Properties

Label 4001.2.a.b.1.29
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.29
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.21700 q^{2} +0.365824 q^{3} +2.91510 q^{4} +2.81066 q^{5} -0.811033 q^{6} -0.497651 q^{7} -2.02878 q^{8} -2.86617 q^{9} +O(q^{10})\) \(q-2.21700 q^{2} +0.365824 q^{3} +2.91510 q^{4} +2.81066 q^{5} -0.811033 q^{6} -0.497651 q^{7} -2.02878 q^{8} -2.86617 q^{9} -6.23125 q^{10} +4.45060 q^{11} +1.06641 q^{12} -2.00286 q^{13} +1.10329 q^{14} +1.02821 q^{15} -1.33240 q^{16} +5.19461 q^{17} +6.35431 q^{18} -5.56713 q^{19} +8.19336 q^{20} -0.182053 q^{21} -9.86699 q^{22} +4.82647 q^{23} -0.742175 q^{24} +2.89983 q^{25} +4.44034 q^{26} -2.14599 q^{27} -1.45070 q^{28} -3.04267 q^{29} -2.27954 q^{30} -2.64110 q^{31} +7.01148 q^{32} +1.62814 q^{33} -11.5165 q^{34} -1.39873 q^{35} -8.35518 q^{36} +1.70848 q^{37} +12.3423 q^{38} -0.732693 q^{39} -5.70220 q^{40} +9.42310 q^{41} +0.403611 q^{42} +4.27362 q^{43} +12.9739 q^{44} -8.05585 q^{45} -10.7003 q^{46} +1.23819 q^{47} -0.487423 q^{48} -6.75234 q^{49} -6.42892 q^{50} +1.90031 q^{51} -5.83852 q^{52} -11.4657 q^{53} +4.75766 q^{54} +12.5091 q^{55} +1.00962 q^{56} -2.03659 q^{57} +6.74561 q^{58} +10.1871 q^{59} +2.99733 q^{60} +3.77568 q^{61} +5.85533 q^{62} +1.42635 q^{63} -12.8797 q^{64} -5.62935 q^{65} -3.60958 q^{66} -5.13248 q^{67} +15.1428 q^{68} +1.76564 q^{69} +3.10098 q^{70} +16.0868 q^{71} +5.81482 q^{72} +2.84487 q^{73} -3.78770 q^{74} +1.06083 q^{75} -16.2287 q^{76} -2.21484 q^{77} +1.62438 q^{78} -12.0950 q^{79} -3.74492 q^{80} +7.81346 q^{81} -20.8910 q^{82} -5.14999 q^{83} -0.530701 q^{84} +14.6003 q^{85} -9.47463 q^{86} -1.11308 q^{87} -9.02927 q^{88} +8.87946 q^{89} +17.8598 q^{90} +0.996723 q^{91} +14.0696 q^{92} -0.966178 q^{93} -2.74507 q^{94} -15.6473 q^{95} +2.56497 q^{96} +9.95199 q^{97} +14.9700 q^{98} -12.7562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21700 −1.56766 −0.783829 0.620977i \(-0.786736\pi\)
−0.783829 + 0.620977i \(0.786736\pi\)
\(3\) 0.365824 0.211209 0.105604 0.994408i \(-0.466322\pi\)
0.105604 + 0.994408i \(0.466322\pi\)
\(4\) 2.91510 1.45755
\(5\) 2.81066 1.25697 0.628483 0.777823i \(-0.283676\pi\)
0.628483 + 0.777823i \(0.283676\pi\)
\(6\) −0.811033 −0.331103
\(7\) −0.497651 −0.188094 −0.0940471 0.995568i \(-0.529980\pi\)
−0.0940471 + 0.995568i \(0.529980\pi\)
\(8\) −2.02878 −0.717281
\(9\) −2.86617 −0.955391
\(10\) −6.23125 −1.97049
\(11\) 4.45060 1.34191 0.670953 0.741500i \(-0.265885\pi\)
0.670953 + 0.741500i \(0.265885\pi\)
\(12\) 1.06641 0.307847
\(13\) −2.00286 −0.555492 −0.277746 0.960654i \(-0.589587\pi\)
−0.277746 + 0.960654i \(0.589587\pi\)
\(14\) 1.10329 0.294867
\(15\) 1.02821 0.265482
\(16\) −1.33240 −0.333099
\(17\) 5.19461 1.25988 0.629938 0.776645i \(-0.283080\pi\)
0.629938 + 0.776645i \(0.283080\pi\)
\(18\) 6.35431 1.49773
\(19\) −5.56713 −1.27719 −0.638594 0.769544i \(-0.720484\pi\)
−0.638594 + 0.769544i \(0.720484\pi\)
\(20\) 8.19336 1.83209
\(21\) −0.182053 −0.0397271
\(22\) −9.86699 −2.10365
\(23\) 4.82647 1.00639 0.503195 0.864173i \(-0.332158\pi\)
0.503195 + 0.864173i \(0.332158\pi\)
\(24\) −0.742175 −0.151496
\(25\) 2.89983 0.579965
\(26\) 4.44034 0.870822
\(27\) −2.14599 −0.412995
\(28\) −1.45070 −0.274157
\(29\) −3.04267 −0.565010 −0.282505 0.959266i \(-0.591165\pi\)
−0.282505 + 0.959266i \(0.591165\pi\)
\(30\) −2.27954 −0.416185
\(31\) −2.64110 −0.474356 −0.237178 0.971466i \(-0.576222\pi\)
−0.237178 + 0.971466i \(0.576222\pi\)
\(32\) 7.01148 1.23947
\(33\) 1.62814 0.283422
\(34\) −11.5165 −1.97506
\(35\) −1.39873 −0.236428
\(36\) −8.35518 −1.39253
\(37\) 1.70848 0.280872 0.140436 0.990090i \(-0.455150\pi\)
0.140436 + 0.990090i \(0.455150\pi\)
\(38\) 12.3423 2.00219
\(39\) −0.732693 −0.117325
\(40\) −5.70220 −0.901598
\(41\) 9.42310 1.47164 0.735820 0.677177i \(-0.236797\pi\)
0.735820 + 0.677177i \(0.236797\pi\)
\(42\) 0.403611 0.0622785
\(43\) 4.27362 0.651721 0.325861 0.945418i \(-0.394346\pi\)
0.325861 + 0.945418i \(0.394346\pi\)
\(44\) 12.9739 1.95589
\(45\) −8.05585 −1.20089
\(46\) −10.7003 −1.57767
\(47\) 1.23819 0.180609 0.0903043 0.995914i \(-0.471216\pi\)
0.0903043 + 0.995914i \(0.471216\pi\)
\(48\) −0.487423 −0.0703534
\(49\) −6.75234 −0.964621
\(50\) −6.42892 −0.909187
\(51\) 1.90031 0.266097
\(52\) −5.83852 −0.809658
\(53\) −11.4657 −1.57493 −0.787467 0.616356i \(-0.788608\pi\)
−0.787467 + 0.616356i \(0.788608\pi\)
\(54\) 4.75766 0.647435
\(55\) 12.5091 1.68673
\(56\) 1.00962 0.134916
\(57\) −2.03659 −0.269753
\(58\) 6.74561 0.885742
\(59\) 10.1871 1.32625 0.663125 0.748509i \(-0.269230\pi\)
0.663125 + 0.748509i \(0.269230\pi\)
\(60\) 2.99733 0.386953
\(61\) 3.77568 0.483426 0.241713 0.970348i \(-0.422291\pi\)
0.241713 + 0.970348i \(0.422291\pi\)
\(62\) 5.85533 0.743627
\(63\) 1.42635 0.179704
\(64\) −12.8797 −1.60996
\(65\) −5.62935 −0.698235
\(66\) −3.60958 −0.444309
\(67\) −5.13248 −0.627032 −0.313516 0.949583i \(-0.601507\pi\)
−0.313516 + 0.949583i \(0.601507\pi\)
\(68\) 15.1428 1.83633
\(69\) 1.76564 0.212558
\(70\) 3.10098 0.370638
\(71\) 16.0868 1.90916 0.954579 0.297960i \(-0.0963060\pi\)
0.954579 + 0.297960i \(0.0963060\pi\)
\(72\) 5.81482 0.685283
\(73\) 2.84487 0.332967 0.166484 0.986044i \(-0.446759\pi\)
0.166484 + 0.986044i \(0.446759\pi\)
\(74\) −3.78770 −0.440312
\(75\) 1.06083 0.122494
\(76\) −16.2287 −1.86156
\(77\) −2.21484 −0.252405
\(78\) 1.62438 0.183925
\(79\) −12.0950 −1.36079 −0.680396 0.732845i \(-0.738192\pi\)
−0.680396 + 0.732845i \(0.738192\pi\)
\(80\) −3.74492 −0.418695
\(81\) 7.81346 0.868163
\(82\) −20.8910 −2.30703
\(83\) −5.14999 −0.565285 −0.282642 0.959225i \(-0.591211\pi\)
−0.282642 + 0.959225i \(0.591211\pi\)
\(84\) −0.530701 −0.0579042
\(85\) 14.6003 1.58362
\(86\) −9.47463 −1.02168
\(87\) −1.11308 −0.119335
\(88\) −9.02927 −0.962523
\(89\) 8.87946 0.941221 0.470610 0.882341i \(-0.344034\pi\)
0.470610 + 0.882341i \(0.344034\pi\)
\(90\) 17.8598 1.88259
\(91\) 0.996723 0.104485
\(92\) 14.0696 1.46686
\(93\) −0.966178 −0.100188
\(94\) −2.74507 −0.283132
\(95\) −15.6473 −1.60538
\(96\) 2.56497 0.261786
\(97\) 9.95199 1.01047 0.505236 0.862982i \(-0.331406\pi\)
0.505236 + 0.862982i \(0.331406\pi\)
\(98\) 14.9700 1.51219
\(99\) −12.7562 −1.28205
\(100\) 8.45328 0.845328
\(101\) 10.7383 1.06850 0.534252 0.845326i \(-0.320594\pi\)
0.534252 + 0.845326i \(0.320594\pi\)
\(102\) −4.21299 −0.417149
\(103\) 12.0097 1.18335 0.591674 0.806177i \(-0.298467\pi\)
0.591674 + 0.806177i \(0.298467\pi\)
\(104\) 4.06335 0.398444
\(105\) −0.511688 −0.0499357
\(106\) 25.4195 2.46896
\(107\) 11.3375 1.09604 0.548020 0.836466i \(-0.315382\pi\)
0.548020 + 0.836466i \(0.315382\pi\)
\(108\) −6.25576 −0.601961
\(109\) 17.2438 1.65166 0.825828 0.563922i \(-0.190708\pi\)
0.825828 + 0.563922i \(0.190708\pi\)
\(110\) −27.7328 −2.64422
\(111\) 0.625003 0.0593227
\(112\) 0.663068 0.0626541
\(113\) 14.9172 1.40329 0.701644 0.712528i \(-0.252450\pi\)
0.701644 + 0.712528i \(0.252450\pi\)
\(114\) 4.51512 0.422880
\(115\) 13.5656 1.26500
\(116\) −8.86969 −0.823530
\(117\) 5.74053 0.530712
\(118\) −22.5849 −2.07910
\(119\) −2.58510 −0.236976
\(120\) −2.08600 −0.190425
\(121\) 8.80784 0.800713
\(122\) −8.37068 −0.757846
\(123\) 3.44720 0.310823
\(124\) −7.69907 −0.691397
\(125\) −5.90288 −0.527970
\(126\) −3.16223 −0.281714
\(127\) 8.39595 0.745020 0.372510 0.928028i \(-0.378497\pi\)
0.372510 + 0.928028i \(0.378497\pi\)
\(128\) 14.5313 1.28440
\(129\) 1.56339 0.137649
\(130\) 12.4803 1.09459
\(131\) −9.40775 −0.821959 −0.410980 0.911645i \(-0.634813\pi\)
−0.410980 + 0.911645i \(0.634813\pi\)
\(132\) 4.74618 0.413102
\(133\) 2.77049 0.240232
\(134\) 11.3787 0.982971
\(135\) −6.03165 −0.519121
\(136\) −10.5387 −0.903685
\(137\) 8.43309 0.720487 0.360244 0.932858i \(-0.382694\pi\)
0.360244 + 0.932858i \(0.382694\pi\)
\(138\) −3.91443 −0.333218
\(139\) −6.95296 −0.589742 −0.294871 0.955537i \(-0.595277\pi\)
−0.294871 + 0.955537i \(0.595277\pi\)
\(140\) −4.07743 −0.344606
\(141\) 0.452959 0.0381461
\(142\) −35.6646 −2.99290
\(143\) −8.91391 −0.745419
\(144\) 3.81888 0.318240
\(145\) −8.55193 −0.710199
\(146\) −6.30709 −0.521979
\(147\) −2.47017 −0.203736
\(148\) 4.98039 0.409385
\(149\) −5.62980 −0.461211 −0.230606 0.973047i \(-0.574071\pi\)
−0.230606 + 0.973047i \(0.574071\pi\)
\(150\) −2.35185 −0.192028
\(151\) −13.0527 −1.06222 −0.531108 0.847304i \(-0.678224\pi\)
−0.531108 + 0.847304i \(0.678224\pi\)
\(152\) 11.2945 0.916102
\(153\) −14.8886 −1.20368
\(154\) 4.91031 0.395684
\(155\) −7.42325 −0.596250
\(156\) −2.13587 −0.171007
\(157\) −12.8484 −1.02541 −0.512706 0.858564i \(-0.671357\pi\)
−0.512706 + 0.858564i \(0.671357\pi\)
\(158\) 26.8146 2.13325
\(159\) −4.19443 −0.332640
\(160\) 19.7069 1.55797
\(161\) −2.40190 −0.189296
\(162\) −17.3225 −1.36098
\(163\) −5.25420 −0.411541 −0.205770 0.978600i \(-0.565970\pi\)
−0.205770 + 0.978600i \(0.565970\pi\)
\(164\) 27.4693 2.14499
\(165\) 4.57614 0.356252
\(166\) 11.4175 0.886173
\(167\) 5.68137 0.439637 0.219819 0.975541i \(-0.429453\pi\)
0.219819 + 0.975541i \(0.429453\pi\)
\(168\) 0.369344 0.0284955
\(169\) −8.98857 −0.691428
\(170\) −32.3689 −2.48258
\(171\) 15.9564 1.22021
\(172\) 12.4580 0.949916
\(173\) 14.1023 1.07218 0.536090 0.844161i \(-0.319901\pi\)
0.536090 + 0.844161i \(0.319901\pi\)
\(174\) 2.46771 0.187076
\(175\) −1.44310 −0.109088
\(176\) −5.92997 −0.446988
\(177\) 3.72669 0.280115
\(178\) −19.6858 −1.47551
\(179\) −24.2263 −1.81076 −0.905381 0.424600i \(-0.860415\pi\)
−0.905381 + 0.424600i \(0.860415\pi\)
\(180\) −23.4836 −1.75036
\(181\) −13.5637 −1.00818 −0.504089 0.863652i \(-0.668172\pi\)
−0.504089 + 0.863652i \(0.668172\pi\)
\(182\) −2.20974 −0.163797
\(183\) 1.38123 0.102104
\(184\) −9.79183 −0.721863
\(185\) 4.80196 0.353047
\(186\) 2.14202 0.157061
\(187\) 23.1191 1.69064
\(188\) 3.60944 0.263246
\(189\) 1.06795 0.0776821
\(190\) 34.6902 2.51669
\(191\) 22.9796 1.66275 0.831373 0.555715i \(-0.187555\pi\)
0.831373 + 0.555715i \(0.187555\pi\)
\(192\) −4.71169 −0.340037
\(193\) −1.23120 −0.0886235 −0.0443118 0.999018i \(-0.514109\pi\)
−0.0443118 + 0.999018i \(0.514109\pi\)
\(194\) −22.0636 −1.58407
\(195\) −2.05935 −0.147473
\(196\) −19.6837 −1.40598
\(197\) −7.68849 −0.547783 −0.273891 0.961761i \(-0.588311\pi\)
−0.273891 + 0.961761i \(0.588311\pi\)
\(198\) 28.2805 2.00981
\(199\) 19.0580 1.35099 0.675494 0.737366i \(-0.263930\pi\)
0.675494 + 0.737366i \(0.263930\pi\)
\(200\) −5.88310 −0.415998
\(201\) −1.87758 −0.132435
\(202\) −23.8069 −1.67505
\(203\) 1.51419 0.106275
\(204\) 5.53960 0.387849
\(205\) 26.4852 1.84980
\(206\) −26.6255 −1.85509
\(207\) −13.8335 −0.961495
\(208\) 2.66860 0.185034
\(209\) −24.7771 −1.71387
\(210\) 1.13441 0.0782820
\(211\) 4.40958 0.303568 0.151784 0.988414i \(-0.451498\pi\)
0.151784 + 0.988414i \(0.451498\pi\)
\(212\) −33.4236 −2.29554
\(213\) 5.88495 0.403230
\(214\) −25.1353 −1.71821
\(215\) 12.0117 0.819192
\(216\) 4.35373 0.296234
\(217\) 1.31435 0.0892236
\(218\) −38.2295 −2.58923
\(219\) 1.04072 0.0703256
\(220\) 36.4654 2.45849
\(221\) −10.4040 −0.699852
\(222\) −1.38563 −0.0929976
\(223\) −2.38168 −0.159489 −0.0797447 0.996815i \(-0.525410\pi\)
−0.0797447 + 0.996815i \(0.525410\pi\)
\(224\) −3.48927 −0.233136
\(225\) −8.31140 −0.554094
\(226\) −33.0714 −2.19987
\(227\) −9.35137 −0.620672 −0.310336 0.950627i \(-0.600442\pi\)
−0.310336 + 0.950627i \(0.600442\pi\)
\(228\) −5.93686 −0.393178
\(229\) 18.4579 1.21973 0.609865 0.792505i \(-0.291224\pi\)
0.609865 + 0.792505i \(0.291224\pi\)
\(230\) −30.0749 −1.98308
\(231\) −0.810243 −0.0533101
\(232\) 6.17290 0.405271
\(233\) −9.61225 −0.629719 −0.314860 0.949138i \(-0.601957\pi\)
−0.314860 + 0.949138i \(0.601957\pi\)
\(234\) −12.7268 −0.831975
\(235\) 3.48013 0.227019
\(236\) 29.6964 1.93307
\(237\) −4.42463 −0.287411
\(238\) 5.73117 0.371497
\(239\) 8.92695 0.577436 0.288718 0.957414i \(-0.406771\pi\)
0.288718 + 0.957414i \(0.406771\pi\)
\(240\) −1.36998 −0.0884319
\(241\) −3.90210 −0.251357 −0.125678 0.992071i \(-0.540111\pi\)
−0.125678 + 0.992071i \(0.540111\pi\)
\(242\) −19.5270 −1.25524
\(243\) 9.29631 0.596359
\(244\) 11.0065 0.704617
\(245\) −18.9786 −1.21250
\(246\) −7.64244 −0.487264
\(247\) 11.1502 0.709468
\(248\) 5.35820 0.340246
\(249\) −1.88399 −0.119393
\(250\) 13.0867 0.827675
\(251\) −15.4281 −0.973814 −0.486907 0.873454i \(-0.661875\pi\)
−0.486907 + 0.873454i \(0.661875\pi\)
\(252\) 4.15796 0.261927
\(253\) 21.4807 1.35048
\(254\) −18.6138 −1.16794
\(255\) 5.34114 0.334475
\(256\) −6.45658 −0.403536
\(257\) −22.4270 −1.39896 −0.699478 0.714654i \(-0.746584\pi\)
−0.699478 + 0.714654i \(0.746584\pi\)
\(258\) −3.46605 −0.215787
\(259\) −0.850226 −0.0528305
\(260\) −16.4101 −1.01771
\(261\) 8.72083 0.539806
\(262\) 20.8570 1.28855
\(263\) −0.840588 −0.0518328 −0.0259164 0.999664i \(-0.508250\pi\)
−0.0259164 + 0.999664i \(0.508250\pi\)
\(264\) −3.30312 −0.203293
\(265\) −32.2262 −1.97964
\(266\) −6.14217 −0.376601
\(267\) 3.24832 0.198794
\(268\) −14.9617 −0.913930
\(269\) −23.7175 −1.44608 −0.723040 0.690806i \(-0.757256\pi\)
−0.723040 + 0.690806i \(0.757256\pi\)
\(270\) 13.3722 0.813804
\(271\) 26.1155 1.58640 0.793202 0.608959i \(-0.208413\pi\)
0.793202 + 0.608959i \(0.208413\pi\)
\(272\) −6.92128 −0.419664
\(273\) 0.364625 0.0220681
\(274\) −18.6962 −1.12948
\(275\) 12.9060 0.778259
\(276\) 5.14701 0.309814
\(277\) −25.3763 −1.52471 −0.762357 0.647156i \(-0.775958\pi\)
−0.762357 + 0.647156i \(0.775958\pi\)
\(278\) 15.4147 0.924514
\(279\) 7.56985 0.453195
\(280\) 2.83771 0.169585
\(281\) 30.5131 1.82026 0.910131 0.414322i \(-0.135981\pi\)
0.910131 + 0.414322i \(0.135981\pi\)
\(282\) −1.00421 −0.0598000
\(283\) −15.6512 −0.930365 −0.465183 0.885215i \(-0.654011\pi\)
−0.465183 + 0.885215i \(0.654011\pi\)
\(284\) 46.8947 2.78269
\(285\) −5.72417 −0.339070
\(286\) 19.7622 1.16856
\(287\) −4.68941 −0.276807
\(288\) −20.0961 −1.18417
\(289\) 9.98393 0.587290
\(290\) 18.9596 1.11335
\(291\) 3.64068 0.213420
\(292\) 8.29309 0.485316
\(293\) −19.5960 −1.14481 −0.572406 0.819970i \(-0.693990\pi\)
−0.572406 + 0.819970i \(0.693990\pi\)
\(294\) 5.47637 0.319388
\(295\) 28.6325 1.66705
\(296\) −3.46612 −0.201464
\(297\) −9.55093 −0.554201
\(298\) 12.4813 0.723021
\(299\) −9.66673 −0.559042
\(300\) 3.09241 0.178541
\(301\) −2.12677 −0.122585
\(302\) 28.9379 1.66519
\(303\) 3.92834 0.225677
\(304\) 7.41763 0.425430
\(305\) 10.6122 0.607650
\(306\) 33.0081 1.88695
\(307\) 21.1550 1.20738 0.603689 0.797220i \(-0.293697\pi\)
0.603689 + 0.797220i \(0.293697\pi\)
\(308\) −6.45649 −0.367893
\(309\) 4.39343 0.249933
\(310\) 16.4574 0.934715
\(311\) 32.8451 1.86248 0.931239 0.364410i \(-0.118729\pi\)
0.931239 + 0.364410i \(0.118729\pi\)
\(312\) 1.48647 0.0841548
\(313\) 5.25756 0.297175 0.148588 0.988899i \(-0.452527\pi\)
0.148588 + 0.988899i \(0.452527\pi\)
\(314\) 28.4849 1.60749
\(315\) 4.00900 0.225881
\(316\) −35.2581 −1.98342
\(317\) 31.6990 1.78039 0.890197 0.455576i \(-0.150567\pi\)
0.890197 + 0.455576i \(0.150567\pi\)
\(318\) 9.29905 0.521465
\(319\) −13.5417 −0.758191
\(320\) −36.2004 −2.02366
\(321\) 4.14754 0.231493
\(322\) 5.32501 0.296751
\(323\) −28.9190 −1.60910
\(324\) 22.7770 1.26539
\(325\) −5.80794 −0.322166
\(326\) 11.6486 0.645155
\(327\) 6.30819 0.348844
\(328\) −19.1174 −1.05558
\(329\) −0.616186 −0.0339714
\(330\) −10.1453 −0.558481
\(331\) −16.5764 −0.911120 −0.455560 0.890205i \(-0.650561\pi\)
−0.455560 + 0.890205i \(0.650561\pi\)
\(332\) −15.0127 −0.823931
\(333\) −4.89680 −0.268343
\(334\) −12.5956 −0.689201
\(335\) −14.4257 −0.788158
\(336\) 0.242566 0.0132331
\(337\) 36.0895 1.96592 0.982959 0.183825i \(-0.0588479\pi\)
0.982959 + 0.183825i \(0.0588479\pi\)
\(338\) 19.9277 1.08392
\(339\) 5.45705 0.296386
\(340\) 42.5613 2.30821
\(341\) −11.7545 −0.636541
\(342\) −35.3753 −1.91288
\(343\) 6.84386 0.369534
\(344\) −8.67022 −0.467467
\(345\) 4.96262 0.267178
\(346\) −31.2649 −1.68081
\(347\) −30.1062 −1.61619 −0.808093 0.589054i \(-0.799500\pi\)
−0.808093 + 0.589054i \(0.799500\pi\)
\(348\) −3.24475 −0.173937
\(349\) −34.4658 −1.84491 −0.922455 0.386104i \(-0.873821\pi\)
−0.922455 + 0.386104i \(0.873821\pi\)
\(350\) 3.19936 0.171013
\(351\) 4.29810 0.229416
\(352\) 31.2053 1.66325
\(353\) 19.0134 1.01198 0.505990 0.862539i \(-0.331127\pi\)
0.505990 + 0.862539i \(0.331127\pi\)
\(354\) −8.26208 −0.439125
\(355\) 45.2147 2.39975
\(356\) 25.8845 1.37188
\(357\) −0.945691 −0.0500513
\(358\) 53.7099 2.83865
\(359\) 37.4606 1.97709 0.988547 0.150913i \(-0.0482213\pi\)
0.988547 + 0.150913i \(0.0482213\pi\)
\(360\) 16.3435 0.861378
\(361\) 11.9929 0.631207
\(362\) 30.0707 1.58048
\(363\) 3.22212 0.169117
\(364\) 2.90554 0.152292
\(365\) 7.99598 0.418529
\(366\) −3.06220 −0.160064
\(367\) 8.83409 0.461136 0.230568 0.973056i \(-0.425942\pi\)
0.230568 + 0.973056i \(0.425942\pi\)
\(368\) −6.43078 −0.335228
\(369\) −27.0082 −1.40599
\(370\) −10.6460 −0.553457
\(371\) 5.70591 0.296236
\(372\) −2.81651 −0.146029
\(373\) −18.5727 −0.961656 −0.480828 0.876815i \(-0.659664\pi\)
−0.480828 + 0.876815i \(0.659664\pi\)
\(374\) −51.2551 −2.65034
\(375\) −2.15942 −0.111512
\(376\) −2.51201 −0.129547
\(377\) 6.09404 0.313859
\(378\) −2.36765 −0.121779
\(379\) 10.8376 0.556691 0.278345 0.960481i \(-0.410214\pi\)
0.278345 + 0.960481i \(0.410214\pi\)
\(380\) −45.6135 −2.33992
\(381\) 3.07144 0.157355
\(382\) −50.9458 −2.60662
\(383\) 24.6609 1.26011 0.630056 0.776549i \(-0.283032\pi\)
0.630056 + 0.776549i \(0.283032\pi\)
\(384\) 5.31590 0.271276
\(385\) −6.22518 −0.317265
\(386\) 2.72957 0.138931
\(387\) −12.2489 −0.622649
\(388\) 29.0110 1.47281
\(389\) 23.6603 1.19963 0.599813 0.800140i \(-0.295241\pi\)
0.599813 + 0.800140i \(0.295241\pi\)
\(390\) 4.56559 0.231188
\(391\) 25.0716 1.26793
\(392\) 13.6990 0.691904
\(393\) −3.44158 −0.173605
\(394\) 17.0454 0.858735
\(395\) −33.9949 −1.71047
\(396\) −37.1855 −1.86864
\(397\) 2.36371 0.118631 0.0593157 0.998239i \(-0.481108\pi\)
0.0593157 + 0.998239i \(0.481108\pi\)
\(398\) −42.2517 −2.11789
\(399\) 1.01351 0.0507390
\(400\) −3.86372 −0.193186
\(401\) 30.8622 1.54119 0.770593 0.637328i \(-0.219960\pi\)
0.770593 + 0.637328i \(0.219960\pi\)
\(402\) 4.16261 0.207612
\(403\) 5.28975 0.263501
\(404\) 31.3033 1.55740
\(405\) 21.9610 1.09125
\(406\) −3.35696 −0.166603
\(407\) 7.60376 0.376904
\(408\) −3.85531 −0.190866
\(409\) −20.4684 −1.01210 −0.506049 0.862505i \(-0.668894\pi\)
−0.506049 + 0.862505i \(0.668894\pi\)
\(410\) −58.7177 −2.89986
\(411\) 3.08503 0.152173
\(412\) 35.0094 1.72479
\(413\) −5.06962 −0.249460
\(414\) 30.6689 1.50729
\(415\) −14.4749 −0.710544
\(416\) −14.0430 −0.688514
\(417\) −2.54356 −0.124559
\(418\) 54.9308 2.68675
\(419\) 35.1238 1.71591 0.857956 0.513724i \(-0.171734\pi\)
0.857956 + 0.513724i \(0.171734\pi\)
\(420\) −1.49162 −0.0727837
\(421\) 14.7872 0.720683 0.360342 0.932820i \(-0.382660\pi\)
0.360342 + 0.932820i \(0.382660\pi\)
\(422\) −9.77604 −0.475890
\(423\) −3.54887 −0.172552
\(424\) 23.2613 1.12967
\(425\) 15.0635 0.730685
\(426\) −13.0470 −0.632127
\(427\) −1.87897 −0.0909296
\(428\) 33.0500 1.59753
\(429\) −3.26092 −0.157439
\(430\) −26.6300 −1.28421
\(431\) 6.98802 0.336601 0.168301 0.985736i \(-0.446172\pi\)
0.168301 + 0.985736i \(0.446172\pi\)
\(432\) 2.85931 0.137568
\(433\) 2.83323 0.136156 0.0680782 0.997680i \(-0.478313\pi\)
0.0680782 + 0.997680i \(0.478313\pi\)
\(434\) −2.91391 −0.139872
\(435\) −3.12850 −0.150000
\(436\) 50.2674 2.40737
\(437\) −26.8696 −1.28535
\(438\) −2.30729 −0.110246
\(439\) 37.7169 1.80013 0.900066 0.435755i \(-0.143518\pi\)
0.900066 + 0.435755i \(0.143518\pi\)
\(440\) −25.3782 −1.20986
\(441\) 19.3534 0.921590
\(442\) 23.0658 1.09713
\(443\) 25.8786 1.22953 0.614766 0.788710i \(-0.289251\pi\)
0.614766 + 0.788710i \(0.289251\pi\)
\(444\) 1.82195 0.0864657
\(445\) 24.9572 1.18308
\(446\) 5.28020 0.250025
\(447\) −2.05952 −0.0974117
\(448\) 6.40958 0.302824
\(449\) 39.7352 1.87522 0.937610 0.347689i \(-0.113034\pi\)
0.937610 + 0.347689i \(0.113034\pi\)
\(450\) 18.4264 0.868629
\(451\) 41.9384 1.97480
\(452\) 43.4850 2.04536
\(453\) −4.77500 −0.224349
\(454\) 20.7320 0.973001
\(455\) 2.80145 0.131334
\(456\) 4.13178 0.193489
\(457\) 5.09670 0.238414 0.119207 0.992869i \(-0.461965\pi\)
0.119207 + 0.992869i \(0.461965\pi\)
\(458\) −40.9211 −1.91212
\(459\) −11.1476 −0.520323
\(460\) 39.5450 1.84380
\(461\) −24.4950 −1.14085 −0.570423 0.821351i \(-0.693221\pi\)
−0.570423 + 0.821351i \(0.693221\pi\)
\(462\) 1.79631 0.0835719
\(463\) −37.0768 −1.72310 −0.861552 0.507670i \(-0.830507\pi\)
−0.861552 + 0.507670i \(0.830507\pi\)
\(464\) 4.05405 0.188204
\(465\) −2.71560 −0.125933
\(466\) 21.3104 0.987184
\(467\) −34.9945 −1.61935 −0.809677 0.586876i \(-0.800358\pi\)
−0.809677 + 0.586876i \(0.800358\pi\)
\(468\) 16.7342 0.773539
\(469\) 2.55418 0.117941
\(470\) −7.71546 −0.355888
\(471\) −4.70024 −0.216576
\(472\) −20.6674 −0.951293
\(473\) 19.0202 0.874549
\(474\) 9.80942 0.450562
\(475\) −16.1437 −0.740724
\(476\) −7.53582 −0.345404
\(477\) 32.8627 1.50468
\(478\) −19.7911 −0.905222
\(479\) −26.3152 −1.20237 −0.601185 0.799110i \(-0.705305\pi\)
−0.601185 + 0.799110i \(0.705305\pi\)
\(480\) 7.20926 0.329056
\(481\) −3.42184 −0.156022
\(482\) 8.65097 0.394041
\(483\) −0.878672 −0.0399809
\(484\) 25.6757 1.16708
\(485\) 27.9717 1.27013
\(486\) −20.6099 −0.934886
\(487\) −2.81618 −0.127613 −0.0638066 0.997962i \(-0.520324\pi\)
−0.0638066 + 0.997962i \(0.520324\pi\)
\(488\) −7.66000 −0.346752
\(489\) −1.92211 −0.0869209
\(490\) 42.0755 1.90078
\(491\) −38.7046 −1.74671 −0.873356 0.487082i \(-0.838061\pi\)
−0.873356 + 0.487082i \(0.838061\pi\)
\(492\) 10.0489 0.453040
\(493\) −15.8055 −0.711843
\(494\) −24.7199 −1.11220
\(495\) −35.8533 −1.61149
\(496\) 3.51900 0.158008
\(497\) −8.00563 −0.359101
\(498\) 4.17681 0.187167
\(499\) 40.6016 1.81758 0.908790 0.417254i \(-0.137008\pi\)
0.908790 + 0.417254i \(0.137008\pi\)
\(500\) −17.2075 −0.769542
\(501\) 2.07838 0.0928552
\(502\) 34.2042 1.52661
\(503\) −18.3406 −0.817767 −0.408884 0.912587i \(-0.634082\pi\)
−0.408884 + 0.912587i \(0.634082\pi\)
\(504\) −2.89375 −0.128898
\(505\) 30.1818 1.34307
\(506\) −47.6228 −2.11709
\(507\) −3.28823 −0.146036
\(508\) 24.4750 1.08590
\(509\) 11.4105 0.505760 0.252880 0.967498i \(-0.418622\pi\)
0.252880 + 0.967498i \(0.418622\pi\)
\(510\) −11.8413 −0.524342
\(511\) −1.41575 −0.0626292
\(512\) −14.7483 −0.651791
\(513\) 11.9470 0.527472
\(514\) 49.7206 2.19308
\(515\) 33.7552 1.48743
\(516\) 4.55745 0.200630
\(517\) 5.51069 0.242360
\(518\) 1.88495 0.0828201
\(519\) 5.15897 0.226454
\(520\) 11.4207 0.500831
\(521\) −6.92978 −0.303599 −0.151799 0.988411i \(-0.548507\pi\)
−0.151799 + 0.988411i \(0.548507\pi\)
\(522\) −19.3341 −0.846230
\(523\) −11.1293 −0.486650 −0.243325 0.969945i \(-0.578238\pi\)
−0.243325 + 0.969945i \(0.578238\pi\)
\(524\) −27.4245 −1.19805
\(525\) −0.527921 −0.0230404
\(526\) 1.86358 0.0812561
\(527\) −13.7195 −0.597630
\(528\) −2.16932 −0.0944077
\(529\) 0.294842 0.0128192
\(530\) 71.4456 3.10340
\(531\) −29.1980 −1.26709
\(532\) 8.07624 0.350149
\(533\) −18.8731 −0.817485
\(534\) −7.20153 −0.311641
\(535\) 31.8659 1.37768
\(536\) 10.4126 0.449758
\(537\) −8.86258 −0.382448
\(538\) 52.5817 2.26696
\(539\) −30.0520 −1.29443
\(540\) −17.5828 −0.756645
\(541\) −9.44965 −0.406272 −0.203136 0.979150i \(-0.565113\pi\)
−0.203136 + 0.979150i \(0.565113\pi\)
\(542\) −57.8981 −2.48694
\(543\) −4.96191 −0.212936
\(544\) 36.4219 1.56157
\(545\) 48.4665 2.07608
\(546\) −0.808375 −0.0345952
\(547\) 20.3596 0.870514 0.435257 0.900306i \(-0.356658\pi\)
0.435257 + 0.900306i \(0.356658\pi\)
\(548\) 24.5833 1.05015
\(549\) −10.8217 −0.461861
\(550\) −28.6126 −1.22004
\(551\) 16.9390 0.721624
\(552\) −3.58209 −0.152464
\(553\) 6.01907 0.255957
\(554\) 56.2593 2.39023
\(555\) 1.75667 0.0745666
\(556\) −20.2686 −0.859578
\(557\) −23.6312 −1.00129 −0.500644 0.865653i \(-0.666903\pi\)
−0.500644 + 0.865653i \(0.666903\pi\)
\(558\) −16.7824 −0.710455
\(559\) −8.55945 −0.362026
\(560\) 1.86366 0.0787541
\(561\) 8.45753 0.357077
\(562\) −67.6477 −2.85355
\(563\) −14.6097 −0.615728 −0.307864 0.951430i \(-0.599614\pi\)
−0.307864 + 0.951430i \(0.599614\pi\)
\(564\) 1.32042 0.0555998
\(565\) 41.9271 1.76389
\(566\) 34.6987 1.45849
\(567\) −3.88838 −0.163296
\(568\) −32.6366 −1.36940
\(569\) 3.08716 0.129420 0.0647102 0.997904i \(-0.479388\pi\)
0.0647102 + 0.997904i \(0.479388\pi\)
\(570\) 12.6905 0.531546
\(571\) 24.0448 1.00624 0.503121 0.864216i \(-0.332185\pi\)
0.503121 + 0.864216i \(0.332185\pi\)
\(572\) −25.9849 −1.08648
\(573\) 8.40649 0.351186
\(574\) 10.3964 0.433939
\(575\) 13.9959 0.583671
\(576\) 36.9154 1.53814
\(577\) −34.0354 −1.41691 −0.708455 0.705756i \(-0.750608\pi\)
−0.708455 + 0.705756i \(0.750608\pi\)
\(578\) −22.1344 −0.920669
\(579\) −0.450402 −0.0187180
\(580\) −24.9297 −1.03515
\(581\) 2.56290 0.106327
\(582\) −8.07138 −0.334570
\(583\) −51.0292 −2.11341
\(584\) −5.77161 −0.238831
\(585\) 16.1347 0.667088
\(586\) 43.4444 1.79467
\(587\) 13.9403 0.575379 0.287689 0.957724i \(-0.407113\pi\)
0.287689 + 0.957724i \(0.407113\pi\)
\(588\) −7.20079 −0.296955
\(589\) 14.7034 0.605841
\(590\) −63.4784 −2.61336
\(591\) −2.81264 −0.115696
\(592\) −2.27637 −0.0935584
\(593\) −45.0631 −1.85052 −0.925259 0.379335i \(-0.876153\pi\)
−0.925259 + 0.379335i \(0.876153\pi\)
\(594\) 21.1744 0.868797
\(595\) −7.26584 −0.297870
\(596\) −16.4114 −0.672238
\(597\) 6.97188 0.285340
\(598\) 21.4312 0.876386
\(599\) 18.8110 0.768597 0.384298 0.923209i \(-0.374443\pi\)
0.384298 + 0.923209i \(0.374443\pi\)
\(600\) −2.15218 −0.0878623
\(601\) 31.1413 1.27028 0.635139 0.772398i \(-0.280943\pi\)
0.635139 + 0.772398i \(0.280943\pi\)
\(602\) 4.71506 0.192171
\(603\) 14.7106 0.599061
\(604\) −38.0500 −1.54823
\(605\) 24.7559 1.00647
\(606\) −8.70913 −0.353784
\(607\) 5.69455 0.231135 0.115567 0.993300i \(-0.463131\pi\)
0.115567 + 0.993300i \(0.463131\pi\)
\(608\) −39.0338 −1.58303
\(609\) 0.553926 0.0224462
\(610\) −23.5272 −0.952587
\(611\) −2.47992 −0.100327
\(612\) −43.4018 −1.75442
\(613\) −45.3709 −1.83251 −0.916257 0.400592i \(-0.868805\pi\)
−0.916257 + 0.400592i \(0.868805\pi\)
\(614\) −46.9006 −1.89276
\(615\) 9.68891 0.390694
\(616\) 4.49342 0.181045
\(617\) 6.79248 0.273455 0.136727 0.990609i \(-0.456342\pi\)
0.136727 + 0.990609i \(0.456342\pi\)
\(618\) −9.74024 −0.391810
\(619\) 10.9342 0.439481 0.219741 0.975558i \(-0.429479\pi\)
0.219741 + 0.975558i \(0.429479\pi\)
\(620\) −21.6395 −0.869063
\(621\) −10.3575 −0.415634
\(622\) −72.8177 −2.91973
\(623\) −4.41887 −0.177038
\(624\) 0.976238 0.0390808
\(625\) −31.0901 −1.24361
\(626\) −11.6560 −0.465869
\(627\) −9.06405 −0.361983
\(628\) −37.4543 −1.49459
\(629\) 8.87488 0.353865
\(630\) −8.88795 −0.354105
\(631\) −19.2251 −0.765341 −0.382670 0.923885i \(-0.624995\pi\)
−0.382670 + 0.923885i \(0.624995\pi\)
\(632\) 24.5380 0.976069
\(633\) 1.61313 0.0641161
\(634\) −70.2768 −2.79105
\(635\) 23.5982 0.936465
\(636\) −12.2272 −0.484839
\(637\) 13.5240 0.535839
\(638\) 30.0220 1.18858
\(639\) −46.1077 −1.82399
\(640\) 40.8426 1.61444
\(641\) 12.2946 0.485608 0.242804 0.970075i \(-0.421933\pi\)
0.242804 + 0.970075i \(0.421933\pi\)
\(642\) −9.19509 −0.362901
\(643\) −14.5822 −0.575066 −0.287533 0.957771i \(-0.592835\pi\)
−0.287533 + 0.957771i \(0.592835\pi\)
\(644\) −7.00177 −0.275908
\(645\) 4.39417 0.173020
\(646\) 64.1136 2.52252
\(647\) 20.9376 0.823142 0.411571 0.911378i \(-0.364980\pi\)
0.411571 + 0.911378i \(0.364980\pi\)
\(648\) −15.8518 −0.622716
\(649\) 45.3388 1.77970
\(650\) 12.8762 0.505046
\(651\) 0.480819 0.0188448
\(652\) −15.3165 −0.599841
\(653\) 27.5327 1.07744 0.538719 0.842486i \(-0.318909\pi\)
0.538719 + 0.842486i \(0.318909\pi\)
\(654\) −13.9853 −0.546868
\(655\) −26.4420 −1.03318
\(656\) −12.5553 −0.490203
\(657\) −8.15390 −0.318114
\(658\) 1.36609 0.0532555
\(659\) 12.4193 0.483785 0.241893 0.970303i \(-0.422232\pi\)
0.241893 + 0.970303i \(0.422232\pi\)
\(660\) 13.3399 0.519255
\(661\) −2.22396 −0.0865021 −0.0432511 0.999064i \(-0.513772\pi\)
−0.0432511 + 0.999064i \(0.513772\pi\)
\(662\) 36.7499 1.42832
\(663\) −3.80605 −0.147815
\(664\) 10.4482 0.405468
\(665\) 7.78690 0.301963
\(666\) 10.8562 0.420670
\(667\) −14.6854 −0.568620
\(668\) 16.5617 0.640793
\(669\) −0.871277 −0.0336855
\(670\) 31.9817 1.23556
\(671\) 16.8040 0.648712
\(672\) −1.27646 −0.0492404
\(673\) −32.3718 −1.24784 −0.623920 0.781488i \(-0.714461\pi\)
−0.623920 + 0.781488i \(0.714461\pi\)
\(674\) −80.0104 −3.08189
\(675\) −6.22299 −0.239523
\(676\) −26.2026 −1.00779
\(677\) 30.3272 1.16557 0.582784 0.812627i \(-0.301963\pi\)
0.582784 + 0.812627i \(0.301963\pi\)
\(678\) −12.0983 −0.464632
\(679\) −4.95261 −0.190064
\(680\) −29.6207 −1.13590
\(681\) −3.42096 −0.131091
\(682\) 26.0597 0.997879
\(683\) 25.3359 0.969452 0.484726 0.874666i \(-0.338919\pi\)
0.484726 + 0.874666i \(0.338919\pi\)
\(684\) 46.5144 1.77852
\(685\) 23.7026 0.905629
\(686\) −15.1729 −0.579302
\(687\) 6.75233 0.257617
\(688\) −5.69416 −0.217088
\(689\) 22.9641 0.874864
\(690\) −11.0021 −0.418844
\(691\) 22.9999 0.874958 0.437479 0.899229i \(-0.355872\pi\)
0.437479 + 0.899229i \(0.355872\pi\)
\(692\) 41.1097 1.56275
\(693\) 6.34813 0.241145
\(694\) 66.7456 2.53363
\(695\) −19.5424 −0.741286
\(696\) 2.25820 0.0855967
\(697\) 48.9493 1.85409
\(698\) 76.4107 2.89219
\(699\) −3.51639 −0.133002
\(700\) −4.20678 −0.159001
\(701\) −13.0035 −0.491134 −0.245567 0.969380i \(-0.578974\pi\)
−0.245567 + 0.969380i \(0.578974\pi\)
\(702\) −9.52890 −0.359645
\(703\) −9.51133 −0.358727
\(704\) −57.3223 −2.16041
\(705\) 1.27312 0.0479483
\(706\) −42.1527 −1.58644
\(707\) −5.34393 −0.200979
\(708\) 10.8637 0.408282
\(709\) −10.9808 −0.412392 −0.206196 0.978511i \(-0.566109\pi\)
−0.206196 + 0.978511i \(0.566109\pi\)
\(710\) −100.241 −3.76198
\(711\) 34.6663 1.30009
\(712\) −18.0144 −0.675119
\(713\) −12.7472 −0.477387
\(714\) 2.09660 0.0784633
\(715\) −25.0540 −0.936967
\(716\) −70.6222 −2.63927
\(717\) 3.26569 0.121959
\(718\) −83.0502 −3.09941
\(719\) 20.8023 0.775794 0.387897 0.921703i \(-0.373202\pi\)
0.387897 + 0.921703i \(0.373202\pi\)
\(720\) 10.7336 0.400017
\(721\) −5.97663 −0.222581
\(722\) −26.5884 −0.989517
\(723\) −1.42748 −0.0530887
\(724\) −39.5394 −1.46947
\(725\) −8.82322 −0.327686
\(726\) −7.14345 −0.265118
\(727\) 23.9110 0.886811 0.443405 0.896321i \(-0.353770\pi\)
0.443405 + 0.896321i \(0.353770\pi\)
\(728\) −2.02213 −0.0749450
\(729\) −20.0396 −0.742207
\(730\) −17.7271 −0.656110
\(731\) 22.1998 0.821089
\(732\) 4.02643 0.148821
\(733\) 18.2961 0.675783 0.337891 0.941185i \(-0.390286\pi\)
0.337891 + 0.941185i \(0.390286\pi\)
\(734\) −19.5852 −0.722903
\(735\) −6.94281 −0.256090
\(736\) 33.8407 1.24739
\(737\) −22.8426 −0.841418
\(738\) 59.8773 2.20411
\(739\) 5.28788 0.194518 0.0972590 0.995259i \(-0.468992\pi\)
0.0972590 + 0.995259i \(0.468992\pi\)
\(740\) 13.9982 0.514584
\(741\) 4.07900 0.149846
\(742\) −12.6500 −0.464397
\(743\) 5.39567 0.197948 0.0989740 0.995090i \(-0.468444\pi\)
0.0989740 + 0.995090i \(0.468444\pi\)
\(744\) 1.96016 0.0718629
\(745\) −15.8235 −0.579727
\(746\) 41.1756 1.50755
\(747\) 14.7608 0.540068
\(748\) 67.3945 2.46419
\(749\) −5.64212 −0.206159
\(750\) 4.78743 0.174812
\(751\) −19.3478 −0.706010 −0.353005 0.935622i \(-0.614840\pi\)
−0.353005 + 0.935622i \(0.614840\pi\)
\(752\) −1.64976 −0.0601606
\(753\) −5.64398 −0.205678
\(754\) −13.5105 −0.492023
\(755\) −36.6868 −1.33517
\(756\) 3.11318 0.113225
\(757\) −43.5090 −1.58136 −0.790680 0.612230i \(-0.790273\pi\)
−0.790680 + 0.612230i \(0.790273\pi\)
\(758\) −24.0270 −0.872700
\(759\) 7.85816 0.285233
\(760\) 31.7449 1.15151
\(761\) 7.18963 0.260624 0.130312 0.991473i \(-0.458402\pi\)
0.130312 + 0.991473i \(0.458402\pi\)
\(762\) −6.80939 −0.246678
\(763\) −8.58139 −0.310667
\(764\) 66.9878 2.42353
\(765\) −41.8469 −1.51298
\(766\) −54.6733 −1.97543
\(767\) −20.4033 −0.736721
\(768\) −2.36197 −0.0852303
\(769\) 19.3679 0.698426 0.349213 0.937043i \(-0.386449\pi\)
0.349213 + 0.937043i \(0.386449\pi\)
\(770\) 13.8012 0.497362
\(771\) −8.20432 −0.295471
\(772\) −3.58906 −0.129173
\(773\) 42.9751 1.54571 0.772854 0.634584i \(-0.218828\pi\)
0.772854 + 0.634584i \(0.218828\pi\)
\(774\) 27.1559 0.976100
\(775\) −7.65874 −0.275110
\(776\) −20.1903 −0.724791
\(777\) −0.311033 −0.0111583
\(778\) −52.4550 −1.88060
\(779\) −52.4596 −1.87956
\(780\) −6.00322 −0.214950
\(781\) 71.5961 2.56191
\(782\) −55.5838 −1.98767
\(783\) 6.52954 0.233347
\(784\) 8.99680 0.321314
\(785\) −36.1124 −1.28891
\(786\) 7.62999 0.272153
\(787\) 9.52179 0.339415 0.169708 0.985494i \(-0.445718\pi\)
0.169708 + 0.985494i \(0.445718\pi\)
\(788\) −22.4127 −0.798420
\(789\) −0.307507 −0.0109475
\(790\) 75.3668 2.68143
\(791\) −7.42353 −0.263950
\(792\) 25.8794 0.919586
\(793\) −7.56214 −0.268539
\(794\) −5.24036 −0.185973
\(795\) −11.7891 −0.418117
\(796\) 55.5560 1.96913
\(797\) −24.9984 −0.885489 −0.442745 0.896648i \(-0.645995\pi\)
−0.442745 + 0.896648i \(0.645995\pi\)
\(798\) −2.24695 −0.0795413
\(799\) 6.43191 0.227544
\(800\) 20.3321 0.718847
\(801\) −25.4501 −0.899234
\(802\) −68.4216 −2.41605
\(803\) 12.6614 0.446811
\(804\) −5.47334 −0.193030
\(805\) −6.75092 −0.237939
\(806\) −11.7274 −0.413079
\(807\) −8.67642 −0.305425
\(808\) −21.7857 −0.766416
\(809\) −18.6563 −0.655922 −0.327961 0.944691i \(-0.606361\pi\)
−0.327961 + 0.944691i \(0.606361\pi\)
\(810\) −48.6876 −1.71071
\(811\) −32.1045 −1.12734 −0.563671 0.826000i \(-0.690611\pi\)
−0.563671 + 0.826000i \(0.690611\pi\)
\(812\) 4.41401 0.154901
\(813\) 9.55368 0.335062
\(814\) −16.8576 −0.590857
\(815\) −14.7678 −0.517293
\(816\) −2.53197 −0.0886367
\(817\) −23.7918 −0.832370
\(818\) 45.3785 1.58662
\(819\) −2.85678 −0.0998240
\(820\) 77.2068 2.69618
\(821\) 31.9294 1.11434 0.557172 0.830397i \(-0.311886\pi\)
0.557172 + 0.830397i \(0.311886\pi\)
\(822\) −6.83951 −0.238555
\(823\) −17.9305 −0.625016 −0.312508 0.949915i \(-0.601169\pi\)
−0.312508 + 0.949915i \(0.601169\pi\)
\(824\) −24.3649 −0.848793
\(825\) 4.72131 0.164375
\(826\) 11.2394 0.391068
\(827\) 5.87465 0.204282 0.102141 0.994770i \(-0.467431\pi\)
0.102141 + 0.994770i \(0.467431\pi\)
\(828\) −40.3260 −1.40143
\(829\) −39.0940 −1.35779 −0.678895 0.734235i \(-0.737541\pi\)
−0.678895 + 0.734235i \(0.737541\pi\)
\(830\) 32.0909 1.11389
\(831\) −9.28326 −0.322033
\(832\) 25.7961 0.894320
\(833\) −35.0758 −1.21530
\(834\) 5.63908 0.195265
\(835\) 15.9684 0.552610
\(836\) −72.2276 −2.49804
\(837\) 5.66777 0.195907
\(838\) −77.8696 −2.68996
\(839\) −3.90927 −0.134963 −0.0674815 0.997721i \(-0.521496\pi\)
−0.0674815 + 0.997721i \(0.521496\pi\)
\(840\) 1.03810 0.0358179
\(841\) −19.7421 −0.680764
\(842\) −32.7832 −1.12978
\(843\) 11.1624 0.384455
\(844\) 12.8544 0.442465
\(845\) −25.2638 −0.869102
\(846\) 7.86784 0.270502
\(847\) −4.38323 −0.150610
\(848\) 15.2769 0.524610
\(849\) −5.72557 −0.196501
\(850\) −33.3957 −1.14546
\(851\) 8.24593 0.282667
\(852\) 17.1552 0.587728
\(853\) 11.1564 0.381988 0.190994 0.981591i \(-0.438829\pi\)
0.190994 + 0.981591i \(0.438829\pi\)
\(854\) 4.16568 0.142546
\(855\) 44.8479 1.53377
\(856\) −23.0013 −0.786167
\(857\) −33.1545 −1.13253 −0.566267 0.824222i \(-0.691613\pi\)
−0.566267 + 0.824222i \(0.691613\pi\)
\(858\) 7.22947 0.246810
\(859\) 37.6497 1.28459 0.642295 0.766457i \(-0.277982\pi\)
0.642295 + 0.766457i \(0.277982\pi\)
\(860\) 35.0153 1.19401
\(861\) −1.71550 −0.0584641
\(862\) −15.4925 −0.527675
\(863\) −49.9751 −1.70117 −0.850587 0.525835i \(-0.823753\pi\)
−0.850587 + 0.525835i \(0.823753\pi\)
\(864\) −15.0465 −0.511894
\(865\) 39.6369 1.34769
\(866\) −6.28128 −0.213446
\(867\) 3.65236 0.124041
\(868\) 3.83145 0.130048
\(869\) −53.8299 −1.82605
\(870\) 6.93589 0.235149
\(871\) 10.2796 0.348311
\(872\) −34.9838 −1.18470
\(873\) −28.5241 −0.965395
\(874\) 59.5700 2.01498
\(875\) 2.93757 0.0993081
\(876\) 3.03381 0.102503
\(877\) 30.3207 1.02386 0.511929 0.859028i \(-0.328931\pi\)
0.511929 + 0.859028i \(0.328931\pi\)
\(878\) −83.6185 −2.82199
\(879\) −7.16870 −0.241794
\(880\) −16.6671 −0.561849
\(881\) −3.49837 −0.117863 −0.0589315 0.998262i \(-0.518769\pi\)
−0.0589315 + 0.998262i \(0.518769\pi\)
\(882\) −42.9065 −1.44474
\(883\) −23.2890 −0.783738 −0.391869 0.920021i \(-0.628171\pi\)
−0.391869 + 0.920021i \(0.628171\pi\)
\(884\) −30.3288 −1.02007
\(885\) 10.4745 0.352095
\(886\) −57.3730 −1.92748
\(887\) −0.700030 −0.0235047 −0.0117524 0.999931i \(-0.503741\pi\)
−0.0117524 + 0.999931i \(0.503741\pi\)
\(888\) −1.26799 −0.0425510
\(889\) −4.17825 −0.140134
\(890\) −55.3301 −1.85467
\(891\) 34.7746 1.16499
\(892\) −6.94284 −0.232464
\(893\) −6.89316 −0.230671
\(894\) 4.56595 0.152708
\(895\) −68.0921 −2.27607
\(896\) −7.23151 −0.241588
\(897\) −3.53632 −0.118074
\(898\) −88.0930 −2.93970
\(899\) 8.03601 0.268016
\(900\) −24.2286 −0.807619
\(901\) −59.5598 −1.98422
\(902\) −92.9776 −3.09582
\(903\) −0.778024 −0.0258910
\(904\) −30.2636 −1.00655
\(905\) −38.1229 −1.26725
\(906\) 10.5862 0.351703
\(907\) −31.1663 −1.03486 −0.517431 0.855725i \(-0.673111\pi\)
−0.517431 + 0.855725i \(0.673111\pi\)
\(908\) −27.2602 −0.904660
\(909\) −30.7779 −1.02084
\(910\) −6.21082 −0.205887
\(911\) 44.9647 1.48975 0.744874 0.667205i \(-0.232509\pi\)
0.744874 + 0.667205i \(0.232509\pi\)
\(912\) 2.71355 0.0898545
\(913\) −22.9206 −0.758560
\(914\) −11.2994 −0.373751
\(915\) 3.88218 0.128341
\(916\) 53.8065 1.77782
\(917\) 4.68177 0.154606
\(918\) 24.7142 0.815689
\(919\) −22.3892 −0.738552 −0.369276 0.929320i \(-0.620394\pi\)
−0.369276 + 0.929320i \(0.620394\pi\)
\(920\) −27.5215 −0.907358
\(921\) 7.73900 0.255009
\(922\) 54.3055 1.78846
\(923\) −32.2196 −1.06052
\(924\) −2.36194 −0.0777021
\(925\) 4.95430 0.162896
\(926\) 82.1993 2.70124
\(927\) −34.4218 −1.13056
\(928\) −21.3336 −0.700311
\(929\) 9.50966 0.312002 0.156001 0.987757i \(-0.450140\pi\)
0.156001 + 0.987757i \(0.450140\pi\)
\(930\) 6.02050 0.197420
\(931\) 37.5912 1.23200
\(932\) −28.0206 −0.917847
\(933\) 12.0155 0.393371
\(934\) 77.5830 2.53859
\(935\) 64.9800 2.12507
\(936\) −11.6463 −0.380670
\(937\) 19.6391 0.641583 0.320791 0.947150i \(-0.396051\pi\)
0.320791 + 0.947150i \(0.396051\pi\)
\(938\) −5.66262 −0.184891
\(939\) 1.92334 0.0627659
\(940\) 10.1449 0.330891
\(941\) 36.8201 1.20030 0.600151 0.799887i \(-0.295107\pi\)
0.600151 + 0.799887i \(0.295107\pi\)
\(942\) 10.4204 0.339516
\(943\) 45.4803 1.48104
\(944\) −13.5733 −0.441773
\(945\) 3.00165 0.0976438
\(946\) −42.1678 −1.37099
\(947\) 3.76703 0.122412 0.0612060 0.998125i \(-0.480505\pi\)
0.0612060 + 0.998125i \(0.480505\pi\)
\(948\) −12.8982 −0.418915
\(949\) −5.69787 −0.184961
\(950\) 35.7906 1.16120
\(951\) 11.5963 0.376035
\(952\) 5.24459 0.169978
\(953\) −4.90914 −0.159023 −0.0795113 0.996834i \(-0.525336\pi\)
−0.0795113 + 0.996834i \(0.525336\pi\)
\(954\) −72.8566 −2.35882
\(955\) 64.5879 2.09002
\(956\) 26.0229 0.841642
\(957\) −4.95389 −0.160136
\(958\) 58.3408 1.88490
\(959\) −4.19673 −0.135520
\(960\) −13.2430 −0.427415
\(961\) −24.0246 −0.774986
\(962\) 7.58623 0.244590
\(963\) −32.4953 −1.04715
\(964\) −11.3750 −0.366365
\(965\) −3.46048 −0.111397
\(966\) 1.94802 0.0626764
\(967\) 40.5043 1.30253 0.651266 0.758850i \(-0.274238\pi\)
0.651266 + 0.758850i \(0.274238\pi\)
\(968\) −17.8691 −0.574336
\(969\) −10.5793 −0.339855
\(970\) −62.0133 −1.99113
\(971\) 20.0468 0.643332 0.321666 0.946853i \(-0.395757\pi\)
0.321666 + 0.946853i \(0.395757\pi\)
\(972\) 27.0997 0.869222
\(973\) 3.46014 0.110927
\(974\) 6.24347 0.200054
\(975\) −2.12468 −0.0680443
\(976\) −5.03070 −0.161029
\(977\) −37.9158 −1.21303 −0.606516 0.795071i \(-0.707433\pi\)
−0.606516 + 0.795071i \(0.707433\pi\)
\(978\) 4.26133 0.136262
\(979\) 39.5189 1.26303
\(980\) −55.3244 −1.76727
\(981\) −49.4237 −1.57798
\(982\) 85.8081 2.73825
\(983\) 22.8675 0.729359 0.364680 0.931133i \(-0.381178\pi\)
0.364680 + 0.931133i \(0.381178\pi\)
\(984\) −6.99359 −0.222947
\(985\) −21.6098 −0.688544
\(986\) 35.0408 1.11593
\(987\) −0.225416 −0.00717506
\(988\) 32.5038 1.03408
\(989\) 20.6265 0.655885
\(990\) 79.4870 2.52626
\(991\) 48.4051 1.53764 0.768819 0.639466i \(-0.220844\pi\)
0.768819 + 0.639466i \(0.220844\pi\)
\(992\) −18.5180 −0.587948
\(993\) −6.06404 −0.192436
\(994\) 17.7485 0.562948
\(995\) 53.5657 1.69815
\(996\) −5.49202 −0.174021
\(997\) 1.21389 0.0384443 0.0192222 0.999815i \(-0.493881\pi\)
0.0192222 + 0.999815i \(0.493881\pi\)
\(998\) −90.0139 −2.84934
\(999\) −3.66638 −0.115999
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 4001.2.a.b.1.29 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.29 184 1.1 even 1 trivial