Properties

Label 6010.2.a.i.1.16
Level $6010$
Weight $2$
Character 6010.1
Self dual yes
Analytic conductor $47.990$
Analytic rank $1$
Dimension $29$
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] = [6010,2,Mod(1,6010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6010.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: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.296108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.296108 q^{6} -4.13577 q^{7} -1.00000 q^{8} -2.91232 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.296108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.296108 q^{6} -4.13577 q^{7} -1.00000 q^{8} -2.91232 q^{9} +1.00000 q^{10} -0.822860 q^{11} -0.296108 q^{12} +3.99861 q^{13} +4.13577 q^{14} +0.296108 q^{15} +1.00000 q^{16} +0.706145 q^{17} +2.91232 q^{18} -7.10481 q^{19} -1.00000 q^{20} +1.22463 q^{21} +0.822860 q^{22} +1.64986 q^{23} +0.296108 q^{24} +1.00000 q^{25} -3.99861 q^{26} +1.75069 q^{27} -4.13577 q^{28} +5.42043 q^{29} -0.296108 q^{30} +9.32030 q^{31} -1.00000 q^{32} +0.243656 q^{33} -0.706145 q^{34} +4.13577 q^{35} -2.91232 q^{36} +8.12172 q^{37} +7.10481 q^{38} -1.18402 q^{39} +1.00000 q^{40} -3.09551 q^{41} -1.22463 q^{42} +1.99945 q^{43} -0.822860 q^{44} +2.91232 q^{45} -1.64986 q^{46} -6.03806 q^{47} -0.296108 q^{48} +10.1046 q^{49} -1.00000 q^{50} -0.209095 q^{51} +3.99861 q^{52} -9.56029 q^{53} -1.75069 q^{54} +0.822860 q^{55} +4.13577 q^{56} +2.10379 q^{57} -5.42043 q^{58} +13.5316 q^{59} +0.296108 q^{60} +1.75683 q^{61} -9.32030 q^{62} +12.0447 q^{63} +1.00000 q^{64} -3.99861 q^{65} -0.243656 q^{66} +3.37580 q^{67} +0.706145 q^{68} -0.488536 q^{69} -4.13577 q^{70} -9.49307 q^{71} +2.91232 q^{72} -2.28444 q^{73} -8.12172 q^{74} -0.296108 q^{75} -7.10481 q^{76} +3.40316 q^{77} +1.18402 q^{78} -10.1450 q^{79} -1.00000 q^{80} +8.21857 q^{81} +3.09551 q^{82} +4.37454 q^{83} +1.22463 q^{84} -0.706145 q^{85} -1.99945 q^{86} -1.60503 q^{87} +0.822860 q^{88} +17.8609 q^{89} -2.91232 q^{90} -16.5373 q^{91} +1.64986 q^{92} -2.75981 q^{93} +6.03806 q^{94} +7.10481 q^{95} +0.296108 q^{96} -4.31564 q^{97} -10.1046 q^{98} +2.39643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 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
\(3\) −0.296108 −0.170958 −0.0854790 0.996340i \(-0.527242\pi\)
−0.0854790 + 0.996340i \(0.527242\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.296108 0.120886
\(7\) −4.13577 −1.56317 −0.781586 0.623797i \(-0.785589\pi\)
−0.781586 + 0.623797i \(0.785589\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.91232 −0.970773
\(10\) 1.00000 0.316228
\(11\) −0.822860 −0.248102 −0.124051 0.992276i \(-0.539589\pi\)
−0.124051 + 0.992276i \(0.539589\pi\)
\(12\) −0.296108 −0.0854790
\(13\) 3.99861 1.10902 0.554508 0.832179i \(-0.312907\pi\)
0.554508 + 0.832179i \(0.312907\pi\)
\(14\) 4.13577 1.10533
\(15\) 0.296108 0.0764548
\(16\) 1.00000 0.250000
\(17\) 0.706145 0.171265 0.0856326 0.996327i \(-0.472709\pi\)
0.0856326 + 0.996327i \(0.472709\pi\)
\(18\) 2.91232 0.686440
\(19\) −7.10481 −1.62995 −0.814977 0.579493i \(-0.803251\pi\)
−0.814977 + 0.579493i \(0.803251\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.22463 0.267237
\(22\) 0.822860 0.175434
\(23\) 1.64986 0.344019 0.172009 0.985095i \(-0.444974\pi\)
0.172009 + 0.985095i \(0.444974\pi\)
\(24\) 0.296108 0.0604428
\(25\) 1.00000 0.200000
\(26\) −3.99861 −0.784192
\(27\) 1.75069 0.336920
\(28\) −4.13577 −0.781586
\(29\) 5.42043 1.00655 0.503274 0.864127i \(-0.332129\pi\)
0.503274 + 0.864127i \(0.332129\pi\)
\(30\) −0.296108 −0.0540617
\(31\) 9.32030 1.67397 0.836987 0.547222i \(-0.184315\pi\)
0.836987 + 0.547222i \(0.184315\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.243656 0.0424150
\(34\) −0.706145 −0.121103
\(35\) 4.13577 0.699072
\(36\) −2.91232 −0.485387
\(37\) 8.12172 1.33520 0.667601 0.744519i \(-0.267321\pi\)
0.667601 + 0.744519i \(0.267321\pi\)
\(38\) 7.10481 1.15255
\(39\) −1.18402 −0.189595
\(40\) 1.00000 0.158114
\(41\) −3.09551 −0.483437 −0.241719 0.970346i \(-0.577711\pi\)
−0.241719 + 0.970346i \(0.577711\pi\)
\(42\) −1.22463 −0.188965
\(43\) 1.99945 0.304914 0.152457 0.988310i \(-0.451281\pi\)
0.152457 + 0.988310i \(0.451281\pi\)
\(44\) −0.822860 −0.124051
\(45\) 2.91232 0.434143
\(46\) −1.64986 −0.243258
\(47\) −6.03806 −0.880741 −0.440370 0.897816i \(-0.645153\pi\)
−0.440370 + 0.897816i \(0.645153\pi\)
\(48\) −0.296108 −0.0427395
\(49\) 10.1046 1.44351
\(50\) −1.00000 −0.141421
\(51\) −0.209095 −0.0292792
\(52\) 3.99861 0.554508
\(53\) −9.56029 −1.31321 −0.656604 0.754236i \(-0.728007\pi\)
−0.656604 + 0.754236i \(0.728007\pi\)
\(54\) −1.75069 −0.238238
\(55\) 0.822860 0.110954
\(56\) 4.13577 0.552665
\(57\) 2.10379 0.278654
\(58\) −5.42043 −0.711737
\(59\) 13.5316 1.76166 0.880832 0.473428i \(-0.156984\pi\)
0.880832 + 0.473428i \(0.156984\pi\)
\(60\) 0.296108 0.0382274
\(61\) 1.75683 0.224939 0.112470 0.993655i \(-0.464124\pi\)
0.112470 + 0.993655i \(0.464124\pi\)
\(62\) −9.32030 −1.18368
\(63\) 12.0447 1.51749
\(64\) 1.00000 0.125000
\(65\) −3.99861 −0.495967
\(66\) −0.243656 −0.0299919
\(67\) 3.37580 0.412419 0.206210 0.978508i \(-0.433887\pi\)
0.206210 + 0.978508i \(0.433887\pi\)
\(68\) 0.706145 0.0856326
\(69\) −0.488536 −0.0588128
\(70\) −4.13577 −0.494319
\(71\) −9.49307 −1.12662 −0.563310 0.826246i \(-0.690472\pi\)
−0.563310 + 0.826246i \(0.690472\pi\)
\(72\) 2.91232 0.343220
\(73\) −2.28444 −0.267373 −0.133686 0.991024i \(-0.542682\pi\)
−0.133686 + 0.991024i \(0.542682\pi\)
\(74\) −8.12172 −0.944131
\(75\) −0.296108 −0.0341916
\(76\) −7.10481 −0.814977
\(77\) 3.40316 0.387826
\(78\) 1.18402 0.134064
\(79\) −10.1450 −1.14140 −0.570700 0.821159i \(-0.693328\pi\)
−0.570700 + 0.821159i \(0.693328\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.21857 0.913174
\(82\) 3.09551 0.341842
\(83\) 4.37454 0.480168 0.240084 0.970752i \(-0.422825\pi\)
0.240084 + 0.970752i \(0.422825\pi\)
\(84\) 1.22463 0.133618
\(85\) −0.706145 −0.0765922
\(86\) −1.99945 −0.215607
\(87\) −1.60503 −0.172077
\(88\) 0.822860 0.0877172
\(89\) 17.8609 1.89325 0.946627 0.322332i \(-0.104467\pi\)
0.946627 + 0.322332i \(0.104467\pi\)
\(90\) −2.91232 −0.306985
\(91\) −16.5373 −1.73358
\(92\) 1.64986 0.172009
\(93\) −2.75981 −0.286179
\(94\) 6.03806 0.622778
\(95\) 7.10481 0.728938
\(96\) 0.296108 0.0302214
\(97\) −4.31564 −0.438187 −0.219093 0.975704i \(-0.570310\pi\)
−0.219093 + 0.975704i \(0.570310\pi\)
\(98\) −10.1046 −1.02071
\(99\) 2.39643 0.240851
\(100\) 1.00000 0.100000
\(101\) 2.44498 0.243285 0.121642 0.992574i \(-0.461184\pi\)
0.121642 + 0.992574i \(0.461184\pi\)
\(102\) 0.209095 0.0207035
\(103\) 4.50202 0.443597 0.221799 0.975092i \(-0.428807\pi\)
0.221799 + 0.975092i \(0.428807\pi\)
\(104\) −3.99861 −0.392096
\(105\) −1.22463 −0.119512
\(106\) 9.56029 0.928578
\(107\) −11.3731 −1.09948 −0.549738 0.835337i \(-0.685273\pi\)
−0.549738 + 0.835337i \(0.685273\pi\)
\(108\) 1.75069 0.168460
\(109\) 10.0190 0.959644 0.479822 0.877366i \(-0.340701\pi\)
0.479822 + 0.877366i \(0.340701\pi\)
\(110\) −0.822860 −0.0784567
\(111\) −2.40491 −0.228264
\(112\) −4.13577 −0.390793
\(113\) 4.40252 0.414154 0.207077 0.978325i \(-0.433605\pi\)
0.207077 + 0.978325i \(0.433605\pi\)
\(114\) −2.10379 −0.197038
\(115\) −1.64986 −0.153850
\(116\) 5.42043 0.503274
\(117\) −11.6452 −1.07660
\(118\) −13.5316 −1.24569
\(119\) −2.92045 −0.267717
\(120\) −0.296108 −0.0270308
\(121\) −10.3229 −0.938446
\(122\) −1.75683 −0.159056
\(123\) 0.916605 0.0826475
\(124\) 9.32030 0.836987
\(125\) −1.00000 −0.0894427
\(126\) −12.0447 −1.07302
\(127\) −15.2948 −1.35720 −0.678598 0.734510i \(-0.737412\pi\)
−0.678598 + 0.734510i \(0.737412\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.592055 −0.0521275
\(130\) 3.99861 0.350701
\(131\) 3.96317 0.346263 0.173132 0.984899i \(-0.444611\pi\)
0.173132 + 0.984899i \(0.444611\pi\)
\(132\) 0.243656 0.0212075
\(133\) 29.3838 2.54790
\(134\) −3.37580 −0.291624
\(135\) −1.75069 −0.150675
\(136\) −0.706145 −0.0605514
\(137\) −4.62278 −0.394951 −0.197475 0.980308i \(-0.563274\pi\)
−0.197475 + 0.980308i \(0.563274\pi\)
\(138\) 0.488536 0.0415869
\(139\) 14.5029 1.23012 0.615061 0.788479i \(-0.289131\pi\)
0.615061 + 0.788479i \(0.289131\pi\)
\(140\) 4.13577 0.349536
\(141\) 1.78792 0.150570
\(142\) 9.49307 0.796641
\(143\) −3.29030 −0.275149
\(144\) −2.91232 −0.242693
\(145\) −5.42043 −0.450142
\(146\) 2.28444 0.189061
\(147\) −2.99204 −0.246779
\(148\) 8.12172 0.667601
\(149\) −1.37553 −0.112688 −0.0563438 0.998411i \(-0.517944\pi\)
−0.0563438 + 0.998411i \(0.517944\pi\)
\(150\) 0.296108 0.0241771
\(151\) −20.5910 −1.67567 −0.837834 0.545925i \(-0.816178\pi\)
−0.837834 + 0.545925i \(0.816178\pi\)
\(152\) 7.10481 0.576276
\(153\) −2.05652 −0.166260
\(154\) −3.40316 −0.274234
\(155\) −9.32030 −0.748624
\(156\) −1.18402 −0.0947975
\(157\) −10.0317 −0.800619 −0.400310 0.916380i \(-0.631097\pi\)
−0.400310 + 0.916380i \(0.631097\pi\)
\(158\) 10.1450 0.807092
\(159\) 2.83088 0.224503
\(160\) 1.00000 0.0790569
\(161\) −6.82342 −0.537761
\(162\) −8.21857 −0.645712
\(163\) 6.90312 0.540694 0.270347 0.962763i \(-0.412862\pi\)
0.270347 + 0.962763i \(0.412862\pi\)
\(164\) −3.09551 −0.241719
\(165\) −0.243656 −0.0189686
\(166\) −4.37454 −0.339530
\(167\) −11.7018 −0.905510 −0.452755 0.891635i \(-0.649559\pi\)
−0.452755 + 0.891635i \(0.649559\pi\)
\(168\) −1.22463 −0.0944825
\(169\) 2.98889 0.229915
\(170\) 0.706145 0.0541588
\(171\) 20.6915 1.58232
\(172\) 1.99945 0.152457
\(173\) −17.2942 −1.31485 −0.657425 0.753520i \(-0.728354\pi\)
−0.657425 + 0.753520i \(0.728354\pi\)
\(174\) 1.60503 0.121677
\(175\) −4.13577 −0.312635
\(176\) −0.822860 −0.0620254
\(177\) −4.00682 −0.301171
\(178\) −17.8609 −1.33873
\(179\) −13.4637 −1.00633 −0.503163 0.864192i \(-0.667830\pi\)
−0.503163 + 0.864192i \(0.667830\pi\)
\(180\) 2.91232 0.217072
\(181\) −8.63696 −0.641980 −0.320990 0.947083i \(-0.604016\pi\)
−0.320990 + 0.947083i \(0.604016\pi\)
\(182\) 16.5373 1.22583
\(183\) −0.520212 −0.0384551
\(184\) −1.64986 −0.121629
\(185\) −8.12172 −0.597121
\(186\) 2.75981 0.202359
\(187\) −0.581059 −0.0424912
\(188\) −6.03806 −0.440370
\(189\) −7.24042 −0.526663
\(190\) −7.10481 −0.515437
\(191\) 19.6582 1.42241 0.711207 0.702983i \(-0.248149\pi\)
0.711207 + 0.702983i \(0.248149\pi\)
\(192\) −0.296108 −0.0213698
\(193\) 8.04192 0.578870 0.289435 0.957198i \(-0.406533\pi\)
0.289435 + 0.957198i \(0.406533\pi\)
\(194\) 4.31564 0.309845
\(195\) 1.18402 0.0847895
\(196\) 10.1046 0.721754
\(197\) 5.98586 0.426475 0.213237 0.977000i \(-0.431599\pi\)
0.213237 + 0.977000i \(0.431599\pi\)
\(198\) −2.39643 −0.170307
\(199\) −14.4209 −1.02227 −0.511135 0.859500i \(-0.670775\pi\)
−0.511135 + 0.859500i \(0.670775\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −0.999600 −0.0705064
\(202\) −2.44498 −0.172028
\(203\) −22.4176 −1.57341
\(204\) −0.209095 −0.0146396
\(205\) 3.09551 0.216200
\(206\) −4.50202 −0.313671
\(207\) −4.80491 −0.333964
\(208\) 3.99861 0.277254
\(209\) 5.84626 0.404394
\(210\) 1.22463 0.0845077
\(211\) −15.9423 −1.09752 −0.548758 0.835981i \(-0.684899\pi\)
−0.548758 + 0.835981i \(0.684899\pi\)
\(212\) −9.56029 −0.656604
\(213\) 2.81097 0.192605
\(214\) 11.3731 0.777447
\(215\) −1.99945 −0.136362
\(216\) −1.75069 −0.119119
\(217\) −38.5466 −2.61671
\(218\) −10.0190 −0.678570
\(219\) 0.676439 0.0457095
\(220\) 0.822860 0.0554772
\(221\) 2.82360 0.189936
\(222\) 2.40491 0.161407
\(223\) −22.3927 −1.49952 −0.749761 0.661708i \(-0.769832\pi\)
−0.749761 + 0.661708i \(0.769832\pi\)
\(224\) 4.13577 0.276332
\(225\) −2.91232 −0.194155
\(226\) −4.40252 −0.292851
\(227\) −25.4914 −1.69193 −0.845963 0.533242i \(-0.820973\pi\)
−0.845963 + 0.533242i \(0.820973\pi\)
\(228\) 2.10379 0.139327
\(229\) 14.2915 0.944406 0.472203 0.881490i \(-0.343459\pi\)
0.472203 + 0.881490i \(0.343459\pi\)
\(230\) 1.64986 0.108788
\(231\) −1.00770 −0.0663019
\(232\) −5.42043 −0.355868
\(233\) −8.74153 −0.572677 −0.286338 0.958129i \(-0.592438\pi\)
−0.286338 + 0.958129i \(0.592438\pi\)
\(234\) 11.6452 0.761273
\(235\) 6.03806 0.393879
\(236\) 13.5316 0.880832
\(237\) 3.00401 0.195132
\(238\) 2.92045 0.189305
\(239\) 12.0802 0.781403 0.390702 0.920517i \(-0.372232\pi\)
0.390702 + 0.920517i \(0.372232\pi\)
\(240\) 0.296108 0.0191137
\(241\) 26.0973 1.68107 0.840537 0.541754i \(-0.182240\pi\)
0.840537 + 0.541754i \(0.182240\pi\)
\(242\) 10.3229 0.663581
\(243\) −7.68564 −0.493034
\(244\) 1.75683 0.112470
\(245\) −10.1046 −0.645557
\(246\) −0.916605 −0.0584406
\(247\) −28.4094 −1.80764
\(248\) −9.32030 −0.591839
\(249\) −1.29534 −0.0820886
\(250\) 1.00000 0.0632456
\(251\) −20.6946 −1.30623 −0.653115 0.757259i \(-0.726538\pi\)
−0.653115 + 0.757259i \(0.726538\pi\)
\(252\) 12.0447 0.758743
\(253\) −1.35760 −0.0853517
\(254\) 15.2948 0.959682
\(255\) 0.209095 0.0130940
\(256\) 1.00000 0.0625000
\(257\) 7.82529 0.488128 0.244064 0.969759i \(-0.421519\pi\)
0.244064 + 0.969759i \(0.421519\pi\)
\(258\) 0.592055 0.0368597
\(259\) −33.5895 −2.08715
\(260\) −3.99861 −0.247983
\(261\) −15.7860 −0.977130
\(262\) −3.96317 −0.244845
\(263\) 15.9940 0.986232 0.493116 0.869964i \(-0.335858\pi\)
0.493116 + 0.869964i \(0.335858\pi\)
\(264\) −0.243656 −0.0149960
\(265\) 9.56029 0.587284
\(266\) −29.3838 −1.80164
\(267\) −5.28876 −0.323667
\(268\) 3.37580 0.206210
\(269\) 17.2558 1.05210 0.526051 0.850453i \(-0.323672\pi\)
0.526051 + 0.850453i \(0.323672\pi\)
\(270\) 1.75069 0.106543
\(271\) 11.3627 0.690236 0.345118 0.938559i \(-0.387839\pi\)
0.345118 + 0.938559i \(0.387839\pi\)
\(272\) 0.706145 0.0428163
\(273\) 4.89683 0.296370
\(274\) 4.62278 0.279272
\(275\) −0.822860 −0.0496204
\(276\) −0.488536 −0.0294064
\(277\) 18.4155 1.10648 0.553240 0.833022i \(-0.313391\pi\)
0.553240 + 0.833022i \(0.313391\pi\)
\(278\) −14.5029 −0.869828
\(279\) −27.1437 −1.62505
\(280\) −4.13577 −0.247159
\(281\) 1.48925 0.0888410 0.0444205 0.999013i \(-0.485856\pi\)
0.0444205 + 0.999013i \(0.485856\pi\)
\(282\) −1.78792 −0.106469
\(283\) 19.5290 1.16088 0.580438 0.814304i \(-0.302881\pi\)
0.580438 + 0.814304i \(0.302881\pi\)
\(284\) −9.49307 −0.563310
\(285\) −2.10379 −0.124618
\(286\) 3.29030 0.194559
\(287\) 12.8023 0.755696
\(288\) 2.91232 0.171610
\(289\) −16.5014 −0.970668
\(290\) 5.42043 0.318298
\(291\) 1.27790 0.0749115
\(292\) −2.28444 −0.133686
\(293\) −20.1562 −1.17754 −0.588770 0.808301i \(-0.700388\pi\)
−0.588770 + 0.808301i \(0.700388\pi\)
\(294\) 2.99204 0.174499
\(295\) −13.5316 −0.787840
\(296\) −8.12172 −0.472065
\(297\) −1.44057 −0.0835903
\(298\) 1.37553 0.0796822
\(299\) 6.59714 0.381522
\(300\) −0.296108 −0.0170958
\(301\) −8.26928 −0.476633
\(302\) 20.5910 1.18488
\(303\) −0.723978 −0.0415914
\(304\) −7.10481 −0.407489
\(305\) −1.75683 −0.100596
\(306\) 2.05652 0.117563
\(307\) −29.9663 −1.71027 −0.855133 0.518408i \(-0.826525\pi\)
−0.855133 + 0.518408i \(0.826525\pi\)
\(308\) 3.40316 0.193913
\(309\) −1.33308 −0.0758365
\(310\) 9.32030 0.529357
\(311\) −0.121878 −0.00691105 −0.00345553 0.999994i \(-0.501100\pi\)
−0.00345553 + 0.999994i \(0.501100\pi\)
\(312\) 1.18402 0.0670320
\(313\) 12.5030 0.706714 0.353357 0.935489i \(-0.385040\pi\)
0.353357 + 0.935489i \(0.385040\pi\)
\(314\) 10.0317 0.566123
\(315\) −12.0447 −0.678640
\(316\) −10.1450 −0.570700
\(317\) −22.3371 −1.25458 −0.627288 0.778787i \(-0.715835\pi\)
−0.627288 + 0.778787i \(0.715835\pi\)
\(318\) −2.83088 −0.158748
\(319\) −4.46025 −0.249726
\(320\) −1.00000 −0.0559017
\(321\) 3.36766 0.187964
\(322\) 6.82342 0.380254
\(323\) −5.01702 −0.279155
\(324\) 8.21857 0.456587
\(325\) 3.99861 0.221803
\(326\) −6.90312 −0.382329
\(327\) −2.96670 −0.164059
\(328\) 3.09551 0.170921
\(329\) 24.9720 1.37675
\(330\) 0.243656 0.0134128
\(331\) 25.6526 1.40999 0.704997 0.709210i \(-0.250948\pi\)
0.704997 + 0.709210i \(0.250948\pi\)
\(332\) 4.37454 0.240084
\(333\) −23.6530 −1.29618
\(334\) 11.7018 0.640292
\(335\) −3.37580 −0.184439
\(336\) 1.22463 0.0668092
\(337\) −19.2644 −1.04940 −0.524700 0.851287i \(-0.675823\pi\)
−0.524700 + 0.851287i \(0.675823\pi\)
\(338\) −2.98889 −0.162574
\(339\) −1.30362 −0.0708030
\(340\) −0.706145 −0.0382961
\(341\) −7.66930 −0.415316
\(342\) −20.6915 −1.11887
\(343\) −12.8397 −0.693280
\(344\) −1.99945 −0.107803
\(345\) 0.488536 0.0263019
\(346\) 17.2942 0.929740
\(347\) −17.9569 −0.963977 −0.481989 0.876177i \(-0.660085\pi\)
−0.481989 + 0.876177i \(0.660085\pi\)
\(348\) −1.60503 −0.0860387
\(349\) −4.82970 −0.258528 −0.129264 0.991610i \(-0.541261\pi\)
−0.129264 + 0.991610i \(0.541261\pi\)
\(350\) 4.13577 0.221066
\(351\) 7.00031 0.373649
\(352\) 0.822860 0.0438586
\(353\) 8.09667 0.430942 0.215471 0.976510i \(-0.430871\pi\)
0.215471 + 0.976510i \(0.430871\pi\)
\(354\) 4.00682 0.212960
\(355\) 9.49307 0.503840
\(356\) 17.8609 0.946627
\(357\) 0.864768 0.0457684
\(358\) 13.4637 0.711579
\(359\) −3.71498 −0.196069 −0.0980347 0.995183i \(-0.531256\pi\)
−0.0980347 + 0.995183i \(0.531256\pi\)
\(360\) −2.91232 −0.153493
\(361\) 31.4783 1.65675
\(362\) 8.63696 0.453949
\(363\) 3.05669 0.160435
\(364\) −16.5373 −0.866791
\(365\) 2.28444 0.119573
\(366\) 0.520212 0.0271919
\(367\) −5.56678 −0.290584 −0.145292 0.989389i \(-0.546412\pi\)
−0.145292 + 0.989389i \(0.546412\pi\)
\(368\) 1.64986 0.0860047
\(369\) 9.01511 0.469308
\(370\) 8.12172 0.422228
\(371\) 39.5391 2.05277
\(372\) −2.75981 −0.143090
\(373\) 0.0486608 0.00251956 0.00125978 0.999999i \(-0.499599\pi\)
0.00125978 + 0.999999i \(0.499599\pi\)
\(374\) 0.581059 0.0300458
\(375\) 0.296108 0.0152910
\(376\) 6.03806 0.311389
\(377\) 21.6742 1.11628
\(378\) 7.24042 0.372407
\(379\) 31.7768 1.63227 0.816133 0.577863i \(-0.196113\pi\)
0.816133 + 0.577863i \(0.196113\pi\)
\(380\) 7.10481 0.364469
\(381\) 4.52892 0.232024
\(382\) −19.6582 −1.00580
\(383\) 31.6798 1.61876 0.809380 0.587285i \(-0.199803\pi\)
0.809380 + 0.587285i \(0.199803\pi\)
\(384\) 0.296108 0.0151107
\(385\) −3.40316 −0.173441
\(386\) −8.04192 −0.409323
\(387\) −5.82305 −0.296002
\(388\) −4.31564 −0.219093
\(389\) 39.1623 1.98561 0.992803 0.119756i \(-0.0382114\pi\)
0.992803 + 0.119756i \(0.0382114\pi\)
\(390\) −1.18402 −0.0599552
\(391\) 1.16504 0.0589185
\(392\) −10.1046 −0.510357
\(393\) −1.17353 −0.0591965
\(394\) −5.98586 −0.301563
\(395\) 10.1450 0.510450
\(396\) 2.39643 0.120425
\(397\) 8.06487 0.404764 0.202382 0.979307i \(-0.435132\pi\)
0.202382 + 0.979307i \(0.435132\pi\)
\(398\) 14.4209 0.722854
\(399\) −8.70078 −0.435584
\(400\) 1.00000 0.0500000
\(401\) −12.4473 −0.621588 −0.310794 0.950477i \(-0.600595\pi\)
−0.310794 + 0.950477i \(0.600595\pi\)
\(402\) 0.999600 0.0498555
\(403\) 37.2682 1.85646
\(404\) 2.44498 0.121642
\(405\) −8.21857 −0.408384
\(406\) 22.4176 1.11257
\(407\) −6.68304 −0.331266
\(408\) 0.209095 0.0103517
\(409\) 13.8530 0.684987 0.342493 0.939520i \(-0.388729\pi\)
0.342493 + 0.939520i \(0.388729\pi\)
\(410\) −3.09551 −0.152876
\(411\) 1.36884 0.0675200
\(412\) 4.50202 0.221799
\(413\) −55.9635 −2.75379
\(414\) 4.80491 0.236148
\(415\) −4.37454 −0.214738
\(416\) −3.99861 −0.196048
\(417\) −4.29443 −0.210299
\(418\) −5.84626 −0.285950
\(419\) 33.8364 1.65302 0.826508 0.562925i \(-0.190324\pi\)
0.826508 + 0.562925i \(0.190324\pi\)
\(420\) −1.22463 −0.0597560
\(421\) 29.1105 1.41876 0.709379 0.704827i \(-0.248976\pi\)
0.709379 + 0.704827i \(0.248976\pi\)
\(422\) 15.9423 0.776061
\(423\) 17.5847 0.855000
\(424\) 9.56029 0.464289
\(425\) 0.706145 0.0342531
\(426\) −2.81097 −0.136192
\(427\) −7.26584 −0.351619
\(428\) −11.3731 −0.549738
\(429\) 0.974284 0.0470389
\(430\) 1.99945 0.0964223
\(431\) −27.7288 −1.33565 −0.667825 0.744318i \(-0.732775\pi\)
−0.667825 + 0.744318i \(0.732775\pi\)
\(432\) 1.75069 0.0842299
\(433\) −20.0254 −0.962361 −0.481180 0.876622i \(-0.659792\pi\)
−0.481180 + 0.876622i \(0.659792\pi\)
\(434\) 38.5466 1.85029
\(435\) 1.60503 0.0769554
\(436\) 10.0190 0.479822
\(437\) −11.7219 −0.560735
\(438\) −0.676439 −0.0323215
\(439\) 17.4058 0.830734 0.415367 0.909654i \(-0.363653\pi\)
0.415367 + 0.909654i \(0.363653\pi\)
\(440\) −0.822860 −0.0392283
\(441\) −29.4277 −1.40132
\(442\) −2.82360 −0.134305
\(443\) −34.8435 −1.65546 −0.827732 0.561123i \(-0.810369\pi\)
−0.827732 + 0.561123i \(0.810369\pi\)
\(444\) −2.40491 −0.114132
\(445\) −17.8609 −0.846689
\(446\) 22.3927 1.06032
\(447\) 0.407305 0.0192648
\(448\) −4.13577 −0.195397
\(449\) −32.0077 −1.51053 −0.755267 0.655417i \(-0.772493\pi\)
−0.755267 + 0.655417i \(0.772493\pi\)
\(450\) 2.91232 0.137288
\(451\) 2.54717 0.119942
\(452\) 4.40252 0.207077
\(453\) 6.09715 0.286469
\(454\) 25.4914 1.19637
\(455\) 16.5373 0.775282
\(456\) −2.10379 −0.0985190
\(457\) −10.1150 −0.473158 −0.236579 0.971612i \(-0.576026\pi\)
−0.236579 + 0.971612i \(0.576026\pi\)
\(458\) −14.2915 −0.667796
\(459\) 1.23624 0.0577026
\(460\) −1.64986 −0.0769250
\(461\) −25.7053 −1.19721 −0.598607 0.801043i \(-0.704279\pi\)
−0.598607 + 0.801043i \(0.704279\pi\)
\(462\) 1.00770 0.0468826
\(463\) −26.4196 −1.22782 −0.613912 0.789374i \(-0.710405\pi\)
−0.613912 + 0.789374i \(0.710405\pi\)
\(464\) 5.42043 0.251637
\(465\) 2.75981 0.127983
\(466\) 8.74153 0.404944
\(467\) 5.55271 0.256949 0.128474 0.991713i \(-0.458992\pi\)
0.128474 + 0.991713i \(0.458992\pi\)
\(468\) −11.6452 −0.538301
\(469\) −13.9615 −0.644682
\(470\) −6.03806 −0.278515
\(471\) 2.97048 0.136872
\(472\) −13.5316 −0.622843
\(473\) −1.64527 −0.0756497
\(474\) −3.00401 −0.137979
\(475\) −7.10481 −0.325991
\(476\) −2.92045 −0.133859
\(477\) 27.8426 1.27483
\(478\) −12.0802 −0.552535
\(479\) −33.0201 −1.50873 −0.754363 0.656458i \(-0.772054\pi\)
−0.754363 + 0.656458i \(0.772054\pi\)
\(480\) −0.296108 −0.0135154
\(481\) 32.4756 1.48076
\(482\) −26.0973 −1.18870
\(483\) 2.02047 0.0919345
\(484\) −10.3229 −0.469223
\(485\) 4.31564 0.195963
\(486\) 7.68564 0.348628
\(487\) 12.6051 0.571192 0.285596 0.958350i \(-0.407808\pi\)
0.285596 + 0.958350i \(0.407808\pi\)
\(488\) −1.75683 −0.0795280
\(489\) −2.04407 −0.0924360
\(490\) 10.1046 0.456477
\(491\) 9.50398 0.428909 0.214454 0.976734i \(-0.431203\pi\)
0.214454 + 0.976734i \(0.431203\pi\)
\(492\) 0.916605 0.0413237
\(493\) 3.82761 0.172387
\(494\) 28.4094 1.27820
\(495\) −2.39643 −0.107712
\(496\) 9.32030 0.418494
\(497\) 39.2611 1.76110
\(498\) 1.29534 0.0580454
\(499\) 1.73969 0.0778793 0.0389396 0.999242i \(-0.487602\pi\)
0.0389396 + 0.999242i \(0.487602\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 3.46499 0.154804
\(502\) 20.6946 0.923644
\(503\) −37.4195 −1.66845 −0.834226 0.551422i \(-0.814085\pi\)
−0.834226 + 0.551422i \(0.814085\pi\)
\(504\) −12.0447 −0.536512
\(505\) −2.44498 −0.108800
\(506\) 1.35760 0.0603528
\(507\) −0.885036 −0.0393058
\(508\) −15.2948 −0.678598
\(509\) −22.4908 −0.996886 −0.498443 0.866923i \(-0.666095\pi\)
−0.498443 + 0.866923i \(0.666095\pi\)
\(510\) −0.209095 −0.00925889
\(511\) 9.44789 0.417950
\(512\) −1.00000 −0.0441942
\(513\) −12.4383 −0.549163
\(514\) −7.82529 −0.345159
\(515\) −4.50202 −0.198383
\(516\) −0.592055 −0.0260637
\(517\) 4.96848 0.218513
\(518\) 33.5895 1.47584
\(519\) 5.12094 0.224784
\(520\) 3.99861 0.175351
\(521\) −37.5682 −1.64589 −0.822947 0.568118i \(-0.807672\pi\)
−0.822947 + 0.568118i \(0.807672\pi\)
\(522\) 15.7860 0.690935
\(523\) 6.93113 0.303077 0.151539 0.988451i \(-0.451577\pi\)
0.151539 + 0.988451i \(0.451577\pi\)
\(524\) 3.96317 0.173132
\(525\) 1.22463 0.0534474
\(526\) −15.9940 −0.697371
\(527\) 6.58148 0.286694
\(528\) 0.243656 0.0106037
\(529\) −20.2780 −0.881651
\(530\) −9.56029 −0.415273
\(531\) −39.4084 −1.71018
\(532\) 29.3838 1.27395
\(533\) −12.3777 −0.536139
\(534\) 5.28876 0.228867
\(535\) 11.3731 0.491701
\(536\) −3.37580 −0.145812
\(537\) 3.98671 0.172039
\(538\) −17.2558 −0.743948
\(539\) −8.31464 −0.358137
\(540\) −1.75069 −0.0753375
\(541\) −11.1664 −0.480080 −0.240040 0.970763i \(-0.577161\pi\)
−0.240040 + 0.970763i \(0.577161\pi\)
\(542\) −11.3627 −0.488071
\(543\) 2.55747 0.109752
\(544\) −0.706145 −0.0302757
\(545\) −10.0190 −0.429166
\(546\) −4.89683 −0.209565
\(547\) 11.7714 0.503311 0.251655 0.967817i \(-0.419025\pi\)
0.251655 + 0.967817i \(0.419025\pi\)
\(548\) −4.62278 −0.197475
\(549\) −5.11645 −0.218365
\(550\) 0.822860 0.0350869
\(551\) −38.5111 −1.64063
\(552\) 0.488536 0.0207935
\(553\) 41.9573 1.78421
\(554\) −18.4155 −0.782400
\(555\) 2.40491 0.102083
\(556\) 14.5029 0.615061
\(557\) −21.8550 −0.926028 −0.463014 0.886351i \(-0.653232\pi\)
−0.463014 + 0.886351i \(0.653232\pi\)
\(558\) 27.1437 1.14908
\(559\) 7.99504 0.338154
\(560\) 4.13577 0.174768
\(561\) 0.172056 0.00726421
\(562\) −1.48925 −0.0628200
\(563\) −11.2852 −0.475616 −0.237808 0.971312i \(-0.576429\pi\)
−0.237808 + 0.971312i \(0.576429\pi\)
\(564\) 1.78792 0.0752849
\(565\) −4.40252 −0.185216
\(566\) −19.5290 −0.820863
\(567\) −33.9901 −1.42745
\(568\) 9.49307 0.398320
\(569\) −3.54576 −0.148646 −0.0743229 0.997234i \(-0.523680\pi\)
−0.0743229 + 0.997234i \(0.523680\pi\)
\(570\) 2.10379 0.0881181
\(571\) 6.12529 0.256335 0.128168 0.991753i \(-0.459090\pi\)
0.128168 + 0.991753i \(0.459090\pi\)
\(572\) −3.29030 −0.137574
\(573\) −5.82094 −0.243173
\(574\) −12.8023 −0.534358
\(575\) 1.64986 0.0688038
\(576\) −2.91232 −0.121347
\(577\) −5.43131 −0.226108 −0.113054 0.993589i \(-0.536063\pi\)
−0.113054 + 0.993589i \(0.536063\pi\)
\(578\) 16.5014 0.686366
\(579\) −2.38128 −0.0989625
\(580\) −5.42043 −0.225071
\(581\) −18.0921 −0.750586
\(582\) −1.27790 −0.0529705
\(583\) 7.86679 0.325809
\(584\) 2.28444 0.0945306
\(585\) 11.6452 0.481471
\(586\) 20.1562 0.832646
\(587\) −10.7921 −0.445438 −0.222719 0.974883i \(-0.571493\pi\)
−0.222719 + 0.974883i \(0.571493\pi\)
\(588\) −2.99204 −0.123390
\(589\) −66.2189 −2.72850
\(590\) 13.5316 0.557087
\(591\) −1.77246 −0.0729093
\(592\) 8.12172 0.333801
\(593\) −15.6129 −0.641144 −0.320572 0.947224i \(-0.603875\pi\)
−0.320572 + 0.947224i \(0.603875\pi\)
\(594\) 1.44057 0.0591073
\(595\) 2.92045 0.119727
\(596\) −1.37553 −0.0563438
\(597\) 4.27014 0.174765
\(598\) −6.59714 −0.269777
\(599\) 16.2243 0.662907 0.331454 0.943472i \(-0.392461\pi\)
0.331454 + 0.943472i \(0.392461\pi\)
\(600\) 0.296108 0.0120886
\(601\) −1.00000 −0.0407909
\(602\) 8.26928 0.337031
\(603\) −9.83140 −0.400366
\(604\) −20.5910 −0.837834
\(605\) 10.3229 0.419686
\(606\) 0.723978 0.0294096
\(607\) −28.6329 −1.16217 −0.581087 0.813841i \(-0.697372\pi\)
−0.581087 + 0.813841i \(0.697372\pi\)
\(608\) 7.10481 0.288138
\(609\) 6.63803 0.268987
\(610\) 1.75683 0.0711320
\(611\) −24.1438 −0.976755
\(612\) −2.05652 −0.0831299
\(613\) 38.8736 1.57009 0.785046 0.619438i \(-0.212639\pi\)
0.785046 + 0.619438i \(0.212639\pi\)
\(614\) 29.9663 1.20934
\(615\) −0.916605 −0.0369611
\(616\) −3.40316 −0.137117
\(617\) −14.3262 −0.576751 −0.288375 0.957517i \(-0.593115\pi\)
−0.288375 + 0.957517i \(0.593115\pi\)
\(618\) 1.33308 0.0536245
\(619\) 28.5541 1.14769 0.573843 0.818965i \(-0.305452\pi\)
0.573843 + 0.818965i \(0.305452\pi\)
\(620\) −9.32030 −0.374312
\(621\) 2.88838 0.115907
\(622\) 0.121878 0.00488685
\(623\) −73.8686 −2.95948
\(624\) −1.18402 −0.0473988
\(625\) 1.00000 0.0400000
\(626\) −12.5030 −0.499722
\(627\) −1.73113 −0.0691345
\(628\) −10.0317 −0.400310
\(629\) 5.73511 0.228674
\(630\) 12.0447 0.479871
\(631\) −31.2959 −1.24587 −0.622936 0.782273i \(-0.714060\pi\)
−0.622936 + 0.782273i \(0.714060\pi\)
\(632\) 10.1450 0.403546
\(633\) 4.72066 0.187629
\(634\) 22.3371 0.887119
\(635\) 15.2948 0.606956
\(636\) 2.83088 0.112252
\(637\) 40.4042 1.60087
\(638\) 4.46025 0.176583
\(639\) 27.6469 1.09369
\(640\) 1.00000 0.0395285
\(641\) −12.3622 −0.488277 −0.244138 0.969740i \(-0.578505\pi\)
−0.244138 + 0.969740i \(0.578505\pi\)
\(642\) −3.36766 −0.132911
\(643\) −16.2820 −0.642099 −0.321050 0.947062i \(-0.604036\pi\)
−0.321050 + 0.947062i \(0.604036\pi\)
\(644\) −6.82342 −0.268880
\(645\) 0.592055 0.0233121
\(646\) 5.01702 0.197392
\(647\) −18.3327 −0.720731 −0.360366 0.932811i \(-0.617348\pi\)
−0.360366 + 0.932811i \(0.617348\pi\)
\(648\) −8.21857 −0.322856
\(649\) −11.1346 −0.437072
\(650\) −3.99861 −0.156838
\(651\) 11.4139 0.447348
\(652\) 6.90312 0.270347
\(653\) −38.2637 −1.49737 −0.748687 0.662924i \(-0.769315\pi\)
−0.748687 + 0.662924i \(0.769315\pi\)
\(654\) 2.96670 0.116007
\(655\) −3.96317 −0.154854
\(656\) −3.09551 −0.120859
\(657\) 6.65301 0.259558
\(658\) −24.9720 −0.973509
\(659\) −33.5330 −1.30626 −0.653131 0.757245i \(-0.726545\pi\)
−0.653131 + 0.757245i \(0.726545\pi\)
\(660\) −0.243656 −0.00948428
\(661\) 24.9749 0.971412 0.485706 0.874122i \(-0.338563\pi\)
0.485706 + 0.874122i \(0.338563\pi\)
\(662\) −25.6526 −0.997016
\(663\) −0.836090 −0.0324710
\(664\) −4.37454 −0.169765
\(665\) −29.3838 −1.13946
\(666\) 23.6530 0.916537
\(667\) 8.94293 0.346271
\(668\) −11.7018 −0.452755
\(669\) 6.63064 0.256355
\(670\) 3.37580 0.130418
\(671\) −1.44563 −0.0558078
\(672\) −1.22463 −0.0472413
\(673\) 30.6584 1.18179 0.590897 0.806747i \(-0.298774\pi\)
0.590897 + 0.806747i \(0.298774\pi\)
\(674\) 19.2644 0.742038
\(675\) 1.75069 0.0673839
\(676\) 2.98889 0.114957
\(677\) −22.2925 −0.856769 −0.428384 0.903597i \(-0.640917\pi\)
−0.428384 + 0.903597i \(0.640917\pi\)
\(678\) 1.30362 0.0500653
\(679\) 17.8485 0.684961
\(680\) 0.706145 0.0270794
\(681\) 7.54821 0.289248
\(682\) 7.66930 0.293673
\(683\) 21.3750 0.817892 0.408946 0.912559i \(-0.365896\pi\)
0.408946 + 0.912559i \(0.365896\pi\)
\(684\) 20.6915 0.791158
\(685\) 4.62278 0.176627
\(686\) 12.8397 0.490223
\(687\) −4.23181 −0.161454
\(688\) 1.99945 0.0762285
\(689\) −38.2279 −1.45637
\(690\) −0.488536 −0.0185982
\(691\) 5.34740 0.203425 0.101712 0.994814i \(-0.467568\pi\)
0.101712 + 0.994814i \(0.467568\pi\)
\(692\) −17.2942 −0.657425
\(693\) −9.91109 −0.376491
\(694\) 17.9569 0.681635
\(695\) −14.5029 −0.550127
\(696\) 1.60503 0.0608386
\(697\) −2.18588 −0.0827960
\(698\) 4.82970 0.182807
\(699\) 2.58844 0.0979037
\(700\) −4.13577 −0.156317
\(701\) −27.4229 −1.03575 −0.517874 0.855457i \(-0.673276\pi\)
−0.517874 + 0.855457i \(0.673276\pi\)
\(702\) −7.00031 −0.264210
\(703\) −57.7032 −2.17632
\(704\) −0.822860 −0.0310127
\(705\) −1.78792 −0.0673368
\(706\) −8.09667 −0.304722
\(707\) −10.1119 −0.380296
\(708\) −4.00682 −0.150585
\(709\) 21.1429 0.794039 0.397019 0.917810i \(-0.370045\pi\)
0.397019 + 0.917810i \(0.370045\pi\)
\(710\) −9.49307 −0.356269
\(711\) 29.5454 1.10804
\(712\) −17.8609 −0.669366
\(713\) 15.3772 0.575879
\(714\) −0.864768 −0.0323631
\(715\) 3.29030 0.123050
\(716\) −13.4637 −0.503163
\(717\) −3.57704 −0.133587
\(718\) 3.71498 0.138642
\(719\) −20.2239 −0.754223 −0.377111 0.926168i \(-0.623083\pi\)
−0.377111 + 0.926168i \(0.623083\pi\)
\(720\) 2.91232 0.108536
\(721\) −18.6193 −0.693419
\(722\) −31.4783 −1.17150
\(723\) −7.72762 −0.287393
\(724\) −8.63696 −0.320990
\(725\) 5.42043 0.201310
\(726\) −3.05669 −0.113445
\(727\) −27.1280 −1.00612 −0.503062 0.864251i \(-0.667793\pi\)
−0.503062 + 0.864251i \(0.667793\pi\)
\(728\) 16.5373 0.612914
\(729\) −22.3799 −0.828886
\(730\) −2.28444 −0.0845507
\(731\) 1.41190 0.0522212
\(732\) −0.520212 −0.0192276
\(733\) 27.9836 1.03360 0.516800 0.856106i \(-0.327123\pi\)
0.516800 + 0.856106i \(0.327123\pi\)
\(734\) 5.56678 0.205474
\(735\) 2.99204 0.110363
\(736\) −1.64986 −0.0608145
\(737\) −2.77781 −0.102322
\(738\) −9.01511 −0.331851
\(739\) −33.7585 −1.24183 −0.620913 0.783880i \(-0.713238\pi\)
−0.620913 + 0.783880i \(0.713238\pi\)
\(740\) −8.12172 −0.298560
\(741\) 8.41224 0.309031
\(742\) −39.5391 −1.45153
\(743\) 19.2666 0.706821 0.353411 0.935468i \(-0.385022\pi\)
0.353411 + 0.935468i \(0.385022\pi\)
\(744\) 2.75981 0.101180
\(745\) 1.37553 0.0503954
\(746\) −0.0486608 −0.00178160
\(747\) −12.7401 −0.466135
\(748\) −0.581059 −0.0212456
\(749\) 47.0364 1.71867
\(750\) −0.296108 −0.0108123
\(751\) 0.636085 0.0232111 0.0116055 0.999933i \(-0.496306\pi\)
0.0116055 + 0.999933i \(0.496306\pi\)
\(752\) −6.03806 −0.220185
\(753\) 6.12783 0.223310
\(754\) −21.6742 −0.789327
\(755\) 20.5910 0.749382
\(756\) −7.24042 −0.263332
\(757\) 6.52218 0.237053 0.118526 0.992951i \(-0.462183\pi\)
0.118526 + 0.992951i \(0.462183\pi\)
\(758\) −31.7768 −1.15419
\(759\) 0.401997 0.0145916
\(760\) −7.10481 −0.257718
\(761\) 3.77881 0.136982 0.0684909 0.997652i \(-0.478182\pi\)
0.0684909 + 0.997652i \(0.478182\pi\)
\(762\) −4.52892 −0.164065
\(763\) −41.4361 −1.50009
\(764\) 19.6582 0.711207
\(765\) 2.05652 0.0743536
\(766\) −31.6798 −1.14464
\(767\) 54.1076 1.95371
\(768\) −0.296108 −0.0106849
\(769\) 0.555843 0.0200442 0.0100221 0.999950i \(-0.496810\pi\)
0.0100221 + 0.999950i \(0.496810\pi\)
\(770\) 3.40316 0.122641
\(771\) −2.31713 −0.0834495
\(772\) 8.04192 0.289435
\(773\) −5.06431 −0.182151 −0.0910753 0.995844i \(-0.529030\pi\)
−0.0910753 + 0.995844i \(0.529030\pi\)
\(774\) 5.82305 0.209305
\(775\) 9.32030 0.334795
\(776\) 4.31564 0.154922
\(777\) 9.94613 0.356815
\(778\) −39.1623 −1.40404
\(779\) 21.9930 0.787981
\(780\) 1.18402 0.0423947
\(781\) 7.81147 0.279516
\(782\) −1.16504 −0.0416617
\(783\) 9.48946 0.339126
\(784\) 10.1046 0.360877
\(785\) 10.0317 0.358048
\(786\) 1.17353 0.0418583
\(787\) 33.9465 1.21006 0.605030 0.796202i \(-0.293161\pi\)
0.605030 + 0.796202i \(0.293161\pi\)
\(788\) 5.98586 0.213237
\(789\) −4.73595 −0.168604
\(790\) −10.1450 −0.360942
\(791\) −18.2078 −0.647395
\(792\) −2.39643 −0.0851535
\(793\) 7.02488 0.249461
\(794\) −8.06487 −0.286212
\(795\) −2.83088 −0.100401
\(796\) −14.4209 −0.511135
\(797\) 29.6491 1.05022 0.525112 0.851033i \(-0.324023\pi\)
0.525112 + 0.851033i \(0.324023\pi\)
\(798\) 8.70078 0.308004
\(799\) −4.26374 −0.150840
\(800\) −1.00000 −0.0353553
\(801\) −52.0167 −1.83792
\(802\) 12.4473 0.439529
\(803\) 1.87977 0.0663357
\(804\) −0.999600 −0.0352532
\(805\) 6.82342 0.240494
\(806\) −37.2682 −1.31272
\(807\) −5.10957 −0.179865
\(808\) −2.44498 −0.0860141
\(809\) −51.1694 −1.79902 −0.899509 0.436901i \(-0.856076\pi\)
−0.899509 + 0.436901i \(0.856076\pi\)
\(810\) 8.21857 0.288771
\(811\) 9.31015 0.326923 0.163462 0.986550i \(-0.447734\pi\)
0.163462 + 0.986550i \(0.447734\pi\)
\(812\) −22.4176 −0.786704
\(813\) −3.36459 −0.118001
\(814\) 6.68304 0.234241
\(815\) −6.90312 −0.241806
\(816\) −0.209095 −0.00731979
\(817\) −14.2057 −0.496996
\(818\) −13.8530 −0.484359
\(819\) 48.1620 1.68292
\(820\) 3.09551 0.108100
\(821\) −29.7388 −1.03789 −0.518945 0.854808i \(-0.673675\pi\)
−0.518945 + 0.854808i \(0.673675\pi\)
\(822\) −1.36884 −0.0477439
\(823\) −34.1657 −1.19094 −0.595470 0.803377i \(-0.703034\pi\)
−0.595470 + 0.803377i \(0.703034\pi\)
\(824\) −4.50202 −0.156835
\(825\) 0.243656 0.00848300
\(826\) 55.9635 1.94722
\(827\) 9.18166 0.319278 0.159639 0.987175i \(-0.448967\pi\)
0.159639 + 0.987175i \(0.448967\pi\)
\(828\) −4.80491 −0.166982
\(829\) 34.3418 1.19274 0.596370 0.802710i \(-0.296609\pi\)
0.596370 + 0.802710i \(0.296609\pi\)
\(830\) 4.37454 0.151843
\(831\) −5.45298 −0.189162
\(832\) 3.99861 0.138627
\(833\) 7.13528 0.247223
\(834\) 4.29443 0.148704
\(835\) 11.7018 0.404956
\(836\) 5.84626 0.202197
\(837\) 16.3169 0.563995
\(838\) −33.8364 −1.16886
\(839\) −25.5692 −0.882748 −0.441374 0.897323i \(-0.645509\pi\)
−0.441374 + 0.897323i \(0.645509\pi\)
\(840\) 1.22463 0.0422539
\(841\) 0.381014 0.0131384
\(842\) −29.1105 −1.00321
\(843\) −0.440978 −0.0151881
\(844\) −15.9423 −0.548758
\(845\) −2.98889 −0.102821
\(846\) −17.5847 −0.604576
\(847\) 42.6931 1.46695
\(848\) −9.56029 −0.328302
\(849\) −5.78268 −0.198461
\(850\) −0.706145 −0.0242206
\(851\) 13.3997 0.459335
\(852\) 2.81097 0.0963024
\(853\) −23.9968 −0.821633 −0.410817 0.911718i \(-0.634756\pi\)
−0.410817 + 0.911718i \(0.634756\pi\)
\(854\) 7.26584 0.248632
\(855\) −20.6915 −0.707633
\(856\) 11.3731 0.388724
\(857\) −44.2671 −1.51214 −0.756068 0.654493i \(-0.772882\pi\)
−0.756068 + 0.654493i \(0.772882\pi\)
\(858\) −0.974284 −0.0332615
\(859\) −3.76483 −0.128454 −0.0642271 0.997935i \(-0.520458\pi\)
−0.0642271 + 0.997935i \(0.520458\pi\)
\(860\) −1.99945 −0.0681808
\(861\) −3.79086 −0.129192
\(862\) 27.7288 0.944448
\(863\) 37.7084 1.28361 0.641805 0.766868i \(-0.278186\pi\)
0.641805 + 0.766868i \(0.278186\pi\)
\(864\) −1.75069 −0.0595595
\(865\) 17.2942 0.588019
\(866\) 20.0254 0.680492
\(867\) 4.88618 0.165944
\(868\) −38.5466 −1.30836
\(869\) 8.34791 0.283183
\(870\) −1.60503 −0.0544157
\(871\) 13.4985 0.457379
\(872\) −10.0190 −0.339285
\(873\) 12.5685 0.425380
\(874\) 11.7219 0.396500
\(875\) 4.13577 0.139814
\(876\) 0.676439 0.0228548
\(877\) 20.4230 0.689634 0.344817 0.938670i \(-0.387941\pi\)
0.344817 + 0.938670i \(0.387941\pi\)
\(878\) −17.4058 −0.587417
\(879\) 5.96842 0.201310
\(880\) 0.822860 0.0277386
\(881\) 47.9464 1.61535 0.807677 0.589625i \(-0.200724\pi\)
0.807677 + 0.589625i \(0.200724\pi\)
\(882\) 29.4277 0.990882
\(883\) 42.4944 1.43005 0.715025 0.699098i \(-0.246415\pi\)
0.715025 + 0.699098i \(0.246415\pi\)
\(884\) 2.82360 0.0949679
\(885\) 4.00682 0.134688
\(886\) 34.8435 1.17059
\(887\) 29.9976 1.00722 0.503610 0.863931i \(-0.332005\pi\)
0.503610 + 0.863931i \(0.332005\pi\)
\(888\) 2.40491 0.0807034
\(889\) 63.2558 2.12153
\(890\) 17.8609 0.598699
\(891\) −6.76273 −0.226560
\(892\) −22.3927 −0.749761
\(893\) 42.8992 1.43557
\(894\) −0.407305 −0.0136223
\(895\) 13.4637 0.450042
\(896\) 4.13577 0.138166
\(897\) −1.95346 −0.0652243
\(898\) 32.0077 1.06811
\(899\) 50.5200 1.68494
\(900\) −2.91232 −0.0970773
\(901\) −6.75095 −0.224907
\(902\) −2.54717 −0.0848115
\(903\) 2.44860 0.0814843
\(904\) −4.40252 −0.146426
\(905\) 8.63696 0.287102
\(906\) −6.09715 −0.202564
\(907\) −53.4495 −1.77476 −0.887380 0.461038i \(-0.847477\pi\)
−0.887380 + 0.461038i \(0.847477\pi\)
\(908\) −25.4914 −0.845963
\(909\) −7.12056 −0.236174
\(910\) −16.5373 −0.548207
\(911\) 15.2363 0.504801 0.252401 0.967623i \(-0.418780\pi\)
0.252401 + 0.967623i \(0.418780\pi\)
\(912\) 2.10379 0.0696634
\(913\) −3.59964 −0.119131
\(914\) 10.1150 0.334573
\(915\) 0.520212 0.0171977
\(916\) 14.2915 0.472203
\(917\) −16.3907 −0.541269
\(918\) −1.23624 −0.0408019
\(919\) 55.2002 1.82089 0.910443 0.413634i \(-0.135741\pi\)
0.910443 + 0.413634i \(0.135741\pi\)
\(920\) 1.64986 0.0543942
\(921\) 8.87326 0.292384
\(922\) 25.7053 0.846558
\(923\) −37.9591 −1.24944
\(924\) −1.00770 −0.0331510
\(925\) 8.12172 0.267040
\(926\) 26.4196 0.868203
\(927\) −13.1113 −0.430633
\(928\) −5.42043 −0.177934
\(929\) −17.0622 −0.559791 −0.279896 0.960030i \(-0.590300\pi\)
−0.279896 + 0.960030i \(0.590300\pi\)
\(930\) −2.75981 −0.0904979
\(931\) −71.7909 −2.35285
\(932\) −8.74153 −0.286338
\(933\) 0.0360890 0.00118150
\(934\) −5.55271 −0.181690
\(935\) 0.581059 0.0190026
\(936\) 11.6452 0.380636
\(937\) 39.0453 1.27556 0.637778 0.770221i \(-0.279854\pi\)
0.637778 + 0.770221i \(0.279854\pi\)
\(938\) 13.9615 0.455859
\(939\) −3.70225 −0.120818
\(940\) 6.03806 0.196940
\(941\) 12.4496 0.405844 0.202922 0.979195i \(-0.434956\pi\)
0.202922 + 0.979195i \(0.434956\pi\)
\(942\) −2.97048 −0.0967833
\(943\) −5.10715 −0.166312
\(944\) 13.5316 0.440416
\(945\) 7.24042 0.235531
\(946\) 1.64527 0.0534924
\(947\) −19.8281 −0.644328 −0.322164 0.946684i \(-0.604410\pi\)
−0.322164 + 0.946684i \(0.604410\pi\)
\(948\) 3.00401 0.0975658
\(949\) −9.13457 −0.296521
\(950\) 7.10481 0.230510
\(951\) 6.61419 0.214480
\(952\) 2.92045 0.0946523
\(953\) 35.6756 1.15565 0.577823 0.816162i \(-0.303902\pi\)
0.577823 + 0.816162i \(0.303902\pi\)
\(954\) −27.8426 −0.901438
\(955\) −19.6582 −0.636123
\(956\) 12.0802 0.390702
\(957\) 1.32072 0.0426927
\(958\) 33.0201 1.06683
\(959\) 19.1187 0.617376
\(960\) 0.296108 0.00955684
\(961\) 55.8679 1.80219
\(962\) −32.4756 −1.04706
\(963\) 33.1220 1.06734
\(964\) 26.0973 0.840537
\(965\) −8.04192 −0.258879
\(966\) −2.02047 −0.0650075
\(967\) −56.7690 −1.82557 −0.912784 0.408442i \(-0.866072\pi\)
−0.912784 + 0.408442i \(0.866072\pi\)
\(968\) 10.3229 0.331791
\(969\) 1.48558 0.0477237
\(970\) −4.31564 −0.138567
\(971\) −30.5244 −0.979575 −0.489788 0.871842i \(-0.662926\pi\)
−0.489788 + 0.871842i \(0.662926\pi\)
\(972\) −7.68564 −0.246517
\(973\) −59.9807 −1.92289
\(974\) −12.6051 −0.403894
\(975\) −1.18402 −0.0379190
\(976\) 1.75683 0.0562348
\(977\) −1.53158 −0.0489997 −0.0244999 0.999700i \(-0.507799\pi\)
−0.0244999 + 0.999700i \(0.507799\pi\)
\(978\) 2.04407 0.0653621
\(979\) −14.6970 −0.469719
\(980\) −10.1046 −0.322778
\(981\) −29.1785 −0.931596
\(982\) −9.50398 −0.303284
\(983\) 0.964359 0.0307583 0.0153791 0.999882i \(-0.495104\pi\)
0.0153791 + 0.999882i \(0.495104\pi\)
\(984\) −0.916605 −0.0292203
\(985\) −5.98586 −0.190725
\(986\) −3.82761 −0.121896
\(987\) −7.39440 −0.235366
\(988\) −28.4094 −0.903822
\(989\) 3.29881 0.104896
\(990\) 2.39643 0.0761636
\(991\) −38.5148 −1.22346 −0.611732 0.791065i \(-0.709527\pi\)
−0.611732 + 0.791065i \(0.709527\pi\)
\(992\) −9.32030 −0.295920
\(993\) −7.59594 −0.241050
\(994\) −39.2611 −1.24529
\(995\) 14.4209 0.457173
\(996\) −1.29534 −0.0410443
\(997\) −12.6946 −0.402043 −0.201021 0.979587i \(-0.564426\pi\)
−0.201021 + 0.979587i \(0.564426\pi\)
\(998\) −1.73969 −0.0550690
\(999\) 14.2186 0.449856
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 6010.2.a.i.1.16 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6010.2.a.i.1.16 29 1.1 even 1 trivial