Properties

Label 8034.2.a.s.1.10
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $1$
Dimension $10$
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] = [8034,2,Mod(1,8034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.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: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-4.04714\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.30484 q^{5} +1.00000 q^{6} -3.32584 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.30484 q^{5} +1.00000 q^{6} -3.32584 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.30484 q^{10} -2.99032 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.32584 q^{14} -4.30484 q^{15} +1.00000 q^{16} +7.37298 q^{17} -1.00000 q^{18} +1.56088 q^{19} +4.30484 q^{20} +3.32584 q^{21} +2.99032 q^{22} -3.98856 q^{23} +1.00000 q^{24} +13.5316 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.32584 q^{28} -5.10669 q^{29} +4.30484 q^{30} -6.12120 q^{31} -1.00000 q^{32} +2.99032 q^{33} -7.37298 q^{34} -14.3172 q^{35} +1.00000 q^{36} -5.21790 q^{37} -1.56088 q^{38} +1.00000 q^{39} -4.30484 q^{40} -1.29895 q^{41} -3.32584 q^{42} -2.11927 q^{43} -2.99032 q^{44} +4.30484 q^{45} +3.98856 q^{46} +10.0352 q^{47} -1.00000 q^{48} +4.06120 q^{49} -13.5316 q^{50} -7.37298 q^{51} -1.00000 q^{52} -8.84758 q^{53} +1.00000 q^{54} -12.8729 q^{55} +3.32584 q^{56} -1.56088 q^{57} +5.10669 q^{58} +3.83269 q^{59} -4.30484 q^{60} +4.47557 q^{61} +6.12120 q^{62} -3.32584 q^{63} +1.00000 q^{64} -4.30484 q^{65} -2.99032 q^{66} +1.76088 q^{67} +7.37298 q^{68} +3.98856 q^{69} +14.3172 q^{70} -10.4599 q^{71} -1.00000 q^{72} +9.29221 q^{73} +5.21790 q^{74} -13.5316 q^{75} +1.56088 q^{76} +9.94533 q^{77} -1.00000 q^{78} +12.4331 q^{79} +4.30484 q^{80} +1.00000 q^{81} +1.29895 q^{82} -7.29642 q^{83} +3.32584 q^{84} +31.7395 q^{85} +2.11927 q^{86} +5.10669 q^{87} +2.99032 q^{88} +0.220099 q^{89} -4.30484 q^{90} +3.32584 q^{91} -3.98856 q^{92} +6.12120 q^{93} -10.0352 q^{94} +6.71933 q^{95} +1.00000 q^{96} -10.6956 q^{97} -4.06120 q^{98} -2.99032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 4.30484 1.92518 0.962591 0.270959i \(-0.0873407\pi\)
0.962591 + 0.270959i \(0.0873407\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.32584 −1.25705 −0.628524 0.777790i \(-0.716341\pi\)
−0.628524 + 0.777790i \(0.716341\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −4.30484 −1.36131
\(11\) −2.99032 −0.901616 −0.450808 0.892621i \(-0.648864\pi\)
−0.450808 + 0.892621i \(0.648864\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) 3.32584 0.888868
\(15\) −4.30484 −1.11150
\(16\) 1.00000 0.250000
\(17\) 7.37298 1.78821 0.894105 0.447858i \(-0.147813\pi\)
0.894105 + 0.447858i \(0.147813\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.56088 0.358090 0.179045 0.983841i \(-0.442699\pi\)
0.179045 + 0.983841i \(0.442699\pi\)
\(20\) 4.30484 0.962591
\(21\) 3.32584 0.725757
\(22\) 2.99032 0.637539
\(23\) −3.98856 −0.831673 −0.415836 0.909439i \(-0.636511\pi\)
−0.415836 + 0.909439i \(0.636511\pi\)
\(24\) 1.00000 0.204124
\(25\) 13.5316 2.70633
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) −3.32584 −0.628524
\(29\) −5.10669 −0.948289 −0.474144 0.880447i \(-0.657243\pi\)
−0.474144 + 0.880447i \(0.657243\pi\)
\(30\) 4.30484 0.785952
\(31\) −6.12120 −1.09940 −0.549700 0.835362i \(-0.685258\pi\)
−0.549700 + 0.835362i \(0.685258\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.99032 0.520549
\(34\) −7.37298 −1.26446
\(35\) −14.3172 −2.42005
\(36\) 1.00000 0.166667
\(37\) −5.21790 −0.857818 −0.428909 0.903348i \(-0.641102\pi\)
−0.428909 + 0.903348i \(0.641102\pi\)
\(38\) −1.56088 −0.253208
\(39\) 1.00000 0.160128
\(40\) −4.30484 −0.680655
\(41\) −1.29895 −0.202863 −0.101431 0.994843i \(-0.532342\pi\)
−0.101431 + 0.994843i \(0.532342\pi\)
\(42\) −3.32584 −0.513188
\(43\) −2.11927 −0.323185 −0.161593 0.986858i \(-0.551663\pi\)
−0.161593 + 0.986858i \(0.551663\pi\)
\(44\) −2.99032 −0.450808
\(45\) 4.30484 0.641727
\(46\) 3.98856 0.588081
\(47\) 10.0352 1.46379 0.731893 0.681419i \(-0.238637\pi\)
0.731893 + 0.681419i \(0.238637\pi\)
\(48\) −1.00000 −0.144338
\(49\) 4.06120 0.580171
\(50\) −13.5316 −1.91366
\(51\) −7.37298 −1.03242
\(52\) −1.00000 −0.138675
\(53\) −8.84758 −1.21531 −0.607654 0.794202i \(-0.707889\pi\)
−0.607654 + 0.794202i \(0.707889\pi\)
\(54\) 1.00000 0.136083
\(55\) −12.8729 −1.73578
\(56\) 3.32584 0.444434
\(57\) −1.56088 −0.206743
\(58\) 5.10669 0.670541
\(59\) 3.83269 0.498973 0.249487 0.968378i \(-0.419738\pi\)
0.249487 + 0.968378i \(0.419738\pi\)
\(60\) −4.30484 −0.555752
\(61\) 4.47557 0.573039 0.286519 0.958074i \(-0.407502\pi\)
0.286519 + 0.958074i \(0.407502\pi\)
\(62\) 6.12120 0.777393
\(63\) −3.32584 −0.419016
\(64\) 1.00000 0.125000
\(65\) −4.30484 −0.533949
\(66\) −2.99032 −0.368083
\(67\) 1.76088 0.215125 0.107563 0.994198i \(-0.465695\pi\)
0.107563 + 0.994198i \(0.465695\pi\)
\(68\) 7.37298 0.894105
\(69\) 3.98856 0.480166
\(70\) 14.3172 1.71123
\(71\) −10.4599 −1.24136 −0.620682 0.784062i \(-0.713144\pi\)
−0.620682 + 0.784062i \(0.713144\pi\)
\(72\) −1.00000 −0.117851
\(73\) 9.29221 1.08757 0.543785 0.839224i \(-0.316991\pi\)
0.543785 + 0.839224i \(0.316991\pi\)
\(74\) 5.21790 0.606569
\(75\) −13.5316 −1.56250
\(76\) 1.56088 0.179045
\(77\) 9.94533 1.13338
\(78\) −1.00000 −0.113228
\(79\) 12.4331 1.39884 0.699418 0.714713i \(-0.253442\pi\)
0.699418 + 0.714713i \(0.253442\pi\)
\(80\) 4.30484 0.481295
\(81\) 1.00000 0.111111
\(82\) 1.29895 0.143445
\(83\) −7.29642 −0.800886 −0.400443 0.916322i \(-0.631144\pi\)
−0.400443 + 0.916322i \(0.631144\pi\)
\(84\) 3.32584 0.362879
\(85\) 31.7395 3.44263
\(86\) 2.11927 0.228526
\(87\) 5.10669 0.547495
\(88\) 2.99032 0.318770
\(89\) 0.220099 0.0233304 0.0116652 0.999932i \(-0.496287\pi\)
0.0116652 + 0.999932i \(0.496287\pi\)
\(90\) −4.30484 −0.453770
\(91\) 3.32584 0.348643
\(92\) −3.98856 −0.415836
\(93\) 6.12120 0.634739
\(94\) −10.0352 −1.03505
\(95\) 6.71933 0.689389
\(96\) 1.00000 0.102062
\(97\) −10.6956 −1.08597 −0.542985 0.839742i \(-0.682706\pi\)
−0.542985 + 0.839742i \(0.682706\pi\)
\(98\) −4.06120 −0.410243
\(99\) −2.99032 −0.300539
\(100\) 13.5316 1.35316
\(101\) −19.7975 −1.96992 −0.984961 0.172776i \(-0.944726\pi\)
−0.984961 + 0.172776i \(0.944726\pi\)
\(102\) 7.37298 0.730034
\(103\) −1.00000 −0.0985329
\(104\) 1.00000 0.0980581
\(105\) 14.3172 1.39721
\(106\) 8.84758 0.859353
\(107\) 7.21479 0.697481 0.348740 0.937219i \(-0.386610\pi\)
0.348740 + 0.937219i \(0.386610\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −4.48414 −0.429503 −0.214751 0.976669i \(-0.568894\pi\)
−0.214751 + 0.976669i \(0.568894\pi\)
\(110\) 12.8729 1.22738
\(111\) 5.21790 0.495261
\(112\) −3.32584 −0.314262
\(113\) −13.7149 −1.29018 −0.645092 0.764105i \(-0.723181\pi\)
−0.645092 + 0.764105i \(0.723181\pi\)
\(114\) 1.56088 0.146190
\(115\) −17.1701 −1.60112
\(116\) −5.10669 −0.474144
\(117\) −1.00000 −0.0924500
\(118\) −3.83269 −0.352827
\(119\) −24.5213 −2.24787
\(120\) 4.30484 0.392976
\(121\) −2.05796 −0.187088
\(122\) −4.47557 −0.405200
\(123\) 1.29895 0.117123
\(124\) −6.12120 −0.549700
\(125\) 36.7273 3.28499
\(126\) 3.32584 0.296289
\(127\) 6.88336 0.610800 0.305400 0.952224i \(-0.401210\pi\)
0.305400 + 0.952224i \(0.401210\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.11927 0.186591
\(130\) 4.30484 0.377559
\(131\) −4.41826 −0.386025 −0.193013 0.981196i \(-0.561826\pi\)
−0.193013 + 0.981196i \(0.561826\pi\)
\(132\) 2.99032 0.260274
\(133\) −5.19123 −0.450137
\(134\) −1.76088 −0.152116
\(135\) −4.30484 −0.370501
\(136\) −7.37298 −0.632228
\(137\) 1.04246 0.0890637 0.0445318 0.999008i \(-0.485820\pi\)
0.0445318 + 0.999008i \(0.485820\pi\)
\(138\) −3.98856 −0.339529
\(139\) 2.48271 0.210581 0.105290 0.994442i \(-0.466423\pi\)
0.105290 + 0.994442i \(0.466423\pi\)
\(140\) −14.3172 −1.21002
\(141\) −10.0352 −0.845117
\(142\) 10.4599 0.877777
\(143\) 2.99032 0.250063
\(144\) 1.00000 0.0833333
\(145\) −21.9835 −1.82563
\(146\) −9.29221 −0.769028
\(147\) −4.06120 −0.334962
\(148\) −5.21790 −0.428909
\(149\) 11.6489 0.954316 0.477158 0.878818i \(-0.341667\pi\)
0.477158 + 0.878818i \(0.341667\pi\)
\(150\) 13.5316 1.10485
\(151\) −9.39427 −0.764495 −0.382247 0.924060i \(-0.624850\pi\)
−0.382247 + 0.924060i \(0.624850\pi\)
\(152\) −1.56088 −0.126604
\(153\) 7.37298 0.596070
\(154\) −9.94533 −0.801418
\(155\) −26.3508 −2.11655
\(156\) 1.00000 0.0800641
\(157\) 7.98927 0.637613 0.318806 0.947820i \(-0.396718\pi\)
0.318806 + 0.947820i \(0.396718\pi\)
\(158\) −12.4331 −0.989127
\(159\) 8.84758 0.701658
\(160\) −4.30484 −0.340327
\(161\) 13.2653 1.04545
\(162\) −1.00000 −0.0785674
\(163\) −22.6367 −1.77304 −0.886522 0.462686i \(-0.846886\pi\)
−0.886522 + 0.462686i \(0.846886\pi\)
\(164\) −1.29895 −0.101431
\(165\) 12.8729 1.00215
\(166\) 7.29642 0.566312
\(167\) −10.0191 −0.775298 −0.387649 0.921807i \(-0.626713\pi\)
−0.387649 + 0.921807i \(0.626713\pi\)
\(168\) −3.32584 −0.256594
\(169\) 1.00000 0.0769231
\(170\) −31.7395 −2.43431
\(171\) 1.56088 0.119363
\(172\) −2.11927 −0.161593
\(173\) −6.74785 −0.513030 −0.256515 0.966540i \(-0.582574\pi\)
−0.256515 + 0.966540i \(0.582574\pi\)
\(174\) −5.10669 −0.387137
\(175\) −45.0040 −3.40198
\(176\) −2.99032 −0.225404
\(177\) −3.83269 −0.288082
\(178\) −0.220099 −0.0164971
\(179\) 7.52216 0.562232 0.281116 0.959674i \(-0.409295\pi\)
0.281116 + 0.959674i \(0.409295\pi\)
\(180\) 4.30484 0.320864
\(181\) 2.55602 0.189987 0.0949936 0.995478i \(-0.469717\pi\)
0.0949936 + 0.995478i \(0.469717\pi\)
\(182\) −3.32584 −0.246528
\(183\) −4.47557 −0.330844
\(184\) 3.98856 0.294041
\(185\) −22.4622 −1.65146
\(186\) −6.12120 −0.448828
\(187\) −22.0476 −1.61228
\(188\) 10.0352 0.731893
\(189\) 3.32584 0.241919
\(190\) −6.71933 −0.487471
\(191\) −8.59420 −0.621855 −0.310927 0.950434i \(-0.600640\pi\)
−0.310927 + 0.950434i \(0.600640\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 12.7715 0.919313 0.459656 0.888097i \(-0.347973\pi\)
0.459656 + 0.888097i \(0.347973\pi\)
\(194\) 10.6956 0.767897
\(195\) 4.30484 0.308276
\(196\) 4.06120 0.290086
\(197\) −5.83763 −0.415914 −0.207957 0.978138i \(-0.566681\pi\)
−0.207957 + 0.978138i \(0.566681\pi\)
\(198\) 2.99032 0.212513
\(199\) 7.01930 0.497585 0.248792 0.968557i \(-0.419966\pi\)
0.248792 + 0.968557i \(0.419966\pi\)
\(200\) −13.5316 −0.956830
\(201\) −1.76088 −0.124203
\(202\) 19.7975 1.39295
\(203\) 16.9840 1.19204
\(204\) −7.37298 −0.516212
\(205\) −5.59179 −0.390547
\(206\) 1.00000 0.0696733
\(207\) −3.98856 −0.277224
\(208\) −1.00000 −0.0693375
\(209\) −4.66753 −0.322860
\(210\) −14.3172 −0.987980
\(211\) −26.6852 −1.83709 −0.918543 0.395320i \(-0.870634\pi\)
−0.918543 + 0.395320i \(0.870634\pi\)
\(212\) −8.84758 −0.607654
\(213\) 10.4599 0.716702
\(214\) −7.21479 −0.493193
\(215\) −9.12310 −0.622190
\(216\) 1.00000 0.0680414
\(217\) 20.3581 1.38200
\(218\) 4.48414 0.303704
\(219\) −9.29221 −0.627909
\(220\) −12.8729 −0.867888
\(221\) −7.37298 −0.495960
\(222\) −5.21790 −0.350203
\(223\) −18.5806 −1.24425 −0.622125 0.782918i \(-0.713731\pi\)
−0.622125 + 0.782918i \(0.713731\pi\)
\(224\) 3.32584 0.222217
\(225\) 13.5316 0.902108
\(226\) 13.7149 0.912298
\(227\) 1.22947 0.0816030 0.0408015 0.999167i \(-0.487009\pi\)
0.0408015 + 0.999167i \(0.487009\pi\)
\(228\) −1.56088 −0.103372
\(229\) 22.9718 1.51802 0.759008 0.651081i \(-0.225684\pi\)
0.759008 + 0.651081i \(0.225684\pi\)
\(230\) 17.1701 1.13216
\(231\) −9.94533 −0.654355
\(232\) 5.10669 0.335271
\(233\) −0.967978 −0.0634144 −0.0317072 0.999497i \(-0.510094\pi\)
−0.0317072 + 0.999497i \(0.510094\pi\)
\(234\) 1.00000 0.0653720
\(235\) 43.2000 2.81806
\(236\) 3.83269 0.249487
\(237\) −12.4331 −0.807619
\(238\) 24.5213 1.58948
\(239\) −23.9676 −1.55033 −0.775166 0.631757i \(-0.782334\pi\)
−0.775166 + 0.631757i \(0.782334\pi\)
\(240\) −4.30484 −0.277876
\(241\) −22.4990 −1.44929 −0.724645 0.689123i \(-0.757996\pi\)
−0.724645 + 0.689123i \(0.757996\pi\)
\(242\) 2.05796 0.132291
\(243\) −1.00000 −0.0641500
\(244\) 4.47557 0.286519
\(245\) 17.4828 1.11694
\(246\) −1.29895 −0.0828183
\(247\) −1.56088 −0.0993163
\(248\) 6.12120 0.388697
\(249\) 7.29642 0.462392
\(250\) −36.7273 −2.32284
\(251\) 25.7307 1.62411 0.812055 0.583581i \(-0.198349\pi\)
0.812055 + 0.583581i \(0.198349\pi\)
\(252\) −3.32584 −0.209508
\(253\) 11.9271 0.749850
\(254\) −6.88336 −0.431901
\(255\) −31.7395 −1.98760
\(256\) 1.00000 0.0625000
\(257\) 20.1726 1.25833 0.629165 0.777272i \(-0.283397\pi\)
0.629165 + 0.777272i \(0.283397\pi\)
\(258\) −2.11927 −0.131940
\(259\) 17.3539 1.07832
\(260\) −4.30484 −0.266975
\(261\) −5.10669 −0.316096
\(262\) 4.41826 0.272961
\(263\) −22.0673 −1.36073 −0.680364 0.732875i \(-0.738178\pi\)
−0.680364 + 0.732875i \(0.738178\pi\)
\(264\) −2.99032 −0.184042
\(265\) −38.0874 −2.33969
\(266\) 5.19123 0.318295
\(267\) −0.220099 −0.0134698
\(268\) 1.76088 0.107563
\(269\) 10.9730 0.669038 0.334519 0.942389i \(-0.391426\pi\)
0.334519 + 0.942389i \(0.391426\pi\)
\(270\) 4.30484 0.261984
\(271\) −18.4643 −1.12163 −0.560813 0.827942i \(-0.689512\pi\)
−0.560813 + 0.827942i \(0.689512\pi\)
\(272\) 7.37298 0.447052
\(273\) −3.32584 −0.201289
\(274\) −1.04246 −0.0629775
\(275\) −40.4639 −2.44007
\(276\) 3.98856 0.240083
\(277\) −14.5293 −0.872984 −0.436492 0.899708i \(-0.643779\pi\)
−0.436492 + 0.899708i \(0.643779\pi\)
\(278\) −2.48271 −0.148903
\(279\) −6.12120 −0.366467
\(280\) 14.3172 0.855616
\(281\) −15.7883 −0.941854 −0.470927 0.882172i \(-0.656080\pi\)
−0.470927 + 0.882172i \(0.656080\pi\)
\(282\) 10.0352 0.597588
\(283\) 18.1693 1.08005 0.540026 0.841649i \(-0.318415\pi\)
0.540026 + 0.841649i \(0.318415\pi\)
\(284\) −10.4599 −0.620682
\(285\) −6.71933 −0.398019
\(286\) −2.99032 −0.176822
\(287\) 4.32011 0.255008
\(288\) −1.00000 −0.0589256
\(289\) 37.3608 2.19769
\(290\) 21.9835 1.29091
\(291\) 10.6956 0.626986
\(292\) 9.29221 0.543785
\(293\) −3.82927 −0.223708 −0.111854 0.993725i \(-0.535679\pi\)
−0.111854 + 0.993725i \(0.535679\pi\)
\(294\) 4.06120 0.236854
\(295\) 16.4991 0.960614
\(296\) 5.21790 0.303284
\(297\) 2.99032 0.173516
\(298\) −11.6489 −0.674803
\(299\) 3.98856 0.230664
\(300\) −13.5316 −0.781249
\(301\) 7.04834 0.406259
\(302\) 9.39427 0.540579
\(303\) 19.7975 1.13734
\(304\) 1.56088 0.0895225
\(305\) 19.2666 1.10320
\(306\) −7.37298 −0.421485
\(307\) −16.8905 −0.963992 −0.481996 0.876173i \(-0.660088\pi\)
−0.481996 + 0.876173i \(0.660088\pi\)
\(308\) 9.94533 0.566688
\(309\) 1.00000 0.0568880
\(310\) 26.3508 1.49662
\(311\) 2.23173 0.126550 0.0632748 0.997996i \(-0.479846\pi\)
0.0632748 + 0.997996i \(0.479846\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −5.72536 −0.323616 −0.161808 0.986822i \(-0.551733\pi\)
−0.161808 + 0.986822i \(0.551733\pi\)
\(314\) −7.98927 −0.450860
\(315\) −14.3172 −0.806682
\(316\) 12.4331 0.699418
\(317\) 4.04068 0.226947 0.113474 0.993541i \(-0.463802\pi\)
0.113474 + 0.993541i \(0.463802\pi\)
\(318\) −8.84758 −0.496147
\(319\) 15.2707 0.854993
\(320\) 4.30484 0.240648
\(321\) −7.21479 −0.402691
\(322\) −13.2653 −0.739247
\(323\) 11.5083 0.640340
\(324\) 1.00000 0.0555556
\(325\) −13.5316 −0.750600
\(326\) 22.6367 1.25373
\(327\) 4.48414 0.247974
\(328\) 1.29895 0.0717227
\(329\) −33.3755 −1.84005
\(330\) −12.8729 −0.708627
\(331\) 11.2057 0.615922 0.307961 0.951399i \(-0.400353\pi\)
0.307961 + 0.951399i \(0.400353\pi\)
\(332\) −7.29642 −0.400443
\(333\) −5.21790 −0.285939
\(334\) 10.0191 0.548219
\(335\) 7.58028 0.414155
\(336\) 3.32584 0.181439
\(337\) −15.9410 −0.868363 −0.434182 0.900825i \(-0.642962\pi\)
−0.434182 + 0.900825i \(0.642962\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 13.7149 0.744888
\(340\) 31.7395 1.72131
\(341\) 18.3044 0.991237
\(342\) −1.56088 −0.0844027
\(343\) 9.77398 0.527745
\(344\) 2.11927 0.114263
\(345\) 17.1701 0.924408
\(346\) 6.74785 0.362767
\(347\) 24.4975 1.31510 0.657548 0.753413i \(-0.271594\pi\)
0.657548 + 0.753413i \(0.271594\pi\)
\(348\) 5.10669 0.273747
\(349\) −4.60506 −0.246503 −0.123252 0.992375i \(-0.539332\pi\)
−0.123252 + 0.992375i \(0.539332\pi\)
\(350\) 45.0040 2.40556
\(351\) 1.00000 0.0533761
\(352\) 2.99032 0.159385
\(353\) 7.92700 0.421912 0.210956 0.977496i \(-0.432342\pi\)
0.210956 + 0.977496i \(0.432342\pi\)
\(354\) 3.83269 0.203705
\(355\) −45.0283 −2.38985
\(356\) 0.220099 0.0116652
\(357\) 24.5213 1.29781
\(358\) −7.52216 −0.397558
\(359\) −16.5493 −0.873438 −0.436719 0.899598i \(-0.643860\pi\)
−0.436719 + 0.899598i \(0.643860\pi\)
\(360\) −4.30484 −0.226885
\(361\) −16.5637 −0.871771
\(362\) −2.55602 −0.134341
\(363\) 2.05796 0.108015
\(364\) 3.32584 0.174321
\(365\) 40.0014 2.09377
\(366\) 4.47557 0.233942
\(367\) 2.43300 0.127002 0.0635009 0.997982i \(-0.479773\pi\)
0.0635009 + 0.997982i \(0.479773\pi\)
\(368\) −3.98856 −0.207918
\(369\) −1.29895 −0.0676208
\(370\) 22.4622 1.16776
\(371\) 29.4256 1.52770
\(372\) 6.12120 0.317370
\(373\) 18.4891 0.957330 0.478665 0.877998i \(-0.341121\pi\)
0.478665 + 0.877998i \(0.341121\pi\)
\(374\) 22.0476 1.14005
\(375\) −36.7273 −1.89659
\(376\) −10.0352 −0.517527
\(377\) 5.10669 0.263008
\(378\) −3.32584 −0.171063
\(379\) 8.19688 0.421046 0.210523 0.977589i \(-0.432483\pi\)
0.210523 + 0.977589i \(0.432483\pi\)
\(380\) 6.71933 0.344694
\(381\) −6.88336 −0.352645
\(382\) 8.59420 0.439718
\(383\) 1.76663 0.0902704 0.0451352 0.998981i \(-0.485628\pi\)
0.0451352 + 0.998981i \(0.485628\pi\)
\(384\) 1.00000 0.0510310
\(385\) 42.8130 2.18195
\(386\) −12.7715 −0.650052
\(387\) −2.11927 −0.107728
\(388\) −10.6956 −0.542985
\(389\) −13.1999 −0.669260 −0.334630 0.942350i \(-0.608611\pi\)
−0.334630 + 0.942350i \(0.608611\pi\)
\(390\) −4.30484 −0.217984
\(391\) −29.4076 −1.48721
\(392\) −4.06120 −0.205122
\(393\) 4.41826 0.222872
\(394\) 5.83763 0.294095
\(395\) 53.5226 2.69301
\(396\) −2.99032 −0.150269
\(397\) 7.07627 0.355148 0.177574 0.984107i \(-0.443175\pi\)
0.177574 + 0.984107i \(0.443175\pi\)
\(398\) −7.01930 −0.351846
\(399\) 5.19123 0.259887
\(400\) 13.5316 0.676581
\(401\) 33.5184 1.67383 0.836914 0.547334i \(-0.184357\pi\)
0.836914 + 0.547334i \(0.184357\pi\)
\(402\) 1.76088 0.0878245
\(403\) 6.12120 0.304919
\(404\) −19.7975 −0.984961
\(405\) 4.30484 0.213909
\(406\) −16.9840 −0.842903
\(407\) 15.6032 0.773423
\(408\) 7.37298 0.365017
\(409\) −26.8161 −1.32597 −0.662986 0.748632i \(-0.730711\pi\)
−0.662986 + 0.748632i \(0.730711\pi\)
\(410\) 5.59179 0.276159
\(411\) −1.04246 −0.0514209
\(412\) −1.00000 −0.0492665
\(413\) −12.7469 −0.627234
\(414\) 3.98856 0.196027
\(415\) −31.4099 −1.54185
\(416\) 1.00000 0.0490290
\(417\) −2.48271 −0.121579
\(418\) 4.66753 0.228296
\(419\) −29.2983 −1.43131 −0.715657 0.698452i \(-0.753872\pi\)
−0.715657 + 0.698452i \(0.753872\pi\)
\(420\) 14.3172 0.698607
\(421\) −34.2832 −1.67086 −0.835429 0.549598i \(-0.814781\pi\)
−0.835429 + 0.549598i \(0.814781\pi\)
\(422\) 26.6852 1.29902
\(423\) 10.0352 0.487929
\(424\) 8.84758 0.429676
\(425\) 99.7684 4.83948
\(426\) −10.4599 −0.506785
\(427\) −14.8850 −0.720337
\(428\) 7.21479 0.348740
\(429\) −2.99032 −0.144374
\(430\) 9.12310 0.439955
\(431\) 7.96742 0.383777 0.191889 0.981417i \(-0.438539\pi\)
0.191889 + 0.981417i \(0.438539\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 4.95655 0.238196 0.119098 0.992882i \(-0.462000\pi\)
0.119098 + 0.992882i \(0.462000\pi\)
\(434\) −20.3581 −0.977221
\(435\) 21.9835 1.05403
\(436\) −4.48414 −0.214751
\(437\) −6.22566 −0.297814
\(438\) 9.29221 0.443999
\(439\) −31.5089 −1.50384 −0.751918 0.659256i \(-0.770871\pi\)
−0.751918 + 0.659256i \(0.770871\pi\)
\(440\) 12.8729 0.613689
\(441\) 4.06120 0.193390
\(442\) 7.37298 0.350697
\(443\) 31.4030 1.49200 0.746000 0.665946i \(-0.231972\pi\)
0.746000 + 0.665946i \(0.231972\pi\)
\(444\) 5.21790 0.247631
\(445\) 0.947490 0.0449154
\(446\) 18.5806 0.879818
\(447\) −11.6489 −0.550975
\(448\) −3.32584 −0.157131
\(449\) −28.1392 −1.32797 −0.663985 0.747746i \(-0.731136\pi\)
−0.663985 + 0.747746i \(0.731136\pi\)
\(450\) −13.5316 −0.637887
\(451\) 3.88429 0.182904
\(452\) −13.7149 −0.645092
\(453\) 9.39427 0.441381
\(454\) −1.22947 −0.0577021
\(455\) 14.3172 0.671200
\(456\) 1.56088 0.0730948
\(457\) 27.3601 1.27985 0.639925 0.768437i \(-0.278965\pi\)
0.639925 + 0.768437i \(0.278965\pi\)
\(458\) −22.9718 −1.07340
\(459\) −7.37298 −0.344141
\(460\) −17.1701 −0.800561
\(461\) −14.1704 −0.659983 −0.329992 0.943984i \(-0.607046\pi\)
−0.329992 + 0.943984i \(0.607046\pi\)
\(462\) 9.94533 0.462699
\(463\) −42.2795 −1.96490 −0.982448 0.186535i \(-0.940274\pi\)
−0.982448 + 0.186535i \(0.940274\pi\)
\(464\) −5.10669 −0.237072
\(465\) 26.3508 1.22199
\(466\) 0.967978 0.0448407
\(467\) −2.38852 −0.110528 −0.0552638 0.998472i \(-0.517600\pi\)
−0.0552638 + 0.998472i \(0.517600\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −5.85639 −0.270423
\(470\) −43.2000 −1.99267
\(471\) −7.98927 −0.368126
\(472\) −3.83269 −0.176414
\(473\) 6.33729 0.291389
\(474\) 12.4331 0.571073
\(475\) 21.1212 0.969108
\(476\) −24.5213 −1.12393
\(477\) −8.84758 −0.405103
\(478\) 23.9676 1.09625
\(479\) −31.2618 −1.42839 −0.714195 0.699947i \(-0.753207\pi\)
−0.714195 + 0.699947i \(0.753207\pi\)
\(480\) 4.30484 0.196488
\(481\) 5.21790 0.237916
\(482\) 22.4990 1.02480
\(483\) −13.2653 −0.603593
\(484\) −2.05796 −0.0935439
\(485\) −46.0427 −2.09069
\(486\) 1.00000 0.0453609
\(487\) 9.37604 0.424869 0.212434 0.977175i \(-0.431861\pi\)
0.212434 + 0.977175i \(0.431861\pi\)
\(488\) −4.47557 −0.202600
\(489\) 22.6367 1.02367
\(490\) −17.4828 −0.789793
\(491\) −27.2778 −1.23103 −0.615515 0.788125i \(-0.711052\pi\)
−0.615515 + 0.788125i \(0.711052\pi\)
\(492\) 1.29895 0.0585614
\(493\) −37.6515 −1.69574
\(494\) 1.56088 0.0702273
\(495\) −12.8729 −0.578592
\(496\) −6.12120 −0.274850
\(497\) 34.7880 1.56046
\(498\) −7.29642 −0.326961
\(499\) −6.22981 −0.278885 −0.139442 0.990230i \(-0.544531\pi\)
−0.139442 + 0.990230i \(0.544531\pi\)
\(500\) 36.7273 1.64249
\(501\) 10.0191 0.447619
\(502\) −25.7307 −1.14842
\(503\) 29.8429 1.33063 0.665314 0.746564i \(-0.268298\pi\)
0.665314 + 0.746564i \(0.268298\pi\)
\(504\) 3.32584 0.148145
\(505\) −85.2249 −3.79246
\(506\) −11.9271 −0.530224
\(507\) −1.00000 −0.0444116
\(508\) 6.88336 0.305400
\(509\) 3.79641 0.168273 0.0841365 0.996454i \(-0.473187\pi\)
0.0841365 + 0.996454i \(0.473187\pi\)
\(510\) 31.7395 1.40545
\(511\) −30.9044 −1.36713
\(512\) −1.00000 −0.0441942
\(513\) −1.56088 −0.0689145
\(514\) −20.1726 −0.889773
\(515\) −4.30484 −0.189694
\(516\) 2.11927 0.0932955
\(517\) −30.0085 −1.31977
\(518\) −17.3539 −0.762486
\(519\) 6.74785 0.296198
\(520\) 4.30484 0.188780
\(521\) 3.96799 0.173841 0.0869203 0.996215i \(-0.472297\pi\)
0.0869203 + 0.996215i \(0.472297\pi\)
\(522\) 5.10669 0.223514
\(523\) −38.8836 −1.70026 −0.850130 0.526573i \(-0.823477\pi\)
−0.850130 + 0.526573i \(0.823477\pi\)
\(524\) −4.41826 −0.193013
\(525\) 45.0040 1.96414
\(526\) 22.0673 0.962180
\(527\) −45.1315 −1.96596
\(528\) 2.99032 0.130137
\(529\) −7.09137 −0.308321
\(530\) 38.0874 1.65441
\(531\) 3.83269 0.166324
\(532\) −5.19123 −0.225068
\(533\) 1.29895 0.0562639
\(534\) 0.220099 0.00952461
\(535\) 31.0585 1.34278
\(536\) −1.76088 −0.0760582
\(537\) −7.52216 −0.324605
\(538\) −10.9730 −0.473082
\(539\) −12.1443 −0.523092
\(540\) −4.30484 −0.185251
\(541\) −8.71614 −0.374736 −0.187368 0.982290i \(-0.559996\pi\)
−0.187368 + 0.982290i \(0.559996\pi\)
\(542\) 18.4643 0.793110
\(543\) −2.55602 −0.109689
\(544\) −7.37298 −0.316114
\(545\) −19.3035 −0.826871
\(546\) 3.32584 0.142333
\(547\) −5.82757 −0.249169 −0.124584 0.992209i \(-0.539760\pi\)
−0.124584 + 0.992209i \(0.539760\pi\)
\(548\) 1.04246 0.0445318
\(549\) 4.47557 0.191013
\(550\) 40.4639 1.72539
\(551\) −7.97092 −0.339573
\(552\) −3.98856 −0.169764
\(553\) −41.3506 −1.75841
\(554\) 14.5293 0.617293
\(555\) 22.4622 0.953468
\(556\) 2.48271 0.105290
\(557\) 27.4278 1.16215 0.581077 0.813848i \(-0.302631\pi\)
0.581077 + 0.813848i \(0.302631\pi\)
\(558\) 6.12120 0.259131
\(559\) 2.11927 0.0896354
\(560\) −14.3172 −0.605012
\(561\) 22.0476 0.930850
\(562\) 15.7883 0.665991
\(563\) 14.8220 0.624674 0.312337 0.949971i \(-0.398888\pi\)
0.312337 + 0.949971i \(0.398888\pi\)
\(564\) −10.0352 −0.422559
\(565\) −59.0402 −2.48384
\(566\) −18.1693 −0.763712
\(567\) −3.32584 −0.139672
\(568\) 10.4599 0.438889
\(569\) 19.0046 0.796714 0.398357 0.917230i \(-0.369581\pi\)
0.398357 + 0.917230i \(0.369581\pi\)
\(570\) 6.71933 0.281442
\(571\) −4.68766 −0.196173 −0.0980863 0.995178i \(-0.531272\pi\)
−0.0980863 + 0.995178i \(0.531272\pi\)
\(572\) 2.99032 0.125032
\(573\) 8.59420 0.359028
\(574\) −4.32011 −0.180318
\(575\) −53.9717 −2.25078
\(576\) 1.00000 0.0416667
\(577\) −34.3823 −1.43135 −0.715676 0.698433i \(-0.753881\pi\)
−0.715676 + 0.698433i \(0.753881\pi\)
\(578\) −37.3608 −1.55400
\(579\) −12.7715 −0.530765
\(580\) −21.9835 −0.912814
\(581\) 24.2667 1.00675
\(582\) −10.6956 −0.443346
\(583\) 26.4571 1.09574
\(584\) −9.29221 −0.384514
\(585\) −4.30484 −0.177983
\(586\) 3.82927 0.158185
\(587\) −35.2121 −1.45336 −0.726680 0.686976i \(-0.758938\pi\)
−0.726680 + 0.686976i \(0.758938\pi\)
\(588\) −4.06120 −0.167481
\(589\) −9.55445 −0.393684
\(590\) −16.4991 −0.679257
\(591\) 5.83763 0.240128
\(592\) −5.21790 −0.214454
\(593\) 10.1964 0.418717 0.209358 0.977839i \(-0.432862\pi\)
0.209358 + 0.977839i \(0.432862\pi\)
\(594\) −2.99032 −0.122694
\(595\) −105.560 −4.32755
\(596\) 11.6489 0.477158
\(597\) −7.01930 −0.287281
\(598\) −3.98856 −0.163104
\(599\) −10.1752 −0.415746 −0.207873 0.978156i \(-0.566654\pi\)
−0.207873 + 0.978156i \(0.566654\pi\)
\(600\) 13.5316 0.552426
\(601\) −32.2687 −1.31627 −0.658133 0.752902i \(-0.728654\pi\)
−0.658133 + 0.752902i \(0.728654\pi\)
\(602\) −7.04834 −0.287269
\(603\) 1.76088 0.0717084
\(604\) −9.39427 −0.382247
\(605\) −8.85920 −0.360178
\(606\) −19.7975 −0.804217
\(607\) 21.8134 0.885380 0.442690 0.896675i \(-0.354024\pi\)
0.442690 + 0.896675i \(0.354024\pi\)
\(608\) −1.56088 −0.0633020
\(609\) −16.9840 −0.688227
\(610\) −19.2666 −0.780083
\(611\) −10.0352 −0.405981
\(612\) 7.37298 0.298035
\(613\) 12.3559 0.499049 0.249524 0.968369i \(-0.419726\pi\)
0.249524 + 0.968369i \(0.419726\pi\)
\(614\) 16.8905 0.681645
\(615\) 5.59179 0.225483
\(616\) −9.94533 −0.400709
\(617\) 39.8625 1.60480 0.802401 0.596785i \(-0.203556\pi\)
0.802401 + 0.596785i \(0.203556\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 24.8162 0.997448 0.498724 0.866761i \(-0.333802\pi\)
0.498724 + 0.866761i \(0.333802\pi\)
\(620\) −26.3508 −1.05827
\(621\) 3.98856 0.160055
\(622\) −2.23173 −0.0894840
\(623\) −0.732014 −0.0293275
\(624\) 1.00000 0.0400320
\(625\) 90.4468 3.61787
\(626\) 5.72536 0.228831
\(627\) 4.66753 0.186403
\(628\) 7.98927 0.318806
\(629\) −38.4715 −1.53396
\(630\) 14.3172 0.570411
\(631\) −33.5627 −1.33611 −0.668055 0.744112i \(-0.732873\pi\)
−0.668055 + 0.744112i \(0.732873\pi\)
\(632\) −12.4331 −0.494563
\(633\) 26.6852 1.06064
\(634\) −4.04068 −0.160476
\(635\) 29.6318 1.17590
\(636\) 8.84758 0.350829
\(637\) −4.06120 −0.160911
\(638\) −15.2707 −0.604571
\(639\) −10.4599 −0.413788
\(640\) −4.30484 −0.170164
\(641\) −28.5203 −1.12649 −0.563243 0.826291i \(-0.690447\pi\)
−0.563243 + 0.826291i \(0.690447\pi\)
\(642\) 7.21479 0.284745
\(643\) 30.9929 1.22224 0.611120 0.791538i \(-0.290719\pi\)
0.611120 + 0.791538i \(0.290719\pi\)
\(644\) 13.2653 0.522726
\(645\) 9.12310 0.359222
\(646\) −11.5083 −0.452789
\(647\) −8.18516 −0.321792 −0.160896 0.986971i \(-0.551438\pi\)
−0.160896 + 0.986971i \(0.551438\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −11.4610 −0.449883
\(650\) 13.5316 0.530754
\(651\) −20.3581 −0.797898
\(652\) −22.6367 −0.886522
\(653\) −21.0639 −0.824294 −0.412147 0.911117i \(-0.635221\pi\)
−0.412147 + 0.911117i \(0.635221\pi\)
\(654\) −4.48414 −0.175344
\(655\) −19.0199 −0.743169
\(656\) −1.29895 −0.0507156
\(657\) 9.29221 0.362524
\(658\) 33.3755 1.30111
\(659\) 42.0600 1.63842 0.819212 0.573490i \(-0.194411\pi\)
0.819212 + 0.573490i \(0.194411\pi\)
\(660\) 12.8729 0.501075
\(661\) −13.7964 −0.536619 −0.268310 0.963333i \(-0.586465\pi\)
−0.268310 + 0.963333i \(0.586465\pi\)
\(662\) −11.2057 −0.435523
\(663\) 7.37298 0.286343
\(664\) 7.29642 0.283156
\(665\) −22.3474 −0.866595
\(666\) 5.21790 0.202190
\(667\) 20.3684 0.788666
\(668\) −10.0191 −0.387649
\(669\) 18.5806 0.718368
\(670\) −7.58028 −0.292852
\(671\) −13.3834 −0.516661
\(672\) −3.32584 −0.128297
\(673\) −14.6214 −0.563615 −0.281807 0.959471i \(-0.590934\pi\)
−0.281807 + 0.959471i \(0.590934\pi\)
\(674\) 15.9410 0.614026
\(675\) −13.5316 −0.520833
\(676\) 1.00000 0.0384615
\(677\) −6.64862 −0.255527 −0.127764 0.991805i \(-0.540780\pi\)
−0.127764 + 0.991805i \(0.540780\pi\)
\(678\) −13.7149 −0.526716
\(679\) 35.5717 1.36512
\(680\) −31.7395 −1.21715
\(681\) −1.22947 −0.0471135
\(682\) −18.3044 −0.700911
\(683\) 42.8630 1.64011 0.820053 0.572288i \(-0.193944\pi\)
0.820053 + 0.572288i \(0.193944\pi\)
\(684\) 1.56088 0.0596817
\(685\) 4.48764 0.171464
\(686\) −9.77398 −0.373172
\(687\) −22.9718 −0.876427
\(688\) −2.11927 −0.0807963
\(689\) 8.84758 0.337066
\(690\) −17.1701 −0.653655
\(691\) 17.9411 0.682511 0.341256 0.939971i \(-0.389148\pi\)
0.341256 + 0.939971i \(0.389148\pi\)
\(692\) −6.74785 −0.256515
\(693\) 9.94533 0.377792
\(694\) −24.4975 −0.929913
\(695\) 10.6877 0.405406
\(696\) −5.10669 −0.193569
\(697\) −9.57716 −0.362761
\(698\) 4.60506 0.174304
\(699\) 0.967978 0.0366123
\(700\) −45.0040 −1.70099
\(701\) 37.7810 1.42697 0.713485 0.700671i \(-0.247116\pi\)
0.713485 + 0.700671i \(0.247116\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −8.14451 −0.307176
\(704\) −2.99032 −0.112702
\(705\) −43.2000 −1.62700
\(706\) −7.92700 −0.298337
\(707\) 65.8432 2.47629
\(708\) −3.83269 −0.144041
\(709\) −20.9024 −0.785007 −0.392504 0.919750i \(-0.628391\pi\)
−0.392504 + 0.919750i \(0.628391\pi\)
\(710\) 45.0283 1.68988
\(711\) 12.4331 0.466279
\(712\) −0.220099 −0.00824856
\(713\) 24.4148 0.914341
\(714\) −24.5213 −0.917688
\(715\) 12.8729 0.481418
\(716\) 7.52216 0.281116
\(717\) 23.9676 0.895085
\(718\) 16.5493 0.617614
\(719\) 25.2877 0.943071 0.471536 0.881847i \(-0.343700\pi\)
0.471536 + 0.881847i \(0.343700\pi\)
\(720\) 4.30484 0.160432
\(721\) 3.32584 0.123861
\(722\) 16.5637 0.616436
\(723\) 22.4990 0.836748
\(724\) 2.55602 0.0949936
\(725\) −69.1018 −2.56638
\(726\) −2.05796 −0.0763782
\(727\) 27.9994 1.03844 0.519220 0.854641i \(-0.326223\pi\)
0.519220 + 0.854641i \(0.326223\pi\)
\(728\) −3.32584 −0.123264
\(729\) 1.00000 0.0370370
\(730\) −40.0014 −1.48052
\(731\) −15.6253 −0.577923
\(732\) −4.47557 −0.165422
\(733\) −47.3618 −1.74935 −0.874674 0.484712i \(-0.838924\pi\)
−0.874674 + 0.484712i \(0.838924\pi\)
\(734\) −2.43300 −0.0898038
\(735\) −17.4828 −0.644863
\(736\) 3.98856 0.147020
\(737\) −5.26559 −0.193960
\(738\) 1.29895 0.0478152
\(739\) −13.5407 −0.498103 −0.249051 0.968490i \(-0.580119\pi\)
−0.249051 + 0.968490i \(0.580119\pi\)
\(740\) −22.4622 −0.825728
\(741\) 1.56088 0.0573403
\(742\) −29.4256 −1.08025
\(743\) −23.4603 −0.860676 −0.430338 0.902668i \(-0.641606\pi\)
−0.430338 + 0.902668i \(0.641606\pi\)
\(744\) −6.12120 −0.224414
\(745\) 50.1467 1.83723
\(746\) −18.4891 −0.676935
\(747\) −7.29642 −0.266962
\(748\) −22.0476 −0.806140
\(749\) −23.9952 −0.876767
\(750\) 36.7273 1.34109
\(751\) −21.3600 −0.779436 −0.389718 0.920934i \(-0.627428\pi\)
−0.389718 + 0.920934i \(0.627428\pi\)
\(752\) 10.0352 0.365947
\(753\) −25.7307 −0.937680
\(754\) −5.10669 −0.185975
\(755\) −40.4408 −1.47179
\(756\) 3.32584 0.120960
\(757\) −23.0970 −0.839475 −0.419737 0.907646i \(-0.637878\pi\)
−0.419737 + 0.907646i \(0.637878\pi\)
\(758\) −8.19688 −0.297724
\(759\) −11.9271 −0.432926
\(760\) −6.71933 −0.243736
\(761\) −36.3536 −1.31782 −0.658909 0.752222i \(-0.728982\pi\)
−0.658909 + 0.752222i \(0.728982\pi\)
\(762\) 6.88336 0.249358
\(763\) 14.9135 0.539906
\(764\) −8.59420 −0.310927
\(765\) 31.7395 1.14754
\(766\) −1.76663 −0.0638308
\(767\) −3.83269 −0.138390
\(768\) −1.00000 −0.0360844
\(769\) 30.5206 1.10060 0.550301 0.834966i \(-0.314513\pi\)
0.550301 + 0.834966i \(0.314513\pi\)
\(770\) −42.8130 −1.54287
\(771\) −20.1726 −0.726497
\(772\) 12.7715 0.459656
\(773\) −36.6077 −1.31669 −0.658344 0.752717i \(-0.728743\pi\)
−0.658344 + 0.752717i \(0.728743\pi\)
\(774\) 2.11927 0.0761754
\(775\) −82.8298 −2.97533
\(776\) 10.6956 0.383949
\(777\) −17.3539 −0.622568
\(778\) 13.1999 0.473238
\(779\) −2.02751 −0.0726431
\(780\) 4.30484 0.154138
\(781\) 31.2786 1.11923
\(782\) 29.4076 1.05161
\(783\) 5.10669 0.182498
\(784\) 4.06120 0.145043
\(785\) 34.3925 1.22752
\(786\) −4.41826 −0.157594
\(787\) 1.66558 0.0593714 0.0296857 0.999559i \(-0.490549\pi\)
0.0296857 + 0.999559i \(0.490549\pi\)
\(788\) −5.83763 −0.207957
\(789\) 22.0673 0.785616
\(790\) −53.5226 −1.90425
\(791\) 45.6134 1.62182
\(792\) 2.99032 0.106257
\(793\) −4.47557 −0.158932
\(794\) −7.07627 −0.251128
\(795\) 38.0874 1.35082
\(796\) 7.01930 0.248792
\(797\) 42.0267 1.48866 0.744331 0.667811i \(-0.232768\pi\)
0.744331 + 0.667811i \(0.232768\pi\)
\(798\) −5.19123 −0.183768
\(799\) 73.9894 2.61756
\(800\) −13.5316 −0.478415
\(801\) 0.220099 0.00777682
\(802\) −33.5184 −1.18358
\(803\) −27.7867 −0.980572
\(804\) −1.76088 −0.0621013
\(805\) 57.1050 2.01269
\(806\) −6.12120 −0.215610
\(807\) −10.9730 −0.386270
\(808\) 19.7975 0.696473
\(809\) 38.2429 1.34455 0.672275 0.740302i \(-0.265317\pi\)
0.672275 + 0.740302i \(0.265317\pi\)
\(810\) −4.30484 −0.151257
\(811\) −10.4223 −0.365978 −0.182989 0.983115i \(-0.558577\pi\)
−0.182989 + 0.983115i \(0.558577\pi\)
\(812\) 16.9840 0.596022
\(813\) 18.4643 0.647572
\(814\) −15.6032 −0.546892
\(815\) −97.4474 −3.41343
\(816\) −7.37298 −0.258106
\(817\) −3.30792 −0.115729
\(818\) 26.8161 0.937603
\(819\) 3.32584 0.116214
\(820\) −5.59179 −0.195274
\(821\) 14.6432 0.511052 0.255526 0.966802i \(-0.417751\pi\)
0.255526 + 0.966802i \(0.417751\pi\)
\(822\) 1.04246 0.0363601
\(823\) −27.0111 −0.941547 −0.470774 0.882254i \(-0.656025\pi\)
−0.470774 + 0.882254i \(0.656025\pi\)
\(824\) 1.00000 0.0348367
\(825\) 40.4639 1.40877
\(826\) 12.7469 0.443521
\(827\) 8.35498 0.290531 0.145266 0.989393i \(-0.453596\pi\)
0.145266 + 0.989393i \(0.453596\pi\)
\(828\) −3.98856 −0.138612
\(829\) −32.0899 −1.11453 −0.557264 0.830335i \(-0.688149\pi\)
−0.557264 + 0.830335i \(0.688149\pi\)
\(830\) 31.4099 1.09025
\(831\) 14.5293 0.504017
\(832\) −1.00000 −0.0346688
\(833\) 29.9431 1.03747
\(834\) 2.48271 0.0859692
\(835\) −43.1304 −1.49259
\(836\) −4.66753 −0.161430
\(837\) 6.12120 0.211580
\(838\) 29.2983 1.01209
\(839\) −25.5252 −0.881229 −0.440615 0.897696i \(-0.645239\pi\)
−0.440615 + 0.897696i \(0.645239\pi\)
\(840\) −14.3172 −0.493990
\(841\) −2.92171 −0.100749
\(842\) 34.2832 1.18148
\(843\) 15.7883 0.543780
\(844\) −26.6852 −0.918543
\(845\) 4.30484 0.148091
\(846\) −10.0352 −0.345018
\(847\) 6.84446 0.235178
\(848\) −8.84758 −0.303827
\(849\) −18.1693 −0.623568
\(850\) −99.7684 −3.42203
\(851\) 20.8119 0.713424
\(852\) 10.4599 0.358351
\(853\) −39.7735 −1.36182 −0.680910 0.732367i \(-0.738416\pi\)
−0.680910 + 0.732367i \(0.738416\pi\)
\(854\) 14.8850 0.509355
\(855\) 6.71933 0.229796
\(856\) −7.21479 −0.246597
\(857\) −20.8272 −0.711445 −0.355723 0.934592i \(-0.615765\pi\)
−0.355723 + 0.934592i \(0.615765\pi\)
\(858\) 2.99032 0.102088
\(859\) 28.1578 0.960733 0.480367 0.877068i \(-0.340504\pi\)
0.480367 + 0.877068i \(0.340504\pi\)
\(860\) −9.12310 −0.311095
\(861\) −4.32011 −0.147229
\(862\) −7.96742 −0.271371
\(863\) 34.1892 1.16382 0.581908 0.813255i \(-0.302307\pi\)
0.581908 + 0.813255i \(0.302307\pi\)
\(864\) 1.00000 0.0340207
\(865\) −29.0484 −0.987675
\(866\) −4.95655 −0.168430
\(867\) −37.3608 −1.26884
\(868\) 20.3581 0.691000
\(869\) −37.1791 −1.26121
\(870\) −21.9835 −0.745310
\(871\) −1.76088 −0.0596650
\(872\) 4.48414 0.151852
\(873\) −10.6956 −0.361990
\(874\) 6.22566 0.210586
\(875\) −122.149 −4.12939
\(876\) −9.29221 −0.313955
\(877\) −22.8923 −0.773017 −0.386509 0.922286i \(-0.626319\pi\)
−0.386509 + 0.922286i \(0.626319\pi\)
\(878\) 31.5089 1.06337
\(879\) 3.82927 0.129158
\(880\) −12.8729 −0.433944
\(881\) −41.5807 −1.40089 −0.700444 0.713707i \(-0.747015\pi\)
−0.700444 + 0.713707i \(0.747015\pi\)
\(882\) −4.06120 −0.136748
\(883\) 8.47194 0.285103 0.142552 0.989787i \(-0.454469\pi\)
0.142552 + 0.989787i \(0.454469\pi\)
\(884\) −7.37298 −0.247980
\(885\) −16.4991 −0.554611
\(886\) −31.4030 −1.05500
\(887\) 28.3749 0.952735 0.476368 0.879246i \(-0.341953\pi\)
0.476368 + 0.879246i \(0.341953\pi\)
\(888\) −5.21790 −0.175101
\(889\) −22.8929 −0.767805
\(890\) −0.947490 −0.0317599
\(891\) −2.99032 −0.100180
\(892\) −18.5806 −0.622125
\(893\) 15.6638 0.524167
\(894\) 11.6489 0.389598
\(895\) 32.3817 1.08240
\(896\) 3.32584 0.111108
\(897\) −3.98856 −0.133174
\(898\) 28.1392 0.939016
\(899\) 31.2591 1.04255
\(900\) 13.5316 0.451054
\(901\) −65.2330 −2.17323
\(902\) −3.88429 −0.129333
\(903\) −7.04834 −0.234554
\(904\) 13.7149 0.456149
\(905\) 11.0032 0.365760
\(906\) −9.39427 −0.312104
\(907\) −7.70609 −0.255877 −0.127938 0.991782i \(-0.540836\pi\)
−0.127938 + 0.991782i \(0.540836\pi\)
\(908\) 1.22947 0.0408015
\(909\) −19.7975 −0.656641
\(910\) −14.3172 −0.474610
\(911\) −38.2938 −1.26873 −0.634364 0.773034i \(-0.718738\pi\)
−0.634364 + 0.773034i \(0.718738\pi\)
\(912\) −1.56088 −0.0516859
\(913\) 21.8187 0.722092
\(914\) −27.3601 −0.904991
\(915\) −19.2666 −0.636935
\(916\) 22.9718 0.759008
\(917\) 14.6944 0.485253
\(918\) 7.37298 0.243345
\(919\) 12.2865 0.405294 0.202647 0.979252i \(-0.435046\pi\)
0.202647 + 0.979252i \(0.435046\pi\)
\(920\) 17.1701 0.566082
\(921\) 16.8905 0.556561
\(922\) 14.1704 0.466679
\(923\) 10.4599 0.344293
\(924\) −9.94533 −0.327177
\(925\) −70.6067 −2.32153
\(926\) 42.2795 1.38939
\(927\) −1.00000 −0.0328443
\(928\) 5.10669 0.167635
\(929\) −16.9963 −0.557629 −0.278815 0.960345i \(-0.589942\pi\)
−0.278815 + 0.960345i \(0.589942\pi\)
\(930\) −26.3508 −0.864076
\(931\) 6.33904 0.207754
\(932\) −0.967978 −0.0317072
\(933\) −2.23173 −0.0730634
\(934\) 2.38852 0.0781548
\(935\) −94.9113 −3.10393
\(936\) 1.00000 0.0326860
\(937\) −48.7121 −1.59135 −0.795677 0.605721i \(-0.792885\pi\)
−0.795677 + 0.605721i \(0.792885\pi\)
\(938\) 5.85639 0.191218
\(939\) 5.72536 0.186840
\(940\) 43.2000 1.40903
\(941\) −55.2320 −1.80051 −0.900255 0.435362i \(-0.856620\pi\)
−0.900255 + 0.435362i \(0.856620\pi\)
\(942\) 7.98927 0.260304
\(943\) 5.18096 0.168715
\(944\) 3.83269 0.124743
\(945\) 14.3172 0.465738
\(946\) −6.33729 −0.206043
\(947\) 54.4116 1.76814 0.884070 0.467354i \(-0.154793\pi\)
0.884070 + 0.467354i \(0.154793\pi\)
\(948\) −12.4331 −0.403809
\(949\) −9.29221 −0.301638
\(950\) −21.1212 −0.685263
\(951\) −4.04068 −0.131028
\(952\) 24.5213 0.794741
\(953\) −40.6163 −1.31569 −0.657846 0.753153i \(-0.728532\pi\)
−0.657846 + 0.753153i \(0.728532\pi\)
\(954\) 8.84758 0.286451
\(955\) −36.9966 −1.19718
\(956\) −23.9676 −0.775166
\(957\) −15.2707 −0.493630
\(958\) 31.2618 1.01002
\(959\) −3.46707 −0.111957
\(960\) −4.30484 −0.138938
\(961\) 6.46911 0.208681
\(962\) −5.21790 −0.168232
\(963\) 7.21479 0.232494
\(964\) −22.4990 −0.724645
\(965\) 54.9792 1.76984
\(966\) 13.2653 0.426804
\(967\) −16.5401 −0.531894 −0.265947 0.963988i \(-0.585685\pi\)
−0.265947 + 0.963988i \(0.585685\pi\)
\(968\) 2.05796 0.0661455
\(969\) −11.5083 −0.369701
\(970\) 46.0427 1.47834
\(971\) −41.7009 −1.33825 −0.669123 0.743152i \(-0.733330\pi\)
−0.669123 + 0.743152i \(0.733330\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −8.25709 −0.264710
\(974\) −9.37604 −0.300428
\(975\) 13.5316 0.433359
\(976\) 4.47557 0.143260
\(977\) 4.78150 0.152974 0.0764868 0.997071i \(-0.475630\pi\)
0.0764868 + 0.997071i \(0.475630\pi\)
\(978\) −22.6367 −0.723842
\(979\) −0.658167 −0.0210351
\(980\) 17.4828 0.558468
\(981\) −4.48414 −0.143168
\(982\) 27.2778 0.870470
\(983\) −40.8081 −1.30158 −0.650788 0.759260i \(-0.725561\pi\)
−0.650788 + 0.759260i \(0.725561\pi\)
\(984\) −1.29895 −0.0414091
\(985\) −25.1300 −0.800710
\(986\) 37.6515 1.19907
\(987\) 33.3755 1.06235
\(988\) −1.56088 −0.0496582
\(989\) 8.45282 0.268784
\(990\) 12.8729 0.409126
\(991\) 58.8569 1.86965 0.934826 0.355106i \(-0.115555\pi\)
0.934826 + 0.355106i \(0.115555\pi\)
\(992\) 6.12120 0.194348
\(993\) −11.2057 −0.355603
\(994\) −34.7880 −1.10341
\(995\) 30.2169 0.957941
\(996\) 7.29642 0.231196
\(997\) −18.7423 −0.593574 −0.296787 0.954944i \(-0.595915\pi\)
−0.296787 + 0.954944i \(0.595915\pi\)
\(998\) 6.22981 0.197201
\(999\) 5.21790 0.165087
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 8034.2.a.s.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.s.1.10 10 1.1 even 1 trivial