Properties

Label 2001.2.a.m.1.3
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $1$
Dimension $14$
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] = [2001,2,Mod(1,2001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, 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("2001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.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: \(15.9780654445\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} - 939 x^{5} - 717 x^{4} + 604 x^{3} + 352 x^{2} - 128 x - 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.05175\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.05175 q^{2} -1.00000 q^{3} +2.20969 q^{4} +3.75134 q^{5} +2.05175 q^{6} -2.35999 q^{7} -0.430233 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.05175 q^{2} -1.00000 q^{3} +2.20969 q^{4} +3.75134 q^{5} +2.05175 q^{6} -2.35999 q^{7} -0.430233 q^{8} +1.00000 q^{9} -7.69683 q^{10} +3.27231 q^{11} -2.20969 q^{12} +4.29495 q^{13} +4.84211 q^{14} -3.75134 q^{15} -3.53665 q^{16} -5.05332 q^{17} -2.05175 q^{18} -7.69400 q^{19} +8.28931 q^{20} +2.35999 q^{21} -6.71396 q^{22} -1.00000 q^{23} +0.430233 q^{24} +9.07257 q^{25} -8.81218 q^{26} -1.00000 q^{27} -5.21484 q^{28} -1.00000 q^{29} +7.69683 q^{30} -8.24396 q^{31} +8.11680 q^{32} -3.27231 q^{33} +10.3682 q^{34} -8.85312 q^{35} +2.20969 q^{36} -7.63881 q^{37} +15.7862 q^{38} -4.29495 q^{39} -1.61395 q^{40} -6.80211 q^{41} -4.84211 q^{42} +5.31051 q^{43} +7.23078 q^{44} +3.75134 q^{45} +2.05175 q^{46} -10.1012 q^{47} +3.53665 q^{48} -1.43046 q^{49} -18.6147 q^{50} +5.05332 q^{51} +9.49051 q^{52} -8.31770 q^{53} +2.05175 q^{54} +12.2755 q^{55} +1.01535 q^{56} +7.69400 q^{57} +2.05175 q^{58} -6.64175 q^{59} -8.28931 q^{60} -4.78113 q^{61} +16.9146 q^{62} -2.35999 q^{63} -9.58036 q^{64} +16.1118 q^{65} +6.71396 q^{66} +15.3363 q^{67} -11.1663 q^{68} +1.00000 q^{69} +18.1644 q^{70} -11.2487 q^{71} -0.430233 q^{72} +11.2463 q^{73} +15.6729 q^{74} -9.07257 q^{75} -17.0014 q^{76} -7.72260 q^{77} +8.81218 q^{78} +1.65332 q^{79} -13.2672 q^{80} +1.00000 q^{81} +13.9563 q^{82} +4.90299 q^{83} +5.21484 q^{84} -18.9567 q^{85} -10.8959 q^{86} +1.00000 q^{87} -1.40785 q^{88} +8.43075 q^{89} -7.69683 q^{90} -10.1360 q^{91} -2.20969 q^{92} +8.24396 q^{93} +20.7251 q^{94} -28.8628 q^{95} -8.11680 q^{96} +8.12503 q^{97} +2.93494 q^{98} +3.27231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05175 −1.45081 −0.725404 0.688323i \(-0.758347\pi\)
−0.725404 + 0.688323i \(0.758347\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.20969 1.10485
\(5\) 3.75134 1.67765 0.838826 0.544400i \(-0.183243\pi\)
0.838826 + 0.544400i \(0.183243\pi\)
\(6\) 2.05175 0.837625
\(7\) −2.35999 −0.891992 −0.445996 0.895035i \(-0.647150\pi\)
−0.445996 + 0.895035i \(0.647150\pi\)
\(8\) −0.430233 −0.152110
\(9\) 1.00000 0.333333
\(10\) −7.69683 −2.43395
\(11\) 3.27231 0.986637 0.493319 0.869849i \(-0.335784\pi\)
0.493319 + 0.869849i \(0.335784\pi\)
\(12\) −2.20969 −0.637883
\(13\) 4.29495 1.19121 0.595603 0.803279i \(-0.296913\pi\)
0.595603 + 0.803279i \(0.296913\pi\)
\(14\) 4.84211 1.29411
\(15\) −3.75134 −0.968593
\(16\) −3.53665 −0.884162
\(17\) −5.05332 −1.22561 −0.612805 0.790235i \(-0.709959\pi\)
−0.612805 + 0.790235i \(0.709959\pi\)
\(18\) −2.05175 −0.483603
\(19\) −7.69400 −1.76513 −0.882563 0.470195i \(-0.844184\pi\)
−0.882563 + 0.470195i \(0.844184\pi\)
\(20\) 8.28931 1.85355
\(21\) 2.35999 0.514992
\(22\) −6.71396 −1.43142
\(23\) −1.00000 −0.208514
\(24\) 0.430233 0.0878210
\(25\) 9.07257 1.81451
\(26\) −8.81218 −1.72821
\(27\) −1.00000 −0.192450
\(28\) −5.21484 −0.985513
\(29\) −1.00000 −0.185695
\(30\) 7.69683 1.40524
\(31\) −8.24396 −1.48066 −0.740329 0.672244i \(-0.765330\pi\)
−0.740329 + 0.672244i \(0.765330\pi\)
\(32\) 8.11680 1.43486
\(33\) −3.27231 −0.569635
\(34\) 10.3682 1.77812
\(35\) −8.85312 −1.49645
\(36\) 2.20969 0.368282
\(37\) −7.63881 −1.25581 −0.627906 0.778289i \(-0.716088\pi\)
−0.627906 + 0.778289i \(0.716088\pi\)
\(38\) 15.7862 2.56086
\(39\) −4.29495 −0.687743
\(40\) −1.61395 −0.255188
\(41\) −6.80211 −1.06231 −0.531156 0.847274i \(-0.678242\pi\)
−0.531156 + 0.847274i \(0.678242\pi\)
\(42\) −4.84211 −0.747154
\(43\) 5.31051 0.809846 0.404923 0.914351i \(-0.367298\pi\)
0.404923 + 0.914351i \(0.367298\pi\)
\(44\) 7.23078 1.09008
\(45\) 3.75134 0.559217
\(46\) 2.05175 0.302514
\(47\) −10.1012 −1.47341 −0.736704 0.676215i \(-0.763619\pi\)
−0.736704 + 0.676215i \(0.763619\pi\)
\(48\) 3.53665 0.510471
\(49\) −1.43046 −0.204351
\(50\) −18.6147 −2.63251
\(51\) 5.05332 0.707606
\(52\) 9.49051 1.31610
\(53\) −8.31770 −1.14252 −0.571262 0.820768i \(-0.693546\pi\)
−0.571262 + 0.820768i \(0.693546\pi\)
\(54\) 2.05175 0.279208
\(55\) 12.2755 1.65523
\(56\) 1.01535 0.135681
\(57\) 7.69400 1.01910
\(58\) 2.05175 0.269408
\(59\) −6.64175 −0.864683 −0.432341 0.901710i \(-0.642312\pi\)
−0.432341 + 0.901710i \(0.642312\pi\)
\(60\) −8.28931 −1.07014
\(61\) −4.78113 −0.612161 −0.306081 0.952006i \(-0.599018\pi\)
−0.306081 + 0.952006i \(0.599018\pi\)
\(62\) 16.9146 2.14815
\(63\) −2.35999 −0.297331
\(64\) −9.58036 −1.19755
\(65\) 16.1118 1.99843
\(66\) 6.71396 0.826432
\(67\) 15.3363 1.87363 0.936815 0.349826i \(-0.113759\pi\)
0.936815 + 0.349826i \(0.113759\pi\)
\(68\) −11.1663 −1.35411
\(69\) 1.00000 0.120386
\(70\) 18.1644 2.17106
\(71\) −11.2487 −1.33497 −0.667487 0.744621i \(-0.732630\pi\)
−0.667487 + 0.744621i \(0.732630\pi\)
\(72\) −0.430233 −0.0507035
\(73\) 11.2463 1.31627 0.658137 0.752898i \(-0.271345\pi\)
0.658137 + 0.752898i \(0.271345\pi\)
\(74\) 15.6729 1.82194
\(75\) −9.07257 −1.04761
\(76\) −17.0014 −1.95019
\(77\) −7.72260 −0.880072
\(78\) 8.81218 0.997783
\(79\) 1.65332 0.186013 0.0930065 0.995665i \(-0.470352\pi\)
0.0930065 + 0.995665i \(0.470352\pi\)
\(80\) −13.2672 −1.48332
\(81\) 1.00000 0.111111
\(82\) 13.9563 1.54121
\(83\) 4.90299 0.538173 0.269086 0.963116i \(-0.413278\pi\)
0.269086 + 0.963116i \(0.413278\pi\)
\(84\) 5.21484 0.568986
\(85\) −18.9567 −2.05614
\(86\) −10.8959 −1.17493
\(87\) 1.00000 0.107211
\(88\) −1.40785 −0.150078
\(89\) 8.43075 0.893657 0.446829 0.894620i \(-0.352553\pi\)
0.446829 + 0.894620i \(0.352553\pi\)
\(90\) −7.69683 −0.811317
\(91\) −10.1360 −1.06254
\(92\) −2.20969 −0.230376
\(93\) 8.24396 0.854859
\(94\) 20.7251 2.13763
\(95\) −28.8628 −2.96127
\(96\) −8.11680 −0.828417
\(97\) 8.12503 0.824972 0.412486 0.910964i \(-0.364661\pi\)
0.412486 + 0.910964i \(0.364661\pi\)
\(98\) 2.93494 0.296474
\(99\) 3.27231 0.328879
\(100\) 20.0476 2.00476
\(101\) −3.48161 −0.346433 −0.173217 0.984884i \(-0.555416\pi\)
−0.173217 + 0.984884i \(0.555416\pi\)
\(102\) −10.3682 −1.02660
\(103\) −17.8318 −1.75702 −0.878508 0.477728i \(-0.841461\pi\)
−0.878508 + 0.477728i \(0.841461\pi\)
\(104\) −1.84783 −0.181195
\(105\) 8.85312 0.863976
\(106\) 17.0659 1.65758
\(107\) 5.22489 0.505109 0.252555 0.967583i \(-0.418729\pi\)
0.252555 + 0.967583i \(0.418729\pi\)
\(108\) −2.20969 −0.212628
\(109\) 12.9348 1.23892 0.619462 0.785026i \(-0.287351\pi\)
0.619462 + 0.785026i \(0.287351\pi\)
\(110\) −25.1864 −2.40143
\(111\) 7.63881 0.725043
\(112\) 8.34645 0.788665
\(113\) 9.19380 0.864880 0.432440 0.901663i \(-0.357653\pi\)
0.432440 + 0.901663i \(0.357653\pi\)
\(114\) −15.7862 −1.47851
\(115\) −3.75134 −0.349815
\(116\) −2.20969 −0.205165
\(117\) 4.29495 0.397068
\(118\) 13.6272 1.25449
\(119\) 11.9258 1.09323
\(120\) 1.61395 0.147333
\(121\) −0.292011 −0.0265465
\(122\) 9.80970 0.888129
\(123\) 6.80211 0.613326
\(124\) −18.2166 −1.63590
\(125\) 15.2776 1.36647
\(126\) 4.84211 0.431370
\(127\) −9.90131 −0.878599 −0.439299 0.898341i \(-0.644773\pi\)
−0.439299 + 0.898341i \(0.644773\pi\)
\(128\) 3.42295 0.302549
\(129\) −5.31051 −0.467565
\(130\) −33.0575 −2.89933
\(131\) −0.700093 −0.0611674 −0.0305837 0.999532i \(-0.509737\pi\)
−0.0305837 + 0.999532i \(0.509737\pi\)
\(132\) −7.23078 −0.629359
\(133\) 18.1578 1.57448
\(134\) −31.4663 −2.71828
\(135\) −3.75134 −0.322864
\(136\) 2.17410 0.186428
\(137\) 10.2345 0.874393 0.437197 0.899366i \(-0.355971\pi\)
0.437197 + 0.899366i \(0.355971\pi\)
\(138\) −2.05175 −0.174657
\(139\) 16.2668 1.37973 0.689867 0.723936i \(-0.257669\pi\)
0.689867 + 0.723936i \(0.257669\pi\)
\(140\) −19.5627 −1.65335
\(141\) 10.1012 0.850673
\(142\) 23.0795 1.93679
\(143\) 14.0544 1.17529
\(144\) −3.53665 −0.294721
\(145\) −3.75134 −0.311532
\(146\) −23.0745 −1.90966
\(147\) 1.43046 0.117982
\(148\) −16.8794 −1.38748
\(149\) −22.1027 −1.81072 −0.905361 0.424643i \(-0.860400\pi\)
−0.905361 + 0.424643i \(0.860400\pi\)
\(150\) 18.6147 1.51988
\(151\) −7.14219 −0.581223 −0.290612 0.956841i \(-0.593859\pi\)
−0.290612 + 0.956841i \(0.593859\pi\)
\(152\) 3.31021 0.268494
\(153\) −5.05332 −0.408536
\(154\) 15.8449 1.27682
\(155\) −30.9259 −2.48403
\(156\) −9.49051 −0.759849
\(157\) 7.21404 0.575743 0.287871 0.957669i \(-0.407052\pi\)
0.287871 + 0.957669i \(0.407052\pi\)
\(158\) −3.39220 −0.269869
\(159\) 8.31770 0.659637
\(160\) 30.4489 2.40720
\(161\) 2.35999 0.185993
\(162\) −2.05175 −0.161201
\(163\) −21.6596 −1.69651 −0.848257 0.529585i \(-0.822348\pi\)
−0.848257 + 0.529585i \(0.822348\pi\)
\(164\) −15.0306 −1.17369
\(165\) −12.2755 −0.955650
\(166\) −10.0597 −0.780786
\(167\) −8.81880 −0.682419 −0.341210 0.939987i \(-0.610837\pi\)
−0.341210 + 0.939987i \(0.610837\pi\)
\(168\) −1.01535 −0.0783356
\(169\) 5.44660 0.418969
\(170\) 38.8945 2.98307
\(171\) −7.69400 −0.588375
\(172\) 11.7346 0.894754
\(173\) −11.4038 −0.867017 −0.433509 0.901149i \(-0.642725\pi\)
−0.433509 + 0.901149i \(0.642725\pi\)
\(174\) −2.05175 −0.155543
\(175\) −21.4112 −1.61853
\(176\) −11.5730 −0.872348
\(177\) 6.64175 0.499225
\(178\) −17.2978 −1.29653
\(179\) −7.78942 −0.582208 −0.291104 0.956691i \(-0.594023\pi\)
−0.291104 + 0.956691i \(0.594023\pi\)
\(180\) 8.28931 0.617848
\(181\) 7.78005 0.578287 0.289143 0.957286i \(-0.406630\pi\)
0.289143 + 0.957286i \(0.406630\pi\)
\(182\) 20.7966 1.54155
\(183\) 4.78113 0.353431
\(184\) 0.430233 0.0317172
\(185\) −28.6558 −2.10681
\(186\) −16.9146 −1.24024
\(187\) −16.5360 −1.20923
\(188\) −22.3205 −1.62789
\(189\) 2.35999 0.171664
\(190\) 59.2194 4.29623
\(191\) −19.1511 −1.38573 −0.692863 0.721070i \(-0.743651\pi\)
−0.692863 + 0.721070i \(0.743651\pi\)
\(192\) 9.58036 0.691403
\(193\) 11.4412 0.823552 0.411776 0.911285i \(-0.364909\pi\)
0.411776 + 0.911285i \(0.364909\pi\)
\(194\) −16.6705 −1.19688
\(195\) −16.1118 −1.15379
\(196\) −3.16087 −0.225776
\(197\) −8.28753 −0.590462 −0.295231 0.955426i \(-0.595397\pi\)
−0.295231 + 0.955426i \(0.595397\pi\)
\(198\) −6.71396 −0.477141
\(199\) −5.51469 −0.390926 −0.195463 0.980711i \(-0.562621\pi\)
−0.195463 + 0.980711i \(0.562621\pi\)
\(200\) −3.90332 −0.276007
\(201\) −15.3363 −1.08174
\(202\) 7.14340 0.502608
\(203\) 2.35999 0.165639
\(204\) 11.1663 0.781795
\(205\) −25.5170 −1.78219
\(206\) 36.5864 2.54909
\(207\) −1.00000 −0.0695048
\(208\) −15.1897 −1.05322
\(209\) −25.1771 −1.74154
\(210\) −18.1644 −1.25346
\(211\) −19.1656 −1.31941 −0.659706 0.751524i \(-0.729319\pi\)
−0.659706 + 0.751524i \(0.729319\pi\)
\(212\) −18.3795 −1.26231
\(213\) 11.2487 0.770748
\(214\) −10.7202 −0.732817
\(215\) 19.9216 1.35864
\(216\) 0.430233 0.0292737
\(217\) 19.4556 1.32074
\(218\) −26.5389 −1.79744
\(219\) −11.2463 −0.759951
\(220\) 27.1252 1.82878
\(221\) −21.7037 −1.45995
\(222\) −15.6729 −1.05190
\(223\) 2.24920 0.150617 0.0753087 0.997160i \(-0.476006\pi\)
0.0753087 + 0.997160i \(0.476006\pi\)
\(224\) −19.1555 −1.27988
\(225\) 9.07257 0.604838
\(226\) −18.8634 −1.25477
\(227\) 22.0599 1.46417 0.732084 0.681214i \(-0.238548\pi\)
0.732084 + 0.681214i \(0.238548\pi\)
\(228\) 17.0014 1.12594
\(229\) 11.0208 0.728278 0.364139 0.931345i \(-0.381363\pi\)
0.364139 + 0.931345i \(0.381363\pi\)
\(230\) 7.69683 0.507514
\(231\) 7.72260 0.508110
\(232\) 0.430233 0.0282462
\(233\) 16.8106 1.10130 0.550650 0.834737i \(-0.314380\pi\)
0.550650 + 0.834737i \(0.314380\pi\)
\(234\) −8.81218 −0.576070
\(235\) −37.8930 −2.47187
\(236\) −14.6762 −0.955341
\(237\) −1.65332 −0.107395
\(238\) −24.4687 −1.58607
\(239\) 0.695292 0.0449747 0.0224873 0.999747i \(-0.492841\pi\)
0.0224873 + 0.999747i \(0.492841\pi\)
\(240\) 13.2672 0.856393
\(241\) −17.3711 −1.11897 −0.559485 0.828840i \(-0.689001\pi\)
−0.559485 + 0.828840i \(0.689001\pi\)
\(242\) 0.599135 0.0385139
\(243\) −1.00000 −0.0641500
\(244\) −10.5648 −0.676343
\(245\) −5.36613 −0.342830
\(246\) −13.9563 −0.889818
\(247\) −33.0454 −2.10263
\(248\) 3.54682 0.225224
\(249\) −4.90299 −0.310714
\(250\) −31.3459 −1.98249
\(251\) −22.7680 −1.43710 −0.718551 0.695474i \(-0.755194\pi\)
−0.718551 + 0.695474i \(0.755194\pi\)
\(252\) −5.21484 −0.328504
\(253\) −3.27231 −0.205728
\(254\) 20.3150 1.27468
\(255\) 18.9567 1.18712
\(256\) 12.1377 0.758605
\(257\) 14.0147 0.874211 0.437105 0.899410i \(-0.356004\pi\)
0.437105 + 0.899410i \(0.356004\pi\)
\(258\) 10.8959 0.678347
\(259\) 18.0275 1.12017
\(260\) 35.6022 2.20795
\(261\) −1.00000 −0.0618984
\(262\) 1.43642 0.0887422
\(263\) −15.9795 −0.985341 −0.492671 0.870216i \(-0.663979\pi\)
−0.492671 + 0.870216i \(0.663979\pi\)
\(264\) 1.40785 0.0866475
\(265\) −31.2026 −1.91676
\(266\) −37.2552 −2.28426
\(267\) −8.43075 −0.515953
\(268\) 33.8885 2.07007
\(269\) 6.05875 0.369409 0.184704 0.982794i \(-0.440867\pi\)
0.184704 + 0.982794i \(0.440867\pi\)
\(270\) 7.69683 0.468414
\(271\) 22.0833 1.34146 0.670731 0.741700i \(-0.265980\pi\)
0.670731 + 0.741700i \(0.265980\pi\)
\(272\) 17.8718 1.08364
\(273\) 10.1360 0.613461
\(274\) −20.9987 −1.26858
\(275\) 29.6882 1.79027
\(276\) 2.20969 0.133008
\(277\) 1.07848 0.0647993 0.0323997 0.999475i \(-0.489685\pi\)
0.0323997 + 0.999475i \(0.489685\pi\)
\(278\) −33.3755 −2.00173
\(279\) −8.24396 −0.493553
\(280\) 3.80891 0.227626
\(281\) −19.6635 −1.17303 −0.586514 0.809939i \(-0.699500\pi\)
−0.586514 + 0.809939i \(0.699500\pi\)
\(282\) −20.7251 −1.23416
\(283\) 19.6493 1.16803 0.584014 0.811743i \(-0.301481\pi\)
0.584014 + 0.811743i \(0.301481\pi\)
\(284\) −24.8561 −1.47494
\(285\) 28.8628 1.70969
\(286\) −28.8361 −1.70512
\(287\) 16.0529 0.947573
\(288\) 8.11680 0.478287
\(289\) 8.53600 0.502117
\(290\) 7.69683 0.451973
\(291\) −8.12503 −0.476298
\(292\) 24.8507 1.45428
\(293\) −19.6322 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(294\) −2.93494 −0.171169
\(295\) −24.9155 −1.45064
\(296\) 3.28647 0.191022
\(297\) −3.27231 −0.189878
\(298\) 45.3492 2.62701
\(299\) −4.29495 −0.248383
\(300\) −20.0476 −1.15745
\(301\) −12.5327 −0.722376
\(302\) 14.6540 0.843244
\(303\) 3.48161 0.200013
\(304\) 27.2110 1.56066
\(305\) −17.9357 −1.02699
\(306\) 10.3682 0.592708
\(307\) −7.90639 −0.451242 −0.225621 0.974215i \(-0.572441\pi\)
−0.225621 + 0.974215i \(0.572441\pi\)
\(308\) −17.0646 −0.972344
\(309\) 17.8318 1.01441
\(310\) 63.4523 3.60385
\(311\) 22.5093 1.27638 0.638192 0.769878i \(-0.279683\pi\)
0.638192 + 0.769878i \(0.279683\pi\)
\(312\) 1.84783 0.104613
\(313\) 10.5353 0.595488 0.297744 0.954646i \(-0.403766\pi\)
0.297744 + 0.954646i \(0.403766\pi\)
\(314\) −14.8014 −0.835293
\(315\) −8.85312 −0.498817
\(316\) 3.65333 0.205516
\(317\) −0.622592 −0.0349683 −0.0174841 0.999847i \(-0.505566\pi\)
−0.0174841 + 0.999847i \(0.505566\pi\)
\(318\) −17.0659 −0.957007
\(319\) −3.27231 −0.183214
\(320\) −35.9392 −2.00906
\(321\) −5.22489 −0.291625
\(322\) −4.84211 −0.269840
\(323\) 38.8802 2.16335
\(324\) 2.20969 0.122761
\(325\) 38.9663 2.16146
\(326\) 44.4402 2.46132
\(327\) −12.9348 −0.715293
\(328\) 2.92649 0.161589
\(329\) 23.8387 1.31427
\(330\) 25.1864 1.38646
\(331\) 2.04097 0.112182 0.0560909 0.998426i \(-0.482136\pi\)
0.0560909 + 0.998426i \(0.482136\pi\)
\(332\) 10.8341 0.594598
\(333\) −7.63881 −0.418604
\(334\) 18.0940 0.990060
\(335\) 57.5318 3.14330
\(336\) −8.34645 −0.455336
\(337\) −7.27857 −0.396489 −0.198245 0.980153i \(-0.563524\pi\)
−0.198245 + 0.980153i \(0.563524\pi\)
\(338\) −11.1751 −0.607844
\(339\) −9.19380 −0.499338
\(340\) −41.8885 −2.27172
\(341\) −26.9768 −1.46087
\(342\) 15.7862 0.853620
\(343\) 19.8958 1.07427
\(344\) −2.28476 −0.123186
\(345\) 3.75134 0.201966
\(346\) 23.3978 1.25788
\(347\) −4.86768 −0.261311 −0.130655 0.991428i \(-0.541708\pi\)
−0.130655 + 0.991428i \(0.541708\pi\)
\(348\) 2.20969 0.118452
\(349\) 16.2572 0.870228 0.435114 0.900375i \(-0.356708\pi\)
0.435114 + 0.900375i \(0.356708\pi\)
\(350\) 43.9304 2.34818
\(351\) −4.29495 −0.229248
\(352\) 26.5606 1.41569
\(353\) 13.1198 0.698295 0.349148 0.937068i \(-0.386471\pi\)
0.349148 + 0.937068i \(0.386471\pi\)
\(354\) −13.6272 −0.724280
\(355\) −42.1977 −2.23962
\(356\) 18.6293 0.987353
\(357\) −11.9258 −0.631178
\(358\) 15.9820 0.844673
\(359\) 31.5273 1.66395 0.831974 0.554814i \(-0.187211\pi\)
0.831974 + 0.554814i \(0.187211\pi\)
\(360\) −1.61395 −0.0850627
\(361\) 40.1977 2.11567
\(362\) −15.9627 −0.838983
\(363\) 0.292011 0.0153266
\(364\) −22.3975 −1.17395
\(365\) 42.1885 2.20825
\(366\) −9.80970 −0.512761
\(367\) 23.9006 1.24760 0.623800 0.781584i \(-0.285588\pi\)
0.623800 + 0.781584i \(0.285588\pi\)
\(368\) 3.53665 0.184361
\(369\) −6.80211 −0.354104
\(370\) 58.7946 3.05659
\(371\) 19.6297 1.01912
\(372\) 18.2166 0.944487
\(373\) −5.72709 −0.296538 −0.148269 0.988947i \(-0.547370\pi\)
−0.148269 + 0.988947i \(0.547370\pi\)
\(374\) 33.9278 1.75436
\(375\) −15.2776 −0.788933
\(376\) 4.34586 0.224121
\(377\) −4.29495 −0.221201
\(378\) −4.84211 −0.249051
\(379\) −34.1260 −1.75293 −0.876467 0.481462i \(-0.840106\pi\)
−0.876467 + 0.481462i \(0.840106\pi\)
\(380\) −63.7779 −3.27174
\(381\) 9.90131 0.507259
\(382\) 39.2933 2.01042
\(383\) 28.4932 1.45593 0.727967 0.685613i \(-0.240466\pi\)
0.727967 + 0.685613i \(0.240466\pi\)
\(384\) −3.42295 −0.174677
\(385\) −28.9701 −1.47645
\(386\) −23.4744 −1.19482
\(387\) 5.31051 0.269949
\(388\) 17.9538 0.911466
\(389\) −34.1307 −1.73050 −0.865248 0.501344i \(-0.832839\pi\)
−0.865248 + 0.501344i \(0.832839\pi\)
\(390\) 33.0575 1.67393
\(391\) 5.05332 0.255557
\(392\) 0.615430 0.0310839
\(393\) 0.700093 0.0353150
\(394\) 17.0040 0.856648
\(395\) 6.20217 0.312065
\(396\) 7.23078 0.363361
\(397\) −0.398698 −0.0200101 −0.0100050 0.999950i \(-0.503185\pi\)
−0.0100050 + 0.999950i \(0.503185\pi\)
\(398\) 11.3148 0.567158
\(399\) −18.1578 −0.909025
\(400\) −32.0865 −1.60433
\(401\) 18.7059 0.934129 0.467064 0.884223i \(-0.345312\pi\)
0.467064 + 0.884223i \(0.345312\pi\)
\(402\) 31.4663 1.56940
\(403\) −35.4074 −1.76377
\(404\) −7.69328 −0.382755
\(405\) 3.75134 0.186406
\(406\) −4.84211 −0.240310
\(407\) −24.9965 −1.23903
\(408\) −2.17410 −0.107634
\(409\) 13.7661 0.680688 0.340344 0.940301i \(-0.389456\pi\)
0.340344 + 0.940301i \(0.389456\pi\)
\(410\) 52.3547 2.58561
\(411\) −10.2345 −0.504831
\(412\) −39.4027 −1.94123
\(413\) 15.6745 0.771290
\(414\) 2.05175 0.100838
\(415\) 18.3928 0.902866
\(416\) 34.8612 1.70921
\(417\) −16.2668 −0.796589
\(418\) 51.6573 2.52664
\(419\) −7.80433 −0.381266 −0.190633 0.981661i \(-0.561054\pi\)
−0.190633 + 0.981661i \(0.561054\pi\)
\(420\) 19.5627 0.954560
\(421\) 4.95845 0.241660 0.120830 0.992673i \(-0.461444\pi\)
0.120830 + 0.992673i \(0.461444\pi\)
\(422\) 39.3230 1.91421
\(423\) −10.1012 −0.491136
\(424\) 3.57855 0.173790
\(425\) −45.8466 −2.22389
\(426\) −23.0795 −1.11821
\(427\) 11.2834 0.546043
\(428\) 11.5454 0.558067
\(429\) −14.0544 −0.678553
\(430\) −40.8741 −1.97113
\(431\) 14.3407 0.690769 0.345384 0.938461i \(-0.387749\pi\)
0.345384 + 0.938461i \(0.387749\pi\)
\(432\) 3.53665 0.170157
\(433\) −20.2753 −0.974371 −0.487185 0.873299i \(-0.661976\pi\)
−0.487185 + 0.873299i \(0.661976\pi\)
\(434\) −39.9182 −1.91613
\(435\) 3.75134 0.179863
\(436\) 28.5818 1.36882
\(437\) 7.69400 0.368054
\(438\) 23.0745 1.10254
\(439\) 11.2623 0.537523 0.268761 0.963207i \(-0.413386\pi\)
0.268761 + 0.963207i \(0.413386\pi\)
\(440\) −5.28135 −0.251778
\(441\) −1.43046 −0.0681170
\(442\) 44.5307 2.11811
\(443\) −8.69105 −0.412924 −0.206462 0.978455i \(-0.566195\pi\)
−0.206462 + 0.978455i \(0.566195\pi\)
\(444\) 16.8794 0.801061
\(445\) 31.6266 1.49925
\(446\) −4.61480 −0.218517
\(447\) 22.1027 1.04542
\(448\) 22.6095 1.06820
\(449\) −26.7449 −1.26217 −0.631085 0.775714i \(-0.717390\pi\)
−0.631085 + 0.775714i \(0.717390\pi\)
\(450\) −18.6147 −0.877504
\(451\) −22.2586 −1.04812
\(452\) 20.3154 0.955558
\(453\) 7.14219 0.335569
\(454\) −45.2615 −2.12423
\(455\) −38.0237 −1.78258
\(456\) −3.31021 −0.155015
\(457\) −18.2879 −0.855473 −0.427736 0.903904i \(-0.640689\pi\)
−0.427736 + 0.903904i \(0.640689\pi\)
\(458\) −22.6120 −1.05659
\(459\) 5.05332 0.235869
\(460\) −8.28931 −0.386491
\(461\) 0.584892 0.0272411 0.0136206 0.999907i \(-0.495664\pi\)
0.0136206 + 0.999907i \(0.495664\pi\)
\(462\) −15.8449 −0.737170
\(463\) −37.2767 −1.73240 −0.866198 0.499701i \(-0.833443\pi\)
−0.866198 + 0.499701i \(0.833443\pi\)
\(464\) 3.53665 0.164185
\(465\) 30.9259 1.43416
\(466\) −34.4912 −1.59777
\(467\) −29.1928 −1.35088 −0.675440 0.737415i \(-0.736046\pi\)
−0.675440 + 0.737415i \(0.736046\pi\)
\(468\) 9.49051 0.438699
\(469\) −36.1935 −1.67126
\(470\) 77.7471 3.58621
\(471\) −7.21404 −0.332405
\(472\) 2.85750 0.131527
\(473\) 17.3776 0.799024
\(474\) 3.39220 0.155809
\(475\) −69.8044 −3.20285
\(476\) 26.3522 1.20785
\(477\) −8.31770 −0.380841
\(478\) −1.42657 −0.0652496
\(479\) 31.5875 1.44327 0.721636 0.692273i \(-0.243391\pi\)
0.721636 + 0.692273i \(0.243391\pi\)
\(480\) −30.4489 −1.38980
\(481\) −32.8083 −1.49593
\(482\) 35.6412 1.62341
\(483\) −2.35999 −0.107383
\(484\) −0.645255 −0.0293298
\(485\) 30.4798 1.38401
\(486\) 2.05175 0.0930694
\(487\) −25.0991 −1.13735 −0.568674 0.822563i \(-0.692543\pi\)
−0.568674 + 0.822563i \(0.692543\pi\)
\(488\) 2.05700 0.0931161
\(489\) 21.6596 0.979483
\(490\) 11.0100 0.497380
\(491\) −10.8979 −0.491815 −0.245908 0.969293i \(-0.579086\pi\)
−0.245908 + 0.969293i \(0.579086\pi\)
\(492\) 15.0306 0.677630
\(493\) 5.05332 0.227590
\(494\) 67.8009 3.05051
\(495\) 12.2755 0.551745
\(496\) 29.1560 1.30914
\(497\) 26.5468 1.19079
\(498\) 10.0597 0.450787
\(499\) −23.4104 −1.04799 −0.523997 0.851720i \(-0.675560\pi\)
−0.523997 + 0.851720i \(0.675560\pi\)
\(500\) 33.7588 1.50974
\(501\) 8.81880 0.393995
\(502\) 46.7143 2.08496
\(503\) −11.4338 −0.509807 −0.254903 0.966966i \(-0.582044\pi\)
−0.254903 + 0.966966i \(0.582044\pi\)
\(504\) 1.01535 0.0452271
\(505\) −13.0607 −0.581194
\(506\) 6.71396 0.298472
\(507\) −5.44660 −0.241892
\(508\) −21.8788 −0.970716
\(509\) −0.942475 −0.0417745 −0.0208872 0.999782i \(-0.506649\pi\)
−0.0208872 + 0.999782i \(0.506649\pi\)
\(510\) −38.8945 −1.72228
\(511\) −26.5410 −1.17411
\(512\) −31.7494 −1.40314
\(513\) 7.69400 0.339699
\(514\) −28.7546 −1.26831
\(515\) −66.8931 −2.94766
\(516\) −11.7346 −0.516587
\(517\) −33.0542 −1.45372
\(518\) −36.9880 −1.62516
\(519\) 11.4038 0.500573
\(520\) −6.93184 −0.303981
\(521\) 12.0132 0.526307 0.263154 0.964754i \(-0.415237\pi\)
0.263154 + 0.964754i \(0.415237\pi\)
\(522\) 2.05175 0.0898028
\(523\) 24.2290 1.05946 0.529731 0.848166i \(-0.322293\pi\)
0.529731 + 0.848166i \(0.322293\pi\)
\(524\) −1.54699 −0.0675806
\(525\) 21.4112 0.934460
\(526\) 32.7861 1.42954
\(527\) 41.6593 1.81471
\(528\) 11.5730 0.503650
\(529\) 1.00000 0.0434783
\(530\) 64.0199 2.78085
\(531\) −6.64175 −0.288228
\(532\) 40.1230 1.73955
\(533\) −29.2147 −1.26543
\(534\) 17.2978 0.748550
\(535\) 19.6003 0.847397
\(536\) −6.59819 −0.284998
\(537\) 7.78942 0.336138
\(538\) −12.4311 −0.535941
\(539\) −4.68089 −0.201620
\(540\) −8.28931 −0.356715
\(541\) 25.5374 1.09794 0.548969 0.835842i \(-0.315020\pi\)
0.548969 + 0.835842i \(0.315020\pi\)
\(542\) −45.3094 −1.94621
\(543\) −7.78005 −0.333874
\(544\) −41.0167 −1.75858
\(545\) 48.5227 2.07848
\(546\) −20.7966 −0.890014
\(547\) 12.3290 0.527150 0.263575 0.964639i \(-0.415098\pi\)
0.263575 + 0.964639i \(0.415098\pi\)
\(548\) 22.6151 0.966069
\(549\) −4.78113 −0.204054
\(550\) −60.9129 −2.59734
\(551\) 7.69400 0.327776
\(552\) −0.430233 −0.0183119
\(553\) −3.90182 −0.165922
\(554\) −2.21277 −0.0940114
\(555\) 28.6558 1.21637
\(556\) 35.9446 1.52439
\(557\) −41.4675 −1.75703 −0.878516 0.477712i \(-0.841466\pi\)
−0.878516 + 0.477712i \(0.841466\pi\)
\(558\) 16.9146 0.716051
\(559\) 22.8084 0.964692
\(560\) 31.3104 1.32311
\(561\) 16.5360 0.698150
\(562\) 40.3447 1.70184
\(563\) 7.39212 0.311541 0.155770 0.987793i \(-0.450214\pi\)
0.155770 + 0.987793i \(0.450214\pi\)
\(564\) 22.3205 0.939862
\(565\) 34.4891 1.45097
\(566\) −40.3155 −1.69459
\(567\) −2.35999 −0.0991102
\(568\) 4.83956 0.203063
\(569\) −6.57511 −0.275643 −0.137821 0.990457i \(-0.544010\pi\)
−0.137821 + 0.990457i \(0.544010\pi\)
\(570\) −59.2194 −2.48043
\(571\) 39.1977 1.64037 0.820186 0.572097i \(-0.193870\pi\)
0.820186 + 0.572097i \(0.193870\pi\)
\(572\) 31.0559 1.29851
\(573\) 19.1511 0.800049
\(574\) −32.9366 −1.37475
\(575\) −9.07257 −0.378352
\(576\) −9.58036 −0.399182
\(577\) −8.73676 −0.363716 −0.181858 0.983325i \(-0.558211\pi\)
−0.181858 + 0.983325i \(0.558211\pi\)
\(578\) −17.5138 −0.728476
\(579\) −11.4412 −0.475478
\(580\) −8.28931 −0.344195
\(581\) −11.5710 −0.480046
\(582\) 16.6705 0.691017
\(583\) −27.2181 −1.12726
\(584\) −4.83851 −0.200219
\(585\) 16.1118 0.666142
\(586\) 40.2804 1.66397
\(587\) −12.6202 −0.520893 −0.260447 0.965488i \(-0.583870\pi\)
−0.260447 + 0.965488i \(0.583870\pi\)
\(588\) 3.16087 0.130352
\(589\) 63.4290 2.61355
\(590\) 51.1204 2.10460
\(591\) 8.28753 0.340904
\(592\) 27.0158 1.11034
\(593\) 25.6149 1.05188 0.525939 0.850522i \(-0.323714\pi\)
0.525939 + 0.850522i \(0.323714\pi\)
\(594\) 6.71396 0.275477
\(595\) 44.7376 1.83406
\(596\) −48.8401 −2.00057
\(597\) 5.51469 0.225701
\(598\) 8.81218 0.360357
\(599\) −25.0727 −1.02444 −0.512222 0.858853i \(-0.671177\pi\)
−0.512222 + 0.858853i \(0.671177\pi\)
\(600\) 3.90332 0.159352
\(601\) 14.8990 0.607742 0.303871 0.952713i \(-0.401721\pi\)
0.303871 + 0.952713i \(0.401721\pi\)
\(602\) 25.7141 1.04803
\(603\) 15.3363 0.624543
\(604\) −15.7820 −0.642162
\(605\) −1.09543 −0.0445358
\(606\) −7.14340 −0.290181
\(607\) 24.3673 0.989036 0.494518 0.869167i \(-0.335345\pi\)
0.494518 + 0.869167i \(0.335345\pi\)
\(608\) −62.4507 −2.53271
\(609\) −2.35999 −0.0956315
\(610\) 36.7996 1.48997
\(611\) −43.3841 −1.75513
\(612\) −11.1663 −0.451369
\(613\) −27.3595 −1.10504 −0.552521 0.833499i \(-0.686334\pi\)
−0.552521 + 0.833499i \(0.686334\pi\)
\(614\) 16.2220 0.654665
\(615\) 25.5170 1.02895
\(616\) 3.32252 0.133868
\(617\) 14.1553 0.569869 0.284935 0.958547i \(-0.408028\pi\)
0.284935 + 0.958547i \(0.408028\pi\)
\(618\) −36.5864 −1.47172
\(619\) 25.6702 1.03177 0.515886 0.856657i \(-0.327463\pi\)
0.515886 + 0.856657i \(0.327463\pi\)
\(620\) −68.3367 −2.74447
\(621\) 1.00000 0.0401286
\(622\) −46.1834 −1.85179
\(623\) −19.8965 −0.797135
\(624\) 15.1897 0.608076
\(625\) 11.9487 0.477949
\(626\) −21.6158 −0.863940
\(627\) 25.1771 1.00548
\(628\) 15.9408 0.636107
\(629\) 38.6013 1.53913
\(630\) 18.1644 0.723688
\(631\) −36.6673 −1.45970 −0.729851 0.683606i \(-0.760411\pi\)
−0.729851 + 0.683606i \(0.760411\pi\)
\(632\) −0.711313 −0.0282945
\(633\) 19.1656 0.761763
\(634\) 1.27741 0.0507323
\(635\) −37.1432 −1.47398
\(636\) 18.3795 0.728797
\(637\) −6.14374 −0.243424
\(638\) 6.71396 0.265808
\(639\) −11.2487 −0.444991
\(640\) 12.8407 0.507571
\(641\) −7.88987 −0.311631 −0.155816 0.987786i \(-0.549801\pi\)
−0.155816 + 0.987786i \(0.549801\pi\)
\(642\) 10.7202 0.423092
\(643\) −15.0059 −0.591774 −0.295887 0.955223i \(-0.595615\pi\)
−0.295887 + 0.955223i \(0.595615\pi\)
\(644\) 5.21484 0.205494
\(645\) −19.9216 −0.784411
\(646\) −79.7726 −3.13861
\(647\) 36.5839 1.43826 0.719131 0.694875i \(-0.244540\pi\)
0.719131 + 0.694875i \(0.244540\pi\)
\(648\) −0.430233 −0.0169012
\(649\) −21.7339 −0.853128
\(650\) −79.9491 −3.13586
\(651\) −19.4556 −0.762527
\(652\) −47.8611 −1.87439
\(653\) −21.5028 −0.841470 −0.420735 0.907184i \(-0.638228\pi\)
−0.420735 + 0.907184i \(0.638228\pi\)
\(654\) 26.5389 1.03775
\(655\) −2.62629 −0.102618
\(656\) 24.0567 0.939255
\(657\) 11.2463 0.438758
\(658\) −48.9111 −1.90675
\(659\) −20.9402 −0.815716 −0.407858 0.913045i \(-0.633724\pi\)
−0.407858 + 0.913045i \(0.633724\pi\)
\(660\) −27.1252 −1.05585
\(661\) −29.4919 −1.14710 −0.573551 0.819170i \(-0.694434\pi\)
−0.573551 + 0.819170i \(0.694434\pi\)
\(662\) −4.18756 −0.162754
\(663\) 21.7037 0.842903
\(664\) −2.10943 −0.0818617
\(665\) 68.1160 2.64142
\(666\) 15.6729 0.607314
\(667\) 1.00000 0.0387202
\(668\) −19.4868 −0.753968
\(669\) −2.24920 −0.0869590
\(670\) −118.041 −4.56032
\(671\) −15.6453 −0.603981
\(672\) 19.1555 0.738941
\(673\) 33.3572 1.28583 0.642913 0.765939i \(-0.277726\pi\)
0.642913 + 0.765939i \(0.277726\pi\)
\(674\) 14.9338 0.575230
\(675\) −9.07257 −0.349204
\(676\) 12.0353 0.462896
\(677\) 17.4062 0.668975 0.334488 0.942400i \(-0.391437\pi\)
0.334488 + 0.942400i \(0.391437\pi\)
\(678\) 18.8634 0.724445
\(679\) −19.1750 −0.735868
\(680\) 8.15581 0.312761
\(681\) −22.0599 −0.845338
\(682\) 55.3497 2.11945
\(683\) 34.7410 1.32933 0.664664 0.747142i \(-0.268575\pi\)
0.664664 + 0.747142i \(0.268575\pi\)
\(684\) −17.0014 −0.650063
\(685\) 38.3932 1.46693
\(686\) −40.8212 −1.55856
\(687\) −11.0208 −0.420471
\(688\) −18.7814 −0.716035
\(689\) −35.7241 −1.36098
\(690\) −7.69683 −0.293013
\(691\) −12.4183 −0.472416 −0.236208 0.971703i \(-0.575905\pi\)
−0.236208 + 0.971703i \(0.575905\pi\)
\(692\) −25.1989 −0.957920
\(693\) −7.72260 −0.293357
\(694\) 9.98728 0.379112
\(695\) 61.0224 2.31471
\(696\) −0.430233 −0.0163079
\(697\) 34.3732 1.30198
\(698\) −33.3558 −1.26253
\(699\) −16.8106 −0.635835
\(700\) −47.3120 −1.78823
\(701\) 31.4022 1.18605 0.593023 0.805186i \(-0.297934\pi\)
0.593023 + 0.805186i \(0.297934\pi\)
\(702\) 8.81218 0.332594
\(703\) 58.7730 2.21667
\(704\) −31.3499 −1.18154
\(705\) 37.8930 1.42713
\(706\) −26.9185 −1.01309
\(707\) 8.21656 0.309015
\(708\) 14.6762 0.551566
\(709\) −47.4665 −1.78264 −0.891322 0.453372i \(-0.850221\pi\)
−0.891322 + 0.453372i \(0.850221\pi\)
\(710\) 86.5793 3.24926
\(711\) 1.65332 0.0620044
\(712\) −3.62719 −0.135935
\(713\) 8.24396 0.308739
\(714\) 24.4687 0.915719
\(715\) 52.7229 1.97172
\(716\) −17.2122 −0.643250
\(717\) −0.695292 −0.0259661
\(718\) −64.6863 −2.41407
\(719\) −30.3339 −1.13126 −0.565632 0.824658i \(-0.691368\pi\)
−0.565632 + 0.824658i \(0.691368\pi\)
\(720\) −13.2672 −0.494439
\(721\) 42.0827 1.56724
\(722\) −82.4757 −3.06943
\(723\) 17.3711 0.646038
\(724\) 17.1915 0.638917
\(725\) −9.07257 −0.336947
\(726\) −0.599135 −0.0222360
\(727\) 37.0949 1.37577 0.687887 0.725818i \(-0.258538\pi\)
0.687887 + 0.725818i \(0.258538\pi\)
\(728\) 4.36086 0.161624
\(729\) 1.00000 0.0370370
\(730\) −86.5605 −3.20375
\(731\) −26.8357 −0.992554
\(732\) 10.5648 0.390487
\(733\) 39.3141 1.45210 0.726049 0.687643i \(-0.241354\pi\)
0.726049 + 0.687643i \(0.241354\pi\)
\(734\) −49.0381 −1.81003
\(735\) 5.36613 0.197933
\(736\) −8.11680 −0.299189
\(737\) 50.1851 1.84859
\(738\) 13.9563 0.513737
\(739\) 15.6659 0.576280 0.288140 0.957588i \(-0.406963\pi\)
0.288140 + 0.957588i \(0.406963\pi\)
\(740\) −63.3204 −2.32770
\(741\) 33.0454 1.21395
\(742\) −40.2753 −1.47855
\(743\) 27.8413 1.02140 0.510698 0.859760i \(-0.329387\pi\)
0.510698 + 0.859760i \(0.329387\pi\)
\(744\) −3.54682 −0.130033
\(745\) −82.9147 −3.03776
\(746\) 11.7506 0.430219
\(747\) 4.90299 0.179391
\(748\) −36.5394 −1.33601
\(749\) −12.3307 −0.450553
\(750\) 31.3459 1.14459
\(751\) −38.0674 −1.38910 −0.694550 0.719444i \(-0.744397\pi\)
−0.694550 + 0.719444i \(0.744397\pi\)
\(752\) 35.7243 1.30273
\(753\) 22.7680 0.829711
\(754\) 8.81218 0.320921
\(755\) −26.7928 −0.975090
\(756\) 5.21484 0.189662
\(757\) −3.87374 −0.140793 −0.0703967 0.997519i \(-0.522427\pi\)
−0.0703967 + 0.997519i \(0.522427\pi\)
\(758\) 70.0181 2.54317
\(759\) 3.27231 0.118777
\(760\) 12.4178 0.450439
\(761\) −11.0651 −0.401109 −0.200554 0.979683i \(-0.564274\pi\)
−0.200554 + 0.979683i \(0.564274\pi\)
\(762\) −20.3150 −0.735936
\(763\) −30.5259 −1.10511
\(764\) −42.3180 −1.53101
\(765\) −18.9567 −0.685382
\(766\) −58.4610 −2.11228
\(767\) −28.5260 −1.03001
\(768\) −12.1377 −0.437981
\(769\) 36.4401 1.31406 0.657032 0.753862i \(-0.271812\pi\)
0.657032 + 0.753862i \(0.271812\pi\)
\(770\) 59.4396 2.14205
\(771\) −14.0147 −0.504726
\(772\) 25.2814 0.909898
\(773\) −43.9907 −1.58224 −0.791118 0.611663i \(-0.790501\pi\)
−0.791118 + 0.611663i \(0.790501\pi\)
\(774\) −10.8959 −0.391644
\(775\) −74.7939 −2.68668
\(776\) −3.49566 −0.125487
\(777\) −18.0275 −0.646733
\(778\) 70.0278 2.51062
\(779\) 52.3355 1.87511
\(780\) −35.6022 −1.27476
\(781\) −36.8092 −1.31714
\(782\) −10.3682 −0.370764
\(783\) 1.00000 0.0357371
\(784\) 5.05902 0.180679
\(785\) 27.0623 0.965896
\(786\) −1.43642 −0.0512354
\(787\) −8.32724 −0.296834 −0.148417 0.988925i \(-0.547418\pi\)
−0.148417 + 0.988925i \(0.547418\pi\)
\(788\) −18.3129 −0.652370
\(789\) 15.9795 0.568887
\(790\) −12.7253 −0.452747
\(791\) −21.6972 −0.771465
\(792\) −1.40785 −0.0500259
\(793\) −20.5347 −0.729209
\(794\) 0.818029 0.0290308
\(795\) 31.2026 1.10664
\(796\) −12.1858 −0.431913
\(797\) −39.5518 −1.40100 −0.700499 0.713653i \(-0.747039\pi\)
−0.700499 + 0.713653i \(0.747039\pi\)
\(798\) 37.2552 1.31882
\(799\) 51.0445 1.80582
\(800\) 73.6402 2.60358
\(801\) 8.43075 0.297886
\(802\) −38.3799 −1.35524
\(803\) 36.8012 1.29869
\(804\) −33.8885 −1.19516
\(805\) 8.85312 0.312032
\(806\) 72.6472 2.55889
\(807\) −6.05875 −0.213278
\(808\) 1.49790 0.0526961
\(809\) −4.41022 −0.155055 −0.0775275 0.996990i \(-0.524703\pi\)
−0.0775275 + 0.996990i \(0.524703\pi\)
\(810\) −7.69683 −0.270439
\(811\) −10.0306 −0.352223 −0.176111 0.984370i \(-0.556352\pi\)
−0.176111 + 0.984370i \(0.556352\pi\)
\(812\) 5.21484 0.183005
\(813\) −22.0833 −0.774494
\(814\) 51.2867 1.79760
\(815\) −81.2528 −2.84616
\(816\) −17.8718 −0.625638
\(817\) −40.8591 −1.42948
\(818\) −28.2446 −0.987548
\(819\) −10.1360 −0.354182
\(820\) −56.3848 −1.96904
\(821\) −25.8478 −0.902094 −0.451047 0.892500i \(-0.648949\pi\)
−0.451047 + 0.892500i \(0.648949\pi\)
\(822\) 20.9987 0.732413
\(823\) 13.8287 0.482037 0.241018 0.970521i \(-0.422519\pi\)
0.241018 + 0.970521i \(0.422519\pi\)
\(824\) 7.67182 0.267260
\(825\) −29.6882 −1.03361
\(826\) −32.1601 −1.11899
\(827\) 12.5175 0.435276 0.217638 0.976030i \(-0.430165\pi\)
0.217638 + 0.976030i \(0.430165\pi\)
\(828\) −2.20969 −0.0767921
\(829\) 34.8545 1.21055 0.605273 0.796018i \(-0.293064\pi\)
0.605273 + 0.796018i \(0.293064\pi\)
\(830\) −37.7375 −1.30989
\(831\) −1.07848 −0.0374119
\(832\) −41.1472 −1.42652
\(833\) 7.22855 0.250454
\(834\) 33.3755 1.15570
\(835\) −33.0823 −1.14486
\(836\) −55.6337 −1.92413
\(837\) 8.24396 0.284953
\(838\) 16.0126 0.553144
\(839\) −30.4417 −1.05097 −0.525483 0.850804i \(-0.676115\pi\)
−0.525483 + 0.850804i \(0.676115\pi\)
\(840\) −3.80891 −0.131420
\(841\) 1.00000 0.0344828
\(842\) −10.1735 −0.350602
\(843\) 19.6635 0.677248
\(844\) −42.3500 −1.45775
\(845\) 20.4321 0.702885
\(846\) 20.7251 0.712545
\(847\) 0.689143 0.0236792
\(848\) 29.4168 1.01018
\(849\) −19.6493 −0.674362
\(850\) 94.0659 3.22643
\(851\) 7.63881 0.261855
\(852\) 24.8561 0.851557
\(853\) 7.79943 0.267047 0.133524 0.991046i \(-0.457371\pi\)
0.133524 + 0.991046i \(0.457371\pi\)
\(854\) −23.1508 −0.792203
\(855\) −28.8628 −0.987088
\(856\) −2.24792 −0.0768323
\(857\) 15.8702 0.542115 0.271058 0.962563i \(-0.412627\pi\)
0.271058 + 0.962563i \(0.412627\pi\)
\(858\) 28.8361 0.984450
\(859\) 7.93953 0.270893 0.135447 0.990785i \(-0.456753\pi\)
0.135447 + 0.990785i \(0.456753\pi\)
\(860\) 44.0205 1.50109
\(861\) −16.0529 −0.547081
\(862\) −29.4236 −1.00217
\(863\) 36.0705 1.22786 0.613928 0.789362i \(-0.289589\pi\)
0.613928 + 0.789362i \(0.289589\pi\)
\(864\) −8.11680 −0.276139
\(865\) −42.7797 −1.45455
\(866\) 41.6000 1.41363
\(867\) −8.53600 −0.289898
\(868\) 42.9910 1.45921
\(869\) 5.41017 0.183527
\(870\) −7.69683 −0.260947
\(871\) 65.8687 2.23188
\(872\) −5.56496 −0.188453
\(873\) 8.12503 0.274991
\(874\) −15.7862 −0.533976
\(875\) −36.0550 −1.21888
\(876\) −24.8507 −0.839629
\(877\) −9.29593 −0.313901 −0.156951 0.987606i \(-0.550166\pi\)
−0.156951 + 0.987606i \(0.550166\pi\)
\(878\) −23.1076 −0.779842
\(879\) 19.6322 0.662177
\(880\) −43.4143 −1.46350
\(881\) 19.7875 0.666657 0.333329 0.942811i \(-0.391828\pi\)
0.333329 + 0.942811i \(0.391828\pi\)
\(882\) 2.93494 0.0988247
\(883\) 36.9124 1.24220 0.621101 0.783731i \(-0.286686\pi\)
0.621101 + 0.783731i \(0.286686\pi\)
\(884\) −47.9586 −1.61302
\(885\) 24.9155 0.837525
\(886\) 17.8319 0.599074
\(887\) −5.46715 −0.183569 −0.0917845 0.995779i \(-0.529257\pi\)
−0.0917845 + 0.995779i \(0.529257\pi\)
\(888\) −3.28647 −0.110287
\(889\) 23.3670 0.783703
\(890\) −64.8900 −2.17512
\(891\) 3.27231 0.109626
\(892\) 4.97003 0.166409
\(893\) 77.7185 2.60075
\(894\) −45.3492 −1.51671
\(895\) −29.2208 −0.976743
\(896\) −8.07812 −0.269871
\(897\) 4.29495 0.143404
\(898\) 54.8739 1.83117
\(899\) 8.24396 0.274951
\(900\) 20.0476 0.668253
\(901\) 42.0320 1.40029
\(902\) 45.6691 1.52062
\(903\) 12.5327 0.417064
\(904\) −3.95548 −0.131557
\(905\) 29.1856 0.970164
\(906\) −14.6540 −0.486847
\(907\) 1.43927 0.0477903 0.0238952 0.999714i \(-0.492393\pi\)
0.0238952 + 0.999714i \(0.492393\pi\)
\(908\) 48.7456 1.61768
\(909\) −3.48161 −0.115478
\(910\) 78.0153 2.58618
\(911\) −45.8742 −1.51988 −0.759941 0.649993i \(-0.774772\pi\)
−0.759941 + 0.649993i \(0.774772\pi\)
\(912\) −27.2110 −0.901046
\(913\) 16.0441 0.530981
\(914\) 37.5223 1.24113
\(915\) 17.9357 0.592935
\(916\) 24.3526 0.804634
\(917\) 1.65221 0.0545608
\(918\) −10.3682 −0.342200
\(919\) 22.7859 0.751637 0.375818 0.926693i \(-0.377362\pi\)
0.375818 + 0.926693i \(0.377362\pi\)
\(920\) 1.61395 0.0532104
\(921\) 7.90639 0.260525
\(922\) −1.20005 −0.0395217
\(923\) −48.3126 −1.59023
\(924\) 17.0646 0.561383
\(925\) −69.3036 −2.27869
\(926\) 76.4826 2.51337
\(927\) −17.8318 −0.585672
\(928\) −8.11680 −0.266447
\(929\) 27.0810 0.888499 0.444250 0.895903i \(-0.353470\pi\)
0.444250 + 0.895903i \(0.353470\pi\)
\(930\) −63.4523 −2.08068
\(931\) 11.0059 0.360705
\(932\) 37.1462 1.21677
\(933\) −22.5093 −0.736920
\(934\) 59.8964 1.95987
\(935\) −62.0322 −2.02867
\(936\) −1.84783 −0.0603982
\(937\) −39.3374 −1.28510 −0.642549 0.766245i \(-0.722123\pi\)
−0.642549 + 0.766245i \(0.722123\pi\)
\(938\) 74.2602 2.42468
\(939\) −10.5353 −0.343805
\(940\) −83.7318 −2.73103
\(941\) −54.4213 −1.77408 −0.887041 0.461690i \(-0.847243\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(942\) 14.8014 0.482256
\(943\) 6.80211 0.221507
\(944\) 23.4896 0.764520
\(945\) 8.85312 0.287992
\(946\) −35.6546 −1.15923
\(947\) −30.7692 −0.999866 −0.499933 0.866064i \(-0.666642\pi\)
−0.499933 + 0.866064i \(0.666642\pi\)
\(948\) −3.65333 −0.118655
\(949\) 48.3021 1.56795
\(950\) 143.221 4.64672
\(951\) 0.622592 0.0201889
\(952\) −5.13086 −0.166292
\(953\) −7.40619 −0.239910 −0.119955 0.992779i \(-0.538275\pi\)
−0.119955 + 0.992779i \(0.538275\pi\)
\(954\) 17.0659 0.552528
\(955\) −71.8424 −2.32476
\(956\) 1.53638 0.0496901
\(957\) 3.27231 0.105779
\(958\) −64.8098 −2.09391
\(959\) −24.1533 −0.779952
\(960\) 35.9392 1.15993
\(961\) 36.9629 1.19235
\(962\) 67.3145 2.17031
\(963\) 5.22489 0.168370
\(964\) −38.3848 −1.23629
\(965\) 42.9197 1.38163
\(966\) 4.84211 0.155792
\(967\) −48.3624 −1.55523 −0.777614 0.628742i \(-0.783570\pi\)
−0.777614 + 0.628742i \(0.783570\pi\)
\(968\) 0.125633 0.00403800
\(969\) −38.8802 −1.24901
\(970\) −62.5369 −2.00794
\(971\) 12.6667 0.406494 0.203247 0.979127i \(-0.434850\pi\)
0.203247 + 0.979127i \(0.434850\pi\)
\(972\) −2.20969 −0.0708759
\(973\) −38.3895 −1.23071
\(974\) 51.4971 1.65007
\(975\) −38.9663 −1.24792
\(976\) 16.9092 0.541250
\(977\) −55.1668 −1.76494 −0.882472 0.470365i \(-0.844122\pi\)
−0.882472 + 0.470365i \(0.844122\pi\)
\(978\) −44.4402 −1.42104
\(979\) 27.5880 0.881716
\(980\) −11.8575 −0.378774
\(981\) 12.9348 0.412975
\(982\) 22.3598 0.713530
\(983\) −50.7397 −1.61834 −0.809172 0.587571i \(-0.800084\pi\)
−0.809172 + 0.587571i \(0.800084\pi\)
\(984\) −2.92649 −0.0932932
\(985\) −31.0894 −0.990590
\(986\) −10.3682 −0.330189
\(987\) −23.8387 −0.758793
\(988\) −73.0200 −2.32308
\(989\) −5.31051 −0.168865
\(990\) −25.1864 −0.800476
\(991\) 15.7634 0.500741 0.250371 0.968150i \(-0.419448\pi\)
0.250371 + 0.968150i \(0.419448\pi\)
\(992\) −66.9145 −2.12454
\(993\) −2.04097 −0.0647682
\(994\) −54.4674 −1.72760
\(995\) −20.6875 −0.655837
\(996\) −10.8341 −0.343291
\(997\) 43.2959 1.37119 0.685597 0.727981i \(-0.259541\pi\)
0.685597 + 0.727981i \(0.259541\pi\)
\(998\) 48.0324 1.52044
\(999\) 7.63881 0.241681
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 2001.2.a.m.1.3 14
3.2 odd 2 6003.2.a.p.1.12 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.m.1.3 14 1.1 even 1 trivial
6003.2.a.p.1.12 14 3.2 odd 2