Properties

Label 6013.2.a.c.1.17
Level $6013$
Weight $2$
Character 6013.1
Self dual yes
Analytic conductor $48.014$
Analytic rank $1$
Dimension $104$
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] = [6013,2,Mod(1,6013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6013, 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("6013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6013 = 7 \cdot 859 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6013.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: \(48.0140467354\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.32315 q^{2} +1.73935 q^{3} +3.39700 q^{4} +3.06159 q^{5} -4.04076 q^{6} -1.00000 q^{7} -3.24544 q^{8} +0.0253336 q^{9} +O(q^{10})\) \(q-2.32315 q^{2} +1.73935 q^{3} +3.39700 q^{4} +3.06159 q^{5} -4.04076 q^{6} -1.00000 q^{7} -3.24544 q^{8} +0.0253336 q^{9} -7.11252 q^{10} +2.06097 q^{11} +5.90857 q^{12} -0.884192 q^{13} +2.32315 q^{14} +5.32517 q^{15} +0.745624 q^{16} +4.69427 q^{17} -0.0588535 q^{18} -6.61397 q^{19} +10.4002 q^{20} -1.73935 q^{21} -4.78792 q^{22} +6.07691 q^{23} -5.64495 q^{24} +4.37333 q^{25} +2.05411 q^{26} -5.17398 q^{27} -3.39700 q^{28} -5.10968 q^{29} -12.3711 q^{30} -7.85495 q^{31} +4.75869 q^{32} +3.58474 q^{33} -10.9055 q^{34} -3.06159 q^{35} +0.0860582 q^{36} -9.91398 q^{37} +15.3652 q^{38} -1.53792 q^{39} -9.93621 q^{40} -1.44396 q^{41} +4.04076 q^{42} -10.0263 q^{43} +7.00111 q^{44} +0.0775609 q^{45} -14.1175 q^{46} -10.0511 q^{47} +1.29690 q^{48} +1.00000 q^{49} -10.1599 q^{50} +8.16497 q^{51} -3.00360 q^{52} -2.62722 q^{53} +12.0199 q^{54} +6.30983 q^{55} +3.24544 q^{56} -11.5040 q^{57} +11.8705 q^{58} -5.96037 q^{59} +18.0896 q^{60} -8.54092 q^{61} +18.2482 q^{62} -0.0253336 q^{63} -12.5464 q^{64} -2.70703 q^{65} -8.32786 q^{66} +7.99440 q^{67} +15.9465 q^{68} +10.5699 q^{69} +7.11252 q^{70} -5.11844 q^{71} -0.0822185 q^{72} -8.12457 q^{73} +23.0316 q^{74} +7.60675 q^{75} -22.4677 q^{76} -2.06097 q^{77} +3.57280 q^{78} -2.16221 q^{79} +2.28280 q^{80} -9.07536 q^{81} +3.35453 q^{82} +12.3065 q^{83} -5.90857 q^{84} +14.3719 q^{85} +23.2927 q^{86} -8.88751 q^{87} -6.68874 q^{88} +6.23287 q^{89} -0.180185 q^{90} +0.884192 q^{91} +20.6433 q^{92} -13.6625 q^{93} +23.3502 q^{94} -20.2493 q^{95} +8.27702 q^{96} -12.9710 q^{97} -2.32315 q^{98} +0.0522116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32315 −1.64271 −0.821356 0.570416i \(-0.806782\pi\)
−0.821356 + 0.570416i \(0.806782\pi\)
\(3\) 1.73935 1.00421 0.502107 0.864806i \(-0.332558\pi\)
0.502107 + 0.864806i \(0.332558\pi\)
\(4\) 3.39700 1.69850
\(5\) 3.06159 1.36918 0.684592 0.728926i \(-0.259980\pi\)
0.684592 + 0.728926i \(0.259980\pi\)
\(6\) −4.04076 −1.64963
\(7\) −1.00000 −0.377964
\(8\) −3.24544 −1.14744
\(9\) 0.0253336 0.00844452
\(10\) −7.11252 −2.24918
\(11\) 2.06097 0.621404 0.310702 0.950507i \(-0.399436\pi\)
0.310702 + 0.950507i \(0.399436\pi\)
\(12\) 5.90857 1.70566
\(13\) −0.884192 −0.245231 −0.122615 0.992454i \(-0.539128\pi\)
−0.122615 + 0.992454i \(0.539128\pi\)
\(14\) 2.32315 0.620887
\(15\) 5.32517 1.37495
\(16\) 0.745624 0.186406
\(17\) 4.69427 1.13853 0.569264 0.822155i \(-0.307228\pi\)
0.569264 + 0.822155i \(0.307228\pi\)
\(18\) −0.0588535 −0.0138719
\(19\) −6.61397 −1.51735 −0.758675 0.651470i \(-0.774153\pi\)
−0.758675 + 0.651470i \(0.774153\pi\)
\(20\) 10.4002 2.32556
\(21\) −1.73935 −0.379557
\(22\) −4.78792 −1.02079
\(23\) 6.07691 1.26712 0.633561 0.773692i \(-0.281592\pi\)
0.633561 + 0.773692i \(0.281592\pi\)
\(24\) −5.64495 −1.15227
\(25\) 4.37333 0.874666
\(26\) 2.05411 0.402843
\(27\) −5.17398 −0.995733
\(28\) −3.39700 −0.641973
\(29\) −5.10968 −0.948843 −0.474422 0.880298i \(-0.657343\pi\)
−0.474422 + 0.880298i \(0.657343\pi\)
\(30\) −12.3711 −2.25865
\(31\) −7.85495 −1.41079 −0.705395 0.708814i \(-0.749230\pi\)
−0.705395 + 0.708814i \(0.749230\pi\)
\(32\) 4.75869 0.841225
\(33\) 3.58474 0.624023
\(34\) −10.9055 −1.87027
\(35\) −3.06159 −0.517503
\(36\) 0.0860582 0.0143430
\(37\) −9.91398 −1.62985 −0.814925 0.579567i \(-0.803222\pi\)
−0.814925 + 0.579567i \(0.803222\pi\)
\(38\) 15.3652 2.49257
\(39\) −1.53792 −0.246264
\(40\) −9.93621 −1.57105
\(41\) −1.44396 −0.225509 −0.112755 0.993623i \(-0.535967\pi\)
−0.112755 + 0.993623i \(0.535967\pi\)
\(42\) 4.04076 0.623503
\(43\) −10.0263 −1.52900 −0.764502 0.644622i \(-0.777015\pi\)
−0.764502 + 0.644622i \(0.777015\pi\)
\(44\) 7.00111 1.05546
\(45\) 0.0775609 0.0115621
\(46\) −14.1175 −2.08152
\(47\) −10.0511 −1.46610 −0.733052 0.680173i \(-0.761905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(48\) 1.29690 0.187191
\(49\) 1.00000 0.142857
\(50\) −10.1599 −1.43682
\(51\) 8.16497 1.14332
\(52\) −3.00360 −0.416525
\(53\) −2.62722 −0.360877 −0.180438 0.983586i \(-0.557752\pi\)
−0.180438 + 0.983586i \(0.557752\pi\)
\(54\) 12.0199 1.63570
\(55\) 6.30983 0.850817
\(56\) 3.24544 0.433690
\(57\) −11.5040 −1.52374
\(58\) 11.8705 1.55868
\(59\) −5.96037 −0.775974 −0.387987 0.921665i \(-0.626829\pi\)
−0.387987 + 0.921665i \(0.626829\pi\)
\(60\) 18.0896 2.33536
\(61\) −8.54092 −1.09355 −0.546777 0.837279i \(-0.684145\pi\)
−0.546777 + 0.837279i \(0.684145\pi\)
\(62\) 18.2482 2.31752
\(63\) −0.0253336 −0.00319173
\(64\) −12.5464 −1.56830
\(65\) −2.70703 −0.335766
\(66\) −8.32786 −1.02509
\(67\) 7.99440 0.976671 0.488335 0.872656i \(-0.337604\pi\)
0.488335 + 0.872656i \(0.337604\pi\)
\(68\) 15.9465 1.93379
\(69\) 10.5699 1.27246
\(70\) 7.11252 0.850108
\(71\) −5.11844 −0.607446 −0.303723 0.952760i \(-0.598230\pi\)
−0.303723 + 0.952760i \(0.598230\pi\)
\(72\) −0.0822185 −0.00968955
\(73\) −8.12457 −0.950909 −0.475455 0.879740i \(-0.657716\pi\)
−0.475455 + 0.879740i \(0.657716\pi\)
\(74\) 23.0316 2.67737
\(75\) 7.60675 0.878351
\(76\) −22.4677 −2.57722
\(77\) −2.06097 −0.234869
\(78\) 3.57280 0.404541
\(79\) −2.16221 −0.243267 −0.121634 0.992575i \(-0.538813\pi\)
−0.121634 + 0.992575i \(0.538813\pi\)
\(80\) 2.28280 0.255224
\(81\) −9.07536 −1.00837
\(82\) 3.35453 0.370446
\(83\) 12.3065 1.35082 0.675408 0.737444i \(-0.263967\pi\)
0.675408 + 0.737444i \(0.263967\pi\)
\(84\) −5.90857 −0.644678
\(85\) 14.3719 1.55885
\(86\) 23.2927 2.51171
\(87\) −8.88751 −0.952841
\(88\) −6.68874 −0.713022
\(89\) 6.23287 0.660683 0.330341 0.943862i \(-0.392836\pi\)
0.330341 + 0.943862i \(0.392836\pi\)
\(90\) −0.180185 −0.0189932
\(91\) 0.884192 0.0926885
\(92\) 20.6433 2.15221
\(93\) −13.6625 −1.41673
\(94\) 23.3502 2.40839
\(95\) −20.2493 −2.07753
\(96\) 8.27702 0.844770
\(97\) −12.9710 −1.31700 −0.658502 0.752579i \(-0.728810\pi\)
−0.658502 + 0.752579i \(0.728810\pi\)
\(98\) −2.32315 −0.234673
\(99\) 0.0522116 0.00524746
\(100\) 14.8562 1.48562
\(101\) 7.47567 0.743857 0.371928 0.928261i \(-0.378697\pi\)
0.371928 + 0.928261i \(0.378697\pi\)
\(102\) −18.9684 −1.87815
\(103\) −19.4840 −1.91981 −0.959906 0.280323i \(-0.909558\pi\)
−0.959906 + 0.280323i \(0.909558\pi\)
\(104\) 2.86959 0.281387
\(105\) −5.32517 −0.519684
\(106\) 6.10342 0.592817
\(107\) 17.6296 1.70432 0.852160 0.523282i \(-0.175293\pi\)
0.852160 + 0.523282i \(0.175293\pi\)
\(108\) −17.5760 −1.69125
\(109\) 6.95439 0.666110 0.333055 0.942907i \(-0.391921\pi\)
0.333055 + 0.942907i \(0.391921\pi\)
\(110\) −14.6586 −1.39765
\(111\) −17.2439 −1.63672
\(112\) −0.745624 −0.0704549
\(113\) −8.85733 −0.833228 −0.416614 0.909083i \(-0.636783\pi\)
−0.416614 + 0.909083i \(0.636783\pi\)
\(114\) 26.7255 2.50307
\(115\) 18.6050 1.73492
\(116\) −17.3576 −1.61161
\(117\) −0.0223997 −0.00207085
\(118\) 13.8468 1.27470
\(119\) −4.69427 −0.430323
\(120\) −17.2825 −1.57767
\(121\) −6.75242 −0.613857
\(122\) 19.8418 1.79639
\(123\) −2.51155 −0.226459
\(124\) −26.6833 −2.39623
\(125\) −1.91861 −0.171605
\(126\) 0.0588535 0.00524309
\(127\) 10.4228 0.924877 0.462439 0.886651i \(-0.346975\pi\)
0.462439 + 0.886651i \(0.346975\pi\)
\(128\) 19.6297 1.73503
\(129\) −17.4393 −1.53545
\(130\) 6.28883 0.551567
\(131\) −4.60012 −0.401914 −0.200957 0.979600i \(-0.564405\pi\)
−0.200957 + 0.979600i \(0.564405\pi\)
\(132\) 12.1774 1.05990
\(133\) 6.61397 0.573504
\(134\) −18.5721 −1.60439
\(135\) −15.8406 −1.36334
\(136\) −15.2350 −1.30639
\(137\) 8.02917 0.685978 0.342989 0.939339i \(-0.388561\pi\)
0.342989 + 0.939339i \(0.388561\pi\)
\(138\) −24.5553 −2.09029
\(139\) 5.45904 0.463030 0.231515 0.972831i \(-0.425632\pi\)
0.231515 + 0.972831i \(0.425632\pi\)
\(140\) −10.4002 −0.878980
\(141\) −17.4824 −1.47228
\(142\) 11.8909 0.997859
\(143\) −1.82229 −0.152387
\(144\) 0.0188893 0.00157411
\(145\) −15.6437 −1.29914
\(146\) 18.8746 1.56207
\(147\) 1.73935 0.143459
\(148\) −33.6778 −2.76830
\(149\) 2.85330 0.233751 0.116876 0.993147i \(-0.462712\pi\)
0.116876 + 0.993147i \(0.462712\pi\)
\(150\) −17.6716 −1.44288
\(151\) 3.17905 0.258707 0.129354 0.991599i \(-0.458710\pi\)
0.129354 + 0.991599i \(0.458710\pi\)
\(152\) 21.4653 1.74106
\(153\) 0.118923 0.00961432
\(154\) 4.78792 0.385822
\(155\) −24.0486 −1.93163
\(156\) −5.22431 −0.418280
\(157\) 16.4550 1.31325 0.656625 0.754217i \(-0.271984\pi\)
0.656625 + 0.754217i \(0.271984\pi\)
\(158\) 5.02312 0.399618
\(159\) −4.56966 −0.362397
\(160\) 14.5692 1.15179
\(161\) −6.07691 −0.478927
\(162\) 21.0834 1.65647
\(163\) −17.8968 −1.40179 −0.700893 0.713266i \(-0.747215\pi\)
−0.700893 + 0.713266i \(0.747215\pi\)
\(164\) −4.90515 −0.383028
\(165\) 10.9750 0.854402
\(166\) −28.5899 −2.21900
\(167\) −2.39694 −0.185481 −0.0927404 0.995690i \(-0.529563\pi\)
−0.0927404 + 0.995690i \(0.529563\pi\)
\(168\) 5.64495 0.435518
\(169\) −12.2182 −0.939862
\(170\) −33.3881 −2.56075
\(171\) −0.167555 −0.0128133
\(172\) −34.0595 −2.59701
\(173\) 24.7394 1.88090 0.940450 0.339933i \(-0.110404\pi\)
0.940450 + 0.339933i \(0.110404\pi\)
\(174\) 20.6470 1.56524
\(175\) −4.37333 −0.330593
\(176\) 1.53671 0.115834
\(177\) −10.3672 −0.779243
\(178\) −14.4799 −1.08531
\(179\) −24.8924 −1.86054 −0.930272 0.366871i \(-0.880429\pi\)
−0.930272 + 0.366871i \(0.880429\pi\)
\(180\) 0.263475 0.0196382
\(181\) 6.79276 0.504902 0.252451 0.967610i \(-0.418763\pi\)
0.252451 + 0.967610i \(0.418763\pi\)
\(182\) −2.05411 −0.152260
\(183\) −14.8556 −1.09816
\(184\) −19.7222 −1.45394
\(185\) −30.3526 −2.23156
\(186\) 31.7399 2.32729
\(187\) 9.67473 0.707486
\(188\) −34.1436 −2.49018
\(189\) 5.17398 0.376352
\(190\) 47.0420 3.41279
\(191\) 10.2100 0.738769 0.369384 0.929277i \(-0.379569\pi\)
0.369384 + 0.929277i \(0.379569\pi\)
\(192\) −21.8225 −1.57490
\(193\) 20.5579 1.47979 0.739895 0.672722i \(-0.234875\pi\)
0.739895 + 0.672722i \(0.234875\pi\)
\(194\) 30.1335 2.16346
\(195\) −4.70847 −0.337181
\(196\) 3.39700 0.242643
\(197\) −13.8711 −0.988277 −0.494139 0.869383i \(-0.664516\pi\)
−0.494139 + 0.869383i \(0.664516\pi\)
\(198\) −0.121295 −0.00862006
\(199\) 17.7999 1.26180 0.630900 0.775864i \(-0.282686\pi\)
0.630900 + 0.775864i \(0.282686\pi\)
\(200\) −14.1934 −1.00362
\(201\) 13.9050 0.980786
\(202\) −17.3671 −1.22194
\(203\) 5.10968 0.358629
\(204\) 27.7364 1.94194
\(205\) −4.42082 −0.308764
\(206\) 45.2641 3.15370
\(207\) 0.153950 0.0107002
\(208\) −0.659275 −0.0457125
\(209\) −13.6312 −0.942888
\(210\) 12.3711 0.853690
\(211\) −17.6608 −1.21582 −0.607910 0.794006i \(-0.707992\pi\)
−0.607910 + 0.794006i \(0.707992\pi\)
\(212\) −8.92469 −0.612950
\(213\) −8.90274 −0.610006
\(214\) −40.9562 −2.79970
\(215\) −30.6965 −2.09349
\(216\) 16.7919 1.14254
\(217\) 7.85495 0.533228
\(218\) −16.1561 −1.09423
\(219\) −14.1315 −0.954916
\(220\) 21.4345 1.44511
\(221\) −4.15063 −0.279202
\(222\) 40.0600 2.68865
\(223\) −4.00578 −0.268247 −0.134124 0.990965i \(-0.542822\pi\)
−0.134124 + 0.990965i \(0.542822\pi\)
\(224\) −4.75869 −0.317953
\(225\) 0.110792 0.00738613
\(226\) 20.5769 1.36875
\(227\) 7.00929 0.465223 0.232611 0.972570i \(-0.425273\pi\)
0.232611 + 0.972570i \(0.425273\pi\)
\(228\) −39.0791 −2.58808
\(229\) 4.82238 0.318672 0.159336 0.987224i \(-0.449065\pi\)
0.159336 + 0.987224i \(0.449065\pi\)
\(230\) −43.2221 −2.84998
\(231\) −3.58474 −0.235858
\(232\) 16.5832 1.08874
\(233\) 6.24966 0.409429 0.204714 0.978822i \(-0.434373\pi\)
0.204714 + 0.978822i \(0.434373\pi\)
\(234\) 0.0520378 0.00340182
\(235\) −30.7723 −2.00737
\(236\) −20.2474 −1.31799
\(237\) −3.76083 −0.244292
\(238\) 10.9055 0.706897
\(239\) −17.0974 −1.10594 −0.552968 0.833202i \(-0.686505\pi\)
−0.552968 + 0.833202i \(0.686505\pi\)
\(240\) 3.97058 0.256300
\(241\) −16.0006 −1.03069 −0.515344 0.856984i \(-0.672336\pi\)
−0.515344 + 0.856984i \(0.672336\pi\)
\(242\) 15.6869 1.00839
\(243\) −0.263267 −0.0168886
\(244\) −29.0135 −1.85740
\(245\) 3.06159 0.195598
\(246\) 5.83471 0.372007
\(247\) 5.84802 0.372101
\(248\) 25.4928 1.61879
\(249\) 21.4053 1.35651
\(250\) 4.45720 0.281898
\(251\) 26.3702 1.66447 0.832237 0.554420i \(-0.187060\pi\)
0.832237 + 0.554420i \(0.187060\pi\)
\(252\) −0.0860582 −0.00542115
\(253\) 12.5243 0.787396
\(254\) −24.2138 −1.51931
\(255\) 24.9978 1.56542
\(256\) −20.5098 −1.28186
\(257\) −28.8048 −1.79680 −0.898398 0.439181i \(-0.855269\pi\)
−0.898398 + 0.439181i \(0.855269\pi\)
\(258\) 40.5140 2.52229
\(259\) 9.91398 0.616025
\(260\) −9.19579 −0.570299
\(261\) −0.129446 −0.00801252
\(262\) 10.6867 0.660229
\(263\) 15.3175 0.944519 0.472260 0.881460i \(-0.343438\pi\)
0.472260 + 0.881460i \(0.343438\pi\)
\(264\) −11.6341 −0.716026
\(265\) −8.04348 −0.494107
\(266\) −15.3652 −0.942102
\(267\) 10.8411 0.663466
\(268\) 27.1570 1.65888
\(269\) 28.8371 1.75823 0.879116 0.476608i \(-0.158134\pi\)
0.879116 + 0.476608i \(0.158134\pi\)
\(270\) 36.8000 2.23958
\(271\) −0.295646 −0.0179592 −0.00897961 0.999960i \(-0.502858\pi\)
−0.00897961 + 0.999960i \(0.502858\pi\)
\(272\) 3.50016 0.212228
\(273\) 1.53792 0.0930790
\(274\) −18.6529 −1.12686
\(275\) 9.01328 0.543521
\(276\) 35.9058 2.16128
\(277\) 28.0470 1.68518 0.842590 0.538555i \(-0.181030\pi\)
0.842590 + 0.538555i \(0.181030\pi\)
\(278\) −12.6821 −0.760624
\(279\) −0.198994 −0.0119134
\(280\) 9.93621 0.593802
\(281\) −13.9797 −0.833957 −0.416979 0.908916i \(-0.636911\pi\)
−0.416979 + 0.908916i \(0.636911\pi\)
\(282\) 40.6141 2.41853
\(283\) 2.65985 0.158112 0.0790559 0.996870i \(-0.474809\pi\)
0.0790559 + 0.996870i \(0.474809\pi\)
\(284\) −17.3873 −1.03175
\(285\) −35.2205 −2.08628
\(286\) 4.23344 0.250329
\(287\) 1.44396 0.0852344
\(288\) 0.120554 0.00710374
\(289\) 5.03617 0.296246
\(290\) 36.3427 2.13411
\(291\) −22.5611 −1.32255
\(292\) −27.5992 −1.61512
\(293\) 25.9655 1.51692 0.758460 0.651719i \(-0.225952\pi\)
0.758460 + 0.651719i \(0.225952\pi\)
\(294\) −4.04076 −0.235662
\(295\) −18.2482 −1.06245
\(296\) 32.1753 1.87015
\(297\) −10.6634 −0.618753
\(298\) −6.62862 −0.383986
\(299\) −5.37315 −0.310737
\(300\) 25.8401 1.49188
\(301\) 10.0263 0.577909
\(302\) −7.38539 −0.424981
\(303\) 13.0028 0.746991
\(304\) −4.93154 −0.282843
\(305\) −26.1488 −1.49728
\(306\) −0.276274 −0.0157936
\(307\) −7.88495 −0.450018 −0.225009 0.974357i \(-0.572241\pi\)
−0.225009 + 0.974357i \(0.572241\pi\)
\(308\) −7.00111 −0.398925
\(309\) −33.8894 −1.92790
\(310\) 55.8684 3.17311
\(311\) −31.2910 −1.77435 −0.887176 0.461431i \(-0.847336\pi\)
−0.887176 + 0.461431i \(0.847336\pi\)
\(312\) 4.99122 0.282572
\(313\) 5.35827 0.302867 0.151434 0.988467i \(-0.451611\pi\)
0.151434 + 0.988467i \(0.451611\pi\)
\(314\) −38.2273 −2.15729
\(315\) −0.0775609 −0.00437006
\(316\) −7.34503 −0.413190
\(317\) 5.38115 0.302235 0.151118 0.988516i \(-0.451713\pi\)
0.151118 + 0.988516i \(0.451713\pi\)
\(318\) 10.6160 0.595314
\(319\) −10.5309 −0.589615
\(320\) −38.4118 −2.14729
\(321\) 30.6640 1.71150
\(322\) 14.1175 0.786740
\(323\) −31.0478 −1.72754
\(324\) −30.8290 −1.71272
\(325\) −3.86686 −0.214495
\(326\) 41.5769 2.30273
\(327\) 12.0961 0.668916
\(328\) 4.68630 0.258757
\(329\) 10.0511 0.554135
\(330\) −25.4965 −1.40354
\(331\) −4.50073 −0.247383 −0.123691 0.992321i \(-0.539473\pi\)
−0.123691 + 0.992321i \(0.539473\pi\)
\(332\) 41.8053 2.29436
\(333\) −0.251156 −0.0137633
\(334\) 5.56844 0.304692
\(335\) 24.4756 1.33724
\(336\) −1.29690 −0.0707517
\(337\) 35.8161 1.95103 0.975514 0.219935i \(-0.0705847\pi\)
0.975514 + 0.219935i \(0.0705847\pi\)
\(338\) 28.3847 1.54392
\(339\) −15.4060 −0.836739
\(340\) 48.8215 2.64772
\(341\) −16.1888 −0.876671
\(342\) 0.389256 0.0210485
\(343\) −1.00000 −0.0539949
\(344\) 32.5399 1.75443
\(345\) 32.3606 1.74223
\(346\) −57.4731 −3.08978
\(347\) 23.7280 1.27378 0.636892 0.770953i \(-0.280220\pi\)
0.636892 + 0.770953i \(0.280220\pi\)
\(348\) −30.1909 −1.61840
\(349\) 20.2816 1.08565 0.542824 0.839847i \(-0.317355\pi\)
0.542824 + 0.839847i \(0.317355\pi\)
\(350\) 10.1599 0.543068
\(351\) 4.57479 0.244184
\(352\) 9.80749 0.522741
\(353\) 20.0201 1.06556 0.532780 0.846254i \(-0.321147\pi\)
0.532780 + 0.846254i \(0.321147\pi\)
\(354\) 24.0844 1.28007
\(355\) −15.6705 −0.831706
\(356\) 21.1731 1.12217
\(357\) −8.16497 −0.432136
\(358\) 57.8286 3.05634
\(359\) −4.07508 −0.215075 −0.107537 0.994201i \(-0.534297\pi\)
−0.107537 + 0.994201i \(0.534297\pi\)
\(360\) −0.251719 −0.0132668
\(361\) 24.7446 1.30235
\(362\) −15.7806 −0.829409
\(363\) −11.7448 −0.616443
\(364\) 3.00360 0.157431
\(365\) −24.8741 −1.30197
\(366\) 34.5118 1.80396
\(367\) 8.55206 0.446414 0.223207 0.974771i \(-0.428347\pi\)
0.223207 + 0.974771i \(0.428347\pi\)
\(368\) 4.53109 0.236199
\(369\) −0.0365807 −0.00190432
\(370\) 70.5134 3.66582
\(371\) 2.62722 0.136399
\(372\) −46.4115 −2.40633
\(373\) 5.63015 0.291518 0.145759 0.989320i \(-0.453438\pi\)
0.145759 + 0.989320i \(0.453438\pi\)
\(374\) −22.4758 −1.16220
\(375\) −3.33712 −0.172328
\(376\) 32.6202 1.68226
\(377\) 4.51793 0.232685
\(378\) −12.0199 −0.618237
\(379\) 3.26015 0.167462 0.0837312 0.996488i \(-0.473316\pi\)
0.0837312 + 0.996488i \(0.473316\pi\)
\(380\) −68.7868 −3.52869
\(381\) 18.1289 0.928774
\(382\) −23.7193 −1.21358
\(383\) 34.2169 1.74840 0.874201 0.485564i \(-0.161386\pi\)
0.874201 + 0.485564i \(0.161386\pi\)
\(384\) 34.1428 1.74234
\(385\) −6.30983 −0.321579
\(386\) −47.7590 −2.43087
\(387\) −0.254003 −0.0129117
\(388\) −44.0625 −2.23693
\(389\) 3.88942 0.197201 0.0986007 0.995127i \(-0.468563\pi\)
0.0986007 + 0.995127i \(0.468563\pi\)
\(390\) 10.9385 0.553891
\(391\) 28.5266 1.44265
\(392\) −3.24544 −0.163920
\(393\) −8.00121 −0.403608
\(394\) 32.2247 1.62345
\(395\) −6.61980 −0.333078
\(396\) 0.177363 0.00891282
\(397\) 34.6189 1.73747 0.868736 0.495275i \(-0.164933\pi\)
0.868736 + 0.495275i \(0.164933\pi\)
\(398\) −41.3517 −2.07277
\(399\) 11.5040 0.575921
\(400\) 3.26086 0.163043
\(401\) 11.4096 0.569767 0.284884 0.958562i \(-0.408045\pi\)
0.284884 + 0.958562i \(0.408045\pi\)
\(402\) −32.3034 −1.61115
\(403\) 6.94528 0.345969
\(404\) 25.3949 1.26344
\(405\) −27.7850 −1.38065
\(406\) −11.8705 −0.589124
\(407\) −20.4324 −1.01280
\(408\) −26.4989 −1.31189
\(409\) −27.5113 −1.36034 −0.680172 0.733052i \(-0.738095\pi\)
−0.680172 + 0.733052i \(0.738095\pi\)
\(410\) 10.2702 0.507209
\(411\) 13.9655 0.688868
\(412\) −66.1871 −3.26080
\(413\) 5.96037 0.293291
\(414\) −0.357647 −0.0175774
\(415\) 37.6775 1.84952
\(416\) −4.20759 −0.206294
\(417\) 9.49517 0.464980
\(418\) 31.6672 1.54889
\(419\) 33.9004 1.65614 0.828071 0.560623i \(-0.189438\pi\)
0.828071 + 0.560623i \(0.189438\pi\)
\(420\) −18.0896 −0.882683
\(421\) −29.5310 −1.43925 −0.719627 0.694361i \(-0.755687\pi\)
−0.719627 + 0.694361i \(0.755687\pi\)
\(422\) 41.0286 1.99724
\(423\) −0.254630 −0.0123805
\(424\) 8.52650 0.414083
\(425\) 20.5296 0.995832
\(426\) 20.6824 1.00206
\(427\) 8.54092 0.413324
\(428\) 59.8879 2.89479
\(429\) −3.16959 −0.153029
\(430\) 71.3125 3.43900
\(431\) −5.40775 −0.260482 −0.130241 0.991482i \(-0.541575\pi\)
−0.130241 + 0.991482i \(0.541575\pi\)
\(432\) −3.85785 −0.185611
\(433\) −21.1114 −1.01455 −0.507276 0.861784i \(-0.669347\pi\)
−0.507276 + 0.861784i \(0.669347\pi\)
\(434\) −18.2482 −0.875941
\(435\) −27.2099 −1.30462
\(436\) 23.6241 1.13139
\(437\) −40.1925 −1.92267
\(438\) 32.8294 1.56865
\(439\) 7.65621 0.365411 0.182706 0.983168i \(-0.441514\pi\)
0.182706 + 0.983168i \(0.441514\pi\)
\(440\) −20.4782 −0.976259
\(441\) 0.0253336 0.00120636
\(442\) 9.64253 0.458648
\(443\) −25.7033 −1.22120 −0.610601 0.791938i \(-0.709072\pi\)
−0.610601 + 0.791938i \(0.709072\pi\)
\(444\) −58.5775 −2.77997
\(445\) 19.0825 0.904596
\(446\) 9.30602 0.440653
\(447\) 4.96288 0.234736
\(448\) 12.5464 0.592760
\(449\) 13.3918 0.631996 0.315998 0.948760i \(-0.397661\pi\)
0.315998 + 0.948760i \(0.397661\pi\)
\(450\) −0.257386 −0.0121333
\(451\) −2.97596 −0.140132
\(452\) −30.0884 −1.41524
\(453\) 5.52947 0.259797
\(454\) −16.2836 −0.764227
\(455\) 2.70703 0.126908
\(456\) 37.3356 1.74840
\(457\) −32.0863 −1.50093 −0.750466 0.660909i \(-0.770171\pi\)
−0.750466 + 0.660909i \(0.770171\pi\)
\(458\) −11.2031 −0.523486
\(459\) −24.2881 −1.13367
\(460\) 63.2012 2.94677
\(461\) 6.41971 0.298996 0.149498 0.988762i \(-0.452234\pi\)
0.149498 + 0.988762i \(0.452234\pi\)
\(462\) 8.32786 0.387447
\(463\) −38.3267 −1.78119 −0.890595 0.454797i \(-0.849712\pi\)
−0.890595 + 0.454797i \(0.849712\pi\)
\(464\) −3.80990 −0.176870
\(465\) −41.8289 −1.93977
\(466\) −14.5189 −0.672574
\(467\) −28.0367 −1.29739 −0.648693 0.761050i \(-0.724684\pi\)
−0.648693 + 0.761050i \(0.724684\pi\)
\(468\) −0.0760919 −0.00351735
\(469\) −7.99440 −0.369147
\(470\) 71.4886 3.29752
\(471\) 28.6209 1.31878
\(472\) 19.3440 0.890381
\(473\) −20.6639 −0.950129
\(474\) 8.73696 0.401302
\(475\) −28.9251 −1.32717
\(476\) −15.9465 −0.730904
\(477\) −0.0665569 −0.00304743
\(478\) 39.7197 1.81673
\(479\) −20.3528 −0.929943 −0.464972 0.885326i \(-0.653935\pi\)
−0.464972 + 0.885326i \(0.653935\pi\)
\(480\) 25.3408 1.15665
\(481\) 8.76586 0.399689
\(482\) 37.1717 1.69312
\(483\) −10.5699 −0.480945
\(484\) −22.9380 −1.04264
\(485\) −39.7118 −1.80322
\(486\) 0.611607 0.0277431
\(487\) −8.64816 −0.391886 −0.195943 0.980615i \(-0.562777\pi\)
−0.195943 + 0.980615i \(0.562777\pi\)
\(488\) 27.7191 1.25478
\(489\) −31.1288 −1.40769
\(490\) −7.11252 −0.321311
\(491\) 6.68506 0.301692 0.150846 0.988557i \(-0.451800\pi\)
0.150846 + 0.988557i \(0.451800\pi\)
\(492\) −8.53176 −0.384641
\(493\) −23.9862 −1.08028
\(494\) −13.5858 −0.611254
\(495\) 0.159850 0.00718474
\(496\) −5.85684 −0.262980
\(497\) 5.11844 0.229593
\(498\) −49.7277 −2.22835
\(499\) 42.2531 1.89151 0.945754 0.324884i \(-0.105325\pi\)
0.945754 + 0.324884i \(0.105325\pi\)
\(500\) −6.51751 −0.291472
\(501\) −4.16912 −0.186262
\(502\) −61.2619 −2.73425
\(503\) −13.5222 −0.602926 −0.301463 0.953478i \(-0.597475\pi\)
−0.301463 + 0.953478i \(0.597475\pi\)
\(504\) 0.0822185 0.00366231
\(505\) 22.8874 1.01848
\(506\) −29.0958 −1.29346
\(507\) −21.2517 −0.943822
\(508\) 35.4064 1.57091
\(509\) 35.7174 1.58314 0.791572 0.611075i \(-0.209263\pi\)
0.791572 + 0.611075i \(0.209263\pi\)
\(510\) −58.0735 −2.57154
\(511\) 8.12457 0.359410
\(512\) 8.38795 0.370699
\(513\) 34.2206 1.51088
\(514\) 66.9178 2.95162
\(515\) −59.6519 −2.62858
\(516\) −59.2414 −2.60796
\(517\) −20.7150 −0.911043
\(518\) −23.0316 −1.01195
\(519\) 43.0304 1.88882
\(520\) 8.78551 0.385270
\(521\) 17.9359 0.785786 0.392893 0.919584i \(-0.371474\pi\)
0.392893 + 0.919584i \(0.371474\pi\)
\(522\) 0.300722 0.0131623
\(523\) −9.20478 −0.402497 −0.201249 0.979540i \(-0.564500\pi\)
−0.201249 + 0.979540i \(0.564500\pi\)
\(524\) −15.6266 −0.682652
\(525\) −7.60675 −0.331986
\(526\) −35.5848 −1.55157
\(527\) −36.8732 −1.60622
\(528\) 2.67287 0.116322
\(529\) 13.9288 0.605600
\(530\) 18.6862 0.811675
\(531\) −0.150997 −0.00655273
\(532\) 22.4677 0.974098
\(533\) 1.27674 0.0553017
\(534\) −25.1855 −1.08988
\(535\) 53.9746 2.33353
\(536\) −25.9453 −1.12067
\(537\) −43.2965 −1.86838
\(538\) −66.9929 −2.88827
\(539\) 2.06097 0.0887721
\(540\) −53.8106 −2.31564
\(541\) 2.33347 0.100324 0.0501619 0.998741i \(-0.484026\pi\)
0.0501619 + 0.998741i \(0.484026\pi\)
\(542\) 0.686829 0.0295018
\(543\) 11.8150 0.507030
\(544\) 22.3386 0.957758
\(545\) 21.2915 0.912027
\(546\) −3.57280 −0.152902
\(547\) 16.8512 0.720504 0.360252 0.932855i \(-0.382691\pi\)
0.360252 + 0.932855i \(0.382691\pi\)
\(548\) 27.2751 1.16513
\(549\) −0.216372 −0.00923453
\(550\) −20.9392 −0.892849
\(551\) 33.7953 1.43973
\(552\) −34.3039 −1.46007
\(553\) 2.16221 0.0919465
\(554\) −65.1572 −2.76827
\(555\) −52.7937 −2.24097
\(556\) 18.5444 0.786456
\(557\) −30.7324 −1.30217 −0.651087 0.759003i \(-0.725687\pi\)
−0.651087 + 0.759003i \(0.725687\pi\)
\(558\) 0.462291 0.0195703
\(559\) 8.86521 0.374958
\(560\) −2.28280 −0.0964657
\(561\) 16.8277 0.710467
\(562\) 32.4768 1.36995
\(563\) −32.1862 −1.35649 −0.678243 0.734838i \(-0.737258\pi\)
−0.678243 + 0.734838i \(0.737258\pi\)
\(564\) −59.3876 −2.50067
\(565\) −27.1175 −1.14084
\(566\) −6.17922 −0.259732
\(567\) 9.07536 0.381129
\(568\) 16.6116 0.697006
\(569\) 34.0146 1.42597 0.712984 0.701181i \(-0.247343\pi\)
0.712984 + 0.701181i \(0.247343\pi\)
\(570\) 81.8224 3.42716
\(571\) −36.4868 −1.52692 −0.763462 0.645852i \(-0.776502\pi\)
−0.763462 + 0.645852i \(0.776502\pi\)
\(572\) −6.19032 −0.258830
\(573\) 17.7587 0.741881
\(574\) −3.35453 −0.140016
\(575\) 26.5763 1.10831
\(576\) −0.317844 −0.0132435
\(577\) −20.7746 −0.864857 −0.432429 0.901668i \(-0.642343\pi\)
−0.432429 + 0.901668i \(0.642343\pi\)
\(578\) −11.6998 −0.486646
\(579\) 35.7574 1.48603
\(580\) −53.1418 −2.20659
\(581\) −12.3065 −0.510561
\(582\) 52.4126 2.17257
\(583\) −5.41462 −0.224250
\(584\) 26.3678 1.09111
\(585\) −0.0685787 −0.00283538
\(586\) −60.3216 −2.49186
\(587\) 3.52820 0.145625 0.0728123 0.997346i \(-0.476803\pi\)
0.0728123 + 0.997346i \(0.476803\pi\)
\(588\) 5.90857 0.243665
\(589\) 51.9524 2.14066
\(590\) 42.3932 1.74530
\(591\) −24.1267 −0.992441
\(592\) −7.39211 −0.303814
\(593\) 42.7442 1.75529 0.877646 0.479309i \(-0.159113\pi\)
0.877646 + 0.479309i \(0.159113\pi\)
\(594\) 24.7726 1.01643
\(595\) −14.3719 −0.589192
\(596\) 9.69265 0.397027
\(597\) 30.9602 1.26712
\(598\) 12.4826 0.510452
\(599\) −15.4713 −0.632141 −0.316071 0.948736i \(-0.602364\pi\)
−0.316071 + 0.948736i \(0.602364\pi\)
\(600\) −24.6872 −1.00785
\(601\) 18.1397 0.739933 0.369967 0.929045i \(-0.379369\pi\)
0.369967 + 0.929045i \(0.379369\pi\)
\(602\) −23.2927 −0.949338
\(603\) 0.202526 0.00824751
\(604\) 10.7992 0.439415
\(605\) −20.6731 −0.840483
\(606\) −30.2074 −1.22709
\(607\) −17.9881 −0.730115 −0.365057 0.930985i \(-0.618951\pi\)
−0.365057 + 0.930985i \(0.618951\pi\)
\(608\) −31.4738 −1.27643
\(609\) 8.88751 0.360140
\(610\) 60.7475 2.45959
\(611\) 8.88710 0.359533
\(612\) 0.403980 0.0163299
\(613\) −15.2541 −0.616108 −0.308054 0.951369i \(-0.599678\pi\)
−0.308054 + 0.951369i \(0.599678\pi\)
\(614\) 18.3179 0.739250
\(615\) −7.68935 −0.310064
\(616\) 6.68874 0.269497
\(617\) −16.6211 −0.669141 −0.334571 0.942371i \(-0.608591\pi\)
−0.334571 + 0.942371i \(0.608591\pi\)
\(618\) 78.7300 3.16698
\(619\) 45.3224 1.82166 0.910830 0.412782i \(-0.135443\pi\)
0.910830 + 0.412782i \(0.135443\pi\)
\(620\) −81.6932 −3.28088
\(621\) −31.4418 −1.26172
\(622\) 72.6936 2.91475
\(623\) −6.23287 −0.249715
\(624\) −1.14671 −0.0459051
\(625\) −27.7406 −1.10963
\(626\) −12.4480 −0.497524
\(627\) −23.7094 −0.946860
\(628\) 55.8976 2.23056
\(629\) −46.5389 −1.85563
\(630\) 0.180185 0.00717875
\(631\) 21.5872 0.859374 0.429687 0.902978i \(-0.358624\pi\)
0.429687 + 0.902978i \(0.358624\pi\)
\(632\) 7.01732 0.279134
\(633\) −30.7183 −1.22094
\(634\) −12.5012 −0.496486
\(635\) 31.9105 1.26633
\(636\) −15.5231 −0.615533
\(637\) −0.884192 −0.0350329
\(638\) 24.4647 0.968568
\(639\) −0.129668 −0.00512959
\(640\) 60.0980 2.37558
\(641\) −38.8820 −1.53575 −0.767873 0.640602i \(-0.778685\pi\)
−0.767873 + 0.640602i \(0.778685\pi\)
\(642\) −71.2370 −2.81150
\(643\) −35.7062 −1.40811 −0.704057 0.710144i \(-0.748630\pi\)
−0.704057 + 0.710144i \(0.748630\pi\)
\(644\) −20.6433 −0.813459
\(645\) −53.3920 −2.10231
\(646\) 72.1285 2.83786
\(647\) −23.0677 −0.906887 −0.453443 0.891285i \(-0.649805\pi\)
−0.453443 + 0.891285i \(0.649805\pi\)
\(648\) 29.4535 1.15704
\(649\) −12.2841 −0.482194
\(650\) 8.98328 0.352353
\(651\) 13.6625 0.535475
\(652\) −60.7955 −2.38094
\(653\) −3.59950 −0.140859 −0.0704297 0.997517i \(-0.522437\pi\)
−0.0704297 + 0.997517i \(0.522437\pi\)
\(654\) −28.1010 −1.09884
\(655\) −14.0837 −0.550295
\(656\) −1.07665 −0.0420363
\(657\) −0.205824 −0.00802997
\(658\) −23.3502 −0.910284
\(659\) 47.0382 1.83235 0.916174 0.400780i \(-0.131261\pi\)
0.916174 + 0.400780i \(0.131261\pi\)
\(660\) 37.2821 1.45120
\(661\) −19.5162 −0.759091 −0.379546 0.925173i \(-0.623920\pi\)
−0.379546 + 0.925173i \(0.623920\pi\)
\(662\) 10.4558 0.406378
\(663\) −7.21940 −0.280378
\(664\) −39.9401 −1.54998
\(665\) 20.2493 0.785233
\(666\) 0.583473 0.0226091
\(667\) −31.0510 −1.20230
\(668\) −8.14242 −0.315040
\(669\) −6.96746 −0.269377
\(670\) −56.8603 −2.19670
\(671\) −17.6025 −0.679539
\(672\) −8.27702 −0.319293
\(673\) −0.570063 −0.0219743 −0.0109871 0.999940i \(-0.503497\pi\)
−0.0109871 + 0.999940i \(0.503497\pi\)
\(674\) −83.2061 −3.20498
\(675\) −22.6275 −0.870934
\(676\) −41.5053 −1.59636
\(677\) −39.2953 −1.51024 −0.755121 0.655586i \(-0.772422\pi\)
−0.755121 + 0.655586i \(0.772422\pi\)
\(678\) 35.7904 1.37452
\(679\) 12.9710 0.497781
\(680\) −46.6432 −1.78869
\(681\) 12.1916 0.467183
\(682\) 37.6089 1.44012
\(683\) −15.2252 −0.582577 −0.291288 0.956635i \(-0.594084\pi\)
−0.291288 + 0.956635i \(0.594084\pi\)
\(684\) −0.569186 −0.0217634
\(685\) 24.5820 0.939230
\(686\) 2.32315 0.0886981
\(687\) 8.38780 0.320015
\(688\) −7.47588 −0.285015
\(689\) 2.32297 0.0884981
\(690\) −75.1783 −2.86199
\(691\) 1.37795 0.0524195 0.0262098 0.999656i \(-0.491656\pi\)
0.0262098 + 0.999656i \(0.491656\pi\)
\(692\) 84.0397 3.19471
\(693\) −0.0522116 −0.00198335
\(694\) −55.1236 −2.09246
\(695\) 16.7133 0.633973
\(696\) 28.8439 1.09332
\(697\) −6.77835 −0.256748
\(698\) −47.1170 −1.78341
\(699\) 10.8703 0.411154
\(700\) −14.8562 −0.561512
\(701\) −13.4507 −0.508026 −0.254013 0.967201i \(-0.581751\pi\)
−0.254013 + 0.967201i \(0.581751\pi\)
\(702\) −10.6279 −0.401124
\(703\) 65.5708 2.47305
\(704\) −25.8576 −0.974546
\(705\) −53.5238 −2.01582
\(706\) −46.5095 −1.75041
\(707\) −7.47567 −0.281151
\(708\) −35.2173 −1.32355
\(709\) 26.3310 0.988881 0.494440 0.869212i \(-0.335373\pi\)
0.494440 + 0.869212i \(0.335373\pi\)
\(710\) 36.4050 1.36625
\(711\) −0.0547764 −0.00205428
\(712\) −20.2284 −0.758092
\(713\) −47.7338 −1.78764
\(714\) 18.9684 0.709875
\(715\) −5.57910 −0.208646
\(716\) −84.5595 −3.16014
\(717\) −29.7383 −1.11060
\(718\) 9.46701 0.353306
\(719\) 40.7114 1.51828 0.759140 0.650927i \(-0.225620\pi\)
0.759140 + 0.650927i \(0.225620\pi\)
\(720\) 0.0578313 0.00215525
\(721\) 19.4840 0.725621
\(722\) −57.4854 −2.13939
\(723\) −27.8306 −1.03503
\(724\) 23.0750 0.857577
\(725\) −22.3463 −0.829921
\(726\) 27.2849 1.01264
\(727\) 8.52507 0.316177 0.158089 0.987425i \(-0.449467\pi\)
0.158089 + 0.987425i \(0.449467\pi\)
\(728\) −2.86959 −0.106354
\(729\) 26.7682 0.991413
\(730\) 57.7862 2.13876
\(731\) −47.0664 −1.74081
\(732\) −50.4647 −1.86523
\(733\) −9.96215 −0.367960 −0.183980 0.982930i \(-0.558898\pi\)
−0.183980 + 0.982930i \(0.558898\pi\)
\(734\) −19.8677 −0.733329
\(735\) 5.32517 0.196422
\(736\) 28.9181 1.06594
\(737\) 16.4762 0.606908
\(738\) 0.0849823 0.00312824
\(739\) 0.612502 0.0225313 0.0112656 0.999937i \(-0.496414\pi\)
0.0112656 + 0.999937i \(0.496414\pi\)
\(740\) −103.108 −3.79032
\(741\) 10.1717 0.373668
\(742\) −6.10342 −0.224064
\(743\) 11.7103 0.429610 0.214805 0.976657i \(-0.431088\pi\)
0.214805 + 0.976657i \(0.431088\pi\)
\(744\) 44.3408 1.62561
\(745\) 8.73562 0.320048
\(746\) −13.0797 −0.478880
\(747\) 0.311768 0.0114070
\(748\) 32.8651 1.20167
\(749\) −17.6296 −0.644172
\(750\) 7.75262 0.283086
\(751\) −32.5115 −1.18636 −0.593180 0.805070i \(-0.702128\pi\)
−0.593180 + 0.805070i \(0.702128\pi\)
\(752\) −7.49434 −0.273291
\(753\) 45.8670 1.67149
\(754\) −10.4958 −0.382235
\(755\) 9.73294 0.354218
\(756\) 17.5760 0.639234
\(757\) 14.7155 0.534843 0.267422 0.963580i \(-0.413828\pi\)
0.267422 + 0.963580i \(0.413828\pi\)
\(758\) −7.57379 −0.275092
\(759\) 21.7841 0.790713
\(760\) 65.7178 2.38384
\(761\) −32.4647 −1.17684 −0.588422 0.808554i \(-0.700251\pi\)
−0.588422 + 0.808554i \(0.700251\pi\)
\(762\) −42.1162 −1.52571
\(763\) −6.95439 −0.251766
\(764\) 34.6834 1.25480
\(765\) 0.364092 0.0131638
\(766\) −79.4908 −2.87212
\(767\) 5.27011 0.190293
\(768\) −35.6737 −1.28726
\(769\) −42.2398 −1.52321 −0.761604 0.648043i \(-0.775588\pi\)
−0.761604 + 0.648043i \(0.775588\pi\)
\(770\) 14.6586 0.528261
\(771\) −50.1017 −1.80437
\(772\) 69.8353 2.51343
\(773\) −36.9608 −1.32939 −0.664694 0.747116i \(-0.731438\pi\)
−0.664694 + 0.747116i \(0.731438\pi\)
\(774\) 0.590086 0.0212102
\(775\) −34.3523 −1.23397
\(776\) 42.0966 1.51118
\(777\) 17.2439 0.618621
\(778\) −9.03568 −0.323945
\(779\) 9.55033 0.342176
\(780\) −15.9947 −0.572702
\(781\) −10.5489 −0.377470
\(782\) −66.2715 −2.36987
\(783\) 26.4374 0.944795
\(784\) 0.745624 0.0266294
\(785\) 50.3784 1.79808
\(786\) 18.5880 0.663011
\(787\) −18.7479 −0.668292 −0.334146 0.942521i \(-0.608448\pi\)
−0.334146 + 0.942521i \(0.608448\pi\)
\(788\) −47.1203 −1.67859
\(789\) 26.6425 0.948499
\(790\) 15.3787 0.547151
\(791\) 8.85733 0.314931
\(792\) −0.169450 −0.00602113
\(793\) 7.55181 0.268173
\(794\) −80.4247 −2.85417
\(795\) −13.9904 −0.496189
\(796\) 60.4663 2.14317
\(797\) −25.8851 −0.916897 −0.458448 0.888721i \(-0.651595\pi\)
−0.458448 + 0.888721i \(0.651595\pi\)
\(798\) −26.7255 −0.946072
\(799\) −47.1826 −1.66920
\(800\) 20.8113 0.735791
\(801\) 0.157901 0.00557915
\(802\) −26.5061 −0.935964
\(803\) −16.7445 −0.590899
\(804\) 47.2355 1.66587
\(805\) −18.6050 −0.655740
\(806\) −16.1349 −0.568327
\(807\) 50.1578 1.76564
\(808\) −24.2618 −0.853528
\(809\) 0.0816777 0.00287163 0.00143582 0.999999i \(-0.499543\pi\)
0.00143582 + 0.999999i \(0.499543\pi\)
\(810\) 64.5486 2.26801
\(811\) −19.6446 −0.689816 −0.344908 0.938637i \(-0.612090\pi\)
−0.344908 + 0.938637i \(0.612090\pi\)
\(812\) 17.3576 0.609132
\(813\) −0.514232 −0.0180349
\(814\) 47.4674 1.66373
\(815\) −54.7927 −1.91930
\(816\) 6.08800 0.213123
\(817\) 66.3140 2.32003
\(818\) 63.9127 2.23465
\(819\) 0.0223997 0.000782709 0
\(820\) −15.0175 −0.524435
\(821\) −29.4710 −1.02855 −0.514273 0.857626i \(-0.671938\pi\)
−0.514273 + 0.857626i \(0.671938\pi\)
\(822\) −32.4439 −1.13161
\(823\) −51.9968 −1.81249 −0.906247 0.422748i \(-0.861066\pi\)
−0.906247 + 0.422748i \(0.861066\pi\)
\(824\) 63.2340 2.20286
\(825\) 15.6772 0.545811
\(826\) −13.8468 −0.481792
\(827\) −7.85703 −0.273216 −0.136608 0.990625i \(-0.543620\pi\)
−0.136608 + 0.990625i \(0.543620\pi\)
\(828\) 0.522967 0.0181744
\(829\) −42.8275 −1.48746 −0.743730 0.668480i \(-0.766945\pi\)
−0.743730 + 0.668480i \(0.766945\pi\)
\(830\) −87.5304 −3.03822
\(831\) 48.7835 1.69228
\(832\) 11.0934 0.384594
\(833\) 4.69427 0.162647
\(834\) −22.0587 −0.763829
\(835\) −7.33845 −0.253958
\(836\) −46.3051 −1.60150
\(837\) 40.6413 1.40477
\(838\) −78.7555 −2.72057
\(839\) 35.6886 1.23211 0.616053 0.787704i \(-0.288731\pi\)
0.616053 + 0.787704i \(0.288731\pi\)
\(840\) 17.2825 0.596304
\(841\) −2.89120 −0.0996966
\(842\) 68.6049 2.36428
\(843\) −24.3155 −0.837471
\(844\) −59.9938 −2.06507
\(845\) −37.4071 −1.28684
\(846\) 0.591543 0.0203377
\(847\) 6.75242 0.232016
\(848\) −1.95892 −0.0672696
\(849\) 4.62641 0.158778
\(850\) −47.6932 −1.63586
\(851\) −60.2464 −2.06522
\(852\) −30.2426 −1.03610
\(853\) 12.7148 0.435347 0.217673 0.976022i \(-0.430153\pi\)
0.217673 + 0.976022i \(0.430153\pi\)
\(854\) −19.8418 −0.678972
\(855\) −0.512986 −0.0175438
\(856\) −57.2159 −1.95560
\(857\) 43.3587 1.48110 0.740552 0.671999i \(-0.234564\pi\)
0.740552 + 0.671999i \(0.234564\pi\)
\(858\) 7.36343 0.251383
\(859\) −1.00000 −0.0341196
\(860\) −104.276 −3.55579
\(861\) 2.51155 0.0855935
\(862\) 12.5630 0.427897
\(863\) −26.0261 −0.885939 −0.442969 0.896537i \(-0.646075\pi\)
−0.442969 + 0.896537i \(0.646075\pi\)
\(864\) −24.6214 −0.837636
\(865\) 75.7418 2.57530
\(866\) 49.0449 1.66661
\(867\) 8.75966 0.297494
\(868\) 26.6833 0.905689
\(869\) −4.45624 −0.151167
\(870\) 63.2126 2.14311
\(871\) −7.06858 −0.239510
\(872\) −22.5701 −0.764319
\(873\) −0.328601 −0.0111215
\(874\) 93.3730 3.15839
\(875\) 1.91861 0.0648607
\(876\) −48.0046 −1.62193
\(877\) 15.7967 0.533418 0.266709 0.963777i \(-0.414064\pi\)
0.266709 + 0.963777i \(0.414064\pi\)
\(878\) −17.7865 −0.600265
\(879\) 45.1631 1.52331
\(880\) 4.70476 0.158597
\(881\) −15.0221 −0.506106 −0.253053 0.967452i \(-0.581435\pi\)
−0.253053 + 0.967452i \(0.581435\pi\)
\(882\) −0.0588535 −0.00198170
\(883\) 2.19915 0.0740072 0.0370036 0.999315i \(-0.488219\pi\)
0.0370036 + 0.999315i \(0.488219\pi\)
\(884\) −14.0997 −0.474225
\(885\) −31.7400 −1.06693
\(886\) 59.7126 2.00608
\(887\) 23.2978 0.782265 0.391132 0.920334i \(-0.372083\pi\)
0.391132 + 0.920334i \(0.372083\pi\)
\(888\) 55.9640 1.87803
\(889\) −10.4228 −0.349571
\(890\) −44.3314 −1.48599
\(891\) −18.7040 −0.626608
\(892\) −13.6077 −0.455618
\(893\) 66.4777 2.22459
\(894\) −11.5295 −0.385603
\(895\) −76.2102 −2.54743
\(896\) −19.6297 −0.655781
\(897\) −9.34578 −0.312047
\(898\) −31.1110 −1.03819
\(899\) 40.1362 1.33862
\(900\) 0.376361 0.0125454
\(901\) −12.3329 −0.410868
\(902\) 6.91358 0.230197
\(903\) 17.4393 0.580344
\(904\) 28.7460 0.956076
\(905\) 20.7967 0.691304
\(906\) −12.8458 −0.426772
\(907\) 27.2122 0.903568 0.451784 0.892127i \(-0.350788\pi\)
0.451784 + 0.892127i \(0.350788\pi\)
\(908\) 23.8106 0.790182
\(909\) 0.189385 0.00628151
\(910\) −6.28883 −0.208473
\(911\) −22.3310 −0.739860 −0.369930 0.929060i \(-0.620618\pi\)
−0.369930 + 0.929060i \(0.620618\pi\)
\(912\) −8.57766 −0.284035
\(913\) 25.3633 0.839404
\(914\) 74.5411 2.46560
\(915\) −45.4819 −1.50358
\(916\) 16.3816 0.541265
\(917\) 4.60012 0.151909
\(918\) 56.4247 1.86229
\(919\) −29.0316 −0.957665 −0.478832 0.877906i \(-0.658940\pi\)
−0.478832 + 0.877906i \(0.658940\pi\)
\(920\) −60.3814 −1.99072
\(921\) −13.7147 −0.451914
\(922\) −14.9139 −0.491163
\(923\) 4.52568 0.148964
\(924\) −12.1774 −0.400606
\(925\) −43.3571 −1.42557
\(926\) 89.0384 2.92598
\(927\) −0.493598 −0.0162119
\(928\) −24.3154 −0.798191
\(929\) 32.0249 1.05070 0.525352 0.850885i \(-0.323934\pi\)
0.525352 + 0.850885i \(0.323934\pi\)
\(930\) 97.1747 3.18648
\(931\) −6.61397 −0.216764
\(932\) 21.2301 0.695416
\(933\) −54.4260 −1.78183
\(934\) 65.1334 2.13123
\(935\) 29.6200 0.968679
\(936\) 0.0726969 0.00237617
\(937\) 11.0748 0.361799 0.180900 0.983502i \(-0.442099\pi\)
0.180900 + 0.983502i \(0.442099\pi\)
\(938\) 18.5721 0.606402
\(939\) 9.31990 0.304143
\(940\) −104.534 −3.40951
\(941\) 42.5748 1.38790 0.693950 0.720023i \(-0.255869\pi\)
0.693950 + 0.720023i \(0.255869\pi\)
\(942\) −66.4906 −2.16638
\(943\) −8.77483 −0.285748
\(944\) −4.44420 −0.144646
\(945\) 15.8406 0.515295
\(946\) 48.0053 1.56079
\(947\) −23.7632 −0.772200 −0.386100 0.922457i \(-0.626178\pi\)
−0.386100 + 0.922457i \(0.626178\pi\)
\(948\) −12.7756 −0.414931
\(949\) 7.18368 0.233192
\(950\) 67.1972 2.18016
\(951\) 9.35969 0.303509
\(952\) 15.2350 0.493768
\(953\) 19.1639 0.620780 0.310390 0.950609i \(-0.399540\pi\)
0.310390 + 0.950609i \(0.399540\pi\)
\(954\) 0.154621 0.00500605
\(955\) 31.2588 1.01151
\(956\) −58.0798 −1.87843
\(957\) −18.3168 −0.592100
\(958\) 47.2825 1.52763
\(959\) −8.02917 −0.259275
\(960\) −66.8116 −2.15633
\(961\) 30.7002 0.990328
\(962\) −20.3644 −0.656574
\(963\) 0.446621 0.0143922
\(964\) −54.3540 −1.75062
\(965\) 62.9399 2.02611
\(966\) 24.5553 0.790054
\(967\) 3.20953 0.103212 0.0516058 0.998668i \(-0.483566\pi\)
0.0516058 + 0.998668i \(0.483566\pi\)
\(968\) 21.9146 0.704362
\(969\) −54.0029 −1.73482
\(970\) 92.2564 2.96217
\(971\) 9.62335 0.308828 0.154414 0.988006i \(-0.450651\pi\)
0.154414 + 0.988006i \(0.450651\pi\)
\(972\) −0.894319 −0.0286853
\(973\) −5.45904 −0.175009
\(974\) 20.0909 0.643755
\(975\) −6.72582 −0.215399
\(976\) −6.36832 −0.203845
\(977\) −14.4061 −0.460893 −0.230446 0.973085i \(-0.574019\pi\)
−0.230446 + 0.973085i \(0.574019\pi\)
\(978\) 72.3167 2.31243
\(979\) 12.8457 0.410551
\(980\) 10.4002 0.332223
\(981\) 0.176179 0.00562497
\(982\) −15.5304 −0.495594
\(983\) −20.0242 −0.638674 −0.319337 0.947641i \(-0.603460\pi\)
−0.319337 + 0.947641i \(0.603460\pi\)
\(984\) 8.15110 0.259848
\(985\) −42.4677 −1.35313
\(986\) 55.7234 1.77460
\(987\) 17.4824 0.556470
\(988\) 19.8657 0.632013
\(989\) −60.9292 −1.93743
\(990\) −0.371356 −0.0118025
\(991\) −4.19638 −0.133302 −0.0666512 0.997776i \(-0.521231\pi\)
−0.0666512 + 0.997776i \(0.521231\pi\)
\(992\) −37.3792 −1.18679
\(993\) −7.82834 −0.248425
\(994\) −11.8909 −0.377155
\(995\) 54.4959 1.72764
\(996\) 72.7140 2.30403
\(997\) −28.1424 −0.891278 −0.445639 0.895213i \(-0.647023\pi\)
−0.445639 + 0.895213i \(0.647023\pi\)
\(998\) −98.1600 −3.10720
\(999\) 51.2948 1.62289
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 6013.2.a.c.1.17 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6013.2.a.c.1.17 104 1.1 even 1 trivial