Properties

Label 1339.2.a.e.1.11
Level $1339$
Weight $2$
Character 1339.1
Self dual yes
Analytic conductor $10.692$
Analytic rank $1$
Dimension $21$
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] = [1339,2,Mod(1,1339)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1339, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1339.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.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: \(10.6919688306\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 1339.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.0264721 q^{2} -1.87769 q^{3} -1.99930 q^{4} +2.52751 q^{5} +0.0497063 q^{6} -1.16160 q^{7} +0.105870 q^{8} +0.525708 q^{9} +O(q^{10})\) \(q-0.0264721 q^{2} -1.87769 q^{3} -1.99930 q^{4} +2.52751 q^{5} +0.0497063 q^{6} -1.16160 q^{7} +0.105870 q^{8} +0.525708 q^{9} -0.0669085 q^{10} +0.665143 q^{11} +3.75406 q^{12} -1.00000 q^{13} +0.0307500 q^{14} -4.74587 q^{15} +3.99580 q^{16} -0.273990 q^{17} -0.0139166 q^{18} +6.34288 q^{19} -5.05325 q^{20} +2.18112 q^{21} -0.0176077 q^{22} -4.90600 q^{23} -0.198791 q^{24} +1.38831 q^{25} +0.0264721 q^{26} +4.64595 q^{27} +2.32238 q^{28} -1.80420 q^{29} +0.125633 q^{30} -0.915299 q^{31} -0.317517 q^{32} -1.24893 q^{33} +0.00725308 q^{34} -2.93595 q^{35} -1.05105 q^{36} -1.13362 q^{37} -0.167910 q^{38} +1.87769 q^{39} +0.267587 q^{40} -11.7774 q^{41} -0.0577388 q^{42} +1.90151 q^{43} -1.32982 q^{44} +1.32873 q^{45} +0.129872 q^{46} +8.92385 q^{47} -7.50285 q^{48} -5.65069 q^{49} -0.0367514 q^{50} +0.514467 q^{51} +1.99930 q^{52} +2.31382 q^{53} -0.122988 q^{54} +1.68115 q^{55} -0.122978 q^{56} -11.9100 q^{57} +0.0477610 q^{58} +9.78985 q^{59} +9.48842 q^{60} -12.3026 q^{61} +0.0242299 q^{62} -0.610662 q^{63} -7.98319 q^{64} -2.52751 q^{65} +0.0330618 q^{66} -13.4446 q^{67} +0.547787 q^{68} +9.21194 q^{69} +0.0777209 q^{70} -11.1693 q^{71} +0.0556567 q^{72} +4.99515 q^{73} +0.0300093 q^{74} -2.60680 q^{75} -12.6813 q^{76} -0.772629 q^{77} -0.0497063 q^{78} -14.1648 q^{79} +10.0994 q^{80} -10.3008 q^{81} +0.311771 q^{82} -1.68710 q^{83} -4.36071 q^{84} -0.692511 q^{85} -0.0503369 q^{86} +3.38772 q^{87} +0.0704186 q^{88} +2.04119 q^{89} -0.0351744 q^{90} +1.16160 q^{91} +9.80857 q^{92} +1.71865 q^{93} -0.236233 q^{94} +16.0317 q^{95} +0.596197 q^{96} -19.1043 q^{97} +0.149586 q^{98} +0.349671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0264721 −0.0187186 −0.00935930 0.999956i \(-0.502979\pi\)
−0.00935930 + 0.999956i \(0.502979\pi\)
\(3\) −1.87769 −1.08408 −0.542042 0.840352i \(-0.682348\pi\)
−0.542042 + 0.840352i \(0.682348\pi\)
\(4\) −1.99930 −0.999650
\(5\) 2.52751 1.13034 0.565168 0.824976i \(-0.308811\pi\)
0.565168 + 0.824976i \(0.308811\pi\)
\(6\) 0.0497063 0.0202925
\(7\) −1.16160 −0.439043 −0.219522 0.975608i \(-0.570450\pi\)
−0.219522 + 0.975608i \(0.570450\pi\)
\(8\) 0.105870 0.0374307
\(9\) 0.525708 0.175236
\(10\) −0.0669085 −0.0211583
\(11\) 0.665143 0.200548 0.100274 0.994960i \(-0.468028\pi\)
0.100274 + 0.994960i \(0.468028\pi\)
\(12\) 3.75406 1.08370
\(13\) −1.00000 −0.277350
\(14\) 0.0307500 0.00821828
\(15\) −4.74587 −1.22538
\(16\) 3.99580 0.998949
\(17\) −0.273990 −0.0664522 −0.0332261 0.999448i \(-0.510578\pi\)
−0.0332261 + 0.999448i \(0.510578\pi\)
\(18\) −0.0139166 −0.00328017
\(19\) 6.34288 1.45516 0.727579 0.686024i \(-0.240646\pi\)
0.727579 + 0.686024i \(0.240646\pi\)
\(20\) −5.05325 −1.12994
\(21\) 2.18112 0.475959
\(22\) −0.0176077 −0.00375398
\(23\) −4.90600 −1.02297 −0.511486 0.859292i \(-0.670905\pi\)
−0.511486 + 0.859292i \(0.670905\pi\)
\(24\) −0.198791 −0.0405779
\(25\) 1.38831 0.277661
\(26\) 0.0264721 0.00519161
\(27\) 4.64595 0.894113
\(28\) 2.32238 0.438889
\(29\) −1.80420 −0.335032 −0.167516 0.985869i \(-0.553575\pi\)
−0.167516 + 0.985869i \(0.553575\pi\)
\(30\) 0.125633 0.0229374
\(31\) −0.915299 −0.164393 −0.0821963 0.996616i \(-0.526193\pi\)
−0.0821963 + 0.996616i \(0.526193\pi\)
\(32\) −0.317517 −0.0561296
\(33\) −1.24893 −0.217411
\(34\) 0.00725308 0.00124389
\(35\) −2.93595 −0.496267
\(36\) −1.05105 −0.175175
\(37\) −1.13362 −0.186366 −0.0931829 0.995649i \(-0.529704\pi\)
−0.0931829 + 0.995649i \(0.529704\pi\)
\(38\) −0.167910 −0.0272385
\(39\) 1.87769 0.300671
\(40\) 0.267587 0.0423093
\(41\) −11.7774 −1.83931 −0.919657 0.392723i \(-0.871533\pi\)
−0.919657 + 0.392723i \(0.871533\pi\)
\(42\) −0.0577388 −0.00890929
\(43\) 1.90151 0.289977 0.144988 0.989433i \(-0.453685\pi\)
0.144988 + 0.989433i \(0.453685\pi\)
\(44\) −1.32982 −0.200478
\(45\) 1.32873 0.198076
\(46\) 0.129872 0.0191486
\(47\) 8.92385 1.30168 0.650838 0.759216i \(-0.274417\pi\)
0.650838 + 0.759216i \(0.274417\pi\)
\(48\) −7.50285 −1.08294
\(49\) −5.65069 −0.807241
\(50\) −0.0367514 −0.00519743
\(51\) 0.514467 0.0720397
\(52\) 1.99930 0.277253
\(53\) 2.31382 0.317828 0.158914 0.987292i \(-0.449201\pi\)
0.158914 + 0.987292i \(0.449201\pi\)
\(54\) −0.122988 −0.0167365
\(55\) 1.68115 0.226687
\(56\) −0.122978 −0.0164337
\(57\) −11.9100 −1.57751
\(58\) 0.0477610 0.00627132
\(59\) 9.78985 1.27453 0.637265 0.770645i \(-0.280066\pi\)
0.637265 + 0.770645i \(0.280066\pi\)
\(60\) 9.48842 1.22495
\(61\) −12.3026 −1.57519 −0.787595 0.616193i \(-0.788674\pi\)
−0.787595 + 0.616193i \(0.788674\pi\)
\(62\) 0.0242299 0.00307720
\(63\) −0.610662 −0.0769362
\(64\) −7.98319 −0.997898
\(65\) −2.52751 −0.313499
\(66\) 0.0330618 0.00406963
\(67\) −13.4446 −1.64252 −0.821260 0.570555i \(-0.806728\pi\)
−0.821260 + 0.570555i \(0.806728\pi\)
\(68\) 0.547787 0.0664290
\(69\) 9.21194 1.10899
\(70\) 0.0777209 0.00928942
\(71\) −11.1693 −1.32556 −0.662779 0.748815i \(-0.730623\pi\)
−0.662779 + 0.748815i \(0.730623\pi\)
\(72\) 0.0556567 0.00655920
\(73\) 4.99515 0.584638 0.292319 0.956321i \(-0.405573\pi\)
0.292319 + 0.956321i \(0.405573\pi\)
\(74\) 0.0300093 0.00348851
\(75\) −2.60680 −0.301008
\(76\) −12.6813 −1.45465
\(77\) −0.772629 −0.0880492
\(78\) −0.0497063 −0.00562813
\(79\) −14.1648 −1.59366 −0.796832 0.604201i \(-0.793492\pi\)
−0.796832 + 0.604201i \(0.793492\pi\)
\(80\) 10.0994 1.12915
\(81\) −10.3008 −1.14453
\(82\) 0.311771 0.0344294
\(83\) −1.68710 −0.185183 −0.0925916 0.995704i \(-0.529515\pi\)
−0.0925916 + 0.995704i \(0.529515\pi\)
\(84\) −4.36071 −0.475792
\(85\) −0.692511 −0.0751134
\(86\) −0.0503369 −0.00542797
\(87\) 3.38772 0.363202
\(88\) 0.0704186 0.00750665
\(89\) 2.04119 0.216366 0.108183 0.994131i \(-0.465497\pi\)
0.108183 + 0.994131i \(0.465497\pi\)
\(90\) −0.0351744 −0.00370770
\(91\) 1.16160 0.121769
\(92\) 9.80857 1.02261
\(93\) 1.71865 0.178215
\(94\) −0.236233 −0.0243656
\(95\) 16.0317 1.64482
\(96\) 0.596197 0.0608491
\(97\) −19.1043 −1.93975 −0.969875 0.243604i \(-0.921670\pi\)
−0.969875 + 0.243604i \(0.921670\pi\)
\(98\) 0.149586 0.0151104
\(99\) 0.349671 0.0351432
\(100\) −2.77564 −0.277564
\(101\) −10.8816 −1.08275 −0.541377 0.840780i \(-0.682097\pi\)
−0.541377 + 0.840780i \(0.682097\pi\)
\(102\) −0.0136190 −0.00134848
\(103\) −1.00000 −0.0985329
\(104\) −0.105870 −0.0103814
\(105\) 5.51280 0.537994
\(106\) −0.0612518 −0.00594930
\(107\) 1.93815 0.187368 0.0936838 0.995602i \(-0.470136\pi\)
0.0936838 + 0.995602i \(0.470136\pi\)
\(108\) −9.28864 −0.893799
\(109\) −0.415219 −0.0397707 −0.0198854 0.999802i \(-0.506330\pi\)
−0.0198854 + 0.999802i \(0.506330\pi\)
\(110\) −0.0445037 −0.00424326
\(111\) 2.12858 0.202036
\(112\) −4.64151 −0.438582
\(113\) −2.07720 −0.195407 −0.0977035 0.995216i \(-0.531150\pi\)
−0.0977035 + 0.995216i \(0.531150\pi\)
\(114\) 0.315282 0.0295288
\(115\) −12.4000 −1.15630
\(116\) 3.60714 0.334914
\(117\) −0.525708 −0.0486017
\(118\) −0.259158 −0.0238574
\(119\) 0.318266 0.0291754
\(120\) −0.502445 −0.0458667
\(121\) −10.5576 −0.959780
\(122\) 0.325677 0.0294854
\(123\) 22.1142 1.99397
\(124\) 1.82996 0.164335
\(125\) −9.12859 −0.816486
\(126\) 0.0161655 0.00144014
\(127\) 3.34549 0.296864 0.148432 0.988923i \(-0.452577\pi\)
0.148432 + 0.988923i \(0.452577\pi\)
\(128\) 0.846366 0.0748089
\(129\) −3.57043 −0.314359
\(130\) 0.0669085 0.00586827
\(131\) 2.97858 0.260240 0.130120 0.991498i \(-0.458464\pi\)
0.130120 + 0.991498i \(0.458464\pi\)
\(132\) 2.49698 0.217335
\(133\) −7.36789 −0.638877
\(134\) 0.355907 0.0307457
\(135\) 11.7427 1.01065
\(136\) −0.0290073 −0.00248735
\(137\) −13.2508 −1.13210 −0.566048 0.824372i \(-0.691528\pi\)
−0.566048 + 0.824372i \(0.691528\pi\)
\(138\) −0.243859 −0.0207587
\(139\) 10.6139 0.900262 0.450131 0.892962i \(-0.351377\pi\)
0.450131 + 0.892962i \(0.351377\pi\)
\(140\) 5.86985 0.496093
\(141\) −16.7562 −1.41113
\(142\) 0.295676 0.0248126
\(143\) −0.665143 −0.0556220
\(144\) 2.10062 0.175052
\(145\) −4.56013 −0.378699
\(146\) −0.132232 −0.0109436
\(147\) 10.6102 0.875116
\(148\) 2.26644 0.186300
\(149\) −17.6602 −1.44678 −0.723390 0.690439i \(-0.757417\pi\)
−0.723390 + 0.690439i \(0.757417\pi\)
\(150\) 0.0690076 0.00563445
\(151\) −13.8272 −1.12524 −0.562622 0.826714i \(-0.690207\pi\)
−0.562622 + 0.826714i \(0.690207\pi\)
\(152\) 0.671520 0.0544675
\(153\) −0.144039 −0.0116448
\(154\) 0.0204531 0.00164816
\(155\) −2.31343 −0.185819
\(156\) −3.75406 −0.300565
\(157\) 16.3694 1.30642 0.653211 0.757176i \(-0.273421\pi\)
0.653211 + 0.757176i \(0.273421\pi\)
\(158\) 0.374972 0.0298312
\(159\) −4.34464 −0.344552
\(160\) −0.802527 −0.0634453
\(161\) 5.69881 0.449129
\(162\) 0.272683 0.0214240
\(163\) 15.5596 1.21872 0.609360 0.792894i \(-0.291426\pi\)
0.609360 + 0.792894i \(0.291426\pi\)
\(164\) 23.5465 1.83867
\(165\) −3.15668 −0.245747
\(166\) 0.0446611 0.00346637
\(167\) −1.98668 −0.153734 −0.0768671 0.997041i \(-0.524492\pi\)
−0.0768671 + 0.997041i \(0.524492\pi\)
\(168\) 0.230915 0.0178155
\(169\) 1.00000 0.0769231
\(170\) 0.0183322 0.00140602
\(171\) 3.33451 0.254996
\(172\) −3.80168 −0.289875
\(173\) 15.6300 1.18833 0.594164 0.804344i \(-0.297483\pi\)
0.594164 + 0.804344i \(0.297483\pi\)
\(174\) −0.0896802 −0.00679864
\(175\) −1.61266 −0.121905
\(176\) 2.65777 0.200337
\(177\) −18.3823 −1.38170
\(178\) −0.0540347 −0.00405007
\(179\) 15.3182 1.14493 0.572467 0.819928i \(-0.305986\pi\)
0.572467 + 0.819928i \(0.305986\pi\)
\(180\) −2.65653 −0.198006
\(181\) 2.77898 0.206560 0.103280 0.994652i \(-0.467066\pi\)
0.103280 + 0.994652i \(0.467066\pi\)
\(182\) −0.0307500 −0.00227934
\(183\) 23.1005 1.70764
\(184\) −0.519398 −0.0382905
\(185\) −2.86523 −0.210656
\(186\) −0.0454962 −0.00333594
\(187\) −0.182242 −0.0133269
\(188\) −17.8414 −1.30122
\(189\) −5.39672 −0.392554
\(190\) −0.424393 −0.0307887
\(191\) −15.2138 −1.10083 −0.550416 0.834890i \(-0.685531\pi\)
−0.550416 + 0.834890i \(0.685531\pi\)
\(192\) 14.9899 1.08180
\(193\) 6.89410 0.496248 0.248124 0.968728i \(-0.420186\pi\)
0.248124 + 0.968728i \(0.420186\pi\)
\(194\) 0.505732 0.0363094
\(195\) 4.74587 0.339859
\(196\) 11.2974 0.806958
\(197\) 2.21792 0.158020 0.0790101 0.996874i \(-0.474824\pi\)
0.0790101 + 0.996874i \(0.474824\pi\)
\(198\) −0.00925653 −0.000657833 0
\(199\) 9.73336 0.689980 0.344990 0.938606i \(-0.387882\pi\)
0.344990 + 0.938606i \(0.387882\pi\)
\(200\) 0.146980 0.0103930
\(201\) 25.2447 1.78063
\(202\) 0.288058 0.0202677
\(203\) 2.09576 0.147093
\(204\) −1.02857 −0.0720145
\(205\) −29.7674 −2.07904
\(206\) 0.0264721 0.00184440
\(207\) −2.57913 −0.179262
\(208\) −3.99580 −0.277059
\(209\) 4.21892 0.291829
\(210\) −0.145935 −0.0100705
\(211\) 14.1331 0.972961 0.486481 0.873691i \(-0.338280\pi\)
0.486481 + 0.873691i \(0.338280\pi\)
\(212\) −4.62602 −0.317717
\(213\) 20.9725 1.43701
\(214\) −0.0513068 −0.00350726
\(215\) 4.80608 0.327772
\(216\) 0.491866 0.0334672
\(217\) 1.06321 0.0721754
\(218\) 0.0109917 0.000744453 0
\(219\) −9.37933 −0.633796
\(220\) −3.36113 −0.226607
\(221\) 0.273990 0.0184305
\(222\) −0.0563480 −0.00378183
\(223\) −17.5433 −1.17479 −0.587393 0.809302i \(-0.699846\pi\)
−0.587393 + 0.809302i \(0.699846\pi\)
\(224\) 0.368827 0.0246433
\(225\) 0.729844 0.0486563
\(226\) 0.0549880 0.00365775
\(227\) 2.38137 0.158057 0.0790284 0.996872i \(-0.474818\pi\)
0.0790284 + 0.996872i \(0.474818\pi\)
\(228\) 23.8116 1.57696
\(229\) 16.3212 1.07853 0.539267 0.842135i \(-0.318701\pi\)
0.539267 + 0.842135i \(0.318701\pi\)
\(230\) 0.328253 0.0216444
\(231\) 1.45076 0.0954527
\(232\) −0.191010 −0.0125405
\(233\) 8.02615 0.525810 0.262905 0.964822i \(-0.415319\pi\)
0.262905 + 0.964822i \(0.415319\pi\)
\(234\) 0.0139166 0.000909757 0
\(235\) 22.5551 1.47133
\(236\) −19.5728 −1.27408
\(237\) 26.5971 1.72766
\(238\) −0.00842517 −0.000546123 0
\(239\) −11.4228 −0.738881 −0.369440 0.929254i \(-0.620451\pi\)
−0.369440 + 0.929254i \(0.620451\pi\)
\(240\) −18.9635 −1.22409
\(241\) 19.1046 1.23064 0.615319 0.788278i \(-0.289027\pi\)
0.615319 + 0.788278i \(0.289027\pi\)
\(242\) 0.279482 0.0179658
\(243\) 5.40376 0.346651
\(244\) 24.5966 1.57464
\(245\) −14.2822 −0.912454
\(246\) −0.585409 −0.0373243
\(247\) −6.34288 −0.403588
\(248\) −0.0969026 −0.00615332
\(249\) 3.16784 0.200754
\(250\) 0.241653 0.0152835
\(251\) 1.23750 0.0781105 0.0390553 0.999237i \(-0.487565\pi\)
0.0390553 + 0.999237i \(0.487565\pi\)
\(252\) 1.22090 0.0769092
\(253\) −3.26319 −0.205155
\(254\) −0.0885622 −0.00555689
\(255\) 1.30032 0.0814292
\(256\) 15.9440 0.996498
\(257\) 12.2839 0.766249 0.383124 0.923697i \(-0.374848\pi\)
0.383124 + 0.923697i \(0.374848\pi\)
\(258\) 0.0945169 0.00588437
\(259\) 1.31681 0.0818226
\(260\) 5.05325 0.313389
\(261\) −0.948483 −0.0587096
\(262\) −0.0788493 −0.00487133
\(263\) −7.40087 −0.456357 −0.228179 0.973619i \(-0.573277\pi\)
−0.228179 + 0.973619i \(0.573277\pi\)
\(264\) −0.132224 −0.00813783
\(265\) 5.84821 0.359253
\(266\) 0.195044 0.0119589
\(267\) −3.83272 −0.234559
\(268\) 26.8798 1.64194
\(269\) −9.73367 −0.593472 −0.296736 0.954959i \(-0.595898\pi\)
−0.296736 + 0.954959i \(0.595898\pi\)
\(270\) −0.310853 −0.0189179
\(271\) −14.0883 −0.855801 −0.427901 0.903826i \(-0.640747\pi\)
−0.427901 + 0.903826i \(0.640747\pi\)
\(272\) −1.09481 −0.0663824
\(273\) −2.18112 −0.132007
\(274\) 0.350778 0.0211913
\(275\) 0.923422 0.0556844
\(276\) −18.4174 −1.10860
\(277\) 22.3287 1.34160 0.670800 0.741639i \(-0.265951\pi\)
0.670800 + 0.741639i \(0.265951\pi\)
\(278\) −0.280973 −0.0168517
\(279\) −0.481180 −0.0288075
\(280\) −0.310829 −0.0185756
\(281\) 31.5303 1.88094 0.940469 0.339879i \(-0.110386\pi\)
0.940469 + 0.339879i \(0.110386\pi\)
\(282\) 0.443572 0.0264143
\(283\) 29.7311 1.76733 0.883665 0.468121i \(-0.155069\pi\)
0.883665 + 0.468121i \(0.155069\pi\)
\(284\) 22.3309 1.32509
\(285\) −30.1025 −1.78312
\(286\) 0.0176077 0.00104117
\(287\) 13.6806 0.807538
\(288\) −0.166921 −0.00983593
\(289\) −16.9249 −0.995584
\(290\) 0.120716 0.00708871
\(291\) 35.8719 2.10285
\(292\) −9.98680 −0.584433
\(293\) −1.75503 −0.102530 −0.0512649 0.998685i \(-0.516325\pi\)
−0.0512649 + 0.998685i \(0.516325\pi\)
\(294\) −0.280875 −0.0163810
\(295\) 24.7440 1.44065
\(296\) −0.120016 −0.00697579
\(297\) 3.09022 0.179313
\(298\) 0.467503 0.0270817
\(299\) 4.90600 0.283721
\(300\) 5.21178 0.300902
\(301\) −2.20879 −0.127312
\(302\) 0.366036 0.0210630
\(303\) 20.4321 1.17380
\(304\) 25.3449 1.45363
\(305\) −31.0950 −1.78050
\(306\) 0.00381300 0.000217975 0
\(307\) −25.0177 −1.42784 −0.713919 0.700228i \(-0.753082\pi\)
−0.713919 + 0.700228i \(0.753082\pi\)
\(308\) 1.54472 0.0880184
\(309\) 1.87769 0.106818
\(310\) 0.0612413 0.00347827
\(311\) −26.0663 −1.47808 −0.739041 0.673660i \(-0.764721\pi\)
−0.739041 + 0.673660i \(0.764721\pi\)
\(312\) 0.198791 0.0112543
\(313\) −18.3238 −1.03572 −0.517862 0.855464i \(-0.673272\pi\)
−0.517862 + 0.855464i \(0.673272\pi\)
\(314\) −0.433333 −0.0244544
\(315\) −1.54345 −0.0869638
\(316\) 28.3197 1.59311
\(317\) 2.91049 0.163469 0.0817346 0.996654i \(-0.473954\pi\)
0.0817346 + 0.996654i \(0.473954\pi\)
\(318\) 0.115012 0.00644953
\(319\) −1.20005 −0.0671899
\(320\) −20.1776 −1.12796
\(321\) −3.63923 −0.203122
\(322\) −0.150859 −0.00840707
\(323\) −1.73788 −0.0966985
\(324\) 20.5943 1.14413
\(325\) −1.38831 −0.0770094
\(326\) −0.411895 −0.0228127
\(327\) 0.779651 0.0431148
\(328\) −1.24687 −0.0688467
\(329\) −10.3659 −0.571492
\(330\) 0.0835640 0.00460005
\(331\) −20.4831 −1.12585 −0.562927 0.826507i \(-0.690325\pi\)
−0.562927 + 0.826507i \(0.690325\pi\)
\(332\) 3.37301 0.185118
\(333\) −0.595952 −0.0326580
\(334\) 0.0525917 0.00287769
\(335\) −33.9814 −1.85660
\(336\) 8.71531 0.475459
\(337\) −20.9638 −1.14197 −0.570986 0.820960i \(-0.693439\pi\)
−0.570986 + 0.820960i \(0.693439\pi\)
\(338\) −0.0264721 −0.00143989
\(339\) 3.90034 0.211837
\(340\) 1.38454 0.0750871
\(341\) −0.608804 −0.0329686
\(342\) −0.0882714 −0.00477317
\(343\) 14.6950 0.793457
\(344\) 0.201312 0.0108540
\(345\) 23.2833 1.25353
\(346\) −0.413759 −0.0222438
\(347\) −18.2463 −0.979511 −0.489755 0.871860i \(-0.662914\pi\)
−0.489755 + 0.871860i \(0.662914\pi\)
\(348\) −6.77307 −0.363075
\(349\) −34.0706 −1.82376 −0.911878 0.410462i \(-0.865367\pi\)
−0.911878 + 0.410462i \(0.865367\pi\)
\(350\) 0.0426904 0.00228190
\(351\) −4.64595 −0.247982
\(352\) −0.211194 −0.0112567
\(353\) −25.4823 −1.35629 −0.678144 0.734929i \(-0.737215\pi\)
−0.678144 + 0.734929i \(0.737215\pi\)
\(354\) 0.486618 0.0258634
\(355\) −28.2306 −1.49833
\(356\) −4.08095 −0.216290
\(357\) −0.597604 −0.0316286
\(358\) −0.405505 −0.0214316
\(359\) 4.20677 0.222025 0.111012 0.993819i \(-0.464591\pi\)
0.111012 + 0.993819i \(0.464591\pi\)
\(360\) 0.140673 0.00741411
\(361\) 21.2322 1.11748
\(362\) −0.0735656 −0.00386652
\(363\) 19.8238 1.04048
\(364\) −2.32238 −0.121726
\(365\) 12.6253 0.660838
\(366\) −0.611519 −0.0319646
\(367\) 27.8945 1.45608 0.728042 0.685533i \(-0.240431\pi\)
0.728042 + 0.685533i \(0.240431\pi\)
\(368\) −19.6034 −1.02190
\(369\) −6.19145 −0.322314
\(370\) 0.0758487 0.00394319
\(371\) −2.68773 −0.139540
\(372\) −3.43609 −0.178153
\(373\) −30.9092 −1.60042 −0.800208 0.599723i \(-0.795277\pi\)
−0.800208 + 0.599723i \(0.795277\pi\)
\(374\) 0.00482434 0.000249460 0
\(375\) 17.1406 0.885139
\(376\) 0.944767 0.0487226
\(377\) 1.80420 0.0929210
\(378\) 0.142863 0.00734806
\(379\) −5.21292 −0.267770 −0.133885 0.990997i \(-0.542745\pi\)
−0.133885 + 0.990997i \(0.542745\pi\)
\(380\) −32.0522 −1.64424
\(381\) −6.28178 −0.321826
\(382\) 0.402742 0.0206061
\(383\) −17.0700 −0.872235 −0.436118 0.899890i \(-0.643647\pi\)
−0.436118 + 0.899890i \(0.643647\pi\)
\(384\) −1.58921 −0.0810990
\(385\) −1.95283 −0.0995253
\(386\) −0.182501 −0.00928907
\(387\) 0.999637 0.0508144
\(388\) 38.1953 1.93907
\(389\) −7.66444 −0.388603 −0.194301 0.980942i \(-0.562244\pi\)
−0.194301 + 0.980942i \(0.562244\pi\)
\(390\) −0.125633 −0.00636169
\(391\) 1.34419 0.0679788
\(392\) −0.598238 −0.0302156
\(393\) −5.59284 −0.282121
\(394\) −0.0587130 −0.00295792
\(395\) −35.8017 −1.80138
\(396\) −0.699097 −0.0351309
\(397\) −17.1066 −0.858556 −0.429278 0.903172i \(-0.641232\pi\)
−0.429278 + 0.903172i \(0.641232\pi\)
\(398\) −0.257663 −0.0129155
\(399\) 13.8346 0.692596
\(400\) 5.54739 0.277369
\(401\) −31.7593 −1.58598 −0.792991 0.609233i \(-0.791477\pi\)
−0.792991 + 0.609233i \(0.791477\pi\)
\(402\) −0.668282 −0.0333309
\(403\) 0.915299 0.0455943
\(404\) 21.7555 1.08238
\(405\) −26.0353 −1.29370
\(406\) −0.0554791 −0.00275338
\(407\) −0.754018 −0.0373753
\(408\) 0.0544665 0.00269650
\(409\) 9.36485 0.463062 0.231531 0.972828i \(-0.425627\pi\)
0.231531 + 0.972828i \(0.425627\pi\)
\(410\) 0.788005 0.0389168
\(411\) 24.8809 1.22729
\(412\) 1.99930 0.0984984
\(413\) −11.3719 −0.559574
\(414\) 0.0682749 0.00335553
\(415\) −4.26416 −0.209319
\(416\) 0.317517 0.0155675
\(417\) −19.9297 −0.975959
\(418\) −0.111684 −0.00546263
\(419\) 34.2734 1.67437 0.837183 0.546922i \(-0.184201\pi\)
0.837183 + 0.546922i \(0.184201\pi\)
\(420\) −11.0217 −0.537806
\(421\) −20.4077 −0.994609 −0.497305 0.867576i \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(422\) −0.374132 −0.0182125
\(423\) 4.69134 0.228101
\(424\) 0.244964 0.0118965
\(425\) −0.380382 −0.0184512
\(426\) −0.555187 −0.0268989
\(427\) 14.2907 0.691577
\(428\) −3.87493 −0.187302
\(429\) 1.24893 0.0602989
\(430\) −0.127227 −0.00613543
\(431\) −29.9027 −1.44036 −0.720182 0.693785i \(-0.755942\pi\)
−0.720182 + 0.693785i \(0.755942\pi\)
\(432\) 18.5642 0.893173
\(433\) 18.2765 0.878312 0.439156 0.898411i \(-0.355278\pi\)
0.439156 + 0.898411i \(0.355278\pi\)
\(434\) −0.0281454 −0.00135102
\(435\) 8.56250 0.410541
\(436\) 0.830146 0.0397568
\(437\) −31.1182 −1.48859
\(438\) 0.248291 0.0118638
\(439\) 23.9802 1.14451 0.572255 0.820076i \(-0.306069\pi\)
0.572255 + 0.820076i \(0.306069\pi\)
\(440\) 0.177984 0.00848504
\(441\) −2.97061 −0.141458
\(442\) −0.00725308 −0.000344994 0
\(443\) 24.8953 1.18281 0.591406 0.806374i \(-0.298573\pi\)
0.591406 + 0.806374i \(0.298573\pi\)
\(444\) −4.25567 −0.201965
\(445\) 5.15913 0.244566
\(446\) 0.464408 0.0219904
\(447\) 33.1603 1.56843
\(448\) 9.27326 0.438120
\(449\) −8.50644 −0.401444 −0.200722 0.979648i \(-0.564329\pi\)
−0.200722 + 0.979648i \(0.564329\pi\)
\(450\) −0.0193205 −0.000910778 0
\(451\) −7.83362 −0.368871
\(452\) 4.15295 0.195339
\(453\) 25.9632 1.21986
\(454\) −0.0630398 −0.00295860
\(455\) 2.93595 0.137640
\(456\) −1.26091 −0.0590473
\(457\) −24.6845 −1.15469 −0.577347 0.816499i \(-0.695912\pi\)
−0.577347 + 0.816499i \(0.695912\pi\)
\(458\) −0.432056 −0.0201886
\(459\) −1.27294 −0.0594158
\(460\) 24.7912 1.15590
\(461\) 27.3082 1.27187 0.635935 0.771742i \(-0.280614\pi\)
0.635935 + 0.771742i \(0.280614\pi\)
\(462\) −0.0384046 −0.00178674
\(463\) 12.2607 0.569805 0.284902 0.958557i \(-0.408039\pi\)
0.284902 + 0.958557i \(0.408039\pi\)
\(464\) −7.20922 −0.334679
\(465\) 4.34389 0.201443
\(466\) −0.212469 −0.00984244
\(467\) −1.56547 −0.0724415 −0.0362207 0.999344i \(-0.511532\pi\)
−0.0362207 + 0.999344i \(0.511532\pi\)
\(468\) 1.05105 0.0485847
\(469\) 15.6172 0.721137
\(470\) −0.597081 −0.0275413
\(471\) −30.7367 −1.41627
\(472\) 1.03645 0.0477065
\(473\) 1.26477 0.0581543
\(474\) −0.704080 −0.0323395
\(475\) 8.80587 0.404041
\(476\) −0.636309 −0.0291652
\(477\) 1.21640 0.0556949
\(478\) 0.302386 0.0138308
\(479\) 30.1358 1.37694 0.688469 0.725266i \(-0.258283\pi\)
0.688469 + 0.725266i \(0.258283\pi\)
\(480\) 1.50689 0.0687800
\(481\) 1.13362 0.0516886
\(482\) −0.505740 −0.0230358
\(483\) −10.7006 −0.486893
\(484\) 21.1078 0.959444
\(485\) −48.2864 −2.19257
\(486\) −0.143049 −0.00648883
\(487\) 12.0921 0.547943 0.273972 0.961738i \(-0.411663\pi\)
0.273972 + 0.961738i \(0.411663\pi\)
\(488\) −1.30248 −0.0589604
\(489\) −29.2160 −1.32119
\(490\) 0.378079 0.0170799
\(491\) −27.0980 −1.22292 −0.611459 0.791276i \(-0.709417\pi\)
−0.611459 + 0.791276i \(0.709417\pi\)
\(492\) −44.2129 −1.99327
\(493\) 0.494332 0.0222636
\(494\) 0.167910 0.00755461
\(495\) 0.883797 0.0397237
\(496\) −3.65735 −0.164220
\(497\) 12.9743 0.581977
\(498\) −0.0838595 −0.00375783
\(499\) 18.1906 0.814324 0.407162 0.913356i \(-0.366519\pi\)
0.407162 + 0.913356i \(0.366519\pi\)
\(500\) 18.2508 0.816200
\(501\) 3.73037 0.166661
\(502\) −0.0327593 −0.00146212
\(503\) −3.39831 −0.151523 −0.0757615 0.997126i \(-0.524139\pi\)
−0.0757615 + 0.997126i \(0.524139\pi\)
\(504\) −0.0646507 −0.00287977
\(505\) −27.5032 −1.22388
\(506\) 0.0863836 0.00384022
\(507\) −1.87769 −0.0833910
\(508\) −6.68864 −0.296760
\(509\) −17.7501 −0.786759 −0.393379 0.919376i \(-0.628694\pi\)
−0.393379 + 0.919376i \(0.628694\pi\)
\(510\) −0.0344222 −0.00152424
\(511\) −5.80236 −0.256681
\(512\) −2.11480 −0.0934619
\(513\) 29.4687 1.30107
\(514\) −0.325181 −0.0143431
\(515\) −2.52751 −0.111375
\(516\) 7.13836 0.314249
\(517\) 5.93563 0.261049
\(518\) −0.0348587 −0.00153160
\(519\) −29.3483 −1.28825
\(520\) −0.267587 −0.0117345
\(521\) 18.4586 0.808688 0.404344 0.914607i \(-0.367500\pi\)
0.404344 + 0.914607i \(0.367500\pi\)
\(522\) 0.0251083 0.00109896
\(523\) 6.30900 0.275874 0.137937 0.990441i \(-0.455953\pi\)
0.137937 + 0.990441i \(0.455953\pi\)
\(524\) −5.95507 −0.260149
\(525\) 3.02806 0.132155
\(526\) 0.195917 0.00854238
\(527\) 0.250782 0.0109243
\(528\) −4.99047 −0.217182
\(529\) 1.06885 0.0464719
\(530\) −0.154814 −0.00672471
\(531\) 5.14661 0.223344
\(532\) 14.7306 0.638653
\(533\) 11.7774 0.510134
\(534\) 0.101460 0.00439061
\(535\) 4.89868 0.211789
\(536\) −1.42338 −0.0614806
\(537\) −28.7628 −1.24120
\(538\) 0.257671 0.0111090
\(539\) −3.75851 −0.161891
\(540\) −23.4771 −1.01029
\(541\) 25.1022 1.07923 0.539614 0.841912i \(-0.318570\pi\)
0.539614 + 0.841912i \(0.318570\pi\)
\(542\) 0.372946 0.0160194
\(543\) −5.21806 −0.223928
\(544\) 0.0869963 0.00372994
\(545\) −1.04947 −0.0449543
\(546\) 0.0577388 0.00247099
\(547\) −23.2214 −0.992875 −0.496438 0.868072i \(-0.665359\pi\)
−0.496438 + 0.868072i \(0.665359\pi\)
\(548\) 26.4924 1.13170
\(549\) −6.46759 −0.276030
\(550\) −0.0244449 −0.00104234
\(551\) −11.4438 −0.487524
\(552\) 0.975267 0.0415101
\(553\) 16.4538 0.699687
\(554\) −0.591087 −0.0251129
\(555\) 5.38001 0.228369
\(556\) −21.2204 −0.899947
\(557\) 15.0923 0.639482 0.319741 0.947505i \(-0.396404\pi\)
0.319741 + 0.947505i \(0.396404\pi\)
\(558\) 0.0127379 0.000539236 0
\(559\) −1.90151 −0.0804251
\(560\) −11.7315 −0.495745
\(561\) 0.342194 0.0144474
\(562\) −0.834673 −0.0352085
\(563\) −42.9093 −1.80841 −0.904206 0.427096i \(-0.859537\pi\)
−0.904206 + 0.427096i \(0.859537\pi\)
\(564\) 33.5006 1.41063
\(565\) −5.25016 −0.220876
\(566\) −0.787044 −0.0330819
\(567\) 11.9653 0.502497
\(568\) −1.18250 −0.0496165
\(569\) 13.6945 0.574103 0.287052 0.957915i \(-0.407325\pi\)
0.287052 + 0.957915i \(0.407325\pi\)
\(570\) 0.796877 0.0333775
\(571\) −13.5970 −0.569018 −0.284509 0.958673i \(-0.591831\pi\)
−0.284509 + 0.958673i \(0.591831\pi\)
\(572\) 1.32982 0.0556025
\(573\) 28.5668 1.19339
\(574\) −0.362153 −0.0151160
\(575\) −6.81103 −0.284040
\(576\) −4.19683 −0.174868
\(577\) 1.50292 0.0625673 0.0312837 0.999511i \(-0.490040\pi\)
0.0312837 + 0.999511i \(0.490040\pi\)
\(578\) 0.448039 0.0186359
\(579\) −12.9450 −0.537974
\(580\) 9.11707 0.378566
\(581\) 1.95973 0.0813034
\(582\) −0.949606 −0.0393624
\(583\) 1.53902 0.0637398
\(584\) 0.528836 0.0218834
\(585\) −1.32873 −0.0549363
\(586\) 0.0464593 0.00191922
\(587\) 37.0399 1.52880 0.764401 0.644742i \(-0.223035\pi\)
0.764401 + 0.644742i \(0.223035\pi\)
\(588\) −21.2130 −0.874810
\(589\) −5.80564 −0.239217
\(590\) −0.655025 −0.0269669
\(591\) −4.16456 −0.171307
\(592\) −4.52971 −0.186170
\(593\) 26.4248 1.08514 0.542568 0.840012i \(-0.317452\pi\)
0.542568 + 0.840012i \(0.317452\pi\)
\(594\) −0.0818046 −0.00335648
\(595\) 0.804420 0.0329780
\(596\) 35.3080 1.44627
\(597\) −18.2762 −0.747995
\(598\) −0.129872 −0.00531087
\(599\) 4.30567 0.175925 0.0879625 0.996124i \(-0.471964\pi\)
0.0879625 + 0.996124i \(0.471964\pi\)
\(600\) −0.275982 −0.0112669
\(601\) 8.02478 0.327338 0.163669 0.986515i \(-0.447667\pi\)
0.163669 + 0.986515i \(0.447667\pi\)
\(602\) 0.0584713 0.00238311
\(603\) −7.06794 −0.287829
\(604\) 27.6448 1.12485
\(605\) −26.6844 −1.08488
\(606\) −0.540882 −0.0219718
\(607\) −4.42667 −0.179673 −0.0898365 0.995957i \(-0.528634\pi\)
−0.0898365 + 0.995957i \(0.528634\pi\)
\(608\) −2.01397 −0.0816774
\(609\) −3.93518 −0.159461
\(610\) 0.823151 0.0333284
\(611\) −8.92385 −0.361020
\(612\) 0.287976 0.0116407
\(613\) 10.7965 0.436066 0.218033 0.975941i \(-0.430036\pi\)
0.218033 + 0.975941i \(0.430036\pi\)
\(614\) 0.662272 0.0267271
\(615\) 55.8938 2.25386
\(616\) −0.0817981 −0.00329574
\(617\) 18.1610 0.731133 0.365567 0.930785i \(-0.380875\pi\)
0.365567 + 0.930785i \(0.380875\pi\)
\(618\) −0.0497063 −0.00199948
\(619\) 17.2708 0.694170 0.347085 0.937834i \(-0.387171\pi\)
0.347085 + 0.937834i \(0.387171\pi\)
\(620\) 4.62523 0.185754
\(621\) −22.7930 −0.914652
\(622\) 0.690029 0.0276676
\(623\) −2.37105 −0.0949939
\(624\) 7.50285 0.300355
\(625\) −30.0141 −1.20057
\(626\) 0.485071 0.0193873
\(627\) −7.92182 −0.316367
\(628\) −32.7274 −1.30596
\(629\) 0.310600 0.0123844
\(630\) 0.0408585 0.00162784
\(631\) 12.4101 0.494040 0.247020 0.969010i \(-0.420549\pi\)
0.247020 + 0.969010i \(0.420549\pi\)
\(632\) −1.49963 −0.0596519
\(633\) −26.5375 −1.05477
\(634\) −0.0770467 −0.00305992
\(635\) 8.45576 0.335557
\(636\) 8.68623 0.344431
\(637\) 5.65069 0.223888
\(638\) 0.0317679 0.00125770
\(639\) −5.87182 −0.232286
\(640\) 2.13920 0.0845592
\(641\) 31.8180 1.25674 0.628368 0.777916i \(-0.283723\pi\)
0.628368 + 0.777916i \(0.283723\pi\)
\(642\) 0.0963381 0.00380216
\(643\) −14.1932 −0.559725 −0.279863 0.960040i \(-0.590289\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(644\) −11.3936 −0.448971
\(645\) −9.02431 −0.355332
\(646\) 0.0460055 0.00181006
\(647\) −5.19642 −0.204292 −0.102146 0.994769i \(-0.532571\pi\)
−0.102146 + 0.994769i \(0.532571\pi\)
\(648\) −1.09054 −0.0428405
\(649\) 6.51165 0.255605
\(650\) 0.0367514 0.00144151
\(651\) −1.99638 −0.0782441
\(652\) −31.1083 −1.21829
\(653\) 8.00734 0.313351 0.156676 0.987650i \(-0.449922\pi\)
0.156676 + 0.987650i \(0.449922\pi\)
\(654\) −0.0206390 −0.000807049 0
\(655\) 7.52839 0.294159
\(656\) −47.0599 −1.83738
\(657\) 2.62599 0.102450
\(658\) 0.274408 0.0106975
\(659\) −40.9699 −1.59596 −0.797981 0.602683i \(-0.794098\pi\)
−0.797981 + 0.602683i \(0.794098\pi\)
\(660\) 6.31115 0.245661
\(661\) 20.3039 0.789728 0.394864 0.918740i \(-0.370792\pi\)
0.394864 + 0.918740i \(0.370792\pi\)
\(662\) 0.542231 0.0210744
\(663\) −0.514467 −0.0199802
\(664\) −0.178613 −0.00693153
\(665\) −18.6224 −0.722146
\(666\) 0.0157761 0.000611312 0
\(667\) 8.85141 0.342728
\(668\) 3.97197 0.153680
\(669\) 32.9408 1.27357
\(670\) 0.899558 0.0347530
\(671\) −8.18301 −0.315901
\(672\) −0.692542 −0.0267154
\(673\) 27.7916 1.07129 0.535644 0.844444i \(-0.320069\pi\)
0.535644 + 0.844444i \(0.320069\pi\)
\(674\) 0.554957 0.0213761
\(675\) 6.45000 0.248260
\(676\) −1.99930 −0.0768961
\(677\) 29.4085 1.13026 0.565129 0.825002i \(-0.308826\pi\)
0.565129 + 0.825002i \(0.308826\pi\)
\(678\) −0.103250 −0.00396530
\(679\) 22.1916 0.851634
\(680\) −0.0733161 −0.00281154
\(681\) −4.47146 −0.171347
\(682\) 0.0161163 0.000617127 0
\(683\) 12.6764 0.485047 0.242524 0.970146i \(-0.422025\pi\)
0.242524 + 0.970146i \(0.422025\pi\)
\(684\) −6.66668 −0.254907
\(685\) −33.4916 −1.27965
\(686\) −0.389008 −0.0148524
\(687\) −30.6461 −1.16922
\(688\) 7.59803 0.289672
\(689\) −2.31382 −0.0881496
\(690\) −0.616357 −0.0234643
\(691\) 23.9852 0.912439 0.456219 0.889867i \(-0.349203\pi\)
0.456219 + 0.889867i \(0.349203\pi\)
\(692\) −31.2491 −1.18791
\(693\) −0.406177 −0.0154294
\(694\) 0.483017 0.0183351
\(695\) 26.8268 1.01760
\(696\) 0.358658 0.0135949
\(697\) 3.22687 0.122226
\(698\) 0.901920 0.0341382
\(699\) −15.0706 −0.570022
\(700\) 3.22418 0.121863
\(701\) −43.5421 −1.64456 −0.822280 0.569083i \(-0.807298\pi\)
−0.822280 + 0.569083i \(0.807298\pi\)
\(702\) 0.122988 0.00464188
\(703\) −7.19041 −0.271192
\(704\) −5.30996 −0.200127
\(705\) −42.3514 −1.59505
\(706\) 0.674571 0.0253878
\(707\) 12.6400 0.475376
\(708\) 36.7517 1.38121
\(709\) 22.5445 0.846678 0.423339 0.905971i \(-0.360858\pi\)
0.423339 + 0.905971i \(0.360858\pi\)
\(710\) 0.747325 0.0280466
\(711\) −7.44655 −0.279267
\(712\) 0.216101 0.00809872
\(713\) 4.49046 0.168169
\(714\) 0.0158198 0.000592043 0
\(715\) −1.68115 −0.0628716
\(716\) −30.6256 −1.14453
\(717\) 21.4485 0.801008
\(718\) −0.111362 −0.00415600
\(719\) −29.6930 −1.10736 −0.553680 0.832729i \(-0.686777\pi\)
−0.553680 + 0.832729i \(0.686777\pi\)
\(720\) 5.30934 0.197868
\(721\) 1.16160 0.0432602
\(722\) −0.562061 −0.0209177
\(723\) −35.8725 −1.33411
\(724\) −5.55602 −0.206488
\(725\) −2.50478 −0.0930253
\(726\) −0.524779 −0.0194764
\(727\) 0.0713199 0.00264511 0.00132255 0.999999i \(-0.499579\pi\)
0.00132255 + 0.999999i \(0.499579\pi\)
\(728\) 0.122978 0.00455788
\(729\) 20.7557 0.768730
\(730\) −0.334218 −0.0123700
\(731\) −0.520993 −0.0192696
\(732\) −46.1848 −1.70704
\(733\) −25.7162 −0.949850 −0.474925 0.880026i \(-0.657525\pi\)
−0.474925 + 0.880026i \(0.657525\pi\)
\(734\) −0.738427 −0.0272558
\(735\) 26.8174 0.989176
\(736\) 1.55774 0.0574190
\(737\) −8.94258 −0.329404
\(738\) 0.163901 0.00603327
\(739\) −41.2789 −1.51847 −0.759234 0.650817i \(-0.774426\pi\)
−0.759234 + 0.650817i \(0.774426\pi\)
\(740\) 5.72846 0.210582
\(741\) 11.9100 0.437523
\(742\) 0.0711500 0.00261200
\(743\) 40.7379 1.49453 0.747264 0.664527i \(-0.231367\pi\)
0.747264 + 0.664527i \(0.231367\pi\)
\(744\) 0.181953 0.00667071
\(745\) −44.6363 −1.63535
\(746\) 0.818230 0.0299575
\(747\) −0.886921 −0.0324508
\(748\) 0.364357 0.0133222
\(749\) −2.25135 −0.0822625
\(750\) −0.453749 −0.0165686
\(751\) −33.6914 −1.22942 −0.614708 0.788755i \(-0.710726\pi\)
−0.614708 + 0.788755i \(0.710726\pi\)
\(752\) 35.6579 1.30031
\(753\) −2.32364 −0.0846783
\(754\) −0.0477610 −0.00173935
\(755\) −34.9485 −1.27190
\(756\) 10.7897 0.392416
\(757\) 41.7799 1.51852 0.759258 0.650790i \(-0.225562\pi\)
0.759258 + 0.650790i \(0.225562\pi\)
\(758\) 0.137997 0.00501227
\(759\) 6.12725 0.222405
\(760\) 1.69727 0.0615666
\(761\) −26.3942 −0.956791 −0.478395 0.878145i \(-0.658781\pi\)
−0.478395 + 0.878145i \(0.658781\pi\)
\(762\) 0.166292 0.00602413
\(763\) 0.482317 0.0174611
\(764\) 30.4170 1.10045
\(765\) −0.364059 −0.0131626
\(766\) 0.451878 0.0163270
\(767\) −9.78985 −0.353491
\(768\) −29.9378 −1.08029
\(769\) 10.0084 0.360911 0.180456 0.983583i \(-0.442243\pi\)
0.180456 + 0.983583i \(0.442243\pi\)
\(770\) 0.0516955 0.00186298
\(771\) −23.0653 −0.830677
\(772\) −13.7834 −0.496074
\(773\) 7.73312 0.278141 0.139071 0.990282i \(-0.455589\pi\)
0.139071 + 0.990282i \(0.455589\pi\)
\(774\) −0.0264625 −0.000951175 0
\(775\) −1.27072 −0.0456455
\(776\) −2.02257 −0.0726061
\(777\) −2.47256 −0.0887025
\(778\) 0.202894 0.00727410
\(779\) −74.7024 −2.67649
\(780\) −9.48842 −0.339740
\(781\) −7.42921 −0.265838
\(782\) −0.0355836 −0.00127247
\(783\) −8.38222 −0.299556
\(784\) −22.5790 −0.806393
\(785\) 41.3739 1.47670
\(786\) 0.148054 0.00528092
\(787\) −3.06461 −0.109241 −0.0546207 0.998507i \(-0.517395\pi\)
−0.0546207 + 0.998507i \(0.517395\pi\)
\(788\) −4.43428 −0.157965
\(789\) 13.8965 0.494729
\(790\) 0.947746 0.0337193
\(791\) 2.41288 0.0857921
\(792\) 0.0370196 0.00131543
\(793\) 12.3026 0.436879
\(794\) 0.452848 0.0160710
\(795\) −10.9811 −0.389460
\(796\) −19.4599 −0.689738
\(797\) −36.4767 −1.29207 −0.646035 0.763308i \(-0.723574\pi\)
−0.646035 + 0.763308i \(0.723574\pi\)
\(798\) −0.366231 −0.0129644
\(799\) −2.44504 −0.0864994
\(800\) −0.440811 −0.0155850
\(801\) 1.07307 0.0379151
\(802\) 0.840735 0.0296874
\(803\) 3.32249 0.117248
\(804\) −50.4718 −1.78000
\(805\) 14.4038 0.507667
\(806\) −0.0242299 −0.000853462 0
\(807\) 18.2768 0.643373
\(808\) −1.15203 −0.0405282
\(809\) −44.0720 −1.54949 −0.774744 0.632275i \(-0.782121\pi\)
−0.774744 + 0.632275i \(0.782121\pi\)
\(810\) 0.689208 0.0242163
\(811\) 29.5356 1.03713 0.518567 0.855037i \(-0.326466\pi\)
0.518567 + 0.855037i \(0.326466\pi\)
\(812\) −4.19004 −0.147042
\(813\) 26.4534 0.927760
\(814\) 0.0199604 0.000699613 0
\(815\) 39.3270 1.37756
\(816\) 2.05570 0.0719640
\(817\) 12.0610 0.421962
\(818\) −0.247907 −0.00866788
\(819\) 0.610662 0.0213383
\(820\) 59.5139 2.07832
\(821\) −46.6122 −1.62678 −0.813388 0.581722i \(-0.802379\pi\)
−0.813388 + 0.581722i \(0.802379\pi\)
\(822\) −0.658651 −0.0229731
\(823\) 26.3732 0.919311 0.459656 0.888097i \(-0.347973\pi\)
0.459656 + 0.888097i \(0.347973\pi\)
\(824\) −0.105870 −0.00368815
\(825\) −1.73390 −0.0603666
\(826\) 0.301038 0.0104744
\(827\) −10.5308 −0.366192 −0.183096 0.983095i \(-0.558612\pi\)
−0.183096 + 0.983095i \(0.558612\pi\)
\(828\) 5.15644 0.179199
\(829\) 11.8489 0.411529 0.205764 0.978602i \(-0.434032\pi\)
0.205764 + 0.978602i \(0.434032\pi\)
\(830\) 0.112881 0.00391817
\(831\) −41.9262 −1.45441
\(832\) 7.98319 0.276767
\(833\) 1.54823 0.0536430
\(834\) 0.527580 0.0182686
\(835\) −5.02136 −0.173771
\(836\) −8.43489 −0.291727
\(837\) −4.25243 −0.146985
\(838\) −0.907290 −0.0313418
\(839\) −26.8766 −0.927883 −0.463941 0.885866i \(-0.653565\pi\)
−0.463941 + 0.885866i \(0.653565\pi\)
\(840\) 0.583639 0.0201375
\(841\) −25.7449 −0.887754
\(842\) 0.540234 0.0186177
\(843\) −59.2040 −2.03909
\(844\) −28.2562 −0.972620
\(845\) 2.52751 0.0869490
\(846\) −0.124190 −0.00426973
\(847\) 12.2637 0.421385
\(848\) 9.24556 0.317494
\(849\) −55.8257 −1.91593
\(850\) 0.0100695 0.000345381 0
\(851\) 5.56153 0.190647
\(852\) −41.9304 −1.43651
\(853\) −15.6788 −0.536832 −0.268416 0.963303i \(-0.586500\pi\)
−0.268416 + 0.963303i \(0.586500\pi\)
\(854\) −0.378306 −0.0129454
\(855\) 8.42800 0.288231
\(856\) 0.205191 0.00701329
\(857\) −50.2928 −1.71797 −0.858984 0.512002i \(-0.828904\pi\)
−0.858984 + 0.512002i \(0.828904\pi\)
\(858\) −0.0330618 −0.00112871
\(859\) −8.65814 −0.295412 −0.147706 0.989031i \(-0.547189\pi\)
−0.147706 + 0.989031i \(0.547189\pi\)
\(860\) −9.60878 −0.327657
\(861\) −25.6878 −0.875438
\(862\) 0.791589 0.0269616
\(863\) 24.1610 0.822450 0.411225 0.911534i \(-0.365101\pi\)
0.411225 + 0.911534i \(0.365101\pi\)
\(864\) −1.47517 −0.0501862
\(865\) 39.5050 1.34321
\(866\) −0.483817 −0.0164408
\(867\) 31.7797 1.07930
\(868\) −2.12568 −0.0721501
\(869\) −9.42161 −0.319606
\(870\) −0.226668 −0.00768475
\(871\) 13.4446 0.455553
\(872\) −0.0439591 −0.00148864
\(873\) −10.0433 −0.339914
\(874\) 0.823764 0.0278642
\(875\) 10.6038 0.358473
\(876\) 18.7521 0.633574
\(877\) 28.7207 0.969830 0.484915 0.874561i \(-0.338851\pi\)
0.484915 + 0.874561i \(0.338851\pi\)
\(878\) −0.634805 −0.0214236
\(879\) 3.29540 0.111151
\(880\) 6.71755 0.226449
\(881\) −47.6364 −1.60491 −0.802455 0.596712i \(-0.796473\pi\)
−0.802455 + 0.596712i \(0.796473\pi\)
\(882\) 0.0786384 0.00264789
\(883\) 56.3760 1.89720 0.948602 0.316472i \(-0.102498\pi\)
0.948602 + 0.316472i \(0.102498\pi\)
\(884\) −0.547787 −0.0184241
\(885\) −46.4614 −1.56178
\(886\) −0.659032 −0.0221406
\(887\) −6.51770 −0.218843 −0.109422 0.993995i \(-0.534900\pi\)
−0.109422 + 0.993995i \(0.534900\pi\)
\(888\) 0.225353 0.00756234
\(889\) −3.88612 −0.130336
\(890\) −0.136573 −0.00457794
\(891\) −6.85147 −0.229533
\(892\) 35.0743 1.17438
\(893\) 56.6029 1.89414
\(894\) −0.877824 −0.0293588
\(895\) 38.7169 1.29416
\(896\) −0.983137 −0.0328443
\(897\) −9.21194 −0.307578
\(898\) 0.225183 0.00751447
\(899\) 1.65138 0.0550767
\(900\) −1.45918 −0.0486392
\(901\) −0.633963 −0.0211204
\(902\) 0.207372 0.00690475
\(903\) 4.14741 0.138017
\(904\) −0.219913 −0.00731421
\(905\) 7.02391 0.233483
\(906\) −0.687301 −0.0228340
\(907\) 37.8942 1.25826 0.629129 0.777301i \(-0.283412\pi\)
0.629129 + 0.777301i \(0.283412\pi\)
\(908\) −4.76106 −0.158001
\(909\) −5.72052 −0.189738
\(910\) −0.0777209 −0.00257642
\(911\) −36.0556 −1.19457 −0.597287 0.802027i \(-0.703755\pi\)
−0.597287 + 0.802027i \(0.703755\pi\)
\(912\) −47.5897 −1.57585
\(913\) −1.12216 −0.0371381
\(914\) 0.653452 0.0216143
\(915\) 58.3867 1.93021
\(916\) −32.6309 −1.07816
\(917\) −3.45991 −0.114256
\(918\) 0.0336974 0.00111218
\(919\) 37.2801 1.22976 0.614878 0.788622i \(-0.289205\pi\)
0.614878 + 0.788622i \(0.289205\pi\)
\(920\) −1.31278 −0.0432812
\(921\) 46.9755 1.54789
\(922\) −0.722906 −0.0238077
\(923\) 11.1693 0.367644
\(924\) −2.90049 −0.0954192
\(925\) −1.57381 −0.0517466
\(926\) −0.324567 −0.0106659
\(927\) −0.525708 −0.0172665
\(928\) 0.572864 0.0188052
\(929\) 30.7339 1.00835 0.504173 0.863603i \(-0.331797\pi\)
0.504173 + 0.863603i \(0.331797\pi\)
\(930\) −0.114992 −0.00377074
\(931\) −35.8417 −1.17466
\(932\) −16.0467 −0.525626
\(933\) 48.9443 1.60236
\(934\) 0.0414414 0.00135600
\(935\) −0.460619 −0.0150639
\(936\) −0.0556567 −0.00181919
\(937\) −15.1454 −0.494778 −0.247389 0.968916i \(-0.579573\pi\)
−0.247389 + 0.968916i \(0.579573\pi\)
\(938\) −0.413421 −0.0134987
\(939\) 34.4064 1.12281
\(940\) −45.0944 −1.47082
\(941\) −8.57099 −0.279406 −0.139703 0.990193i \(-0.544615\pi\)
−0.139703 + 0.990193i \(0.544615\pi\)
\(942\) 0.813664 0.0265106
\(943\) 57.7797 1.88157
\(944\) 39.1183 1.27319
\(945\) −13.6403 −0.443718
\(946\) −0.0334812 −0.00108857
\(947\) −19.1228 −0.621408 −0.310704 0.950507i \(-0.600565\pi\)
−0.310704 + 0.950507i \(0.600565\pi\)
\(948\) −53.1755 −1.72706
\(949\) −4.99515 −0.162149
\(950\) −0.233110 −0.00756308
\(951\) −5.46498 −0.177214
\(952\) 0.0336948 0.00109205
\(953\) 9.70290 0.314308 0.157154 0.987574i \(-0.449768\pi\)
0.157154 + 0.987574i \(0.449768\pi\)
\(954\) −0.0322006 −0.00104253
\(955\) −38.4530 −1.24431
\(956\) 22.8376 0.738622
\(957\) 2.25332 0.0728395
\(958\) −0.797757 −0.0257744
\(959\) 15.3922 0.497039
\(960\) 37.8872 1.22280
\(961\) −30.1622 −0.972975
\(962\) −0.0300093 −0.000967538 0
\(963\) 1.01890 0.0328336
\(964\) −38.1959 −1.23021
\(965\) 17.4249 0.560927
\(966\) 0.283267 0.00911396
\(967\) 39.0287 1.25508 0.627539 0.778585i \(-0.284062\pi\)
0.627539 + 0.778585i \(0.284062\pi\)
\(968\) −1.11773 −0.0359252
\(969\) 3.26320 0.104829
\(970\) 1.27824 0.0410419
\(971\) −10.2814 −0.329947 −0.164974 0.986298i \(-0.552754\pi\)
−0.164974 + 0.986298i \(0.552754\pi\)
\(972\) −10.8037 −0.346530
\(973\) −12.3291 −0.395254
\(974\) −0.320102 −0.0102567
\(975\) 2.60680 0.0834846
\(976\) −49.1588 −1.57354
\(977\) 35.6529 1.14064 0.570318 0.821424i \(-0.306820\pi\)
0.570318 + 0.821424i \(0.306820\pi\)
\(978\) 0.773410 0.0247309
\(979\) 1.35768 0.0433918
\(980\) 28.5543 0.912135
\(981\) −0.218284 −0.00696927
\(982\) 0.717342 0.0228913
\(983\) −14.2218 −0.453606 −0.226803 0.973941i \(-0.572827\pi\)
−0.226803 + 0.973941i \(0.572827\pi\)
\(984\) 2.34123 0.0746355
\(985\) 5.60581 0.178616
\(986\) −0.0130860 −0.000416744 0
\(987\) 19.4640 0.619545
\(988\) 12.6813 0.403447
\(989\) −9.32879 −0.296638
\(990\) −0.0233960 −0.000743573 0
\(991\) −21.0208 −0.667749 −0.333874 0.942618i \(-0.608356\pi\)
−0.333874 + 0.942618i \(0.608356\pi\)
\(992\) 0.290623 0.00922729
\(993\) 38.4609 1.22052
\(994\) −0.343457 −0.0108938
\(995\) 24.6012 0.779909
\(996\) −6.33347 −0.200684
\(997\) 16.9039 0.535353 0.267676 0.963509i \(-0.413744\pi\)
0.267676 + 0.963509i \(0.413744\pi\)
\(998\) −0.481544 −0.0152430
\(999\) −5.26673 −0.166632
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 1339.2.a.e.1.11 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1339.2.a.e.1.11 21 1.1 even 1 trivial