Properties

Label 1441.4.a.b.1.10
Level $1441$
Weight $4$
Character 1441.1
Self dual yes
Analytic conductor $85.022$
Analytic rank $1$
Dimension $79$
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] = [1441,4,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1441.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1441.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: \(85.0217523183\)
Analytic rank: \(1\)
Dimension: \(79\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.81294 q^{2} +2.88277 q^{3} +15.1644 q^{4} -12.4285 q^{5} -13.8746 q^{6} -12.7070 q^{7} -34.4818 q^{8} -18.6896 q^{9} +O(q^{10})\) \(q-4.81294 q^{2} +2.88277 q^{3} +15.1644 q^{4} -12.4285 q^{5} -13.8746 q^{6} -12.7070 q^{7} -34.4818 q^{8} -18.6896 q^{9} +59.8178 q^{10} +11.0000 q^{11} +43.7155 q^{12} +69.0410 q^{13} +61.1579 q^{14} -35.8286 q^{15} +44.6437 q^{16} -79.5521 q^{17} +89.9520 q^{18} +112.287 q^{19} -188.471 q^{20} -36.6313 q^{21} -52.9423 q^{22} -122.870 q^{23} -99.4032 q^{24} +29.4683 q^{25} -332.290 q^{26} -131.713 q^{27} -192.694 q^{28} -146.473 q^{29} +172.441 q^{30} +198.735 q^{31} +60.9869 q^{32} +31.7105 q^{33} +382.879 q^{34} +157.929 q^{35} -283.417 q^{36} +265.049 q^{37} -540.429 q^{38} +199.030 q^{39} +428.558 q^{40} +26.8558 q^{41} +176.304 q^{42} -6.45965 q^{43} +166.808 q^{44} +232.284 q^{45} +591.366 q^{46} +495.176 q^{47} +128.698 q^{48} -181.533 q^{49} -141.829 q^{50} -229.331 q^{51} +1046.97 q^{52} -5.15724 q^{53} +633.926 q^{54} -136.714 q^{55} +438.159 q^{56} +323.697 q^{57} +704.967 q^{58} +108.052 q^{59} -543.320 q^{60} +109.201 q^{61} -956.502 q^{62} +237.488 q^{63} -650.676 q^{64} -858.079 q^{65} -152.621 q^{66} +269.510 q^{67} -1206.36 q^{68} -354.207 q^{69} -760.103 q^{70} -33.3057 q^{71} +644.452 q^{72} -481.037 q^{73} -1275.67 q^{74} +84.9505 q^{75} +1702.76 q^{76} -139.777 q^{77} -957.918 q^{78} +694.397 q^{79} -554.856 q^{80} +124.921 q^{81} -129.255 q^{82} +1483.15 q^{83} -555.492 q^{84} +988.715 q^{85} +31.0899 q^{86} -422.249 q^{87} -379.300 q^{88} -1242.93 q^{89} -1117.97 q^{90} -877.303 q^{91} -1863.25 q^{92} +572.909 q^{93} -2383.25 q^{94} -1395.56 q^{95} +175.811 q^{96} -994.914 q^{97} +873.707 q^{98} -205.586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.81294 −1.70163 −0.850816 0.525464i \(-0.823892\pi\)
−0.850816 + 0.525464i \(0.823892\pi\)
\(3\) 2.88277 0.554790 0.277395 0.960756i \(-0.410529\pi\)
0.277395 + 0.960756i \(0.410529\pi\)
\(4\) 15.1644 1.89555
\(5\) −12.4285 −1.11164 −0.555821 0.831302i \(-0.687596\pi\)
−0.555821 + 0.831302i \(0.687596\pi\)
\(6\) −13.8746 −0.944048
\(7\) −12.7070 −0.686112 −0.343056 0.939315i \(-0.611462\pi\)
−0.343056 + 0.939315i \(0.611462\pi\)
\(8\) −34.4818 −1.52389
\(9\) −18.6896 −0.692208
\(10\) 59.8178 1.89160
\(11\) 11.0000 0.301511
\(12\) 43.7155 1.05163
\(13\) 69.0410 1.47296 0.736482 0.676457i \(-0.236485\pi\)
0.736482 + 0.676457i \(0.236485\pi\)
\(14\) 61.1579 1.16751
\(15\) −35.8286 −0.616728
\(16\) 44.6437 0.697558
\(17\) −79.5521 −1.13495 −0.567477 0.823389i \(-0.692080\pi\)
−0.567477 + 0.823389i \(0.692080\pi\)
\(18\) 89.9520 1.17788
\(19\) 112.287 1.35581 0.677904 0.735151i \(-0.262889\pi\)
0.677904 + 0.735151i \(0.262889\pi\)
\(20\) −188.471 −2.10717
\(21\) −36.6313 −0.380648
\(22\) −52.9423 −0.513061
\(23\) −122.870 −1.11392 −0.556961 0.830539i \(-0.688033\pi\)
−0.556961 + 0.830539i \(0.688033\pi\)
\(24\) −99.4032 −0.845442
\(25\) 29.4683 0.235747
\(26\) −332.290 −2.50644
\(27\) −131.713 −0.938820
\(28\) −192.694 −1.30056
\(29\) −146.473 −0.937910 −0.468955 0.883222i \(-0.655369\pi\)
−0.468955 + 0.883222i \(0.655369\pi\)
\(30\) 172.441 1.04944
\(31\) 198.735 1.15142 0.575709 0.817655i \(-0.304726\pi\)
0.575709 + 0.817655i \(0.304726\pi\)
\(32\) 60.9869 0.336908
\(33\) 31.7105 0.167275
\(34\) 382.879 1.93127
\(35\) 157.929 0.762711
\(36\) −283.417 −1.31211
\(37\) 265.049 1.17767 0.588836 0.808253i \(-0.299586\pi\)
0.588836 + 0.808253i \(0.299586\pi\)
\(38\) −540.429 −2.30708
\(39\) 199.030 0.817186
\(40\) 428.558 1.69402
\(41\) 26.8558 0.102297 0.0511484 0.998691i \(-0.483712\pi\)
0.0511484 + 0.998691i \(0.483712\pi\)
\(42\) 176.304 0.647723
\(43\) −6.45965 −0.0229090 −0.0114545 0.999934i \(-0.503646\pi\)
−0.0114545 + 0.999934i \(0.503646\pi\)
\(44\) 166.808 0.571530
\(45\) 232.284 0.769487
\(46\) 591.366 1.89548
\(47\) 495.176 1.53678 0.768392 0.639979i \(-0.221057\pi\)
0.768392 + 0.639979i \(0.221057\pi\)
\(48\) 128.698 0.386998
\(49\) −181.533 −0.529250
\(50\) −141.829 −0.401154
\(51\) −229.331 −0.629661
\(52\) 1046.97 2.79208
\(53\) −5.15724 −0.0133661 −0.00668303 0.999978i \(-0.502127\pi\)
−0.00668303 + 0.999978i \(0.502127\pi\)
\(54\) 633.926 1.59753
\(55\) −136.714 −0.335173
\(56\) 438.159 1.04556
\(57\) 323.697 0.752188
\(58\) 704.967 1.59598
\(59\) 108.052 0.238426 0.119213 0.992869i \(-0.461963\pi\)
0.119213 + 0.992869i \(0.461963\pi\)
\(60\) −543.320 −1.16904
\(61\) 109.201 0.229210 0.114605 0.993411i \(-0.463440\pi\)
0.114605 + 0.993411i \(0.463440\pi\)
\(62\) −956.502 −1.95929
\(63\) 237.488 0.474932
\(64\) −650.676 −1.27085
\(65\) −858.079 −1.63741
\(66\) −152.621 −0.284641
\(67\) 269.510 0.491431 0.245715 0.969342i \(-0.420977\pi\)
0.245715 + 0.969342i \(0.420977\pi\)
\(68\) −1206.36 −2.15136
\(69\) −354.207 −0.617992
\(70\) −760.103 −1.29785
\(71\) −33.3057 −0.0556713 −0.0278356 0.999613i \(-0.508862\pi\)
−0.0278356 + 0.999613i \(0.508862\pi\)
\(72\) 644.452 1.05485
\(73\) −481.037 −0.771249 −0.385624 0.922656i \(-0.626014\pi\)
−0.385624 + 0.922656i \(0.626014\pi\)
\(74\) −1275.67 −2.00396
\(75\) 84.9505 0.130790
\(76\) 1702.76 2.57000
\(77\) −139.777 −0.206871
\(78\) −957.918 −1.39055
\(79\) 694.397 0.988934 0.494467 0.869196i \(-0.335363\pi\)
0.494467 + 0.869196i \(0.335363\pi\)
\(80\) −554.856 −0.775434
\(81\) 124.921 0.171360
\(82\) −129.255 −0.174071
\(83\) 1483.15 1.96141 0.980706 0.195490i \(-0.0626298\pi\)
0.980706 + 0.195490i \(0.0626298\pi\)
\(84\) −555.492 −0.721537
\(85\) 988.715 1.26166
\(86\) 31.0899 0.0389827
\(87\) −422.249 −0.520343
\(88\) −379.300 −0.459472
\(89\) −1242.93 −1.48034 −0.740170 0.672420i \(-0.765255\pi\)
−0.740170 + 0.672420i \(0.765255\pi\)
\(90\) −1117.97 −1.30938
\(91\) −877.303 −1.01062
\(92\) −1863.25 −2.11149
\(93\) 572.909 0.638795
\(94\) −2383.25 −2.61504
\(95\) −1395.56 −1.50717
\(96\) 175.811 0.186913
\(97\) −994.914 −1.04142 −0.520712 0.853732i \(-0.674334\pi\)
−0.520712 + 0.853732i \(0.674334\pi\)
\(98\) 873.707 0.900589
\(99\) −205.586 −0.208709
\(100\) 446.869 0.446869
\(101\) 1093.92 1.07772 0.538858 0.842396i \(-0.318856\pi\)
0.538858 + 0.842396i \(0.318856\pi\)
\(102\) 1103.75 1.07145
\(103\) 722.486 0.691152 0.345576 0.938391i \(-0.387684\pi\)
0.345576 + 0.938391i \(0.387684\pi\)
\(104\) −2380.66 −2.24464
\(105\) 455.274 0.423144
\(106\) 24.8215 0.0227441
\(107\) −1371.36 −1.23901 −0.619505 0.784993i \(-0.712667\pi\)
−0.619505 + 0.784993i \(0.712667\pi\)
\(108\) −1997.35 −1.77958
\(109\) 592.866 0.520975 0.260488 0.965477i \(-0.416117\pi\)
0.260488 + 0.965477i \(0.416117\pi\)
\(110\) 657.995 0.570340
\(111\) 764.078 0.653361
\(112\) −567.287 −0.478603
\(113\) 327.515 0.272655 0.136327 0.990664i \(-0.456470\pi\)
0.136327 + 0.990664i \(0.456470\pi\)
\(114\) −1557.94 −1.27995
\(115\) 1527.09 1.23828
\(116\) −2221.18 −1.77786
\(117\) −1290.35 −1.01960
\(118\) −520.047 −0.405714
\(119\) 1010.87 0.778705
\(120\) 1235.44 0.939828
\(121\) 121.000 0.0909091
\(122\) −525.580 −0.390031
\(123\) 77.4191 0.0567532
\(124\) 3013.70 2.18257
\(125\) 1187.32 0.849576
\(126\) −1143.02 −0.808160
\(127\) 23.2120 0.0162184 0.00810919 0.999967i \(-0.497419\pi\)
0.00810919 + 0.999967i \(0.497419\pi\)
\(128\) 2643.77 1.82561
\(129\) −18.6217 −0.0127097
\(130\) 4129.88 2.78627
\(131\) −131.000 −0.0873704
\(132\) 480.871 0.317079
\(133\) −1426.82 −0.930236
\(134\) −1297.13 −0.836234
\(135\) 1637.00 1.04363
\(136\) 2743.10 1.72955
\(137\) −9.30853 −0.00580498 −0.00290249 0.999996i \(-0.500924\pi\)
−0.00290249 + 0.999996i \(0.500924\pi\)
\(138\) 1704.78 1.05160
\(139\) −1774.82 −1.08301 −0.541506 0.840697i \(-0.682146\pi\)
−0.541506 + 0.840697i \(0.682146\pi\)
\(140\) 2394.90 1.44576
\(141\) 1427.48 0.852592
\(142\) 160.298 0.0947320
\(143\) 759.451 0.444116
\(144\) −834.374 −0.482855
\(145\) 1820.45 1.04262
\(146\) 2315.20 1.31238
\(147\) −523.318 −0.293623
\(148\) 4019.31 2.23234
\(149\) −842.339 −0.463135 −0.231567 0.972819i \(-0.574385\pi\)
−0.231567 + 0.972819i \(0.574385\pi\)
\(150\) −408.862 −0.222556
\(151\) −2773.37 −1.49466 −0.747331 0.664452i \(-0.768665\pi\)
−0.747331 + 0.664452i \(0.768665\pi\)
\(152\) −3871.85 −2.06611
\(153\) 1486.80 0.785624
\(154\) 672.737 0.352017
\(155\) −2469.99 −1.27996
\(156\) 3018.17 1.54902
\(157\) −2130.05 −1.08278 −0.541391 0.840771i \(-0.682102\pi\)
−0.541391 + 0.840771i \(0.682102\pi\)
\(158\) −3342.09 −1.68280
\(159\) −14.8671 −0.00741535
\(160\) −757.977 −0.374521
\(161\) 1561.31 0.764275
\(162\) −601.239 −0.291591
\(163\) 3457.25 1.66130 0.830652 0.556792i \(-0.187968\pi\)
0.830652 + 0.556792i \(0.187968\pi\)
\(164\) 407.252 0.193909
\(165\) −394.115 −0.185950
\(166\) −7138.32 −3.33760
\(167\) 1359.97 0.630167 0.315083 0.949064i \(-0.397968\pi\)
0.315083 + 0.949064i \(0.397968\pi\)
\(168\) 1263.11 0.580068
\(169\) 2569.67 1.16962
\(170\) −4758.63 −2.14688
\(171\) −2098.60 −0.938501
\(172\) −97.9567 −0.0434252
\(173\) −967.698 −0.425276 −0.212638 0.977131i \(-0.568206\pi\)
−0.212638 + 0.977131i \(0.568206\pi\)
\(174\) 2032.26 0.885433
\(175\) −374.453 −0.161749
\(176\) 491.081 0.210322
\(177\) 311.489 0.132276
\(178\) 5982.14 2.51899
\(179\) −3121.28 −1.30333 −0.651663 0.758509i \(-0.725928\pi\)
−0.651663 + 0.758509i \(0.725928\pi\)
\(180\) 3522.45 1.45860
\(181\) 673.200 0.276456 0.138228 0.990400i \(-0.455859\pi\)
0.138228 + 0.990400i \(0.455859\pi\)
\(182\) 4222.41 1.71970
\(183\) 314.803 0.127163
\(184\) 4236.78 1.69750
\(185\) −3294.17 −1.30915
\(186\) −2757.38 −1.08699
\(187\) −875.073 −0.342201
\(188\) 7509.05 2.91305
\(189\) 1673.67 0.644136
\(190\) 6716.74 2.56465
\(191\) 2224.34 0.842658 0.421329 0.906908i \(-0.361564\pi\)
0.421329 + 0.906908i \(0.361564\pi\)
\(192\) −1875.75 −0.705056
\(193\) −1442.29 −0.537918 −0.268959 0.963152i \(-0.586680\pi\)
−0.268959 + 0.963152i \(0.586680\pi\)
\(194\) 4788.46 1.77212
\(195\) −2473.65 −0.908418
\(196\) −2752.84 −1.00322
\(197\) 1557.92 0.563438 0.281719 0.959497i \(-0.409095\pi\)
0.281719 + 0.959497i \(0.409095\pi\)
\(198\) 989.472 0.355145
\(199\) 2261.71 0.805671 0.402835 0.915272i \(-0.368025\pi\)
0.402835 + 0.915272i \(0.368025\pi\)
\(200\) −1016.12 −0.359253
\(201\) 776.936 0.272641
\(202\) −5264.99 −1.83388
\(203\) 1861.23 0.643512
\(204\) −3477.66 −1.19355
\(205\) −333.778 −0.113717
\(206\) −3477.28 −1.17609
\(207\) 2296.39 0.771065
\(208\) 3082.25 1.02748
\(209\) 1235.15 0.408791
\(210\) −2191.20 −0.720036
\(211\) 3227.11 1.05291 0.526454 0.850204i \(-0.323521\pi\)
0.526454 + 0.850204i \(0.323521\pi\)
\(212\) −78.2064 −0.0253360
\(213\) −96.0128 −0.0308859
\(214\) 6600.26 2.10834
\(215\) 80.2840 0.0254666
\(216\) 4541.70 1.43066
\(217\) −2525.33 −0.790001
\(218\) −2853.43 −0.886508
\(219\) −1386.72 −0.427881
\(220\) −2073.18 −0.635336
\(221\) −5492.36 −1.67175
\(222\) −3677.46 −1.11178
\(223\) 1205.99 0.362150 0.181075 0.983469i \(-0.442042\pi\)
0.181075 + 0.983469i \(0.442042\pi\)
\(224\) −774.959 −0.231157
\(225\) −550.752 −0.163186
\(226\) −1576.31 −0.463958
\(227\) −2479.50 −0.724979 −0.362490 0.931988i \(-0.618073\pi\)
−0.362490 + 0.931988i \(0.618073\pi\)
\(228\) 4908.67 1.42581
\(229\) −3428.15 −0.989250 −0.494625 0.869106i \(-0.664695\pi\)
−0.494625 + 0.869106i \(0.664695\pi\)
\(230\) −7349.81 −2.10710
\(231\) −402.945 −0.114770
\(232\) 5050.66 1.42928
\(233\) −1951.25 −0.548630 −0.274315 0.961640i \(-0.588451\pi\)
−0.274315 + 0.961640i \(0.588451\pi\)
\(234\) 6210.38 1.73498
\(235\) −6154.31 −1.70835
\(236\) 1638.54 0.451949
\(237\) 2001.79 0.548651
\(238\) −4865.24 −1.32507
\(239\) −4077.36 −1.10352 −0.551762 0.834002i \(-0.686044\pi\)
−0.551762 + 0.834002i \(0.686044\pi\)
\(240\) −1599.52 −0.430203
\(241\) −3335.97 −0.891653 −0.445827 0.895119i \(-0.647090\pi\)
−0.445827 + 0.895119i \(0.647090\pi\)
\(242\) −582.366 −0.154694
\(243\) 3916.37 1.03389
\(244\) 1655.97 0.434479
\(245\) 2256.19 0.588336
\(246\) −372.614 −0.0965731
\(247\) 7752.39 1.99706
\(248\) −6852.76 −1.75464
\(249\) 4275.59 1.08817
\(250\) −5714.49 −1.44566
\(251\) 5700.17 1.43343 0.716717 0.697365i \(-0.245644\pi\)
0.716717 + 0.697365i \(0.245644\pi\)
\(252\) 3601.37 0.900258
\(253\) −1351.57 −0.335860
\(254\) −111.718 −0.0275977
\(255\) 2850.24 0.699957
\(256\) −7518.90 −1.83567
\(257\) 957.717 0.232454 0.116227 0.993223i \(-0.462920\pi\)
0.116227 + 0.993223i \(0.462920\pi\)
\(258\) 89.6252 0.0216272
\(259\) −3367.98 −0.808015
\(260\) −13012.2 −3.10379
\(261\) 2737.53 0.649229
\(262\) 630.495 0.148672
\(263\) −3477.86 −0.815414 −0.407707 0.913113i \(-0.633672\pi\)
−0.407707 + 0.913113i \(0.633672\pi\)
\(264\) −1093.44 −0.254910
\(265\) 64.0969 0.0148583
\(266\) 6867.22 1.58292
\(267\) −3583.08 −0.821277
\(268\) 4086.95 0.931531
\(269\) −7097.25 −1.60865 −0.804326 0.594189i \(-0.797473\pi\)
−0.804326 + 0.594189i \(0.797473\pi\)
\(270\) −7878.77 −1.77588
\(271\) −7743.09 −1.73564 −0.867821 0.496877i \(-0.834480\pi\)
−0.867821 + 0.496877i \(0.834480\pi\)
\(272\) −3551.50 −0.791696
\(273\) −2529.07 −0.560681
\(274\) 44.8014 0.00987793
\(275\) 324.152 0.0710803
\(276\) −5371.33 −1.17143
\(277\) −1739.02 −0.377212 −0.188606 0.982053i \(-0.560397\pi\)
−0.188606 + 0.982053i \(0.560397\pi\)
\(278\) 8542.12 1.84289
\(279\) −3714.29 −0.797020
\(280\) −5445.68 −1.16229
\(281\) −6087.61 −1.29237 −0.646186 0.763180i \(-0.723637\pi\)
−0.646186 + 0.763180i \(0.723637\pi\)
\(282\) −6870.38 −1.45080
\(283\) −7485.51 −1.57232 −0.786161 0.618021i \(-0.787935\pi\)
−0.786161 + 0.618021i \(0.787935\pi\)
\(284\) −505.061 −0.105528
\(285\) −4023.08 −0.836164
\(286\) −3655.19 −0.755721
\(287\) −341.256 −0.0701871
\(288\) −1139.82 −0.233211
\(289\) 1415.53 0.288119
\(290\) −8761.70 −1.77416
\(291\) −2868.11 −0.577772
\(292\) −7294.64 −1.46194
\(293\) −5674.34 −1.13139 −0.565697 0.824613i \(-0.691393\pi\)
−0.565697 + 0.824613i \(0.691393\pi\)
\(294\) 2518.70 0.499638
\(295\) −1342.92 −0.265044
\(296\) −9139.38 −1.79465
\(297\) −1448.84 −0.283065
\(298\) 4054.13 0.788085
\(299\) −8483.08 −1.64077
\(300\) 1288.22 0.247919
\(301\) 82.0826 0.0157182
\(302\) 13348.1 2.54336
\(303\) 3153.53 0.597907
\(304\) 5012.90 0.945754
\(305\) −1357.21 −0.254799
\(306\) −7155.87 −1.33684
\(307\) −972.535 −0.180800 −0.0903999 0.995906i \(-0.528815\pi\)
−0.0903999 + 0.995906i \(0.528815\pi\)
\(308\) −2119.63 −0.392133
\(309\) 2082.76 0.383444
\(310\) 11887.9 2.17803
\(311\) 1657.27 0.302171 0.151086 0.988521i \(-0.451723\pi\)
0.151086 + 0.988521i \(0.451723\pi\)
\(312\) −6862.90 −1.24531
\(313\) −4397.59 −0.794143 −0.397071 0.917788i \(-0.629973\pi\)
−0.397071 + 0.917788i \(0.629973\pi\)
\(314\) 10251.8 1.84250
\(315\) −2951.63 −0.527954
\(316\) 10530.1 1.87457
\(317\) 540.436 0.0957537 0.0478768 0.998853i \(-0.484754\pi\)
0.0478768 + 0.998853i \(0.484754\pi\)
\(318\) 71.5547 0.0126182
\(319\) −1611.21 −0.282791
\(320\) 8086.95 1.41273
\(321\) −3953.31 −0.687390
\(322\) −7514.48 −1.30051
\(323\) −8932.64 −1.53878
\(324\) 1894.36 0.324821
\(325\) 2034.52 0.347247
\(326\) −16639.5 −2.82693
\(327\) 1709.10 0.289032
\(328\) −926.036 −0.155890
\(329\) −6292.19 −1.05441
\(330\) 1896.85 0.316419
\(331\) 9335.25 1.55019 0.775093 0.631847i \(-0.217703\pi\)
0.775093 + 0.631847i \(0.217703\pi\)
\(332\) 22491.1 3.71795
\(333\) −4953.67 −0.815194
\(334\) −6545.47 −1.07231
\(335\) −3349.61 −0.546295
\(336\) −1635.36 −0.265524
\(337\) −8699.39 −1.40619 −0.703095 0.711096i \(-0.748199\pi\)
−0.703095 + 0.711096i \(0.748199\pi\)
\(338\) −12367.6 −1.99027
\(339\) 944.151 0.151266
\(340\) 14993.3 2.39154
\(341\) 2186.09 0.347165
\(342\) 10100.4 1.59698
\(343\) 6665.22 1.04924
\(344\) 222.741 0.0349109
\(345\) 4402.27 0.686986
\(346\) 4657.47 0.723663
\(347\) −9167.24 −1.41822 −0.709111 0.705097i \(-0.750903\pi\)
−0.709111 + 0.705097i \(0.750903\pi\)
\(348\) −6403.15 −0.986337
\(349\) −4725.44 −0.724777 −0.362389 0.932027i \(-0.618039\pi\)
−0.362389 + 0.932027i \(0.618039\pi\)
\(350\) 1802.22 0.275237
\(351\) −9093.59 −1.38285
\(352\) 670.856 0.101582
\(353\) 4341.29 0.654570 0.327285 0.944926i \(-0.393866\pi\)
0.327285 + 0.944926i \(0.393866\pi\)
\(354\) −1499.18 −0.225086
\(355\) 413.941 0.0618865
\(356\) −18848.3 −2.80606
\(357\) 2914.10 0.432018
\(358\) 15022.5 2.21778
\(359\) 1253.74 0.184317 0.0921585 0.995744i \(-0.470623\pi\)
0.0921585 + 0.995744i \(0.470623\pi\)
\(360\) −8009.59 −1.17262
\(361\) 5749.31 0.838213
\(362\) −3240.07 −0.470426
\(363\) 348.816 0.0504355
\(364\) −13303.8 −1.91568
\(365\) 5978.59 0.857352
\(366\) −1515.13 −0.216385
\(367\) 1426.36 0.202875 0.101438 0.994842i \(-0.467656\pi\)
0.101438 + 0.994842i \(0.467656\pi\)
\(368\) −5485.38 −0.777025
\(369\) −501.924 −0.0708107
\(370\) 15854.7 2.22769
\(371\) 65.5329 0.00917061
\(372\) 8687.82 1.21087
\(373\) 856.823 0.118940 0.0594700 0.998230i \(-0.481059\pi\)
0.0594700 + 0.998230i \(0.481059\pi\)
\(374\) 4211.67 0.582301
\(375\) 3422.77 0.471336
\(376\) −17074.6 −2.34190
\(377\) −10112.7 −1.38151
\(378\) −8055.28 −1.09608
\(379\) 7789.36 1.05571 0.527853 0.849336i \(-0.322997\pi\)
0.527853 + 0.849336i \(0.322997\pi\)
\(380\) −21162.8 −2.85692
\(381\) 66.9150 0.00899780
\(382\) −10705.6 −1.43389
\(383\) 2844.39 0.379482 0.189741 0.981834i \(-0.439235\pi\)
0.189741 + 0.981834i \(0.439235\pi\)
\(384\) 7621.39 1.01283
\(385\) 1737.22 0.229966
\(386\) 6941.65 0.915338
\(387\) 120.728 0.0158578
\(388\) −15087.3 −1.97407
\(389\) −5069.27 −0.660725 −0.330363 0.943854i \(-0.607171\pi\)
−0.330363 + 0.943854i \(0.607171\pi\)
\(390\) 11905.5 1.54579
\(391\) 9774.57 1.26425
\(392\) 6259.58 0.806522
\(393\) −377.643 −0.0484722
\(394\) −7498.18 −0.958764
\(395\) −8630.34 −1.09934
\(396\) −3117.58 −0.395617
\(397\) 2861.62 0.361764 0.180882 0.983505i \(-0.442105\pi\)
0.180882 + 0.983505i \(0.442105\pi\)
\(398\) −10885.5 −1.37095
\(399\) −4113.21 −0.516086
\(400\) 1315.58 0.164447
\(401\) −3081.80 −0.383785 −0.191892 0.981416i \(-0.561462\pi\)
−0.191892 + 0.981416i \(0.561462\pi\)
\(402\) −3739.35 −0.463934
\(403\) 13720.9 1.69600
\(404\) 16588.7 2.04287
\(405\) −1552.59 −0.190491
\(406\) −8958.00 −1.09502
\(407\) 2915.54 0.355081
\(408\) 7907.73 0.959537
\(409\) 490.037 0.0592440 0.0296220 0.999561i \(-0.490570\pi\)
0.0296220 + 0.999561i \(0.490570\pi\)
\(410\) 1606.45 0.193505
\(411\) −26.8344 −0.00322054
\(412\) 10956.1 1.31011
\(413\) −1373.01 −0.163587
\(414\) −11052.4 −1.31207
\(415\) −18433.4 −2.18039
\(416\) 4210.60 0.496254
\(417\) −5116.42 −0.600844
\(418\) −5944.72 −0.695612
\(419\) 807.157 0.0941103 0.0470552 0.998892i \(-0.485016\pi\)
0.0470552 + 0.998892i \(0.485016\pi\)
\(420\) 6903.95 0.802091
\(421\) −13416.7 −1.55318 −0.776589 0.630007i \(-0.783052\pi\)
−0.776589 + 0.630007i \(0.783052\pi\)
\(422\) −15531.9 −1.79166
\(423\) −9254.65 −1.06377
\(424\) 177.831 0.0203685
\(425\) −2344.27 −0.267562
\(426\) 462.104 0.0525564
\(427\) −1387.62 −0.157264
\(428\) −20795.8 −2.34860
\(429\) 2189.33 0.246391
\(430\) −386.402 −0.0433348
\(431\) −14006.6 −1.56537 −0.782685 0.622418i \(-0.786150\pi\)
−0.782685 + 0.622418i \(0.786150\pi\)
\(432\) −5880.15 −0.654882
\(433\) −1046.71 −0.116170 −0.0580852 0.998312i \(-0.518499\pi\)
−0.0580852 + 0.998312i \(0.518499\pi\)
\(434\) 12154.2 1.34429
\(435\) 5247.94 0.578435
\(436\) 8990.46 0.987534
\(437\) −13796.7 −1.51026
\(438\) 6674.21 0.728096
\(439\) 11960.3 1.30030 0.650151 0.759805i \(-0.274706\pi\)
0.650151 + 0.759805i \(0.274706\pi\)
\(440\) 4714.14 0.510768
\(441\) 3392.78 0.366351
\(442\) 26434.4 2.84470
\(443\) −57.0715 −0.00612087 −0.00306044 0.999995i \(-0.500974\pi\)
−0.00306044 + 0.999995i \(0.500974\pi\)
\(444\) 11586.8 1.23848
\(445\) 15447.8 1.64561
\(446\) −5804.38 −0.616245
\(447\) −2428.27 −0.256943
\(448\) 8268.12 0.871947
\(449\) 15533.0 1.63263 0.816314 0.577609i \(-0.196014\pi\)
0.816314 + 0.577609i \(0.196014\pi\)
\(450\) 2650.74 0.277682
\(451\) 295.414 0.0308436
\(452\) 4966.56 0.516830
\(453\) −7995.01 −0.829223
\(454\) 11933.7 1.23365
\(455\) 10903.6 1.12345
\(456\) −11161.7 −1.14626
\(457\) 8667.99 0.887246 0.443623 0.896213i \(-0.353693\pi\)
0.443623 + 0.896213i \(0.353693\pi\)
\(458\) 16499.5 1.68334
\(459\) 10478.0 1.06552
\(460\) 23157.5 2.34722
\(461\) −11264.1 −1.13801 −0.569005 0.822334i \(-0.692671\pi\)
−0.569005 + 0.822334i \(0.692671\pi\)
\(462\) 1939.35 0.195296
\(463\) −17534.4 −1.76003 −0.880015 0.474946i \(-0.842468\pi\)
−0.880015 + 0.474946i \(0.842468\pi\)
\(464\) −6539.11 −0.654247
\(465\) −7120.42 −0.710111
\(466\) 9391.26 0.933566
\(467\) 496.301 0.0491779 0.0245889 0.999698i \(-0.492172\pi\)
0.0245889 + 0.999698i \(0.492172\pi\)
\(468\) −19567.4 −1.93270
\(469\) −3424.65 −0.337177
\(470\) 29620.3 2.90699
\(471\) −6140.46 −0.600717
\(472\) −3725.82 −0.363336
\(473\) −71.0562 −0.00690733
\(474\) −9634.50 −0.933602
\(475\) 3308.90 0.319627
\(476\) 15329.2 1.47607
\(477\) 96.3868 0.00925209
\(478\) 19624.1 1.87779
\(479\) −20243.2 −1.93097 −0.965485 0.260458i \(-0.916126\pi\)
−0.965485 + 0.260458i \(0.916126\pi\)
\(480\) −2185.08 −0.207781
\(481\) 18299.3 1.73467
\(482\) 16055.8 1.51727
\(483\) 4500.89 0.424012
\(484\) 1834.89 0.172323
\(485\) 12365.3 1.15769
\(486\) −18849.2 −1.75930
\(487\) 3880.42 0.361065 0.180532 0.983569i \(-0.442218\pi\)
0.180532 + 0.983569i \(0.442218\pi\)
\(488\) −3765.46 −0.349292
\(489\) 9966.47 0.921675
\(490\) −10858.9 −1.00113
\(491\) −3238.53 −0.297664 −0.148832 0.988863i \(-0.547551\pi\)
−0.148832 + 0.988863i \(0.547551\pi\)
\(492\) 1174.01 0.107579
\(493\) 11652.3 1.06448
\(494\) −37311.8 −3.39825
\(495\) 2555.13 0.232009
\(496\) 8872.29 0.803180
\(497\) 423.215 0.0381967
\(498\) −20578.2 −1.85167
\(499\) −6473.71 −0.580768 −0.290384 0.956910i \(-0.593783\pi\)
−0.290384 + 0.956910i \(0.593783\pi\)
\(500\) 18005.0 1.61041
\(501\) 3920.49 0.349610
\(502\) −27434.6 −2.43917
\(503\) 5199.63 0.460915 0.230457 0.973082i \(-0.425978\pi\)
0.230457 + 0.973082i \(0.425978\pi\)
\(504\) −8189.03 −0.723747
\(505\) −13595.9 −1.19803
\(506\) 6505.03 0.571510
\(507\) 7407.76 0.648896
\(508\) 351.996 0.0307428
\(509\) −4993.37 −0.434827 −0.217414 0.976080i \(-0.569762\pi\)
−0.217414 + 0.976080i \(0.569762\pi\)
\(510\) −13718.0 −1.19107
\(511\) 6112.53 0.529163
\(512\) 15037.9 1.29802
\(513\) −14789.6 −1.27286
\(514\) −4609.44 −0.395552
\(515\) −8979.44 −0.768313
\(516\) −282.387 −0.0240919
\(517\) 5446.94 0.463358
\(518\) 16209.9 1.37494
\(519\) −2789.66 −0.235939
\(520\) 29588.1 2.49524
\(521\) −8412.30 −0.707389 −0.353694 0.935361i \(-0.615075\pi\)
−0.353694 + 0.935361i \(0.615075\pi\)
\(522\) −13175.6 −1.10475
\(523\) 4110.76 0.343692 0.171846 0.985124i \(-0.445027\pi\)
0.171846 + 0.985124i \(0.445027\pi\)
\(524\) −1986.54 −0.165615
\(525\) −1079.46 −0.0897365
\(526\) 16738.7 1.38753
\(527\) −15809.8 −1.30681
\(528\) 1415.68 0.116684
\(529\) 2930.06 0.240820
\(530\) −308.494 −0.0252833
\(531\) −2019.45 −0.165041
\(532\) −21636.9 −1.76331
\(533\) 1854.15 0.150680
\(534\) 17245.2 1.39751
\(535\) 17043.9 1.37733
\(536\) −9293.19 −0.748889
\(537\) −8997.94 −0.723072
\(538\) 34158.7 2.73733
\(539\) −1996.86 −0.159575
\(540\) 24824.1 1.97825
\(541\) −5569.83 −0.442635 −0.221318 0.975202i \(-0.571036\pi\)
−0.221318 + 0.975202i \(0.571036\pi\)
\(542\) 37267.0 2.95342
\(543\) 1940.68 0.153375
\(544\) −4851.63 −0.382375
\(545\) −7368.46 −0.579138
\(546\) 12172.2 0.954073
\(547\) −10562.9 −0.825658 −0.412829 0.910809i \(-0.635459\pi\)
−0.412829 + 0.910809i \(0.635459\pi\)
\(548\) −141.158 −0.0110036
\(549\) −2040.93 −0.158661
\(550\) −1560.12 −0.120952
\(551\) −16447.0 −1.27163
\(552\) 12213.7 0.941755
\(553\) −8823.69 −0.678520
\(554\) 8369.80 0.641875
\(555\) −9496.36 −0.726303
\(556\) −26914.1 −2.05290
\(557\) −12272.7 −0.933596 −0.466798 0.884364i \(-0.654592\pi\)
−0.466798 + 0.884364i \(0.654592\pi\)
\(558\) 17876.7 1.35623
\(559\) −445.981 −0.0337442
\(560\) 7050.54 0.532035
\(561\) −2522.64 −0.189850
\(562\) 29299.3 2.19914
\(563\) −7340.77 −0.549514 −0.274757 0.961514i \(-0.588597\pi\)
−0.274757 + 0.961514i \(0.588597\pi\)
\(564\) 21646.9 1.61613
\(565\) −4070.52 −0.303094
\(566\) 36027.3 2.67551
\(567\) −1587.37 −0.117572
\(568\) 1148.44 0.0848372
\(569\) 22051.9 1.62471 0.812356 0.583161i \(-0.198184\pi\)
0.812356 + 0.583161i \(0.198184\pi\)
\(570\) 19362.8 1.42284
\(571\) −11672.6 −0.855485 −0.427742 0.903901i \(-0.640691\pi\)
−0.427742 + 0.903901i \(0.640691\pi\)
\(572\) 11516.6 0.841843
\(573\) 6412.27 0.467498
\(574\) 1642.44 0.119433
\(575\) −3620.78 −0.262603
\(576\) 12160.9 0.879694
\(577\) −17850.3 −1.28790 −0.643950 0.765068i \(-0.722705\pi\)
−0.643950 + 0.765068i \(0.722705\pi\)
\(578\) −6812.86 −0.490273
\(579\) −4157.79 −0.298431
\(580\) 27606.0 1.97634
\(581\) −18846.4 −1.34575
\(582\) 13804.0 0.983155
\(583\) −56.7296 −0.00403002
\(584\) 16587.0 1.17530
\(585\) 16037.2 1.13343
\(586\) 27310.3 1.92522
\(587\) −876.228 −0.0616112 −0.0308056 0.999525i \(-0.509807\pi\)
−0.0308056 + 0.999525i \(0.509807\pi\)
\(588\) −7935.80 −0.556576
\(589\) 22315.3 1.56110
\(590\) 6463.42 0.451008
\(591\) 4491.13 0.312590
\(592\) 11832.8 0.821495
\(593\) 1897.12 0.131375 0.0656877 0.997840i \(-0.479076\pi\)
0.0656877 + 0.997840i \(0.479076\pi\)
\(594\) 6973.19 0.481672
\(595\) −12563.6 −0.865641
\(596\) −12773.6 −0.877895
\(597\) 6520.00 0.446978
\(598\) 40828.6 2.79198
\(599\) −20724.9 −1.41368 −0.706841 0.707373i \(-0.749880\pi\)
−0.706841 + 0.707373i \(0.749880\pi\)
\(600\) −2929.25 −0.199310
\(601\) −2916.81 −0.197969 −0.0989844 0.995089i \(-0.531559\pi\)
−0.0989844 + 0.995089i \(0.531559\pi\)
\(602\) −395.059 −0.0267465
\(603\) −5037.04 −0.340172
\(604\) −42056.5 −2.83320
\(605\) −1503.85 −0.101058
\(606\) −15177.8 −1.01742
\(607\) 27913.0 1.86648 0.933241 0.359250i \(-0.116968\pi\)
0.933241 + 0.359250i \(0.116968\pi\)
\(608\) 6848.02 0.456783
\(609\) 5365.51 0.357014
\(610\) 6532.19 0.433575
\(611\) 34187.5 2.26363
\(612\) 22546.4 1.48919
\(613\) −318.939 −0.0210144 −0.0105072 0.999945i \(-0.503345\pi\)
−0.0105072 + 0.999945i \(0.503345\pi\)
\(614\) 4680.76 0.307655
\(615\) −962.206 −0.0630892
\(616\) 4819.75 0.315249
\(617\) −16978.6 −1.10784 −0.553918 0.832572i \(-0.686868\pi\)
−0.553918 + 0.832572i \(0.686868\pi\)
\(618\) −10024.2 −0.652481
\(619\) 26132.1 1.69683 0.848414 0.529333i \(-0.177558\pi\)
0.848414 + 0.529333i \(0.177558\pi\)
\(620\) −37455.9 −2.42623
\(621\) 16183.6 1.04577
\(622\) −7976.35 −0.514184
\(623\) 15793.9 1.01568
\(624\) 8885.43 0.570035
\(625\) −18440.2 −1.18017
\(626\) 21165.4 1.35134
\(627\) 3560.67 0.226793
\(628\) −32301.0 −2.05247
\(629\) −21085.2 −1.33660
\(630\) 14206.0 0.898384
\(631\) 29730.0 1.87565 0.937823 0.347113i \(-0.112838\pi\)
0.937823 + 0.347113i \(0.112838\pi\)
\(632\) −23944.1 −1.50703
\(633\) 9303.04 0.584143
\(634\) −2601.09 −0.162937
\(635\) −288.491 −0.0180290
\(636\) −225.451 −0.0140562
\(637\) −12533.2 −0.779567
\(638\) 7754.64 0.481205
\(639\) 622.471 0.0385361
\(640\) −32858.2 −2.02943
\(641\) 5481.24 0.337747 0.168874 0.985638i \(-0.445987\pi\)
0.168874 + 0.985638i \(0.445987\pi\)
\(642\) 19027.1 1.16969
\(643\) 25418.2 1.55893 0.779467 0.626443i \(-0.215490\pi\)
0.779467 + 0.626443i \(0.215490\pi\)
\(644\) 23676.3 1.44872
\(645\) 231.441 0.0141286
\(646\) 42992.3 2.61843
\(647\) −12725.8 −0.773267 −0.386633 0.922234i \(-0.626362\pi\)
−0.386633 + 0.922234i \(0.626362\pi\)
\(648\) −4307.51 −0.261135
\(649\) 1188.57 0.0718882
\(650\) −9792.05 −0.590886
\(651\) −7279.94 −0.438285
\(652\) 52427.1 3.14908
\(653\) 15378.7 0.921617 0.460808 0.887500i \(-0.347560\pi\)
0.460808 + 0.887500i \(0.347560\pi\)
\(654\) −8225.79 −0.491826
\(655\) 1628.14 0.0971246
\(656\) 1198.94 0.0713579
\(657\) 8990.40 0.533865
\(658\) 30283.9 1.79421
\(659\) 3097.56 0.183101 0.0915507 0.995800i \(-0.470818\pi\)
0.0915507 + 0.995800i \(0.470818\pi\)
\(660\) −5976.52 −0.352478
\(661\) −22527.3 −1.32558 −0.662792 0.748803i \(-0.730629\pi\)
−0.662792 + 0.748803i \(0.730629\pi\)
\(662\) −44930.0 −2.63785
\(663\) −15833.2 −0.927468
\(664\) −51141.8 −2.98898
\(665\) 17733.3 1.03409
\(666\) 23841.7 1.38716
\(667\) 17997.2 1.04476
\(668\) 20623.2 1.19451
\(669\) 3476.61 0.200917
\(670\) 16121.5 0.929593
\(671\) 1201.22 0.0691094
\(672\) −2234.03 −0.128243
\(673\) 6391.49 0.366083 0.183041 0.983105i \(-0.441406\pi\)
0.183041 + 0.983105i \(0.441406\pi\)
\(674\) 41869.6 2.39282
\(675\) −3881.36 −0.221324
\(676\) 38967.4 2.21708
\(677\) −19747.0 −1.12103 −0.560517 0.828143i \(-0.689398\pi\)
−0.560517 + 0.828143i \(0.689398\pi\)
\(678\) −4544.14 −0.257399
\(679\) 12642.3 0.714534
\(680\) −34092.7 −1.92264
\(681\) −7147.84 −0.402211
\(682\) −10521.5 −0.590748
\(683\) 17156.1 0.961144 0.480572 0.876955i \(-0.340429\pi\)
0.480572 + 0.876955i \(0.340429\pi\)
\(684\) −31823.9 −1.77897
\(685\) 115.691 0.00645305
\(686\) −32079.3 −1.78541
\(687\) −9882.57 −0.548826
\(688\) −288.383 −0.0159804
\(689\) −356.061 −0.0196877
\(690\) −21187.9 −1.16900
\(691\) −5754.63 −0.316811 −0.158405 0.987374i \(-0.550635\pi\)
−0.158405 + 0.987374i \(0.550635\pi\)
\(692\) −14674.6 −0.806132
\(693\) 2612.37 0.143197
\(694\) 44121.4 2.41329
\(695\) 22058.5 1.20392
\(696\) 14559.9 0.792949
\(697\) −2136.43 −0.116102
\(698\) 22743.3 1.23330
\(699\) −5625.02 −0.304374
\(700\) −5678.36 −0.306603
\(701\) −34405.6 −1.85375 −0.926877 0.375366i \(-0.877517\pi\)
−0.926877 + 0.375366i \(0.877517\pi\)
\(702\) 43766.9 2.35310
\(703\) 29761.5 1.59670
\(704\) −7157.44 −0.383176
\(705\) −17741.5 −0.947777
\(706\) −20894.4 −1.11384
\(707\) −13900.4 −0.739435
\(708\) 4723.54 0.250737
\(709\) −5247.78 −0.277976 −0.138988 0.990294i \(-0.544385\pi\)
−0.138988 + 0.990294i \(0.544385\pi\)
\(710\) −1992.27 −0.105308
\(711\) −12978.0 −0.684548
\(712\) 42858.4 2.25588
\(713\) −24418.6 −1.28259
\(714\) −14025.4 −0.735135
\(715\) −9438.86 −0.493697
\(716\) −47332.3 −2.47052
\(717\) −11754.1 −0.612224
\(718\) −6034.17 −0.313640
\(719\) −11261.5 −0.584122 −0.292061 0.956400i \(-0.594341\pi\)
−0.292061 + 0.956400i \(0.594341\pi\)
\(720\) 10370.0 0.536762
\(721\) −9180.61 −0.474208
\(722\) −27671.1 −1.42633
\(723\) −9616.83 −0.494680
\(724\) 10208.7 0.524036
\(725\) −4316.32 −0.221109
\(726\) −1678.83 −0.0858226
\(727\) 20408.8 1.04115 0.520577 0.853815i \(-0.325717\pi\)
0.520577 + 0.853815i \(0.325717\pi\)
\(728\) 30251.0 1.54008
\(729\) 7917.12 0.402231
\(730\) −28774.6 −1.45890
\(731\) 513.879 0.0260007
\(732\) 4773.80 0.241045
\(733\) 16343.4 0.823543 0.411772 0.911287i \(-0.364910\pi\)
0.411772 + 0.911287i \(0.364910\pi\)
\(734\) −6864.96 −0.345219
\(735\) 6504.07 0.326403
\(736\) −7493.47 −0.375289
\(737\) 2964.61 0.148172
\(738\) 2415.73 0.120494
\(739\) 20458.1 1.01836 0.509178 0.860662i \(-0.329950\pi\)
0.509178 + 0.860662i \(0.329950\pi\)
\(740\) −49954.2 −2.48156
\(741\) 22348.4 1.10795
\(742\) −315.406 −0.0156050
\(743\) 31227.7 1.54190 0.770952 0.636894i \(-0.219781\pi\)
0.770952 + 0.636894i \(0.219781\pi\)
\(744\) −19754.9 −0.973456
\(745\) 10469.0 0.514840
\(746\) −4123.84 −0.202392
\(747\) −27719.6 −1.35770
\(748\) −13269.9 −0.648660
\(749\) 17425.8 0.850100
\(750\) −16473.6 −0.802040
\(751\) −10031.8 −0.487436 −0.243718 0.969846i \(-0.578367\pi\)
−0.243718 + 0.969846i \(0.578367\pi\)
\(752\) 22106.5 1.07200
\(753\) 16432.3 0.795254
\(754\) 48671.7 2.35082
\(755\) 34468.9 1.66153
\(756\) 25380.2 1.22099
\(757\) −38647.7 −1.85558 −0.927790 0.373102i \(-0.878294\pi\)
−0.927790 + 0.373102i \(0.878294\pi\)
\(758\) −37489.7 −1.79642
\(759\) −3896.27 −0.186332
\(760\) 48121.4 2.29677
\(761\) −489.763 −0.0233297 −0.0116649 0.999932i \(-0.503713\pi\)
−0.0116649 + 0.999932i \(0.503713\pi\)
\(762\) −322.058 −0.0153109
\(763\) −7533.54 −0.357447
\(764\) 33730.8 1.59730
\(765\) −18478.7 −0.873332
\(766\) −13689.9 −0.645738
\(767\) 7460.01 0.351193
\(768\) −21675.3 −1.01841
\(769\) −674.895 −0.0316481 −0.0158240 0.999875i \(-0.505037\pi\)
−0.0158240 + 0.999875i \(0.505037\pi\)
\(770\) −8361.13 −0.391317
\(771\) 2760.88 0.128963
\(772\) −21871.4 −1.01965
\(773\) 30397.0 1.41437 0.707183 0.707030i \(-0.249966\pi\)
0.707183 + 0.707030i \(0.249966\pi\)
\(774\) −581.059 −0.0269841
\(775\) 5856.40 0.271443
\(776\) 34306.4 1.58702
\(777\) −9709.11 −0.448279
\(778\) 24398.1 1.12431
\(779\) 3015.55 0.138695
\(780\) −37511.4 −1.72195
\(781\) −366.363 −0.0167855
\(782\) −47044.4 −2.15128
\(783\) 19292.4 0.880529
\(784\) −8104.30 −0.369183
\(785\) 26473.4 1.20367
\(786\) 1817.57 0.0824819
\(787\) −5662.68 −0.256484 −0.128242 0.991743i \(-0.540933\pi\)
−0.128242 + 0.991743i \(0.540933\pi\)
\(788\) 23624.9 1.06802
\(789\) −10025.9 −0.452384
\(790\) 41537.3 1.87067
\(791\) −4161.72 −0.187072
\(792\) 7088.97 0.318050
\(793\) 7539.38 0.337618
\(794\) −13772.8 −0.615590
\(795\) 184.777 0.00824322
\(796\) 34297.5 1.52719
\(797\) −26107.2 −1.16031 −0.580153 0.814507i \(-0.697007\pi\)
−0.580153 + 0.814507i \(0.697007\pi\)
\(798\) 19796.6 0.878187
\(799\) −39392.3 −1.74418
\(800\) 1797.18 0.0794250
\(801\) 23229.9 1.02470
\(802\) 14832.5 0.653060
\(803\) −5291.41 −0.232540
\(804\) 11781.8 0.516804
\(805\) −19404.7 −0.849599
\(806\) −66037.9 −2.88596
\(807\) −20459.8 −0.892464
\(808\) −37720.4 −1.64233
\(809\) 28202.3 1.22564 0.612818 0.790224i \(-0.290036\pi\)
0.612818 + 0.790224i \(0.290036\pi\)
\(810\) 7472.52 0.324145
\(811\) −18137.7 −0.785327 −0.392663 0.919682i \(-0.628446\pi\)
−0.392663 + 0.919682i \(0.628446\pi\)
\(812\) 28224.5 1.21981
\(813\) −22321.6 −0.962917
\(814\) −14032.3 −0.604218
\(815\) −42968.5 −1.84677
\(816\) −10238.2 −0.439225
\(817\) −725.333 −0.0310602
\(818\) −2358.52 −0.100811
\(819\) 16396.5 0.699558
\(820\) −5061.54 −0.215557
\(821\) −12795.3 −0.543920 −0.271960 0.962309i \(-0.587672\pi\)
−0.271960 + 0.962309i \(0.587672\pi\)
\(822\) 129.152 0.00548018
\(823\) −16164.3 −0.684631 −0.342315 0.939585i \(-0.611211\pi\)
−0.342315 + 0.939585i \(0.611211\pi\)
\(824\) −24912.6 −1.05324
\(825\) 934.456 0.0394346
\(826\) 6608.22 0.278365
\(827\) −5621.29 −0.236362 −0.118181 0.992992i \(-0.537706\pi\)
−0.118181 + 0.992992i \(0.537706\pi\)
\(828\) 34823.4 1.46159
\(829\) −39059.8 −1.63643 −0.818217 0.574910i \(-0.805037\pi\)
−0.818217 + 0.574910i \(0.805037\pi\)
\(830\) 88718.9 3.71021
\(831\) −5013.20 −0.209273
\(832\) −44923.4 −1.87192
\(833\) 14441.3 0.600674
\(834\) 24625.0 1.02242
\(835\) −16902.5 −0.700519
\(836\) 18730.4 0.774884
\(837\) −26176.0 −1.08097
\(838\) −3884.80 −0.160141
\(839\) −8129.04 −0.334500 −0.167250 0.985915i \(-0.553489\pi\)
−0.167250 + 0.985915i \(0.553489\pi\)
\(840\) −15698.7 −0.644827
\(841\) −2934.58 −0.120324
\(842\) 64573.6 2.64294
\(843\) −17549.2 −0.716995
\(844\) 48937.2 1.99584
\(845\) −31937.2 −1.30020
\(846\) 44542.1 1.81015
\(847\) −1537.54 −0.0623738
\(848\) −230.238 −0.00932360
\(849\) −21579.0 −0.872309
\(850\) 11282.8 0.455291
\(851\) −32566.6 −1.31183
\(852\) −1455.98 −0.0585457
\(853\) −36159.4 −1.45144 −0.725719 0.687992i \(-0.758493\pi\)
−0.725719 + 0.687992i \(0.758493\pi\)
\(854\) 6678.53 0.267605
\(855\) 26082.5 1.04328
\(856\) 47286.9 1.88812
\(857\) 40431.4 1.61157 0.805783 0.592211i \(-0.201745\pi\)
0.805783 + 0.592211i \(0.201745\pi\)
\(858\) −10537.1 −0.419266
\(859\) −31565.4 −1.25378 −0.626891 0.779107i \(-0.715673\pi\)
−0.626891 + 0.779107i \(0.715673\pi\)
\(860\) 1217.46 0.0482732
\(861\) −983.763 −0.0389391
\(862\) 67412.9 2.66368
\(863\) 40280.1 1.58882 0.794410 0.607382i \(-0.207780\pi\)
0.794410 + 0.607382i \(0.207780\pi\)
\(864\) −8032.76 −0.316296
\(865\) 12027.1 0.472754
\(866\) 5037.76 0.197679
\(867\) 4080.65 0.159846
\(868\) −38295.0 −1.49749
\(869\) 7638.37 0.298175
\(870\) −25258.0 −0.984284
\(871\) 18607.2 0.723860
\(872\) −20443.1 −0.793911
\(873\) 18594.6 0.720882
\(874\) 66402.6 2.56991
\(875\) −15087.2 −0.582904
\(876\) −21028.8 −0.811070
\(877\) 73.3545 0.00282441 0.00141220 0.999999i \(-0.499550\pi\)
0.00141220 + 0.999999i \(0.499550\pi\)
\(878\) −57564.1 −2.21263
\(879\) −16357.8 −0.627686
\(880\) −6103.41 −0.233802
\(881\) −23041.7 −0.881153 −0.440576 0.897715i \(-0.645226\pi\)
−0.440576 + 0.897715i \(0.645226\pi\)
\(882\) −16329.2 −0.623395
\(883\) −5593.41 −0.213175 −0.106587 0.994303i \(-0.533992\pi\)
−0.106587 + 0.994303i \(0.533992\pi\)
\(884\) −83288.3 −3.16888
\(885\) −3871.35 −0.147044
\(886\) 274.682 0.0104155
\(887\) 36177.4 1.36947 0.684734 0.728793i \(-0.259918\pi\)
0.684734 + 0.728793i \(0.259918\pi\)
\(888\) −26346.8 −0.995653
\(889\) −294.955 −0.0111276
\(890\) −74349.2 −2.80022
\(891\) 1374.14 0.0516670
\(892\) 18288.2 0.686472
\(893\) 55601.7 2.08358
\(894\) 11687.1 0.437222
\(895\) 38792.9 1.44883
\(896\) −33594.3 −1.25258
\(897\) −24454.8 −0.910281
\(898\) −74759.6 −2.77813
\(899\) −29109.4 −1.07993
\(900\) −8351.82 −0.309327
\(901\) 410.269 0.0151699
\(902\) −1421.81 −0.0524845
\(903\) 236.626 0.00872028
\(904\) −11293.3 −0.415497
\(905\) −8366.88 −0.307320
\(906\) 38479.5 1.41103
\(907\) 372.408 0.0136335 0.00681675 0.999977i \(-0.497830\pi\)
0.00681675 + 0.999977i \(0.497830\pi\)
\(908\) −37600.1 −1.37423
\(909\) −20445.0 −0.746004
\(910\) −52478.3 −1.91169
\(911\) −10956.7 −0.398476 −0.199238 0.979951i \(-0.563847\pi\)
−0.199238 + 0.979951i \(0.563847\pi\)
\(912\) 14451.0 0.524695
\(913\) 16314.7 0.591388
\(914\) −41718.5 −1.50977
\(915\) −3912.54 −0.141360
\(916\) −51985.8 −1.87517
\(917\) 1664.61 0.0599459
\(918\) −50430.1 −1.81312
\(919\) −16477.5 −0.591452 −0.295726 0.955273i \(-0.595561\pi\)
−0.295726 + 0.955273i \(0.595561\pi\)
\(920\) −52657.0 −1.88701
\(921\) −2803.60 −0.100306
\(922\) 54213.5 1.93647
\(923\) −2299.46 −0.0820018
\(924\) −6110.41 −0.217552
\(925\) 7810.57 0.277632
\(926\) 84392.2 2.99492
\(927\) −13503.0 −0.478421
\(928\) −8932.95 −0.315990
\(929\) 22853.7 0.807111 0.403556 0.914955i \(-0.367774\pi\)
0.403556 + 0.914955i \(0.367774\pi\)
\(930\) 34270.2 1.20835
\(931\) −20383.7 −0.717561
\(932\) −29589.6 −1.03995
\(933\) 4777.54 0.167642
\(934\) −2388.67 −0.0836826
\(935\) 10875.9 0.380405
\(936\) 44493.6 1.55376
\(937\) −23823.3 −0.830602 −0.415301 0.909684i \(-0.636324\pi\)
−0.415301 + 0.909684i \(0.636324\pi\)
\(938\) 16482.7 0.573750
\(939\) −12677.3 −0.440583
\(940\) −93326.4 −3.23827
\(941\) −13339.6 −0.462124 −0.231062 0.972939i \(-0.574220\pi\)
−0.231062 + 0.972939i \(0.574220\pi\)
\(942\) 29553.7 1.02220
\(943\) −3299.77 −0.113951
\(944\) 4823.83 0.166316
\(945\) −20801.3 −0.716048
\(946\) 341.989 0.0117537
\(947\) −14119.9 −0.484514 −0.242257 0.970212i \(-0.577888\pi\)
−0.242257 + 0.970212i \(0.577888\pi\)
\(948\) 30355.9 1.03999
\(949\) −33211.3 −1.13602
\(950\) −15925.5 −0.543887
\(951\) 1557.96 0.0531232
\(952\) −34856.5 −1.18667
\(953\) 25335.3 0.861167 0.430584 0.902551i \(-0.358308\pi\)
0.430584 + 0.902551i \(0.358308\pi\)
\(954\) −463.904 −0.0157436
\(955\) −27645.3 −0.936734
\(956\) −61830.7 −2.09178
\(957\) −4644.74 −0.156889
\(958\) 97429.3 3.28580
\(959\) 118.283 0.00398286
\(960\) 23312.8 0.783769
\(961\) 9704.77 0.325762
\(962\) −88073.4 −2.95177
\(963\) 25630.1 0.857653
\(964\) −50587.9 −1.69017
\(965\) 17925.5 0.597972
\(966\) −21662.5 −0.721512
\(967\) 21854.1 0.726764 0.363382 0.931640i \(-0.381622\pi\)
0.363382 + 0.931640i \(0.381622\pi\)
\(968\) −4172.30 −0.138536
\(969\) −25750.8 −0.853699
\(970\) −59513.5 −1.96996
\(971\) 23044.6 0.761622 0.380811 0.924653i \(-0.375645\pi\)
0.380811 + 0.924653i \(0.375645\pi\)
\(972\) 59389.3 1.95979
\(973\) 22552.6 0.743068
\(974\) −18676.2 −0.614399
\(975\) 5865.07 0.192649
\(976\) 4875.16 0.159887
\(977\) 59011.4 1.93239 0.966193 0.257820i \(-0.0830042\pi\)
0.966193 + 0.257820i \(0.0830042\pi\)
\(978\) −47968.0 −1.56835
\(979\) −13672.2 −0.446339
\(980\) 34213.7 1.11522
\(981\) −11080.4 −0.360623
\(982\) 15586.9 0.506514
\(983\) −4203.76 −0.136398 −0.0681989 0.997672i \(-0.521725\pi\)
−0.0681989 + 0.997672i \(0.521725\pi\)
\(984\) −2669.55 −0.0864860
\(985\) −19362.7 −0.626341
\(986\) −56081.6 −1.81136
\(987\) −18139.0 −0.584974
\(988\) 117560. 3.78552
\(989\) 793.698 0.0255188
\(990\) −12297.7 −0.394794
\(991\) 25120.7 0.805233 0.402616 0.915369i \(-0.368101\pi\)
0.402616 + 0.915369i \(0.368101\pi\)
\(992\) 12120.3 0.387922
\(993\) 26911.4 0.860028
\(994\) −2036.91 −0.0649968
\(995\) −28109.8 −0.895617
\(996\) 64836.8 2.06268
\(997\) −24088.4 −0.765182 −0.382591 0.923918i \(-0.624968\pi\)
−0.382591 + 0.923918i \(0.624968\pi\)
\(998\) 31157.6 0.988252
\(999\) −34910.4 −1.10562
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 1441.4.a.b.1.10 79
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.4.a.b.1.10 79 1.1 even 1 trivial