Properties

Label 6015.2.a.c.1.19
Level $6015$
Weight $2$
Character 6015.1
Self dual yes
Analytic conductor $48.030$
Analytic rank $1$
Dimension $28$
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] = [6015,2,Mod(1,6015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6015, 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("6015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6015.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: \(48.0300168158\)
Analytic rank: \(1\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 6015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.894188 q^{2} +1.00000 q^{3} -1.20043 q^{4} -1.00000 q^{5} +0.894188 q^{6} -1.23837 q^{7} -2.86178 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.894188 q^{2} +1.00000 q^{3} -1.20043 q^{4} -1.00000 q^{5} +0.894188 q^{6} -1.23837 q^{7} -2.86178 q^{8} +1.00000 q^{9} -0.894188 q^{10} -2.33822 q^{11} -1.20043 q^{12} +2.73582 q^{13} -1.10734 q^{14} -1.00000 q^{15} -0.158119 q^{16} +2.62798 q^{17} +0.894188 q^{18} +6.44686 q^{19} +1.20043 q^{20} -1.23837 q^{21} -2.09081 q^{22} +0.252290 q^{23} -2.86178 q^{24} +1.00000 q^{25} +2.44634 q^{26} +1.00000 q^{27} +1.48658 q^{28} -4.04780 q^{29} -0.894188 q^{30} -3.99704 q^{31} +5.58218 q^{32} -2.33822 q^{33} +2.34991 q^{34} +1.23837 q^{35} -1.20043 q^{36} -5.94314 q^{37} +5.76471 q^{38} +2.73582 q^{39} +2.86178 q^{40} -7.32162 q^{41} -1.10734 q^{42} -6.68308 q^{43} +2.80686 q^{44} -1.00000 q^{45} +0.225594 q^{46} +9.58108 q^{47} -0.158119 q^{48} -5.46643 q^{49} +0.894188 q^{50} +2.62798 q^{51} -3.28416 q^{52} +7.13339 q^{53} +0.894188 q^{54} +2.33822 q^{55} +3.54396 q^{56} +6.44686 q^{57} -3.61950 q^{58} -13.0441 q^{59} +1.20043 q^{60} +8.58250 q^{61} -3.57411 q^{62} -1.23837 q^{63} +5.30776 q^{64} -2.73582 q^{65} -2.09081 q^{66} +2.37402 q^{67} -3.15470 q^{68} +0.252290 q^{69} +1.10734 q^{70} -8.87660 q^{71} -2.86178 q^{72} -12.6997 q^{73} -5.31429 q^{74} +1.00000 q^{75} -7.73899 q^{76} +2.89559 q^{77} +2.44634 q^{78} +5.00742 q^{79} +0.158119 q^{80} +1.00000 q^{81} -6.54691 q^{82} +15.7216 q^{83} +1.48658 q^{84} -2.62798 q^{85} -5.97593 q^{86} -4.04780 q^{87} +6.69147 q^{88} -0.511577 q^{89} -0.894188 q^{90} -3.38797 q^{91} -0.302855 q^{92} -3.99704 q^{93} +8.56729 q^{94} -6.44686 q^{95} +5.58218 q^{96} -8.25939 q^{97} -4.88802 q^{98} -2.33822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.894188 0.632287 0.316143 0.948711i \(-0.397612\pi\)
0.316143 + 0.948711i \(0.397612\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.20043 −0.600214
\(5\) −1.00000 −0.447214
\(6\) 0.894188 0.365051
\(7\) −1.23837 −0.468061 −0.234031 0.972229i \(-0.575192\pi\)
−0.234031 + 0.972229i \(0.575192\pi\)
\(8\) −2.86178 −1.01179
\(9\) 1.00000 0.333333
\(10\) −0.894188 −0.282767
\(11\) −2.33822 −0.704999 −0.352499 0.935812i \(-0.614668\pi\)
−0.352499 + 0.935812i \(0.614668\pi\)
\(12\) −1.20043 −0.346534
\(13\) 2.73582 0.758781 0.379390 0.925237i \(-0.376134\pi\)
0.379390 + 0.925237i \(0.376134\pi\)
\(14\) −1.10734 −0.295949
\(15\) −1.00000 −0.258199
\(16\) −0.158119 −0.0395298
\(17\) 2.62798 0.637380 0.318690 0.947859i \(-0.396757\pi\)
0.318690 + 0.947859i \(0.396757\pi\)
\(18\) 0.894188 0.210762
\(19\) 6.44686 1.47901 0.739506 0.673150i \(-0.235059\pi\)
0.739506 + 0.673150i \(0.235059\pi\)
\(20\) 1.20043 0.268424
\(21\) −1.23837 −0.270235
\(22\) −2.09081 −0.445761
\(23\) 0.252290 0.0526060 0.0263030 0.999654i \(-0.491627\pi\)
0.0263030 + 0.999654i \(0.491627\pi\)
\(24\) −2.86178 −0.584159
\(25\) 1.00000 0.200000
\(26\) 2.44634 0.479767
\(27\) 1.00000 0.192450
\(28\) 1.48658 0.280937
\(29\) −4.04780 −0.751658 −0.375829 0.926689i \(-0.622642\pi\)
−0.375829 + 0.926689i \(0.622642\pi\)
\(30\) −0.894188 −0.163256
\(31\) −3.99704 −0.717890 −0.358945 0.933359i \(-0.616863\pi\)
−0.358945 + 0.933359i \(0.616863\pi\)
\(32\) 5.58218 0.986799
\(33\) −2.33822 −0.407031
\(34\) 2.34991 0.403007
\(35\) 1.23837 0.209323
\(36\) −1.20043 −0.200071
\(37\) −5.94314 −0.977046 −0.488523 0.872551i \(-0.662464\pi\)
−0.488523 + 0.872551i \(0.662464\pi\)
\(38\) 5.76471 0.935159
\(39\) 2.73582 0.438082
\(40\) 2.86178 0.452488
\(41\) −7.32162 −1.14344 −0.571722 0.820447i \(-0.693725\pi\)
−0.571722 + 0.820447i \(0.693725\pi\)
\(42\) −1.10734 −0.170866
\(43\) −6.68308 −1.01916 −0.509580 0.860423i \(-0.670199\pi\)
−0.509580 + 0.860423i \(0.670199\pi\)
\(44\) 2.80686 0.423150
\(45\) −1.00000 −0.149071
\(46\) 0.225594 0.0332621
\(47\) 9.58108 1.39754 0.698772 0.715344i \(-0.253730\pi\)
0.698772 + 0.715344i \(0.253730\pi\)
\(48\) −0.158119 −0.0228226
\(49\) −5.46643 −0.780919
\(50\) 0.894188 0.126457
\(51\) 2.62798 0.367991
\(52\) −3.28416 −0.455431
\(53\) 7.13339 0.979847 0.489924 0.871765i \(-0.337025\pi\)
0.489924 + 0.871765i \(0.337025\pi\)
\(54\) 0.894188 0.121684
\(55\) 2.33822 0.315285
\(56\) 3.54396 0.473581
\(57\) 6.44686 0.853907
\(58\) −3.61950 −0.475263
\(59\) −13.0441 −1.69820 −0.849099 0.528233i \(-0.822855\pi\)
−0.849099 + 0.528233i \(0.822855\pi\)
\(60\) 1.20043 0.154975
\(61\) 8.58250 1.09888 0.549438 0.835534i \(-0.314842\pi\)
0.549438 + 0.835534i \(0.314842\pi\)
\(62\) −3.57411 −0.453912
\(63\) −1.23837 −0.156020
\(64\) 5.30776 0.663470
\(65\) −2.73582 −0.339337
\(66\) −2.09081 −0.257360
\(67\) 2.37402 0.290032 0.145016 0.989429i \(-0.453677\pi\)
0.145016 + 0.989429i \(0.453677\pi\)
\(68\) −3.15470 −0.382564
\(69\) 0.252290 0.0303721
\(70\) 1.10734 0.132352
\(71\) −8.87660 −1.05346 −0.526729 0.850033i \(-0.676582\pi\)
−0.526729 + 0.850033i \(0.676582\pi\)
\(72\) −2.86178 −0.337265
\(73\) −12.6997 −1.48638 −0.743192 0.669078i \(-0.766689\pi\)
−0.743192 + 0.669078i \(0.766689\pi\)
\(74\) −5.31429 −0.617773
\(75\) 1.00000 0.115470
\(76\) −7.73899 −0.887723
\(77\) 2.89559 0.329983
\(78\) 2.44634 0.276993
\(79\) 5.00742 0.563379 0.281690 0.959506i \(-0.409105\pi\)
0.281690 + 0.959506i \(0.409105\pi\)
\(80\) 0.158119 0.0176783
\(81\) 1.00000 0.111111
\(82\) −6.54691 −0.722985
\(83\) 15.7216 1.72567 0.862836 0.505484i \(-0.168686\pi\)
0.862836 + 0.505484i \(0.168686\pi\)
\(84\) 1.48658 0.162199
\(85\) −2.62798 −0.285045
\(86\) −5.97593 −0.644401
\(87\) −4.04780 −0.433970
\(88\) 6.69147 0.713313
\(89\) −0.511577 −0.0542271 −0.0271135 0.999632i \(-0.508632\pi\)
−0.0271135 + 0.999632i \(0.508632\pi\)
\(90\) −0.894188 −0.0942557
\(91\) −3.38797 −0.355156
\(92\) −0.302855 −0.0315748
\(93\) −3.99704 −0.414474
\(94\) 8.56729 0.883649
\(95\) −6.44686 −0.661434
\(96\) 5.58218 0.569729
\(97\) −8.25939 −0.838614 −0.419307 0.907845i \(-0.637727\pi\)
−0.419307 + 0.907845i \(0.637727\pi\)
\(98\) −4.88802 −0.493764
\(99\) −2.33822 −0.235000
\(100\) −1.20043 −0.120043
\(101\) 8.20247 0.816177 0.408088 0.912942i \(-0.366196\pi\)
0.408088 + 0.912942i \(0.366196\pi\)
\(102\) 2.34991 0.232676
\(103\) −13.5598 −1.33609 −0.668045 0.744121i \(-0.732869\pi\)
−0.668045 + 0.744121i \(0.732869\pi\)
\(104\) −7.82933 −0.767729
\(105\) 1.23837 0.120853
\(106\) 6.37860 0.619544
\(107\) −1.07130 −0.103567 −0.0517833 0.998658i \(-0.516491\pi\)
−0.0517833 + 0.998658i \(0.516491\pi\)
\(108\) −1.20043 −0.115511
\(109\) −6.38693 −0.611757 −0.305878 0.952071i \(-0.598950\pi\)
−0.305878 + 0.952071i \(0.598950\pi\)
\(110\) 2.09081 0.199351
\(111\) −5.94314 −0.564098
\(112\) 0.195811 0.0185024
\(113\) 7.79616 0.733401 0.366701 0.930339i \(-0.380487\pi\)
0.366701 + 0.930339i \(0.380487\pi\)
\(114\) 5.76471 0.539914
\(115\) −0.252290 −0.0235261
\(116\) 4.85909 0.451156
\(117\) 2.73582 0.252927
\(118\) −11.6639 −1.07375
\(119\) −3.25443 −0.298333
\(120\) 2.86178 0.261244
\(121\) −5.53274 −0.502977
\(122\) 7.67437 0.694805
\(123\) −7.32162 −0.660168
\(124\) 4.79816 0.430887
\(125\) −1.00000 −0.0894427
\(126\) −1.10734 −0.0986496
\(127\) −4.50707 −0.399938 −0.199969 0.979802i \(-0.564084\pi\)
−0.199969 + 0.979802i \(0.564084\pi\)
\(128\) −6.41823 −0.567296
\(129\) −6.68308 −0.588412
\(130\) −2.44634 −0.214558
\(131\) 9.83424 0.859222 0.429611 0.903014i \(-0.358651\pi\)
0.429611 + 0.903014i \(0.358651\pi\)
\(132\) 2.80686 0.244306
\(133\) −7.98362 −0.692268
\(134\) 2.12282 0.183383
\(135\) −1.00000 −0.0860663
\(136\) −7.52073 −0.644897
\(137\) 7.76121 0.663085 0.331543 0.943440i \(-0.392431\pi\)
0.331543 + 0.943440i \(0.392431\pi\)
\(138\) 0.225594 0.0192039
\(139\) −20.5265 −1.74103 −0.870517 0.492139i \(-0.836215\pi\)
−0.870517 + 0.492139i \(0.836215\pi\)
\(140\) −1.48658 −0.125639
\(141\) 9.58108 0.806873
\(142\) −7.93735 −0.666088
\(143\) −6.39695 −0.534940
\(144\) −0.158119 −0.0131766
\(145\) 4.04780 0.336152
\(146\) −11.3559 −0.939821
\(147\) −5.46643 −0.450864
\(148\) 7.13431 0.586437
\(149\) −7.19674 −0.589580 −0.294790 0.955562i \(-0.595250\pi\)
−0.294790 + 0.955562i \(0.595250\pi\)
\(150\) 0.894188 0.0730102
\(151\) −17.6348 −1.43510 −0.717548 0.696509i \(-0.754736\pi\)
−0.717548 + 0.696509i \(0.754736\pi\)
\(152\) −18.4495 −1.49645
\(153\) 2.62798 0.212460
\(154\) 2.58920 0.208644
\(155\) 3.99704 0.321050
\(156\) −3.28416 −0.262943
\(157\) −14.1066 −1.12583 −0.562913 0.826516i \(-0.690319\pi\)
−0.562913 + 0.826516i \(0.690319\pi\)
\(158\) 4.47758 0.356217
\(159\) 7.13339 0.565715
\(160\) −5.58218 −0.441310
\(161\) −0.312429 −0.0246228
\(162\) 0.894188 0.0702541
\(163\) −16.7070 −1.30859 −0.654296 0.756238i \(-0.727035\pi\)
−0.654296 + 0.756238i \(0.727035\pi\)
\(164\) 8.78907 0.686311
\(165\) 2.33822 0.182030
\(166\) 14.0581 1.09112
\(167\) −20.7124 −1.60277 −0.801386 0.598148i \(-0.795904\pi\)
−0.801386 + 0.598148i \(0.795904\pi\)
\(168\) 3.54396 0.273422
\(169\) −5.51528 −0.424252
\(170\) −2.34991 −0.180230
\(171\) 6.44686 0.493004
\(172\) 8.02255 0.611714
\(173\) −11.0999 −0.843908 −0.421954 0.906617i \(-0.638656\pi\)
−0.421954 + 0.906617i \(0.638656\pi\)
\(174\) −3.61950 −0.274393
\(175\) −1.23837 −0.0936122
\(176\) 0.369717 0.0278685
\(177\) −13.0441 −0.980456
\(178\) −0.457446 −0.0342871
\(179\) −22.6227 −1.69090 −0.845448 0.534057i \(-0.820667\pi\)
−0.845448 + 0.534057i \(0.820667\pi\)
\(180\) 1.20043 0.0894746
\(181\) −21.9859 −1.63420 −0.817099 0.576498i \(-0.804419\pi\)
−0.817099 + 0.576498i \(0.804419\pi\)
\(182\) −3.02948 −0.224560
\(183\) 8.58250 0.634436
\(184\) −0.721998 −0.0532264
\(185\) 5.94314 0.436948
\(186\) −3.57411 −0.262066
\(187\) −6.14480 −0.449352
\(188\) −11.5014 −0.838825
\(189\) −1.23837 −0.0900784
\(190\) −5.76471 −0.418216
\(191\) −3.62710 −0.262448 −0.131224 0.991353i \(-0.541891\pi\)
−0.131224 + 0.991353i \(0.541891\pi\)
\(192\) 5.30776 0.383055
\(193\) 18.8754 1.35868 0.679340 0.733824i \(-0.262266\pi\)
0.679340 + 0.733824i \(0.262266\pi\)
\(194\) −7.38545 −0.530244
\(195\) −2.73582 −0.195916
\(196\) 6.56205 0.468718
\(197\) −10.4283 −0.742987 −0.371494 0.928436i \(-0.621154\pi\)
−0.371494 + 0.928436i \(0.621154\pi\)
\(198\) −2.09081 −0.148587
\(199\) 24.7050 1.75129 0.875646 0.482953i \(-0.160436\pi\)
0.875646 + 0.482953i \(0.160436\pi\)
\(200\) −2.86178 −0.202359
\(201\) 2.37402 0.167450
\(202\) 7.33455 0.516057
\(203\) 5.01269 0.351822
\(204\) −3.15470 −0.220874
\(205\) 7.32162 0.511364
\(206\) −12.1250 −0.844792
\(207\) 0.252290 0.0175353
\(208\) −0.432586 −0.0299945
\(209\) −15.0742 −1.04270
\(210\) 1.10734 0.0764136
\(211\) −6.11184 −0.420756 −0.210378 0.977620i \(-0.567469\pi\)
−0.210378 + 0.977620i \(0.567469\pi\)
\(212\) −8.56312 −0.588118
\(213\) −8.87660 −0.608215
\(214\) −0.957945 −0.0654838
\(215\) 6.68308 0.455782
\(216\) −2.86178 −0.194720
\(217\) 4.94983 0.336016
\(218\) −5.71112 −0.386806
\(219\) −12.6997 −0.858165
\(220\) −2.80686 −0.189238
\(221\) 7.18970 0.483632
\(222\) −5.31429 −0.356672
\(223\) 1.81356 0.121445 0.0607225 0.998155i \(-0.480660\pi\)
0.0607225 + 0.998155i \(0.480660\pi\)
\(224\) −6.91282 −0.461882
\(225\) 1.00000 0.0666667
\(226\) 6.97124 0.463720
\(227\) −4.82939 −0.320538 −0.160269 0.987073i \(-0.551236\pi\)
−0.160269 + 0.987073i \(0.551236\pi\)
\(228\) −7.73899 −0.512527
\(229\) −3.75378 −0.248057 −0.124028 0.992279i \(-0.539581\pi\)
−0.124028 + 0.992279i \(0.539581\pi\)
\(230\) −0.225594 −0.0148752
\(231\) 2.89559 0.190516
\(232\) 11.5839 0.760523
\(233\) −7.14068 −0.467801 −0.233901 0.972261i \(-0.575149\pi\)
−0.233901 + 0.972261i \(0.575149\pi\)
\(234\) 2.44634 0.159922
\(235\) −9.58108 −0.625001
\(236\) 15.6585 1.01928
\(237\) 5.00742 0.325267
\(238\) −2.91007 −0.188632
\(239\) −18.6288 −1.20500 −0.602499 0.798119i \(-0.705828\pi\)
−0.602499 + 0.798119i \(0.705828\pi\)
\(240\) 0.158119 0.0102066
\(241\) 22.4227 1.44437 0.722186 0.691699i \(-0.243138\pi\)
0.722186 + 0.691699i \(0.243138\pi\)
\(242\) −4.94731 −0.318025
\(243\) 1.00000 0.0641500
\(244\) −10.3027 −0.659560
\(245\) 5.46643 0.349238
\(246\) −6.54691 −0.417415
\(247\) 17.6375 1.12225
\(248\) 11.4387 0.726356
\(249\) 15.7216 0.996317
\(250\) −0.894188 −0.0565534
\(251\) 15.6303 0.986576 0.493288 0.869866i \(-0.335795\pi\)
0.493288 + 0.869866i \(0.335795\pi\)
\(252\) 1.48658 0.0936456
\(253\) −0.589908 −0.0370872
\(254\) −4.03017 −0.252875
\(255\) −2.62798 −0.164571
\(256\) −16.3546 −1.02216
\(257\) −9.45626 −0.589865 −0.294933 0.955518i \(-0.595297\pi\)
−0.294933 + 0.955518i \(0.595297\pi\)
\(258\) −5.97593 −0.372045
\(259\) 7.35983 0.457317
\(260\) 3.28416 0.203675
\(261\) −4.04780 −0.250553
\(262\) 8.79366 0.543274
\(263\) 0.547871 0.0337832 0.0168916 0.999857i \(-0.494623\pi\)
0.0168916 + 0.999857i \(0.494623\pi\)
\(264\) 6.69147 0.411832
\(265\) −7.13339 −0.438201
\(266\) −7.13886 −0.437711
\(267\) −0.511577 −0.0313080
\(268\) −2.84983 −0.174081
\(269\) −0.925980 −0.0564580 −0.0282290 0.999601i \(-0.508987\pi\)
−0.0282290 + 0.999601i \(0.508987\pi\)
\(270\) −0.894188 −0.0544186
\(271\) 1.09783 0.0666882 0.0333441 0.999444i \(-0.489384\pi\)
0.0333441 + 0.999444i \(0.489384\pi\)
\(272\) −0.415535 −0.0251955
\(273\) −3.38797 −0.205049
\(274\) 6.93999 0.419260
\(275\) −2.33822 −0.141000
\(276\) −0.302855 −0.0182297
\(277\) −18.3973 −1.10539 −0.552693 0.833385i \(-0.686400\pi\)
−0.552693 + 0.833385i \(0.686400\pi\)
\(278\) −18.3545 −1.10083
\(279\) −3.99704 −0.239297
\(280\) −3.54396 −0.211792
\(281\) 10.9689 0.654348 0.327174 0.944964i \(-0.393904\pi\)
0.327174 + 0.944964i \(0.393904\pi\)
\(282\) 8.56729 0.510175
\(283\) 14.9113 0.886388 0.443194 0.896426i \(-0.353845\pi\)
0.443194 + 0.896426i \(0.353845\pi\)
\(284\) 10.6557 0.632300
\(285\) −6.44686 −0.381879
\(286\) −5.72007 −0.338235
\(287\) 9.06690 0.535202
\(288\) 5.58218 0.328933
\(289\) −10.0937 −0.593747
\(290\) 3.61950 0.212544
\(291\) −8.25939 −0.484174
\(292\) 15.2450 0.892149
\(293\) 21.8589 1.27701 0.638504 0.769618i \(-0.279554\pi\)
0.638504 + 0.769618i \(0.279554\pi\)
\(294\) −4.88802 −0.285075
\(295\) 13.0441 0.759458
\(296\) 17.0080 0.988569
\(297\) −2.33822 −0.135677
\(298\) −6.43524 −0.372783
\(299\) 0.690219 0.0399164
\(300\) −1.20043 −0.0693067
\(301\) 8.27614 0.477029
\(302\) −15.7688 −0.907392
\(303\) 8.20247 0.471220
\(304\) −1.01937 −0.0584651
\(305\) −8.58250 −0.491432
\(306\) 2.34991 0.134336
\(307\) −3.59398 −0.205119 −0.102560 0.994727i \(-0.532703\pi\)
−0.102560 + 0.994727i \(0.532703\pi\)
\(308\) −3.47594 −0.198060
\(309\) −13.5598 −0.771392
\(310\) 3.57411 0.202996
\(311\) 14.1229 0.800839 0.400419 0.916332i \(-0.368864\pi\)
0.400419 + 0.916332i \(0.368864\pi\)
\(312\) −7.82933 −0.443249
\(313\) 0.158146 0.00893895 0.00446947 0.999990i \(-0.498577\pi\)
0.00446947 + 0.999990i \(0.498577\pi\)
\(314\) −12.6139 −0.711845
\(315\) 1.23837 0.0697744
\(316\) −6.01105 −0.338148
\(317\) 1.95832 0.109990 0.0549952 0.998487i \(-0.482486\pi\)
0.0549952 + 0.998487i \(0.482486\pi\)
\(318\) 6.37860 0.357694
\(319\) 9.46464 0.529918
\(320\) −5.30776 −0.296713
\(321\) −1.07130 −0.0597942
\(322\) −0.279370 −0.0155687
\(323\) 16.9423 0.942692
\(324\) −1.20043 −0.0666904
\(325\) 2.73582 0.151756
\(326\) −14.9392 −0.827405
\(327\) −6.38693 −0.353198
\(328\) 20.9529 1.15693
\(329\) −11.8650 −0.654136
\(330\) 2.09081 0.115095
\(331\) −3.56211 −0.195791 −0.0978955 0.995197i \(-0.531211\pi\)
−0.0978955 + 0.995197i \(0.531211\pi\)
\(332\) −18.8727 −1.03577
\(333\) −5.94314 −0.325682
\(334\) −18.5208 −1.01341
\(335\) −2.37402 −0.129706
\(336\) 0.195811 0.0106824
\(337\) −15.8481 −0.863299 −0.431649 0.902041i \(-0.642068\pi\)
−0.431649 + 0.902041i \(0.642068\pi\)
\(338\) −4.93169 −0.268249
\(339\) 7.79616 0.423429
\(340\) 3.15470 0.171088
\(341\) 9.34595 0.506111
\(342\) 5.76471 0.311720
\(343\) 15.4381 0.833579
\(344\) 19.1255 1.03118
\(345\) −0.252290 −0.0135828
\(346\) −9.92538 −0.533592
\(347\) −13.4216 −0.720511 −0.360256 0.932854i \(-0.617311\pi\)
−0.360256 + 0.932854i \(0.617311\pi\)
\(348\) 4.85909 0.260475
\(349\) 4.04184 0.216355 0.108177 0.994132i \(-0.465499\pi\)
0.108177 + 0.994132i \(0.465499\pi\)
\(350\) −1.10734 −0.0591897
\(351\) 2.73582 0.146027
\(352\) −13.0523 −0.695693
\(353\) −6.67569 −0.355311 −0.177656 0.984093i \(-0.556851\pi\)
−0.177656 + 0.984093i \(0.556851\pi\)
\(354\) −11.6639 −0.619929
\(355\) 8.87660 0.471121
\(356\) 0.614112 0.0325478
\(357\) −3.25443 −0.172242
\(358\) −20.2289 −1.06913
\(359\) 20.1867 1.06541 0.532707 0.846300i \(-0.321175\pi\)
0.532707 + 0.846300i \(0.321175\pi\)
\(360\) 2.86178 0.150829
\(361\) 22.5620 1.18747
\(362\) −19.6595 −1.03328
\(363\) −5.53274 −0.290394
\(364\) 4.06701 0.213169
\(365\) 12.6997 0.664732
\(366\) 7.67437 0.401146
\(367\) 9.43628 0.492570 0.246285 0.969197i \(-0.420790\pi\)
0.246285 + 0.969197i \(0.420790\pi\)
\(368\) −0.0398919 −0.00207951
\(369\) −7.32162 −0.381148
\(370\) 5.31429 0.276277
\(371\) −8.83380 −0.458628
\(372\) 4.79816 0.248773
\(373\) 18.2109 0.942923 0.471461 0.881887i \(-0.343727\pi\)
0.471461 + 0.881887i \(0.343727\pi\)
\(374\) −5.49461 −0.284119
\(375\) −1.00000 −0.0516398
\(376\) −27.4190 −1.41403
\(377\) −11.0741 −0.570344
\(378\) −1.10734 −0.0569554
\(379\) −5.25106 −0.269729 −0.134864 0.990864i \(-0.543060\pi\)
−0.134864 + 0.990864i \(0.543060\pi\)
\(380\) 7.73899 0.397002
\(381\) −4.50707 −0.230904
\(382\) −3.24331 −0.165942
\(383\) 27.3701 1.39854 0.699272 0.714855i \(-0.253507\pi\)
0.699272 + 0.714855i \(0.253507\pi\)
\(384\) −6.41823 −0.327529
\(385\) −2.89559 −0.147573
\(386\) 16.8782 0.859075
\(387\) −6.68308 −0.339720
\(388\) 9.91480 0.503348
\(389\) −27.0288 −1.37041 −0.685207 0.728349i \(-0.740288\pi\)
−0.685207 + 0.728349i \(0.740288\pi\)
\(390\) −2.44634 −0.123875
\(391\) 0.663013 0.0335300
\(392\) 15.6438 0.790129
\(393\) 9.83424 0.496072
\(394\) −9.32488 −0.469781
\(395\) −5.00742 −0.251951
\(396\) 2.80686 0.141050
\(397\) −9.61301 −0.482463 −0.241232 0.970468i \(-0.577551\pi\)
−0.241232 + 0.970468i \(0.577551\pi\)
\(398\) 22.0909 1.10732
\(399\) −7.98362 −0.399681
\(400\) −0.158119 −0.00790597
\(401\) 1.00000 0.0499376
\(402\) 2.12282 0.105876
\(403\) −10.9352 −0.544721
\(404\) −9.84647 −0.489880
\(405\) −1.00000 −0.0496904
\(406\) 4.48229 0.222452
\(407\) 13.8964 0.688817
\(408\) −7.52073 −0.372331
\(409\) 36.3963 1.79968 0.899841 0.436218i \(-0.143682\pi\)
0.899841 + 0.436218i \(0.143682\pi\)
\(410\) 6.54691 0.323329
\(411\) 7.76121 0.382832
\(412\) 16.2776 0.801940
\(413\) 16.1535 0.794861
\(414\) 0.225594 0.0110874
\(415\) −15.7216 −0.771744
\(416\) 15.2719 0.748764
\(417\) −20.5265 −1.00519
\(418\) −13.4791 −0.659286
\(419\) 17.9732 0.878050 0.439025 0.898475i \(-0.355324\pi\)
0.439025 + 0.898475i \(0.355324\pi\)
\(420\) −1.48658 −0.0725375
\(421\) −7.56122 −0.368511 −0.184256 0.982878i \(-0.558987\pi\)
−0.184256 + 0.982878i \(0.558987\pi\)
\(422\) −5.46513 −0.266038
\(423\) 9.58108 0.465848
\(424\) −20.4142 −0.991403
\(425\) 2.62798 0.127476
\(426\) −7.93735 −0.384566
\(427\) −10.6283 −0.514341
\(428\) 1.28602 0.0621621
\(429\) −6.39695 −0.308847
\(430\) 5.97593 0.288185
\(431\) 38.1848 1.83930 0.919649 0.392742i \(-0.128474\pi\)
0.919649 + 0.392742i \(0.128474\pi\)
\(432\) −0.158119 −0.00760752
\(433\) 14.8475 0.713525 0.356762 0.934195i \(-0.383881\pi\)
0.356762 + 0.934195i \(0.383881\pi\)
\(434\) 4.42608 0.212459
\(435\) 4.04780 0.194077
\(436\) 7.66704 0.367185
\(437\) 1.62648 0.0778049
\(438\) −11.3559 −0.542606
\(439\) 4.53100 0.216253 0.108126 0.994137i \(-0.465515\pi\)
0.108126 + 0.994137i \(0.465515\pi\)
\(440\) −6.69147 −0.319003
\(441\) −5.46643 −0.260306
\(442\) 6.42895 0.305794
\(443\) 4.37559 0.207891 0.103945 0.994583i \(-0.466853\pi\)
0.103945 + 0.994583i \(0.466853\pi\)
\(444\) 7.13431 0.338579
\(445\) 0.511577 0.0242511
\(446\) 1.62166 0.0767880
\(447\) −7.19674 −0.340394
\(448\) −6.57299 −0.310544
\(449\) −14.4095 −0.680027 −0.340014 0.940420i \(-0.610432\pi\)
−0.340014 + 0.940420i \(0.610432\pi\)
\(450\) 0.894188 0.0421524
\(451\) 17.1195 0.806127
\(452\) −9.35873 −0.440197
\(453\) −17.6348 −0.828553
\(454\) −4.31838 −0.202672
\(455\) 3.38797 0.158830
\(456\) −18.4495 −0.863978
\(457\) 23.8458 1.11546 0.557729 0.830023i \(-0.311673\pi\)
0.557729 + 0.830023i \(0.311673\pi\)
\(458\) −3.35658 −0.156843
\(459\) 2.62798 0.122664
\(460\) 0.302855 0.0141207
\(461\) 2.05310 0.0956226 0.0478113 0.998856i \(-0.484775\pi\)
0.0478113 + 0.998856i \(0.484775\pi\)
\(462\) 2.58920 0.120460
\(463\) −4.02036 −0.186842 −0.0934210 0.995627i \(-0.529780\pi\)
−0.0934210 + 0.995627i \(0.529780\pi\)
\(464\) 0.640036 0.0297129
\(465\) 3.99704 0.185358
\(466\) −6.38511 −0.295784
\(467\) −12.1488 −0.562178 −0.281089 0.959682i \(-0.590696\pi\)
−0.281089 + 0.959682i \(0.590696\pi\)
\(468\) −3.28416 −0.151810
\(469\) −2.93992 −0.135753
\(470\) −8.56729 −0.395180
\(471\) −14.1066 −0.649996
\(472\) 37.3294 1.71823
\(473\) 15.6265 0.718507
\(474\) 4.47758 0.205662
\(475\) 6.44686 0.295802
\(476\) 3.90670 0.179063
\(477\) 7.13339 0.326616
\(478\) −16.6577 −0.761905
\(479\) 5.23016 0.238972 0.119486 0.992836i \(-0.461875\pi\)
0.119486 + 0.992836i \(0.461875\pi\)
\(480\) −5.58218 −0.254791
\(481\) −16.2594 −0.741364
\(482\) 20.0501 0.913257
\(483\) −0.312429 −0.0142160
\(484\) 6.64165 0.301893
\(485\) 8.25939 0.375040
\(486\) 0.894188 0.0405612
\(487\) −19.2870 −0.873979 −0.436989 0.899467i \(-0.643955\pi\)
−0.436989 + 0.899467i \(0.643955\pi\)
\(488\) −24.5613 −1.11184
\(489\) −16.7070 −0.755516
\(490\) 4.88802 0.220818
\(491\) −9.18328 −0.414436 −0.207218 0.978295i \(-0.566441\pi\)
−0.207218 + 0.978295i \(0.566441\pi\)
\(492\) 8.78907 0.396242
\(493\) −10.6376 −0.479092
\(494\) 15.7712 0.709580
\(495\) 2.33822 0.105095
\(496\) 0.632009 0.0283781
\(497\) 10.9925 0.493083
\(498\) 14.0581 0.629958
\(499\) −8.60218 −0.385087 −0.192543 0.981288i \(-0.561674\pi\)
−0.192543 + 0.981288i \(0.561674\pi\)
\(500\) 1.20043 0.0536847
\(501\) −20.7124 −0.925361
\(502\) 13.9764 0.623799
\(503\) 4.71685 0.210314 0.105157 0.994456i \(-0.466465\pi\)
0.105157 + 0.994456i \(0.466465\pi\)
\(504\) 3.54396 0.157860
\(505\) −8.20247 −0.365005
\(506\) −0.527488 −0.0234497
\(507\) −5.51528 −0.244942
\(508\) 5.41041 0.240048
\(509\) −11.6534 −0.516527 −0.258264 0.966074i \(-0.583150\pi\)
−0.258264 + 0.966074i \(0.583150\pi\)
\(510\) −2.34991 −0.104056
\(511\) 15.7269 0.695719
\(512\) −1.78766 −0.0790041
\(513\) 6.44686 0.284636
\(514\) −8.45567 −0.372964
\(515\) 13.5598 0.597518
\(516\) 8.02255 0.353173
\(517\) −22.4027 −0.985268
\(518\) 6.58107 0.289156
\(519\) −11.0999 −0.487231
\(520\) 7.82933 0.343339
\(521\) 14.5413 0.637064 0.318532 0.947912i \(-0.396810\pi\)
0.318532 + 0.947912i \(0.396810\pi\)
\(522\) −3.61950 −0.158421
\(523\) −24.4936 −1.07103 −0.535515 0.844526i \(-0.679883\pi\)
−0.535515 + 0.844526i \(0.679883\pi\)
\(524\) −11.8053 −0.515717
\(525\) −1.23837 −0.0540470
\(526\) 0.489899 0.0213606
\(527\) −10.5042 −0.457568
\(528\) 0.369717 0.0160899
\(529\) −22.9363 −0.997233
\(530\) −6.37860 −0.277069
\(531\) −13.0441 −0.566066
\(532\) 9.58375 0.415508
\(533\) −20.0307 −0.867624
\(534\) −0.457446 −0.0197956
\(535\) 1.07130 0.0463164
\(536\) −6.79392 −0.293453
\(537\) −22.6227 −0.976240
\(538\) −0.828000 −0.0356976
\(539\) 12.7817 0.550547
\(540\) 1.20043 0.0516582
\(541\) −10.6550 −0.458095 −0.229048 0.973415i \(-0.573561\pi\)
−0.229048 + 0.973415i \(0.573561\pi\)
\(542\) 0.981663 0.0421660
\(543\) −21.9859 −0.943504
\(544\) 14.6699 0.628966
\(545\) 6.38693 0.273586
\(546\) −3.02948 −0.129650
\(547\) −13.5171 −0.577947 −0.288974 0.957337i \(-0.593314\pi\)
−0.288974 + 0.957337i \(0.593314\pi\)
\(548\) −9.31677 −0.397993
\(549\) 8.58250 0.366292
\(550\) −2.09081 −0.0891523
\(551\) −26.0956 −1.11171
\(552\) −0.721998 −0.0307303
\(553\) −6.20106 −0.263696
\(554\) −16.4506 −0.698921
\(555\) 5.94314 0.252272
\(556\) 24.6406 1.04499
\(557\) 15.8094 0.669865 0.334933 0.942242i \(-0.391286\pi\)
0.334933 + 0.942242i \(0.391286\pi\)
\(558\) −3.57411 −0.151304
\(559\) −18.2837 −0.773319
\(560\) −0.195811 −0.00827451
\(561\) −6.14480 −0.259434
\(562\) 9.80824 0.413736
\(563\) −9.59235 −0.404270 −0.202135 0.979358i \(-0.564788\pi\)
−0.202135 + 0.979358i \(0.564788\pi\)
\(564\) −11.5014 −0.484296
\(565\) −7.79616 −0.327987
\(566\) 13.3336 0.560451
\(567\) −1.23837 −0.0520068
\(568\) 25.4029 1.06588
\(569\) −25.6094 −1.07360 −0.536800 0.843709i \(-0.680367\pi\)
−0.536800 + 0.843709i \(0.680367\pi\)
\(570\) −5.76471 −0.241457
\(571\) 35.5587 1.48809 0.744043 0.668132i \(-0.232906\pi\)
0.744043 + 0.668132i \(0.232906\pi\)
\(572\) 7.67907 0.321078
\(573\) −3.62710 −0.151524
\(574\) 8.10751 0.338401
\(575\) 0.252290 0.0105212
\(576\) 5.30776 0.221157
\(577\) −12.9952 −0.540997 −0.270498 0.962720i \(-0.587188\pi\)
−0.270498 + 0.962720i \(0.587188\pi\)
\(578\) −9.02566 −0.375418
\(579\) 18.8754 0.784434
\(580\) −4.85909 −0.201763
\(581\) −19.4692 −0.807720
\(582\) −7.38545 −0.306137
\(583\) −16.6794 −0.690791
\(584\) 36.3437 1.50391
\(585\) −2.73582 −0.113112
\(586\) 19.5459 0.807435
\(587\) 19.0102 0.784636 0.392318 0.919830i \(-0.371673\pi\)
0.392318 + 0.919830i \(0.371673\pi\)
\(588\) 6.56205 0.270615
\(589\) −25.7684 −1.06177
\(590\) 11.6639 0.480195
\(591\) −10.4283 −0.428964
\(592\) 0.939726 0.0386225
\(593\) 16.6492 0.683702 0.341851 0.939754i \(-0.388946\pi\)
0.341851 + 0.939754i \(0.388946\pi\)
\(594\) −2.09081 −0.0857868
\(595\) 3.25443 0.133418
\(596\) 8.63916 0.353874
\(597\) 24.7050 1.01111
\(598\) 0.617186 0.0252386
\(599\) −2.54859 −0.104133 −0.0520663 0.998644i \(-0.516581\pi\)
−0.0520663 + 0.998644i \(0.516581\pi\)
\(600\) −2.86178 −0.116832
\(601\) −5.38650 −0.219720 −0.109860 0.993947i \(-0.535040\pi\)
−0.109860 + 0.993947i \(0.535040\pi\)
\(602\) 7.40043 0.301619
\(603\) 2.37402 0.0966774
\(604\) 21.1693 0.861365
\(605\) 5.53274 0.224938
\(606\) 7.33455 0.297946
\(607\) 27.2500 1.10604 0.553021 0.833167i \(-0.313475\pi\)
0.553021 + 0.833167i \(0.313475\pi\)
\(608\) 35.9875 1.45949
\(609\) 5.01269 0.203124
\(610\) −7.67437 −0.310726
\(611\) 26.2121 1.06043
\(612\) −3.15470 −0.127521
\(613\) 27.8673 1.12555 0.562775 0.826610i \(-0.309734\pi\)
0.562775 + 0.826610i \(0.309734\pi\)
\(614\) −3.21369 −0.129694
\(615\) 7.32162 0.295236
\(616\) −8.28654 −0.333874
\(617\) −3.90079 −0.157040 −0.0785199 0.996913i \(-0.525019\pi\)
−0.0785199 + 0.996913i \(0.525019\pi\)
\(618\) −12.1250 −0.487741
\(619\) 23.0232 0.925379 0.462689 0.886520i \(-0.346885\pi\)
0.462689 + 0.886520i \(0.346885\pi\)
\(620\) −4.79816 −0.192699
\(621\) 0.252290 0.0101240
\(622\) 12.6286 0.506360
\(623\) 0.633524 0.0253816
\(624\) −0.432586 −0.0173173
\(625\) 1.00000 0.0400000
\(626\) 0.141412 0.00565198
\(627\) −15.0742 −0.602004
\(628\) 16.9339 0.675736
\(629\) −15.6185 −0.622750
\(630\) 1.10734 0.0441174
\(631\) −28.5584 −1.13689 −0.568447 0.822720i \(-0.692455\pi\)
−0.568447 + 0.822720i \(0.692455\pi\)
\(632\) −14.3302 −0.570023
\(633\) −6.11184 −0.242924
\(634\) 1.75111 0.0695454
\(635\) 4.50707 0.178858
\(636\) −8.56312 −0.339550
\(637\) −14.9552 −0.592546
\(638\) 8.46317 0.335060
\(639\) −8.87660 −0.351153
\(640\) 6.41823 0.253703
\(641\) 6.40836 0.253115 0.126558 0.991959i \(-0.459607\pi\)
0.126558 + 0.991959i \(0.459607\pi\)
\(642\) −0.957945 −0.0378071
\(643\) 49.0025 1.93247 0.966234 0.257665i \(-0.0829531\pi\)
0.966234 + 0.257665i \(0.0829531\pi\)
\(644\) 0.375048 0.0147790
\(645\) 6.68308 0.263146
\(646\) 15.1496 0.596052
\(647\) −17.0173 −0.669020 −0.334510 0.942392i \(-0.608571\pi\)
−0.334510 + 0.942392i \(0.608571\pi\)
\(648\) −2.86178 −0.112422
\(649\) 30.5000 1.19723
\(650\) 2.44634 0.0959534
\(651\) 4.94983 0.193999
\(652\) 20.0555 0.785435
\(653\) −0.168620 −0.00659862 −0.00329931 0.999995i \(-0.501050\pi\)
−0.00329931 + 0.999995i \(0.501050\pi\)
\(654\) −5.71112 −0.223322
\(655\) −9.83424 −0.384256
\(656\) 1.15769 0.0452002
\(657\) −12.6997 −0.495462
\(658\) −10.6095 −0.413602
\(659\) −6.27007 −0.244247 −0.122124 0.992515i \(-0.538970\pi\)
−0.122124 + 0.992515i \(0.538970\pi\)
\(660\) −2.80686 −0.109257
\(661\) 36.3017 1.41197 0.705986 0.708225i \(-0.250504\pi\)
0.705986 + 0.708225i \(0.250504\pi\)
\(662\) −3.18519 −0.123796
\(663\) 7.18970 0.279225
\(664\) −44.9919 −1.74602
\(665\) 7.98362 0.309591
\(666\) −5.31429 −0.205924
\(667\) −1.02122 −0.0395417
\(668\) 24.8637 0.962005
\(669\) 1.81356 0.0701163
\(670\) −2.12282 −0.0820116
\(671\) −20.0677 −0.774706
\(672\) −6.91282 −0.266668
\(673\) −36.9261 −1.42340 −0.711698 0.702485i \(-0.752074\pi\)
−0.711698 + 0.702485i \(0.752074\pi\)
\(674\) −14.1711 −0.545852
\(675\) 1.00000 0.0384900
\(676\) 6.62069 0.254642
\(677\) −6.02639 −0.231613 −0.115807 0.993272i \(-0.536945\pi\)
−0.115807 + 0.993272i \(0.536945\pi\)
\(678\) 6.97124 0.267729
\(679\) 10.2282 0.392523
\(680\) 7.52073 0.288407
\(681\) −4.82939 −0.185062
\(682\) 8.35704 0.320007
\(683\) 23.9474 0.916323 0.458161 0.888869i \(-0.348508\pi\)
0.458161 + 0.888869i \(0.348508\pi\)
\(684\) −7.73899 −0.295908
\(685\) −7.76121 −0.296541
\(686\) 13.8046 0.527061
\(687\) −3.75378 −0.143216
\(688\) 1.05672 0.0402872
\(689\) 19.5157 0.743489
\(690\) −0.225594 −0.00858823
\(691\) 34.0282 1.29449 0.647247 0.762281i \(-0.275920\pi\)
0.647247 + 0.762281i \(0.275920\pi\)
\(692\) 13.3246 0.506525
\(693\) 2.89559 0.109994
\(694\) −12.0015 −0.455570
\(695\) 20.5265 0.778614
\(696\) 11.5839 0.439088
\(697\) −19.2411 −0.728809
\(698\) 3.61417 0.136798
\(699\) −7.14068 −0.270085
\(700\) 1.48658 0.0561873
\(701\) −38.8971 −1.46912 −0.734561 0.678542i \(-0.762612\pi\)
−0.734561 + 0.678542i \(0.762612\pi\)
\(702\) 2.44634 0.0923312
\(703\) −38.3146 −1.44506
\(704\) −12.4107 −0.467746
\(705\) −9.58108 −0.360845
\(706\) −5.96932 −0.224658
\(707\) −10.1577 −0.382020
\(708\) 15.6585 0.588483
\(709\) −24.2856 −0.912064 −0.456032 0.889963i \(-0.650730\pi\)
−0.456032 + 0.889963i \(0.650730\pi\)
\(710\) 7.93735 0.297884
\(711\) 5.00742 0.187793
\(712\) 1.46402 0.0548666
\(713\) −1.00841 −0.0377653
\(714\) −2.91007 −0.108907
\(715\) 6.39695 0.239232
\(716\) 27.1569 1.01490
\(717\) −18.6288 −0.695706
\(718\) 18.0507 0.673647
\(719\) 30.3900 1.13336 0.566678 0.823939i \(-0.308228\pi\)
0.566678 + 0.823939i \(0.308228\pi\)
\(720\) 0.158119 0.00589276
\(721\) 16.7921 0.625372
\(722\) 20.1747 0.750824
\(723\) 22.4227 0.833908
\(724\) 26.3925 0.980868
\(725\) −4.04780 −0.150332
\(726\) −4.94731 −0.183612
\(727\) 3.98401 0.147759 0.0738793 0.997267i \(-0.476462\pi\)
0.0738793 + 0.997267i \(0.476462\pi\)
\(728\) 9.69564 0.359344
\(729\) 1.00000 0.0370370
\(730\) 11.3559 0.420301
\(731\) −17.5630 −0.649592
\(732\) −10.3027 −0.380797
\(733\) 42.7431 1.57875 0.789376 0.613910i \(-0.210404\pi\)
0.789376 + 0.613910i \(0.210404\pi\)
\(734\) 8.43781 0.311445
\(735\) 5.46643 0.201632
\(736\) 1.40833 0.0519116
\(737\) −5.55096 −0.204472
\(738\) −6.54691 −0.240995
\(739\) −38.6570 −1.42202 −0.711010 0.703182i \(-0.751762\pi\)
−0.711010 + 0.703182i \(0.751762\pi\)
\(740\) −7.13431 −0.262262
\(741\) 17.6375 0.647928
\(742\) −7.89908 −0.289984
\(743\) 48.0976 1.76453 0.882265 0.470752i \(-0.156017\pi\)
0.882265 + 0.470752i \(0.156017\pi\)
\(744\) 11.4387 0.419362
\(745\) 7.19674 0.263668
\(746\) 16.2839 0.596197
\(747\) 15.7216 0.575224
\(748\) 7.37638 0.269707
\(749\) 1.32667 0.0484755
\(750\) −0.894188 −0.0326511
\(751\) −46.7733 −1.70678 −0.853391 0.521272i \(-0.825458\pi\)
−0.853391 + 0.521272i \(0.825458\pi\)
\(752\) −1.51495 −0.0552447
\(753\) 15.6303 0.569600
\(754\) −9.90230 −0.360621
\(755\) 17.6348 0.641795
\(756\) 1.48658 0.0540663
\(757\) 5.76736 0.209618 0.104809 0.994492i \(-0.466577\pi\)
0.104809 + 0.994492i \(0.466577\pi\)
\(758\) −4.69544 −0.170546
\(759\) −0.589908 −0.0214123
\(760\) 18.4495 0.669235
\(761\) 14.9700 0.542662 0.271331 0.962486i \(-0.412536\pi\)
0.271331 + 0.962486i \(0.412536\pi\)
\(762\) −4.03017 −0.145998
\(763\) 7.90940 0.286340
\(764\) 4.35407 0.157525
\(765\) −2.62798 −0.0950150
\(766\) 24.4740 0.884281
\(767\) −35.6864 −1.28856
\(768\) −16.3546 −0.590147
\(769\) −35.5597 −1.28232 −0.641158 0.767409i \(-0.721546\pi\)
−0.641158 + 0.767409i \(0.721546\pi\)
\(770\) −2.58920 −0.0933082
\(771\) −9.45626 −0.340559
\(772\) −22.6585 −0.815498
\(773\) −11.3942 −0.409821 −0.204911 0.978781i \(-0.565690\pi\)
−0.204911 + 0.978781i \(0.565690\pi\)
\(774\) −5.97593 −0.214800
\(775\) −3.99704 −0.143578
\(776\) 23.6366 0.848504
\(777\) 7.35983 0.264032
\(778\) −24.1688 −0.866494
\(779\) −47.2015 −1.69117
\(780\) 3.28416 0.117592
\(781\) 20.7554 0.742687
\(782\) 0.592858 0.0212006
\(783\) −4.04780 −0.144657
\(784\) 0.864349 0.0308696
\(785\) 14.1066 0.503485
\(786\) 8.79366 0.313660
\(787\) 15.8265 0.564153 0.282076 0.959392i \(-0.408977\pi\)
0.282076 + 0.959392i \(0.408977\pi\)
\(788\) 12.5184 0.445951
\(789\) 0.547871 0.0195047
\(790\) −4.47758 −0.159305
\(791\) −9.65456 −0.343277
\(792\) 6.69147 0.237771
\(793\) 23.4802 0.833806
\(794\) −8.59584 −0.305055
\(795\) −7.13339 −0.252995
\(796\) −29.6566 −1.05115
\(797\) 6.49567 0.230088 0.115044 0.993360i \(-0.463299\pi\)
0.115044 + 0.993360i \(0.463299\pi\)
\(798\) −7.13886 −0.252713
\(799\) 25.1789 0.890767
\(800\) 5.58218 0.197360
\(801\) −0.511577 −0.0180757
\(802\) 0.894188 0.0315749
\(803\) 29.6946 1.04790
\(804\) −2.84983 −0.100506
\(805\) 0.312429 0.0110117
\(806\) −9.77812 −0.344420
\(807\) −0.925980 −0.0325960
\(808\) −23.4737 −0.825802
\(809\) −11.3612 −0.399439 −0.199719 0.979853i \(-0.564003\pi\)
−0.199719 + 0.979853i \(0.564003\pi\)
\(810\) −0.894188 −0.0314186
\(811\) −3.57942 −0.125690 −0.0628452 0.998023i \(-0.520017\pi\)
−0.0628452 + 0.998023i \(0.520017\pi\)
\(812\) −6.01737 −0.211168
\(813\) 1.09783 0.0385024
\(814\) 12.4260 0.435530
\(815\) 16.7070 0.585220
\(816\) −0.415535 −0.0145466
\(817\) −43.0849 −1.50735
\(818\) 32.5452 1.13791
\(819\) −3.38797 −0.118385
\(820\) −8.78907 −0.306928
\(821\) 36.7564 1.28281 0.641404 0.767203i \(-0.278352\pi\)
0.641404 + 0.767203i \(0.278352\pi\)
\(822\) 6.93999 0.242060
\(823\) −43.1865 −1.50539 −0.752693 0.658371i \(-0.771246\pi\)
−0.752693 + 0.658371i \(0.771246\pi\)
\(824\) 38.8053 1.35185
\(825\) −2.33822 −0.0814063
\(826\) 14.4443 0.502580
\(827\) −49.2282 −1.71183 −0.855916 0.517115i \(-0.827006\pi\)
−0.855916 + 0.517115i \(0.827006\pi\)
\(828\) −0.302855 −0.0105249
\(829\) −17.3300 −0.601895 −0.300948 0.953641i \(-0.597303\pi\)
−0.300948 + 0.953641i \(0.597303\pi\)
\(830\) −14.0581 −0.487963
\(831\) −18.3973 −0.638195
\(832\) 14.5211 0.503428
\(833\) −14.3657 −0.497742
\(834\) −18.3545 −0.635566
\(835\) 20.7124 0.716781
\(836\) 18.0954 0.625844
\(837\) −3.99704 −0.138158
\(838\) 16.0715 0.555179
\(839\) 48.5427 1.67588 0.837940 0.545762i \(-0.183760\pi\)
0.837940 + 0.545762i \(0.183760\pi\)
\(840\) −3.54396 −0.122278
\(841\) −12.6153 −0.435010
\(842\) −6.76115 −0.233005
\(843\) 10.9689 0.377788
\(844\) 7.33681 0.252544
\(845\) 5.51528 0.189731
\(846\) 8.56729 0.294550
\(847\) 6.85160 0.235424
\(848\) −1.12793 −0.0387332
\(849\) 14.9113 0.511756
\(850\) 2.34991 0.0806014
\(851\) −1.49939 −0.0513985
\(852\) 10.6557 0.365059
\(853\) −37.3764 −1.27974 −0.639872 0.768482i \(-0.721012\pi\)
−0.639872 + 0.768482i \(0.721012\pi\)
\(854\) −9.50373 −0.325211
\(855\) −6.44686 −0.220478
\(856\) 3.06583 0.104788
\(857\) −10.1630 −0.347162 −0.173581 0.984820i \(-0.555534\pi\)
−0.173581 + 0.984820i \(0.555534\pi\)
\(858\) −5.72007 −0.195280
\(859\) −45.9498 −1.56779 −0.783894 0.620895i \(-0.786769\pi\)
−0.783894 + 0.620895i \(0.786769\pi\)
\(860\) −8.02255 −0.273567
\(861\) 9.06690 0.308999
\(862\) 34.1444 1.16296
\(863\) 36.5510 1.24421 0.622105 0.782934i \(-0.286278\pi\)
0.622105 + 0.782934i \(0.286278\pi\)
\(864\) 5.58218 0.189910
\(865\) 11.0999 0.377407
\(866\) 13.2764 0.451152
\(867\) −10.0937 −0.342800
\(868\) −5.94191 −0.201682
\(869\) −11.7084 −0.397182
\(870\) 3.61950 0.122712
\(871\) 6.49488 0.220071
\(872\) 18.2780 0.618972
\(873\) −8.25939 −0.279538
\(874\) 1.45438 0.0491950
\(875\) 1.23837 0.0418647
\(876\) 15.2450 0.515082
\(877\) 6.64708 0.224456 0.112228 0.993682i \(-0.464201\pi\)
0.112228 + 0.993682i \(0.464201\pi\)
\(878\) 4.05157 0.136734
\(879\) 21.8589 0.737281
\(880\) −0.369717 −0.0124632
\(881\) −33.7476 −1.13698 −0.568492 0.822689i \(-0.692473\pi\)
−0.568492 + 0.822689i \(0.692473\pi\)
\(882\) −4.88802 −0.164588
\(883\) −44.1013 −1.48413 −0.742063 0.670330i \(-0.766153\pi\)
−0.742063 + 0.670330i \(0.766153\pi\)
\(884\) −8.63071 −0.290282
\(885\) 13.0441 0.438473
\(886\) 3.91260 0.131446
\(887\) 26.1653 0.878544 0.439272 0.898354i \(-0.355237\pi\)
0.439272 + 0.898354i \(0.355237\pi\)
\(888\) 17.0080 0.570751
\(889\) 5.58143 0.187195
\(890\) 0.457446 0.0153336
\(891\) −2.33822 −0.0783332
\(892\) −2.17705 −0.0728930
\(893\) 61.7679 2.06698
\(894\) −6.43524 −0.215227
\(895\) 22.6227 0.756192
\(896\) 7.94816 0.265529
\(897\) 0.690219 0.0230458
\(898\) −12.8848 −0.429972
\(899\) 16.1792 0.539608
\(900\) −1.20043 −0.0400142
\(901\) 18.7465 0.624535
\(902\) 15.3081 0.509704
\(903\) 8.27614 0.275413
\(904\) −22.3109 −0.742051
\(905\) 21.9859 0.730835
\(906\) −15.7688 −0.523883
\(907\) 7.53650 0.250245 0.125123 0.992141i \(-0.460068\pi\)
0.125123 + 0.992141i \(0.460068\pi\)
\(908\) 5.79733 0.192391
\(909\) 8.20247 0.272059
\(910\) 3.02948 0.100426
\(911\) 21.9719 0.727962 0.363981 0.931406i \(-0.381417\pi\)
0.363981 + 0.931406i \(0.381417\pi\)
\(912\) −1.01937 −0.0337548
\(913\) −36.7606 −1.21660
\(914\) 21.3226 0.705289
\(915\) −8.58250 −0.283729
\(916\) 4.50614 0.148887
\(917\) −12.1785 −0.402168
\(918\) 2.34991 0.0775587
\(919\) 8.33852 0.275062 0.137531 0.990497i \(-0.456083\pi\)
0.137531 + 0.990497i \(0.456083\pi\)
\(920\) 0.721998 0.0238036
\(921\) −3.59398 −0.118426
\(922\) 1.83586 0.0604609
\(923\) −24.2848 −0.799344
\(924\) −3.47594 −0.114350
\(925\) −5.94314 −0.195409
\(926\) −3.59496 −0.118138
\(927\) −13.5598 −0.445364
\(928\) −22.5956 −0.741736
\(929\) 23.3917 0.767457 0.383728 0.923446i \(-0.374640\pi\)
0.383728 + 0.923446i \(0.374640\pi\)
\(930\) 3.57411 0.117200
\(931\) −35.2413 −1.15499
\(932\) 8.57186 0.280781
\(933\) 14.1229 0.462365
\(934\) −10.8633 −0.355458
\(935\) 6.14480 0.200956
\(936\) −7.82933 −0.255910
\(937\) −42.7989 −1.39818 −0.699090 0.715034i \(-0.746411\pi\)
−0.699090 + 0.715034i \(0.746411\pi\)
\(938\) −2.62884 −0.0858346
\(939\) 0.158146 0.00516090
\(940\) 11.5014 0.375134
\(941\) 4.46473 0.145546 0.0727730 0.997349i \(-0.476815\pi\)
0.0727730 + 0.997349i \(0.476815\pi\)
\(942\) −12.6139 −0.410984
\(943\) −1.84717 −0.0601521
\(944\) 2.06253 0.0671295
\(945\) 1.23837 0.0402843
\(946\) 13.9730 0.454302
\(947\) −0.0122997 −0.000399687 0 −0.000199843 1.00000i \(-0.500064\pi\)
−0.000199843 1.00000i \(0.500064\pi\)
\(948\) −6.01105 −0.195230
\(949\) −34.7441 −1.12784
\(950\) 5.76471 0.187032
\(951\) 1.95832 0.0635029
\(952\) 9.31347 0.301851
\(953\) −35.0610 −1.13574 −0.567869 0.823119i \(-0.692232\pi\)
−0.567869 + 0.823119i \(0.692232\pi\)
\(954\) 6.37860 0.206515
\(955\) 3.62710 0.117370
\(956\) 22.3626 0.723257
\(957\) 9.46464 0.305948
\(958\) 4.67675 0.151099
\(959\) −9.61128 −0.310364
\(960\) −5.30776 −0.171307
\(961\) −15.0237 −0.484635
\(962\) −14.5389 −0.468754
\(963\) −1.07130 −0.0345222
\(964\) −26.9168 −0.866932
\(965\) −18.8754 −0.607620
\(966\) −0.279370 −0.00898858
\(967\) 30.1640 0.970009 0.485004 0.874512i \(-0.338818\pi\)
0.485004 + 0.874512i \(0.338818\pi\)
\(968\) 15.8335 0.508908
\(969\) 16.9423 0.544263
\(970\) 7.38545 0.237132
\(971\) 55.5418 1.78242 0.891210 0.453590i \(-0.149857\pi\)
0.891210 + 0.453590i \(0.149857\pi\)
\(972\) −1.20043 −0.0385037
\(973\) 25.4194 0.814910
\(974\) −17.2462 −0.552605
\(975\) 2.73582 0.0876164
\(976\) −1.35706 −0.0434384
\(977\) −55.1344 −1.76390 −0.881952 0.471339i \(-0.843771\pi\)
−0.881952 + 0.471339i \(0.843771\pi\)
\(978\) −14.9392 −0.477703
\(979\) 1.19618 0.0382300
\(980\) −6.56205 −0.209617
\(981\) −6.38693 −0.203919
\(982\) −8.21158 −0.262042
\(983\) −6.30521 −0.201105 −0.100553 0.994932i \(-0.532061\pi\)
−0.100553 + 0.994932i \(0.532061\pi\)
\(984\) 20.9529 0.667954
\(985\) 10.4283 0.332274
\(986\) −9.51199 −0.302923
\(987\) −11.8650 −0.377666
\(988\) −21.1725 −0.673587
\(989\) −1.68607 −0.0536139
\(990\) 2.09081 0.0664502
\(991\) 26.3922 0.838377 0.419189 0.907899i \(-0.362315\pi\)
0.419189 + 0.907899i \(0.362315\pi\)
\(992\) −22.3122 −0.708413
\(993\) −3.56211 −0.113040
\(994\) 9.82941 0.311770
\(995\) −24.7050 −0.783202
\(996\) −18.8727 −0.598003
\(997\) 46.1483 1.46153 0.730766 0.682628i \(-0.239163\pi\)
0.730766 + 0.682628i \(0.239163\pi\)
\(998\) −7.69197 −0.243485
\(999\) −5.94314 −0.188033
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 6015.2.a.c.1.19 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6015.2.a.c.1.19 28 1.1 even 1 trivial