Properties

Label 1502.2.a.g.1.3
Level $1502$
Weight $2$
Character 1502.1
Self dual yes
Analytic conductor $11.994$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1502,2,Mod(1,1502)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1502.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1502 = 2 \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1502.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: \(11.9935303836\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + 5490 x^{8} - 2787 x^{7} - 10540 x^{6} + 1919 x^{5} + 10822 x^{4} + 132 x^{3} + \cdots + 864 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.25035\) of defining polynomial
Character \(\chi\) \(=\) 1502.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.25035 q^{3} +1.00000 q^{4} -3.07514 q^{5} -1.25035 q^{6} -0.487959 q^{7} +1.00000 q^{8} -1.43661 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.25035 q^{3} +1.00000 q^{4} -3.07514 q^{5} -1.25035 q^{6} -0.487959 q^{7} +1.00000 q^{8} -1.43661 q^{9} -3.07514 q^{10} -4.26766 q^{11} -1.25035 q^{12} -2.00084 q^{13} -0.487959 q^{14} +3.84501 q^{15} +1.00000 q^{16} +4.08581 q^{17} -1.43661 q^{18} +8.04310 q^{19} -3.07514 q^{20} +0.610122 q^{21} -4.26766 q^{22} -0.0257712 q^{23} -1.25035 q^{24} +4.45648 q^{25} -2.00084 q^{26} +5.54734 q^{27} -0.487959 q^{28} +9.96727 q^{29} +3.84501 q^{30} +0.393455 q^{31} +1.00000 q^{32} +5.33608 q^{33} +4.08581 q^{34} +1.50054 q^{35} -1.43661 q^{36} +10.0185 q^{37} +8.04310 q^{38} +2.50175 q^{39} -3.07514 q^{40} -4.52723 q^{41} +0.610122 q^{42} -4.16008 q^{43} -4.26766 q^{44} +4.41779 q^{45} -0.0257712 q^{46} -0.996759 q^{47} -1.25035 q^{48} -6.76190 q^{49} +4.45648 q^{50} -5.10871 q^{51} -2.00084 q^{52} -5.88337 q^{53} +5.54734 q^{54} +13.1236 q^{55} -0.487959 q^{56} -10.0567 q^{57} +9.96727 q^{58} +6.63589 q^{59} +3.84501 q^{60} -4.39227 q^{61} +0.393455 q^{62} +0.701010 q^{63} +1.00000 q^{64} +6.15285 q^{65} +5.33608 q^{66} +11.7016 q^{67} +4.08581 q^{68} +0.0322231 q^{69} +1.50054 q^{70} -0.816623 q^{71} -1.43661 q^{72} +1.75200 q^{73} +10.0185 q^{74} -5.57218 q^{75} +8.04310 q^{76} +2.08244 q^{77} +2.50175 q^{78} +1.76038 q^{79} -3.07514 q^{80} -2.62629 q^{81} -4.52723 q^{82} -17.9525 q^{83} +0.610122 q^{84} -12.5644 q^{85} -4.16008 q^{86} -12.4626 q^{87} -4.26766 q^{88} +5.54121 q^{89} +4.41779 q^{90} +0.976327 q^{91} -0.0257712 q^{92} -0.491958 q^{93} -0.996759 q^{94} -24.7337 q^{95} -1.25035 q^{96} +10.5413 q^{97} -6.76190 q^{98} +6.13098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 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
\(3\) −1.25035 −0.721892 −0.360946 0.932587i \(-0.617546\pi\)
−0.360946 + 0.932587i \(0.617546\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.07514 −1.37524 −0.687622 0.726069i \(-0.741345\pi\)
−0.687622 + 0.726069i \(0.741345\pi\)
\(6\) −1.25035 −0.510455
\(7\) −0.487959 −0.184431 −0.0922157 0.995739i \(-0.529395\pi\)
−0.0922157 + 0.995739i \(0.529395\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.43661 −0.478872
\(10\) −3.07514 −0.972444
\(11\) −4.26766 −1.28675 −0.643374 0.765552i \(-0.722466\pi\)
−0.643374 + 0.765552i \(0.722466\pi\)
\(12\) −1.25035 −0.360946
\(13\) −2.00084 −0.554932 −0.277466 0.960735i \(-0.589495\pi\)
−0.277466 + 0.960735i \(0.589495\pi\)
\(14\) −0.487959 −0.130413
\(15\) 3.84501 0.992778
\(16\) 1.00000 0.250000
\(17\) 4.08581 0.990955 0.495478 0.868621i \(-0.334993\pi\)
0.495478 + 0.868621i \(0.334993\pi\)
\(18\) −1.43661 −0.338613
\(19\) 8.04310 1.84521 0.922607 0.385741i \(-0.126054\pi\)
0.922607 + 0.385741i \(0.126054\pi\)
\(20\) −3.07514 −0.687622
\(21\) 0.610122 0.133140
\(22\) −4.26766 −0.909868
\(23\) −0.0257712 −0.00537366 −0.00268683 0.999996i \(-0.500855\pi\)
−0.00268683 + 0.999996i \(0.500855\pi\)
\(24\) −1.25035 −0.255227
\(25\) 4.45648 0.891296
\(26\) −2.00084 −0.392396
\(27\) 5.54734 1.06759
\(28\) −0.487959 −0.0922157
\(29\) 9.96727 1.85088 0.925438 0.378900i \(-0.123698\pi\)
0.925438 + 0.378900i \(0.123698\pi\)
\(30\) 3.84501 0.702000
\(31\) 0.393455 0.0706666 0.0353333 0.999376i \(-0.488751\pi\)
0.0353333 + 0.999376i \(0.488751\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.33608 0.928893
\(34\) 4.08581 0.700711
\(35\) 1.50054 0.253638
\(36\) −1.43661 −0.239436
\(37\) 10.0185 1.64703 0.823514 0.567297i \(-0.192011\pi\)
0.823514 + 0.567297i \(0.192011\pi\)
\(38\) 8.04310 1.30476
\(39\) 2.50175 0.400601
\(40\) −3.07514 −0.486222
\(41\) −4.52723 −0.707034 −0.353517 0.935428i \(-0.615014\pi\)
−0.353517 + 0.935428i \(0.615014\pi\)
\(42\) 0.610122 0.0941439
\(43\) −4.16008 −0.634406 −0.317203 0.948358i \(-0.602744\pi\)
−0.317203 + 0.948358i \(0.602744\pi\)
\(44\) −4.26766 −0.643374
\(45\) 4.41779 0.658565
\(46\) −0.0257712 −0.00379975
\(47\) −0.996759 −0.145392 −0.0726961 0.997354i \(-0.523160\pi\)
−0.0726961 + 0.997354i \(0.523160\pi\)
\(48\) −1.25035 −0.180473
\(49\) −6.76190 −0.965985
\(50\) 4.45648 0.630242
\(51\) −5.10871 −0.715363
\(52\) −2.00084 −0.277466
\(53\) −5.88337 −0.808142 −0.404071 0.914728i \(-0.632405\pi\)
−0.404071 + 0.914728i \(0.632405\pi\)
\(54\) 5.54734 0.754897
\(55\) 13.1236 1.76959
\(56\) −0.487959 −0.0652063
\(57\) −10.0567 −1.33205
\(58\) 9.96727 1.30877
\(59\) 6.63589 0.863919 0.431960 0.901893i \(-0.357822\pi\)
0.431960 + 0.901893i \(0.357822\pi\)
\(60\) 3.84501 0.496389
\(61\) −4.39227 −0.562373 −0.281186 0.959653i \(-0.590728\pi\)
−0.281186 + 0.959653i \(0.590728\pi\)
\(62\) 0.393455 0.0499688
\(63\) 0.701010 0.0883189
\(64\) 1.00000 0.125000
\(65\) 6.15285 0.763167
\(66\) 5.33608 0.656826
\(67\) 11.7016 1.42958 0.714791 0.699338i \(-0.246522\pi\)
0.714791 + 0.699338i \(0.246522\pi\)
\(68\) 4.08581 0.495478
\(69\) 0.0322231 0.00387920
\(70\) 1.50054 0.179349
\(71\) −0.816623 −0.0969153 −0.0484577 0.998825i \(-0.515431\pi\)
−0.0484577 + 0.998825i \(0.515431\pi\)
\(72\) −1.43661 −0.169307
\(73\) 1.75200 0.205056 0.102528 0.994730i \(-0.467307\pi\)
0.102528 + 0.994730i \(0.467307\pi\)
\(74\) 10.0185 1.16462
\(75\) −5.57218 −0.643420
\(76\) 8.04310 0.922607
\(77\) 2.08244 0.237316
\(78\) 2.50175 0.283268
\(79\) 1.76038 0.198058 0.0990292 0.995085i \(-0.468426\pi\)
0.0990292 + 0.995085i \(0.468426\pi\)
\(80\) −3.07514 −0.343811
\(81\) −2.62629 −0.291810
\(82\) −4.52723 −0.499949
\(83\) −17.9525 −1.97054 −0.985272 0.170993i \(-0.945303\pi\)
−0.985272 + 0.170993i \(0.945303\pi\)
\(84\) 0.610122 0.0665698
\(85\) −12.5644 −1.36281
\(86\) −4.16008 −0.448593
\(87\) −12.4626 −1.33613
\(88\) −4.26766 −0.454934
\(89\) 5.54121 0.587368 0.293684 0.955903i \(-0.405119\pi\)
0.293684 + 0.955903i \(0.405119\pi\)
\(90\) 4.41779 0.465676
\(91\) 0.976327 0.102347
\(92\) −0.0257712 −0.00268683
\(93\) −0.491958 −0.0510137
\(94\) −0.996759 −0.102808
\(95\) −24.7337 −2.53762
\(96\) −1.25035 −0.127614
\(97\) 10.5413 1.07031 0.535155 0.844754i \(-0.320253\pi\)
0.535155 + 0.844754i \(0.320253\pi\)
\(98\) −6.76190 −0.683055
\(99\) 6.13098 0.616187
\(100\) 4.45648 0.445648
\(101\) 6.67517 0.664204 0.332102 0.943243i \(-0.392242\pi\)
0.332102 + 0.943243i \(0.392242\pi\)
\(102\) −5.10871 −0.505838
\(103\) 11.9804 1.18047 0.590233 0.807233i \(-0.299036\pi\)
0.590233 + 0.807233i \(0.299036\pi\)
\(104\) −2.00084 −0.196198
\(105\) −1.87621 −0.183099
\(106\) −5.88337 −0.571443
\(107\) 7.35926 0.711447 0.355723 0.934591i \(-0.384235\pi\)
0.355723 + 0.934591i \(0.384235\pi\)
\(108\) 5.54734 0.533793
\(109\) 7.21073 0.690663 0.345332 0.938481i \(-0.387766\pi\)
0.345332 + 0.938481i \(0.387766\pi\)
\(110\) 13.1236 1.25129
\(111\) −12.5266 −1.18898
\(112\) −0.487959 −0.0461078
\(113\) −1.34213 −0.126257 −0.0631287 0.998005i \(-0.520108\pi\)
−0.0631287 + 0.998005i \(0.520108\pi\)
\(114\) −10.0567 −0.941899
\(115\) 0.0792499 0.00739009
\(116\) 9.96727 0.925438
\(117\) 2.87443 0.265741
\(118\) 6.63589 0.610883
\(119\) −1.99371 −0.182763
\(120\) 3.84501 0.351000
\(121\) 7.21290 0.655718
\(122\) −4.39227 −0.397657
\(123\) 5.66064 0.510403
\(124\) 0.393455 0.0353333
\(125\) 1.67140 0.149494
\(126\) 0.701010 0.0624509
\(127\) −10.3758 −0.920702 −0.460351 0.887737i \(-0.652276\pi\)
−0.460351 + 0.887737i \(0.652276\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.20157 0.457973
\(130\) 6.15285 0.539641
\(131\) 2.44482 0.213605 0.106803 0.994280i \(-0.465939\pi\)
0.106803 + 0.994280i \(0.465939\pi\)
\(132\) 5.33608 0.464446
\(133\) −3.92471 −0.340315
\(134\) 11.7016 1.01087
\(135\) −17.0588 −1.46819
\(136\) 4.08581 0.350356
\(137\) 6.38733 0.545707 0.272853 0.962056i \(-0.412033\pi\)
0.272853 + 0.962056i \(0.412033\pi\)
\(138\) 0.0322231 0.00274301
\(139\) 13.8060 1.17101 0.585504 0.810670i \(-0.300897\pi\)
0.585504 + 0.810670i \(0.300897\pi\)
\(140\) 1.50054 0.126819
\(141\) 1.24630 0.104958
\(142\) −0.816623 −0.0685295
\(143\) 8.53889 0.714058
\(144\) −1.43661 −0.119718
\(145\) −30.6507 −2.54541
\(146\) 1.75200 0.144996
\(147\) 8.45476 0.697337
\(148\) 10.0185 0.823514
\(149\) −12.3706 −1.01344 −0.506720 0.862111i \(-0.669142\pi\)
−0.506720 + 0.862111i \(0.669142\pi\)
\(150\) −5.57218 −0.454966
\(151\) 6.20066 0.504603 0.252301 0.967649i \(-0.418813\pi\)
0.252301 + 0.967649i \(0.418813\pi\)
\(152\) 8.04310 0.652382
\(153\) −5.86974 −0.474540
\(154\) 2.08244 0.167808
\(155\) −1.20993 −0.0971838
\(156\) 2.50175 0.200301
\(157\) 0.364004 0.0290507 0.0145253 0.999895i \(-0.495376\pi\)
0.0145253 + 0.999895i \(0.495376\pi\)
\(158\) 1.76038 0.140048
\(159\) 7.35629 0.583392
\(160\) −3.07514 −0.243111
\(161\) 0.0125753 0.000991070 0
\(162\) −2.62629 −0.206341
\(163\) 20.4860 1.60459 0.802294 0.596930i \(-0.203613\pi\)
0.802294 + 0.596930i \(0.203613\pi\)
\(164\) −4.52723 −0.353517
\(165\) −16.4092 −1.27745
\(166\) −17.9525 −1.39339
\(167\) 11.4706 0.887618 0.443809 0.896121i \(-0.353627\pi\)
0.443809 + 0.896121i \(0.353627\pi\)
\(168\) 0.610122 0.0470719
\(169\) −8.99665 −0.692050
\(170\) −12.5644 −0.963649
\(171\) −11.5548 −0.883621
\(172\) −4.16008 −0.317203
\(173\) −9.37883 −0.713059 −0.356530 0.934284i \(-0.616040\pi\)
−0.356530 + 0.934284i \(0.616040\pi\)
\(174\) −12.4626 −0.944788
\(175\) −2.17458 −0.164383
\(176\) −4.26766 −0.321687
\(177\) −8.29721 −0.623657
\(178\) 5.54121 0.415332
\(179\) −11.3854 −0.850982 −0.425491 0.904963i \(-0.639899\pi\)
−0.425491 + 0.904963i \(0.639899\pi\)
\(180\) 4.41779 0.329283
\(181\) 16.9420 1.25929 0.629644 0.776883i \(-0.283201\pi\)
0.629644 + 0.776883i \(0.283201\pi\)
\(182\) 0.976327 0.0723702
\(183\) 5.49189 0.405972
\(184\) −0.0257712 −0.00189987
\(185\) −30.8082 −2.26506
\(186\) −0.491958 −0.0360721
\(187\) −17.4369 −1.27511
\(188\) −0.996759 −0.0726961
\(189\) −2.70688 −0.196896
\(190\) −24.7337 −1.79437
\(191\) 3.61845 0.261822 0.130911 0.991394i \(-0.458210\pi\)
0.130911 + 0.991394i \(0.458210\pi\)
\(192\) −1.25035 −0.0902365
\(193\) −13.7420 −0.989172 −0.494586 0.869129i \(-0.664680\pi\)
−0.494586 + 0.869129i \(0.664680\pi\)
\(194\) 10.5413 0.756823
\(195\) −7.69324 −0.550925
\(196\) −6.76190 −0.482993
\(197\) −5.57990 −0.397551 −0.198776 0.980045i \(-0.563697\pi\)
−0.198776 + 0.980045i \(0.563697\pi\)
\(198\) 6.13098 0.435710
\(199\) 22.2676 1.57850 0.789252 0.614069i \(-0.210468\pi\)
0.789252 + 0.614069i \(0.210468\pi\)
\(200\) 4.45648 0.315121
\(201\) −14.6312 −1.03200
\(202\) 6.67517 0.469663
\(203\) −4.86362 −0.341359
\(204\) −5.10871 −0.357682
\(205\) 13.9219 0.972345
\(206\) 11.9804 0.834716
\(207\) 0.0370232 0.00257329
\(208\) −2.00084 −0.138733
\(209\) −34.3252 −2.37432
\(210\) −1.87621 −0.129471
\(211\) −21.3358 −1.46882 −0.734409 0.678707i \(-0.762541\pi\)
−0.734409 + 0.678707i \(0.762541\pi\)
\(212\) −5.88337 −0.404071
\(213\) 1.02107 0.0699624
\(214\) 7.35926 0.503069
\(215\) 12.7928 0.872464
\(216\) 5.54734 0.377449
\(217\) −0.191990 −0.0130331
\(218\) 7.21073 0.488373
\(219\) −2.19062 −0.148028
\(220\) 13.1236 0.884796
\(221\) −8.17505 −0.549913
\(222\) −12.5266 −0.840733
\(223\) 15.2924 1.02405 0.512026 0.858970i \(-0.328895\pi\)
0.512026 + 0.858970i \(0.328895\pi\)
\(224\) −0.487959 −0.0326032
\(225\) −6.40225 −0.426816
\(226\) −1.34213 −0.0892775
\(227\) 6.22212 0.412976 0.206488 0.978449i \(-0.433796\pi\)
0.206488 + 0.978449i \(0.433796\pi\)
\(228\) −10.0567 −0.666023
\(229\) −1.20776 −0.0798113 −0.0399056 0.999203i \(-0.512706\pi\)
−0.0399056 + 0.999203i \(0.512706\pi\)
\(230\) 0.0792499 0.00522558
\(231\) −2.60379 −0.171317
\(232\) 9.96727 0.654383
\(233\) −25.1341 −1.64659 −0.823294 0.567616i \(-0.807866\pi\)
−0.823294 + 0.567616i \(0.807866\pi\)
\(234\) 2.87443 0.187907
\(235\) 3.06517 0.199950
\(236\) 6.63589 0.431960
\(237\) −2.20110 −0.142977
\(238\) −1.99371 −0.129233
\(239\) −23.6571 −1.53025 −0.765125 0.643882i \(-0.777323\pi\)
−0.765125 + 0.643882i \(0.777323\pi\)
\(240\) 3.84501 0.248194
\(241\) −15.1358 −0.974982 −0.487491 0.873128i \(-0.662088\pi\)
−0.487491 + 0.873128i \(0.662088\pi\)
\(242\) 7.21290 0.463663
\(243\) −13.3582 −0.856930
\(244\) −4.39227 −0.281186
\(245\) 20.7938 1.32847
\(246\) 5.66064 0.360909
\(247\) −16.0929 −1.02397
\(248\) 0.393455 0.0249844
\(249\) 22.4470 1.42252
\(250\) 1.67140 0.105709
\(251\) 23.0807 1.45684 0.728419 0.685132i \(-0.240256\pi\)
0.728419 + 0.685132i \(0.240256\pi\)
\(252\) 0.701010 0.0441595
\(253\) 0.109982 0.00691454
\(254\) −10.3758 −0.651035
\(255\) 15.7100 0.983799
\(256\) 1.00000 0.0625000
\(257\) −5.54349 −0.345793 −0.172897 0.984940i \(-0.555313\pi\)
−0.172897 + 0.984940i \(0.555313\pi\)
\(258\) 5.20157 0.323836
\(259\) −4.88861 −0.303763
\(260\) 6.15285 0.381584
\(261\) −14.3191 −0.886332
\(262\) 2.44482 0.151042
\(263\) 16.2519 1.00214 0.501068 0.865408i \(-0.332941\pi\)
0.501068 + 0.865408i \(0.332941\pi\)
\(264\) 5.33608 0.328413
\(265\) 18.0922 1.11139
\(266\) −3.92471 −0.240639
\(267\) −6.92848 −0.424016
\(268\) 11.7016 0.714791
\(269\) 13.0504 0.795695 0.397848 0.917452i \(-0.369757\pi\)
0.397848 + 0.917452i \(0.369757\pi\)
\(270\) −17.0588 −1.03817
\(271\) −8.91362 −0.541464 −0.270732 0.962655i \(-0.587266\pi\)
−0.270732 + 0.962655i \(0.587266\pi\)
\(272\) 4.08581 0.247739
\(273\) −1.22075 −0.0738834
\(274\) 6.38733 0.385873
\(275\) −19.0187 −1.14687
\(276\) 0.0322231 0.00193960
\(277\) 31.3497 1.88362 0.941811 0.336142i \(-0.109122\pi\)
0.941811 + 0.336142i \(0.109122\pi\)
\(278\) 13.8060 0.828028
\(279\) −0.565243 −0.0338402
\(280\) 1.50054 0.0896746
\(281\) −11.2573 −0.671554 −0.335777 0.941942i \(-0.608999\pi\)
−0.335777 + 0.941942i \(0.608999\pi\)
\(282\) 1.24630 0.0742162
\(283\) 18.9390 1.12580 0.562902 0.826523i \(-0.309685\pi\)
0.562902 + 0.826523i \(0.309685\pi\)
\(284\) −0.816623 −0.0484577
\(285\) 30.9258 1.83189
\(286\) 8.53889 0.504915
\(287\) 2.20910 0.130399
\(288\) −1.43661 −0.0846533
\(289\) −0.306124 −0.0180073
\(290\) −30.6507 −1.79987
\(291\) −13.1804 −0.772648
\(292\) 1.75200 0.102528
\(293\) 22.0162 1.28620 0.643099 0.765783i \(-0.277648\pi\)
0.643099 + 0.765783i \(0.277648\pi\)
\(294\) 8.45476 0.493092
\(295\) −20.4063 −1.18810
\(296\) 10.0185 0.582312
\(297\) −23.6741 −1.37371
\(298\) −12.3706 −0.716610
\(299\) 0.0515639 0.00298202
\(300\) −5.57218 −0.321710
\(301\) 2.02995 0.117004
\(302\) 6.20066 0.356808
\(303\) −8.34633 −0.479484
\(304\) 8.04310 0.461304
\(305\) 13.5068 0.773400
\(306\) −5.86974 −0.335551
\(307\) 27.0103 1.54156 0.770779 0.637103i \(-0.219867\pi\)
0.770779 + 0.637103i \(0.219867\pi\)
\(308\) 2.08244 0.118658
\(309\) −14.9798 −0.852170
\(310\) −1.20993 −0.0687193
\(311\) 19.1623 1.08659 0.543296 0.839541i \(-0.317176\pi\)
0.543296 + 0.839541i \(0.317176\pi\)
\(312\) 2.50175 0.141634
\(313\) −2.27801 −0.128761 −0.0643803 0.997925i \(-0.520507\pi\)
−0.0643803 + 0.997925i \(0.520507\pi\)
\(314\) 0.364004 0.0205419
\(315\) −2.15570 −0.121460
\(316\) 1.76038 0.0990292
\(317\) −23.8258 −1.33819 −0.669095 0.743177i \(-0.733318\pi\)
−0.669095 + 0.743177i \(0.733318\pi\)
\(318\) 7.35629 0.412520
\(319\) −42.5369 −2.38161
\(320\) −3.07514 −0.171906
\(321\) −9.20168 −0.513588
\(322\) 0.0125753 0.000700793 0
\(323\) 32.8626 1.82853
\(324\) −2.62629 −0.145905
\(325\) −8.91669 −0.494609
\(326\) 20.4860 1.13461
\(327\) −9.01597 −0.498584
\(328\) −4.52723 −0.249974
\(329\) 0.486378 0.0268149
\(330\) −16.4092 −0.903297
\(331\) 27.3893 1.50545 0.752727 0.658333i \(-0.228738\pi\)
0.752727 + 0.658333i \(0.228738\pi\)
\(332\) −17.9525 −0.985272
\(333\) −14.3927 −0.788715
\(334\) 11.4706 0.627641
\(335\) −35.9842 −1.96602
\(336\) 0.610122 0.0332849
\(337\) −7.97092 −0.434204 −0.217102 0.976149i \(-0.569660\pi\)
−0.217102 + 0.976149i \(0.569660\pi\)
\(338\) −8.99665 −0.489353
\(339\) 1.67814 0.0911442
\(340\) −12.5644 −0.681403
\(341\) −1.67913 −0.0909301
\(342\) −11.5548 −0.624814
\(343\) 6.71525 0.362589
\(344\) −4.16008 −0.224297
\(345\) −0.0990904 −0.00533485
\(346\) −9.37883 −0.504209
\(347\) 12.4240 0.666955 0.333478 0.942758i \(-0.391778\pi\)
0.333478 + 0.942758i \(0.391778\pi\)
\(348\) −12.4626 −0.668066
\(349\) 14.3433 0.767781 0.383890 0.923379i \(-0.374584\pi\)
0.383890 + 0.923379i \(0.374584\pi\)
\(350\) −2.17458 −0.116236
\(351\) −11.0993 −0.592438
\(352\) −4.26766 −0.227467
\(353\) −4.12403 −0.219500 −0.109750 0.993959i \(-0.535005\pi\)
−0.109750 + 0.993959i \(0.535005\pi\)
\(354\) −8.29721 −0.440992
\(355\) 2.51123 0.133282
\(356\) 5.54121 0.293684
\(357\) 2.49284 0.131935
\(358\) −11.3854 −0.601735
\(359\) −16.4658 −0.869030 −0.434515 0.900665i \(-0.643080\pi\)
−0.434515 + 0.900665i \(0.643080\pi\)
\(360\) 4.41779 0.232838
\(361\) 45.6915 2.40482
\(362\) 16.9420 0.890452
\(363\) −9.01868 −0.473358
\(364\) 0.976327 0.0511734
\(365\) −5.38764 −0.282002
\(366\) 5.49189 0.287066
\(367\) 14.9541 0.780600 0.390300 0.920688i \(-0.372371\pi\)
0.390300 + 0.920688i \(0.372371\pi\)
\(368\) −0.0257712 −0.00134341
\(369\) 6.50388 0.338579
\(370\) −30.8082 −1.60164
\(371\) 2.87084 0.149047
\(372\) −0.491958 −0.0255068
\(373\) −13.6234 −0.705393 −0.352696 0.935738i \(-0.614735\pi\)
−0.352696 + 0.935738i \(0.614735\pi\)
\(374\) −17.4369 −0.901638
\(375\) −2.08984 −0.107919
\(376\) −0.996759 −0.0514039
\(377\) −19.9429 −1.02711
\(378\) −2.70688 −0.139227
\(379\) 8.55606 0.439495 0.219748 0.975557i \(-0.429477\pi\)
0.219748 + 0.975557i \(0.429477\pi\)
\(380\) −24.7337 −1.26881
\(381\) 12.9734 0.664648
\(382\) 3.61845 0.185136
\(383\) −18.9528 −0.968445 −0.484222 0.874945i \(-0.660897\pi\)
−0.484222 + 0.874945i \(0.660897\pi\)
\(384\) −1.25035 −0.0638069
\(385\) −6.40380 −0.326368
\(386\) −13.7420 −0.699451
\(387\) 5.97643 0.303799
\(388\) 10.5413 0.535155
\(389\) 27.1610 1.37712 0.688559 0.725181i \(-0.258244\pi\)
0.688559 + 0.725181i \(0.258244\pi\)
\(390\) −7.69324 −0.389562
\(391\) −0.105296 −0.00532505
\(392\) −6.76190 −0.341527
\(393\) −3.05690 −0.154200
\(394\) −5.57990 −0.281111
\(395\) −5.41342 −0.272379
\(396\) 6.13098 0.308093
\(397\) 17.0314 0.854782 0.427391 0.904067i \(-0.359433\pi\)
0.427391 + 0.904067i \(0.359433\pi\)
\(398\) 22.2676 1.11617
\(399\) 4.90727 0.245671
\(400\) 4.45648 0.222824
\(401\) −16.0489 −0.801442 −0.400721 0.916200i \(-0.631240\pi\)
−0.400721 + 0.916200i \(0.631240\pi\)
\(402\) −14.6312 −0.729737
\(403\) −0.787239 −0.0392152
\(404\) 6.67517 0.332102
\(405\) 8.07622 0.401310
\(406\) −4.86362 −0.241378
\(407\) −42.7554 −2.11931
\(408\) −5.10871 −0.252919
\(409\) 0.780928 0.0386144 0.0193072 0.999814i \(-0.493854\pi\)
0.0193072 + 0.999814i \(0.493854\pi\)
\(410\) 13.9219 0.687551
\(411\) −7.98643 −0.393942
\(412\) 11.9804 0.590233
\(413\) −3.23804 −0.159334
\(414\) 0.0370232 0.00181959
\(415\) 55.2065 2.70998
\(416\) −2.00084 −0.0980991
\(417\) −17.2624 −0.845342
\(418\) −34.3252 −1.67890
\(419\) 19.4074 0.948114 0.474057 0.880494i \(-0.342789\pi\)
0.474057 + 0.880494i \(0.342789\pi\)
\(420\) −1.87621 −0.0915497
\(421\) −17.1074 −0.833765 −0.416882 0.908960i \(-0.636877\pi\)
−0.416882 + 0.908960i \(0.636877\pi\)
\(422\) −21.3358 −1.03861
\(423\) 1.43196 0.0696242
\(424\) −5.88337 −0.285721
\(425\) 18.2084 0.883235
\(426\) 1.02107 0.0494709
\(427\) 2.14325 0.103719
\(428\) 7.35926 0.355723
\(429\) −10.6766 −0.515473
\(430\) 12.7928 0.616925
\(431\) 9.53381 0.459227 0.229614 0.973282i \(-0.426254\pi\)
0.229614 + 0.973282i \(0.426254\pi\)
\(432\) 5.54734 0.266896
\(433\) −36.1544 −1.73747 −0.868735 0.495277i \(-0.835067\pi\)
−0.868735 + 0.495277i \(0.835067\pi\)
\(434\) −0.191990 −0.00921582
\(435\) 38.3243 1.83751
\(436\) 7.21073 0.345332
\(437\) −0.207280 −0.00991555
\(438\) −2.19062 −0.104672
\(439\) −6.91667 −0.330115 −0.165057 0.986284i \(-0.552781\pi\)
−0.165057 + 0.986284i \(0.552781\pi\)
\(440\) 13.1236 0.625645
\(441\) 9.71424 0.462583
\(442\) −8.17505 −0.388847
\(443\) 23.1969 1.10212 0.551058 0.834467i \(-0.314224\pi\)
0.551058 + 0.834467i \(0.314224\pi\)
\(444\) −12.5266 −0.594488
\(445\) −17.0400 −0.807774
\(446\) 15.2924 0.724114
\(447\) 15.4676 0.731594
\(448\) −0.487959 −0.0230539
\(449\) −8.22895 −0.388348 −0.194174 0.980967i \(-0.562203\pi\)
−0.194174 + 0.980967i \(0.562203\pi\)
\(450\) −6.40225 −0.301805
\(451\) 19.3207 0.909774
\(452\) −1.34213 −0.0631287
\(453\) −7.75303 −0.364269
\(454\) 6.22212 0.292018
\(455\) −3.00234 −0.140752
\(456\) −10.0567 −0.470949
\(457\) −28.1009 −1.31450 −0.657252 0.753671i \(-0.728281\pi\)
−0.657252 + 0.753671i \(0.728281\pi\)
\(458\) −1.20776 −0.0564351
\(459\) 22.6654 1.05793
\(460\) 0.0792499 0.00369504
\(461\) −9.95374 −0.463592 −0.231796 0.972764i \(-0.574460\pi\)
−0.231796 + 0.972764i \(0.574460\pi\)
\(462\) −2.60379 −0.121139
\(463\) 2.26105 0.105080 0.0525399 0.998619i \(-0.483268\pi\)
0.0525399 + 0.998619i \(0.483268\pi\)
\(464\) 9.96727 0.462719
\(465\) 1.51284 0.0701562
\(466\) −25.1341 −1.16431
\(467\) −22.1707 −1.02594 −0.512970 0.858407i \(-0.671455\pi\)
−0.512970 + 0.858407i \(0.671455\pi\)
\(468\) 2.87443 0.132871
\(469\) −5.70992 −0.263660
\(470\) 3.06517 0.141386
\(471\) −0.455134 −0.0209715
\(472\) 6.63589 0.305442
\(473\) 17.7538 0.816321
\(474\) −2.20110 −0.101100
\(475\) 35.8439 1.64463
\(476\) −1.99371 −0.0913816
\(477\) 8.45213 0.386996
\(478\) −23.6571 −1.08205
\(479\) −7.54080 −0.344548 −0.172274 0.985049i \(-0.555111\pi\)
−0.172274 + 0.985049i \(0.555111\pi\)
\(480\) 3.84501 0.175500
\(481\) −20.0453 −0.913988
\(482\) −15.1358 −0.689417
\(483\) −0.0157235 −0.000715446 0
\(484\) 7.21290 0.327859
\(485\) −32.4161 −1.47194
\(486\) −13.3582 −0.605941
\(487\) 19.2978 0.874467 0.437233 0.899348i \(-0.355958\pi\)
0.437233 + 0.899348i \(0.355958\pi\)
\(488\) −4.39227 −0.198829
\(489\) −25.6147 −1.15834
\(490\) 20.7938 0.939367
\(491\) 3.53482 0.159524 0.0797621 0.996814i \(-0.474584\pi\)
0.0797621 + 0.996814i \(0.474584\pi\)
\(492\) 5.66064 0.255201
\(493\) 40.7244 1.83413
\(494\) −16.0929 −0.724055
\(495\) −18.8536 −0.847407
\(496\) 0.393455 0.0176667
\(497\) 0.398479 0.0178742
\(498\) 22.4470 1.00587
\(499\) −0.943200 −0.0422234 −0.0211117 0.999777i \(-0.506721\pi\)
−0.0211117 + 0.999777i \(0.506721\pi\)
\(500\) 1.67140 0.0747472
\(501\) −14.3423 −0.640765
\(502\) 23.0807 1.03014
\(503\) 37.4162 1.66831 0.834154 0.551532i \(-0.185956\pi\)
0.834154 + 0.551532i \(0.185956\pi\)
\(504\) 0.701010 0.0312255
\(505\) −20.5271 −0.913443
\(506\) 0.109982 0.00488932
\(507\) 11.2490 0.499586
\(508\) −10.3758 −0.460351
\(509\) −16.5233 −0.732380 −0.366190 0.930540i \(-0.619338\pi\)
−0.366190 + 0.930540i \(0.619338\pi\)
\(510\) 15.7100 0.695651
\(511\) −0.854904 −0.0378187
\(512\) 1.00000 0.0441942
\(513\) 44.6178 1.96992
\(514\) −5.54349 −0.244513
\(515\) −36.8415 −1.62343
\(516\) 5.20157 0.228987
\(517\) 4.25383 0.187083
\(518\) −4.88861 −0.214793
\(519\) 11.7269 0.514752
\(520\) 6.15285 0.269820
\(521\) 15.0883 0.661030 0.330515 0.943801i \(-0.392778\pi\)
0.330515 + 0.943801i \(0.392778\pi\)
\(522\) −14.3191 −0.626731
\(523\) −9.97432 −0.436147 −0.218073 0.975932i \(-0.569977\pi\)
−0.218073 + 0.975932i \(0.569977\pi\)
\(524\) 2.44482 0.106803
\(525\) 2.71900 0.118667
\(526\) 16.2519 0.708617
\(527\) 1.60758 0.0700275
\(528\) 5.33608 0.232223
\(529\) −22.9993 −0.999971
\(530\) 18.0922 0.785873
\(531\) −9.53322 −0.413706
\(532\) −3.92471 −0.170158
\(533\) 9.05824 0.392356
\(534\) −6.92848 −0.299825
\(535\) −22.6308 −0.978413
\(536\) 11.7016 0.505434
\(537\) 14.2357 0.614317
\(538\) 13.0504 0.562641
\(539\) 28.8575 1.24298
\(540\) −17.0588 −0.734096
\(541\) −34.5081 −1.48362 −0.741810 0.670610i \(-0.766032\pi\)
−0.741810 + 0.670610i \(0.766032\pi\)
\(542\) −8.91362 −0.382873
\(543\) −21.1835 −0.909071
\(544\) 4.08581 0.175178
\(545\) −22.1740 −0.949830
\(546\) −1.22075 −0.0522435
\(547\) −5.30310 −0.226744 −0.113372 0.993553i \(-0.536165\pi\)
−0.113372 + 0.993553i \(0.536165\pi\)
\(548\) 6.38733 0.272853
\(549\) 6.31000 0.269304
\(550\) −19.0187 −0.810962
\(551\) 80.1678 3.41526
\(552\) 0.0322231 0.00137150
\(553\) −0.858994 −0.0365282
\(554\) 31.3497 1.33192
\(555\) 38.5212 1.63513
\(556\) 13.8060 0.585504
\(557\) 5.82931 0.246996 0.123498 0.992345i \(-0.460589\pi\)
0.123498 + 0.992345i \(0.460589\pi\)
\(558\) −0.565243 −0.0239287
\(559\) 8.32364 0.352053
\(560\) 1.50054 0.0634095
\(561\) 21.8022 0.920491
\(562\) −11.2573 −0.474860
\(563\) 13.9047 0.586011 0.293006 0.956111i \(-0.405344\pi\)
0.293006 + 0.956111i \(0.405344\pi\)
\(564\) 1.24630 0.0524788
\(565\) 4.12725 0.173635
\(566\) 18.9390 0.796064
\(567\) 1.28152 0.0538190
\(568\) −0.816623 −0.0342647
\(569\) 39.9841 1.67622 0.838110 0.545501i \(-0.183661\pi\)
0.838110 + 0.545501i \(0.183661\pi\)
\(570\) 30.9258 1.29534
\(571\) −40.1158 −1.67879 −0.839397 0.543518i \(-0.817092\pi\)
−0.839397 + 0.543518i \(0.817092\pi\)
\(572\) 8.53889 0.357029
\(573\) −4.52434 −0.189007
\(574\) 2.20910 0.0922062
\(575\) −0.114849 −0.00478952
\(576\) −1.43661 −0.0598590
\(577\) 42.6589 1.77591 0.887957 0.459926i \(-0.152124\pi\)
0.887957 + 0.459926i \(0.152124\pi\)
\(578\) −0.306124 −0.0127331
\(579\) 17.1824 0.714076
\(580\) −30.6507 −1.27270
\(581\) 8.76010 0.363430
\(582\) −13.1804 −0.546345
\(583\) 25.1082 1.03987
\(584\) 1.75200 0.0724982
\(585\) −8.83928 −0.365459
\(586\) 22.0162 0.909480
\(587\) −26.5806 −1.09710 −0.548549 0.836118i \(-0.684820\pi\)
−0.548549 + 0.836118i \(0.684820\pi\)
\(588\) 8.45476 0.348669
\(589\) 3.16460 0.130395
\(590\) −20.4063 −0.840113
\(591\) 6.97685 0.286989
\(592\) 10.0185 0.411757
\(593\) −30.0581 −1.23434 −0.617169 0.786831i \(-0.711720\pi\)
−0.617169 + 0.786831i \(0.711720\pi\)
\(594\) −23.6741 −0.971362
\(595\) 6.13094 0.251344
\(596\) −12.3706 −0.506720
\(597\) −27.8423 −1.13951
\(598\) 0.0515639 0.00210860
\(599\) 0.721394 0.0294753 0.0147377 0.999891i \(-0.495309\pi\)
0.0147377 + 0.999891i \(0.495309\pi\)
\(600\) −5.57218 −0.227483
\(601\) 25.1413 1.02553 0.512767 0.858528i \(-0.328621\pi\)
0.512767 + 0.858528i \(0.328621\pi\)
\(602\) 2.02995 0.0827346
\(603\) −16.8107 −0.684587
\(604\) 6.20066 0.252301
\(605\) −22.1807 −0.901773
\(606\) −8.34633 −0.339046
\(607\) −25.5188 −1.03578 −0.517889 0.855448i \(-0.673282\pi\)
−0.517889 + 0.855448i \(0.673282\pi\)
\(608\) 8.04310 0.326191
\(609\) 6.08125 0.246425
\(610\) 13.5068 0.546876
\(611\) 1.99435 0.0806828
\(612\) −5.86974 −0.237270
\(613\) 44.3356 1.79070 0.895349 0.445365i \(-0.146926\pi\)
0.895349 + 0.445365i \(0.146926\pi\)
\(614\) 27.0103 1.09005
\(615\) −17.4072 −0.701928
\(616\) 2.08244 0.0839040
\(617\) −3.80538 −0.153199 −0.0765994 0.997062i \(-0.524406\pi\)
−0.0765994 + 0.997062i \(0.524406\pi\)
\(618\) −14.9798 −0.602575
\(619\) −2.83337 −0.113883 −0.0569413 0.998378i \(-0.518135\pi\)
−0.0569413 + 0.998378i \(0.518135\pi\)
\(620\) −1.20993 −0.0485919
\(621\) −0.142961 −0.00573684
\(622\) 19.1623 0.768336
\(623\) −2.70389 −0.108329
\(624\) 2.50175 0.100150
\(625\) −27.4222 −1.09689
\(626\) −2.27801 −0.0910475
\(627\) 42.9187 1.71401
\(628\) 0.364004 0.0145253
\(629\) 40.9336 1.63213
\(630\) −2.15570 −0.0858852
\(631\) −7.54691 −0.300438 −0.150219 0.988653i \(-0.547998\pi\)
−0.150219 + 0.988653i \(0.547998\pi\)
\(632\) 1.76038 0.0700242
\(633\) 26.6773 1.06033
\(634\) −23.8258 −0.946243
\(635\) 31.9070 1.26619
\(636\) 7.35629 0.291696
\(637\) 13.5294 0.536056
\(638\) −42.5369 −1.68405
\(639\) 1.17317 0.0464100
\(640\) −3.07514 −0.121556
\(641\) −31.0501 −1.22641 −0.613203 0.789925i \(-0.710119\pi\)
−0.613203 + 0.789925i \(0.710119\pi\)
\(642\) −9.20168 −0.363161
\(643\) 43.4217 1.71239 0.856193 0.516656i \(-0.172823\pi\)
0.856193 + 0.516656i \(0.172823\pi\)
\(644\) 0.0125753 0.000495535 0
\(645\) −15.9956 −0.629825
\(646\) 32.8626 1.29296
\(647\) 11.3056 0.444470 0.222235 0.974993i \(-0.428665\pi\)
0.222235 + 0.974993i \(0.428665\pi\)
\(648\) −2.62629 −0.103171
\(649\) −28.3197 −1.11165
\(650\) −8.91669 −0.349741
\(651\) 0.240056 0.00940852
\(652\) 20.4860 0.802294
\(653\) 23.1531 0.906051 0.453025 0.891498i \(-0.350345\pi\)
0.453025 + 0.891498i \(0.350345\pi\)
\(654\) −9.01597 −0.352552
\(655\) −7.51818 −0.293759
\(656\) −4.52723 −0.176759
\(657\) −2.51695 −0.0981955
\(658\) 0.486378 0.0189610
\(659\) −24.1765 −0.941782 −0.470891 0.882191i \(-0.656068\pi\)
−0.470891 + 0.882191i \(0.656068\pi\)
\(660\) −16.4092 −0.638727
\(661\) −41.0112 −1.59515 −0.797575 0.603219i \(-0.793884\pi\)
−0.797575 + 0.603219i \(0.793884\pi\)
\(662\) 27.3893 1.06452
\(663\) 10.2217 0.396978
\(664\) −17.9525 −0.696693
\(665\) 12.0690 0.468017
\(666\) −14.3927 −0.557705
\(667\) −0.256868 −0.00994597
\(668\) 11.4706 0.443809
\(669\) −19.1209 −0.739255
\(670\) −35.9842 −1.39019
\(671\) 18.7447 0.723631
\(672\) 0.610122 0.0235360
\(673\) 26.5236 1.02241 0.511204 0.859459i \(-0.329200\pi\)
0.511204 + 0.859459i \(0.329200\pi\)
\(674\) −7.97092 −0.307028
\(675\) 24.7216 0.951535
\(676\) −8.99665 −0.346025
\(677\) −18.9379 −0.727843 −0.363922 0.931430i \(-0.618562\pi\)
−0.363922 + 0.931430i \(0.618562\pi\)
\(678\) 1.67814 0.0644487
\(679\) −5.14374 −0.197399
\(680\) −12.5644 −0.481825
\(681\) −7.77985 −0.298125
\(682\) −1.67913 −0.0642973
\(683\) −26.2998 −1.00633 −0.503166 0.864190i \(-0.667832\pi\)
−0.503166 + 0.864190i \(0.667832\pi\)
\(684\) −11.5548 −0.441810
\(685\) −19.6419 −0.750480
\(686\) 6.71525 0.256389
\(687\) 1.51013 0.0576151
\(688\) −4.16008 −0.158602
\(689\) 11.7717 0.448464
\(690\) −0.0990904 −0.00377231
\(691\) −28.7667 −1.09434 −0.547168 0.837023i \(-0.684294\pi\)
−0.547168 + 0.837023i \(0.684294\pi\)
\(692\) −9.37883 −0.356530
\(693\) −2.99167 −0.113644
\(694\) 12.4240 0.471609
\(695\) −42.4553 −1.61042
\(696\) −12.4626 −0.472394
\(697\) −18.4974 −0.700639
\(698\) 14.3433 0.542903
\(699\) 31.4265 1.18866
\(700\) −2.17458 −0.0821915
\(701\) −12.2711 −0.463473 −0.231737 0.972779i \(-0.574441\pi\)
−0.231737 + 0.972779i \(0.574441\pi\)
\(702\) −11.0993 −0.418917
\(703\) 80.5796 3.03912
\(704\) −4.26766 −0.160843
\(705\) −3.83255 −0.144342
\(706\) −4.12403 −0.155210
\(707\) −3.25721 −0.122500
\(708\) −8.29721 −0.311828
\(709\) −12.3020 −0.462010 −0.231005 0.972953i \(-0.574201\pi\)
−0.231005 + 0.972953i \(0.574201\pi\)
\(710\) 2.51123 0.0942448
\(711\) −2.52899 −0.0948445
\(712\) 5.54121 0.207666
\(713\) −0.0101398 −0.000379738 0
\(714\) 2.49284 0.0932924
\(715\) −26.2583 −0.982003
\(716\) −11.3854 −0.425491
\(717\) 29.5797 1.10467
\(718\) −16.4658 −0.614497
\(719\) 9.14406 0.341016 0.170508 0.985356i \(-0.445459\pi\)
0.170508 + 0.985356i \(0.445459\pi\)
\(720\) 4.41779 0.164641
\(721\) −5.84596 −0.217715
\(722\) 45.6915 1.70046
\(723\) 18.9251 0.703832
\(724\) 16.9420 0.629644
\(725\) 44.4189 1.64968
\(726\) −9.01868 −0.334715
\(727\) 0.913119 0.0338657 0.0169329 0.999857i \(-0.494610\pi\)
0.0169329 + 0.999857i \(0.494610\pi\)
\(728\) 0.976327 0.0361851
\(729\) 24.5814 0.910422
\(730\) −5.38764 −0.199406
\(731\) −16.9973 −0.628668
\(732\) 5.49189 0.202986
\(733\) −17.6523 −0.652002 −0.326001 0.945369i \(-0.605701\pi\)
−0.326001 + 0.945369i \(0.605701\pi\)
\(734\) 14.9541 0.551967
\(735\) −25.9996 −0.959009
\(736\) −0.0257712 −0.000949937 0
\(737\) −49.9386 −1.83951
\(738\) 6.50388 0.239411
\(739\) 49.7299 1.82934 0.914671 0.404198i \(-0.132449\pi\)
0.914671 + 0.404198i \(0.132449\pi\)
\(740\) −30.8082 −1.13253
\(741\) 20.1219 0.739195
\(742\) 2.87084 0.105392
\(743\) 50.3686 1.84784 0.923922 0.382580i \(-0.124964\pi\)
0.923922 + 0.382580i \(0.124964\pi\)
\(744\) −0.491958 −0.0180361
\(745\) 38.0413 1.39373
\(746\) −13.6234 −0.498788
\(747\) 25.7909 0.943638
\(748\) −17.4369 −0.637555
\(749\) −3.59102 −0.131213
\(750\) −2.08984 −0.0763102
\(751\) −1.00000 −0.0364905
\(752\) −0.996759 −0.0363481
\(753\) −28.8590 −1.05168
\(754\) −19.9429 −0.726277
\(755\) −19.0679 −0.693952
\(756\) −2.70688 −0.0984481
\(757\) −25.7409 −0.935567 −0.467784 0.883843i \(-0.654947\pi\)
−0.467784 + 0.883843i \(0.654947\pi\)
\(758\) 8.55606 0.310770
\(759\) −0.137517 −0.00499155
\(760\) −24.7337 −0.897184
\(761\) 34.9639 1.26744 0.633719 0.773563i \(-0.281527\pi\)
0.633719 + 0.773563i \(0.281527\pi\)
\(762\) 12.9734 0.469977
\(763\) −3.51855 −0.127380
\(764\) 3.61845 0.130911
\(765\) 18.0503 0.652609
\(766\) −18.9528 −0.684794
\(767\) −13.2773 −0.479417
\(768\) −1.25035 −0.0451183
\(769\) −12.4021 −0.447232 −0.223616 0.974677i \(-0.571786\pi\)
−0.223616 + 0.974677i \(0.571786\pi\)
\(770\) −6.40380 −0.230777
\(771\) 6.93132 0.249626
\(772\) −13.7420 −0.494586
\(773\) −19.5835 −0.704370 −0.352185 0.935930i \(-0.614561\pi\)
−0.352185 + 0.935930i \(0.614561\pi\)
\(774\) 5.97643 0.214818
\(775\) 1.75342 0.0629849
\(776\) 10.5413 0.378412
\(777\) 6.11249 0.219284
\(778\) 27.1610 0.973769
\(779\) −36.4130 −1.30463
\(780\) −7.69324 −0.275462
\(781\) 3.48507 0.124706
\(782\) −0.105296 −0.00376538
\(783\) 55.2918 1.97597
\(784\) −6.76190 −0.241496
\(785\) −1.11936 −0.0399518
\(786\) −3.05690 −0.109036
\(787\) −10.2413 −0.365064 −0.182532 0.983200i \(-0.558429\pi\)
−0.182532 + 0.983200i \(0.558429\pi\)
\(788\) −5.57990 −0.198776
\(789\) −20.3207 −0.723434
\(790\) −5.41342 −0.192601
\(791\) 0.654907 0.0232858
\(792\) 6.13098 0.217855
\(793\) 8.78822 0.312079
\(794\) 17.0314 0.604422
\(795\) −22.6216 −0.802306
\(796\) 22.2676 0.789252
\(797\) −8.14107 −0.288372 −0.144186 0.989551i \(-0.546056\pi\)
−0.144186 + 0.989551i \(0.546056\pi\)
\(798\) 4.90727 0.173716
\(799\) −4.07257 −0.144077
\(800\) 4.45648 0.157560
\(801\) −7.96059 −0.281274
\(802\) −16.0489 −0.566705
\(803\) −7.47693 −0.263855
\(804\) −14.6312 −0.516002
\(805\) −0.0386707 −0.00136296
\(806\) −0.787239 −0.0277293
\(807\) −16.3176 −0.574406
\(808\) 6.67517 0.234832
\(809\) −46.5791 −1.63763 −0.818817 0.574055i \(-0.805370\pi\)
−0.818817 + 0.574055i \(0.805370\pi\)
\(810\) 8.07622 0.283769
\(811\) −40.6312 −1.42675 −0.713377 0.700780i \(-0.752835\pi\)
−0.713377 + 0.700780i \(0.752835\pi\)
\(812\) −4.86362 −0.170680
\(813\) 11.1452 0.390879
\(814\) −42.7554 −1.49858
\(815\) −62.9973 −2.20670
\(816\) −5.10871 −0.178841
\(817\) −33.4600 −1.17062
\(818\) 0.780928 0.0273045
\(819\) −1.40261 −0.0490110
\(820\) 13.9219 0.486172
\(821\) 30.0352 1.04824 0.524119 0.851645i \(-0.324395\pi\)
0.524119 + 0.851645i \(0.324395\pi\)
\(822\) −7.98643 −0.278559
\(823\) −25.6172 −0.892958 −0.446479 0.894794i \(-0.647322\pi\)
−0.446479 + 0.894794i \(0.647322\pi\)
\(824\) 11.9804 0.417358
\(825\) 23.7801 0.827919
\(826\) −3.23804 −0.112666
\(827\) 17.0234 0.591961 0.295980 0.955194i \(-0.404354\pi\)
0.295980 + 0.955194i \(0.404354\pi\)
\(828\) 0.0370232 0.00128665
\(829\) −26.2810 −0.912776 −0.456388 0.889781i \(-0.650857\pi\)
−0.456388 + 0.889781i \(0.650857\pi\)
\(830\) 55.2065 1.91624
\(831\) −39.1983 −1.35977
\(832\) −2.00084 −0.0693665
\(833\) −27.6278 −0.957248
\(834\) −17.2624 −0.597747
\(835\) −35.2736 −1.22069
\(836\) −34.3252 −1.18716
\(837\) 2.18263 0.0754427
\(838\) 19.4074 0.670418
\(839\) 12.7311 0.439526 0.219763 0.975553i \(-0.429472\pi\)
0.219763 + 0.975553i \(0.429472\pi\)
\(840\) −1.87621 −0.0647354
\(841\) 70.3464 2.42574
\(842\) −17.1074 −0.589561
\(843\) 14.0756 0.484790
\(844\) −21.3358 −0.734409
\(845\) 27.6660 0.951738
\(846\) 1.43196 0.0492318
\(847\) −3.51960 −0.120935
\(848\) −5.88337 −0.202036
\(849\) −23.6804 −0.812710
\(850\) 18.2084 0.624541
\(851\) −0.258188 −0.00885056
\(852\) 1.02107 0.0349812
\(853\) 43.7636 1.49844 0.749219 0.662322i \(-0.230429\pi\)
0.749219 + 0.662322i \(0.230429\pi\)
\(854\) 2.14325 0.0733405
\(855\) 35.5327 1.21519
\(856\) 7.35926 0.251534
\(857\) 35.2258 1.20329 0.601645 0.798763i \(-0.294512\pi\)
0.601645 + 0.798763i \(0.294512\pi\)
\(858\) −10.6766 −0.364494
\(859\) 28.9699 0.988439 0.494220 0.869337i \(-0.335454\pi\)
0.494220 + 0.869337i \(0.335454\pi\)
\(860\) 12.7928 0.436232
\(861\) −2.76216 −0.0941342
\(862\) 9.53381 0.324723
\(863\) 47.5013 1.61696 0.808481 0.588522i \(-0.200290\pi\)
0.808481 + 0.588522i \(0.200290\pi\)
\(864\) 5.54734 0.188724
\(865\) 28.8412 0.980631
\(866\) −36.1544 −1.22858
\(867\) 0.382763 0.0129993
\(868\) −0.191990 −0.00651657
\(869\) −7.51270 −0.254851
\(870\) 38.3243 1.29931
\(871\) −23.4131 −0.793321
\(872\) 7.21073 0.244186
\(873\) −15.1438 −0.512541
\(874\) −0.207280 −0.00701135
\(875\) −0.815574 −0.0275714
\(876\) −2.19062 −0.0740142
\(877\) 32.3786 1.09335 0.546674 0.837345i \(-0.315894\pi\)
0.546674 + 0.837345i \(0.315894\pi\)
\(878\) −6.91667 −0.233426
\(879\) −27.5280 −0.928497
\(880\) 13.1236 0.442398
\(881\) −9.73501 −0.327981 −0.163990 0.986462i \(-0.552437\pi\)
−0.163990 + 0.986462i \(0.552437\pi\)
\(882\) 9.71424 0.327095
\(883\) 25.1596 0.846687 0.423344 0.905969i \(-0.360856\pi\)
0.423344 + 0.905969i \(0.360856\pi\)
\(884\) −8.17505 −0.274957
\(885\) 25.5151 0.857680
\(886\) 23.1969 0.779314
\(887\) 31.6471 1.06261 0.531303 0.847182i \(-0.321702\pi\)
0.531303 + 0.847182i \(0.321702\pi\)
\(888\) −12.5266 −0.420366
\(889\) 5.06296 0.169806
\(890\) −17.0400 −0.571182
\(891\) 11.2081 0.375486
\(892\) 15.2924 0.512026
\(893\) −8.01704 −0.268280
\(894\) 15.4676 0.517315
\(895\) 35.0116 1.17031
\(896\) −0.487959 −0.0163016
\(897\) −0.0644731 −0.00215269
\(898\) −8.22895 −0.274603
\(899\) 3.92167 0.130795
\(900\) −6.40225 −0.213408
\(901\) −24.0383 −0.800833
\(902\) 19.3207 0.643308
\(903\) −2.53816 −0.0844646
\(904\) −1.34213 −0.0446387
\(905\) −52.0990 −1.73183
\(906\) −7.75303 −0.257577
\(907\) 14.5931 0.484557 0.242279 0.970207i \(-0.422105\pi\)
0.242279 + 0.970207i \(0.422105\pi\)
\(908\) 6.22212 0.206488
\(909\) −9.58965 −0.318069
\(910\) −3.00234 −0.0995266
\(911\) −16.9317 −0.560972 −0.280486 0.959858i \(-0.590496\pi\)
−0.280486 + 0.959858i \(0.590496\pi\)
\(912\) −10.0567 −0.333011
\(913\) 76.6152 2.53559
\(914\) −28.1009 −0.929494
\(915\) −16.8883 −0.558311
\(916\) −1.20776 −0.0399056
\(917\) −1.19298 −0.0393955
\(918\) 22.6654 0.748070
\(919\) −40.9232 −1.34993 −0.674966 0.737849i \(-0.735842\pi\)
−0.674966 + 0.737849i \(0.735842\pi\)
\(920\) 0.0792499 0.00261279
\(921\) −33.7724 −1.11284
\(922\) −9.95374 −0.327809
\(923\) 1.63393 0.0537814
\(924\) −2.60379 −0.0856585
\(925\) 44.6471 1.46799
\(926\) 2.26105 0.0743026
\(927\) −17.2113 −0.565292
\(928\) 9.96727 0.327192
\(929\) 22.5424 0.739591 0.369796 0.929113i \(-0.379428\pi\)
0.369796 + 0.929113i \(0.379428\pi\)
\(930\) 1.51284 0.0496080
\(931\) −54.3866 −1.78245
\(932\) −25.1341 −0.823294
\(933\) −23.9596 −0.784402
\(934\) −22.1707 −0.725449
\(935\) 53.6208 1.75359
\(936\) 2.87443 0.0939537
\(937\) −36.6526 −1.19739 −0.598693 0.800978i \(-0.704313\pi\)
−0.598693 + 0.800978i \(0.704313\pi\)
\(938\) −5.70992 −0.186436
\(939\) 2.84831 0.0929512
\(940\) 3.06517 0.0999749
\(941\) 12.0701 0.393473 0.196737 0.980456i \(-0.436966\pi\)
0.196737 + 0.980456i \(0.436966\pi\)
\(942\) −0.455134 −0.0148291
\(943\) 0.116672 0.00379936
\(944\) 6.63589 0.215980
\(945\) 8.32402 0.270780
\(946\) 17.7538 0.577226
\(947\) 45.2139 1.46925 0.734627 0.678472i \(-0.237357\pi\)
0.734627 + 0.678472i \(0.237357\pi\)
\(948\) −2.20110 −0.0714884
\(949\) −3.50546 −0.113792
\(950\) 35.8439 1.16293
\(951\) 29.7907 0.966029
\(952\) −1.99371 −0.0646166
\(953\) −57.9368 −1.87676 −0.938378 0.345611i \(-0.887672\pi\)
−0.938378 + 0.345611i \(0.887672\pi\)
\(954\) 8.45213 0.273648
\(955\) −11.1272 −0.360069
\(956\) −23.6571 −0.765125
\(957\) 53.1862 1.71926
\(958\) −7.54080 −0.243632
\(959\) −3.11676 −0.100645
\(960\) 3.84501 0.124097
\(961\) −30.8452 −0.995006
\(962\) −20.0453 −0.646287
\(963\) −10.5724 −0.340692
\(964\) −15.1358 −0.487491
\(965\) 42.2586 1.36035
\(966\) −0.0157235 −0.000505897 0
\(967\) −28.2229 −0.907587 −0.453793 0.891107i \(-0.649930\pi\)
−0.453793 + 0.891107i \(0.649930\pi\)
\(968\) 7.21290 0.231831
\(969\) −41.0899 −1.32000
\(970\) −32.4161 −1.04082
\(971\) 7.15962 0.229763 0.114882 0.993379i \(-0.463351\pi\)
0.114882 + 0.993379i \(0.463351\pi\)
\(972\) −13.3582 −0.428465
\(973\) −6.73676 −0.215971
\(974\) 19.2978 0.618341
\(975\) 11.1490 0.357054
\(976\) −4.39227 −0.140593
\(977\) 22.7509 0.727865 0.363933 0.931425i \(-0.381434\pi\)
0.363933 + 0.931425i \(0.381434\pi\)
\(978\) −25.6147 −0.819069
\(979\) −23.6480 −0.755794
\(980\) 20.7938 0.664233
\(981\) −10.3590 −0.330739
\(982\) 3.53482 0.112801
\(983\) 24.8512 0.792631 0.396315 0.918114i \(-0.370289\pi\)
0.396315 + 0.918114i \(0.370289\pi\)
\(984\) 5.66064 0.180455
\(985\) 17.1590 0.546730
\(986\) 40.7244 1.29693
\(987\) −0.608145 −0.0193575
\(988\) −16.0929 −0.511984
\(989\) 0.107210 0.00340908
\(990\) −18.8536 −0.599207
\(991\) −2.89525 −0.0919706 −0.0459853 0.998942i \(-0.514643\pi\)
−0.0459853 + 0.998942i \(0.514643\pi\)
\(992\) 0.393455 0.0124922
\(993\) −34.2464 −1.08678
\(994\) 0.398479 0.0126390
\(995\) −68.4758 −2.17083
\(996\) 22.4470 0.711260
\(997\) 46.6409 1.47713 0.738565 0.674182i \(-0.235504\pi\)
0.738565 + 0.674182i \(0.235504\pi\)
\(998\) −0.943200 −0.0298565
\(999\) 55.5759 1.75834
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 1502.2.a.g.1.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1502.2.a.g.1.3 16 1.1 even 1 trivial