Properties

Label 4029.2.a.g.1.15
Level $4029$
Weight $2$
Character 4029.1
Self dual yes
Analytic conductor $32.172$
Analytic rank $1$
Dimension $22$
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] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.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: \(32.1717269744\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 4029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.13663 q^{2} -1.00000 q^{3} -0.708075 q^{4} +0.214323 q^{5} -1.13663 q^{6} -3.67011 q^{7} -3.07808 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.13663 q^{2} -1.00000 q^{3} -0.708075 q^{4} +0.214323 q^{5} -1.13663 q^{6} -3.67011 q^{7} -3.07808 q^{8} +1.00000 q^{9} +0.243606 q^{10} +1.55131 q^{11} +0.708075 q^{12} +4.74297 q^{13} -4.17155 q^{14} -0.214323 q^{15} -2.08248 q^{16} -1.00000 q^{17} +1.13663 q^{18} +2.11286 q^{19} -0.151757 q^{20} +3.67011 q^{21} +1.76326 q^{22} +6.11579 q^{23} +3.07808 q^{24} -4.95407 q^{25} +5.39099 q^{26} -1.00000 q^{27} +2.59871 q^{28} +2.33087 q^{29} -0.243606 q^{30} +2.34245 q^{31} +3.78915 q^{32} -1.55131 q^{33} -1.13663 q^{34} -0.786588 q^{35} -0.708075 q^{36} -1.25736 q^{37} +2.40153 q^{38} -4.74297 q^{39} -0.659702 q^{40} -5.50155 q^{41} +4.17155 q^{42} -1.86178 q^{43} -1.09844 q^{44} +0.214323 q^{45} +6.95138 q^{46} -11.7711 q^{47} +2.08248 q^{48} +6.46968 q^{49} -5.63093 q^{50} +1.00000 q^{51} -3.35838 q^{52} +10.9367 q^{53} -1.13663 q^{54} +0.332481 q^{55} +11.2969 q^{56} -2.11286 q^{57} +2.64933 q^{58} -9.95337 q^{59} +0.151757 q^{60} +0.941200 q^{61} +2.66249 q^{62} -3.67011 q^{63} +8.47181 q^{64} +1.01653 q^{65} -1.76326 q^{66} -9.40312 q^{67} +0.708075 q^{68} -6.11579 q^{69} -0.894059 q^{70} -11.5189 q^{71} -3.07808 q^{72} +8.55533 q^{73} -1.42916 q^{74} +4.95407 q^{75} -1.49606 q^{76} -5.69347 q^{77} -5.39099 q^{78} -1.00000 q^{79} -0.446323 q^{80} +1.00000 q^{81} -6.25322 q^{82} +0.671241 q^{83} -2.59871 q^{84} -0.214323 q^{85} -2.11615 q^{86} -2.33087 q^{87} -4.77505 q^{88} +9.15637 q^{89} +0.243606 q^{90} -17.4072 q^{91} -4.33044 q^{92} -2.34245 q^{93} -13.3794 q^{94} +0.452834 q^{95} -3.78915 q^{96} -9.74734 q^{97} +7.35362 q^{98} +1.55131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.13663 0.803718 0.401859 0.915702i \(-0.368364\pi\)
0.401859 + 0.915702i \(0.368364\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.708075 −0.354038
\(5\) 0.214323 0.0958482 0.0479241 0.998851i \(-0.484739\pi\)
0.0479241 + 0.998851i \(0.484739\pi\)
\(6\) −1.13663 −0.464027
\(7\) −3.67011 −1.38717 −0.693585 0.720375i \(-0.743970\pi\)
−0.693585 + 0.720375i \(0.743970\pi\)
\(8\) −3.07808 −1.08826
\(9\) 1.00000 0.333333
\(10\) 0.243606 0.0770349
\(11\) 1.55131 0.467738 0.233869 0.972268i \(-0.424861\pi\)
0.233869 + 0.972268i \(0.424861\pi\)
\(12\) 0.708075 0.204404
\(13\) 4.74297 1.31546 0.657731 0.753253i \(-0.271516\pi\)
0.657731 + 0.753253i \(0.271516\pi\)
\(14\) −4.17155 −1.11489
\(15\) −0.214323 −0.0553380
\(16\) −2.08248 −0.520620
\(17\) −1.00000 −0.242536
\(18\) 1.13663 0.267906
\(19\) 2.11286 0.484722 0.242361 0.970186i \(-0.422078\pi\)
0.242361 + 0.970186i \(0.422078\pi\)
\(20\) −0.151757 −0.0339339
\(21\) 3.67011 0.800883
\(22\) 1.76326 0.375929
\(23\) 6.11579 1.27523 0.637615 0.770355i \(-0.279921\pi\)
0.637615 + 0.770355i \(0.279921\pi\)
\(24\) 3.07808 0.628310
\(25\) −4.95407 −0.990813
\(26\) 5.39099 1.05726
\(27\) −1.00000 −0.192450
\(28\) 2.59871 0.491110
\(29\) 2.33087 0.432832 0.216416 0.976301i \(-0.430563\pi\)
0.216416 + 0.976301i \(0.430563\pi\)
\(30\) −0.243606 −0.0444761
\(31\) 2.34245 0.420716 0.210358 0.977624i \(-0.432537\pi\)
0.210358 + 0.977624i \(0.432537\pi\)
\(32\) 3.78915 0.669833
\(33\) −1.55131 −0.270048
\(34\) −1.13663 −0.194930
\(35\) −0.786588 −0.132958
\(36\) −0.708075 −0.118013
\(37\) −1.25736 −0.206709 −0.103355 0.994645i \(-0.532958\pi\)
−0.103355 + 0.994645i \(0.532958\pi\)
\(38\) 2.40153 0.389580
\(39\) −4.74297 −0.759483
\(40\) −0.659702 −0.104308
\(41\) −5.50155 −0.859199 −0.429599 0.903020i \(-0.641345\pi\)
−0.429599 + 0.903020i \(0.641345\pi\)
\(42\) 4.17155 0.643684
\(43\) −1.86178 −0.283919 −0.141959 0.989873i \(-0.545340\pi\)
−0.141959 + 0.989873i \(0.545340\pi\)
\(44\) −1.09844 −0.165597
\(45\) 0.214323 0.0319494
\(46\) 6.95138 1.02492
\(47\) −11.7711 −1.71699 −0.858497 0.512819i \(-0.828601\pi\)
−0.858497 + 0.512819i \(0.828601\pi\)
\(48\) 2.08248 0.300580
\(49\) 6.46968 0.924240
\(50\) −5.63093 −0.796334
\(51\) 1.00000 0.140028
\(52\) −3.35838 −0.465723
\(53\) 10.9367 1.50227 0.751134 0.660150i \(-0.229507\pi\)
0.751134 + 0.660150i \(0.229507\pi\)
\(54\) −1.13663 −0.154676
\(55\) 0.332481 0.0448318
\(56\) 11.2969 1.50961
\(57\) −2.11286 −0.279855
\(58\) 2.64933 0.347875
\(59\) −9.95337 −1.29582 −0.647909 0.761718i \(-0.724356\pi\)
−0.647909 + 0.761718i \(0.724356\pi\)
\(60\) 0.151757 0.0195917
\(61\) 0.941200 0.120508 0.0602542 0.998183i \(-0.480809\pi\)
0.0602542 + 0.998183i \(0.480809\pi\)
\(62\) 2.66249 0.338137
\(63\) −3.67011 −0.462390
\(64\) 8.47181 1.05898
\(65\) 1.01653 0.126085
\(66\) −1.76326 −0.217043
\(67\) −9.40312 −1.14877 −0.574387 0.818584i \(-0.694760\pi\)
−0.574387 + 0.818584i \(0.694760\pi\)
\(68\) 0.708075 0.0858668
\(69\) −6.11579 −0.736254
\(70\) −0.894059 −0.106860
\(71\) −11.5189 −1.36704 −0.683521 0.729931i \(-0.739552\pi\)
−0.683521 + 0.729931i \(0.739552\pi\)
\(72\) −3.07808 −0.362755
\(73\) 8.55533 1.00133 0.500663 0.865642i \(-0.333090\pi\)
0.500663 + 0.865642i \(0.333090\pi\)
\(74\) −1.42916 −0.166136
\(75\) 4.95407 0.572046
\(76\) −1.49606 −0.171610
\(77\) −5.69347 −0.648831
\(78\) −5.39099 −0.610410
\(79\) −1.00000 −0.112509
\(80\) −0.446323 −0.0499004
\(81\) 1.00000 0.111111
\(82\) −6.25322 −0.690553
\(83\) 0.671241 0.0736783 0.0368391 0.999321i \(-0.488271\pi\)
0.0368391 + 0.999321i \(0.488271\pi\)
\(84\) −2.59871 −0.283543
\(85\) −0.214323 −0.0232466
\(86\) −2.11615 −0.228190
\(87\) −2.33087 −0.249896
\(88\) −4.77505 −0.509022
\(89\) 9.15637 0.970573 0.485287 0.874355i \(-0.338715\pi\)
0.485287 + 0.874355i \(0.338715\pi\)
\(90\) 0.243606 0.0256783
\(91\) −17.4072 −1.82477
\(92\) −4.33044 −0.451479
\(93\) −2.34245 −0.242900
\(94\) −13.3794 −1.37998
\(95\) 0.452834 0.0464597
\(96\) −3.78915 −0.386728
\(97\) −9.74734 −0.989692 −0.494846 0.868981i \(-0.664776\pi\)
−0.494846 + 0.868981i \(0.664776\pi\)
\(98\) 7.35362 0.742828
\(99\) 1.55131 0.155913
\(100\) 3.50785 0.350785
\(101\) −7.11071 −0.707542 −0.353771 0.935332i \(-0.615101\pi\)
−0.353771 + 0.935332i \(0.615101\pi\)
\(102\) 1.13663 0.112543
\(103\) −16.2637 −1.60251 −0.801253 0.598325i \(-0.795833\pi\)
−0.801253 + 0.598325i \(0.795833\pi\)
\(104\) −14.5992 −1.43157
\(105\) 0.786588 0.0767631
\(106\) 12.4309 1.20740
\(107\) 1.70968 0.165281 0.0826406 0.996579i \(-0.473665\pi\)
0.0826406 + 0.996579i \(0.473665\pi\)
\(108\) 0.708075 0.0681346
\(109\) −12.4469 −1.19220 −0.596099 0.802911i \(-0.703283\pi\)
−0.596099 + 0.802911i \(0.703283\pi\)
\(110\) 0.377908 0.0360321
\(111\) 1.25736 0.119344
\(112\) 7.64292 0.722188
\(113\) −17.4918 −1.64549 −0.822745 0.568411i \(-0.807558\pi\)
−0.822745 + 0.568411i \(0.807558\pi\)
\(114\) −2.40153 −0.224924
\(115\) 1.31075 0.122228
\(116\) −1.65043 −0.153239
\(117\) 4.74297 0.438487
\(118\) −11.3133 −1.04147
\(119\) 3.67011 0.336438
\(120\) 0.659702 0.0602223
\(121\) −8.59344 −0.781222
\(122\) 1.06980 0.0968547
\(123\) 5.50155 0.496058
\(124\) −1.65863 −0.148949
\(125\) −2.13339 −0.190816
\(126\) −4.17155 −0.371631
\(127\) 6.09114 0.540502 0.270251 0.962790i \(-0.412893\pi\)
0.270251 + 0.962790i \(0.412893\pi\)
\(128\) 2.05101 0.181285
\(129\) 1.86178 0.163920
\(130\) 1.15541 0.101336
\(131\) −7.73013 −0.675384 −0.337692 0.941257i \(-0.609646\pi\)
−0.337692 + 0.941257i \(0.609646\pi\)
\(132\) 1.09844 0.0956073
\(133\) −7.75441 −0.672392
\(134\) −10.6879 −0.923290
\(135\) −0.214323 −0.0184460
\(136\) 3.07808 0.263943
\(137\) 16.9300 1.44643 0.723215 0.690623i \(-0.242664\pi\)
0.723215 + 0.690623i \(0.242664\pi\)
\(138\) −6.95138 −0.591741
\(139\) 12.7928 1.08507 0.542534 0.840034i \(-0.317465\pi\)
0.542534 + 0.840034i \(0.317465\pi\)
\(140\) 0.556964 0.0470720
\(141\) 11.7711 0.991307
\(142\) −13.0927 −1.09872
\(143\) 7.35781 0.615291
\(144\) −2.08248 −0.173540
\(145\) 0.499559 0.0414861
\(146\) 9.72423 0.804783
\(147\) −6.46968 −0.533610
\(148\) 0.890308 0.0731829
\(149\) −12.0048 −0.983468 −0.491734 0.870745i \(-0.663637\pi\)
−0.491734 + 0.870745i \(0.663637\pi\)
\(150\) 5.63093 0.459764
\(151\) −4.54958 −0.370240 −0.185120 0.982716i \(-0.559267\pi\)
−0.185120 + 0.982716i \(0.559267\pi\)
\(152\) −6.50353 −0.527506
\(153\) −1.00000 −0.0808452
\(154\) −6.47136 −0.521477
\(155\) 0.502040 0.0403248
\(156\) 3.35838 0.268885
\(157\) −8.32921 −0.664744 −0.332372 0.943148i \(-0.607849\pi\)
−0.332372 + 0.943148i \(0.607849\pi\)
\(158\) −1.13663 −0.0904253
\(159\) −10.9367 −0.867334
\(160\) 0.812101 0.0642023
\(161\) −22.4456 −1.76896
\(162\) 1.13663 0.0893020
\(163\) 5.47361 0.428726 0.214363 0.976754i \(-0.431232\pi\)
0.214363 + 0.976754i \(0.431232\pi\)
\(164\) 3.89552 0.304189
\(165\) −0.332481 −0.0258836
\(166\) 0.762952 0.0592166
\(167\) −9.15869 −0.708721 −0.354360 0.935109i \(-0.615301\pi\)
−0.354360 + 0.935109i \(0.615301\pi\)
\(168\) −11.2969 −0.871572
\(169\) 9.49574 0.730441
\(170\) −0.243606 −0.0186837
\(171\) 2.11286 0.161574
\(172\) 1.31828 0.100518
\(173\) 12.0426 0.915578 0.457789 0.889061i \(-0.348641\pi\)
0.457789 + 0.889061i \(0.348641\pi\)
\(174\) −2.64933 −0.200846
\(175\) 18.1819 1.37443
\(176\) −3.23057 −0.243513
\(177\) 9.95337 0.748141
\(178\) 10.4074 0.780067
\(179\) −7.94145 −0.593572 −0.296786 0.954944i \(-0.595915\pi\)
−0.296786 + 0.954944i \(0.595915\pi\)
\(180\) −0.151757 −0.0113113
\(181\) 25.8212 1.91927 0.959636 0.281245i \(-0.0907472\pi\)
0.959636 + 0.281245i \(0.0907472\pi\)
\(182\) −19.7855 −1.46660
\(183\) −0.941200 −0.0695755
\(184\) −18.8249 −1.38779
\(185\) −0.269482 −0.0198127
\(186\) −2.66249 −0.195223
\(187\) −1.55131 −0.113443
\(188\) 8.33484 0.607881
\(189\) 3.67011 0.266961
\(190\) 0.514704 0.0373405
\(191\) −16.3757 −1.18490 −0.592452 0.805606i \(-0.701840\pi\)
−0.592452 + 0.805606i \(0.701840\pi\)
\(192\) −8.47181 −0.611400
\(193\) −3.74152 −0.269320 −0.134660 0.990892i \(-0.542994\pi\)
−0.134660 + 0.990892i \(0.542994\pi\)
\(194\) −11.0791 −0.795433
\(195\) −1.01653 −0.0727950
\(196\) −4.58102 −0.327216
\(197\) −2.82332 −0.201153 −0.100577 0.994929i \(-0.532069\pi\)
−0.100577 + 0.994929i \(0.532069\pi\)
\(198\) 1.76326 0.125310
\(199\) −12.3050 −0.872275 −0.436138 0.899880i \(-0.643654\pi\)
−0.436138 + 0.899880i \(0.643654\pi\)
\(200\) 15.2490 1.07827
\(201\) 9.40312 0.663245
\(202\) −8.08223 −0.568664
\(203\) −8.55454 −0.600411
\(204\) −0.708075 −0.0495752
\(205\) −1.17911 −0.0823526
\(206\) −18.4857 −1.28796
\(207\) 6.11579 0.425077
\(208\) −9.87713 −0.684855
\(209\) 3.27770 0.226723
\(210\) 0.894059 0.0616959
\(211\) 22.1380 1.52405 0.762023 0.647550i \(-0.224206\pi\)
0.762023 + 0.647550i \(0.224206\pi\)
\(212\) −7.74399 −0.531859
\(213\) 11.5189 0.789262
\(214\) 1.94327 0.132839
\(215\) −0.399022 −0.0272131
\(216\) 3.07808 0.209437
\(217\) −8.59702 −0.583604
\(218\) −14.1475 −0.958191
\(219\) −8.55533 −0.578116
\(220\) −0.235422 −0.0158721
\(221\) −4.74297 −0.319047
\(222\) 1.42916 0.0959186
\(223\) 9.31754 0.623948 0.311974 0.950091i \(-0.399010\pi\)
0.311974 + 0.950091i \(0.399010\pi\)
\(224\) −13.9066 −0.929172
\(225\) −4.95407 −0.330271
\(226\) −19.8817 −1.32251
\(227\) −6.76431 −0.448963 −0.224482 0.974478i \(-0.572069\pi\)
−0.224482 + 0.974478i \(0.572069\pi\)
\(228\) 1.49606 0.0990791
\(229\) −21.6557 −1.43105 −0.715523 0.698589i \(-0.753812\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(230\) 1.48984 0.0982372
\(231\) 5.69347 0.374603
\(232\) −7.17460 −0.471035
\(233\) −3.67388 −0.240684 −0.120342 0.992732i \(-0.538399\pi\)
−0.120342 + 0.992732i \(0.538399\pi\)
\(234\) 5.39099 0.352420
\(235\) −2.52282 −0.164571
\(236\) 7.04774 0.458769
\(237\) 1.00000 0.0649570
\(238\) 4.17155 0.270401
\(239\) 3.05888 0.197862 0.0989312 0.995094i \(-0.468458\pi\)
0.0989312 + 0.995094i \(0.468458\pi\)
\(240\) 0.446323 0.0288100
\(241\) 1.60800 0.103580 0.0517902 0.998658i \(-0.483507\pi\)
0.0517902 + 0.998658i \(0.483507\pi\)
\(242\) −9.76755 −0.627882
\(243\) −1.00000 −0.0641500
\(244\) −0.666441 −0.0426645
\(245\) 1.38660 0.0885867
\(246\) 6.25322 0.398691
\(247\) 10.0212 0.637634
\(248\) −7.21022 −0.457850
\(249\) −0.671241 −0.0425382
\(250\) −2.42487 −0.153362
\(251\) 10.9970 0.694122 0.347061 0.937843i \(-0.387180\pi\)
0.347061 + 0.937843i \(0.387180\pi\)
\(252\) 2.59871 0.163703
\(253\) 9.48748 0.596473
\(254\) 6.92337 0.434411
\(255\) 0.214323 0.0134214
\(256\) −14.6124 −0.913274
\(257\) −28.0759 −1.75133 −0.875663 0.482923i \(-0.839575\pi\)
−0.875663 + 0.482923i \(0.839575\pi\)
\(258\) 2.11615 0.131746
\(259\) 4.61466 0.286741
\(260\) −0.719778 −0.0446387
\(261\) 2.33087 0.144277
\(262\) −8.78628 −0.542818
\(263\) −8.20013 −0.505642 −0.252821 0.967513i \(-0.581358\pi\)
−0.252821 + 0.967513i \(0.581358\pi\)
\(264\) 4.77505 0.293884
\(265\) 2.34398 0.143990
\(266\) −8.81388 −0.540414
\(267\) −9.15637 −0.560361
\(268\) 6.65812 0.406710
\(269\) −9.93169 −0.605546 −0.302773 0.953063i \(-0.597912\pi\)
−0.302773 + 0.953063i \(0.597912\pi\)
\(270\) −0.243606 −0.0148254
\(271\) −15.1264 −0.918866 −0.459433 0.888212i \(-0.651947\pi\)
−0.459433 + 0.888212i \(0.651947\pi\)
\(272\) 2.08248 0.126269
\(273\) 17.4072 1.05353
\(274\) 19.2431 1.16252
\(275\) −7.68529 −0.463441
\(276\) 4.33044 0.260662
\(277\) 15.3924 0.924840 0.462420 0.886661i \(-0.346981\pi\)
0.462420 + 0.886661i \(0.346981\pi\)
\(278\) 14.5406 0.872088
\(279\) 2.34245 0.140239
\(280\) 2.42118 0.144693
\(281\) 1.50282 0.0896505 0.0448253 0.998995i \(-0.485727\pi\)
0.0448253 + 0.998995i \(0.485727\pi\)
\(282\) 13.3794 0.796731
\(283\) 29.0096 1.72444 0.862220 0.506534i \(-0.169074\pi\)
0.862220 + 0.506534i \(0.169074\pi\)
\(284\) 8.15625 0.483984
\(285\) −0.452834 −0.0268235
\(286\) 8.36310 0.494521
\(287\) 20.1913 1.19185
\(288\) 3.78915 0.223278
\(289\) 1.00000 0.0588235
\(290\) 0.567813 0.0333431
\(291\) 9.74734 0.571399
\(292\) −6.05782 −0.354507
\(293\) −16.1990 −0.946355 −0.473178 0.880967i \(-0.656893\pi\)
−0.473178 + 0.880967i \(0.656893\pi\)
\(294\) −7.35362 −0.428872
\(295\) −2.13324 −0.124202
\(296\) 3.87026 0.224954
\(297\) −1.55131 −0.0900161
\(298\) −13.6450 −0.790431
\(299\) 29.0070 1.67752
\(300\) −3.50785 −0.202526
\(301\) 6.83292 0.393843
\(302\) −5.17118 −0.297568
\(303\) 7.11071 0.408499
\(304\) −4.39998 −0.252356
\(305\) 0.201721 0.0115505
\(306\) −1.13663 −0.0649767
\(307\) −8.81308 −0.502989 −0.251495 0.967859i \(-0.580922\pi\)
−0.251495 + 0.967859i \(0.580922\pi\)
\(308\) 4.03141 0.229711
\(309\) 16.2637 0.925208
\(310\) 0.570633 0.0324098
\(311\) −18.4789 −1.04784 −0.523921 0.851767i \(-0.675531\pi\)
−0.523921 + 0.851767i \(0.675531\pi\)
\(312\) 14.5992 0.826518
\(313\) −14.5072 −0.819996 −0.409998 0.912086i \(-0.634471\pi\)
−0.409998 + 0.912086i \(0.634471\pi\)
\(314\) −9.46722 −0.534266
\(315\) −0.786588 −0.0443192
\(316\) 0.708075 0.0398324
\(317\) 16.4750 0.925330 0.462665 0.886533i \(-0.346893\pi\)
0.462665 + 0.886533i \(0.346893\pi\)
\(318\) −12.4309 −0.697092
\(319\) 3.61590 0.202452
\(320\) 1.81570 0.101501
\(321\) −1.70968 −0.0954252
\(322\) −25.5123 −1.42174
\(323\) −2.11286 −0.117562
\(324\) −0.708075 −0.0393375
\(325\) −23.4970 −1.30338
\(326\) 6.22147 0.344575
\(327\) 12.4469 0.688316
\(328\) 16.9342 0.935035
\(329\) 43.2012 2.38176
\(330\) −0.377908 −0.0208031
\(331\) −19.5599 −1.07511 −0.537554 0.843229i \(-0.680652\pi\)
−0.537554 + 0.843229i \(0.680652\pi\)
\(332\) −0.475289 −0.0260849
\(333\) −1.25736 −0.0689031
\(334\) −10.4100 −0.569612
\(335\) −2.01531 −0.110108
\(336\) −7.64292 −0.416955
\(337\) −8.28556 −0.451343 −0.225672 0.974203i \(-0.572458\pi\)
−0.225672 + 0.974203i \(0.572458\pi\)
\(338\) 10.7931 0.587069
\(339\) 17.4918 0.950024
\(340\) 0.151757 0.00823017
\(341\) 3.63386 0.196784
\(342\) 2.40153 0.129860
\(343\) 1.94633 0.105092
\(344\) 5.73069 0.308978
\(345\) −1.31075 −0.0705686
\(346\) 13.6879 0.735867
\(347\) 29.3419 1.57515 0.787577 0.616216i \(-0.211335\pi\)
0.787577 + 0.616216i \(0.211335\pi\)
\(348\) 1.65043 0.0884725
\(349\) 21.7187 1.16257 0.581287 0.813699i \(-0.302549\pi\)
0.581287 + 0.813699i \(0.302549\pi\)
\(350\) 20.6661 1.10465
\(351\) −4.74297 −0.253161
\(352\) 5.87814 0.313306
\(353\) 24.7560 1.31763 0.658814 0.752306i \(-0.271059\pi\)
0.658814 + 0.752306i \(0.271059\pi\)
\(354\) 11.3133 0.601294
\(355\) −2.46876 −0.131028
\(356\) −6.48340 −0.343620
\(357\) −3.67011 −0.194243
\(358\) −9.02648 −0.477064
\(359\) −9.57224 −0.505204 −0.252602 0.967570i \(-0.581286\pi\)
−0.252602 + 0.967570i \(0.581286\pi\)
\(360\) −0.659702 −0.0347694
\(361\) −14.5358 −0.765044
\(362\) 29.3491 1.54255
\(363\) 8.59344 0.451038
\(364\) 12.3256 0.646037
\(365\) 1.83360 0.0959752
\(366\) −1.06980 −0.0559191
\(367\) −27.1320 −1.41628 −0.708139 0.706073i \(-0.750465\pi\)
−0.708139 + 0.706073i \(0.750465\pi\)
\(368\) −12.7360 −0.663910
\(369\) −5.50155 −0.286400
\(370\) −0.306301 −0.0159238
\(371\) −40.1387 −2.08390
\(372\) 1.65863 0.0859958
\(373\) −2.78783 −0.144348 −0.0721741 0.997392i \(-0.522994\pi\)
−0.0721741 + 0.997392i \(0.522994\pi\)
\(374\) −1.76326 −0.0911762
\(375\) 2.13339 0.110168
\(376\) 36.2324 1.86854
\(377\) 11.0552 0.569374
\(378\) 4.17155 0.214561
\(379\) 5.41556 0.278178 0.139089 0.990280i \(-0.455583\pi\)
0.139089 + 0.990280i \(0.455583\pi\)
\(380\) −0.320640 −0.0164485
\(381\) −6.09114 −0.312059
\(382\) −18.6131 −0.952328
\(383\) −18.9645 −0.969040 −0.484520 0.874780i \(-0.661006\pi\)
−0.484520 + 0.874780i \(0.661006\pi\)
\(384\) −2.05101 −0.104665
\(385\) −1.22024 −0.0621893
\(386\) −4.25271 −0.216457
\(387\) −1.86178 −0.0946395
\(388\) 6.90185 0.350388
\(389\) −9.49053 −0.481189 −0.240594 0.970626i \(-0.577342\pi\)
−0.240594 + 0.970626i \(0.577342\pi\)
\(390\) −1.15541 −0.0585066
\(391\) −6.11579 −0.309289
\(392\) −19.9142 −1.00582
\(393\) 7.73013 0.389933
\(394\) −3.20907 −0.161670
\(395\) −0.214323 −0.0107838
\(396\) −1.09844 −0.0551989
\(397\) 16.9087 0.848625 0.424313 0.905516i \(-0.360516\pi\)
0.424313 + 0.905516i \(0.360516\pi\)
\(398\) −13.9862 −0.701063
\(399\) 7.75441 0.388206
\(400\) 10.3167 0.515837
\(401\) −7.42429 −0.370751 −0.185376 0.982668i \(-0.559350\pi\)
−0.185376 + 0.982668i \(0.559350\pi\)
\(402\) 10.6879 0.533062
\(403\) 11.1101 0.553436
\(404\) 5.03492 0.250497
\(405\) 0.214323 0.0106498
\(406\) −9.72334 −0.482561
\(407\) −1.95056 −0.0966857
\(408\) −3.07808 −0.152387
\(409\) 11.8120 0.584065 0.292032 0.956408i \(-0.405668\pi\)
0.292032 + 0.956408i \(0.405668\pi\)
\(410\) −1.34021 −0.0661882
\(411\) −16.9300 −0.835096
\(412\) 11.5159 0.567348
\(413\) 36.5299 1.79752
\(414\) 6.95138 0.341642
\(415\) 0.143862 0.00706193
\(416\) 17.9718 0.881140
\(417\) −12.7928 −0.626464
\(418\) 3.72552 0.182221
\(419\) 19.1553 0.935797 0.467899 0.883782i \(-0.345011\pi\)
0.467899 + 0.883782i \(0.345011\pi\)
\(420\) −0.556964 −0.0271770
\(421\) −8.29817 −0.404428 −0.202214 0.979341i \(-0.564814\pi\)
−0.202214 + 0.979341i \(0.564814\pi\)
\(422\) 25.1627 1.22490
\(423\) −11.7711 −0.572331
\(424\) −33.6639 −1.63486
\(425\) 4.95407 0.240307
\(426\) 13.0927 0.634344
\(427\) −3.45431 −0.167166
\(428\) −1.21058 −0.0585158
\(429\) −7.35781 −0.355239
\(430\) −0.453540 −0.0218716
\(431\) 9.27257 0.446644 0.223322 0.974745i \(-0.428310\pi\)
0.223322 + 0.974745i \(0.428310\pi\)
\(432\) 2.08248 0.100193
\(433\) −19.2380 −0.924519 −0.462260 0.886745i \(-0.652961\pi\)
−0.462260 + 0.886745i \(0.652961\pi\)
\(434\) −9.77162 −0.469053
\(435\) −0.499559 −0.0239520
\(436\) 8.81335 0.422083
\(437\) 12.9218 0.618132
\(438\) −9.72423 −0.464642
\(439\) −22.9217 −1.09399 −0.546996 0.837135i \(-0.684229\pi\)
−0.546996 + 0.837135i \(0.684229\pi\)
\(440\) −1.02340 −0.0487888
\(441\) 6.46968 0.308080
\(442\) −5.39099 −0.256423
\(443\) 27.1028 1.28769 0.643847 0.765155i \(-0.277337\pi\)
0.643847 + 0.765155i \(0.277337\pi\)
\(444\) −0.890308 −0.0422522
\(445\) 1.96242 0.0930277
\(446\) 10.5906 0.501478
\(447\) 12.0048 0.567806
\(448\) −31.0924 −1.46898
\(449\) 37.2215 1.75659 0.878296 0.478118i \(-0.158681\pi\)
0.878296 + 0.478118i \(0.158681\pi\)
\(450\) −5.63093 −0.265445
\(451\) −8.53462 −0.401879
\(452\) 12.3855 0.582565
\(453\) 4.54958 0.213758
\(454\) −7.68851 −0.360840
\(455\) −3.73076 −0.174901
\(456\) 6.50353 0.304556
\(457\) −7.49997 −0.350834 −0.175417 0.984494i \(-0.556127\pi\)
−0.175417 + 0.984494i \(0.556127\pi\)
\(458\) −24.6145 −1.15016
\(459\) 1.00000 0.0466760
\(460\) −0.928113 −0.0432735
\(461\) 35.7101 1.66319 0.831593 0.555386i \(-0.187429\pi\)
0.831593 + 0.555386i \(0.187429\pi\)
\(462\) 6.47136 0.301075
\(463\) −37.5659 −1.74583 −0.872917 0.487869i \(-0.837774\pi\)
−0.872917 + 0.487869i \(0.837774\pi\)
\(464\) −4.85399 −0.225341
\(465\) −0.502040 −0.0232815
\(466\) −4.17584 −0.193442
\(467\) −6.87574 −0.318171 −0.159086 0.987265i \(-0.550855\pi\)
−0.159086 + 0.987265i \(0.550855\pi\)
\(468\) −3.35838 −0.155241
\(469\) 34.5105 1.59355
\(470\) −2.86751 −0.132268
\(471\) 8.32921 0.383790
\(472\) 30.6372 1.41019
\(473\) −2.88820 −0.132799
\(474\) 1.13663 0.0522071
\(475\) −10.4672 −0.480269
\(476\) −2.59871 −0.119112
\(477\) 10.9367 0.500756
\(478\) 3.47681 0.159026
\(479\) −12.1106 −0.553347 −0.276673 0.960964i \(-0.589232\pi\)
−0.276673 + 0.960964i \(0.589232\pi\)
\(480\) −0.812101 −0.0370672
\(481\) −5.96364 −0.271918
\(482\) 1.82770 0.0832494
\(483\) 22.4456 1.02131
\(484\) 6.08480 0.276582
\(485\) −2.08908 −0.0948602
\(486\) −1.13663 −0.0515585
\(487\) −18.9233 −0.857494 −0.428747 0.903424i \(-0.641045\pi\)
−0.428747 + 0.903424i \(0.641045\pi\)
\(488\) −2.89709 −0.131145
\(489\) −5.47361 −0.247525
\(490\) 1.57605 0.0711987
\(491\) −31.8196 −1.43600 −0.717998 0.696045i \(-0.754941\pi\)
−0.717998 + 0.696045i \(0.754941\pi\)
\(492\) −3.89552 −0.175623
\(493\) −2.33087 −0.104977
\(494\) 11.3904 0.512478
\(495\) 0.332481 0.0149439
\(496\) −4.87809 −0.219033
\(497\) 42.2756 1.89632
\(498\) −0.762952 −0.0341887
\(499\) −13.7156 −0.613994 −0.306997 0.951710i \(-0.599324\pi\)
−0.306997 + 0.951710i \(0.599324\pi\)
\(500\) 1.51060 0.0675560
\(501\) 9.15869 0.409180
\(502\) 12.4995 0.557878
\(503\) −38.5264 −1.71781 −0.858904 0.512137i \(-0.828854\pi\)
−0.858904 + 0.512137i \(0.828854\pi\)
\(504\) 11.2969 0.503202
\(505\) −1.52399 −0.0678166
\(506\) 10.7837 0.479396
\(507\) −9.49574 −0.421721
\(508\) −4.31299 −0.191358
\(509\) 14.0220 0.621516 0.310758 0.950489i \(-0.399417\pi\)
0.310758 + 0.950489i \(0.399417\pi\)
\(510\) 0.243606 0.0107870
\(511\) −31.3990 −1.38901
\(512\) −20.7109 −0.915300
\(513\) −2.11286 −0.0932849
\(514\) −31.9119 −1.40757
\(515\) −3.48568 −0.153597
\(516\) −1.31828 −0.0580340
\(517\) −18.2607 −0.803103
\(518\) 5.24515 0.230459
\(519\) −12.0426 −0.528609
\(520\) −3.12895 −0.137213
\(521\) −5.75596 −0.252173 −0.126087 0.992019i \(-0.540242\pi\)
−0.126087 + 0.992019i \(0.540242\pi\)
\(522\) 2.64933 0.115958
\(523\) −14.8685 −0.650155 −0.325077 0.945687i \(-0.605390\pi\)
−0.325077 + 0.945687i \(0.605390\pi\)
\(524\) 5.47351 0.239111
\(525\) −18.1819 −0.793525
\(526\) −9.32051 −0.406393
\(527\) −2.34245 −0.102039
\(528\) 3.23057 0.140592
\(529\) 14.4029 0.626211
\(530\) 2.66423 0.115727
\(531\) −9.95337 −0.431939
\(532\) 5.49071 0.238052
\(533\) −26.0937 −1.13024
\(534\) −10.4074 −0.450372
\(535\) 0.366424 0.0158419
\(536\) 28.9435 1.25017
\(537\) 7.94145 0.342699
\(538\) −11.2886 −0.486688
\(539\) 10.0365 0.432302
\(540\) 0.151757 0.00653057
\(541\) −21.2889 −0.915279 −0.457640 0.889138i \(-0.651305\pi\)
−0.457640 + 0.889138i \(0.651305\pi\)
\(542\) −17.1931 −0.738509
\(543\) −25.8212 −1.10809
\(544\) −3.78915 −0.162458
\(545\) −2.66766 −0.114270
\(546\) 19.7855 0.846742
\(547\) −42.6972 −1.82560 −0.912801 0.408405i \(-0.866085\pi\)
−0.912801 + 0.408405i \(0.866085\pi\)
\(548\) −11.9877 −0.512090
\(549\) 0.941200 0.0401694
\(550\) −8.73532 −0.372475
\(551\) 4.92480 0.209803
\(552\) 18.8249 0.801239
\(553\) 3.67011 0.156069
\(554\) 17.4955 0.743311
\(555\) 0.269482 0.0114389
\(556\) −9.05824 −0.384155
\(557\) 16.9010 0.716119 0.358059 0.933699i \(-0.383439\pi\)
0.358059 + 0.933699i \(0.383439\pi\)
\(558\) 2.66249 0.112712
\(559\) −8.83035 −0.373484
\(560\) 1.63805 0.0692204
\(561\) 1.55131 0.0654964
\(562\) 1.70814 0.0720537
\(563\) 8.33678 0.351353 0.175677 0.984448i \(-0.443789\pi\)
0.175677 + 0.984448i \(0.443789\pi\)
\(564\) −8.33484 −0.350960
\(565\) −3.74889 −0.157717
\(566\) 32.9731 1.38596
\(567\) −3.67011 −0.154130
\(568\) 35.4560 1.48770
\(569\) 14.8310 0.621748 0.310874 0.950451i \(-0.399378\pi\)
0.310874 + 0.950451i \(0.399378\pi\)
\(570\) −0.514704 −0.0215586
\(571\) −1.08522 −0.0454151 −0.0227075 0.999742i \(-0.507229\pi\)
−0.0227075 + 0.999742i \(0.507229\pi\)
\(572\) −5.20989 −0.217836
\(573\) 16.3757 0.684104
\(574\) 22.9500 0.957914
\(575\) −30.2980 −1.26351
\(576\) 8.47181 0.352992
\(577\) 18.7475 0.780467 0.390234 0.920716i \(-0.372394\pi\)
0.390234 + 0.920716i \(0.372394\pi\)
\(578\) 1.13663 0.0472775
\(579\) 3.74152 0.155492
\(580\) −0.353726 −0.0146877
\(581\) −2.46353 −0.102204
\(582\) 11.0791 0.459244
\(583\) 16.9662 0.702667
\(584\) −26.3340 −1.08971
\(585\) 1.01653 0.0420282
\(586\) −18.4122 −0.760603
\(587\) 13.9597 0.576180 0.288090 0.957603i \(-0.406980\pi\)
0.288090 + 0.957603i \(0.406980\pi\)
\(588\) 4.58102 0.188918
\(589\) 4.94925 0.203930
\(590\) −2.42470 −0.0998232
\(591\) 2.82332 0.116136
\(592\) 2.61843 0.107617
\(593\) 18.3434 0.753274 0.376637 0.926361i \(-0.377080\pi\)
0.376637 + 0.926361i \(0.377080\pi\)
\(594\) −1.76326 −0.0723476
\(595\) 0.786588 0.0322470
\(596\) 8.50028 0.348185
\(597\) 12.3050 0.503608
\(598\) 32.9702 1.34825
\(599\) −25.9189 −1.05902 −0.529510 0.848304i \(-0.677624\pi\)
−0.529510 + 0.848304i \(0.677624\pi\)
\(600\) −15.2490 −0.622537
\(601\) −27.6931 −1.12963 −0.564813 0.825219i \(-0.691052\pi\)
−0.564813 + 0.825219i \(0.691052\pi\)
\(602\) 7.76650 0.316539
\(603\) −9.40312 −0.382925
\(604\) 3.22145 0.131079
\(605\) −1.84177 −0.0748786
\(606\) 8.08223 0.328318
\(607\) −3.27046 −0.132744 −0.0663718 0.997795i \(-0.521142\pi\)
−0.0663718 + 0.997795i \(0.521142\pi\)
\(608\) 8.00592 0.324683
\(609\) 8.55454 0.346648
\(610\) 0.229282 0.00928334
\(611\) −55.8300 −2.25864
\(612\) 0.708075 0.0286223
\(613\) 20.1956 0.815691 0.407846 0.913051i \(-0.366280\pi\)
0.407846 + 0.913051i \(0.366280\pi\)
\(614\) −10.0172 −0.404261
\(615\) 1.17911 0.0475463
\(616\) 17.5249 0.706100
\(617\) −2.40284 −0.0967346 −0.0483673 0.998830i \(-0.515402\pi\)
−0.0483673 + 0.998830i \(0.515402\pi\)
\(618\) 18.4857 0.743606
\(619\) −6.22988 −0.250400 −0.125200 0.992132i \(-0.539957\pi\)
−0.125200 + 0.992132i \(0.539957\pi\)
\(620\) −0.355482 −0.0142765
\(621\) −6.11579 −0.245418
\(622\) −21.0037 −0.842170
\(623\) −33.6049 −1.34635
\(624\) 9.87713 0.395401
\(625\) 24.3131 0.972524
\(626\) −16.4893 −0.659045
\(627\) −3.27770 −0.130899
\(628\) 5.89771 0.235344
\(629\) 1.25736 0.0501344
\(630\) −0.894059 −0.0356201
\(631\) −21.7900 −0.867447 −0.433724 0.901046i \(-0.642801\pi\)
−0.433724 + 0.901046i \(0.642801\pi\)
\(632\) 3.07808 0.122439
\(633\) −22.1380 −0.879908
\(634\) 18.7260 0.743704
\(635\) 1.30547 0.0518061
\(636\) 7.74399 0.307069
\(637\) 30.6855 1.21580
\(638\) 4.10994 0.162714
\(639\) −11.5189 −0.455681
\(640\) 0.439578 0.0173758
\(641\) −18.8533 −0.744660 −0.372330 0.928100i \(-0.621441\pi\)
−0.372330 + 0.928100i \(0.621441\pi\)
\(642\) −1.94327 −0.0766949
\(643\) 17.6240 0.695023 0.347512 0.937676i \(-0.387027\pi\)
0.347512 + 0.937676i \(0.387027\pi\)
\(644\) 15.8932 0.626279
\(645\) 0.399022 0.0157115
\(646\) −2.40153 −0.0944870
\(647\) 18.7515 0.737199 0.368599 0.929588i \(-0.379837\pi\)
0.368599 + 0.929588i \(0.379837\pi\)
\(648\) −3.07808 −0.120918
\(649\) −15.4408 −0.606103
\(650\) −26.7073 −1.04755
\(651\) 8.59702 0.336944
\(652\) −3.87573 −0.151785
\(653\) −0.452815 −0.0177200 −0.00886002 0.999961i \(-0.502820\pi\)
−0.00886002 + 0.999961i \(0.502820\pi\)
\(654\) 14.1475 0.553212
\(655\) −1.65674 −0.0647343
\(656\) 11.4569 0.447316
\(657\) 8.55533 0.333775
\(658\) 49.1038 1.91426
\(659\) −35.0830 −1.36664 −0.683321 0.730118i \(-0.739465\pi\)
−0.683321 + 0.730118i \(0.739465\pi\)
\(660\) 0.235422 0.00916379
\(661\) −26.3800 −1.02606 −0.513031 0.858370i \(-0.671478\pi\)
−0.513031 + 0.858370i \(0.671478\pi\)
\(662\) −22.2323 −0.864084
\(663\) 4.74297 0.184202
\(664\) −2.06613 −0.0801815
\(665\) −1.66195 −0.0644476
\(666\) −1.42916 −0.0553787
\(667\) 14.2551 0.551960
\(668\) 6.48505 0.250914
\(669\) −9.31754 −0.360237
\(670\) −2.29065 −0.0884957
\(671\) 1.46009 0.0563663
\(672\) 13.9066 0.536458
\(673\) −11.5724 −0.446082 −0.223041 0.974809i \(-0.571598\pi\)
−0.223041 + 0.974809i \(0.571598\pi\)
\(674\) −9.41761 −0.362753
\(675\) 4.95407 0.190682
\(676\) −6.72370 −0.258604
\(677\) 7.16339 0.275311 0.137656 0.990480i \(-0.456043\pi\)
0.137656 + 0.990480i \(0.456043\pi\)
\(678\) 19.8817 0.763551
\(679\) 35.7738 1.37287
\(680\) 0.659702 0.0252984
\(681\) 6.76431 0.259209
\(682\) 4.13035 0.158159
\(683\) 20.0088 0.765614 0.382807 0.923828i \(-0.374957\pi\)
0.382807 + 0.923828i \(0.374957\pi\)
\(684\) −1.49606 −0.0572033
\(685\) 3.62849 0.138638
\(686\) 2.21226 0.0844643
\(687\) 21.6557 0.826215
\(688\) 3.87711 0.147814
\(689\) 51.8723 1.97618
\(690\) −1.48984 −0.0567172
\(691\) 18.2957 0.695999 0.348000 0.937495i \(-0.386861\pi\)
0.348000 + 0.937495i \(0.386861\pi\)
\(692\) −8.52704 −0.324149
\(693\) −5.69347 −0.216277
\(694\) 33.3508 1.26598
\(695\) 2.74178 0.104002
\(696\) 7.17460 0.271952
\(697\) 5.50155 0.208386
\(698\) 24.6861 0.934381
\(699\) 3.67388 0.138959
\(700\) −12.8742 −0.486599
\(701\) 22.2297 0.839604 0.419802 0.907616i \(-0.362100\pi\)
0.419802 + 0.907616i \(0.362100\pi\)
\(702\) −5.39099 −0.203470
\(703\) −2.65663 −0.100197
\(704\) 13.1424 0.495323
\(705\) 2.52282 0.0950149
\(706\) 28.1383 1.05900
\(707\) 26.0971 0.981481
\(708\) −7.04774 −0.264870
\(709\) −22.7261 −0.853496 −0.426748 0.904371i \(-0.640341\pi\)
−0.426748 + 0.904371i \(0.640341\pi\)
\(710\) −2.80607 −0.105310
\(711\) −1.00000 −0.0375029
\(712\) −28.1840 −1.05624
\(713\) 14.3259 0.536509
\(714\) −4.17155 −0.156116
\(715\) 1.57695 0.0589745
\(716\) 5.62315 0.210147
\(717\) −3.05888 −0.114236
\(718\) −10.8801 −0.406041
\(719\) 44.8953 1.67431 0.837155 0.546965i \(-0.184217\pi\)
0.837155 + 0.546965i \(0.184217\pi\)
\(720\) −0.446323 −0.0166335
\(721\) 59.6894 2.22295
\(722\) −16.5218 −0.614880
\(723\) −1.60800 −0.0598021
\(724\) −18.2833 −0.679495
\(725\) −11.5473 −0.428856
\(726\) 9.76755 0.362508
\(727\) −29.3350 −1.08797 −0.543987 0.839093i \(-0.683086\pi\)
−0.543987 + 0.839093i \(0.683086\pi\)
\(728\) 53.5807 1.98583
\(729\) 1.00000 0.0370370
\(730\) 2.08413 0.0771370
\(731\) 1.86178 0.0688604
\(732\) 0.666441 0.0246324
\(733\) 4.31493 0.159376 0.0796878 0.996820i \(-0.474608\pi\)
0.0796878 + 0.996820i \(0.474608\pi\)
\(734\) −30.8390 −1.13829
\(735\) −1.38660 −0.0511455
\(736\) 23.1736 0.854191
\(737\) −14.5872 −0.537325
\(738\) −6.25322 −0.230184
\(739\) 6.03080 0.221847 0.110923 0.993829i \(-0.464619\pi\)
0.110923 + 0.993829i \(0.464619\pi\)
\(740\) 0.190814 0.00701445
\(741\) −10.0212 −0.368138
\(742\) −45.6228 −1.67487
\(743\) −32.2327 −1.18250 −0.591252 0.806487i \(-0.701366\pi\)
−0.591252 + 0.806487i \(0.701366\pi\)
\(744\) 7.21022 0.264340
\(745\) −2.57290 −0.0942636
\(746\) −3.16872 −0.116015
\(747\) 0.671241 0.0245594
\(748\) 1.09844 0.0401631
\(749\) −6.27472 −0.229273
\(750\) 2.42487 0.0885436
\(751\) 12.4853 0.455595 0.227798 0.973708i \(-0.426848\pi\)
0.227798 + 0.973708i \(0.426848\pi\)
\(752\) 24.5131 0.893901
\(753\) −10.9970 −0.400752
\(754\) 12.5657 0.457616
\(755\) −0.975080 −0.0354868
\(756\) −2.59871 −0.0945142
\(757\) 44.0976 1.60275 0.801377 0.598159i \(-0.204101\pi\)
0.801377 + 0.598159i \(0.204101\pi\)
\(758\) 6.15548 0.223577
\(759\) −9.48748 −0.344374
\(760\) −1.39386 −0.0505605
\(761\) 17.3048 0.627299 0.313650 0.949539i \(-0.398448\pi\)
0.313650 + 0.949539i \(0.398448\pi\)
\(762\) −6.92337 −0.250807
\(763\) 45.6815 1.65378
\(764\) 11.5952 0.419501
\(765\) −0.214323 −0.00774886
\(766\) −21.5556 −0.778835
\(767\) −47.2085 −1.70460
\(768\) 14.6124 0.527279
\(769\) −33.8806 −1.22177 −0.610883 0.791721i \(-0.709185\pi\)
−0.610883 + 0.791721i \(0.709185\pi\)
\(770\) −1.38696 −0.0499826
\(771\) 28.0759 1.01113
\(772\) 2.64928 0.0953495
\(773\) 32.9682 1.18578 0.592892 0.805282i \(-0.297986\pi\)
0.592892 + 0.805282i \(0.297986\pi\)
\(774\) −2.11615 −0.0760635
\(775\) −11.6046 −0.416850
\(776\) 30.0030 1.07705
\(777\) −4.61466 −0.165550
\(778\) −10.7872 −0.386740
\(779\) −11.6240 −0.416473
\(780\) 0.719778 0.0257722
\(781\) −17.8694 −0.639417
\(782\) −6.95138 −0.248581
\(783\) −2.33087 −0.0832985
\(784\) −13.4730 −0.481177
\(785\) −1.78514 −0.0637144
\(786\) 8.78628 0.313396
\(787\) 45.4079 1.61862 0.809309 0.587383i \(-0.199842\pi\)
0.809309 + 0.587383i \(0.199842\pi\)
\(788\) 1.99912 0.0712158
\(789\) 8.20013 0.291933
\(790\) −0.243606 −0.00866710
\(791\) 64.1967 2.28257
\(792\) −4.77505 −0.169674
\(793\) 4.46408 0.158524
\(794\) 19.2190 0.682055
\(795\) −2.34398 −0.0831324
\(796\) 8.71284 0.308818
\(797\) 36.4726 1.29192 0.645962 0.763369i \(-0.276456\pi\)
0.645962 + 0.763369i \(0.276456\pi\)
\(798\) 8.81388 0.312008
\(799\) 11.7711 0.416432
\(800\) −18.7717 −0.663679
\(801\) 9.15637 0.323524
\(802\) −8.43866 −0.297979
\(803\) 13.2720 0.468358
\(804\) −6.65812 −0.234814
\(805\) −4.81061 −0.169552
\(806\) 12.6281 0.444806
\(807\) 9.93169 0.349612
\(808\) 21.8873 0.769992
\(809\) 1.26737 0.0445583 0.0222792 0.999752i \(-0.492908\pi\)
0.0222792 + 0.999752i \(0.492908\pi\)
\(810\) 0.243606 0.00855943
\(811\) 0.375933 0.0132008 0.00660039 0.999978i \(-0.497899\pi\)
0.00660039 + 0.999978i \(0.497899\pi\)
\(812\) 6.05726 0.212568
\(813\) 15.1264 0.530508
\(814\) −2.21706 −0.0777080
\(815\) 1.17312 0.0410926
\(816\) −2.08248 −0.0729013
\(817\) −3.93367 −0.137622
\(818\) 13.4258 0.469423
\(819\) −17.4072 −0.608257
\(820\) 0.834899 0.0291559
\(821\) 24.5833 0.857962 0.428981 0.903313i \(-0.358873\pi\)
0.428981 + 0.903313i \(0.358873\pi\)
\(822\) −19.2431 −0.671182
\(823\) −12.1301 −0.422829 −0.211414 0.977397i \(-0.567807\pi\)
−0.211414 + 0.977397i \(0.567807\pi\)
\(824\) 50.0608 1.74395
\(825\) 7.68529 0.267568
\(826\) 41.5210 1.44470
\(827\) 49.0258 1.70480 0.852398 0.522894i \(-0.175148\pi\)
0.852398 + 0.522894i \(0.175148\pi\)
\(828\) −4.33044 −0.150493
\(829\) −37.0272 −1.28601 −0.643004 0.765863i \(-0.722312\pi\)
−0.643004 + 0.765863i \(0.722312\pi\)
\(830\) 0.163518 0.00567580
\(831\) −15.3924 −0.533957
\(832\) 40.1815 1.39304
\(833\) −6.46968 −0.224161
\(834\) −14.5406 −0.503500
\(835\) −1.96292 −0.0679296
\(836\) −2.32086 −0.0802685
\(837\) −2.34245 −0.0809667
\(838\) 21.7725 0.752117
\(839\) 57.2941 1.97801 0.989005 0.147879i \(-0.0472447\pi\)
0.989005 + 0.147879i \(0.0472447\pi\)
\(840\) −2.42118 −0.0835386
\(841\) −23.5670 −0.812657
\(842\) −9.43194 −0.325046
\(843\) −1.50282 −0.0517598
\(844\) −15.6754 −0.539570
\(845\) 2.03516 0.0700115
\(846\) −13.3794 −0.459993
\(847\) 31.5388 1.08369
\(848\) −22.7754 −0.782110
\(849\) −29.0096 −0.995606
\(850\) 5.63093 0.193139
\(851\) −7.68977 −0.263602
\(852\) −8.15625 −0.279429
\(853\) 23.9065 0.818542 0.409271 0.912413i \(-0.365783\pi\)
0.409271 + 0.912413i \(0.365783\pi\)
\(854\) −3.92626 −0.134354
\(855\) 0.452834 0.0154866
\(856\) −5.26253 −0.179870
\(857\) 22.7745 0.777962 0.388981 0.921246i \(-0.372827\pi\)
0.388981 + 0.921246i \(0.372827\pi\)
\(858\) −8.36310 −0.285512
\(859\) −32.6260 −1.11318 −0.556592 0.830786i \(-0.687891\pi\)
−0.556592 + 0.830786i \(0.687891\pi\)
\(860\) 0.282538 0.00963445
\(861\) −20.1913 −0.688117
\(862\) 10.5395 0.358976
\(863\) −23.0547 −0.784792 −0.392396 0.919796i \(-0.628354\pi\)
−0.392396 + 0.919796i \(0.628354\pi\)
\(864\) −3.78915 −0.128909
\(865\) 2.58100 0.0877565
\(866\) −21.8665 −0.743053
\(867\) −1.00000 −0.0339618
\(868\) 6.08734 0.206618
\(869\) −1.55131 −0.0526246
\(870\) −0.567813 −0.0192507
\(871\) −44.5987 −1.51117
\(872\) 38.3125 1.29743
\(873\) −9.74734 −0.329897
\(874\) 14.6873 0.496804
\(875\) 7.82975 0.264694
\(876\) 6.05782 0.204675
\(877\) −29.6363 −1.00075 −0.500374 0.865810i \(-0.666804\pi\)
−0.500374 + 0.865810i \(0.666804\pi\)
\(878\) −26.0535 −0.879261
\(879\) 16.1990 0.546378
\(880\) −0.692385 −0.0233403
\(881\) −4.90474 −0.165245 −0.0826225 0.996581i \(-0.526330\pi\)
−0.0826225 + 0.996581i \(0.526330\pi\)
\(882\) 7.35362 0.247609
\(883\) −11.4422 −0.385062 −0.192531 0.981291i \(-0.561670\pi\)
−0.192531 + 0.981291i \(0.561670\pi\)
\(884\) 3.35838 0.112955
\(885\) 2.13324 0.0717079
\(886\) 30.8058 1.03494
\(887\) −33.8172 −1.13547 −0.567735 0.823211i \(-0.692180\pi\)
−0.567735 + 0.823211i \(0.692180\pi\)
\(888\) −3.87026 −0.129877
\(889\) −22.3551 −0.749767
\(890\) 2.23054 0.0747680
\(891\) 1.55131 0.0519708
\(892\) −6.59752 −0.220901
\(893\) −24.8707 −0.832265
\(894\) 13.6450 0.456356
\(895\) −1.70204 −0.0568928
\(896\) −7.52741 −0.251473
\(897\) −29.0070 −0.968515
\(898\) 42.3070 1.41180
\(899\) 5.45994 0.182099
\(900\) 3.50785 0.116928
\(901\) −10.9367 −0.364353
\(902\) −9.70069 −0.322998
\(903\) −6.83292 −0.227385
\(904\) 53.8411 1.79073
\(905\) 5.53407 0.183959
\(906\) 5.17118 0.171801
\(907\) 5.05307 0.167785 0.0838923 0.996475i \(-0.473265\pi\)
0.0838923 + 0.996475i \(0.473265\pi\)
\(908\) 4.78964 0.158950
\(909\) −7.11071 −0.235847
\(910\) −4.24049 −0.140571
\(911\) 12.0225 0.398324 0.199162 0.979967i \(-0.436178\pi\)
0.199162 + 0.979967i \(0.436178\pi\)
\(912\) 4.39998 0.145698
\(913\) 1.04130 0.0344621
\(914\) −8.52468 −0.281971
\(915\) −0.201721 −0.00666869
\(916\) 15.3338 0.506645
\(917\) 28.3704 0.936873
\(918\) 1.13663 0.0375143
\(919\) −21.5359 −0.710404 −0.355202 0.934790i \(-0.615588\pi\)
−0.355202 + 0.934790i \(0.615588\pi\)
\(920\) −4.03460 −0.133017
\(921\) 8.81308 0.290401
\(922\) 40.5891 1.33673
\(923\) −54.6338 −1.79829
\(924\) −4.03141 −0.132624
\(925\) 6.22906 0.204810
\(926\) −42.6984 −1.40316
\(927\) −16.2637 −0.534169
\(928\) 8.83202 0.289925
\(929\) −24.6960 −0.810248 −0.405124 0.914262i \(-0.632772\pi\)
−0.405124 + 0.914262i \(0.632772\pi\)
\(930\) −0.570633 −0.0187118
\(931\) 13.6695 0.448000
\(932\) 2.60139 0.0852112
\(933\) 18.4789 0.604972
\(934\) −7.81517 −0.255720
\(935\) −0.332481 −0.0108733
\(936\) −14.5992 −0.477190
\(937\) −42.7377 −1.39618 −0.698090 0.716010i \(-0.745967\pi\)
−0.698090 + 0.716010i \(0.745967\pi\)
\(938\) 39.2256 1.28076
\(939\) 14.5072 0.473425
\(940\) 1.78635 0.0582642
\(941\) 11.2561 0.366937 0.183469 0.983026i \(-0.441267\pi\)
0.183469 + 0.983026i \(0.441267\pi\)
\(942\) 9.46722 0.308459
\(943\) −33.6463 −1.09568
\(944\) 20.7277 0.674628
\(945\) 0.786588 0.0255877
\(946\) −3.28281 −0.106733
\(947\) 13.1347 0.426820 0.213410 0.976963i \(-0.431543\pi\)
0.213410 + 0.976963i \(0.431543\pi\)
\(948\) −0.708075 −0.0229972
\(949\) 40.5777 1.31721
\(950\) −11.8974 −0.386001
\(951\) −16.4750 −0.534239
\(952\) −11.2969 −0.366134
\(953\) 37.0193 1.19917 0.599586 0.800311i \(-0.295332\pi\)
0.599586 + 0.800311i \(0.295332\pi\)
\(954\) 12.4309 0.402466
\(955\) −3.50969 −0.113571
\(956\) −2.16592 −0.0700507
\(957\) −3.61590 −0.116886
\(958\) −13.7652 −0.444735
\(959\) −62.1350 −2.00644
\(960\) −1.81570 −0.0586016
\(961\) −25.5130 −0.822998
\(962\) −6.77844 −0.218546
\(963\) 1.70968 0.0550937
\(964\) −1.13858 −0.0366714
\(965\) −0.801893 −0.0258138
\(966\) 25.5123 0.820845
\(967\) 4.49043 0.144402 0.0722012 0.997390i \(-0.476998\pi\)
0.0722012 + 0.997390i \(0.476998\pi\)
\(968\) 26.4513 0.850175
\(969\) 2.11286 0.0678747
\(970\) −2.37451 −0.0762408
\(971\) −44.7509 −1.43612 −0.718062 0.695979i \(-0.754971\pi\)
−0.718062 + 0.695979i \(0.754971\pi\)
\(972\) 0.708075 0.0227115
\(973\) −46.9508 −1.50517
\(974\) −21.5087 −0.689184
\(975\) 23.4970 0.752505
\(976\) −1.96003 −0.0627390
\(977\) 50.2998 1.60923 0.804616 0.593796i \(-0.202371\pi\)
0.804616 + 0.593796i \(0.202371\pi\)
\(978\) −6.22147 −0.198941
\(979\) 14.2044 0.453974
\(980\) −0.981818 −0.0313630
\(981\) −12.4469 −0.397399
\(982\) −36.1670 −1.15414
\(983\) −12.9761 −0.413873 −0.206936 0.978354i \(-0.566349\pi\)
−0.206936 + 0.978354i \(0.566349\pi\)
\(984\) −16.9342 −0.539843
\(985\) −0.605102 −0.0192802
\(986\) −2.64933 −0.0843720
\(987\) −43.2012 −1.37511
\(988\) −7.09577 −0.225747
\(989\) −11.3862 −0.362061
\(990\) 0.377908 0.0120107
\(991\) 21.3996 0.679779 0.339890 0.940465i \(-0.389610\pi\)
0.339890 + 0.940465i \(0.389610\pi\)
\(992\) 8.87587 0.281809
\(993\) 19.5599 0.620714
\(994\) 48.0516 1.52411
\(995\) −2.63723 −0.0836060
\(996\) 0.475289 0.0150601
\(997\) −24.3735 −0.771918 −0.385959 0.922516i \(-0.626129\pi\)
−0.385959 + 0.922516i \(0.626129\pi\)
\(998\) −15.5895 −0.493478
\(999\) 1.25736 0.0397812
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 4029.2.a.g.1.15 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.g.1.15 22 1.1 even 1 trivial