Properties

Label 1881.2.a.k.1.5
Level $1881$
Weight $2$
Character 1881.1
Self dual yes
Analytic conductor $15.020$
Analytic rank $0$
Dimension $5$
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] = [1881,2,Mod(1,1881)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1881, 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("1881.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1881.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: \(15.0198606202\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.246832.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 209)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.245526\) of defining polynomial
Character \(\chi\) \(=\) 1881.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.18524 q^{2} +2.77529 q^{4} +3.43077 q^{5} +3.93972 q^{7} +1.69419 q^{8} +O(q^{10})\) \(q+2.18524 q^{2} +2.77529 q^{4} +3.43077 q^{5} +3.93972 q^{7} +1.69419 q^{8} +7.49706 q^{10} -1.00000 q^{11} +3.31182 q^{13} +8.60924 q^{14} -1.84836 q^{16} -2.80637 q^{17} -1.00000 q^{19} +9.52137 q^{20} -2.18524 q^{22} -6.88998 q^{23} +6.77018 q^{25} +7.23713 q^{26} +10.9338 q^{28} -5.67979 q^{29} +2.51864 q^{31} -7.42749 q^{32} -6.13259 q^{34} +13.5163 q^{35} -6.39893 q^{37} -2.18524 q^{38} +5.81238 q^{40} -0.560629 q^{41} -9.40080 q^{43} -2.77529 q^{44} -15.0563 q^{46} +12.1742 q^{47} +8.52137 q^{49} +14.7945 q^{50} +9.19126 q^{52} -5.68316 q^{53} -3.43077 q^{55} +6.67463 q^{56} -12.4117 q^{58} -4.35730 q^{59} -3.56412 q^{61} +5.50384 q^{62} -12.5342 q^{64} +11.3621 q^{65} -9.95563 q^{67} -7.78847 q^{68} +29.5363 q^{70} +11.4671 q^{71} -8.95834 q^{73} -13.9832 q^{74} -2.77529 q^{76} -3.93972 q^{77} +8.49105 q^{79} -6.34128 q^{80} -1.22511 q^{82} +5.21960 q^{83} -9.62799 q^{85} -20.5430 q^{86} -1.69419 q^{88} +7.28423 q^{89} +13.0476 q^{91} -19.1217 q^{92} +26.6036 q^{94} -3.43077 q^{95} +10.6574 q^{97} +18.6213 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{2} + 6 q^{4} + 5 q^{5} + 6 q^{7} - 6 q^{8} + 12 q^{10} - 5 q^{11} + 4 q^{13} + 14 q^{14} + 8 q^{16} + 4 q^{17} - 5 q^{19} + 8 q^{20} + 2 q^{22} - 3 q^{23} + 6 q^{25} + 6 q^{26} - 10 q^{28} - 10 q^{29} + 11 q^{31} - 14 q^{32} - 4 q^{34} + 8 q^{35} + q^{37} + 2 q^{38} - 16 q^{40} - 2 q^{41} + 20 q^{43} - 6 q^{44} - 4 q^{46} + 20 q^{47} + 3 q^{49} + 32 q^{50} + 6 q^{52} + 14 q^{53} - 5 q^{55} + 38 q^{56} - 6 q^{58} - 3 q^{59} - 10 q^{61} + 6 q^{62} + 9 q^{67} - 24 q^{68} + 50 q^{70} - 23 q^{71} - 8 q^{74} - 6 q^{76} - 6 q^{77} + 44 q^{79} + 18 q^{80} - 30 q^{82} + 14 q^{83} - 12 q^{85} - 52 q^{86} + 6 q^{88} + 27 q^{89} + 24 q^{91} - 58 q^{92} - 8 q^{94} - 5 q^{95} + 15 q^{97} + 10 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18524 1.54520 0.772600 0.634893i \(-0.218956\pi\)
0.772600 + 0.634893i \(0.218956\pi\)
\(3\) 0 0
\(4\) 2.77529 1.38764
\(5\) 3.43077 1.53429 0.767143 0.641476i \(-0.221678\pi\)
0.767143 + 0.641476i \(0.221678\pi\)
\(6\) 0 0
\(7\) 3.93972 1.48907 0.744537 0.667582i \(-0.232671\pi\)
0.744537 + 0.667582i \(0.232671\pi\)
\(8\) 1.69419 0.598987
\(9\) 0 0
\(10\) 7.49706 2.37078
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 3.31182 0.918534 0.459267 0.888298i \(-0.348112\pi\)
0.459267 + 0.888298i \(0.348112\pi\)
\(14\) 8.60924 2.30092
\(15\) 0 0
\(16\) −1.84836 −0.462089
\(17\) −2.80637 −0.680644 −0.340322 0.940309i \(-0.610536\pi\)
−0.340322 + 0.940309i \(0.610536\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 9.52137 2.12904
\(21\) 0 0
\(22\) −2.18524 −0.465895
\(23\) −6.88998 −1.43666 −0.718330 0.695702i \(-0.755093\pi\)
−0.718330 + 0.695702i \(0.755093\pi\)
\(24\) 0 0
\(25\) 6.77018 1.35404
\(26\) 7.23713 1.41932
\(27\) 0 0
\(28\) 10.9338 2.06630
\(29\) −5.67979 −1.05471 −0.527355 0.849645i \(-0.676816\pi\)
−0.527355 + 0.849645i \(0.676816\pi\)
\(30\) 0 0
\(31\) 2.51864 0.452361 0.226180 0.974085i \(-0.427376\pi\)
0.226180 + 0.974085i \(0.427376\pi\)
\(32\) −7.42749 −1.31301
\(33\) 0 0
\(34\) −6.13259 −1.05173
\(35\) 13.5163 2.28466
\(36\) 0 0
\(37\) −6.39893 −1.05198 −0.525989 0.850491i \(-0.676305\pi\)
−0.525989 + 0.850491i \(0.676305\pi\)
\(38\) −2.18524 −0.354493
\(39\) 0 0
\(40\) 5.81238 0.919018
\(41\) −0.560629 −0.0875555 −0.0437778 0.999041i \(-0.513939\pi\)
−0.0437778 + 0.999041i \(0.513939\pi\)
\(42\) 0 0
\(43\) −9.40080 −1.43361 −0.716805 0.697274i \(-0.754396\pi\)
−0.716805 + 0.697274i \(0.754396\pi\)
\(44\) −2.77529 −0.418390
\(45\) 0 0
\(46\) −15.0563 −2.21993
\(47\) 12.1742 1.77579 0.887896 0.460044i \(-0.152166\pi\)
0.887896 + 0.460044i \(0.152166\pi\)
\(48\) 0 0
\(49\) 8.52137 1.21734
\(50\) 14.7945 2.09226
\(51\) 0 0
\(52\) 9.19126 1.27460
\(53\) −5.68316 −0.780643 −0.390321 0.920679i \(-0.627636\pi\)
−0.390321 + 0.920679i \(0.627636\pi\)
\(54\) 0 0
\(55\) −3.43077 −0.462605
\(56\) 6.67463 0.891935
\(57\) 0 0
\(58\) −12.4117 −1.62974
\(59\) −4.35730 −0.567273 −0.283636 0.958932i \(-0.591541\pi\)
−0.283636 + 0.958932i \(0.591541\pi\)
\(60\) 0 0
\(61\) −3.56412 −0.456339 −0.228169 0.973621i \(-0.573274\pi\)
−0.228169 + 0.973621i \(0.573274\pi\)
\(62\) 5.50384 0.698988
\(63\) 0 0
\(64\) −12.5342 −1.56677
\(65\) 11.3621 1.40929
\(66\) 0 0
\(67\) −9.95563 −1.21627 −0.608137 0.793832i \(-0.708083\pi\)
−0.608137 + 0.793832i \(0.708083\pi\)
\(68\) −7.78847 −0.944491
\(69\) 0 0
\(70\) 29.5363 3.53026
\(71\) 11.4671 1.36089 0.680447 0.732797i \(-0.261786\pi\)
0.680447 + 0.732797i \(0.261786\pi\)
\(72\) 0 0
\(73\) −8.95834 −1.04849 −0.524247 0.851566i \(-0.675653\pi\)
−0.524247 + 0.851566i \(0.675653\pi\)
\(74\) −13.9832 −1.62552
\(75\) 0 0
\(76\) −2.77529 −0.318347
\(77\) −3.93972 −0.448972
\(78\) 0 0
\(79\) 8.49105 0.955318 0.477659 0.878545i \(-0.341485\pi\)
0.477659 + 0.878545i \(0.341485\pi\)
\(80\) −6.34128 −0.708977
\(81\) 0 0
\(82\) −1.22511 −0.135291
\(83\) 5.21960 0.572926 0.286463 0.958091i \(-0.407520\pi\)
0.286463 + 0.958091i \(0.407520\pi\)
\(84\) 0 0
\(85\) −9.62799 −1.04430
\(86\) −20.5430 −2.21521
\(87\) 0 0
\(88\) −1.69419 −0.180601
\(89\) 7.28423 0.772127 0.386064 0.922472i \(-0.373834\pi\)
0.386064 + 0.922472i \(0.373834\pi\)
\(90\) 0 0
\(91\) 13.0476 1.36776
\(92\) −19.1217 −1.99357
\(93\) 0 0
\(94\) 26.6036 2.74395
\(95\) −3.43077 −0.351989
\(96\) 0 0
\(97\) 10.6574 1.08209 0.541045 0.840993i \(-0.318029\pi\)
0.541045 + 0.840993i \(0.318029\pi\)
\(98\) 18.6213 1.88103
\(99\) 0 0
\(100\) 18.7892 1.87892
\(101\) 11.4716 1.14147 0.570735 0.821134i \(-0.306658\pi\)
0.570735 + 0.821134i \(0.306658\pi\)
\(102\) 0 0
\(103\) 18.3034 1.80349 0.901745 0.432268i \(-0.142286\pi\)
0.901745 + 0.432268i \(0.142286\pi\)
\(104\) 5.61086 0.550190
\(105\) 0 0
\(106\) −12.4191 −1.20625
\(107\) −1.38838 −0.134220 −0.0671100 0.997746i \(-0.521378\pi\)
−0.0671100 + 0.997746i \(0.521378\pi\)
\(108\) 0 0
\(109\) −0.412113 −0.0394732 −0.0197366 0.999805i \(-0.506283\pi\)
−0.0197366 + 0.999805i \(0.506283\pi\)
\(110\) −7.49706 −0.714817
\(111\) 0 0
\(112\) −7.28200 −0.688084
\(113\) 6.54003 0.615234 0.307617 0.951510i \(-0.400468\pi\)
0.307617 + 0.951510i \(0.400468\pi\)
\(114\) 0 0
\(115\) −23.6379 −2.20425
\(116\) −15.7630 −1.46356
\(117\) 0 0
\(118\) −9.52177 −0.876550
\(119\) −11.0563 −1.01353
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −7.78847 −0.705135
\(123\) 0 0
\(124\) 6.98995 0.627716
\(125\) 6.07307 0.543192
\(126\) 0 0
\(127\) 9.08005 0.805724 0.402862 0.915261i \(-0.368015\pi\)
0.402862 + 0.915261i \(0.368015\pi\)
\(128\) −12.5352 −1.10797
\(129\) 0 0
\(130\) 24.8289 2.17764
\(131\) 10.3876 0.907571 0.453785 0.891111i \(-0.350073\pi\)
0.453785 + 0.891111i \(0.350073\pi\)
\(132\) 0 0
\(133\) −3.93972 −0.341617
\(134\) −21.7555 −1.87939
\(135\) 0 0
\(136\) −4.75452 −0.407697
\(137\) 0.798293 0.0682028 0.0341014 0.999418i \(-0.489143\pi\)
0.0341014 + 0.999418i \(0.489143\pi\)
\(138\) 0 0
\(139\) 5.03184 0.426795 0.213398 0.976965i \(-0.431547\pi\)
0.213398 + 0.976965i \(0.431547\pi\)
\(140\) 37.5115 3.17030
\(141\) 0 0
\(142\) 25.0584 2.10285
\(143\) −3.31182 −0.276948
\(144\) 0 0
\(145\) −19.4860 −1.61823
\(146\) −19.5761 −1.62013
\(147\) 0 0
\(148\) −17.7589 −1.45977
\(149\) −19.8351 −1.62496 −0.812479 0.582991i \(-0.801882\pi\)
−0.812479 + 0.582991i \(0.801882\pi\)
\(150\) 0 0
\(151\) 22.5447 1.83466 0.917331 0.398125i \(-0.130339\pi\)
0.917331 + 0.398125i \(0.130339\pi\)
\(152\) −1.69419 −0.137417
\(153\) 0 0
\(154\) −8.60924 −0.693752
\(155\) 8.64087 0.694051
\(156\) 0 0
\(157\) −11.8013 −0.941843 −0.470921 0.882175i \(-0.656078\pi\)
−0.470921 + 0.882175i \(0.656078\pi\)
\(158\) 18.5550 1.47616
\(159\) 0 0
\(160\) −25.4820 −2.01453
\(161\) −27.1446 −2.13929
\(162\) 0 0
\(163\) −24.8395 −1.94558 −0.972789 0.231691i \(-0.925574\pi\)
−0.972789 + 0.231691i \(0.925574\pi\)
\(164\) −1.55591 −0.121496
\(165\) 0 0
\(166\) 11.4061 0.885285
\(167\) 2.79938 0.216623 0.108311 0.994117i \(-0.465456\pi\)
0.108311 + 0.994117i \(0.465456\pi\)
\(168\) 0 0
\(169\) −2.03184 −0.156295
\(170\) −21.0395 −1.61366
\(171\) 0 0
\(172\) −26.0899 −1.98934
\(173\) 6.43926 0.489568 0.244784 0.969578i \(-0.421283\pi\)
0.244784 + 0.969578i \(0.421283\pi\)
\(174\) 0 0
\(175\) 26.6726 2.01626
\(176\) 1.84836 0.139325
\(177\) 0 0
\(178\) 15.9178 1.19309
\(179\) −12.5241 −0.936095 −0.468048 0.883703i \(-0.655042\pi\)
−0.468048 + 0.883703i \(0.655042\pi\)
\(180\) 0 0
\(181\) 13.7515 1.02214 0.511071 0.859538i \(-0.329249\pi\)
0.511071 + 0.859538i \(0.329249\pi\)
\(182\) 28.5123 2.11347
\(183\) 0 0
\(184\) −11.6729 −0.860541
\(185\) −21.9533 −1.61404
\(186\) 0 0
\(187\) 2.80637 0.205222
\(188\) 33.7869 2.46417
\(189\) 0 0
\(190\) −7.49706 −0.543894
\(191\) −3.10678 −0.224799 −0.112399 0.993663i \(-0.535854\pi\)
−0.112399 + 0.993663i \(0.535854\pi\)
\(192\) 0 0
\(193\) −0.747815 −0.0538289 −0.0269144 0.999638i \(-0.508568\pi\)
−0.0269144 + 0.999638i \(0.508568\pi\)
\(194\) 23.2889 1.67205
\(195\) 0 0
\(196\) 23.6492 1.68923
\(197\) 3.41798 0.243521 0.121761 0.992559i \(-0.461146\pi\)
0.121761 + 0.992559i \(0.461146\pi\)
\(198\) 0 0
\(199\) 5.36785 0.380517 0.190258 0.981734i \(-0.439067\pi\)
0.190258 + 0.981734i \(0.439067\pi\)
\(200\) 11.4700 0.811049
\(201\) 0 0
\(202\) 25.0683 1.76380
\(203\) −22.3768 −1.57054
\(204\) 0 0
\(205\) −1.92339 −0.134335
\(206\) 39.9974 2.78675
\(207\) 0 0
\(208\) −6.12142 −0.424444
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 2.55492 0.175888 0.0879441 0.996125i \(-0.471970\pi\)
0.0879441 + 0.996125i \(0.471970\pi\)
\(212\) −15.7724 −1.08325
\(213\) 0 0
\(214\) −3.03395 −0.207397
\(215\) −32.2520 −2.19957
\(216\) 0 0
\(217\) 9.92272 0.673598
\(218\) −0.900566 −0.0609940
\(219\) 0 0
\(220\) −9.52137 −0.641931
\(221\) −9.29418 −0.625194
\(222\) 0 0
\(223\) −24.9404 −1.67013 −0.835066 0.550149i \(-0.814571\pi\)
−0.835066 + 0.550149i \(0.814571\pi\)
\(224\) −29.2622 −1.95516
\(225\) 0 0
\(226\) 14.2915 0.950660
\(227\) 22.8254 1.51497 0.757487 0.652851i \(-0.226427\pi\)
0.757487 + 0.652851i \(0.226427\pi\)
\(228\) 0 0
\(229\) −0.603546 −0.0398834 −0.0199417 0.999801i \(-0.506348\pi\)
−0.0199417 + 0.999801i \(0.506348\pi\)
\(230\) −51.6546 −3.40601
\(231\) 0 0
\(232\) −9.62264 −0.631757
\(233\) −17.3705 −1.13798 −0.568988 0.822346i \(-0.692665\pi\)
−0.568988 + 0.822346i \(0.692665\pi\)
\(234\) 0 0
\(235\) 41.7669 2.72457
\(236\) −12.0928 −0.787172
\(237\) 0 0
\(238\) −24.1607 −1.56610
\(239\) −7.23486 −0.467984 −0.233992 0.972238i \(-0.575179\pi\)
−0.233992 + 0.972238i \(0.575179\pi\)
\(240\) 0 0
\(241\) −12.2034 −0.786090 −0.393045 0.919519i \(-0.628578\pi\)
−0.393045 + 0.919519i \(0.628578\pi\)
\(242\) 2.18524 0.140473
\(243\) 0 0
\(244\) −9.89146 −0.633236
\(245\) 29.2349 1.86775
\(246\) 0 0
\(247\) −3.31182 −0.210726
\(248\) 4.26705 0.270958
\(249\) 0 0
\(250\) 13.2711 0.839340
\(251\) 14.0923 0.889499 0.444750 0.895655i \(-0.353293\pi\)
0.444750 + 0.895655i \(0.353293\pi\)
\(252\) 0 0
\(253\) 6.88998 0.433169
\(254\) 19.8421 1.24501
\(255\) 0 0
\(256\) −2.32415 −0.145259
\(257\) −0.440920 −0.0275038 −0.0137519 0.999905i \(-0.504378\pi\)
−0.0137519 + 0.999905i \(0.504378\pi\)
\(258\) 0 0
\(259\) −25.2100 −1.56647
\(260\) 31.5331 1.95560
\(261\) 0 0
\(262\) 22.6995 1.40238
\(263\) 15.0661 0.929016 0.464508 0.885569i \(-0.346231\pi\)
0.464508 + 0.885569i \(0.346231\pi\)
\(264\) 0 0
\(265\) −19.4976 −1.19773
\(266\) −8.60924 −0.527866
\(267\) 0 0
\(268\) −27.6297 −1.68775
\(269\) 7.25751 0.442498 0.221249 0.975217i \(-0.428987\pi\)
0.221249 + 0.975217i \(0.428987\pi\)
\(270\) 0 0
\(271\) −16.8878 −1.02586 −0.512931 0.858430i \(-0.671440\pi\)
−0.512931 + 0.858430i \(0.671440\pi\)
\(272\) 5.18716 0.314518
\(273\) 0 0
\(274\) 1.74446 0.105387
\(275\) −6.77018 −0.408257
\(276\) 0 0
\(277\) −15.3818 −0.924204 −0.462102 0.886827i \(-0.652905\pi\)
−0.462102 + 0.886827i \(0.652905\pi\)
\(278\) 10.9958 0.659484
\(279\) 0 0
\(280\) 22.8991 1.36848
\(281\) 25.8974 1.54491 0.772456 0.635069i \(-0.219028\pi\)
0.772456 + 0.635069i \(0.219028\pi\)
\(282\) 0 0
\(283\) 18.6882 1.11090 0.555450 0.831550i \(-0.312546\pi\)
0.555450 + 0.831550i \(0.312546\pi\)
\(284\) 31.8245 1.88844
\(285\) 0 0
\(286\) −7.23713 −0.427941
\(287\) −2.20872 −0.130377
\(288\) 0 0
\(289\) −9.12431 −0.536724
\(290\) −42.5817 −2.50049
\(291\) 0 0
\(292\) −24.8620 −1.45494
\(293\) −26.7471 −1.56258 −0.781291 0.624167i \(-0.785439\pi\)
−0.781291 + 0.624167i \(0.785439\pi\)
\(294\) 0 0
\(295\) −14.9489 −0.870359
\(296\) −10.8410 −0.630121
\(297\) 0 0
\(298\) −43.3446 −2.51088
\(299\) −22.8184 −1.31962
\(300\) 0 0
\(301\) −37.0365 −2.13475
\(302\) 49.2657 2.83492
\(303\) 0 0
\(304\) 1.84836 0.106010
\(305\) −12.2277 −0.700155
\(306\) 0 0
\(307\) 22.6415 1.29222 0.646109 0.763245i \(-0.276395\pi\)
0.646109 + 0.763245i \(0.276395\pi\)
\(308\) −10.9338 −0.623014
\(309\) 0 0
\(310\) 18.8824 1.07245
\(311\) 1.38723 0.0786628 0.0393314 0.999226i \(-0.487477\pi\)
0.0393314 + 0.999226i \(0.487477\pi\)
\(312\) 0 0
\(313\) 12.9018 0.729255 0.364627 0.931153i \(-0.381196\pi\)
0.364627 + 0.931153i \(0.381196\pi\)
\(314\) −25.7886 −1.45534
\(315\) 0 0
\(316\) 23.5651 1.32564
\(317\) 19.0712 1.07114 0.535572 0.844489i \(-0.320096\pi\)
0.535572 + 0.844489i \(0.320096\pi\)
\(318\) 0 0
\(319\) 5.67979 0.318007
\(320\) −43.0018 −2.40387
\(321\) 0 0
\(322\) −59.3175 −3.30564
\(323\) 2.80637 0.156150
\(324\) 0 0
\(325\) 22.4216 1.24373
\(326\) −54.2803 −3.00631
\(327\) 0 0
\(328\) −0.949812 −0.0524446
\(329\) 47.9630 2.64428
\(330\) 0 0
\(331\) −12.4616 −0.684952 −0.342476 0.939527i \(-0.611265\pi\)
−0.342476 + 0.939527i \(0.611265\pi\)
\(332\) 14.4859 0.795017
\(333\) 0 0
\(334\) 6.11733 0.334725
\(335\) −34.1555 −1.86611
\(336\) 0 0
\(337\) −0.401035 −0.0218458 −0.0109229 0.999940i \(-0.503477\pi\)
−0.0109229 + 0.999940i \(0.503477\pi\)
\(338\) −4.44006 −0.241508
\(339\) 0 0
\(340\) −26.7204 −1.44912
\(341\) −2.51864 −0.136392
\(342\) 0 0
\(343\) 5.99377 0.323633
\(344\) −15.9268 −0.858713
\(345\) 0 0
\(346\) 14.0713 0.756480
\(347\) −1.06608 −0.0572304 −0.0286152 0.999591i \(-0.509110\pi\)
−0.0286152 + 0.999591i \(0.509110\pi\)
\(348\) 0 0
\(349\) 22.2695 1.19206 0.596029 0.802963i \(-0.296744\pi\)
0.596029 + 0.802963i \(0.296744\pi\)
\(350\) 58.2861 3.11552
\(351\) 0 0
\(352\) 7.42749 0.395886
\(353\) −12.3631 −0.658023 −0.329012 0.944326i \(-0.606716\pi\)
−0.329012 + 0.944326i \(0.606716\pi\)
\(354\) 0 0
\(355\) 39.3410 2.08800
\(356\) 20.2158 1.07144
\(357\) 0 0
\(358\) −27.3682 −1.44645
\(359\) −32.1914 −1.69899 −0.849497 0.527593i \(-0.823095\pi\)
−0.849497 + 0.527593i \(0.823095\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 30.0504 1.57941
\(363\) 0 0
\(364\) 36.2109 1.89797
\(365\) −30.7340 −1.60869
\(366\) 0 0
\(367\) −18.9777 −0.990628 −0.495314 0.868714i \(-0.664947\pi\)
−0.495314 + 0.868714i \(0.664947\pi\)
\(368\) 12.7351 0.663865
\(369\) 0 0
\(370\) −47.9732 −2.49401
\(371\) −22.3901 −1.16243
\(372\) 0 0
\(373\) 1.15238 0.0596678 0.0298339 0.999555i \(-0.490502\pi\)
0.0298339 + 0.999555i \(0.490502\pi\)
\(374\) 6.13259 0.317109
\(375\) 0 0
\(376\) 20.6254 1.06368
\(377\) −18.8104 −0.968787
\(378\) 0 0
\(379\) 13.5365 0.695325 0.347663 0.937620i \(-0.386975\pi\)
0.347663 + 0.937620i \(0.386975\pi\)
\(380\) −9.52137 −0.488436
\(381\) 0 0
\(382\) −6.78907 −0.347359
\(383\) −13.1671 −0.672809 −0.336404 0.941718i \(-0.609211\pi\)
−0.336404 + 0.941718i \(0.609211\pi\)
\(384\) 0 0
\(385\) −13.5163 −0.688852
\(386\) −1.63416 −0.0831764
\(387\) 0 0
\(388\) 29.5772 1.50156
\(389\) −0.223588 −0.0113364 −0.00566819 0.999984i \(-0.501804\pi\)
−0.00566819 + 0.999984i \(0.501804\pi\)
\(390\) 0 0
\(391\) 19.3358 0.977854
\(392\) 14.4368 0.729170
\(393\) 0 0
\(394\) 7.46913 0.376289
\(395\) 29.1308 1.46573
\(396\) 0 0
\(397\) −21.6504 −1.08660 −0.543301 0.839538i \(-0.682826\pi\)
−0.543301 + 0.839538i \(0.682826\pi\)
\(398\) 11.7301 0.587975
\(399\) 0 0
\(400\) −12.5137 −0.625685
\(401\) −1.30180 −0.0650089 −0.0325045 0.999472i \(-0.510348\pi\)
−0.0325045 + 0.999472i \(0.510348\pi\)
\(402\) 0 0
\(403\) 8.34128 0.415509
\(404\) 31.8371 1.58395
\(405\) 0 0
\(406\) −48.8986 −2.42680
\(407\) 6.39893 0.317183
\(408\) 0 0
\(409\) −2.15631 −0.106622 −0.0533112 0.998578i \(-0.516978\pi\)
−0.0533112 + 0.998578i \(0.516978\pi\)
\(410\) −4.20307 −0.207575
\(411\) 0 0
\(412\) 50.7973 2.50260
\(413\) −17.1665 −0.844710
\(414\) 0 0
\(415\) 17.9073 0.879032
\(416\) −24.5985 −1.20604
\(417\) 0 0
\(418\) 2.18524 0.106884
\(419\) 29.6335 1.44769 0.723844 0.689963i \(-0.242373\pi\)
0.723844 + 0.689963i \(0.242373\pi\)
\(420\) 0 0
\(421\) −5.25385 −0.256057 −0.128028 0.991770i \(-0.540865\pi\)
−0.128028 + 0.991770i \(0.540865\pi\)
\(422\) 5.58313 0.271782
\(423\) 0 0
\(424\) −9.62837 −0.467595
\(425\) −18.9996 −0.921616
\(426\) 0 0
\(427\) −14.0416 −0.679522
\(428\) −3.85316 −0.186249
\(429\) 0 0
\(430\) −70.4784 −3.39877
\(431\) −17.8489 −0.859752 −0.429876 0.902888i \(-0.641443\pi\)
−0.429876 + 0.902888i \(0.641443\pi\)
\(432\) 0 0
\(433\) −0.696383 −0.0334660 −0.0167330 0.999860i \(-0.505327\pi\)
−0.0167330 + 0.999860i \(0.505327\pi\)
\(434\) 21.6836 1.04084
\(435\) 0 0
\(436\) −1.14373 −0.0547748
\(437\) 6.88998 0.329593
\(438\) 0 0
\(439\) −24.8210 −1.18464 −0.592321 0.805702i \(-0.701788\pi\)
−0.592321 + 0.805702i \(0.701788\pi\)
\(440\) −5.81238 −0.277094
\(441\) 0 0
\(442\) −20.3100 −0.966050
\(443\) 3.93424 0.186922 0.0934608 0.995623i \(-0.470207\pi\)
0.0934608 + 0.995623i \(0.470207\pi\)
\(444\) 0 0
\(445\) 24.9905 1.18466
\(446\) −54.5008 −2.58069
\(447\) 0 0
\(448\) −49.3810 −2.33303
\(449\) −6.13394 −0.289479 −0.144739 0.989470i \(-0.546234\pi\)
−0.144739 + 0.989470i \(0.546234\pi\)
\(450\) 0 0
\(451\) 0.560629 0.0263990
\(452\) 18.1505 0.853725
\(453\) 0 0
\(454\) 49.8790 2.34094
\(455\) 44.7634 2.09854
\(456\) 0 0
\(457\) 8.40189 0.393024 0.196512 0.980501i \(-0.437039\pi\)
0.196512 + 0.980501i \(0.437039\pi\)
\(458\) −1.31889 −0.0616279
\(459\) 0 0
\(460\) −65.6021 −3.05871
\(461\) −25.9903 −1.21049 −0.605246 0.796039i \(-0.706925\pi\)
−0.605246 + 0.796039i \(0.706925\pi\)
\(462\) 0 0
\(463\) 19.3724 0.900311 0.450155 0.892950i \(-0.351369\pi\)
0.450155 + 0.892950i \(0.351369\pi\)
\(464\) 10.4983 0.487370
\(465\) 0 0
\(466\) −37.9587 −1.75840
\(467\) 34.6720 1.60443 0.802214 0.597037i \(-0.203655\pi\)
0.802214 + 0.597037i \(0.203655\pi\)
\(468\) 0 0
\(469\) −39.2224 −1.81112
\(470\) 91.2709 4.21001
\(471\) 0 0
\(472\) −7.38210 −0.339789
\(473\) 9.40080 0.432249
\(474\) 0 0
\(475\) −6.77018 −0.310637
\(476\) −30.6844 −1.40642
\(477\) 0 0
\(478\) −15.8099 −0.723130
\(479\) −23.2352 −1.06164 −0.530821 0.847484i \(-0.678117\pi\)
−0.530821 + 0.847484i \(0.678117\pi\)
\(480\) 0 0
\(481\) −21.1921 −0.966277
\(482\) −26.6674 −1.21467
\(483\) 0 0
\(484\) 2.77529 0.126149
\(485\) 36.5629 1.66024
\(486\) 0 0
\(487\) 14.2680 0.646545 0.323272 0.946306i \(-0.395217\pi\)
0.323272 + 0.946306i \(0.395217\pi\)
\(488\) −6.03830 −0.273341
\(489\) 0 0
\(490\) 63.8853 2.88604
\(491\) −41.6168 −1.87814 −0.939071 0.343724i \(-0.888311\pi\)
−0.939071 + 0.343724i \(0.888311\pi\)
\(492\) 0 0
\(493\) 15.9396 0.717882
\(494\) −7.23713 −0.325614
\(495\) 0 0
\(496\) −4.65534 −0.209031
\(497\) 45.1771 2.02647
\(498\) 0 0
\(499\) 19.9664 0.893820 0.446910 0.894579i \(-0.352524\pi\)
0.446910 + 0.894579i \(0.352524\pi\)
\(500\) 16.8545 0.753757
\(501\) 0 0
\(502\) 30.7951 1.37445
\(503\) −2.31362 −0.103159 −0.0515797 0.998669i \(-0.516426\pi\)
−0.0515797 + 0.998669i \(0.516426\pi\)
\(504\) 0 0
\(505\) 39.3565 1.75134
\(506\) 15.0563 0.669334
\(507\) 0 0
\(508\) 25.1998 1.11806
\(509\) 13.2009 0.585120 0.292560 0.956247i \(-0.405493\pi\)
0.292560 + 0.956247i \(0.405493\pi\)
\(510\) 0 0
\(511\) −35.2933 −1.56128
\(512\) 19.9916 0.883511
\(513\) 0 0
\(514\) −0.963517 −0.0424989
\(515\) 62.7948 2.76707
\(516\) 0 0
\(517\) −12.1742 −0.535421
\(518\) −55.0899 −2.42051
\(519\) 0 0
\(520\) 19.2496 0.844149
\(521\) 15.6498 0.685629 0.342814 0.939403i \(-0.388620\pi\)
0.342814 + 0.939403i \(0.388620\pi\)
\(522\) 0 0
\(523\) −17.7350 −0.775498 −0.387749 0.921765i \(-0.626747\pi\)
−0.387749 + 0.921765i \(0.626747\pi\)
\(524\) 28.8286 1.25938
\(525\) 0 0
\(526\) 32.9231 1.43552
\(527\) −7.06822 −0.307897
\(528\) 0 0
\(529\) 24.4719 1.06399
\(530\) −42.6071 −1.85073
\(531\) 0 0
\(532\) −10.9338 −0.474042
\(533\) −1.85670 −0.0804227
\(534\) 0 0
\(535\) −4.76322 −0.205932
\(536\) −16.8667 −0.728532
\(537\) 0 0
\(538\) 15.8594 0.683748
\(539\) −8.52137 −0.367041
\(540\) 0 0
\(541\) −34.5196 −1.48412 −0.742058 0.670336i \(-0.766150\pi\)
−0.742058 + 0.670336i \(0.766150\pi\)
\(542\) −36.9040 −1.58516
\(543\) 0 0
\(544\) 20.8442 0.893690
\(545\) −1.41386 −0.0605632
\(546\) 0 0
\(547\) 1.99561 0.0853263 0.0426632 0.999090i \(-0.486416\pi\)
0.0426632 + 0.999090i \(0.486416\pi\)
\(548\) 2.21549 0.0946411
\(549\) 0 0
\(550\) −14.7945 −0.630839
\(551\) 5.67979 0.241967
\(552\) 0 0
\(553\) 33.4523 1.42254
\(554\) −33.6130 −1.42808
\(555\) 0 0
\(556\) 13.9648 0.592239
\(557\) 23.5272 0.996881 0.498440 0.866924i \(-0.333906\pi\)
0.498440 + 0.866924i \(0.333906\pi\)
\(558\) 0 0
\(559\) −31.1338 −1.31682
\(560\) −24.9829 −1.05572
\(561\) 0 0
\(562\) 56.5922 2.38720
\(563\) −14.2122 −0.598972 −0.299486 0.954101i \(-0.596815\pi\)
−0.299486 + 0.954101i \(0.596815\pi\)
\(564\) 0 0
\(565\) 22.4373 0.943945
\(566\) 40.8383 1.71656
\(567\) 0 0
\(568\) 19.4275 0.815158
\(569\) −22.1906 −0.930277 −0.465138 0.885238i \(-0.653995\pi\)
−0.465138 + 0.885238i \(0.653995\pi\)
\(570\) 0 0
\(571\) 8.67954 0.363227 0.181614 0.983370i \(-0.441868\pi\)
0.181614 + 0.983370i \(0.441868\pi\)
\(572\) −9.19126 −0.384306
\(573\) 0 0
\(574\) −4.82659 −0.201458
\(575\) −46.6464 −1.94529
\(576\) 0 0
\(577\) 40.9150 1.70331 0.851657 0.524100i \(-0.175598\pi\)
0.851657 + 0.524100i \(0.175598\pi\)
\(578\) −19.9388 −0.829346
\(579\) 0 0
\(580\) −54.0794 −2.24552
\(581\) 20.5638 0.853128
\(582\) 0 0
\(583\) 5.68316 0.235373
\(584\) −15.1771 −0.628034
\(585\) 0 0
\(586\) −58.4489 −2.41450
\(587\) 21.2684 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(588\) 0 0
\(589\) −2.51864 −0.103779
\(590\) −32.6670 −1.34488
\(591\) 0 0
\(592\) 11.8275 0.486107
\(593\) 23.0212 0.945368 0.472684 0.881232i \(-0.343285\pi\)
0.472684 + 0.881232i \(0.343285\pi\)
\(594\) 0 0
\(595\) −37.9316 −1.55504
\(596\) −55.0482 −2.25486
\(597\) 0 0
\(598\) −49.8637 −2.03908
\(599\) 41.6249 1.70075 0.850374 0.526179i \(-0.176376\pi\)
0.850374 + 0.526179i \(0.176376\pi\)
\(600\) 0 0
\(601\) −20.8629 −0.851016 −0.425508 0.904955i \(-0.639905\pi\)
−0.425508 + 0.904955i \(0.639905\pi\)
\(602\) −80.9338 −3.29861
\(603\) 0 0
\(604\) 62.5680 2.54586
\(605\) 3.43077 0.139481
\(606\) 0 0
\(607\) −0.146703 −0.00595450 −0.00297725 0.999996i \(-0.500948\pi\)
−0.00297725 + 0.999996i \(0.500948\pi\)
\(608\) 7.42749 0.301224
\(609\) 0 0
\(610\) −26.7204 −1.08188
\(611\) 40.3188 1.63113
\(612\) 0 0
\(613\) −18.3393 −0.740716 −0.370358 0.928889i \(-0.620765\pi\)
−0.370358 + 0.928889i \(0.620765\pi\)
\(614\) 49.4772 1.99674
\(615\) 0 0
\(616\) −6.67463 −0.268929
\(617\) −4.12050 −0.165885 −0.0829425 0.996554i \(-0.526432\pi\)
−0.0829425 + 0.996554i \(0.526432\pi\)
\(618\) 0 0
\(619\) 28.5699 1.14832 0.574161 0.818743i \(-0.305328\pi\)
0.574161 + 0.818743i \(0.305328\pi\)
\(620\) 23.9809 0.963096
\(621\) 0 0
\(622\) 3.03144 0.121550
\(623\) 28.6978 1.14975
\(624\) 0 0
\(625\) −13.0156 −0.520624
\(626\) 28.1937 1.12684
\(627\) 0 0
\(628\) −32.7519 −1.30694
\(629\) 17.9577 0.716022
\(630\) 0 0
\(631\) 33.9323 1.35082 0.675412 0.737441i \(-0.263966\pi\)
0.675412 + 0.737441i \(0.263966\pi\)
\(632\) 14.3855 0.572223
\(633\) 0 0
\(634\) 41.6752 1.65513
\(635\) 31.1516 1.23621
\(636\) 0 0
\(637\) 28.2213 1.11817
\(638\) 12.4117 0.491385
\(639\) 0 0
\(640\) −43.0054 −1.69994
\(641\) −19.7694 −0.780844 −0.390422 0.920636i \(-0.627671\pi\)
−0.390422 + 0.920636i \(0.627671\pi\)
\(642\) 0 0
\(643\) 36.7642 1.44984 0.724920 0.688833i \(-0.241877\pi\)
0.724920 + 0.688833i \(0.241877\pi\)
\(644\) −75.3340 −2.96858
\(645\) 0 0
\(646\) 6.13259 0.241284
\(647\) −24.9430 −0.980610 −0.490305 0.871551i \(-0.663115\pi\)
−0.490305 + 0.871551i \(0.663115\pi\)
\(648\) 0 0
\(649\) 4.35730 0.171039
\(650\) 48.9967 1.92181
\(651\) 0 0
\(652\) −68.9367 −2.69977
\(653\) −8.60802 −0.336858 −0.168429 0.985714i \(-0.553869\pi\)
−0.168429 + 0.985714i \(0.553869\pi\)
\(654\) 0 0
\(655\) 35.6375 1.39247
\(656\) 1.03624 0.0404584
\(657\) 0 0
\(658\) 104.811 4.08595
\(659\) −27.7805 −1.08217 −0.541087 0.840967i \(-0.681987\pi\)
−0.541087 + 0.840967i \(0.681987\pi\)
\(660\) 0 0
\(661\) 30.8037 1.19812 0.599062 0.800702i \(-0.295540\pi\)
0.599062 + 0.800702i \(0.295540\pi\)
\(662\) −27.2316 −1.05839
\(663\) 0 0
\(664\) 8.84300 0.343175
\(665\) −13.5163 −0.524138
\(666\) 0 0
\(667\) 39.1336 1.51526
\(668\) 7.76909 0.300595
\(669\) 0 0
\(670\) −74.6380 −2.88352
\(671\) 3.56412 0.137591
\(672\) 0 0
\(673\) 15.2015 0.585974 0.292987 0.956116i \(-0.405351\pi\)
0.292987 + 0.956116i \(0.405351\pi\)
\(674\) −0.876359 −0.0337561
\(675\) 0 0
\(676\) −5.63894 −0.216882
\(677\) 9.49027 0.364741 0.182370 0.983230i \(-0.441623\pi\)
0.182370 + 0.983230i \(0.441623\pi\)
\(678\) 0 0
\(679\) 41.9870 1.61131
\(680\) −16.3117 −0.625523
\(681\) 0 0
\(682\) −5.50384 −0.210753
\(683\) −15.0960 −0.577631 −0.288816 0.957385i \(-0.593261\pi\)
−0.288816 + 0.957385i \(0.593261\pi\)
\(684\) 0 0
\(685\) 2.73876 0.104643
\(686\) 13.0978 0.500078
\(687\) 0 0
\(688\) 17.3760 0.662455
\(689\) −18.8216 −0.717047
\(690\) 0 0
\(691\) 3.46673 0.131881 0.0659403 0.997824i \(-0.478995\pi\)
0.0659403 + 0.997824i \(0.478995\pi\)
\(692\) 17.8708 0.679345
\(693\) 0 0
\(694\) −2.32965 −0.0884325
\(695\) 17.2631 0.654826
\(696\) 0 0
\(697\) 1.57333 0.0595941
\(698\) 48.6643 1.84197
\(699\) 0 0
\(700\) 74.0241 2.79785
\(701\) 26.2612 0.991872 0.495936 0.868359i \(-0.334825\pi\)
0.495936 + 0.868359i \(0.334825\pi\)
\(702\) 0 0
\(703\) 6.39893 0.241340
\(704\) 12.5342 0.472399
\(705\) 0 0
\(706\) −27.0165 −1.01678
\(707\) 45.1950 1.69973
\(708\) 0 0
\(709\) −20.1488 −0.756704 −0.378352 0.925662i \(-0.623509\pi\)
−0.378352 + 0.925662i \(0.623509\pi\)
\(710\) 85.9696 3.22638
\(711\) 0 0
\(712\) 12.3409 0.462494
\(713\) −17.3534 −0.649889
\(714\) 0 0
\(715\) −11.3621 −0.424918
\(716\) −34.7580 −1.29897
\(717\) 0 0
\(718\) −70.3459 −2.62529
\(719\) 43.4738 1.62130 0.810650 0.585532i \(-0.199114\pi\)
0.810650 + 0.585532i \(0.199114\pi\)
\(720\) 0 0
\(721\) 72.1103 2.68553
\(722\) 2.18524 0.0813263
\(723\) 0 0
\(724\) 38.1644 1.41837
\(725\) −38.4532 −1.42811
\(726\) 0 0
\(727\) 9.55640 0.354427 0.177214 0.984172i \(-0.443292\pi\)
0.177214 + 0.984172i \(0.443292\pi\)
\(728\) 22.1052 0.819273
\(729\) 0 0
\(730\) −67.1612 −2.48575
\(731\) 26.3821 0.975777
\(732\) 0 0
\(733\) −20.3072 −0.750065 −0.375032 0.927012i \(-0.622368\pi\)
−0.375032 + 0.927012i \(0.622368\pi\)
\(734\) −41.4709 −1.53072
\(735\) 0 0
\(736\) 51.1753 1.88635
\(737\) 9.95563 0.366720
\(738\) 0 0
\(739\) −6.60855 −0.243099 −0.121550 0.992585i \(-0.538786\pi\)
−0.121550 + 0.992585i \(0.538786\pi\)
\(740\) −60.9266 −2.23971
\(741\) 0 0
\(742\) −48.9277 −1.79619
\(743\) 39.1431 1.43602 0.718010 0.696033i \(-0.245053\pi\)
0.718010 + 0.696033i \(0.245053\pi\)
\(744\) 0 0
\(745\) −68.0498 −2.49315
\(746\) 2.51822 0.0921988
\(747\) 0 0
\(748\) 7.78847 0.284775
\(749\) −5.46983 −0.199863
\(750\) 0 0
\(751\) 43.2173 1.57702 0.788511 0.615020i \(-0.210852\pi\)
0.788511 + 0.615020i \(0.210852\pi\)
\(752\) −22.5023 −0.820574
\(753\) 0 0
\(754\) −41.1054 −1.49697
\(755\) 77.3457 2.81490
\(756\) 0 0
\(757\) 9.93714 0.361171 0.180586 0.983559i \(-0.442201\pi\)
0.180586 + 0.983559i \(0.442201\pi\)
\(758\) 29.5806 1.07442
\(759\) 0 0
\(760\) −5.81238 −0.210837
\(761\) −14.5829 −0.528630 −0.264315 0.964436i \(-0.585146\pi\)
−0.264315 + 0.964436i \(0.585146\pi\)
\(762\) 0 0
\(763\) −1.62361 −0.0587785
\(764\) −8.62221 −0.311941
\(765\) 0 0
\(766\) −28.7734 −1.03962
\(767\) −14.4306 −0.521059
\(768\) 0 0
\(769\) −11.8924 −0.428853 −0.214426 0.976740i \(-0.568788\pi\)
−0.214426 + 0.976740i \(0.568788\pi\)
\(770\) −29.5363 −1.06441
\(771\) 0 0
\(772\) −2.07540 −0.0746953
\(773\) −15.0935 −0.542876 −0.271438 0.962456i \(-0.587499\pi\)
−0.271438 + 0.962456i \(0.587499\pi\)
\(774\) 0 0
\(775\) 17.0516 0.612513
\(776\) 18.0556 0.648158
\(777\) 0 0
\(778\) −0.488595 −0.0175170
\(779\) 0.560629 0.0200866
\(780\) 0 0
\(781\) −11.4671 −0.410325
\(782\) 42.2534 1.51098
\(783\) 0 0
\(784\) −15.7505 −0.562519
\(785\) −40.4874 −1.44506
\(786\) 0 0
\(787\) −5.98214 −0.213240 −0.106620 0.994300i \(-0.534003\pi\)
−0.106620 + 0.994300i \(0.534003\pi\)
\(788\) 9.48589 0.337921
\(789\) 0 0
\(790\) 63.6580 2.26485
\(791\) 25.7659 0.916128
\(792\) 0 0
\(793\) −11.8037 −0.419163
\(794\) −47.3114 −1.67902
\(795\) 0 0
\(796\) 14.8973 0.528022
\(797\) −24.2718 −0.859751 −0.429876 0.902888i \(-0.641443\pi\)
−0.429876 + 0.902888i \(0.641443\pi\)
\(798\) 0 0
\(799\) −34.1653 −1.20868
\(800\) −50.2854 −1.77786
\(801\) 0 0
\(802\) −2.84476 −0.100452
\(803\) 8.95834 0.316133
\(804\) 0 0
\(805\) −93.1268 −3.28229
\(806\) 18.2277 0.642044
\(807\) 0 0
\(808\) 19.4351 0.683726
\(809\) 17.9557 0.631289 0.315644 0.948878i \(-0.397779\pi\)
0.315644 + 0.948878i \(0.397779\pi\)
\(810\) 0 0
\(811\) 5.48300 0.192534 0.0962671 0.995356i \(-0.469310\pi\)
0.0962671 + 0.995356i \(0.469310\pi\)
\(812\) −62.1019 −2.17935
\(813\) 0 0
\(814\) 13.9832 0.490111
\(815\) −85.2185 −2.98508
\(816\) 0 0
\(817\) 9.40080 0.328892
\(818\) −4.71205 −0.164753
\(819\) 0 0
\(820\) −5.33795 −0.186409
\(821\) −52.6324 −1.83688 −0.918441 0.395558i \(-0.870551\pi\)
−0.918441 + 0.395558i \(0.870551\pi\)
\(822\) 0 0
\(823\) −20.4784 −0.713831 −0.356916 0.934137i \(-0.616172\pi\)
−0.356916 + 0.934137i \(0.616172\pi\)
\(824\) 31.0095 1.08027
\(825\) 0 0
\(826\) −37.5131 −1.30525
\(827\) 0.359755 0.0125099 0.00625496 0.999980i \(-0.498009\pi\)
0.00625496 + 0.999980i \(0.498009\pi\)
\(828\) 0 0
\(829\) 22.7422 0.789870 0.394935 0.918709i \(-0.370767\pi\)
0.394935 + 0.918709i \(0.370767\pi\)
\(830\) 39.1317 1.35828
\(831\) 0 0
\(832\) −41.5109 −1.43913
\(833\) −23.9141 −0.828574
\(834\) 0 0
\(835\) 9.60403 0.332361
\(836\) 2.77529 0.0959853
\(837\) 0 0
\(838\) 64.7563 2.23697
\(839\) −13.1616 −0.454388 −0.227194 0.973849i \(-0.572955\pi\)
−0.227194 + 0.973849i \(0.572955\pi\)
\(840\) 0 0
\(841\) 3.25998 0.112413
\(842\) −11.4809 −0.395659
\(843\) 0 0
\(844\) 7.09065 0.244070
\(845\) −6.97077 −0.239802
\(846\) 0 0
\(847\) 3.93972 0.135370
\(848\) 10.5045 0.360726
\(849\) 0 0
\(850\) −41.5187 −1.42408
\(851\) 44.0885 1.51133
\(852\) 0 0
\(853\) −36.9102 −1.26378 −0.631891 0.775057i \(-0.717721\pi\)
−0.631891 + 0.775057i \(0.717721\pi\)
\(854\) −30.6844 −1.05000
\(855\) 0 0
\(856\) −2.35218 −0.0803960
\(857\) −24.3615 −0.832174 −0.416087 0.909325i \(-0.636599\pi\)
−0.416087 + 0.909325i \(0.636599\pi\)
\(858\) 0 0
\(859\) −7.69750 −0.262635 −0.131318 0.991340i \(-0.541921\pi\)
−0.131318 + 0.991340i \(0.541921\pi\)
\(860\) −89.5085 −3.05222
\(861\) 0 0
\(862\) −39.0042 −1.32849
\(863\) 29.0225 0.987937 0.493969 0.869480i \(-0.335546\pi\)
0.493969 + 0.869480i \(0.335546\pi\)
\(864\) 0 0
\(865\) 22.0916 0.751137
\(866\) −1.52177 −0.0517117
\(867\) 0 0
\(868\) 27.5384 0.934714
\(869\) −8.49105 −0.288039
\(870\) 0 0
\(871\) −32.9713 −1.11719
\(872\) −0.698197 −0.0236439
\(873\) 0 0
\(874\) 15.0563 0.509286
\(875\) 23.9262 0.808852
\(876\) 0 0
\(877\) −36.0010 −1.21567 −0.607834 0.794064i \(-0.707961\pi\)
−0.607834 + 0.794064i \(0.707961\pi\)
\(878\) −54.2399 −1.83051
\(879\) 0 0
\(880\) 6.34128 0.213765
\(881\) 15.3587 0.517448 0.258724 0.965951i \(-0.416698\pi\)
0.258724 + 0.965951i \(0.416698\pi\)
\(882\) 0 0
\(883\) 40.2870 1.35577 0.677883 0.735170i \(-0.262898\pi\)
0.677883 + 0.735170i \(0.262898\pi\)
\(884\) −25.7940 −0.867547
\(885\) 0 0
\(886\) 8.59728 0.288831
\(887\) 7.09855 0.238346 0.119173 0.992874i \(-0.461976\pi\)
0.119173 + 0.992874i \(0.461976\pi\)
\(888\) 0 0
\(889\) 35.7728 1.19978
\(890\) 54.6104 1.83054
\(891\) 0 0
\(892\) −69.2168 −2.31755
\(893\) −12.1742 −0.407395
\(894\) 0 0
\(895\) −42.9673 −1.43624
\(896\) −49.3851 −1.64984
\(897\) 0 0
\(898\) −13.4042 −0.447302
\(899\) −14.3053 −0.477110
\(900\) 0 0
\(901\) 15.9490 0.531339
\(902\) 1.22511 0.0407917
\(903\) 0 0
\(904\) 11.0801 0.368517
\(905\) 47.1783 1.56826
\(906\) 0 0
\(907\) 28.4435 0.944452 0.472226 0.881478i \(-0.343451\pi\)
0.472226 + 0.881478i \(0.343451\pi\)
\(908\) 63.3470 2.10224
\(909\) 0 0
\(910\) 97.8190 3.24267
\(911\) −49.5740 −1.64246 −0.821230 0.570598i \(-0.806712\pi\)
−0.821230 + 0.570598i \(0.806712\pi\)
\(912\) 0 0
\(913\) −5.21960 −0.172744
\(914\) 18.3602 0.607301
\(915\) 0 0
\(916\) −1.67501 −0.0553440
\(917\) 40.9243 1.35144
\(918\) 0 0
\(919\) 17.8421 0.588556 0.294278 0.955720i \(-0.404921\pi\)
0.294278 + 0.955720i \(0.404921\pi\)
\(920\) −40.0472 −1.32032
\(921\) 0 0
\(922\) −56.7952 −1.87045
\(923\) 37.9770 1.25003
\(924\) 0 0
\(925\) −43.3219 −1.42441
\(926\) 42.3334 1.39116
\(927\) 0 0
\(928\) 42.1865 1.38484
\(929\) −36.0244 −1.18192 −0.590961 0.806700i \(-0.701251\pi\)
−0.590961 + 0.806700i \(0.701251\pi\)
\(930\) 0 0
\(931\) −8.52137 −0.279277
\(932\) −48.2080 −1.57911
\(933\) 0 0
\(934\) 75.7667 2.47916
\(935\) 9.62799 0.314869
\(936\) 0 0
\(937\) −3.50371 −0.114461 −0.0572307 0.998361i \(-0.518227\pi\)
−0.0572307 + 0.998361i \(0.518227\pi\)
\(938\) −85.7104 −2.79854
\(939\) 0 0
\(940\) 115.915 3.78074
\(941\) −44.2074 −1.44112 −0.720560 0.693392i \(-0.756115\pi\)
−0.720560 + 0.693392i \(0.756115\pi\)
\(942\) 0 0
\(943\) 3.86272 0.125788
\(944\) 8.05385 0.262130
\(945\) 0 0
\(946\) 20.5430 0.667912
\(947\) −37.9515 −1.23326 −0.616629 0.787254i \(-0.711502\pi\)
−0.616629 + 0.787254i \(0.711502\pi\)
\(948\) 0 0
\(949\) −29.6684 −0.963077
\(950\) −14.7945 −0.479996
\(951\) 0 0
\(952\) −18.7315 −0.607090
\(953\) −13.0303 −0.422094 −0.211047 0.977476i \(-0.567687\pi\)
−0.211047 + 0.977476i \(0.567687\pi\)
\(954\) 0 0
\(955\) −10.6586 −0.344906
\(956\) −20.0788 −0.649396
\(957\) 0 0
\(958\) −50.7745 −1.64045
\(959\) 3.14505 0.101559
\(960\) 0 0
\(961\) −24.6565 −0.795370
\(962\) −46.3099 −1.49309
\(963\) 0 0
\(964\) −33.8679 −1.09081
\(965\) −2.56558 −0.0825889
\(966\) 0 0
\(967\) 24.0504 0.773409 0.386705 0.922204i \(-0.373613\pi\)
0.386705 + 0.922204i \(0.373613\pi\)
\(968\) 1.69419 0.0544534
\(969\) 0 0
\(970\) 79.8989 2.56540
\(971\) −54.1335 −1.73723 −0.868614 0.495490i \(-0.834988\pi\)
−0.868614 + 0.495490i \(0.834988\pi\)
\(972\) 0 0
\(973\) 19.8240 0.635529
\(974\) 31.1791 0.999041
\(975\) 0 0
\(976\) 6.58776 0.210869
\(977\) 50.2507 1.60766 0.803832 0.594857i \(-0.202791\pi\)
0.803832 + 0.594857i \(0.202791\pi\)
\(978\) 0 0
\(979\) −7.28423 −0.232805
\(980\) 81.1351 2.59177
\(981\) 0 0
\(982\) −90.9429 −2.90210
\(983\) −6.64633 −0.211985 −0.105993 0.994367i \(-0.533802\pi\)
−0.105993 + 0.994367i \(0.533802\pi\)
\(984\) 0 0
\(985\) 11.7263 0.373631
\(986\) 34.8318 1.10927
\(987\) 0 0
\(988\) −9.19126 −0.292413
\(989\) 64.7714 2.05961
\(990\) 0 0
\(991\) 51.7993 1.64546 0.822729 0.568434i \(-0.192451\pi\)
0.822729 + 0.568434i \(0.192451\pi\)
\(992\) −18.7072 −0.593953
\(993\) 0 0
\(994\) 98.7230 3.13130
\(995\) 18.4159 0.583822
\(996\) 0 0
\(997\) −14.2042 −0.449851 −0.224925 0.974376i \(-0.572214\pi\)
−0.224925 + 0.974376i \(0.572214\pi\)
\(998\) 43.6315 1.38113
\(999\) 0 0
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 1881.2.a.k.1.5 5
3.2 odd 2 209.2.a.c.1.1 5
12.11 even 2 3344.2.a.t.1.2 5
15.14 odd 2 5225.2.a.h.1.5 5
33.32 even 2 2299.2.a.n.1.5 5
57.56 even 2 3971.2.a.h.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.c.1.1 5 3.2 odd 2
1881.2.a.k.1.5 5 1.1 even 1 trivial
2299.2.a.n.1.5 5 33.32 even 2
3344.2.a.t.1.2 5 12.11 even 2
3971.2.a.h.1.5 5 57.56 even 2
5225.2.a.h.1.5 5 15.14 odd 2