Properties

Label 2013.2.a.h.1.6
Level $2013$
Weight $2$
Character 2013.1
Self dual yes
Analytic conductor $16.074$
Analytic rank $0$
Dimension $14$
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] = [2013,2,Mod(1,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, 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("2013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.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: \(16.0738859269\)
Analytic rank: \(0\)
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: \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.546298\) of defining polynomial
Character \(\chi\) \(=\) 2013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.546298 q^{2} -1.00000 q^{3} -1.70156 q^{4} -0.842631 q^{5} +0.546298 q^{6} -4.19208 q^{7} +2.02216 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.546298 q^{2} -1.00000 q^{3} -1.70156 q^{4} -0.842631 q^{5} +0.546298 q^{6} -4.19208 q^{7} +2.02216 q^{8} +1.00000 q^{9} +0.460328 q^{10} -1.00000 q^{11} +1.70156 q^{12} -5.95974 q^{13} +2.29012 q^{14} +0.842631 q^{15} +2.29842 q^{16} +0.386200 q^{17} -0.546298 q^{18} -2.95453 q^{19} +1.43379 q^{20} +4.19208 q^{21} +0.546298 q^{22} -0.974992 q^{23} -2.02216 q^{24} -4.28997 q^{25} +3.25580 q^{26} -1.00000 q^{27} +7.13306 q^{28} -10.0563 q^{29} -0.460328 q^{30} -10.6290 q^{31} -5.29993 q^{32} +1.00000 q^{33} -0.210980 q^{34} +3.53237 q^{35} -1.70156 q^{36} -3.16781 q^{37} +1.61405 q^{38} +5.95974 q^{39} -1.70393 q^{40} -1.29317 q^{41} -2.29012 q^{42} -4.99709 q^{43} +1.70156 q^{44} -0.842631 q^{45} +0.532636 q^{46} +7.87272 q^{47} -2.29842 q^{48} +10.5735 q^{49} +2.34361 q^{50} -0.386200 q^{51} +10.1408 q^{52} +0.370002 q^{53} +0.546298 q^{54} +0.842631 q^{55} -8.47703 q^{56} +2.95453 q^{57} +5.49376 q^{58} +13.7723 q^{59} -1.43379 q^{60} +1.00000 q^{61} +5.80661 q^{62} -4.19208 q^{63} -1.70149 q^{64} +5.02186 q^{65} -0.546298 q^{66} +9.80901 q^{67} -0.657141 q^{68} +0.974992 q^{69} -1.92973 q^{70} -4.36706 q^{71} +2.02216 q^{72} -2.06518 q^{73} +1.73057 q^{74} +4.28997 q^{75} +5.02730 q^{76} +4.19208 q^{77} -3.25580 q^{78} -8.67552 q^{79} -1.93672 q^{80} +1.00000 q^{81} +0.706457 q^{82} -7.09673 q^{83} -7.13306 q^{84} -0.325424 q^{85} +2.72990 q^{86} +10.0563 q^{87} -2.02216 q^{88} -7.42432 q^{89} +0.460328 q^{90} +24.9837 q^{91} +1.65901 q^{92} +10.6290 q^{93} -4.30086 q^{94} +2.48957 q^{95} +5.29993 q^{96} -6.00940 q^{97} -5.77628 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.546298 −0.386291 −0.193146 0.981170i \(-0.561869\pi\)
−0.193146 + 0.981170i \(0.561869\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.70156 −0.850779
\(5\) −0.842631 −0.376836 −0.188418 0.982089i \(-0.560336\pi\)
−0.188418 + 0.982089i \(0.560336\pi\)
\(6\) 0.546298 0.223025
\(7\) −4.19208 −1.58446 −0.792228 0.610226i \(-0.791079\pi\)
−0.792228 + 0.610226i \(0.791079\pi\)
\(8\) 2.02216 0.714940
\(9\) 1.00000 0.333333
\(10\) 0.460328 0.145568
\(11\) −1.00000 −0.301511
\(12\) 1.70156 0.491198
\(13\) −5.95974 −1.65293 −0.826467 0.562985i \(-0.809653\pi\)
−0.826467 + 0.562985i \(0.809653\pi\)
\(14\) 2.29012 0.612061
\(15\) 0.842631 0.217566
\(16\) 2.29842 0.574604
\(17\) 0.386200 0.0936672 0.0468336 0.998903i \(-0.485087\pi\)
0.0468336 + 0.998903i \(0.485087\pi\)
\(18\) −0.546298 −0.128764
\(19\) −2.95453 −0.677815 −0.338907 0.940820i \(-0.610057\pi\)
−0.338907 + 0.940820i \(0.610057\pi\)
\(20\) 1.43379 0.320604
\(21\) 4.19208 0.914786
\(22\) 0.546298 0.116471
\(23\) −0.974992 −0.203300 −0.101650 0.994820i \(-0.532412\pi\)
−0.101650 + 0.994820i \(0.532412\pi\)
\(24\) −2.02216 −0.412771
\(25\) −4.28997 −0.857995
\(26\) 3.25580 0.638514
\(27\) −1.00000 −0.192450
\(28\) 7.13306 1.34802
\(29\) −10.0563 −1.86741 −0.933707 0.358038i \(-0.883446\pi\)
−0.933707 + 0.358038i \(0.883446\pi\)
\(30\) −0.460328 −0.0840440
\(31\) −10.6290 −1.90902 −0.954512 0.298171i \(-0.903623\pi\)
−0.954512 + 0.298171i \(0.903623\pi\)
\(32\) −5.29993 −0.936904
\(33\) 1.00000 0.174078
\(34\) −0.210980 −0.0361828
\(35\) 3.53237 0.597080
\(36\) −1.70156 −0.283593
\(37\) −3.16781 −0.520785 −0.260392 0.965503i \(-0.583852\pi\)
−0.260392 + 0.965503i \(0.583852\pi\)
\(38\) 1.61405 0.261834
\(39\) 5.95974 0.954322
\(40\) −1.70393 −0.269415
\(41\) −1.29317 −0.201959 −0.100980 0.994888i \(-0.532198\pi\)
−0.100980 + 0.994888i \(0.532198\pi\)
\(42\) −2.29012 −0.353374
\(43\) −4.99709 −0.762050 −0.381025 0.924565i \(-0.624429\pi\)
−0.381025 + 0.924565i \(0.624429\pi\)
\(44\) 1.70156 0.256520
\(45\) −0.842631 −0.125612
\(46\) 0.532636 0.0785330
\(47\) 7.87272 1.14835 0.574177 0.818731i \(-0.305322\pi\)
0.574177 + 0.818731i \(0.305322\pi\)
\(48\) −2.29842 −0.331748
\(49\) 10.5735 1.51050
\(50\) 2.34361 0.331436
\(51\) −0.386200 −0.0540788
\(52\) 10.1408 1.40628
\(53\) 0.370002 0.0508237 0.0254119 0.999677i \(-0.491910\pi\)
0.0254119 + 0.999677i \(0.491910\pi\)
\(54\) 0.546298 0.0743418
\(55\) 0.842631 0.113620
\(56\) −8.47703 −1.13279
\(57\) 2.95453 0.391337
\(58\) 5.49376 0.721366
\(59\) 13.7723 1.79299 0.896497 0.443049i \(-0.146103\pi\)
0.896497 + 0.443049i \(0.146103\pi\)
\(60\) −1.43379 −0.185101
\(61\) 1.00000 0.128037
\(62\) 5.80661 0.737440
\(63\) −4.19208 −0.528152
\(64\) −1.70149 −0.212686
\(65\) 5.02186 0.622885
\(66\) −0.546298 −0.0672447
\(67\) 9.80901 1.19836 0.599181 0.800614i \(-0.295493\pi\)
0.599181 + 0.800614i \(0.295493\pi\)
\(68\) −0.657141 −0.0796901
\(69\) 0.974992 0.117375
\(70\) −1.92973 −0.230647
\(71\) −4.36706 −0.518274 −0.259137 0.965841i \(-0.583438\pi\)
−0.259137 + 0.965841i \(0.583438\pi\)
\(72\) 2.02216 0.238313
\(73\) −2.06518 −0.241711 −0.120855 0.992670i \(-0.538564\pi\)
−0.120855 + 0.992670i \(0.538564\pi\)
\(74\) 1.73057 0.201175
\(75\) 4.28997 0.495363
\(76\) 5.02730 0.576671
\(77\) 4.19208 0.477731
\(78\) −3.25580 −0.368646
\(79\) −8.67552 −0.976072 −0.488036 0.872823i \(-0.662287\pi\)
−0.488036 + 0.872823i \(0.662287\pi\)
\(80\) −1.93672 −0.216531
\(81\) 1.00000 0.111111
\(82\) 0.706457 0.0780151
\(83\) −7.09673 −0.778967 −0.389483 0.921033i \(-0.627346\pi\)
−0.389483 + 0.921033i \(0.627346\pi\)
\(84\) −7.13306 −0.778281
\(85\) −0.325424 −0.0352972
\(86\) 2.72990 0.294373
\(87\) 10.0563 1.07815
\(88\) −2.02216 −0.215562
\(89\) −7.42432 −0.786976 −0.393488 0.919330i \(-0.628732\pi\)
−0.393488 + 0.919330i \(0.628732\pi\)
\(90\) 0.460328 0.0485228
\(91\) 24.9837 2.61900
\(92\) 1.65901 0.172963
\(93\) 10.6290 1.10218
\(94\) −4.30086 −0.443599
\(95\) 2.48957 0.255425
\(96\) 5.29993 0.540922
\(97\) −6.00940 −0.610162 −0.305081 0.952326i \(-0.598684\pi\)
−0.305081 + 0.952326i \(0.598684\pi\)
\(98\) −5.77628 −0.583493
\(99\) −1.00000 −0.100504
\(100\) 7.29964 0.729964
\(101\) −18.1851 −1.80948 −0.904742 0.425961i \(-0.859936\pi\)
−0.904742 + 0.425961i \(0.859936\pi\)
\(102\) 0.210980 0.0208902
\(103\) 10.9494 1.07887 0.539436 0.842026i \(-0.318637\pi\)
0.539436 + 0.842026i \(0.318637\pi\)
\(104\) −12.0515 −1.18175
\(105\) −3.53237 −0.344724
\(106\) −0.202132 −0.0196328
\(107\) 2.84318 0.274860 0.137430 0.990511i \(-0.456116\pi\)
0.137430 + 0.990511i \(0.456116\pi\)
\(108\) 1.70156 0.163733
\(109\) 19.4494 1.86291 0.931456 0.363855i \(-0.118540\pi\)
0.931456 + 0.363855i \(0.118540\pi\)
\(110\) −0.460328 −0.0438905
\(111\) 3.16781 0.300675
\(112\) −9.63513 −0.910434
\(113\) 8.08952 0.760998 0.380499 0.924781i \(-0.375752\pi\)
0.380499 + 0.924781i \(0.375752\pi\)
\(114\) −1.61405 −0.151170
\(115\) 0.821558 0.0766107
\(116\) 17.1114 1.58876
\(117\) −5.95974 −0.550978
\(118\) −7.52376 −0.692618
\(119\) −1.61898 −0.148411
\(120\) 1.70393 0.155547
\(121\) 1.00000 0.0909091
\(122\) −0.546298 −0.0494595
\(123\) 1.29317 0.116601
\(124\) 18.0859 1.62416
\(125\) 7.82802 0.700159
\(126\) 2.29012 0.204020
\(127\) 1.18990 0.105587 0.0527934 0.998605i \(-0.483188\pi\)
0.0527934 + 0.998605i \(0.483188\pi\)
\(128\) 11.5294 1.01906
\(129\) 4.99709 0.439970
\(130\) −2.74343 −0.240615
\(131\) −0.232276 −0.0202940 −0.0101470 0.999949i \(-0.503230\pi\)
−0.0101470 + 0.999949i \(0.503230\pi\)
\(132\) −1.70156 −0.148102
\(133\) 12.3856 1.07397
\(134\) −5.35865 −0.462917
\(135\) 0.842631 0.0725221
\(136\) 0.780956 0.0669664
\(137\) −13.7946 −1.17855 −0.589276 0.807932i \(-0.700587\pi\)
−0.589276 + 0.807932i \(0.700587\pi\)
\(138\) −0.532636 −0.0453410
\(139\) 10.2427 0.868777 0.434388 0.900726i \(-0.356965\pi\)
0.434388 + 0.900726i \(0.356965\pi\)
\(140\) −6.01053 −0.507983
\(141\) −7.87272 −0.663003
\(142\) 2.38572 0.200205
\(143\) 5.95974 0.498378
\(144\) 2.29842 0.191535
\(145\) 8.47377 0.703709
\(146\) 1.12820 0.0933708
\(147\) −10.5735 −0.872087
\(148\) 5.39021 0.443073
\(149\) −2.70615 −0.221697 −0.110848 0.993837i \(-0.535357\pi\)
−0.110848 + 0.993837i \(0.535357\pi\)
\(150\) −2.34361 −0.191355
\(151\) −15.6416 −1.27290 −0.636448 0.771319i \(-0.719597\pi\)
−0.636448 + 0.771319i \(0.719597\pi\)
\(152\) −5.97451 −0.484597
\(153\) 0.386200 0.0312224
\(154\) −2.29012 −0.184543
\(155\) 8.95632 0.719389
\(156\) −10.1408 −0.811917
\(157\) 3.50083 0.279397 0.139698 0.990194i \(-0.455387\pi\)
0.139698 + 0.990194i \(0.455387\pi\)
\(158\) 4.73942 0.377048
\(159\) −0.370002 −0.0293431
\(160\) 4.46589 0.353059
\(161\) 4.08724 0.322120
\(162\) −0.546298 −0.0429213
\(163\) 16.8255 1.31788 0.658938 0.752197i \(-0.271006\pi\)
0.658938 + 0.752197i \(0.271006\pi\)
\(164\) 2.20040 0.171823
\(165\) −0.842631 −0.0655987
\(166\) 3.87693 0.300908
\(167\) 18.1086 1.40129 0.700645 0.713510i \(-0.252896\pi\)
0.700645 + 0.713510i \(0.252896\pi\)
\(168\) 8.47703 0.654017
\(169\) 22.5185 1.73219
\(170\) 0.177778 0.0136350
\(171\) −2.95453 −0.225938
\(172\) 8.50285 0.648336
\(173\) −9.84724 −0.748672 −0.374336 0.927293i \(-0.622129\pi\)
−0.374336 + 0.927293i \(0.622129\pi\)
\(174\) −5.49376 −0.416481
\(175\) 17.9839 1.35945
\(176\) −2.29842 −0.173250
\(177\) −13.7723 −1.03519
\(178\) 4.05589 0.304002
\(179\) −10.0310 −0.749749 −0.374875 0.927075i \(-0.622314\pi\)
−0.374875 + 0.927075i \(0.622314\pi\)
\(180\) 1.43379 0.106868
\(181\) −13.2298 −0.983362 −0.491681 0.870775i \(-0.663617\pi\)
−0.491681 + 0.870775i \(0.663617\pi\)
\(182\) −13.6485 −1.01170
\(183\) −1.00000 −0.0739221
\(184\) −1.97158 −0.145347
\(185\) 2.66929 0.196250
\(186\) −5.80661 −0.425761
\(187\) −0.386200 −0.0282417
\(188\) −13.3959 −0.976996
\(189\) 4.19208 0.304929
\(190\) −1.36005 −0.0986684
\(191\) −26.0670 −1.88614 −0.943069 0.332596i \(-0.892075\pi\)
−0.943069 + 0.332596i \(0.892075\pi\)
\(192\) 1.70149 0.122794
\(193\) −1.64976 −0.118752 −0.0593760 0.998236i \(-0.518911\pi\)
−0.0593760 + 0.998236i \(0.518911\pi\)
\(194\) 3.28292 0.235700
\(195\) −5.02186 −0.359623
\(196\) −17.9914 −1.28510
\(197\) −15.0092 −1.06936 −0.534681 0.845054i \(-0.679568\pi\)
−0.534681 + 0.845054i \(0.679568\pi\)
\(198\) 0.546298 0.0388237
\(199\) 0.432727 0.0306752 0.0153376 0.999882i \(-0.495118\pi\)
0.0153376 + 0.999882i \(0.495118\pi\)
\(200\) −8.67499 −0.613415
\(201\) −9.80901 −0.691874
\(202\) 9.93448 0.698988
\(203\) 42.1569 2.95883
\(204\) 0.657141 0.0460091
\(205\) 1.08967 0.0761055
\(206\) −5.98162 −0.416759
\(207\) −0.974992 −0.0677666
\(208\) −13.6980 −0.949783
\(209\) 2.95453 0.204369
\(210\) 1.92973 0.133164
\(211\) −5.99457 −0.412683 −0.206342 0.978480i \(-0.566156\pi\)
−0.206342 + 0.978480i \(0.566156\pi\)
\(212\) −0.629580 −0.0432398
\(213\) 4.36706 0.299226
\(214\) −1.55322 −0.106176
\(215\) 4.21070 0.287168
\(216\) −2.02216 −0.137590
\(217\) 44.5576 3.02476
\(218\) −10.6252 −0.719626
\(219\) 2.06518 0.139552
\(220\) −1.43379 −0.0966658
\(221\) −2.30165 −0.154826
\(222\) −1.73057 −0.116148
\(223\) 1.20744 0.0808559 0.0404280 0.999182i \(-0.487128\pi\)
0.0404280 + 0.999182i \(0.487128\pi\)
\(224\) 22.2177 1.48448
\(225\) −4.28997 −0.285998
\(226\) −4.41929 −0.293967
\(227\) 3.17333 0.210621 0.105311 0.994439i \(-0.466416\pi\)
0.105311 + 0.994439i \(0.466416\pi\)
\(228\) −5.02730 −0.332941
\(229\) −26.1824 −1.73018 −0.865091 0.501614i \(-0.832740\pi\)
−0.865091 + 0.501614i \(0.832740\pi\)
\(230\) −0.448816 −0.0295940
\(231\) −4.19208 −0.275818
\(232\) −20.3355 −1.33509
\(233\) 15.3586 1.00617 0.503087 0.864236i \(-0.332197\pi\)
0.503087 + 0.864236i \(0.332197\pi\)
\(234\) 3.25580 0.212838
\(235\) −6.63380 −0.432741
\(236\) −23.4343 −1.52544
\(237\) 8.67552 0.563535
\(238\) 0.884445 0.0573301
\(239\) −6.48318 −0.419362 −0.209681 0.977770i \(-0.567243\pi\)
−0.209681 + 0.977770i \(0.567243\pi\)
\(240\) 1.93672 0.125014
\(241\) −2.05017 −0.132063 −0.0660315 0.997818i \(-0.521034\pi\)
−0.0660315 + 0.997818i \(0.521034\pi\)
\(242\) −0.546298 −0.0351174
\(243\) −1.00000 −0.0641500
\(244\) −1.70156 −0.108931
\(245\) −8.90955 −0.569210
\(246\) −0.706457 −0.0450421
\(247\) 17.6082 1.12038
\(248\) −21.4935 −1.36484
\(249\) 7.09673 0.449737
\(250\) −4.27643 −0.270465
\(251\) 0.403663 0.0254790 0.0127395 0.999919i \(-0.495945\pi\)
0.0127395 + 0.999919i \(0.495945\pi\)
\(252\) 7.13306 0.449340
\(253\) 0.974992 0.0612972
\(254\) −0.650042 −0.0407873
\(255\) 0.325424 0.0203788
\(256\) −2.89551 −0.180969
\(257\) −3.52100 −0.219634 −0.109817 0.993952i \(-0.535027\pi\)
−0.109817 + 0.993952i \(0.535027\pi\)
\(258\) −2.72990 −0.169956
\(259\) 13.2797 0.825160
\(260\) −8.54498 −0.529937
\(261\) −10.0563 −0.622471
\(262\) 0.126892 0.00783940
\(263\) 25.3122 1.56082 0.780408 0.625271i \(-0.215012\pi\)
0.780408 + 0.625271i \(0.215012\pi\)
\(264\) 2.02216 0.124455
\(265\) −0.311775 −0.0191522
\(266\) −6.76623 −0.414864
\(267\) 7.42432 0.454361
\(268\) −16.6906 −1.01954
\(269\) 26.8357 1.63620 0.818100 0.575076i \(-0.195028\pi\)
0.818100 + 0.575076i \(0.195028\pi\)
\(270\) −0.460328 −0.0280147
\(271\) −8.80885 −0.535099 −0.267550 0.963544i \(-0.586214\pi\)
−0.267550 + 0.963544i \(0.586214\pi\)
\(272\) 0.887648 0.0538215
\(273\) −24.9837 −1.51208
\(274\) 7.53597 0.455264
\(275\) 4.28997 0.258695
\(276\) −1.65901 −0.0998604
\(277\) 21.3581 1.28328 0.641641 0.767005i \(-0.278254\pi\)
0.641641 + 0.767005i \(0.278254\pi\)
\(278\) −5.59559 −0.335601
\(279\) −10.6290 −0.636342
\(280\) 7.14300 0.426876
\(281\) −29.9872 −1.78889 −0.894444 0.447181i \(-0.852428\pi\)
−0.894444 + 0.447181i \(0.852428\pi\)
\(282\) 4.30086 0.256112
\(283\) 10.0912 0.599862 0.299931 0.953961i \(-0.403036\pi\)
0.299931 + 0.953961i \(0.403036\pi\)
\(284\) 7.43080 0.440937
\(285\) −2.48957 −0.147470
\(286\) −3.25580 −0.192519
\(287\) 5.42107 0.319996
\(288\) −5.29993 −0.312301
\(289\) −16.8508 −0.991226
\(290\) −4.62921 −0.271837
\(291\) 6.00940 0.352277
\(292\) 3.51402 0.205643
\(293\) −11.7387 −0.685783 −0.342892 0.939375i \(-0.611406\pi\)
−0.342892 + 0.939375i \(0.611406\pi\)
\(294\) 5.77628 0.336880
\(295\) −11.6049 −0.675665
\(296\) −6.40580 −0.372330
\(297\) 1.00000 0.0580259
\(298\) 1.47837 0.0856395
\(299\) 5.81070 0.336041
\(300\) −7.29964 −0.421445
\(301\) 20.9482 1.20743
\(302\) 8.54499 0.491709
\(303\) 18.1851 1.04471
\(304\) −6.79073 −0.389475
\(305\) −0.842631 −0.0482489
\(306\) −0.210980 −0.0120609
\(307\) 12.1646 0.694269 0.347135 0.937815i \(-0.387155\pi\)
0.347135 + 0.937815i \(0.387155\pi\)
\(308\) −7.13306 −0.406444
\(309\) −10.9494 −0.622887
\(310\) −4.89282 −0.277894
\(311\) −10.4238 −0.591079 −0.295539 0.955331i \(-0.595499\pi\)
−0.295539 + 0.955331i \(0.595499\pi\)
\(312\) 12.0515 0.682283
\(313\) −3.70708 −0.209536 −0.104768 0.994497i \(-0.533410\pi\)
−0.104768 + 0.994497i \(0.533410\pi\)
\(314\) −1.91250 −0.107928
\(315\) 3.53237 0.199027
\(316\) 14.7619 0.830422
\(317\) −17.7635 −0.997696 −0.498848 0.866690i \(-0.666243\pi\)
−0.498848 + 0.866690i \(0.666243\pi\)
\(318\) 0.202132 0.0113350
\(319\) 10.0563 0.563046
\(320\) 1.43373 0.0801477
\(321\) −2.84318 −0.158691
\(322\) −2.23285 −0.124432
\(323\) −1.14104 −0.0634890
\(324\) −1.70156 −0.0945310
\(325\) 25.5671 1.41821
\(326\) −9.19176 −0.509084
\(327\) −19.4494 −1.07555
\(328\) −2.61499 −0.144389
\(329\) −33.0030 −1.81952
\(330\) 0.460328 0.0253402
\(331\) 25.2813 1.38959 0.694794 0.719209i \(-0.255496\pi\)
0.694794 + 0.719209i \(0.255496\pi\)
\(332\) 12.0755 0.662729
\(333\) −3.16781 −0.173595
\(334\) −9.89273 −0.541306
\(335\) −8.26538 −0.451586
\(336\) 9.63513 0.525640
\(337\) −15.8267 −0.862134 −0.431067 0.902320i \(-0.641863\pi\)
−0.431067 + 0.902320i \(0.641863\pi\)
\(338\) −12.3018 −0.669130
\(339\) −8.08952 −0.439363
\(340\) 0.553727 0.0300301
\(341\) 10.6290 0.575593
\(342\) 1.61405 0.0872780
\(343\) −14.9804 −0.808863
\(344\) −10.1049 −0.544820
\(345\) −0.821558 −0.0442312
\(346\) 5.37953 0.289205
\(347\) −14.2210 −0.763424 −0.381712 0.924281i \(-0.624665\pi\)
−0.381712 + 0.924281i \(0.624665\pi\)
\(348\) −17.1114 −0.917269
\(349\) 20.6858 1.10728 0.553642 0.832755i \(-0.313238\pi\)
0.553642 + 0.832755i \(0.313238\pi\)
\(350\) −9.82457 −0.525145
\(351\) 5.95974 0.318107
\(352\) 5.29993 0.282487
\(353\) −13.3604 −0.711102 −0.355551 0.934657i \(-0.615707\pi\)
−0.355551 + 0.934657i \(0.615707\pi\)
\(354\) 7.52376 0.399883
\(355\) 3.67981 0.195304
\(356\) 12.6329 0.669543
\(357\) 1.61898 0.0856854
\(358\) 5.47990 0.289622
\(359\) −10.9660 −0.578761 −0.289381 0.957214i \(-0.593449\pi\)
−0.289381 + 0.957214i \(0.593449\pi\)
\(360\) −1.70393 −0.0898050
\(361\) −10.2708 −0.540567
\(362\) 7.22741 0.379864
\(363\) −1.00000 −0.0524864
\(364\) −42.5112 −2.22819
\(365\) 1.74018 0.0910854
\(366\) 0.546298 0.0285555
\(367\) −18.2275 −0.951468 −0.475734 0.879589i \(-0.657818\pi\)
−0.475734 + 0.879589i \(0.657818\pi\)
\(368\) −2.24094 −0.116817
\(369\) −1.29317 −0.0673198
\(370\) −1.45823 −0.0758098
\(371\) −1.55108 −0.0805279
\(372\) −18.0859 −0.937708
\(373\) −14.3974 −0.745467 −0.372733 0.927938i \(-0.621579\pi\)
−0.372733 + 0.927938i \(0.621579\pi\)
\(374\) 0.210980 0.0109095
\(375\) −7.82802 −0.404237
\(376\) 15.9199 0.821005
\(377\) 59.9331 3.08671
\(378\) −2.29012 −0.117791
\(379\) 11.1418 0.572316 0.286158 0.958182i \(-0.407622\pi\)
0.286158 + 0.958182i \(0.407622\pi\)
\(380\) −4.23616 −0.217310
\(381\) −1.18990 −0.0609606
\(382\) 14.2403 0.728599
\(383\) −13.6433 −0.697140 −0.348570 0.937283i \(-0.613333\pi\)
−0.348570 + 0.937283i \(0.613333\pi\)
\(384\) −11.5294 −0.588356
\(385\) −3.53237 −0.180026
\(386\) 0.901260 0.0458729
\(387\) −4.99709 −0.254017
\(388\) 10.2253 0.519113
\(389\) 23.6998 1.20163 0.600814 0.799389i \(-0.294843\pi\)
0.600814 + 0.799389i \(0.294843\pi\)
\(390\) 2.74343 0.138919
\(391\) −0.376542 −0.0190425
\(392\) 21.3812 1.07992
\(393\) 0.232276 0.0117168
\(394\) 8.19951 0.413086
\(395\) 7.31026 0.367819
\(396\) 1.70156 0.0855065
\(397\) −19.8855 −0.998023 −0.499011 0.866595i \(-0.666303\pi\)
−0.499011 + 0.866595i \(0.666303\pi\)
\(398\) −0.236398 −0.0118496
\(399\) −12.3856 −0.620055
\(400\) −9.86014 −0.493007
\(401\) −15.1693 −0.757517 −0.378758 0.925496i \(-0.623649\pi\)
−0.378758 + 0.925496i \(0.623649\pi\)
\(402\) 5.35865 0.267265
\(403\) 63.3461 3.15549
\(404\) 30.9430 1.53947
\(405\) −0.842631 −0.0418707
\(406\) −23.0302 −1.14297
\(407\) 3.16781 0.157022
\(408\) −0.780956 −0.0386631
\(409\) −20.3853 −1.00799 −0.503995 0.863706i \(-0.668137\pi\)
−0.503995 + 0.863706i \(0.668137\pi\)
\(410\) −0.595282 −0.0293989
\(411\) 13.7946 0.680437
\(412\) −18.6310 −0.917882
\(413\) −57.7343 −2.84092
\(414\) 0.532636 0.0261777
\(415\) 5.97992 0.293543
\(416\) 31.5862 1.54864
\(417\) −10.2427 −0.501588
\(418\) −1.61405 −0.0789459
\(419\) 19.1519 0.935633 0.467817 0.883826i \(-0.345041\pi\)
0.467817 + 0.883826i \(0.345041\pi\)
\(420\) 6.01053 0.293284
\(421\) −8.29681 −0.404362 −0.202181 0.979348i \(-0.564803\pi\)
−0.202181 + 0.979348i \(0.564803\pi\)
\(422\) 3.27482 0.159416
\(423\) 7.87272 0.382785
\(424\) 0.748202 0.0363359
\(425\) −1.65679 −0.0803660
\(426\) −2.38572 −0.115588
\(427\) −4.19208 −0.202869
\(428\) −4.83783 −0.233845
\(429\) −5.95974 −0.287739
\(430\) −2.30030 −0.110930
\(431\) −17.6981 −0.852485 −0.426243 0.904609i \(-0.640163\pi\)
−0.426243 + 0.904609i \(0.640163\pi\)
\(432\) −2.29842 −0.110583
\(433\) 5.57917 0.268118 0.134059 0.990973i \(-0.457199\pi\)
0.134059 + 0.990973i \(0.457199\pi\)
\(434\) −24.3417 −1.16844
\(435\) −8.47377 −0.406286
\(436\) −33.0942 −1.58493
\(437\) 2.88064 0.137800
\(438\) −1.12820 −0.0539077
\(439\) −6.90623 −0.329616 −0.164808 0.986326i \(-0.552701\pi\)
−0.164808 + 0.986326i \(0.552701\pi\)
\(440\) 1.70393 0.0812317
\(441\) 10.5735 0.503500
\(442\) 1.25739 0.0598078
\(443\) 8.54914 0.406182 0.203091 0.979160i \(-0.434901\pi\)
0.203091 + 0.979160i \(0.434901\pi\)
\(444\) −5.39021 −0.255808
\(445\) 6.25596 0.296561
\(446\) −0.659621 −0.0312339
\(447\) 2.70615 0.127997
\(448\) 7.13276 0.336991
\(449\) −22.1028 −1.04309 −0.521547 0.853223i \(-0.674645\pi\)
−0.521547 + 0.853223i \(0.674645\pi\)
\(450\) 2.34361 0.110479
\(451\) 1.29317 0.0608930
\(452\) −13.7648 −0.647441
\(453\) 15.6416 0.734907
\(454\) −1.73358 −0.0813611
\(455\) −21.0520 −0.986933
\(456\) 5.97451 0.279782
\(457\) −12.2492 −0.572995 −0.286497 0.958081i \(-0.592491\pi\)
−0.286497 + 0.958081i \(0.592491\pi\)
\(458\) 14.3034 0.668355
\(459\) −0.386200 −0.0180263
\(460\) −1.39793 −0.0651788
\(461\) −5.51693 −0.256949 −0.128475 0.991713i \(-0.541008\pi\)
−0.128475 + 0.991713i \(0.541008\pi\)
\(462\) 2.29012 0.106546
\(463\) −39.0620 −1.81536 −0.907682 0.419659i \(-0.862150\pi\)
−0.907682 + 0.419659i \(0.862150\pi\)
\(464\) −23.1136 −1.07302
\(465\) −8.95632 −0.415339
\(466\) −8.39037 −0.388676
\(467\) −15.4534 −0.715099 −0.357550 0.933894i \(-0.616388\pi\)
−0.357550 + 0.933894i \(0.616388\pi\)
\(468\) 10.1408 0.468761
\(469\) −41.1201 −1.89875
\(470\) 3.62403 0.167164
\(471\) −3.50083 −0.161310
\(472\) 27.8496 1.28188
\(473\) 4.99709 0.229767
\(474\) −4.73942 −0.217689
\(475\) 12.6748 0.581561
\(476\) 2.75479 0.126265
\(477\) 0.370002 0.0169412
\(478\) 3.54175 0.161996
\(479\) 19.2183 0.878106 0.439053 0.898461i \(-0.355314\pi\)
0.439053 + 0.898461i \(0.355314\pi\)
\(480\) −4.46589 −0.203839
\(481\) 18.8793 0.860823
\(482\) 1.12000 0.0510148
\(483\) −4.08724 −0.185976
\(484\) −1.70156 −0.0773435
\(485\) 5.06370 0.229931
\(486\) 0.546298 0.0247806
\(487\) −5.36667 −0.243187 −0.121594 0.992580i \(-0.538800\pi\)
−0.121594 + 0.992580i \(0.538800\pi\)
\(488\) 2.02216 0.0915387
\(489\) −16.8255 −0.760876
\(490\) 4.86727 0.219881
\(491\) −30.3986 −1.37187 −0.685936 0.727662i \(-0.740607\pi\)
−0.685936 + 0.727662i \(0.740607\pi\)
\(492\) −2.20040 −0.0992019
\(493\) −3.88375 −0.174915
\(494\) −9.61933 −0.432794
\(495\) 0.842631 0.0378734
\(496\) −24.4299 −1.09693
\(497\) 18.3070 0.821182
\(498\) −3.87693 −0.173729
\(499\) −17.0924 −0.765160 −0.382580 0.923922i \(-0.624964\pi\)
−0.382580 + 0.923922i \(0.624964\pi\)
\(500\) −13.3198 −0.595681
\(501\) −18.1086 −0.809035
\(502\) −0.220521 −0.00984231
\(503\) 32.1659 1.43421 0.717103 0.696967i \(-0.245468\pi\)
0.717103 + 0.696967i \(0.245468\pi\)
\(504\) −8.47703 −0.377597
\(505\) 15.3233 0.681878
\(506\) −0.532636 −0.0236786
\(507\) −22.5185 −1.00008
\(508\) −2.02469 −0.0898310
\(509\) 20.2801 0.898900 0.449450 0.893306i \(-0.351620\pi\)
0.449450 + 0.893306i \(0.351620\pi\)
\(510\) −0.177778 −0.00787216
\(511\) 8.65739 0.382980
\(512\) −21.4770 −0.949156
\(513\) 2.95453 0.130446
\(514\) 1.92352 0.0848428
\(515\) −9.22627 −0.406558
\(516\) −8.50285 −0.374317
\(517\) −7.87272 −0.346242
\(518\) −7.25467 −0.318752
\(519\) 9.84724 0.432246
\(520\) 10.1550 0.445325
\(521\) 27.3063 1.19631 0.598156 0.801380i \(-0.295900\pi\)
0.598156 + 0.801380i \(0.295900\pi\)
\(522\) 5.49376 0.240455
\(523\) −23.5138 −1.02819 −0.514093 0.857734i \(-0.671871\pi\)
−0.514093 + 0.857734i \(0.671871\pi\)
\(524\) 0.395230 0.0172657
\(525\) −17.9839 −0.784881
\(526\) −13.8280 −0.602929
\(527\) −4.10492 −0.178813
\(528\) 2.29842 0.100026
\(529\) −22.0494 −0.958669
\(530\) 0.170322 0.00739833
\(531\) 13.7723 0.597665
\(532\) −21.0748 −0.913709
\(533\) 7.70696 0.333825
\(534\) −4.05589 −0.175516
\(535\) −2.39575 −0.103577
\(536\) 19.8353 0.856757
\(537\) 10.0310 0.432868
\(538\) −14.6603 −0.632050
\(539\) −10.5735 −0.455433
\(540\) −1.43379 −0.0617003
\(541\) 21.3883 0.919556 0.459778 0.888034i \(-0.347929\pi\)
0.459778 + 0.888034i \(0.347929\pi\)
\(542\) 4.81226 0.206704
\(543\) 13.2298 0.567744
\(544\) −2.04683 −0.0877572
\(545\) −16.3886 −0.702012
\(546\) 13.6485 0.584104
\(547\) −18.4841 −0.790322 −0.395161 0.918612i \(-0.629311\pi\)
−0.395161 + 0.918612i \(0.629311\pi\)
\(548\) 23.4723 1.00269
\(549\) 1.00000 0.0426790
\(550\) −2.34361 −0.0999317
\(551\) 29.7117 1.26576
\(552\) 1.97158 0.0839162
\(553\) 36.3684 1.54654
\(554\) −11.6679 −0.495721
\(555\) −2.66929 −0.113305
\(556\) −17.4286 −0.739137
\(557\) −24.4886 −1.03762 −0.518808 0.854891i \(-0.673624\pi\)
−0.518808 + 0.854891i \(0.673624\pi\)
\(558\) 5.80661 0.245813
\(559\) 29.7814 1.25962
\(560\) 8.11886 0.343084
\(561\) 0.386200 0.0163054
\(562\) 16.3820 0.691032
\(563\) −20.3211 −0.856433 −0.428216 0.903676i \(-0.640858\pi\)
−0.428216 + 0.903676i \(0.640858\pi\)
\(564\) 13.3959 0.564069
\(565\) −6.81648 −0.286771
\(566\) −5.51283 −0.231721
\(567\) −4.19208 −0.176051
\(568\) −8.83086 −0.370535
\(569\) −24.7529 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(570\) 1.36005 0.0569663
\(571\) 10.7099 0.448195 0.224098 0.974567i \(-0.428057\pi\)
0.224098 + 0.974567i \(0.428057\pi\)
\(572\) −10.1408 −0.424010
\(573\) 26.0670 1.08896
\(574\) −2.96152 −0.123612
\(575\) 4.18269 0.174430
\(576\) −1.70149 −0.0708953
\(577\) −4.97286 −0.207023 −0.103512 0.994628i \(-0.533008\pi\)
−0.103512 + 0.994628i \(0.533008\pi\)
\(578\) 9.20559 0.382902
\(579\) 1.64976 0.0685616
\(580\) −14.4186 −0.598701
\(581\) 29.7500 1.23424
\(582\) −3.28292 −0.136082
\(583\) −0.370002 −0.0153239
\(584\) −4.17611 −0.172809
\(585\) 5.02186 0.207628
\(586\) 6.41284 0.264912
\(587\) 2.13571 0.0881502 0.0440751 0.999028i \(-0.485966\pi\)
0.0440751 + 0.999028i \(0.485966\pi\)
\(588\) 17.9914 0.741953
\(589\) 31.4037 1.29397
\(590\) 6.33975 0.261003
\(591\) 15.0092 0.617397
\(592\) −7.28094 −0.299245
\(593\) 13.9935 0.574646 0.287323 0.957834i \(-0.407235\pi\)
0.287323 + 0.957834i \(0.407235\pi\)
\(594\) −0.546298 −0.0224149
\(595\) 1.36420 0.0559268
\(596\) 4.60468 0.188615
\(597\) −0.432727 −0.0177103
\(598\) −3.17437 −0.129810
\(599\) −27.2804 −1.11465 −0.557324 0.830295i \(-0.688172\pi\)
−0.557324 + 0.830295i \(0.688172\pi\)
\(600\) 8.67499 0.354155
\(601\) 38.7081 1.57894 0.789468 0.613791i \(-0.210356\pi\)
0.789468 + 0.613791i \(0.210356\pi\)
\(602\) −11.4440 −0.466421
\(603\) 9.80901 0.399454
\(604\) 26.6151 1.08295
\(605\) −0.842631 −0.0342578
\(606\) −9.93448 −0.403561
\(607\) 27.3959 1.11197 0.555983 0.831194i \(-0.312342\pi\)
0.555983 + 0.831194i \(0.312342\pi\)
\(608\) 15.6588 0.635048
\(609\) −42.1569 −1.70828
\(610\) 0.460328 0.0186381
\(611\) −46.9194 −1.89815
\(612\) −0.657141 −0.0265634
\(613\) 8.56875 0.346088 0.173044 0.984914i \(-0.444640\pi\)
0.173044 + 0.984914i \(0.444640\pi\)
\(614\) −6.64549 −0.268190
\(615\) −1.08967 −0.0439395
\(616\) 8.47703 0.341549
\(617\) 45.6108 1.83622 0.918112 0.396322i \(-0.129713\pi\)
0.918112 + 0.396322i \(0.129713\pi\)
\(618\) 5.98162 0.240616
\(619\) 36.2410 1.45665 0.728325 0.685232i \(-0.240299\pi\)
0.728325 + 0.685232i \(0.240299\pi\)
\(620\) −15.2397 −0.612041
\(621\) 0.974992 0.0391251
\(622\) 5.69450 0.228329
\(623\) 31.1233 1.24693
\(624\) 13.6980 0.548357
\(625\) 14.8537 0.594150
\(626\) 2.02517 0.0809421
\(627\) −2.95453 −0.117992
\(628\) −5.95686 −0.237705
\(629\) −1.22341 −0.0487804
\(630\) −1.92973 −0.0768822
\(631\) −5.90488 −0.235070 −0.117535 0.993069i \(-0.537499\pi\)
−0.117535 + 0.993069i \(0.537499\pi\)
\(632\) −17.5432 −0.697833
\(633\) 5.99457 0.238263
\(634\) 9.70415 0.385401
\(635\) −1.00265 −0.0397889
\(636\) 0.629580 0.0249645
\(637\) −63.0153 −2.49676
\(638\) −5.49376 −0.217500
\(639\) −4.36706 −0.172758
\(640\) −9.71501 −0.384020
\(641\) −27.6940 −1.09385 −0.546923 0.837183i \(-0.684201\pi\)
−0.546923 + 0.837183i \(0.684201\pi\)
\(642\) 1.55322 0.0613008
\(643\) 39.7962 1.56941 0.784704 0.619871i \(-0.212815\pi\)
0.784704 + 0.619871i \(0.212815\pi\)
\(644\) −6.95467 −0.274053
\(645\) −4.21070 −0.165796
\(646\) 0.623347 0.0245253
\(647\) 35.8326 1.40872 0.704362 0.709841i \(-0.251233\pi\)
0.704362 + 0.709841i \(0.251233\pi\)
\(648\) 2.02216 0.0794378
\(649\) −13.7723 −0.540608
\(650\) −13.9673 −0.547842
\(651\) −44.5576 −1.74635
\(652\) −28.6296 −1.12122
\(653\) 3.93565 0.154014 0.0770070 0.997031i \(-0.475464\pi\)
0.0770070 + 0.997031i \(0.475464\pi\)
\(654\) 10.6252 0.415477
\(655\) 0.195723 0.00764751
\(656\) −2.97224 −0.116047
\(657\) −2.06518 −0.0805703
\(658\) 18.0295 0.702864
\(659\) −1.14603 −0.0446429 −0.0223215 0.999751i \(-0.507106\pi\)
−0.0223215 + 0.999751i \(0.507106\pi\)
\(660\) 1.43379 0.0558100
\(661\) −21.1185 −0.821414 −0.410707 0.911767i \(-0.634718\pi\)
−0.410707 + 0.911767i \(0.634718\pi\)
\(662\) −13.8112 −0.536786
\(663\) 2.30165 0.0893887
\(664\) −14.3507 −0.556915
\(665\) −10.4365 −0.404709
\(666\) 1.73057 0.0670582
\(667\) 9.80484 0.379645
\(668\) −30.8129 −1.19219
\(669\) −1.20744 −0.0466822
\(670\) 4.51536 0.174444
\(671\) −1.00000 −0.0386046
\(672\) −22.2177 −0.857067
\(673\) −50.2053 −1.93527 −0.967636 0.252349i \(-0.918797\pi\)
−0.967636 + 0.252349i \(0.918797\pi\)
\(674\) 8.64609 0.333035
\(675\) 4.28997 0.165121
\(676\) −38.3165 −1.47371
\(677\) −15.0864 −0.579819 −0.289910 0.957054i \(-0.593625\pi\)
−0.289910 + 0.957054i \(0.593625\pi\)
\(678\) 4.41929 0.169722
\(679\) 25.1918 0.966774
\(680\) −0.658057 −0.0252353
\(681\) −3.17333 −0.121602
\(682\) −5.80661 −0.222346
\(683\) 48.5108 1.85621 0.928107 0.372314i \(-0.121436\pi\)
0.928107 + 0.372314i \(0.121436\pi\)
\(684\) 5.02730 0.192224
\(685\) 11.6238 0.444121
\(686\) 8.18375 0.312457
\(687\) 26.1824 0.998922
\(688\) −11.4854 −0.437877
\(689\) −2.20512 −0.0840083
\(690\) 0.448816 0.0170861
\(691\) −28.3558 −1.07871 −0.539353 0.842080i \(-0.681331\pi\)
−0.539353 + 0.842080i \(0.681331\pi\)
\(692\) 16.7557 0.636954
\(693\) 4.19208 0.159244
\(694\) 7.76891 0.294904
\(695\) −8.63084 −0.327386
\(696\) 20.3355 0.770814
\(697\) −0.499422 −0.0189170
\(698\) −11.3006 −0.427734
\(699\) −15.3586 −0.580915
\(700\) −30.6006 −1.15660
\(701\) −4.65092 −0.175663 −0.0878313 0.996135i \(-0.527994\pi\)
−0.0878313 + 0.996135i \(0.527994\pi\)
\(702\) −3.25580 −0.122882
\(703\) 9.35937 0.352995
\(704\) 1.70149 0.0641272
\(705\) 6.63380 0.249843
\(706\) 7.29876 0.274692
\(707\) 76.2332 2.86705
\(708\) 23.4343 0.880715
\(709\) 47.0222 1.76595 0.882977 0.469416i \(-0.155536\pi\)
0.882977 + 0.469416i \(0.155536\pi\)
\(710\) −2.01028 −0.0754443
\(711\) −8.67552 −0.325357
\(712\) −15.0131 −0.562641
\(713\) 10.3632 0.388104
\(714\) −0.884445 −0.0330995
\(715\) −5.02186 −0.187807
\(716\) 17.0683 0.637871
\(717\) 6.48318 0.242119
\(718\) 5.99069 0.223570
\(719\) 8.60663 0.320973 0.160487 0.987038i \(-0.448694\pi\)
0.160487 + 0.987038i \(0.448694\pi\)
\(720\) −1.93672 −0.0721771
\(721\) −45.9005 −1.70943
\(722\) 5.61091 0.208816
\(723\) 2.05017 0.0762466
\(724\) 22.5112 0.836624
\(725\) 43.1414 1.60223
\(726\) 0.546298 0.0202750
\(727\) 29.4993 1.09407 0.547034 0.837110i \(-0.315757\pi\)
0.547034 + 0.837110i \(0.315757\pi\)
\(728\) 50.5209 1.87243
\(729\) 1.00000 0.0370370
\(730\) −0.950659 −0.0351855
\(731\) −1.92988 −0.0713791
\(732\) 1.70156 0.0628914
\(733\) −42.0201 −1.55205 −0.776025 0.630702i \(-0.782767\pi\)
−0.776025 + 0.630702i \(0.782767\pi\)
\(734\) 9.95766 0.367544
\(735\) 8.90955 0.328634
\(736\) 5.16739 0.190473
\(737\) −9.80901 −0.361320
\(738\) 0.706457 0.0260050
\(739\) 50.8992 1.87236 0.936179 0.351523i \(-0.114336\pi\)
0.936179 + 0.351523i \(0.114336\pi\)
\(740\) −4.54196 −0.166966
\(741\) −17.6082 −0.646854
\(742\) 0.847351 0.0311072
\(743\) −4.44260 −0.162983 −0.0814916 0.996674i \(-0.525968\pi\)
−0.0814916 + 0.996674i \(0.525968\pi\)
\(744\) 21.4935 0.787989
\(745\) 2.28029 0.0835433
\(746\) 7.86525 0.287967
\(747\) −7.09673 −0.259656
\(748\) 0.657141 0.0240275
\(749\) −11.9188 −0.435504
\(750\) 4.27643 0.156153
\(751\) 3.39662 0.123944 0.0619722 0.998078i \(-0.480261\pi\)
0.0619722 + 0.998078i \(0.480261\pi\)
\(752\) 18.0948 0.659849
\(753\) −0.403663 −0.0147103
\(754\) −32.7414 −1.19237
\(755\) 13.1801 0.479673
\(756\) −7.13306 −0.259427
\(757\) 13.8258 0.502508 0.251254 0.967921i \(-0.419157\pi\)
0.251254 + 0.967921i \(0.419157\pi\)
\(758\) −6.08675 −0.221081
\(759\) −0.974992 −0.0353900
\(760\) 5.03431 0.182613
\(761\) −34.7597 −1.26004 −0.630018 0.776580i \(-0.716953\pi\)
−0.630018 + 0.776580i \(0.716953\pi\)
\(762\) 0.650042 0.0235485
\(763\) −81.5332 −2.95170
\(764\) 44.3544 1.60469
\(765\) −0.325424 −0.0117657
\(766\) 7.45331 0.269299
\(767\) −82.0790 −2.96370
\(768\) 2.89551 0.104483
\(769\) −1.09955 −0.0396507 −0.0198254 0.999803i \(-0.506311\pi\)
−0.0198254 + 0.999803i \(0.506311\pi\)
\(770\) 1.92973 0.0695426
\(771\) 3.52100 0.126806
\(772\) 2.80716 0.101032
\(773\) −13.8425 −0.497879 −0.248939 0.968519i \(-0.580082\pi\)
−0.248939 + 0.968519i \(0.580082\pi\)
\(774\) 2.72990 0.0981244
\(775\) 45.5981 1.63793
\(776\) −12.1519 −0.436229
\(777\) −13.2797 −0.476406
\(778\) −12.9472 −0.464178
\(779\) 3.82071 0.136891
\(780\) 8.54498 0.305960
\(781\) 4.36706 0.156266
\(782\) 0.205704 0.00735596
\(783\) 10.0563 0.359384
\(784\) 24.3023 0.867939
\(785\) −2.94991 −0.105287
\(786\) −0.126892 −0.00452608
\(787\) −33.6766 −1.20044 −0.600220 0.799835i \(-0.704920\pi\)
−0.600220 + 0.799835i \(0.704920\pi\)
\(788\) 25.5391 0.909792
\(789\) −25.3122 −0.901137
\(790\) −3.99358 −0.142085
\(791\) −33.9119 −1.20577
\(792\) −2.02216 −0.0718542
\(793\) −5.95974 −0.211637
\(794\) 10.8634 0.385528
\(795\) 0.311775 0.0110575
\(796\) −0.736310 −0.0260978
\(797\) −1.47756 −0.0523377 −0.0261689 0.999658i \(-0.508331\pi\)
−0.0261689 + 0.999658i \(0.508331\pi\)
\(798\) 6.76623 0.239522
\(799\) 3.04044 0.107563
\(800\) 22.7366 0.803859
\(801\) −7.42432 −0.262325
\(802\) 8.28694 0.292622
\(803\) 2.06518 0.0728786
\(804\) 16.6906 0.588632
\(805\) −3.44403 −0.121386
\(806\) −34.6059 −1.21894
\(807\) −26.8357 −0.944660
\(808\) −36.7731 −1.29367
\(809\) 26.0611 0.916260 0.458130 0.888885i \(-0.348519\pi\)
0.458130 + 0.888885i \(0.348519\pi\)
\(810\) 0.460328 0.0161743
\(811\) 21.1286 0.741925 0.370962 0.928648i \(-0.379028\pi\)
0.370962 + 0.928648i \(0.379028\pi\)
\(812\) −71.7324 −2.51731
\(813\) 8.80885 0.308940
\(814\) −1.73057 −0.0606564
\(815\) −14.1777 −0.496623
\(816\) −0.887648 −0.0310739
\(817\) 14.7640 0.516529
\(818\) 11.1365 0.389378
\(819\) 24.9837 0.873000
\(820\) −1.85413 −0.0647490
\(821\) −46.0338 −1.60659 −0.803295 0.595582i \(-0.796922\pi\)
−0.803295 + 0.595582i \(0.796922\pi\)
\(822\) −7.53597 −0.262847
\(823\) −23.0217 −0.802488 −0.401244 0.915971i \(-0.631422\pi\)
−0.401244 + 0.915971i \(0.631422\pi\)
\(824\) 22.1413 0.771329
\(825\) −4.28997 −0.149358
\(826\) 31.5402 1.09742
\(827\) −15.9583 −0.554923 −0.277461 0.960737i \(-0.589493\pi\)
−0.277461 + 0.960737i \(0.589493\pi\)
\(828\) 1.65901 0.0576544
\(829\) −36.0118 −1.25074 −0.625370 0.780328i \(-0.715052\pi\)
−0.625370 + 0.780328i \(0.715052\pi\)
\(830\) −3.26682 −0.113393
\(831\) −21.3581 −0.740904
\(832\) 10.1404 0.351556
\(833\) 4.08348 0.141484
\(834\) 5.59559 0.193759
\(835\) −15.2589 −0.528056
\(836\) −5.02730 −0.173873
\(837\) 10.6290 0.367392
\(838\) −10.4627 −0.361427
\(839\) 34.2082 1.18100 0.590499 0.807038i \(-0.298931\pi\)
0.590499 + 0.807038i \(0.298931\pi\)
\(840\) −7.14300 −0.246457
\(841\) 72.1298 2.48723
\(842\) 4.53253 0.156201
\(843\) 29.9872 1.03281
\(844\) 10.2001 0.351102
\(845\) −18.9748 −0.652752
\(846\) −4.30086 −0.147866
\(847\) −4.19208 −0.144041
\(848\) 0.850419 0.0292035
\(849\) −10.0912 −0.346330
\(850\) 0.905100 0.0310447
\(851\) 3.08859 0.105875
\(852\) −7.43080 −0.254575
\(853\) 11.3190 0.387554 0.193777 0.981046i \(-0.437926\pi\)
0.193777 + 0.981046i \(0.437926\pi\)
\(854\) 2.29012 0.0783664
\(855\) 2.48957 0.0851417
\(856\) 5.74935 0.196509
\(857\) 43.3860 1.48204 0.741019 0.671485i \(-0.234343\pi\)
0.741019 + 0.671485i \(0.234343\pi\)
\(858\) 3.25580 0.111151
\(859\) −25.6339 −0.874617 −0.437308 0.899312i \(-0.644068\pi\)
−0.437308 + 0.899312i \(0.644068\pi\)
\(860\) −7.16476 −0.244316
\(861\) −5.42107 −0.184750
\(862\) 9.66842 0.329308
\(863\) 16.0782 0.547309 0.273654 0.961828i \(-0.411768\pi\)
0.273654 + 0.961828i \(0.411768\pi\)
\(864\) 5.29993 0.180307
\(865\) 8.29759 0.282126
\(866\) −3.04789 −0.103572
\(867\) 16.8508 0.572285
\(868\) −75.8173 −2.57341
\(869\) 8.67552 0.294297
\(870\) 4.62921 0.156945
\(871\) −58.4592 −1.98081
\(872\) 39.3296 1.33187
\(873\) −6.00940 −0.203387
\(874\) −1.57369 −0.0532308
\(875\) −32.8156 −1.10937
\(876\) −3.51402 −0.118728
\(877\) −17.4124 −0.587974 −0.293987 0.955809i \(-0.594982\pi\)
−0.293987 + 0.955809i \(0.594982\pi\)
\(878\) 3.77286 0.127328
\(879\) 11.7387 0.395937
\(880\) 1.93672 0.0652867
\(881\) −41.4135 −1.39526 −0.697628 0.716460i \(-0.745761\pi\)
−0.697628 + 0.716460i \(0.745761\pi\)
\(882\) −5.77628 −0.194498
\(883\) −49.5096 −1.66613 −0.833066 0.553174i \(-0.813416\pi\)
−0.833066 + 0.553174i \(0.813416\pi\)
\(884\) 3.91639 0.131722
\(885\) 11.6049 0.390095
\(886\) −4.67038 −0.156905
\(887\) −48.4377 −1.62638 −0.813190 0.581999i \(-0.802271\pi\)
−0.813190 + 0.581999i \(0.802271\pi\)
\(888\) 6.40580 0.214965
\(889\) −4.98816 −0.167298
\(890\) −3.41762 −0.114559
\(891\) −1.00000 −0.0335013
\(892\) −2.05452 −0.0687905
\(893\) −23.2602 −0.778372
\(894\) −1.47837 −0.0494440
\(895\) 8.45240 0.282533
\(896\) −48.3320 −1.61466
\(897\) −5.81070 −0.194014
\(898\) 12.0747 0.402938
\(899\) 106.889 3.56494
\(900\) 7.29964 0.243321
\(901\) 0.142895 0.00476052
\(902\) −0.706457 −0.0235224
\(903\) −20.9482 −0.697112
\(904\) 16.3583 0.544068
\(905\) 11.1478 0.370566
\(906\) −8.54499 −0.283888
\(907\) 50.1623 1.66561 0.832807 0.553564i \(-0.186733\pi\)
0.832807 + 0.553564i \(0.186733\pi\)
\(908\) −5.39960 −0.179192
\(909\) −18.1851 −0.603161
\(910\) 11.5007 0.381244
\(911\) −19.2889 −0.639071 −0.319536 0.947574i \(-0.603527\pi\)
−0.319536 + 0.947574i \(0.603527\pi\)
\(912\) 6.79073 0.224864
\(913\) 7.09673 0.234867
\(914\) 6.69173 0.221343
\(915\) 0.842631 0.0278565
\(916\) 44.5509 1.47200
\(917\) 0.973717 0.0321550
\(918\) 0.210980 0.00696339
\(919\) −43.7882 −1.44444 −0.722220 0.691663i \(-0.756878\pi\)
−0.722220 + 0.691663i \(0.756878\pi\)
\(920\) 1.66132 0.0547720
\(921\) −12.1646 −0.400837
\(922\) 3.01389 0.0992572
\(923\) 26.0265 0.856673
\(924\) 7.13306 0.234660
\(925\) 13.5898 0.446830
\(926\) 21.3395 0.701259
\(927\) 10.9494 0.359624
\(928\) 53.2979 1.74959
\(929\) −27.0615 −0.887858 −0.443929 0.896062i \(-0.646416\pi\)
−0.443929 + 0.896062i \(0.646416\pi\)
\(930\) 4.89282 0.160442
\(931\) −31.2397 −1.02384
\(932\) −26.1335 −0.856032
\(933\) 10.4238 0.341260
\(934\) 8.44218 0.276237
\(935\) 0.325424 0.0106425
\(936\) −12.0515 −0.393916
\(937\) 2.66965 0.0872137 0.0436068 0.999049i \(-0.486115\pi\)
0.0436068 + 0.999049i \(0.486115\pi\)
\(938\) 22.4639 0.733471
\(939\) 3.70708 0.120976
\(940\) 11.2878 0.368167
\(941\) −31.2522 −1.01879 −0.509397 0.860532i \(-0.670132\pi\)
−0.509397 + 0.860532i \(0.670132\pi\)
\(942\) 1.91250 0.0623125
\(943\) 1.26083 0.0410583
\(944\) 31.6544 1.03026
\(945\) −3.53237 −0.114908
\(946\) −2.72990 −0.0887568
\(947\) −6.67071 −0.216769 −0.108384 0.994109i \(-0.534568\pi\)
−0.108384 + 0.994109i \(0.534568\pi\)
\(948\) −14.7619 −0.479444
\(949\) 12.3079 0.399532
\(950\) −6.92424 −0.224652
\(951\) 17.7635 0.576020
\(952\) −3.27383 −0.106105
\(953\) 14.3407 0.464540 0.232270 0.972651i \(-0.425385\pi\)
0.232270 + 0.972651i \(0.425385\pi\)
\(954\) −0.202132 −0.00654425
\(955\) 21.9648 0.710765
\(956\) 11.0315 0.356785
\(957\) −10.0563 −0.325075
\(958\) −10.4989 −0.339205
\(959\) 57.8280 1.86736
\(960\) −1.43373 −0.0462733
\(961\) 81.9756 2.64438
\(962\) −10.3137 −0.332528
\(963\) 2.84318 0.0916201
\(964\) 3.48848 0.112356
\(965\) 1.39014 0.0447501
\(966\) 2.23285 0.0718408
\(967\) 33.8580 1.08880 0.544400 0.838826i \(-0.316757\pi\)
0.544400 + 0.838826i \(0.316757\pi\)
\(968\) 2.02216 0.0649945
\(969\) 1.14104 0.0366554
\(970\) −2.76629 −0.0888203
\(971\) 23.2171 0.745074 0.372537 0.928017i \(-0.378488\pi\)
0.372537 + 0.928017i \(0.378488\pi\)
\(972\) 1.70156 0.0545775
\(973\) −42.9383 −1.37654
\(974\) 2.93180 0.0939411
\(975\) −25.5671 −0.818803
\(976\) 2.29842 0.0735705
\(977\) 11.4832 0.367381 0.183690 0.982984i \(-0.441196\pi\)
0.183690 + 0.982984i \(0.441196\pi\)
\(978\) 9.19176 0.293920
\(979\) 7.42432 0.237282
\(980\) 15.1601 0.484272
\(981\) 19.4494 0.620970
\(982\) 16.6067 0.529942
\(983\) −2.32576 −0.0741803 −0.0370901 0.999312i \(-0.511809\pi\)
−0.0370901 + 0.999312i \(0.511809\pi\)
\(984\) 2.61499 0.0833629
\(985\) 12.6472 0.402974
\(986\) 2.12169 0.0675683
\(987\) 33.0030 1.05050
\(988\) −29.9614 −0.953199
\(989\) 4.87213 0.154925
\(990\) −0.460328 −0.0146302
\(991\) −27.4890 −0.873218 −0.436609 0.899651i \(-0.643821\pi\)
−0.436609 + 0.899651i \(0.643821\pi\)
\(992\) 56.3330 1.78857
\(993\) −25.2813 −0.802279
\(994\) −10.0011 −0.317216
\(995\) −0.364629 −0.0115595
\(996\) −12.0755 −0.382627
\(997\) −0.204845 −0.00648751 −0.00324375 0.999995i \(-0.501033\pi\)
−0.00324375 + 0.999995i \(0.501033\pi\)
\(998\) 9.33754 0.295575
\(999\) 3.16781 0.100225
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 2013.2.a.h.1.6 14
3.2 odd 2 6039.2.a.j.1.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.h.1.6 14 1.1 even 1 trivial
6039.2.a.j.1.9 14 3.2 odd 2