Properties

Label 6047.2.a.b.1.8
Level $6047$
Weight $2$
Character 6047.1
Self dual yes
Analytic conductor $48.286$
Analytic rank $0$
Dimension $287$
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] = [6047,2,Mod(1,6047)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6047.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6047 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6047.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: \(48.2855381023\)
Analytic rank: \(0\)
Dimension: \(287\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 6047.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.69052 q^{2} -1.22455 q^{3} +5.23892 q^{4} +3.48449 q^{5} +3.29468 q^{6} +4.74165 q^{7} -8.71440 q^{8} -1.50048 q^{9} +O(q^{10})\) \(q-2.69052 q^{2} -1.22455 q^{3} +5.23892 q^{4} +3.48449 q^{5} +3.29468 q^{6} +4.74165 q^{7} -8.71440 q^{8} -1.50048 q^{9} -9.37511 q^{10} -0.101858 q^{11} -6.41532 q^{12} +3.70807 q^{13} -12.7575 q^{14} -4.26693 q^{15} +12.9685 q^{16} +1.84612 q^{17} +4.03707 q^{18} +6.19824 q^{19} +18.2550 q^{20} -5.80639 q^{21} +0.274051 q^{22} -0.771298 q^{23} +10.6712 q^{24} +7.14168 q^{25} -9.97666 q^{26} +5.51106 q^{27} +24.8411 q^{28} -7.94169 q^{29} +11.4803 q^{30} +9.88585 q^{31} -17.4631 q^{32} +0.124730 q^{33} -4.96702 q^{34} +16.5222 q^{35} -7.86088 q^{36} +8.20300 q^{37} -16.6765 q^{38} -4.54072 q^{39} -30.3652 q^{40} +0.0528848 q^{41} +15.6222 q^{42} -5.27439 q^{43} -0.533625 q^{44} -5.22840 q^{45} +2.07520 q^{46} -10.3434 q^{47} -15.8805 q^{48} +15.4832 q^{49} -19.2149 q^{50} -2.26066 q^{51} +19.4263 q^{52} +2.93474 q^{53} -14.8276 q^{54} -0.354923 q^{55} -41.3206 q^{56} -7.59005 q^{57} +21.3673 q^{58} -2.85944 q^{59} -22.3541 q^{60} -7.44599 q^{61} -26.5981 q^{62} -7.11474 q^{63} +21.0481 q^{64} +12.9208 q^{65} -0.335589 q^{66} -8.72133 q^{67} +9.67166 q^{68} +0.944493 q^{69} -44.4535 q^{70} +16.6740 q^{71} +13.0758 q^{72} -4.16063 q^{73} -22.0704 q^{74} -8.74534 q^{75} +32.4721 q^{76} -0.482974 q^{77} +12.2169 q^{78} +7.63338 q^{79} +45.1885 q^{80} -2.24714 q^{81} -0.142288 q^{82} -2.61134 q^{83} -30.4192 q^{84} +6.43278 q^{85} +14.1909 q^{86} +9.72500 q^{87} +0.887630 q^{88} +5.30060 q^{89} +14.0671 q^{90} +17.5824 q^{91} -4.04077 q^{92} -12.1057 q^{93} +27.8292 q^{94} +21.5977 q^{95} +21.3845 q^{96} +11.8985 q^{97} -41.6580 q^{98} +0.152835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69052 −1.90249 −0.951244 0.308439i \(-0.900193\pi\)
−0.951244 + 0.308439i \(0.900193\pi\)
\(3\) −1.22455 −0.706994 −0.353497 0.935436i \(-0.615008\pi\)
−0.353497 + 0.935436i \(0.615008\pi\)
\(4\) 5.23892 2.61946
\(5\) 3.48449 1.55831 0.779156 0.626830i \(-0.215648\pi\)
0.779156 + 0.626830i \(0.215648\pi\)
\(6\) 3.29468 1.34505
\(7\) 4.74165 1.79218 0.896088 0.443877i \(-0.146397\pi\)
0.896088 + 0.443877i \(0.146397\pi\)
\(8\) −8.71440 −3.08100
\(9\) −1.50048 −0.500159
\(10\) −9.37511 −2.96467
\(11\) −0.101858 −0.0307113 −0.0153556 0.999882i \(-0.504888\pi\)
−0.0153556 + 0.999882i \(0.504888\pi\)
\(12\) −6.41532 −1.85194
\(13\) 3.70807 1.02843 0.514217 0.857660i \(-0.328082\pi\)
0.514217 + 0.857660i \(0.328082\pi\)
\(14\) −12.7575 −3.40959
\(15\) −4.26693 −1.10172
\(16\) 12.9685 3.24211
\(17\) 1.84612 0.447749 0.223875 0.974618i \(-0.428129\pi\)
0.223875 + 0.974618i \(0.428129\pi\)
\(18\) 4.03707 0.951547
\(19\) 6.19824 1.42197 0.710987 0.703205i \(-0.248249\pi\)
0.710987 + 0.703205i \(0.248249\pi\)
\(20\) 18.2550 4.08194
\(21\) −5.80639 −1.26706
\(22\) 0.274051 0.0584279
\(23\) −0.771298 −0.160827 −0.0804134 0.996762i \(-0.525624\pi\)
−0.0804134 + 0.996762i \(0.525624\pi\)
\(24\) 10.6712 2.17825
\(25\) 7.14168 1.42834
\(26\) −9.97666 −1.95658
\(27\) 5.51106 1.06060
\(28\) 24.8411 4.69453
\(29\) −7.94169 −1.47474 −0.737368 0.675492i \(-0.763931\pi\)
−0.737368 + 0.675492i \(0.763931\pi\)
\(30\) 11.4803 2.09600
\(31\) 9.88585 1.77555 0.887776 0.460276i \(-0.152250\pi\)
0.887776 + 0.460276i \(0.152250\pi\)
\(32\) −17.4631 −3.08708
\(33\) 0.124730 0.0217127
\(34\) −4.96702 −0.851837
\(35\) 16.5222 2.79277
\(36\) −7.86088 −1.31015
\(37\) 8.20300 1.34856 0.674282 0.738474i \(-0.264453\pi\)
0.674282 + 0.738474i \(0.264453\pi\)
\(38\) −16.6765 −2.70529
\(39\) −4.54072 −0.727098
\(40\) −30.3652 −4.80116
\(41\) 0.0528848 0.00825922 0.00412961 0.999991i \(-0.498686\pi\)
0.00412961 + 0.999991i \(0.498686\pi\)
\(42\) 15.6222 2.41056
\(43\) −5.27439 −0.804337 −0.402168 0.915566i \(-0.631743\pi\)
−0.402168 + 0.915566i \(0.631743\pi\)
\(44\) −0.533625 −0.0804470
\(45\) −5.22840 −0.779404
\(46\) 2.07520 0.305971
\(47\) −10.3434 −1.50874 −0.754372 0.656448i \(-0.772058\pi\)
−0.754372 + 0.656448i \(0.772058\pi\)
\(48\) −15.8805 −2.29216
\(49\) 15.4832 2.21189
\(50\) −19.2149 −2.71739
\(51\) −2.26066 −0.316556
\(52\) 19.4263 2.69394
\(53\) 2.93474 0.403117 0.201559 0.979476i \(-0.435399\pi\)
0.201559 + 0.979476i \(0.435399\pi\)
\(54\) −14.8276 −2.01779
\(55\) −0.354923 −0.0478578
\(56\) −41.3206 −5.52170
\(57\) −7.59005 −1.00533
\(58\) 21.3673 2.80567
\(59\) −2.85944 −0.372267 −0.186134 0.982524i \(-0.559596\pi\)
−0.186134 + 0.982524i \(0.559596\pi\)
\(60\) −22.3541 −2.88591
\(61\) −7.44599 −0.953362 −0.476681 0.879076i \(-0.658160\pi\)
−0.476681 + 0.879076i \(0.658160\pi\)
\(62\) −26.5981 −3.37797
\(63\) −7.11474 −0.896373
\(64\) 21.0481 2.63101
\(65\) 12.9208 1.60262
\(66\) −0.335589 −0.0413082
\(67\) −8.72133 −1.06548 −0.532740 0.846279i \(-0.678838\pi\)
−0.532740 + 0.846279i \(0.678838\pi\)
\(68\) 9.67166 1.17286
\(69\) 0.944493 0.113704
\(70\) −44.4535 −5.31321
\(71\) 16.6740 1.97884 0.989422 0.145067i \(-0.0463399\pi\)
0.989422 + 0.145067i \(0.0463399\pi\)
\(72\) 13.0758 1.54099
\(73\) −4.16063 −0.486965 −0.243482 0.969905i \(-0.578290\pi\)
−0.243482 + 0.969905i \(0.578290\pi\)
\(74\) −22.0704 −2.56563
\(75\) −8.74534 −1.00982
\(76\) 32.4721 3.72480
\(77\) −0.482974 −0.0550400
\(78\) 12.2169 1.38329
\(79\) 7.63338 0.858823 0.429411 0.903109i \(-0.358721\pi\)
0.429411 + 0.903109i \(0.358721\pi\)
\(80\) 45.1885 5.05222
\(81\) −2.24714 −0.249682
\(82\) −0.142288 −0.0157131
\(83\) −2.61134 −0.286632 −0.143316 0.989677i \(-0.545776\pi\)
−0.143316 + 0.989677i \(0.545776\pi\)
\(84\) −30.4192 −3.31901
\(85\) 6.43278 0.697733
\(86\) 14.1909 1.53024
\(87\) 9.72500 1.04263
\(88\) 0.887630 0.0946216
\(89\) 5.30060 0.561862 0.280931 0.959728i \(-0.409357\pi\)
0.280931 + 0.959728i \(0.409357\pi\)
\(90\) 14.0671 1.48281
\(91\) 17.5824 1.84314
\(92\) −4.04077 −0.421279
\(93\) −12.1057 −1.25530
\(94\) 27.8292 2.87037
\(95\) 21.5977 2.21588
\(96\) 21.3845 2.18255
\(97\) 11.8985 1.20810 0.604052 0.796945i \(-0.293552\pi\)
0.604052 + 0.796945i \(0.293552\pi\)
\(98\) −41.6580 −4.20810
\(99\) 0.152835 0.0153605
\(100\) 37.4147 3.74147
\(101\) 9.08359 0.903851 0.451925 0.892056i \(-0.350737\pi\)
0.451925 + 0.892056i \(0.350737\pi\)
\(102\) 6.08237 0.602244
\(103\) −3.89449 −0.383735 −0.191868 0.981421i \(-0.561454\pi\)
−0.191868 + 0.981421i \(0.561454\pi\)
\(104\) −32.3136 −3.16861
\(105\) −20.2323 −1.97447
\(106\) −7.89598 −0.766925
\(107\) −12.4086 −1.19959 −0.599793 0.800155i \(-0.704750\pi\)
−0.599793 + 0.800155i \(0.704750\pi\)
\(108\) 28.8720 2.77821
\(109\) −15.3937 −1.47445 −0.737223 0.675650i \(-0.763863\pi\)
−0.737223 + 0.675650i \(0.763863\pi\)
\(110\) 0.954928 0.0910488
\(111\) −10.0450 −0.953427
\(112\) 61.4919 5.81043
\(113\) 8.93885 0.840896 0.420448 0.907317i \(-0.361873\pi\)
0.420448 + 0.907317i \(0.361873\pi\)
\(114\) 20.4212 1.91262
\(115\) −2.68758 −0.250618
\(116\) −41.6059 −3.86301
\(117\) −5.56388 −0.514381
\(118\) 7.69339 0.708234
\(119\) 8.75364 0.802445
\(120\) 37.1837 3.39440
\(121\) −10.9896 −0.999057
\(122\) 20.0336 1.81376
\(123\) −0.0647601 −0.00583922
\(124\) 51.7912 4.65099
\(125\) 7.46265 0.667480
\(126\) 19.1424 1.70534
\(127\) 16.3849 1.45393 0.726964 0.686675i \(-0.240931\pi\)
0.726964 + 0.686675i \(0.240931\pi\)
\(128\) −21.7042 −1.91839
\(129\) 6.45875 0.568662
\(130\) −34.7636 −3.04897
\(131\) 10.4649 0.914323 0.457162 0.889384i \(-0.348866\pi\)
0.457162 + 0.889384i \(0.348866\pi\)
\(132\) 0.653451 0.0568756
\(133\) 29.3899 2.54843
\(134\) 23.4649 2.02706
\(135\) 19.2032 1.65275
\(136\) −16.0878 −1.37952
\(137\) 8.26403 0.706044 0.353022 0.935615i \(-0.385154\pi\)
0.353022 + 0.935615i \(0.385154\pi\)
\(138\) −2.54118 −0.216320
\(139\) −21.4749 −1.82148 −0.910740 0.412981i \(-0.864488\pi\)
−0.910740 + 0.412981i \(0.864488\pi\)
\(140\) 86.5587 7.31554
\(141\) 12.6660 1.06667
\(142\) −44.8619 −3.76473
\(143\) −0.377696 −0.0315846
\(144\) −19.4589 −1.62157
\(145\) −27.6728 −2.29810
\(146\) 11.1943 0.926445
\(147\) −18.9600 −1.56379
\(148\) 42.9748 3.53251
\(149\) 9.35958 0.766767 0.383383 0.923589i \(-0.374759\pi\)
0.383383 + 0.923589i \(0.374759\pi\)
\(150\) 23.5296 1.92118
\(151\) 15.1816 1.23546 0.617731 0.786390i \(-0.288052\pi\)
0.617731 + 0.786390i \(0.288052\pi\)
\(152\) −54.0139 −4.38111
\(153\) −2.77006 −0.223946
\(154\) 1.29945 0.104713
\(155\) 34.4472 2.76686
\(156\) −23.7885 −1.90460
\(157\) −15.4687 −1.23454 −0.617270 0.786752i \(-0.711761\pi\)
−0.617270 + 0.786752i \(0.711761\pi\)
\(158\) −20.5378 −1.63390
\(159\) −3.59373 −0.285001
\(160\) −60.8502 −4.81063
\(161\) −3.65723 −0.288230
\(162\) 6.04598 0.475017
\(163\) 14.0081 1.09720 0.548601 0.836085i \(-0.315161\pi\)
0.548601 + 0.836085i \(0.315161\pi\)
\(164\) 0.277059 0.0216347
\(165\) 0.434621 0.0338352
\(166\) 7.02587 0.545313
\(167\) 6.61321 0.511746 0.255873 0.966710i \(-0.417637\pi\)
0.255873 + 0.966710i \(0.417637\pi\)
\(168\) 50.5992 3.90381
\(169\) 0.749815 0.0576781
\(170\) −17.3075 −1.32743
\(171\) −9.30032 −0.711213
\(172\) −27.6321 −2.10693
\(173\) −11.5099 −0.875081 −0.437540 0.899199i \(-0.644150\pi\)
−0.437540 + 0.899199i \(0.644150\pi\)
\(174\) −26.1654 −1.98359
\(175\) 33.8633 2.55983
\(176\) −1.32094 −0.0995695
\(177\) 3.50152 0.263191
\(178\) −14.2614 −1.06894
\(179\) −4.51739 −0.337645 −0.168823 0.985646i \(-0.553997\pi\)
−0.168823 + 0.985646i \(0.553997\pi\)
\(180\) −27.3912 −2.04162
\(181\) −9.54177 −0.709234 −0.354617 0.935012i \(-0.615389\pi\)
−0.354617 + 0.935012i \(0.615389\pi\)
\(182\) −47.3058 −3.50654
\(183\) 9.11799 0.674021
\(184\) 6.72140 0.495508
\(185\) 28.5833 2.10148
\(186\) 32.5707 2.38820
\(187\) −0.188041 −0.0137510
\(188\) −54.1884 −3.95209
\(189\) 26.1315 1.90079
\(190\) −58.1092 −4.21568
\(191\) 6.36925 0.460863 0.230431 0.973089i \(-0.425986\pi\)
0.230431 + 0.973089i \(0.425986\pi\)
\(192\) −25.7745 −1.86011
\(193\) 14.3046 1.02967 0.514835 0.857290i \(-0.327853\pi\)
0.514835 + 0.857290i \(0.327853\pi\)
\(194\) −32.0131 −2.29840
\(195\) −15.8221 −1.13304
\(196\) 81.1155 5.79396
\(197\) 9.00492 0.641574 0.320787 0.947151i \(-0.396053\pi\)
0.320787 + 0.947151i \(0.396053\pi\)
\(198\) −0.411207 −0.0292232
\(199\) −10.3462 −0.733424 −0.366712 0.930335i \(-0.619517\pi\)
−0.366712 + 0.930335i \(0.619517\pi\)
\(200\) −62.2354 −4.40071
\(201\) 10.6797 0.753288
\(202\) −24.4396 −1.71957
\(203\) −37.6567 −2.64298
\(204\) −11.8434 −0.829206
\(205\) 0.184277 0.0128704
\(206\) 10.4782 0.730051
\(207\) 1.15732 0.0804390
\(208\) 48.0880 3.33430
\(209\) −0.631339 −0.0436707
\(210\) 54.4355 3.75641
\(211\) −9.06806 −0.624271 −0.312136 0.950038i \(-0.601044\pi\)
−0.312136 + 0.950038i \(0.601044\pi\)
\(212\) 15.3749 1.05595
\(213\) −20.4182 −1.39903
\(214\) 33.3857 2.28220
\(215\) −18.3786 −1.25341
\(216\) −48.0256 −3.26773
\(217\) 46.8753 3.18210
\(218\) 41.4170 2.80511
\(219\) 5.09490 0.344281
\(220\) −1.85941 −0.125362
\(221\) 6.84554 0.460481
\(222\) 27.0263 1.81388
\(223\) −11.5714 −0.774878 −0.387439 0.921895i \(-0.626640\pi\)
−0.387439 + 0.921895i \(0.626640\pi\)
\(224\) −82.8041 −5.53258
\(225\) −10.7159 −0.714395
\(226\) −24.0502 −1.59979
\(227\) 16.7767 1.11351 0.556755 0.830677i \(-0.312046\pi\)
0.556755 + 0.830677i \(0.312046\pi\)
\(228\) −39.7637 −2.63341
\(229\) −8.12271 −0.536764 −0.268382 0.963313i \(-0.586489\pi\)
−0.268382 + 0.963313i \(0.586489\pi\)
\(230\) 7.23100 0.476798
\(231\) 0.591426 0.0389130
\(232\) 69.2071 4.54367
\(233\) 15.2388 0.998328 0.499164 0.866507i \(-0.333640\pi\)
0.499164 + 0.866507i \(0.333640\pi\)
\(234\) 14.9698 0.978604
\(235\) −36.0416 −2.35109
\(236\) −14.9804 −0.975139
\(237\) −9.34746 −0.607183
\(238\) −23.5519 −1.52664
\(239\) −27.7155 −1.79276 −0.896382 0.443282i \(-0.853814\pi\)
−0.896382 + 0.443282i \(0.853814\pi\)
\(240\) −55.3355 −3.57189
\(241\) −15.5764 −1.00336 −0.501682 0.865052i \(-0.667285\pi\)
−0.501682 + 0.865052i \(0.667285\pi\)
\(242\) 29.5679 1.90069
\(243\) −13.7814 −0.884080
\(244\) −39.0090 −2.49729
\(245\) 53.9512 3.44682
\(246\) 0.174239 0.0111090
\(247\) 22.9835 1.46241
\(248\) −86.1492 −5.47048
\(249\) 3.19771 0.202647
\(250\) −20.0784 −1.26987
\(251\) −7.64429 −0.482503 −0.241252 0.970463i \(-0.577558\pi\)
−0.241252 + 0.970463i \(0.577558\pi\)
\(252\) −37.2735 −2.34801
\(253\) 0.0785628 0.00493920
\(254\) −44.0841 −2.76608
\(255\) −7.87726 −0.493293
\(256\) 16.2993 1.01871
\(257\) 5.08550 0.317225 0.158613 0.987341i \(-0.449298\pi\)
0.158613 + 0.987341i \(0.449298\pi\)
\(258\) −17.3774 −1.08187
\(259\) 38.8957 2.41686
\(260\) 67.6908 4.19800
\(261\) 11.9163 0.737602
\(262\) −28.1561 −1.73949
\(263\) 14.3888 0.887252 0.443626 0.896212i \(-0.353692\pi\)
0.443626 + 0.896212i \(0.353692\pi\)
\(264\) −1.08695 −0.0668970
\(265\) 10.2261 0.628182
\(266\) −79.0742 −4.84835
\(267\) −6.49085 −0.397234
\(268\) −45.6904 −2.79098
\(269\) 1.68319 0.102626 0.0513130 0.998683i \(-0.483659\pi\)
0.0513130 + 0.998683i \(0.483659\pi\)
\(270\) −51.6668 −3.14434
\(271\) −23.7938 −1.44537 −0.722686 0.691177i \(-0.757093\pi\)
−0.722686 + 0.691177i \(0.757093\pi\)
\(272\) 23.9413 1.45165
\(273\) −21.5305 −1.30309
\(274\) −22.2346 −1.34324
\(275\) −0.727436 −0.0438660
\(276\) 4.94813 0.297842
\(277\) −1.13517 −0.0682057 −0.0341028 0.999418i \(-0.510857\pi\)
−0.0341028 + 0.999418i \(0.510857\pi\)
\(278\) 57.7788 3.46534
\(279\) −14.8335 −0.888058
\(280\) −143.981 −8.60453
\(281\) −9.92821 −0.592268 −0.296134 0.955146i \(-0.595697\pi\)
−0.296134 + 0.955146i \(0.595697\pi\)
\(282\) −34.0783 −2.02933
\(283\) 8.82254 0.524445 0.262223 0.965007i \(-0.415545\pi\)
0.262223 + 0.965007i \(0.415545\pi\)
\(284\) 87.3539 5.18350
\(285\) −26.4475 −1.56661
\(286\) 1.01620 0.0600893
\(287\) 0.250761 0.0148020
\(288\) 26.2030 1.54403
\(289\) −13.5919 −0.799521
\(290\) 74.4542 4.37210
\(291\) −14.5702 −0.854123
\(292\) −21.7972 −1.27559
\(293\) −9.50459 −0.555264 −0.277632 0.960688i \(-0.589550\pi\)
−0.277632 + 0.960688i \(0.589550\pi\)
\(294\) 51.0124 2.97510
\(295\) −9.96369 −0.580108
\(296\) −71.4841 −4.15493
\(297\) −0.561345 −0.0325725
\(298\) −25.1822 −1.45876
\(299\) −2.86003 −0.165400
\(300\) −45.8161 −2.64520
\(301\) −25.0093 −1.44151
\(302\) −40.8465 −2.35045
\(303\) −11.1233 −0.639017
\(304\) 80.3816 4.61020
\(305\) −25.9455 −1.48563
\(306\) 7.45290 0.426054
\(307\) 8.38054 0.478302 0.239151 0.970982i \(-0.423131\pi\)
0.239151 + 0.970982i \(0.423131\pi\)
\(308\) −2.53026 −0.144175
\(309\) 4.76899 0.271299
\(310\) −92.6809 −5.26392
\(311\) −22.5970 −1.28136 −0.640680 0.767808i \(-0.721347\pi\)
−0.640680 + 0.767808i \(0.721347\pi\)
\(312\) 39.5697 2.24019
\(313\) −1.68212 −0.0950790 −0.0475395 0.998869i \(-0.515138\pi\)
−0.0475395 + 0.998869i \(0.515138\pi\)
\(314\) 41.6190 2.34870
\(315\) −24.7912 −1.39683
\(316\) 39.9907 2.24965
\(317\) −18.2743 −1.02639 −0.513194 0.858272i \(-0.671538\pi\)
−0.513194 + 0.858272i \(0.671538\pi\)
\(318\) 9.66902 0.542212
\(319\) 0.808924 0.0452910
\(320\) 73.3419 4.09994
\(321\) 15.1950 0.848101
\(322\) 9.83986 0.548354
\(323\) 11.4427 0.636687
\(324\) −11.7726 −0.654032
\(325\) 26.4819 1.46895
\(326\) −37.6892 −2.08741
\(327\) 18.8503 1.04242
\(328\) −0.460859 −0.0254467
\(329\) −49.0449 −2.70393
\(330\) −1.16936 −0.0643710
\(331\) −9.89268 −0.543751 −0.271875 0.962332i \(-0.587644\pi\)
−0.271875 + 0.962332i \(0.587644\pi\)
\(332\) −13.6806 −0.750820
\(333\) −12.3084 −0.674497
\(334\) −17.7930 −0.973590
\(335\) −30.3894 −1.66035
\(336\) −75.2999 −4.10794
\(337\) −6.25247 −0.340594 −0.170297 0.985393i \(-0.554473\pi\)
−0.170297 + 0.985393i \(0.554473\pi\)
\(338\) −2.01740 −0.109732
\(339\) −10.9461 −0.594509
\(340\) 33.7008 1.82768
\(341\) −1.00695 −0.0545295
\(342\) 25.0227 1.35307
\(343\) 40.2246 2.17192
\(344\) 45.9631 2.47817
\(345\) 3.29108 0.177186
\(346\) 30.9676 1.66483
\(347\) 17.1445 0.920364 0.460182 0.887824i \(-0.347784\pi\)
0.460182 + 0.887824i \(0.347784\pi\)
\(348\) 50.9485 2.73113
\(349\) −32.4368 −1.73630 −0.868150 0.496302i \(-0.834691\pi\)
−0.868150 + 0.496302i \(0.834691\pi\)
\(350\) −91.1101 −4.87004
\(351\) 20.4354 1.09076
\(352\) 1.77876 0.0948081
\(353\) 25.9028 1.37867 0.689333 0.724445i \(-0.257904\pi\)
0.689333 + 0.724445i \(0.257904\pi\)
\(354\) −9.42094 −0.500717
\(355\) 58.1005 3.08366
\(356\) 27.7694 1.47178
\(357\) −10.7193 −0.567324
\(358\) 12.1541 0.642366
\(359\) −9.41033 −0.496658 −0.248329 0.968676i \(-0.579881\pi\)
−0.248329 + 0.968676i \(0.579881\pi\)
\(360\) 45.5623 2.40135
\(361\) 19.4182 1.02201
\(362\) 25.6724 1.34931
\(363\) 13.4573 0.706327
\(364\) 92.1127 4.82802
\(365\) −14.4977 −0.758843
\(366\) −24.5322 −1.28232
\(367\) 7.98013 0.416559 0.208280 0.978069i \(-0.433214\pi\)
0.208280 + 0.978069i \(0.433214\pi\)
\(368\) −10.0025 −0.521419
\(369\) −0.0793524 −0.00413092
\(370\) −76.9040 −3.99805
\(371\) 13.9155 0.722456
\(372\) −63.4209 −3.28822
\(373\) −27.7050 −1.43451 −0.717255 0.696811i \(-0.754602\pi\)
−0.717255 + 0.696811i \(0.754602\pi\)
\(374\) 0.505930 0.0261610
\(375\) −9.13839 −0.471904
\(376\) 90.1367 4.64844
\(377\) −29.4484 −1.51667
\(378\) −70.3075 −3.61623
\(379\) 8.04396 0.413191 0.206595 0.978426i \(-0.433762\pi\)
0.206595 + 0.978426i \(0.433762\pi\)
\(380\) 113.149 5.80441
\(381\) −20.0642 −1.02792
\(382\) −17.1366 −0.876786
\(383\) −5.00399 −0.255692 −0.127846 0.991794i \(-0.540806\pi\)
−0.127846 + 0.991794i \(0.540806\pi\)
\(384\) 26.5778 1.35629
\(385\) −1.68292 −0.0857695
\(386\) −38.4869 −1.95893
\(387\) 7.91410 0.402296
\(388\) 62.3350 3.16458
\(389\) −25.6084 −1.29840 −0.649200 0.760618i \(-0.724896\pi\)
−0.649200 + 0.760618i \(0.724896\pi\)
\(390\) 42.5698 2.15560
\(391\) −1.42391 −0.0720101
\(392\) −134.927 −6.81485
\(393\) −12.8148 −0.646421
\(394\) −24.2280 −1.22059
\(395\) 26.5985 1.33831
\(396\) 0.800692 0.0402363
\(397\) 30.9302 1.55234 0.776172 0.630521i \(-0.217159\pi\)
0.776172 + 0.630521i \(0.217159\pi\)
\(398\) 27.8367 1.39533
\(399\) −35.9894 −1.80172
\(400\) 92.6165 4.63082
\(401\) 12.6558 0.632001 0.316001 0.948759i \(-0.397660\pi\)
0.316001 + 0.948759i \(0.397660\pi\)
\(402\) −28.7340 −1.43312
\(403\) 36.6575 1.82604
\(404\) 47.5882 2.36760
\(405\) −7.83013 −0.389082
\(406\) 101.316 5.02825
\(407\) −0.835539 −0.0414162
\(408\) 19.7003 0.975310
\(409\) 31.2671 1.54606 0.773029 0.634370i \(-0.218740\pi\)
0.773029 + 0.634370i \(0.218740\pi\)
\(410\) −0.495801 −0.0244858
\(411\) −10.1197 −0.499169
\(412\) −20.4029 −1.00518
\(413\) −13.5585 −0.667168
\(414\) −3.11379 −0.153034
\(415\) −9.09918 −0.446661
\(416\) −64.7546 −3.17486
\(417\) 26.2971 1.28778
\(418\) 1.69863 0.0830829
\(419\) 11.9524 0.583911 0.291955 0.956432i \(-0.405694\pi\)
0.291955 + 0.956432i \(0.405694\pi\)
\(420\) −105.995 −5.17205
\(421\) 30.4104 1.48211 0.741057 0.671442i \(-0.234325\pi\)
0.741057 + 0.671442i \(0.234325\pi\)
\(422\) 24.3978 1.18767
\(423\) 15.5201 0.754612
\(424\) −25.5745 −1.24201
\(425\) 13.1844 0.639536
\(426\) 54.9356 2.66164
\(427\) −35.3063 −1.70859
\(428\) −65.0078 −3.14227
\(429\) 0.462508 0.0223301
\(430\) 49.4480 2.38459
\(431\) −10.8315 −0.521735 −0.260868 0.965375i \(-0.584009\pi\)
−0.260868 + 0.965375i \(0.584009\pi\)
\(432\) 71.4699 3.43860
\(433\) 28.8223 1.38511 0.692555 0.721365i \(-0.256485\pi\)
0.692555 + 0.721365i \(0.256485\pi\)
\(434\) −126.119 −6.05391
\(435\) 33.8867 1.62474
\(436\) −80.6462 −3.86225
\(437\) −4.78069 −0.228691
\(438\) −13.7079 −0.654991
\(439\) 2.88085 0.137496 0.0687478 0.997634i \(-0.478100\pi\)
0.0687478 + 0.997634i \(0.478100\pi\)
\(440\) 3.09294 0.147450
\(441\) −23.2323 −1.10630
\(442\) −18.4181 −0.876059
\(443\) −31.0601 −1.47571 −0.737855 0.674959i \(-0.764161\pi\)
−0.737855 + 0.674959i \(0.764161\pi\)
\(444\) −52.6248 −2.49746
\(445\) 18.4699 0.875557
\(446\) 31.1331 1.47420
\(447\) −11.4613 −0.542100
\(448\) 99.8027 4.71524
\(449\) −8.93178 −0.421517 −0.210758 0.977538i \(-0.567593\pi\)
−0.210758 + 0.977538i \(0.567593\pi\)
\(450\) 28.8315 1.35913
\(451\) −0.00538673 −0.000253651 0
\(452\) 46.8299 2.20269
\(453\) −18.5906 −0.873464
\(454\) −45.1381 −2.11844
\(455\) 61.2657 2.87218
\(456\) 66.1427 3.09742
\(457\) −27.6639 −1.29406 −0.647032 0.762463i \(-0.723990\pi\)
−0.647032 + 0.762463i \(0.723990\pi\)
\(458\) 21.8544 1.02119
\(459\) 10.1741 0.474884
\(460\) −14.0800 −0.656485
\(461\) 28.3363 1.31975 0.659877 0.751374i \(-0.270608\pi\)
0.659877 + 0.751374i \(0.270608\pi\)
\(462\) −1.59125 −0.0740315
\(463\) −24.3654 −1.13236 −0.566179 0.824282i \(-0.691579\pi\)
−0.566179 + 0.824282i \(0.691579\pi\)
\(464\) −102.991 −4.78126
\(465\) −42.1823 −1.95616
\(466\) −41.0004 −1.89931
\(467\) 16.6816 0.771933 0.385967 0.922513i \(-0.373868\pi\)
0.385967 + 0.922513i \(0.373868\pi\)
\(468\) −29.1487 −1.34740
\(469\) −41.3535 −1.90953
\(470\) 96.9707 4.47292
\(471\) 18.9422 0.872812
\(472\) 24.9183 1.14696
\(473\) 0.537238 0.0247022
\(474\) 25.1496 1.15516
\(475\) 44.2658 2.03106
\(476\) 45.8596 2.10197
\(477\) −4.40350 −0.201623
\(478\) 74.5691 3.41071
\(479\) −23.1977 −1.05993 −0.529964 0.848020i \(-0.677795\pi\)
−0.529964 + 0.848020i \(0.677795\pi\)
\(480\) 74.5141 3.40109
\(481\) 30.4173 1.38691
\(482\) 41.9087 1.90889
\(483\) 4.47846 0.203777
\(484\) −57.5738 −2.61699
\(485\) 41.4600 1.88260
\(486\) 37.0793 1.68195
\(487\) −5.42166 −0.245679 −0.122839 0.992427i \(-0.539200\pi\)
−0.122839 + 0.992427i \(0.539200\pi\)
\(488\) 64.8873 2.93731
\(489\) −17.1537 −0.775715
\(490\) −145.157 −6.55753
\(491\) 35.3271 1.59429 0.797145 0.603788i \(-0.206343\pi\)
0.797145 + 0.603788i \(0.206343\pi\)
\(492\) −0.339273 −0.0152956
\(493\) −14.6613 −0.660311
\(494\) −61.8378 −2.78221
\(495\) 0.532553 0.0239365
\(496\) 128.204 5.75654
\(497\) 79.0624 3.54643
\(498\) −8.60353 −0.385533
\(499\) −4.73592 −0.212009 −0.106004 0.994366i \(-0.533806\pi\)
−0.106004 + 0.994366i \(0.533806\pi\)
\(500\) 39.0962 1.74844
\(501\) −8.09821 −0.361801
\(502\) 20.5672 0.917957
\(503\) −26.7346 −1.19204 −0.596019 0.802971i \(-0.703252\pi\)
−0.596019 + 0.802971i \(0.703252\pi\)
\(504\) 62.0006 2.76173
\(505\) 31.6517 1.40848
\(506\) −0.211375 −0.00939677
\(507\) −0.918186 −0.0407781
\(508\) 85.8394 3.80851
\(509\) −22.8187 −1.01142 −0.505710 0.862703i \(-0.668770\pi\)
−0.505710 + 0.862703i \(0.668770\pi\)
\(510\) 21.1939 0.938484
\(511\) −19.7282 −0.872726
\(512\) −0.445477 −0.0196875
\(513\) 34.1589 1.50815
\(514\) −13.6827 −0.603517
\(515\) −13.5703 −0.597979
\(516\) 33.8369 1.48959
\(517\) 1.05356 0.0463355
\(518\) −104.650 −4.59805
\(519\) 14.0944 0.618677
\(520\) −112.597 −4.93768
\(521\) 17.4065 0.762592 0.381296 0.924453i \(-0.375478\pi\)
0.381296 + 0.924453i \(0.375478\pi\)
\(522\) −32.0612 −1.40328
\(523\) 23.6414 1.03377 0.516884 0.856056i \(-0.327092\pi\)
0.516884 + 0.856056i \(0.327092\pi\)
\(524\) 54.8248 2.39503
\(525\) −41.4673 −1.80978
\(526\) −38.7135 −1.68799
\(527\) 18.2504 0.795002
\(528\) 1.61756 0.0703951
\(529\) −22.4051 −0.974135
\(530\) −27.5135 −1.19511
\(531\) 4.29052 0.186193
\(532\) 153.971 6.67550
\(533\) 0.196101 0.00849407
\(534\) 17.4638 0.755732
\(535\) −43.2377 −1.86933
\(536\) 76.0011 3.28275
\(537\) 5.53176 0.238713
\(538\) −4.52867 −0.195245
\(539\) −1.57709 −0.0679301
\(540\) 100.604 4.32932
\(541\) 23.3037 1.00190 0.500951 0.865475i \(-0.332984\pi\)
0.500951 + 0.865475i \(0.332984\pi\)
\(542\) 64.0179 2.74980
\(543\) 11.6844 0.501424
\(544\) −32.2390 −1.38224
\(545\) −53.6391 −2.29765
\(546\) 57.9284 2.47911
\(547\) −20.2022 −0.863782 −0.431891 0.901926i \(-0.642153\pi\)
−0.431891 + 0.901926i \(0.642153\pi\)
\(548\) 43.2946 1.84945
\(549\) 11.1725 0.476833
\(550\) 1.95718 0.0834546
\(551\) −49.2245 −2.09703
\(552\) −8.23069 −0.350321
\(553\) 36.1948 1.53916
\(554\) 3.05420 0.129761
\(555\) −35.0016 −1.48574
\(556\) −112.505 −4.77129
\(557\) −25.7948 −1.09296 −0.546481 0.837471i \(-0.684033\pi\)
−0.546481 + 0.837471i \(0.684033\pi\)
\(558\) 39.9099 1.68952
\(559\) −19.5578 −0.827208
\(560\) 214.268 9.05447
\(561\) 0.230266 0.00972185
\(562\) 26.7121 1.12678
\(563\) 22.4751 0.947214 0.473607 0.880736i \(-0.342952\pi\)
0.473607 + 0.880736i \(0.342952\pi\)
\(564\) 66.3564 2.79411
\(565\) 31.1473 1.31038
\(566\) −23.7372 −0.997751
\(567\) −10.6551 −0.447474
\(568\) −145.304 −6.09683
\(569\) −34.5715 −1.44931 −0.724657 0.689110i \(-0.758002\pi\)
−0.724657 + 0.689110i \(0.758002\pi\)
\(570\) 71.1576 2.98046
\(571\) −7.49016 −0.313454 −0.156727 0.987642i \(-0.550094\pi\)
−0.156727 + 0.987642i \(0.550094\pi\)
\(572\) −1.97872 −0.0827345
\(573\) −7.79946 −0.325827
\(574\) −0.674679 −0.0281606
\(575\) −5.50836 −0.229715
\(576\) −31.5822 −1.31593
\(577\) −39.4227 −1.64119 −0.820594 0.571512i \(-0.806357\pi\)
−0.820594 + 0.571512i \(0.806357\pi\)
\(578\) 36.5692 1.52108
\(579\) −17.5167 −0.727970
\(580\) −144.975 −6.01978
\(581\) −12.3820 −0.513694
\(582\) 39.2016 1.62496
\(583\) −0.298926 −0.0123802
\(584\) 36.2574 1.50034
\(585\) −19.3873 −0.801566
\(586\) 25.5723 1.05638
\(587\) 8.28897 0.342122 0.171061 0.985260i \(-0.445280\pi\)
0.171061 + 0.985260i \(0.445280\pi\)
\(588\) −99.3300 −4.09630
\(589\) 61.2749 2.52479
\(590\) 26.8075 1.10365
\(591\) −11.0270 −0.453589
\(592\) 106.380 4.37220
\(593\) 26.7614 1.09896 0.549480 0.835507i \(-0.314826\pi\)
0.549480 + 0.835507i \(0.314826\pi\)
\(594\) 1.51031 0.0619688
\(595\) 30.5020 1.25046
\(596\) 49.0341 2.00851
\(597\) 12.6695 0.518526
\(598\) 7.69498 0.314671
\(599\) −35.3536 −1.44451 −0.722255 0.691627i \(-0.756894\pi\)
−0.722255 + 0.691627i \(0.756894\pi\)
\(600\) 76.2104 3.11127
\(601\) 30.0631 1.22630 0.613150 0.789966i \(-0.289902\pi\)
0.613150 + 0.789966i \(0.289902\pi\)
\(602\) 67.2882 2.74246
\(603\) 13.0862 0.532909
\(604\) 79.5352 3.23624
\(605\) −38.2932 −1.55684
\(606\) 29.9275 1.21572
\(607\) −32.4269 −1.31617 −0.658084 0.752945i \(-0.728633\pi\)
−0.658084 + 0.752945i \(0.728633\pi\)
\(608\) −108.241 −4.38974
\(609\) 46.1125 1.86857
\(610\) 69.8070 2.82640
\(611\) −38.3542 −1.55164
\(612\) −14.5121 −0.586617
\(613\) 3.78794 0.152993 0.0764967 0.997070i \(-0.475627\pi\)
0.0764967 + 0.997070i \(0.475627\pi\)
\(614\) −22.5480 −0.909965
\(615\) −0.225656 −0.00909932
\(616\) 4.20883 0.169579
\(617\) −15.4029 −0.620098 −0.310049 0.950721i \(-0.600345\pi\)
−0.310049 + 0.950721i \(0.600345\pi\)
\(618\) −12.8311 −0.516142
\(619\) −28.5500 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(620\) 180.466 7.24769
\(621\) −4.25067 −0.170574
\(622\) 60.7978 2.43777
\(623\) 25.1336 1.00696
\(624\) −58.8861 −2.35733
\(625\) −9.70484 −0.388194
\(626\) 4.52578 0.180887
\(627\) 0.773107 0.0308749
\(628\) −81.0395 −3.23383
\(629\) 15.1437 0.603818
\(630\) 66.7014 2.65745
\(631\) −28.2180 −1.12334 −0.561670 0.827361i \(-0.689841\pi\)
−0.561670 + 0.827361i \(0.689841\pi\)
\(632\) −66.5203 −2.64604
\(633\) 11.1043 0.441356
\(634\) 49.1675 1.95269
\(635\) 57.0932 2.26567
\(636\) −18.8273 −0.746550
\(637\) 57.4130 2.27479
\(638\) −2.17643 −0.0861657
\(639\) −25.0190 −0.989737
\(640\) −75.6279 −2.98946
\(641\) 14.2454 0.562660 0.281330 0.959611i \(-0.409225\pi\)
0.281330 + 0.959611i \(0.409225\pi\)
\(642\) −40.8824 −1.61350
\(643\) 30.0818 1.18631 0.593156 0.805088i \(-0.297882\pi\)
0.593156 + 0.805088i \(0.297882\pi\)
\(644\) −19.1599 −0.755007
\(645\) 22.5055 0.886152
\(646\) −30.7868 −1.21129
\(647\) −34.1451 −1.34238 −0.671192 0.741284i \(-0.734217\pi\)
−0.671192 + 0.741284i \(0.734217\pi\)
\(648\) 19.5824 0.769271
\(649\) 0.291256 0.0114328
\(650\) −71.2501 −2.79466
\(651\) −57.4011 −2.24973
\(652\) 73.3875 2.87408
\(653\) 46.1820 1.80724 0.903621 0.428334i \(-0.140899\pi\)
0.903621 + 0.428334i \(0.140899\pi\)
\(654\) −50.7172 −1.98320
\(655\) 36.4649 1.42480
\(656\) 0.685834 0.0267773
\(657\) 6.24293 0.243560
\(658\) 131.956 5.14420
\(659\) −18.2059 −0.709201 −0.354600 0.935018i \(-0.615383\pi\)
−0.354600 + 0.935018i \(0.615383\pi\)
\(660\) 2.27694 0.0886299
\(661\) −22.6590 −0.881334 −0.440667 0.897671i \(-0.645258\pi\)
−0.440667 + 0.897671i \(0.645258\pi\)
\(662\) 26.6165 1.03448
\(663\) −8.38270 −0.325557
\(664\) 22.7562 0.883113
\(665\) 102.409 3.97124
\(666\) 33.1161 1.28322
\(667\) 6.12541 0.237177
\(668\) 34.6461 1.34050
\(669\) 14.1698 0.547834
\(670\) 81.7634 3.15880
\(671\) 0.758433 0.0292790
\(672\) 101.398 3.91150
\(673\) 15.2435 0.587592 0.293796 0.955868i \(-0.405081\pi\)
0.293796 + 0.955868i \(0.405081\pi\)
\(674\) 16.8224 0.647976
\(675\) 39.3582 1.51490
\(676\) 3.92822 0.151085
\(677\) −12.8476 −0.493775 −0.246888 0.969044i \(-0.579408\pi\)
−0.246888 + 0.969044i \(0.579408\pi\)
\(678\) 29.4507 1.13105
\(679\) 56.4183 2.16514
\(680\) −56.0578 −2.14972
\(681\) −20.5439 −0.787245
\(682\) 2.70923 0.103742
\(683\) 11.6100 0.444243 0.222121 0.975019i \(-0.428702\pi\)
0.222121 + 0.975019i \(0.428702\pi\)
\(684\) −48.7236 −1.86299
\(685\) 28.7959 1.10024
\(686\) −108.225 −4.13206
\(687\) 9.94667 0.379489
\(688\) −68.4007 −2.60775
\(689\) 10.8822 0.414580
\(690\) −8.85473 −0.337094
\(691\) −27.7625 −1.05614 −0.528068 0.849202i \(-0.677083\pi\)
−0.528068 + 0.849202i \(0.677083\pi\)
\(692\) −60.2994 −2.29224
\(693\) 0.724692 0.0275288
\(694\) −46.1277 −1.75098
\(695\) −74.8292 −2.83843
\(696\) −84.7475 −3.21235
\(697\) 0.0976315 0.00369806
\(698\) 87.2719 3.30329
\(699\) −18.6607 −0.705812
\(700\) 177.407 6.70537
\(701\) −32.5900 −1.23091 −0.615453 0.788173i \(-0.711027\pi\)
−0.615453 + 0.788173i \(0.711027\pi\)
\(702\) −54.9820 −2.07516
\(703\) 50.8441 1.91762
\(704\) −2.14391 −0.0808018
\(705\) 44.1347 1.66221
\(706\) −69.6920 −2.62289
\(707\) 43.0712 1.61986
\(708\) 18.3442 0.689418
\(709\) 5.99547 0.225165 0.112582 0.993642i \(-0.464088\pi\)
0.112582 + 0.993642i \(0.464088\pi\)
\(710\) −156.321 −5.86662
\(711\) −11.4537 −0.429548
\(712\) −46.1915 −1.73110
\(713\) −7.62494 −0.285556
\(714\) 28.8404 1.07933
\(715\) −1.31608 −0.0492186
\(716\) −23.6662 −0.884448
\(717\) 33.9390 1.26747
\(718\) 25.3187 0.944886
\(719\) −37.1135 −1.38410 −0.692050 0.721850i \(-0.743292\pi\)
−0.692050 + 0.721850i \(0.743292\pi\)
\(720\) −67.8042 −2.52691
\(721\) −18.4663 −0.687720
\(722\) −52.2451 −1.94436
\(723\) 19.0741 0.709372
\(724\) −49.9886 −1.85781
\(725\) −56.7170 −2.10642
\(726\) −36.2073 −1.34378
\(727\) −1.46708 −0.0544110 −0.0272055 0.999630i \(-0.508661\pi\)
−0.0272055 + 0.999630i \(0.508661\pi\)
\(728\) −153.220 −5.67871
\(729\) 23.6175 0.874722
\(730\) 39.0063 1.44369
\(731\) −9.73714 −0.360141
\(732\) 47.7684 1.76557
\(733\) 40.8976 1.51059 0.755295 0.655386i \(-0.227494\pi\)
0.755295 + 0.655386i \(0.227494\pi\)
\(734\) −21.4707 −0.792499
\(735\) −66.0660 −2.43688
\(736\) 13.4693 0.496485
\(737\) 0.888336 0.0327223
\(738\) 0.213500 0.00785903
\(739\) 1.22727 0.0451457 0.0225728 0.999745i \(-0.492814\pi\)
0.0225728 + 0.999745i \(0.492814\pi\)
\(740\) 149.745 5.50475
\(741\) −28.1445 −1.03391
\(742\) −37.4400 −1.37446
\(743\) −30.3102 −1.11197 −0.555986 0.831192i \(-0.687659\pi\)
−0.555986 + 0.831192i \(0.687659\pi\)
\(744\) 105.494 3.86760
\(745\) 32.6134 1.19486
\(746\) 74.5409 2.72914
\(747\) 3.91825 0.143361
\(748\) −0.985134 −0.0360201
\(749\) −58.8373 −2.14987
\(750\) 24.5871 0.897793
\(751\) 25.3132 0.923693 0.461847 0.886960i \(-0.347187\pi\)
0.461847 + 0.886960i \(0.347187\pi\)
\(752\) −134.138 −4.89152
\(753\) 9.36082 0.341127
\(754\) 79.2316 2.88544
\(755\) 52.9001 1.92523
\(756\) 136.901 4.97904
\(757\) 14.6495 0.532446 0.266223 0.963911i \(-0.414224\pi\)
0.266223 + 0.963911i \(0.414224\pi\)
\(758\) −21.6425 −0.786090
\(759\) −0.0962041 −0.00349199
\(760\) −188.211 −6.82713
\(761\) 15.0204 0.544487 0.272244 0.962228i \(-0.412234\pi\)
0.272244 + 0.962228i \(0.412234\pi\)
\(762\) 53.9832 1.95560
\(763\) −72.9913 −2.64246
\(764\) 33.3680 1.20721
\(765\) −9.65223 −0.348977
\(766\) 13.4634 0.486451
\(767\) −10.6030 −0.382852
\(768\) −19.9594 −0.720222
\(769\) 4.96410 0.179010 0.0895050 0.995986i \(-0.471471\pi\)
0.0895050 + 0.995986i \(0.471471\pi\)
\(770\) 4.52794 0.163175
\(771\) −6.22745 −0.224276
\(772\) 74.9408 2.69718
\(773\) 43.8007 1.57540 0.787701 0.616058i \(-0.211271\pi\)
0.787701 + 0.616058i \(0.211271\pi\)
\(774\) −21.2931 −0.765364
\(775\) 70.6016 2.53608
\(776\) −103.688 −3.72218
\(777\) −47.6298 −1.70871
\(778\) 68.9001 2.47019
\(779\) 0.327793 0.0117444
\(780\) −82.8908 −2.96797
\(781\) −1.69838 −0.0607729
\(782\) 3.83106 0.136998
\(783\) −43.7671 −1.56411
\(784\) 200.794 7.17120
\(785\) −53.9007 −1.92380
\(786\) 34.4785 1.22981
\(787\) −26.6270 −0.949152 −0.474576 0.880215i \(-0.657399\pi\)
−0.474576 + 0.880215i \(0.657399\pi\)
\(788\) 47.1761 1.68058
\(789\) −17.6198 −0.627282
\(790\) −71.5638 −2.54612
\(791\) 42.3849 1.50703
\(792\) −1.33187 −0.0473259
\(793\) −27.6103 −0.980470
\(794\) −83.2186 −2.95332
\(795\) −12.5223 −0.444121
\(796\) −54.2030 −1.92117
\(797\) 49.4424 1.75134 0.875670 0.482910i \(-0.160420\pi\)
0.875670 + 0.482910i \(0.160420\pi\)
\(798\) 96.8303 3.42776
\(799\) −19.0952 −0.675538
\(800\) −124.716 −4.40938
\(801\) −7.95343 −0.281021
\(802\) −34.0508 −1.20238
\(803\) 0.423793 0.0149553
\(804\) 55.9501 1.97321
\(805\) −12.7436 −0.449152
\(806\) −98.6278 −3.47402
\(807\) −2.06115 −0.0725560
\(808\) −79.1580 −2.78477
\(809\) 9.48953 0.333634 0.166817 0.985988i \(-0.446651\pi\)
0.166817 + 0.985988i \(0.446651\pi\)
\(810\) 21.0671 0.740224
\(811\) −18.4162 −0.646681 −0.323340 0.946283i \(-0.604806\pi\)
−0.323340 + 0.946283i \(0.604806\pi\)
\(812\) −197.281 −6.92319
\(813\) 29.1367 1.02187
\(814\) 2.24804 0.0787937
\(815\) 48.8112 1.70978
\(816\) −29.3173 −1.02631
\(817\) −32.6919 −1.14375
\(818\) −84.1249 −2.94136
\(819\) −26.3820 −0.921861
\(820\) 0.965411 0.0337136
\(821\) −9.97256 −0.348045 −0.174022 0.984742i \(-0.555677\pi\)
−0.174022 + 0.984742i \(0.555677\pi\)
\(822\) 27.2274 0.949663
\(823\) −15.7357 −0.548511 −0.274256 0.961657i \(-0.588431\pi\)
−0.274256 + 0.961657i \(0.588431\pi\)
\(824\) 33.9381 1.18229
\(825\) 0.890782 0.0310130
\(826\) 36.4793 1.26928
\(827\) −38.2246 −1.32920 −0.664601 0.747199i \(-0.731398\pi\)
−0.664601 + 0.747199i \(0.731398\pi\)
\(828\) 6.06308 0.210707
\(829\) 49.3887 1.71534 0.857670 0.514200i \(-0.171911\pi\)
0.857670 + 0.514200i \(0.171911\pi\)
\(830\) 24.4816 0.849768
\(831\) 1.39007 0.0482210
\(832\) 78.0479 2.70583
\(833\) 28.5839 0.990372
\(834\) −70.7530 −2.44998
\(835\) 23.0437 0.797459
\(836\) −3.30754 −0.114394
\(837\) 54.4815 1.88316
\(838\) −32.1581 −1.11088
\(839\) −18.5985 −0.642091 −0.321046 0.947064i \(-0.604034\pi\)
−0.321046 + 0.947064i \(0.604034\pi\)
\(840\) 176.312 6.08335
\(841\) 34.0705 1.17484
\(842\) −81.8200 −2.81970
\(843\) 12.1576 0.418730
\(844\) −47.5069 −1.63525
\(845\) 2.61272 0.0898804
\(846\) −41.7571 −1.43564
\(847\) −52.1090 −1.79048
\(848\) 38.0590 1.30695
\(849\) −10.8036 −0.370780
\(850\) −35.4729 −1.21671
\(851\) −6.32696 −0.216885
\(852\) −106.969 −3.66471
\(853\) −52.4880 −1.79715 −0.898577 0.438815i \(-0.855398\pi\)
−0.898577 + 0.438815i \(0.855398\pi\)
\(854\) 94.9924 3.25057
\(855\) −32.4069 −1.10829
\(856\) 108.134 3.69593
\(857\) 45.9719 1.57037 0.785185 0.619262i \(-0.212568\pi\)
0.785185 + 0.619262i \(0.212568\pi\)
\(858\) −1.24439 −0.0424828
\(859\) −44.6790 −1.52443 −0.762213 0.647326i \(-0.775887\pi\)
−0.762213 + 0.647326i \(0.775887\pi\)
\(860\) −96.2838 −3.28325
\(861\) −0.307070 −0.0104649
\(862\) 29.1424 0.992595
\(863\) −0.948035 −0.0322715 −0.0161357 0.999870i \(-0.505136\pi\)
−0.0161357 + 0.999870i \(0.505136\pi\)
\(864\) −96.2404 −3.27417
\(865\) −40.1061 −1.36365
\(866\) −77.5470 −2.63516
\(867\) 16.6439 0.565257
\(868\) 245.576 8.33538
\(869\) −0.777520 −0.0263756
\(870\) −91.1729 −3.09105
\(871\) −32.3393 −1.09578
\(872\) 134.146 4.54277
\(873\) −17.8534 −0.604245
\(874\) 12.8626 0.435083
\(875\) 35.3853 1.19624
\(876\) 26.6918 0.901831
\(877\) −44.1850 −1.49202 −0.746011 0.665933i \(-0.768034\pi\)
−0.746011 + 0.665933i \(0.768034\pi\)
\(878\) −7.75100 −0.261584
\(879\) 11.6388 0.392568
\(880\) −4.60280 −0.155160
\(881\) −38.4387 −1.29503 −0.647516 0.762052i \(-0.724192\pi\)
−0.647516 + 0.762052i \(0.724192\pi\)
\(882\) 62.5069 2.10472
\(883\) 49.9110 1.67964 0.839819 0.542866i \(-0.182661\pi\)
0.839819 + 0.542866i \(0.182661\pi\)
\(884\) 35.8632 1.20621
\(885\) 12.2010 0.410133
\(886\) 83.5680 2.80752
\(887\) 4.34039 0.145736 0.0728681 0.997342i \(-0.476785\pi\)
0.0728681 + 0.997342i \(0.476785\pi\)
\(888\) 87.5359 2.93751
\(889\) 77.6916 2.60569
\(890\) −49.6937 −1.66574
\(891\) 0.228888 0.00766805
\(892\) −60.6216 −2.02976
\(893\) −64.1110 −2.14539
\(894\) 30.8368 1.03134
\(895\) −15.7408 −0.526157
\(896\) −102.914 −3.43810
\(897\) 3.50225 0.116937
\(898\) 24.0312 0.801931
\(899\) −78.5104 −2.61847
\(900\) −56.1399 −1.87133
\(901\) 5.41786 0.180495
\(902\) 0.0144931 0.000482569 0
\(903\) 30.6252 1.01914
\(904\) −77.8966 −2.59080
\(905\) −33.2482 −1.10521
\(906\) 50.0185 1.66175
\(907\) −47.7832 −1.58662 −0.793308 0.608821i \(-0.791643\pi\)
−0.793308 + 0.608821i \(0.791643\pi\)
\(908\) 87.8919 2.91679
\(909\) −13.6297 −0.452069
\(910\) −164.837 −5.46429
\(911\) 45.3177 1.50144 0.750721 0.660619i \(-0.229706\pi\)
0.750721 + 0.660619i \(0.229706\pi\)
\(912\) −98.4312 −3.25938
\(913\) 0.265985 0.00880283
\(914\) 74.4305 2.46194
\(915\) 31.7716 1.05034
\(916\) −42.5543 −1.40603
\(917\) 49.6209 1.63863
\(918\) −27.3736 −0.903462
\(919\) 10.9476 0.361128 0.180564 0.983563i \(-0.442208\pi\)
0.180564 + 0.983563i \(0.442208\pi\)
\(920\) 23.4207 0.772156
\(921\) −10.2624 −0.338157
\(922\) −76.2396 −2.51082
\(923\) 61.8285 2.03511
\(924\) 3.09843 0.101931
\(925\) 58.5831 1.92620
\(926\) 65.5558 2.15430
\(927\) 5.84359 0.191929
\(928\) 138.687 4.55262
\(929\) 24.3472 0.798804 0.399402 0.916776i \(-0.369218\pi\)
0.399402 + 0.916776i \(0.369218\pi\)
\(930\) 113.492 3.72156
\(931\) 95.9688 3.14525
\(932\) 79.8350 2.61508
\(933\) 27.6712 0.905914
\(934\) −44.8823 −1.46859
\(935\) −0.655229 −0.0214283
\(936\) 48.4859 1.58481
\(937\) 55.8733 1.82530 0.912650 0.408742i \(-0.134032\pi\)
0.912650 + 0.408742i \(0.134032\pi\)
\(938\) 111.263 3.63285
\(939\) 2.05984 0.0672203
\(940\) −188.819 −6.15859
\(941\) 21.7427 0.708793 0.354396 0.935095i \(-0.384686\pi\)
0.354396 + 0.935095i \(0.384686\pi\)
\(942\) −50.9645 −1.66051
\(943\) −0.0407900 −0.00132830
\(944\) −37.0825 −1.20693
\(945\) 91.0550 2.96202
\(946\) −1.44545 −0.0469957
\(947\) −23.8511 −0.775056 −0.387528 0.921858i \(-0.626671\pi\)
−0.387528 + 0.921858i \(0.626671\pi\)
\(948\) −48.9706 −1.59049
\(949\) −15.4279 −0.500812
\(950\) −119.098 −3.86406
\(951\) 22.3778 0.725651
\(952\) −76.2827 −2.47234
\(953\) −6.65749 −0.215657 −0.107829 0.994169i \(-0.534390\pi\)
−0.107829 + 0.994169i \(0.534390\pi\)
\(954\) 11.8477 0.383585
\(955\) 22.1936 0.718168
\(956\) −145.199 −4.69607
\(957\) −0.990568 −0.0320205
\(958\) 62.4139 2.01650
\(959\) 39.1851 1.26535
\(960\) −89.8109 −2.89863
\(961\) 66.7301 2.15258
\(962\) −81.8385 −2.63858
\(963\) 18.6188 0.599984
\(964\) −81.6035 −2.62827
\(965\) 49.8443 1.60455
\(966\) −12.0494 −0.387683
\(967\) 40.0480 1.28786 0.643929 0.765086i \(-0.277303\pi\)
0.643929 + 0.765086i \(0.277303\pi\)
\(968\) 95.7679 3.07810
\(969\) −14.0121 −0.450134
\(970\) −111.549 −3.58163
\(971\) 34.7644 1.11564 0.557821 0.829962i \(-0.311638\pi\)
0.557821 + 0.829962i \(0.311638\pi\)
\(972\) −72.1999 −2.31581
\(973\) −101.827 −3.26441
\(974\) 14.5871 0.467401
\(975\) −32.4284 −1.03854
\(976\) −96.5630 −3.09091
\(977\) −35.3718 −1.13164 −0.565822 0.824527i \(-0.691441\pi\)
−0.565822 + 0.824527i \(0.691441\pi\)
\(978\) 46.1523 1.47579
\(979\) −0.539908 −0.0172555
\(980\) 282.646 9.02880
\(981\) 23.0978 0.737457
\(982\) −95.0484 −3.03312
\(983\) 35.0144 1.11678 0.558392 0.829577i \(-0.311418\pi\)
0.558392 + 0.829577i \(0.311418\pi\)
\(984\) 0.564345 0.0179907
\(985\) 31.3776 0.999772
\(986\) 39.4466 1.25623
\(987\) 60.0579 1.91166
\(988\) 120.409 3.83072
\(989\) 4.06813 0.129359
\(990\) −1.43285 −0.0455389
\(991\) 51.4127 1.63318 0.816589 0.577220i \(-0.195862\pi\)
0.816589 + 0.577220i \(0.195862\pi\)
\(992\) −172.638 −5.48126
\(993\) 12.1141 0.384429
\(994\) −212.719 −6.74705
\(995\) −36.0513 −1.14290
\(996\) 16.7526 0.530826
\(997\) 27.7549 0.879007 0.439503 0.898241i \(-0.355154\pi\)
0.439503 + 0.898241i \(0.355154\pi\)
\(998\) 12.7421 0.403344
\(999\) 45.2072 1.43029
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 6047.2.a.b.1.8 287
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6047.2.a.b.1.8 287 1.1 even 1 trivial