975i \(0.502250\pi\)
\(660\) −0.179617 −0.00699160
\(661\) 9.07466 0.352963 0.176482 0.984304i \(-0.443528\pi\)
0.176482 + 0.984304i \(0.443528\pi\)
\(662\) −13.2395 −0.514569
\(663\) 27.8517 1.08167
\(664\) 32.0924 1.24542
\(665\) 1.54444 0.0598906
\(666\) −10.5969 −0.410621
\(667\) 1.00000 0.0387202
\(668\) −0.294516 −0.0113952
\(669\) 9.70226 0.375111
\(670\) −25.8423 −0.998375
\(671\) −5.09552 −0.196710
\(672\) 0.339439 0.0130942
\(673\) −25.6908 −0.990308 −0.495154 0.868805i \(-0.664888\pi\)
−0.495154 + 0.868805i \(0.664888\pi\)
\(674\) −3.45534 −0.133095
\(675\) −3.71636 −0.143043
\(676\) −0.0414495 −0.00159421
\(677\) −2.75399 −0.105844 −0.0529222 0.998599i \(-0.516854\pi\)
−0.0529222 + 0.998599i \(0.516854\pi\)
\(678\) 28.2016 1.08308
\(679\) 6.09848 0.234038
\(680\) 23.7681 0.911467
\(681\) −20.8423 −0.798679
\(682\) −30.7189 −1.17629
\(683\) −7.37036 −0.282019 −0.141009 0.990008i \(-0.545035\pi\)
−0.141009 + 0.990008i \(0.545035\pi\)
\(684\) 0.0224359 0.000857857 0
\(685\) 13.2155 0.504939
\(686\) −27.7392 −1.05909
\(687\) 11.7579 0.448592
\(688\) 50.3315 1.91887
\(689\) −17.4026 −0.662988
\(690\) 1.58963 0.0605163
\(691\) −0.879847 −0.0334710 −0.0167355 0.999860i \(-0.505327\pi\)
−0.0167355 + 0.999860i \(0.505327\pi\)
\(692\) −0.458179 −0.0174173
\(693\) −9.63238 −0.365904
\(694\) 19.1468 0.726803
\(695\) 11.5406 0.437758
\(696\) −2.85021 −0.108037
\(697\) −73.8718 −2.79809
\(698\) −49.7941 −1.88473
\(699\) −0.963016 −0.0364246
\(700\) −0.223021 −0.00842941
\(701\) 37.0825 1.40059 0.700293 0.713855i \(-0.253053\pi\)
0.700293 + 0.713855i \(0.253053\pi\)
\(702\) −5.30922 −0.200383
\(703\) −5.39181 −0.203356
\(704\) 40.9699 1.54411
\(705\) −1.32398 −0.0498639
\(706\) 34.1214 1.28418
\(707\) 2.71875 0.102249
\(708\) −0.140476 −0.00527939
\(709\) −19.9284 −0.748426 −0.374213 0.927343i \(-0.622087\pi\)
−0.374213 + 0.927343i \(0.622087\pi\)
\(710\) −21.7820 −0.817464
\(711\) −0.947565 −0.0355365
\(712\) −27.5549 −1.03266
\(713\) −4.34024 −0.162543
\(714\) 19.7192 0.737973
\(715\) 21.6268 0.808796
\(716\) −0.0542370 −0.00202693
\(717\) −28.8074 −1.07583
\(718\) 35.1706 1.31256
\(719\) −7.28652 −0.271741 −0.135871 0.990727i \(-0.543383\pi\)
−0.135871 + 0.990727i \(0.543383\pi\)
\(720\) −4.45957 −0.166199
\(721\) 7.91009 0.294587
\(722\) 25.9431 0.965500
\(723\) 11.7498 0.436979
\(724\) 0.380561 0.0141435
\(725\) 3.71636 0.138022
\(726\) −20.2697 −0.752280
\(727\) 41.8878 1.55353 0.776766 0.629790i \(-0.216859\pi\)
0.776766 + 0.629790i \(0.216859\pi\)
\(728\) −20.5944 −0.763278
\(729\) 1.00000 0.0370370
\(730\) −22.6675 −0.838964
\(731\) −94.1163 −3.48102
\(732\) 0.0317456 0.00117335
\(733\) 6.92995 0.255964 0.127982 0.991777i \(-0.459150\pi\)
0.127982 + 0.991777i \(0.459150\pi\)
\(734\) −6.91952 −0.255404
\(735\) −3.79984 −0.140159
\(736\) 0.177765 0.00655249
\(737\) 82.0070 3.02077
\(738\) 14.0818 0.518357
\(739\) 41.3802 1.52220 0.761098 0.648637i \(-0.224661\pi\)
0.761098 + 0.648637i \(0.224661\pi\)
\(740\) −0.268927 −0.00988596
\(741\) −2.70139 −0.0992379
\(742\) −12.3212 −0.452325
\(743\) 21.4539 0.787068 0.393534 0.919310i \(-0.371252\pi\)
0.393534 + 0.919310i \(0.371252\pi\)
\(744\) 12.3706 0.453528
\(745\) −4.01798 −0.147207
\(746\) 16.0364 0.587133
\(747\) 11.2596 0.411969
\(748\) −1.16688 −0.0426652
\(749\) −1.33685 −0.0488476
\(750\) 13.8558 0.505943
\(751\) 48.2066 1.75908 0.879542 0.475821i \(-0.157849\pi\)
0.879542 + 0.475821i \(0.157849\pi\)
\(752\) 4.59973 0.167735
\(753\) 15.1439 0.551873
\(754\) 5.30922 0.193350
\(755\) 10.2295 0.372289
\(756\) 0.0600106 0.00218256
\(757\) 21.8131 0.792811 0.396406 0.918075i \(-0.370257\pi\)
0.396406 + 0.918075i \(0.370257\pi\)
\(758\) −15.6562 −0.568659
\(759\) −5.04448 −0.183103
\(760\) −2.30531 −0.0836225
\(761\) −1.72952 −0.0626949 −0.0313475 0.999509i \(-0.509980\pi\)
−0.0313475 + 0.999509i \(0.509980\pi\)
\(762\) −3.51238 −0.127240
\(763\) −17.6218 −0.637952
\(764\) −0.569961 −0.0206205
\(765\) 8.33908 0.301500
\(766\) 1.91831 0.0693113
\(767\) 16.9139 0.610726
\(768\) −0.754075 −0.0272103
\(769\) −1.19902 −0.0432377 −0.0216188 0.999766i \(-0.506882\pi\)
−0.0216188 + 0.999766i \(0.506882\pi\)
\(770\) 15.3119 0.551804
\(771\) −7.48604 −0.269603
\(772\) 0.143454 0.00516302
\(773\) 14.0133 0.504023 0.252011 0.967724i \(-0.418908\pi\)
0.252011 + 0.967724i \(0.418908\pi\)
\(774\) 17.9409 0.644871
\(775\) −16.1299 −0.579403
\(776\) −9.10294 −0.326776
\(777\) −14.4218 −0.517379
\(778\) −15.8497 −0.568238
\(779\) 7.16495 0.256711
\(780\) −0.134737 −0.00482436
\(781\) 69.1223 2.47339
\(782\) 10.3270 0.369292
\(783\) −1.00000 −0.0357371
\(784\) 13.2013 0.471475
\(785\) −19.2388 −0.686661
\(786\) 7.66604 0.273439
\(787\) 11.0327 0.393273 0.196637 0.980476i \(-0.436998\pi\)
0.196637 + 0.980476i \(0.436998\pi\)
\(788\) 0.0828822 0.00295256
\(789\) −0.748198 −0.0266366
\(790\) 1.50628 0.0535910
\(791\) 38.3809 1.36467
\(792\) 14.3778 0.510894
\(793\) −3.82232 −0.135734
\(794\) −31.9851 −1.13511
\(795\) −5.21052 −0.184798
\(796\) 0.682547 0.0241922
\(797\) 26.2929 0.931341 0.465670 0.884958i \(-0.345813\pi\)
0.465670 + 0.884958i \(0.345813\pi\)
\(798\) −1.91260 −0.0677054
\(799\) −8.60116 −0.304287
\(800\) 0.660638 0.0233571
\(801\) −9.66768 −0.341591
\(802\) −20.5781 −0.726637
\(803\) 71.9324 2.53844
\(804\) −0.510911 −0.0180185
\(805\) 2.16340 0.0762500
\(806\) −23.0432 −0.811664
\(807\) 5.29003 0.186218
\(808\) −4.05816 −0.142766
\(809\) −29.4769 −1.03635 −0.518176 0.855274i \(-0.673389\pi\)
−0.518176 + 0.855274i \(0.673389\pi\)
\(810\) −1.58963 −0.0558540
\(811\) −1.87348 −0.0657866 −0.0328933 0.999459i \(-0.510472\pi\)
−0.0328933 + 0.999459i \(0.510472\pi\)
\(812\) −0.0600106 −0.00210596
\(813\) 25.5087 0.894628
\(814\) −53.4558 −1.87363
\(815\) 8.65263 0.303088
\(816\) −28.9714 −1.01420
\(817\) 9.12851 0.319366
\(818\) 39.6236 1.38541
\(819\) −7.22556 −0.252481
\(820\) 0.357366 0.0124798
\(821\) 30.2249 1.05486 0.527429 0.849599i \(-0.323156\pi\)
0.527429 + 0.849599i \(0.323156\pi\)
\(822\) −16.3659 −0.570826
\(823\) −52.7186 −1.83765 −0.918827 0.394661i \(-0.870862\pi\)
−0.918827 + 0.394661i \(0.870862\pi\)
\(824\) −11.8071 −0.411318
\(825\) −18.7471 −0.652692
\(826\) 11.9752 0.416670
\(827\) −22.5735 −0.784957 −0.392479 0.919761i \(-0.628382\pi\)
−0.392479 + 0.919761i \(0.628382\pi\)
\(828\) 0.0314276 0.00109218
\(829\) 21.7513 0.755453 0.377727 0.925917i \(-0.376706\pi\)
0.377727 + 0.925917i \(0.376706\pi\)
\(830\) −17.8987 −0.621272
\(831\) −11.7482 −0.407542
\(832\) 30.7329 1.06547
\(833\) −24.6855 −0.855302
\(834\) −14.2916 −0.494879
\(835\) 10.6174 0.367431
\(836\) 0.113177 0.00391432
\(837\) 4.34024 0.150021
\(838\) −6.56811 −0.226892
\(839\) −2.97271 −0.102629 −0.0513146 0.998683i \(-0.516341\pi\)
−0.0513146 + 0.998683i \(0.516341\pi\)
\(840\) −6.16616 −0.212753
\(841\) 1.00000 0.0344828
\(842\) 31.9093 1.09967
\(843\) −12.3525 −0.425444
\(844\) −0.426272 −0.0146729
\(845\) 1.49427 0.0514045
\(846\) 1.63959 0.0563703
\(847\) −27.5860 −0.947866
\(848\) 18.1023 0.621634
\(849\) 7.72479 0.265114
\(850\) 38.3788 1.31638
\(851\) −7.55271 −0.258904
\(852\) −0.430638 −0.0147534
\(853\) −30.9077 −1.05826 −0.529130 0.848540i \(-0.677482\pi\)
−0.529130 + 0.848540i \(0.677482\pi\)
\(854\) −2.70623 −0.0926053
\(855\) −0.808822 −0.0276611
\(856\) 1.99547 0.0682036
\(857\) −34.0716 −1.16387 −0.581933 0.813237i \(-0.697703\pi\)
−0.581933 + 0.813237i \(0.697703\pi\)
\(858\) −26.7822 −0.914331
\(859\) −46.6389 −1.59130 −0.795650 0.605757i \(-0.792871\pi\)
−0.795650 + 0.605757i \(0.792871\pi\)
\(860\) 0.455302 0.0155257
\(861\) 19.1645 0.653125
\(862\) −1.95103 −0.0664525
\(863\) −6.08275 −0.207059 −0.103530 0.994626i \(-0.533014\pi\)
−0.103530 + 0.994626i \(0.533014\pi\)
\(864\) −0.177765 −0.00604768
\(865\) 16.5175 0.561612
\(866\) 31.3548 1.06548
\(867\) 37.1744 1.26251
\(868\) 0.260460 0.00884059
\(869\) −4.77998 −0.162150
\(870\) 1.58963 0.0538936
\(871\) 61.5161 2.08440
\(872\) 26.3033 0.890743
\(873\) −3.19378 −0.108093
\(874\) −1.00163 −0.0338807
\(875\) 18.8570 0.637484
\(876\) −0.448145 −0.0151414
\(877\) 32.2078 1.08758 0.543791 0.839221i \(-0.316988\pi\)
0.543791 + 0.839221i \(0.316988\pi\)
\(878\) 42.9349 1.44898
\(879\) 19.8822 0.670610
\(880\) −22.4962 −0.758348
\(881\) −15.9775 −0.538296 −0.269148 0.963099i \(-0.586742\pi\)
−0.269148 + 0.963099i \(0.586742\pi\)
\(882\) 4.70566 0.158448
\(883\) −52.3366 −1.76127 −0.880633 0.473798i \(-0.842883\pi\)
−0.880633 + 0.473798i \(0.842883\pi\)
\(884\) −0.875312 −0.0294399
\(885\) 5.06420 0.170231
\(886\) 14.0422 0.471756
\(887\) −34.9470 −1.17340 −0.586702 0.809803i \(-0.699574\pi\)
−0.586702 + 0.809803i \(0.699574\pi\)
\(888\) 21.5268 0.722393
\(889\) −4.78017 −0.160322
\(890\) 15.3681 0.515138
\(891\) 5.04448 0.168997
\(892\) −0.304918 −0.0102094
\(893\) 0.834241 0.0279168
\(894\) 4.97579 0.166415
\(895\) 1.95527 0.0653573
\(896\) 21.0802 0.704241
\(897\) −3.78403 −0.126345
\(898\) 37.0956 1.23790
\(899\) −4.34024 −0.144755
\(900\) 0.116796 0.00389321
\(901\) −33.8499 −1.12770
\(902\) 71.0352 2.36521
\(903\) 24.4166 0.812532
\(904\) −57.2895 −1.90542
\(905\) −13.7194 −0.456048
\(906\) −12.6680 −0.420866
\(907\) 34.1605 1.13428 0.567140 0.823622i \(-0.308050\pi\)
0.567140 + 0.823622i \(0.308050\pi\)
\(908\) 0.655023 0.0217377
\(909\) −1.42381 −0.0472248
\(910\) 11.4860 0.380757
\(911\) −47.2422 −1.56520 −0.782601 0.622523i \(-0.786108\pi\)
−0.782601 + 0.622523i \(0.786108\pi\)
\(912\) 2.80999 0.0930480
\(913\) 56.7991 1.87977
\(914\) 19.5773 0.647560
\(915\) −1.14444 −0.0378340
\(916\) −0.369523 −0.0122094
\(917\) 10.4331 0.344530
\(918\) −10.3270 −0.340841
\(919\) −57.8655 −1.90881 −0.954403 0.298522i \(-0.903506\pi\)
−0.954403 + 0.298522i \(0.903506\pi\)
\(920\) −3.22922 −0.106464
\(921\) −23.7258 −0.781790
\(922\) 16.4481 0.541690
\(923\) 51.8509 1.70669
\(924\) 0.302722 0.00995883
\(925\) −28.0686 −0.922891
\(926\) 20.6077 0.677211
\(927\) −4.14252 −0.136058
\(928\) 0.177765 0.00583541
\(929\) −4.71461 −0.154681 −0.0773406 0.997005i \(-0.524643\pi\)
−0.0773406 + 0.997005i \(0.524643\pi\)
\(930\) −6.89938 −0.226240
\(931\) 2.39429 0.0784697
\(932\) 0.0302653 0.000991372 0
\(933\) 18.1409 0.593907
\(934\) −35.2444 −1.15323
\(935\) 42.0663 1.37572
\(936\) 10.7853 0.352528
\(937\) −43.2695 −1.41355 −0.706776 0.707437i \(-0.749851\pi\)
−0.706776 + 0.707437i \(0.749851\pi\)
\(938\) 43.5539 1.42208
\(939\) 9.20479 0.300387
\(940\) 0.0416094 0.00135715
\(941\) 26.7756 0.872858 0.436429 0.899739i \(-0.356243\pi\)
0.436429 + 0.899739i \(0.356243\pi\)
\(942\) 23.8249 0.776259
\(943\) 10.0365 0.326833
\(944\) −17.5939 −0.572633
\(945\) −2.16340 −0.0703755
\(946\) 90.5024 2.94249
\(947\) 28.1314 0.914148 0.457074 0.889429i \(-0.348898\pi\)
0.457074 + 0.889429i \(0.348898\pi\)
\(948\) 0.0297797 0.000967199 0
\(949\) 53.9588 1.75158
\(950\) −3.72243 −0.120771
\(951\) −17.6458 −0.572205
\(952\) −40.0582 −1.29829
\(953\) −20.0115 −0.648238 −0.324119 0.946016i \(-0.605068\pi\)
−0.324119 + 0.946016i \(0.605068\pi\)
\(954\) 6.45262 0.208911
\(955\) 20.5473 0.664895
\(956\) 0.905346 0.0292810
\(957\) −5.04448 −0.163065
\(958\) 15.6001 0.504015
\(959\) −22.2731 −0.719235
\(960\) 9.20173 0.296984
\(961\) −12.1624 −0.392334
\(962\) −40.0990 −1.29284
\(963\) 0.700112 0.0225608
\(964\) −0.369267 −0.0118933
\(965\) −5.17157 −0.166479
\(966\) −2.67912 −0.0861993
\(967\) −40.3456 −1.29743 −0.648714 0.761032i \(-0.724693\pi\)
−0.648714 + 0.761032i \(0.724693\pi\)
\(968\) 41.1765 1.32346
\(969\) −5.25447 −0.168798
\(970\) 5.07693 0.163010
\(971\) −14.3640 −0.460961 −0.230481 0.973077i \(-0.574030\pi\)
−0.230481 + 0.973077i \(0.574030\pi\)
\(972\) −0.0314276 −0.00100804
\(973\) −19.4501 −0.623543
\(974\) 44.3927 1.42244
\(975\) −14.0628 −0.450371
\(976\) 3.97598 0.127268
\(977\) −26.5524 −0.849487 −0.424744 0.905314i \(-0.639636\pi\)
−0.424744 + 0.905314i \(0.639636\pi\)
\(978\) −10.7153 −0.342636
\(979\) −48.7685 −1.55865
\(980\) 0.119420 0.00381473
\(981\) 9.22855 0.294645
\(982\) −6.27898 −0.200370
\(983\) 21.8041 0.695441 0.347721 0.937598i \(-0.386956\pi\)
0.347721 + 0.937598i \(0.386956\pi\)
\(984\) −28.6061 −0.911928
\(985\) −2.98794 −0.0952036
\(986\) 10.3270 0.328878
\(987\) 2.23139 0.0710261
\(988\) 0.0848980 0.00270097
\(989\) 12.7870 0.406602
\(990\) −8.01887 −0.254856
\(991\) 30.5663 0.970969 0.485485 0.874245i \(-0.338643\pi\)
0.485485 + 0.874245i \(0.338643\pi\)
\(992\) −0.771541 −0.0244964
\(993\) 9.43619 0.299448
\(994\) 36.7108 1.16440
\(995\) −24.6061 −0.780065
\(996\) −0.353863 −0.0112126
\(997\) −37.1186 −1.17556 −0.587779 0.809021i \(-0.699998\pi\)
−0.587779 + 0.809021i \(0.699998\pi\)
\(998\) 35.0113 1.10826
\(999\) 7.55271 0.238957
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 2001.2.a.n.1.6 16
3.2 odd 2 6003.2.a.r.1.11 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.n.1.6 16 1.1 even 1 trivial
6003.2.a.r.1.11 16 3.2 odd 2