Properties

Label 6014.2.a.f.1.10
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $22$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.531212 q^{3} +1.00000 q^{4} +1.86385 q^{5} +0.531212 q^{6} -4.06404 q^{7} -1.00000 q^{8} -2.71781 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.531212 q^{3} +1.00000 q^{4} +1.86385 q^{5} +0.531212 q^{6} -4.06404 q^{7} -1.00000 q^{8} -2.71781 q^{9} -1.86385 q^{10} +2.15501 q^{11} -0.531212 q^{12} +0.240812 q^{13} +4.06404 q^{14} -0.990100 q^{15} +1.00000 q^{16} +5.05056 q^{17} +2.71781 q^{18} -2.35517 q^{19} +1.86385 q^{20} +2.15886 q^{21} -2.15501 q^{22} +6.69545 q^{23} +0.531212 q^{24} -1.52606 q^{25} -0.240812 q^{26} +3.03737 q^{27} -4.06404 q^{28} -7.35248 q^{29} +0.990100 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.14477 q^{33} -5.05056 q^{34} -7.57475 q^{35} -2.71781 q^{36} +1.51194 q^{37} +2.35517 q^{38} -0.127922 q^{39} -1.86385 q^{40} +0.437600 q^{41} -2.15886 q^{42} -2.73910 q^{43} +2.15501 q^{44} -5.06560 q^{45} -6.69545 q^{46} -11.2456 q^{47} -0.531212 q^{48} +9.51638 q^{49} +1.52606 q^{50} -2.68292 q^{51} +0.240812 q^{52} -10.9375 q^{53} -3.03737 q^{54} +4.01662 q^{55} +4.06404 q^{56} +1.25109 q^{57} +7.35248 q^{58} +9.67425 q^{59} -0.990100 q^{60} +15.2735 q^{61} -1.00000 q^{62} +11.0453 q^{63} +1.00000 q^{64} +0.448838 q^{65} +1.14477 q^{66} +3.34422 q^{67} +5.05056 q^{68} -3.55670 q^{69} +7.57475 q^{70} +1.95372 q^{71} +2.71781 q^{72} +1.25545 q^{73} -1.51194 q^{74} +0.810663 q^{75} -2.35517 q^{76} -8.75805 q^{77} +0.127922 q^{78} +6.32603 q^{79} +1.86385 q^{80} +6.53995 q^{81} -0.437600 q^{82} +9.96182 q^{83} +2.15886 q^{84} +9.41349 q^{85} +2.73910 q^{86} +3.90573 q^{87} -2.15501 q^{88} -14.0185 q^{89} +5.06560 q^{90} -0.978669 q^{91} +6.69545 q^{92} -0.531212 q^{93} +11.2456 q^{94} -4.38968 q^{95} +0.531212 q^{96} +1.00000 q^{97} -9.51638 q^{98} -5.85692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 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
\(3\) −0.531212 −0.306695 −0.153348 0.988172i \(-0.549005\pi\)
−0.153348 + 0.988172i \(0.549005\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.86385 0.833539 0.416770 0.909012i \(-0.363162\pi\)
0.416770 + 0.909012i \(0.363162\pi\)
\(6\) 0.531212 0.216866
\(7\) −4.06404 −1.53606 −0.768031 0.640413i \(-0.778763\pi\)
−0.768031 + 0.640413i \(0.778763\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.71781 −0.905938
\(10\) −1.86385 −0.589401
\(11\) 2.15501 0.649761 0.324880 0.945755i \(-0.394676\pi\)
0.324880 + 0.945755i \(0.394676\pi\)
\(12\) −0.531212 −0.153348
\(13\) 0.240812 0.0667892 0.0333946 0.999442i \(-0.489368\pi\)
0.0333946 + 0.999442i \(0.489368\pi\)
\(14\) 4.06404 1.08616
\(15\) −0.990100 −0.255643
\(16\) 1.00000 0.250000
\(17\) 5.05056 1.22494 0.612470 0.790493i \(-0.290176\pi\)
0.612470 + 0.790493i \(0.290176\pi\)
\(18\) 2.71781 0.640595
\(19\) −2.35517 −0.540312 −0.270156 0.962817i \(-0.587075\pi\)
−0.270156 + 0.962817i \(0.587075\pi\)
\(20\) 1.86385 0.416770
\(21\) 2.15886 0.471103
\(22\) −2.15501 −0.459450
\(23\) 6.69545 1.39610 0.698048 0.716051i \(-0.254052\pi\)
0.698048 + 0.716051i \(0.254052\pi\)
\(24\) 0.531212 0.108433
\(25\) −1.52606 −0.305213
\(26\) −0.240812 −0.0472271
\(27\) 3.03737 0.584542
\(28\) −4.06404 −0.768031
\(29\) −7.35248 −1.36532 −0.682661 0.730736i \(-0.739177\pi\)
−0.682661 + 0.730736i \(0.739177\pi\)
\(30\) 0.990100 0.180767
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) −1.14477 −0.199279
\(34\) −5.05056 −0.866164
\(35\) −7.57475 −1.28037
\(36\) −2.71781 −0.452969
\(37\) 1.51194 0.248561 0.124280 0.992247i \(-0.460338\pi\)
0.124280 + 0.992247i \(0.460338\pi\)
\(38\) 2.35517 0.382058
\(39\) −0.127922 −0.0204840
\(40\) −1.86385 −0.294701
\(41\) 0.437600 0.0683416 0.0341708 0.999416i \(-0.489121\pi\)
0.0341708 + 0.999416i \(0.489121\pi\)
\(42\) −2.15886 −0.333120
\(43\) −2.73910 −0.417709 −0.208854 0.977947i \(-0.566973\pi\)
−0.208854 + 0.977947i \(0.566973\pi\)
\(44\) 2.15501 0.324880
\(45\) −5.06560 −0.755135
\(46\) −6.69545 −0.987190
\(47\) −11.2456 −1.64034 −0.820168 0.572123i \(-0.806120\pi\)
−0.820168 + 0.572123i \(0.806120\pi\)
\(48\) −0.531212 −0.0766739
\(49\) 9.51638 1.35948
\(50\) 1.52606 0.215818
\(51\) −2.68292 −0.375684
\(52\) 0.240812 0.0333946
\(53\) −10.9375 −1.50238 −0.751190 0.660086i \(-0.770520\pi\)
−0.751190 + 0.660086i \(0.770520\pi\)
\(54\) −3.03737 −0.413334
\(55\) 4.01662 0.541601
\(56\) 4.06404 0.543080
\(57\) 1.25109 0.165711
\(58\) 7.35248 0.965428
\(59\) 9.67425 1.25948 0.629740 0.776806i \(-0.283161\pi\)
0.629740 + 0.776806i \(0.283161\pi\)
\(60\) −0.990100 −0.127821
\(61\) 15.2735 1.95557 0.977785 0.209611i \(-0.0672199\pi\)
0.977785 + 0.209611i \(0.0672199\pi\)
\(62\) −1.00000 −0.127000
\(63\) 11.0453 1.39158
\(64\) 1.00000 0.125000
\(65\) 0.448838 0.0556714
\(66\) 1.14477 0.140911
\(67\) 3.34422 0.408562 0.204281 0.978912i \(-0.434514\pi\)
0.204281 + 0.978912i \(0.434514\pi\)
\(68\) 5.05056 0.612470
\(69\) −3.55670 −0.428177
\(70\) 7.57475 0.905356
\(71\) 1.95372 0.231864 0.115932 0.993257i \(-0.463014\pi\)
0.115932 + 0.993257i \(0.463014\pi\)
\(72\) 2.71781 0.320297
\(73\) 1.25545 0.146939 0.0734696 0.997297i \(-0.476593\pi\)
0.0734696 + 0.997297i \(0.476593\pi\)
\(74\) −1.51194 −0.175759
\(75\) 0.810663 0.0936073
\(76\) −2.35517 −0.270156
\(77\) −8.75805 −0.998072
\(78\) 0.127922 0.0144843
\(79\) 6.32603 0.711734 0.355867 0.934537i \(-0.384186\pi\)
0.355867 + 0.934537i \(0.384186\pi\)
\(80\) 1.86385 0.208385
\(81\) 6.53995 0.726661
\(82\) −0.437600 −0.0483248
\(83\) 9.96182 1.09345 0.546726 0.837312i \(-0.315874\pi\)
0.546726 + 0.837312i \(0.315874\pi\)
\(84\) 2.15886 0.235551
\(85\) 9.41349 1.02104
\(86\) 2.73910 0.295365
\(87\) 3.90573 0.418738
\(88\) −2.15501 −0.229725
\(89\) −14.0185 −1.48596 −0.742978 0.669316i \(-0.766587\pi\)
−0.742978 + 0.669316i \(0.766587\pi\)
\(90\) 5.06560 0.533961
\(91\) −0.978669 −0.102592
\(92\) 6.69545 0.698048
\(93\) −0.531212 −0.0550841
\(94\) 11.2456 1.15989
\(95\) −4.38968 −0.450371
\(96\) 0.531212 0.0542166
\(97\) 1.00000 0.101535
\(98\) −9.51638 −0.961300
\(99\) −5.85692 −0.588643
\(100\) −1.52606 −0.152606
\(101\) −5.00795 −0.498310 −0.249155 0.968464i \(-0.580153\pi\)
−0.249155 + 0.968464i \(0.580153\pi\)
\(102\) 2.68292 0.265649
\(103\) 11.1096 1.09466 0.547329 0.836918i \(-0.315645\pi\)
0.547329 + 0.836918i \(0.315645\pi\)
\(104\) −0.240812 −0.0236136
\(105\) 4.02380 0.392683
\(106\) 10.9375 1.06234
\(107\) −5.19849 −0.502557 −0.251279 0.967915i \(-0.580851\pi\)
−0.251279 + 0.967915i \(0.580851\pi\)
\(108\) 3.03737 0.292271
\(109\) −17.4332 −1.66979 −0.834897 0.550407i \(-0.814473\pi\)
−0.834897 + 0.550407i \(0.814473\pi\)
\(110\) −4.01662 −0.382970
\(111\) −0.803159 −0.0762325
\(112\) −4.06404 −0.384015
\(113\) −1.86512 −0.175456 −0.0877280 0.996144i \(-0.527961\pi\)
−0.0877280 + 0.996144i \(0.527961\pi\)
\(114\) −1.25109 −0.117176
\(115\) 12.4793 1.16370
\(116\) −7.35248 −0.682661
\(117\) −0.654482 −0.0605069
\(118\) −9.67425 −0.890587
\(119\) −20.5257 −1.88158
\(120\) 0.990100 0.0903833
\(121\) −6.35592 −0.577811
\(122\) −15.2735 −1.38280
\(123\) −0.232458 −0.0209601
\(124\) 1.00000 0.0898027
\(125\) −12.1636 −1.08795
\(126\) −11.0453 −0.983993
\(127\) −9.43734 −0.837429 −0.418714 0.908118i \(-0.637519\pi\)
−0.418714 + 0.908118i \(0.637519\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.45504 0.128109
\(130\) −0.448838 −0.0393657
\(131\) −3.80936 −0.332826 −0.166413 0.986056i \(-0.553218\pi\)
−0.166413 + 0.986056i \(0.553218\pi\)
\(132\) −1.14477 −0.0996393
\(133\) 9.57148 0.829953
\(134\) −3.34422 −0.288897
\(135\) 5.66120 0.487239
\(136\) −5.05056 −0.433082
\(137\) −9.27362 −0.792299 −0.396149 0.918186i \(-0.629654\pi\)
−0.396149 + 0.918186i \(0.629654\pi\)
\(138\) 3.55670 0.302767
\(139\) 0.598622 0.0507745 0.0253872 0.999678i \(-0.491918\pi\)
0.0253872 + 0.999678i \(0.491918\pi\)
\(140\) −7.57475 −0.640183
\(141\) 5.97378 0.503083
\(142\) −1.95372 −0.163953
\(143\) 0.518953 0.0433970
\(144\) −2.71781 −0.226484
\(145\) −13.7039 −1.13805
\(146\) −1.25545 −0.103902
\(147\) −5.05522 −0.416947
\(148\) 1.51194 0.124280
\(149\) 15.0404 1.23215 0.616077 0.787686i \(-0.288721\pi\)
0.616077 + 0.787686i \(0.288721\pi\)
\(150\) −0.810663 −0.0661904
\(151\) −2.61615 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(152\) 2.35517 0.191029
\(153\) −13.7265 −1.10972
\(154\) 8.75805 0.705744
\(155\) 1.86385 0.149708
\(156\) −0.127922 −0.0102420
\(157\) 14.3268 1.14340 0.571702 0.820461i \(-0.306283\pi\)
0.571702 + 0.820461i \(0.306283\pi\)
\(158\) −6.32603 −0.503272
\(159\) 5.81013 0.460773
\(160\) −1.86385 −0.147350
\(161\) −27.2105 −2.14449
\(162\) −6.53995 −0.513827
\(163\) −21.7235 −1.70151 −0.850756 0.525560i \(-0.823856\pi\)
−0.850756 + 0.525560i \(0.823856\pi\)
\(164\) 0.437600 0.0341708
\(165\) −2.13368 −0.166107
\(166\) −9.96182 −0.773187
\(167\) 7.18386 0.555904 0.277952 0.960595i \(-0.410344\pi\)
0.277952 + 0.960595i \(0.410344\pi\)
\(168\) −2.15886 −0.166560
\(169\) −12.9420 −0.995539
\(170\) −9.41349 −0.721982
\(171\) 6.40090 0.489489
\(172\) −2.73910 −0.208854
\(173\) 15.9336 1.21141 0.605703 0.795691i \(-0.292892\pi\)
0.605703 + 0.795691i \(0.292892\pi\)
\(174\) −3.90573 −0.296092
\(175\) 6.20198 0.468825
\(176\) 2.15501 0.162440
\(177\) −5.13908 −0.386277
\(178\) 14.0185 1.05073
\(179\) −13.9130 −1.03990 −0.519952 0.854195i \(-0.674050\pi\)
−0.519952 + 0.854195i \(0.674050\pi\)
\(180\) −5.06560 −0.377567
\(181\) 7.67066 0.570156 0.285078 0.958504i \(-0.407981\pi\)
0.285078 + 0.958504i \(0.407981\pi\)
\(182\) 0.978669 0.0725438
\(183\) −8.11346 −0.599764
\(184\) −6.69545 −0.493595
\(185\) 2.81802 0.207185
\(186\) 0.531212 0.0389504
\(187\) 10.8840 0.795919
\(188\) −11.2456 −0.820168
\(189\) −12.3440 −0.897893
\(190\) 4.38968 0.318461
\(191\) −21.9540 −1.58853 −0.794267 0.607568i \(-0.792145\pi\)
−0.794267 + 0.607568i \(0.792145\pi\)
\(192\) −0.531212 −0.0383369
\(193\) 4.32134 0.311057 0.155528 0.987831i \(-0.450292\pi\)
0.155528 + 0.987831i \(0.450292\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −0.238428 −0.0170742
\(196\) 9.51638 0.679742
\(197\) −19.4316 −1.38444 −0.692222 0.721684i \(-0.743368\pi\)
−0.692222 + 0.721684i \(0.743368\pi\)
\(198\) 5.85692 0.416233
\(199\) 5.99771 0.425167 0.212583 0.977143i \(-0.431812\pi\)
0.212583 + 0.977143i \(0.431812\pi\)
\(200\) 1.52606 0.107909
\(201\) −1.77649 −0.125304
\(202\) 5.00795 0.352358
\(203\) 29.8807 2.09722
\(204\) −2.68292 −0.187842
\(205\) 0.815620 0.0569654
\(206\) −11.1096 −0.774040
\(207\) −18.1970 −1.26478
\(208\) 0.240812 0.0166973
\(209\) −5.07541 −0.351074
\(210\) −4.02380 −0.277669
\(211\) 10.5332 0.725135 0.362567 0.931958i \(-0.381900\pi\)
0.362567 + 0.931958i \(0.381900\pi\)
\(212\) −10.9375 −0.751190
\(213\) −1.03784 −0.0711117
\(214\) 5.19849 0.355362
\(215\) −5.10527 −0.348176
\(216\) −3.03737 −0.206667
\(217\) −4.06404 −0.275885
\(218\) 17.4332 1.18072
\(219\) −0.666909 −0.0450656
\(220\) 4.01662 0.270800
\(221\) 1.21624 0.0818129
\(222\) 0.803159 0.0539045
\(223\) 14.8409 0.993820 0.496910 0.867802i \(-0.334468\pi\)
0.496910 + 0.867802i \(0.334468\pi\)
\(224\) 4.06404 0.271540
\(225\) 4.14756 0.276504
\(226\) 1.86512 0.124066
\(227\) 11.4527 0.760143 0.380072 0.924957i \(-0.375899\pi\)
0.380072 + 0.924957i \(0.375899\pi\)
\(228\) 1.25109 0.0828557
\(229\) −14.1093 −0.932370 −0.466185 0.884687i \(-0.654372\pi\)
−0.466185 + 0.884687i \(0.654372\pi\)
\(230\) −12.4793 −0.822861
\(231\) 4.65238 0.306104
\(232\) 7.35248 0.482714
\(233\) −17.7045 −1.15986 −0.579931 0.814666i \(-0.696921\pi\)
−0.579931 + 0.814666i \(0.696921\pi\)
\(234\) 0.654482 0.0427848
\(235\) −20.9601 −1.36728
\(236\) 9.67425 0.629740
\(237\) −3.36046 −0.218286
\(238\) 20.5257 1.33048
\(239\) 10.8794 0.703731 0.351865 0.936051i \(-0.385548\pi\)
0.351865 + 0.936051i \(0.385548\pi\)
\(240\) −0.990100 −0.0639107
\(241\) −23.9685 −1.54395 −0.771973 0.635655i \(-0.780730\pi\)
−0.771973 + 0.635655i \(0.780730\pi\)
\(242\) 6.35592 0.408574
\(243\) −12.5862 −0.807406
\(244\) 15.2735 0.977785
\(245\) 17.7371 1.13318
\(246\) 0.232458 0.0148210
\(247\) −0.567153 −0.0360871
\(248\) −1.00000 −0.0635001
\(249\) −5.29184 −0.335357
\(250\) 12.1636 0.769294
\(251\) 20.6521 1.30355 0.651775 0.758412i \(-0.274025\pi\)
0.651775 + 0.758412i \(0.274025\pi\)
\(252\) 11.0453 0.695788
\(253\) 14.4288 0.907129
\(254\) 9.43734 0.592152
\(255\) −5.00056 −0.313147
\(256\) 1.00000 0.0625000
\(257\) 14.2771 0.890578 0.445289 0.895387i \(-0.353101\pi\)
0.445289 + 0.895387i \(0.353101\pi\)
\(258\) −1.45504 −0.0905870
\(259\) −6.14456 −0.381805
\(260\) 0.448838 0.0278357
\(261\) 19.9827 1.23690
\(262\) 3.80936 0.235343
\(263\) −15.8164 −0.975282 −0.487641 0.873044i \(-0.662142\pi\)
−0.487641 + 0.873044i \(0.662142\pi\)
\(264\) 1.14477 0.0704556
\(265\) −20.3858 −1.25229
\(266\) −9.57148 −0.586865
\(267\) 7.44678 0.455736
\(268\) 3.34422 0.204281
\(269\) −31.4323 −1.91646 −0.958231 0.285995i \(-0.907676\pi\)
−0.958231 + 0.285995i \(0.907676\pi\)
\(270\) −5.66120 −0.344530
\(271\) −10.1062 −0.613911 −0.306955 0.951724i \(-0.599310\pi\)
−0.306955 + 0.951724i \(0.599310\pi\)
\(272\) 5.05056 0.306235
\(273\) 0.519881 0.0314646
\(274\) 9.27362 0.560240
\(275\) −3.28869 −0.198315
\(276\) −3.55670 −0.214088
\(277\) −3.04574 −0.183001 −0.0915005 0.995805i \(-0.529166\pi\)
−0.0915005 + 0.995805i \(0.529166\pi\)
\(278\) −0.598622 −0.0359030
\(279\) −2.71781 −0.162711
\(280\) 7.57475 0.452678
\(281\) −21.8794 −1.30522 −0.652608 0.757696i \(-0.726325\pi\)
−0.652608 + 0.757696i \(0.726325\pi\)
\(282\) −5.97378 −0.355734
\(283\) 8.90262 0.529206 0.264603 0.964357i \(-0.414759\pi\)
0.264603 + 0.964357i \(0.414759\pi\)
\(284\) 1.95372 0.115932
\(285\) 2.33185 0.138127
\(286\) −0.518953 −0.0306863
\(287\) −1.77842 −0.104977
\(288\) 2.71781 0.160149
\(289\) 8.50817 0.500480
\(290\) 13.7039 0.804722
\(291\) −0.531212 −0.0311402
\(292\) 1.25545 0.0734696
\(293\) −19.5925 −1.14461 −0.572304 0.820041i \(-0.693950\pi\)
−0.572304 + 0.820041i \(0.693950\pi\)
\(294\) 5.05522 0.294826
\(295\) 18.0314 1.04983
\(296\) −1.51194 −0.0878795
\(297\) 6.54557 0.379813
\(298\) −15.0404 −0.871264
\(299\) 1.61234 0.0932443
\(300\) 0.810663 0.0468037
\(301\) 11.1318 0.641626
\(302\) 2.61615 0.150542
\(303\) 2.66028 0.152829
\(304\) −2.35517 −0.135078
\(305\) 28.4675 1.63004
\(306\) 13.7265 0.784691
\(307\) −32.2620 −1.84129 −0.920646 0.390399i \(-0.872337\pi\)
−0.920646 + 0.390399i \(0.872337\pi\)
\(308\) −8.75805 −0.499036
\(309\) −5.90153 −0.335727
\(310\) −1.86385 −0.105860
\(311\) −18.8003 −1.06607 −0.533033 0.846094i \(-0.678948\pi\)
−0.533033 + 0.846094i \(0.678948\pi\)
\(312\) 0.127922 0.00724217
\(313\) −11.9552 −0.675748 −0.337874 0.941191i \(-0.609708\pi\)
−0.337874 + 0.941191i \(0.609708\pi\)
\(314\) −14.3268 −0.808509
\(315\) 20.5868 1.15993
\(316\) 6.32603 0.355867
\(317\) −14.1818 −0.796527 −0.398263 0.917271i \(-0.630387\pi\)
−0.398263 + 0.917271i \(0.630387\pi\)
\(318\) −5.81013 −0.325816
\(319\) −15.8447 −0.887132
\(320\) 1.86385 0.104192
\(321\) 2.76150 0.154132
\(322\) 27.2105 1.51638
\(323\) −11.8949 −0.661851
\(324\) 6.53995 0.363331
\(325\) −0.367494 −0.0203849
\(326\) 21.7235 1.20315
\(327\) 9.26070 0.512118
\(328\) −0.437600 −0.0241624
\(329\) 45.7024 2.51965
\(330\) 2.13368 0.117455
\(331\) −35.6196 −1.95783 −0.978916 0.204265i \(-0.934520\pi\)
−0.978916 + 0.204265i \(0.934520\pi\)
\(332\) 9.96182 0.546726
\(333\) −4.10916 −0.225181
\(334\) −7.18386 −0.393083
\(335\) 6.23312 0.340552
\(336\) 2.15886 0.117776
\(337\) −13.4426 −0.732264 −0.366132 0.930563i \(-0.619318\pi\)
−0.366132 + 0.930563i \(0.619318\pi\)
\(338\) 12.9420 0.703953
\(339\) 0.990775 0.0538115
\(340\) 9.41349 0.510518
\(341\) 2.15501 0.116700
\(342\) −6.40090 −0.346121
\(343\) −10.2267 −0.552188
\(344\) 2.73910 0.147682
\(345\) −6.62916 −0.356902
\(346\) −15.9336 −0.856594
\(347\) 4.58164 0.245955 0.122978 0.992409i \(-0.460756\pi\)
0.122978 + 0.992409i \(0.460756\pi\)
\(348\) 3.90573 0.209369
\(349\) 26.1860 1.40170 0.700851 0.713307i \(-0.252804\pi\)
0.700851 + 0.713307i \(0.252804\pi\)
\(350\) −6.20198 −0.331510
\(351\) 0.731436 0.0390411
\(352\) −2.15501 −0.114863
\(353\) −8.49199 −0.451983 −0.225991 0.974129i \(-0.572562\pi\)
−0.225991 + 0.974129i \(0.572562\pi\)
\(354\) 5.13908 0.273139
\(355\) 3.64145 0.193268
\(356\) −14.0185 −0.742978
\(357\) 10.9035 0.577073
\(358\) 13.9130 0.735324
\(359\) 13.2984 0.701862 0.350931 0.936401i \(-0.385865\pi\)
0.350931 + 0.936401i \(0.385865\pi\)
\(360\) 5.06560 0.266980
\(361\) −13.4532 −0.708063
\(362\) −7.67066 −0.403161
\(363\) 3.37634 0.177212
\(364\) −0.978669 −0.0512962
\(365\) 2.33997 0.122479
\(366\) 8.11346 0.424097
\(367\) −21.5352 −1.12413 −0.562065 0.827093i \(-0.689993\pi\)
−0.562065 + 0.827093i \(0.689993\pi\)
\(368\) 6.69545 0.349024
\(369\) −1.18931 −0.0619132
\(370\) −2.81802 −0.146502
\(371\) 44.4504 2.30775
\(372\) −0.531212 −0.0275421
\(373\) 25.5012 1.32040 0.660200 0.751090i \(-0.270472\pi\)
0.660200 + 0.751090i \(0.270472\pi\)
\(374\) −10.8840 −0.562799
\(375\) 6.46145 0.333668
\(376\) 11.2456 0.579946
\(377\) −1.77057 −0.0911888
\(378\) 12.3440 0.634906
\(379\) −2.19932 −0.112972 −0.0564858 0.998403i \(-0.517990\pi\)
−0.0564858 + 0.998403i \(0.517990\pi\)
\(380\) −4.38968 −0.225186
\(381\) 5.01323 0.256836
\(382\) 21.9540 1.12326
\(383\) 29.0342 1.48358 0.741789 0.670633i \(-0.233978\pi\)
0.741789 + 0.670633i \(0.233978\pi\)
\(384\) 0.531212 0.0271083
\(385\) −16.3237 −0.831932
\(386\) −4.32134 −0.219950
\(387\) 7.44436 0.378418
\(388\) 1.00000 0.0507673
\(389\) −17.1770 −0.870907 −0.435453 0.900211i \(-0.643412\pi\)
−0.435453 + 0.900211i \(0.643412\pi\)
\(390\) 0.238428 0.0120733
\(391\) 33.8158 1.71014
\(392\) −9.51638 −0.480650
\(393\) 2.02358 0.102076
\(394\) 19.4316 0.978950
\(395\) 11.7908 0.593258
\(396\) −5.85692 −0.294321
\(397\) 5.42066 0.272055 0.136027 0.990705i \(-0.456566\pi\)
0.136027 + 0.990705i \(0.456566\pi\)
\(398\) −5.99771 −0.300638
\(399\) −5.08449 −0.254543
\(400\) −1.52606 −0.0763032
\(401\) 19.7790 0.987715 0.493858 0.869543i \(-0.335586\pi\)
0.493858 + 0.869543i \(0.335586\pi\)
\(402\) 1.77649 0.0886033
\(403\) 0.240812 0.0119957
\(404\) −5.00795 −0.249155
\(405\) 12.1895 0.605701
\(406\) −29.8807 −1.48296
\(407\) 3.25824 0.161505
\(408\) 2.68292 0.132824
\(409\) −30.9625 −1.53100 −0.765499 0.643437i \(-0.777508\pi\)
−0.765499 + 0.643437i \(0.777508\pi\)
\(410\) −0.815620 −0.0402806
\(411\) 4.92626 0.242994
\(412\) 11.1096 0.547329
\(413\) −39.3165 −1.93464
\(414\) 18.1970 0.894333
\(415\) 18.5673 0.911435
\(416\) −0.240812 −0.0118068
\(417\) −0.317995 −0.0155723
\(418\) 5.07541 0.248247
\(419\) −32.8771 −1.60615 −0.803075 0.595879i \(-0.796804\pi\)
−0.803075 + 0.595879i \(0.796804\pi\)
\(420\) 4.02380 0.196341
\(421\) −16.5914 −0.808613 −0.404306 0.914624i \(-0.632487\pi\)
−0.404306 + 0.914624i \(0.632487\pi\)
\(422\) −10.5332 −0.512748
\(423\) 30.5634 1.48604
\(424\) 10.9375 0.531172
\(425\) −7.70748 −0.373868
\(426\) 1.03784 0.0502836
\(427\) −62.0720 −3.00387
\(428\) −5.19849 −0.251279
\(429\) −0.275674 −0.0133097
\(430\) 5.10527 0.246198
\(431\) 22.0837 1.06374 0.531868 0.846827i \(-0.321490\pi\)
0.531868 + 0.846827i \(0.321490\pi\)
\(432\) 3.03737 0.146136
\(433\) −12.5493 −0.603082 −0.301541 0.953453i \(-0.597501\pi\)
−0.301541 + 0.953453i \(0.597501\pi\)
\(434\) 4.06404 0.195080
\(435\) 7.27969 0.349034
\(436\) −17.4332 −0.834897
\(437\) −15.7689 −0.754328
\(438\) 0.666909 0.0318662
\(439\) −16.1761 −0.772044 −0.386022 0.922490i \(-0.626151\pi\)
−0.386022 + 0.922490i \(0.626151\pi\)
\(440\) −4.01662 −0.191485
\(441\) −25.8638 −1.23161
\(442\) −1.21624 −0.0578504
\(443\) 4.03243 0.191586 0.0957932 0.995401i \(-0.469461\pi\)
0.0957932 + 0.995401i \(0.469461\pi\)
\(444\) −0.803159 −0.0381162
\(445\) −26.1283 −1.23860
\(446\) −14.8409 −0.702737
\(447\) −7.98962 −0.377896
\(448\) −4.06404 −0.192008
\(449\) 25.5043 1.20362 0.601811 0.798639i \(-0.294446\pi\)
0.601811 + 0.798639i \(0.294446\pi\)
\(450\) −4.14756 −0.195518
\(451\) 0.943033 0.0444057
\(452\) −1.86512 −0.0877280
\(453\) 1.38973 0.0652951
\(454\) −11.4527 −0.537502
\(455\) −1.82409 −0.0855147
\(456\) −1.25109 −0.0585878
\(457\) −21.2751 −0.995208 −0.497604 0.867404i \(-0.665787\pi\)
−0.497604 + 0.867404i \(0.665787\pi\)
\(458\) 14.1093 0.659285
\(459\) 15.3404 0.716030
\(460\) 12.4793 0.581851
\(461\) −21.4885 −1.00082 −0.500410 0.865789i \(-0.666817\pi\)
−0.500410 + 0.865789i \(0.666817\pi\)
\(462\) −4.65238 −0.216448
\(463\) 10.9892 0.510711 0.255356 0.966847i \(-0.417807\pi\)
0.255356 + 0.966847i \(0.417807\pi\)
\(464\) −7.35248 −0.341330
\(465\) −0.990100 −0.0459148
\(466\) 17.7045 0.820146
\(467\) −1.30362 −0.0603246 −0.0301623 0.999545i \(-0.509602\pi\)
−0.0301623 + 0.999545i \(0.509602\pi\)
\(468\) −0.654482 −0.0302535
\(469\) −13.5910 −0.627575
\(470\) 20.9601 0.966815
\(471\) −7.61058 −0.350677
\(472\) −9.67425 −0.445294
\(473\) −5.90279 −0.271411
\(474\) 3.36046 0.154351
\(475\) 3.59413 0.164910
\(476\) −20.5257 −0.940792
\(477\) 29.7261 1.36106
\(478\) −10.8794 −0.497613
\(479\) −9.66601 −0.441651 −0.220826 0.975313i \(-0.570875\pi\)
−0.220826 + 0.975313i \(0.570875\pi\)
\(480\) 0.990100 0.0451917
\(481\) 0.364093 0.0166012
\(482\) 23.9685 1.09174
\(483\) 14.4546 0.657705
\(484\) −6.35592 −0.288905
\(485\) 1.86385 0.0846331
\(486\) 12.5862 0.570922
\(487\) 13.2452 0.600197 0.300098 0.953908i \(-0.402981\pi\)
0.300098 + 0.953908i \(0.402981\pi\)
\(488\) −15.2735 −0.691398
\(489\) 11.5398 0.521846
\(490\) −17.7371 −0.801281
\(491\) 20.0511 0.904894 0.452447 0.891791i \(-0.350551\pi\)
0.452447 + 0.891791i \(0.350551\pi\)
\(492\) −0.232458 −0.0104800
\(493\) −37.1341 −1.67244
\(494\) 0.567153 0.0255174
\(495\) −10.9164 −0.490657
\(496\) 1.00000 0.0449013
\(497\) −7.94000 −0.356158
\(498\) 5.29184 0.237133
\(499\) −26.4689 −1.18491 −0.592455 0.805604i \(-0.701841\pi\)
−0.592455 + 0.805604i \(0.701841\pi\)
\(500\) −12.1636 −0.543973
\(501\) −3.81615 −0.170493
\(502\) −20.6521 −0.921749
\(503\) −5.09601 −0.227220 −0.113610 0.993525i \(-0.536241\pi\)
−0.113610 + 0.993525i \(0.536241\pi\)
\(504\) −11.0453 −0.491996
\(505\) −9.33407 −0.415361
\(506\) −14.4288 −0.641437
\(507\) 6.87495 0.305327
\(508\) −9.43734 −0.418714
\(509\) −15.1369 −0.670930 −0.335465 0.942053i \(-0.608893\pi\)
−0.335465 + 0.942053i \(0.608893\pi\)
\(510\) 5.00056 0.221428
\(511\) −5.10219 −0.225707
\(512\) −1.00000 −0.0441942
\(513\) −7.15352 −0.315835
\(514\) −14.2771 −0.629734
\(515\) 20.7066 0.912440
\(516\) 1.45504 0.0640547
\(517\) −24.2343 −1.06583
\(518\) 6.14456 0.269977
\(519\) −8.46410 −0.371533
\(520\) −0.448838 −0.0196828
\(521\) 22.1551 0.970631 0.485316 0.874339i \(-0.338705\pi\)
0.485316 + 0.874339i \(0.338705\pi\)
\(522\) −19.9827 −0.874618
\(523\) 14.9344 0.653035 0.326518 0.945191i \(-0.394125\pi\)
0.326518 + 0.945191i \(0.394125\pi\)
\(524\) −3.80936 −0.166413
\(525\) −3.29456 −0.143787
\(526\) 15.8164 0.689628
\(527\) 5.05056 0.220006
\(528\) −1.14477 −0.0498197
\(529\) 21.8290 0.949087
\(530\) 20.3858 0.885504
\(531\) −26.2928 −1.14101
\(532\) 9.57148 0.414976
\(533\) 0.105379 0.00456448
\(534\) −7.44678 −0.322254
\(535\) −9.68921 −0.418901
\(536\) −3.34422 −0.144448
\(537\) 7.39074 0.318934
\(538\) 31.4323 1.35514
\(539\) 20.5079 0.883339
\(540\) 5.66120 0.243619
\(541\) 9.13240 0.392632 0.196316 0.980541i \(-0.437102\pi\)
0.196316 + 0.980541i \(0.437102\pi\)
\(542\) 10.1062 0.434100
\(543\) −4.07475 −0.174864
\(544\) −5.05056 −0.216541
\(545\) −32.4928 −1.39184
\(546\) −0.519881 −0.0222488
\(547\) 3.98086 0.170209 0.0851047 0.996372i \(-0.472878\pi\)
0.0851047 + 0.996372i \(0.472878\pi\)
\(548\) −9.27362 −0.396149
\(549\) −41.5105 −1.77162
\(550\) 3.28869 0.140230
\(551\) 17.3163 0.737700
\(552\) 3.55670 0.151383
\(553\) −25.7092 −1.09327
\(554\) 3.04574 0.129401
\(555\) −1.49697 −0.0635427
\(556\) 0.598622 0.0253872
\(557\) −27.2244 −1.15354 −0.576768 0.816908i \(-0.695686\pi\)
−0.576768 + 0.816908i \(0.695686\pi\)
\(558\) 2.71781 0.115054
\(559\) −0.659608 −0.0278984
\(560\) −7.57475 −0.320092
\(561\) −5.78172 −0.244105
\(562\) 21.8794 0.922927
\(563\) 26.4386 1.11425 0.557127 0.830427i \(-0.311904\pi\)
0.557127 + 0.830427i \(0.311904\pi\)
\(564\) 5.97378 0.251542
\(565\) −3.47631 −0.146249
\(566\) −8.90262 −0.374205
\(567\) −26.5786 −1.11620
\(568\) −1.95372 −0.0819764
\(569\) 20.5608 0.861953 0.430976 0.902363i \(-0.358169\pi\)
0.430976 + 0.902363i \(0.358169\pi\)
\(570\) −2.33185 −0.0976704
\(571\) −1.90737 −0.0798208 −0.0399104 0.999203i \(-0.512707\pi\)
−0.0399104 + 0.999203i \(0.512707\pi\)
\(572\) 0.518953 0.0216985
\(573\) 11.6622 0.487196
\(574\) 1.77842 0.0742299
\(575\) −10.2177 −0.426107
\(576\) −2.71781 −0.113242
\(577\) 26.6219 1.10828 0.554142 0.832422i \(-0.313046\pi\)
0.554142 + 0.832422i \(0.313046\pi\)
\(578\) −8.50817 −0.353893
\(579\) −2.29555 −0.0953997
\(580\) −13.7039 −0.569024
\(581\) −40.4852 −1.67961
\(582\) 0.531212 0.0220194
\(583\) −23.5704 −0.976188
\(584\) −1.25545 −0.0519508
\(585\) −1.21986 −0.0504349
\(586\) 19.5925 0.809360
\(587\) −17.4559 −0.720480 −0.360240 0.932860i \(-0.617305\pi\)
−0.360240 + 0.932860i \(0.617305\pi\)
\(588\) −5.05522 −0.208474
\(589\) −2.35517 −0.0970430
\(590\) −18.0314 −0.742339
\(591\) 10.3223 0.424603
\(592\) 1.51194 0.0621402
\(593\) 36.1070 1.48274 0.741368 0.671099i \(-0.234177\pi\)
0.741368 + 0.671099i \(0.234177\pi\)
\(594\) −6.54557 −0.268568
\(595\) −38.2567 −1.56837
\(596\) 15.0404 0.616077
\(597\) −3.18606 −0.130397
\(598\) −1.61234 −0.0659337
\(599\) 5.59080 0.228434 0.114217 0.993456i \(-0.463564\pi\)
0.114217 + 0.993456i \(0.463564\pi\)
\(600\) −0.810663 −0.0330952
\(601\) 12.5228 0.510815 0.255408 0.966833i \(-0.417790\pi\)
0.255408 + 0.966833i \(0.417790\pi\)
\(602\) −11.1318 −0.453698
\(603\) −9.08897 −0.370131
\(604\) −2.61615 −0.106449
\(605\) −11.8465 −0.481628
\(606\) −2.66028 −0.108067
\(607\) 8.42948 0.342142 0.171071 0.985259i \(-0.445277\pi\)
0.171071 + 0.985259i \(0.445277\pi\)
\(608\) 2.35517 0.0955146
\(609\) −15.8730 −0.643207
\(610\) −28.4675 −1.15261
\(611\) −2.70807 −0.109557
\(612\) −13.7265 −0.554860
\(613\) 10.4446 0.421855 0.210927 0.977502i \(-0.432352\pi\)
0.210927 + 0.977502i \(0.432352\pi\)
\(614\) 32.2620 1.30199
\(615\) −0.433267 −0.0174710
\(616\) 8.75805 0.352872
\(617\) 1.61686 0.0650922 0.0325461 0.999470i \(-0.489638\pi\)
0.0325461 + 0.999470i \(0.489638\pi\)
\(618\) 5.90153 0.237395
\(619\) 5.28772 0.212531 0.106266 0.994338i \(-0.466111\pi\)
0.106266 + 0.994338i \(0.466111\pi\)
\(620\) 1.86385 0.0748540
\(621\) 20.3366 0.816078
\(622\) 18.8003 0.753822
\(623\) 56.9716 2.28252
\(624\) −0.127922 −0.00512099
\(625\) −15.0408 −0.601633
\(626\) 11.9552 0.477826
\(627\) 2.69612 0.107673
\(628\) 14.3268 0.571702
\(629\) 7.63613 0.304472
\(630\) −20.5868 −0.820196
\(631\) 7.79917 0.310480 0.155240 0.987877i \(-0.450385\pi\)
0.155240 + 0.987877i \(0.450385\pi\)
\(632\) −6.32603 −0.251636
\(633\) −5.59536 −0.222396
\(634\) 14.1818 0.563230
\(635\) −17.5898 −0.698030
\(636\) 5.81013 0.230387
\(637\) 2.29166 0.0907989
\(638\) 15.8447 0.627297
\(639\) −5.30985 −0.210055
\(640\) −1.86385 −0.0736751
\(641\) −35.0667 −1.38505 −0.692525 0.721394i \(-0.743502\pi\)
−0.692525 + 0.721394i \(0.743502\pi\)
\(642\) −2.76150 −0.108988
\(643\) −13.3830 −0.527772 −0.263886 0.964554i \(-0.585004\pi\)
−0.263886 + 0.964554i \(0.585004\pi\)
\(644\) −27.2105 −1.07225
\(645\) 2.71198 0.106784
\(646\) 11.8949 0.467999
\(647\) 14.4181 0.566836 0.283418 0.958997i \(-0.408532\pi\)
0.283418 + 0.958997i \(0.408532\pi\)
\(648\) −6.53995 −0.256914
\(649\) 20.8481 0.818361
\(650\) 0.367494 0.0144143
\(651\) 2.15886 0.0846126
\(652\) −21.7235 −0.850756
\(653\) −17.6995 −0.692633 −0.346317 0.938118i \(-0.612568\pi\)
−0.346317 + 0.938118i \(0.612568\pi\)
\(654\) −9.26070 −0.362122
\(655\) −7.10008 −0.277423
\(656\) 0.437600 0.0170854
\(657\) −3.41207 −0.133118
\(658\) −45.7024 −1.78167
\(659\) −9.55989 −0.372401 −0.186200 0.982512i \(-0.559617\pi\)
−0.186200 + 0.982512i \(0.559617\pi\)
\(660\) −2.13368 −0.0830533
\(661\) −36.9183 −1.43596 −0.717978 0.696066i \(-0.754932\pi\)
−0.717978 + 0.696066i \(0.754932\pi\)
\(662\) 35.6196 1.38440
\(663\) −0.646079 −0.0250916
\(664\) −9.96182 −0.386593
\(665\) 17.8398 0.691798
\(666\) 4.10916 0.159227
\(667\) −49.2281 −1.90612
\(668\) 7.18386 0.277952
\(669\) −7.88366 −0.304800
\(670\) −6.23312 −0.240807
\(671\) 32.9146 1.27065
\(672\) −2.15886 −0.0832800
\(673\) −13.9201 −0.536581 −0.268290 0.963338i \(-0.586459\pi\)
−0.268290 + 0.963338i \(0.586459\pi\)
\(674\) 13.4426 0.517789
\(675\) −4.63522 −0.178410
\(676\) −12.9420 −0.497770
\(677\) 13.3426 0.512798 0.256399 0.966571i \(-0.417464\pi\)
0.256399 + 0.966571i \(0.417464\pi\)
\(678\) −0.990775 −0.0380505
\(679\) −4.06404 −0.155963
\(680\) −9.41349 −0.360991
\(681\) −6.08382 −0.233132
\(682\) −2.15501 −0.0825197
\(683\) 18.6396 0.713226 0.356613 0.934252i \(-0.383931\pi\)
0.356613 + 0.934252i \(0.383931\pi\)
\(684\) 6.40090 0.244745
\(685\) −17.2846 −0.660412
\(686\) 10.2267 0.390456
\(687\) 7.49504 0.285954
\(688\) −2.73910 −0.104427
\(689\) −2.63388 −0.100343
\(690\) 6.62916 0.252368
\(691\) −25.2602 −0.960945 −0.480472 0.877010i \(-0.659535\pi\)
−0.480472 + 0.877010i \(0.659535\pi\)
\(692\) 15.9336 0.605703
\(693\) 23.8027 0.904191
\(694\) −4.58164 −0.173917
\(695\) 1.11574 0.0423225
\(696\) −3.90573 −0.148046
\(697\) 2.21012 0.0837144
\(698\) −26.1860 −0.991153
\(699\) 9.40486 0.355724
\(700\) 6.20198 0.234413
\(701\) −29.4721 −1.11315 −0.556573 0.830799i \(-0.687884\pi\)
−0.556573 + 0.830799i \(0.687884\pi\)
\(702\) −0.731436 −0.0276063
\(703\) −3.56086 −0.134300
\(704\) 2.15501 0.0812201
\(705\) 11.1342 0.419340
\(706\) 8.49199 0.319600
\(707\) 20.3525 0.765434
\(708\) −5.13908 −0.193138
\(709\) −40.4421 −1.51884 −0.759418 0.650603i \(-0.774516\pi\)
−0.759418 + 0.650603i \(0.774516\pi\)
\(710\) −3.64145 −0.136661
\(711\) −17.1930 −0.644787
\(712\) 14.0185 0.525364
\(713\) 6.69545 0.250746
\(714\) −10.9035 −0.408052
\(715\) 0.967251 0.0361731
\(716\) −13.9130 −0.519952
\(717\) −5.77927 −0.215831
\(718\) −13.2984 −0.496291
\(719\) 5.73213 0.213773 0.106886 0.994271i \(-0.465912\pi\)
0.106886 + 0.994271i \(0.465912\pi\)
\(720\) −5.06560 −0.188784
\(721\) −45.1497 −1.68146
\(722\) 13.4532 0.500676
\(723\) 12.7324 0.473521
\(724\) 7.67066 0.285078
\(725\) 11.2204 0.416713
\(726\) −3.37634 −0.125308
\(727\) 31.8915 1.18279 0.591395 0.806382i \(-0.298578\pi\)
0.591395 + 0.806382i \(0.298578\pi\)
\(728\) 0.978669 0.0362719
\(729\) −12.9339 −0.479034
\(730\) −2.33997 −0.0866061
\(731\) −13.8340 −0.511668
\(732\) −8.11346 −0.299882
\(733\) −34.3205 −1.26766 −0.633828 0.773474i \(-0.718517\pi\)
−0.633828 + 0.773474i \(0.718517\pi\)
\(734\) 21.5352 0.794880
\(735\) −9.42217 −0.347542
\(736\) −6.69545 −0.246797
\(737\) 7.20684 0.265467
\(738\) 1.18931 0.0437793
\(739\) −33.8462 −1.24505 −0.622526 0.782599i \(-0.713893\pi\)
−0.622526 + 0.782599i \(0.713893\pi\)
\(740\) 2.81802 0.103593
\(741\) 0.301278 0.0110677
\(742\) −44.4504 −1.63182
\(743\) −28.2921 −1.03793 −0.518967 0.854794i \(-0.673683\pi\)
−0.518967 + 0.854794i \(0.673683\pi\)
\(744\) 0.531212 0.0194752
\(745\) 28.0330 1.02705
\(746\) −25.5012 −0.933664
\(747\) −27.0744 −0.990599
\(748\) 10.8840 0.397959
\(749\) 21.1269 0.771959
\(750\) −6.46145 −0.235939
\(751\) −28.4785 −1.03920 −0.519598 0.854411i \(-0.673918\pi\)
−0.519598 + 0.854411i \(0.673918\pi\)
\(752\) −11.2456 −0.410084
\(753\) −10.9707 −0.399793
\(754\) 1.77057 0.0644802
\(755\) −4.87610 −0.177460
\(756\) −12.3440 −0.448946
\(757\) −22.6135 −0.821903 −0.410951 0.911657i \(-0.634803\pi\)
−0.410951 + 0.911657i \(0.634803\pi\)
\(758\) 2.19932 0.0798830
\(759\) −7.66474 −0.278212
\(760\) 4.38968 0.159230
\(761\) −34.7144 −1.25840 −0.629199 0.777245i \(-0.716617\pi\)
−0.629199 + 0.777245i \(0.716617\pi\)
\(762\) −5.01323 −0.181610
\(763\) 70.8490 2.56490
\(764\) −21.9540 −0.794267
\(765\) −25.5841 −0.924995
\(766\) −29.0342 −1.04905
\(767\) 2.32968 0.0841197
\(768\) −0.531212 −0.0191685
\(769\) 0.645198 0.0232664 0.0116332 0.999932i \(-0.496297\pi\)
0.0116332 + 0.999932i \(0.496297\pi\)
\(770\) 16.3237 0.588265
\(771\) −7.58414 −0.273136
\(772\) 4.32134 0.155528
\(773\) 7.58398 0.272777 0.136388 0.990655i \(-0.456450\pi\)
0.136388 + 0.990655i \(0.456450\pi\)
\(774\) −7.44436 −0.267582
\(775\) −1.52606 −0.0548178
\(776\) −1.00000 −0.0358979
\(777\) 3.26407 0.117098
\(778\) 17.1770 0.615824
\(779\) −1.03062 −0.0369258
\(780\) −0.238428 −0.00853709
\(781\) 4.21030 0.150656
\(782\) −33.8158 −1.20925
\(783\) −22.3322 −0.798088
\(784\) 9.51638 0.339871
\(785\) 26.7030 0.953073
\(786\) −2.02358 −0.0721787
\(787\) −3.19935 −0.114044 −0.0570222 0.998373i \(-0.518161\pi\)
−0.0570222 + 0.998373i \(0.518161\pi\)
\(788\) −19.4316 −0.692222
\(789\) 8.40187 0.299114
\(790\) −11.7908 −0.419497
\(791\) 7.57992 0.269511
\(792\) 5.85692 0.208117
\(793\) 3.67804 0.130611
\(794\) −5.42066 −0.192372
\(795\) 10.8292 0.384072
\(796\) 5.99771 0.212583
\(797\) 3.47876 0.123224 0.0616120 0.998100i \(-0.480376\pi\)
0.0616120 + 0.998100i \(0.480376\pi\)
\(798\) 5.08449 0.179989
\(799\) −56.7964 −2.00931
\(800\) 1.52606 0.0539545
\(801\) 38.0996 1.34618
\(802\) −19.7790 −0.698420
\(803\) 2.70551 0.0954753
\(804\) −1.77649 −0.0626520
\(805\) −50.7163 −1.78752
\(806\) −0.240812 −0.00848224
\(807\) 16.6972 0.587770
\(808\) 5.00795 0.176179
\(809\) −28.0693 −0.986863 −0.493432 0.869785i \(-0.664258\pi\)
−0.493432 + 0.869785i \(0.664258\pi\)
\(810\) −12.1895 −0.428295
\(811\) 8.34633 0.293079 0.146540 0.989205i \(-0.453186\pi\)
0.146540 + 0.989205i \(0.453186\pi\)
\(812\) 29.8807 1.04861
\(813\) 5.36856 0.188284
\(814\) −3.25824 −0.114201
\(815\) −40.4893 −1.41828
\(816\) −2.68292 −0.0939209
\(817\) 6.45103 0.225693
\(818\) 30.9625 1.08258
\(819\) 2.65984 0.0929423
\(820\) 0.815620 0.0284827
\(821\) 31.9483 1.11500 0.557501 0.830176i \(-0.311760\pi\)
0.557501 + 0.830176i \(0.311760\pi\)
\(822\) −4.92626 −0.171823
\(823\) 11.6495 0.406076 0.203038 0.979171i \(-0.434919\pi\)
0.203038 + 0.979171i \(0.434919\pi\)
\(824\) −11.1096 −0.387020
\(825\) 1.74699 0.0608224
\(826\) 39.3165 1.36800
\(827\) −4.86571 −0.169197 −0.0845986 0.996415i \(-0.526961\pi\)
−0.0845986 + 0.996415i \(0.526961\pi\)
\(828\) −18.1970 −0.632389
\(829\) −30.2881 −1.05195 −0.525975 0.850500i \(-0.676299\pi\)
−0.525975 + 0.850500i \(0.676299\pi\)
\(830\) −18.5673 −0.644482
\(831\) 1.61794 0.0561256
\(832\) 0.240812 0.00834866
\(833\) 48.0631 1.66529
\(834\) 0.317995 0.0110113
\(835\) 13.3896 0.463368
\(836\) −5.07541 −0.175537
\(837\) 3.03737 0.104987
\(838\) 32.8771 1.13572
\(839\) 43.3356 1.49611 0.748055 0.663636i \(-0.230988\pi\)
0.748055 + 0.663636i \(0.230988\pi\)
\(840\) −4.02380 −0.138834
\(841\) 25.0590 0.864102
\(842\) 16.5914 0.571776
\(843\) 11.6226 0.400304
\(844\) 10.5332 0.362567
\(845\) −24.1220 −0.829821
\(846\) −30.5634 −1.05079
\(847\) 25.8307 0.887553
\(848\) −10.9375 −0.375595
\(849\) −4.72918 −0.162305
\(850\) 7.70748 0.264364
\(851\) 10.1231 0.347015
\(852\) −1.03784 −0.0355558
\(853\) 23.6902 0.811137 0.405569 0.914065i \(-0.367074\pi\)
0.405569 + 0.914065i \(0.367074\pi\)
\(854\) 62.0720 2.12406
\(855\) 11.9303 0.408009
\(856\) 5.19849 0.177681
\(857\) −44.5713 −1.52253 −0.761263 0.648443i \(-0.775420\pi\)
−0.761263 + 0.648443i \(0.775420\pi\)
\(858\) 0.275674 0.00941136
\(859\) 3.79116 0.129353 0.0646763 0.997906i \(-0.479399\pi\)
0.0646763 + 0.997906i \(0.479399\pi\)
\(860\) −5.10527 −0.174088
\(861\) 0.944719 0.0321959
\(862\) −22.0837 −0.752175
\(863\) −10.2311 −0.348271 −0.174136 0.984722i \(-0.555713\pi\)
−0.174136 + 0.984722i \(0.555713\pi\)
\(864\) −3.03737 −0.103333
\(865\) 29.6978 1.00975
\(866\) 12.5493 0.426443
\(867\) −4.51964 −0.153495
\(868\) −4.06404 −0.137942
\(869\) 13.6327 0.462457
\(870\) −7.27969 −0.246804
\(871\) 0.805329 0.0272875
\(872\) 17.4332 0.590361
\(873\) −2.71781 −0.0919841
\(874\) 15.7689 0.533391
\(875\) 49.4333 1.67115
\(876\) −0.666909 −0.0225328
\(877\) 8.30377 0.280398 0.140199 0.990123i \(-0.455226\pi\)
0.140199 + 0.990123i \(0.455226\pi\)
\(878\) 16.1761 0.545917
\(879\) 10.4078 0.351046
\(880\) 4.01662 0.135400
\(881\) 2.17468 0.0732669 0.0366334 0.999329i \(-0.488337\pi\)
0.0366334 + 0.999329i \(0.488337\pi\)
\(882\) 25.8638 0.870878
\(883\) 17.3317 0.583258 0.291629 0.956532i \(-0.405803\pi\)
0.291629 + 0.956532i \(0.405803\pi\)
\(884\) 1.21624 0.0409064
\(885\) −9.57847 −0.321977
\(886\) −4.03243 −0.135472
\(887\) 5.05505 0.169732 0.0848660 0.996392i \(-0.472954\pi\)
0.0848660 + 0.996392i \(0.472954\pi\)
\(888\) 0.803159 0.0269522
\(889\) 38.3537 1.28634
\(890\) 26.1283 0.875824
\(891\) 14.0937 0.472156
\(892\) 14.8409 0.496910
\(893\) 26.4852 0.886293
\(894\) 7.98962 0.267213
\(895\) −25.9317 −0.866801
\(896\) 4.06404 0.135770
\(897\) −0.856497 −0.0285976
\(898\) −25.5043 −0.851089
\(899\) −7.35248 −0.245219
\(900\) 4.14756 0.138252
\(901\) −55.2405 −1.84033
\(902\) −0.943033 −0.0313996
\(903\) −5.91334 −0.196784
\(904\) 1.86512 0.0620330
\(905\) 14.2970 0.475247
\(906\) −1.38973 −0.0461706
\(907\) −6.71882 −0.223095 −0.111547 0.993759i \(-0.535581\pi\)
−0.111547 + 0.993759i \(0.535581\pi\)
\(908\) 11.4527 0.380072
\(909\) 13.6107 0.451438
\(910\) 1.82409 0.0604680
\(911\) 7.13853 0.236510 0.118255 0.992983i \(-0.462270\pi\)
0.118255 + 0.992983i \(0.462270\pi\)
\(912\) 1.25109 0.0414278
\(913\) 21.4678 0.710482
\(914\) 21.2751 0.703718
\(915\) −15.1223 −0.499927
\(916\) −14.1093 −0.466185
\(917\) 15.4814 0.511240
\(918\) −15.3404 −0.506310
\(919\) −24.4581 −0.806798 −0.403399 0.915024i \(-0.632171\pi\)
−0.403399 + 0.915024i \(0.632171\pi\)
\(920\) −12.4793 −0.411431
\(921\) 17.1380 0.564716
\(922\) 21.4885 0.707687
\(923\) 0.470480 0.0154860
\(924\) 4.65238 0.153052
\(925\) −2.30731 −0.0758639
\(926\) −10.9892 −0.361127
\(927\) −30.1937 −0.991692
\(928\) 7.35248 0.241357
\(929\) −31.3613 −1.02893 −0.514465 0.857511i \(-0.672009\pi\)
−0.514465 + 0.857511i \(0.672009\pi\)
\(930\) 0.990100 0.0324666
\(931\) −22.4127 −0.734546
\(932\) −17.7045 −0.579931
\(933\) 9.98693 0.326958
\(934\) 1.30362 0.0426559
\(935\) 20.2862 0.663429
\(936\) 0.654482 0.0213924
\(937\) 51.1150 1.66986 0.834928 0.550360i \(-0.185509\pi\)
0.834928 + 0.550360i \(0.185509\pi\)
\(938\) 13.5910 0.443763
\(939\) 6.35074 0.207249
\(940\) −20.9601 −0.683642
\(941\) 41.6596 1.35807 0.679033 0.734108i \(-0.262399\pi\)
0.679033 + 0.734108i \(0.262399\pi\)
\(942\) 7.61058 0.247966
\(943\) 2.92993 0.0954115
\(944\) 9.67425 0.314870
\(945\) −23.0073 −0.748429
\(946\) 5.90279 0.191916
\(947\) −50.2070 −1.63151 −0.815754 0.578399i \(-0.803678\pi\)
−0.815754 + 0.578399i \(0.803678\pi\)
\(948\) −3.36046 −0.109143
\(949\) 0.302327 0.00981395
\(950\) −3.59413 −0.116609
\(951\) 7.53352 0.244291
\(952\) 20.5257 0.665240
\(953\) 17.4563 0.565466 0.282733 0.959199i \(-0.408759\pi\)
0.282733 + 0.959199i \(0.408759\pi\)
\(954\) −29.7261 −0.962417
\(955\) −40.9189 −1.32411
\(956\) 10.8794 0.351865
\(957\) 8.41689 0.272079
\(958\) 9.66601 0.312294
\(959\) 37.6883 1.21702
\(960\) −0.990100 −0.0319553
\(961\) 1.00000 0.0322581
\(962\) −0.364093 −0.0117388
\(963\) 14.1285 0.455286
\(964\) −23.9685 −0.771973
\(965\) 8.05432 0.259278
\(966\) −14.4546 −0.465068
\(967\) −15.2711 −0.491085 −0.245543 0.969386i \(-0.578966\pi\)
−0.245543 + 0.969386i \(0.578966\pi\)
\(968\) 6.35592 0.204287
\(969\) 6.31872 0.202987
\(970\) −1.86385 −0.0598446
\(971\) 10.0477 0.322445 0.161223 0.986918i \(-0.448456\pi\)
0.161223 + 0.986918i \(0.448456\pi\)
\(972\) −12.5862 −0.403703
\(973\) −2.43282 −0.0779927
\(974\) −13.2452 −0.424403
\(975\) 0.195218 0.00625196
\(976\) 15.2735 0.488892
\(977\) −14.2628 −0.456307 −0.228154 0.973625i \(-0.573269\pi\)
−0.228154 + 0.973625i \(0.573269\pi\)
\(978\) −11.5398 −0.369001
\(979\) −30.2100 −0.965515
\(980\) 17.7371 0.566591
\(981\) 47.3801 1.51273
\(982\) −20.0511 −0.639857
\(983\) 44.8520 1.43056 0.715279 0.698839i \(-0.246300\pi\)
0.715279 + 0.698839i \(0.246300\pi\)
\(984\) 0.232458 0.00741050
\(985\) −36.2176 −1.15399
\(986\) 37.1341 1.18259
\(987\) −24.2777 −0.772767
\(988\) −0.567153 −0.0180435
\(989\) −18.3395 −0.583162
\(990\) 10.9164 0.346947
\(991\) −3.76510 −0.119602 −0.0598011 0.998210i \(-0.519047\pi\)
−0.0598011 + 0.998210i \(0.519047\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 18.9216 0.600458
\(994\) 7.94000 0.251841
\(995\) 11.1788 0.354393
\(996\) −5.29184 −0.167678
\(997\) −6.19708 −0.196264 −0.0981318 0.995173i \(-0.531287\pi\)
−0.0981318 + 0.995173i \(0.531287\pi\)
\(998\) 26.4689 0.837858
\(999\) 4.59231 0.145294
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 6014.2.a.f.1.10 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.f.1.10 22 1.1 even 1 trivial