Properties

Label 5610.2.a.bo.1.2
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $1$
Dimension $2$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 10 \) 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 1.2
Root \(-2.70156\) of defining polynomial
Character \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +4.70156 q^{13} -2.70156 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.70156 q^{19} -1.00000 q^{20} -2.70156 q^{21} -1.00000 q^{22} -8.70156 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.70156 q^{26} -1.00000 q^{27} +2.70156 q^{28} +2.00000 q^{29} -1.00000 q^{30} +0.701562 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -2.70156 q^{35} +1.00000 q^{36} +10.7016 q^{37} +4.70156 q^{38} -4.70156 q^{39} +1.00000 q^{40} -9.40312 q^{41} +2.70156 q^{42} -7.40312 q^{43} +1.00000 q^{44} -1.00000 q^{45} +8.70156 q^{46} -9.40312 q^{47} -1.00000 q^{48} +0.298438 q^{49} -1.00000 q^{50} -1.00000 q^{51} +4.70156 q^{52} +2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -2.70156 q^{56} +4.70156 q^{57} -2.00000 q^{58} -0.596876 q^{59} +1.00000 q^{60} +1.29844 q^{61} -0.701562 q^{62} +2.70156 q^{63} +1.00000 q^{64} -4.70156 q^{65} +1.00000 q^{66} -14.7016 q^{67} +1.00000 q^{68} +8.70156 q^{69} +2.70156 q^{70} -12.8062 q^{71} -1.00000 q^{72} -8.00000 q^{73} -10.7016 q^{74} -1.00000 q^{75} -4.70156 q^{76} +2.70156 q^{77} +4.70156 q^{78} -5.40312 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.40312 q^{82} -3.29844 q^{83} -2.70156 q^{84} -1.00000 q^{85} +7.40312 q^{86} -2.00000 q^{87} -1.00000 q^{88} +14.0000 q^{89} +1.00000 q^{90} +12.7016 q^{91} -8.70156 q^{92} -0.701562 q^{93} +9.40312 q^{94} +4.70156 q^{95} +1.00000 q^{96} +3.29844 q^{97} -0.298438 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} + q^{21} - 2 q^{22} - 11 q^{23} + 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - q^{28} + 4 q^{29} - 2 q^{30} - 5 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} + q^{35} + 2 q^{36} + 15 q^{37} + 3 q^{38} - 3 q^{39} + 2 q^{40} - 6 q^{41} - q^{42} - 2 q^{43} + 2 q^{44} - 2 q^{45} + 11 q^{46} - 6 q^{47} - 2 q^{48} + 7 q^{49} - 2 q^{50} - 2 q^{51} + 3 q^{52} + 4 q^{53} + 2 q^{54} - 2 q^{55} + q^{56} + 3 q^{57} - 4 q^{58} - 14 q^{59} + 2 q^{60} + 9 q^{61} + 5 q^{62} - q^{63} + 2 q^{64} - 3 q^{65} + 2 q^{66} - 23 q^{67} + 2 q^{68} + 11 q^{69} - q^{70} - 2 q^{72} - 16 q^{73} - 15 q^{74} - 2 q^{75} - 3 q^{76} - q^{77} + 3 q^{78} + 2 q^{79} - 2 q^{80} + 2 q^{81} + 6 q^{82} - 13 q^{83} + q^{84} - 2 q^{85} + 2 q^{86} - 4 q^{87} - 2 q^{88} + 28 q^{89} + 2 q^{90} + 19 q^{91} - 11 q^{92} + 5 q^{93} + 6 q^{94} + 3 q^{95} + 2 q^{96} + 13 q^{97} - 7 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 2.70156 1.02109 0.510547 0.859850i \(-0.329443\pi\)
0.510547 + 0.859850i \(0.329443\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) −1.00000 −0.288675
\(13\) 4.70156 1.30398 0.651989 0.758228i \(-0.273935\pi\)
0.651989 + 0.758228i \(0.273935\pi\)
\(14\) −2.70156 −0.722023
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) −4.70156 −1.07861 −0.539306 0.842110i \(-0.681313\pi\)
−0.539306 + 0.842110i \(0.681313\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.70156 −0.589529
\(22\) −1.00000 −0.213201
\(23\) −8.70156 −1.81440 −0.907201 0.420698i \(-0.861785\pi\)
−0.907201 + 0.420698i \(0.861785\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −4.70156 −0.922052
\(27\) −1.00000 −0.192450
\(28\) 2.70156 0.510547
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0.701562 0.126004 0.0630021 0.998013i \(-0.479933\pi\)
0.0630021 + 0.998013i \(0.479933\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −1.00000 −0.171499
\(35\) −2.70156 −0.456647
\(36\) 1.00000 0.166667
\(37\) 10.7016 1.75933 0.879663 0.475598i \(-0.157768\pi\)
0.879663 + 0.475598i \(0.157768\pi\)
\(38\) 4.70156 0.762694
\(39\) −4.70156 −0.752852
\(40\) 1.00000 0.158114
\(41\) −9.40312 −1.46852 −0.734261 0.678868i \(-0.762471\pi\)
−0.734261 + 0.678868i \(0.762471\pi\)
\(42\) 2.70156 0.416860
\(43\) −7.40312 −1.12897 −0.564483 0.825445i \(-0.690924\pi\)
−0.564483 + 0.825445i \(0.690924\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) 8.70156 1.28298
\(47\) −9.40312 −1.37159 −0.685793 0.727796i \(-0.740545\pi\)
−0.685793 + 0.727796i \(0.740545\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0.298438 0.0426340
\(50\) −1.00000 −0.141421
\(51\) −1.00000 −0.140028
\(52\) 4.70156 0.651989
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) −2.70156 −0.361011
\(57\) 4.70156 0.622737
\(58\) −2.00000 −0.262613
\(59\) −0.596876 −0.0777066 −0.0388533 0.999245i \(-0.512371\pi\)
−0.0388533 + 0.999245i \(0.512371\pi\)
\(60\) 1.00000 0.129099
\(61\) 1.29844 0.166248 0.0831240 0.996539i \(-0.473510\pi\)
0.0831240 + 0.996539i \(0.473510\pi\)
\(62\) −0.701562 −0.0890985
\(63\) 2.70156 0.340365
\(64\) 1.00000 0.125000
\(65\) −4.70156 −0.583157
\(66\) 1.00000 0.123091
\(67\) −14.7016 −1.79608 −0.898041 0.439912i \(-0.855010\pi\)
−0.898041 + 0.439912i \(0.855010\pi\)
\(68\) 1.00000 0.121268
\(69\) 8.70156 1.04754
\(70\) 2.70156 0.322898
\(71\) −12.8062 −1.51982 −0.759911 0.650027i \(-0.774758\pi\)
−0.759911 + 0.650027i \(0.774758\pi\)
\(72\) −1.00000 −0.117851
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) −10.7016 −1.24403
\(75\) −1.00000 −0.115470
\(76\) −4.70156 −0.539306
\(77\) 2.70156 0.307872
\(78\) 4.70156 0.532347
\(79\) −5.40312 −0.607899 −0.303949 0.952688i \(-0.598305\pi\)
−0.303949 + 0.952688i \(0.598305\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 9.40312 1.03840
\(83\) −3.29844 −0.362051 −0.181025 0.983478i \(-0.557942\pi\)
−0.181025 + 0.983478i \(0.557942\pi\)
\(84\) −2.70156 −0.294765
\(85\) −1.00000 −0.108465
\(86\) 7.40312 0.798299
\(87\) −2.00000 −0.214423
\(88\) −1.00000 −0.106600
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 1.00000 0.105409
\(91\) 12.7016 1.33149
\(92\) −8.70156 −0.907201
\(93\) −0.701562 −0.0727486
\(94\) 9.40312 0.969858
\(95\) 4.70156 0.482370
\(96\) 1.00000 0.102062
\(97\) 3.29844 0.334906 0.167453 0.985880i \(-0.446446\pi\)
0.167453 + 0.985880i \(0.446446\pi\)
\(98\) −0.298438 −0.0301468
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) 9.40312 0.935646 0.467823 0.883822i \(-0.345039\pi\)
0.467823 + 0.883822i \(0.345039\pi\)
\(102\) 1.00000 0.0990148
\(103\) −2.10469 −0.207381 −0.103690 0.994610i \(-0.533065\pi\)
−0.103690 + 0.994610i \(0.533065\pi\)
\(104\) −4.70156 −0.461026
\(105\) 2.70156 0.263645
\(106\) −2.00000 −0.194257
\(107\) 5.40312 0.522340 0.261170 0.965293i \(-0.415892\pi\)
0.261170 + 0.965293i \(0.415892\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −4.10469 −0.393158 −0.196579 0.980488i \(-0.562983\pi\)
−0.196579 + 0.980488i \(0.562983\pi\)
\(110\) 1.00000 0.0953463
\(111\) −10.7016 −1.01575
\(112\) 2.70156 0.255274
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −4.70156 −0.440342
\(115\) 8.70156 0.811425
\(116\) 2.00000 0.185695
\(117\) 4.70156 0.434660
\(118\) 0.596876 0.0549469
\(119\) 2.70156 0.247652
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −1.29844 −0.117555
\(123\) 9.40312 0.847851
\(124\) 0.701562 0.0630021
\(125\) −1.00000 −0.0894427
\(126\) −2.70156 −0.240674
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.40312 0.651809
\(130\) 4.70156 0.412354
\(131\) −6.10469 −0.533369 −0.266684 0.963784i \(-0.585928\pi\)
−0.266684 + 0.963784i \(0.585928\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −12.7016 −1.10137
\(134\) 14.7016 1.27002
\(135\) 1.00000 0.0860663
\(136\) −1.00000 −0.0857493
\(137\) 0.104686 0.00894396 0.00447198 0.999990i \(-0.498577\pi\)
0.00447198 + 0.999990i \(0.498577\pi\)
\(138\) −8.70156 −0.740726
\(139\) 21.4031 1.81539 0.907695 0.419631i \(-0.137841\pi\)
0.907695 + 0.419631i \(0.137841\pi\)
\(140\) −2.70156 −0.228324
\(141\) 9.40312 0.791886
\(142\) 12.8062 1.07468
\(143\) 4.70156 0.393164
\(144\) 1.00000 0.0833333
\(145\) −2.00000 −0.166091
\(146\) 8.00000 0.662085
\(147\) −0.298438 −0.0246147
\(148\) 10.7016 0.879663
\(149\) −12.7016 −1.04055 −0.520276 0.853998i \(-0.674171\pi\)
−0.520276 + 0.853998i \(0.674171\pi\)
\(150\) 1.00000 0.0816497
\(151\) 15.5078 1.26201 0.631004 0.775780i \(-0.282643\pi\)
0.631004 + 0.775780i \(0.282643\pi\)
\(152\) 4.70156 0.381347
\(153\) 1.00000 0.0808452
\(154\) −2.70156 −0.217698
\(155\) −0.701562 −0.0563508
\(156\) −4.70156 −0.376426
\(157\) −12.0000 −0.957704 −0.478852 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 5.40312 0.429849
\(159\) −2.00000 −0.158610
\(160\) 1.00000 0.0790569
\(161\) −23.5078 −1.85268
\(162\) −1.00000 −0.0785674
\(163\) 10.8062 0.846411 0.423205 0.906034i \(-0.360905\pi\)
0.423205 + 0.906034i \(0.360905\pi\)
\(164\) −9.40312 −0.734261
\(165\) 1.00000 0.0778499
\(166\) 3.29844 0.256008
\(167\) 6.80625 0.526683 0.263342 0.964703i \(-0.415175\pi\)
0.263342 + 0.964703i \(0.415175\pi\)
\(168\) 2.70156 0.208430
\(169\) 9.10469 0.700360
\(170\) 1.00000 0.0766965
\(171\) −4.70156 −0.359537
\(172\) −7.40312 −0.564483
\(173\) −25.5078 −1.93932 −0.969661 0.244452i \(-0.921392\pi\)
−0.969661 + 0.244452i \(0.921392\pi\)
\(174\) 2.00000 0.151620
\(175\) 2.70156 0.204219
\(176\) 1.00000 0.0753778
\(177\) 0.596876 0.0448639
\(178\) −14.0000 −1.04934
\(179\) 16.1047 1.20372 0.601860 0.798601i \(-0.294426\pi\)
0.601860 + 0.798601i \(0.294426\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 3.40312 0.252952 0.126476 0.991970i \(-0.459633\pi\)
0.126476 + 0.991970i \(0.459633\pi\)
\(182\) −12.7016 −0.941502
\(183\) −1.29844 −0.0959833
\(184\) 8.70156 0.641488
\(185\) −10.7016 −0.786794
\(186\) 0.701562 0.0514410
\(187\) 1.00000 0.0731272
\(188\) −9.40312 −0.685793
\(189\) −2.70156 −0.196510
\(190\) −4.70156 −0.341087
\(191\) −1.19375 −0.0863768 −0.0431884 0.999067i \(-0.513752\pi\)
−0.0431884 + 0.999067i \(0.513752\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −12.0000 −0.863779 −0.431889 0.901927i \(-0.642153\pi\)
−0.431889 + 0.901927i \(0.642153\pi\)
\(194\) −3.29844 −0.236814
\(195\) 4.70156 0.336686
\(196\) 0.298438 0.0213170
\(197\) −22.7016 −1.61742 −0.808710 0.588208i \(-0.799834\pi\)
−0.808710 + 0.588208i \(0.799834\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 8.70156 0.616837 0.308419 0.951251i \(-0.400200\pi\)
0.308419 + 0.951251i \(0.400200\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 14.7016 1.03697
\(202\) −9.40312 −0.661602
\(203\) 5.40312 0.379225
\(204\) −1.00000 −0.0700140
\(205\) 9.40312 0.656743
\(206\) 2.10469 0.146640
\(207\) −8.70156 −0.604800
\(208\) 4.70156 0.325995
\(209\) −4.70156 −0.325214
\(210\) −2.70156 −0.186425
\(211\) −16.2094 −1.11590 −0.557950 0.829875i \(-0.688412\pi\)
−0.557950 + 0.829875i \(0.688412\pi\)
\(212\) 2.00000 0.137361
\(213\) 12.8062 0.877470
\(214\) −5.40312 −0.369350
\(215\) 7.40312 0.504889
\(216\) 1.00000 0.0680414
\(217\) 1.89531 0.128662
\(218\) 4.10469 0.278004
\(219\) 8.00000 0.540590
\(220\) −1.00000 −0.0674200
\(221\) 4.70156 0.316261
\(222\) 10.7016 0.718242
\(223\) −19.5078 −1.30634 −0.653170 0.757211i \(-0.726561\pi\)
−0.653170 + 0.757211i \(0.726561\pi\)
\(224\) −2.70156 −0.180506
\(225\) 1.00000 0.0666667
\(226\) −2.00000 −0.133038
\(227\) −24.2094 −1.60683 −0.803416 0.595418i \(-0.796987\pi\)
−0.803416 + 0.595418i \(0.796987\pi\)
\(228\) 4.70156 0.311369
\(229\) 1.29844 0.0858032 0.0429016 0.999079i \(-0.486340\pi\)
0.0429016 + 0.999079i \(0.486340\pi\)
\(230\) −8.70156 −0.573764
\(231\) −2.70156 −0.177750
\(232\) −2.00000 −0.131306
\(233\) 12.8062 0.838965 0.419483 0.907763i \(-0.362212\pi\)
0.419483 + 0.907763i \(0.362212\pi\)
\(234\) −4.70156 −0.307351
\(235\) 9.40312 0.613392
\(236\) −0.596876 −0.0388533
\(237\) 5.40312 0.350971
\(238\) −2.70156 −0.175116
\(239\) −9.40312 −0.608238 −0.304119 0.952634i \(-0.598362\pi\)
−0.304119 + 0.952634i \(0.598362\pi\)
\(240\) 1.00000 0.0645497
\(241\) 10.7016 0.689348 0.344674 0.938722i \(-0.387989\pi\)
0.344674 + 0.938722i \(0.387989\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 1.29844 0.0831240
\(245\) −0.298438 −0.0190665
\(246\) −9.40312 −0.599521
\(247\) −22.1047 −1.40649
\(248\) −0.701562 −0.0445492
\(249\) 3.29844 0.209030
\(250\) 1.00000 0.0632456
\(251\) −11.8953 −0.750826 −0.375413 0.926858i \(-0.622499\pi\)
−0.375413 + 0.926858i \(0.622499\pi\)
\(252\) 2.70156 0.170182
\(253\) −8.70156 −0.547063
\(254\) −4.00000 −0.250982
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 27.6125 1.72242 0.861210 0.508249i \(-0.169707\pi\)
0.861210 + 0.508249i \(0.169707\pi\)
\(258\) −7.40312 −0.460898
\(259\) 28.9109 1.79644
\(260\) −4.70156 −0.291579
\(261\) 2.00000 0.123797
\(262\) 6.10469 0.377149
\(263\) −22.1047 −1.36303 −0.681517 0.731803i \(-0.738679\pi\)
−0.681517 + 0.731803i \(0.738679\pi\)
\(264\) 1.00000 0.0615457
\(265\) −2.00000 −0.122859
\(266\) 12.7016 0.778783
\(267\) −14.0000 −0.856786
\(268\) −14.7016 −0.898041
\(269\) −5.50781 −0.335817 −0.167909 0.985803i \(-0.553701\pi\)
−0.167909 + 0.985803i \(0.553701\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −10.8062 −0.656433 −0.328216 0.944603i \(-0.606448\pi\)
−0.328216 + 0.944603i \(0.606448\pi\)
\(272\) 1.00000 0.0606339
\(273\) −12.7016 −0.768734
\(274\) −0.104686 −0.00632433
\(275\) 1.00000 0.0603023
\(276\) 8.70156 0.523772
\(277\) 0.596876 0.0358628 0.0179314 0.999839i \(-0.494292\pi\)
0.0179314 + 0.999839i \(0.494292\pi\)
\(278\) −21.4031 −1.28367
\(279\) 0.701562 0.0420014
\(280\) 2.70156 0.161449
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −9.40312 −0.559948
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) −12.8062 −0.759911
\(285\) −4.70156 −0.278497
\(286\) −4.70156 −0.278009
\(287\) −25.4031 −1.49950
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 2.00000 0.117444
\(291\) −3.29844 −0.193358
\(292\) −8.00000 −0.468165
\(293\) 8.59688 0.502235 0.251117 0.967957i \(-0.419202\pi\)
0.251117 + 0.967957i \(0.419202\pi\)
\(294\) 0.298438 0.0174053
\(295\) 0.596876 0.0347515
\(296\) −10.7016 −0.622016
\(297\) −1.00000 −0.0580259
\(298\) 12.7016 0.735782
\(299\) −40.9109 −2.36594
\(300\) −1.00000 −0.0577350
\(301\) −20.0000 −1.15278
\(302\) −15.5078 −0.892374
\(303\) −9.40312 −0.540195
\(304\) −4.70156 −0.269653
\(305\) −1.29844 −0.0743483
\(306\) −1.00000 −0.0571662
\(307\) −15.4031 −0.879103 −0.439551 0.898217i \(-0.644863\pi\)
−0.439551 + 0.898217i \(0.644863\pi\)
\(308\) 2.70156 0.153936
\(309\) 2.10469 0.119731
\(310\) 0.701562 0.0398461
\(311\) 20.8062 1.17981 0.589907 0.807471i \(-0.299164\pi\)
0.589907 + 0.807471i \(0.299164\pi\)
\(312\) 4.70156 0.266174
\(313\) −24.9109 −1.40805 −0.704025 0.710176i \(-0.748616\pi\)
−0.704025 + 0.710176i \(0.748616\pi\)
\(314\) 12.0000 0.677199
\(315\) −2.70156 −0.152216
\(316\) −5.40312 −0.303949
\(317\) 14.0000 0.786318 0.393159 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(318\) 2.00000 0.112154
\(319\) 2.00000 0.111979
\(320\) −1.00000 −0.0559017
\(321\) −5.40312 −0.301573
\(322\) 23.5078 1.31004
\(323\) −4.70156 −0.261602
\(324\) 1.00000 0.0555556
\(325\) 4.70156 0.260796
\(326\) −10.8062 −0.598503
\(327\) 4.10469 0.226990
\(328\) 9.40312 0.519201
\(329\) −25.4031 −1.40052
\(330\) −1.00000 −0.0550482
\(331\) 29.6125 1.62765 0.813825 0.581110i \(-0.197381\pi\)
0.813825 + 0.581110i \(0.197381\pi\)
\(332\) −3.29844 −0.181025
\(333\) 10.7016 0.586442
\(334\) −6.80625 −0.372421
\(335\) 14.7016 0.803232
\(336\) −2.70156 −0.147382
\(337\) 10.8062 0.588654 0.294327 0.955705i \(-0.404905\pi\)
0.294327 + 0.955705i \(0.404905\pi\)
\(338\) −9.10469 −0.495230
\(339\) −2.00000 −0.108625
\(340\) −1.00000 −0.0542326
\(341\) 0.701562 0.0379917
\(342\) 4.70156 0.254231
\(343\) −18.1047 −0.977561
\(344\) 7.40312 0.399150
\(345\) −8.70156 −0.468476
\(346\) 25.5078 1.37131
\(347\) 5.40312 0.290055 0.145027 0.989428i \(-0.453673\pi\)
0.145027 + 0.989428i \(0.453673\pi\)
\(348\) −2.00000 −0.107211
\(349\) −31.6125 −1.69218 −0.846089 0.533042i \(-0.821049\pi\)
−0.846089 + 0.533042i \(0.821049\pi\)
\(350\) −2.70156 −0.144405
\(351\) −4.70156 −0.250951
\(352\) −1.00000 −0.0533002
\(353\) 29.5078 1.57054 0.785271 0.619152i \(-0.212524\pi\)
0.785271 + 0.619152i \(0.212524\pi\)
\(354\) −0.596876 −0.0317236
\(355\) 12.8062 0.679685
\(356\) 14.0000 0.741999
\(357\) −2.70156 −0.142982
\(358\) −16.1047 −0.851159
\(359\) 35.0156 1.84805 0.924027 0.382327i \(-0.124877\pi\)
0.924027 + 0.382327i \(0.124877\pi\)
\(360\) 1.00000 0.0527046
\(361\) 3.10469 0.163405
\(362\) −3.40312 −0.178864
\(363\) −1.00000 −0.0524864
\(364\) 12.7016 0.665743
\(365\) 8.00000 0.418739
\(366\) 1.29844 0.0678704
\(367\) −19.4031 −1.01283 −0.506417 0.862288i \(-0.669030\pi\)
−0.506417 + 0.862288i \(0.669030\pi\)
\(368\) −8.70156 −0.453600
\(369\) −9.40312 −0.489507
\(370\) 10.7016 0.556348
\(371\) 5.40312 0.280516
\(372\) −0.701562 −0.0363743
\(373\) −2.59688 −0.134461 −0.0672306 0.997737i \(-0.521416\pi\)
−0.0672306 + 0.997737i \(0.521416\pi\)
\(374\) −1.00000 −0.0517088
\(375\) 1.00000 0.0516398
\(376\) 9.40312 0.484929
\(377\) 9.40312 0.484286
\(378\) 2.70156 0.138953
\(379\) 30.3141 1.55713 0.778564 0.627565i \(-0.215948\pi\)
0.778564 + 0.627565i \(0.215948\pi\)
\(380\) 4.70156 0.241185
\(381\) −4.00000 −0.204926
\(382\) 1.19375 0.0610776
\(383\) −22.5969 −1.15465 −0.577323 0.816516i \(-0.695903\pi\)
−0.577323 + 0.816516i \(0.695903\pi\)
\(384\) 1.00000 0.0510310
\(385\) −2.70156 −0.137684
\(386\) 12.0000 0.610784
\(387\) −7.40312 −0.376322
\(388\) 3.29844 0.167453
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) −4.70156 −0.238073
\(391\) −8.70156 −0.440057
\(392\) −0.298438 −0.0150734
\(393\) 6.10469 0.307941
\(394\) 22.7016 1.14369
\(395\) 5.40312 0.271861
\(396\) 1.00000 0.0502519
\(397\) −12.8062 −0.642727 −0.321364 0.946956i \(-0.604141\pi\)
−0.321364 + 0.946956i \(0.604141\pi\)
\(398\) −8.70156 −0.436170
\(399\) 12.7016 0.635873
\(400\) 1.00000 0.0500000
\(401\) 6.10469 0.304853 0.152427 0.988315i \(-0.451291\pi\)
0.152427 + 0.988315i \(0.451291\pi\)
\(402\) −14.7016 −0.733247
\(403\) 3.29844 0.164307
\(404\) 9.40312 0.467823
\(405\) −1.00000 −0.0496904
\(406\) −5.40312 −0.268153
\(407\) 10.7016 0.530457
\(408\) 1.00000 0.0495074
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) −9.40312 −0.464387
\(411\) −0.104686 −0.00516380
\(412\) −2.10469 −0.103690
\(413\) −1.61250 −0.0793458
\(414\) 8.70156 0.427658
\(415\) 3.29844 0.161914
\(416\) −4.70156 −0.230513
\(417\) −21.4031 −1.04812
\(418\) 4.70156 0.229961
\(419\) −5.19375 −0.253731 −0.126866 0.991920i \(-0.540492\pi\)
−0.126866 + 0.991920i \(0.540492\pi\)
\(420\) 2.70156 0.131823
\(421\) −14.7016 −0.716510 −0.358255 0.933624i \(-0.616628\pi\)
−0.358255 + 0.933624i \(0.616628\pi\)
\(422\) 16.2094 0.789060
\(423\) −9.40312 −0.457196
\(424\) −2.00000 −0.0971286
\(425\) 1.00000 0.0485071
\(426\) −12.8062 −0.620465
\(427\) 3.50781 0.169755
\(428\) 5.40312 0.261170
\(429\) −4.70156 −0.226994
\(430\) −7.40312 −0.357010
\(431\) 2.20937 0.106422 0.0532109 0.998583i \(-0.483054\pi\)
0.0532109 + 0.998583i \(0.483054\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) −1.89531 −0.0909780
\(435\) 2.00000 0.0958927
\(436\) −4.10469 −0.196579
\(437\) 40.9109 1.95704
\(438\) −8.00000 −0.382255
\(439\) 40.2094 1.91909 0.959544 0.281558i \(-0.0908511\pi\)
0.959544 + 0.281558i \(0.0908511\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0.298438 0.0142113
\(442\) −4.70156 −0.223631
\(443\) −24.2094 −1.15022 −0.575111 0.818075i \(-0.695041\pi\)
−0.575111 + 0.818075i \(0.695041\pi\)
\(444\) −10.7016 −0.507874
\(445\) −14.0000 −0.663664
\(446\) 19.5078 0.923722
\(447\) 12.7016 0.600763
\(448\) 2.70156 0.127637
\(449\) −27.2984 −1.28829 −0.644146 0.764902i \(-0.722787\pi\)
−0.644146 + 0.764902i \(0.722787\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −9.40312 −0.442776
\(452\) 2.00000 0.0940721
\(453\) −15.5078 −0.728621
\(454\) 24.2094 1.13620
\(455\) −12.7016 −0.595458
\(456\) −4.70156 −0.220171
\(457\) −16.1047 −0.753345 −0.376673 0.926346i \(-0.622932\pi\)
−0.376673 + 0.926346i \(0.622932\pi\)
\(458\) −1.29844 −0.0606720
\(459\) −1.00000 −0.0466760
\(460\) 8.70156 0.405712
\(461\) −37.4031 −1.74204 −0.871019 0.491250i \(-0.836540\pi\)
−0.871019 + 0.491250i \(0.836540\pi\)
\(462\) 2.70156 0.125688
\(463\) −24.7016 −1.14798 −0.573989 0.818863i \(-0.694605\pi\)
−0.573989 + 0.818863i \(0.694605\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0.701562 0.0325342
\(466\) −12.8062 −0.593238
\(467\) −34.8062 −1.61064 −0.805321 0.592840i \(-0.798007\pi\)
−0.805321 + 0.592840i \(0.798007\pi\)
\(468\) 4.70156 0.217330
\(469\) −39.7172 −1.83397
\(470\) −9.40312 −0.433734
\(471\) 12.0000 0.552931
\(472\) 0.596876 0.0274734
\(473\) −7.40312 −0.340396
\(474\) −5.40312 −0.248174
\(475\) −4.70156 −0.215722
\(476\) 2.70156 0.123826
\(477\) 2.00000 0.0915737
\(478\) 9.40312 0.430089
\(479\) −14.9109 −0.681298 −0.340649 0.940191i \(-0.610647\pi\)
−0.340649 + 0.940191i \(0.610647\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 50.3141 2.29412
\(482\) −10.7016 −0.487443
\(483\) 23.5078 1.06964
\(484\) 1.00000 0.0454545
\(485\) −3.29844 −0.149774
\(486\) 1.00000 0.0453609
\(487\) −18.2094 −0.825145 −0.412573 0.910925i \(-0.635370\pi\)
−0.412573 + 0.910925i \(0.635370\pi\)
\(488\) −1.29844 −0.0587775
\(489\) −10.8062 −0.488675
\(490\) 0.298438 0.0134820
\(491\) −12.8062 −0.577938 −0.288969 0.957338i \(-0.593312\pi\)
−0.288969 + 0.957338i \(0.593312\pi\)
\(492\) 9.40312 0.423926
\(493\) 2.00000 0.0900755
\(494\) 22.1047 0.994537
\(495\) −1.00000 −0.0449467
\(496\) 0.701562 0.0315011
\(497\) −34.5969 −1.55188
\(498\) −3.29844 −0.147807
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −6.80625 −0.304081
\(502\) 11.8953 0.530914
\(503\) 10.8062 0.481827 0.240913 0.970547i \(-0.422553\pi\)
0.240913 + 0.970547i \(0.422553\pi\)
\(504\) −2.70156 −0.120337
\(505\) −9.40312 −0.418434
\(506\) 8.70156 0.386832
\(507\) −9.10469 −0.404353
\(508\) 4.00000 0.177471
\(509\) −8.20937 −0.363874 −0.181937 0.983310i \(-0.558237\pi\)
−0.181937 + 0.983310i \(0.558237\pi\)
\(510\) −1.00000 −0.0442807
\(511\) −21.6125 −0.956081
\(512\) −1.00000 −0.0441942
\(513\) 4.70156 0.207579
\(514\) −27.6125 −1.21794
\(515\) 2.10469 0.0927436
\(516\) 7.40312 0.325904
\(517\) −9.40312 −0.413549
\(518\) −28.9109 −1.27027
\(519\) 25.5078 1.11967
\(520\) 4.70156 0.206177
\(521\) 30.1047 1.31891 0.659455 0.751744i \(-0.270787\pi\)
0.659455 + 0.751744i \(0.270787\pi\)
\(522\) −2.00000 −0.0875376
\(523\) −22.2094 −0.971148 −0.485574 0.874196i \(-0.661389\pi\)
−0.485574 + 0.874196i \(0.661389\pi\)
\(524\) −6.10469 −0.266684
\(525\) −2.70156 −0.117906
\(526\) 22.1047 0.963810
\(527\) 0.701562 0.0305605
\(528\) −1.00000 −0.0435194
\(529\) 52.7172 2.29205
\(530\) 2.00000 0.0868744
\(531\) −0.596876 −0.0259022
\(532\) −12.7016 −0.550683
\(533\) −44.2094 −1.91492
\(534\) 14.0000 0.605839
\(535\) −5.40312 −0.233597
\(536\) 14.7016 0.635011
\(537\) −16.1047 −0.694969
\(538\) 5.50781 0.237459
\(539\) 0.298438 0.0128546
\(540\) 1.00000 0.0430331
\(541\) 16.8062 0.722557 0.361279 0.932458i \(-0.382340\pi\)
0.361279 + 0.932458i \(0.382340\pi\)
\(542\) 10.8062 0.464168
\(543\) −3.40312 −0.146042
\(544\) −1.00000 −0.0428746
\(545\) 4.10469 0.175825
\(546\) 12.7016 0.543577
\(547\) −10.1047 −0.432045 −0.216023 0.976388i \(-0.569308\pi\)
−0.216023 + 0.976388i \(0.569308\pi\)
\(548\) 0.104686 0.00447198
\(549\) 1.29844 0.0554160
\(550\) −1.00000 −0.0426401
\(551\) −9.40312 −0.400587
\(552\) −8.70156 −0.370363
\(553\) −14.5969 −0.620722
\(554\) −0.596876 −0.0253588
\(555\) 10.7016 0.454256
\(556\) 21.4031 0.907695
\(557\) 10.2094 0.432585 0.216293 0.976329i \(-0.430604\pi\)
0.216293 + 0.976329i \(0.430604\pi\)
\(558\) −0.701562 −0.0296995
\(559\) −34.8062 −1.47215
\(560\) −2.70156 −0.114162
\(561\) −1.00000 −0.0422200
\(562\) 10.0000 0.421825
\(563\) −17.8953 −0.754198 −0.377099 0.926173i \(-0.623078\pi\)
−0.377099 + 0.926173i \(0.623078\pi\)
\(564\) 9.40312 0.395943
\(565\) −2.00000 −0.0841406
\(566\) −12.0000 −0.504398
\(567\) 2.70156 0.113455
\(568\) 12.8062 0.537338
\(569\) 10.4922 0.439855 0.219928 0.975516i \(-0.429418\pi\)
0.219928 + 0.975516i \(0.429418\pi\)
\(570\) 4.70156 0.196927
\(571\) −45.4031 −1.90006 −0.950031 0.312156i \(-0.898949\pi\)
−0.950031 + 0.312156i \(0.898949\pi\)
\(572\) 4.70156 0.196582
\(573\) 1.19375 0.0498697
\(574\) 25.4031 1.06031
\(575\) −8.70156 −0.362880
\(576\) 1.00000 0.0416667
\(577\) −23.6125 −0.983001 −0.491501 0.870877i \(-0.663551\pi\)
−0.491501 + 0.870877i \(0.663551\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 12.0000 0.498703
\(580\) −2.00000 −0.0830455
\(581\) −8.91093 −0.369688
\(582\) 3.29844 0.136725
\(583\) 2.00000 0.0828315
\(584\) 8.00000 0.331042
\(585\) −4.70156 −0.194386
\(586\) −8.59688 −0.355134
\(587\) −37.4031 −1.54379 −0.771896 0.635749i \(-0.780691\pi\)
−0.771896 + 0.635749i \(0.780691\pi\)
\(588\) −0.298438 −0.0123074
\(589\) −3.29844 −0.135910
\(590\) −0.596876 −0.0245730
\(591\) 22.7016 0.933817
\(592\) 10.7016 0.439831
\(593\) −15.1938 −0.623933 −0.311966 0.950093i \(-0.600988\pi\)
−0.311966 + 0.950093i \(0.600988\pi\)
\(594\) 1.00000 0.0410305
\(595\) −2.70156 −0.110753
\(596\) −12.7016 −0.520276
\(597\) −8.70156 −0.356131
\(598\) 40.9109 1.67297
\(599\) −8.70156 −0.355536 −0.177768 0.984072i \(-0.556888\pi\)
−0.177768 + 0.984072i \(0.556888\pi\)
\(600\) 1.00000 0.0408248
\(601\) 1.50781 0.0615049 0.0307524 0.999527i \(-0.490210\pi\)
0.0307524 + 0.999527i \(0.490210\pi\)
\(602\) 20.0000 0.815139
\(603\) −14.7016 −0.598694
\(604\) 15.5078 0.631004
\(605\) −1.00000 −0.0406558
\(606\) 9.40312 0.381976
\(607\) 18.7016 0.759073 0.379536 0.925177i \(-0.376083\pi\)
0.379536 + 0.925177i \(0.376083\pi\)
\(608\) 4.70156 0.190674
\(609\) −5.40312 −0.218946
\(610\) 1.29844 0.0525722
\(611\) −44.2094 −1.78852
\(612\) 1.00000 0.0404226
\(613\) 26.5969 1.07424 0.537119 0.843507i \(-0.319513\pi\)
0.537119 + 0.843507i \(0.319513\pi\)
\(614\) 15.4031 0.621620
\(615\) −9.40312 −0.379171
\(616\) −2.70156 −0.108849
\(617\) 3.61250 0.145434 0.0727168 0.997353i \(-0.476833\pi\)
0.0727168 + 0.997353i \(0.476833\pi\)
\(618\) −2.10469 −0.0846629
\(619\) −14.3141 −0.575331 −0.287665 0.957731i \(-0.592879\pi\)
−0.287665 + 0.957731i \(0.592879\pi\)
\(620\) −0.701562 −0.0281754
\(621\) 8.70156 0.349182
\(622\) −20.8062 −0.834255
\(623\) 37.8219 1.51530
\(624\) −4.70156 −0.188213
\(625\) 1.00000 0.0400000
\(626\) 24.9109 0.995641
\(627\) 4.70156 0.187762
\(628\) −12.0000 −0.478852
\(629\) 10.7016 0.426699
\(630\) 2.70156 0.107633
\(631\) −36.2094 −1.44147 −0.720736 0.693209i \(-0.756196\pi\)
−0.720736 + 0.693209i \(0.756196\pi\)
\(632\) 5.40312 0.214925
\(633\) 16.2094 0.644265
\(634\) −14.0000 −0.556011
\(635\) −4.00000 −0.158735
\(636\) −2.00000 −0.0793052
\(637\) 1.40312 0.0555938
\(638\) −2.00000 −0.0791808
\(639\) −12.8062 −0.506607
\(640\) 1.00000 0.0395285
\(641\) −4.20937 −0.166260 −0.0831301 0.996539i \(-0.526492\pi\)
−0.0831301 + 0.996539i \(0.526492\pi\)
\(642\) 5.40312 0.213244
\(643\) 21.6125 0.852314 0.426157 0.904649i \(-0.359867\pi\)
0.426157 + 0.904649i \(0.359867\pi\)
\(644\) −23.5078 −0.926338
\(645\) −7.40312 −0.291498
\(646\) 4.70156 0.184980
\(647\) 41.4031 1.62772 0.813862 0.581058i \(-0.197361\pi\)
0.813862 + 0.581058i \(0.197361\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −0.596876 −0.0234294
\(650\) −4.70156 −0.184410
\(651\) −1.89531 −0.0742832
\(652\) 10.8062 0.423205
\(653\) −26.2094 −1.02565 −0.512826 0.858493i \(-0.671401\pi\)
−0.512826 + 0.858493i \(0.671401\pi\)
\(654\) −4.10469 −0.160506
\(655\) 6.10469 0.238530
\(656\) −9.40312 −0.367130
\(657\) −8.00000 −0.312110
\(658\) 25.4031 0.990317
\(659\) 24.8062 0.966314 0.483157 0.875534i \(-0.339490\pi\)
0.483157 + 0.875534i \(0.339490\pi\)
\(660\) 1.00000 0.0389249
\(661\) 6.70156 0.260661 0.130330 0.991471i \(-0.458396\pi\)
0.130330 + 0.991471i \(0.458396\pi\)
\(662\) −29.6125 −1.15092
\(663\) −4.70156 −0.182594
\(664\) 3.29844 0.128004
\(665\) 12.7016 0.492545
\(666\) −10.7016 −0.414677
\(667\) −17.4031 −0.673852
\(668\) 6.80625 0.263342
\(669\) 19.5078 0.754216
\(670\) −14.7016 −0.567971
\(671\) 1.29844 0.0501256
\(672\) 2.70156 0.104215
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) −10.8062 −0.416241
\(675\) −1.00000 −0.0384900
\(676\) 9.10469 0.350180
\(677\) −50.4187 −1.93775 −0.968875 0.247551i \(-0.920374\pi\)
−0.968875 + 0.247551i \(0.920374\pi\)
\(678\) 2.00000 0.0768095
\(679\) 8.91093 0.341970
\(680\) 1.00000 0.0383482
\(681\) 24.2094 0.927705
\(682\) −0.701562 −0.0268642
\(683\) −27.5078 −1.05256 −0.526279 0.850312i \(-0.676413\pi\)
−0.526279 + 0.850312i \(0.676413\pi\)
\(684\) −4.70156 −0.179769
\(685\) −0.104686 −0.00399986
\(686\) 18.1047 0.691240
\(687\) −1.29844 −0.0495385
\(688\) −7.40312 −0.282241
\(689\) 9.40312 0.358231
\(690\) 8.70156 0.331263
\(691\) 39.7172 1.51091 0.755456 0.655199i \(-0.227415\pi\)
0.755456 + 0.655199i \(0.227415\pi\)
\(692\) −25.5078 −0.969661
\(693\) 2.70156 0.102624
\(694\) −5.40312 −0.205100
\(695\) −21.4031 −0.811867
\(696\) 2.00000 0.0758098
\(697\) −9.40312 −0.356169
\(698\) 31.6125 1.19655
\(699\) −12.8062 −0.484377
\(700\) 2.70156 0.102109
\(701\) 0.209373 0.00790790 0.00395395 0.999992i \(-0.498741\pi\)
0.00395395 + 0.999992i \(0.498741\pi\)
\(702\) 4.70156 0.177449
\(703\) −50.3141 −1.89763
\(704\) 1.00000 0.0376889
\(705\) −9.40312 −0.354142
\(706\) −29.5078 −1.11054
\(707\) 25.4031 0.955383
\(708\) 0.596876 0.0224320
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) −12.8062 −0.480610
\(711\) −5.40312 −0.202633
\(712\) −14.0000 −0.524672
\(713\) −6.10469 −0.228622
\(714\) 2.70156 0.101103
\(715\) −4.70156 −0.175828
\(716\) 16.1047 0.601860
\(717\) 9.40312 0.351166
\(718\) −35.0156 −1.30677
\(719\) 46.4187 1.73113 0.865564 0.500799i \(-0.166960\pi\)
0.865564 + 0.500799i \(0.166960\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −5.68594 −0.211756
\(722\) −3.10469 −0.115544
\(723\) −10.7016 −0.397995
\(724\) 3.40312 0.126476
\(725\) 2.00000 0.0742781
\(726\) 1.00000 0.0371135
\(727\) 30.8062 1.14254 0.571270 0.820762i \(-0.306451\pi\)
0.571270 + 0.820762i \(0.306451\pi\)
\(728\) −12.7016 −0.470751
\(729\) 1.00000 0.0370370
\(730\) −8.00000 −0.296093
\(731\) −7.40312 −0.273814
\(732\) −1.29844 −0.0479916
\(733\) 44.9109 1.65882 0.829412 0.558638i \(-0.188676\pi\)
0.829412 + 0.558638i \(0.188676\pi\)
\(734\) 19.4031 0.716182
\(735\) 0.298438 0.0110080
\(736\) 8.70156 0.320744
\(737\) −14.7016 −0.541539
\(738\) 9.40312 0.346134
\(739\) 27.5078 1.01189 0.505946 0.862565i \(-0.331144\pi\)
0.505946 + 0.862565i \(0.331144\pi\)
\(740\) −10.7016 −0.393397
\(741\) 22.1047 0.812036
\(742\) −5.40312 −0.198355
\(743\) 44.4187 1.62957 0.814783 0.579766i \(-0.196856\pi\)
0.814783 + 0.579766i \(0.196856\pi\)
\(744\) 0.701562 0.0257205
\(745\) 12.7016 0.465349
\(746\) 2.59688 0.0950784
\(747\) −3.29844 −0.120684
\(748\) 1.00000 0.0365636
\(749\) 14.5969 0.533358
\(750\) −1.00000 −0.0365148
\(751\) 21.6125 0.788651 0.394326 0.918971i \(-0.370978\pi\)
0.394326 + 0.918971i \(0.370978\pi\)
\(752\) −9.40312 −0.342897
\(753\) 11.8953 0.433489
\(754\) −9.40312 −0.342442
\(755\) −15.5078 −0.564387
\(756\) −2.70156 −0.0982549
\(757\) 10.5969 0.385150 0.192575 0.981282i \(-0.438316\pi\)
0.192575 + 0.981282i \(0.438316\pi\)
\(758\) −30.3141 −1.10106
\(759\) 8.70156 0.315847
\(760\) −4.70156 −0.170544
\(761\) 8.10469 0.293795 0.146897 0.989152i \(-0.453071\pi\)
0.146897 + 0.989152i \(0.453071\pi\)
\(762\) 4.00000 0.144905
\(763\) −11.0891 −0.401451
\(764\) −1.19375 −0.0431884
\(765\) −1.00000 −0.0361551
\(766\) 22.5969 0.816458
\(767\) −2.80625 −0.101328
\(768\) −1.00000 −0.0360844
\(769\) −6.20937 −0.223916 −0.111958 0.993713i \(-0.535712\pi\)
−0.111958 + 0.993713i \(0.535712\pi\)
\(770\) 2.70156 0.0973575
\(771\) −27.6125 −0.994440
\(772\) −12.0000 −0.431889
\(773\) 17.5078 0.629712 0.314856 0.949139i \(-0.398044\pi\)
0.314856 + 0.949139i \(0.398044\pi\)
\(774\) 7.40312 0.266100
\(775\) 0.701562 0.0252009
\(776\) −3.29844 −0.118407
\(777\) −28.9109 −1.03717
\(778\) 12.0000 0.430221
\(779\) 44.2094 1.58397
\(780\) 4.70156 0.168343
\(781\) −12.8062 −0.458244
\(782\) 8.70156 0.311167
\(783\) −2.00000 −0.0714742
\(784\) 0.298438 0.0106585
\(785\) 12.0000 0.428298
\(786\) −6.10469 −0.217747
\(787\) 27.7172 0.988011 0.494005 0.869459i \(-0.335532\pi\)
0.494005 + 0.869459i \(0.335532\pi\)
\(788\) −22.7016 −0.808710
\(789\) 22.1047 0.786948
\(790\) −5.40312 −0.192235
\(791\) 5.40312 0.192113
\(792\) −1.00000 −0.0355335
\(793\) 6.10469 0.216784
\(794\) 12.8062 0.454477
\(795\) 2.00000 0.0709327
\(796\) 8.70156 0.308419
\(797\) −44.3141 −1.56968 −0.784842 0.619696i \(-0.787256\pi\)
−0.784842 + 0.619696i \(0.787256\pi\)
\(798\) −12.7016 −0.449630
\(799\) −9.40312 −0.332659
\(800\) −1.00000 −0.0353553
\(801\) 14.0000 0.494666
\(802\) −6.10469 −0.215564
\(803\) −8.00000 −0.282314
\(804\) 14.7016 0.518484
\(805\) 23.5078 0.828541
\(806\) −3.29844 −0.116183
\(807\) 5.50781 0.193884
\(808\) −9.40312 −0.330801
\(809\) 25.4031 0.893126 0.446563 0.894752i \(-0.352648\pi\)
0.446563 + 0.894752i \(0.352648\pi\)
\(810\) 1.00000 0.0351364
\(811\) 37.4031 1.31340 0.656701 0.754151i \(-0.271952\pi\)
0.656701 + 0.754151i \(0.271952\pi\)
\(812\) 5.40312 0.189612
\(813\) 10.8062 0.378992
\(814\) −10.7016 −0.375090
\(815\) −10.8062 −0.378526
\(816\) −1.00000 −0.0350070
\(817\) 34.8062 1.21772
\(818\) −6.00000 −0.209785
\(819\) 12.7016 0.443828
\(820\) 9.40312 0.328371
\(821\) −31.6125 −1.10328 −0.551642 0.834081i \(-0.685998\pi\)
−0.551642 + 0.834081i \(0.685998\pi\)
\(822\) 0.104686 0.00365136
\(823\) 6.00000 0.209147 0.104573 0.994517i \(-0.466652\pi\)
0.104573 + 0.994517i \(0.466652\pi\)
\(824\) 2.10469 0.0733202
\(825\) −1.00000 −0.0348155
\(826\) 1.61250 0.0561059
\(827\) 8.20937 0.285468 0.142734 0.989761i \(-0.454411\pi\)
0.142734 + 0.989761i \(0.454411\pi\)
\(828\) −8.70156 −0.302400
\(829\) −23.8953 −0.829919 −0.414959 0.909840i \(-0.636204\pi\)
−0.414959 + 0.909840i \(0.636204\pi\)
\(830\) −3.29844 −0.114490
\(831\) −0.596876 −0.0207054
\(832\) 4.70156 0.162997
\(833\) 0.298438 0.0103403
\(834\) 21.4031 0.741130
\(835\) −6.80625 −0.235540
\(836\) −4.70156 −0.162607
\(837\) −0.701562 −0.0242495
\(838\) 5.19375 0.179415
\(839\) 54.2094 1.87152 0.935758 0.352644i \(-0.114717\pi\)
0.935758 + 0.352644i \(0.114717\pi\)
\(840\) −2.70156 −0.0932127
\(841\) −25.0000 −0.862069
\(842\) 14.7016 0.506649
\(843\) 10.0000 0.344418
\(844\) −16.2094 −0.557950
\(845\) −9.10469 −0.313211
\(846\) 9.40312 0.323286
\(847\) 2.70156 0.0928268
\(848\) 2.00000 0.0686803
\(849\) −12.0000 −0.411839
\(850\) −1.00000 −0.0342997
\(851\) −93.1203 −3.19212
\(852\) 12.8062 0.438735
\(853\) 11.4031 0.390436 0.195218 0.980760i \(-0.437459\pi\)
0.195218 + 0.980760i \(0.437459\pi\)
\(854\) −3.50781 −0.120035
\(855\) 4.70156 0.160790
\(856\) −5.40312 −0.184675
\(857\) 45.2984 1.54737 0.773683 0.633573i \(-0.218413\pi\)
0.773683 + 0.633573i \(0.218413\pi\)
\(858\) 4.70156 0.160509
\(859\) 56.4187 1.92498 0.962491 0.271312i \(-0.0874576\pi\)
0.962491 + 0.271312i \(0.0874576\pi\)
\(860\) 7.40312 0.252444
\(861\) 25.4031 0.865736
\(862\) −2.20937 −0.0752515
\(863\) −16.0000 −0.544646 −0.272323 0.962206i \(-0.587792\pi\)
−0.272323 + 0.962206i \(0.587792\pi\)
\(864\) 1.00000 0.0340207
\(865\) 25.5078 0.867292
\(866\) 18.0000 0.611665
\(867\) −1.00000 −0.0339618
\(868\) 1.89531 0.0643311
\(869\) −5.40312 −0.183288
\(870\) −2.00000 −0.0678064
\(871\) −69.1203 −2.34205
\(872\) 4.10469 0.139002
\(873\) 3.29844 0.111635
\(874\) −40.9109 −1.38383
\(875\) −2.70156 −0.0913295
\(876\) 8.00000 0.270295
\(877\) −7.40312 −0.249986 −0.124993 0.992158i \(-0.539891\pi\)
−0.124993 + 0.992158i \(0.539891\pi\)
\(878\) −40.2094 −1.35700
\(879\) −8.59688 −0.289965
\(880\) −1.00000 −0.0337100
\(881\) −17.4031 −0.586326 −0.293163 0.956062i \(-0.594708\pi\)
−0.293163 + 0.956062i \(0.594708\pi\)
\(882\) −0.298438 −0.0100489
\(883\) −53.0156 −1.78412 −0.892059 0.451919i \(-0.850740\pi\)
−0.892059 + 0.451919i \(0.850740\pi\)
\(884\) 4.70156 0.158131
\(885\) −0.596876 −0.0200638
\(886\) 24.2094 0.813330
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 10.7016 0.359121
\(889\) 10.8062 0.362430
\(890\) 14.0000 0.469281
\(891\) 1.00000 0.0335013
\(892\) −19.5078 −0.653170
\(893\) 44.2094 1.47941
\(894\) −12.7016 −0.424804
\(895\) −16.1047 −0.538320
\(896\) −2.70156 −0.0902529
\(897\) 40.9109 1.36598
\(898\) 27.2984 0.910961
\(899\) 1.40312 0.0467968
\(900\) 1.00000 0.0333333
\(901\) 2.00000 0.0666297
\(902\) 9.40312 0.313090
\(903\) 20.0000 0.665558
\(904\) −2.00000 −0.0665190
\(905\) −3.40312 −0.113124
\(906\) 15.5078 0.515212
\(907\) −48.0000 −1.59381 −0.796907 0.604102i \(-0.793532\pi\)
−0.796907 + 0.604102i \(0.793532\pi\)
\(908\) −24.2094 −0.803416
\(909\) 9.40312 0.311882
\(910\) 12.7016 0.421053
\(911\) −35.4031 −1.17296 −0.586479 0.809964i \(-0.699486\pi\)
−0.586479 + 0.809964i \(0.699486\pi\)
\(912\) 4.70156 0.155684
\(913\) −3.29844 −0.109162
\(914\) 16.1047 0.532696
\(915\) 1.29844 0.0429250
\(916\) 1.29844 0.0429016
\(917\) −16.4922 −0.544620
\(918\) 1.00000 0.0330049
\(919\) 28.7016 0.946777 0.473389 0.880854i \(-0.343031\pi\)
0.473389 + 0.880854i \(0.343031\pi\)
\(920\) −8.70156 −0.286882
\(921\) 15.4031 0.507550
\(922\) 37.4031 1.23181
\(923\) −60.2094 −1.98182
\(924\) −2.70156 −0.0888749
\(925\) 10.7016 0.351865
\(926\) 24.7016 0.811744
\(927\) −2.10469 −0.0691270
\(928\) −2.00000 −0.0656532
\(929\) 32.7016 1.07290 0.536452 0.843931i \(-0.319764\pi\)
0.536452 + 0.843931i \(0.319764\pi\)
\(930\) −0.701562 −0.0230051
\(931\) −1.40312 −0.0459855
\(932\) 12.8062 0.419483
\(933\) −20.8062 −0.681166
\(934\) 34.8062 1.13890
\(935\) −1.00000 −0.0327035
\(936\) −4.70156 −0.153675
\(937\) 29.5078 0.963978 0.481989 0.876177i \(-0.339914\pi\)
0.481989 + 0.876177i \(0.339914\pi\)
\(938\) 39.7172 1.29681
\(939\) 24.9109 0.812938
\(940\) 9.40312 0.306696
\(941\) 15.4031 0.502127 0.251064 0.967971i \(-0.419220\pi\)
0.251064 + 0.967971i \(0.419220\pi\)
\(942\) −12.0000 −0.390981
\(943\) 81.8219 2.66449
\(944\) −0.596876 −0.0194267
\(945\) 2.70156 0.0878818
\(946\) 7.40312 0.240696
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) 5.40312 0.175485
\(949\) −37.6125 −1.22095
\(950\) 4.70156 0.152539
\(951\) −14.0000 −0.453981
\(952\) −2.70156 −0.0875581
\(953\) −39.8219 −1.28996 −0.644978 0.764201i \(-0.723134\pi\)
−0.644978 + 0.764201i \(0.723134\pi\)
\(954\) −2.00000 −0.0647524
\(955\) 1.19375 0.0386289
\(956\) −9.40312 −0.304119
\(957\) −2.00000 −0.0646508
\(958\) 14.9109 0.481750
\(959\) 0.282817 0.00913263
\(960\) 1.00000 0.0322749
\(961\) −30.5078 −0.984123
\(962\) −50.3141 −1.62219
\(963\) 5.40312 0.174113
\(964\) 10.7016 0.344674
\(965\) 12.0000 0.386294
\(966\) −23.5078 −0.756351
\(967\) −4.20937 −0.135364 −0.0676822 0.997707i \(-0.521560\pi\)
−0.0676822 + 0.997707i \(0.521560\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 4.70156 0.151036
\(970\) 3.29844 0.105906
\(971\) −33.7172 −1.08204 −0.541018 0.841011i \(-0.681961\pi\)
−0.541018 + 0.841011i \(0.681961\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 57.8219 1.85368
\(974\) 18.2094 0.583466
\(975\) −4.70156 −0.150570
\(976\) 1.29844 0.0415620
\(977\) −48.5234 −1.55240 −0.776201 0.630485i \(-0.782856\pi\)
−0.776201 + 0.630485i \(0.782856\pi\)
\(978\) 10.8062 0.345546
\(979\) 14.0000 0.447442
\(980\) −0.298438 −0.00953325
\(981\) −4.10469 −0.131053
\(982\) 12.8062 0.408664
\(983\) −26.8062 −0.854987 −0.427493 0.904019i \(-0.640603\pi\)
−0.427493 + 0.904019i \(0.640603\pi\)
\(984\) −9.40312 −0.299761
\(985\) 22.7016 0.723332
\(986\) −2.00000 −0.0636930
\(987\) 25.4031 0.808590
\(988\) −22.1047 −0.703244
\(989\) 64.4187 2.04840
\(990\) 1.00000 0.0317821
\(991\) −3.50781 −0.111429 −0.0557146 0.998447i \(-0.517744\pi\)
−0.0557146 + 0.998447i \(0.517744\pi\)
\(992\) −0.701562 −0.0222746
\(993\) −29.6125 −0.939724
\(994\) 34.5969 1.09735
\(995\) −8.70156 −0.275858
\(996\) 3.29844 0.104515
\(997\) −18.0000 −0.570066 −0.285033 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) 36.0000 1.13956
\(999\) −10.7016 −0.338582
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 5610.2.a.bo.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.bo.1.2 2 1.1 even 1 trivial