Properties

Label 6031.2.a.c.1.17
Level $6031$
Weight $2$
Character 6031.1
Self dual yes
Analytic conductor $48.158$
Analytic rank $1$
Dimension $110$
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] = [6031,2,Mod(1,6031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6031, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6031 = 37 \cdot 163 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6031.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: \(48.1577774590\)
Analytic rank: \(1\)
Dimension: \(110\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.13628 q^{2} -0.861354 q^{3} +2.56370 q^{4} +1.50403 q^{5} +1.84010 q^{6} -3.07386 q^{7} -1.20423 q^{8} -2.25807 q^{9} +O(q^{10})\) \(q-2.13628 q^{2} -0.861354 q^{3} +2.56370 q^{4} +1.50403 q^{5} +1.84010 q^{6} -3.07386 q^{7} -1.20423 q^{8} -2.25807 q^{9} -3.21303 q^{10} -1.80814 q^{11} -2.20826 q^{12} +1.56008 q^{13} +6.56664 q^{14} -1.29550 q^{15} -2.55483 q^{16} -5.85280 q^{17} +4.82387 q^{18} -4.73888 q^{19} +3.85588 q^{20} +2.64768 q^{21} +3.86271 q^{22} +4.68229 q^{23} +1.03727 q^{24} -2.73790 q^{25} -3.33278 q^{26} +4.52906 q^{27} -7.88047 q^{28} +3.88648 q^{29} +2.76756 q^{30} +6.05166 q^{31} +7.86630 q^{32} +1.55745 q^{33} +12.5032 q^{34} -4.62317 q^{35} -5.78902 q^{36} -1.00000 q^{37} +10.1236 q^{38} -1.34378 q^{39} -1.81119 q^{40} +5.01348 q^{41} -5.65620 q^{42} -1.88723 q^{43} -4.63554 q^{44} -3.39620 q^{45} -10.0027 q^{46} +6.96769 q^{47} +2.20062 q^{48} +2.44862 q^{49} +5.84892 q^{50} +5.04134 q^{51} +3.99959 q^{52} +4.59970 q^{53} -9.67535 q^{54} -2.71950 q^{55} +3.70163 q^{56} +4.08185 q^{57} -8.30262 q^{58} +7.15569 q^{59} -3.32128 q^{60} +13.7289 q^{61} -12.9281 q^{62} +6.94099 q^{63} -11.6950 q^{64} +2.34641 q^{65} -3.32716 q^{66} -8.22758 q^{67} -15.0048 q^{68} -4.03311 q^{69} +9.87641 q^{70} -4.95883 q^{71} +2.71923 q^{72} +16.1812 q^{73} +2.13628 q^{74} +2.35830 q^{75} -12.1491 q^{76} +5.55798 q^{77} +2.87070 q^{78} +9.56083 q^{79} -3.84254 q^{80} +2.87308 q^{81} -10.7102 q^{82} +5.83991 q^{83} +6.78787 q^{84} -8.80278 q^{85} +4.03166 q^{86} -3.34764 q^{87} +2.17742 q^{88} +4.75958 q^{89} +7.25524 q^{90} -4.79547 q^{91} +12.0040 q^{92} -5.21263 q^{93} -14.8850 q^{94} -7.12741 q^{95} -6.77568 q^{96} -10.2835 q^{97} -5.23095 q^{98} +4.08291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13628 −1.51058 −0.755290 0.655391i \(-0.772504\pi\)
−0.755290 + 0.655391i \(0.772504\pi\)
\(3\) −0.861354 −0.497303 −0.248652 0.968593i \(-0.579987\pi\)
−0.248652 + 0.968593i \(0.579987\pi\)
\(4\) 2.56370 1.28185
\(5\) 1.50403 0.672622 0.336311 0.941751i \(-0.390821\pi\)
0.336311 + 0.941751i \(0.390821\pi\)
\(6\) 1.84010 0.751216
\(7\) −3.07386 −1.16181 −0.580905 0.813971i \(-0.697301\pi\)
−0.580905 + 0.813971i \(0.697301\pi\)
\(8\) −1.20423 −0.425759
\(9\) −2.25807 −0.752689
\(10\) −3.21303 −1.01605
\(11\) −1.80814 −0.545176 −0.272588 0.962131i \(-0.587880\pi\)
−0.272588 + 0.962131i \(0.587880\pi\)
\(12\) −2.20826 −0.637469
\(13\) 1.56008 0.432689 0.216344 0.976317i \(-0.430587\pi\)
0.216344 + 0.976317i \(0.430587\pi\)
\(14\) 6.56664 1.75501
\(15\) −1.29550 −0.334497
\(16\) −2.55483 −0.638708
\(17\) −5.85280 −1.41951 −0.709756 0.704447i \(-0.751195\pi\)
−0.709756 + 0.704447i \(0.751195\pi\)
\(18\) 4.82387 1.13700
\(19\) −4.73888 −1.08717 −0.543586 0.839353i \(-0.682934\pi\)
−0.543586 + 0.839353i \(0.682934\pi\)
\(20\) 3.85588 0.862201
\(21\) 2.64768 0.577772
\(22\) 3.86271 0.823532
\(23\) 4.68229 0.976324 0.488162 0.872753i \(-0.337668\pi\)
0.488162 + 0.872753i \(0.337668\pi\)
\(24\) 1.03727 0.211731
\(25\) −2.73790 −0.547580
\(26\) −3.33278 −0.653611
\(27\) 4.52906 0.871618
\(28\) −7.88047 −1.48927
\(29\) 3.88648 0.721702 0.360851 0.932624i \(-0.382486\pi\)
0.360851 + 0.932624i \(0.382486\pi\)
\(30\) 2.76756 0.505285
\(31\) 6.05166 1.08691 0.543455 0.839438i \(-0.317116\pi\)
0.543455 + 0.839438i \(0.317116\pi\)
\(32\) 7.86630 1.39058
\(33\) 1.55745 0.271118
\(34\) 12.5032 2.14429
\(35\) −4.62317 −0.781459
\(36\) −5.78902 −0.964836
\(37\) −1.00000 −0.164399
\(38\) 10.1236 1.64226
\(39\) −1.34378 −0.215178
\(40\) −1.81119 −0.286375
\(41\) 5.01348 0.782975 0.391487 0.920183i \(-0.371961\pi\)
0.391487 + 0.920183i \(0.371961\pi\)
\(42\) −5.65620 −0.872771
\(43\) −1.88723 −0.287800 −0.143900 0.989592i \(-0.545964\pi\)
−0.143900 + 0.989592i \(0.545964\pi\)
\(44\) −4.63554 −0.698834
\(45\) −3.39620 −0.506276
\(46\) −10.0027 −1.47482
\(47\) 6.96769 1.01634 0.508171 0.861256i \(-0.330322\pi\)
0.508171 + 0.861256i \(0.330322\pi\)
\(48\) 2.20062 0.317632
\(49\) 2.44862 0.349803
\(50\) 5.84892 0.827163
\(51\) 5.04134 0.705928
\(52\) 3.99959 0.554643
\(53\) 4.59970 0.631817 0.315908 0.948790i \(-0.397691\pi\)
0.315908 + 0.948790i \(0.397691\pi\)
\(54\) −9.67535 −1.31665
\(55\) −2.71950 −0.366697
\(56\) 3.70163 0.494651
\(57\) 4.08185 0.540655
\(58\) −8.30262 −1.09019
\(59\) 7.15569 0.931592 0.465796 0.884892i \(-0.345768\pi\)
0.465796 + 0.884892i \(0.345768\pi\)
\(60\) −3.32128 −0.428776
\(61\) 13.7289 1.75781 0.878904 0.476998i \(-0.158275\pi\)
0.878904 + 0.476998i \(0.158275\pi\)
\(62\) −12.9281 −1.64187
\(63\) 6.94099 0.874482
\(64\) −11.6950 −1.46187
\(65\) 2.34641 0.291036
\(66\) −3.32716 −0.409545
\(67\) −8.22758 −1.00516 −0.502579 0.864531i \(-0.667616\pi\)
−0.502579 + 0.864531i \(0.667616\pi\)
\(68\) −15.0048 −1.81960
\(69\) −4.03311 −0.485529
\(70\) 9.87641 1.18046
\(71\) −4.95883 −0.588505 −0.294253 0.955728i \(-0.595071\pi\)
−0.294253 + 0.955728i \(0.595071\pi\)
\(72\) 2.71923 0.320464
\(73\) 16.1812 1.89386 0.946931 0.321436i \(-0.104166\pi\)
0.946931 + 0.321436i \(0.104166\pi\)
\(74\) 2.13628 0.248338
\(75\) 2.35830 0.272313
\(76\) −12.1491 −1.39359
\(77\) 5.55798 0.633391
\(78\) 2.87070 0.325043
\(79\) 9.56083 1.07568 0.537839 0.843048i \(-0.319241\pi\)
0.537839 + 0.843048i \(0.319241\pi\)
\(80\) −3.84254 −0.429609
\(81\) 2.87308 0.319231
\(82\) −10.7102 −1.18275
\(83\) 5.83991 0.641013 0.320507 0.947246i \(-0.396147\pi\)
0.320507 + 0.947246i \(0.396147\pi\)
\(84\) 6.78787 0.740618
\(85\) −8.80278 −0.954796
\(86\) 4.03166 0.434745
\(87\) −3.34764 −0.358905
\(88\) 2.17742 0.232114
\(89\) 4.75958 0.504514 0.252257 0.967660i \(-0.418827\pi\)
0.252257 + 0.967660i \(0.418827\pi\)
\(90\) 7.25524 0.764770
\(91\) −4.79547 −0.502702
\(92\) 12.0040 1.25150
\(93\) −5.21263 −0.540524
\(94\) −14.8850 −1.53527
\(95\) −7.12741 −0.731256
\(96\) −6.77568 −0.691539
\(97\) −10.2835 −1.04413 −0.522066 0.852905i \(-0.674839\pi\)
−0.522066 + 0.852905i \(0.674839\pi\)
\(98\) −5.23095 −0.528405
\(99\) 4.08291 0.410348
\(100\) −7.01916 −0.701916
\(101\) −17.2754 −1.71897 −0.859483 0.511164i \(-0.829215\pi\)
−0.859483 + 0.511164i \(0.829215\pi\)
\(102\) −10.7697 −1.06636
\(103\) −0.330529 −0.0325680 −0.0162840 0.999867i \(-0.505184\pi\)
−0.0162840 + 0.999867i \(0.505184\pi\)
\(104\) −1.87869 −0.184221
\(105\) 3.98219 0.388622
\(106\) −9.82625 −0.954410
\(107\) 0.979488 0.0946906 0.0473453 0.998879i \(-0.484924\pi\)
0.0473453 + 0.998879i \(0.484924\pi\)
\(108\) 11.6112 1.11728
\(109\) −0.177182 −0.0169709 −0.00848546 0.999964i \(-0.502701\pi\)
−0.00848546 + 0.999964i \(0.502701\pi\)
\(110\) 5.80962 0.553925
\(111\) 0.861354 0.0817562
\(112\) 7.85320 0.742058
\(113\) −16.5884 −1.56051 −0.780254 0.625462i \(-0.784910\pi\)
−0.780254 + 0.625462i \(0.784910\pi\)
\(114\) −8.71999 −0.816702
\(115\) 7.04229 0.656697
\(116\) 9.96378 0.925114
\(117\) −3.52277 −0.325680
\(118\) −15.2866 −1.40724
\(119\) 17.9907 1.64920
\(120\) 1.56008 0.142415
\(121\) −7.73062 −0.702783
\(122\) −29.3289 −2.65531
\(123\) −4.31839 −0.389376
\(124\) 15.5147 1.39326
\(125\) −11.6380 −1.04094
\(126\) −14.8279 −1.32098
\(127\) −0.646451 −0.0573632 −0.0286816 0.999589i \(-0.509131\pi\)
−0.0286816 + 0.999589i \(0.509131\pi\)
\(128\) 9.25117 0.817696
\(129\) 1.62557 0.143124
\(130\) −5.01259 −0.439633
\(131\) 9.53249 0.832857 0.416429 0.909168i \(-0.363282\pi\)
0.416429 + 0.909168i \(0.363282\pi\)
\(132\) 3.99285 0.347533
\(133\) 14.5666 1.26309
\(134\) 17.5764 1.51837
\(135\) 6.81184 0.586270
\(136\) 7.04811 0.604370
\(137\) −7.89736 −0.674717 −0.337359 0.941376i \(-0.609534\pi\)
−0.337359 + 0.941376i \(0.609534\pi\)
\(138\) 8.61586 0.733430
\(139\) −12.8766 −1.09218 −0.546088 0.837728i \(-0.683884\pi\)
−0.546088 + 0.837728i \(0.683884\pi\)
\(140\) −11.8524 −1.00171
\(141\) −6.00165 −0.505430
\(142\) 10.5935 0.888984
\(143\) −2.82085 −0.235891
\(144\) 5.76899 0.480749
\(145\) 5.84538 0.485432
\(146\) −34.5675 −2.86083
\(147\) −2.10913 −0.173958
\(148\) −2.56370 −0.210735
\(149\) −14.8877 −1.21965 −0.609824 0.792537i \(-0.708760\pi\)
−0.609824 + 0.792537i \(0.708760\pi\)
\(150\) −5.03800 −0.411351
\(151\) −4.57817 −0.372566 −0.186283 0.982496i \(-0.559644\pi\)
−0.186283 + 0.982496i \(0.559644\pi\)
\(152\) 5.70669 0.462874
\(153\) 13.2160 1.06845
\(154\) −11.8734 −0.956787
\(155\) 9.10187 0.731080
\(156\) −3.44506 −0.275826
\(157\) 14.9052 1.18956 0.594782 0.803887i \(-0.297238\pi\)
0.594782 + 0.803887i \(0.297238\pi\)
\(158\) −20.4246 −1.62490
\(159\) −3.96197 −0.314205
\(160\) 11.8311 0.935334
\(161\) −14.3927 −1.13430
\(162\) −6.13771 −0.482224
\(163\) −1.00000 −0.0783260
\(164\) 12.8531 1.00366
\(165\) 2.34245 0.182360
\(166\) −12.4757 −0.968301
\(167\) 20.1670 1.56057 0.780284 0.625426i \(-0.215075\pi\)
0.780284 + 0.625426i \(0.215075\pi\)
\(168\) −3.18842 −0.245992
\(169\) −10.5661 −0.812780
\(170\) 18.8052 1.44229
\(171\) 10.7007 0.818304
\(172\) −4.83830 −0.368917
\(173\) 2.77070 0.210653 0.105326 0.994438i \(-0.466411\pi\)
0.105326 + 0.994438i \(0.466411\pi\)
\(174\) 7.15150 0.542154
\(175\) 8.41592 0.636184
\(176\) 4.61951 0.348208
\(177\) −6.16359 −0.463284
\(178\) −10.1678 −0.762109
\(179\) 23.4233 1.75074 0.875372 0.483451i \(-0.160617\pi\)
0.875372 + 0.483451i \(0.160617\pi\)
\(180\) −8.70685 −0.648970
\(181\) 6.06222 0.450601 0.225301 0.974289i \(-0.427664\pi\)
0.225301 + 0.974289i \(0.427664\pi\)
\(182\) 10.2445 0.759372
\(183\) −11.8255 −0.874164
\(184\) −5.63854 −0.415679
\(185\) −1.50403 −0.110578
\(186\) 11.1356 0.816505
\(187\) 10.5827 0.773884
\(188\) 17.8631 1.30280
\(189\) −13.9217 −1.01265
\(190\) 15.2262 1.10462
\(191\) −13.6800 −0.989853 −0.494926 0.868935i \(-0.664805\pi\)
−0.494926 + 0.868935i \(0.664805\pi\)
\(192\) 10.0735 0.726994
\(193\) −4.72926 −0.340420 −0.170210 0.985408i \(-0.554445\pi\)
−0.170210 + 0.985408i \(0.554445\pi\)
\(194\) 21.9685 1.57724
\(195\) −2.02109 −0.144733
\(196\) 6.27754 0.448395
\(197\) −21.5882 −1.53809 −0.769047 0.639192i \(-0.779269\pi\)
−0.769047 + 0.639192i \(0.779269\pi\)
\(198\) −8.72225 −0.619864
\(199\) −21.5374 −1.52675 −0.763375 0.645956i \(-0.776459\pi\)
−0.763375 + 0.645956i \(0.776459\pi\)
\(200\) 3.29705 0.233137
\(201\) 7.08686 0.499869
\(202\) 36.9051 2.59664
\(203\) −11.9465 −0.838480
\(204\) 12.9245 0.904895
\(205\) 7.54042 0.526646
\(206\) 0.706103 0.0491965
\(207\) −10.5729 −0.734869
\(208\) −3.98575 −0.276362
\(209\) 8.56857 0.592700
\(210\) −8.50709 −0.587045
\(211\) −6.16563 −0.424459 −0.212230 0.977220i \(-0.568073\pi\)
−0.212230 + 0.977220i \(0.568073\pi\)
\(212\) 11.7923 0.809895
\(213\) 4.27131 0.292666
\(214\) −2.09246 −0.143038
\(215\) −2.83845 −0.193581
\(216\) −5.45402 −0.371099
\(217\) −18.6020 −1.26278
\(218\) 0.378510 0.0256359
\(219\) −13.9377 −0.941824
\(220\) −6.97199 −0.470051
\(221\) −9.13085 −0.614207
\(222\) −1.84010 −0.123499
\(223\) 1.89843 0.127128 0.0635641 0.997978i \(-0.479753\pi\)
0.0635641 + 0.997978i \(0.479753\pi\)
\(224\) −24.1799 −1.61559
\(225\) 6.18236 0.412157
\(226\) 35.4376 2.35727
\(227\) 12.8688 0.854133 0.427067 0.904220i \(-0.359547\pi\)
0.427067 + 0.904220i \(0.359547\pi\)
\(228\) 10.4647 0.693039
\(229\) 8.54671 0.564782 0.282391 0.959299i \(-0.408872\pi\)
0.282391 + 0.959299i \(0.408872\pi\)
\(230\) −15.0443 −0.991993
\(231\) −4.78739 −0.314987
\(232\) −4.68021 −0.307271
\(233\) −22.5414 −1.47674 −0.738370 0.674396i \(-0.764404\pi\)
−0.738370 + 0.674396i \(0.764404\pi\)
\(234\) 7.52563 0.491966
\(235\) 10.4796 0.683614
\(236\) 18.3451 1.19416
\(237\) −8.23527 −0.534938
\(238\) −38.4332 −2.49126
\(239\) −7.60840 −0.492146 −0.246073 0.969251i \(-0.579140\pi\)
−0.246073 + 0.969251i \(0.579140\pi\)
\(240\) 3.30979 0.213646
\(241\) −4.94063 −0.318254 −0.159127 0.987258i \(-0.550868\pi\)
−0.159127 + 0.987258i \(0.550868\pi\)
\(242\) 16.5148 1.06161
\(243\) −16.0619 −1.03037
\(244\) 35.1969 2.25325
\(245\) 3.68280 0.235285
\(246\) 9.22530 0.588183
\(247\) −7.39304 −0.470408
\(248\) −7.28759 −0.462762
\(249\) −5.03023 −0.318778
\(250\) 24.8621 1.57242
\(251\) 5.05769 0.319239 0.159619 0.987179i \(-0.448973\pi\)
0.159619 + 0.987179i \(0.448973\pi\)
\(252\) 17.7946 1.12096
\(253\) −8.46624 −0.532268
\(254\) 1.38100 0.0866518
\(255\) 7.58231 0.474823
\(256\) 3.62684 0.226678
\(257\) 18.9308 1.18087 0.590435 0.807085i \(-0.298956\pi\)
0.590435 + 0.807085i \(0.298956\pi\)
\(258\) −3.47269 −0.216200
\(259\) 3.07386 0.191000
\(260\) 6.01549 0.373065
\(261\) −8.77594 −0.543217
\(262\) −20.3641 −1.25810
\(263\) 5.58788 0.344563 0.172282 0.985048i \(-0.444886\pi\)
0.172282 + 0.985048i \(0.444886\pi\)
\(264\) −1.87553 −0.115431
\(265\) 6.91807 0.424974
\(266\) −31.1185 −1.90800
\(267\) −4.09968 −0.250896
\(268\) −21.0931 −1.28846
\(269\) −6.82385 −0.416058 −0.208029 0.978123i \(-0.566705\pi\)
−0.208029 + 0.978123i \(0.566705\pi\)
\(270\) −14.5520 −0.885607
\(271\) −14.5790 −0.885613 −0.442807 0.896617i \(-0.646017\pi\)
−0.442807 + 0.896617i \(0.646017\pi\)
\(272\) 14.9529 0.906655
\(273\) 4.13060 0.249995
\(274\) 16.8710 1.01921
\(275\) 4.95051 0.298527
\(276\) −10.3397 −0.622376
\(277\) 25.4534 1.52934 0.764672 0.644420i \(-0.222901\pi\)
0.764672 + 0.644420i \(0.222901\pi\)
\(278\) 27.5080 1.64982
\(279\) −13.6651 −0.818106
\(280\) 5.56736 0.332713
\(281\) −18.7019 −1.11566 −0.557831 0.829954i \(-0.688366\pi\)
−0.557831 + 0.829954i \(0.688366\pi\)
\(282\) 12.8212 0.763493
\(283\) 14.4768 0.860554 0.430277 0.902697i \(-0.358416\pi\)
0.430277 + 0.902697i \(0.358416\pi\)
\(284\) −12.7130 −0.754376
\(285\) 6.13922 0.363656
\(286\) 6.02614 0.356333
\(287\) −15.4108 −0.909668
\(288\) −17.7627 −1.04667
\(289\) 17.2553 1.01502
\(290\) −12.4874 −0.733284
\(291\) 8.85774 0.519250
\(292\) 41.4837 2.42765
\(293\) −3.40397 −0.198862 −0.0994310 0.995044i \(-0.531702\pi\)
−0.0994310 + 0.995044i \(0.531702\pi\)
\(294\) 4.50570 0.262778
\(295\) 10.7624 0.626609
\(296\) 1.20423 0.0699944
\(297\) −8.18919 −0.475185
\(298\) 31.8043 1.84237
\(299\) 7.30475 0.422444
\(300\) 6.04598 0.349065
\(301\) 5.80108 0.334369
\(302\) 9.78026 0.562790
\(303\) 14.8802 0.854848
\(304\) 12.1070 0.694386
\(305\) 20.6487 1.18234
\(306\) −28.2332 −1.61398
\(307\) −31.3361 −1.78844 −0.894221 0.447625i \(-0.852270\pi\)
−0.894221 + 0.447625i \(0.852270\pi\)
\(308\) 14.2490 0.811913
\(309\) 0.284702 0.0161962
\(310\) −19.4442 −1.10435
\(311\) 1.14417 0.0648799 0.0324399 0.999474i \(-0.489672\pi\)
0.0324399 + 0.999474i \(0.489672\pi\)
\(312\) 1.61822 0.0916138
\(313\) 32.5807 1.84157 0.920784 0.390073i \(-0.127550\pi\)
0.920784 + 0.390073i \(0.127550\pi\)
\(314\) −31.8417 −1.79693
\(315\) 10.4394 0.588196
\(316\) 24.5111 1.37886
\(317\) −20.3265 −1.14165 −0.570825 0.821071i \(-0.693377\pi\)
−0.570825 + 0.821071i \(0.693377\pi\)
\(318\) 8.46389 0.474631
\(319\) −7.02732 −0.393454
\(320\) −17.5896 −0.983287
\(321\) −0.843686 −0.0470900
\(322\) 30.7469 1.71346
\(323\) 27.7357 1.54326
\(324\) 7.36572 0.409207
\(325\) −4.27134 −0.236932
\(326\) 2.13628 0.118318
\(327\) 0.152616 0.00843969
\(328\) −6.03738 −0.333359
\(329\) −21.4177 −1.18080
\(330\) −5.00414 −0.275469
\(331\) 18.1496 0.997592 0.498796 0.866719i \(-0.333776\pi\)
0.498796 + 0.866719i \(0.333776\pi\)
\(332\) 14.9718 0.821684
\(333\) 2.25807 0.123741
\(334\) −43.0824 −2.35736
\(335\) −12.3745 −0.676092
\(336\) −6.76439 −0.369028
\(337\) −35.9417 −1.95787 −0.978934 0.204178i \(-0.934548\pi\)
−0.978934 + 0.204178i \(0.934548\pi\)
\(338\) 22.5723 1.22777
\(339\) 14.2885 0.776046
\(340\) −22.5677 −1.22391
\(341\) −10.9423 −0.592558
\(342\) −22.8597 −1.23611
\(343\) 13.9903 0.755406
\(344\) 2.27266 0.122533
\(345\) −6.06591 −0.326578
\(346\) −5.91900 −0.318208
\(347\) −22.9431 −1.23165 −0.615824 0.787883i \(-0.711177\pi\)
−0.615824 + 0.787883i \(0.711177\pi\)
\(348\) −8.58235 −0.460062
\(349\) −11.5807 −0.619901 −0.309950 0.950753i \(-0.600312\pi\)
−0.309950 + 0.950753i \(0.600312\pi\)
\(350\) −17.9788 −0.961006
\(351\) 7.06571 0.377139
\(352\) −14.2234 −0.758110
\(353\) 17.4702 0.929847 0.464924 0.885351i \(-0.346082\pi\)
0.464924 + 0.885351i \(0.346082\pi\)
\(354\) 13.1672 0.699827
\(355\) −7.45823 −0.395842
\(356\) 12.2021 0.646712
\(357\) −15.4964 −0.820155
\(358\) −50.0389 −2.64464
\(359\) 17.2379 0.909781 0.454890 0.890547i \(-0.349678\pi\)
0.454890 + 0.890547i \(0.349678\pi\)
\(360\) 4.08980 0.215551
\(361\) 3.45696 0.181945
\(362\) −12.9506 −0.680669
\(363\) 6.65880 0.349496
\(364\) −12.2942 −0.644390
\(365\) 24.3369 1.27385
\(366\) 25.2625 1.32049
\(367\) 10.1832 0.531561 0.265781 0.964034i \(-0.414370\pi\)
0.265781 + 0.964034i \(0.414370\pi\)
\(368\) −11.9625 −0.623586
\(369\) −11.3208 −0.589337
\(370\) 3.21303 0.167037
\(371\) −14.1388 −0.734051
\(372\) −13.3636 −0.692872
\(373\) 25.2556 1.30768 0.653842 0.756631i \(-0.273156\pi\)
0.653842 + 0.756631i \(0.273156\pi\)
\(374\) −22.6076 −1.16901
\(375\) 10.0245 0.517661
\(376\) −8.39069 −0.432717
\(377\) 6.06323 0.312272
\(378\) 29.7407 1.52970
\(379\) −22.8613 −1.17431 −0.587154 0.809475i \(-0.699752\pi\)
−0.587154 + 0.809475i \(0.699752\pi\)
\(380\) −18.2726 −0.937362
\(381\) 0.556823 0.0285269
\(382\) 29.2244 1.49525
\(383\) 5.13943 0.262613 0.131306 0.991342i \(-0.458083\pi\)
0.131306 + 0.991342i \(0.458083\pi\)
\(384\) −7.96854 −0.406643
\(385\) 8.35936 0.426033
\(386\) 10.1030 0.514231
\(387\) 4.26150 0.216624
\(388\) −26.3639 −1.33842
\(389\) 35.2080 1.78512 0.892559 0.450931i \(-0.148908\pi\)
0.892559 + 0.450931i \(0.148908\pi\)
\(390\) 4.31762 0.218631
\(391\) −27.4045 −1.38590
\(392\) −2.94870 −0.148932
\(393\) −8.21085 −0.414183
\(394\) 46.1184 2.32341
\(395\) 14.3798 0.723525
\(396\) 10.4674 0.526005
\(397\) 27.4755 1.37895 0.689477 0.724308i \(-0.257840\pi\)
0.689477 + 0.724308i \(0.257840\pi\)
\(398\) 46.0101 2.30628
\(399\) −12.5470 −0.628138
\(400\) 6.99487 0.349744
\(401\) −17.1495 −0.856407 −0.428203 0.903682i \(-0.640853\pi\)
−0.428203 + 0.903682i \(0.640853\pi\)
\(402\) −15.1395 −0.755091
\(403\) 9.44109 0.470294
\(404\) −44.2890 −2.20346
\(405\) 4.32119 0.214722
\(406\) 25.5211 1.26659
\(407\) 1.80814 0.0896264
\(408\) −6.07092 −0.300555
\(409\) 23.5970 1.16679 0.583397 0.812187i \(-0.301723\pi\)
0.583397 + 0.812187i \(0.301723\pi\)
\(410\) −16.1085 −0.795541
\(411\) 6.80243 0.335539
\(412\) −0.847378 −0.0417473
\(413\) −21.9956 −1.08233
\(414\) 22.5867 1.11008
\(415\) 8.78339 0.431160
\(416\) 12.2721 0.601688
\(417\) 11.0913 0.543143
\(418\) −18.3049 −0.895321
\(419\) −13.1801 −0.643888 −0.321944 0.946759i \(-0.604336\pi\)
−0.321944 + 0.946759i \(0.604336\pi\)
\(420\) 10.2092 0.498156
\(421\) −19.8361 −0.966753 −0.483377 0.875413i \(-0.660590\pi\)
−0.483377 + 0.875413i \(0.660590\pi\)
\(422\) 13.1715 0.641180
\(423\) −15.7335 −0.764990
\(424\) −5.53909 −0.269002
\(425\) 16.0244 0.777296
\(426\) −9.12473 −0.442095
\(427\) −42.2008 −2.04224
\(428\) 2.51112 0.121379
\(429\) 2.42975 0.117310
\(430\) 6.06373 0.292419
\(431\) 17.3934 0.837810 0.418905 0.908030i \(-0.362414\pi\)
0.418905 + 0.908030i \(0.362414\pi\)
\(432\) −11.5710 −0.556710
\(433\) −12.5269 −0.602002 −0.301001 0.953624i \(-0.597321\pi\)
−0.301001 + 0.953624i \(0.597321\pi\)
\(434\) 39.7391 1.90754
\(435\) −5.03494 −0.241407
\(436\) −0.454241 −0.0217542
\(437\) −22.1888 −1.06143
\(438\) 29.7749 1.42270
\(439\) −4.43921 −0.211872 −0.105936 0.994373i \(-0.533784\pi\)
−0.105936 + 0.994373i \(0.533784\pi\)
\(440\) 3.27490 0.156125
\(441\) −5.52915 −0.263293
\(442\) 19.5061 0.927809
\(443\) 1.11323 0.0528911 0.0264456 0.999650i \(-0.491581\pi\)
0.0264456 + 0.999650i \(0.491581\pi\)
\(444\) 2.20826 0.104799
\(445\) 7.15854 0.339347
\(446\) −4.05558 −0.192037
\(447\) 12.8236 0.606535
\(448\) 35.9487 1.69842
\(449\) −18.1387 −0.856017 −0.428009 0.903775i \(-0.640785\pi\)
−0.428009 + 0.903775i \(0.640785\pi\)
\(450\) −13.2073 −0.622597
\(451\) −9.06510 −0.426859
\(452\) −42.5278 −2.00034
\(453\) 3.94342 0.185278
\(454\) −27.4914 −1.29024
\(455\) −7.21253 −0.338129
\(456\) −4.91548 −0.230189
\(457\) 39.7129 1.85769 0.928845 0.370469i \(-0.120803\pi\)
0.928845 + 0.370469i \(0.120803\pi\)
\(458\) −18.2582 −0.853149
\(459\) −26.5077 −1.23727
\(460\) 18.0543 0.841788
\(461\) −38.7701 −1.80570 −0.902852 0.429952i \(-0.858531\pi\)
−0.902852 + 0.429952i \(0.858531\pi\)
\(462\) 10.2272 0.475813
\(463\) −25.8031 −1.19917 −0.599586 0.800311i \(-0.704668\pi\)
−0.599586 + 0.800311i \(0.704668\pi\)
\(464\) −9.92931 −0.460957
\(465\) −7.83994 −0.363569
\(466\) 48.1549 2.23073
\(467\) 20.8600 0.965286 0.482643 0.875817i \(-0.339677\pi\)
0.482643 + 0.875817i \(0.339677\pi\)
\(468\) −9.03134 −0.417474
\(469\) 25.2904 1.16780
\(470\) −22.3874 −1.03265
\(471\) −12.8387 −0.591574
\(472\) −8.61709 −0.396634
\(473\) 3.41238 0.156902
\(474\) 17.5929 0.808067
\(475\) 12.9746 0.595314
\(476\) 46.1228 2.11404
\(477\) −10.3864 −0.475562
\(478\) 16.2537 0.743426
\(479\) −4.39948 −0.201017 −0.100509 0.994936i \(-0.532047\pi\)
−0.100509 + 0.994936i \(0.532047\pi\)
\(480\) −10.1908 −0.465145
\(481\) −1.56008 −0.0711336
\(482\) 10.5546 0.480748
\(483\) 12.3972 0.564093
\(484\) −19.8190 −0.900864
\(485\) −15.4667 −0.702306
\(486\) 34.3128 1.55646
\(487\) 3.14012 0.142292 0.0711461 0.997466i \(-0.477334\pi\)
0.0711461 + 0.997466i \(0.477334\pi\)
\(488\) −16.5328 −0.748403
\(489\) 0.861354 0.0389518
\(490\) −7.86749 −0.355417
\(491\) −39.1019 −1.76464 −0.882322 0.470646i \(-0.844021\pi\)
−0.882322 + 0.470646i \(0.844021\pi\)
\(492\) −11.0711 −0.499122
\(493\) −22.7468 −1.02446
\(494\) 15.7936 0.710588
\(495\) 6.14082 0.276009
\(496\) −15.4610 −0.694219
\(497\) 15.2428 0.683731
\(498\) 10.7460 0.481539
\(499\) 12.5714 0.562772 0.281386 0.959595i \(-0.409206\pi\)
0.281386 + 0.959595i \(0.409206\pi\)
\(500\) −29.8364 −1.33433
\(501\) −17.3709 −0.776075
\(502\) −10.8047 −0.482235
\(503\) 22.1614 0.988127 0.494063 0.869426i \(-0.335511\pi\)
0.494063 + 0.869426i \(0.335511\pi\)
\(504\) −8.35854 −0.372319
\(505\) −25.9827 −1.15621
\(506\) 18.0863 0.804034
\(507\) 9.10120 0.404198
\(508\) −1.65731 −0.0735312
\(509\) 1.68174 0.0745420 0.0372710 0.999305i \(-0.488134\pi\)
0.0372710 + 0.999305i \(0.488134\pi\)
\(510\) −16.1980 −0.717258
\(511\) −49.7387 −2.20031
\(512\) −26.2503 −1.16011
\(513\) −21.4627 −0.947600
\(514\) −40.4415 −1.78380
\(515\) −0.497125 −0.0219059
\(516\) 4.16749 0.183464
\(517\) −12.5986 −0.554085
\(518\) −6.56664 −0.288521
\(519\) −2.38656 −0.104758
\(520\) −2.82561 −0.123911
\(521\) −23.4398 −1.02692 −0.513459 0.858114i \(-0.671636\pi\)
−0.513459 + 0.858114i \(0.671636\pi\)
\(522\) 18.7479 0.820573
\(523\) 10.4211 0.455684 0.227842 0.973698i \(-0.426833\pi\)
0.227842 + 0.973698i \(0.426833\pi\)
\(524\) 24.4385 1.06760
\(525\) −7.24909 −0.316376
\(526\) −11.9373 −0.520490
\(527\) −35.4192 −1.54288
\(528\) −3.97903 −0.173165
\(529\) −1.07620 −0.0467915
\(530\) −14.7790 −0.641957
\(531\) −16.1580 −0.701199
\(532\) 37.3446 1.61909
\(533\) 7.82145 0.338784
\(534\) 8.75808 0.378999
\(535\) 1.47318 0.0636910
\(536\) 9.90788 0.427955
\(537\) −20.1758 −0.870650
\(538\) 14.5777 0.628488
\(539\) −4.42746 −0.190704
\(540\) 17.4635 0.751510
\(541\) −22.7892 −0.979785 −0.489893 0.871783i \(-0.662964\pi\)
−0.489893 + 0.871783i \(0.662964\pi\)
\(542\) 31.1449 1.33779
\(543\) −5.22172 −0.224085
\(544\) −46.0399 −1.97394
\(545\) −0.266486 −0.0114150
\(546\) −8.82414 −0.377638
\(547\) 30.2551 1.29362 0.646808 0.762653i \(-0.276103\pi\)
0.646808 + 0.762653i \(0.276103\pi\)
\(548\) −20.2465 −0.864887
\(549\) −31.0009 −1.32308
\(550\) −10.5757 −0.450949
\(551\) −18.4176 −0.784614
\(552\) 4.85678 0.206718
\(553\) −29.3887 −1.24973
\(554\) −54.3756 −2.31020
\(555\) 1.29550 0.0549910
\(556\) −33.0117 −1.40001
\(557\) −38.9178 −1.64900 −0.824500 0.565862i \(-0.808543\pi\)
−0.824500 + 0.565862i \(0.808543\pi\)
\(558\) 29.1924 1.23581
\(559\) −2.94423 −0.124528
\(560\) 11.8114 0.499124
\(561\) −9.11546 −0.384855
\(562\) 39.9526 1.68530
\(563\) −20.0995 −0.847093 −0.423547 0.905874i \(-0.639215\pi\)
−0.423547 + 0.905874i \(0.639215\pi\)
\(564\) −15.3864 −0.647886
\(565\) −24.9495 −1.04963
\(566\) −30.9264 −1.29994
\(567\) −8.83144 −0.370886
\(568\) 5.97157 0.250561
\(569\) 8.88209 0.372357 0.186178 0.982516i \(-0.440390\pi\)
0.186178 + 0.982516i \(0.440390\pi\)
\(570\) −13.1151 −0.549332
\(571\) −3.08809 −0.129233 −0.0646163 0.997910i \(-0.520582\pi\)
−0.0646163 + 0.997910i \(0.520582\pi\)
\(572\) −7.23183 −0.302378
\(573\) 11.7834 0.492257
\(574\) 32.9217 1.37413
\(575\) −12.8196 −0.534615
\(576\) 26.4081 1.10034
\(577\) 9.49723 0.395375 0.197687 0.980265i \(-0.436657\pi\)
0.197687 + 0.980265i \(0.436657\pi\)
\(578\) −36.8622 −1.53326
\(579\) 4.07357 0.169292
\(580\) 14.9858 0.622252
\(581\) −17.9511 −0.744736
\(582\) −18.9226 −0.784369
\(583\) −8.31691 −0.344451
\(584\) −19.4858 −0.806329
\(585\) −5.29835 −0.219060
\(586\) 7.27184 0.300397
\(587\) −14.5936 −0.602343 −0.301171 0.953570i \(-0.597378\pi\)
−0.301171 + 0.953570i \(0.597378\pi\)
\(588\) −5.40718 −0.222989
\(589\) −28.6781 −1.18166
\(590\) −22.9915 −0.946543
\(591\) 18.5951 0.764899
\(592\) 2.55483 0.105003
\(593\) 9.70102 0.398373 0.199187 0.979962i \(-0.436170\pi\)
0.199187 + 0.979962i \(0.436170\pi\)
\(594\) 17.4944 0.717805
\(595\) 27.0585 1.10929
\(596\) −38.1676 −1.56341
\(597\) 18.5514 0.759257
\(598\) −15.6050 −0.638136
\(599\) −44.2925 −1.80974 −0.904871 0.425686i \(-0.860033\pi\)
−0.904871 + 0.425686i \(0.860033\pi\)
\(600\) −2.83993 −0.115940
\(601\) 19.5791 0.798647 0.399324 0.916810i \(-0.369245\pi\)
0.399324 + 0.916810i \(0.369245\pi\)
\(602\) −12.3928 −0.505091
\(603\) 18.5784 0.756572
\(604\) −11.7371 −0.477574
\(605\) −11.6271 −0.472708
\(606\) −31.7884 −1.29132
\(607\) −18.9130 −0.767656 −0.383828 0.923405i \(-0.625395\pi\)
−0.383828 + 0.923405i \(0.625395\pi\)
\(608\) −37.2774 −1.51180
\(609\) 10.2902 0.416979
\(610\) −44.1114 −1.78602
\(611\) 10.8702 0.439760
\(612\) 33.8820 1.36960
\(613\) −3.93350 −0.158873 −0.0794364 0.996840i \(-0.525312\pi\)
−0.0794364 + 0.996840i \(0.525312\pi\)
\(614\) 66.9427 2.70159
\(615\) −6.49498 −0.261903
\(616\) −6.69308 −0.269672
\(617\) −13.5226 −0.544399 −0.272200 0.962241i \(-0.587751\pi\)
−0.272200 + 0.962241i \(0.587751\pi\)
\(618\) −0.608205 −0.0244656
\(619\) 43.6578 1.75475 0.877377 0.479801i \(-0.159291\pi\)
0.877377 + 0.479801i \(0.159291\pi\)
\(620\) 23.3345 0.937136
\(621\) 21.2064 0.850982
\(622\) −2.44427 −0.0980063
\(623\) −14.6303 −0.586150
\(624\) 3.43314 0.137436
\(625\) −3.81442 −0.152577
\(626\) −69.6015 −2.78183
\(627\) −7.38058 −0.294752
\(628\) 38.2125 1.52484
\(629\) 5.85280 0.233366
\(630\) −22.3016 −0.888517
\(631\) −11.4879 −0.457327 −0.228664 0.973505i \(-0.573436\pi\)
−0.228664 + 0.973505i \(0.573436\pi\)
\(632\) −11.5134 −0.457980
\(633\) 5.31079 0.211085
\(634\) 43.4232 1.72455
\(635\) −0.972281 −0.0385838
\(636\) −10.1573 −0.402764
\(637\) 3.82005 0.151356
\(638\) 15.0123 0.594344
\(639\) 11.1974 0.442962
\(640\) 13.9140 0.550000
\(641\) −29.1193 −1.15014 −0.575071 0.818104i \(-0.695025\pi\)
−0.575071 + 0.818104i \(0.695025\pi\)
\(642\) 1.80235 0.0711331
\(643\) 48.1988 1.90078 0.950388 0.311067i \(-0.100686\pi\)
0.950388 + 0.311067i \(0.100686\pi\)
\(644\) −36.8986 −1.45401
\(645\) 2.44491 0.0962683
\(646\) −59.2513 −2.33121
\(647\) 11.7233 0.460891 0.230445 0.973085i \(-0.425982\pi\)
0.230445 + 0.973085i \(0.425982\pi\)
\(648\) −3.45984 −0.135915
\(649\) −12.9385 −0.507881
\(650\) 9.12480 0.357904
\(651\) 16.0229 0.627987
\(652\) −2.56370 −0.100402
\(653\) −36.7252 −1.43717 −0.718584 0.695440i \(-0.755209\pi\)
−0.718584 + 0.695440i \(0.755209\pi\)
\(654\) −0.326031 −0.0127488
\(655\) 14.3371 0.560198
\(656\) −12.8086 −0.500092
\(657\) −36.5382 −1.42549
\(658\) 45.7543 1.78369
\(659\) −17.2769 −0.673014 −0.336507 0.941681i \(-0.609246\pi\)
−0.336507 + 0.941681i \(0.609246\pi\)
\(660\) 6.00535 0.233758
\(661\) −35.1251 −1.36621 −0.683103 0.730322i \(-0.739370\pi\)
−0.683103 + 0.730322i \(0.739370\pi\)
\(662\) −38.7727 −1.50694
\(663\) 7.86490 0.305447
\(664\) −7.03258 −0.272917
\(665\) 21.9087 0.849581
\(666\) −4.82387 −0.186921
\(667\) 18.1976 0.704615
\(668\) 51.7021 2.00042
\(669\) −1.63522 −0.0632212
\(670\) 26.4355 1.02129
\(671\) −24.8239 −0.958315
\(672\) 20.8275 0.803438
\(673\) −41.2185 −1.58886 −0.794428 0.607359i \(-0.792229\pi\)
−0.794428 + 0.607359i \(0.792229\pi\)
\(674\) 76.7816 2.95752
\(675\) −12.4001 −0.477280
\(676\) −27.0885 −1.04186
\(677\) −44.6147 −1.71468 −0.857341 0.514749i \(-0.827885\pi\)
−0.857341 + 0.514749i \(0.827885\pi\)
\(678\) −30.5243 −1.17228
\(679\) 31.6101 1.21308
\(680\) 10.6006 0.406513
\(681\) −11.0846 −0.424763
\(682\) 23.3758 0.895105
\(683\) −6.56790 −0.251314 −0.125657 0.992074i \(-0.540104\pi\)
−0.125657 + 0.992074i \(0.540104\pi\)
\(684\) 27.4334 1.04894
\(685\) −11.8779 −0.453830
\(686\) −29.8872 −1.14110
\(687\) −7.36175 −0.280868
\(688\) 4.82156 0.183820
\(689\) 7.17590 0.273380
\(690\) 12.9585 0.493321
\(691\) 12.4604 0.474016 0.237008 0.971508i \(-0.423833\pi\)
0.237008 + 0.971508i \(0.423833\pi\)
\(692\) 7.10326 0.270025
\(693\) −12.5503 −0.476747
\(694\) 49.0129 1.86050
\(695\) −19.3667 −0.734622
\(696\) 4.03132 0.152807
\(697\) −29.3429 −1.11144
\(698\) 24.7396 0.936410
\(699\) 19.4162 0.734387
\(700\) 21.5759 0.815493
\(701\) −30.9476 −1.16888 −0.584438 0.811439i \(-0.698685\pi\)
−0.584438 + 0.811439i \(0.698685\pi\)
\(702\) −15.0943 −0.569699
\(703\) 4.73888 0.178730
\(704\) 21.1462 0.796977
\(705\) −9.02665 −0.339963
\(706\) −37.3214 −1.40461
\(707\) 53.1022 1.99711
\(708\) −15.8016 −0.593861
\(709\) −3.15529 −0.118499 −0.0592497 0.998243i \(-0.518871\pi\)
−0.0592497 + 0.998243i \(0.518871\pi\)
\(710\) 15.9329 0.597950
\(711\) −21.5890 −0.809651
\(712\) −5.73162 −0.214801
\(713\) 28.3356 1.06118
\(714\) 33.1046 1.23891
\(715\) −4.24264 −0.158666
\(716\) 60.0505 2.24419
\(717\) 6.55353 0.244746
\(718\) −36.8250 −1.37430
\(719\) 34.4768 1.28577 0.642883 0.765964i \(-0.277738\pi\)
0.642883 + 0.765964i \(0.277738\pi\)
\(720\) 8.67672 0.323362
\(721\) 1.01600 0.0378378
\(722\) −7.38504 −0.274843
\(723\) 4.25564 0.158269
\(724\) 15.5417 0.577604
\(725\) −10.6408 −0.395189
\(726\) −14.2251 −0.527942
\(727\) 5.44394 0.201905 0.100952 0.994891i \(-0.467811\pi\)
0.100952 + 0.994891i \(0.467811\pi\)
\(728\) 5.77485 0.214030
\(729\) 5.21577 0.193177
\(730\) −51.9906 −1.92426
\(731\) 11.0456 0.408536
\(732\) −30.3170 −1.12055
\(733\) −42.7675 −1.57965 −0.789827 0.613329i \(-0.789830\pi\)
−0.789827 + 0.613329i \(0.789830\pi\)
\(734\) −21.7543 −0.802965
\(735\) −3.17219 −0.117008
\(736\) 36.8323 1.35766
\(737\) 14.8766 0.547988
\(738\) 24.1844 0.890240
\(739\) −27.8389 −1.02407 −0.512036 0.858964i \(-0.671108\pi\)
−0.512036 + 0.858964i \(0.671108\pi\)
\(740\) −3.85588 −0.141745
\(741\) 6.36802 0.233935
\(742\) 30.2045 1.10884
\(743\) −44.0846 −1.61731 −0.808653 0.588286i \(-0.799803\pi\)
−0.808653 + 0.588286i \(0.799803\pi\)
\(744\) 6.27719 0.230133
\(745\) −22.3915 −0.820362
\(746\) −53.9530 −1.97536
\(747\) −13.1869 −0.482484
\(748\) 27.1309 0.992004
\(749\) −3.01081 −0.110013
\(750\) −21.4151 −0.781968
\(751\) 34.0298 1.24176 0.620882 0.783904i \(-0.286774\pi\)
0.620882 + 0.783904i \(0.286774\pi\)
\(752\) −17.8013 −0.649146
\(753\) −4.35646 −0.158758
\(754\) −12.9528 −0.471712
\(755\) −6.88569 −0.250596
\(756\) −35.6911 −1.29807
\(757\) −18.1340 −0.659092 −0.329546 0.944139i \(-0.606896\pi\)
−0.329546 + 0.944139i \(0.606896\pi\)
\(758\) 48.8383 1.77389
\(759\) 7.29244 0.264699
\(760\) 8.58303 0.311339
\(761\) −9.13881 −0.331282 −0.165641 0.986186i \(-0.552969\pi\)
−0.165641 + 0.986186i \(0.552969\pi\)
\(762\) −1.18953 −0.0430922
\(763\) 0.544631 0.0197170
\(764\) −35.0715 −1.26884
\(765\) 19.8773 0.718665
\(766\) −10.9793 −0.396698
\(767\) 11.1635 0.403089
\(768\) −3.12400 −0.112728
\(769\) 41.0704 1.48104 0.740518 0.672037i \(-0.234580\pi\)
0.740518 + 0.672037i \(0.234580\pi\)
\(770\) −17.8580 −0.643556
\(771\) −16.3061 −0.587250
\(772\) −12.1244 −0.436368
\(773\) −0.718435 −0.0258403 −0.0129201 0.999917i \(-0.504113\pi\)
−0.0129201 + 0.999917i \(0.504113\pi\)
\(774\) −9.10376 −0.327228
\(775\) −16.5688 −0.595170
\(776\) 12.3837 0.444549
\(777\) −2.64768 −0.0949851
\(778\) −75.2143 −2.69656
\(779\) −23.7583 −0.851229
\(780\) −5.18147 −0.185526
\(781\) 8.96628 0.320839
\(782\) 58.5437 2.09352
\(783\) 17.6021 0.629048
\(784\) −6.25582 −0.223422
\(785\) 22.4178 0.800127
\(786\) 17.5407 0.625656
\(787\) −1.94168 −0.0692135 −0.0346067 0.999401i \(-0.511018\pi\)
−0.0346067 + 0.999401i \(0.511018\pi\)
\(788\) −55.3457 −1.97161
\(789\) −4.81314 −0.171352
\(790\) −30.7192 −1.09294
\(791\) 50.9905 1.81302
\(792\) −4.91676 −0.174709
\(793\) 21.4182 0.760584
\(794\) −58.6954 −2.08302
\(795\) −5.95891 −0.211341
\(796\) −55.2156 −1.95707
\(797\) 42.9732 1.52219 0.761094 0.648641i \(-0.224662\pi\)
0.761094 + 0.648641i \(0.224662\pi\)
\(798\) 26.8040 0.948853
\(799\) −40.7805 −1.44271
\(800\) −21.5371 −0.761453
\(801\) −10.7474 −0.379742
\(802\) 36.6362 1.29367
\(803\) −29.2579 −1.03249
\(804\) 18.1686 0.640757
\(805\) −21.6470 −0.762957
\(806\) −20.1688 −0.710417
\(807\) 5.87776 0.206907
\(808\) 20.8035 0.731866
\(809\) −42.1542 −1.48206 −0.741031 0.671471i \(-0.765663\pi\)
−0.741031 + 0.671471i \(0.765663\pi\)
\(810\) −9.23129 −0.324354
\(811\) −39.0880 −1.37257 −0.686283 0.727335i \(-0.740759\pi\)
−0.686283 + 0.727335i \(0.740759\pi\)
\(812\) −30.6273 −1.07481
\(813\) 12.5577 0.440418
\(814\) −3.86271 −0.135388
\(815\) −1.50403 −0.0526838
\(816\) −12.8798 −0.450882
\(817\) 8.94335 0.312888
\(818\) −50.4098 −1.76254
\(819\) 10.8285 0.378379
\(820\) 19.3314 0.675082
\(821\) −17.3874 −0.606826 −0.303413 0.952859i \(-0.598126\pi\)
−0.303413 + 0.952859i \(0.598126\pi\)
\(822\) −14.5319 −0.506859
\(823\) 36.6943 1.27908 0.639541 0.768757i \(-0.279125\pi\)
0.639541 + 0.768757i \(0.279125\pi\)
\(824\) 0.398032 0.0138661
\(825\) −4.26415 −0.148459
\(826\) 46.9888 1.63495
\(827\) −4.52228 −0.157255 −0.0786276 0.996904i \(-0.525054\pi\)
−0.0786276 + 0.996904i \(0.525054\pi\)
\(828\) −27.1058 −0.941993
\(829\) −49.2312 −1.70987 −0.854935 0.518736i \(-0.826403\pi\)
−0.854935 + 0.518736i \(0.826403\pi\)
\(830\) −18.7638 −0.651301
\(831\) −21.9244 −0.760548
\(832\) −18.2451 −0.632536
\(833\) −14.3313 −0.496550
\(834\) −23.6941 −0.820461
\(835\) 30.3317 1.04967
\(836\) 21.9673 0.759754
\(837\) 27.4084 0.947371
\(838\) 28.1563 0.972644
\(839\) −10.0115 −0.345635 −0.172818 0.984954i \(-0.555287\pi\)
−0.172818 + 0.984954i \(0.555287\pi\)
\(840\) −4.79547 −0.165459
\(841\) −13.8953 −0.479147
\(842\) 42.3755 1.46036
\(843\) 16.1090 0.554822
\(844\) −15.8068 −0.544094
\(845\) −15.8918 −0.546694
\(846\) 33.6112 1.15558
\(847\) 23.7628 0.816501
\(848\) −11.7515 −0.403547
\(849\) −12.4696 −0.427956
\(850\) −34.2326 −1.17417
\(851\) −4.68229 −0.160507
\(852\) 10.9504 0.375154
\(853\) −11.2609 −0.385566 −0.192783 0.981241i \(-0.561751\pi\)
−0.192783 + 0.981241i \(0.561751\pi\)
\(854\) 90.1528 3.08497
\(855\) 16.0942 0.550409
\(856\) −1.17953 −0.0403154
\(857\) 23.6931 0.809339 0.404670 0.914463i \(-0.367387\pi\)
0.404670 + 0.914463i \(0.367387\pi\)
\(858\) −5.19064 −0.177206
\(859\) −46.4974 −1.58647 −0.793235 0.608916i \(-0.791605\pi\)
−0.793235 + 0.608916i \(0.791605\pi\)
\(860\) −7.27694 −0.248142
\(861\) 13.2741 0.452381
\(862\) −37.1572 −1.26558
\(863\) 53.9120 1.83518 0.917592 0.397523i \(-0.130130\pi\)
0.917592 + 0.397523i \(0.130130\pi\)
\(864\) 35.6270 1.21205
\(865\) 4.16722 0.141690
\(866\) 26.7609 0.909373
\(867\) −14.8629 −0.504771
\(868\) −47.6899 −1.61870
\(869\) −17.2874 −0.586434
\(870\) 10.7561 0.364665
\(871\) −12.8357 −0.434921
\(872\) 0.213367 0.00722552
\(873\) 23.2209 0.785907
\(874\) 47.4015 1.60338
\(875\) 35.7737 1.20937
\(876\) −35.7322 −1.20728
\(877\) −27.4341 −0.926385 −0.463192 0.886258i \(-0.653296\pi\)
−0.463192 + 0.886258i \(0.653296\pi\)
\(878\) 9.48340 0.320049
\(879\) 2.93202 0.0988947
\(880\) 6.94787 0.234213
\(881\) 21.8568 0.736374 0.368187 0.929752i \(-0.379979\pi\)
0.368187 + 0.929752i \(0.379979\pi\)
\(882\) 11.8118 0.397725
\(883\) 51.9615 1.74864 0.874321 0.485348i \(-0.161307\pi\)
0.874321 + 0.485348i \(0.161307\pi\)
\(884\) −23.4088 −0.787323
\(885\) −9.27021 −0.311615
\(886\) −2.37817 −0.0798962
\(887\) −23.5921 −0.792147 −0.396073 0.918219i \(-0.629627\pi\)
−0.396073 + 0.918219i \(0.629627\pi\)
\(888\) −1.03727 −0.0348084
\(889\) 1.98710 0.0666452
\(890\) −15.2927 −0.512611
\(891\) −5.19494 −0.174037
\(892\) 4.86700 0.162959
\(893\) −33.0190 −1.10494
\(894\) −27.3948 −0.916219
\(895\) 35.2294 1.17759
\(896\) −28.4368 −0.950007
\(897\) −6.29198 −0.210083
\(898\) 38.7494 1.29308
\(899\) 23.5197 0.784425
\(900\) 15.8497 0.528325
\(901\) −26.9211 −0.896872
\(902\) 19.3656 0.644804
\(903\) −4.99679 −0.166283
\(904\) 19.9763 0.664401
\(905\) 9.11775 0.303084
\(906\) −8.42427 −0.279878
\(907\) 5.28546 0.175501 0.0877505 0.996142i \(-0.472032\pi\)
0.0877505 + 0.996142i \(0.472032\pi\)
\(908\) 32.9918 1.09487
\(909\) 39.0090 1.29385
\(910\) 15.4080 0.510770
\(911\) 11.3593 0.376351 0.188175 0.982135i \(-0.439743\pi\)
0.188175 + 0.982135i \(0.439743\pi\)
\(912\) −10.4285 −0.345321
\(913\) −10.5594 −0.349465
\(914\) −84.8379 −2.80619
\(915\) −17.7858 −0.587982
\(916\) 21.9112 0.723967
\(917\) −29.3015 −0.967622
\(918\) 56.6279 1.86900
\(919\) 54.3921 1.79423 0.897115 0.441797i \(-0.145659\pi\)
0.897115 + 0.441797i \(0.145659\pi\)
\(920\) −8.48053 −0.279595
\(921\) 26.9914 0.889399
\(922\) 82.8239 2.72766
\(923\) −7.73619 −0.254640
\(924\) −12.2735 −0.403767
\(925\) 2.73790 0.0900215
\(926\) 55.1227 1.81144
\(927\) 0.746357 0.0245136
\(928\) 30.5722 1.00358
\(929\) −6.36264 −0.208751 −0.104376 0.994538i \(-0.533284\pi\)
−0.104376 + 0.994538i \(0.533284\pi\)
\(930\) 16.7483 0.549199
\(931\) −11.6037 −0.380296
\(932\) −57.7896 −1.89296
\(933\) −0.985535 −0.0322650
\(934\) −44.5629 −1.45814
\(935\) 15.9167 0.520531
\(936\) 4.24222 0.138661
\(937\) 16.8228 0.549577 0.274788 0.961505i \(-0.411392\pi\)
0.274788 + 0.961505i \(0.411392\pi\)
\(938\) −54.0275 −1.76406
\(939\) −28.0635 −0.915818
\(940\) 26.8666 0.876292
\(941\) −36.5857 −1.19266 −0.596330 0.802739i \(-0.703375\pi\)
−0.596330 + 0.802739i \(0.703375\pi\)
\(942\) 27.4270 0.893620
\(943\) 23.4746 0.764437
\(944\) −18.2816 −0.595015
\(945\) −20.9386 −0.681134
\(946\) −7.28982 −0.237012
\(947\) −22.7184 −0.738247 −0.369124 0.929380i \(-0.620342\pi\)
−0.369124 + 0.929380i \(0.620342\pi\)
\(948\) −21.1128 −0.685711
\(949\) 25.2439 0.819453
\(950\) −27.7173 −0.899269
\(951\) 17.5083 0.567747
\(952\) −21.6649 −0.702164
\(953\) 20.9042 0.677154 0.338577 0.940939i \(-0.390054\pi\)
0.338577 + 0.940939i \(0.390054\pi\)
\(954\) 22.1883 0.718374
\(955\) −20.5752 −0.665797
\(956\) −19.5057 −0.630859
\(957\) 6.05301 0.195666
\(958\) 9.39854 0.303653
\(959\) 24.2754 0.783894
\(960\) 15.1509 0.488992
\(961\) 5.62263 0.181375
\(962\) 3.33278 0.107453
\(963\) −2.21175 −0.0712726
\(964\) −12.6663 −0.407955
\(965\) −7.11295 −0.228974
\(966\) −26.4839 −0.852107
\(967\) 43.3065 1.39264 0.696321 0.717730i \(-0.254819\pi\)
0.696321 + 0.717730i \(0.254819\pi\)
\(968\) 9.30943 0.299216
\(969\) −23.8903 −0.767466
\(970\) 33.0412 1.06089
\(971\) −21.8133 −0.700023 −0.350011 0.936745i \(-0.613822\pi\)
−0.350011 + 0.936745i \(0.613822\pi\)
\(972\) −41.1780 −1.32078
\(973\) 39.5808 1.26890
\(974\) −6.70817 −0.214944
\(975\) 3.67914 0.117827
\(976\) −35.0751 −1.12273
\(977\) 3.15259 0.100860 0.0504302 0.998728i \(-0.483941\pi\)
0.0504302 + 0.998728i \(0.483941\pi\)
\(978\) −1.84010 −0.0588398
\(979\) −8.60600 −0.275049
\(980\) 9.44159 0.301601
\(981\) 0.400088 0.0127738
\(982\) 83.5327 2.66564
\(983\) 9.92042 0.316412 0.158206 0.987406i \(-0.449429\pi\)
0.158206 + 0.987406i \(0.449429\pi\)
\(984\) 5.20032 0.165780
\(985\) −32.4692 −1.03456
\(986\) 48.5936 1.54754
\(987\) 18.4482 0.587214
\(988\) −18.9535 −0.602993
\(989\) −8.83655 −0.280986
\(990\) −13.1185 −0.416934
\(991\) 56.8811 1.80689 0.903444 0.428705i \(-0.141030\pi\)
0.903444 + 0.428705i \(0.141030\pi\)
\(992\) 47.6042 1.51144
\(993\) −15.6332 −0.496106
\(994\) −32.5629 −1.03283
\(995\) −32.3929 −1.02692
\(996\) −12.8960 −0.408626
\(997\) 57.4344 1.81897 0.909484 0.415740i \(-0.136477\pi\)
0.909484 + 0.415740i \(0.136477\pi\)
\(998\) −26.8560 −0.850112
\(999\) −4.52906 −0.143293
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 6031.2.a.c.1.17 110
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6031.2.a.c.1.17 110 1.1 even 1 trivial