Properties

Label 1502.2.a.h.1.5
Level $1502$
Weight $2$
Character 1502.1
Self dual yes
Analytic conductor $11.994$
Analytic rank $0$
Dimension $19$
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: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} - 11338 x^{11} - 56744 x^{10} + 50183 x^{9} + 120237 x^{8} - 102992 x^{7} + \cdots + 4222 \) 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 1.5
Root \(-1.64365\) 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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.64365 q^{3} +1.00000 q^{4} -0.210142 q^{5} +1.64365 q^{6} -4.29873 q^{7} -1.00000 q^{8} -0.298402 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.64365 q^{3} +1.00000 q^{4} -0.210142 q^{5} +1.64365 q^{6} -4.29873 q^{7} -1.00000 q^{8} -0.298402 q^{9} +0.210142 q^{10} -5.53220 q^{11} -1.64365 q^{12} +1.08532 q^{13} +4.29873 q^{14} +0.345400 q^{15} +1.00000 q^{16} -3.80403 q^{17} +0.298402 q^{18} -7.09967 q^{19} -0.210142 q^{20} +7.06562 q^{21} +5.53220 q^{22} +2.95120 q^{23} +1.64365 q^{24} -4.95584 q^{25} -1.08532 q^{26} +5.42143 q^{27} -4.29873 q^{28} -3.08121 q^{29} -0.345400 q^{30} +6.63740 q^{31} -1.00000 q^{32} +9.09302 q^{33} +3.80403 q^{34} +0.903343 q^{35} -0.298402 q^{36} +4.14968 q^{37} +7.09967 q^{38} -1.78389 q^{39} +0.210142 q^{40} +2.73766 q^{41} -7.06562 q^{42} -11.9305 q^{43} -5.53220 q^{44} +0.0627068 q^{45} -2.95120 q^{46} -6.80185 q^{47} -1.64365 q^{48} +11.4791 q^{49} +4.95584 q^{50} +6.25251 q^{51} +1.08532 q^{52} +3.05280 q^{53} -5.42143 q^{54} +1.16255 q^{55} +4.29873 q^{56} +11.6694 q^{57} +3.08121 q^{58} -9.49532 q^{59} +0.345400 q^{60} -2.70135 q^{61} -6.63740 q^{62} +1.28275 q^{63} +1.00000 q^{64} -0.228072 q^{65} -9.09302 q^{66} +15.7797 q^{67} -3.80403 q^{68} -4.85076 q^{69} -0.903343 q^{70} -5.51340 q^{71} +0.298402 q^{72} +3.31672 q^{73} -4.14968 q^{74} +8.14569 q^{75} -7.09967 q^{76} +23.7814 q^{77} +1.78389 q^{78} -7.06174 q^{79} -0.210142 q^{80} -8.01575 q^{81} -2.73766 q^{82} +4.61960 q^{83} +7.06562 q^{84} +0.799386 q^{85} +11.9305 q^{86} +5.06444 q^{87} +5.53220 q^{88} -11.7469 q^{89} -0.0627068 q^{90} -4.66551 q^{91} +2.95120 q^{92} -10.9096 q^{93} +6.80185 q^{94} +1.49194 q^{95} +1.64365 q^{96} -0.942349 q^{97} -11.4791 q^{98} +1.65082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 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
\(3\) −1.64365 −0.948964 −0.474482 0.880265i \(-0.657365\pi\)
−0.474482 + 0.880265i \(0.657365\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.210142 −0.0939783 −0.0469891 0.998895i \(-0.514963\pi\)
−0.0469891 + 0.998895i \(0.514963\pi\)
\(6\) 1.64365 0.671019
\(7\) −4.29873 −1.62477 −0.812384 0.583123i \(-0.801830\pi\)
−0.812384 + 0.583123i \(0.801830\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.298402 −0.0994674
\(10\) 0.210142 0.0664527
\(11\) −5.53220 −1.66802 −0.834010 0.551749i \(-0.813961\pi\)
−0.834010 + 0.551749i \(0.813961\pi\)
\(12\) −1.64365 −0.474482
\(13\) 1.08532 0.301014 0.150507 0.988609i \(-0.451909\pi\)
0.150507 + 0.988609i \(0.451909\pi\)
\(14\) 4.29873 1.14888
\(15\) 0.345400 0.0891820
\(16\) 1.00000 0.250000
\(17\) −3.80403 −0.922612 −0.461306 0.887241i \(-0.652619\pi\)
−0.461306 + 0.887241i \(0.652619\pi\)
\(18\) 0.298402 0.0703341
\(19\) −7.09967 −1.62878 −0.814388 0.580321i \(-0.802927\pi\)
−0.814388 + 0.580321i \(0.802927\pi\)
\(20\) −0.210142 −0.0469891
\(21\) 7.06562 1.54185
\(22\) 5.53220 1.17947
\(23\) 2.95120 0.615369 0.307684 0.951489i \(-0.400446\pi\)
0.307684 + 0.951489i \(0.400446\pi\)
\(24\) 1.64365 0.335509
\(25\) −4.95584 −0.991168
\(26\) −1.08532 −0.212849
\(27\) 5.42143 1.04335
\(28\) −4.29873 −0.812384
\(29\) −3.08121 −0.572166 −0.286083 0.958205i \(-0.592353\pi\)
−0.286083 + 0.958205i \(0.592353\pi\)
\(30\) −0.345400 −0.0630612
\(31\) 6.63740 1.19211 0.596056 0.802943i \(-0.296734\pi\)
0.596056 + 0.802943i \(0.296734\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.09302 1.58289
\(34\) 3.80403 0.652386
\(35\) 0.903343 0.152693
\(36\) −0.298402 −0.0497337
\(37\) 4.14968 0.682203 0.341101 0.940026i \(-0.389200\pi\)
0.341101 + 0.940026i \(0.389200\pi\)
\(38\) 7.09967 1.15172
\(39\) −1.78389 −0.285652
\(40\) 0.210142 0.0332263
\(41\) 2.73766 0.427550 0.213775 0.976883i \(-0.431424\pi\)
0.213775 + 0.976883i \(0.431424\pi\)
\(42\) −7.06562 −1.09025
\(43\) −11.9305 −1.81938 −0.909691 0.415286i \(-0.863681\pi\)
−0.909691 + 0.415286i \(0.863681\pi\)
\(44\) −5.53220 −0.834010
\(45\) 0.0627068 0.00934778
\(46\) −2.95120 −0.435131
\(47\) −6.80185 −0.992151 −0.496076 0.868279i \(-0.665226\pi\)
−0.496076 + 0.868279i \(0.665226\pi\)
\(48\) −1.64365 −0.237241
\(49\) 11.4791 1.63987
\(50\) 4.95584 0.700862
\(51\) 6.25251 0.875526
\(52\) 1.08532 0.150507
\(53\) 3.05280 0.419334 0.209667 0.977773i \(-0.432762\pi\)
0.209667 + 0.977773i \(0.432762\pi\)
\(54\) −5.42143 −0.737763
\(55\) 1.16255 0.156758
\(56\) 4.29873 0.574442
\(57\) 11.6694 1.54565
\(58\) 3.08121 0.404582
\(59\) −9.49532 −1.23619 −0.618093 0.786105i \(-0.712094\pi\)
−0.618093 + 0.786105i \(0.712094\pi\)
\(60\) 0.345400 0.0445910
\(61\) −2.70135 −0.345872 −0.172936 0.984933i \(-0.555325\pi\)
−0.172936 + 0.984933i \(0.555325\pi\)
\(62\) −6.63740 −0.842951
\(63\) 1.28275 0.161611
\(64\) 1.00000 0.125000
\(65\) −0.228072 −0.0282888
\(66\) −9.09302 −1.11927
\(67\) 15.7797 1.92780 0.963898 0.266273i \(-0.0857923\pi\)
0.963898 + 0.266273i \(0.0857923\pi\)
\(68\) −3.80403 −0.461306
\(69\) −4.85076 −0.583963
\(70\) −0.903343 −0.107970
\(71\) −5.51340 −0.654320 −0.327160 0.944969i \(-0.606092\pi\)
−0.327160 + 0.944969i \(0.606092\pi\)
\(72\) 0.298402 0.0351671
\(73\) 3.31672 0.388193 0.194096 0.980982i \(-0.437823\pi\)
0.194096 + 0.980982i \(0.437823\pi\)
\(74\) −4.14968 −0.482390
\(75\) 8.14569 0.940583
\(76\) −7.09967 −0.814388
\(77\) 23.7814 2.71015
\(78\) 1.78389 0.201986
\(79\) −7.06174 −0.794508 −0.397254 0.917709i \(-0.630037\pi\)
−0.397254 + 0.917709i \(0.630037\pi\)
\(80\) −0.210142 −0.0234946
\(81\) −8.01575 −0.890639
\(82\) −2.73766 −0.302324
\(83\) 4.61960 0.507067 0.253534 0.967327i \(-0.418407\pi\)
0.253534 + 0.967327i \(0.418407\pi\)
\(84\) 7.06562 0.770923
\(85\) 0.799386 0.0867055
\(86\) 11.9305 1.28650
\(87\) 5.06444 0.542965
\(88\) 5.53220 0.589734
\(89\) −11.7469 −1.24517 −0.622583 0.782554i \(-0.713917\pi\)
−0.622583 + 0.782554i \(0.713917\pi\)
\(90\) −0.0627068 −0.00660988
\(91\) −4.66551 −0.489078
\(92\) 2.95120 0.307684
\(93\) −10.9096 −1.13127
\(94\) 6.80185 0.701557
\(95\) 1.49194 0.153070
\(96\) 1.64365 0.167755
\(97\) −0.942349 −0.0956810 −0.0478405 0.998855i \(-0.515234\pi\)
−0.0478405 + 0.998855i \(0.515234\pi\)
\(98\) −11.4791 −1.15956
\(99\) 1.65082 0.165914
\(100\) −4.95584 −0.495584
\(101\) 15.8815 1.58027 0.790134 0.612935i \(-0.210011\pi\)
0.790134 + 0.612935i \(0.210011\pi\)
\(102\) −6.25251 −0.619090
\(103\) −0.796754 −0.0785065 −0.0392532 0.999229i \(-0.512498\pi\)
−0.0392532 + 0.999229i \(0.512498\pi\)
\(104\) −1.08532 −0.106425
\(105\) −1.48478 −0.144900
\(106\) −3.05280 −0.296514
\(107\) −14.3543 −1.38768 −0.693842 0.720127i \(-0.744083\pi\)
−0.693842 + 0.720127i \(0.744083\pi\)
\(108\) 5.42143 0.521677
\(109\) 6.51756 0.624269 0.312134 0.950038i \(-0.398956\pi\)
0.312134 + 0.950038i \(0.398956\pi\)
\(110\) −1.16255 −0.110844
\(111\) −6.82064 −0.647386
\(112\) −4.29873 −0.406192
\(113\) 1.99662 0.187826 0.0939129 0.995580i \(-0.470062\pi\)
0.0939129 + 0.995580i \(0.470062\pi\)
\(114\) −11.6694 −1.09294
\(115\) −0.620171 −0.0578313
\(116\) −3.08121 −0.286083
\(117\) −0.323863 −0.0299411
\(118\) 9.49532 0.874115
\(119\) 16.3525 1.49903
\(120\) −0.345400 −0.0315306
\(121\) 19.6052 1.78229
\(122\) 2.70135 0.244568
\(123\) −4.49976 −0.405730
\(124\) 6.63740 0.596056
\(125\) 2.09214 0.187127
\(126\) −1.28275 −0.114277
\(127\) 10.8564 0.963348 0.481674 0.876350i \(-0.340029\pi\)
0.481674 + 0.876350i \(0.340029\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 19.6096 1.72653
\(130\) 0.228072 0.0200032
\(131\) −16.4182 −1.43446 −0.717232 0.696834i \(-0.754591\pi\)
−0.717232 + 0.696834i \(0.754591\pi\)
\(132\) 9.09302 0.791446
\(133\) 30.5196 2.64638
\(134\) −15.7797 −1.36316
\(135\) −1.13927 −0.0980527
\(136\) 3.80403 0.326193
\(137\) 22.5222 1.92420 0.962100 0.272697i \(-0.0879155\pi\)
0.962100 + 0.272697i \(0.0879155\pi\)
\(138\) 4.85076 0.412924
\(139\) −12.3368 −1.04639 −0.523197 0.852212i \(-0.675261\pi\)
−0.523197 + 0.852212i \(0.675261\pi\)
\(140\) 0.903343 0.0763464
\(141\) 11.1799 0.941516
\(142\) 5.51340 0.462674
\(143\) −6.00422 −0.502098
\(144\) −0.298402 −0.0248669
\(145\) 0.647491 0.0537712
\(146\) −3.31672 −0.274494
\(147\) −18.8676 −1.55618
\(148\) 4.14968 0.341101
\(149\) 3.36969 0.276056 0.138028 0.990428i \(-0.455924\pi\)
0.138028 + 0.990428i \(0.455924\pi\)
\(150\) −8.14569 −0.665092
\(151\) 19.6668 1.60046 0.800230 0.599694i \(-0.204711\pi\)
0.800230 + 0.599694i \(0.204711\pi\)
\(152\) 7.09967 0.575859
\(153\) 1.13513 0.0917699
\(154\) −23.7814 −1.91636
\(155\) −1.39480 −0.112033
\(156\) −1.78389 −0.142826
\(157\) 22.7381 1.81470 0.907349 0.420378i \(-0.138102\pi\)
0.907349 + 0.420378i \(0.138102\pi\)
\(158\) 7.06174 0.561802
\(159\) −5.01774 −0.397933
\(160\) 0.210142 0.0166132
\(161\) −12.6864 −0.999831
\(162\) 8.01575 0.629777
\(163\) −0.524356 −0.0410708 −0.0205354 0.999789i \(-0.506537\pi\)
−0.0205354 + 0.999789i \(0.506537\pi\)
\(164\) 2.73766 0.213775
\(165\) −1.91082 −0.148757
\(166\) −4.61960 −0.358551
\(167\) 7.09344 0.548907 0.274453 0.961600i \(-0.411503\pi\)
0.274453 + 0.961600i \(0.411503\pi\)
\(168\) −7.06562 −0.545125
\(169\) −11.8221 −0.909391
\(170\) −0.799386 −0.0613101
\(171\) 2.11856 0.162010
\(172\) −11.9305 −0.909691
\(173\) −20.1340 −1.53076 −0.765381 0.643577i \(-0.777450\pi\)
−0.765381 + 0.643577i \(0.777450\pi\)
\(174\) −5.06444 −0.383934
\(175\) 21.3038 1.61042
\(176\) −5.53220 −0.417005
\(177\) 15.6070 1.17310
\(178\) 11.7469 0.880465
\(179\) −13.3020 −0.994242 −0.497121 0.867681i \(-0.665609\pi\)
−0.497121 + 0.867681i \(0.665609\pi\)
\(180\) 0.0627068 0.00467389
\(181\) −18.2102 −1.35355 −0.676776 0.736189i \(-0.736623\pi\)
−0.676776 + 0.736189i \(0.736623\pi\)
\(182\) 4.66551 0.345830
\(183\) 4.44008 0.328220
\(184\) −2.95120 −0.217566
\(185\) −0.872021 −0.0641123
\(186\) 10.9096 0.799930
\(187\) 21.0446 1.53894
\(188\) −6.80185 −0.496076
\(189\) −23.3053 −1.69521
\(190\) −1.49194 −0.108237
\(191\) 15.2620 1.10432 0.552158 0.833739i \(-0.313805\pi\)
0.552158 + 0.833739i \(0.313805\pi\)
\(192\) −1.64365 −0.118620
\(193\) −9.87710 −0.710969 −0.355485 0.934682i \(-0.615684\pi\)
−0.355485 + 0.934682i \(0.615684\pi\)
\(194\) 0.942349 0.0676567
\(195\) 0.374871 0.0268450
\(196\) 11.4791 0.819935
\(197\) 17.9712 1.28039 0.640197 0.768210i \(-0.278853\pi\)
0.640197 + 0.768210i \(0.278853\pi\)
\(198\) −1.65082 −0.117319
\(199\) 22.5180 1.59626 0.798129 0.602486i \(-0.205823\pi\)
0.798129 + 0.602486i \(0.205823\pi\)
\(200\) 4.95584 0.350431
\(201\) −25.9363 −1.82941
\(202\) −15.8815 −1.11742
\(203\) 13.2453 0.929637
\(204\) 6.25251 0.437763
\(205\) −0.575296 −0.0401804
\(206\) 0.796754 0.0555125
\(207\) −0.880646 −0.0612091
\(208\) 1.08532 0.0752535
\(209\) 39.2768 2.71683
\(210\) 1.48478 0.102460
\(211\) 7.71129 0.530867 0.265433 0.964129i \(-0.414485\pi\)
0.265433 + 0.964129i \(0.414485\pi\)
\(212\) 3.05280 0.209667
\(213\) 9.06212 0.620926
\(214\) 14.3543 0.981241
\(215\) 2.50709 0.170982
\(216\) −5.42143 −0.368882
\(217\) −28.5324 −1.93691
\(218\) −6.51756 −0.441425
\(219\) −5.45154 −0.368381
\(220\) 1.16255 0.0783789
\(221\) −4.12860 −0.277719
\(222\) 6.82064 0.457771
\(223\) 7.65080 0.512335 0.256168 0.966632i \(-0.417540\pi\)
0.256168 + 0.966632i \(0.417540\pi\)
\(224\) 4.29873 0.287221
\(225\) 1.47883 0.0985890
\(226\) −1.99662 −0.132813
\(227\) −13.2776 −0.881266 −0.440633 0.897687i \(-0.645246\pi\)
−0.440633 + 0.897687i \(0.645246\pi\)
\(228\) 11.6694 0.772825
\(229\) −6.61574 −0.437180 −0.218590 0.975817i \(-0.570146\pi\)
−0.218590 + 0.975817i \(0.570146\pi\)
\(230\) 0.620171 0.0408929
\(231\) −39.0884 −2.57183
\(232\) 3.08121 0.202291
\(233\) −17.6112 −1.15375 −0.576873 0.816834i \(-0.695727\pi\)
−0.576873 + 0.816834i \(0.695727\pi\)
\(234\) 0.323863 0.0211716
\(235\) 1.42935 0.0932407
\(236\) −9.49532 −0.618093
\(237\) 11.6071 0.753960
\(238\) −16.3525 −1.05997
\(239\) 4.20632 0.272084 0.136042 0.990703i \(-0.456562\pi\)
0.136042 + 0.990703i \(0.456562\pi\)
\(240\) 0.345400 0.0222955
\(241\) −24.0169 −1.54706 −0.773531 0.633759i \(-0.781511\pi\)
−0.773531 + 0.633759i \(0.781511\pi\)
\(242\) −19.6052 −1.26027
\(243\) −3.08918 −0.198171
\(244\) −2.70135 −0.172936
\(245\) −2.41224 −0.154112
\(246\) 4.49976 0.286894
\(247\) −7.70543 −0.490284
\(248\) −6.63740 −0.421475
\(249\) −7.59303 −0.481189
\(250\) −2.09214 −0.132318
\(251\) −15.5276 −0.980092 −0.490046 0.871697i \(-0.663020\pi\)
−0.490046 + 0.871697i \(0.663020\pi\)
\(252\) 1.28275 0.0808057
\(253\) −16.3266 −1.02645
\(254\) −10.8564 −0.681190
\(255\) −1.31391 −0.0822804
\(256\) 1.00000 0.0625000
\(257\) −5.67507 −0.354001 −0.177001 0.984211i \(-0.556639\pi\)
−0.177001 + 0.984211i \(0.556639\pi\)
\(258\) −19.6096 −1.22084
\(259\) −17.8384 −1.10842
\(260\) −0.228072 −0.0141444
\(261\) 0.919440 0.0569119
\(262\) 16.4182 1.01432
\(263\) −23.2605 −1.43430 −0.717151 0.696917i \(-0.754554\pi\)
−0.717151 + 0.696917i \(0.754554\pi\)
\(264\) −9.09302 −0.559637
\(265\) −0.641520 −0.0394083
\(266\) −30.5196 −1.87127
\(267\) 19.3078 1.18162
\(268\) 15.7797 0.963898
\(269\) −3.18536 −0.194215 −0.0971074 0.995274i \(-0.530959\pi\)
−0.0971074 + 0.995274i \(0.530959\pi\)
\(270\) 1.13927 0.0693337
\(271\) −25.4698 −1.54718 −0.773589 0.633687i \(-0.781541\pi\)
−0.773589 + 0.633687i \(0.781541\pi\)
\(272\) −3.80403 −0.230653
\(273\) 7.66848 0.464117
\(274\) −22.5222 −1.36061
\(275\) 27.4167 1.65329
\(276\) −4.85076 −0.291981
\(277\) 16.5221 0.992719 0.496359 0.868117i \(-0.334670\pi\)
0.496359 + 0.868117i \(0.334670\pi\)
\(278\) 12.3368 0.739912
\(279\) −1.98062 −0.118576
\(280\) −0.903343 −0.0539851
\(281\) −26.9021 −1.60485 −0.802424 0.596755i \(-0.796457\pi\)
−0.802424 + 0.596755i \(0.796457\pi\)
\(282\) −11.1799 −0.665752
\(283\) −6.89172 −0.409670 −0.204835 0.978796i \(-0.565666\pi\)
−0.204835 + 0.978796i \(0.565666\pi\)
\(284\) −5.51340 −0.327160
\(285\) −2.45223 −0.145257
\(286\) 6.00422 0.355037
\(287\) −11.7684 −0.694669
\(288\) 0.298402 0.0175835
\(289\) −2.52937 −0.148786
\(290\) −0.647491 −0.0380220
\(291\) 1.54889 0.0907978
\(292\) 3.31672 0.194096
\(293\) 16.9443 0.989895 0.494948 0.868923i \(-0.335187\pi\)
0.494948 + 0.868923i \(0.335187\pi\)
\(294\) 18.8676 1.10038
\(295\) 1.99536 0.116175
\(296\) −4.14968 −0.241195
\(297\) −29.9924 −1.74034
\(298\) −3.36969 −0.195201
\(299\) 3.20301 0.185235
\(300\) 8.14569 0.470291
\(301\) 51.2859 2.95607
\(302\) −19.6668 −1.13170
\(303\) −26.1037 −1.49962
\(304\) −7.09967 −0.407194
\(305\) 0.567666 0.0325045
\(306\) −1.13513 −0.0648911
\(307\) 26.7963 1.52934 0.764672 0.644420i \(-0.222901\pi\)
0.764672 + 0.644420i \(0.222901\pi\)
\(308\) 23.7814 1.35507
\(309\) 1.30959 0.0744998
\(310\) 1.39480 0.0792191
\(311\) 10.1369 0.574810 0.287405 0.957809i \(-0.407207\pi\)
0.287405 + 0.957809i \(0.407207\pi\)
\(312\) 1.78389 0.100993
\(313\) 7.82461 0.442273 0.221136 0.975243i \(-0.429023\pi\)
0.221136 + 0.975243i \(0.429023\pi\)
\(314\) −22.7381 −1.28319
\(315\) −0.269560 −0.0151880
\(316\) −7.06174 −0.397254
\(317\) −29.0296 −1.63046 −0.815231 0.579136i \(-0.803390\pi\)
−0.815231 + 0.579136i \(0.803390\pi\)
\(318\) 5.01774 0.281381
\(319\) 17.0459 0.954385
\(320\) −0.210142 −0.0117473
\(321\) 23.5935 1.31686
\(322\) 12.6864 0.706987
\(323\) 27.0073 1.50273
\(324\) −8.01575 −0.445319
\(325\) −5.37868 −0.298356
\(326\) 0.524356 0.0290414
\(327\) −10.7126 −0.592409
\(328\) −2.73766 −0.151162
\(329\) 29.2393 1.61202
\(330\) 1.91082 0.105187
\(331\) −14.7746 −0.812087 −0.406044 0.913854i \(-0.633092\pi\)
−0.406044 + 0.913854i \(0.633092\pi\)
\(332\) 4.61960 0.253534
\(333\) −1.23827 −0.0678570
\(334\) −7.09344 −0.388136
\(335\) −3.31597 −0.181171
\(336\) 7.06562 0.385461
\(337\) −8.26719 −0.450342 −0.225171 0.974319i \(-0.572294\pi\)
−0.225171 + 0.974319i \(0.572294\pi\)
\(338\) 11.8221 0.643036
\(339\) −3.28175 −0.178240
\(340\) 0.799386 0.0433528
\(341\) −36.7194 −1.98847
\(342\) −2.11856 −0.114558
\(343\) −19.2544 −1.03964
\(344\) 11.9305 0.643248
\(345\) 1.01935 0.0548798
\(346\) 20.1340 1.08241
\(347\) −10.9550 −0.588095 −0.294048 0.955791i \(-0.595002\pi\)
−0.294048 + 0.955791i \(0.595002\pi\)
\(348\) 5.06444 0.271482
\(349\) −7.67321 −0.410737 −0.205369 0.978685i \(-0.565839\pi\)
−0.205369 + 0.978685i \(0.565839\pi\)
\(350\) −21.3038 −1.13874
\(351\) 5.88400 0.314065
\(352\) 5.53220 0.294867
\(353\) −18.3730 −0.977895 −0.488947 0.872313i \(-0.662619\pi\)
−0.488947 + 0.872313i \(0.662619\pi\)
\(354\) −15.6070 −0.829504
\(355\) 1.15860 0.0614919
\(356\) −11.7469 −0.622583
\(357\) −26.8778 −1.42253
\(358\) 13.3020 0.703035
\(359\) −19.6442 −1.03678 −0.518391 0.855144i \(-0.673469\pi\)
−0.518391 + 0.855144i \(0.673469\pi\)
\(360\) −0.0627068 −0.00330494
\(361\) 31.4053 1.65291
\(362\) 18.2102 0.957105
\(363\) −32.2242 −1.69133
\(364\) −4.66551 −0.244539
\(365\) −0.696982 −0.0364817
\(366\) −4.44008 −0.232087
\(367\) 21.5291 1.12381 0.561904 0.827203i \(-0.310069\pi\)
0.561904 + 0.827203i \(0.310069\pi\)
\(368\) 2.95120 0.153842
\(369\) −0.816923 −0.0425273
\(370\) 0.872021 0.0453342
\(371\) −13.1231 −0.681320
\(372\) −10.9096 −0.565636
\(373\) −14.6387 −0.757963 −0.378981 0.925404i \(-0.623726\pi\)
−0.378981 + 0.925404i \(0.623726\pi\)
\(374\) −21.0446 −1.08819
\(375\) −3.43875 −0.177576
\(376\) 6.80185 0.350778
\(377\) −3.34410 −0.172230
\(378\) 23.3053 1.19869
\(379\) −2.19800 −0.112904 −0.0564519 0.998405i \(-0.517979\pi\)
−0.0564519 + 0.998405i \(0.517979\pi\)
\(380\) 1.49194 0.0765348
\(381\) −17.8441 −0.914183
\(382\) −15.2620 −0.780869
\(383\) −19.2884 −0.985590 −0.492795 0.870145i \(-0.664025\pi\)
−0.492795 + 0.870145i \(0.664025\pi\)
\(384\) 1.64365 0.0838774
\(385\) −4.99747 −0.254695
\(386\) 9.87710 0.502731
\(387\) 3.56008 0.180969
\(388\) −0.942349 −0.0478405
\(389\) −22.3365 −1.13251 −0.566253 0.824232i \(-0.691607\pi\)
−0.566253 + 0.824232i \(0.691607\pi\)
\(390\) −0.374871 −0.0189823
\(391\) −11.2265 −0.567747
\(392\) −11.4791 −0.579781
\(393\) 26.9858 1.36126
\(394\) −17.9712 −0.905376
\(395\) 1.48397 0.0746665
\(396\) 1.65082 0.0829569
\(397\) 33.8282 1.69779 0.848895 0.528562i \(-0.177268\pi\)
0.848895 + 0.528562i \(0.177268\pi\)
\(398\) −22.5180 −1.12873
\(399\) −50.1636 −2.51132
\(400\) −4.95584 −0.247792
\(401\) 26.8410 1.34038 0.670188 0.742192i \(-0.266214\pi\)
0.670188 + 0.742192i \(0.266214\pi\)
\(402\) 25.9363 1.29359
\(403\) 7.20372 0.358843
\(404\) 15.8815 0.790134
\(405\) 1.68444 0.0837007
\(406\) −13.2453 −0.657352
\(407\) −22.9568 −1.13793
\(408\) −6.25251 −0.309545
\(409\) −15.4994 −0.766397 −0.383199 0.923666i \(-0.625178\pi\)
−0.383199 + 0.923666i \(0.625178\pi\)
\(410\) 0.575296 0.0284119
\(411\) −37.0187 −1.82600
\(412\) −0.796754 −0.0392532
\(413\) 40.8178 2.00851
\(414\) 0.880646 0.0432814
\(415\) −0.970772 −0.0476533
\(416\) −1.08532 −0.0532123
\(417\) 20.2774 0.992990
\(418\) −39.2768 −1.92109
\(419\) 10.4030 0.508218 0.254109 0.967176i \(-0.418218\pi\)
0.254109 + 0.967176i \(0.418218\pi\)
\(420\) −1.48478 −0.0724500
\(421\) −9.76094 −0.475719 −0.237860 0.971300i \(-0.576446\pi\)
−0.237860 + 0.971300i \(0.576446\pi\)
\(422\) −7.71129 −0.375380
\(423\) 2.02969 0.0986868
\(424\) −3.05280 −0.148257
\(425\) 18.8522 0.914464
\(426\) −9.06212 −0.439061
\(427\) 11.6124 0.561962
\(428\) −14.3543 −0.693842
\(429\) 9.86885 0.476473
\(430\) −2.50709 −0.120903
\(431\) −9.18053 −0.442210 −0.221105 0.975250i \(-0.570966\pi\)
−0.221105 + 0.975250i \(0.570966\pi\)
\(432\) 5.42143 0.260839
\(433\) 26.8684 1.29121 0.645607 0.763670i \(-0.276604\pi\)
0.645607 + 0.763670i \(0.276604\pi\)
\(434\) 28.5324 1.36960
\(435\) −1.06425 −0.0510269
\(436\) 6.51756 0.312134
\(437\) −20.9526 −1.00230
\(438\) 5.45154 0.260485
\(439\) 21.0844 1.00630 0.503152 0.864198i \(-0.332174\pi\)
0.503152 + 0.864198i \(0.332174\pi\)
\(440\) −1.16255 −0.0554222
\(441\) −3.42539 −0.163114
\(442\) 4.12860 0.196377
\(443\) −37.0110 −1.75845 −0.879223 0.476410i \(-0.841938\pi\)
−0.879223 + 0.476410i \(0.841938\pi\)
\(444\) −6.82064 −0.323693
\(445\) 2.46851 0.117019
\(446\) −7.65080 −0.362276
\(447\) −5.53860 −0.261967
\(448\) −4.29873 −0.203096
\(449\) −0.401494 −0.0189477 −0.00947384 0.999955i \(-0.503016\pi\)
−0.00947384 + 0.999955i \(0.503016\pi\)
\(450\) −1.47883 −0.0697129
\(451\) −15.1453 −0.713162
\(452\) 1.99662 0.0939129
\(453\) −32.3254 −1.51878
\(454\) 13.2776 0.623149
\(455\) 0.980418 0.0459627
\(456\) −11.6694 −0.546470
\(457\) −15.4830 −0.724265 −0.362133 0.932127i \(-0.617951\pi\)
−0.362133 + 0.932127i \(0.617951\pi\)
\(458\) 6.61574 0.309133
\(459\) −20.6233 −0.962612
\(460\) −0.620171 −0.0289156
\(461\) 13.4457 0.626229 0.313115 0.949715i \(-0.398628\pi\)
0.313115 + 0.949715i \(0.398628\pi\)
\(462\) 39.0884 1.81856
\(463\) 37.6315 1.74888 0.874442 0.485130i \(-0.161228\pi\)
0.874442 + 0.485130i \(0.161228\pi\)
\(464\) −3.08121 −0.143041
\(465\) 2.29256 0.106315
\(466\) 17.6112 0.815821
\(467\) 30.1127 1.39345 0.696725 0.717338i \(-0.254640\pi\)
0.696725 + 0.717338i \(0.254640\pi\)
\(468\) −0.323863 −0.0149706
\(469\) −67.8326 −3.13222
\(470\) −1.42935 −0.0659311
\(471\) −37.3736 −1.72208
\(472\) 9.49532 0.437058
\(473\) 66.0018 3.03477
\(474\) −11.6071 −0.533130
\(475\) 35.1848 1.61439
\(476\) 16.3525 0.749515
\(477\) −0.910961 −0.0417100
\(478\) −4.20632 −0.192393
\(479\) 3.74467 0.171098 0.0855491 0.996334i \(-0.472736\pi\)
0.0855491 + 0.996334i \(0.472736\pi\)
\(480\) −0.345400 −0.0157653
\(481\) 4.50374 0.205353
\(482\) 24.0169 1.09394
\(483\) 20.8521 0.948803
\(484\) 19.6052 0.891146
\(485\) 0.198027 0.00899194
\(486\) 3.08918 0.140128
\(487\) 14.1799 0.642552 0.321276 0.946986i \(-0.395888\pi\)
0.321276 + 0.946986i \(0.395888\pi\)
\(488\) 2.70135 0.122284
\(489\) 0.861860 0.0389747
\(490\) 2.41224 0.108974
\(491\) −34.2896 −1.54747 −0.773734 0.633511i \(-0.781613\pi\)
−0.773734 + 0.633511i \(0.781613\pi\)
\(492\) −4.49976 −0.202865
\(493\) 11.7210 0.527887
\(494\) 7.70543 0.346683
\(495\) −0.346907 −0.0155923
\(496\) 6.63740 0.298028
\(497\) 23.7006 1.06312
\(498\) 7.59303 0.340252
\(499\) 11.8419 0.530115 0.265057 0.964233i \(-0.414609\pi\)
0.265057 + 0.964233i \(0.414609\pi\)
\(500\) 2.09214 0.0935633
\(501\) −11.6592 −0.520893
\(502\) 15.5276 0.693029
\(503\) −2.80121 −0.124900 −0.0624499 0.998048i \(-0.519891\pi\)
−0.0624499 + 0.998048i \(0.519891\pi\)
\(504\) −1.28275 −0.0571383
\(505\) −3.33737 −0.148511
\(506\) 16.3266 0.725808
\(507\) 19.4314 0.862979
\(508\) 10.8564 0.481674
\(509\) 6.49918 0.288071 0.144036 0.989573i \(-0.453992\pi\)
0.144036 + 0.989573i \(0.453992\pi\)
\(510\) 1.31391 0.0581811
\(511\) −14.2577 −0.630723
\(512\) −1.00000 −0.0441942
\(513\) −38.4904 −1.69939
\(514\) 5.67507 0.250317
\(515\) 0.167431 0.00737790
\(516\) 19.6096 0.863264
\(517\) 37.6292 1.65493
\(518\) 17.8384 0.783772
\(519\) 33.0934 1.45264
\(520\) 0.228072 0.0100016
\(521\) 25.8051 1.13054 0.565271 0.824905i \(-0.308772\pi\)
0.565271 + 0.824905i \(0.308772\pi\)
\(522\) −0.919440 −0.0402428
\(523\) 22.5447 0.985812 0.492906 0.870083i \(-0.335935\pi\)
0.492906 + 0.870083i \(0.335935\pi\)
\(524\) −16.4182 −0.717232
\(525\) −35.0161 −1.52823
\(526\) 23.2605 1.01421
\(527\) −25.2489 −1.09986
\(528\) 9.09302 0.395723
\(529\) −14.2904 −0.621322
\(530\) 0.641520 0.0278658
\(531\) 2.83343 0.122960
\(532\) 30.5196 1.32319
\(533\) 2.97124 0.128699
\(534\) −19.3078 −0.835530
\(535\) 3.01644 0.130412
\(536\) −15.7797 −0.681579
\(537\) 21.8640 0.943499
\(538\) 3.18536 0.137331
\(539\) −63.5046 −2.73534
\(540\) −1.13927 −0.0490264
\(541\) 15.9763 0.686876 0.343438 0.939175i \(-0.388408\pi\)
0.343438 + 0.939175i \(0.388408\pi\)
\(542\) 25.4698 1.09402
\(543\) 29.9312 1.28447
\(544\) 3.80403 0.163096
\(545\) −1.36961 −0.0586677
\(546\) −7.66848 −0.328181
\(547\) 7.75254 0.331475 0.165737 0.986170i \(-0.447000\pi\)
0.165737 + 0.986170i \(0.447000\pi\)
\(548\) 22.5222 0.962100
\(549\) 0.806088 0.0344030
\(550\) −27.4167 −1.16905
\(551\) 21.8756 0.931930
\(552\) 4.85076 0.206462
\(553\) 30.3565 1.29089
\(554\) −16.5221 −0.701958
\(555\) 1.43330 0.0608402
\(556\) −12.3368 −0.523197
\(557\) −3.24760 −0.137605 −0.0688026 0.997630i \(-0.521918\pi\)
−0.0688026 + 0.997630i \(0.521918\pi\)
\(558\) 1.98062 0.0838462
\(559\) −12.9484 −0.547660
\(560\) 0.903343 0.0381732
\(561\) −34.5901 −1.46040
\(562\) 26.9021 1.13480
\(563\) 14.7866 0.623183 0.311591 0.950216i \(-0.399138\pi\)
0.311591 + 0.950216i \(0.399138\pi\)
\(564\) 11.1799 0.470758
\(565\) −0.419573 −0.0176516
\(566\) 6.89172 0.289681
\(567\) 34.4575 1.44708
\(568\) 5.51340 0.231337
\(569\) −17.0785 −0.715970 −0.357985 0.933727i \(-0.616536\pi\)
−0.357985 + 0.933727i \(0.616536\pi\)
\(570\) 2.45223 0.102713
\(571\) 14.4469 0.604585 0.302293 0.953215i \(-0.402248\pi\)
0.302293 + 0.953215i \(0.402248\pi\)
\(572\) −6.00422 −0.251049
\(573\) −25.0854 −1.04796
\(574\) 11.7684 0.491205
\(575\) −14.6257 −0.609934
\(576\) −0.298402 −0.0124334
\(577\) 31.9489 1.33005 0.665024 0.746822i \(-0.268421\pi\)
0.665024 + 0.746822i \(0.268421\pi\)
\(578\) 2.52937 0.105208
\(579\) 16.2345 0.674684
\(580\) 0.647491 0.0268856
\(581\) −19.8584 −0.823866
\(582\) −1.54889 −0.0642038
\(583\) −16.8887 −0.699457
\(584\) −3.31672 −0.137247
\(585\) 0.0680571 0.00281381
\(586\) −16.9443 −0.699962
\(587\) −12.9026 −0.532548 −0.266274 0.963897i \(-0.585793\pi\)
−0.266274 + 0.963897i \(0.585793\pi\)
\(588\) −18.8676 −0.778088
\(589\) −47.1233 −1.94168
\(590\) −1.99536 −0.0821478
\(591\) −29.5384 −1.21505
\(592\) 4.14968 0.170551
\(593\) 21.6512 0.889108 0.444554 0.895752i \(-0.353362\pi\)
0.444554 + 0.895752i \(0.353362\pi\)
\(594\) 29.9924 1.23060
\(595\) −3.43634 −0.140876
\(596\) 3.36969 0.138028
\(597\) −37.0118 −1.51479
\(598\) −3.20301 −0.130981
\(599\) −37.8688 −1.54728 −0.773640 0.633626i \(-0.781566\pi\)
−0.773640 + 0.633626i \(0.781566\pi\)
\(600\) −8.14569 −0.332546
\(601\) 7.71790 0.314820 0.157410 0.987533i \(-0.449686\pi\)
0.157410 + 0.987533i \(0.449686\pi\)
\(602\) −51.2859 −2.09026
\(603\) −4.70869 −0.191753
\(604\) 19.6668 0.800230
\(605\) −4.11988 −0.167497
\(606\) 26.1037 1.06039
\(607\) 11.5734 0.469750 0.234875 0.972026i \(-0.424532\pi\)
0.234875 + 0.972026i \(0.424532\pi\)
\(608\) 7.09967 0.287930
\(609\) −21.7707 −0.882192
\(610\) −0.567666 −0.0229841
\(611\) −7.38219 −0.298652
\(612\) 1.13513 0.0458850
\(613\) −11.2636 −0.454934 −0.227467 0.973786i \(-0.573044\pi\)
−0.227467 + 0.973786i \(0.573044\pi\)
\(614\) −26.7963 −1.08141
\(615\) 0.945588 0.0381298
\(616\) −23.7814 −0.958181
\(617\) −33.5643 −1.35125 −0.675625 0.737246i \(-0.736126\pi\)
−0.675625 + 0.737246i \(0.736126\pi\)
\(618\) −1.30959 −0.0526793
\(619\) −33.2642 −1.33700 −0.668501 0.743711i \(-0.733064\pi\)
−0.668501 + 0.743711i \(0.733064\pi\)
\(620\) −1.39480 −0.0560163
\(621\) 15.9997 0.642048
\(622\) −10.1369 −0.406452
\(623\) 50.4966 2.02311
\(624\) −1.78389 −0.0714129
\(625\) 24.3396 0.973582
\(626\) −7.82461 −0.312734
\(627\) −64.5574 −2.57818
\(628\) 22.7381 0.907349
\(629\) −15.7855 −0.629409
\(630\) 0.269560 0.0107395
\(631\) −5.81031 −0.231305 −0.115652 0.993290i \(-0.536896\pi\)
−0.115652 + 0.993290i \(0.536896\pi\)
\(632\) 7.06174 0.280901
\(633\) −12.6747 −0.503774
\(634\) 29.0296 1.15291
\(635\) −2.28138 −0.0905338
\(636\) −5.01774 −0.198966
\(637\) 12.4585 0.493624
\(638\) −17.0459 −0.674852
\(639\) 1.64521 0.0650835
\(640\) 0.210142 0.00830659
\(641\) 11.1411 0.440049 0.220024 0.975494i \(-0.429386\pi\)
0.220024 + 0.975494i \(0.429386\pi\)
\(642\) −23.5935 −0.931162
\(643\) 16.1937 0.638617 0.319309 0.947651i \(-0.396549\pi\)
0.319309 + 0.947651i \(0.396549\pi\)
\(644\) −12.6864 −0.499915
\(645\) −4.12079 −0.162256
\(646\) −27.0073 −1.06259
\(647\) −6.74976 −0.265360 −0.132680 0.991159i \(-0.542358\pi\)
−0.132680 + 0.991159i \(0.542358\pi\)
\(648\) 8.01575 0.314888
\(649\) 52.5300 2.06198
\(650\) 5.37868 0.210969
\(651\) 46.8974 1.83805
\(652\) −0.524356 −0.0205354
\(653\) −4.57421 −0.179003 −0.0895014 0.995987i \(-0.528527\pi\)
−0.0895014 + 0.995987i \(0.528527\pi\)
\(654\) 10.7126 0.418896
\(655\) 3.45015 0.134809
\(656\) 2.73766 0.106888
\(657\) −0.989718 −0.0386126
\(658\) −29.2393 −1.13987
\(659\) 1.97216 0.0768244 0.0384122 0.999262i \(-0.487770\pi\)
0.0384122 + 0.999262i \(0.487770\pi\)
\(660\) −1.91082 −0.0743787
\(661\) 17.3944 0.676564 0.338282 0.941045i \(-0.390154\pi\)
0.338282 + 0.941045i \(0.390154\pi\)
\(662\) 14.7746 0.574232
\(663\) 6.78598 0.263546
\(664\) −4.61960 −0.179275
\(665\) −6.41344 −0.248702
\(666\) 1.23827 0.0479821
\(667\) −9.09327 −0.352093
\(668\) 7.09344 0.274453
\(669\) −12.5753 −0.486188
\(670\) 3.31597 0.128107
\(671\) 14.9444 0.576922
\(672\) −7.06562 −0.272562
\(673\) 24.4371 0.941980 0.470990 0.882138i \(-0.343897\pi\)
0.470990 + 0.882138i \(0.343897\pi\)
\(674\) 8.26719 0.318440
\(675\) −26.8677 −1.03414
\(676\) −11.8221 −0.454695
\(677\) −45.1930 −1.73691 −0.868454 0.495771i \(-0.834886\pi\)
−0.868454 + 0.495771i \(0.834886\pi\)
\(678\) 3.28175 0.126035
\(679\) 4.05090 0.155459
\(680\) −0.799386 −0.0306550
\(681\) 21.8238 0.836290
\(682\) 36.7194 1.40606
\(683\) 17.9571 0.687108 0.343554 0.939133i \(-0.388369\pi\)
0.343554 + 0.939133i \(0.388369\pi\)
\(684\) 2.11856 0.0810051
\(685\) −4.73285 −0.180833
\(686\) 19.2544 0.735136
\(687\) 10.8740 0.414868
\(688\) −11.9305 −0.454845
\(689\) 3.31327 0.126225
\(690\) −1.01935 −0.0388059
\(691\) 26.8021 1.01960 0.509801 0.860292i \(-0.329719\pi\)
0.509801 + 0.860292i \(0.329719\pi\)
\(692\) −20.1340 −0.765381
\(693\) −7.09644 −0.269571
\(694\) 10.9550 0.415846
\(695\) 2.59248 0.0983383
\(696\) −5.06444 −0.191967
\(697\) −10.4141 −0.394463
\(698\) 7.67321 0.290435
\(699\) 28.9466 1.09486
\(700\) 21.3038 0.805209
\(701\) 29.2426 1.10448 0.552238 0.833687i \(-0.313774\pi\)
0.552238 + 0.833687i \(0.313774\pi\)
\(702\) −5.88400 −0.222077
\(703\) −29.4613 −1.11116
\(704\) −5.53220 −0.208503
\(705\) −2.34936 −0.0884821
\(706\) 18.3730 0.691476
\(707\) −68.2702 −2.56757
\(708\) 15.6070 0.586548
\(709\) −12.8858 −0.483935 −0.241967 0.970284i \(-0.577793\pi\)
−0.241967 + 0.970284i \(0.577793\pi\)
\(710\) −1.15860 −0.0434813
\(711\) 2.10724 0.0790277
\(712\) 11.7469 0.440233
\(713\) 19.5883 0.733588
\(714\) 26.8778 1.00588
\(715\) 1.26174 0.0471863
\(716\) −13.3020 −0.497121
\(717\) −6.91373 −0.258198
\(718\) 19.6442 0.733115
\(719\) 8.42286 0.314120 0.157060 0.987589i \(-0.449798\pi\)
0.157060 + 0.987589i \(0.449798\pi\)
\(720\) 0.0627068 0.00233695
\(721\) 3.42503 0.127555
\(722\) −31.4053 −1.16878
\(723\) 39.4754 1.46811
\(724\) −18.2102 −0.676776
\(725\) 15.2700 0.567113
\(726\) 32.2242 1.19595
\(727\) −23.7113 −0.879405 −0.439702 0.898144i \(-0.644916\pi\)
−0.439702 + 0.898144i \(0.644916\pi\)
\(728\) 4.66551 0.172915
\(729\) 29.1248 1.07870
\(730\) 0.696982 0.0257965
\(731\) 45.3839 1.67858
\(732\) 4.44008 0.164110
\(733\) −1.53367 −0.0566473 −0.0283236 0.999599i \(-0.509017\pi\)
−0.0283236 + 0.999599i \(0.509017\pi\)
\(734\) −21.5291 −0.794652
\(735\) 3.96488 0.146247
\(736\) −2.95120 −0.108783
\(737\) −87.2963 −3.21560
\(738\) 0.816923 0.0300714
\(739\) −28.6951 −1.05557 −0.527783 0.849380i \(-0.676976\pi\)
−0.527783 + 0.849380i \(0.676976\pi\)
\(740\) −0.872021 −0.0320561
\(741\) 12.6651 0.465262
\(742\) 13.1231 0.481766
\(743\) 38.6729 1.41877 0.709385 0.704821i \(-0.248973\pi\)
0.709385 + 0.704821i \(0.248973\pi\)
\(744\) 10.9096 0.399965
\(745\) −0.708113 −0.0259433
\(746\) 14.6387 0.535960
\(747\) −1.37850 −0.0504367
\(748\) 21.0446 0.769468
\(749\) 61.7053 2.25466
\(750\) 3.43875 0.125565
\(751\) 1.00000 0.0364905
\(752\) −6.80185 −0.248038
\(753\) 25.5219 0.930072
\(754\) 3.34410 0.121785
\(755\) −4.13281 −0.150408
\(756\) −23.3053 −0.847605
\(757\) −26.2491 −0.954040 −0.477020 0.878892i \(-0.658283\pi\)
−0.477020 + 0.878892i \(0.658283\pi\)
\(758\) 2.19800 0.0798350
\(759\) 26.8354 0.974062
\(760\) −1.49194 −0.0541183
\(761\) 40.8421 1.48053 0.740263 0.672317i \(-0.234701\pi\)
0.740263 + 0.672317i \(0.234701\pi\)
\(762\) 17.8441 0.646425
\(763\) −28.0172 −1.01429
\(764\) 15.2620 0.552158
\(765\) −0.238539 −0.00862438
\(766\) 19.2884 0.696917
\(767\) −10.3055 −0.372109
\(768\) −1.64365 −0.0593102
\(769\) 1.81384 0.0654088 0.0327044 0.999465i \(-0.489588\pi\)
0.0327044 + 0.999465i \(0.489588\pi\)
\(770\) 4.99747 0.180096
\(771\) 9.32785 0.335934
\(772\) −9.87710 −0.355485
\(773\) −34.5877 −1.24403 −0.622016 0.783004i \(-0.713686\pi\)
−0.622016 + 0.783004i \(0.713686\pi\)
\(774\) −3.56008 −0.127965
\(775\) −32.8939 −1.18158
\(776\) 0.942349 0.0338283
\(777\) 29.3201 1.05185
\(778\) 22.3365 0.800802
\(779\) −19.4365 −0.696383
\(780\) 0.374871 0.0134225
\(781\) 30.5012 1.09142
\(782\) 11.2265 0.401458
\(783\) −16.7046 −0.596972
\(784\) 11.4791 0.409967
\(785\) −4.77823 −0.170542
\(786\) −26.9858 −0.962553
\(787\) −9.25606 −0.329943 −0.164972 0.986298i \(-0.552753\pi\)
−0.164972 + 0.986298i \(0.552753\pi\)
\(788\) 17.9712 0.640197
\(789\) 38.2322 1.36110
\(790\) −1.48397 −0.0527972
\(791\) −8.58292 −0.305173
\(792\) −1.65082 −0.0586594
\(793\) −2.93183 −0.104112
\(794\) −33.8282 −1.20052
\(795\) 1.05444 0.0373970
\(796\) 22.5180 0.798129
\(797\) −49.7407 −1.76191 −0.880953 0.473204i \(-0.843097\pi\)
−0.880953 + 0.473204i \(0.843097\pi\)
\(798\) 50.1636 1.77577
\(799\) 25.8744 0.915371
\(800\) 4.95584 0.175215
\(801\) 3.50529 0.123853
\(802\) −26.8410 −0.947789
\(803\) −18.3488 −0.647514
\(804\) −25.9363 −0.914704
\(805\) 2.66595 0.0939624
\(806\) −7.20372 −0.253740
\(807\) 5.23563 0.184303
\(808\) −15.8815 −0.558709
\(809\) 13.3531 0.469469 0.234734 0.972060i \(-0.424578\pi\)
0.234734 + 0.972060i \(0.424578\pi\)
\(810\) −1.68444 −0.0591853
\(811\) 3.83503 0.134666 0.0673330 0.997731i \(-0.478551\pi\)
0.0673330 + 0.997731i \(0.478551\pi\)
\(812\) 13.2453 0.464818
\(813\) 41.8635 1.46822
\(814\) 22.9568 0.804637
\(815\) 0.110189 0.00385976
\(816\) 6.25251 0.218881
\(817\) 84.7025 2.96336
\(818\) 15.4994 0.541925
\(819\) 1.39220 0.0486473
\(820\) −0.575296 −0.0200902
\(821\) −15.3533 −0.535832 −0.267916 0.963442i \(-0.586335\pi\)
−0.267916 + 0.963442i \(0.586335\pi\)
\(822\) 37.0187 1.29117
\(823\) −29.9003 −1.04226 −0.521129 0.853478i \(-0.674489\pi\)
−0.521129 + 0.853478i \(0.674489\pi\)
\(824\) 0.796754 0.0277562
\(825\) −45.0636 −1.56891
\(826\) −40.8178 −1.42023
\(827\) 53.7563 1.86929 0.934644 0.355585i \(-0.115718\pi\)
0.934644 + 0.355585i \(0.115718\pi\)
\(828\) −0.880646 −0.0306046
\(829\) 6.40991 0.222625 0.111313 0.993785i \(-0.464494\pi\)
0.111313 + 0.993785i \(0.464494\pi\)
\(830\) 0.970772 0.0336960
\(831\) −27.1567 −0.942054
\(832\) 1.08532 0.0376268
\(833\) −43.6668 −1.51296
\(834\) −20.2774 −0.702150
\(835\) −1.49063 −0.0515853
\(836\) 39.2768 1.35842
\(837\) 35.9842 1.24380
\(838\) −10.4030 −0.359365
\(839\) 12.4566 0.430048 0.215024 0.976609i \(-0.431017\pi\)
0.215024 + 0.976609i \(0.431017\pi\)
\(840\) 1.48478 0.0512299
\(841\) −19.5062 −0.672626
\(842\) 9.76094 0.336384
\(843\) 44.2178 1.52294
\(844\) 7.71129 0.265433
\(845\) 2.48431 0.0854630
\(846\) −2.02969 −0.0697821
\(847\) −84.2776 −2.89581
\(848\) 3.05280 0.104833
\(849\) 11.3276 0.388763
\(850\) −18.8522 −0.646624
\(851\) 12.2465 0.419806
\(852\) 9.06212 0.310463
\(853\) 25.3375 0.867539 0.433769 0.901024i \(-0.357183\pi\)
0.433769 + 0.901024i \(0.357183\pi\)
\(854\) −11.6124 −0.397367
\(855\) −0.445198 −0.0152254
\(856\) 14.3543 0.490620
\(857\) 18.0280 0.615826 0.307913 0.951415i \(-0.400369\pi\)
0.307913 + 0.951415i \(0.400369\pi\)
\(858\) −9.86885 −0.336917
\(859\) −12.7900 −0.436389 −0.218195 0.975905i \(-0.570017\pi\)
−0.218195 + 0.975905i \(0.570017\pi\)
\(860\) 2.50709 0.0854912
\(861\) 19.3433 0.659216
\(862\) 9.18053 0.312690
\(863\) 34.9638 1.19018 0.595090 0.803659i \(-0.297116\pi\)
0.595090 + 0.803659i \(0.297116\pi\)
\(864\) −5.42143 −0.184441
\(865\) 4.23101 0.143858
\(866\) −26.8684 −0.913026
\(867\) 4.15740 0.141193
\(868\) −28.5324 −0.968453
\(869\) 39.0670 1.32526
\(870\) 1.06425 0.0360815
\(871\) 17.1260 0.580294
\(872\) −6.51756 −0.220712
\(873\) 0.281199 0.00951715
\(874\) 20.9526 0.708731
\(875\) −8.99354 −0.304037
\(876\) −5.45154 −0.184191
\(877\) −23.9968 −0.810313 −0.405157 0.914247i \(-0.632783\pi\)
−0.405157 + 0.914247i \(0.632783\pi\)
\(878\) −21.0844 −0.711564
\(879\) −27.8505 −0.939375
\(880\) 1.16255 0.0391894
\(881\) −12.6147 −0.425001 −0.212500 0.977161i \(-0.568161\pi\)
−0.212500 + 0.977161i \(0.568161\pi\)
\(882\) 3.42539 0.115339
\(883\) −14.7897 −0.497712 −0.248856 0.968541i \(-0.580055\pi\)
−0.248856 + 0.968541i \(0.580055\pi\)
\(884\) −4.12860 −0.138860
\(885\) −3.27969 −0.110246
\(886\) 37.0110 1.24341
\(887\) 22.7477 0.763793 0.381896 0.924205i \(-0.375271\pi\)
0.381896 + 0.924205i \(0.375271\pi\)
\(888\) 6.82064 0.228886
\(889\) −46.6687 −1.56522
\(890\) −2.46851 −0.0827446
\(891\) 44.3447 1.48560
\(892\) 7.65080 0.256168
\(893\) 48.2909 1.61599
\(894\) 5.53860 0.185239
\(895\) 2.79532 0.0934371
\(896\) 4.29873 0.143611
\(897\) −5.26463 −0.175781
\(898\) 0.401494 0.0133980
\(899\) −20.4512 −0.682086
\(900\) 1.47883 0.0492945
\(901\) −11.6129 −0.386882
\(902\) 15.1453 0.504282
\(903\) −84.2963 −2.80521
\(904\) −1.99662 −0.0664065
\(905\) 3.82672 0.127204
\(906\) 32.3254 1.07394
\(907\) −33.7575 −1.12090 −0.560450 0.828188i \(-0.689372\pi\)
−0.560450 + 0.828188i \(0.689372\pi\)
\(908\) −13.2776 −0.440633
\(909\) −4.73907 −0.157185
\(910\) −0.980418 −0.0325005
\(911\) 39.3121 1.30247 0.651235 0.758877i \(-0.274251\pi\)
0.651235 + 0.758877i \(0.274251\pi\)
\(912\) 11.6694 0.386412
\(913\) −25.5566 −0.845799
\(914\) 15.4830 0.512133
\(915\) −0.933047 −0.0308456
\(916\) −6.61574 −0.218590
\(917\) 70.5774 2.33067
\(918\) 20.6233 0.680670
\(919\) 35.7082 1.17791 0.588953 0.808167i \(-0.299540\pi\)
0.588953 + 0.808167i \(0.299540\pi\)
\(920\) 0.620171 0.0204464
\(921\) −44.0438 −1.45129
\(922\) −13.4457 −0.442811
\(923\) −5.98381 −0.196960
\(924\) −39.0884 −1.28592
\(925\) −20.5651 −0.676178
\(926\) −37.6315 −1.23665
\(927\) 0.237753 0.00780884
\(928\) 3.08121 0.101146
\(929\) 48.8337 1.60218 0.801091 0.598542i \(-0.204253\pi\)
0.801091 + 0.598542i \(0.204253\pi\)
\(930\) −2.29256 −0.0751760
\(931\) −81.4977 −2.67098
\(932\) −17.6112 −0.576873
\(933\) −16.6615 −0.545474
\(934\) −30.1127 −0.985318
\(935\) −4.42236 −0.144627
\(936\) 0.323863 0.0105858
\(937\) −36.5109 −1.19276 −0.596379 0.802703i \(-0.703395\pi\)
−0.596379 + 0.802703i \(0.703395\pi\)
\(938\) 67.8326 2.21481
\(939\) −12.8609 −0.419701
\(940\) 1.42935 0.0466203
\(941\) 3.25315 0.106050 0.0530249 0.998593i \(-0.483114\pi\)
0.0530249 + 0.998593i \(0.483114\pi\)
\(942\) 37.3736 1.21770
\(943\) 8.07938 0.263101
\(944\) −9.49532 −0.309046
\(945\) 4.89741 0.159313
\(946\) −66.0018 −2.14590
\(947\) 16.3429 0.531074 0.265537 0.964101i \(-0.414451\pi\)
0.265537 + 0.964101i \(0.414451\pi\)
\(948\) 11.6071 0.376980
\(949\) 3.59971 0.116852
\(950\) −35.1848 −1.14155
\(951\) 47.7145 1.54725
\(952\) −16.3525 −0.529987
\(953\) 35.3966 1.14661 0.573304 0.819343i \(-0.305662\pi\)
0.573304 + 0.819343i \(0.305662\pi\)
\(954\) 0.910961 0.0294935
\(955\) −3.20717 −0.103782
\(956\) 4.20632 0.136042
\(957\) −28.0175 −0.905677
\(958\) −3.74467 −0.120985
\(959\) −96.8168 −3.12638
\(960\) 0.345400 0.0111478
\(961\) 13.0551 0.421132
\(962\) −4.50374 −0.145206
\(963\) 4.28336 0.138029
\(964\) −24.0169 −0.773531
\(965\) 2.07559 0.0668157
\(966\) −20.8521 −0.670905
\(967\) 33.2805 1.07023 0.535115 0.844779i \(-0.320268\pi\)
0.535115 + 0.844779i \(0.320268\pi\)
\(968\) −19.6052 −0.630136
\(969\) −44.3907 −1.42604
\(970\) −0.198027 −0.00635826
\(971\) 48.2451 1.54826 0.774129 0.633028i \(-0.218188\pi\)
0.774129 + 0.633028i \(0.218188\pi\)
\(972\) −3.08918 −0.0990854
\(973\) 53.0326 1.70015
\(974\) −14.1799 −0.454353
\(975\) 8.84069 0.283129
\(976\) −2.70135 −0.0864680
\(977\) 19.4436 0.622056 0.311028 0.950401i \(-0.399327\pi\)
0.311028 + 0.950401i \(0.399327\pi\)
\(978\) −0.861860 −0.0275593
\(979\) 64.9860 2.07696
\(980\) −2.41224 −0.0770561
\(981\) −1.94485 −0.0620944
\(982\) 34.2896 1.09422
\(983\) −44.1183 −1.40716 −0.703578 0.710618i \(-0.748415\pi\)
−0.703578 + 0.710618i \(0.748415\pi\)
\(984\) 4.49976 0.143447
\(985\) −3.77650 −0.120329
\(986\) −11.7210 −0.373273
\(987\) −48.0593 −1.52974
\(988\) −7.70543 −0.245142
\(989\) −35.2093 −1.11959
\(990\) 0.346907 0.0110254
\(991\) 15.0817 0.479086 0.239543 0.970886i \(-0.423002\pi\)
0.239543 + 0.970886i \(0.423002\pi\)
\(992\) −6.63740 −0.210738
\(993\) 24.2844 0.770642
\(994\) −23.7006 −0.751738
\(995\) −4.73197 −0.150014
\(996\) −7.59303 −0.240594
\(997\) −28.0852 −0.889466 −0.444733 0.895663i \(-0.646701\pi\)
−0.444733 + 0.895663i \(0.646701\pi\)
\(998\) −11.8419 −0.374848
\(999\) 22.4972 0.711780
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.h.1.5 19
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1502.2.a.h.1.5 19 1.1 even 1 trivial