Properties

Label 2541.2.a.bo.1.4
Level $2541$
Weight $2$
Character 2541.1
Self dual yes
Analytic conductor $20.290$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2541,2,Mod(1,2541)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2541.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2541.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: \(20.2899871536\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.7488.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.698857\) of defining polynomial
Character \(\chi\) \(=\) 2541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} +4.64136 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} +4.64136 q^{8} +1.00000 q^{9} +8.34022 q^{10} -3.90931 q^{12} -6.11977 q^{13} +2.43091 q^{14} -3.43091 q^{15} +3.46410 q^{16} +3.21046 q^{17} +2.43091 q^{18} +6.34022 q^{19} +13.4125 q^{20} -1.00000 q^{21} -0.210456 q^{23} -4.64136 q^{24} +6.77113 q^{25} -14.8766 q^{26} -1.00000 q^{27} +3.90931 q^{28} +2.74635 q^{29} -8.34022 q^{30} +4.64136 q^{31} -0.861816 q^{32} +7.80432 q^{34} +3.43091 q^{35} +3.90931 q^{36} -9.37341 q^{37} +15.4125 q^{38} +6.11977 q^{39} +15.9241 q^{40} +11.9484 q^{41} -2.43091 q^{42} +7.12976 q^{43} +3.43091 q^{45} -0.511599 q^{46} -5.91520 q^{47} -3.46410 q^{48} +1.00000 q^{49} +16.4600 q^{50} -3.21046 q^{51} -23.9241 q^{52} -6.35452 q^{53} -2.43091 q^{54} +4.64136 q^{56} -6.34022 q^{57} +6.67613 q^{58} -11.8232 q^{59} -13.4125 q^{60} +9.20204 q^{61} +11.2827 q^{62} +1.00000 q^{63} -9.02320 q^{64} -20.9964 q^{65} -3.89042 q^{67} +12.5507 q^{68} +0.210456 q^{69} +8.34022 q^{70} -5.19458 q^{71} +4.64136 q^{72} -13.1747 q^{73} -22.7859 q^{74} -6.77113 q^{75} +24.7859 q^{76} +14.8766 q^{78} -4.33022 q^{79} +11.8850 q^{80} +1.00000 q^{81} +29.0454 q^{82} -0.737935 q^{83} -3.90931 q^{84} +11.0148 q^{85} +17.3318 q^{86} -2.74635 q^{87} -9.34453 q^{89} +8.34022 q^{90} -6.11977 q^{91} -0.822738 q^{92} -4.64136 q^{93} -14.3793 q^{94} +21.7527 q^{95} +0.861816 q^{96} +12.0534 q^{97} +2.43091 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{9} + 14 q^{10} - 4 q^{12} - 2 q^{13} + 2 q^{14} - 6 q^{15} + 2 q^{17} + 2 q^{18} + 6 q^{19} + 8 q^{20} - 4 q^{21} + 10 q^{23} - 4 q^{27} + 4 q^{28} + 14 q^{29} - 14 q^{30} + 12 q^{32} - 2 q^{34} + 6 q^{35} + 4 q^{36} - 12 q^{37} + 16 q^{38} + 2 q^{39} + 8 q^{40} + 16 q^{41} - 2 q^{42} + 20 q^{43} + 6 q^{45} + 8 q^{46} + 2 q^{47} + 4 q^{49} + 24 q^{50} - 2 q^{51} - 40 q^{52} - 16 q^{53} - 2 q^{54} - 6 q^{57} - 8 q^{58} + 2 q^{59} - 8 q^{60} + 2 q^{61} + 8 q^{62} + 4 q^{63} - 16 q^{64} - 2 q^{65} - 20 q^{67} + 20 q^{68} - 10 q^{69} + 14 q^{70} - 10 q^{71} - 10 q^{73} - 20 q^{74} + 28 q^{76} + 16 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} + 18 q^{83} - 4 q^{84} + 26 q^{86} - 14 q^{87} - 14 q^{89} + 14 q^{90} - 2 q^{91} - 8 q^{92} - 18 q^{94} + 22 q^{95} - 12 q^{96} + 38 q^{97} + 2 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.43091 1.71891 0.859456 0.511210i \(-0.170803\pi\)
0.859456 + 0.511210i \(0.170803\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.90931 1.95466
\(5\) 3.43091 1.53435 0.767174 0.641439i \(-0.221662\pi\)
0.767174 + 0.641439i \(0.221662\pi\)
\(6\) −2.43091 −0.992414
\(7\) 1.00000 0.377964
\(8\) 4.64136 1.64097
\(9\) 1.00000 0.333333
\(10\) 8.34022 2.63741
\(11\) 0 0
\(12\) −3.90931 −1.12852
\(13\) −6.11977 −1.69732 −0.848659 0.528940i \(-0.822590\pi\)
−0.848659 + 0.528940i \(0.822590\pi\)
\(14\) 2.43091 0.649687
\(15\) −3.43091 −0.885857
\(16\) 3.46410 0.866025
\(17\) 3.21046 0.778650 0.389325 0.921100i \(-0.372708\pi\)
0.389325 + 0.921100i \(0.372708\pi\)
\(18\) 2.43091 0.572970
\(19\) 6.34022 1.45455 0.727273 0.686348i \(-0.240787\pi\)
0.727273 + 0.686348i \(0.240787\pi\)
\(20\) 13.4125 2.99912
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −0.210456 −0.0438831 −0.0219415 0.999759i \(-0.506985\pi\)
−0.0219415 + 0.999759i \(0.506985\pi\)
\(24\) −4.64136 −0.947414
\(25\) 6.77113 1.35423
\(26\) −14.8766 −2.91754
\(27\) −1.00000 −0.192450
\(28\) 3.90931 0.738791
\(29\) 2.74635 0.509985 0.254993 0.966943i \(-0.417927\pi\)
0.254993 + 0.966943i \(0.417927\pi\)
\(30\) −8.34022 −1.52271
\(31\) 4.64136 0.833614 0.416807 0.908995i \(-0.363149\pi\)
0.416807 + 0.908995i \(0.363149\pi\)
\(32\) −0.861816 −0.152349
\(33\) 0 0
\(34\) 7.80432 1.33843
\(35\) 3.43091 0.579929
\(36\) 3.90931 0.651552
\(37\) −9.37341 −1.54098 −0.770490 0.637452i \(-0.779988\pi\)
−0.770490 + 0.637452i \(0.779988\pi\)
\(38\) 15.4125 2.50024
\(39\) 6.11977 0.979947
\(40\) 15.9241 2.51782
\(41\) 11.9484 1.86603 0.933013 0.359844i \(-0.117170\pi\)
0.933013 + 0.359844i \(0.117170\pi\)
\(42\) −2.43091 −0.375097
\(43\) 7.12976 1.08728 0.543639 0.839319i \(-0.317046\pi\)
0.543639 + 0.839319i \(0.317046\pi\)
\(44\) 0 0
\(45\) 3.43091 0.511450
\(46\) −0.511599 −0.0754311
\(47\) −5.91520 −0.862820 −0.431410 0.902156i \(-0.641984\pi\)
−0.431410 + 0.902156i \(0.641984\pi\)
\(48\) −3.46410 −0.500000
\(49\) 1.00000 0.142857
\(50\) 16.4600 2.32779
\(51\) −3.21046 −0.449554
\(52\) −23.9241 −3.31767
\(53\) −6.35452 −0.872861 −0.436431 0.899738i \(-0.643758\pi\)
−0.436431 + 0.899738i \(0.643758\pi\)
\(54\) −2.43091 −0.330805
\(55\) 0 0
\(56\) 4.64136 0.620228
\(57\) −6.34022 −0.839783
\(58\) 6.67613 0.876619
\(59\) −11.8232 −1.53925 −0.769626 0.638495i \(-0.779557\pi\)
−0.769626 + 0.638495i \(0.779557\pi\)
\(60\) −13.4125 −1.73155
\(61\) 9.20204 1.17820 0.589100 0.808060i \(-0.299482\pi\)
0.589100 + 0.808060i \(0.299482\pi\)
\(62\) 11.2827 1.43291
\(63\) 1.00000 0.125988
\(64\) −9.02320 −1.12790
\(65\) −20.9964 −2.60428
\(66\) 0 0
\(67\) −3.89042 −0.475291 −0.237645 0.971352i \(-0.576376\pi\)
−0.237645 + 0.971352i \(0.576376\pi\)
\(68\) 12.5507 1.52199
\(69\) 0.210456 0.0253359
\(70\) 8.34022 0.996847
\(71\) −5.19458 −0.616483 −0.308241 0.951308i \(-0.599740\pi\)
−0.308241 + 0.951308i \(0.599740\pi\)
\(72\) 4.64136 0.546990
\(73\) −13.1747 −1.54199 −0.770993 0.636844i \(-0.780239\pi\)
−0.770993 + 0.636844i \(0.780239\pi\)
\(74\) −22.7859 −2.64881
\(75\) −6.77113 −0.781863
\(76\) 24.7859 2.84314
\(77\) 0 0
\(78\) 14.8766 1.68444
\(79\) −4.33022 −0.487188 −0.243594 0.969877i \(-0.578326\pi\)
−0.243594 + 0.969877i \(0.578326\pi\)
\(80\) 11.8850 1.32878
\(81\) 1.00000 0.111111
\(82\) 29.0454 3.20753
\(83\) −0.737935 −0.0809989 −0.0404994 0.999180i \(-0.512895\pi\)
−0.0404994 + 0.999180i \(0.512895\pi\)
\(84\) −3.90931 −0.426541
\(85\) 11.0148 1.19472
\(86\) 17.3318 1.86894
\(87\) −2.74635 −0.294440
\(88\) 0 0
\(89\) −9.34453 −0.990518 −0.495259 0.868745i \(-0.664927\pi\)
−0.495259 + 0.868745i \(0.664927\pi\)
\(90\) 8.34022 0.879136
\(91\) −6.11977 −0.641526
\(92\) −0.822738 −0.0857764
\(93\) −4.64136 −0.481287
\(94\) −14.3793 −1.48311
\(95\) 21.7527 2.23178
\(96\) 0.861816 0.0879587
\(97\) 12.0534 1.22384 0.611918 0.790921i \(-0.290398\pi\)
0.611918 + 0.790921i \(0.290398\pi\)
\(98\) 2.43091 0.245559
\(99\) 0 0
\(100\) 26.4705 2.64705
\(101\) −1.58798 −0.158010 −0.0790051 0.996874i \(-0.525174\pi\)
−0.0790051 + 0.996874i \(0.525174\pi\)
\(102\) −7.80432 −0.772743
\(103\) 9.42249 0.928425 0.464213 0.885724i \(-0.346337\pi\)
0.464213 + 0.885724i \(0.346337\pi\)
\(104\) −28.4041 −2.78525
\(105\) −3.43091 −0.334822
\(106\) −15.4473 −1.50037
\(107\) 7.03319 0.679925 0.339962 0.940439i \(-0.389586\pi\)
0.339962 + 0.940439i \(0.389586\pi\)
\(108\) −3.90931 −0.376174
\(109\) −2.37040 −0.227044 −0.113522 0.993536i \(-0.536213\pi\)
−0.113522 + 0.993536i \(0.536213\pi\)
\(110\) 0 0
\(111\) 9.37341 0.889685
\(112\) 3.46410 0.327327
\(113\) 0.409144 0.0384890 0.0192445 0.999815i \(-0.493874\pi\)
0.0192445 + 0.999815i \(0.493874\pi\)
\(114\) −15.4125 −1.44351
\(115\) −0.722055 −0.0673320
\(116\) 10.7364 0.996846
\(117\) −6.11977 −0.565773
\(118\) −28.7411 −2.64584
\(119\) 3.21046 0.294302
\(120\) −15.9241 −1.45366
\(121\) 0 0
\(122\) 22.3693 2.02522
\(123\) −11.9484 −1.07735
\(124\) 18.1445 1.62943
\(125\) 6.07658 0.543506
\(126\) 2.43091 0.216562
\(127\) −19.5307 −1.73307 −0.866534 0.499118i \(-0.833657\pi\)
−0.866534 + 0.499118i \(0.833657\pi\)
\(128\) −20.2109 −1.78641
\(129\) −7.12976 −0.627741
\(130\) −51.0402 −4.47652
\(131\) 19.3750 1.69280 0.846400 0.532547i \(-0.178765\pi\)
0.846400 + 0.532547i \(0.178765\pi\)
\(132\) 0 0
\(133\) 6.34022 0.549767
\(134\) −9.45726 −0.816983
\(135\) −3.43091 −0.295286
\(136\) 14.9009 1.27774
\(137\) −6.14277 −0.524812 −0.262406 0.964958i \(-0.584516\pi\)
−0.262406 + 0.964958i \(0.584516\pi\)
\(138\) 0.511599 0.0435502
\(139\) 6.77065 0.574279 0.287140 0.957889i \(-0.407296\pi\)
0.287140 + 0.957889i \(0.407296\pi\)
\(140\) 13.4125 1.13356
\(141\) 5.91520 0.498149
\(142\) −12.6275 −1.05968
\(143\) 0 0
\(144\) 3.46410 0.288675
\(145\) 9.42249 0.782495
\(146\) −32.0265 −2.65054
\(147\) −1.00000 −0.0824786
\(148\) −36.6436 −3.01209
\(149\) −17.8204 −1.45990 −0.729952 0.683498i \(-0.760458\pi\)
−0.729952 + 0.683498i \(0.760458\pi\)
\(150\) −16.4600 −1.34395
\(151\) 0.610705 0.0496985 0.0248493 0.999691i \(-0.492089\pi\)
0.0248493 + 0.999691i \(0.492089\pi\)
\(152\) 29.4273 2.38687
\(153\) 3.21046 0.259550
\(154\) 0 0
\(155\) 15.9241 1.27905
\(156\) 23.9241 1.91546
\(157\) 6.82274 0.544514 0.272257 0.962225i \(-0.412230\pi\)
0.272257 + 0.962225i \(0.412230\pi\)
\(158\) −10.5264 −0.837434
\(159\) 6.35452 0.503947
\(160\) −2.95681 −0.233756
\(161\) −0.210456 −0.0165862
\(162\) 2.43091 0.190990
\(163\) −12.0738 −0.945697 −0.472848 0.881144i \(-0.656774\pi\)
−0.472848 + 0.881144i \(0.656774\pi\)
\(164\) 46.7100 3.64744
\(165\) 0 0
\(166\) −1.79385 −0.139230
\(167\) −2.89932 −0.224356 −0.112178 0.993688i \(-0.535783\pi\)
−0.112178 + 0.993688i \(0.535783\pi\)
\(168\) −4.64136 −0.358089
\(169\) 24.4516 1.88089
\(170\) 26.7759 2.05362
\(171\) 6.34022 0.484849
\(172\) 27.8725 2.12526
\(173\) −14.5713 −1.10784 −0.553919 0.832570i \(-0.686868\pi\)
−0.553919 + 0.832570i \(0.686868\pi\)
\(174\) −6.67613 −0.506116
\(175\) 6.77113 0.511849
\(176\) 0 0
\(177\) 11.8232 0.888687
\(178\) −22.7157 −1.70261
\(179\) 18.9082 1.41327 0.706633 0.707580i \(-0.250213\pi\)
0.706633 + 0.707580i \(0.250213\pi\)
\(180\) 13.4125 0.999708
\(181\) 15.7713 1.17227 0.586137 0.810212i \(-0.300648\pi\)
0.586137 + 0.810212i \(0.300648\pi\)
\(182\) −14.8766 −1.10273
\(183\) −9.20204 −0.680234
\(184\) −0.976802 −0.0720108
\(185\) −32.1593 −2.36440
\(186\) −11.2827 −0.827290
\(187\) 0 0
\(188\) −23.1244 −1.68652
\(189\) −1.00000 −0.0727393
\(190\) 52.8788 3.83623
\(191\) −19.5132 −1.41192 −0.705962 0.708250i \(-0.749485\pi\)
−0.705962 + 0.708250i \(0.749485\pi\)
\(192\) 9.02320 0.651193
\(193\) −22.9830 −1.65435 −0.827177 0.561942i \(-0.810055\pi\)
−0.827177 + 0.561942i \(0.810055\pi\)
\(194\) 29.3007 2.10366
\(195\) 20.9964 1.50358
\(196\) 3.90931 0.279237
\(197\) 11.3218 0.806645 0.403323 0.915058i \(-0.367855\pi\)
0.403323 + 0.915058i \(0.367855\pi\)
\(198\) 0 0
\(199\) −6.43837 −0.456404 −0.228202 0.973614i \(-0.573285\pi\)
−0.228202 + 0.973614i \(0.573285\pi\)
\(200\) 31.4273 2.22224
\(201\) 3.89042 0.274409
\(202\) −3.86024 −0.271605
\(203\) 2.74635 0.192756
\(204\) −12.5507 −0.878723
\(205\) 40.9938 2.86313
\(206\) 22.9052 1.59588
\(207\) −0.210456 −0.0146277
\(208\) −21.1995 −1.46992
\(209\) 0 0
\(210\) −8.34022 −0.575530
\(211\) 20.1287 1.38571 0.692857 0.721075i \(-0.256352\pi\)
0.692857 + 0.721075i \(0.256352\pi\)
\(212\) −24.8418 −1.70614
\(213\) 5.19458 0.355926
\(214\) 17.0970 1.16873
\(215\) 24.4616 1.66826
\(216\) −4.64136 −0.315805
\(217\) 4.64136 0.315076
\(218\) −5.76223 −0.390268
\(219\) 13.1747 0.890266
\(220\) 0 0
\(221\) −19.6472 −1.32162
\(222\) 22.7859 1.52929
\(223\) −20.8691 −1.39750 −0.698750 0.715366i \(-0.746260\pi\)
−0.698750 + 0.715366i \(0.746260\pi\)
\(224\) −0.861816 −0.0575825
\(225\) 6.77113 0.451409
\(226\) 0.994591 0.0661592
\(227\) 3.06892 0.203692 0.101846 0.994800i \(-0.467525\pi\)
0.101846 + 0.994800i \(0.467525\pi\)
\(228\) −24.7859 −1.64149
\(229\) −8.35768 −0.552291 −0.276145 0.961116i \(-0.589057\pi\)
−0.276145 + 0.961116i \(0.589057\pi\)
\(230\) −1.75525 −0.115738
\(231\) 0 0
\(232\) 12.7468 0.836870
\(233\) −5.50270 −0.360494 −0.180247 0.983621i \(-0.557690\pi\)
−0.180247 + 0.983621i \(0.557690\pi\)
\(234\) −14.8766 −0.972513
\(235\) −20.2945 −1.32387
\(236\) −46.2206 −3.00871
\(237\) 4.33022 0.281278
\(238\) 7.80432 0.505879
\(239\) 2.30368 0.149013 0.0745063 0.997221i \(-0.476262\pi\)
0.0745063 + 0.997221i \(0.476262\pi\)
\(240\) −11.8850 −0.767174
\(241\) −10.3602 −0.667360 −0.333680 0.942686i \(-0.608290\pi\)
−0.333680 + 0.942686i \(0.608290\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 35.9736 2.30298
\(245\) 3.43091 0.219193
\(246\) −29.0454 −1.85187
\(247\) −38.8007 −2.46883
\(248\) 21.5423 1.36793
\(249\) 0.737935 0.0467647
\(250\) 14.7716 0.934238
\(251\) 11.2627 0.710898 0.355449 0.934696i \(-0.384328\pi\)
0.355449 + 0.934696i \(0.384328\pi\)
\(252\) 3.90931 0.246264
\(253\) 0 0
\(254\) −47.4773 −2.97899
\(255\) −11.0148 −0.689772
\(256\) −31.0845 −1.94278
\(257\) −15.2643 −0.952162 −0.476081 0.879402i \(-0.657943\pi\)
−0.476081 + 0.879402i \(0.657943\pi\)
\(258\) −17.3318 −1.07903
\(259\) −9.37341 −0.582436
\(260\) −82.0814 −5.09047
\(261\) 2.74635 0.169995
\(262\) 47.0988 2.90977
\(263\) −8.45315 −0.521243 −0.260622 0.965441i \(-0.583928\pi\)
−0.260622 + 0.965441i \(0.583928\pi\)
\(264\) 0 0
\(265\) −21.8018 −1.33927
\(266\) 15.4125 0.945001
\(267\) 9.34453 0.571876
\(268\) −15.2089 −0.929030
\(269\) −21.3987 −1.30470 −0.652350 0.757918i \(-0.726217\pi\)
−0.652350 + 0.757918i \(0.726217\pi\)
\(270\) −8.34022 −0.507570
\(271\) 26.2414 1.59405 0.797026 0.603946i \(-0.206406\pi\)
0.797026 + 0.603946i \(0.206406\pi\)
\(272\) 11.1213 0.674331
\(273\) 6.11977 0.370385
\(274\) −14.9325 −0.902106
\(275\) 0 0
\(276\) 0.822738 0.0495230
\(277\) −18.5696 −1.11574 −0.557869 0.829929i \(-0.688381\pi\)
−0.557869 + 0.829929i \(0.688381\pi\)
\(278\) 16.4588 0.987135
\(279\) 4.64136 0.277871
\(280\) 15.9241 0.951646
\(281\) 4.24906 0.253478 0.126739 0.991936i \(-0.459549\pi\)
0.126739 + 0.991936i \(0.459549\pi\)
\(282\) 14.3793 0.856275
\(283\) 20.5277 1.22024 0.610122 0.792308i \(-0.291121\pi\)
0.610122 + 0.792308i \(0.291121\pi\)
\(284\) −20.3072 −1.20501
\(285\) −21.7527 −1.28852
\(286\) 0 0
\(287\) 11.9484 0.705291
\(288\) −0.861816 −0.0507830
\(289\) −6.69297 −0.393704
\(290\) 22.9052 1.34504
\(291\) −12.0534 −0.706582
\(292\) −51.5041 −3.01405
\(293\) −21.2022 −1.23865 −0.619324 0.785136i \(-0.712593\pi\)
−0.619324 + 0.785136i \(0.712593\pi\)
\(294\) −2.43091 −0.141773
\(295\) −40.5644 −2.36175
\(296\) −43.5054 −2.52870
\(297\) 0 0
\(298\) −43.3197 −2.50945
\(299\) 1.28794 0.0744836
\(300\) −26.4705 −1.52827
\(301\) 7.12976 0.410953
\(302\) 1.48457 0.0854273
\(303\) 1.58798 0.0912272
\(304\) 21.9632 1.25967
\(305\) 31.5713 1.80777
\(306\) 7.80432 0.446143
\(307\) 23.0007 1.31272 0.656359 0.754449i \(-0.272096\pi\)
0.656359 + 0.754449i \(0.272096\pi\)
\(308\) 0 0
\(309\) −9.42249 −0.536027
\(310\) 38.7100 2.19858
\(311\) 7.36753 0.417774 0.208887 0.977940i \(-0.433016\pi\)
0.208887 + 0.977940i \(0.433016\pi\)
\(312\) 28.4041 1.60806
\(313\) −4.80590 −0.271645 −0.135823 0.990733i \(-0.543368\pi\)
−0.135823 + 0.990733i \(0.543368\pi\)
\(314\) 16.5854 0.935971
\(315\) 3.43091 0.193310
\(316\) −16.9282 −0.952286
\(317\) −1.54178 −0.0865951 −0.0432976 0.999062i \(-0.513786\pi\)
−0.0432976 + 0.999062i \(0.513786\pi\)
\(318\) 15.4473 0.866239
\(319\) 0 0
\(320\) −30.9578 −1.73059
\(321\) −7.03319 −0.392555
\(322\) −0.511599 −0.0285103
\(323\) 20.3550 1.13258
\(324\) 3.90931 0.217184
\(325\) −41.4377 −2.29855
\(326\) −29.3504 −1.62557
\(327\) 2.37040 0.131084
\(328\) 55.4568 3.06209
\(329\) −5.91520 −0.326115
\(330\) 0 0
\(331\) −12.8925 −0.708634 −0.354317 0.935125i \(-0.615287\pi\)
−0.354317 + 0.935125i \(0.615287\pi\)
\(332\) −2.88482 −0.158325
\(333\) −9.37341 −0.513660
\(334\) −7.04797 −0.385648
\(335\) −13.3477 −0.729262
\(336\) −3.46410 −0.188982
\(337\) −18.6475 −1.01580 −0.507898 0.861417i \(-0.669577\pi\)
−0.507898 + 0.861417i \(0.669577\pi\)
\(338\) 59.4395 3.23308
\(339\) −0.409144 −0.0222216
\(340\) 43.0602 2.33527
\(341\) 0 0
\(342\) 15.4125 0.833412
\(343\) 1.00000 0.0539949
\(344\) 33.0918 1.78419
\(345\) 0.722055 0.0388741
\(346\) −35.4216 −1.90428
\(347\) 12.4700 0.669424 0.334712 0.942320i \(-0.391361\pi\)
0.334712 + 0.942320i \(0.391361\pi\)
\(348\) −10.7364 −0.575529
\(349\) 5.11087 0.273579 0.136789 0.990600i \(-0.456322\pi\)
0.136789 + 0.990600i \(0.456322\pi\)
\(350\) 16.4600 0.879823
\(351\) 6.11977 0.326649
\(352\) 0 0
\(353\) 26.7386 1.42315 0.711576 0.702609i \(-0.247982\pi\)
0.711576 + 0.702609i \(0.247982\pi\)
\(354\) 28.7411 1.52757
\(355\) −17.8221 −0.945899
\(356\) −36.5307 −1.93612
\(357\) −3.21046 −0.169915
\(358\) 45.9641 2.42928
\(359\) 0.873109 0.0460809 0.0230405 0.999735i \(-0.492665\pi\)
0.0230405 + 0.999735i \(0.492665\pi\)
\(360\) 15.9241 0.839273
\(361\) 21.1984 1.11571
\(362\) 38.3386 2.01503
\(363\) 0 0
\(364\) −23.9241 −1.25396
\(365\) −45.2013 −2.36594
\(366\) −22.3693 −1.16926
\(367\) 12.4644 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(368\) −0.729041 −0.0380039
\(369\) 11.9484 0.622008
\(370\) −78.1763 −4.06419
\(371\) −6.35452 −0.329910
\(372\) −18.1445 −0.940751
\(373\) −2.27617 −0.117856 −0.0589279 0.998262i \(-0.518768\pi\)
−0.0589279 + 0.998262i \(0.518768\pi\)
\(374\) 0 0
\(375\) −6.07658 −0.313793
\(376\) −27.4546 −1.41586
\(377\) −16.8071 −0.865607
\(378\) −2.43091 −0.125032
\(379\) 20.7575 1.06624 0.533120 0.846039i \(-0.321019\pi\)
0.533120 + 0.846039i \(0.321019\pi\)
\(380\) 85.0382 4.36237
\(381\) 19.5307 1.00059
\(382\) −47.4347 −2.42697
\(383\) −17.8498 −0.912080 −0.456040 0.889959i \(-0.650733\pi\)
−0.456040 + 0.889959i \(0.650733\pi\)
\(384\) 20.2109 1.03138
\(385\) 0 0
\(386\) −55.8696 −2.84369
\(387\) 7.12976 0.362426
\(388\) 47.1204 2.39218
\(389\) −8.23954 −0.417761 −0.208881 0.977941i \(-0.566982\pi\)
−0.208881 + 0.977941i \(0.566982\pi\)
\(390\) 51.0402 2.58452
\(391\) −0.675659 −0.0341696
\(392\) 4.64136 0.234424
\(393\) −19.3750 −0.977339
\(394\) 27.5223 1.38655
\(395\) −14.8566 −0.747517
\(396\) 0 0
\(397\) −16.1445 −0.810271 −0.405136 0.914257i \(-0.632776\pi\)
−0.405136 + 0.914257i \(0.632776\pi\)
\(398\) −15.6511 −0.784518
\(399\) −6.34022 −0.317408
\(400\) 23.4559 1.17279
\(401\) 27.5236 1.37446 0.687231 0.726439i \(-0.258826\pi\)
0.687231 + 0.726439i \(0.258826\pi\)
\(402\) 9.45726 0.471685
\(403\) −28.4041 −1.41491
\(404\) −6.20792 −0.308856
\(405\) 3.43091 0.170483
\(406\) 6.67613 0.331331
\(407\) 0 0
\(408\) −14.9009 −0.737704
\(409\) −17.1270 −0.846877 −0.423439 0.905925i \(-0.639177\pi\)
−0.423439 + 0.905925i \(0.639177\pi\)
\(410\) 99.6522 4.92147
\(411\) 6.14277 0.303001
\(412\) 36.8355 1.81475
\(413\) −11.8232 −0.581782
\(414\) −0.511599 −0.0251437
\(415\) −2.53179 −0.124281
\(416\) 5.27411 0.258585
\(417\) −6.77065 −0.331560
\(418\) 0 0
\(419\) 14.3995 0.703461 0.351730 0.936101i \(-0.385593\pi\)
0.351730 + 0.936101i \(0.385593\pi\)
\(420\) −13.4125 −0.654463
\(421\) −11.0695 −0.539496 −0.269748 0.962931i \(-0.586940\pi\)
−0.269748 + 0.962931i \(0.586940\pi\)
\(422\) 48.9309 2.38192
\(423\) −5.91520 −0.287607
\(424\) −29.4937 −1.43234
\(425\) 21.7384 1.05447
\(426\) 12.6275 0.611806
\(427\) 9.20204 0.445318
\(428\) 27.4950 1.32902
\(429\) 0 0
\(430\) 59.4638 2.86760
\(431\) 15.6173 0.752257 0.376128 0.926568i \(-0.377255\pi\)
0.376128 + 0.926568i \(0.377255\pi\)
\(432\) −3.46410 −0.166667
\(433\) 2.17439 0.104494 0.0522472 0.998634i \(-0.483362\pi\)
0.0522472 + 0.998634i \(0.483362\pi\)
\(434\) 11.2827 0.541588
\(435\) −9.42249 −0.451774
\(436\) −9.26665 −0.443792
\(437\) −1.33434 −0.0638300
\(438\) 32.0265 1.53029
\(439\) −9.44726 −0.450893 −0.225447 0.974256i \(-0.572384\pi\)
−0.225447 + 0.974256i \(0.572384\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) −47.7606 −2.27174
\(443\) 8.08725 0.384237 0.192118 0.981372i \(-0.438464\pi\)
0.192118 + 0.981372i \(0.438464\pi\)
\(444\) 36.6436 1.73903
\(445\) −32.0602 −1.51980
\(446\) −50.7309 −2.40218
\(447\) 17.8204 0.842876
\(448\) −9.02320 −0.426306
\(449\) −28.5845 −1.34899 −0.674494 0.738280i \(-0.735638\pi\)
−0.674494 + 0.738280i \(0.735638\pi\)
\(450\) 16.4600 0.775931
\(451\) 0 0
\(452\) 1.59947 0.0752328
\(453\) −0.610705 −0.0286934
\(454\) 7.46027 0.350128
\(455\) −20.9964 −0.984325
\(456\) −29.4273 −1.37806
\(457\) 8.25713 0.386252 0.193126 0.981174i \(-0.438137\pi\)
0.193126 + 0.981174i \(0.438137\pi\)
\(458\) −20.3167 −0.949339
\(459\) −3.21046 −0.149851
\(460\) −2.82274 −0.131611
\(461\) −13.3346 −0.621055 −0.310527 0.950564i \(-0.600506\pi\)
−0.310527 + 0.950564i \(0.600506\pi\)
\(462\) 0 0
\(463\) 26.6479 1.23843 0.619217 0.785220i \(-0.287450\pi\)
0.619217 + 0.785220i \(0.287450\pi\)
\(464\) 9.51365 0.441660
\(465\) −15.9241 −0.738462
\(466\) −13.3766 −0.619658
\(467\) 28.8194 1.33360 0.666801 0.745236i \(-0.267663\pi\)
0.666801 + 0.745236i \(0.267663\pi\)
\(468\) −23.9241 −1.10589
\(469\) −3.89042 −0.179643
\(470\) −49.3340 −2.27561
\(471\) −6.82274 −0.314375
\(472\) −54.8758 −2.52586
\(473\) 0 0
\(474\) 10.5264 0.483493
\(475\) 42.9304 1.96978
\(476\) 12.5507 0.575259
\(477\) −6.35452 −0.290954
\(478\) 5.60003 0.256139
\(479\) 7.03430 0.321405 0.160703 0.987003i \(-0.448624\pi\)
0.160703 + 0.987003i \(0.448624\pi\)
\(480\) 2.95681 0.134959
\(481\) 57.3631 2.61553
\(482\) −25.1847 −1.14713
\(483\) 0.210456 0.00957607
\(484\) 0 0
\(485\) 41.3540 1.87779
\(486\) −2.43091 −0.110268
\(487\) −15.1823 −0.687977 −0.343988 0.938974i \(-0.611778\pi\)
−0.343988 + 0.938974i \(0.611778\pi\)
\(488\) 42.7100 1.93339
\(489\) 12.0738 0.545998
\(490\) 8.34022 0.376773
\(491\) −15.6173 −0.704801 −0.352400 0.935849i \(-0.614634\pi\)
−0.352400 + 0.935849i \(0.614634\pi\)
\(492\) −46.7100 −2.10585
\(493\) 8.81705 0.397100
\(494\) −94.3209 −4.24370
\(495\) 0 0
\(496\) 16.0782 0.721930
\(497\) −5.19458 −0.233009
\(498\) 1.79385 0.0803844
\(499\) 9.99383 0.447385 0.223693 0.974660i \(-0.428189\pi\)
0.223693 + 0.974660i \(0.428189\pi\)
\(500\) 23.7552 1.06237
\(501\) 2.89932 0.129532
\(502\) 27.3787 1.22197
\(503\) −13.6115 −0.606908 −0.303454 0.952846i \(-0.598140\pi\)
−0.303454 + 0.952846i \(0.598140\pi\)
\(504\) 4.64136 0.206743
\(505\) −5.44822 −0.242443
\(506\) 0 0
\(507\) −24.4516 −1.08593
\(508\) −76.3516 −3.38755
\(509\) −20.5379 −0.910325 −0.455162 0.890408i \(-0.650419\pi\)
−0.455162 + 0.890408i \(0.650419\pi\)
\(510\) −26.7759 −1.18566
\(511\) −13.1747 −0.582816
\(512\) −35.1417 −1.55306
\(513\) −6.34022 −0.279928
\(514\) −37.1061 −1.63668
\(515\) 32.3277 1.42453
\(516\) −27.8725 −1.22702
\(517\) 0 0
\(518\) −22.7859 −1.00116
\(519\) 14.5713 0.639611
\(520\) −97.4518 −4.27354
\(521\) 14.7483 0.646133 0.323067 0.946376i \(-0.395286\pi\)
0.323067 + 0.946376i \(0.395286\pi\)
\(522\) 6.67613 0.292206
\(523\) −22.1029 −0.966494 −0.483247 0.875484i \(-0.660543\pi\)
−0.483247 + 0.875484i \(0.660543\pi\)
\(524\) 75.7429 3.30884
\(525\) −6.77113 −0.295516
\(526\) −20.5488 −0.895971
\(527\) 14.9009 0.649093
\(528\) 0 0
\(529\) −22.9557 −0.998074
\(530\) −52.9981 −2.30209
\(531\) −11.8232 −0.513084
\(532\) 24.7859 1.07461
\(533\) −73.1214 −3.16724
\(534\) 22.7157 0.983004
\(535\) 24.1302 1.04324
\(536\) −18.0569 −0.779938
\(537\) −18.9082 −0.815950
\(538\) −52.0182 −2.24266
\(539\) 0 0
\(540\) −13.4125 −0.577182
\(541\) 6.86201 0.295021 0.147510 0.989060i \(-0.452874\pi\)
0.147510 + 0.989060i \(0.452874\pi\)
\(542\) 63.7904 2.74003
\(543\) −15.7713 −0.676812
\(544\) −2.76682 −0.118626
\(545\) −8.13264 −0.348364
\(546\) 14.8766 0.636659
\(547\) −24.7425 −1.05791 −0.528957 0.848649i \(-0.677417\pi\)
−0.528957 + 0.848649i \(0.677417\pi\)
\(548\) −24.0140 −1.02583
\(549\) 9.20204 0.392733
\(550\) 0 0
\(551\) 17.4125 0.741797
\(552\) 0.976802 0.0415755
\(553\) −4.33022 −0.184140
\(554\) −45.1409 −1.91785
\(555\) 32.1593 1.36509
\(556\) 26.4686 1.12252
\(557\) 4.14961 0.175825 0.0879124 0.996128i \(-0.471980\pi\)
0.0879124 + 0.996128i \(0.471980\pi\)
\(558\) 11.2827 0.477636
\(559\) −43.6325 −1.84546
\(560\) 11.8850 0.502233
\(561\) 0 0
\(562\) 10.3291 0.435706
\(563\) −2.86455 −0.120726 −0.0603631 0.998176i \(-0.519226\pi\)
−0.0603631 + 0.998176i \(0.519226\pi\)
\(564\) 23.1244 0.973711
\(565\) 1.40373 0.0590556
\(566\) 49.9009 2.09749
\(567\) 1.00000 0.0419961
\(568\) −24.1099 −1.01163
\(569\) −10.5736 −0.443268 −0.221634 0.975130i \(-0.571139\pi\)
−0.221634 + 0.975130i \(0.571139\pi\)
\(570\) −52.8788 −2.21485
\(571\) 27.2490 1.14034 0.570169 0.821528i \(-0.306878\pi\)
0.570169 + 0.821528i \(0.306878\pi\)
\(572\) 0 0
\(573\) 19.5132 0.815175
\(574\) 29.0454 1.21233
\(575\) −1.42502 −0.0594276
\(576\) −9.02320 −0.375967
\(577\) −29.8593 −1.24306 −0.621530 0.783390i \(-0.713489\pi\)
−0.621530 + 0.783390i \(0.713489\pi\)
\(578\) −16.2700 −0.676743
\(579\) 22.9830 0.955142
\(580\) 36.8355 1.52951
\(581\) −0.737935 −0.0306147
\(582\) −29.3007 −1.21455
\(583\) 0 0
\(584\) −61.1487 −2.53035
\(585\) −20.9964 −0.868093
\(586\) −51.5407 −2.12913
\(587\) 10.4659 0.431973 0.215986 0.976396i \(-0.430703\pi\)
0.215986 + 0.976396i \(0.430703\pi\)
\(588\) −3.90931 −0.161217
\(589\) 29.4273 1.21253
\(590\) −98.6082 −4.05964
\(591\) −11.3218 −0.465717
\(592\) −32.4705 −1.33453
\(593\) 36.5059 1.49912 0.749559 0.661938i \(-0.230266\pi\)
0.749559 + 0.661938i \(0.230266\pi\)
\(594\) 0 0
\(595\) 11.0148 0.451562
\(596\) −69.6655 −2.85361
\(597\) 6.43837 0.263505
\(598\) 3.13087 0.128031
\(599\) 9.49586 0.387990 0.193995 0.981002i \(-0.437855\pi\)
0.193995 + 0.981002i \(0.437855\pi\)
\(600\) −31.4273 −1.28301
\(601\) −7.98125 −0.325562 −0.162781 0.986662i \(-0.552046\pi\)
−0.162781 + 0.986662i \(0.552046\pi\)
\(602\) 17.3318 0.706391
\(603\) −3.89042 −0.158430
\(604\) 2.38744 0.0971435
\(605\) 0 0
\(606\) 3.86024 0.156811
\(607\) 32.4406 1.31672 0.658362 0.752701i \(-0.271250\pi\)
0.658362 + 0.752701i \(0.271250\pi\)
\(608\) −5.46410 −0.221599
\(609\) −2.74635 −0.111288
\(610\) 76.7470 3.10740
\(611\) 36.1996 1.46448
\(612\) 12.5507 0.507331
\(613\) 33.0240 1.33382 0.666912 0.745136i \(-0.267616\pi\)
0.666912 + 0.745136i \(0.267616\pi\)
\(614\) 55.9125 2.25645
\(615\) −40.9938 −1.65303
\(616\) 0 0
\(617\) 48.7478 1.96251 0.981256 0.192710i \(-0.0617275\pi\)
0.981256 + 0.192710i \(0.0617275\pi\)
\(618\) −22.9052 −0.921382
\(619\) −1.29320 −0.0519780 −0.0259890 0.999662i \(-0.508273\pi\)
−0.0259890 + 0.999662i \(0.508273\pi\)
\(620\) 62.2523 2.50011
\(621\) 0.210456 0.00844530
\(622\) 17.9098 0.718117
\(623\) −9.34453 −0.374381
\(624\) 21.1995 0.848659
\(625\) −13.0075 −0.520298
\(626\) −11.6827 −0.466935
\(627\) 0 0
\(628\) 26.6722 1.06434
\(629\) −30.0929 −1.19988
\(630\) 8.34022 0.332282
\(631\) −18.7715 −0.747280 −0.373640 0.927574i \(-0.621891\pi\)
−0.373640 + 0.927574i \(0.621891\pi\)
\(632\) −20.0981 −0.799461
\(633\) −20.1287 −0.800043
\(634\) −3.74793 −0.148849
\(635\) −67.0080 −2.65913
\(636\) 24.8418 0.985042
\(637\) −6.11977 −0.242474
\(638\) 0 0
\(639\) −5.19458 −0.205494
\(640\) −69.3418 −2.74098
\(641\) −17.9563 −0.709232 −0.354616 0.935012i \(-0.615388\pi\)
−0.354616 + 0.935012i \(0.615388\pi\)
\(642\) −17.0970 −0.674767
\(643\) 23.2796 0.918057 0.459028 0.888422i \(-0.348198\pi\)
0.459028 + 0.888422i \(0.348198\pi\)
\(644\) −0.822738 −0.0324204
\(645\) −24.4616 −0.963173
\(646\) 49.4811 1.94681
\(647\) −42.2211 −1.65988 −0.829942 0.557850i \(-0.811626\pi\)
−0.829942 + 0.557850i \(0.811626\pi\)
\(648\) 4.64136 0.182330
\(649\) 0 0
\(650\) −100.731 −3.95101
\(651\) −4.64136 −0.181909
\(652\) −47.2005 −1.84851
\(653\) −1.27048 −0.0497179 −0.0248590 0.999691i \(-0.507914\pi\)
−0.0248590 + 0.999691i \(0.507914\pi\)
\(654\) 5.76223 0.225321
\(655\) 66.4738 2.59735
\(656\) 41.3904 1.61603
\(657\) −13.1747 −0.513995
\(658\) −14.3793 −0.560563
\(659\) 35.1838 1.37056 0.685282 0.728278i \(-0.259679\pi\)
0.685282 + 0.728278i \(0.259679\pi\)
\(660\) 0 0
\(661\) 2.90089 0.112832 0.0564158 0.998407i \(-0.482033\pi\)
0.0564158 + 0.998407i \(0.482033\pi\)
\(662\) −31.3404 −1.21808
\(663\) 19.6472 0.763036
\(664\) −3.42502 −0.132917
\(665\) 21.7527 0.843534
\(666\) −22.7859 −0.882936
\(667\) −0.577986 −0.0223797
\(668\) −11.3343 −0.438539
\(669\) 20.8691 0.806847
\(670\) −32.4470 −1.25354
\(671\) 0 0
\(672\) 0.861816 0.0332453
\(673\) 37.1846 1.43336 0.716680 0.697402i \(-0.245661\pi\)
0.716680 + 0.697402i \(0.245661\pi\)
\(674\) −45.3304 −1.74606
\(675\) −6.77113 −0.260621
\(676\) 95.5888 3.67649
\(677\) 26.7675 1.02876 0.514379 0.857563i \(-0.328022\pi\)
0.514379 + 0.857563i \(0.328022\pi\)
\(678\) −0.994591 −0.0381970
\(679\) 12.0534 0.462566
\(680\) 51.1236 1.96050
\(681\) −3.06892 −0.117601
\(682\) 0 0
\(683\) 40.9076 1.56529 0.782643 0.622471i \(-0.213871\pi\)
0.782643 + 0.622471i \(0.213871\pi\)
\(684\) 24.7859 0.947713
\(685\) −21.0753 −0.805245
\(686\) 2.43091 0.0928125
\(687\) 8.35768 0.318865
\(688\) 24.6982 0.941611
\(689\) 38.8882 1.48152
\(690\) 1.75525 0.0668212
\(691\) 41.0267 1.56073 0.780365 0.625324i \(-0.215033\pi\)
0.780365 + 0.625324i \(0.215033\pi\)
\(692\) −56.9639 −2.16544
\(693\) 0 0
\(694\) 30.3134 1.15068
\(695\) 23.2295 0.881145
\(696\) −12.7468 −0.483167
\(697\) 38.3598 1.45298
\(698\) 12.4241 0.470258
\(699\) 5.50270 0.208131
\(700\) 26.4705 1.00049
\(701\) 18.6482 0.704333 0.352167 0.935937i \(-0.385445\pi\)
0.352167 + 0.935937i \(0.385445\pi\)
\(702\) 14.8766 0.561481
\(703\) −59.4295 −2.24143
\(704\) 0 0
\(705\) 20.2945 0.764335
\(706\) 64.9991 2.44627
\(707\) −1.58798 −0.0597222
\(708\) 46.2206 1.73708
\(709\) −35.4041 −1.32963 −0.664814 0.747009i \(-0.731489\pi\)
−0.664814 + 0.747009i \(0.731489\pi\)
\(710\) −43.3239 −1.62592
\(711\) −4.33022 −0.162396
\(712\) −43.3714 −1.62541
\(713\) −0.976802 −0.0365815
\(714\) −7.80432 −0.292069
\(715\) 0 0
\(716\) 73.9181 2.76245
\(717\) −2.30368 −0.0860324
\(718\) 2.12245 0.0792090
\(719\) 22.9482 0.855823 0.427912 0.903821i \(-0.359249\pi\)
0.427912 + 0.903821i \(0.359249\pi\)
\(720\) 11.8850 0.442928
\(721\) 9.42249 0.350912
\(722\) 51.5314 1.91780
\(723\) 10.3602 0.385300
\(724\) 61.6550 2.29139
\(725\) 18.5959 0.690635
\(726\) 0 0
\(727\) 4.75027 0.176178 0.0880889 0.996113i \(-0.471924\pi\)
0.0880889 + 0.996113i \(0.471924\pi\)
\(728\) −28.4041 −1.05272
\(729\) 1.00000 0.0370370
\(730\) −109.880 −4.06685
\(731\) 22.8898 0.846610
\(732\) −35.9736 −1.32962
\(733\) −26.7529 −0.988141 −0.494071 0.869422i \(-0.664492\pi\)
−0.494071 + 0.869422i \(0.664492\pi\)
\(734\) 30.2998 1.11838
\(735\) −3.43091 −0.126551
\(736\) 0.181374 0.00668554
\(737\) 0 0
\(738\) 29.0454 1.06918
\(739\) −4.44616 −0.163555 −0.0817773 0.996651i \(-0.526060\pi\)
−0.0817773 + 0.996651i \(0.526060\pi\)
\(740\) −125.721 −4.62159
\(741\) 38.8007 1.42538
\(742\) −15.4473 −0.567087
\(743\) 8.17268 0.299826 0.149913 0.988699i \(-0.452101\pi\)
0.149913 + 0.988699i \(0.452101\pi\)
\(744\) −21.5423 −0.789777
\(745\) −61.1401 −2.24000
\(746\) −5.53317 −0.202584
\(747\) −0.737935 −0.0269996
\(748\) 0 0
\(749\) 7.03319 0.256987
\(750\) −14.7716 −0.539383
\(751\) −23.9396 −0.873568 −0.436784 0.899566i \(-0.643883\pi\)
−0.436784 + 0.899566i \(0.643883\pi\)
\(752\) −20.4908 −0.747224
\(753\) −11.2627 −0.410437
\(754\) −40.8564 −1.48790
\(755\) 2.09527 0.0762548
\(756\) −3.90931 −0.142180
\(757\) 19.9431 0.724845 0.362423 0.932014i \(-0.381950\pi\)
0.362423 + 0.932014i \(0.381950\pi\)
\(758\) 50.4596 1.83277
\(759\) 0 0
\(760\) 100.962 3.66229
\(761\) 10.2909 0.373044 0.186522 0.982451i \(-0.440278\pi\)
0.186522 + 0.982451i \(0.440278\pi\)
\(762\) 47.4773 1.71992
\(763\) −2.37040 −0.0858144
\(764\) −76.2831 −2.75983
\(765\) 11.0148 0.398240
\(766\) −43.3911 −1.56778
\(767\) 72.3553 2.61260
\(768\) 31.0845 1.12167
\(769\) −39.4073 −1.42106 −0.710531 0.703665i \(-0.751545\pi\)
−0.710531 + 0.703665i \(0.751545\pi\)
\(770\) 0 0
\(771\) 15.2643 0.549731
\(772\) −89.8478 −3.23369
\(773\) 22.7516 0.818317 0.409158 0.912463i \(-0.365822\pi\)
0.409158 + 0.912463i \(0.365822\pi\)
\(774\) 17.3318 0.622979
\(775\) 31.4273 1.12890
\(776\) 55.9441 2.00828
\(777\) 9.37341 0.336269
\(778\) −20.0296 −0.718094
\(779\) 75.7554 2.71422
\(780\) 82.0814 2.93898
\(781\) 0 0
\(782\) −1.64247 −0.0587344
\(783\) −2.74635 −0.0981467
\(784\) 3.46410 0.123718
\(785\) 23.4082 0.835474
\(786\) −47.0988 −1.67996
\(787\) −36.2328 −1.29156 −0.645780 0.763524i \(-0.723467\pi\)
−0.645780 + 0.763524i \(0.723467\pi\)
\(788\) 44.2605 1.57671
\(789\) 8.45315 0.300940
\(790\) −36.1150 −1.28492
\(791\) 0.409144 0.0145475
\(792\) 0 0
\(793\) −56.3143 −1.99978
\(794\) −39.2459 −1.39278
\(795\) 21.8018 0.773230
\(796\) −25.1696 −0.892113
\(797\) 21.3161 0.755054 0.377527 0.925999i \(-0.376775\pi\)
0.377527 + 0.925999i \(0.376775\pi\)
\(798\) −15.4125 −0.545596
\(799\) −18.9905 −0.671835
\(800\) −5.83546 −0.206315
\(801\) −9.34453 −0.330173
\(802\) 66.9072 2.36258
\(803\) 0 0
\(804\) 15.2089 0.536376
\(805\) −0.722055 −0.0254491
\(806\) −69.0477 −2.43210
\(807\) 21.3987 0.753269
\(808\) −7.37040 −0.259290
\(809\) −37.6282 −1.32294 −0.661469 0.749973i \(-0.730067\pi\)
−0.661469 + 0.749973i \(0.730067\pi\)
\(810\) 8.34022 0.293045
\(811\) −3.04195 −0.106817 −0.0534087 0.998573i \(-0.517009\pi\)
−0.0534087 + 0.998573i \(0.517009\pi\)
\(812\) 10.7364 0.376772
\(813\) −26.2414 −0.920326
\(814\) 0 0
\(815\) −41.4243 −1.45103
\(816\) −11.1213 −0.389325
\(817\) 45.2043 1.58150
\(818\) −41.6342 −1.45571
\(819\) −6.11977 −0.213842
\(820\) 160.258 5.59644
\(821\) 37.2094 1.29862 0.649309 0.760525i \(-0.275058\pi\)
0.649309 + 0.760525i \(0.275058\pi\)
\(822\) 14.9325 0.520831
\(823\) −36.4957 −1.27216 −0.636080 0.771623i \(-0.719445\pi\)
−0.636080 + 0.771623i \(0.719445\pi\)
\(824\) 43.7332 1.52352
\(825\) 0 0
\(826\) −28.7411 −1.00003
\(827\) 52.8436 1.83755 0.918776 0.394779i \(-0.129179\pi\)
0.918776 + 0.394779i \(0.129179\pi\)
\(828\) −0.822738 −0.0285921
\(829\) −43.4225 −1.50813 −0.754063 0.656802i \(-0.771909\pi\)
−0.754063 + 0.656802i \(0.771909\pi\)
\(830\) −6.15454 −0.213627
\(831\) 18.5696 0.644171
\(832\) 55.2199 1.91441
\(833\) 3.21046 0.111236
\(834\) −16.4588 −0.569923
\(835\) −9.94729 −0.344240
\(836\) 0 0
\(837\) −4.64136 −0.160429
\(838\) 35.0038 1.20919
\(839\) 27.6102 0.953211 0.476605 0.879117i \(-0.341867\pi\)
0.476605 + 0.879117i \(0.341867\pi\)
\(840\) −15.9241 −0.549433
\(841\) −21.4575 −0.739915
\(842\) −26.9090 −0.927347
\(843\) −4.24906 −0.146345
\(844\) 78.6892 2.70860
\(845\) 83.8911 2.88594
\(846\) −14.3793 −0.494370
\(847\) 0 0
\(848\) −22.0127 −0.755920
\(849\) −20.5277 −0.704508
\(850\) 52.8441 1.81254
\(851\) 1.97269 0.0676229
\(852\) 20.3072 0.695714
\(853\) 22.4005 0.766980 0.383490 0.923545i \(-0.374722\pi\)
0.383490 + 0.923545i \(0.374722\pi\)
\(854\) 22.3693 0.765462
\(855\) 21.7527 0.743927
\(856\) 32.6436 1.11574
\(857\) −8.30018 −0.283529 −0.141764 0.989900i \(-0.545278\pi\)
−0.141764 + 0.989900i \(0.545278\pi\)
\(858\) 0 0
\(859\) 5.09088 0.173699 0.0868493 0.996221i \(-0.472320\pi\)
0.0868493 + 0.996221i \(0.472320\pi\)
\(860\) 95.6279 3.26088
\(861\) −11.9484 −0.407200
\(862\) 37.9641 1.29306
\(863\) 44.7322 1.52270 0.761352 0.648339i \(-0.224536\pi\)
0.761352 + 0.648339i \(0.224536\pi\)
\(864\) 0.861816 0.0293196
\(865\) −49.9929 −1.69981
\(866\) 5.28574 0.179617
\(867\) 6.69297 0.227305
\(868\) 18.1445 0.615866
\(869\) 0 0
\(870\) −22.9052 −0.776559
\(871\) 23.8085 0.806720
\(872\) −11.0019 −0.372572
\(873\) 12.0534 0.407945
\(874\) −3.24365 −0.109718
\(875\) 6.07658 0.205426
\(876\) 51.5041 1.74016
\(877\) −8.54938 −0.288692 −0.144346 0.989527i \(-0.546108\pi\)
−0.144346 + 0.989527i \(0.546108\pi\)
\(878\) −22.9654 −0.775046
\(879\) 21.2022 0.715134
\(880\) 0 0
\(881\) 38.1169 1.28419 0.642095 0.766625i \(-0.278065\pi\)
0.642095 + 0.766625i \(0.278065\pi\)
\(882\) 2.43091 0.0818529
\(883\) 2.36088 0.0794500 0.0397250 0.999211i \(-0.487352\pi\)
0.0397250 + 0.999211i \(0.487352\pi\)
\(884\) −76.8072 −2.58331
\(885\) 40.5644 1.36356
\(886\) 19.6593 0.660469
\(887\) 11.5996 0.389477 0.194738 0.980855i \(-0.437614\pi\)
0.194738 + 0.980855i \(0.437614\pi\)
\(888\) 43.5054 1.45995
\(889\) −19.5307 −0.655038
\(890\) −77.9354 −2.61240
\(891\) 0 0
\(892\) −81.5840 −2.73163
\(893\) −37.5037 −1.25501
\(894\) 43.3197 1.44883
\(895\) 64.8723 2.16844
\(896\) −20.2109 −0.675200
\(897\) −1.28794 −0.0430031
\(898\) −69.4864 −2.31879
\(899\) 12.7468 0.425131
\(900\) 26.4705 0.882349
\(901\) −20.4009 −0.679653
\(902\) 0 0
\(903\) −7.12976 −0.237264
\(904\) 1.89899 0.0631593
\(905\) 54.1100 1.79868
\(906\) −1.48457 −0.0493215
\(907\) −5.25241 −0.174403 −0.0872017 0.996191i \(-0.527792\pi\)
−0.0872017 + 0.996191i \(0.527792\pi\)
\(908\) 11.9974 0.398147
\(909\) −1.58798 −0.0526701
\(910\) −51.0402 −1.69197
\(911\) 14.4254 0.477934 0.238967 0.971028i \(-0.423191\pi\)
0.238967 + 0.971028i \(0.423191\pi\)
\(912\) −21.9632 −0.727273
\(913\) 0 0
\(914\) 20.0723 0.663933
\(915\) −31.5713 −1.04372
\(916\) −32.6728 −1.07954
\(917\) 19.3750 0.639819
\(918\) −7.80432 −0.257581
\(919\) −0.440140 −0.0145189 −0.00725945 0.999974i \(-0.502311\pi\)
−0.00725945 + 0.999974i \(0.502311\pi\)
\(920\) −3.35132 −0.110490
\(921\) −23.0007 −0.757898
\(922\) −32.4152 −1.06754
\(923\) 31.7896 1.04637
\(924\) 0 0
\(925\) −63.4686 −2.08683
\(926\) 64.7786 2.12876
\(927\) 9.42249 0.309475
\(928\) −2.36685 −0.0776957
\(929\) −44.8443 −1.47130 −0.735648 0.677364i \(-0.763122\pi\)
−0.735648 + 0.677364i \(0.763122\pi\)
\(930\) −38.7100 −1.26935
\(931\) 6.34022 0.207792
\(932\) −21.5118 −0.704642
\(933\) −7.36753 −0.241202
\(934\) 70.0573 2.29234
\(935\) 0 0
\(936\) −28.4041 −0.928416
\(937\) −25.6547 −0.838103 −0.419051 0.907963i \(-0.637637\pi\)
−0.419051 + 0.907963i \(0.637637\pi\)
\(938\) −9.45726 −0.308790
\(939\) 4.80590 0.156835
\(940\) −79.3375 −2.58771
\(941\) 47.6122 1.55211 0.776056 0.630663i \(-0.217217\pi\)
0.776056 + 0.630663i \(0.217217\pi\)
\(942\) −16.5854 −0.540383
\(943\) −2.51461 −0.0818869
\(944\) −40.9568 −1.33303
\(945\) −3.43091 −0.111607
\(946\) 0 0
\(947\) −43.8549 −1.42509 −0.712546 0.701625i \(-0.752458\pi\)
−0.712546 + 0.701625i \(0.752458\pi\)
\(948\) 16.9282 0.549802
\(949\) 80.6263 2.61724
\(950\) 104.360 3.38588
\(951\) 1.54178 0.0499957
\(952\) 14.9009 0.482941
\(953\) 30.5035 0.988106 0.494053 0.869432i \(-0.335515\pi\)
0.494053 + 0.869432i \(0.335515\pi\)
\(954\) −15.4473 −0.500124
\(955\) −66.9479 −2.16638
\(956\) 9.00580 0.291268
\(957\) 0 0
\(958\) 17.0997 0.552467
\(959\) −6.14277 −0.198360
\(960\) 30.9578 0.999157
\(961\) −9.45774 −0.305088
\(962\) 139.444 4.49587
\(963\) 7.03319 0.226642
\(964\) −40.5013 −1.30446
\(965\) −78.8526 −2.53836
\(966\) 0.511599 0.0164604
\(967\) 14.1404 0.454726 0.227363 0.973810i \(-0.426990\pi\)
0.227363 + 0.973810i \(0.426990\pi\)
\(968\) 0 0
\(969\) −20.3550 −0.653897
\(970\) 100.528 3.22776
\(971\) 18.1712 0.583141 0.291571 0.956549i \(-0.405822\pi\)
0.291571 + 0.956549i \(0.405822\pi\)
\(972\) −3.90931 −0.125391
\(973\) 6.77065 0.217057
\(974\) −36.9068 −1.18257
\(975\) 41.4377 1.32707
\(976\) 31.8768 1.02035
\(977\) 47.4599 1.51838 0.759188 0.650871i \(-0.225596\pi\)
0.759188 + 0.650871i \(0.225596\pi\)
\(978\) 29.3504 0.938523
\(979\) 0 0
\(980\) 13.4125 0.428446
\(981\) −2.37040 −0.0756812
\(982\) −37.9643 −1.21149
\(983\) 53.8977 1.71907 0.859535 0.511076i \(-0.170753\pi\)
0.859535 + 0.511076i \(0.170753\pi\)
\(984\) −55.4568 −1.76790
\(985\) 38.8441 1.23767
\(986\) 21.4334 0.682580
\(987\) 5.91520 0.188283
\(988\) −151.684 −4.82571
\(989\) −1.50050 −0.0477132
\(990\) 0 0
\(991\) −5.06529 −0.160904 −0.0804521 0.996758i \(-0.525636\pi\)
−0.0804521 + 0.996758i \(0.525636\pi\)
\(992\) −4.00000 −0.127000
\(993\) 12.8925 0.409130
\(994\) −12.6275 −0.400521
\(995\) −22.0894 −0.700283
\(996\) 2.88482 0.0914090
\(997\) 14.8081 0.468979 0.234489 0.972119i \(-0.424658\pi\)
0.234489 + 0.972119i \(0.424658\pi\)
\(998\) 24.2941 0.769015
\(999\) 9.37341 0.296562
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 2541.2.a.bo.1.4 yes 4
3.2 odd 2 7623.2.a.cf.1.1 4
11.10 odd 2 2541.2.a.bk.1.1 4
33.32 even 2 7623.2.a.cm.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2541.2.a.bk.1.1 4 11.10 odd 2
2541.2.a.bo.1.4 yes 4 1.1 even 1 trivial
7623.2.a.cf.1.1 4 3.2 odd 2
7623.2.a.cm.1.4 4 33.32 even 2