Properties

Label 6013.2.a.f.1.3
Level $6013$
Weight $2$
Character 6013.1
Self dual yes
Analytic conductor $48.014$
Analytic rank $0$
Dimension $110$
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: \(0\)
Dimension: \(110\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
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)
 
\(f(q)\) \(=\) \(q-2.64365 q^{2} +1.43905 q^{3} +4.98889 q^{4} +0.402261 q^{5} -3.80434 q^{6} -1.00000 q^{7} -7.90158 q^{8} -0.929138 q^{9} +O(q^{10})\) \(q-2.64365 q^{2} +1.43905 q^{3} +4.98889 q^{4} +0.402261 q^{5} -3.80434 q^{6} -1.00000 q^{7} -7.90158 q^{8} -0.929138 q^{9} -1.06344 q^{10} -0.489443 q^{11} +7.17926 q^{12} -6.45702 q^{13} +2.64365 q^{14} +0.578873 q^{15} +10.9112 q^{16} -1.62326 q^{17} +2.45632 q^{18} -0.818199 q^{19} +2.00684 q^{20} -1.43905 q^{21} +1.29392 q^{22} +5.22279 q^{23} -11.3708 q^{24} -4.83819 q^{25} +17.0701 q^{26} -5.65422 q^{27} -4.98889 q^{28} -8.57274 q^{29} -1.53034 q^{30} +6.80611 q^{31} -13.0423 q^{32} -0.704333 q^{33} +4.29134 q^{34} -0.402261 q^{35} -4.63537 q^{36} +5.90364 q^{37} +2.16303 q^{38} -9.29197 q^{39} -3.17850 q^{40} +5.29790 q^{41} +3.80434 q^{42} +6.73364 q^{43} -2.44178 q^{44} -0.373756 q^{45} -13.8072 q^{46} -3.93916 q^{47} +15.7018 q^{48} +1.00000 q^{49} +12.7905 q^{50} -2.33595 q^{51} -32.2134 q^{52} +12.1186 q^{53} +14.9478 q^{54} -0.196884 q^{55} +7.90158 q^{56} -1.17743 q^{57} +22.6633 q^{58} -12.2165 q^{59} +2.88794 q^{60} -3.99370 q^{61} -17.9930 q^{62} +0.929138 q^{63} +12.6569 q^{64} -2.59741 q^{65} +1.86201 q^{66} -4.87826 q^{67} -8.09827 q^{68} +7.51586 q^{69} +1.06344 q^{70} +16.2985 q^{71} +7.34166 q^{72} -7.32447 q^{73} -15.6071 q^{74} -6.96239 q^{75} -4.08190 q^{76} +0.489443 q^{77} +24.5647 q^{78} -7.49834 q^{79} +4.38917 q^{80} -5.34929 q^{81} -14.0058 q^{82} -11.2101 q^{83} -7.17926 q^{84} -0.652975 q^{85} -17.8014 q^{86} -12.3366 q^{87} +3.86738 q^{88} -5.79688 q^{89} +0.988081 q^{90} +6.45702 q^{91} +26.0559 q^{92} +9.79432 q^{93} +10.4138 q^{94} -0.329130 q^{95} -18.7686 q^{96} +3.31457 q^{97} -2.64365 q^{98} +0.454761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64365 −1.86934 −0.934672 0.355512i \(-0.884307\pi\)
−0.934672 + 0.355512i \(0.884307\pi\)
\(3\) 1.43905 0.830835 0.415418 0.909631i \(-0.363635\pi\)
0.415418 + 0.909631i \(0.363635\pi\)
\(4\) 4.98889 2.49444
\(5\) 0.402261 0.179897 0.0899483 0.995946i \(-0.471330\pi\)
0.0899483 + 0.995946i \(0.471330\pi\)
\(6\) −3.80434 −1.55312
\(7\) −1.00000 −0.377964
\(8\) −7.90158 −2.79363
\(9\) −0.929138 −0.309713
\(10\) −1.06344 −0.336289
\(11\) −0.489443 −0.147573 −0.0737864 0.997274i \(-0.523508\pi\)
−0.0737864 + 0.997274i \(0.523508\pi\)
\(12\) 7.17926 2.07247
\(13\) −6.45702 −1.79086 −0.895428 0.445206i \(-0.853130\pi\)
−0.895428 + 0.445206i \(0.853130\pi\)
\(14\) 2.64365 0.706545
\(15\) 0.578873 0.149464
\(16\) 10.9112 2.72781
\(17\) −1.62326 −0.393699 −0.196849 0.980434i \(-0.563071\pi\)
−0.196849 + 0.980434i \(0.563071\pi\)
\(18\) 2.45632 0.578959
\(19\) −0.818199 −0.187708 −0.0938538 0.995586i \(-0.529919\pi\)
−0.0938538 + 0.995586i \(0.529919\pi\)
\(20\) 2.00684 0.448742
\(21\) −1.43905 −0.314026
\(22\) 1.29392 0.275864
\(23\) 5.22279 1.08903 0.544514 0.838752i \(-0.316714\pi\)
0.544514 + 0.838752i \(0.316714\pi\)
\(24\) −11.3708 −2.32105
\(25\) −4.83819 −0.967637
\(26\) 17.0701 3.34773
\(27\) −5.65422 −1.08816
\(28\) −4.98889 −0.942812
\(29\) −8.57274 −1.59192 −0.795959 0.605351i \(-0.793033\pi\)
−0.795959 + 0.605351i \(0.793033\pi\)
\(30\) −1.53034 −0.279400
\(31\) 6.80611 1.22241 0.611206 0.791471i \(-0.290685\pi\)
0.611206 + 0.791471i \(0.290685\pi\)
\(32\) −13.0423 −2.30558
\(33\) −0.704333 −0.122609
\(34\) 4.29134 0.735958
\(35\) −0.402261 −0.0679945
\(36\) −4.63537 −0.772561
\(37\) 5.90364 0.970552 0.485276 0.874361i \(-0.338719\pi\)
0.485276 + 0.874361i \(0.338719\pi\)
\(38\) 2.16303 0.350890
\(39\) −9.29197 −1.48791
\(40\) −3.17850 −0.502565
\(41\) 5.29790 0.827393 0.413696 0.910415i \(-0.364238\pi\)
0.413696 + 0.910415i \(0.364238\pi\)
\(42\) 3.80434 0.587023
\(43\) 6.73364 1.02687 0.513436 0.858128i \(-0.328373\pi\)
0.513436 + 0.858128i \(0.328373\pi\)
\(44\) −2.44178 −0.368112
\(45\) −0.373756 −0.0557163
\(46\) −13.8072 −2.03577
\(47\) −3.93916 −0.574586 −0.287293 0.957843i \(-0.592755\pi\)
−0.287293 + 0.957843i \(0.592755\pi\)
\(48\) 15.7018 2.26636
\(49\) 1.00000 0.142857
\(50\) 12.7905 1.80885
\(51\) −2.33595 −0.327099
\(52\) −32.2134 −4.46719
\(53\) 12.1186 1.66462 0.832309 0.554312i \(-0.187019\pi\)
0.832309 + 0.554312i \(0.187019\pi\)
\(54\) 14.9478 2.03414
\(55\) −0.196884 −0.0265478
\(56\) 7.90158 1.05589
\(57\) −1.17743 −0.155954
\(58\) 22.6633 2.97584
\(59\) −12.2165 −1.59045 −0.795223 0.606317i \(-0.792646\pi\)
−0.795223 + 0.606317i \(0.792646\pi\)
\(60\) 2.88794 0.372831
\(61\) −3.99370 −0.511340 −0.255670 0.966764i \(-0.582296\pi\)
−0.255670 + 0.966764i \(0.582296\pi\)
\(62\) −17.9930 −2.28511
\(63\) 0.929138 0.117060
\(64\) 12.6569 1.58212
\(65\) −2.59741 −0.322169
\(66\) 1.86201 0.229198
\(67\) −4.87826 −0.595974 −0.297987 0.954570i \(-0.596315\pi\)
−0.297987 + 0.954570i \(0.596315\pi\)
\(68\) −8.09827 −0.982060
\(69\) 7.51586 0.904803
\(70\) 1.06344 0.127105
\(71\) 16.2985 1.93428 0.967138 0.254252i \(-0.0818292\pi\)
0.967138 + 0.254252i \(0.0818292\pi\)
\(72\) 7.34166 0.865223
\(73\) −7.32447 −0.857265 −0.428632 0.903479i \(-0.641004\pi\)
−0.428632 + 0.903479i \(0.641004\pi\)
\(74\) −15.6071 −1.81429
\(75\) −6.96239 −0.803947
\(76\) −4.08190 −0.468226
\(77\) 0.489443 0.0557773
\(78\) 24.5647 2.78141
\(79\) −7.49834 −0.843629 −0.421814 0.906682i \(-0.638607\pi\)
−0.421814 + 0.906682i \(0.638607\pi\)
\(80\) 4.38917 0.490724
\(81\) −5.34929 −0.594365
\(82\) −14.0058 −1.54668
\(83\) −11.2101 −1.23047 −0.615237 0.788342i \(-0.710940\pi\)
−0.615237 + 0.788342i \(0.710940\pi\)
\(84\) −7.17926 −0.783321
\(85\) −0.652975 −0.0708251
\(86\) −17.8014 −1.91957
\(87\) −12.3366 −1.32262
\(88\) 3.86738 0.412264
\(89\) −5.79688 −0.614468 −0.307234 0.951634i \(-0.599404\pi\)
−0.307234 + 0.951634i \(0.599404\pi\)
\(90\) 0.988081 0.104153
\(91\) 6.45702 0.676880
\(92\) 26.0559 2.71652
\(93\) 9.79432 1.01562
\(94\) 10.4138 1.07410
\(95\) −0.329130 −0.0337680
\(96\) −18.7686 −1.91556
\(97\) 3.31457 0.336544 0.168272 0.985741i \(-0.446181\pi\)
0.168272 + 0.985741i \(0.446181\pi\)
\(98\) −2.64365 −0.267049
\(99\) 0.454761 0.0457052
\(100\) −24.1372 −2.41372
\(101\) 1.85159 0.184240 0.0921201 0.995748i \(-0.470636\pi\)
0.0921201 + 0.995748i \(0.470636\pi\)
\(102\) 6.17544 0.611460
\(103\) 6.85532 0.675475 0.337738 0.941240i \(-0.390338\pi\)
0.337738 + 0.941240i \(0.390338\pi\)
\(104\) 51.0207 5.00299
\(105\) −0.578873 −0.0564923
\(106\) −32.0374 −3.11174
\(107\) 4.55624 0.440468 0.220234 0.975447i \(-0.429318\pi\)
0.220234 + 0.975447i \(0.429318\pi\)
\(108\) −28.2083 −2.71434
\(109\) −7.71733 −0.739186 −0.369593 0.929194i \(-0.620503\pi\)
−0.369593 + 0.929194i \(0.620503\pi\)
\(110\) 0.520493 0.0496270
\(111\) 8.49562 0.806369
\(112\) −10.9112 −1.03102
\(113\) 20.5285 1.93116 0.965581 0.260102i \(-0.0837562\pi\)
0.965581 + 0.260102i \(0.0837562\pi\)
\(114\) 3.11271 0.291532
\(115\) 2.10093 0.195912
\(116\) −42.7684 −3.97095
\(117\) 5.99947 0.554651
\(118\) 32.2960 2.97309
\(119\) 1.62326 0.148804
\(120\) −4.57402 −0.417549
\(121\) −10.7604 −0.978222
\(122\) 10.5579 0.955871
\(123\) 7.62393 0.687427
\(124\) 33.9549 3.04924
\(125\) −3.95752 −0.353971
\(126\) −2.45632 −0.218826
\(127\) −9.34859 −0.829553 −0.414777 0.909923i \(-0.636140\pi\)
−0.414777 + 0.909923i \(0.636140\pi\)
\(128\) −7.37582 −0.651937
\(129\) 9.69004 0.853161
\(130\) 6.86664 0.602245
\(131\) 7.23135 0.631806 0.315903 0.948792i \(-0.397693\pi\)
0.315903 + 0.948792i \(0.397693\pi\)
\(132\) −3.51384 −0.305841
\(133\) 0.818199 0.0709468
\(134\) 12.8964 1.11408
\(135\) −2.27447 −0.195756
\(136\) 12.8263 1.09985
\(137\) 9.31540 0.795868 0.397934 0.917414i \(-0.369727\pi\)
0.397934 + 0.917414i \(0.369727\pi\)
\(138\) −19.8693 −1.69139
\(139\) −11.4421 −0.970507 −0.485254 0.874373i \(-0.661273\pi\)
−0.485254 + 0.874373i \(0.661273\pi\)
\(140\) −2.00684 −0.169609
\(141\) −5.66865 −0.477386
\(142\) −43.0875 −3.61583
\(143\) 3.16035 0.264282
\(144\) −10.1380 −0.844837
\(145\) −3.44848 −0.286381
\(146\) 19.3633 1.60252
\(147\) 1.43905 0.118691
\(148\) 29.4526 2.42099
\(149\) 3.06584 0.251163 0.125582 0.992083i \(-0.459920\pi\)
0.125582 + 0.992083i \(0.459920\pi\)
\(150\) 18.4061 1.50285
\(151\) 8.05295 0.655340 0.327670 0.944792i \(-0.393737\pi\)
0.327670 + 0.944792i \(0.393737\pi\)
\(152\) 6.46506 0.524386
\(153\) 1.50823 0.121933
\(154\) −1.29392 −0.104267
\(155\) 2.73783 0.219908
\(156\) −46.3566 −3.71150
\(157\) 4.35562 0.347616 0.173808 0.984780i \(-0.444393\pi\)
0.173808 + 0.984780i \(0.444393\pi\)
\(158\) 19.8230 1.57703
\(159\) 17.4393 1.38302
\(160\) −5.24643 −0.414767
\(161\) −5.22279 −0.411614
\(162\) 14.1417 1.11107
\(163\) 13.9624 1.09362 0.546810 0.837257i \(-0.315842\pi\)
0.546810 + 0.837257i \(0.315842\pi\)
\(164\) 26.4306 2.06389
\(165\) −0.283326 −0.0220569
\(166\) 29.6357 2.30018
\(167\) 10.3733 0.802711 0.401356 0.915922i \(-0.368539\pi\)
0.401356 + 0.915922i \(0.368539\pi\)
\(168\) 11.3708 0.877273
\(169\) 28.6932 2.20717
\(170\) 1.72624 0.132396
\(171\) 0.760220 0.0581355
\(172\) 33.5934 2.56147
\(173\) 18.9115 1.43782 0.718909 0.695105i \(-0.244642\pi\)
0.718909 + 0.695105i \(0.244642\pi\)
\(174\) 32.6136 2.47243
\(175\) 4.83819 0.365732
\(176\) −5.34044 −0.402550
\(177\) −17.5801 −1.32140
\(178\) 15.3249 1.14865
\(179\) −18.2820 −1.36646 −0.683230 0.730204i \(-0.739425\pi\)
−0.683230 + 0.730204i \(0.739425\pi\)
\(180\) −1.86463 −0.138981
\(181\) 1.04329 0.0775472 0.0387736 0.999248i \(-0.487655\pi\)
0.0387736 + 0.999248i \(0.487655\pi\)
\(182\) −17.0701 −1.26532
\(183\) −5.74712 −0.424840
\(184\) −41.2683 −3.04234
\(185\) 2.37480 0.174599
\(186\) −25.8928 −1.89855
\(187\) 0.794495 0.0580992
\(188\) −19.6521 −1.43327
\(189\) 5.65422 0.411284
\(190\) 0.870104 0.0631240
\(191\) 3.99309 0.288929 0.144465 0.989510i \(-0.453854\pi\)
0.144465 + 0.989510i \(0.453854\pi\)
\(192\) 18.2140 1.31448
\(193\) −7.43970 −0.535522 −0.267761 0.963485i \(-0.586284\pi\)
−0.267761 + 0.963485i \(0.586284\pi\)
\(194\) −8.76256 −0.629115
\(195\) −3.73780 −0.267669
\(196\) 4.98889 0.356349
\(197\) 24.0770 1.71541 0.857706 0.514140i \(-0.171889\pi\)
0.857706 + 0.514140i \(0.171889\pi\)
\(198\) −1.20223 −0.0854386
\(199\) 24.1690 1.71330 0.856649 0.515900i \(-0.172542\pi\)
0.856649 + 0.515900i \(0.172542\pi\)
\(200\) 38.2293 2.70322
\(201\) −7.02006 −0.495157
\(202\) −4.89496 −0.344408
\(203\) 8.57274 0.601688
\(204\) −11.6538 −0.815930
\(205\) 2.13114 0.148845
\(206\) −18.1231 −1.26269
\(207\) −4.85270 −0.337286
\(208\) −70.4541 −4.88512
\(209\) 0.400462 0.0277005
\(210\) 1.53034 0.105603
\(211\) 18.9433 1.30411 0.652054 0.758172i \(-0.273907\pi\)
0.652054 + 0.758172i \(0.273907\pi\)
\(212\) 60.4584 4.15230
\(213\) 23.4543 1.60706
\(214\) −12.0451 −0.823387
\(215\) 2.70868 0.184731
\(216\) 44.6773 3.03990
\(217\) −6.80611 −0.462029
\(218\) 20.4019 1.38179
\(219\) −10.5403 −0.712246
\(220\) −0.982233 −0.0662221
\(221\) 10.4814 0.705058
\(222\) −22.4595 −1.50738
\(223\) −25.0809 −1.67954 −0.839771 0.542941i \(-0.817311\pi\)
−0.839771 + 0.542941i \(0.817311\pi\)
\(224\) 13.0423 0.871429
\(225\) 4.49534 0.299690
\(226\) −54.2703 −3.61001
\(227\) −9.90530 −0.657438 −0.328719 0.944428i \(-0.606617\pi\)
−0.328719 + 0.944428i \(0.606617\pi\)
\(228\) −5.87406 −0.389019
\(229\) 19.3330 1.27756 0.638780 0.769390i \(-0.279439\pi\)
0.638780 + 0.769390i \(0.279439\pi\)
\(230\) −5.55412 −0.366228
\(231\) 0.704333 0.0463417
\(232\) 67.7382 4.44723
\(233\) 22.8913 1.49966 0.749829 0.661631i \(-0.230136\pi\)
0.749829 + 0.661631i \(0.230136\pi\)
\(234\) −15.8605 −1.03683
\(235\) −1.58457 −0.103366
\(236\) −60.9465 −3.96728
\(237\) −10.7905 −0.700917
\(238\) −4.29134 −0.278166
\(239\) −0.392340 −0.0253784 −0.0126892 0.999919i \(-0.504039\pi\)
−0.0126892 + 0.999919i \(0.504039\pi\)
\(240\) 6.31623 0.407711
\(241\) −14.5810 −0.939244 −0.469622 0.882868i \(-0.655610\pi\)
−0.469622 + 0.882868i \(0.655610\pi\)
\(242\) 28.4469 1.82863
\(243\) 9.26478 0.594336
\(244\) −19.9241 −1.27551
\(245\) 0.402261 0.0256995
\(246\) −20.1550 −1.28504
\(247\) 5.28313 0.336158
\(248\) −53.7790 −3.41497
\(249\) −16.1319 −1.02232
\(250\) 10.4623 0.661694
\(251\) −0.400107 −0.0252545 −0.0126273 0.999920i \(-0.504019\pi\)
−0.0126273 + 0.999920i \(0.504019\pi\)
\(252\) 4.63537 0.292001
\(253\) −2.55626 −0.160711
\(254\) 24.7144 1.55072
\(255\) −0.939663 −0.0588440
\(256\) −5.81478 −0.363424
\(257\) 14.4821 0.903370 0.451685 0.892177i \(-0.350823\pi\)
0.451685 + 0.892177i \(0.350823\pi\)
\(258\) −25.6171 −1.59485
\(259\) −5.90364 −0.366834
\(260\) −12.9582 −0.803633
\(261\) 7.96526 0.493037
\(262\) −19.1172 −1.18106
\(263\) −5.62754 −0.347009 −0.173505 0.984833i \(-0.555509\pi\)
−0.173505 + 0.984833i \(0.555509\pi\)
\(264\) 5.56534 0.342523
\(265\) 4.87484 0.299459
\(266\) −2.16303 −0.132624
\(267\) −8.34200 −0.510522
\(268\) −24.3371 −1.48663
\(269\) −0.321185 −0.0195830 −0.00979149 0.999952i \(-0.503117\pi\)
−0.00979149 + 0.999952i \(0.503117\pi\)
\(270\) 6.01291 0.365934
\(271\) −7.84217 −0.476378 −0.238189 0.971219i \(-0.576554\pi\)
−0.238189 + 0.971219i \(0.576554\pi\)
\(272\) −17.7118 −1.07394
\(273\) 9.29197 0.562376
\(274\) −24.6267 −1.48775
\(275\) 2.36802 0.142797
\(276\) 37.4958 2.25698
\(277\) 10.2938 0.618493 0.309246 0.950982i \(-0.399923\pi\)
0.309246 + 0.950982i \(0.399923\pi\)
\(278\) 30.2489 1.81421
\(279\) −6.32381 −0.378597
\(280\) 3.17850 0.189952
\(281\) 27.3135 1.62938 0.814692 0.579893i \(-0.196906\pi\)
0.814692 + 0.579893i \(0.196906\pi\)
\(282\) 14.9859 0.892399
\(283\) 28.2761 1.68084 0.840421 0.541934i \(-0.182308\pi\)
0.840421 + 0.541934i \(0.182308\pi\)
\(284\) 81.3114 4.82495
\(285\) −0.473634 −0.0280556
\(286\) −8.35486 −0.494033
\(287\) −5.29790 −0.312725
\(288\) 12.1181 0.714068
\(289\) −14.3650 −0.845001
\(290\) 9.11657 0.535344
\(291\) 4.76983 0.279612
\(292\) −36.5410 −2.13840
\(293\) 2.97080 0.173556 0.0867779 0.996228i \(-0.472343\pi\)
0.0867779 + 0.996228i \(0.472343\pi\)
\(294\) −3.80434 −0.221874
\(295\) −4.91420 −0.286116
\(296\) −46.6480 −2.71136
\(297\) 2.76742 0.160582
\(298\) −8.10500 −0.469510
\(299\) −33.7237 −1.95029
\(300\) −34.7346 −2.00540
\(301\) −6.73364 −0.388121
\(302\) −21.2892 −1.22506
\(303\) 2.66453 0.153073
\(304\) −8.92756 −0.512031
\(305\) −1.60651 −0.0919884
\(306\) −3.98724 −0.227936
\(307\) 3.26723 0.186470 0.0932352 0.995644i \(-0.470279\pi\)
0.0932352 + 0.995644i \(0.470279\pi\)
\(308\) 2.44178 0.139133
\(309\) 9.86515 0.561209
\(310\) −7.23787 −0.411084
\(311\) −14.0354 −0.795873 −0.397937 0.917413i \(-0.630274\pi\)
−0.397937 + 0.917413i \(0.630274\pi\)
\(312\) 73.4213 4.15666
\(313\) −10.9185 −0.617149 −0.308575 0.951200i \(-0.599852\pi\)
−0.308575 + 0.951200i \(0.599852\pi\)
\(314\) −11.5147 −0.649814
\(315\) 0.373756 0.0210588
\(316\) −37.4084 −2.10439
\(317\) 23.0589 1.29512 0.647558 0.762016i \(-0.275790\pi\)
0.647558 + 0.762016i \(0.275790\pi\)
\(318\) −46.1033 −2.58535
\(319\) 4.19587 0.234924
\(320\) 5.09139 0.284618
\(321\) 6.55665 0.365957
\(322\) 13.8072 0.769448
\(323\) 1.32815 0.0739003
\(324\) −26.6870 −1.48261
\(325\) 31.2403 1.73290
\(326\) −36.9117 −2.04435
\(327\) −11.1056 −0.614142
\(328\) −41.8618 −2.31143
\(329\) 3.93916 0.217173
\(330\) 0.749014 0.0412319
\(331\) 6.91231 0.379935 0.189968 0.981790i \(-0.439162\pi\)
0.189968 + 0.981790i \(0.439162\pi\)
\(332\) −55.9262 −3.06935
\(333\) −5.48529 −0.300592
\(334\) −27.4234 −1.50054
\(335\) −1.96233 −0.107214
\(336\) −15.7018 −0.856604
\(337\) 1.49739 0.0815678 0.0407839 0.999168i \(-0.487014\pi\)
0.0407839 + 0.999168i \(0.487014\pi\)
\(338\) −75.8547 −4.12595
\(339\) 29.5416 1.60448
\(340\) −3.25762 −0.176669
\(341\) −3.33120 −0.180395
\(342\) −2.00976 −0.108675
\(343\) −1.00000 −0.0539949
\(344\) −53.2064 −2.86870
\(345\) 3.02334 0.162771
\(346\) −49.9955 −2.68777
\(347\) 25.5669 1.37250 0.686251 0.727365i \(-0.259255\pi\)
0.686251 + 0.727365i \(0.259255\pi\)
\(348\) −61.5459 −3.29921
\(349\) 11.8755 0.635683 0.317841 0.948144i \(-0.397042\pi\)
0.317841 + 0.948144i \(0.397042\pi\)
\(350\) −12.7905 −0.683680
\(351\) 36.5094 1.94873
\(352\) 6.38349 0.340241
\(353\) 25.7095 1.36838 0.684190 0.729304i \(-0.260156\pi\)
0.684190 + 0.729304i \(0.260156\pi\)
\(354\) 46.4756 2.47015
\(355\) 6.55625 0.347970
\(356\) −28.9200 −1.53276
\(357\) 2.33595 0.123632
\(358\) 48.3312 2.55438
\(359\) −18.5032 −0.976563 −0.488281 0.872686i \(-0.662376\pi\)
−0.488281 + 0.872686i \(0.662376\pi\)
\(360\) 2.95326 0.155651
\(361\) −18.3306 −0.964766
\(362\) −2.75810 −0.144962
\(363\) −15.4848 −0.812742
\(364\) 32.2134 1.68844
\(365\) −2.94635 −0.154219
\(366\) 15.1934 0.794171
\(367\) −30.4209 −1.58796 −0.793979 0.607945i \(-0.791994\pi\)
−0.793979 + 0.607945i \(0.791994\pi\)
\(368\) 56.9872 2.97066
\(369\) −4.92248 −0.256254
\(370\) −6.27815 −0.326385
\(371\) −12.1186 −0.629166
\(372\) 48.8628 2.53342
\(373\) −10.3536 −0.536090 −0.268045 0.963406i \(-0.586378\pi\)
−0.268045 + 0.963406i \(0.586378\pi\)
\(374\) −2.10037 −0.108607
\(375\) −5.69506 −0.294092
\(376\) 31.1256 1.60518
\(377\) 55.3544 2.85090
\(378\) −14.9478 −0.768831
\(379\) 5.06788 0.260320 0.130160 0.991493i \(-0.458451\pi\)
0.130160 + 0.991493i \(0.458451\pi\)
\(380\) −1.64199 −0.0842324
\(381\) −13.4531 −0.689222
\(382\) −10.5563 −0.540108
\(383\) −12.9676 −0.662612 −0.331306 0.943523i \(-0.607489\pi\)
−0.331306 + 0.943523i \(0.607489\pi\)
\(384\) −10.6142 −0.541652
\(385\) 0.196884 0.0100341
\(386\) 19.6680 1.00107
\(387\) −6.25649 −0.318035
\(388\) 16.5360 0.839489
\(389\) 19.8330 1.00557 0.502785 0.864411i \(-0.332309\pi\)
0.502785 + 0.864411i \(0.332309\pi\)
\(390\) 9.88144 0.500366
\(391\) −8.47796 −0.428749
\(392\) −7.90158 −0.399090
\(393\) 10.4063 0.524927
\(394\) −63.6511 −3.20670
\(395\) −3.01629 −0.151766
\(396\) 2.26875 0.114009
\(397\) 12.4932 0.627014 0.313507 0.949586i \(-0.398496\pi\)
0.313507 + 0.949586i \(0.398496\pi\)
\(398\) −63.8945 −3.20274
\(399\) 1.17743 0.0589451
\(400\) −52.7906 −2.63953
\(401\) 0.490251 0.0244820 0.0122410 0.999925i \(-0.496103\pi\)
0.0122410 + 0.999925i \(0.496103\pi\)
\(402\) 18.5586 0.925618
\(403\) −43.9472 −2.18917
\(404\) 9.23738 0.459577
\(405\) −2.15181 −0.106924
\(406\) −22.6633 −1.12476
\(407\) −2.88950 −0.143227
\(408\) 18.4577 0.913793
\(409\) 14.2486 0.704546 0.352273 0.935897i \(-0.385409\pi\)
0.352273 + 0.935897i \(0.385409\pi\)
\(410\) −5.63398 −0.278243
\(411\) 13.4053 0.661236
\(412\) 34.2005 1.68494
\(413\) 12.2165 0.601132
\(414\) 12.8288 0.630503
\(415\) −4.50941 −0.221358
\(416\) 84.2148 4.12897
\(417\) −16.4658 −0.806332
\(418\) −1.05868 −0.0517818
\(419\) −25.3305 −1.23747 −0.618737 0.785598i \(-0.712355\pi\)
−0.618737 + 0.785598i \(0.712355\pi\)
\(420\) −2.88794 −0.140917
\(421\) −25.2412 −1.23018 −0.615091 0.788456i \(-0.710881\pi\)
−0.615091 + 0.788456i \(0.710881\pi\)
\(422\) −50.0794 −2.43783
\(423\) 3.66003 0.177957
\(424\) −95.7561 −4.65033
\(425\) 7.85364 0.380958
\(426\) −62.0051 −3.00416
\(427\) 3.99370 0.193268
\(428\) 22.7306 1.09872
\(429\) 4.54790 0.219574
\(430\) −7.16081 −0.345325
\(431\) 40.0857 1.93086 0.965431 0.260658i \(-0.0839397\pi\)
0.965431 + 0.260658i \(0.0839397\pi\)
\(432\) −61.6946 −2.96828
\(433\) −31.6468 −1.52085 −0.760424 0.649427i \(-0.775009\pi\)
−0.760424 + 0.649427i \(0.775009\pi\)
\(434\) 17.9930 0.863690
\(435\) −4.96253 −0.237935
\(436\) −38.5009 −1.84386
\(437\) −4.27328 −0.204419
\(438\) 27.8648 1.33143
\(439\) −13.7798 −0.657673 −0.328837 0.944387i \(-0.606657\pi\)
−0.328837 + 0.944387i \(0.606657\pi\)
\(440\) 1.55570 0.0741649
\(441\) −0.929138 −0.0442447
\(442\) −27.7093 −1.31800
\(443\) −13.8783 −0.659380 −0.329690 0.944089i \(-0.606944\pi\)
−0.329690 + 0.944089i \(0.606944\pi\)
\(444\) 42.3837 2.01144
\(445\) −2.33186 −0.110541
\(446\) 66.3051 3.13964
\(447\) 4.41189 0.208675
\(448\) −12.6569 −0.597984
\(449\) −3.23136 −0.152497 −0.0762486 0.997089i \(-0.524294\pi\)
−0.0762486 + 0.997089i \(0.524294\pi\)
\(450\) −11.8841 −0.560223
\(451\) −2.59302 −0.122101
\(452\) 102.415 4.81718
\(453\) 11.5886 0.544480
\(454\) 26.1862 1.22898
\(455\) 2.59741 0.121768
\(456\) 9.30354 0.435678
\(457\) −2.01677 −0.0943404 −0.0471702 0.998887i \(-0.515020\pi\)
−0.0471702 + 0.998887i \(0.515020\pi\)
\(458\) −51.1097 −2.38820
\(459\) 9.17828 0.428405
\(460\) 10.4813 0.488693
\(461\) −31.7690 −1.47963 −0.739814 0.672811i \(-0.765087\pi\)
−0.739814 + 0.672811i \(0.765087\pi\)
\(462\) −1.86201 −0.0866286
\(463\) 10.0070 0.465065 0.232533 0.972589i \(-0.425299\pi\)
0.232533 + 0.972589i \(0.425299\pi\)
\(464\) −93.5392 −4.34245
\(465\) 3.93987 0.182707
\(466\) −60.5166 −2.80338
\(467\) 11.1922 0.517915 0.258957 0.965889i \(-0.416621\pi\)
0.258957 + 0.965889i \(0.416621\pi\)
\(468\) 29.9307 1.38355
\(469\) 4.87826 0.225257
\(470\) 4.18906 0.193227
\(471\) 6.26795 0.288812
\(472\) 96.5293 4.44312
\(473\) −3.29574 −0.151538
\(474\) 28.5262 1.31025
\(475\) 3.95860 0.181633
\(476\) 8.09827 0.371184
\(477\) −11.2599 −0.515553
\(478\) 1.03721 0.0474409
\(479\) 24.3206 1.11124 0.555619 0.831437i \(-0.312481\pi\)
0.555619 + 0.831437i \(0.312481\pi\)
\(480\) −7.54987 −0.344603
\(481\) −38.1199 −1.73812
\(482\) 38.5470 1.75577
\(483\) −7.51586 −0.341983
\(484\) −53.6827 −2.44012
\(485\) 1.33332 0.0605431
\(486\) −24.4928 −1.11102
\(487\) −20.4072 −0.924737 −0.462368 0.886688i \(-0.653000\pi\)
−0.462368 + 0.886688i \(0.653000\pi\)
\(488\) 31.5565 1.42850
\(489\) 20.0926 0.908619
\(490\) −1.06344 −0.0480412
\(491\) 15.1666 0.684461 0.342230 0.939616i \(-0.388818\pi\)
0.342230 + 0.939616i \(0.388818\pi\)
\(492\) 38.0350 1.71475
\(493\) 13.9158 0.626736
\(494\) −13.9668 −0.628394
\(495\) 0.182932 0.00822220
\(496\) 74.2631 3.33451
\(497\) −16.2985 −0.731088
\(498\) 42.6472 1.91107
\(499\) −21.4156 −0.958693 −0.479346 0.877626i \(-0.659126\pi\)
−0.479346 + 0.877626i \(0.659126\pi\)
\(500\) −19.7436 −0.882962
\(501\) 14.9277 0.666921
\(502\) 1.05774 0.0472093
\(503\) 3.32579 0.148290 0.0741448 0.997247i \(-0.476377\pi\)
0.0741448 + 0.997247i \(0.476377\pi\)
\(504\) −7.34166 −0.327023
\(505\) 0.744823 0.0331442
\(506\) 6.75786 0.300424
\(507\) 41.2909 1.83379
\(508\) −46.6391 −2.06927
\(509\) −23.4678 −1.04019 −0.520095 0.854108i \(-0.674104\pi\)
−0.520095 + 0.854108i \(0.674104\pi\)
\(510\) 2.48414 0.110000
\(511\) 7.32447 0.324016
\(512\) 30.1239 1.33130
\(513\) 4.62628 0.204255
\(514\) −38.2857 −1.68871
\(515\) 2.75763 0.121516
\(516\) 48.3426 2.12816
\(517\) 1.92800 0.0847933
\(518\) 15.6071 0.685739
\(519\) 27.2146 1.19459
\(520\) 20.5236 0.900021
\(521\) 15.7483 0.689946 0.344973 0.938613i \(-0.387888\pi\)
0.344973 + 0.938613i \(0.387888\pi\)
\(522\) −21.0574 −0.921656
\(523\) 1.01217 0.0442593 0.0221296 0.999755i \(-0.492955\pi\)
0.0221296 + 0.999755i \(0.492955\pi\)
\(524\) 36.0764 1.57600
\(525\) 6.96239 0.303863
\(526\) 14.8773 0.648679
\(527\) −11.0481 −0.481262
\(528\) −7.68515 −0.334453
\(529\) 4.27758 0.185982
\(530\) −12.8874 −0.559792
\(531\) 11.3508 0.492581
\(532\) 4.08190 0.176973
\(533\) −34.2087 −1.48174
\(534\) 22.0533 0.954341
\(535\) 1.83280 0.0792388
\(536\) 38.5460 1.66493
\(537\) −26.3087 −1.13530
\(538\) 0.849101 0.0366073
\(539\) −0.489443 −0.0210818
\(540\) −11.3471 −0.488301
\(541\) 37.6945 1.62061 0.810307 0.586005i \(-0.199300\pi\)
0.810307 + 0.586005i \(0.199300\pi\)
\(542\) 20.7320 0.890514
\(543\) 1.50135 0.0644289
\(544\) 21.1711 0.907705
\(545\) −3.10438 −0.132977
\(546\) −24.5647 −1.05127
\(547\) 10.0185 0.428361 0.214180 0.976794i \(-0.431292\pi\)
0.214180 + 0.976794i \(0.431292\pi\)
\(548\) 46.4735 1.98525
\(549\) 3.71069 0.158369
\(550\) −6.26021 −0.266936
\(551\) 7.01420 0.298815
\(552\) −59.3871 −2.52768
\(553\) 7.49834 0.318862
\(554\) −27.2131 −1.15618
\(555\) 3.41746 0.145063
\(556\) −57.0834 −2.42088
\(557\) 40.4574 1.71424 0.857119 0.515119i \(-0.172252\pi\)
0.857119 + 0.515119i \(0.172252\pi\)
\(558\) 16.7180 0.707727
\(559\) −43.4793 −1.83898
\(560\) −4.38917 −0.185476
\(561\) 1.14332 0.0482709
\(562\) −72.2073 −3.04588
\(563\) 34.6290 1.45944 0.729719 0.683747i \(-0.239651\pi\)
0.729719 + 0.683747i \(0.239651\pi\)
\(564\) −28.2803 −1.19081
\(565\) 8.25783 0.347410
\(566\) −74.7523 −3.14207
\(567\) 5.34929 0.224649
\(568\) −128.784 −5.40365
\(569\) 7.58582 0.318014 0.159007 0.987277i \(-0.449171\pi\)
0.159007 + 0.987277i \(0.449171\pi\)
\(570\) 1.25212 0.0524456
\(571\) −23.7976 −0.995900 −0.497950 0.867206i \(-0.665914\pi\)
−0.497950 + 0.867206i \(0.665914\pi\)
\(572\) 15.7666 0.659236
\(573\) 5.74624 0.240053
\(574\) 14.0058 0.584590
\(575\) −25.2688 −1.05378
\(576\) −11.7600 −0.490002
\(577\) −3.93178 −0.163682 −0.0818411 0.996645i \(-0.526080\pi\)
−0.0818411 + 0.996645i \(0.526080\pi\)
\(578\) 37.9761 1.57960
\(579\) −10.7061 −0.444930
\(580\) −17.2041 −0.714361
\(581\) 11.2101 0.465075
\(582\) −12.6098 −0.522691
\(583\) −5.93137 −0.245652
\(584\) 57.8749 2.39488
\(585\) 2.41335 0.0997798
\(586\) −7.85375 −0.324436
\(587\) −13.0092 −0.536949 −0.268474 0.963287i \(-0.586519\pi\)
−0.268474 + 0.963287i \(0.586519\pi\)
\(588\) 7.17926 0.296068
\(589\) −5.56875 −0.229456
\(590\) 12.9914 0.534849
\(591\) 34.6479 1.42523
\(592\) 64.4160 2.64748
\(593\) −4.58168 −0.188147 −0.0940735 0.995565i \(-0.529989\pi\)
−0.0940735 + 0.995565i \(0.529989\pi\)
\(594\) −7.31610 −0.300183
\(595\) 0.652975 0.0267694
\(596\) 15.2951 0.626512
\(597\) 34.7804 1.42347
\(598\) 89.1537 3.64577
\(599\) −37.8001 −1.54447 −0.772235 0.635337i \(-0.780861\pi\)
−0.772235 + 0.635337i \(0.780861\pi\)
\(600\) 55.0139 2.24593
\(601\) −1.26908 −0.0517668 −0.0258834 0.999665i \(-0.508240\pi\)
−0.0258834 + 0.999665i \(0.508240\pi\)
\(602\) 17.8014 0.725531
\(603\) 4.53258 0.184581
\(604\) 40.1753 1.63471
\(605\) −4.32851 −0.175979
\(606\) −7.04409 −0.286146
\(607\) −39.3144 −1.59572 −0.797861 0.602841i \(-0.794035\pi\)
−0.797861 + 0.602841i \(0.794035\pi\)
\(608\) 10.6712 0.432776
\(609\) 12.3366 0.499904
\(610\) 4.24705 0.171958
\(611\) 25.4353 1.02900
\(612\) 7.52441 0.304156
\(613\) 14.3223 0.578472 0.289236 0.957258i \(-0.406599\pi\)
0.289236 + 0.957258i \(0.406599\pi\)
\(614\) −8.63741 −0.348577
\(615\) 3.06681 0.123666
\(616\) −3.86738 −0.155821
\(617\) 11.0111 0.443290 0.221645 0.975127i \(-0.428857\pi\)
0.221645 + 0.975127i \(0.428857\pi\)
\(618\) −26.0800 −1.04909
\(619\) 30.1483 1.21176 0.605881 0.795555i \(-0.292821\pi\)
0.605881 + 0.795555i \(0.292821\pi\)
\(620\) 13.6587 0.548548
\(621\) −29.5308 −1.18503
\(622\) 37.1046 1.48776
\(623\) 5.79688 0.232247
\(624\) −101.387 −4.05873
\(625\) 22.5990 0.903959
\(626\) 28.8647 1.15366
\(627\) 0.576284 0.0230146
\(628\) 21.7297 0.867110
\(629\) −9.58314 −0.382105
\(630\) −0.988081 −0.0393661
\(631\) 21.4260 0.852956 0.426478 0.904498i \(-0.359754\pi\)
0.426478 + 0.904498i \(0.359754\pi\)
\(632\) 59.2487 2.35679
\(633\) 27.2603 1.08350
\(634\) −60.9596 −2.42102
\(635\) −3.76057 −0.149234
\(636\) 87.0026 3.44988
\(637\) −6.45702 −0.255837
\(638\) −11.0924 −0.439153
\(639\) −15.1436 −0.599070
\(640\) −2.96701 −0.117281
\(641\) 31.9478 1.26186 0.630931 0.775839i \(-0.282673\pi\)
0.630931 + 0.775839i \(0.282673\pi\)
\(642\) −17.3335 −0.684099
\(643\) 30.7100 1.21108 0.605542 0.795813i \(-0.292956\pi\)
0.605542 + 0.795813i \(0.292956\pi\)
\(644\) −26.0559 −1.02675
\(645\) 3.89793 0.153481
\(646\) −3.51117 −0.138145
\(647\) 36.0700 1.41806 0.709028 0.705180i \(-0.249134\pi\)
0.709028 + 0.705180i \(0.249134\pi\)
\(648\) 42.2678 1.66044
\(649\) 5.97926 0.234707
\(650\) −82.5884 −3.23938
\(651\) −9.79432 −0.383870
\(652\) 69.6569 2.72798
\(653\) −42.4334 −1.66055 −0.830273 0.557356i \(-0.811816\pi\)
−0.830273 + 0.557356i \(0.811816\pi\)
\(654\) 29.3594 1.14804
\(655\) 2.90889 0.113660
\(656\) 57.8066 2.25697
\(657\) 6.80545 0.265506
\(658\) −10.4138 −0.405971
\(659\) 4.39124 0.171058 0.0855292 0.996336i \(-0.472742\pi\)
0.0855292 + 0.996336i \(0.472742\pi\)
\(660\) −1.41348 −0.0550197
\(661\) 28.0159 1.08969 0.544847 0.838536i \(-0.316588\pi\)
0.544847 + 0.838536i \(0.316588\pi\)
\(662\) −18.2737 −0.710229
\(663\) 15.0833 0.585787
\(664\) 88.5779 3.43749
\(665\) 0.329130 0.0127631
\(666\) 14.5012 0.561910
\(667\) −44.7736 −1.73364
\(668\) 51.7513 2.00232
\(669\) −36.0926 −1.39542
\(670\) 5.18773 0.200419
\(671\) 1.95469 0.0754599
\(672\) 18.7686 0.724014
\(673\) −24.5371 −0.945834 −0.472917 0.881107i \(-0.656799\pi\)
−0.472917 + 0.881107i \(0.656799\pi\)
\(674\) −3.95856 −0.152478
\(675\) 27.3562 1.05294
\(676\) 143.147 5.50565
\(677\) 11.6750 0.448708 0.224354 0.974508i \(-0.427973\pi\)
0.224354 + 0.974508i \(0.427973\pi\)
\(678\) −78.0976 −2.99932
\(679\) −3.31457 −0.127202
\(680\) 5.15953 0.197859
\(681\) −14.2542 −0.546223
\(682\) 8.80654 0.337220
\(683\) 27.8733 1.06654 0.533271 0.845944i \(-0.320963\pi\)
0.533271 + 0.845944i \(0.320963\pi\)
\(684\) 3.79265 0.145016
\(685\) 3.74722 0.143174
\(686\) 2.64365 0.100935
\(687\) 27.8211 1.06144
\(688\) 73.4724 2.80111
\(689\) −78.2501 −2.98109
\(690\) −7.99265 −0.304275
\(691\) 2.46494 0.0937708 0.0468854 0.998900i \(-0.485070\pi\)
0.0468854 + 0.998900i \(0.485070\pi\)
\(692\) 94.3476 3.58656
\(693\) −0.454761 −0.0172749
\(694\) −67.5899 −2.56568
\(695\) −4.60272 −0.174591
\(696\) 97.4786 3.69492
\(697\) −8.59987 −0.325743
\(698\) −31.3948 −1.18831
\(699\) 32.9417 1.24597
\(700\) 24.1372 0.912300
\(701\) −6.53593 −0.246859 −0.123429 0.992353i \(-0.539389\pi\)
−0.123429 + 0.992353i \(0.539389\pi\)
\(702\) −96.5182 −3.64285
\(703\) −4.83035 −0.182180
\(704\) −6.19485 −0.233477
\(705\) −2.28028 −0.0858802
\(706\) −67.9670 −2.55797
\(707\) −1.85159 −0.0696362
\(708\) −87.7050 −3.29616
\(709\) −27.7948 −1.04386 −0.521928 0.852989i \(-0.674787\pi\)
−0.521928 + 0.852989i \(0.674787\pi\)
\(710\) −17.3324 −0.650475
\(711\) 6.96699 0.261283
\(712\) 45.8045 1.71660
\(713\) 35.5469 1.33124
\(714\) −6.17544 −0.231110
\(715\) 1.27129 0.0475434
\(716\) −91.2068 −3.40856
\(717\) −0.564597 −0.0210853
\(718\) 48.9161 1.82553
\(719\) 5.45519 0.203444 0.101722 0.994813i \(-0.467565\pi\)
0.101722 + 0.994813i \(0.467565\pi\)
\(720\) −4.07814 −0.151983
\(721\) −6.85532 −0.255306
\(722\) 48.4596 1.80348
\(723\) −20.9827 −0.780357
\(724\) 5.20486 0.193437
\(725\) 41.4765 1.54040
\(726\) 40.9364 1.51929
\(727\) −34.3782 −1.27502 −0.637508 0.770444i \(-0.720035\pi\)
−0.637508 + 0.770444i \(0.720035\pi\)
\(728\) −51.0207 −1.89095
\(729\) 29.3803 1.08816
\(730\) 7.78912 0.288288
\(731\) −10.9305 −0.404278
\(732\) −28.6718 −1.05974
\(733\) 43.8315 1.61895 0.809476 0.587153i \(-0.199751\pi\)
0.809476 + 0.587153i \(0.199751\pi\)
\(734\) 80.4222 2.96844
\(735\) 0.578873 0.0213521
\(736\) −68.1175 −2.51084
\(737\) 2.38763 0.0879496
\(738\) 13.0133 0.479027
\(739\) 26.5622 0.977108 0.488554 0.872534i \(-0.337525\pi\)
0.488554 + 0.872534i \(0.337525\pi\)
\(740\) 11.8476 0.435528
\(741\) 7.60268 0.279292
\(742\) 32.0374 1.17613
\(743\) 28.1244 1.03178 0.515892 0.856654i \(-0.327461\pi\)
0.515892 + 0.856654i \(0.327461\pi\)
\(744\) −77.3906 −2.83728
\(745\) 1.23327 0.0451834
\(746\) 27.3713 1.00214
\(747\) 10.4158 0.381093
\(748\) 3.96365 0.144925
\(749\) −4.55624 −0.166481
\(750\) 15.0558 0.549759
\(751\) 33.1393 1.20927 0.604636 0.796502i \(-0.293319\pi\)
0.604636 + 0.796502i \(0.293319\pi\)
\(752\) −42.9812 −1.56736
\(753\) −0.575773 −0.0209823
\(754\) −146.338 −5.32930
\(755\) 3.23939 0.117893
\(756\) 28.2083 1.02593
\(757\) −13.4566 −0.489090 −0.244545 0.969638i \(-0.578639\pi\)
−0.244545 + 0.969638i \(0.578639\pi\)
\(758\) −13.3977 −0.486627
\(759\) −3.67859 −0.133524
\(760\) 2.60064 0.0943353
\(761\) −4.34193 −0.157395 −0.0786975 0.996899i \(-0.525076\pi\)
−0.0786975 + 0.996899i \(0.525076\pi\)
\(762\) 35.5652 1.28839
\(763\) 7.71733 0.279386
\(764\) 19.9211 0.720719
\(765\) 0.606704 0.0219354
\(766\) 34.2817 1.23865
\(767\) 78.8819 2.84826
\(768\) −8.36775 −0.301945
\(769\) 3.25027 0.117208 0.0586039 0.998281i \(-0.481335\pi\)
0.0586039 + 0.998281i \(0.481335\pi\)
\(770\) −0.520493 −0.0187573
\(771\) 20.8405 0.750552
\(772\) −37.1159 −1.33583
\(773\) −15.5861 −0.560591 −0.280296 0.959914i \(-0.590433\pi\)
−0.280296 + 0.959914i \(0.590433\pi\)
\(774\) 16.5400 0.594517
\(775\) −32.9292 −1.18285
\(776\) −26.1903 −0.940178
\(777\) −8.49562 −0.304779
\(778\) −52.4314 −1.87976
\(779\) −4.33473 −0.155308
\(780\) −18.6475 −0.667687
\(781\) −7.97719 −0.285446
\(782\) 22.4128 0.801479
\(783\) 48.4722 1.73225
\(784\) 10.9112 0.389687
\(785\) 1.75210 0.0625350
\(786\) −27.5105 −0.981268
\(787\) −16.2109 −0.577857 −0.288929 0.957351i \(-0.593299\pi\)
−0.288929 + 0.957351i \(0.593299\pi\)
\(788\) 120.117 4.27900
\(789\) −8.09831 −0.288307
\(790\) 7.97402 0.283703
\(791\) −20.5285 −0.729911
\(792\) −3.59333 −0.127683
\(793\) 25.7874 0.915737
\(794\) −33.0276 −1.17210
\(795\) 7.01514 0.248801
\(796\) 120.577 4.27373
\(797\) 2.19319 0.0776868 0.0388434 0.999245i \(-0.487633\pi\)
0.0388434 + 0.999245i \(0.487633\pi\)
\(798\) −3.11271 −0.110189
\(799\) 6.39429 0.226214
\(800\) 63.1013 2.23097
\(801\) 5.38611 0.190309
\(802\) −1.29605 −0.0457652
\(803\) 3.58491 0.126509
\(804\) −35.0223 −1.23514
\(805\) −2.10093 −0.0740479
\(806\) 116.181 4.09230
\(807\) −0.462201 −0.0162702
\(808\) −14.6305 −0.514699
\(809\) −47.9315 −1.68518 −0.842592 0.538553i \(-0.818971\pi\)
−0.842592 + 0.538553i \(0.818971\pi\)
\(810\) 5.68864 0.199878
\(811\) 42.4308 1.48995 0.744974 0.667094i \(-0.232462\pi\)
0.744974 + 0.667094i \(0.232462\pi\)
\(812\) 42.7684 1.50088
\(813\) −11.2853 −0.395792
\(814\) 7.63882 0.267740
\(815\) 5.61654 0.196739
\(816\) −25.4881 −0.892263
\(817\) −5.50946 −0.192752
\(818\) −37.6682 −1.31704
\(819\) −5.99947 −0.209638
\(820\) 10.6320 0.371286
\(821\) −43.2450 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(822\) −35.4390 −1.23608
\(823\) 13.5021 0.470652 0.235326 0.971916i \(-0.424384\pi\)
0.235326 + 0.971916i \(0.424384\pi\)
\(824\) −54.1679 −1.88703
\(825\) 3.40769 0.118641
\(826\) −32.2960 −1.12372
\(827\) 46.3065 1.61024 0.805118 0.593115i \(-0.202102\pi\)
0.805118 + 0.593115i \(0.202102\pi\)
\(828\) −24.2096 −0.841341
\(829\) −10.9243 −0.379417 −0.189708 0.981840i \(-0.560754\pi\)
−0.189708 + 0.981840i \(0.560754\pi\)
\(830\) 11.9213 0.413794
\(831\) 14.8132 0.513866
\(832\) −81.7261 −2.83334
\(833\) −1.62326 −0.0562427
\(834\) 43.5297 1.50731
\(835\) 4.17278 0.144405
\(836\) 1.99786 0.0690975
\(837\) −38.4832 −1.33018
\(838\) 66.9649 2.31326
\(839\) −1.40430 −0.0484819 −0.0242409 0.999706i \(-0.507717\pi\)
−0.0242409 + 0.999706i \(0.507717\pi\)
\(840\) 4.57402 0.157819
\(841\) 44.4918 1.53420
\(842\) 66.7289 2.29963
\(843\) 39.3054 1.35375
\(844\) 94.5059 3.25303
\(845\) 11.5421 0.397062
\(846\) −9.67583 −0.332662
\(847\) 10.7604 0.369733
\(848\) 132.229 4.54076
\(849\) 40.6908 1.39650
\(850\) −20.7623 −0.712140
\(851\) 30.8335 1.05696
\(852\) 117.011 4.00873
\(853\) −3.73677 −0.127944 −0.0639722 0.997952i \(-0.520377\pi\)
−0.0639722 + 0.997952i \(0.520377\pi\)
\(854\) −10.5579 −0.361285
\(855\) 0.305807 0.0104584
\(856\) −36.0015 −1.23051
\(857\) −14.6273 −0.499658 −0.249829 0.968290i \(-0.580374\pi\)
−0.249829 + 0.968290i \(0.580374\pi\)
\(858\) −12.0230 −0.410460
\(859\) 1.00000 0.0341196
\(860\) 13.5133 0.460800
\(861\) −7.62393 −0.259823
\(862\) −105.973 −3.60944
\(863\) −46.1094 −1.56958 −0.784792 0.619760i \(-0.787230\pi\)
−0.784792 + 0.619760i \(0.787230\pi\)
\(864\) 73.7443 2.50883
\(865\) 7.60737 0.258658
\(866\) 83.6631 2.84299
\(867\) −20.6720 −0.702057
\(868\) −33.9549 −1.15250
\(869\) 3.67001 0.124497
\(870\) 13.1192 0.444782
\(871\) 31.4990 1.06730
\(872\) 60.9791 2.06501
\(873\) −3.07969 −0.104232
\(874\) 11.2971 0.382129
\(875\) 3.95752 0.133789
\(876\) −52.5843 −1.77666
\(877\) 57.9445 1.95665 0.978324 0.207080i \(-0.0663962\pi\)
0.978324 + 0.207080i \(0.0663962\pi\)
\(878\) 36.4289 1.22942
\(879\) 4.27512 0.144196
\(880\) −2.14825 −0.0724175
\(881\) −36.0607 −1.21492 −0.607459 0.794351i \(-0.707811\pi\)
−0.607459 + 0.794351i \(0.707811\pi\)
\(882\) 2.45632 0.0827085
\(883\) 5.91195 0.198953 0.0994765 0.995040i \(-0.468283\pi\)
0.0994765 + 0.995040i \(0.468283\pi\)
\(884\) 52.2907 1.75873
\(885\) −7.07178 −0.237715
\(886\) 36.6895 1.23261
\(887\) −49.8167 −1.67268 −0.836340 0.548211i \(-0.815309\pi\)
−0.836340 + 0.548211i \(0.815309\pi\)
\(888\) −67.1288 −2.25270
\(889\) 9.34859 0.313542
\(890\) 6.16463 0.206639
\(891\) 2.61817 0.0877121
\(892\) −125.126 −4.18952
\(893\) 3.22302 0.107854
\(894\) −11.6635 −0.390086
\(895\) −7.35413 −0.245821
\(896\) 7.37582 0.246409
\(897\) −48.5301 −1.62037
\(898\) 8.54258 0.285070
\(899\) −58.3470 −1.94598
\(900\) 22.4268 0.747559
\(901\) −19.6717 −0.655358
\(902\) 6.85504 0.228248
\(903\) −9.69004 −0.322464
\(904\) −162.208 −5.39495
\(905\) 0.419675 0.0139505
\(906\) −30.6362 −1.01782
\(907\) −22.3211 −0.741160 −0.370580 0.928801i \(-0.620841\pi\)
−0.370580 + 0.928801i \(0.620841\pi\)
\(908\) −49.4165 −1.63994
\(909\) −1.72038 −0.0570615
\(910\) −6.86664 −0.227627
\(911\) −0.338172 −0.0112041 −0.00560207 0.999984i \(-0.501783\pi\)
−0.00560207 + 0.999984i \(0.501783\pi\)
\(912\) −12.8472 −0.425413
\(913\) 5.48673 0.181584
\(914\) 5.33163 0.176355
\(915\) −2.31184 −0.0764272
\(916\) 96.4501 3.18680
\(917\) −7.23135 −0.238800
\(918\) −24.2642 −0.800837
\(919\) 1.00120 0.0330266 0.0165133 0.999864i \(-0.494743\pi\)
0.0165133 + 0.999864i \(0.494743\pi\)
\(920\) −16.6006 −0.547307
\(921\) 4.70170 0.154926
\(922\) 83.9861 2.76593
\(923\) −105.240 −3.46401
\(924\) 3.51384 0.115597
\(925\) −28.5629 −0.939142
\(926\) −26.4550 −0.869366
\(927\) −6.36954 −0.209203
\(928\) 111.809 3.67030
\(929\) 4.63616 0.152107 0.0760537 0.997104i \(-0.475768\pi\)
0.0760537 + 0.997104i \(0.475768\pi\)
\(930\) −10.4157 −0.341543
\(931\) −0.818199 −0.0268154
\(932\) 114.202 3.74082
\(933\) −20.1976 −0.661239
\(934\) −29.5884 −0.968160
\(935\) 0.319594 0.0104519
\(936\) −47.4053 −1.54949
\(937\) 42.1780 1.37789 0.688947 0.724812i \(-0.258073\pi\)
0.688947 + 0.724812i \(0.258073\pi\)
\(938\) −12.8964 −0.421083
\(939\) −15.7122 −0.512749
\(940\) −7.90526 −0.257841
\(941\) 16.7642 0.546498 0.273249 0.961943i \(-0.411902\pi\)
0.273249 + 0.961943i \(0.411902\pi\)
\(942\) −16.5703 −0.539889
\(943\) 27.6698 0.901054
\(944\) −133.297 −4.33844
\(945\) 2.27447 0.0739886
\(946\) 8.71278 0.283277
\(947\) 61.2497 1.99035 0.995174 0.0981282i \(-0.0312855\pi\)
0.995174 + 0.0981282i \(0.0312855\pi\)
\(948\) −53.8325 −1.74840
\(949\) 47.2943 1.53524
\(950\) −10.4652 −0.339534
\(951\) 33.1829 1.07603
\(952\) −12.8263 −0.415704
\(953\) −49.1554 −1.59230 −0.796150 0.605099i \(-0.793134\pi\)
−0.796150 + 0.605099i \(0.793134\pi\)
\(954\) 29.7671 0.963746
\(955\) 1.60626 0.0519774
\(956\) −1.95734 −0.0633050
\(957\) 6.03806 0.195183
\(958\) −64.2952 −2.07728
\(959\) −9.31540 −0.300810
\(960\) 7.32676 0.236470
\(961\) 15.3231 0.494293
\(962\) 100.776 3.24914
\(963\) −4.23338 −0.136419
\(964\) −72.7429 −2.34289
\(965\) −2.99270 −0.0963385
\(966\) 19.8693 0.639284
\(967\) 37.7498 1.21395 0.606976 0.794720i \(-0.292383\pi\)
0.606976 + 0.794720i \(0.292383\pi\)
\(968\) 85.0245 2.73279
\(969\) 1.91127 0.0613990
\(970\) −3.52484 −0.113176
\(971\) 27.0786 0.868994 0.434497 0.900673i \(-0.356926\pi\)
0.434497 + 0.900673i \(0.356926\pi\)
\(972\) 46.2210 1.48254
\(973\) 11.4421 0.366817
\(974\) 53.9494 1.72865
\(975\) 44.9563 1.43975
\(976\) −43.5762 −1.39484
\(977\) 0.683774 0.0218759 0.0109379 0.999940i \(-0.496518\pi\)
0.0109379 + 0.999940i \(0.496518\pi\)
\(978\) −53.1178 −1.69852
\(979\) 2.83725 0.0906788
\(980\) 2.00684 0.0641060
\(981\) 7.17046 0.228935
\(982\) −40.0953 −1.27949
\(983\) 11.2418 0.358557 0.179279 0.983798i \(-0.442624\pi\)
0.179279 + 0.983798i \(0.442624\pi\)
\(984\) −60.2411 −1.92042
\(985\) 9.68523 0.308597
\(986\) −36.7885 −1.17158
\(987\) 5.66865 0.180435
\(988\) 26.3570 0.838526
\(989\) 35.1684 1.11829
\(990\) −0.483610 −0.0153701
\(991\) 4.41767 0.140332 0.0701660 0.997535i \(-0.477647\pi\)
0.0701660 + 0.997535i \(0.477647\pi\)
\(992\) −88.7676 −2.81837
\(993\) 9.94716 0.315664
\(994\) 43.0875 1.36665
\(995\) 9.72226 0.308217
\(996\) −80.4805 −2.55012
\(997\) −43.2265 −1.36900 −0.684498 0.729014i \(-0.739979\pi\)
−0.684498 + 0.729014i \(0.739979\pi\)
\(998\) 56.6153 1.79213
\(999\) −33.3805 −1.05611
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.f.1.3 110
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6013.2.a.f.1.3 110 1.1 even 1 trivial