Properties

Label 5610.2.a.bo.1.1
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 1.1
Root \(3.70156\) 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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.70156 q^{13} +3.70156 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.70156 q^{19} -1.00000 q^{20} +3.70156 q^{21} -1.00000 q^{22} -2.29844 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.70156 q^{26} -1.00000 q^{27} -3.70156 q^{28} +2.00000 q^{29} -1.00000 q^{30} -5.70156 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +3.70156 q^{35} +1.00000 q^{36} +4.29844 q^{37} -1.70156 q^{38} +1.70156 q^{39} +1.00000 q^{40} +3.40312 q^{41} -3.70156 q^{42} +5.40312 q^{43} +1.00000 q^{44} -1.00000 q^{45} +2.29844 q^{46} +3.40312 q^{47} -1.00000 q^{48} +6.70156 q^{49} -1.00000 q^{50} -1.00000 q^{51} -1.70156 q^{52} +2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +3.70156 q^{56} -1.70156 q^{57} -2.00000 q^{58} -13.4031 q^{59} +1.00000 q^{60} +7.70156 q^{61} +5.70156 q^{62} -3.70156 q^{63} +1.00000 q^{64} +1.70156 q^{65} +1.00000 q^{66} -8.29844 q^{67} +1.00000 q^{68} +2.29844 q^{69} -3.70156 q^{70} +12.8062 q^{71} -1.00000 q^{72} -8.00000 q^{73} -4.29844 q^{74} -1.00000 q^{75} +1.70156 q^{76} -3.70156 q^{77} -1.70156 q^{78} +7.40312 q^{79} -1.00000 q^{80} +1.00000 q^{81} -3.40312 q^{82} -9.70156 q^{83} +3.70156 q^{84} -1.00000 q^{85} -5.40312 q^{86} -2.00000 q^{87} -1.00000 q^{88} +14.0000 q^{89} +1.00000 q^{90} +6.29844 q^{91} -2.29844 q^{92} +5.70156 q^{93} -3.40312 q^{94} -1.70156 q^{95} +1.00000 q^{96} +9.70156 q^{97} -6.70156 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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
\(7\) −3.70156 −1.39906 −0.699529 0.714604i \(-0.746607\pi\)
−0.699529 + 0.714604i \(0.746607\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) −1.00000 −0.288675
\(13\) −1.70156 −0.471928 −0.235964 0.971762i \(-0.575825\pi\)
−0.235964 + 0.971762i \(0.575825\pi\)
\(14\) 3.70156 0.989284
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 1.70156 0.390365 0.195183 0.980767i \(-0.437470\pi\)
0.195183 + 0.980767i \(0.437470\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.70156 0.807747
\(22\) −1.00000 −0.213201
\(23\) −2.29844 −0.479257 −0.239629 0.970865i \(-0.577026\pi\)
−0.239629 + 0.970865i \(0.577026\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 1.70156 0.333704
\(27\) −1.00000 −0.192450
\(28\) −3.70156 −0.699529
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −1.00000 −0.182574
\(31\) −5.70156 −1.02403 −0.512015 0.858976i \(-0.671101\pi\)
−0.512015 + 0.858976i \(0.671101\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −1.00000 −0.171499
\(35\) 3.70156 0.625678
\(36\) 1.00000 0.166667
\(37\) 4.29844 0.706659 0.353329 0.935499i \(-0.385049\pi\)
0.353329 + 0.935499i \(0.385049\pi\)
\(38\) −1.70156 −0.276030
\(39\) 1.70156 0.272468
\(40\) 1.00000 0.158114
\(41\) 3.40312 0.531479 0.265739 0.964045i \(-0.414384\pi\)
0.265739 + 0.964045i \(0.414384\pi\)
\(42\) −3.70156 −0.571163
\(43\) 5.40312 0.823969 0.411984 0.911191i \(-0.364836\pi\)
0.411984 + 0.911191i \(0.364836\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) 2.29844 0.338886
\(47\) 3.40312 0.496397 0.248198 0.968709i \(-0.420162\pi\)
0.248198 + 0.968709i \(0.420162\pi\)
\(48\) −1.00000 −0.144338
\(49\) 6.70156 0.957366
\(50\) −1.00000 −0.141421
\(51\) −1.00000 −0.140028
\(52\) −1.70156 −0.235964
\(53\) 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
\(56\) 3.70156 0.494642
\(57\) −1.70156 −0.225377
\(58\) −2.00000 −0.262613
\(59\) −13.4031 −1.74494 −0.872469 0.488669i \(-0.837482\pi\)
−0.872469 + 0.488669i \(0.837482\pi\)
\(60\) 1.00000 0.129099
\(61\) 7.70156 0.986084 0.493042 0.870006i \(-0.335885\pi\)
0.493042 + 0.870006i \(0.335885\pi\)
\(62\) 5.70156 0.724099
\(63\) −3.70156 −0.466353
\(64\) 1.00000 0.125000
\(65\) 1.70156 0.211053
\(66\) 1.00000 0.123091
\(67\) −8.29844 −1.01382 −0.506908 0.862000i \(-0.669212\pi\)
−0.506908 + 0.862000i \(0.669212\pi\)
\(68\) 1.00000 0.121268
\(69\) 2.29844 0.276699
\(70\) −3.70156 −0.442421
\(71\) 12.8062 1.51982 0.759911 0.650027i \(-0.225242\pi\)
0.759911 + 0.650027i \(0.225242\pi\)
\(72\) −1.00000 −0.117851
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) −4.29844 −0.499683
\(75\) −1.00000 −0.115470
\(76\) 1.70156 0.195183
\(77\) −3.70156 −0.421832
\(78\) −1.70156 −0.192664
\(79\) 7.40312 0.832917 0.416458 0.909155i \(-0.363271\pi\)
0.416458 + 0.909155i \(0.363271\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −3.40312 −0.375812
\(83\) −9.70156 −1.06488 −0.532442 0.846466i \(-0.678726\pi\)
−0.532442 + 0.846466i \(0.678726\pi\)
\(84\) 3.70156 0.403874
\(85\) −1.00000 −0.108465
\(86\) −5.40312 −0.582634
\(87\) −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
\(91\) 6.29844 0.660256
\(92\) −2.29844 −0.239629
\(93\) 5.70156 0.591224
\(94\) −3.40312 −0.351005
\(95\) −1.70156 −0.174577
\(96\) 1.00000 0.102062
\(97\) 9.70156 0.985044 0.492522 0.870300i \(-0.336075\pi\)
0.492522 + 0.870300i \(0.336075\pi\)
\(98\) −6.70156 −0.676960
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) −3.40312 −0.338624 −0.169312 0.985563i \(-0.554154\pi\)
−0.169312 + 0.985563i \(0.554154\pi\)
\(102\) 1.00000 0.0990148
\(103\) 17.1047 1.68537 0.842687 0.538403i \(-0.180972\pi\)
0.842687 + 0.538403i \(0.180972\pi\)
\(104\) 1.70156 0.166852
\(105\) −3.70156 −0.361235
\(106\) −2.00000 −0.194257
\(107\) −7.40312 −0.715687 −0.357844 0.933782i \(-0.616488\pi\)
−0.357844 + 0.933782i \(0.616488\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 15.1047 1.44677 0.723383 0.690447i \(-0.242586\pi\)
0.723383 + 0.690447i \(0.242586\pi\)
\(110\) 1.00000 0.0953463
\(111\) −4.29844 −0.407990
\(112\) −3.70156 −0.349765
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 1.70156 0.159366
\(115\) 2.29844 0.214330
\(116\) 2.00000 0.185695
\(117\) −1.70156 −0.157309
\(118\) 13.4031 1.23386
\(119\) −3.70156 −0.339322
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −7.70156 −0.697267
\(123\) −3.40312 −0.306849
\(124\) −5.70156 −0.512015
\(125\) −1.00000 −0.0894427
\(126\) 3.70156 0.329761
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.40312 −0.475719
\(130\) −1.70156 −0.149237
\(131\) 13.1047 1.14496 0.572481 0.819918i \(-0.305981\pi\)
0.572481 + 0.819918i \(0.305981\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −6.29844 −0.546144
\(134\) 8.29844 0.716876
\(135\) 1.00000 0.0860663
\(136\) −1.00000 −0.0857493
\(137\) −19.1047 −1.63222 −0.816112 0.577894i \(-0.803875\pi\)
−0.816112 + 0.577894i \(0.803875\pi\)
\(138\) −2.29844 −0.195656
\(139\) 8.59688 0.729177 0.364589 0.931169i \(-0.381210\pi\)
0.364589 + 0.931169i \(0.381210\pi\)
\(140\) 3.70156 0.312839
\(141\) −3.40312 −0.286595
\(142\) −12.8062 −1.07468
\(143\) −1.70156 −0.142292
\(144\) 1.00000 0.0833333
\(145\) −2.00000 −0.166091
\(146\) 8.00000 0.662085
\(147\) −6.70156 −0.552736
\(148\) 4.29844 0.353329
\(149\) −6.29844 −0.515988 −0.257994 0.966147i \(-0.583062\pi\)
−0.257994 + 0.966147i \(0.583062\pi\)
\(150\) 1.00000 0.0816497
\(151\) −16.5078 −1.34339 −0.671693 0.740829i \(-0.734433\pi\)
−0.671693 + 0.740829i \(0.734433\pi\)
\(152\) −1.70156 −0.138015
\(153\) 1.00000 0.0808452
\(154\) 3.70156 0.298280
\(155\) 5.70156 0.457960
\(156\) 1.70156 0.136234
\(157\) −12.0000 −0.957704 −0.478852 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) −7.40312 −0.588961
\(159\) −2.00000 −0.158610
\(160\) 1.00000 0.0790569
\(161\) 8.50781 0.670509
\(162\) −1.00000 −0.0785674
\(163\) −14.8062 −1.15971 −0.579857 0.814718i \(-0.696892\pi\)
−0.579857 + 0.814718i \(0.696892\pi\)
\(164\) 3.40312 0.265739
\(165\) 1.00000 0.0778499
\(166\) 9.70156 0.752987
\(167\) −18.8062 −1.45527 −0.727636 0.685964i \(-0.759381\pi\)
−0.727636 + 0.685964i \(0.759381\pi\)
\(168\) −3.70156 −0.285582
\(169\) −10.1047 −0.777284
\(170\) 1.00000 0.0766965
\(171\) 1.70156 0.130122
\(172\) 5.40312 0.411984
\(173\) 6.50781 0.494780 0.247390 0.968916i \(-0.420427\pi\)
0.247390 + 0.968916i \(0.420427\pi\)
\(174\) 2.00000 0.151620
\(175\) −3.70156 −0.279812
\(176\) 1.00000 0.0753778
\(177\) 13.4031 1.00744
\(178\) −14.0000 −1.04934
\(179\) −3.10469 −0.232055 −0.116028 0.993246i \(-0.537016\pi\)
−0.116028 + 0.993246i \(0.537016\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −9.40312 −0.698929 −0.349464 0.936950i \(-0.613636\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(182\) −6.29844 −0.466871
\(183\) −7.70156 −0.569316
\(184\) 2.29844 0.169443
\(185\) −4.29844 −0.316027
\(186\) −5.70156 −0.418059
\(187\) 1.00000 0.0731272
\(188\) 3.40312 0.248198
\(189\) 3.70156 0.269249
\(190\) 1.70156 0.123444
\(191\) −26.8062 −1.93963 −0.969816 0.243838i \(-0.921594\pi\)
−0.969816 + 0.243838i \(0.921594\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −12.0000 −0.863779 −0.431889 0.901927i \(-0.642153\pi\)
−0.431889 + 0.901927i \(0.642153\pi\)
\(194\) −9.70156 −0.696532
\(195\) −1.70156 −0.121851
\(196\) 6.70156 0.478683
\(197\) −16.2984 −1.16122 −0.580608 0.814183i \(-0.697185\pi\)
−0.580608 + 0.814183i \(0.697185\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 2.29844 0.162932 0.0814660 0.996676i \(-0.474040\pi\)
0.0814660 + 0.996676i \(0.474040\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.29844 0.585327
\(202\) 3.40312 0.239443
\(203\) −7.40312 −0.519597
\(204\) −1.00000 −0.0700140
\(205\) −3.40312 −0.237685
\(206\) −17.1047 −1.19174
\(207\) −2.29844 −0.159752
\(208\) −1.70156 −0.117982
\(209\) 1.70156 0.117700
\(210\) 3.70156 0.255432
\(211\) 22.2094 1.52896 0.764478 0.644650i \(-0.222997\pi\)
0.764478 + 0.644650i \(0.222997\pi\)
\(212\) 2.00000 0.137361
\(213\) −12.8062 −0.877470
\(214\) 7.40312 0.506067
\(215\) −5.40312 −0.368490
\(216\) 1.00000 0.0680414
\(217\) 21.1047 1.43268
\(218\) −15.1047 −1.02302
\(219\) 8.00000 0.540590
\(220\) −1.00000 −0.0674200
\(221\) −1.70156 −0.114459
\(222\) 4.29844 0.288492
\(223\) 12.5078 0.837585 0.418792 0.908082i \(-0.362453\pi\)
0.418792 + 0.908082i \(0.362453\pi\)
\(224\) 3.70156 0.247321
\(225\) 1.00000 0.0666667
\(226\) −2.00000 −0.133038
\(227\) 14.2094 0.943109 0.471555 0.881837i \(-0.343693\pi\)
0.471555 + 0.881837i \(0.343693\pi\)
\(228\) −1.70156 −0.112689
\(229\) 7.70156 0.508934 0.254467 0.967082i \(-0.418100\pi\)
0.254467 + 0.967082i \(0.418100\pi\)
\(230\) −2.29844 −0.151555
\(231\) 3.70156 0.243545
\(232\) −2.00000 −0.131306
\(233\) −12.8062 −0.838965 −0.419483 0.907763i \(-0.637788\pi\)
−0.419483 + 0.907763i \(0.637788\pi\)
\(234\) 1.70156 0.111235
\(235\) −3.40312 −0.221995
\(236\) −13.4031 −0.872469
\(237\) −7.40312 −0.480885
\(238\) 3.70156 0.239937
\(239\) 3.40312 0.220130 0.110065 0.993924i \(-0.464894\pi\)
0.110065 + 0.993924i \(0.464894\pi\)
\(240\) 1.00000 0.0645497
\(241\) 4.29844 0.276887 0.138443 0.990370i \(-0.455790\pi\)
0.138443 + 0.990370i \(0.455790\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 7.70156 0.493042
\(245\) −6.70156 −0.428147
\(246\) 3.40312 0.216975
\(247\) −2.89531 −0.184224
\(248\) 5.70156 0.362050
\(249\) 9.70156 0.614812
\(250\) 1.00000 0.0632456
\(251\) −31.1047 −1.96331 −0.981655 0.190665i \(-0.938936\pi\)
−0.981655 + 0.190665i \(0.938936\pi\)
\(252\) −3.70156 −0.233176
\(253\) −2.29844 −0.144502
\(254\) −4.00000 −0.250982
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −23.6125 −1.47291 −0.736454 0.676488i \(-0.763501\pi\)
−0.736454 + 0.676488i \(0.763501\pi\)
\(258\) 5.40312 0.336384
\(259\) −15.9109 −0.988657
\(260\) 1.70156 0.105526
\(261\) 2.00000 0.123797
\(262\) −13.1047 −0.809610
\(263\) −2.89531 −0.178533 −0.0892663 0.996008i \(-0.528452\pi\)
−0.0892663 + 0.996008i \(0.528452\pi\)
\(264\) 1.00000 0.0615457
\(265\) −2.00000 −0.122859
\(266\) 6.29844 0.386182
\(267\) −14.0000 −0.856786
\(268\) −8.29844 −0.506908
\(269\) 26.5078 1.61621 0.808105 0.589039i \(-0.200493\pi\)
0.808105 + 0.589039i \(0.200493\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 14.8062 0.899416 0.449708 0.893176i \(-0.351528\pi\)
0.449708 + 0.893176i \(0.351528\pi\)
\(272\) 1.00000 0.0606339
\(273\) −6.29844 −0.381199
\(274\) 19.1047 1.15416
\(275\) 1.00000 0.0603023
\(276\) 2.29844 0.138350
\(277\) 13.4031 0.805316 0.402658 0.915351i \(-0.368086\pi\)
0.402658 + 0.915351i \(0.368086\pi\)
\(278\) −8.59688 −0.515606
\(279\) −5.70156 −0.341344
\(280\) −3.70156 −0.221211
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 3.40312 0.202653
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) 12.8062 0.759911
\(285\) 1.70156 0.100792
\(286\) 1.70156 0.100615
\(287\) −12.5969 −0.743570
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 2.00000 0.117444
\(291\) −9.70156 −0.568716
\(292\) −8.00000 −0.468165
\(293\) 21.4031 1.25038 0.625192 0.780471i \(-0.285021\pi\)
0.625192 + 0.780471i \(0.285021\pi\)
\(294\) 6.70156 0.390843
\(295\) 13.4031 0.780360
\(296\) −4.29844 −0.249842
\(297\) −1.00000 −0.0580259
\(298\) 6.29844 0.364859
\(299\) 3.91093 0.226175
\(300\) −1.00000 −0.0577350
\(301\) −20.0000 −1.15278
\(302\) 16.5078 0.949918
\(303\) 3.40312 0.195504
\(304\) 1.70156 0.0975913
\(305\) −7.70156 −0.440990
\(306\) −1.00000 −0.0571662
\(307\) −2.59688 −0.148212 −0.0741058 0.997250i \(-0.523610\pi\)
−0.0741058 + 0.997250i \(0.523610\pi\)
\(308\) −3.70156 −0.210916
\(309\) −17.1047 −0.973052
\(310\) −5.70156 −0.323827
\(311\) −4.80625 −0.272537 −0.136269 0.990672i \(-0.543511\pi\)
−0.136269 + 0.990672i \(0.543511\pi\)
\(312\) −1.70156 −0.0963320
\(313\) 19.9109 1.12543 0.562716 0.826650i \(-0.309756\pi\)
0.562716 + 0.826650i \(0.309756\pi\)
\(314\) 12.0000 0.677199
\(315\) 3.70156 0.208559
\(316\) 7.40312 0.416458
\(317\) 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
\(321\) 7.40312 0.413202
\(322\) −8.50781 −0.474122
\(323\) 1.70156 0.0946774
\(324\) 1.00000 0.0555556
\(325\) −1.70156 −0.0943857
\(326\) 14.8062 0.820042
\(327\) −15.1047 −0.835291
\(328\) −3.40312 −0.187906
\(329\) −12.5969 −0.694488
\(330\) −1.00000 −0.0550482
\(331\) −21.6125 −1.18793 −0.593965 0.804491i \(-0.702438\pi\)
−0.593965 + 0.804491i \(0.702438\pi\)
\(332\) −9.70156 −0.532442
\(333\) 4.29844 0.235553
\(334\) 18.8062 1.02903
\(335\) 8.29844 0.453392
\(336\) 3.70156 0.201937
\(337\) −14.8062 −0.806548 −0.403274 0.915079i \(-0.632128\pi\)
−0.403274 + 0.915079i \(0.632128\pi\)
\(338\) 10.1047 0.549622
\(339\) −2.00000 −0.108625
\(340\) −1.00000 −0.0542326
\(341\) −5.70156 −0.308757
\(342\) −1.70156 −0.0920099
\(343\) 1.10469 0.0596475
\(344\) −5.40312 −0.291317
\(345\) −2.29844 −0.123744
\(346\) −6.50781 −0.349862
\(347\) −7.40312 −0.397421 −0.198710 0.980058i \(-0.563675\pi\)
−0.198710 + 0.980058i \(0.563675\pi\)
\(348\) −2.00000 −0.107211
\(349\) 19.6125 1.04983 0.524916 0.851154i \(-0.324097\pi\)
0.524916 + 0.851154i \(0.324097\pi\)
\(350\) 3.70156 0.197857
\(351\) 1.70156 0.0908227
\(352\) −1.00000 −0.0533002
\(353\) −2.50781 −0.133477 −0.0667386 0.997770i \(-0.521259\pi\)
−0.0667386 + 0.997770i \(0.521259\pi\)
\(354\) −13.4031 −0.712368
\(355\) −12.8062 −0.679685
\(356\) 14.0000 0.741999
\(357\) 3.70156 0.195907
\(358\) 3.10469 0.164088
\(359\) −29.0156 −1.53139 −0.765693 0.643206i \(-0.777604\pi\)
−0.765693 + 0.643206i \(0.777604\pi\)
\(360\) 1.00000 0.0527046
\(361\) −16.1047 −0.847615
\(362\) 9.40312 0.494217
\(363\) −1.00000 −0.0524864
\(364\) 6.29844 0.330128
\(365\) 8.00000 0.418739
\(366\) 7.70156 0.402567
\(367\) −6.59688 −0.344354 −0.172177 0.985066i \(-0.555080\pi\)
−0.172177 + 0.985066i \(0.555080\pi\)
\(368\) −2.29844 −0.119814
\(369\) 3.40312 0.177160
\(370\) 4.29844 0.223465
\(371\) −7.40312 −0.384351
\(372\) 5.70156 0.295612
\(373\) −15.4031 −0.797544 −0.398772 0.917050i \(-0.630563\pi\)
−0.398772 + 0.917050i \(0.630563\pi\)
\(374\) −1.00000 −0.0517088
\(375\) 1.00000 0.0516398
\(376\) −3.40312 −0.175503
\(377\) −3.40312 −0.175270
\(378\) −3.70156 −0.190388
\(379\) −27.3141 −1.40303 −0.701514 0.712655i \(-0.747492\pi\)
−0.701514 + 0.712655i \(0.747492\pi\)
\(380\) −1.70156 −0.0872883
\(381\) −4.00000 −0.204926
\(382\) 26.8062 1.37153
\(383\) −35.4031 −1.80902 −0.904508 0.426458i \(-0.859761\pi\)
−0.904508 + 0.426458i \(0.859761\pi\)
\(384\) 1.00000 0.0510310
\(385\) 3.70156 0.188649
\(386\) 12.0000 0.610784
\(387\) 5.40312 0.274656
\(388\) 9.70156 0.492522
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) 1.70156 0.0861619
\(391\) −2.29844 −0.116237
\(392\) −6.70156 −0.338480
\(393\) −13.1047 −0.661044
\(394\) 16.2984 0.821103
\(395\) −7.40312 −0.372492
\(396\) 1.00000 0.0502519
\(397\) 12.8062 0.642727 0.321364 0.946956i \(-0.395859\pi\)
0.321364 + 0.946956i \(0.395859\pi\)
\(398\) −2.29844 −0.115210
\(399\) 6.29844 0.315316
\(400\) 1.00000 0.0500000
\(401\) −13.1047 −0.654417 −0.327208 0.944952i \(-0.606108\pi\)
−0.327208 + 0.944952i \(0.606108\pi\)
\(402\) −8.29844 −0.413888
\(403\) 9.70156 0.483269
\(404\) −3.40312 −0.169312
\(405\) −1.00000 −0.0496904
\(406\) 7.40312 0.367411
\(407\) 4.29844 0.213066
\(408\) 1.00000 0.0495074
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) 3.40312 0.168068
\(411\) 19.1047 0.942365
\(412\) 17.1047 0.842687
\(413\) 49.6125 2.44127
\(414\) 2.29844 0.112962
\(415\) 9.70156 0.476231
\(416\) 1.70156 0.0834259
\(417\) −8.59688 −0.420991
\(418\) −1.70156 −0.0832261
\(419\) −30.8062 −1.50498 −0.752492 0.658602i \(-0.771148\pi\)
−0.752492 + 0.658602i \(0.771148\pi\)
\(420\) −3.70156 −0.180618
\(421\) −8.29844 −0.404441 −0.202221 0.979340i \(-0.564816\pi\)
−0.202221 + 0.979340i \(0.564816\pi\)
\(422\) −22.2094 −1.08114
\(423\) 3.40312 0.165466
\(424\) −2.00000 −0.0971286
\(425\) 1.00000 0.0485071
\(426\) 12.8062 0.620465
\(427\) −28.5078 −1.37959
\(428\) −7.40312 −0.357844
\(429\) 1.70156 0.0821522
\(430\) 5.40312 0.260562
\(431\) −36.2094 −1.74414 −0.872072 0.489377i \(-0.837224\pi\)
−0.872072 + 0.489377i \(0.837224\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) −21.1047 −1.01306
\(435\) 2.00000 0.0958927
\(436\) 15.1047 0.723383
\(437\) −3.91093 −0.187085
\(438\) −8.00000 −0.382255
\(439\) 1.79063 0.0854620 0.0427310 0.999087i \(-0.486394\pi\)
0.0427310 + 0.999087i \(0.486394\pi\)
\(440\) 1.00000 0.0476731
\(441\) 6.70156 0.319122
\(442\) 1.70156 0.0809351
\(443\) 14.2094 0.675108 0.337554 0.941306i \(-0.390400\pi\)
0.337554 + 0.941306i \(0.390400\pi\)
\(444\) −4.29844 −0.203995
\(445\) −14.0000 −0.663664
\(446\) −12.5078 −0.592262
\(447\) 6.29844 0.297906
\(448\) −3.70156 −0.174882
\(449\) −33.7016 −1.59048 −0.795238 0.606298i \(-0.792654\pi\)
−0.795238 + 0.606298i \(0.792654\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 3.40312 0.160247
\(452\) 2.00000 0.0940721
\(453\) 16.5078 0.775605
\(454\) −14.2094 −0.666879
\(455\) −6.29844 −0.295275
\(456\) 1.70156 0.0796829
\(457\) 3.10469 0.145231 0.0726156 0.997360i \(-0.476865\pi\)
0.0726156 + 0.997360i \(0.476865\pi\)
\(458\) −7.70156 −0.359870
\(459\) −1.00000 −0.0466760
\(460\) 2.29844 0.107165
\(461\) −24.5969 −1.14559 −0.572795 0.819698i \(-0.694141\pi\)
−0.572795 + 0.819698i \(0.694141\pi\)
\(462\) −3.70156 −0.172212
\(463\) −18.2984 −0.850401 −0.425200 0.905099i \(-0.639796\pi\)
−0.425200 + 0.905099i \(0.639796\pi\)
\(464\) 2.00000 0.0928477
\(465\) −5.70156 −0.264404
\(466\) 12.8062 0.593238
\(467\) −9.19375 −0.425436 −0.212718 0.977114i \(-0.568232\pi\)
−0.212718 + 0.977114i \(0.568232\pi\)
\(468\) −1.70156 −0.0786547
\(469\) 30.7172 1.41839
\(470\) 3.40312 0.156974
\(471\) 12.0000 0.552931
\(472\) 13.4031 0.616929
\(473\) 5.40312 0.248436
\(474\) 7.40312 0.340037
\(475\) 1.70156 0.0780730
\(476\) −3.70156 −0.169661
\(477\) 2.00000 0.0915737
\(478\) −3.40312 −0.155655
\(479\) 29.9109 1.36667 0.683333 0.730107i \(-0.260530\pi\)
0.683333 + 0.730107i \(0.260530\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −7.31406 −0.333492
\(482\) −4.29844 −0.195788
\(483\) −8.50781 −0.387119
\(484\) 1.00000 0.0454545
\(485\) −9.70156 −0.440525
\(486\) 1.00000 0.0453609
\(487\) 20.2094 0.915774 0.457887 0.889010i \(-0.348606\pi\)
0.457887 + 0.889010i \(0.348606\pi\)
\(488\) −7.70156 −0.348633
\(489\) 14.8062 0.669562
\(490\) 6.70156 0.302746
\(491\) 12.8062 0.577938 0.288969 0.957338i \(-0.406688\pi\)
0.288969 + 0.957338i \(0.406688\pi\)
\(492\) −3.40312 −0.153425
\(493\) 2.00000 0.0900755
\(494\) 2.89531 0.130266
\(495\) −1.00000 −0.0449467
\(496\) −5.70156 −0.256008
\(497\) −47.4031 −2.12632
\(498\) −9.70156 −0.434737
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 18.8062 0.840201
\(502\) 31.1047 1.38827
\(503\) −14.8062 −0.660178 −0.330089 0.943950i \(-0.607079\pi\)
−0.330089 + 0.943950i \(0.607079\pi\)
\(504\) 3.70156 0.164881
\(505\) 3.40312 0.151437
\(506\) 2.29844 0.102178
\(507\) 10.1047 0.448765
\(508\) 4.00000 0.177471
\(509\) 30.2094 1.33901 0.669503 0.742809i \(-0.266507\pi\)
0.669503 + 0.742809i \(0.266507\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 29.6125 1.30998
\(512\) −1.00000 −0.0441942
\(513\) −1.70156 −0.0751258
\(514\) 23.6125 1.04150
\(515\) −17.1047 −0.753723
\(516\) −5.40312 −0.237859
\(517\) 3.40312 0.149669
\(518\) 15.9109 0.699086
\(519\) −6.50781 −0.285661
\(520\) −1.70156 −0.0746184
\(521\) 10.8953 0.477332 0.238666 0.971102i \(-0.423290\pi\)
0.238666 + 0.971102i \(0.423290\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 16.2094 0.708786 0.354393 0.935097i \(-0.384687\pi\)
0.354393 + 0.935097i \(0.384687\pi\)
\(524\) 13.1047 0.572481
\(525\) 3.70156 0.161549
\(526\) 2.89531 0.126242
\(527\) −5.70156 −0.248364
\(528\) −1.00000 −0.0435194
\(529\) −17.7172 −0.770312
\(530\) 2.00000 0.0868744
\(531\) −13.4031 −0.581646
\(532\) −6.29844 −0.273072
\(533\) −5.79063 −0.250820
\(534\) 14.0000 0.605839
\(535\) 7.40312 0.320065
\(536\) 8.29844 0.358438
\(537\) 3.10469 0.133977
\(538\) −26.5078 −1.14283
\(539\) 6.70156 0.288657
\(540\) 1.00000 0.0430331
\(541\) −8.80625 −0.378610 −0.189305 0.981918i \(-0.560624\pi\)
−0.189305 + 0.981918i \(0.560624\pi\)
\(542\) −14.8062 −0.635983
\(543\) 9.40312 0.403527
\(544\) −1.00000 −0.0428746
\(545\) −15.1047 −0.647014
\(546\) 6.29844 0.269548
\(547\) 9.10469 0.389288 0.194644 0.980874i \(-0.437645\pi\)
0.194644 + 0.980874i \(0.437645\pi\)
\(548\) −19.1047 −0.816112
\(549\) 7.70156 0.328695
\(550\) −1.00000 −0.0426401
\(551\) 3.40312 0.144978
\(552\) −2.29844 −0.0978280
\(553\) −27.4031 −1.16530
\(554\) −13.4031 −0.569444
\(555\) 4.29844 0.182459
\(556\) 8.59688 0.364589
\(557\) −28.2094 −1.19527 −0.597635 0.801768i \(-0.703893\pi\)
−0.597635 + 0.801768i \(0.703893\pi\)
\(558\) 5.70156 0.241366
\(559\) −9.19375 −0.388854
\(560\) 3.70156 0.156420
\(561\) −1.00000 −0.0422200
\(562\) 10.0000 0.421825
\(563\) −37.1047 −1.56378 −0.781888 0.623419i \(-0.785743\pi\)
−0.781888 + 0.623419i \(0.785743\pi\)
\(564\) −3.40312 −0.143297
\(565\) −2.00000 −0.0841406
\(566\) −12.0000 −0.504398
\(567\) −3.70156 −0.155451
\(568\) −12.8062 −0.537338
\(569\) 42.5078 1.78202 0.891010 0.453984i \(-0.149998\pi\)
0.891010 + 0.453984i \(0.149998\pi\)
\(570\) −1.70156 −0.0712706
\(571\) −32.5969 −1.36414 −0.682068 0.731288i \(-0.738919\pi\)
−0.682068 + 0.731288i \(0.738919\pi\)
\(572\) −1.70156 −0.0711459
\(573\) 26.8062 1.11985
\(574\) 12.5969 0.525783
\(575\) −2.29844 −0.0958515
\(576\) 1.00000 0.0416667
\(577\) 27.6125 1.14952 0.574762 0.818321i \(-0.305095\pi\)
0.574762 + 0.818321i \(0.305095\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 12.0000 0.498703
\(580\) −2.00000 −0.0830455
\(581\) 35.9109 1.48984
\(582\) 9.70156 0.402143
\(583\) 2.00000 0.0828315
\(584\) 8.00000 0.331042
\(585\) 1.70156 0.0703509
\(586\) −21.4031 −0.884155
\(587\) −24.5969 −1.01522 −0.507611 0.861586i \(-0.669471\pi\)
−0.507611 + 0.861586i \(0.669471\pi\)
\(588\) −6.70156 −0.276368
\(589\) −9.70156 −0.399746
\(590\) −13.4031 −0.551798
\(591\) 16.2984 0.670428
\(592\) 4.29844 0.176665
\(593\) −40.8062 −1.67571 −0.837856 0.545891i \(-0.816191\pi\)
−0.837856 + 0.545891i \(0.816191\pi\)
\(594\) 1.00000 0.0410305
\(595\) 3.70156 0.151749
\(596\) −6.29844 −0.257994
\(597\) −2.29844 −0.0940688
\(598\) −3.91093 −0.159930
\(599\) −2.29844 −0.0939116 −0.0469558 0.998897i \(-0.514952\pi\)
−0.0469558 + 0.998897i \(0.514952\pi\)
\(600\) 1.00000 0.0408248
\(601\) −30.5078 −1.24444 −0.622220 0.782843i \(-0.713769\pi\)
−0.622220 + 0.782843i \(0.713769\pi\)
\(602\) 20.0000 0.815139
\(603\) −8.29844 −0.337939
\(604\) −16.5078 −0.671693
\(605\) −1.00000 −0.0406558
\(606\) −3.40312 −0.138242
\(607\) 12.2984 0.499178 0.249589 0.968352i \(-0.419704\pi\)
0.249589 + 0.968352i \(0.419704\pi\)
\(608\) −1.70156 −0.0690075
\(609\) 7.40312 0.299990
\(610\) 7.70156 0.311827
\(611\) −5.79063 −0.234264
\(612\) 1.00000 0.0404226
\(613\) 39.4031 1.59148 0.795739 0.605640i \(-0.207083\pi\)
0.795739 + 0.605640i \(0.207083\pi\)
\(614\) 2.59688 0.104801
\(615\) 3.40312 0.137227
\(616\) 3.70156 0.149140
\(617\) −47.6125 −1.91681 −0.958403 0.285417i \(-0.907868\pi\)
−0.958403 + 0.285417i \(0.907868\pi\)
\(618\) 17.1047 0.688051
\(619\) 43.3141 1.74094 0.870470 0.492222i \(-0.163815\pi\)
0.870470 + 0.492222i \(0.163815\pi\)
\(620\) 5.70156 0.228980
\(621\) 2.29844 0.0922331
\(622\) 4.80625 0.192713
\(623\) −51.8219 −2.07620
\(624\) 1.70156 0.0681170
\(625\) 1.00000 0.0400000
\(626\) −19.9109 −0.795801
\(627\) −1.70156 −0.0679538
\(628\) −12.0000 −0.478852
\(629\) 4.29844 0.171390
\(630\) −3.70156 −0.147474
\(631\) 2.20937 0.0879537 0.0439769 0.999033i \(-0.485997\pi\)
0.0439769 + 0.999033i \(0.485997\pi\)
\(632\) −7.40312 −0.294480
\(633\) −22.2094 −0.882743
\(634\) −14.0000 −0.556011
\(635\) −4.00000 −0.158735
\(636\) −2.00000 −0.0793052
\(637\) −11.4031 −0.451808
\(638\) −2.00000 −0.0791808
\(639\) 12.8062 0.506607
\(640\) 1.00000 0.0395285
\(641\) 34.2094 1.35119 0.675594 0.737273i \(-0.263887\pi\)
0.675594 + 0.737273i \(0.263887\pi\)
\(642\) −7.40312 −0.292178
\(643\) −29.6125 −1.16780 −0.583901 0.811825i \(-0.698475\pi\)
−0.583901 + 0.811825i \(0.698475\pi\)
\(644\) 8.50781 0.335255
\(645\) 5.40312 0.212748
\(646\) −1.70156 −0.0669471
\(647\) 28.5969 1.12426 0.562130 0.827049i \(-0.309982\pi\)
0.562130 + 0.827049i \(0.309982\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −13.4031 −0.526119
\(650\) 1.70156 0.0667408
\(651\) −21.1047 −0.827158
\(652\) −14.8062 −0.579857
\(653\) 12.2094 0.477790 0.238895 0.971045i \(-0.423215\pi\)
0.238895 + 0.971045i \(0.423215\pi\)
\(654\) 15.1047 0.590640
\(655\) −13.1047 −0.512042
\(656\) 3.40312 0.132870
\(657\) −8.00000 −0.312110
\(658\) 12.5969 0.491077
\(659\) −0.806248 −0.0314070 −0.0157035 0.999877i \(-0.504999\pi\)
−0.0157035 + 0.999877i \(0.504999\pi\)
\(660\) 1.00000 0.0389249
\(661\) 0.298438 0.0116079 0.00580394 0.999983i \(-0.498153\pi\)
0.00580394 + 0.999983i \(0.498153\pi\)
\(662\) 21.6125 0.839994
\(663\) 1.70156 0.0660832
\(664\) 9.70156 0.376494
\(665\) 6.29844 0.244243
\(666\) −4.29844 −0.166561
\(667\) −4.59688 −0.177992
\(668\) −18.8062 −0.727636
\(669\) −12.5078 −0.483580
\(670\) −8.29844 −0.320597
\(671\) 7.70156 0.297316
\(672\) −3.70156 −0.142791
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) 14.8062 0.570315
\(675\) −1.00000 −0.0384900
\(676\) −10.1047 −0.388642
\(677\) 26.4187 1.01535 0.507677 0.861547i \(-0.330504\pi\)
0.507677 + 0.861547i \(0.330504\pi\)
\(678\) 2.00000 0.0768095
\(679\) −35.9109 −1.37814
\(680\) 1.00000 0.0383482
\(681\) −14.2094 −0.544504
\(682\) 5.70156 0.218324
\(683\) 4.50781 0.172487 0.0862433 0.996274i \(-0.472514\pi\)
0.0862433 + 0.996274i \(0.472514\pi\)
\(684\) 1.70156 0.0650609
\(685\) 19.1047 0.729953
\(686\) −1.10469 −0.0421771
\(687\) −7.70156 −0.293833
\(688\) 5.40312 0.205992
\(689\) −3.40312 −0.129649
\(690\) 2.29844 0.0875000
\(691\) −30.7172 −1.16854 −0.584268 0.811561i \(-0.698618\pi\)
−0.584268 + 0.811561i \(0.698618\pi\)
\(692\) 6.50781 0.247390
\(693\) −3.70156 −0.140611
\(694\) 7.40312 0.281019
\(695\) −8.59688 −0.326098
\(696\) 2.00000 0.0758098
\(697\) 3.40312 0.128903
\(698\) −19.6125 −0.742344
\(699\) 12.8062 0.484377
\(700\) −3.70156 −0.139906
\(701\) −38.2094 −1.44315 −0.721574 0.692337i \(-0.756581\pi\)
−0.721574 + 0.692337i \(0.756581\pi\)
\(702\) −1.70156 −0.0642213
\(703\) 7.31406 0.275855
\(704\) 1.00000 0.0376889
\(705\) 3.40312 0.128169
\(706\) 2.50781 0.0943827
\(707\) 12.5969 0.473754
\(708\) 13.4031 0.503720
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 12.8062 0.480610
\(711\) 7.40312 0.277639
\(712\) −14.0000 −0.524672
\(713\) 13.1047 0.490774
\(714\) −3.70156 −0.138527
\(715\) 1.70156 0.0636348
\(716\) −3.10469 −0.116028
\(717\) −3.40312 −0.127092
\(718\) 29.0156 1.08285
\(719\) −30.4187 −1.13443 −0.567214 0.823571i \(-0.691979\pi\)
−0.567214 + 0.823571i \(0.691979\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −63.3141 −2.35794
\(722\) 16.1047 0.599354
\(723\) −4.29844 −0.159861
\(724\) −9.40312 −0.349464
\(725\) 2.00000 0.0742781
\(726\) 1.00000 0.0371135
\(727\) 5.19375 0.192626 0.0963128 0.995351i \(-0.469295\pi\)
0.0963128 + 0.995351i \(0.469295\pi\)
\(728\) −6.29844 −0.233436
\(729\) 1.00000 0.0370370
\(730\) −8.00000 −0.296093
\(731\) 5.40312 0.199842
\(732\) −7.70156 −0.284658
\(733\) 0.0890652 0.00328970 0.00164485 0.999999i \(-0.499476\pi\)
0.00164485 + 0.999999i \(0.499476\pi\)
\(734\) 6.59688 0.243495
\(735\) 6.70156 0.247191
\(736\) 2.29844 0.0847215
\(737\) −8.29844 −0.305677
\(738\) −3.40312 −0.125271
\(739\) −4.50781 −0.165822 −0.0829112 0.996557i \(-0.526422\pi\)
−0.0829112 + 0.996557i \(0.526422\pi\)
\(740\) −4.29844 −0.158014
\(741\) 2.89531 0.106362
\(742\) 7.40312 0.271777
\(743\) −32.4187 −1.18933 −0.594664 0.803974i \(-0.702715\pi\)
−0.594664 + 0.803974i \(0.702715\pi\)
\(744\) −5.70156 −0.209029
\(745\) 6.29844 0.230757
\(746\) 15.4031 0.563948
\(747\) −9.70156 −0.354962
\(748\) 1.00000 0.0365636
\(749\) 27.4031 1.00129
\(750\) −1.00000 −0.0365148
\(751\) −29.6125 −1.08058 −0.540288 0.841480i \(-0.681685\pi\)
−0.540288 + 0.841480i \(0.681685\pi\)
\(752\) 3.40312 0.124099
\(753\) 31.1047 1.13352
\(754\) 3.40312 0.123934
\(755\) 16.5078 0.600781
\(756\) 3.70156 0.134625
\(757\) 23.4031 0.850601 0.425301 0.905052i \(-0.360168\pi\)
0.425301 + 0.905052i \(0.360168\pi\)
\(758\) 27.3141 0.992091
\(759\) 2.29844 0.0834280
\(760\) 1.70156 0.0617221
\(761\) −11.1047 −0.402545 −0.201272 0.979535i \(-0.564508\pi\)
−0.201272 + 0.979535i \(0.564508\pi\)
\(762\) 4.00000 0.144905
\(763\) −55.9109 −2.02411
\(764\) −26.8062 −0.969816
\(765\) −1.00000 −0.0361551
\(766\) 35.4031 1.27917
\(767\) 22.8062 0.823486
\(768\) −1.00000 −0.0360844
\(769\) 32.2094 1.16150 0.580750 0.814082i \(-0.302759\pi\)
0.580750 + 0.814082i \(0.302759\pi\)
\(770\) −3.70156 −0.133395
\(771\) 23.6125 0.850383
\(772\) −12.0000 −0.431889
\(773\) −14.5078 −0.521810 −0.260905 0.965365i \(-0.584021\pi\)
−0.260905 + 0.965365i \(0.584021\pi\)
\(774\) −5.40312 −0.194211
\(775\) −5.70156 −0.204806
\(776\) −9.70156 −0.348266
\(777\) 15.9109 0.570802
\(778\) 12.0000 0.430221
\(779\) 5.79063 0.207471
\(780\) −1.70156 −0.0609257
\(781\) 12.8062 0.458244
\(782\) 2.29844 0.0821920
\(783\) −2.00000 −0.0714742
\(784\) 6.70156 0.239342
\(785\) 12.0000 0.428298
\(786\) 13.1047 0.467429
\(787\) −42.7172 −1.52270 −0.761352 0.648339i \(-0.775464\pi\)
−0.761352 + 0.648339i \(0.775464\pi\)
\(788\) −16.2984 −0.580608
\(789\) 2.89531 0.103076
\(790\) 7.40312 0.263391
\(791\) −7.40312 −0.263225
\(792\) −1.00000 −0.0355335
\(793\) −13.1047 −0.465361
\(794\) −12.8062 −0.454477
\(795\) 2.00000 0.0709327
\(796\) 2.29844 0.0814660
\(797\) 13.3141 0.471608 0.235804 0.971801i \(-0.424228\pi\)
0.235804 + 0.971801i \(0.424228\pi\)
\(798\) −6.29844 −0.222962
\(799\) 3.40312 0.120394
\(800\) −1.00000 −0.0353553
\(801\) 14.0000 0.494666
\(802\) 13.1047 0.462743
\(803\) −8.00000 −0.282314
\(804\) 8.29844 0.292663
\(805\) −8.50781 −0.299861
\(806\) −9.70156 −0.341723
\(807\) −26.5078 −0.933119
\(808\) 3.40312 0.119721
\(809\) 12.5969 0.442883 0.221441 0.975174i \(-0.428924\pi\)
0.221441 + 0.975174i \(0.428924\pi\)
\(810\) 1.00000 0.0351364
\(811\) 24.5969 0.863713 0.431857 0.901942i \(-0.357859\pi\)
0.431857 + 0.901942i \(0.357859\pi\)
\(812\) −7.40312 −0.259799
\(813\) −14.8062 −0.519278
\(814\) −4.29844 −0.150660
\(815\) 14.8062 0.518640
\(816\) −1.00000 −0.0350070
\(817\) 9.19375 0.321649
\(818\) −6.00000 −0.209785
\(819\) 6.29844 0.220085
\(820\) −3.40312 −0.118842
\(821\) 19.6125 0.684481 0.342240 0.939612i \(-0.388814\pi\)
0.342240 + 0.939612i \(0.388814\pi\)
\(822\) −19.1047 −0.666352
\(823\) 6.00000 0.209147 0.104573 0.994517i \(-0.466652\pi\)
0.104573 + 0.994517i \(0.466652\pi\)
\(824\) −17.1047 −0.595870
\(825\) −1.00000 −0.0348155
\(826\) −49.6125 −1.72624
\(827\) −30.2094 −1.05048 −0.525241 0.850953i \(-0.676025\pi\)
−0.525241 + 0.850953i \(0.676025\pi\)
\(828\) −2.29844 −0.0798762
\(829\) −43.1047 −1.49709 −0.748544 0.663085i \(-0.769247\pi\)
−0.748544 + 0.663085i \(0.769247\pi\)
\(830\) −9.70156 −0.336746
\(831\) −13.4031 −0.464949
\(832\) −1.70156 −0.0589911
\(833\) 6.70156 0.232195
\(834\) 8.59688 0.297685
\(835\) 18.8062 0.650817
\(836\) 1.70156 0.0588498
\(837\) 5.70156 0.197075
\(838\) 30.8062 1.06418
\(839\) 15.7906 0.545153 0.272576 0.962134i \(-0.412124\pi\)
0.272576 + 0.962134i \(0.412124\pi\)
\(840\) 3.70156 0.127716
\(841\) −25.0000 −0.862069
\(842\) 8.29844 0.285983
\(843\) 10.0000 0.344418
\(844\) 22.2094 0.764478
\(845\) 10.1047 0.347612
\(846\) −3.40312 −0.117002
\(847\) −3.70156 −0.127187
\(848\) 2.00000 0.0686803
\(849\) −12.0000 −0.411839
\(850\) −1.00000 −0.0342997
\(851\) −9.87969 −0.338671
\(852\) −12.8062 −0.438735
\(853\) −1.40312 −0.0480421 −0.0240210 0.999711i \(-0.507647\pi\)
−0.0240210 + 0.999711i \(0.507647\pi\)
\(854\) 28.5078 0.975517
\(855\) −1.70156 −0.0581922
\(856\) 7.40312 0.253034
\(857\) 51.7016 1.76609 0.883046 0.469287i \(-0.155489\pi\)
0.883046 + 0.469287i \(0.155489\pi\)
\(858\) −1.70156 −0.0580904
\(859\) −20.4187 −0.696679 −0.348339 0.937369i \(-0.613254\pi\)
−0.348339 + 0.937369i \(0.613254\pi\)
\(860\) −5.40312 −0.184245
\(861\) 12.5969 0.429300
\(862\) 36.2094 1.23330
\(863\) −16.0000 −0.544646 −0.272323 0.962206i \(-0.587792\pi\)
−0.272323 + 0.962206i \(0.587792\pi\)
\(864\) 1.00000 0.0340207
\(865\) −6.50781 −0.221272
\(866\) 18.0000 0.611665
\(867\) −1.00000 −0.0339618
\(868\) 21.1047 0.716340
\(869\) 7.40312 0.251134
\(870\) −2.00000 −0.0678064
\(871\) 14.1203 0.478448
\(872\) −15.1047 −0.511509
\(873\) 9.70156 0.328348
\(874\) 3.91093 0.132289
\(875\) 3.70156 0.125136
\(876\) 8.00000 0.270295
\(877\) 5.40312 0.182451 0.0912253 0.995830i \(-0.470922\pi\)
0.0912253 + 0.995830i \(0.470922\pi\)
\(878\) −1.79063 −0.0604307
\(879\) −21.4031 −0.721909
\(880\) −1.00000 −0.0337100
\(881\) −4.59688 −0.154873 −0.0774363 0.996997i \(-0.524673\pi\)
−0.0774363 + 0.996997i \(0.524673\pi\)
\(882\) −6.70156 −0.225653
\(883\) 11.0156 0.370705 0.185353 0.982672i \(-0.440657\pi\)
0.185353 + 0.982672i \(0.440657\pi\)
\(884\) −1.70156 −0.0572297
\(885\) −13.4031 −0.450541
\(886\) −14.2094 −0.477373
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 4.29844 0.144246
\(889\) −14.8062 −0.496586
\(890\) 14.0000 0.469281
\(891\) 1.00000 0.0335013
\(892\) 12.5078 0.418792
\(893\) 5.79063 0.193776
\(894\) −6.29844 −0.210651
\(895\) 3.10469 0.103778
\(896\) 3.70156 0.123661
\(897\) −3.91093 −0.130582
\(898\) 33.7016 1.12464
\(899\) −11.4031 −0.380315
\(900\) 1.00000 0.0333333
\(901\) 2.00000 0.0666297
\(902\) −3.40312 −0.113312
\(903\) 20.0000 0.665558
\(904\) −2.00000 −0.0665190
\(905\) 9.40312 0.312570
\(906\) −16.5078 −0.548435
\(907\) −48.0000 −1.59381 −0.796907 0.604102i \(-0.793532\pi\)
−0.796907 + 0.604102i \(0.793532\pi\)
\(908\) 14.2094 0.471555
\(909\) −3.40312 −0.112875
\(910\) 6.29844 0.208791
\(911\) −22.5969 −0.748668 −0.374334 0.927294i \(-0.622129\pi\)
−0.374334 + 0.927294i \(0.622129\pi\)
\(912\) −1.70156 −0.0563444
\(913\) −9.70156 −0.321075
\(914\) −3.10469 −0.102694
\(915\) 7.70156 0.254606
\(916\) 7.70156 0.254467
\(917\) −48.5078 −1.60187
\(918\) 1.00000 0.0330049
\(919\) 22.2984 0.735558 0.367779 0.929913i \(-0.380118\pi\)
0.367779 + 0.929913i \(0.380118\pi\)
\(920\) −2.29844 −0.0757773
\(921\) 2.59688 0.0855700
\(922\) 24.5969 0.810055
\(923\) −21.7906 −0.717247
\(924\) 3.70156 0.121772
\(925\) 4.29844 0.141332
\(926\) 18.2984 0.601324
\(927\) 17.1047 0.561792
\(928\) −2.00000 −0.0656532
\(929\) 26.2984 0.862824 0.431412 0.902155i \(-0.358016\pi\)
0.431412 + 0.902155i \(0.358016\pi\)
\(930\) 5.70156 0.186962
\(931\) 11.4031 0.373722
\(932\) −12.8062 −0.419483
\(933\) 4.80625 0.157350
\(934\) 9.19375 0.300829
\(935\) −1.00000 −0.0327035
\(936\) 1.70156 0.0556173
\(937\) −2.50781 −0.0819266 −0.0409633 0.999161i \(-0.513043\pi\)
−0.0409633 + 0.999161i \(0.513043\pi\)
\(938\) −30.7172 −1.00295
\(939\) −19.9109 −0.649769
\(940\) −3.40312 −0.110998
\(941\) 2.59688 0.0846557 0.0423279 0.999104i \(-0.486523\pi\)
0.0423279 + 0.999104i \(0.486523\pi\)
\(942\) −12.0000 −0.390981
\(943\) −7.82187 −0.254715
\(944\) −13.4031 −0.436235
\(945\) −3.70156 −0.120412
\(946\) −5.40312 −0.175671
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) −7.40312 −0.240442
\(949\) 13.6125 0.441880
\(950\) −1.70156 −0.0552060
\(951\) −14.0000 −0.453981
\(952\) 3.70156 0.119968
\(953\) 49.8219 1.61389 0.806944 0.590628i \(-0.201120\pi\)
0.806944 + 0.590628i \(0.201120\pi\)
\(954\) −2.00000 −0.0647524
\(955\) 26.8062 0.867430
\(956\) 3.40312 0.110065
\(957\) −2.00000 −0.0646508
\(958\) −29.9109 −0.966378
\(959\) 70.7172 2.28358
\(960\) 1.00000 0.0322749
\(961\) 1.50781 0.0486391
\(962\) 7.31406 0.235815
\(963\) −7.40312 −0.238562
\(964\) 4.29844 0.138443
\(965\) 12.0000 0.386294
\(966\) 8.50781 0.273734
\(967\) 34.2094 1.10010 0.550050 0.835132i \(-0.314609\pi\)
0.550050 + 0.835132i \(0.314609\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −1.70156 −0.0546621
\(970\) 9.70156 0.311498
\(971\) 36.7172 1.17831 0.589155 0.808020i \(-0.299461\pi\)
0.589155 + 0.808020i \(0.299461\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −31.8219 −1.02016
\(974\) −20.2094 −0.647550
\(975\) 1.70156 0.0544936
\(976\) 7.70156 0.246521
\(977\) 47.5234 1.52041 0.760205 0.649684i \(-0.225099\pi\)
0.760205 + 0.649684i \(0.225099\pi\)
\(978\) −14.8062 −0.473452
\(979\) 14.0000 0.447442
\(980\) −6.70156 −0.214074
\(981\) 15.1047 0.482256
\(982\) −12.8062 −0.408664
\(983\) −1.19375 −0.0380748 −0.0190374 0.999819i \(-0.506060\pi\)
−0.0190374 + 0.999819i \(0.506060\pi\)
\(984\) 3.40312 0.108488
\(985\) 16.2984 0.519311
\(986\) −2.00000 −0.0636930
\(987\) 12.5969 0.400963
\(988\) −2.89531 −0.0921122
\(989\) −12.4187 −0.394893
\(990\) 1.00000 0.0317821
\(991\) 28.5078 0.905580 0.452790 0.891617i \(-0.350429\pi\)
0.452790 + 0.891617i \(0.350429\pi\)
\(992\) 5.70156 0.181025
\(993\) 21.6125 0.685852
\(994\) 47.4031 1.50354
\(995\) −2.29844 −0.0728654
\(996\) 9.70156 0.307406
\(997\) −18.0000 −0.570066 −0.285033 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) 36.0000 1.13956
\(999\) −4.29844 −0.135997
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.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.bo.1.1 2 1.1 even 1 trivial