Properties

Label 8030.2.a.bf.1.5
Level $8030$
Weight $2$
Character 8030.1
Self dual yes
Analytic conductor $64.120$
Analytic rank $1$
Dimension $15$
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] = [8030,2,Mod(1,8030)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8030, 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("8030.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8030.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: \(64.1198728231\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 4 x^{14} - 23 x^{13} + 99 x^{12} + 191 x^{11} - 922 x^{10} - 702 x^{9} + 4108 x^{8} + 957 x^{7} - 8875 x^{6} + 479 x^{5} + 7698 x^{4} - 1731 x^{3} - 626 x^{2} + 46 x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.82644\) of defining polynomial
Character \(\chi\) \(=\) 8030.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.82644 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.82644 q^{6} +3.00453 q^{7} +1.00000 q^{8} +0.335869 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.82644 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.82644 q^{6} +3.00453 q^{7} +1.00000 q^{8} +0.335869 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.82644 q^{12} -4.32653 q^{13} +3.00453 q^{14} +1.82644 q^{15} +1.00000 q^{16} -2.32985 q^{17} +0.335869 q^{18} -1.98016 q^{19} -1.00000 q^{20} -5.48759 q^{21} -1.00000 q^{22} +6.29494 q^{23} -1.82644 q^{24} +1.00000 q^{25} -4.32653 q^{26} +4.86586 q^{27} +3.00453 q^{28} +3.78974 q^{29} +1.82644 q^{30} +2.81506 q^{31} +1.00000 q^{32} +1.82644 q^{33} -2.32985 q^{34} -3.00453 q^{35} +0.335869 q^{36} -0.856830 q^{37} -1.98016 q^{38} +7.90214 q^{39} -1.00000 q^{40} -5.60727 q^{41} -5.48759 q^{42} +8.01229 q^{43} -1.00000 q^{44} -0.335869 q^{45} +6.29494 q^{46} -6.59031 q^{47} -1.82644 q^{48} +2.02723 q^{49} +1.00000 q^{50} +4.25533 q^{51} -4.32653 q^{52} -9.34352 q^{53} +4.86586 q^{54} +1.00000 q^{55} +3.00453 q^{56} +3.61664 q^{57} +3.78974 q^{58} +7.84290 q^{59} +1.82644 q^{60} -2.89353 q^{61} +2.81506 q^{62} +1.00913 q^{63} +1.00000 q^{64} +4.32653 q^{65} +1.82644 q^{66} -9.07976 q^{67} -2.32985 q^{68} -11.4973 q^{69} -3.00453 q^{70} +4.45061 q^{71} +0.335869 q^{72} +1.00000 q^{73} -0.856830 q^{74} -1.82644 q^{75} -1.98016 q^{76} -3.00453 q^{77} +7.90214 q^{78} +5.72249 q^{79} -1.00000 q^{80} -9.89480 q^{81} -5.60727 q^{82} -5.58265 q^{83} -5.48759 q^{84} +2.32985 q^{85} +8.01229 q^{86} -6.92171 q^{87} -1.00000 q^{88} -6.01085 q^{89} -0.335869 q^{90} -12.9992 q^{91} +6.29494 q^{92} -5.14152 q^{93} -6.59031 q^{94} +1.98016 q^{95} -1.82644 q^{96} -7.84684 q^{97} +2.02723 q^{98} -0.335869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 15 q^{2} - 4 q^{3} + 15 q^{4} - 15 q^{5} - 4 q^{6} - 6 q^{7} + 15 q^{8} + 17 q^{9} - 15 q^{10} - 15 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{14} + 4 q^{15} + 15 q^{16} + 2 q^{17} + 17 q^{18} - 8 q^{19} - 15 q^{20} - 17 q^{21} - 15 q^{22} - 4 q^{23} - 4 q^{24} + 15 q^{25} - 6 q^{26} - 19 q^{27} - 6 q^{28} - 13 q^{29} + 4 q^{30} - 20 q^{31} + 15 q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 17 q^{36} - 15 q^{37} - 8 q^{38} - 11 q^{39} - 15 q^{40} + 2 q^{41} - 17 q^{42} - 26 q^{43} - 15 q^{44} - 17 q^{45} - 4 q^{46} - 14 q^{47} - 4 q^{48} + 11 q^{49} + 15 q^{50} - 39 q^{51} - 6 q^{52} - 21 q^{53} - 19 q^{54} + 15 q^{55} - 6 q^{56} + q^{57} - 13 q^{58} - 14 q^{59} + 4 q^{60} - 45 q^{61} - 20 q^{62} - 17 q^{63} + 15 q^{64} + 6 q^{65} + 4 q^{66} - 10 q^{67} + 2 q^{68} - 23 q^{69} + 6 q^{70} - 9 q^{71} + 17 q^{72} + 15 q^{73} - 15 q^{74} - 4 q^{75} - 8 q^{76} + 6 q^{77} - 11 q^{78} - 26 q^{79} - 15 q^{80} + 15 q^{81} + 2 q^{82} - 30 q^{83} - 17 q^{84} - 2 q^{85} - 26 q^{86} - 14 q^{87} - 15 q^{88} + 10 q^{89} - 17 q^{90} - 17 q^{91} - 4 q^{92} - 8 q^{93} - 14 q^{94} + 8 q^{95} - 4 q^{96} - 27 q^{97} + 11 q^{98} - 17 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.82644 −1.05449 −0.527247 0.849712i \(-0.676776\pi\)
−0.527247 + 0.849712i \(0.676776\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.82644 −0.745639
\(7\) 3.00453 1.13561 0.567804 0.823164i \(-0.307793\pi\)
0.567804 + 0.823164i \(0.307793\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.335869 0.111956
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.82644 −0.527247
\(13\) −4.32653 −1.19996 −0.599982 0.800013i \(-0.704826\pi\)
−0.599982 + 0.800013i \(0.704826\pi\)
\(14\) 3.00453 0.802996
\(15\) 1.82644 0.471584
\(16\) 1.00000 0.250000
\(17\) −2.32985 −0.565072 −0.282536 0.959257i \(-0.591176\pi\)
−0.282536 + 0.959257i \(0.591176\pi\)
\(18\) 0.335869 0.0791651
\(19\) −1.98016 −0.454281 −0.227140 0.973862i \(-0.572938\pi\)
−0.227140 + 0.973862i \(0.572938\pi\)
\(20\) −1.00000 −0.223607
\(21\) −5.48759 −1.19749
\(22\) −1.00000 −0.213201
\(23\) 6.29494 1.31259 0.656293 0.754506i \(-0.272124\pi\)
0.656293 + 0.754506i \(0.272124\pi\)
\(24\) −1.82644 −0.372820
\(25\) 1.00000 0.200000
\(26\) −4.32653 −0.848503
\(27\) 4.86586 0.936436
\(28\) 3.00453 0.567804
\(29\) 3.78974 0.703736 0.351868 0.936050i \(-0.385547\pi\)
0.351868 + 0.936050i \(0.385547\pi\)
\(30\) 1.82644 0.333460
\(31\) 2.81506 0.505599 0.252800 0.967519i \(-0.418649\pi\)
0.252800 + 0.967519i \(0.418649\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.82644 0.317942
\(34\) −2.32985 −0.399566
\(35\) −3.00453 −0.507859
\(36\) 0.335869 0.0559782
\(37\) −0.856830 −0.140862 −0.0704310 0.997517i \(-0.522437\pi\)
−0.0704310 + 0.997517i \(0.522437\pi\)
\(38\) −1.98016 −0.321225
\(39\) 7.90214 1.26535
\(40\) −1.00000 −0.158114
\(41\) −5.60727 −0.875708 −0.437854 0.899046i \(-0.644261\pi\)
−0.437854 + 0.899046i \(0.644261\pi\)
\(42\) −5.48759 −0.846754
\(43\) 8.01229 1.22186 0.610931 0.791684i \(-0.290795\pi\)
0.610931 + 0.791684i \(0.290795\pi\)
\(44\) −1.00000 −0.150756
\(45\) −0.335869 −0.0500684
\(46\) 6.29494 0.928138
\(47\) −6.59031 −0.961295 −0.480648 0.876914i \(-0.659598\pi\)
−0.480648 + 0.876914i \(0.659598\pi\)
\(48\) −1.82644 −0.263623
\(49\) 2.02723 0.289604
\(50\) 1.00000 0.141421
\(51\) 4.25533 0.595865
\(52\) −4.32653 −0.599982
\(53\) −9.34352 −1.28343 −0.641715 0.766943i \(-0.721777\pi\)
−0.641715 + 0.766943i \(0.721777\pi\)
\(54\) 4.86586 0.662160
\(55\) 1.00000 0.134840
\(56\) 3.00453 0.401498
\(57\) 3.61664 0.479036
\(58\) 3.78974 0.497617
\(59\) 7.84290 1.02106 0.510529 0.859860i \(-0.329450\pi\)
0.510529 + 0.859860i \(0.329450\pi\)
\(60\) 1.82644 0.235792
\(61\) −2.89353 −0.370479 −0.185239 0.982693i \(-0.559306\pi\)
−0.185239 + 0.982693i \(0.559306\pi\)
\(62\) 2.81506 0.357513
\(63\) 1.00913 0.127139
\(64\) 1.00000 0.125000
\(65\) 4.32653 0.536640
\(66\) 1.82644 0.224819
\(67\) −9.07976 −1.10927 −0.554634 0.832094i \(-0.687142\pi\)
−0.554634 + 0.832094i \(0.687142\pi\)
\(68\) −2.32985 −0.282536
\(69\) −11.4973 −1.38411
\(70\) −3.00453 −0.359111
\(71\) 4.45061 0.528191 0.264095 0.964497i \(-0.414927\pi\)
0.264095 + 0.964497i \(0.414927\pi\)
\(72\) 0.335869 0.0395826
\(73\) 1.00000 0.117041
\(74\) −0.856830 −0.0996044
\(75\) −1.82644 −0.210899
\(76\) −1.98016 −0.227140
\(77\) −3.00453 −0.342398
\(78\) 7.90214 0.894741
\(79\) 5.72249 0.643830 0.321915 0.946769i \(-0.395673\pi\)
0.321915 + 0.946769i \(0.395673\pi\)
\(80\) −1.00000 −0.111803
\(81\) −9.89480 −1.09942
\(82\) −5.60727 −0.619219
\(83\) −5.58265 −0.612776 −0.306388 0.951907i \(-0.599120\pi\)
−0.306388 + 0.951907i \(0.599120\pi\)
\(84\) −5.48759 −0.598745
\(85\) 2.32985 0.252708
\(86\) 8.01229 0.863987
\(87\) −6.92171 −0.742085
\(88\) −1.00000 −0.106600
\(89\) −6.01085 −0.637149 −0.318575 0.947898i \(-0.603204\pi\)
−0.318575 + 0.947898i \(0.603204\pi\)
\(90\) −0.335869 −0.0354037
\(91\) −12.9992 −1.36269
\(92\) 6.29494 0.656293
\(93\) −5.14152 −0.533151
\(94\) −6.59031 −0.679739
\(95\) 1.98016 0.203161
\(96\) −1.82644 −0.186410
\(97\) −7.84684 −0.796726 −0.398363 0.917228i \(-0.630422\pi\)
−0.398363 + 0.917228i \(0.630422\pi\)
\(98\) 2.02723 0.204781
\(99\) −0.335869 −0.0337561
\(100\) 1.00000 0.100000
\(101\) −17.0206 −1.69362 −0.846809 0.531897i \(-0.821479\pi\)
−0.846809 + 0.531897i \(0.821479\pi\)
\(102\) 4.25533 0.421340
\(103\) 7.28504 0.717816 0.358908 0.933373i \(-0.383149\pi\)
0.358908 + 0.933373i \(0.383149\pi\)
\(104\) −4.32653 −0.424251
\(105\) 5.48759 0.535534
\(106\) −9.34352 −0.907522
\(107\) 4.10876 0.397209 0.198604 0.980080i \(-0.436359\pi\)
0.198604 + 0.980080i \(0.436359\pi\)
\(108\) 4.86586 0.468218
\(109\) −15.6780 −1.50168 −0.750841 0.660483i \(-0.770352\pi\)
−0.750841 + 0.660483i \(0.770352\pi\)
\(110\) 1.00000 0.0953463
\(111\) 1.56494 0.148538
\(112\) 3.00453 0.283902
\(113\) 14.3410 1.34909 0.674543 0.738235i \(-0.264341\pi\)
0.674543 + 0.738235i \(0.264341\pi\)
\(114\) 3.61664 0.338730
\(115\) −6.29494 −0.587006
\(116\) 3.78974 0.351868
\(117\) −1.45315 −0.134344
\(118\) 7.84290 0.721997
\(119\) −7.00012 −0.641700
\(120\) 1.82644 0.166730
\(121\) 1.00000 0.0909091
\(122\) −2.89353 −0.261968
\(123\) 10.2413 0.923428
\(124\) 2.81506 0.252800
\(125\) −1.00000 −0.0894427
\(126\) 1.00913 0.0899005
\(127\) −11.8099 −1.04795 −0.523977 0.851732i \(-0.675552\pi\)
−0.523977 + 0.851732i \(0.675552\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.6339 −1.28845
\(130\) 4.32653 0.379462
\(131\) 15.2331 1.33093 0.665463 0.746431i \(-0.268234\pi\)
0.665463 + 0.746431i \(0.268234\pi\)
\(132\) 1.82644 0.158971
\(133\) −5.94947 −0.515885
\(134\) −9.07976 −0.784372
\(135\) −4.86586 −0.418787
\(136\) −2.32985 −0.199783
\(137\) 6.96108 0.594726 0.297363 0.954765i \(-0.403893\pi\)
0.297363 + 0.954765i \(0.403893\pi\)
\(138\) −11.4973 −0.978716
\(139\) 0.0908223 0.00770345 0.00385172 0.999993i \(-0.498774\pi\)
0.00385172 + 0.999993i \(0.498774\pi\)
\(140\) −3.00453 −0.253929
\(141\) 12.0368 1.01368
\(142\) 4.45061 0.373487
\(143\) 4.32653 0.361803
\(144\) 0.335869 0.0279891
\(145\) −3.78974 −0.314720
\(146\) 1.00000 0.0827606
\(147\) −3.70260 −0.305385
\(148\) −0.856830 −0.0704310
\(149\) 11.6325 0.952970 0.476485 0.879183i \(-0.341911\pi\)
0.476485 + 0.879183i \(0.341911\pi\)
\(150\) −1.82644 −0.149128
\(151\) −0.737844 −0.0600449 −0.0300224 0.999549i \(-0.509558\pi\)
−0.0300224 + 0.999549i \(0.509558\pi\)
\(152\) −1.98016 −0.160613
\(153\) −0.782526 −0.0632635
\(154\) −3.00453 −0.242112
\(155\) −2.81506 −0.226111
\(156\) 7.90214 0.632677
\(157\) −4.90260 −0.391270 −0.195635 0.980677i \(-0.562677\pi\)
−0.195635 + 0.980677i \(0.562677\pi\)
\(158\) 5.72249 0.455257
\(159\) 17.0653 1.35337
\(160\) −1.00000 −0.0790569
\(161\) 18.9134 1.49058
\(162\) −9.89480 −0.777409
\(163\) −16.7822 −1.31448 −0.657241 0.753681i \(-0.728276\pi\)
−0.657241 + 0.753681i \(0.728276\pi\)
\(164\) −5.60727 −0.437854
\(165\) −1.82644 −0.142188
\(166\) −5.58265 −0.433298
\(167\) −11.4368 −0.885005 −0.442502 0.896767i \(-0.645909\pi\)
−0.442502 + 0.896767i \(0.645909\pi\)
\(168\) −5.48759 −0.423377
\(169\) 5.71889 0.439914
\(170\) 2.32985 0.178692
\(171\) −0.665076 −0.0508597
\(172\) 8.01229 0.610931
\(173\) −20.2277 −1.53788 −0.768941 0.639319i \(-0.779216\pi\)
−0.768941 + 0.639319i \(0.779216\pi\)
\(174\) −6.92171 −0.524733
\(175\) 3.00453 0.227121
\(176\) −1.00000 −0.0753778
\(177\) −14.3246 −1.07670
\(178\) −6.01085 −0.450533
\(179\) −8.05501 −0.602060 −0.301030 0.953615i \(-0.597330\pi\)
−0.301030 + 0.953615i \(0.597330\pi\)
\(180\) −0.335869 −0.0250342
\(181\) −3.96610 −0.294798 −0.147399 0.989077i \(-0.547090\pi\)
−0.147399 + 0.989077i \(0.547090\pi\)
\(182\) −12.9992 −0.963566
\(183\) 5.28485 0.390667
\(184\) 6.29494 0.464069
\(185\) 0.856830 0.0629954
\(186\) −5.14152 −0.376995
\(187\) 2.32985 0.170376
\(188\) −6.59031 −0.480648
\(189\) 14.6197 1.06342
\(190\) 1.98016 0.143656
\(191\) 3.49901 0.253179 0.126590 0.991955i \(-0.459597\pi\)
0.126590 + 0.991955i \(0.459597\pi\)
\(192\) −1.82644 −0.131812
\(193\) −18.0220 −1.29725 −0.648627 0.761106i \(-0.724657\pi\)
−0.648627 + 0.761106i \(0.724657\pi\)
\(194\) −7.84684 −0.563370
\(195\) −7.90214 −0.565884
\(196\) 2.02723 0.144802
\(197\) −14.5436 −1.03619 −0.518093 0.855324i \(-0.673358\pi\)
−0.518093 + 0.855324i \(0.673358\pi\)
\(198\) −0.335869 −0.0238692
\(199\) 3.37427 0.239196 0.119598 0.992822i \(-0.461839\pi\)
0.119598 + 0.992822i \(0.461839\pi\)
\(200\) 1.00000 0.0707107
\(201\) 16.5836 1.16972
\(202\) −17.0206 −1.19757
\(203\) 11.3864 0.799168
\(204\) 4.25533 0.297933
\(205\) 5.60727 0.391628
\(206\) 7.28504 0.507572
\(207\) 2.11428 0.146952
\(208\) −4.32653 −0.299991
\(209\) 1.98016 0.136971
\(210\) 5.48759 0.378680
\(211\) −21.4525 −1.47685 −0.738427 0.674334i \(-0.764431\pi\)
−0.738427 + 0.674334i \(0.764431\pi\)
\(212\) −9.34352 −0.641715
\(213\) −8.12876 −0.556974
\(214\) 4.10876 0.280869
\(215\) −8.01229 −0.546433
\(216\) 4.86586 0.331080
\(217\) 8.45794 0.574162
\(218\) −15.6780 −1.06185
\(219\) −1.82644 −0.123419
\(220\) 1.00000 0.0674200
\(221\) 10.0802 0.678067
\(222\) 1.56494 0.105032
\(223\) 21.6813 1.45189 0.725944 0.687753i \(-0.241403\pi\)
0.725944 + 0.687753i \(0.241403\pi\)
\(224\) 3.00453 0.200749
\(225\) 0.335869 0.0223913
\(226\) 14.3410 0.953948
\(227\) 16.8342 1.11733 0.558664 0.829394i \(-0.311314\pi\)
0.558664 + 0.829394i \(0.311314\pi\)
\(228\) 3.61664 0.239518
\(229\) −20.1367 −1.33067 −0.665336 0.746544i \(-0.731712\pi\)
−0.665336 + 0.746544i \(0.731712\pi\)
\(230\) −6.29494 −0.415076
\(231\) 5.48759 0.361057
\(232\) 3.78974 0.248808
\(233\) 21.0354 1.37808 0.689039 0.724724i \(-0.258033\pi\)
0.689039 + 0.724724i \(0.258033\pi\)
\(234\) −1.45315 −0.0949953
\(235\) 6.59031 0.429904
\(236\) 7.84290 0.510529
\(237\) −10.4518 −0.678914
\(238\) −7.00012 −0.453751
\(239\) −17.5138 −1.13288 −0.566438 0.824104i \(-0.691679\pi\)
−0.566438 + 0.824104i \(0.691679\pi\)
\(240\) 1.82644 0.117896
\(241\) 4.72871 0.304603 0.152301 0.988334i \(-0.451332\pi\)
0.152301 + 0.988334i \(0.451332\pi\)
\(242\) 1.00000 0.0642824
\(243\) 3.47463 0.222897
\(244\) −2.89353 −0.185239
\(245\) −2.02723 −0.129515
\(246\) 10.2413 0.652962
\(247\) 8.56725 0.545121
\(248\) 2.81506 0.178756
\(249\) 10.1964 0.646168
\(250\) −1.00000 −0.0632456
\(251\) −13.9460 −0.880264 −0.440132 0.897933i \(-0.645068\pi\)
−0.440132 + 0.897933i \(0.645068\pi\)
\(252\) 1.00913 0.0635693
\(253\) −6.29494 −0.395760
\(254\) −11.8099 −0.741016
\(255\) −4.25533 −0.266479
\(256\) 1.00000 0.0625000
\(257\) −30.0521 −1.87460 −0.937298 0.348530i \(-0.886681\pi\)
−0.937298 + 0.348530i \(0.886681\pi\)
\(258\) −14.6339 −0.911069
\(259\) −2.57437 −0.159964
\(260\) 4.32653 0.268320
\(261\) 1.27286 0.0787878
\(262\) 15.2331 0.941107
\(263\) 17.1222 1.05580 0.527901 0.849306i \(-0.322979\pi\)
0.527901 + 0.849306i \(0.322979\pi\)
\(264\) 1.82644 0.112409
\(265\) 9.34352 0.573968
\(266\) −5.94947 −0.364785
\(267\) 10.9784 0.671870
\(268\) −9.07976 −0.554634
\(269\) 13.4766 0.821682 0.410841 0.911707i \(-0.365235\pi\)
0.410841 + 0.911707i \(0.365235\pi\)
\(270\) −4.86586 −0.296127
\(271\) −26.7041 −1.62216 −0.811078 0.584938i \(-0.801119\pi\)
−0.811078 + 0.584938i \(0.801119\pi\)
\(272\) −2.32985 −0.141268
\(273\) 23.7422 1.43695
\(274\) 6.96108 0.420534
\(275\) −1.00000 −0.0603023
\(276\) −11.4973 −0.692057
\(277\) 0.768199 0.0461566 0.0230783 0.999734i \(-0.492653\pi\)
0.0230783 + 0.999734i \(0.492653\pi\)
\(278\) 0.0908223 0.00544716
\(279\) 0.945491 0.0566051
\(280\) −3.00453 −0.179555
\(281\) 1.67745 0.100068 0.0500341 0.998748i \(-0.484067\pi\)
0.0500341 + 0.998748i \(0.484067\pi\)
\(282\) 12.0368 0.716780
\(283\) 7.32944 0.435690 0.217845 0.975983i \(-0.430097\pi\)
0.217845 + 0.975983i \(0.430097\pi\)
\(284\) 4.45061 0.264095
\(285\) −3.61664 −0.214231
\(286\) 4.32653 0.255833
\(287\) −16.8472 −0.994460
\(288\) 0.335869 0.0197913
\(289\) −11.5718 −0.680693
\(290\) −3.78974 −0.222541
\(291\) 14.3318 0.840142
\(292\) 1.00000 0.0585206
\(293\) −7.57117 −0.442312 −0.221156 0.975238i \(-0.570983\pi\)
−0.221156 + 0.975238i \(0.570983\pi\)
\(294\) −3.70260 −0.215940
\(295\) −7.84290 −0.456631
\(296\) −0.856830 −0.0498022
\(297\) −4.86586 −0.282346
\(298\) 11.6325 0.673852
\(299\) −27.2353 −1.57506
\(300\) −1.82644 −0.105449
\(301\) 24.0732 1.38756
\(302\) −0.737844 −0.0424582
\(303\) 31.0871 1.78591
\(304\) −1.98016 −0.113570
\(305\) 2.89353 0.165683
\(306\) −0.782526 −0.0447340
\(307\) −26.3131 −1.50177 −0.750884 0.660435i \(-0.770372\pi\)
−0.750884 + 0.660435i \(0.770372\pi\)
\(308\) −3.00453 −0.171199
\(309\) −13.3057 −0.756932
\(310\) −2.81506 −0.159885
\(311\) 9.91646 0.562311 0.281155 0.959662i \(-0.409282\pi\)
0.281155 + 0.959662i \(0.409282\pi\)
\(312\) 7.90214 0.447370
\(313\) 26.8046 1.51509 0.757544 0.652784i \(-0.226399\pi\)
0.757544 + 0.652784i \(0.226399\pi\)
\(314\) −4.90260 −0.276670
\(315\) −1.00913 −0.0568581
\(316\) 5.72249 0.321915
\(317\) 18.8464 1.05852 0.529259 0.848460i \(-0.322470\pi\)
0.529259 + 0.848460i \(0.322470\pi\)
\(318\) 17.0653 0.956977
\(319\) −3.78974 −0.212184
\(320\) −1.00000 −0.0559017
\(321\) −7.50438 −0.418854
\(322\) 18.9134 1.05400
\(323\) 4.61349 0.256702
\(324\) −9.89480 −0.549711
\(325\) −4.32653 −0.239993
\(326\) −16.7822 −0.929479
\(327\) 28.6349 1.58351
\(328\) −5.60727 −0.309610
\(329\) −19.8008 −1.09165
\(330\) −1.82644 −0.100542
\(331\) 31.9810 1.75784 0.878918 0.476973i \(-0.158266\pi\)
0.878918 + 0.476973i \(0.158266\pi\)
\(332\) −5.58265 −0.306388
\(333\) −0.287783 −0.0157704
\(334\) −11.4368 −0.625793
\(335\) 9.07976 0.496080
\(336\) −5.48759 −0.299373
\(337\) −6.25893 −0.340945 −0.170473 0.985362i \(-0.554529\pi\)
−0.170473 + 0.985362i \(0.554529\pi\)
\(338\) 5.71889 0.311066
\(339\) −26.1929 −1.42260
\(340\) 2.32985 0.126354
\(341\) −2.81506 −0.152444
\(342\) −0.665076 −0.0359632
\(343\) −14.9409 −0.806731
\(344\) 8.01229 0.431994
\(345\) 11.4973 0.618994
\(346\) −20.2277 −1.08745
\(347\) −15.9336 −0.855362 −0.427681 0.903930i \(-0.640669\pi\)
−0.427681 + 0.903930i \(0.640669\pi\)
\(348\) −6.92171 −0.371043
\(349\) −22.7662 −1.21865 −0.609324 0.792921i \(-0.708559\pi\)
−0.609324 + 0.792921i \(0.708559\pi\)
\(350\) 3.00453 0.160599
\(351\) −21.0523 −1.12369
\(352\) −1.00000 −0.0533002
\(353\) 3.93216 0.209288 0.104644 0.994510i \(-0.466630\pi\)
0.104644 + 0.994510i \(0.466630\pi\)
\(354\) −14.3246 −0.761341
\(355\) −4.45061 −0.236214
\(356\) −6.01085 −0.318575
\(357\) 12.7853 0.676669
\(358\) −8.05501 −0.425720
\(359\) −19.6647 −1.03787 −0.518933 0.854815i \(-0.673670\pi\)
−0.518933 + 0.854815i \(0.673670\pi\)
\(360\) −0.335869 −0.0177019
\(361\) −15.0789 −0.793629
\(362\) −3.96610 −0.208454
\(363\) −1.82644 −0.0958630
\(364\) −12.9992 −0.681344
\(365\) −1.00000 −0.0523424
\(366\) 5.28485 0.276244
\(367\) 14.0691 0.734402 0.367201 0.930142i \(-0.380316\pi\)
0.367201 + 0.930142i \(0.380316\pi\)
\(368\) 6.29494 0.328146
\(369\) −1.88331 −0.0980411
\(370\) 0.856830 0.0445444
\(371\) −28.0729 −1.45747
\(372\) −5.14152 −0.266576
\(373\) 7.03836 0.364433 0.182216 0.983258i \(-0.441673\pi\)
0.182216 + 0.983258i \(0.441673\pi\)
\(374\) 2.32985 0.120474
\(375\) 1.82644 0.0943168
\(376\) −6.59031 −0.339869
\(377\) −16.3964 −0.844458
\(378\) 14.6197 0.751954
\(379\) 24.9735 1.28280 0.641402 0.767205i \(-0.278353\pi\)
0.641402 + 0.767205i \(0.278353\pi\)
\(380\) 1.98016 0.101580
\(381\) 21.5699 1.10506
\(382\) 3.49901 0.179025
\(383\) −2.32441 −0.118772 −0.0593858 0.998235i \(-0.518914\pi\)
−0.0593858 + 0.998235i \(0.518914\pi\)
\(384\) −1.82644 −0.0932049
\(385\) 3.00453 0.153125
\(386\) −18.0220 −0.917297
\(387\) 2.69108 0.136795
\(388\) −7.84684 −0.398363
\(389\) −10.2655 −0.520483 −0.260241 0.965544i \(-0.583802\pi\)
−0.260241 + 0.965544i \(0.583802\pi\)
\(390\) −7.90214 −0.400140
\(391\) −14.6663 −0.741706
\(392\) 2.02723 0.102390
\(393\) −27.8224 −1.40345
\(394\) −14.5436 −0.732694
\(395\) −5.72249 −0.287929
\(396\) −0.335869 −0.0168781
\(397\) −8.96973 −0.450178 −0.225089 0.974338i \(-0.572267\pi\)
−0.225089 + 0.974338i \(0.572267\pi\)
\(398\) 3.37427 0.169137
\(399\) 10.8663 0.543997
\(400\) 1.00000 0.0500000
\(401\) −27.9889 −1.39770 −0.698849 0.715269i \(-0.746304\pi\)
−0.698849 + 0.715269i \(0.746304\pi\)
\(402\) 16.5836 0.827115
\(403\) −12.1794 −0.606701
\(404\) −17.0206 −0.846809
\(405\) 9.89480 0.491677
\(406\) 11.3864 0.565097
\(407\) 0.856830 0.0424715
\(408\) 4.25533 0.210670
\(409\) −19.0794 −0.943417 −0.471708 0.881755i \(-0.656362\pi\)
−0.471708 + 0.881755i \(0.656362\pi\)
\(410\) 5.60727 0.276923
\(411\) −12.7140 −0.627134
\(412\) 7.28504 0.358908
\(413\) 23.5643 1.15952
\(414\) 2.11428 0.103911
\(415\) 5.58265 0.274042
\(416\) −4.32653 −0.212126
\(417\) −0.165881 −0.00812324
\(418\) 1.98016 0.0968530
\(419\) −32.8434 −1.60450 −0.802251 0.596986i \(-0.796365\pi\)
−0.802251 + 0.596986i \(0.796365\pi\)
\(420\) 5.48759 0.267767
\(421\) 25.4036 1.23809 0.619047 0.785354i \(-0.287519\pi\)
0.619047 + 0.785354i \(0.287519\pi\)
\(422\) −21.4525 −1.04429
\(423\) −2.21348 −0.107623
\(424\) −9.34352 −0.453761
\(425\) −2.32985 −0.113014
\(426\) −8.12876 −0.393840
\(427\) −8.69371 −0.420718
\(428\) 4.10876 0.198604
\(429\) −7.90214 −0.381519
\(430\) −8.01229 −0.386387
\(431\) 28.2811 1.36225 0.681127 0.732165i \(-0.261490\pi\)
0.681127 + 0.732165i \(0.261490\pi\)
\(432\) 4.86586 0.234109
\(433\) −11.4205 −0.548833 −0.274417 0.961611i \(-0.588485\pi\)
−0.274417 + 0.961611i \(0.588485\pi\)
\(434\) 8.45794 0.405994
\(435\) 6.92171 0.331871
\(436\) −15.6780 −0.750841
\(437\) −12.4650 −0.596283
\(438\) −1.82644 −0.0872705
\(439\) −25.6469 −1.22406 −0.612030 0.790835i \(-0.709647\pi\)
−0.612030 + 0.790835i \(0.709647\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0.680883 0.0324230
\(442\) 10.0802 0.479466
\(443\) 34.3263 1.63089 0.815447 0.578832i \(-0.196491\pi\)
0.815447 + 0.578832i \(0.196491\pi\)
\(444\) 1.56494 0.0742690
\(445\) 6.01085 0.284942
\(446\) 21.6813 1.02664
\(447\) −21.2460 −1.00490
\(448\) 3.00453 0.141951
\(449\) −24.9408 −1.17703 −0.588514 0.808487i \(-0.700287\pi\)
−0.588514 + 0.808487i \(0.700287\pi\)
\(450\) 0.335869 0.0158330
\(451\) 5.60727 0.264036
\(452\) 14.3410 0.674543
\(453\) 1.34762 0.0633169
\(454\) 16.8342 0.790070
\(455\) 12.9992 0.609413
\(456\) 3.61664 0.169365
\(457\) 8.81941 0.412554 0.206277 0.978494i \(-0.433865\pi\)
0.206277 + 0.978494i \(0.433865\pi\)
\(458\) −20.1367 −0.940927
\(459\) −11.3368 −0.529154
\(460\) −6.29494 −0.293503
\(461\) −16.4185 −0.764688 −0.382344 0.924020i \(-0.624883\pi\)
−0.382344 + 0.924020i \(0.624883\pi\)
\(462\) 5.48759 0.255306
\(463\) −20.3061 −0.943707 −0.471853 0.881677i \(-0.656415\pi\)
−0.471853 + 0.881677i \(0.656415\pi\)
\(464\) 3.78974 0.175934
\(465\) 5.14152 0.238432
\(466\) 21.0354 0.974448
\(467\) −20.5992 −0.953217 −0.476609 0.879116i \(-0.658134\pi\)
−0.476609 + 0.879116i \(0.658134\pi\)
\(468\) −1.45315 −0.0671719
\(469\) −27.2804 −1.25969
\(470\) 6.59031 0.303988
\(471\) 8.95430 0.412592
\(472\) 7.84290 0.360999
\(473\) −8.01229 −0.368405
\(474\) −10.4518 −0.480065
\(475\) −1.98016 −0.0908562
\(476\) −7.00012 −0.320850
\(477\) −3.13820 −0.143688
\(478\) −17.5138 −0.801064
\(479\) 17.6387 0.805932 0.402966 0.915215i \(-0.367979\pi\)
0.402966 + 0.915215i \(0.367979\pi\)
\(480\) 1.82644 0.0833650
\(481\) 3.70710 0.169029
\(482\) 4.72871 0.215387
\(483\) −34.5441 −1.57181
\(484\) 1.00000 0.0454545
\(485\) 7.84684 0.356307
\(486\) 3.47463 0.157612
\(487\) −5.31105 −0.240666 −0.120333 0.992734i \(-0.538396\pi\)
−0.120333 + 0.992734i \(0.538396\pi\)
\(488\) −2.89353 −0.130984
\(489\) 30.6516 1.38611
\(490\) −2.02723 −0.0915807
\(491\) −34.1717 −1.54215 −0.771073 0.636747i \(-0.780280\pi\)
−0.771073 + 0.636747i \(0.780280\pi\)
\(492\) 10.2413 0.461714
\(493\) −8.82953 −0.397662
\(494\) 8.56725 0.385459
\(495\) 0.335869 0.0150962
\(496\) 2.81506 0.126400
\(497\) 13.3720 0.599817
\(498\) 10.1964 0.456910
\(499\) 3.62548 0.162299 0.0811494 0.996702i \(-0.474141\pi\)
0.0811494 + 0.996702i \(0.474141\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 20.8885 0.933232
\(502\) −13.9460 −0.622440
\(503\) −0.419493 −0.0187043 −0.00935214 0.999956i \(-0.502977\pi\)
−0.00935214 + 0.999956i \(0.502977\pi\)
\(504\) 1.00913 0.0449503
\(505\) 17.0206 0.757409
\(506\) −6.29494 −0.279844
\(507\) −10.4452 −0.463887
\(508\) −11.8099 −0.523977
\(509\) −37.4776 −1.66116 −0.830582 0.556897i \(-0.811992\pi\)
−0.830582 + 0.556897i \(0.811992\pi\)
\(510\) −4.25533 −0.188429
\(511\) 3.00453 0.132913
\(512\) 1.00000 0.0441942
\(513\) −9.63521 −0.425405
\(514\) −30.0521 −1.32554
\(515\) −7.28504 −0.321017
\(516\) −14.6339 −0.644223
\(517\) 6.59031 0.289841
\(518\) −2.57437 −0.113111
\(519\) 36.9446 1.62169
\(520\) 4.32653 0.189731
\(521\) −9.01721 −0.395051 −0.197526 0.980298i \(-0.563291\pi\)
−0.197526 + 0.980298i \(0.563291\pi\)
\(522\) 1.27286 0.0557114
\(523\) −38.0175 −1.66239 −0.831194 0.555983i \(-0.812342\pi\)
−0.831194 + 0.555983i \(0.812342\pi\)
\(524\) 15.2331 0.665463
\(525\) −5.48759 −0.239498
\(526\) 17.1222 0.746564
\(527\) −6.55867 −0.285700
\(528\) 1.82644 0.0794854
\(529\) 16.6263 0.722882
\(530\) 9.34352 0.405856
\(531\) 2.63419 0.114314
\(532\) −5.94947 −0.257942
\(533\) 24.2600 1.05082
\(534\) 10.9784 0.475084
\(535\) −4.10876 −0.177637
\(536\) −9.07976 −0.392186
\(537\) 14.7120 0.634868
\(538\) 13.4766 0.581017
\(539\) −2.02723 −0.0873188
\(540\) −4.86586 −0.209393
\(541\) −4.97669 −0.213965 −0.106982 0.994261i \(-0.534119\pi\)
−0.106982 + 0.994261i \(0.534119\pi\)
\(542\) −26.7041 −1.14704
\(543\) 7.24383 0.310862
\(544\) −2.32985 −0.0998916
\(545\) 15.6780 0.671573
\(546\) 23.7422 1.01607
\(547\) 14.7387 0.630182 0.315091 0.949061i \(-0.397965\pi\)
0.315091 + 0.949061i \(0.397965\pi\)
\(548\) 6.96108 0.297363
\(549\) −0.971848 −0.0414775
\(550\) −1.00000 −0.0426401
\(551\) −7.50430 −0.319694
\(552\) −11.4973 −0.489358
\(553\) 17.1934 0.731138
\(554\) 0.768199 0.0326377
\(555\) −1.56494 −0.0664282
\(556\) 0.0908223 0.00385172
\(557\) −39.2902 −1.66478 −0.832389 0.554192i \(-0.813027\pi\)
−0.832389 + 0.554192i \(0.813027\pi\)
\(558\) 0.945491 0.0400258
\(559\) −34.6654 −1.46619
\(560\) −3.00453 −0.126965
\(561\) −4.25533 −0.179660
\(562\) 1.67745 0.0707588
\(563\) −12.2878 −0.517867 −0.258934 0.965895i \(-0.583371\pi\)
−0.258934 + 0.965895i \(0.583371\pi\)
\(564\) 12.0368 0.506840
\(565\) −14.3410 −0.603330
\(566\) 7.32944 0.308079
\(567\) −29.7293 −1.24851
\(568\) 4.45061 0.186744
\(569\) 31.7088 1.32930 0.664652 0.747153i \(-0.268580\pi\)
0.664652 + 0.747153i \(0.268580\pi\)
\(570\) −3.61664 −0.151485
\(571\) 6.62363 0.277190 0.138595 0.990349i \(-0.455741\pi\)
0.138595 + 0.990349i \(0.455741\pi\)
\(572\) 4.32653 0.180901
\(573\) −6.39072 −0.266976
\(574\) −16.8472 −0.703190
\(575\) 6.29494 0.262517
\(576\) 0.335869 0.0139946
\(577\) −31.0460 −1.29246 −0.646232 0.763141i \(-0.723656\pi\)
−0.646232 + 0.763141i \(0.723656\pi\)
\(578\) −11.5718 −0.481323
\(579\) 32.9161 1.36795
\(580\) −3.78974 −0.157360
\(581\) −16.7733 −0.695872
\(582\) 14.3318 0.594070
\(583\) 9.34352 0.386969
\(584\) 1.00000 0.0413803
\(585\) 1.45315 0.0600803
\(586\) −7.57117 −0.312762
\(587\) −9.30278 −0.383967 −0.191983 0.981398i \(-0.561492\pi\)
−0.191983 + 0.981398i \(0.561492\pi\)
\(588\) −3.70260 −0.152693
\(589\) −5.57428 −0.229684
\(590\) −7.84290 −0.322887
\(591\) 26.5629 1.09265
\(592\) −0.856830 −0.0352155
\(593\) 43.9366 1.80426 0.902131 0.431463i \(-0.142002\pi\)
0.902131 + 0.431463i \(0.142002\pi\)
\(594\) −4.86586 −0.199649
\(595\) 7.00012 0.286977
\(596\) 11.6325 0.476485
\(597\) −6.16289 −0.252230
\(598\) −27.2353 −1.11373
\(599\) 11.0579 0.451815 0.225908 0.974149i \(-0.427465\pi\)
0.225908 + 0.974149i \(0.427465\pi\)
\(600\) −1.82644 −0.0745639
\(601\) −16.8549 −0.687526 −0.343763 0.939056i \(-0.611702\pi\)
−0.343763 + 0.939056i \(0.611702\pi\)
\(602\) 24.0732 0.981150
\(603\) −3.04961 −0.124190
\(604\) −0.737844 −0.0300224
\(605\) −1.00000 −0.0406558
\(606\) 31.0871 1.26283
\(607\) −1.31520 −0.0533824 −0.0266912 0.999644i \(-0.508497\pi\)
−0.0266912 + 0.999644i \(0.508497\pi\)
\(608\) −1.98016 −0.0803063
\(609\) −20.7965 −0.842717
\(610\) 2.89353 0.117156
\(611\) 28.5132 1.15352
\(612\) −0.782526 −0.0316317
\(613\) −22.4731 −0.907680 −0.453840 0.891083i \(-0.649946\pi\)
−0.453840 + 0.891083i \(0.649946\pi\)
\(614\) −26.3131 −1.06191
\(615\) −10.2413 −0.412970
\(616\) −3.00453 −0.121056
\(617\) 32.6429 1.31415 0.657077 0.753823i \(-0.271793\pi\)
0.657077 + 0.753823i \(0.271793\pi\)
\(618\) −13.3057 −0.535232
\(619\) 21.0286 0.845211 0.422605 0.906314i \(-0.361116\pi\)
0.422605 + 0.906314i \(0.361116\pi\)
\(620\) −2.81506 −0.113055
\(621\) 30.6303 1.22915
\(622\) 9.91646 0.397614
\(623\) −18.0598 −0.723551
\(624\) 7.90214 0.316339
\(625\) 1.00000 0.0400000
\(626\) 26.8046 1.07133
\(627\) −3.61664 −0.144435
\(628\) −4.90260 −0.195635
\(629\) 1.99629 0.0795972
\(630\) −1.00913 −0.0402047
\(631\) −5.09926 −0.202998 −0.101499 0.994836i \(-0.532364\pi\)
−0.101499 + 0.994836i \(0.532364\pi\)
\(632\) 5.72249 0.227628
\(633\) 39.1817 1.55733
\(634\) 18.8464 0.748485
\(635\) 11.8099 0.468660
\(636\) 17.0653 0.676685
\(637\) −8.77086 −0.347514
\(638\) −3.78974 −0.150037
\(639\) 1.49482 0.0591343
\(640\) −1.00000 −0.0395285
\(641\) −14.1024 −0.557013 −0.278506 0.960434i \(-0.589839\pi\)
−0.278506 + 0.960434i \(0.589839\pi\)
\(642\) −7.50438 −0.296174
\(643\) 3.29614 0.129987 0.0649935 0.997886i \(-0.479297\pi\)
0.0649935 + 0.997886i \(0.479297\pi\)
\(644\) 18.9134 0.745291
\(645\) 14.6339 0.576211
\(646\) 4.61349 0.181515
\(647\) −46.9087 −1.84417 −0.922086 0.386984i \(-0.873517\pi\)
−0.922086 + 0.386984i \(0.873517\pi\)
\(648\) −9.89480 −0.388704
\(649\) −7.84290 −0.307861
\(650\) −4.32653 −0.169701
\(651\) −15.4479 −0.605450
\(652\) −16.7822 −0.657241
\(653\) 28.8352 1.12841 0.564205 0.825635i \(-0.309183\pi\)
0.564205 + 0.825635i \(0.309183\pi\)
\(654\) 28.6349 1.11971
\(655\) −15.2331 −0.595208
\(656\) −5.60727 −0.218927
\(657\) 0.335869 0.0131035
\(658\) −19.8008 −0.771916
\(659\) −40.4273 −1.57483 −0.787413 0.616426i \(-0.788580\pi\)
−0.787413 + 0.616426i \(0.788580\pi\)
\(660\) −1.82644 −0.0710939
\(661\) 19.0767 0.741998 0.370999 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(662\) 31.9810 1.24298
\(663\) −18.4108 −0.715017
\(664\) −5.58265 −0.216649
\(665\) 5.94947 0.230711
\(666\) −0.287783 −0.0111514
\(667\) 23.8562 0.923714
\(668\) −11.4368 −0.442502
\(669\) −39.5996 −1.53101
\(670\) 9.07976 0.350782
\(671\) 2.89353 0.111704
\(672\) −5.48759 −0.211688
\(673\) 36.8733 1.42136 0.710681 0.703514i \(-0.248387\pi\)
0.710681 + 0.703514i \(0.248387\pi\)
\(674\) −6.25893 −0.241085
\(675\) 4.86586 0.187287
\(676\) 5.71889 0.219957
\(677\) 31.8011 1.22222 0.611108 0.791547i \(-0.290724\pi\)
0.611108 + 0.791547i \(0.290724\pi\)
\(678\) −26.1929 −1.00593
\(679\) −23.5761 −0.904768
\(680\) 2.32985 0.0893458
\(681\) −30.7467 −1.17822
\(682\) −2.81506 −0.107794
\(683\) 5.24583 0.200726 0.100363 0.994951i \(-0.468000\pi\)
0.100363 + 0.994951i \(0.468000\pi\)
\(684\) −0.665076 −0.0254298
\(685\) −6.96108 −0.265969
\(686\) −14.9409 −0.570445
\(687\) 36.7784 1.40318
\(688\) 8.01229 0.305466
\(689\) 40.4250 1.54007
\(690\) 11.4973 0.437695
\(691\) −32.3766 −1.23166 −0.615832 0.787877i \(-0.711180\pi\)
−0.615832 + 0.787877i \(0.711180\pi\)
\(692\) −20.2277 −0.768941
\(693\) −1.00913 −0.0383337
\(694\) −15.9336 −0.604832
\(695\) −0.0908223 −0.00344509
\(696\) −6.92171 −0.262367
\(697\) 13.0641 0.494838
\(698\) −22.7662 −0.861714
\(699\) −38.4199 −1.45317
\(700\) 3.00453 0.113561
\(701\) −17.4489 −0.659035 −0.329517 0.944149i \(-0.606886\pi\)
−0.329517 + 0.944149i \(0.606886\pi\)
\(702\) −21.0523 −0.794569
\(703\) 1.69666 0.0639909
\(704\) −1.00000 −0.0376889
\(705\) −12.0368 −0.453331
\(706\) 3.93216 0.147989
\(707\) −51.1391 −1.92328
\(708\) −14.3246 −0.538350
\(709\) −11.9616 −0.449229 −0.224614 0.974448i \(-0.572112\pi\)
−0.224614 + 0.974448i \(0.572112\pi\)
\(710\) −4.45061 −0.167029
\(711\) 1.92201 0.0720809
\(712\) −6.01085 −0.225266
\(713\) 17.7206 0.663643
\(714\) 12.7853 0.478477
\(715\) −4.32653 −0.161803
\(716\) −8.05501 −0.301030
\(717\) 31.9879 1.19461
\(718\) −19.6647 −0.733882
\(719\) 45.1017 1.68201 0.841006 0.541026i \(-0.181964\pi\)
0.841006 + 0.541026i \(0.181964\pi\)
\(720\) −0.335869 −0.0125171
\(721\) 21.8881 0.815157
\(722\) −15.0789 −0.561180
\(723\) −8.63668 −0.321202
\(724\) −3.96610 −0.147399
\(725\) 3.78974 0.140747
\(726\) −1.82644 −0.0677854
\(727\) −2.90588 −0.107773 −0.0538865 0.998547i \(-0.517161\pi\)
−0.0538865 + 0.998547i \(0.517161\pi\)
\(728\) −12.9992 −0.481783
\(729\) 23.3382 0.864378
\(730\) −1.00000 −0.0370117
\(731\) −18.6675 −0.690441
\(732\) 5.28485 0.195334
\(733\) 31.9119 1.17869 0.589346 0.807881i \(-0.299385\pi\)
0.589346 + 0.807881i \(0.299385\pi\)
\(734\) 14.0691 0.519301
\(735\) 3.70260 0.136572
\(736\) 6.29494 0.232035
\(737\) 9.07976 0.334457
\(738\) −1.88331 −0.0693255
\(739\) −20.5138 −0.754614 −0.377307 0.926088i \(-0.623150\pi\)
−0.377307 + 0.926088i \(0.623150\pi\)
\(740\) 0.856830 0.0314977
\(741\) −15.6475 −0.574826
\(742\) −28.0729 −1.03059
\(743\) 29.3013 1.07496 0.537479 0.843277i \(-0.319377\pi\)
0.537479 + 0.843277i \(0.319377\pi\)
\(744\) −5.14152 −0.188497
\(745\) −11.6325 −0.426181
\(746\) 7.03836 0.257693
\(747\) −1.87504 −0.0686042
\(748\) 2.32985 0.0851879
\(749\) 12.3449 0.451073
\(750\) 1.82644 0.0666920
\(751\) −12.8441 −0.468687 −0.234344 0.972154i \(-0.575294\pi\)
−0.234344 + 0.972154i \(0.575294\pi\)
\(752\) −6.59031 −0.240324
\(753\) 25.4715 0.928232
\(754\) −16.3964 −0.597122
\(755\) 0.737844 0.0268529
\(756\) 14.6197 0.531712
\(757\) −44.1602 −1.60503 −0.802514 0.596633i \(-0.796505\pi\)
−0.802514 + 0.596633i \(0.796505\pi\)
\(758\) 24.9735 0.907079
\(759\) 11.4973 0.417326
\(760\) 1.98016 0.0718281
\(761\) −5.30498 −0.192306 −0.0961528 0.995367i \(-0.530654\pi\)
−0.0961528 + 0.995367i \(0.530654\pi\)
\(762\) 21.5699 0.781397
\(763\) −47.1052 −1.70532
\(764\) 3.49901 0.126590
\(765\) 0.782526 0.0282923
\(766\) −2.32441 −0.0839842
\(767\) −33.9326 −1.22523
\(768\) −1.82644 −0.0659058
\(769\) −37.0814 −1.33719 −0.668595 0.743627i \(-0.733104\pi\)
−0.668595 + 0.743627i \(0.733104\pi\)
\(770\) 3.00453 0.108276
\(771\) 54.8882 1.97675
\(772\) −18.0220 −0.648627
\(773\) −17.4222 −0.626634 −0.313317 0.949649i \(-0.601440\pi\)
−0.313317 + 0.949649i \(0.601440\pi\)
\(774\) 2.69108 0.0967289
\(775\) 2.81506 0.101120
\(776\) −7.84684 −0.281685
\(777\) 4.70193 0.168681
\(778\) −10.2655 −0.368037
\(779\) 11.1033 0.397817
\(780\) −7.90214 −0.282942
\(781\) −4.45061 −0.159255
\(782\) −14.6663 −0.524465
\(783\) 18.4403 0.659004
\(784\) 2.02723 0.0724009
\(785\) 4.90260 0.174981
\(786\) −27.8224 −0.992391
\(787\) 53.2897 1.89957 0.949787 0.312898i \(-0.101300\pi\)
0.949787 + 0.312898i \(0.101300\pi\)
\(788\) −14.5436 −0.518093
\(789\) −31.2726 −1.11334
\(790\) −5.72249 −0.203597
\(791\) 43.0880 1.53203
\(792\) −0.335869 −0.0119346
\(793\) 12.5190 0.444561
\(794\) −8.96973 −0.318324
\(795\) −17.0653 −0.605245
\(796\) 3.37427 0.119598
\(797\) 39.8765 1.41250 0.706250 0.707963i \(-0.250386\pi\)
0.706250 + 0.707963i \(0.250386\pi\)
\(798\) 10.8663 0.384664
\(799\) 15.3545 0.543202
\(800\) 1.00000 0.0353553
\(801\) −2.01886 −0.0713330
\(802\) −27.9889 −0.988322
\(803\) −1.00000 −0.0352892
\(804\) 16.5836 0.584858
\(805\) −18.9134 −0.666609
\(806\) −12.1794 −0.429002
\(807\) −24.6141 −0.866458
\(808\) −17.0206 −0.598784
\(809\) −42.9569 −1.51028 −0.755142 0.655562i \(-0.772432\pi\)
−0.755142 + 0.655562i \(0.772432\pi\)
\(810\) 9.89480 0.347668
\(811\) 6.83735 0.240092 0.120046 0.992768i \(-0.461696\pi\)
0.120046 + 0.992768i \(0.461696\pi\)
\(812\) 11.3864 0.399584
\(813\) 48.7733 1.71055
\(814\) 0.856830 0.0300319
\(815\) 16.7822 0.587854
\(816\) 4.25533 0.148966
\(817\) −15.8656 −0.555069
\(818\) −19.0794 −0.667096
\(819\) −4.36604 −0.152562
\(820\) 5.60727 0.195814
\(821\) 6.83310 0.238477 0.119238 0.992866i \(-0.461955\pi\)
0.119238 + 0.992866i \(0.461955\pi\)
\(822\) −12.7140 −0.443451
\(823\) −0.603298 −0.0210296 −0.0105148 0.999945i \(-0.503347\pi\)
−0.0105148 + 0.999945i \(0.503347\pi\)
\(824\) 7.28504 0.253786
\(825\) 1.82644 0.0635883
\(826\) 23.5643 0.819905
\(827\) 25.3974 0.883155 0.441577 0.897223i \(-0.354419\pi\)
0.441577 + 0.897223i \(0.354419\pi\)
\(828\) 2.11428 0.0734762
\(829\) −10.8485 −0.376784 −0.188392 0.982094i \(-0.560328\pi\)
−0.188392 + 0.982094i \(0.560328\pi\)
\(830\) 5.58265 0.193777
\(831\) −1.40307 −0.0486719
\(832\) −4.32653 −0.149996
\(833\) −4.72314 −0.163647
\(834\) −0.165881 −0.00574400
\(835\) 11.4368 0.395786
\(836\) 1.98016 0.0684854
\(837\) 13.6977 0.473461
\(838\) −32.8434 −1.13455
\(839\) 42.3663 1.46265 0.731324 0.682030i \(-0.238903\pi\)
0.731324 + 0.682030i \(0.238903\pi\)
\(840\) 5.48759 0.189340
\(841\) −14.6379 −0.504755
\(842\) 25.4036 0.875465
\(843\) −3.06375 −0.105521
\(844\) −21.4525 −0.738427
\(845\) −5.71889 −0.196736
\(846\) −2.21348 −0.0761011
\(847\) 3.00453 0.103237
\(848\) −9.34352 −0.320858
\(849\) −13.3868 −0.459432
\(850\) −2.32985 −0.0799133
\(851\) −5.39369 −0.184893
\(852\) −8.12876 −0.278487
\(853\) 40.0418 1.37100 0.685502 0.728071i \(-0.259583\pi\)
0.685502 + 0.728071i \(0.259583\pi\)
\(854\) −8.69371 −0.297493
\(855\) 0.665076 0.0227451
\(856\) 4.10876 0.140434
\(857\) 1.41773 0.0484288 0.0242144 0.999707i \(-0.492292\pi\)
0.0242144 + 0.999707i \(0.492292\pi\)
\(858\) −7.90214 −0.269774
\(859\) −13.3345 −0.454967 −0.227483 0.973782i \(-0.573050\pi\)
−0.227483 + 0.973782i \(0.573050\pi\)
\(860\) −8.01229 −0.273217
\(861\) 30.7704 1.04865
\(862\) 28.2811 0.963260
\(863\) 22.3794 0.761804 0.380902 0.924615i \(-0.375614\pi\)
0.380902 + 0.924615i \(0.375614\pi\)
\(864\) 4.86586 0.165540
\(865\) 20.2277 0.687762
\(866\) −11.4205 −0.388084
\(867\) 21.1351 0.717787
\(868\) 8.45794 0.287081
\(869\) −5.72249 −0.194122
\(870\) 6.92171 0.234668
\(871\) 39.2839 1.33108
\(872\) −15.6780 −0.530925
\(873\) −2.63551 −0.0891986
\(874\) −12.4650 −0.421635
\(875\) −3.00453 −0.101572
\(876\) −1.82644 −0.0617096
\(877\) 5.18944 0.175235 0.0876175 0.996154i \(-0.472075\pi\)
0.0876175 + 0.996154i \(0.472075\pi\)
\(878\) −25.6469 −0.865541
\(879\) 13.8283 0.466415
\(880\) 1.00000 0.0337100
\(881\) 45.0059 1.51629 0.758144 0.652087i \(-0.226106\pi\)
0.758144 + 0.652087i \(0.226106\pi\)
\(882\) 0.680883 0.0229265
\(883\) −32.9850 −1.11003 −0.555016 0.831840i \(-0.687288\pi\)
−0.555016 + 0.831840i \(0.687288\pi\)
\(884\) 10.0802 0.339033
\(885\) 14.3246 0.481515
\(886\) 34.3263 1.15322
\(887\) −16.0608 −0.539267 −0.269634 0.962963i \(-0.586903\pi\)
−0.269634 + 0.962963i \(0.586903\pi\)
\(888\) 1.56494 0.0525161
\(889\) −35.4831 −1.19007
\(890\) 6.01085 0.201484
\(891\) 9.89480 0.331488
\(892\) 21.6813 0.725944
\(893\) 13.0499 0.436698
\(894\) −21.2460 −0.710572
\(895\) 8.05501 0.269249
\(896\) 3.00453 0.100374
\(897\) 49.7435 1.66089
\(898\) −24.9408 −0.832284
\(899\) 10.6683 0.355809
\(900\) 0.335869 0.0111956
\(901\) 21.7690 0.725231
\(902\) 5.60727 0.186702
\(903\) −43.9682 −1.46317
\(904\) 14.3410 0.476974
\(905\) 3.96610 0.131838
\(906\) 1.34762 0.0447718
\(907\) −41.0935 −1.36449 −0.682243 0.731125i \(-0.738996\pi\)
−0.682243 + 0.731125i \(0.738996\pi\)
\(908\) 16.8342 0.558664
\(909\) −5.71671 −0.189611
\(910\) 12.9992 0.430920
\(911\) 52.6723 1.74511 0.872555 0.488515i \(-0.162461\pi\)
0.872555 + 0.488515i \(0.162461\pi\)
\(912\) 3.61664 0.119759
\(913\) 5.58265 0.184759
\(914\) 8.81941 0.291720
\(915\) −5.28485 −0.174712
\(916\) −20.1367 −0.665336
\(917\) 45.7685 1.51141
\(918\) −11.3368 −0.374169
\(919\) 2.69139 0.0887808 0.0443904 0.999014i \(-0.485865\pi\)
0.0443904 + 0.999014i \(0.485865\pi\)
\(920\) −6.29494 −0.207538
\(921\) 48.0592 1.58360
\(922\) −16.4185 −0.540716
\(923\) −19.2557 −0.633810
\(924\) 5.48759 0.180528
\(925\) −0.856830 −0.0281724
\(926\) −20.3061 −0.667301
\(927\) 2.44682 0.0803641
\(928\) 3.78974 0.124404
\(929\) −4.03549 −0.132400 −0.0662000 0.997806i \(-0.521088\pi\)
−0.0662000 + 0.997806i \(0.521088\pi\)
\(930\) 5.14152 0.168597
\(931\) −4.01424 −0.131561
\(932\) 21.0354 0.689039
\(933\) −18.1118 −0.592953
\(934\) −20.5992 −0.674026
\(935\) −2.32985 −0.0761943
\(936\) −1.45315 −0.0474977
\(937\) 36.0105 1.17641 0.588207 0.808711i \(-0.299834\pi\)
0.588207 + 0.808711i \(0.299834\pi\)
\(938\) −27.2804 −0.890738
\(939\) −48.9570 −1.59765
\(940\) 6.59031 0.214952
\(941\) −47.8388 −1.55950 −0.779750 0.626091i \(-0.784654\pi\)
−0.779750 + 0.626091i \(0.784654\pi\)
\(942\) 8.95430 0.291747
\(943\) −35.2974 −1.14944
\(944\) 7.84290 0.255265
\(945\) −14.6197 −0.475577
\(946\) −8.01229 −0.260502
\(947\) 11.9931 0.389723 0.194862 0.980831i \(-0.437574\pi\)
0.194862 + 0.980831i \(0.437574\pi\)
\(948\) −10.4518 −0.339457
\(949\) −4.32653 −0.140445
\(950\) −1.98016 −0.0642450
\(951\) −34.4217 −1.11620
\(952\) −7.00012 −0.226875
\(953\) 4.31087 0.139643 0.0698214 0.997560i \(-0.477757\pi\)
0.0698214 + 0.997560i \(0.477757\pi\)
\(954\) −3.13820 −0.101603
\(955\) −3.49901 −0.113225
\(956\) −17.5138 −0.566438
\(957\) 6.92171 0.223747
\(958\) 17.6387 0.569880
\(959\) 20.9148 0.675375
\(960\) 1.82644 0.0589480
\(961\) −23.0754 −0.744369
\(962\) 3.70710 0.119522
\(963\) 1.38001 0.0444700
\(964\) 4.72871 0.152301
\(965\) 18.0220 0.580150
\(966\) −34.5441 −1.11144
\(967\) 40.1249 1.29033 0.645165 0.764043i \(-0.276789\pi\)
0.645165 + 0.764043i \(0.276789\pi\)
\(968\) 1.00000 0.0321412
\(969\) −8.42625 −0.270690
\(970\) 7.84684 0.251947
\(971\) −9.22327 −0.295989 −0.147994 0.988988i \(-0.547282\pi\)
−0.147994 + 0.988988i \(0.547282\pi\)
\(972\) 3.47463 0.111449
\(973\) 0.272879 0.00874809
\(974\) −5.31105 −0.170177
\(975\) 7.90214 0.253071
\(976\) −2.89353 −0.0926197
\(977\) 1.29895 0.0415569 0.0207785 0.999784i \(-0.493386\pi\)
0.0207785 + 0.999784i \(0.493386\pi\)
\(978\) 30.6516 0.980129
\(979\) 6.01085 0.192108
\(980\) −2.02723 −0.0647574
\(981\) −5.26577 −0.168123
\(982\) −34.1717 −1.09046
\(983\) −21.6788 −0.691446 −0.345723 0.938337i \(-0.612366\pi\)
−0.345723 + 0.938337i \(0.612366\pi\)
\(984\) 10.2413 0.326481
\(985\) 14.5436 0.463396
\(986\) −8.82953 −0.281189
\(987\) 36.1649 1.15114
\(988\) 8.56725 0.272560
\(989\) 50.4369 1.60380
\(990\) 0.335869 0.0106746
\(991\) 19.0629 0.605554 0.302777 0.953061i \(-0.402086\pi\)
0.302777 + 0.953061i \(0.402086\pi\)
\(992\) 2.81506 0.0893782
\(993\) −58.4113 −1.85363
\(994\) 13.3720 0.424135
\(995\) −3.37427 −0.106972
\(996\) 10.1964 0.323084
\(997\) 2.65307 0.0840235 0.0420118 0.999117i \(-0.486623\pi\)
0.0420118 + 0.999117i \(0.486623\pi\)
\(998\) 3.62548 0.114763
\(999\) −4.16922 −0.131908
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 8030.2.a.bf.1.5 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8030.2.a.bf.1.5 15 1.1 even 1 trivial