Properties

Label 6026.2.a.g.1.14
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $21$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.825726 q^{3} +1.00000 q^{4} -2.91252 q^{5} +0.825726 q^{6} -1.72528 q^{7} +1.00000 q^{8} -2.31818 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.825726 q^{3} +1.00000 q^{4} -2.91252 q^{5} +0.825726 q^{6} -1.72528 q^{7} +1.00000 q^{8} -2.31818 q^{9} -2.91252 q^{10} +3.70152 q^{11} +0.825726 q^{12} -4.64552 q^{13} -1.72528 q^{14} -2.40494 q^{15} +1.00000 q^{16} +4.45979 q^{17} -2.31818 q^{18} +8.38053 q^{19} -2.91252 q^{20} -1.42461 q^{21} +3.70152 q^{22} -1.00000 q^{23} +0.825726 q^{24} +3.48278 q^{25} -4.64552 q^{26} -4.39136 q^{27} -1.72528 q^{28} +0.958192 q^{29} -2.40494 q^{30} +0.0262738 q^{31} +1.00000 q^{32} +3.05644 q^{33} +4.45979 q^{34} +5.02490 q^{35} -2.31818 q^{36} +0.0277632 q^{37} +8.38053 q^{38} -3.83593 q^{39} -2.91252 q^{40} -2.57987 q^{41} -1.42461 q^{42} +4.39952 q^{43} +3.70152 q^{44} +6.75174 q^{45} -1.00000 q^{46} -2.76732 q^{47} +0.825726 q^{48} -4.02342 q^{49} +3.48278 q^{50} +3.68256 q^{51} -4.64552 q^{52} -6.42047 q^{53} -4.39136 q^{54} -10.7808 q^{55} -1.72528 q^{56} +6.92002 q^{57} +0.958192 q^{58} -10.5683 q^{59} -2.40494 q^{60} -9.59785 q^{61} +0.0262738 q^{62} +3.99950 q^{63} +1.00000 q^{64} +13.5302 q^{65} +3.05644 q^{66} -6.74945 q^{67} +4.45979 q^{68} -0.825726 q^{69} +5.02490 q^{70} -3.62262 q^{71} -2.31818 q^{72} -0.166419 q^{73} +0.0277632 q^{74} +2.87582 q^{75} +8.38053 q^{76} -6.38615 q^{77} -3.83593 q^{78} -8.12246 q^{79} -2.91252 q^{80} +3.32848 q^{81} -2.57987 q^{82} -4.83091 q^{83} -1.42461 q^{84} -12.9892 q^{85} +4.39952 q^{86} +0.791204 q^{87} +3.70152 q^{88} +0.889547 q^{89} +6.75174 q^{90} +8.01481 q^{91} -1.00000 q^{92} +0.0216950 q^{93} -2.76732 q^{94} -24.4085 q^{95} +0.825726 q^{96} +3.83775 q^{97} -4.02342 q^{98} -8.58078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.825726 0.476733 0.238366 0.971175i \(-0.423388\pi\)
0.238366 + 0.971175i \(0.423388\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.91252 −1.30252 −0.651259 0.758855i \(-0.725759\pi\)
−0.651259 + 0.758855i \(0.725759\pi\)
\(6\) 0.825726 0.337101
\(7\) −1.72528 −0.652093 −0.326047 0.945354i \(-0.605717\pi\)
−0.326047 + 0.945354i \(0.605717\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.31818 −0.772726
\(10\) −2.91252 −0.921020
\(11\) 3.70152 1.11605 0.558025 0.829824i \(-0.311559\pi\)
0.558025 + 0.829824i \(0.311559\pi\)
\(12\) 0.825726 0.238366
\(13\) −4.64552 −1.28844 −0.644218 0.764842i \(-0.722817\pi\)
−0.644218 + 0.764842i \(0.722817\pi\)
\(14\) −1.72528 −0.461100
\(15\) −2.40494 −0.620954
\(16\) 1.00000 0.250000
\(17\) 4.45979 1.08166 0.540829 0.841133i \(-0.318111\pi\)
0.540829 + 0.841133i \(0.318111\pi\)
\(18\) −2.31818 −0.546400
\(19\) 8.38053 1.92263 0.961313 0.275458i \(-0.0888295\pi\)
0.961313 + 0.275458i \(0.0888295\pi\)
\(20\) −2.91252 −0.651259
\(21\) −1.42461 −0.310874
\(22\) 3.70152 0.789167
\(23\) −1.00000 −0.208514
\(24\) 0.825726 0.168551
\(25\) 3.48278 0.696555
\(26\) −4.64552 −0.911062
\(27\) −4.39136 −0.845117
\(28\) −1.72528 −0.326047
\(29\) 0.958192 0.177932 0.0889659 0.996035i \(-0.471644\pi\)
0.0889659 + 0.996035i \(0.471644\pi\)
\(30\) −2.40494 −0.439081
\(31\) 0.0262738 0.00471892 0.00235946 0.999997i \(-0.499249\pi\)
0.00235946 + 0.999997i \(0.499249\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.05644 0.532058
\(34\) 4.45979 0.764847
\(35\) 5.02490 0.849364
\(36\) −2.31818 −0.386363
\(37\) 0.0277632 0.00456425 0.00228212 0.999997i \(-0.499274\pi\)
0.00228212 + 0.999997i \(0.499274\pi\)
\(38\) 8.38053 1.35950
\(39\) −3.83593 −0.614240
\(40\) −2.91252 −0.460510
\(41\) −2.57987 −0.402909 −0.201454 0.979498i \(-0.564567\pi\)
−0.201454 + 0.979498i \(0.564567\pi\)
\(42\) −1.42461 −0.219821
\(43\) 4.39952 0.670921 0.335460 0.942054i \(-0.391108\pi\)
0.335460 + 0.942054i \(0.391108\pi\)
\(44\) 3.70152 0.558025
\(45\) 6.75174 1.00649
\(46\) −1.00000 −0.147442
\(47\) −2.76732 −0.403655 −0.201828 0.979421i \(-0.564688\pi\)
−0.201828 + 0.979421i \(0.564688\pi\)
\(48\) 0.825726 0.119183
\(49\) −4.02342 −0.574774
\(50\) 3.48278 0.492539
\(51\) 3.68256 0.515662
\(52\) −4.64552 −0.644218
\(53\) −6.42047 −0.881919 −0.440960 0.897527i \(-0.645362\pi\)
−0.440960 + 0.897527i \(0.645362\pi\)
\(54\) −4.39136 −0.597588
\(55\) −10.7808 −1.45368
\(56\) −1.72528 −0.230550
\(57\) 6.92002 0.916579
\(58\) 0.958192 0.125817
\(59\) −10.5683 −1.37588 −0.687940 0.725768i \(-0.741485\pi\)
−0.687940 + 0.725768i \(0.741485\pi\)
\(60\) −2.40494 −0.310477
\(61\) −9.59785 −1.22888 −0.614439 0.788964i \(-0.710618\pi\)
−0.614439 + 0.788964i \(0.710618\pi\)
\(62\) 0.0262738 0.00333678
\(63\) 3.99950 0.503889
\(64\) 1.00000 0.125000
\(65\) 13.5302 1.67821
\(66\) 3.05644 0.376222
\(67\) −6.74945 −0.824576 −0.412288 0.911053i \(-0.635270\pi\)
−0.412288 + 0.911053i \(0.635270\pi\)
\(68\) 4.45979 0.540829
\(69\) −0.825726 −0.0994057
\(70\) 5.02490 0.600591
\(71\) −3.62262 −0.429926 −0.214963 0.976622i \(-0.568963\pi\)
−0.214963 + 0.976622i \(0.568963\pi\)
\(72\) −2.31818 −0.273200
\(73\) −0.166419 −0.0194779 −0.00973893 0.999953i \(-0.503100\pi\)
−0.00973893 + 0.999953i \(0.503100\pi\)
\(74\) 0.0277632 0.00322741
\(75\) 2.87582 0.332071
\(76\) 8.38053 0.961313
\(77\) −6.38615 −0.727769
\(78\) −3.83593 −0.434333
\(79\) −8.12246 −0.913848 −0.456924 0.889506i \(-0.651049\pi\)
−0.456924 + 0.889506i \(0.651049\pi\)
\(80\) −2.91252 −0.325630
\(81\) 3.32848 0.369831
\(82\) −2.57987 −0.284899
\(83\) −4.83091 −0.530262 −0.265131 0.964212i \(-0.585415\pi\)
−0.265131 + 0.964212i \(0.585415\pi\)
\(84\) −1.42461 −0.155437
\(85\) −12.9892 −1.40888
\(86\) 4.39952 0.474413
\(87\) 0.791204 0.0848260
\(88\) 3.70152 0.394583
\(89\) 0.889547 0.0942918 0.0471459 0.998888i \(-0.484987\pi\)
0.0471459 + 0.998888i \(0.484987\pi\)
\(90\) 6.75174 0.711696
\(91\) 8.01481 0.840181
\(92\) −1.00000 −0.104257
\(93\) 0.0216950 0.00224966
\(94\) −2.76732 −0.285427
\(95\) −24.4085 −2.50426
\(96\) 0.825726 0.0842753
\(97\) 3.83775 0.389664 0.194832 0.980837i \(-0.437584\pi\)
0.194832 + 0.980837i \(0.437584\pi\)
\(98\) −4.02342 −0.406427
\(99\) −8.58078 −0.862401
\(100\) 3.48278 0.348278
\(101\) −12.9059 −1.28418 −0.642092 0.766628i \(-0.721933\pi\)
−0.642092 + 0.766628i \(0.721933\pi\)
\(102\) 3.68256 0.364628
\(103\) 4.12459 0.406408 0.203204 0.979136i \(-0.434865\pi\)
0.203204 + 0.979136i \(0.434865\pi\)
\(104\) −4.64552 −0.455531
\(105\) 4.14919 0.404920
\(106\) −6.42047 −0.623611
\(107\) −3.70214 −0.357899 −0.178950 0.983858i \(-0.557270\pi\)
−0.178950 + 0.983858i \(0.557270\pi\)
\(108\) −4.39136 −0.422558
\(109\) −10.7316 −1.02790 −0.513949 0.857821i \(-0.671818\pi\)
−0.513949 + 0.857821i \(0.671818\pi\)
\(110\) −10.7808 −1.02790
\(111\) 0.0229248 0.00217593
\(112\) −1.72528 −0.163023
\(113\) −9.91209 −0.932451 −0.466225 0.884666i \(-0.654386\pi\)
−0.466225 + 0.884666i \(0.654386\pi\)
\(114\) 6.92002 0.648119
\(115\) 2.91252 0.271594
\(116\) 0.958192 0.0889659
\(117\) 10.7691 0.995608
\(118\) −10.5683 −0.972894
\(119\) −7.69437 −0.705342
\(120\) −2.40494 −0.219540
\(121\) 2.70126 0.245569
\(122\) −9.59785 −0.868949
\(123\) −2.13027 −0.192080
\(124\) 0.0262738 0.00235946
\(125\) 4.41895 0.395243
\(126\) 3.99950 0.356304
\(127\) −0.314178 −0.0278788 −0.0139394 0.999903i \(-0.504437\pi\)
−0.0139394 + 0.999903i \(0.504437\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.63280 0.319850
\(130\) 13.5302 1.18668
\(131\) 1.00000 0.0873704
\(132\) 3.05644 0.266029
\(133\) −14.4587 −1.25373
\(134\) −6.74945 −0.583064
\(135\) 12.7899 1.10078
\(136\) 4.45979 0.382424
\(137\) −14.7354 −1.25893 −0.629466 0.777028i \(-0.716726\pi\)
−0.629466 + 0.777028i \(0.716726\pi\)
\(138\) −0.825726 −0.0702904
\(139\) −6.44780 −0.546895 −0.273448 0.961887i \(-0.588164\pi\)
−0.273448 + 0.961887i \(0.588164\pi\)
\(140\) 5.02490 0.424682
\(141\) −2.28505 −0.192436
\(142\) −3.62262 −0.304004
\(143\) −17.1955 −1.43796
\(144\) −2.31818 −0.193181
\(145\) −2.79075 −0.231760
\(146\) −0.166419 −0.0137729
\(147\) −3.32224 −0.274014
\(148\) 0.0277632 0.00228212
\(149\) 16.1454 1.32268 0.661340 0.750087i \(-0.269988\pi\)
0.661340 + 0.750087i \(0.269988\pi\)
\(150\) 2.87582 0.234810
\(151\) 1.92980 0.157045 0.0785224 0.996912i \(-0.474980\pi\)
0.0785224 + 0.996912i \(0.474980\pi\)
\(152\) 8.38053 0.679751
\(153\) −10.3386 −0.835824
\(154\) −6.38615 −0.514611
\(155\) −0.0765231 −0.00614648
\(156\) −3.83593 −0.307120
\(157\) −16.6026 −1.32503 −0.662514 0.749049i \(-0.730511\pi\)
−0.662514 + 0.749049i \(0.730511\pi\)
\(158\) −8.12246 −0.646188
\(159\) −5.30155 −0.420440
\(160\) −2.91252 −0.230255
\(161\) 1.72528 0.135971
\(162\) 3.32848 0.261510
\(163\) −1.82033 −0.142579 −0.0712895 0.997456i \(-0.522711\pi\)
−0.0712895 + 0.997456i \(0.522711\pi\)
\(164\) −2.57987 −0.201454
\(165\) −8.90195 −0.693016
\(166\) −4.83091 −0.374952
\(167\) −2.76385 −0.213873 −0.106937 0.994266i \(-0.534104\pi\)
−0.106937 + 0.994266i \(0.534104\pi\)
\(168\) −1.42461 −0.109911
\(169\) 8.58089 0.660068
\(170\) −12.9892 −0.996228
\(171\) −19.4276 −1.48566
\(172\) 4.39952 0.335460
\(173\) 22.8026 1.73365 0.866825 0.498612i \(-0.166157\pi\)
0.866825 + 0.498612i \(0.166157\pi\)
\(174\) 0.791204 0.0599810
\(175\) −6.00875 −0.454219
\(176\) 3.70152 0.279013
\(177\) −8.72654 −0.655927
\(178\) 0.889547 0.0666743
\(179\) 6.71468 0.501879 0.250939 0.968003i \(-0.419261\pi\)
0.250939 + 0.968003i \(0.419261\pi\)
\(180\) 6.75174 0.503245
\(181\) 11.4355 0.849996 0.424998 0.905194i \(-0.360275\pi\)
0.424998 + 0.905194i \(0.360275\pi\)
\(182\) 8.01481 0.594098
\(183\) −7.92519 −0.585847
\(184\) −1.00000 −0.0737210
\(185\) −0.0808610 −0.00594502
\(186\) 0.0216950 0.00159075
\(187\) 16.5080 1.20718
\(188\) −2.76732 −0.201828
\(189\) 7.57630 0.551095
\(190\) −24.4085 −1.77078
\(191\) −18.0493 −1.30600 −0.653001 0.757357i \(-0.726490\pi\)
−0.653001 + 0.757357i \(0.726490\pi\)
\(192\) 0.825726 0.0595916
\(193\) 15.4934 1.11524 0.557619 0.830097i \(-0.311715\pi\)
0.557619 + 0.830097i \(0.311715\pi\)
\(194\) 3.83775 0.275534
\(195\) 11.1722 0.800059
\(196\) −4.02342 −0.287387
\(197\) 15.8107 1.12646 0.563232 0.826299i \(-0.309558\pi\)
0.563232 + 0.826299i \(0.309558\pi\)
\(198\) −8.58078 −0.609810
\(199\) 0.796066 0.0564316 0.0282158 0.999602i \(-0.491017\pi\)
0.0282158 + 0.999602i \(0.491017\pi\)
\(200\) 3.48278 0.246269
\(201\) −5.57319 −0.393103
\(202\) −12.9059 −0.908055
\(203\) −1.65315 −0.116028
\(204\) 3.68256 0.257831
\(205\) 7.51393 0.524796
\(206\) 4.12459 0.287374
\(207\) 2.31818 0.161124
\(208\) −4.64552 −0.322109
\(209\) 31.0207 2.14575
\(210\) 4.14919 0.286322
\(211\) −26.4759 −1.82268 −0.911338 0.411659i \(-0.864950\pi\)
−0.911338 + 0.411659i \(0.864950\pi\)
\(212\) −6.42047 −0.440960
\(213\) −2.99129 −0.204960
\(214\) −3.70214 −0.253073
\(215\) −12.8137 −0.873887
\(216\) −4.39136 −0.298794
\(217\) −0.0453296 −0.00307718
\(218\) −10.7316 −0.726833
\(219\) −0.137416 −0.00928574
\(220\) −10.7808 −0.726838
\(221\) −20.7180 −1.39365
\(222\) 0.0229248 0.00153861
\(223\) −20.0246 −1.34095 −0.670473 0.741934i \(-0.733909\pi\)
−0.670473 + 0.741934i \(0.733909\pi\)
\(224\) −1.72528 −0.115275
\(225\) −8.07369 −0.538246
\(226\) −9.91209 −0.659342
\(227\) −10.7338 −0.712428 −0.356214 0.934404i \(-0.615933\pi\)
−0.356214 + 0.934404i \(0.615933\pi\)
\(228\) 6.92002 0.458290
\(229\) −11.0900 −0.732848 −0.366424 0.930448i \(-0.619418\pi\)
−0.366424 + 0.930448i \(0.619418\pi\)
\(230\) 2.91252 0.192046
\(231\) −5.27321 −0.346952
\(232\) 0.958192 0.0629084
\(233\) −16.4885 −1.08020 −0.540099 0.841601i \(-0.681613\pi\)
−0.540099 + 0.841601i \(0.681613\pi\)
\(234\) 10.7691 0.704001
\(235\) 8.05988 0.525768
\(236\) −10.5683 −0.687940
\(237\) −6.70693 −0.435662
\(238\) −7.69437 −0.498752
\(239\) −20.8880 −1.35113 −0.675565 0.737300i \(-0.736100\pi\)
−0.675565 + 0.737300i \(0.736100\pi\)
\(240\) −2.40494 −0.155238
\(241\) −0.268081 −0.0172686 −0.00863431 0.999963i \(-0.502748\pi\)
−0.00863431 + 0.999963i \(0.502748\pi\)
\(242\) 2.70126 0.173643
\(243\) 15.9225 1.02143
\(244\) −9.59785 −0.614439
\(245\) 11.7183 0.748654
\(246\) −2.13027 −0.135821
\(247\) −38.9320 −2.47718
\(248\) 0.0262738 0.00166839
\(249\) −3.98901 −0.252793
\(250\) 4.41895 0.279479
\(251\) 14.2857 0.901704 0.450852 0.892599i \(-0.351120\pi\)
0.450852 + 0.892599i \(0.351120\pi\)
\(252\) 3.99950 0.251945
\(253\) −3.70152 −0.232713
\(254\) −0.314178 −0.0197133
\(255\) −10.7255 −0.671659
\(256\) 1.00000 0.0625000
\(257\) 28.4449 1.77434 0.887172 0.461439i \(-0.152667\pi\)
0.887172 + 0.461439i \(0.152667\pi\)
\(258\) 3.63280 0.226168
\(259\) −0.0478993 −0.00297632
\(260\) 13.5302 0.839106
\(261\) −2.22126 −0.137492
\(262\) 1.00000 0.0617802
\(263\) −17.2177 −1.06169 −0.530844 0.847470i \(-0.678125\pi\)
−0.530844 + 0.847470i \(0.678125\pi\)
\(264\) 3.05644 0.188111
\(265\) 18.6997 1.14872
\(266\) −14.4587 −0.886522
\(267\) 0.734522 0.0449520
\(268\) −6.74945 −0.412288
\(269\) 2.89267 0.176369 0.0881847 0.996104i \(-0.471893\pi\)
0.0881847 + 0.996104i \(0.471893\pi\)
\(270\) 12.7899 0.778369
\(271\) 22.1434 1.34512 0.672558 0.740044i \(-0.265196\pi\)
0.672558 + 0.740044i \(0.265196\pi\)
\(272\) 4.45979 0.270414
\(273\) 6.61804 0.400542
\(274\) −14.7354 −0.890199
\(275\) 12.8916 0.777391
\(276\) −0.825726 −0.0497028
\(277\) 16.3344 0.981438 0.490719 0.871318i \(-0.336734\pi\)
0.490719 + 0.871318i \(0.336734\pi\)
\(278\) −6.44780 −0.386713
\(279\) −0.0609074 −0.00364643
\(280\) 5.02490 0.300295
\(281\) 17.2067 1.02647 0.513234 0.858249i \(-0.328447\pi\)
0.513234 + 0.858249i \(0.328447\pi\)
\(282\) −2.28505 −0.136073
\(283\) 5.88667 0.349926 0.174963 0.984575i \(-0.444019\pi\)
0.174963 + 0.984575i \(0.444019\pi\)
\(284\) −3.62262 −0.214963
\(285\) −20.1547 −1.19386
\(286\) −17.1955 −1.01679
\(287\) 4.45100 0.262734
\(288\) −2.31818 −0.136600
\(289\) 2.88971 0.169983
\(290\) −2.79075 −0.163879
\(291\) 3.16893 0.185766
\(292\) −0.166419 −0.00973893
\(293\) 18.0716 1.05575 0.527876 0.849321i \(-0.322989\pi\)
0.527876 + 0.849321i \(0.322989\pi\)
\(294\) −3.32224 −0.193757
\(295\) 30.7805 1.79211
\(296\) 0.0277632 0.00161371
\(297\) −16.2547 −0.943193
\(298\) 16.1454 0.935276
\(299\) 4.64552 0.268658
\(300\) 2.87582 0.166035
\(301\) −7.59040 −0.437503
\(302\) 1.92980 0.111047
\(303\) −10.6567 −0.612212
\(304\) 8.38053 0.480657
\(305\) 27.9539 1.60064
\(306\) −10.3386 −0.591017
\(307\) 16.7644 0.956797 0.478398 0.878143i \(-0.341218\pi\)
0.478398 + 0.878143i \(0.341218\pi\)
\(308\) −6.38615 −0.363885
\(309\) 3.40578 0.193748
\(310\) −0.0765231 −0.00434622
\(311\) 9.48145 0.537644 0.268822 0.963190i \(-0.413366\pi\)
0.268822 + 0.963190i \(0.413366\pi\)
\(312\) −3.83593 −0.217167
\(313\) 19.1669 1.08338 0.541689 0.840579i \(-0.317785\pi\)
0.541689 + 0.840579i \(0.317785\pi\)
\(314\) −16.6026 −0.936937
\(315\) −11.6486 −0.656325
\(316\) −8.12246 −0.456924
\(317\) −25.4875 −1.43152 −0.715761 0.698345i \(-0.753920\pi\)
−0.715761 + 0.698345i \(0.753920\pi\)
\(318\) −5.30155 −0.297296
\(319\) 3.54677 0.198581
\(320\) −2.91252 −0.162815
\(321\) −3.05695 −0.170622
\(322\) 1.72528 0.0961459
\(323\) 37.3754 2.07962
\(324\) 3.32848 0.184915
\(325\) −16.1793 −0.897467
\(326\) −1.82033 −0.100819
\(327\) −8.86133 −0.490033
\(328\) −2.57987 −0.142450
\(329\) 4.77439 0.263221
\(330\) −8.90195 −0.490036
\(331\) 18.1211 0.996025 0.498012 0.867170i \(-0.334063\pi\)
0.498012 + 0.867170i \(0.334063\pi\)
\(332\) −4.83091 −0.265131
\(333\) −0.0643601 −0.00352691
\(334\) −2.76385 −0.151231
\(335\) 19.6579 1.07403
\(336\) −1.42461 −0.0777186
\(337\) −29.3256 −1.59747 −0.798733 0.601686i \(-0.794496\pi\)
−0.798733 + 0.601686i \(0.794496\pi\)
\(338\) 8.58089 0.466739
\(339\) −8.18466 −0.444530
\(340\) −12.9892 −0.704440
\(341\) 0.0972531 0.00526655
\(342\) −19.4276 −1.05052
\(343\) 19.0185 1.02690
\(344\) 4.39952 0.237206
\(345\) 2.40494 0.129478
\(346\) 22.8026 1.22588
\(347\) 7.46569 0.400779 0.200390 0.979716i \(-0.435779\pi\)
0.200390 + 0.979716i \(0.435779\pi\)
\(348\) 0.791204 0.0424130
\(349\) −11.4966 −0.615400 −0.307700 0.951483i \(-0.599559\pi\)
−0.307700 + 0.951483i \(0.599559\pi\)
\(350\) −6.00875 −0.321181
\(351\) 20.4001 1.08888
\(352\) 3.70152 0.197292
\(353\) −6.34943 −0.337946 −0.168973 0.985621i \(-0.554045\pi\)
−0.168973 + 0.985621i \(0.554045\pi\)
\(354\) −8.72654 −0.463810
\(355\) 10.5510 0.559987
\(356\) 0.889547 0.0471459
\(357\) −6.35344 −0.336260
\(358\) 6.71468 0.354882
\(359\) −4.27204 −0.225470 −0.112735 0.993625i \(-0.535961\pi\)
−0.112735 + 0.993625i \(0.535961\pi\)
\(360\) 6.75174 0.355848
\(361\) 51.2333 2.69649
\(362\) 11.4355 0.601038
\(363\) 2.23050 0.117071
\(364\) 8.01481 0.420090
\(365\) 0.484699 0.0253703
\(366\) −7.92519 −0.414256
\(367\) −27.5219 −1.43663 −0.718315 0.695718i \(-0.755086\pi\)
−0.718315 + 0.695718i \(0.755086\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 5.98060 0.311338
\(370\) −0.0808610 −0.00420376
\(371\) 11.0771 0.575094
\(372\) 0.0216950 0.00112483
\(373\) 17.6082 0.911720 0.455860 0.890052i \(-0.349332\pi\)
0.455860 + 0.890052i \(0.349332\pi\)
\(374\) 16.5080 0.853608
\(375\) 3.64884 0.188425
\(376\) −2.76732 −0.142714
\(377\) −4.45130 −0.229254
\(378\) 7.57630 0.389683
\(379\) −34.4193 −1.76800 −0.884000 0.467486i \(-0.845160\pi\)
−0.884000 + 0.467486i \(0.845160\pi\)
\(380\) −24.4085 −1.25213
\(381\) −0.259425 −0.0132907
\(382\) −18.0493 −0.923483
\(383\) −14.4656 −0.739158 −0.369579 0.929199i \(-0.620498\pi\)
−0.369579 + 0.929199i \(0.620498\pi\)
\(384\) 0.825726 0.0421376
\(385\) 18.5998 0.947933
\(386\) 15.4934 0.788592
\(387\) −10.1989 −0.518438
\(388\) 3.83775 0.194832
\(389\) −14.7539 −0.748052 −0.374026 0.927418i \(-0.622023\pi\)
−0.374026 + 0.927418i \(0.622023\pi\)
\(390\) 11.1722 0.565727
\(391\) −4.45979 −0.225541
\(392\) −4.02342 −0.203213
\(393\) 0.825726 0.0416524
\(394\) 15.8107 0.796531
\(395\) 23.6568 1.19030
\(396\) −8.58078 −0.431200
\(397\) −1.90888 −0.0958041 −0.0479020 0.998852i \(-0.515254\pi\)
−0.0479020 + 0.998852i \(0.515254\pi\)
\(398\) 0.796066 0.0399032
\(399\) −11.9390 −0.597695
\(400\) 3.48278 0.174139
\(401\) −11.0337 −0.550999 −0.275499 0.961301i \(-0.588843\pi\)
−0.275499 + 0.961301i \(0.588843\pi\)
\(402\) −5.57319 −0.277966
\(403\) −0.122056 −0.00608003
\(404\) −12.9059 −0.642092
\(405\) −9.69425 −0.481711
\(406\) −1.65315 −0.0820443
\(407\) 0.102766 0.00509393
\(408\) 3.68256 0.182314
\(409\) −7.05569 −0.348881 −0.174441 0.984668i \(-0.555812\pi\)
−0.174441 + 0.984668i \(0.555812\pi\)
\(410\) 7.51393 0.371087
\(411\) −12.1674 −0.600174
\(412\) 4.12459 0.203204
\(413\) 18.2333 0.897202
\(414\) 2.31818 0.113932
\(415\) 14.0701 0.690676
\(416\) −4.64552 −0.227766
\(417\) −5.32412 −0.260723
\(418\) 31.0207 1.51727
\(419\) −6.44623 −0.314919 −0.157460 0.987525i \(-0.550330\pi\)
−0.157460 + 0.987525i \(0.550330\pi\)
\(420\) 4.14919 0.202460
\(421\) −30.3425 −1.47880 −0.739401 0.673265i \(-0.764891\pi\)
−0.739401 + 0.673265i \(0.764891\pi\)
\(422\) −26.4759 −1.28883
\(423\) 6.41514 0.311915
\(424\) −6.42047 −0.311806
\(425\) 15.5324 0.753434
\(426\) −2.99129 −0.144928
\(427\) 16.5590 0.801344
\(428\) −3.70214 −0.178950
\(429\) −14.1988 −0.685523
\(430\) −12.8137 −0.617932
\(431\) −8.21996 −0.395942 −0.197971 0.980208i \(-0.563435\pi\)
−0.197971 + 0.980208i \(0.563435\pi\)
\(432\) −4.39136 −0.211279
\(433\) 38.4408 1.84735 0.923673 0.383183i \(-0.125172\pi\)
0.923673 + 0.383183i \(0.125172\pi\)
\(434\) −0.0453296 −0.00217589
\(435\) −2.30440 −0.110487
\(436\) −10.7316 −0.513949
\(437\) −8.38053 −0.400895
\(438\) −0.137416 −0.00656601
\(439\) 11.8125 0.563779 0.281890 0.959447i \(-0.409039\pi\)
0.281890 + 0.959447i \(0.409039\pi\)
\(440\) −10.7808 −0.513952
\(441\) 9.32700 0.444143
\(442\) −20.7180 −0.985457
\(443\) −13.4654 −0.639763 −0.319881 0.947458i \(-0.603643\pi\)
−0.319881 + 0.947458i \(0.603643\pi\)
\(444\) 0.0229248 0.00108796
\(445\) −2.59082 −0.122817
\(446\) −20.0246 −0.948192
\(447\) 13.3316 0.630565
\(448\) −1.72528 −0.0815117
\(449\) −2.87075 −0.135479 −0.0677395 0.997703i \(-0.521579\pi\)
−0.0677395 + 0.997703i \(0.521579\pi\)
\(450\) −8.07369 −0.380597
\(451\) −9.54946 −0.449666
\(452\) −9.91209 −0.466225
\(453\) 1.59348 0.0748684
\(454\) −10.7338 −0.503763
\(455\) −23.3433 −1.09435
\(456\) 6.92002 0.324060
\(457\) 22.9351 1.07286 0.536430 0.843945i \(-0.319773\pi\)
0.536430 + 0.843945i \(0.319773\pi\)
\(458\) −11.0900 −0.518202
\(459\) −19.5845 −0.914127
\(460\) 2.91252 0.135797
\(461\) −7.78624 −0.362641 −0.181321 0.983424i \(-0.558037\pi\)
−0.181321 + 0.983424i \(0.558037\pi\)
\(462\) −5.27321 −0.245332
\(463\) 23.9570 1.11337 0.556687 0.830722i \(-0.312072\pi\)
0.556687 + 0.830722i \(0.312072\pi\)
\(464\) 0.958192 0.0444829
\(465\) −0.0631871 −0.00293023
\(466\) −16.4885 −0.763816
\(467\) −34.5877 −1.60053 −0.800263 0.599649i \(-0.795307\pi\)
−0.800263 + 0.599649i \(0.795307\pi\)
\(468\) 10.7691 0.497804
\(469\) 11.6447 0.537701
\(470\) 8.05988 0.371774
\(471\) −13.7092 −0.631685
\(472\) −10.5683 −0.486447
\(473\) 16.2849 0.748782
\(474\) −6.70693 −0.308059
\(475\) 29.1875 1.33922
\(476\) −7.69437 −0.352671
\(477\) 14.8838 0.681482
\(478\) −20.8880 −0.955393
\(479\) −18.1571 −0.829618 −0.414809 0.909909i \(-0.636152\pi\)
−0.414809 + 0.909909i \(0.636152\pi\)
\(480\) −2.40494 −0.109770
\(481\) −0.128975 −0.00588074
\(482\) −0.268081 −0.0122108
\(483\) 1.42461 0.0648218
\(484\) 2.70126 0.122784
\(485\) −11.1775 −0.507545
\(486\) 15.9225 0.722258
\(487\) 26.3758 1.19520 0.597600 0.801794i \(-0.296121\pi\)
0.597600 + 0.801794i \(0.296121\pi\)
\(488\) −9.59785 −0.434474
\(489\) −1.50309 −0.0679721
\(490\) 11.7183 0.529378
\(491\) 35.7810 1.61477 0.807387 0.590022i \(-0.200881\pi\)
0.807387 + 0.590022i \(0.200881\pi\)
\(492\) −2.13027 −0.0960399
\(493\) 4.27333 0.192461
\(494\) −38.9320 −1.75163
\(495\) 24.9917 1.12329
\(496\) 0.0262738 0.00117973
\(497\) 6.25002 0.280352
\(498\) −3.98901 −0.178752
\(499\) −21.7609 −0.974154 −0.487077 0.873359i \(-0.661937\pi\)
−0.487077 + 0.873359i \(0.661937\pi\)
\(500\) 4.41895 0.197621
\(501\) −2.28218 −0.101960
\(502\) 14.2857 0.637601
\(503\) 13.9850 0.623560 0.311780 0.950154i \(-0.399075\pi\)
0.311780 + 0.950154i \(0.399075\pi\)
\(504\) 3.99950 0.178152
\(505\) 37.5886 1.67267
\(506\) −3.70152 −0.164553
\(507\) 7.08546 0.314676
\(508\) −0.314178 −0.0139394
\(509\) −36.5256 −1.61897 −0.809484 0.587142i \(-0.800253\pi\)
−0.809484 + 0.587142i \(0.800253\pi\)
\(510\) −10.7255 −0.474935
\(511\) 0.287119 0.0127014
\(512\) 1.00000 0.0441942
\(513\) −36.8019 −1.62484
\(514\) 28.4449 1.25465
\(515\) −12.0129 −0.529354
\(516\) 3.63280 0.159925
\(517\) −10.2433 −0.450500
\(518\) −0.0478993 −0.00210457
\(519\) 18.8287 0.826488
\(520\) 13.5302 0.593338
\(521\) −4.41620 −0.193477 −0.0967386 0.995310i \(-0.530841\pi\)
−0.0967386 + 0.995310i \(0.530841\pi\)
\(522\) −2.22126 −0.0972219
\(523\) −32.0404 −1.40103 −0.700515 0.713637i \(-0.747046\pi\)
−0.700515 + 0.713637i \(0.747046\pi\)
\(524\) 1.00000 0.0436852
\(525\) −4.96158 −0.216541
\(526\) −17.2177 −0.750727
\(527\) 0.117176 0.00510425
\(528\) 3.05644 0.133015
\(529\) 1.00000 0.0434783
\(530\) 18.6997 0.812265
\(531\) 24.4993 1.06318
\(532\) −14.4587 −0.626866
\(533\) 11.9849 0.519122
\(534\) 0.734522 0.0317859
\(535\) 10.7826 0.466170
\(536\) −6.74945 −0.291532
\(537\) 5.54448 0.239262
\(538\) 2.89267 0.124712
\(539\) −14.8928 −0.641477
\(540\) 12.7899 0.550390
\(541\) −19.7636 −0.849702 −0.424851 0.905263i \(-0.639674\pi\)
−0.424851 + 0.905263i \(0.639674\pi\)
\(542\) 22.1434 0.951141
\(543\) 9.44260 0.405221
\(544\) 4.45979 0.191212
\(545\) 31.2559 1.33886
\(546\) 6.61804 0.283226
\(547\) −28.0042 −1.19737 −0.598686 0.800984i \(-0.704310\pi\)
−0.598686 + 0.800984i \(0.704310\pi\)
\(548\) −14.7354 −0.629466
\(549\) 22.2495 0.949586
\(550\) 12.8916 0.549698
\(551\) 8.03016 0.342096
\(552\) −0.825726 −0.0351452
\(553\) 14.0135 0.595915
\(554\) 16.3344 0.693981
\(555\) −0.0667690 −0.00283419
\(556\) −6.44780 −0.273448
\(557\) 31.7381 1.34479 0.672394 0.740194i \(-0.265266\pi\)
0.672394 + 0.740194i \(0.265266\pi\)
\(558\) −0.0609074 −0.00257841
\(559\) −20.4381 −0.864439
\(560\) 5.02490 0.212341
\(561\) 13.6311 0.575505
\(562\) 17.2067 0.725823
\(563\) 2.36905 0.0998437 0.0499218 0.998753i \(-0.484103\pi\)
0.0499218 + 0.998753i \(0.484103\pi\)
\(564\) −2.28505 −0.0962179
\(565\) 28.8692 1.21453
\(566\) 5.88667 0.247435
\(567\) −5.74254 −0.241164
\(568\) −3.62262 −0.152002
\(569\) −24.9149 −1.04449 −0.522243 0.852797i \(-0.674905\pi\)
−0.522243 + 0.852797i \(0.674905\pi\)
\(570\) −20.1547 −0.844188
\(571\) −28.5277 −1.19385 −0.596924 0.802298i \(-0.703611\pi\)
−0.596924 + 0.802298i \(0.703611\pi\)
\(572\) −17.1955 −0.718980
\(573\) −14.9038 −0.622614
\(574\) 4.45100 0.185781
\(575\) −3.48278 −0.145242
\(576\) −2.31818 −0.0965907
\(577\) 30.9672 1.28918 0.644590 0.764528i \(-0.277028\pi\)
0.644590 + 0.764528i \(0.277028\pi\)
\(578\) 2.88971 0.120196
\(579\) 12.7933 0.531671
\(580\) −2.79075 −0.115880
\(581\) 8.33466 0.345780
\(582\) 3.16893 0.131356
\(583\) −23.7655 −0.984266
\(584\) −0.166419 −0.00688647
\(585\) −31.3654 −1.29680
\(586\) 18.0716 0.746530
\(587\) 22.4958 0.928501 0.464251 0.885704i \(-0.346324\pi\)
0.464251 + 0.885704i \(0.346324\pi\)
\(588\) −3.32224 −0.137007
\(589\) 0.220189 0.00907272
\(590\) 30.7805 1.26721
\(591\) 13.0553 0.537023
\(592\) 0.0277632 0.00114106
\(593\) 6.62297 0.271973 0.135986 0.990711i \(-0.456580\pi\)
0.135986 + 0.990711i \(0.456580\pi\)
\(594\) −16.2547 −0.666938
\(595\) 22.4100 0.918721
\(596\) 16.1454 0.661340
\(597\) 0.657332 0.0269028
\(598\) 4.64552 0.189970
\(599\) 24.8385 1.01487 0.507436 0.861689i \(-0.330593\pi\)
0.507436 + 0.861689i \(0.330593\pi\)
\(600\) 2.87582 0.117405
\(601\) 8.30968 0.338959 0.169480 0.985534i \(-0.445791\pi\)
0.169480 + 0.985534i \(0.445791\pi\)
\(602\) −7.59040 −0.309361
\(603\) 15.6464 0.637171
\(604\) 1.92980 0.0785224
\(605\) −7.86746 −0.319858
\(606\) −10.6567 −0.432900
\(607\) 35.0562 1.42289 0.711444 0.702743i \(-0.248042\pi\)
0.711444 + 0.702743i \(0.248042\pi\)
\(608\) 8.38053 0.339876
\(609\) −1.36505 −0.0553144
\(610\) 27.9539 1.13182
\(611\) 12.8557 0.520084
\(612\) −10.3386 −0.417912
\(613\) 10.8224 0.437111 0.218555 0.975825i \(-0.429866\pi\)
0.218555 + 0.975825i \(0.429866\pi\)
\(614\) 16.7644 0.676557
\(615\) 6.20445 0.250188
\(616\) −6.38615 −0.257305
\(617\) 6.24292 0.251330 0.125665 0.992073i \(-0.459893\pi\)
0.125665 + 0.992073i \(0.459893\pi\)
\(618\) 3.40578 0.137000
\(619\) 5.19792 0.208922 0.104461 0.994529i \(-0.466688\pi\)
0.104461 + 0.994529i \(0.466688\pi\)
\(620\) −0.0765231 −0.00307324
\(621\) 4.39136 0.176219
\(622\) 9.48145 0.380171
\(623\) −1.53471 −0.0614870
\(624\) −3.83593 −0.153560
\(625\) −30.2842 −1.21137
\(626\) 19.1669 0.766064
\(627\) 25.6146 1.02295
\(628\) −16.6026 −0.662514
\(629\) 0.123818 0.00493695
\(630\) −11.6486 −0.464092
\(631\) −9.74097 −0.387782 −0.193891 0.981023i \(-0.562111\pi\)
−0.193891 + 0.981023i \(0.562111\pi\)
\(632\) −8.12246 −0.323094
\(633\) −21.8618 −0.868930
\(634\) −25.4875 −1.01224
\(635\) 0.915050 0.0363126
\(636\) −5.30155 −0.210220
\(637\) 18.6909 0.740560
\(638\) 3.54677 0.140418
\(639\) 8.39787 0.332215
\(640\) −2.91252 −0.115127
\(641\) −25.2230 −0.996250 −0.498125 0.867105i \(-0.665978\pi\)
−0.498125 + 0.867105i \(0.665978\pi\)
\(642\) −3.05695 −0.120648
\(643\) 10.9839 0.433162 0.216581 0.976265i \(-0.430509\pi\)
0.216581 + 0.976265i \(0.430509\pi\)
\(644\) 1.72528 0.0679854
\(645\) −10.5806 −0.416611
\(646\) 37.3754 1.47052
\(647\) 13.1182 0.515728 0.257864 0.966181i \(-0.416981\pi\)
0.257864 + 0.966181i \(0.416981\pi\)
\(648\) 3.32848 0.130755
\(649\) −39.1189 −1.53555
\(650\) −16.1793 −0.634605
\(651\) −0.0374298 −0.00146699
\(652\) −1.82033 −0.0712895
\(653\) −42.8881 −1.67834 −0.839170 0.543870i \(-0.816959\pi\)
−0.839170 + 0.543870i \(0.816959\pi\)
\(654\) −8.86133 −0.346505
\(655\) −2.91252 −0.113802
\(656\) −2.57987 −0.100727
\(657\) 0.385789 0.0150510
\(658\) 4.77439 0.186125
\(659\) 10.3626 0.403671 0.201836 0.979419i \(-0.435309\pi\)
0.201836 + 0.979419i \(0.435309\pi\)
\(660\) −8.90195 −0.346508
\(661\) 5.10877 0.198708 0.0993541 0.995052i \(-0.468322\pi\)
0.0993541 + 0.995052i \(0.468322\pi\)
\(662\) 18.1211 0.704296
\(663\) −17.1074 −0.664397
\(664\) −4.83091 −0.187476
\(665\) 42.1114 1.63301
\(666\) −0.0643601 −0.00249390
\(667\) −0.958192 −0.0371013
\(668\) −2.76385 −0.106937
\(669\) −16.5348 −0.639273
\(670\) 19.6579 0.759451
\(671\) −35.5266 −1.37149
\(672\) −1.42461 −0.0549554
\(673\) −1.25257 −0.0482830 −0.0241415 0.999709i \(-0.507685\pi\)
−0.0241415 + 0.999709i \(0.507685\pi\)
\(674\) −29.3256 −1.12958
\(675\) −15.2941 −0.588671
\(676\) 8.58089 0.330034
\(677\) 17.0467 0.655158 0.327579 0.944824i \(-0.393767\pi\)
0.327579 + 0.944824i \(0.393767\pi\)
\(678\) −8.18466 −0.314330
\(679\) −6.62118 −0.254098
\(680\) −12.9892 −0.498114
\(681\) −8.86318 −0.339638
\(682\) 0.0972531 0.00372401
\(683\) 7.12925 0.272793 0.136397 0.990654i \(-0.456448\pi\)
0.136397 + 0.990654i \(0.456448\pi\)
\(684\) −19.4276 −0.742831
\(685\) 42.9172 1.63978
\(686\) 19.0185 0.726128
\(687\) −9.15731 −0.349373
\(688\) 4.39952 0.167730
\(689\) 29.8264 1.13630
\(690\) 2.40494 0.0915546
\(691\) −4.74540 −0.180524 −0.0902618 0.995918i \(-0.528770\pi\)
−0.0902618 + 0.995918i \(0.528770\pi\)
\(692\) 22.8026 0.866825
\(693\) 14.8042 0.562366
\(694\) 7.46569 0.283394
\(695\) 18.7794 0.712342
\(696\) 0.791204 0.0299905
\(697\) −11.5057 −0.435809
\(698\) −11.4966 −0.435153
\(699\) −13.6150 −0.514966
\(700\) −6.00875 −0.227110
\(701\) 19.8587 0.750053 0.375027 0.927014i \(-0.377634\pi\)
0.375027 + 0.927014i \(0.377634\pi\)
\(702\) 20.4001 0.769954
\(703\) 0.232671 0.00877534
\(704\) 3.70152 0.139506
\(705\) 6.65525 0.250651
\(706\) −6.34943 −0.238964
\(707\) 22.2662 0.837407
\(708\) −8.72654 −0.327964
\(709\) 13.9649 0.524463 0.262232 0.965005i \(-0.415542\pi\)
0.262232 + 0.965005i \(0.415542\pi\)
\(710\) 10.5510 0.395970
\(711\) 18.8293 0.706154
\(712\) 0.889547 0.0333372
\(713\) −0.0262738 −0.000983963 0
\(714\) −6.35344 −0.237771
\(715\) 50.0823 1.87297
\(716\) 6.71468 0.250939
\(717\) −17.2477 −0.644128
\(718\) −4.27204 −0.159431
\(719\) −42.3501 −1.57939 −0.789697 0.613497i \(-0.789762\pi\)
−0.789697 + 0.613497i \(0.789762\pi\)
\(720\) 6.75174 0.251622
\(721\) −7.11605 −0.265016
\(722\) 51.2333 1.90671
\(723\) −0.221361 −0.00823252
\(724\) 11.4355 0.424998
\(725\) 3.33717 0.123939
\(726\) 2.23050 0.0827815
\(727\) −6.18336 −0.229328 −0.114664 0.993404i \(-0.536579\pi\)
−0.114664 + 0.993404i \(0.536579\pi\)
\(728\) 8.01481 0.297049
\(729\) 3.16217 0.117117
\(730\) 0.484699 0.0179395
\(731\) 19.6209 0.725707
\(732\) −7.92519 −0.292924
\(733\) −1.34665 −0.0497398 −0.0248699 0.999691i \(-0.507917\pi\)
−0.0248699 + 0.999691i \(0.507917\pi\)
\(734\) −27.5219 −1.01585
\(735\) 9.67610 0.356908
\(736\) −1.00000 −0.0368605
\(737\) −24.9832 −0.920269
\(738\) 5.98060 0.220149
\(739\) −38.8738 −1.43000 −0.714999 0.699126i \(-0.753573\pi\)
−0.714999 + 0.699126i \(0.753573\pi\)
\(740\) −0.0808610 −0.00297251
\(741\) −32.1471 −1.18095
\(742\) 11.0771 0.406653
\(743\) 9.35104 0.343056 0.171528 0.985179i \(-0.445130\pi\)
0.171528 + 0.985179i \(0.445130\pi\)
\(744\) 0.0216950 0.000795376 0
\(745\) −47.0237 −1.72281
\(746\) 17.6082 0.644683
\(747\) 11.1989 0.409747
\(748\) 16.5080 0.603592
\(749\) 6.38721 0.233384
\(750\) 3.64884 0.133237
\(751\) −11.8407 −0.432073 −0.216036 0.976385i \(-0.569313\pi\)
−0.216036 + 0.976385i \(0.569313\pi\)
\(752\) −2.76732 −0.100914
\(753\) 11.7961 0.429872
\(754\) −4.45130 −0.162107
\(755\) −5.62058 −0.204554
\(756\) 7.57630 0.275548
\(757\) 10.9057 0.396376 0.198188 0.980164i \(-0.436494\pi\)
0.198188 + 0.980164i \(0.436494\pi\)
\(758\) −34.4193 −1.25017
\(759\) −3.05644 −0.110942
\(760\) −24.4085 −0.885388
\(761\) −9.22732 −0.334490 −0.167245 0.985915i \(-0.553487\pi\)
−0.167245 + 0.985915i \(0.553487\pi\)
\(762\) −0.259425 −0.00939797
\(763\) 18.5149 0.670285
\(764\) −18.0493 −0.653001
\(765\) 30.1113 1.08868
\(766\) −14.4656 −0.522664
\(767\) 49.0954 1.77273
\(768\) 0.825726 0.0297958
\(769\) 17.6746 0.637364 0.318682 0.947862i \(-0.396760\pi\)
0.318682 + 0.947862i \(0.396760\pi\)
\(770\) 18.5998 0.670290
\(771\) 23.4877 0.845888
\(772\) 15.4934 0.557619
\(773\) 26.6069 0.956984 0.478492 0.878092i \(-0.341184\pi\)
0.478492 + 0.878092i \(0.341184\pi\)
\(774\) −10.1989 −0.366591
\(775\) 0.0915059 0.00328699
\(776\) 3.83775 0.137767
\(777\) −0.0395517 −0.00141891
\(778\) −14.7539 −0.528952
\(779\) −21.6207 −0.774643
\(780\) 11.1722 0.400030
\(781\) −13.4092 −0.479819
\(782\) −4.45979 −0.159482
\(783\) −4.20776 −0.150373
\(784\) −4.02342 −0.143694
\(785\) 48.3553 1.72587
\(786\) 0.825726 0.0294527
\(787\) 14.0817 0.501958 0.250979 0.967993i \(-0.419248\pi\)
0.250979 + 0.967993i \(0.419248\pi\)
\(788\) 15.8107 0.563232
\(789\) −14.2171 −0.506142
\(790\) 23.6568 0.841673
\(791\) 17.1011 0.608045
\(792\) −8.58078 −0.304905
\(793\) 44.5870 1.58333
\(794\) −1.90888 −0.0677437
\(795\) 15.4409 0.547631
\(796\) 0.796066 0.0282158
\(797\) −31.6007 −1.11936 −0.559678 0.828710i \(-0.689075\pi\)
−0.559678 + 0.828710i \(0.689075\pi\)
\(798\) −11.9390 −0.422634
\(799\) −12.3417 −0.436617
\(800\) 3.48278 0.123135
\(801\) −2.06213 −0.0728617
\(802\) −11.0337 −0.389615
\(803\) −0.616003 −0.0217383
\(804\) −5.57319 −0.196551
\(805\) −5.02490 −0.177105
\(806\) −0.122056 −0.00429923
\(807\) 2.38855 0.0840811
\(808\) −12.9059 −0.454027
\(809\) 36.5813 1.28613 0.643066 0.765811i \(-0.277662\pi\)
0.643066 + 0.765811i \(0.277662\pi\)
\(810\) −9.69425 −0.340621
\(811\) −8.05806 −0.282957 −0.141478 0.989941i \(-0.545186\pi\)
−0.141478 + 0.989941i \(0.545186\pi\)
\(812\) −1.65315 −0.0580141
\(813\) 18.2844 0.641261
\(814\) 0.102766 0.00360195
\(815\) 5.30174 0.185712
\(816\) 3.68256 0.128915
\(817\) 36.8704 1.28993
\(818\) −7.05569 −0.246696
\(819\) −18.5798 −0.649229
\(820\) 7.51393 0.262398
\(821\) −15.9326 −0.556053 −0.278026 0.960573i \(-0.589680\pi\)
−0.278026 + 0.960573i \(0.589680\pi\)
\(822\) −12.1674 −0.424387
\(823\) −53.5115 −1.86529 −0.932647 0.360791i \(-0.882507\pi\)
−0.932647 + 0.360791i \(0.882507\pi\)
\(824\) 4.12459 0.143687
\(825\) 10.6449 0.370608
\(826\) 18.2333 0.634417
\(827\) 46.6305 1.62150 0.810751 0.585391i \(-0.199059\pi\)
0.810751 + 0.585391i \(0.199059\pi\)
\(828\) 2.31818 0.0805622
\(829\) −42.0387 −1.46006 −0.730032 0.683413i \(-0.760495\pi\)
−0.730032 + 0.683413i \(0.760495\pi\)
\(830\) 14.0701 0.488382
\(831\) 13.4877 0.467884
\(832\) −4.64552 −0.161055
\(833\) −17.9436 −0.621709
\(834\) −5.32412 −0.184359
\(835\) 8.04978 0.278574
\(836\) 31.0207 1.07287
\(837\) −0.115378 −0.00398804
\(838\) −6.44623 −0.222681
\(839\) 7.73543 0.267057 0.133528 0.991045i \(-0.457369\pi\)
0.133528 + 0.991045i \(0.457369\pi\)
\(840\) 4.14919 0.143161
\(841\) −28.0819 −0.968340
\(842\) −30.3425 −1.04567
\(843\) 14.2080 0.489351
\(844\) −26.4759 −0.911338
\(845\) −24.9920 −0.859751
\(846\) 6.41514 0.220557
\(847\) −4.66042 −0.160134
\(848\) −6.42047 −0.220480
\(849\) 4.86077 0.166821
\(850\) 15.5324 0.532758
\(851\) −0.0277632 −0.000951712 0
\(852\) −2.99129 −0.102480
\(853\) −34.9691 −1.19732 −0.598660 0.801003i \(-0.704300\pi\)
−0.598660 + 0.801003i \(0.704300\pi\)
\(854\) 16.5590 0.566636
\(855\) 56.5832 1.93510
\(856\) −3.70214 −0.126536
\(857\) 42.6996 1.45859 0.729295 0.684200i \(-0.239848\pi\)
0.729295 + 0.684200i \(0.239848\pi\)
\(858\) −14.1988 −0.484738
\(859\) −52.0855 −1.77714 −0.888568 0.458745i \(-0.848299\pi\)
−0.888568 + 0.458745i \(0.848299\pi\)
\(860\) −12.8137 −0.436944
\(861\) 3.67530 0.125254
\(862\) −8.21996 −0.279973
\(863\) 0.726688 0.0247367 0.0123684 0.999924i \(-0.496063\pi\)
0.0123684 + 0.999924i \(0.496063\pi\)
\(864\) −4.39136 −0.149397
\(865\) −66.4131 −2.25811
\(866\) 38.4408 1.30627
\(867\) 2.38610 0.0810363
\(868\) −0.0453296 −0.00153859
\(869\) −30.0655 −1.01990
\(870\) −2.30440 −0.0781264
\(871\) 31.3547 1.06241
\(872\) −10.7316 −0.363417
\(873\) −8.89658 −0.301104
\(874\) −8.38053 −0.283476
\(875\) −7.62391 −0.257735
\(876\) −0.137416 −0.00464287
\(877\) −38.4960 −1.29992 −0.649959 0.759969i \(-0.725214\pi\)
−0.649959 + 0.759969i \(0.725214\pi\)
\(878\) 11.8125 0.398652
\(879\) 14.9222 0.503312
\(880\) −10.7808 −0.363419
\(881\) 23.8585 0.803814 0.401907 0.915681i \(-0.368348\pi\)
0.401907 + 0.915681i \(0.368348\pi\)
\(882\) 9.32700 0.314056
\(883\) −17.9819 −0.605141 −0.302570 0.953127i \(-0.597845\pi\)
−0.302570 + 0.953127i \(0.597845\pi\)
\(884\) −20.7180 −0.696823
\(885\) 25.4162 0.854357
\(886\) −13.4654 −0.452380
\(887\) −10.0919 −0.338853 −0.169426 0.985543i \(-0.554192\pi\)
−0.169426 + 0.985543i \(0.554192\pi\)
\(888\) 0.0229248 0.000769307 0
\(889\) 0.542044 0.0181796
\(890\) −2.59082 −0.0868446
\(891\) 12.3204 0.412750
\(892\) −20.0246 −0.670473
\(893\) −23.1916 −0.776078
\(894\) 13.3316 0.445877
\(895\) −19.5566 −0.653706
\(896\) −1.72528 −0.0576375
\(897\) 3.83593 0.128078
\(898\) −2.87075 −0.0957981
\(899\) 0.0251754 0.000839646 0
\(900\) −8.07369 −0.269123
\(901\) −28.6339 −0.953934
\(902\) −9.54946 −0.317962
\(903\) −6.26759 −0.208572
\(904\) −9.91209 −0.329671
\(905\) −33.3062 −1.10714
\(906\) 1.59348 0.0529400
\(907\) 18.6354 0.618777 0.309388 0.950936i \(-0.399876\pi\)
0.309388 + 0.950936i \(0.399876\pi\)
\(908\) −10.7338 −0.356214
\(909\) 29.9181 0.992321
\(910\) −23.3433 −0.773823
\(911\) 8.01001 0.265384 0.132692 0.991157i \(-0.457638\pi\)
0.132692 + 0.991157i \(0.457638\pi\)
\(912\) 6.92002 0.229145
\(913\) −17.8817 −0.591799
\(914\) 22.9351 0.758626
\(915\) 23.0823 0.763077
\(916\) −11.0900 −0.366424
\(917\) −1.72528 −0.0569737
\(918\) −19.5845 −0.646385
\(919\) 12.4560 0.410886 0.205443 0.978669i \(-0.434137\pi\)
0.205443 + 0.978669i \(0.434137\pi\)
\(920\) 2.91252 0.0960230
\(921\) 13.8428 0.456137
\(922\) −7.78624 −0.256426
\(923\) 16.8290 0.553932
\(924\) −5.27321 −0.173476
\(925\) 0.0966931 0.00317925
\(926\) 23.9570 0.787275
\(927\) −9.56152 −0.314042
\(928\) 0.958192 0.0314542
\(929\) −47.9843 −1.57431 −0.787157 0.616753i \(-0.788448\pi\)
−0.787157 + 0.616753i \(0.788448\pi\)
\(930\) −0.0631871 −0.00207199
\(931\) −33.7184 −1.10508
\(932\) −16.4885 −0.540099
\(933\) 7.82907 0.256312
\(934\) −34.5877 −1.13174
\(935\) −48.0799 −1.57238
\(936\) 10.7691 0.352001
\(937\) −39.2493 −1.28222 −0.641109 0.767450i \(-0.721525\pi\)
−0.641109 + 0.767450i \(0.721525\pi\)
\(938\) 11.6447 0.380212
\(939\) 15.8266 0.516482
\(940\) 8.05988 0.262884
\(941\) −33.8853 −1.10463 −0.552314 0.833636i \(-0.686255\pi\)
−0.552314 + 0.833636i \(0.686255\pi\)
\(942\) −13.7092 −0.446669
\(943\) 2.57987 0.0840122
\(944\) −10.5683 −0.343970
\(945\) −22.0661 −0.717812
\(946\) 16.2849 0.529469
\(947\) 5.75179 0.186908 0.0934541 0.995624i \(-0.470209\pi\)
0.0934541 + 0.995624i \(0.470209\pi\)
\(948\) −6.70693 −0.217831
\(949\) 0.773103 0.0250960
\(950\) 29.1875 0.946968
\(951\) −21.0457 −0.682454
\(952\) −7.69437 −0.249376
\(953\) −1.12943 −0.0365860 −0.0182930 0.999833i \(-0.505823\pi\)
−0.0182930 + 0.999833i \(0.505823\pi\)
\(954\) 14.8838 0.481880
\(955\) 52.5690 1.70109
\(956\) −20.8880 −0.675565
\(957\) 2.92866 0.0946700
\(958\) −18.1571 −0.586628
\(959\) 25.4227 0.820941
\(960\) −2.40494 −0.0776192
\(961\) −30.9993 −0.999978
\(962\) −0.128975 −0.00415831
\(963\) 8.58221 0.276558
\(964\) −0.268081 −0.00863431
\(965\) −45.1248 −1.45262
\(966\) 1.42461 0.0458359
\(967\) 10.9368 0.351703 0.175851 0.984417i \(-0.443732\pi\)
0.175851 + 0.984417i \(0.443732\pi\)
\(968\) 2.70126 0.0868217
\(969\) 30.8618 0.991425
\(970\) −11.1775 −0.358889
\(971\) 15.7024 0.503915 0.251957 0.967738i \(-0.418926\pi\)
0.251957 + 0.967738i \(0.418926\pi\)
\(972\) 15.9225 0.510714
\(973\) 11.1242 0.356627
\(974\) 26.3758 0.845135
\(975\) −13.3597 −0.427852
\(976\) −9.59785 −0.307220
\(977\) −8.72265 −0.279062 −0.139531 0.990218i \(-0.544560\pi\)
−0.139531 + 0.990218i \(0.544560\pi\)
\(978\) −1.50309 −0.0480635
\(979\) 3.29268 0.105234
\(980\) 11.7183 0.374327
\(981\) 24.8777 0.794283
\(982\) 35.7810 1.14182
\(983\) −61.2127 −1.95238 −0.976190 0.216916i \(-0.930400\pi\)
−0.976190 + 0.216916i \(0.930400\pi\)
\(984\) −2.13027 −0.0679105
\(985\) −46.0489 −1.46724
\(986\) 4.27333 0.136091
\(987\) 3.94234 0.125486
\(988\) −38.9320 −1.23859
\(989\) −4.39952 −0.139897
\(990\) 24.9917 0.794288
\(991\) −2.13953 −0.0679643 −0.0339821 0.999422i \(-0.510819\pi\)
−0.0339821 + 0.999422i \(0.510819\pi\)
\(992\) 0.0262738 0.000834195 0
\(993\) 14.9630 0.474838
\(994\) 6.25002 0.198239
\(995\) −2.31856 −0.0735033
\(996\) −3.98901 −0.126397
\(997\) 27.2390 0.862669 0.431334 0.902192i \(-0.358043\pi\)
0.431334 + 0.902192i \(0.358043\pi\)
\(998\) −21.7609 −0.688831
\(999\) −0.121918 −0.00385732
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 6026.2.a.g.1.14 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.g.1.14 21 1.1 even 1 trivial