Properties

Label 8014.2.a.d.1.1
Level $8014$
Weight $2$
Character 8014.1
Self dual yes
Analytic conductor $63.992$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8014,2,Mod(1,8014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8014.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: \(63.9921121799\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.16888 q^{3} +1.00000 q^{4} -3.03965 q^{5} -3.16888 q^{6} -1.28246 q^{7} +1.00000 q^{8} +7.04180 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.16888 q^{3} +1.00000 q^{4} -3.03965 q^{5} -3.16888 q^{6} -1.28246 q^{7} +1.00000 q^{8} +7.04180 q^{9} -3.03965 q^{10} +3.46314 q^{11} -3.16888 q^{12} -4.50722 q^{13} -1.28246 q^{14} +9.63228 q^{15} +1.00000 q^{16} +3.23801 q^{17} +7.04180 q^{18} -0.846917 q^{19} -3.03965 q^{20} +4.06395 q^{21} +3.46314 q^{22} -0.287066 q^{23} -3.16888 q^{24} +4.23946 q^{25} -4.50722 q^{26} -12.8080 q^{27} -1.28246 q^{28} +1.25694 q^{29} +9.63228 q^{30} -6.14846 q^{31} +1.00000 q^{32} -10.9743 q^{33} +3.23801 q^{34} +3.89821 q^{35} +7.04180 q^{36} +7.21847 q^{37} -0.846917 q^{38} +14.2828 q^{39} -3.03965 q^{40} -4.83235 q^{41} +4.06395 q^{42} +1.61059 q^{43} +3.46314 q^{44} -21.4046 q^{45} -0.287066 q^{46} +3.12714 q^{47} -3.16888 q^{48} -5.35531 q^{49} +4.23946 q^{50} -10.2608 q^{51} -4.50722 q^{52} -6.99757 q^{53} -12.8080 q^{54} -10.5267 q^{55} -1.28246 q^{56} +2.68378 q^{57} +1.25694 q^{58} +8.82489 q^{59} +9.63228 q^{60} +9.09016 q^{61} -6.14846 q^{62} -9.03080 q^{63} +1.00000 q^{64} +13.7004 q^{65} -10.9743 q^{66} +0.507256 q^{67} +3.23801 q^{68} +0.909678 q^{69} +3.89821 q^{70} -8.65604 q^{71} +7.04180 q^{72} +0.231430 q^{73} +7.21847 q^{74} -13.4343 q^{75} -0.846917 q^{76} -4.44133 q^{77} +14.2828 q^{78} +3.00674 q^{79} -3.03965 q^{80} +19.4615 q^{81} -4.83235 q^{82} -14.5534 q^{83} +4.06395 q^{84} -9.84239 q^{85} +1.61059 q^{86} -3.98308 q^{87} +3.46314 q^{88} -17.1962 q^{89} -21.4046 q^{90} +5.78031 q^{91} -0.287066 q^{92} +19.4837 q^{93} +3.12714 q^{94} +2.57433 q^{95} -3.16888 q^{96} -12.2668 q^{97} -5.35531 q^{98} +24.3867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 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
\(3\) −3.16888 −1.82955 −0.914777 0.403960i \(-0.867634\pi\)
−0.914777 + 0.403960i \(0.867634\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.03965 −1.35937 −0.679686 0.733503i \(-0.737884\pi\)
−0.679686 + 0.733503i \(0.737884\pi\)
\(6\) −3.16888 −1.29369
\(7\) −1.28246 −0.484723 −0.242361 0.970186i \(-0.577922\pi\)
−0.242361 + 0.970186i \(0.577922\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.04180 2.34727
\(10\) −3.03965 −0.961221
\(11\) 3.46314 1.04418 0.522088 0.852892i \(-0.325153\pi\)
0.522088 + 0.852892i \(0.325153\pi\)
\(12\) −3.16888 −0.914777
\(13\) −4.50722 −1.25008 −0.625039 0.780594i \(-0.714917\pi\)
−0.625039 + 0.780594i \(0.714917\pi\)
\(14\) −1.28246 −0.342751
\(15\) 9.63228 2.48704
\(16\) 1.00000 0.250000
\(17\) 3.23801 0.785332 0.392666 0.919681i \(-0.371553\pi\)
0.392666 + 0.919681i \(0.371553\pi\)
\(18\) 7.04180 1.65977
\(19\) −0.846917 −0.194296 −0.0971480 0.995270i \(-0.530972\pi\)
−0.0971480 + 0.995270i \(0.530972\pi\)
\(20\) −3.03965 −0.679686
\(21\) 4.06395 0.886826
\(22\) 3.46314 0.738344
\(23\) −0.287066 −0.0598574 −0.0299287 0.999552i \(-0.509528\pi\)
−0.0299287 + 0.999552i \(0.509528\pi\)
\(24\) −3.16888 −0.646845
\(25\) 4.23946 0.847891
\(26\) −4.50722 −0.883939
\(27\) −12.8080 −2.46489
\(28\) −1.28246 −0.242361
\(29\) 1.25694 0.233407 0.116704 0.993167i \(-0.462767\pi\)
0.116704 + 0.993167i \(0.462767\pi\)
\(30\) 9.63228 1.75860
\(31\) −6.14846 −1.10430 −0.552148 0.833746i \(-0.686192\pi\)
−0.552148 + 0.833746i \(0.686192\pi\)
\(32\) 1.00000 0.176777
\(33\) −10.9743 −1.91038
\(34\) 3.23801 0.555313
\(35\) 3.89821 0.658919
\(36\) 7.04180 1.17363
\(37\) 7.21847 1.18671 0.593354 0.804941i \(-0.297803\pi\)
0.593354 + 0.804941i \(0.297803\pi\)
\(38\) −0.846917 −0.137388
\(39\) 14.2828 2.28708
\(40\) −3.03965 −0.480610
\(41\) −4.83235 −0.754686 −0.377343 0.926074i \(-0.623162\pi\)
−0.377343 + 0.926074i \(0.623162\pi\)
\(42\) 4.06395 0.627081
\(43\) 1.61059 0.245613 0.122807 0.992431i \(-0.460811\pi\)
0.122807 + 0.992431i \(0.460811\pi\)
\(44\) 3.46314 0.522088
\(45\) −21.4046 −3.19081
\(46\) −0.287066 −0.0423256
\(47\) 3.12714 0.456141 0.228070 0.973645i \(-0.426758\pi\)
0.228070 + 0.973645i \(0.426758\pi\)
\(48\) −3.16888 −0.457388
\(49\) −5.35531 −0.765044
\(50\) 4.23946 0.599549
\(51\) −10.2608 −1.43681
\(52\) −4.50722 −0.625039
\(53\) −6.99757 −0.961190 −0.480595 0.876943i \(-0.659579\pi\)
−0.480595 + 0.876943i \(0.659579\pi\)
\(54\) −12.8080 −1.74294
\(55\) −10.5267 −1.41942
\(56\) −1.28246 −0.171375
\(57\) 2.68378 0.355475
\(58\) 1.25694 0.165044
\(59\) 8.82489 1.14890 0.574451 0.818539i \(-0.305215\pi\)
0.574451 + 0.818539i \(0.305215\pi\)
\(60\) 9.63228 1.24352
\(61\) 9.09016 1.16388 0.581938 0.813233i \(-0.302295\pi\)
0.581938 + 0.813233i \(0.302295\pi\)
\(62\) −6.14846 −0.780855
\(63\) −9.03080 −1.13777
\(64\) 1.00000 0.125000
\(65\) 13.7004 1.69932
\(66\) −10.9743 −1.35084
\(67\) 0.507256 0.0619712 0.0309856 0.999520i \(-0.490135\pi\)
0.0309856 + 0.999520i \(0.490135\pi\)
\(68\) 3.23801 0.392666
\(69\) 0.909678 0.109512
\(70\) 3.89821 0.465926
\(71\) −8.65604 −1.02728 −0.513642 0.858005i \(-0.671704\pi\)
−0.513642 + 0.858005i \(0.671704\pi\)
\(72\) 7.04180 0.829884
\(73\) 0.231430 0.0270868 0.0135434 0.999908i \(-0.495689\pi\)
0.0135434 + 0.999908i \(0.495689\pi\)
\(74\) 7.21847 0.839130
\(75\) −13.4343 −1.55126
\(76\) −0.846917 −0.0971480
\(77\) −4.44133 −0.506136
\(78\) 14.2828 1.61721
\(79\) 3.00674 0.338285 0.169142 0.985592i \(-0.445900\pi\)
0.169142 + 0.985592i \(0.445900\pi\)
\(80\) −3.03965 −0.339843
\(81\) 19.4615 2.16239
\(82\) −4.83235 −0.533644
\(83\) −14.5534 −1.59745 −0.798723 0.601698i \(-0.794491\pi\)
−0.798723 + 0.601698i \(0.794491\pi\)
\(84\) 4.06395 0.443413
\(85\) −9.84239 −1.06756
\(86\) 1.61059 0.173675
\(87\) −3.98308 −0.427031
\(88\) 3.46314 0.369172
\(89\) −17.1962 −1.82279 −0.911396 0.411530i \(-0.864994\pi\)
−0.911396 + 0.411530i \(0.864994\pi\)
\(90\) −21.4046 −2.25624
\(91\) 5.78031 0.605941
\(92\) −0.287066 −0.0299287
\(93\) 19.4837 2.02037
\(94\) 3.12714 0.322540
\(95\) 2.57433 0.264120
\(96\) −3.16888 −0.323422
\(97\) −12.2668 −1.24550 −0.622752 0.782419i \(-0.713986\pi\)
−0.622752 + 0.782419i \(0.713986\pi\)
\(98\) −5.35531 −0.540968
\(99\) 24.3867 2.45096
\(100\) 4.23946 0.423946
\(101\) 6.75003 0.671653 0.335826 0.941924i \(-0.390984\pi\)
0.335826 + 0.941924i \(0.390984\pi\)
\(102\) −10.2608 −1.01598
\(103\) 0.260264 0.0256445 0.0128223 0.999918i \(-0.495918\pi\)
0.0128223 + 0.999918i \(0.495918\pi\)
\(104\) −4.50722 −0.441969
\(105\) −12.3530 −1.20553
\(106\) −6.99757 −0.679664
\(107\) −12.2796 −1.18712 −0.593558 0.804791i \(-0.702277\pi\)
−0.593558 + 0.804791i \(0.702277\pi\)
\(108\) −12.8080 −1.23245
\(109\) −3.06057 −0.293150 −0.146575 0.989200i \(-0.546825\pi\)
−0.146575 + 0.989200i \(0.546825\pi\)
\(110\) −10.5267 −1.00368
\(111\) −22.8744 −2.17115
\(112\) −1.28246 −0.121181
\(113\) −14.6944 −1.38233 −0.691165 0.722697i \(-0.742902\pi\)
−0.691165 + 0.722697i \(0.742902\pi\)
\(114\) 2.68378 0.251359
\(115\) 0.872580 0.0813685
\(116\) 1.25694 0.116704
\(117\) −31.7389 −2.93426
\(118\) 8.82489 0.812397
\(119\) −4.15260 −0.380668
\(120\) 9.63228 0.879302
\(121\) 0.993337 0.0903034
\(122\) 9.09016 0.822984
\(123\) 15.3131 1.38074
\(124\) −6.14846 −0.552148
\(125\) 2.31179 0.206773
\(126\) −9.03080 −0.804527
\(127\) −10.8892 −0.966259 −0.483130 0.875549i \(-0.660500\pi\)
−0.483130 + 0.875549i \(0.660500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.10377 −0.449362
\(130\) 13.7004 1.20160
\(131\) 3.51410 0.307028 0.153514 0.988146i \(-0.450941\pi\)
0.153514 + 0.988146i \(0.450941\pi\)
\(132\) −10.9743 −0.955188
\(133\) 1.08613 0.0941797
\(134\) 0.507256 0.0438203
\(135\) 38.9317 3.35071
\(136\) 3.23801 0.277657
\(137\) −16.2368 −1.38720 −0.693600 0.720360i \(-0.743976\pi\)
−0.693600 + 0.720360i \(0.743976\pi\)
\(138\) 0.909678 0.0774369
\(139\) 7.68972 0.652234 0.326117 0.945329i \(-0.394260\pi\)
0.326117 + 0.945329i \(0.394260\pi\)
\(140\) 3.89821 0.329459
\(141\) −9.90954 −0.834534
\(142\) −8.65604 −0.726399
\(143\) −15.6091 −1.30530
\(144\) 7.04180 0.586816
\(145\) −3.82064 −0.317287
\(146\) 0.231430 0.0191533
\(147\) 16.9703 1.39969
\(148\) 7.21847 0.593354
\(149\) 8.62106 0.706265 0.353132 0.935573i \(-0.385117\pi\)
0.353132 + 0.935573i \(0.385117\pi\)
\(150\) −13.4343 −1.09691
\(151\) 21.3163 1.73469 0.867346 0.497706i \(-0.165824\pi\)
0.867346 + 0.497706i \(0.165824\pi\)
\(152\) −0.846917 −0.0686940
\(153\) 22.8014 1.84338
\(154\) −4.44133 −0.357892
\(155\) 18.6892 1.50115
\(156\) 14.2828 1.14354
\(157\) −6.99959 −0.558628 −0.279314 0.960200i \(-0.590107\pi\)
−0.279314 + 0.960200i \(0.590107\pi\)
\(158\) 3.00674 0.239203
\(159\) 22.1745 1.75855
\(160\) −3.03965 −0.240305
\(161\) 0.368150 0.0290143
\(162\) 19.4615 1.52904
\(163\) 22.6419 1.77345 0.886725 0.462296i \(-0.152974\pi\)
0.886725 + 0.462296i \(0.152974\pi\)
\(164\) −4.83235 −0.377343
\(165\) 33.3579 2.59691
\(166\) −14.5534 −1.12957
\(167\) 0.707537 0.0547508 0.0273754 0.999625i \(-0.491285\pi\)
0.0273754 + 0.999625i \(0.491285\pi\)
\(168\) 4.06395 0.313541
\(169\) 7.31503 0.562695
\(170\) −9.84239 −0.754877
\(171\) −5.96381 −0.456064
\(172\) 1.61059 0.122807
\(173\) 6.92283 0.526333 0.263166 0.964750i \(-0.415233\pi\)
0.263166 + 0.964750i \(0.415233\pi\)
\(174\) −3.98308 −0.301957
\(175\) −5.43692 −0.410992
\(176\) 3.46314 0.261044
\(177\) −27.9650 −2.10198
\(178\) −17.1962 −1.28891
\(179\) 5.27002 0.393900 0.196950 0.980414i \(-0.436896\pi\)
0.196950 + 0.980414i \(0.436896\pi\)
\(180\) −21.4046 −1.59540
\(181\) −10.2356 −0.760804 −0.380402 0.924821i \(-0.624214\pi\)
−0.380402 + 0.924821i \(0.624214\pi\)
\(182\) 5.78031 0.428465
\(183\) −28.8056 −2.12937
\(184\) −0.287066 −0.0211628
\(185\) −21.9416 −1.61318
\(186\) 19.4837 1.42862
\(187\) 11.2137 0.820024
\(188\) 3.12714 0.228070
\(189\) 16.4257 1.19479
\(190\) 2.57433 0.186761
\(191\) 4.00758 0.289979 0.144989 0.989433i \(-0.453685\pi\)
0.144989 + 0.989433i \(0.453685\pi\)
\(192\) −3.16888 −0.228694
\(193\) 10.0430 0.722911 0.361455 0.932389i \(-0.382280\pi\)
0.361455 + 0.932389i \(0.382280\pi\)
\(194\) −12.2668 −0.880705
\(195\) −43.4148 −3.10900
\(196\) −5.35531 −0.382522
\(197\) 20.1963 1.43892 0.719462 0.694531i \(-0.244388\pi\)
0.719462 + 0.694531i \(0.244388\pi\)
\(198\) 24.3867 1.73309
\(199\) 8.46992 0.600417 0.300208 0.953874i \(-0.402944\pi\)
0.300208 + 0.953874i \(0.402944\pi\)
\(200\) 4.23946 0.299775
\(201\) −1.60743 −0.113380
\(202\) 6.75003 0.474930
\(203\) −1.61197 −0.113138
\(204\) −10.2608 −0.718403
\(205\) 14.6886 1.02590
\(206\) 0.260264 0.0181334
\(207\) −2.02146 −0.140501
\(208\) −4.50722 −0.312519
\(209\) −2.93299 −0.202879
\(210\) −12.3530 −0.852436
\(211\) 7.40185 0.509564 0.254782 0.966998i \(-0.417996\pi\)
0.254782 + 0.966998i \(0.417996\pi\)
\(212\) −6.99757 −0.480595
\(213\) 27.4300 1.87947
\(214\) −12.2796 −0.839418
\(215\) −4.89563 −0.333879
\(216\) −12.8080 −0.871472
\(217\) 7.88513 0.535278
\(218\) −3.06057 −0.207288
\(219\) −0.733373 −0.0495567
\(220\) −10.5267 −0.709712
\(221\) −14.5944 −0.981726
\(222\) −22.8744 −1.53523
\(223\) −4.66593 −0.312454 −0.156227 0.987721i \(-0.549933\pi\)
−0.156227 + 0.987721i \(0.549933\pi\)
\(224\) −1.28246 −0.0856877
\(225\) 29.8534 1.99023
\(226\) −14.6944 −0.977455
\(227\) −25.5637 −1.69672 −0.848361 0.529418i \(-0.822410\pi\)
−0.848361 + 0.529418i \(0.822410\pi\)
\(228\) 2.68378 0.177737
\(229\) 16.8881 1.11600 0.558000 0.829841i \(-0.311569\pi\)
0.558000 + 0.829841i \(0.311569\pi\)
\(230\) 0.872580 0.0575362
\(231\) 14.0740 0.926003
\(232\) 1.25694 0.0825219
\(233\) 17.2278 1.12863 0.564314 0.825560i \(-0.309141\pi\)
0.564314 + 0.825560i \(0.309141\pi\)
\(234\) −31.7389 −2.07484
\(235\) −9.50542 −0.620065
\(236\) 8.82489 0.574451
\(237\) −9.52800 −0.618910
\(238\) −4.15260 −0.269173
\(239\) 10.2780 0.664827 0.332414 0.943134i \(-0.392137\pi\)
0.332414 + 0.943134i \(0.392137\pi\)
\(240\) 9.63228 0.621761
\(241\) 1.86449 0.120102 0.0600512 0.998195i \(-0.480874\pi\)
0.0600512 + 0.998195i \(0.480874\pi\)
\(242\) 0.993337 0.0638541
\(243\) −23.2473 −1.49131
\(244\) 9.09016 0.581938
\(245\) 16.2782 1.03998
\(246\) 15.3131 0.976330
\(247\) 3.81724 0.242885
\(248\) −6.14846 −0.390428
\(249\) 46.1181 2.92261
\(250\) 2.31179 0.146210
\(251\) 6.05456 0.382161 0.191080 0.981574i \(-0.438801\pi\)
0.191080 + 0.981574i \(0.438801\pi\)
\(252\) −9.03080 −0.568887
\(253\) −0.994150 −0.0625017
\(254\) −10.8892 −0.683248
\(255\) 31.1894 1.95315
\(256\) 1.00000 0.0625000
\(257\) 13.6654 0.852425 0.426213 0.904623i \(-0.359848\pi\)
0.426213 + 0.904623i \(0.359848\pi\)
\(258\) −5.10377 −0.317747
\(259\) −9.25737 −0.575225
\(260\) 13.7004 0.849660
\(261\) 8.85109 0.547869
\(262\) 3.51410 0.217102
\(263\) 0.256730 0.0158306 0.00791531 0.999969i \(-0.497480\pi\)
0.00791531 + 0.999969i \(0.497480\pi\)
\(264\) −10.9743 −0.675420
\(265\) 21.2701 1.30661
\(266\) 1.08613 0.0665951
\(267\) 54.4926 3.33490
\(268\) 0.507256 0.0309856
\(269\) 25.7916 1.57254 0.786271 0.617882i \(-0.212009\pi\)
0.786271 + 0.617882i \(0.212009\pi\)
\(270\) 38.9317 2.36931
\(271\) 27.6172 1.67763 0.838813 0.544419i \(-0.183250\pi\)
0.838813 + 0.544419i \(0.183250\pi\)
\(272\) 3.23801 0.196333
\(273\) −18.3171 −1.10860
\(274\) −16.2368 −0.980899
\(275\) 14.6818 0.885347
\(276\) 0.909678 0.0547562
\(277\) 15.0027 0.901426 0.450713 0.892669i \(-0.351170\pi\)
0.450713 + 0.892669i \(0.351170\pi\)
\(278\) 7.68972 0.461199
\(279\) −43.2962 −2.59208
\(280\) 3.89821 0.232963
\(281\) 14.0305 0.836988 0.418494 0.908220i \(-0.362558\pi\)
0.418494 + 0.908220i \(0.362558\pi\)
\(282\) −9.90954 −0.590105
\(283\) 2.91971 0.173559 0.0867794 0.996228i \(-0.472342\pi\)
0.0867794 + 0.996228i \(0.472342\pi\)
\(284\) −8.65604 −0.513642
\(285\) −8.15773 −0.483222
\(286\) −15.6091 −0.922987
\(287\) 6.19728 0.365814
\(288\) 7.04180 0.414942
\(289\) −6.51532 −0.383254
\(290\) −3.82064 −0.224356
\(291\) 38.8720 2.27872
\(292\) 0.231430 0.0135434
\(293\) 12.7936 0.747413 0.373706 0.927547i \(-0.378087\pi\)
0.373706 + 0.927547i \(0.378087\pi\)
\(294\) 16.9703 0.989729
\(295\) −26.8246 −1.56179
\(296\) 7.21847 0.419565
\(297\) −44.3558 −2.57378
\(298\) 8.62106 0.499405
\(299\) 1.29387 0.0748264
\(300\) −13.4343 −0.775631
\(301\) −2.06552 −0.119054
\(302\) 21.3163 1.22661
\(303\) −21.3900 −1.22882
\(304\) −0.846917 −0.0485740
\(305\) −27.6309 −1.58214
\(306\) 22.8014 1.30347
\(307\) −0.792900 −0.0452532 −0.0226266 0.999744i \(-0.507203\pi\)
−0.0226266 + 0.999744i \(0.507203\pi\)
\(308\) −4.44133 −0.253068
\(309\) −0.824744 −0.0469180
\(310\) 18.6892 1.06147
\(311\) 13.3358 0.756204 0.378102 0.925764i \(-0.376577\pi\)
0.378102 + 0.925764i \(0.376577\pi\)
\(312\) 14.2828 0.808606
\(313\) −12.1971 −0.689423 −0.344712 0.938709i \(-0.612023\pi\)
−0.344712 + 0.938709i \(0.612023\pi\)
\(314\) −6.99959 −0.395010
\(315\) 27.4504 1.54666
\(316\) 3.00674 0.169142
\(317\) 16.9958 0.954580 0.477290 0.878746i \(-0.341619\pi\)
0.477290 + 0.878746i \(0.341619\pi\)
\(318\) 22.1745 1.24348
\(319\) 4.35295 0.243718
\(320\) −3.03965 −0.169921
\(321\) 38.9126 2.17189
\(322\) 0.368150 0.0205162
\(323\) −2.74232 −0.152587
\(324\) 19.4615 1.08119
\(325\) −19.1082 −1.05993
\(326\) 22.6419 1.25402
\(327\) 9.69859 0.536333
\(328\) −4.83235 −0.266822
\(329\) −4.01043 −0.221102
\(330\) 33.3579 1.83629
\(331\) −7.05932 −0.388015 −0.194008 0.981000i \(-0.562149\pi\)
−0.194008 + 0.981000i \(0.562149\pi\)
\(332\) −14.5534 −0.798723
\(333\) 50.8310 2.78552
\(334\) 0.707537 0.0387147
\(335\) −1.54188 −0.0842419
\(336\) 4.06395 0.221707
\(337\) 1.85496 0.101046 0.0505230 0.998723i \(-0.483911\pi\)
0.0505230 + 0.998723i \(0.483911\pi\)
\(338\) 7.31503 0.397885
\(339\) 46.5647 2.52905
\(340\) −9.84239 −0.533779
\(341\) −21.2930 −1.15308
\(342\) −5.96381 −0.322486
\(343\) 15.8451 0.855557
\(344\) 1.61059 0.0868373
\(345\) −2.76510 −0.148868
\(346\) 6.92283 0.372173
\(347\) −1.49193 −0.0800912 −0.0400456 0.999198i \(-0.512750\pi\)
−0.0400456 + 0.999198i \(0.512750\pi\)
\(348\) −3.98308 −0.213515
\(349\) 6.00693 0.321544 0.160772 0.986992i \(-0.448602\pi\)
0.160772 + 0.986992i \(0.448602\pi\)
\(350\) −5.43692 −0.290615
\(351\) 57.7283 3.08131
\(352\) 3.46314 0.184586
\(353\) 25.6381 1.36458 0.682290 0.731082i \(-0.260984\pi\)
0.682290 + 0.731082i \(0.260984\pi\)
\(354\) −27.9650 −1.48632
\(355\) 26.3113 1.39646
\(356\) −17.1962 −0.911396
\(357\) 13.1591 0.696453
\(358\) 5.27002 0.278529
\(359\) −27.1825 −1.43464 −0.717319 0.696745i \(-0.754631\pi\)
−0.717319 + 0.696745i \(0.754631\pi\)
\(360\) −21.4046 −1.12812
\(361\) −18.2827 −0.962249
\(362\) −10.2356 −0.537970
\(363\) −3.14776 −0.165215
\(364\) 5.78031 0.302971
\(365\) −0.703465 −0.0368210
\(366\) −28.8056 −1.50569
\(367\) −14.6711 −0.765828 −0.382914 0.923784i \(-0.625079\pi\)
−0.382914 + 0.923784i \(0.625079\pi\)
\(368\) −0.287066 −0.0149644
\(369\) −34.0284 −1.77145
\(370\) −21.9416 −1.14069
\(371\) 8.97408 0.465911
\(372\) 19.4837 1.01018
\(373\) −0.602150 −0.0311781 −0.0155891 0.999878i \(-0.504962\pi\)
−0.0155891 + 0.999878i \(0.504962\pi\)
\(374\) 11.2137 0.579845
\(375\) −7.32578 −0.378302
\(376\) 3.12714 0.161270
\(377\) −5.66529 −0.291777
\(378\) 16.4257 0.844845
\(379\) −4.61086 −0.236844 −0.118422 0.992963i \(-0.537784\pi\)
−0.118422 + 0.992963i \(0.537784\pi\)
\(380\) 2.57433 0.132060
\(381\) 34.5065 1.76782
\(382\) 4.00758 0.205046
\(383\) −18.2631 −0.933200 −0.466600 0.884468i \(-0.654521\pi\)
−0.466600 + 0.884468i \(0.654521\pi\)
\(384\) −3.16888 −0.161711
\(385\) 13.5001 0.688027
\(386\) 10.0430 0.511175
\(387\) 11.3415 0.576519
\(388\) −12.2668 −0.622752
\(389\) −29.0706 −1.47394 −0.736969 0.675926i \(-0.763744\pi\)
−0.736969 + 0.675926i \(0.763744\pi\)
\(390\) −43.4148 −2.19839
\(391\) −0.929522 −0.0470079
\(392\) −5.35531 −0.270484
\(393\) −11.1357 −0.561724
\(394\) 20.1963 1.01747
\(395\) −9.13943 −0.459855
\(396\) 24.3867 1.22548
\(397\) −8.41968 −0.422571 −0.211286 0.977424i \(-0.567765\pi\)
−0.211286 + 0.977424i \(0.567765\pi\)
\(398\) 8.46992 0.424559
\(399\) −3.44183 −0.172307
\(400\) 4.23946 0.211973
\(401\) −2.69017 −0.134340 −0.0671702 0.997742i \(-0.521397\pi\)
−0.0671702 + 0.997742i \(0.521397\pi\)
\(402\) −1.60743 −0.0801715
\(403\) 27.7125 1.38046
\(404\) 6.75003 0.335826
\(405\) −59.1561 −2.93949
\(406\) −1.61197 −0.0800005
\(407\) 24.9986 1.23913
\(408\) −10.2608 −0.507988
\(409\) 36.9422 1.82668 0.913338 0.407203i \(-0.133496\pi\)
0.913338 + 0.407203i \(0.133496\pi\)
\(410\) 14.6886 0.725420
\(411\) 51.4523 2.53796
\(412\) 0.260264 0.0128223
\(413\) −11.3175 −0.556900
\(414\) −2.02146 −0.0993494
\(415\) 44.2373 2.17152
\(416\) −4.50722 −0.220985
\(417\) −24.3678 −1.19330
\(418\) −2.93299 −0.143457
\(419\) 24.3255 1.18838 0.594190 0.804325i \(-0.297473\pi\)
0.594190 + 0.804325i \(0.297473\pi\)
\(420\) −12.3530 −0.602763
\(421\) −13.7992 −0.672532 −0.336266 0.941767i \(-0.609164\pi\)
−0.336266 + 0.941767i \(0.609164\pi\)
\(422\) 7.40185 0.360316
\(423\) 22.0207 1.07068
\(424\) −6.99757 −0.339832
\(425\) 13.7274 0.665876
\(426\) 27.4300 1.32899
\(427\) −11.6577 −0.564157
\(428\) −12.2796 −0.593558
\(429\) 49.4635 2.38812
\(430\) −4.89563 −0.236088
\(431\) 7.63843 0.367930 0.183965 0.982933i \(-0.441107\pi\)
0.183965 + 0.982933i \(0.441107\pi\)
\(432\) −12.8080 −0.616224
\(433\) −0.237432 −0.0114103 −0.00570514 0.999984i \(-0.501816\pi\)
−0.00570514 + 0.999984i \(0.501816\pi\)
\(434\) 7.88513 0.378498
\(435\) 12.1072 0.580494
\(436\) −3.06057 −0.146575
\(437\) 0.243121 0.0116301
\(438\) −0.733373 −0.0350419
\(439\) 22.7203 1.08438 0.542190 0.840256i \(-0.317595\pi\)
0.542190 + 0.840256i \(0.317595\pi\)
\(440\) −10.5267 −0.501842
\(441\) −37.7110 −1.79576
\(442\) −14.5944 −0.694185
\(443\) 31.7608 1.50900 0.754500 0.656300i \(-0.227880\pi\)
0.754500 + 0.656300i \(0.227880\pi\)
\(444\) −22.8744 −1.08557
\(445\) 52.2703 2.47785
\(446\) −4.66593 −0.220938
\(447\) −27.3191 −1.29215
\(448\) −1.28246 −0.0605904
\(449\) −10.4783 −0.494503 −0.247252 0.968951i \(-0.579527\pi\)
−0.247252 + 0.968951i \(0.579527\pi\)
\(450\) 29.8534 1.40730
\(451\) −16.7351 −0.788025
\(452\) −14.6944 −0.691165
\(453\) −67.5486 −3.17371
\(454\) −25.5637 −1.19976
\(455\) −17.5701 −0.823700
\(456\) 2.68378 0.125679
\(457\) −29.2012 −1.36598 −0.682988 0.730430i \(-0.739320\pi\)
−0.682988 + 0.730430i \(0.739320\pi\)
\(458\) 16.8881 0.789131
\(459\) −41.4723 −1.93576
\(460\) 0.872580 0.0406842
\(461\) −14.6740 −0.683437 −0.341719 0.939802i \(-0.611009\pi\)
−0.341719 + 0.939802i \(0.611009\pi\)
\(462\) 14.0740 0.654783
\(463\) −8.79064 −0.408536 −0.204268 0.978915i \(-0.565481\pi\)
−0.204268 + 0.978915i \(0.565481\pi\)
\(464\) 1.25694 0.0583518
\(465\) −59.2237 −2.74643
\(466\) 17.2278 0.798060
\(467\) 3.63604 0.168256 0.0841279 0.996455i \(-0.473190\pi\)
0.0841279 + 0.996455i \(0.473190\pi\)
\(468\) −31.7389 −1.46713
\(469\) −0.650534 −0.0300389
\(470\) −9.50542 −0.438452
\(471\) 22.1809 1.02204
\(472\) 8.82489 0.406198
\(473\) 5.57771 0.256463
\(474\) −9.52800 −0.437636
\(475\) −3.59047 −0.164742
\(476\) −4.15260 −0.190334
\(477\) −49.2755 −2.25617
\(478\) 10.2780 0.470104
\(479\) 0.241336 0.0110269 0.00551347 0.999985i \(-0.498245\pi\)
0.00551347 + 0.999985i \(0.498245\pi\)
\(480\) 9.63228 0.439651
\(481\) −32.5352 −1.48348
\(482\) 1.86449 0.0849252
\(483\) −1.16662 −0.0530831
\(484\) 0.993337 0.0451517
\(485\) 37.2867 1.69310
\(486\) −23.2473 −1.05452
\(487\) −8.08526 −0.366378 −0.183189 0.983078i \(-0.558642\pi\)
−0.183189 + 0.983078i \(0.558642\pi\)
\(488\) 9.09016 0.411492
\(489\) −71.7495 −3.24462
\(490\) 16.2782 0.735376
\(491\) 10.1812 0.459470 0.229735 0.973253i \(-0.426214\pi\)
0.229735 + 0.973253i \(0.426214\pi\)
\(492\) 15.3131 0.690369
\(493\) 4.06997 0.183302
\(494\) 3.81724 0.171746
\(495\) −74.1270 −3.33176
\(496\) −6.14846 −0.276074
\(497\) 11.1010 0.497948
\(498\) 46.1181 2.06660
\(499\) 15.1985 0.680380 0.340190 0.940357i \(-0.389509\pi\)
0.340190 + 0.940357i \(0.389509\pi\)
\(500\) 2.31179 0.103386
\(501\) −2.24210 −0.100170
\(502\) 6.05456 0.270228
\(503\) 19.8713 0.886018 0.443009 0.896517i \(-0.353911\pi\)
0.443009 + 0.896517i \(0.353911\pi\)
\(504\) −9.03080 −0.402264
\(505\) −20.5177 −0.913026
\(506\) −0.994150 −0.0441954
\(507\) −23.1804 −1.02948
\(508\) −10.8892 −0.483130
\(509\) −21.0381 −0.932496 −0.466248 0.884654i \(-0.654394\pi\)
−0.466248 + 0.884654i \(0.654394\pi\)
\(510\) 31.1894 1.38109
\(511\) −0.296799 −0.0131296
\(512\) 1.00000 0.0441942
\(513\) 10.8473 0.478919
\(514\) 13.6654 0.602756
\(515\) −0.791110 −0.0348605
\(516\) −5.10377 −0.224681
\(517\) 10.8297 0.476291
\(518\) −9.25737 −0.406745
\(519\) −21.9376 −0.962954
\(520\) 13.7004 0.600800
\(521\) −26.2594 −1.15045 −0.575224 0.817996i \(-0.695085\pi\)
−0.575224 + 0.817996i \(0.695085\pi\)
\(522\) 8.85109 0.387402
\(523\) −31.3689 −1.37166 −0.685832 0.727760i \(-0.740562\pi\)
−0.685832 + 0.727760i \(0.740562\pi\)
\(524\) 3.51410 0.153514
\(525\) 17.2289 0.751932
\(526\) 0.256730 0.0111939
\(527\) −19.9087 −0.867239
\(528\) −10.9743 −0.477594
\(529\) −22.9176 −0.996417
\(530\) 21.2701 0.923916
\(531\) 62.1431 2.69678
\(532\) 1.08613 0.0470899
\(533\) 21.7805 0.943417
\(534\) 54.4926 2.35813
\(535\) 37.3257 1.61373
\(536\) 0.507256 0.0219101
\(537\) −16.7001 −0.720661
\(538\) 25.7916 1.11195
\(539\) −18.5462 −0.798840
\(540\) 38.9317 1.67535
\(541\) −9.67287 −0.415869 −0.207935 0.978143i \(-0.566674\pi\)
−0.207935 + 0.978143i \(0.566674\pi\)
\(542\) 27.6172 1.18626
\(543\) 32.4353 1.39193
\(544\) 3.23801 0.138828
\(545\) 9.30307 0.398500
\(546\) −18.3171 −0.783900
\(547\) 23.8349 1.01911 0.509554 0.860439i \(-0.329810\pi\)
0.509554 + 0.860439i \(0.329810\pi\)
\(548\) −16.2368 −0.693600
\(549\) 64.0110 2.73192
\(550\) 14.6818 0.626035
\(551\) −1.06452 −0.0453501
\(552\) 0.909678 0.0387185
\(553\) −3.85601 −0.163974
\(554\) 15.0027 0.637405
\(555\) 69.5303 2.95139
\(556\) 7.68972 0.326117
\(557\) −8.59867 −0.364337 −0.182169 0.983267i \(-0.558312\pi\)
−0.182169 + 0.983267i \(0.558312\pi\)
\(558\) −43.2962 −1.83287
\(559\) −7.25930 −0.307036
\(560\) 3.89821 0.164730
\(561\) −35.5348 −1.50028
\(562\) 14.0305 0.591840
\(563\) 18.3220 0.772182 0.386091 0.922461i \(-0.373825\pi\)
0.386091 + 0.922461i \(0.373825\pi\)
\(564\) −9.90954 −0.417267
\(565\) 44.6657 1.87910
\(566\) 2.91971 0.122725
\(567\) −24.9585 −1.04816
\(568\) −8.65604 −0.363200
\(569\) 10.6598 0.446883 0.223442 0.974717i \(-0.428271\pi\)
0.223442 + 0.974717i \(0.428271\pi\)
\(570\) −8.15773 −0.341690
\(571\) 7.63681 0.319591 0.159795 0.987150i \(-0.448917\pi\)
0.159795 + 0.987150i \(0.448917\pi\)
\(572\) −15.6091 −0.652651
\(573\) −12.6996 −0.530531
\(574\) 6.19728 0.258669
\(575\) −1.21700 −0.0507526
\(576\) 7.04180 0.293408
\(577\) −28.3404 −1.17983 −0.589914 0.807466i \(-0.700838\pi\)
−0.589914 + 0.807466i \(0.700838\pi\)
\(578\) −6.51532 −0.271002
\(579\) −31.8250 −1.32260
\(580\) −3.82064 −0.158644
\(581\) 18.6641 0.774319
\(582\) 38.8720 1.61130
\(583\) −24.2336 −1.00365
\(584\) 0.231430 0.00957663
\(585\) 96.4751 3.98876
\(586\) 12.7936 0.528501
\(587\) 16.3759 0.675907 0.337954 0.941163i \(-0.390265\pi\)
0.337954 + 0.941163i \(0.390265\pi\)
\(588\) 16.9703 0.699844
\(589\) 5.20723 0.214560
\(590\) −26.8246 −1.10435
\(591\) −63.9996 −2.63259
\(592\) 7.21847 0.296677
\(593\) 35.7370 1.46754 0.733771 0.679397i \(-0.237759\pi\)
0.733771 + 0.679397i \(0.237759\pi\)
\(594\) −44.3558 −1.81994
\(595\) 12.6224 0.517470
\(596\) 8.62106 0.353132
\(597\) −26.8402 −1.09849
\(598\) 1.29387 0.0529103
\(599\) 17.5971 0.718999 0.359500 0.933145i \(-0.382947\pi\)
0.359500 + 0.933145i \(0.382947\pi\)
\(600\) −13.4343 −0.548454
\(601\) −18.2459 −0.744266 −0.372133 0.928179i \(-0.621373\pi\)
−0.372133 + 0.928179i \(0.621373\pi\)
\(602\) −2.06552 −0.0841841
\(603\) 3.57200 0.145463
\(604\) 21.3163 0.867346
\(605\) −3.01939 −0.122756
\(606\) −21.3900 −0.868910
\(607\) 8.32651 0.337962 0.168981 0.985619i \(-0.445952\pi\)
0.168981 + 0.985619i \(0.445952\pi\)
\(608\) −0.846917 −0.0343470
\(609\) 5.10813 0.206992
\(610\) −27.6309 −1.11874
\(611\) −14.0947 −0.570212
\(612\) 22.8014 0.921691
\(613\) 25.0195 1.01053 0.505265 0.862964i \(-0.331395\pi\)
0.505265 + 0.862964i \(0.331395\pi\)
\(614\) −0.792900 −0.0319989
\(615\) −46.5465 −1.87694
\(616\) −4.44133 −0.178946
\(617\) 22.9530 0.924052 0.462026 0.886866i \(-0.347123\pi\)
0.462026 + 0.886866i \(0.347123\pi\)
\(618\) −0.824744 −0.0331761
\(619\) 37.2680 1.49793 0.748963 0.662612i \(-0.230552\pi\)
0.748963 + 0.662612i \(0.230552\pi\)
\(620\) 18.6892 0.750574
\(621\) 3.67673 0.147542
\(622\) 13.3358 0.534717
\(623\) 22.0534 0.883549
\(624\) 14.2828 0.571771
\(625\) −28.2243 −1.12897
\(626\) −12.1971 −0.487496
\(627\) 9.29429 0.371178
\(628\) −6.99959 −0.279314
\(629\) 23.3734 0.931960
\(630\) 27.4504 1.09365
\(631\) −1.08594 −0.0432306 −0.0216153 0.999766i \(-0.506881\pi\)
−0.0216153 + 0.999766i \(0.506881\pi\)
\(632\) 3.00674 0.119602
\(633\) −23.4556 −0.932275
\(634\) 16.9958 0.674990
\(635\) 33.0993 1.31351
\(636\) 22.1745 0.879274
\(637\) 24.1375 0.956364
\(638\) 4.35295 0.172335
\(639\) −60.9541 −2.41131
\(640\) −3.03965 −0.120153
\(641\) −33.9464 −1.34080 −0.670401 0.741999i \(-0.733878\pi\)
−0.670401 + 0.741999i \(0.733878\pi\)
\(642\) 38.9126 1.53576
\(643\) 27.0846 1.06811 0.534055 0.845449i \(-0.320667\pi\)
0.534055 + 0.845449i \(0.320667\pi\)
\(644\) 0.368150 0.0145071
\(645\) 15.5137 0.610850
\(646\) −2.74232 −0.107895
\(647\) −25.8657 −1.01688 −0.508442 0.861096i \(-0.669778\pi\)
−0.508442 + 0.861096i \(0.669778\pi\)
\(648\) 19.4615 0.764520
\(649\) 30.5618 1.19966
\(650\) −19.1082 −0.749484
\(651\) −24.9870 −0.979319
\(652\) 22.6419 0.886725
\(653\) 33.5998 1.31486 0.657432 0.753514i \(-0.271643\pi\)
0.657432 + 0.753514i \(0.271643\pi\)
\(654\) 9.69859 0.379245
\(655\) −10.6816 −0.417365
\(656\) −4.83235 −0.188672
\(657\) 1.62968 0.0635799
\(658\) −4.01043 −0.156343
\(659\) 33.4850 1.30439 0.652196 0.758050i \(-0.273848\pi\)
0.652196 + 0.758050i \(0.273848\pi\)
\(660\) 33.3579 1.29846
\(661\) −14.4870 −0.563479 −0.281739 0.959491i \(-0.590911\pi\)
−0.281739 + 0.959491i \(0.590911\pi\)
\(662\) −7.05932 −0.274368
\(663\) 46.2479 1.79612
\(664\) −14.5534 −0.564783
\(665\) −3.30146 −0.128025
\(666\) 50.8310 1.96966
\(667\) −0.360824 −0.0139712
\(668\) 0.707537 0.0273754
\(669\) 14.7858 0.571650
\(670\) −1.54188 −0.0595680
\(671\) 31.4805 1.21529
\(672\) 4.06395 0.156770
\(673\) −4.39816 −0.169537 −0.0847683 0.996401i \(-0.527015\pi\)
−0.0847683 + 0.996401i \(0.527015\pi\)
\(674\) 1.85496 0.0714503
\(675\) −54.2988 −2.08996
\(676\) 7.31503 0.281347
\(677\) −20.3723 −0.782969 −0.391485 0.920185i \(-0.628038\pi\)
−0.391485 + 0.920185i \(0.628038\pi\)
\(678\) 46.5647 1.78831
\(679\) 15.7316 0.603725
\(680\) −9.84239 −0.377439
\(681\) 81.0083 3.10424
\(682\) −21.2930 −0.815350
\(683\) −30.1909 −1.15522 −0.577611 0.816312i \(-0.696015\pi\)
−0.577611 + 0.816312i \(0.696015\pi\)
\(684\) −5.96381 −0.228032
\(685\) 49.3540 1.88572
\(686\) 15.8451 0.604970
\(687\) −53.5165 −2.04178
\(688\) 1.61059 0.0614033
\(689\) 31.5396 1.20156
\(690\) −2.76510 −0.105266
\(691\) 18.4334 0.701239 0.350619 0.936518i \(-0.385971\pi\)
0.350619 + 0.936518i \(0.385971\pi\)
\(692\) 6.92283 0.263166
\(693\) −31.2749 −1.18804
\(694\) −1.49193 −0.0566331
\(695\) −23.3740 −0.886628
\(696\) −3.98308 −0.150978
\(697\) −15.6472 −0.592679
\(698\) 6.00693 0.227366
\(699\) −54.5927 −2.06488
\(700\) −5.43692 −0.205496
\(701\) −48.4633 −1.83043 −0.915217 0.402962i \(-0.867981\pi\)
−0.915217 + 0.402962i \(0.867981\pi\)
\(702\) 57.7283 2.17881
\(703\) −6.11344 −0.230573
\(704\) 3.46314 0.130522
\(705\) 30.1215 1.13444
\(706\) 25.6381 0.964904
\(707\) −8.65661 −0.325565
\(708\) −27.9650 −1.05099
\(709\) 51.5335 1.93538 0.967691 0.252138i \(-0.0811338\pi\)
0.967691 + 0.252138i \(0.0811338\pi\)
\(710\) 26.3113 0.987446
\(711\) 21.1729 0.794044
\(712\) −17.1962 −0.644454
\(713\) 1.76501 0.0661003
\(714\) 13.1591 0.492467
\(715\) 47.4463 1.77439
\(716\) 5.27002 0.196950
\(717\) −32.5697 −1.21634
\(718\) −27.1825 −1.01444
\(719\) −6.06661 −0.226246 −0.113123 0.993581i \(-0.536085\pi\)
−0.113123 + 0.993581i \(0.536085\pi\)
\(720\) −21.4046 −0.797701
\(721\) −0.333777 −0.0124305
\(722\) −18.2827 −0.680413
\(723\) −5.90835 −0.219734
\(724\) −10.2356 −0.380402
\(725\) 5.32873 0.197904
\(726\) −3.14776 −0.116825
\(727\) 26.8418 0.995506 0.497753 0.867319i \(-0.334159\pi\)
0.497753 + 0.867319i \(0.334159\pi\)
\(728\) 5.78031 0.214233
\(729\) 15.2833 0.566048
\(730\) −0.703465 −0.0260364
\(731\) 5.21511 0.192888
\(732\) −28.8056 −1.06469
\(733\) −51.8368 −1.91464 −0.957319 0.289034i \(-0.906666\pi\)
−0.957319 + 0.289034i \(0.906666\pi\)
\(734\) −14.6711 −0.541522
\(735\) −51.5838 −1.90270
\(736\) −0.287066 −0.0105814
\(737\) 1.75670 0.0647089
\(738\) −34.0284 −1.25260
\(739\) 17.2741 0.635437 0.317719 0.948185i \(-0.397083\pi\)
0.317719 + 0.948185i \(0.397083\pi\)
\(740\) −21.9416 −0.806589
\(741\) −12.0964 −0.444371
\(742\) 8.97408 0.329449
\(743\) −26.0173 −0.954482 −0.477241 0.878773i \(-0.658363\pi\)
−0.477241 + 0.878773i \(0.658363\pi\)
\(744\) 19.4837 0.714308
\(745\) −26.2050 −0.960076
\(746\) −0.602150 −0.0220463
\(747\) −102.482 −3.74963
\(748\) 11.2137 0.410012
\(749\) 15.7481 0.575422
\(750\) −7.32578 −0.267500
\(751\) 50.8700 1.85627 0.928136 0.372240i \(-0.121410\pi\)
0.928136 + 0.372240i \(0.121410\pi\)
\(752\) 3.12714 0.114035
\(753\) −19.1862 −0.699183
\(754\) −5.66529 −0.206318
\(755\) −64.7939 −2.35809
\(756\) 16.4257 0.597395
\(757\) −28.4707 −1.03479 −0.517393 0.855748i \(-0.673098\pi\)
−0.517393 + 0.855748i \(0.673098\pi\)
\(758\) −4.61086 −0.167474
\(759\) 3.15034 0.114350
\(760\) 2.57433 0.0933807
\(761\) 33.6279 1.21901 0.609505 0.792782i \(-0.291368\pi\)
0.609505 + 0.792782i \(0.291368\pi\)
\(762\) 34.5065 1.25004
\(763\) 3.92505 0.142096
\(764\) 4.00758 0.144989
\(765\) −69.3081 −2.50584
\(766\) −18.2631 −0.659872
\(767\) −39.7757 −1.43622
\(768\) −3.16888 −0.114347
\(769\) 23.8916 0.861553 0.430777 0.902459i \(-0.358240\pi\)
0.430777 + 0.902459i \(0.358240\pi\)
\(770\) 13.5001 0.486508
\(771\) −43.3041 −1.55956
\(772\) 10.0430 0.361455
\(773\) 2.84455 0.102311 0.0511557 0.998691i \(-0.483710\pi\)
0.0511557 + 0.998691i \(0.483710\pi\)
\(774\) 11.3415 0.407661
\(775\) −26.0661 −0.936323
\(776\) −12.2668 −0.440352
\(777\) 29.3355 1.05240
\(778\) −29.0706 −1.04223
\(779\) 4.09260 0.146633
\(780\) −43.4148 −1.55450
\(781\) −29.9771 −1.07266
\(782\) −0.929522 −0.0332396
\(783\) −16.0988 −0.575324
\(784\) −5.35531 −0.191261
\(785\) 21.2763 0.759384
\(786\) −11.1357 −0.397199
\(787\) 7.49094 0.267023 0.133512 0.991047i \(-0.457375\pi\)
0.133512 + 0.991047i \(0.457375\pi\)
\(788\) 20.1963 0.719462
\(789\) −0.813545 −0.0289630
\(790\) −9.13943 −0.325166
\(791\) 18.8449 0.670047
\(792\) 24.3867 0.866545
\(793\) −40.9713 −1.45493
\(794\) −8.41968 −0.298803
\(795\) −67.4025 −2.39052
\(796\) 8.46992 0.300208
\(797\) −31.0123 −1.09851 −0.549256 0.835654i \(-0.685089\pi\)
−0.549256 + 0.835654i \(0.685089\pi\)
\(798\) −3.44183 −0.121839
\(799\) 10.1257 0.358222
\(800\) 4.23946 0.149887
\(801\) −121.092 −4.27858
\(802\) −2.69017 −0.0949930
\(803\) 0.801474 0.0282834
\(804\) −1.60743 −0.0566898
\(805\) −1.11905 −0.0394412
\(806\) 27.7125 0.976130
\(807\) −81.7305 −2.87705
\(808\) 6.75003 0.237465
\(809\) 16.1090 0.566363 0.283181 0.959066i \(-0.408610\pi\)
0.283181 + 0.959066i \(0.408610\pi\)
\(810\) −59.1561 −2.07853
\(811\) −0.142698 −0.00501080 −0.00250540 0.999997i \(-0.500797\pi\)
−0.00250540 + 0.999997i \(0.500797\pi\)
\(812\) −1.61197 −0.0565689
\(813\) −87.5156 −3.06931
\(814\) 24.9986 0.876199
\(815\) −68.8234 −2.41078
\(816\) −10.2608 −0.359202
\(817\) −1.36404 −0.0477216
\(818\) 36.9422 1.29165
\(819\) 40.7038 1.42231
\(820\) 14.6886 0.512950
\(821\) 3.18240 0.111067 0.0555333 0.998457i \(-0.482314\pi\)
0.0555333 + 0.998457i \(0.482314\pi\)
\(822\) 51.4523 1.79461
\(823\) 33.6306 1.17229 0.586145 0.810206i \(-0.300645\pi\)
0.586145 + 0.810206i \(0.300645\pi\)
\(824\) 0.260264 0.00906671
\(825\) −46.5249 −1.61979
\(826\) −11.3175 −0.393787
\(827\) −44.6141 −1.55138 −0.775692 0.631111i \(-0.782599\pi\)
−0.775692 + 0.631111i \(0.782599\pi\)
\(828\) −2.02146 −0.0702506
\(829\) −0.397951 −0.0138214 −0.00691070 0.999976i \(-0.502200\pi\)
−0.00691070 + 0.999976i \(0.502200\pi\)
\(830\) 44.2373 1.53550
\(831\) −47.5418 −1.64921
\(832\) −4.50722 −0.156260
\(833\) −17.3405 −0.600813
\(834\) −24.3678 −0.843788
\(835\) −2.15066 −0.0744267
\(836\) −2.93299 −0.101440
\(837\) 78.7493 2.72197
\(838\) 24.3255 0.840312
\(839\) 43.1968 1.49132 0.745660 0.666326i \(-0.232134\pi\)
0.745660 + 0.666326i \(0.232134\pi\)
\(840\) −12.3530 −0.426218
\(841\) −27.4201 −0.945521
\(842\) −13.7992 −0.475552
\(843\) −44.4609 −1.53131
\(844\) 7.40185 0.254782
\(845\) −22.2351 −0.764911
\(846\) 22.0207 0.757088
\(847\) −1.27391 −0.0437721
\(848\) −6.99757 −0.240298
\(849\) −9.25221 −0.317535
\(850\) 13.7274 0.470845
\(851\) −2.07218 −0.0710333
\(852\) 27.4300 0.939735
\(853\) −6.47898 −0.221836 −0.110918 0.993830i \(-0.535379\pi\)
−0.110918 + 0.993830i \(0.535379\pi\)
\(854\) −11.6577 −0.398919
\(855\) 18.1279 0.619961
\(856\) −12.2796 −0.419709
\(857\) 9.63433 0.329102 0.164551 0.986369i \(-0.447382\pi\)
0.164551 + 0.986369i \(0.447382\pi\)
\(858\) 49.4635 1.68865
\(859\) 39.4243 1.34514 0.672570 0.740034i \(-0.265190\pi\)
0.672570 + 0.740034i \(0.265190\pi\)
\(860\) −4.89563 −0.166940
\(861\) −19.6384 −0.669276
\(862\) 7.63843 0.260166
\(863\) 12.5077 0.425768 0.212884 0.977077i \(-0.431714\pi\)
0.212884 + 0.977077i \(0.431714\pi\)
\(864\) −12.8080 −0.435736
\(865\) −21.0429 −0.715482
\(866\) −0.237432 −0.00806828
\(867\) 20.6463 0.701184
\(868\) 7.88513 0.267639
\(869\) 10.4128 0.353229
\(870\) 12.1072 0.410471
\(871\) −2.28632 −0.0774689
\(872\) −3.06057 −0.103644
\(873\) −86.3803 −2.92353
\(874\) 0.243121 0.00822369
\(875\) −2.96477 −0.100227
\(876\) −0.733373 −0.0247784
\(877\) −19.0268 −0.642488 −0.321244 0.946996i \(-0.604101\pi\)
−0.321244 + 0.946996i \(0.604101\pi\)
\(878\) 22.7203 0.766773
\(879\) −40.5415 −1.36743
\(880\) −10.5267 −0.354856
\(881\) 4.38011 0.147570 0.0737848 0.997274i \(-0.476492\pi\)
0.0737848 + 0.997274i \(0.476492\pi\)
\(882\) −37.7110 −1.26979
\(883\) −1.03524 −0.0348386 −0.0174193 0.999848i \(-0.505545\pi\)
−0.0174193 + 0.999848i \(0.505545\pi\)
\(884\) −14.5944 −0.490863
\(885\) 85.0038 2.85737
\(886\) 31.7608 1.06702
\(887\) 22.0410 0.740066 0.370033 0.929019i \(-0.379346\pi\)
0.370033 + 0.929019i \(0.379346\pi\)
\(888\) −22.8744 −0.767616
\(889\) 13.9649 0.468368
\(890\) 52.2703 1.75211
\(891\) 67.3979 2.25792
\(892\) −4.66593 −0.156227
\(893\) −2.64843 −0.0886264
\(894\) −27.3191 −0.913688
\(895\) −16.0190 −0.535456
\(896\) −1.28246 −0.0428439
\(897\) −4.10012 −0.136899
\(898\) −10.4783 −0.349667
\(899\) −7.72822 −0.257751
\(900\) 29.8534 0.995113
\(901\) −22.6582 −0.754853
\(902\) −16.7351 −0.557218
\(903\) 6.54537 0.217816
\(904\) −14.6944 −0.488727
\(905\) 31.1125 1.03422
\(906\) −67.5486 −2.24415
\(907\) −29.3125 −0.973306 −0.486653 0.873595i \(-0.661782\pi\)
−0.486653 + 0.873595i \(0.661782\pi\)
\(908\) −25.5637 −0.848361
\(909\) 47.5323 1.57655
\(910\) −17.5701 −0.582444
\(911\) 9.90013 0.328006 0.164003 0.986460i \(-0.447559\pi\)
0.164003 + 0.986460i \(0.447559\pi\)
\(912\) 2.68378 0.0888687
\(913\) −50.4006 −1.66802
\(914\) −29.2012 −0.965891
\(915\) 87.5589 2.89461
\(916\) 16.8881 0.558000
\(917\) −4.50667 −0.148823
\(918\) −41.4723 −1.36879
\(919\) 0.357050 0.0117780 0.00588900 0.999983i \(-0.498125\pi\)
0.00588900 + 0.999983i \(0.498125\pi\)
\(920\) 0.872580 0.0287681
\(921\) 2.51261 0.0827932
\(922\) −14.6740 −0.483263
\(923\) 39.0147 1.28418
\(924\) 14.0740 0.463001
\(925\) 30.6024 1.00620
\(926\) −8.79064 −0.288878
\(927\) 1.83272 0.0601945
\(928\) 1.25694 0.0412610
\(929\) −7.81636 −0.256446 −0.128223 0.991745i \(-0.540927\pi\)
−0.128223 + 0.991745i \(0.540927\pi\)
\(930\) −59.2237 −1.94202
\(931\) 4.53550 0.148645
\(932\) 17.2278 0.564314
\(933\) −42.2596 −1.38352
\(934\) 3.63604 0.118975
\(935\) −34.0856 −1.11472
\(936\) −31.7389 −1.03742
\(937\) −21.7907 −0.711873 −0.355936 0.934510i \(-0.615838\pi\)
−0.355936 + 0.934510i \(0.615838\pi\)
\(938\) −0.650534 −0.0212407
\(939\) 38.6513 1.26134
\(940\) −9.50542 −0.310032
\(941\) 52.0794 1.69774 0.848869 0.528603i \(-0.177284\pi\)
0.848869 + 0.528603i \(0.177284\pi\)
\(942\) 22.1809 0.722692
\(943\) 1.38720 0.0451736
\(944\) 8.82489 0.287226
\(945\) −49.9282 −1.62416
\(946\) 5.57771 0.181347
\(947\) 0.766172 0.0248973 0.0124486 0.999923i \(-0.496037\pi\)
0.0124486 + 0.999923i \(0.496037\pi\)
\(948\) −9.52800 −0.309455
\(949\) −1.04310 −0.0338606
\(950\) −3.59047 −0.116490
\(951\) −53.8577 −1.74646
\(952\) −4.15260 −0.134587
\(953\) 23.4455 0.759473 0.379736 0.925095i \(-0.376015\pi\)
0.379736 + 0.925095i \(0.376015\pi\)
\(954\) −49.2755 −1.59535
\(955\) −12.1816 −0.394189
\(956\) 10.2780 0.332414
\(957\) −13.7940 −0.445895
\(958\) 0.241336 0.00779722
\(959\) 20.8229 0.672408
\(960\) 9.63228 0.310880
\(961\) 6.80357 0.219470
\(962\) −32.5352 −1.04898
\(963\) −86.4706 −2.78648
\(964\) 1.86449 0.0600512
\(965\) −30.5272 −0.982704
\(966\) −1.16662 −0.0375355
\(967\) 12.5254 0.402789 0.201394 0.979510i \(-0.435453\pi\)
0.201394 + 0.979510i \(0.435453\pi\)
\(968\) 0.993337 0.0319271
\(969\) 8.69008 0.279166
\(970\) 37.2867 1.19721
\(971\) 54.2390 1.74061 0.870306 0.492511i \(-0.163921\pi\)
0.870306 + 0.492511i \(0.163921\pi\)
\(972\) −23.2473 −0.745657
\(973\) −9.86173 −0.316153
\(974\) −8.08526 −0.259068
\(975\) 60.5514 1.93920
\(976\) 9.09016 0.290969
\(977\) 41.0382 1.31293 0.656464 0.754357i \(-0.272051\pi\)
0.656464 + 0.754357i \(0.272051\pi\)
\(978\) −71.7495 −2.29429
\(979\) −59.5528 −1.90332
\(980\) 16.2782 0.519989
\(981\) −21.5519 −0.688101
\(982\) 10.1812 0.324895
\(983\) 37.4383 1.19410 0.597048 0.802206i \(-0.296340\pi\)
0.597048 + 0.802206i \(0.296340\pi\)
\(984\) 15.3131 0.488165
\(985\) −61.3895 −1.95603
\(986\) 4.06997 0.129614
\(987\) 12.7086 0.404518
\(988\) 3.81724 0.121443
\(989\) −0.462347 −0.0147018
\(990\) −74.1270 −2.35591
\(991\) −52.5884 −1.67053 −0.835263 0.549851i \(-0.814684\pi\)
−0.835263 + 0.549851i \(0.814684\pi\)
\(992\) −6.14846 −0.195214
\(993\) 22.3701 0.709895
\(994\) 11.1010 0.352102
\(995\) −25.7456 −0.816190
\(996\) 46.1181 1.46131
\(997\) 17.8599 0.565628 0.282814 0.959175i \(-0.408732\pi\)
0.282814 + 0.959175i \(0.408732\pi\)
\(998\) 15.1985 0.481101
\(999\) −92.4539 −2.92511
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 8014.2.a.d.1.1 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8014.2.a.d.1.1 88 1.1 even 1 trivial