Properties

Label 6014.2.a.l.1.15
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $38$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.26563 q^{3} +1.00000 q^{4} +1.94989 q^{5} +1.26563 q^{6} -2.66768 q^{7} -1.00000 q^{8} -1.39817 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.26563 q^{3} +1.00000 q^{4} +1.94989 q^{5} +1.26563 q^{6} -2.66768 q^{7} -1.00000 q^{8} -1.39817 q^{9} -1.94989 q^{10} -5.22737 q^{11} -1.26563 q^{12} -3.09749 q^{13} +2.66768 q^{14} -2.46785 q^{15} +1.00000 q^{16} +2.37272 q^{17} +1.39817 q^{18} +5.22260 q^{19} +1.94989 q^{20} +3.37631 q^{21} +5.22737 q^{22} -6.75349 q^{23} +1.26563 q^{24} -1.19791 q^{25} +3.09749 q^{26} +5.56648 q^{27} -2.66768 q^{28} +9.08445 q^{29} +2.46785 q^{30} +1.00000 q^{31} -1.00000 q^{32} +6.61594 q^{33} -2.37272 q^{34} -5.20170 q^{35} -1.39817 q^{36} -4.41612 q^{37} -5.22260 q^{38} +3.92029 q^{39} -1.94989 q^{40} +7.40463 q^{41} -3.37631 q^{42} -11.3820 q^{43} -5.22737 q^{44} -2.72628 q^{45} +6.75349 q^{46} -10.4992 q^{47} -1.26563 q^{48} +0.116534 q^{49} +1.19791 q^{50} -3.00300 q^{51} -3.09749 q^{52} -9.41301 q^{53} -5.56648 q^{54} -10.1928 q^{55} +2.66768 q^{56} -6.60991 q^{57} -9.08445 q^{58} -14.1437 q^{59} -2.46785 q^{60} +1.37878 q^{61} -1.00000 q^{62} +3.72987 q^{63} +1.00000 q^{64} -6.03978 q^{65} -6.61594 q^{66} -5.35993 q^{67} +2.37272 q^{68} +8.54745 q^{69} +5.20170 q^{70} -5.76766 q^{71} +1.39817 q^{72} -3.88527 q^{73} +4.41612 q^{74} +1.51612 q^{75} +5.22260 q^{76} +13.9450 q^{77} -3.92029 q^{78} +7.72257 q^{79} +1.94989 q^{80} -2.85062 q^{81} -7.40463 q^{82} +10.7802 q^{83} +3.37631 q^{84} +4.62655 q^{85} +11.3820 q^{86} -11.4976 q^{87} +5.22737 q^{88} -10.1291 q^{89} +2.72628 q^{90} +8.26312 q^{91} -6.75349 q^{92} -1.26563 q^{93} +10.4992 q^{94} +10.1835 q^{95} +1.26563 q^{96} -1.00000 q^{97} -0.116534 q^{98} +7.30875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 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
\(3\) −1.26563 −0.730715 −0.365357 0.930867i \(-0.619053\pi\)
−0.365357 + 0.930867i \(0.619053\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.94989 0.872019 0.436009 0.899942i \(-0.356391\pi\)
0.436009 + 0.899942i \(0.356391\pi\)
\(6\) 1.26563 0.516693
\(7\) −2.66768 −1.00829 −0.504145 0.863619i \(-0.668192\pi\)
−0.504145 + 0.863619i \(0.668192\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.39817 −0.466056
\(10\) −1.94989 −0.616610
\(11\) −5.22737 −1.57611 −0.788056 0.615603i \(-0.788912\pi\)
−0.788056 + 0.615603i \(0.788912\pi\)
\(12\) −1.26563 −0.365357
\(13\) −3.09749 −0.859089 −0.429545 0.903046i \(-0.641326\pi\)
−0.429545 + 0.903046i \(0.641326\pi\)
\(14\) 2.66768 0.712968
\(15\) −2.46785 −0.637197
\(16\) 1.00000 0.250000
\(17\) 2.37272 0.575469 0.287735 0.957710i \(-0.407098\pi\)
0.287735 + 0.957710i \(0.407098\pi\)
\(18\) 1.39817 0.329552
\(19\) 5.22260 1.19815 0.599074 0.800694i \(-0.295536\pi\)
0.599074 + 0.800694i \(0.295536\pi\)
\(20\) 1.94989 0.436009
\(21\) 3.37631 0.736772
\(22\) 5.22737 1.11448
\(23\) −6.75349 −1.40820 −0.704100 0.710101i \(-0.748649\pi\)
−0.704100 + 0.710101i \(0.748649\pi\)
\(24\) 1.26563 0.258347
\(25\) −1.19791 −0.239583
\(26\) 3.09749 0.607468
\(27\) 5.56648 1.07127
\(28\) −2.66768 −0.504145
\(29\) 9.08445 1.68694 0.843470 0.537176i \(-0.180509\pi\)
0.843470 + 0.537176i \(0.180509\pi\)
\(30\) 2.46785 0.450566
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) 6.61594 1.15169
\(34\) −2.37272 −0.406918
\(35\) −5.20170 −0.879248
\(36\) −1.39817 −0.233028
\(37\) −4.41612 −0.726006 −0.363003 0.931788i \(-0.618248\pi\)
−0.363003 + 0.931788i \(0.618248\pi\)
\(38\) −5.22260 −0.847218
\(39\) 3.92029 0.627749
\(40\) −1.94989 −0.308305
\(41\) 7.40463 1.15641 0.578204 0.815892i \(-0.303754\pi\)
0.578204 + 0.815892i \(0.303754\pi\)
\(42\) −3.37631 −0.520976
\(43\) −11.3820 −1.73574 −0.867869 0.496794i \(-0.834511\pi\)
−0.867869 + 0.496794i \(0.834511\pi\)
\(44\) −5.22737 −0.788056
\(45\) −2.72628 −0.406410
\(46\) 6.75349 0.995748
\(47\) −10.4992 −1.53146 −0.765729 0.643163i \(-0.777622\pi\)
−0.765729 + 0.643163i \(0.777622\pi\)
\(48\) −1.26563 −0.182679
\(49\) 0.116534 0.0166477
\(50\) 1.19791 0.169411
\(51\) −3.00300 −0.420504
\(52\) −3.09749 −0.429545
\(53\) −9.41301 −1.29298 −0.646488 0.762924i \(-0.723763\pi\)
−0.646488 + 0.762924i \(0.723763\pi\)
\(54\) −5.56648 −0.757501
\(55\) −10.1928 −1.37440
\(56\) 2.66768 0.356484
\(57\) −6.60991 −0.875504
\(58\) −9.08445 −1.19285
\(59\) −14.1437 −1.84135 −0.920675 0.390330i \(-0.872361\pi\)
−0.920675 + 0.390330i \(0.872361\pi\)
\(60\) −2.46785 −0.318598
\(61\) 1.37878 0.176535 0.0882674 0.996097i \(-0.471867\pi\)
0.0882674 + 0.996097i \(0.471867\pi\)
\(62\) −1.00000 −0.127000
\(63\) 3.72987 0.469920
\(64\) 1.00000 0.125000
\(65\) −6.03978 −0.749142
\(66\) −6.61594 −0.814366
\(67\) −5.35993 −0.654819 −0.327410 0.944883i \(-0.606176\pi\)
−0.327410 + 0.944883i \(0.606176\pi\)
\(68\) 2.37272 0.287735
\(69\) 8.54745 1.02899
\(70\) 5.20170 0.621722
\(71\) −5.76766 −0.684495 −0.342248 0.939610i \(-0.611188\pi\)
−0.342248 + 0.939610i \(0.611188\pi\)
\(72\) 1.39817 0.164776
\(73\) −3.88527 −0.454737 −0.227368 0.973809i \(-0.573012\pi\)
−0.227368 + 0.973809i \(0.573012\pi\)
\(74\) 4.41612 0.513363
\(75\) 1.51612 0.175067
\(76\) 5.22260 0.599074
\(77\) 13.9450 1.58918
\(78\) −3.92029 −0.443886
\(79\) 7.72257 0.868857 0.434429 0.900706i \(-0.356950\pi\)
0.434429 + 0.900706i \(0.356950\pi\)
\(80\) 1.94989 0.218005
\(81\) −2.85062 −0.316735
\(82\) −7.40463 −0.817704
\(83\) 10.7802 1.18329 0.591643 0.806200i \(-0.298480\pi\)
0.591643 + 0.806200i \(0.298480\pi\)
\(84\) 3.37631 0.368386
\(85\) 4.62655 0.501820
\(86\) 11.3820 1.22735
\(87\) −11.4976 −1.23267
\(88\) 5.22737 0.557240
\(89\) −10.1291 −1.07369 −0.536843 0.843682i \(-0.680383\pi\)
−0.536843 + 0.843682i \(0.680383\pi\)
\(90\) 2.72628 0.287375
\(91\) 8.26312 0.866211
\(92\) −6.75349 −0.704100
\(93\) −1.26563 −0.131240
\(94\) 10.4992 1.08290
\(95\) 10.1835 1.04481
\(96\) 1.26563 0.129173
\(97\) −1.00000 −0.101535
\(98\) −0.116534 −0.0117717
\(99\) 7.30875 0.734557
\(100\) −1.19791 −0.119791
\(101\) 13.1008 1.30358 0.651789 0.758401i \(-0.274019\pi\)
0.651789 + 0.758401i \(0.274019\pi\)
\(102\) 3.00300 0.297341
\(103\) 5.85042 0.576459 0.288229 0.957561i \(-0.406933\pi\)
0.288229 + 0.957561i \(0.406933\pi\)
\(104\) 3.09749 0.303734
\(105\) 6.58345 0.642479
\(106\) 9.41301 0.914273
\(107\) 5.93015 0.573289 0.286645 0.958037i \(-0.407460\pi\)
0.286645 + 0.958037i \(0.407460\pi\)
\(108\) 5.56648 0.535634
\(109\) 14.7868 1.41632 0.708160 0.706052i \(-0.249526\pi\)
0.708160 + 0.706052i \(0.249526\pi\)
\(110\) 10.1928 0.971847
\(111\) 5.58919 0.530503
\(112\) −2.66768 −0.252072
\(113\) 5.76413 0.542244 0.271122 0.962545i \(-0.412605\pi\)
0.271122 + 0.962545i \(0.412605\pi\)
\(114\) 6.60991 0.619075
\(115\) −13.1686 −1.22798
\(116\) 9.08445 0.843470
\(117\) 4.33082 0.400384
\(118\) 14.1437 1.30203
\(119\) −6.32967 −0.580240
\(120\) 2.46785 0.225283
\(121\) 16.3254 1.48413
\(122\) −1.37878 −0.124829
\(123\) −9.37155 −0.845005
\(124\) 1.00000 0.0898027
\(125\) −12.0853 −1.08094
\(126\) −3.72987 −0.332283
\(127\) −9.18792 −0.815296 −0.407648 0.913139i \(-0.633651\pi\)
−0.407648 + 0.913139i \(0.633651\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 14.4054 1.26833
\(130\) 6.03978 0.529724
\(131\) −5.96717 −0.521354 −0.260677 0.965426i \(-0.583946\pi\)
−0.260677 + 0.965426i \(0.583946\pi\)
\(132\) 6.61594 0.575844
\(133\) −13.9323 −1.20808
\(134\) 5.35993 0.463027
\(135\) 10.8540 0.934167
\(136\) −2.37272 −0.203459
\(137\) −8.95303 −0.764909 −0.382454 0.923974i \(-0.624921\pi\)
−0.382454 + 0.923974i \(0.624921\pi\)
\(138\) −8.54745 −0.727608
\(139\) −11.4499 −0.971166 −0.485583 0.874191i \(-0.661393\pi\)
−0.485583 + 0.874191i \(0.661393\pi\)
\(140\) −5.20170 −0.439624
\(141\) 13.2881 1.11906
\(142\) 5.76766 0.484011
\(143\) 16.1917 1.35402
\(144\) −1.39817 −0.116514
\(145\) 17.7137 1.47104
\(146\) 3.88527 0.321547
\(147\) −0.147489 −0.0121647
\(148\) −4.41612 −0.363003
\(149\) −1.83408 −0.150254 −0.0751269 0.997174i \(-0.523936\pi\)
−0.0751269 + 0.997174i \(0.523936\pi\)
\(150\) −1.51612 −0.123791
\(151\) −11.0204 −0.896824 −0.448412 0.893827i \(-0.648010\pi\)
−0.448412 + 0.893827i \(0.648010\pi\)
\(152\) −5.22260 −0.423609
\(153\) −3.31747 −0.268201
\(154\) −13.9450 −1.12372
\(155\) 1.94989 0.156619
\(156\) 3.92029 0.313875
\(157\) −7.85364 −0.626789 −0.313395 0.949623i \(-0.601466\pi\)
−0.313395 + 0.949623i \(0.601466\pi\)
\(158\) −7.72257 −0.614375
\(159\) 11.9134 0.944797
\(160\) −1.94989 −0.154153
\(161\) 18.0162 1.41987
\(162\) 2.85062 0.223966
\(163\) 13.4381 1.05255 0.526275 0.850314i \(-0.323588\pi\)
0.526275 + 0.850314i \(0.323588\pi\)
\(164\) 7.40463 0.578204
\(165\) 12.9004 1.00429
\(166\) −10.7802 −0.836709
\(167\) 7.11664 0.550702 0.275351 0.961344i \(-0.411206\pi\)
0.275351 + 0.961344i \(0.411206\pi\)
\(168\) −3.37631 −0.260488
\(169\) −3.40555 −0.261965
\(170\) −4.62655 −0.354841
\(171\) −7.30208 −0.558404
\(172\) −11.3820 −0.867869
\(173\) −3.03986 −0.231116 −0.115558 0.993301i \(-0.536866\pi\)
−0.115558 + 0.993301i \(0.536866\pi\)
\(174\) 11.4976 0.871630
\(175\) 3.19566 0.241569
\(176\) −5.22737 −0.394028
\(177\) 17.9007 1.34550
\(178\) 10.1291 0.759211
\(179\) −11.6031 −0.867255 −0.433627 0.901092i \(-0.642767\pi\)
−0.433627 + 0.901092i \(0.642767\pi\)
\(180\) −2.72628 −0.203205
\(181\) 9.58979 0.712804 0.356402 0.934333i \(-0.384003\pi\)
0.356402 + 0.934333i \(0.384003\pi\)
\(182\) −8.26312 −0.612504
\(183\) −1.74503 −0.128997
\(184\) 6.75349 0.497874
\(185\) −8.61096 −0.633091
\(186\) 1.26563 0.0928008
\(187\) −12.4031 −0.907004
\(188\) −10.4992 −0.765729
\(189\) −14.8496 −1.08015
\(190\) −10.1835 −0.738790
\(191\) 12.0863 0.874532 0.437266 0.899332i \(-0.355947\pi\)
0.437266 + 0.899332i \(0.355947\pi\)
\(192\) −1.26563 −0.0913393
\(193\) 5.49083 0.395239 0.197619 0.980279i \(-0.436679\pi\)
0.197619 + 0.980279i \(0.436679\pi\)
\(194\) 1.00000 0.0717958
\(195\) 7.64415 0.547409
\(196\) 0.116534 0.00832383
\(197\) 24.2500 1.72774 0.863869 0.503716i \(-0.168034\pi\)
0.863869 + 0.503716i \(0.168034\pi\)
\(198\) −7.30875 −0.519410
\(199\) 14.0168 0.993626 0.496813 0.867857i \(-0.334503\pi\)
0.496813 + 0.867857i \(0.334503\pi\)
\(200\) 1.19791 0.0847054
\(201\) 6.78371 0.478486
\(202\) −13.1008 −0.921768
\(203\) −24.2344 −1.70092
\(204\) −3.00300 −0.210252
\(205\) 14.4382 1.00841
\(206\) −5.85042 −0.407618
\(207\) 9.44252 0.656301
\(208\) −3.09749 −0.214772
\(209\) −27.3005 −1.88841
\(210\) −6.58345 −0.454301
\(211\) 13.2954 0.915290 0.457645 0.889135i \(-0.348693\pi\)
0.457645 + 0.889135i \(0.348693\pi\)
\(212\) −9.41301 −0.646488
\(213\) 7.29975 0.500171
\(214\) −5.93015 −0.405377
\(215\) −22.1937 −1.51360
\(216\) −5.56648 −0.378751
\(217\) −2.66768 −0.181094
\(218\) −14.7868 −1.00149
\(219\) 4.91734 0.332283
\(220\) −10.1928 −0.687200
\(221\) −7.34948 −0.494380
\(222\) −5.58919 −0.375122
\(223\) 11.5547 0.773757 0.386879 0.922131i \(-0.373553\pi\)
0.386879 + 0.922131i \(0.373553\pi\)
\(224\) 2.66768 0.178242
\(225\) 1.67489 0.111659
\(226\) −5.76413 −0.383424
\(227\) 27.7500 1.84183 0.920915 0.389764i \(-0.127443\pi\)
0.920915 + 0.389764i \(0.127443\pi\)
\(228\) −6.60991 −0.437752
\(229\) −10.3009 −0.680703 −0.340351 0.940298i \(-0.610546\pi\)
−0.340351 + 0.940298i \(0.610546\pi\)
\(230\) 13.1686 0.868311
\(231\) −17.6492 −1.16123
\(232\) −9.08445 −0.596423
\(233\) 11.2048 0.734049 0.367024 0.930211i \(-0.380377\pi\)
0.367024 + 0.930211i \(0.380377\pi\)
\(234\) −4.33082 −0.283114
\(235\) −20.4722 −1.33546
\(236\) −14.1437 −0.920675
\(237\) −9.77396 −0.634887
\(238\) 6.32967 0.410292
\(239\) 27.4050 1.77268 0.886342 0.463032i \(-0.153238\pi\)
0.886342 + 0.463032i \(0.153238\pi\)
\(240\) −2.46785 −0.159299
\(241\) 28.8657 1.85940 0.929700 0.368317i \(-0.120066\pi\)
0.929700 + 0.368317i \(0.120066\pi\)
\(242\) −16.3254 −1.04944
\(243\) −13.0916 −0.839826
\(244\) 1.37878 0.0882674
\(245\) 0.227228 0.0145171
\(246\) 9.37155 0.597508
\(247\) −16.1770 −1.02932
\(248\) −1.00000 −0.0635001
\(249\) −13.6438 −0.864644
\(250\) 12.0853 0.764340
\(251\) 18.0563 1.13970 0.569851 0.821748i \(-0.307001\pi\)
0.569851 + 0.821748i \(0.307001\pi\)
\(252\) 3.72987 0.234960
\(253\) 35.3030 2.21948
\(254\) 9.18792 0.576501
\(255\) −5.85553 −0.366687
\(256\) 1.00000 0.0625000
\(257\) 20.4236 1.27399 0.636995 0.770868i \(-0.280177\pi\)
0.636995 + 0.770868i \(0.280177\pi\)
\(258\) −14.4054 −0.896844
\(259\) 11.7808 0.732024
\(260\) −6.03978 −0.374571
\(261\) −12.7016 −0.786209
\(262\) 5.96717 0.368653
\(263\) −5.85635 −0.361118 −0.180559 0.983564i \(-0.557791\pi\)
−0.180559 + 0.983564i \(0.557791\pi\)
\(264\) −6.61594 −0.407183
\(265\) −18.3544 −1.12750
\(266\) 13.9323 0.854241
\(267\) 12.8198 0.784558
\(268\) −5.35993 −0.327410
\(269\) 26.9843 1.64526 0.822630 0.568577i \(-0.192506\pi\)
0.822630 + 0.568577i \(0.192506\pi\)
\(270\) −10.8540 −0.660555
\(271\) −14.8981 −0.904992 −0.452496 0.891766i \(-0.649466\pi\)
−0.452496 + 0.891766i \(0.649466\pi\)
\(272\) 2.37272 0.143867
\(273\) −10.4581 −0.632953
\(274\) 8.95303 0.540872
\(275\) 6.26195 0.377610
\(276\) 8.54745 0.514496
\(277\) −23.4010 −1.40603 −0.703014 0.711176i \(-0.748163\pi\)
−0.703014 + 0.711176i \(0.748163\pi\)
\(278\) 11.4499 0.686718
\(279\) −1.39817 −0.0837062
\(280\) 5.20170 0.310861
\(281\) −26.8670 −1.60275 −0.801376 0.598160i \(-0.795899\pi\)
−0.801376 + 0.598160i \(0.795899\pi\)
\(282\) −13.2881 −0.791294
\(283\) 19.8041 1.17723 0.588617 0.808412i \(-0.299673\pi\)
0.588617 + 0.808412i \(0.299673\pi\)
\(284\) −5.76766 −0.342248
\(285\) −12.8886 −0.763456
\(286\) −16.1917 −0.957438
\(287\) −19.7532 −1.16599
\(288\) 1.39817 0.0823879
\(289\) −11.3702 −0.668835
\(290\) −17.7137 −1.04018
\(291\) 1.26563 0.0741928
\(292\) −3.88527 −0.227368
\(293\) −0.812185 −0.0474484 −0.0237242 0.999719i \(-0.507552\pi\)
−0.0237242 + 0.999719i \(0.507552\pi\)
\(294\) 0.147489 0.00860173
\(295\) −27.5787 −1.60569
\(296\) 4.41612 0.256682
\(297\) −29.0980 −1.68844
\(298\) 1.83408 0.106246
\(299\) 20.9189 1.20977
\(300\) 1.51612 0.0875334
\(301\) 30.3635 1.75013
\(302\) 11.0204 0.634150
\(303\) −16.5808 −0.952543
\(304\) 5.22260 0.299537
\(305\) 2.68848 0.153942
\(306\) 3.31747 0.189647
\(307\) 25.4624 1.45322 0.726608 0.687052i \(-0.241095\pi\)
0.726608 + 0.687052i \(0.241095\pi\)
\(308\) 13.9450 0.794589
\(309\) −7.40449 −0.421227
\(310\) −1.94989 −0.110747
\(311\) −14.3767 −0.815227 −0.407614 0.913154i \(-0.633639\pi\)
−0.407614 + 0.913154i \(0.633639\pi\)
\(312\) −3.92029 −0.221943
\(313\) 8.18376 0.462573 0.231287 0.972886i \(-0.425706\pi\)
0.231287 + 0.972886i \(0.425706\pi\)
\(314\) 7.85364 0.443207
\(315\) 7.27285 0.409779
\(316\) 7.72257 0.434429
\(317\) −28.2390 −1.58606 −0.793029 0.609184i \(-0.791497\pi\)
−0.793029 + 0.609184i \(0.791497\pi\)
\(318\) −11.9134 −0.668072
\(319\) −47.4878 −2.65881
\(320\) 1.94989 0.109002
\(321\) −7.50540 −0.418911
\(322\) −18.0162 −1.00400
\(323\) 12.3918 0.689497
\(324\) −2.85062 −0.158368
\(325\) 3.71053 0.205823
\(326\) −13.4381 −0.744265
\(327\) −18.7147 −1.03493
\(328\) −7.40463 −0.408852
\(329\) 28.0084 1.54415
\(330\) −12.9004 −0.710143
\(331\) 31.6846 1.74154 0.870772 0.491686i \(-0.163619\pi\)
0.870772 + 0.491686i \(0.163619\pi\)
\(332\) 10.7802 0.591643
\(333\) 6.17448 0.338359
\(334\) −7.11664 −0.389405
\(335\) −10.4513 −0.571015
\(336\) 3.37631 0.184193
\(337\) 15.5577 0.847481 0.423741 0.905784i \(-0.360717\pi\)
0.423741 + 0.905784i \(0.360717\pi\)
\(338\) 3.40555 0.185237
\(339\) −7.29529 −0.396226
\(340\) 4.62655 0.250910
\(341\) −5.22737 −0.283078
\(342\) 7.30208 0.394851
\(343\) 18.3629 0.991504
\(344\) 11.3820 0.613676
\(345\) 16.6666 0.897301
\(346\) 3.03986 0.163424
\(347\) −17.8940 −0.960599 −0.480300 0.877104i \(-0.659472\pi\)
−0.480300 + 0.877104i \(0.659472\pi\)
\(348\) −11.4976 −0.616336
\(349\) −25.4040 −1.35984 −0.679921 0.733285i \(-0.737986\pi\)
−0.679921 + 0.733285i \(0.737986\pi\)
\(350\) −3.19566 −0.170815
\(351\) −17.2421 −0.920316
\(352\) 5.22737 0.278620
\(353\) 0.0373432 0.00198758 0.000993789 1.00000i \(-0.499684\pi\)
0.000993789 1.00000i \(0.499684\pi\)
\(354\) −17.9007 −0.951413
\(355\) −11.2463 −0.596893
\(356\) −10.1291 −0.536843
\(357\) 8.01105 0.423990
\(358\) 11.6031 0.613242
\(359\) 7.83321 0.413421 0.206711 0.978402i \(-0.433724\pi\)
0.206711 + 0.978402i \(0.433724\pi\)
\(360\) 2.72628 0.143688
\(361\) 8.27559 0.435557
\(362\) −9.58979 −0.504028
\(363\) −20.6620 −1.08447
\(364\) 8.26312 0.433105
\(365\) −7.57587 −0.396539
\(366\) 1.74503 0.0912143
\(367\) −26.3646 −1.37622 −0.688109 0.725607i \(-0.741559\pi\)
−0.688109 + 0.725607i \(0.741559\pi\)
\(368\) −6.75349 −0.352050
\(369\) −10.3529 −0.538951
\(370\) 8.61096 0.447663
\(371\) 25.1109 1.30370
\(372\) −1.26563 −0.0656201
\(373\) 27.5033 1.42407 0.712035 0.702144i \(-0.247774\pi\)
0.712035 + 0.702144i \(0.247774\pi\)
\(374\) 12.4031 0.641349
\(375\) 15.2955 0.789858
\(376\) 10.4992 0.541452
\(377\) −28.1390 −1.44923
\(378\) 14.8496 0.763781
\(379\) 17.1114 0.878952 0.439476 0.898254i \(-0.355164\pi\)
0.439476 + 0.898254i \(0.355164\pi\)
\(380\) 10.1835 0.522404
\(381\) 11.6285 0.595749
\(382\) −12.0863 −0.618388
\(383\) −24.0296 −1.22786 −0.613928 0.789362i \(-0.710411\pi\)
−0.613928 + 0.789362i \(0.710411\pi\)
\(384\) 1.26563 0.0645867
\(385\) 27.1912 1.38579
\(386\) −5.49083 −0.279476
\(387\) 15.9139 0.808951
\(388\) −1.00000 −0.0507673
\(389\) −25.9380 −1.31511 −0.657554 0.753407i \(-0.728409\pi\)
−0.657554 + 0.753407i \(0.728409\pi\)
\(390\) −7.64415 −0.387077
\(391\) −16.0242 −0.810376
\(392\) −0.116534 −0.00588584
\(393\) 7.55226 0.380961
\(394\) −24.2500 −1.22170
\(395\) 15.0582 0.757660
\(396\) 7.30875 0.367278
\(397\) 19.8959 0.998548 0.499274 0.866444i \(-0.333600\pi\)
0.499274 + 0.866444i \(0.333600\pi\)
\(398\) −14.0168 −0.702600
\(399\) 17.6331 0.882761
\(400\) −1.19791 −0.0598957
\(401\) 13.3050 0.664418 0.332209 0.943206i \(-0.392206\pi\)
0.332209 + 0.943206i \(0.392206\pi\)
\(402\) −6.78371 −0.338341
\(403\) −3.09749 −0.154297
\(404\) 13.1008 0.651789
\(405\) −5.55840 −0.276199
\(406\) 24.2344 1.20273
\(407\) 23.0847 1.14427
\(408\) 3.00300 0.148671
\(409\) −2.21626 −0.109587 −0.0547936 0.998498i \(-0.517450\pi\)
−0.0547936 + 0.998498i \(0.517450\pi\)
\(410\) −14.4382 −0.713054
\(411\) 11.3313 0.558930
\(412\) 5.85042 0.288229
\(413\) 37.7308 1.85661
\(414\) −9.44252 −0.464075
\(415\) 21.0203 1.03185
\(416\) 3.09749 0.151867
\(417\) 14.4914 0.709645
\(418\) 27.3005 1.33531
\(419\) 0.277866 0.0135746 0.00678732 0.999977i \(-0.497840\pi\)
0.00678732 + 0.999977i \(0.497840\pi\)
\(420\) 6.58345 0.321239
\(421\) 31.4285 1.53173 0.765865 0.643001i \(-0.222311\pi\)
0.765865 + 0.643001i \(0.222311\pi\)
\(422\) −13.2954 −0.647208
\(423\) 14.6796 0.713746
\(424\) 9.41301 0.457136
\(425\) −2.84232 −0.137873
\(426\) −7.29975 −0.353674
\(427\) −3.67815 −0.177998
\(428\) 5.93015 0.286645
\(429\) −20.4928 −0.989403
\(430\) 22.1937 1.07027
\(431\) 34.0903 1.64207 0.821035 0.570877i \(-0.193397\pi\)
0.821035 + 0.570877i \(0.193397\pi\)
\(432\) 5.56648 0.267817
\(433\) 36.9809 1.77719 0.888594 0.458695i \(-0.151683\pi\)
0.888594 + 0.458695i \(0.151683\pi\)
\(434\) 2.66768 0.128053
\(435\) −22.4191 −1.07491
\(436\) 14.7868 0.708160
\(437\) −35.2708 −1.68723
\(438\) −4.91734 −0.234959
\(439\) −1.85530 −0.0885488 −0.0442744 0.999019i \(-0.514098\pi\)
−0.0442744 + 0.999019i \(0.514098\pi\)
\(440\) 10.1928 0.485924
\(441\) −0.162934 −0.00775875
\(442\) 7.34948 0.349579
\(443\) −3.87605 −0.184157 −0.0920783 0.995752i \(-0.529351\pi\)
−0.0920783 + 0.995752i \(0.529351\pi\)
\(444\) 5.58919 0.265251
\(445\) −19.7507 −0.936275
\(446\) −11.5547 −0.547129
\(447\) 2.32128 0.109793
\(448\) −2.66768 −0.126036
\(449\) 1.92416 0.0908069 0.0454034 0.998969i \(-0.485543\pi\)
0.0454034 + 0.998969i \(0.485543\pi\)
\(450\) −1.67489 −0.0789549
\(451\) −38.7067 −1.82263
\(452\) 5.76413 0.271122
\(453\) 13.9477 0.655322
\(454\) −27.7500 −1.30237
\(455\) 16.1122 0.755352
\(456\) 6.60991 0.309537
\(457\) −35.4478 −1.65818 −0.829089 0.559116i \(-0.811141\pi\)
−0.829089 + 0.559116i \(0.811141\pi\)
\(458\) 10.3009 0.481330
\(459\) 13.2077 0.616482
\(460\) −13.1686 −0.613989
\(461\) 0.839413 0.0390954 0.0195477 0.999809i \(-0.493777\pi\)
0.0195477 + 0.999809i \(0.493777\pi\)
\(462\) 17.6492 0.821117
\(463\) −17.4738 −0.812078 −0.406039 0.913856i \(-0.633090\pi\)
−0.406039 + 0.913856i \(0.633090\pi\)
\(464\) 9.08445 0.421735
\(465\) −2.46785 −0.114444
\(466\) −11.2048 −0.519051
\(467\) −17.2684 −0.799086 −0.399543 0.916714i \(-0.630831\pi\)
−0.399543 + 0.916714i \(0.630831\pi\)
\(468\) 4.33082 0.200192
\(469\) 14.2986 0.660247
\(470\) 20.4722 0.944314
\(471\) 9.93985 0.458004
\(472\) 14.1437 0.651016
\(473\) 59.4979 2.73572
\(474\) 9.77396 0.448933
\(475\) −6.25623 −0.287056
\(476\) −6.32967 −0.290120
\(477\) 13.1610 0.602600
\(478\) −27.4050 −1.25348
\(479\) −38.5054 −1.75936 −0.879678 0.475569i \(-0.842242\pi\)
−0.879678 + 0.475569i \(0.842242\pi\)
\(480\) 2.46785 0.112642
\(481\) 13.6789 0.623704
\(482\) −28.8657 −1.31479
\(483\) −22.8019 −1.03752
\(484\) 16.3254 0.742065
\(485\) −1.94989 −0.0885401
\(486\) 13.0916 0.593846
\(487\) 18.3889 0.833282 0.416641 0.909071i \(-0.363207\pi\)
0.416641 + 0.909071i \(0.363207\pi\)
\(488\) −1.37878 −0.0624145
\(489\) −17.0077 −0.769114
\(490\) −0.227228 −0.0102651
\(491\) −0.591152 −0.0266783 −0.0133392 0.999911i \(-0.504246\pi\)
−0.0133392 + 0.999911i \(0.504246\pi\)
\(492\) −9.37155 −0.422502
\(493\) 21.5549 0.970783
\(494\) 16.1770 0.727836
\(495\) 14.2513 0.640548
\(496\) 1.00000 0.0449013
\(497\) 15.3863 0.690170
\(498\) 13.6438 0.611396
\(499\) −25.9442 −1.16142 −0.580710 0.814110i \(-0.697225\pi\)
−0.580710 + 0.814110i \(0.697225\pi\)
\(500\) −12.0853 −0.540470
\(501\) −9.00706 −0.402406
\(502\) −18.0563 −0.805891
\(503\) −34.4315 −1.53523 −0.767613 0.640914i \(-0.778555\pi\)
−0.767613 + 0.640914i \(0.778555\pi\)
\(504\) −3.72987 −0.166142
\(505\) 25.5451 1.13674
\(506\) −35.3030 −1.56941
\(507\) 4.31018 0.191422
\(508\) −9.18792 −0.407648
\(509\) 20.7445 0.919486 0.459743 0.888052i \(-0.347942\pi\)
0.459743 + 0.888052i \(0.347942\pi\)
\(510\) 5.85553 0.259287
\(511\) 10.3647 0.458506
\(512\) −1.00000 −0.0441942
\(513\) 29.0715 1.28354
\(514\) −20.4236 −0.900846
\(515\) 11.4077 0.502683
\(516\) 14.4054 0.634164
\(517\) 54.8830 2.41375
\(518\) −11.7808 −0.517619
\(519\) 3.84735 0.168880
\(520\) 6.03978 0.264862
\(521\) −31.0547 −1.36053 −0.680265 0.732966i \(-0.738135\pi\)
−0.680265 + 0.732966i \(0.738135\pi\)
\(522\) 12.7016 0.555934
\(523\) −36.8872 −1.61297 −0.806483 0.591257i \(-0.798632\pi\)
−0.806483 + 0.591257i \(0.798632\pi\)
\(524\) −5.96717 −0.260677
\(525\) −4.04454 −0.176518
\(526\) 5.85635 0.255349
\(527\) 2.37272 0.103357
\(528\) 6.61594 0.287922
\(529\) 22.6097 0.983028
\(530\) 18.3544 0.797263
\(531\) 19.7752 0.858173
\(532\) −13.9323 −0.604040
\(533\) −22.9358 −0.993458
\(534\) −12.8198 −0.554767
\(535\) 11.5632 0.499919
\(536\) 5.35993 0.231514
\(537\) 14.6853 0.633716
\(538\) −26.9843 −1.16337
\(539\) −0.609165 −0.0262386
\(540\) 10.8540 0.467083
\(541\) 43.9010 1.88745 0.943725 0.330731i \(-0.107295\pi\)
0.943725 + 0.330731i \(0.107295\pi\)
\(542\) 14.8981 0.639926
\(543\) −12.1372 −0.520856
\(544\) −2.37272 −0.101730
\(545\) 28.8327 1.23506
\(546\) 10.4581 0.447565
\(547\) −0.00902360 −0.000385821 0 −0.000192911 1.00000i \(-0.500061\pi\)
−0.000192911 1.00000i \(0.500061\pi\)
\(548\) −8.95303 −0.382454
\(549\) −1.92777 −0.0822751
\(550\) −6.26195 −0.267010
\(551\) 47.4445 2.02120
\(552\) −8.54745 −0.363804
\(553\) −20.6014 −0.876060
\(554\) 23.4010 0.994213
\(555\) 10.8983 0.462608
\(556\) −11.4499 −0.485583
\(557\) 22.5672 0.956201 0.478101 0.878305i \(-0.341325\pi\)
0.478101 + 0.878305i \(0.341325\pi\)
\(558\) 1.39817 0.0591892
\(559\) 35.2556 1.49115
\(560\) −5.20170 −0.219812
\(561\) 15.6978 0.662761
\(562\) 26.8670 1.13332
\(563\) 5.08080 0.214130 0.107065 0.994252i \(-0.465855\pi\)
0.107065 + 0.994252i \(0.465855\pi\)
\(564\) 13.2881 0.559530
\(565\) 11.2394 0.472847
\(566\) −19.8041 −0.832430
\(567\) 7.60454 0.319361
\(568\) 5.76766 0.242006
\(569\) 7.61121 0.319079 0.159539 0.987192i \(-0.448999\pi\)
0.159539 + 0.987192i \(0.448999\pi\)
\(570\) 12.8886 0.539845
\(571\) −25.1865 −1.05402 −0.527012 0.849858i \(-0.676688\pi\)
−0.527012 + 0.849858i \(0.676688\pi\)
\(572\) 16.1917 0.677011
\(573\) −15.2968 −0.639033
\(574\) 19.7532 0.824483
\(575\) 8.09011 0.337381
\(576\) −1.39817 −0.0582570
\(577\) −35.0060 −1.45732 −0.728660 0.684876i \(-0.759856\pi\)
−0.728660 + 0.684876i \(0.759856\pi\)
\(578\) 11.3702 0.472938
\(579\) −6.94939 −0.288807
\(580\) 17.7137 0.735522
\(581\) −28.7583 −1.19309
\(582\) −1.26563 −0.0524622
\(583\) 49.2053 2.03788
\(584\) 3.88527 0.160774
\(585\) 8.44463 0.349142
\(586\) 0.812185 0.0335511
\(587\) 23.2481 0.959550 0.479775 0.877392i \(-0.340718\pi\)
0.479775 + 0.877392i \(0.340718\pi\)
\(588\) −0.147489 −0.00608234
\(589\) 5.22260 0.215194
\(590\) 27.5787 1.13540
\(591\) −30.6916 −1.26248
\(592\) −4.41612 −0.181501
\(593\) 13.3423 0.547902 0.273951 0.961744i \(-0.411669\pi\)
0.273951 + 0.961744i \(0.411669\pi\)
\(594\) 29.0980 1.19391
\(595\) −12.3422 −0.505980
\(596\) −1.83408 −0.0751269
\(597\) −17.7402 −0.726057
\(598\) −20.9189 −0.855437
\(599\) −19.0823 −0.779682 −0.389841 0.920882i \(-0.627470\pi\)
−0.389841 + 0.920882i \(0.627470\pi\)
\(600\) −1.51612 −0.0618954
\(601\) 11.0751 0.451761 0.225881 0.974155i \(-0.427474\pi\)
0.225881 + 0.974155i \(0.427474\pi\)
\(602\) −30.3635 −1.23753
\(603\) 7.49408 0.305183
\(604\) −11.0204 −0.448412
\(605\) 31.8328 1.29419
\(606\) 16.5808 0.673550
\(607\) 19.7998 0.803649 0.401825 0.915717i \(-0.368376\pi\)
0.401825 + 0.915717i \(0.368376\pi\)
\(608\) −5.22260 −0.211805
\(609\) 30.6719 1.24289
\(610\) −2.68848 −0.108853
\(611\) 32.5210 1.31566
\(612\) −3.31747 −0.134101
\(613\) −0.663095 −0.0267821 −0.0133911 0.999910i \(-0.504263\pi\)
−0.0133911 + 0.999910i \(0.504263\pi\)
\(614\) −25.4624 −1.02758
\(615\) −18.2735 −0.736860
\(616\) −13.9450 −0.561859
\(617\) 20.8327 0.838695 0.419347 0.907826i \(-0.362259\pi\)
0.419347 + 0.907826i \(0.362259\pi\)
\(618\) 7.40449 0.297852
\(619\) −26.8026 −1.07729 −0.538644 0.842533i \(-0.681063\pi\)
−0.538644 + 0.842533i \(0.681063\pi\)
\(620\) 1.94989 0.0783096
\(621\) −37.5931 −1.50856
\(622\) 14.3767 0.576453
\(623\) 27.0213 1.08259
\(624\) 3.92029 0.156937
\(625\) −17.5754 −0.703017
\(626\) −8.18376 −0.327089
\(627\) 34.5525 1.37989
\(628\) −7.85364 −0.313395
\(629\) −10.4782 −0.417794
\(630\) −7.27285 −0.289757
\(631\) 22.5507 0.897728 0.448864 0.893600i \(-0.351829\pi\)
0.448864 + 0.893600i \(0.351829\pi\)
\(632\) −7.72257 −0.307187
\(633\) −16.8271 −0.668816
\(634\) 28.2390 1.12151
\(635\) −17.9155 −0.710953
\(636\) 11.9134 0.472399
\(637\) −0.360962 −0.0143018
\(638\) 47.4878 1.88006
\(639\) 8.06416 0.319013
\(640\) −1.94989 −0.0770763
\(641\) 33.0314 1.30466 0.652330 0.757935i \(-0.273791\pi\)
0.652330 + 0.757935i \(0.273791\pi\)
\(642\) 7.50540 0.296215
\(643\) −24.6351 −0.971514 −0.485757 0.874094i \(-0.661456\pi\)
−0.485757 + 0.874094i \(0.661456\pi\)
\(644\) 18.0162 0.709937
\(645\) 28.0891 1.10601
\(646\) −12.3918 −0.487548
\(647\) −18.5484 −0.729213 −0.364607 0.931162i \(-0.618797\pi\)
−0.364607 + 0.931162i \(0.618797\pi\)
\(648\) 2.85062 0.111983
\(649\) 73.9343 2.90217
\(650\) −3.71053 −0.145539
\(651\) 3.37631 0.132328
\(652\) 13.4381 0.526275
\(653\) 47.3735 1.85387 0.926935 0.375222i \(-0.122434\pi\)
0.926935 + 0.375222i \(0.122434\pi\)
\(654\) 18.7147 0.731803
\(655\) −11.6353 −0.454631
\(656\) 7.40463 0.289102
\(657\) 5.43227 0.211933
\(658\) −28.0084 −1.09188
\(659\) 2.23952 0.0872395 0.0436197 0.999048i \(-0.486111\pi\)
0.0436197 + 0.999048i \(0.486111\pi\)
\(660\) 12.9004 0.502147
\(661\) 34.9675 1.36008 0.680038 0.733177i \(-0.261963\pi\)
0.680038 + 0.733177i \(0.261963\pi\)
\(662\) −31.6846 −1.23146
\(663\) 9.30176 0.361250
\(664\) −10.7802 −0.418355
\(665\) −27.1664 −1.05347
\(666\) −6.17448 −0.239256
\(667\) −61.3518 −2.37555
\(668\) 7.11664 0.275351
\(669\) −14.6240 −0.565396
\(670\) 10.4513 0.403768
\(671\) −7.20740 −0.278239
\(672\) −3.37631 −0.130244
\(673\) 6.69011 0.257885 0.128942 0.991652i \(-0.458842\pi\)
0.128942 + 0.991652i \(0.458842\pi\)
\(674\) −15.5577 −0.599260
\(675\) −6.66816 −0.256658
\(676\) −3.40555 −0.130983
\(677\) −33.4012 −1.28371 −0.641857 0.766825i \(-0.721836\pi\)
−0.641857 + 0.766825i \(0.721836\pi\)
\(678\) 7.29529 0.280174
\(679\) 2.66768 0.102376
\(680\) −4.62655 −0.177420
\(681\) −35.1213 −1.34585
\(682\) 5.22737 0.200166
\(683\) −10.5090 −0.402114 −0.201057 0.979580i \(-0.564438\pi\)
−0.201057 + 0.979580i \(0.564438\pi\)
\(684\) −7.30208 −0.279202
\(685\) −17.4575 −0.667015
\(686\) −18.3629 −0.701099
\(687\) 13.0372 0.497400
\(688\) −11.3820 −0.433934
\(689\) 29.1567 1.11078
\(690\) −16.6666 −0.634488
\(691\) −21.1228 −0.803548 −0.401774 0.915739i \(-0.631606\pi\)
−0.401774 + 0.915739i \(0.631606\pi\)
\(692\) −3.03986 −0.115558
\(693\) −19.4974 −0.740646
\(694\) 17.8940 0.679246
\(695\) −22.3260 −0.846875
\(696\) 11.4976 0.435815
\(697\) 17.5691 0.665478
\(698\) 25.4040 0.961554
\(699\) −14.1811 −0.536380
\(700\) 3.19566 0.120785
\(701\) −50.0893 −1.89185 −0.945924 0.324388i \(-0.894842\pi\)
−0.945924 + 0.324388i \(0.894842\pi\)
\(702\) 17.2421 0.650761
\(703\) −23.0636 −0.869862
\(704\) −5.22737 −0.197014
\(705\) 25.9104 0.975841
\(706\) −0.0373432 −0.00140543
\(707\) −34.9488 −1.31438
\(708\) 17.9007 0.672751
\(709\) 27.5526 1.03476 0.517380 0.855756i \(-0.326908\pi\)
0.517380 + 0.855756i \(0.326908\pi\)
\(710\) 11.2463 0.422067
\(711\) −10.7975 −0.404936
\(712\) 10.1291 0.379606
\(713\) −6.75349 −0.252920
\(714\) −8.01105 −0.299806
\(715\) 31.5722 1.18073
\(716\) −11.6031 −0.433627
\(717\) −34.6847 −1.29533
\(718\) −7.83321 −0.292333
\(719\) −5.20954 −0.194283 −0.0971416 0.995271i \(-0.530970\pi\)
−0.0971416 + 0.995271i \(0.530970\pi\)
\(720\) −2.72628 −0.101602
\(721\) −15.6071 −0.581237
\(722\) −8.27559 −0.307985
\(723\) −36.5334 −1.35869
\(724\) 9.58979 0.356402
\(725\) −10.8824 −0.404162
\(726\) 20.6620 0.766840
\(727\) −10.4960 −0.389274 −0.194637 0.980875i \(-0.562353\pi\)
−0.194637 + 0.980875i \(0.562353\pi\)
\(728\) −8.26312 −0.306252
\(729\) 25.1210 0.930408
\(730\) 7.57587 0.280395
\(731\) −27.0063 −0.998864
\(732\) −1.74503 −0.0644983
\(733\) 7.71136 0.284825 0.142413 0.989807i \(-0.454514\pi\)
0.142413 + 0.989807i \(0.454514\pi\)
\(734\) 26.3646 0.973133
\(735\) −0.287588 −0.0106078
\(736\) 6.75349 0.248937
\(737\) 28.0183 1.03207
\(738\) 10.3529 0.381096
\(739\) 47.7675 1.75716 0.878579 0.477598i \(-0.158492\pi\)
0.878579 + 0.477598i \(0.158492\pi\)
\(740\) −8.61096 −0.316545
\(741\) 20.4741 0.752136
\(742\) −25.1109 −0.921852
\(743\) −2.18953 −0.0803262 −0.0401631 0.999193i \(-0.512788\pi\)
−0.0401631 + 0.999193i \(0.512788\pi\)
\(744\) 1.26563 0.0464004
\(745\) −3.57627 −0.131024
\(746\) −27.5033 −1.00697
\(747\) −15.0726 −0.551478
\(748\) −12.4031 −0.453502
\(749\) −15.8198 −0.578042
\(750\) −15.2955 −0.558514
\(751\) 13.6668 0.498708 0.249354 0.968412i \(-0.419782\pi\)
0.249354 + 0.968412i \(0.419782\pi\)
\(752\) −10.4992 −0.382865
\(753\) −22.8526 −0.832797
\(754\) 28.1390 1.02476
\(755\) −21.4885 −0.782047
\(756\) −14.8496 −0.540074
\(757\) 22.1752 0.805972 0.402986 0.915206i \(-0.367972\pi\)
0.402986 + 0.915206i \(0.367972\pi\)
\(758\) −17.1114 −0.621513
\(759\) −44.6807 −1.62181
\(760\) −10.1835 −0.369395
\(761\) −3.24618 −0.117674 −0.0588370 0.998268i \(-0.518739\pi\)
−0.0588370 + 0.998268i \(0.518739\pi\)
\(762\) −11.6285 −0.421258
\(763\) −39.4465 −1.42806
\(764\) 12.0863 0.437266
\(765\) −6.46870 −0.233876
\(766\) 24.0296 0.868225
\(767\) 43.8099 1.58188
\(768\) −1.26563 −0.0456697
\(769\) −29.7308 −1.07212 −0.536060 0.844180i \(-0.680088\pi\)
−0.536060 + 0.844180i \(0.680088\pi\)
\(770\) −27.1912 −0.979903
\(771\) −25.8488 −0.930922
\(772\) 5.49083 0.197619
\(773\) −6.34496 −0.228212 −0.114106 0.993469i \(-0.536400\pi\)
−0.114106 + 0.993469i \(0.536400\pi\)
\(774\) −15.9139 −0.572015
\(775\) −1.19791 −0.0430304
\(776\) 1.00000 0.0358979
\(777\) −14.9102 −0.534900
\(778\) 25.9380 0.929922
\(779\) 38.6714 1.38555
\(780\) 7.64415 0.273705
\(781\) 30.1497 1.07884
\(782\) 16.0242 0.573023
\(783\) 50.5684 1.80717
\(784\) 0.116534 0.00416192
\(785\) −15.3138 −0.546572
\(786\) −7.55226 −0.269380
\(787\) 54.1808 1.93134 0.965668 0.259778i \(-0.0836495\pi\)
0.965668 + 0.259778i \(0.0836495\pi\)
\(788\) 24.2500 0.863869
\(789\) 7.41201 0.263874
\(790\) −15.0582 −0.535747
\(791\) −15.3769 −0.546739
\(792\) −7.30875 −0.259705
\(793\) −4.27076 −0.151659
\(794\) −19.8959 −0.706080
\(795\) 23.2299 0.823881
\(796\) 14.0168 0.496813
\(797\) −35.4082 −1.25422 −0.627111 0.778930i \(-0.715763\pi\)
−0.627111 + 0.778930i \(0.715763\pi\)
\(798\) −17.6331 −0.624206
\(799\) −24.9116 −0.881308
\(800\) 1.19791 0.0423527
\(801\) 14.1622 0.500398
\(802\) −13.3050 −0.469814
\(803\) 20.3098 0.716716
\(804\) 6.78371 0.239243
\(805\) 35.1296 1.23816
\(806\) 3.09749 0.109104
\(807\) −34.1522 −1.20222
\(808\) −13.1008 −0.460884
\(809\) −16.4334 −0.577767 −0.288883 0.957364i \(-0.593284\pi\)
−0.288883 + 0.957364i \(0.593284\pi\)
\(810\) 5.55840 0.195302
\(811\) 18.0429 0.633572 0.316786 0.948497i \(-0.397396\pi\)
0.316786 + 0.948497i \(0.397396\pi\)
\(812\) −24.2344 −0.850462
\(813\) 18.8555 0.661291
\(814\) −23.0847 −0.809118
\(815\) 26.2028 0.917844
\(816\) −3.00300 −0.105126
\(817\) −59.4436 −2.07967
\(818\) 2.21626 0.0774898
\(819\) −11.5532 −0.403703
\(820\) 14.4382 0.504205
\(821\) −27.1615 −0.947944 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(822\) −11.3313 −0.395223
\(823\) −48.5334 −1.69177 −0.845884 0.533367i \(-0.820926\pi\)
−0.845884 + 0.533367i \(0.820926\pi\)
\(824\) −5.85042 −0.203809
\(825\) −7.92534 −0.275925
\(826\) −37.7308 −1.31282
\(827\) 27.8336 0.967869 0.483934 0.875104i \(-0.339207\pi\)
0.483934 + 0.875104i \(0.339207\pi\)
\(828\) 9.44252 0.328150
\(829\) −32.9579 −1.14468 −0.572338 0.820018i \(-0.693963\pi\)
−0.572338 + 0.820018i \(0.693963\pi\)
\(830\) −21.0203 −0.729626
\(831\) 29.6171 1.02741
\(832\) −3.09749 −0.107386
\(833\) 0.276502 0.00958022
\(834\) −14.4914 −0.501795
\(835\) 13.8767 0.480222
\(836\) −27.3005 −0.944207
\(837\) 5.56648 0.192406
\(838\) −0.277866 −0.00959872
\(839\) −7.35979 −0.254088 −0.127044 0.991897i \(-0.540549\pi\)
−0.127044 + 0.991897i \(0.540549\pi\)
\(840\) −6.58345 −0.227151
\(841\) 53.5272 1.84577
\(842\) −31.4285 −1.08310
\(843\) 34.0039 1.17115
\(844\) 13.2954 0.457645
\(845\) −6.64046 −0.228439
\(846\) −14.6796 −0.504695
\(847\) −43.5511 −1.49643
\(848\) −9.41301 −0.323244
\(849\) −25.0648 −0.860222
\(850\) 2.84232 0.0974907
\(851\) 29.8242 1.02236
\(852\) 7.29975 0.250085
\(853\) 35.5826 1.21833 0.609163 0.793045i \(-0.291505\pi\)
0.609163 + 0.793045i \(0.291505\pi\)
\(854\) 3.67815 0.125864
\(855\) −14.2383 −0.486939
\(856\) −5.93015 −0.202688
\(857\) 57.3253 1.95820 0.979098 0.203388i \(-0.0651954\pi\)
0.979098 + 0.203388i \(0.0651954\pi\)
\(858\) 20.4928 0.699614
\(859\) 18.0698 0.616534 0.308267 0.951300i \(-0.400251\pi\)
0.308267 + 0.951300i \(0.400251\pi\)
\(860\) −22.1937 −0.756798
\(861\) 25.0003 0.852009
\(862\) −34.0903 −1.16112
\(863\) 1.51201 0.0514695 0.0257347 0.999669i \(-0.491807\pi\)
0.0257347 + 0.999669i \(0.491807\pi\)
\(864\) −5.56648 −0.189375
\(865\) −5.92740 −0.201538
\(866\) −36.9809 −1.25666
\(867\) 14.3905 0.488727
\(868\) −2.66768 −0.0905471
\(869\) −40.3688 −1.36942
\(870\) 22.4191 0.760078
\(871\) 16.6023 0.562548
\(872\) −14.7868 −0.500745
\(873\) 1.39817 0.0473208
\(874\) 35.2708 1.19305
\(875\) 32.2397 1.08990
\(876\) 4.91734 0.166141
\(877\) −22.1574 −0.748201 −0.374101 0.927388i \(-0.622049\pi\)
−0.374101 + 0.927388i \(0.622049\pi\)
\(878\) 1.85530 0.0626134
\(879\) 1.02793 0.0346712
\(880\) −10.1928 −0.343600
\(881\) −52.4572 −1.76733 −0.883663 0.468123i \(-0.844930\pi\)
−0.883663 + 0.468123i \(0.844930\pi\)
\(882\) 0.162934 0.00548626
\(883\) −34.1132 −1.14800 −0.574001 0.818855i \(-0.694609\pi\)
−0.574001 + 0.818855i \(0.694609\pi\)
\(884\) −7.34948 −0.247190
\(885\) 34.9045 1.17330
\(886\) 3.87605 0.130218
\(887\) −29.7572 −0.999149 −0.499574 0.866271i \(-0.666510\pi\)
−0.499574 + 0.866271i \(0.666510\pi\)
\(888\) −5.58919 −0.187561
\(889\) 24.5105 0.822054
\(890\) 19.7507 0.662047
\(891\) 14.9012 0.499210
\(892\) 11.5547 0.386879
\(893\) −54.8329 −1.83491
\(894\) −2.32128 −0.0776352
\(895\) −22.6248 −0.756263
\(896\) 2.66768 0.0891210
\(897\) −26.4757 −0.883997
\(898\) −1.92416 −0.0642102
\(899\) 9.08445 0.302983
\(900\) 1.67489 0.0558296
\(901\) −22.3345 −0.744069
\(902\) 38.7067 1.28879
\(903\) −38.4292 −1.27884
\(904\) −5.76413 −0.191712
\(905\) 18.6991 0.621578
\(906\) −13.9477 −0.463383
\(907\) 23.5868 0.783185 0.391593 0.920139i \(-0.371924\pi\)
0.391593 + 0.920139i \(0.371924\pi\)
\(908\) 27.7500 0.920915
\(909\) −18.3171 −0.607540
\(910\) −16.1122 −0.534115
\(911\) 30.9659 1.02595 0.512973 0.858405i \(-0.328544\pi\)
0.512973 + 0.858405i \(0.328544\pi\)
\(912\) −6.60991 −0.218876
\(913\) −56.3523 −1.86499
\(914\) 35.4478 1.17251
\(915\) −3.40263 −0.112487
\(916\) −10.3009 −0.340351
\(917\) 15.9185 0.525676
\(918\) −13.2077 −0.435919
\(919\) 32.3256 1.06632 0.533162 0.846013i \(-0.321004\pi\)
0.533162 + 0.846013i \(0.321004\pi\)
\(920\) 13.1686 0.434156
\(921\) −32.2261 −1.06189
\(922\) −0.839413 −0.0276446
\(923\) 17.8653 0.588043
\(924\) −17.6492 −0.580617
\(925\) 5.29014 0.173939
\(926\) 17.4738 0.574226
\(927\) −8.17987 −0.268662
\(928\) −9.08445 −0.298212
\(929\) −2.46694 −0.0809377 −0.0404689 0.999181i \(-0.512885\pi\)
−0.0404689 + 0.999181i \(0.512885\pi\)
\(930\) 2.46785 0.0809241
\(931\) 0.608609 0.0199464
\(932\) 11.2048 0.367024
\(933\) 18.1956 0.595698
\(934\) 17.2684 0.565039
\(935\) −24.1847 −0.790925
\(936\) −4.33082 −0.141557
\(937\) 27.4222 0.895843 0.447922 0.894073i \(-0.352164\pi\)
0.447922 + 0.894073i \(0.352164\pi\)
\(938\) −14.2986 −0.466865
\(939\) −10.3577 −0.338009
\(940\) −20.4722 −0.667731
\(941\) −47.1337 −1.53651 −0.768257 0.640141i \(-0.778876\pi\)
−0.768257 + 0.640141i \(0.778876\pi\)
\(942\) −9.93985 −0.323858
\(943\) −50.0071 −1.62845
\(944\) −14.1437 −0.460337
\(945\) −28.9551 −0.941910
\(946\) −59.4979 −1.93444
\(947\) 12.9777 0.421719 0.210859 0.977516i \(-0.432374\pi\)
0.210859 + 0.977516i \(0.432374\pi\)
\(948\) −9.77396 −0.317443
\(949\) 12.0346 0.390660
\(950\) 6.25623 0.202979
\(951\) 35.7402 1.15896
\(952\) 6.32967 0.205146
\(953\) 53.4647 1.73189 0.865946 0.500138i \(-0.166717\pi\)
0.865946 + 0.500138i \(0.166717\pi\)
\(954\) −13.1610 −0.426103
\(955\) 23.5670 0.762609
\(956\) 27.4050 0.886342
\(957\) 60.1022 1.94283
\(958\) 38.5054 1.24405
\(959\) 23.8838 0.771250
\(960\) −2.46785 −0.0796496
\(961\) 1.00000 0.0322581
\(962\) −13.6789 −0.441025
\(963\) −8.29135 −0.267185
\(964\) 28.8657 0.929700
\(965\) 10.7065 0.344656
\(966\) 22.8019 0.733639
\(967\) 8.44918 0.271707 0.135854 0.990729i \(-0.456622\pi\)
0.135854 + 0.990729i \(0.456622\pi\)
\(968\) −16.3254 −0.524719
\(969\) −15.6835 −0.503826
\(970\) 1.94989 0.0626073
\(971\) −36.1359 −1.15966 −0.579829 0.814738i \(-0.696881\pi\)
−0.579829 + 0.814738i \(0.696881\pi\)
\(972\) −13.0916 −0.419913
\(973\) 30.5446 0.979216
\(974\) −18.3889 −0.589219
\(975\) −4.69618 −0.150398
\(976\) 1.37878 0.0441337
\(977\) 60.3113 1.92953 0.964765 0.263112i \(-0.0847489\pi\)
0.964765 + 0.263112i \(0.0847489\pi\)
\(978\) 17.0077 0.543846
\(979\) 52.9488 1.69225
\(980\) 0.227228 0.00725854
\(981\) −20.6745 −0.660085
\(982\) 0.591152 0.0188644
\(983\) 22.9239 0.731158 0.365579 0.930780i \(-0.380871\pi\)
0.365579 + 0.930780i \(0.380871\pi\)
\(984\) 9.37155 0.298754
\(985\) 47.2848 1.50662
\(986\) −21.5549 −0.686447
\(987\) −35.4484 −1.12834
\(988\) −16.1770 −0.514658
\(989\) 76.8682 2.44427
\(990\) −14.2513 −0.452936
\(991\) −52.5822 −1.67033 −0.835164 0.550001i \(-0.814627\pi\)
−0.835164 + 0.550001i \(0.814627\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −40.1012 −1.27257
\(994\) −15.3863 −0.488024
\(995\) 27.3313 0.866461
\(996\) −13.6438 −0.432322
\(997\) 13.4114 0.424745 0.212372 0.977189i \(-0.431881\pi\)
0.212372 + 0.977189i \(0.431881\pi\)
\(998\) 25.9442 0.821248
\(999\) −24.5822 −0.777747
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 6014.2.a.l.1.15 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.l.1.15 38 1.1 even 1 trivial