Properties

Label 8041.2.a.d.1.13
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $1$
Dimension $62$
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] = [8041,2,Mod(1,8041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8041.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: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(62\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 8041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.89473 q^{2} -0.654571 q^{3} +1.59002 q^{4} +2.95213 q^{5} +1.24024 q^{6} -2.97686 q^{7} +0.776803 q^{8} -2.57154 q^{9} +O(q^{10})\) \(q-1.89473 q^{2} -0.654571 q^{3} +1.59002 q^{4} +2.95213 q^{5} +1.24024 q^{6} -2.97686 q^{7} +0.776803 q^{8} -2.57154 q^{9} -5.59350 q^{10} +1.00000 q^{11} -1.04078 q^{12} -2.31439 q^{13} +5.64036 q^{14} -1.93238 q^{15} -4.65188 q^{16} -1.00000 q^{17} +4.87238 q^{18} +8.06990 q^{19} +4.69394 q^{20} +1.94857 q^{21} -1.89473 q^{22} +1.76109 q^{23} -0.508473 q^{24} +3.71506 q^{25} +4.38516 q^{26} +3.64697 q^{27} -4.73327 q^{28} -4.64475 q^{29} +3.66135 q^{30} -2.51028 q^{31} +7.26047 q^{32} -0.654571 q^{33} +1.89473 q^{34} -8.78807 q^{35} -4.08879 q^{36} -7.64717 q^{37} -15.2903 q^{38} +1.51494 q^{39} +2.29322 q^{40} -0.808864 q^{41} -3.69202 q^{42} +1.00000 q^{43} +1.59002 q^{44} -7.59151 q^{45} -3.33680 q^{46} -0.805861 q^{47} +3.04499 q^{48} +1.86170 q^{49} -7.03906 q^{50} +0.654571 q^{51} -3.67993 q^{52} +11.2784 q^{53} -6.91004 q^{54} +2.95213 q^{55} -2.31243 q^{56} -5.28233 q^{57} +8.80058 q^{58} +8.88704 q^{59} -3.07252 q^{60} -0.148551 q^{61} +4.75631 q^{62} +7.65510 q^{63} -4.45290 q^{64} -6.83239 q^{65} +1.24024 q^{66} -8.30785 q^{67} -1.59002 q^{68} -1.15276 q^{69} +16.6511 q^{70} +1.70595 q^{71} -1.99758 q^{72} +12.9783 q^{73} +14.4894 q^{74} -2.43177 q^{75} +12.8313 q^{76} -2.97686 q^{77} -2.87040 q^{78} -10.0903 q^{79} -13.7329 q^{80} +5.32741 q^{81} +1.53258 q^{82} +13.0959 q^{83} +3.09826 q^{84} -2.95213 q^{85} -1.89473 q^{86} +3.04032 q^{87} +0.776803 q^{88} -7.73489 q^{89} +14.3839 q^{90} +6.88963 q^{91} +2.80017 q^{92} +1.64316 q^{93} +1.52689 q^{94} +23.8234 q^{95} -4.75249 q^{96} -13.9630 q^{97} -3.52742 q^{98} -2.57154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89473 −1.33978 −0.669890 0.742460i \(-0.733659\pi\)
−0.669890 + 0.742460i \(0.733659\pi\)
\(3\) −0.654571 −0.377917 −0.188959 0.981985i \(-0.560511\pi\)
−0.188959 + 0.981985i \(0.560511\pi\)
\(4\) 1.59002 0.795010
\(5\) 2.95213 1.32023 0.660116 0.751164i \(-0.270507\pi\)
0.660116 + 0.751164i \(0.270507\pi\)
\(6\) 1.24024 0.506326
\(7\) −2.97686 −1.12515 −0.562574 0.826747i \(-0.690189\pi\)
−0.562574 + 0.826747i \(0.690189\pi\)
\(8\) 0.776803 0.274641
\(9\) −2.57154 −0.857179
\(10\) −5.59350 −1.76882
\(11\) 1.00000 0.301511
\(12\) −1.04078 −0.300448
\(13\) −2.31439 −0.641897 −0.320949 0.947097i \(-0.604002\pi\)
−0.320949 + 0.947097i \(0.604002\pi\)
\(14\) 5.64036 1.50745
\(15\) −1.93238 −0.498938
\(16\) −4.65188 −1.16297
\(17\) −1.00000 −0.242536
\(18\) 4.87238 1.14843
\(19\) 8.06990 1.85136 0.925682 0.378304i \(-0.123492\pi\)
0.925682 + 0.378304i \(0.123492\pi\)
\(20\) 4.69394 1.04960
\(21\) 1.94857 0.425212
\(22\) −1.89473 −0.403959
\(23\) 1.76109 0.367213 0.183606 0.983000i \(-0.441223\pi\)
0.183606 + 0.983000i \(0.441223\pi\)
\(24\) −0.508473 −0.103792
\(25\) 3.71506 0.743012
\(26\) 4.38516 0.860001
\(27\) 3.64697 0.701859
\(28\) −4.73327 −0.894504
\(29\) −4.64475 −0.862509 −0.431255 0.902230i \(-0.641929\pi\)
−0.431255 + 0.902230i \(0.641929\pi\)
\(30\) 3.66135 0.668467
\(31\) −2.51028 −0.450859 −0.225430 0.974259i \(-0.572379\pi\)
−0.225430 + 0.974259i \(0.572379\pi\)
\(32\) 7.26047 1.28348
\(33\) −0.654571 −0.113946
\(34\) 1.89473 0.324944
\(35\) −8.78807 −1.48546
\(36\) −4.08879 −0.681466
\(37\) −7.64717 −1.25719 −0.628593 0.777734i \(-0.716369\pi\)
−0.628593 + 0.777734i \(0.716369\pi\)
\(38\) −15.2903 −2.48042
\(39\) 1.51494 0.242584
\(40\) 2.29322 0.362590
\(41\) −0.808864 −0.126323 −0.0631617 0.998003i \(-0.520118\pi\)
−0.0631617 + 0.998003i \(0.520118\pi\)
\(42\) −3.69202 −0.569691
\(43\) 1.00000 0.152499
\(44\) 1.59002 0.239705
\(45\) −7.59151 −1.13167
\(46\) −3.33680 −0.491984
\(47\) −0.805861 −0.117547 −0.0587734 0.998271i \(-0.518719\pi\)
−0.0587734 + 0.998271i \(0.518719\pi\)
\(48\) 3.04499 0.439506
\(49\) 1.86170 0.265957
\(50\) −7.03906 −0.995473
\(51\) 0.654571 0.0916583
\(52\) −3.67993 −0.510315
\(53\) 11.2784 1.54920 0.774602 0.632449i \(-0.217950\pi\)
0.774602 + 0.632449i \(0.217950\pi\)
\(54\) −6.91004 −0.940337
\(55\) 2.95213 0.398065
\(56\) −2.31243 −0.309012
\(57\) −5.28233 −0.699662
\(58\) 8.80058 1.15557
\(59\) 8.88704 1.15699 0.578497 0.815684i \(-0.303639\pi\)
0.578497 + 0.815684i \(0.303639\pi\)
\(60\) −3.07252 −0.396661
\(61\) −0.148551 −0.0190200 −0.00951001 0.999955i \(-0.503027\pi\)
−0.00951001 + 0.999955i \(0.503027\pi\)
\(62\) 4.75631 0.604052
\(63\) 7.65510 0.964453
\(64\) −4.45290 −0.556613
\(65\) −6.83239 −0.847453
\(66\) 1.24024 0.152663
\(67\) −8.30785 −1.01497 −0.507483 0.861662i \(-0.669424\pi\)
−0.507483 + 0.861662i \(0.669424\pi\)
\(68\) −1.59002 −0.192818
\(69\) −1.15276 −0.138776
\(70\) 16.6511 1.99018
\(71\) 1.70595 0.202459 0.101230 0.994863i \(-0.467722\pi\)
0.101230 + 0.994863i \(0.467722\pi\)
\(72\) −1.99758 −0.235417
\(73\) 12.9783 1.51900 0.759499 0.650509i \(-0.225444\pi\)
0.759499 + 0.650509i \(0.225444\pi\)
\(74\) 14.4894 1.68435
\(75\) −2.43177 −0.280797
\(76\) 12.8313 1.47185
\(77\) −2.97686 −0.339245
\(78\) −2.87040 −0.325009
\(79\) −10.0903 −1.13524 −0.567622 0.823289i \(-0.692137\pi\)
−0.567622 + 0.823289i \(0.692137\pi\)
\(80\) −13.7329 −1.53539
\(81\) 5.32741 0.591934
\(82\) 1.53258 0.169245
\(83\) 13.0959 1.43746 0.718731 0.695288i \(-0.244723\pi\)
0.718731 + 0.695288i \(0.244723\pi\)
\(84\) 3.09826 0.338048
\(85\) −2.95213 −0.320203
\(86\) −1.89473 −0.204315
\(87\) 3.04032 0.325957
\(88\) 0.776803 0.0828075
\(89\) −7.73489 −0.819897 −0.409949 0.912109i \(-0.634453\pi\)
−0.409949 + 0.912109i \(0.634453\pi\)
\(90\) 14.3839 1.51620
\(91\) 6.88963 0.722229
\(92\) 2.80017 0.291938
\(93\) 1.64316 0.170387
\(94\) 1.52689 0.157487
\(95\) 23.8234 2.44423
\(96\) −4.75249 −0.485049
\(97\) −13.9630 −1.41773 −0.708866 0.705343i \(-0.750793\pi\)
−0.708866 + 0.705343i \(0.750793\pi\)
\(98\) −3.52742 −0.356324
\(99\) −2.57154 −0.258449
\(100\) 5.90702 0.590702
\(101\) −12.4410 −1.23793 −0.618964 0.785419i \(-0.712447\pi\)
−0.618964 + 0.785419i \(0.712447\pi\)
\(102\) −1.24024 −0.122802
\(103\) 12.7577 1.25706 0.628528 0.777787i \(-0.283658\pi\)
0.628528 + 0.777787i \(0.283658\pi\)
\(104\) −1.79783 −0.176292
\(105\) 5.75242 0.561379
\(106\) −21.3695 −2.07559
\(107\) 4.30060 0.415755 0.207877 0.978155i \(-0.433344\pi\)
0.207877 + 0.978155i \(0.433344\pi\)
\(108\) 5.79875 0.557985
\(109\) 1.16601 0.111683 0.0558416 0.998440i \(-0.482216\pi\)
0.0558416 + 0.998440i \(0.482216\pi\)
\(110\) −5.59350 −0.533319
\(111\) 5.00562 0.475112
\(112\) 13.8480 1.30851
\(113\) 7.02879 0.661213 0.330606 0.943769i \(-0.392747\pi\)
0.330606 + 0.943769i \(0.392747\pi\)
\(114\) 10.0086 0.937393
\(115\) 5.19896 0.484806
\(116\) −7.38525 −0.685704
\(117\) 5.95155 0.550221
\(118\) −16.8386 −1.55012
\(119\) 2.97686 0.272888
\(120\) −1.50108 −0.137029
\(121\) 1.00000 0.0909091
\(122\) 0.281465 0.0254826
\(123\) 0.529459 0.0477397
\(124\) −3.99139 −0.358438
\(125\) −3.79330 −0.339283
\(126\) −14.5044 −1.29215
\(127\) −4.02695 −0.357334 −0.178667 0.983910i \(-0.557179\pi\)
−0.178667 + 0.983910i \(0.557179\pi\)
\(128\) −6.08386 −0.537742
\(129\) −0.654571 −0.0576318
\(130\) 12.9456 1.13540
\(131\) 5.25164 0.458838 0.229419 0.973328i \(-0.426317\pi\)
0.229419 + 0.973328i \(0.426317\pi\)
\(132\) −1.04078 −0.0905884
\(133\) −24.0230 −2.08306
\(134\) 15.7412 1.35983
\(135\) 10.7663 0.926617
\(136\) −0.776803 −0.0666103
\(137\) 3.88496 0.331915 0.165957 0.986133i \(-0.446929\pi\)
0.165957 + 0.986133i \(0.446929\pi\)
\(138\) 2.18417 0.185929
\(139\) 2.69022 0.228182 0.114091 0.993470i \(-0.463604\pi\)
0.114091 + 0.993470i \(0.463604\pi\)
\(140\) −13.9732 −1.18095
\(141\) 0.527493 0.0444230
\(142\) −3.23232 −0.271251
\(143\) −2.31439 −0.193539
\(144\) 11.9625 0.996872
\(145\) −13.7119 −1.13871
\(146\) −24.5905 −2.03512
\(147\) −1.21861 −0.100510
\(148\) −12.1591 −0.999476
\(149\) 11.1826 0.916118 0.458059 0.888922i \(-0.348545\pi\)
0.458059 + 0.888922i \(0.348545\pi\)
\(150\) 4.60757 0.376206
\(151\) −15.0744 −1.22674 −0.613368 0.789797i \(-0.710186\pi\)
−0.613368 + 0.789797i \(0.710186\pi\)
\(152\) 6.26873 0.508461
\(153\) 2.57154 0.207896
\(154\) 5.64036 0.454513
\(155\) −7.41066 −0.595239
\(156\) 2.40878 0.192857
\(157\) −1.80903 −0.144376 −0.0721881 0.997391i \(-0.522998\pi\)
−0.0721881 + 0.997391i \(0.522998\pi\)
\(158\) 19.1184 1.52098
\(159\) −7.38250 −0.585471
\(160\) 21.4338 1.69449
\(161\) −5.24252 −0.413168
\(162\) −10.0940 −0.793061
\(163\) −23.8752 −1.87005 −0.935026 0.354579i \(-0.884624\pi\)
−0.935026 + 0.354579i \(0.884624\pi\)
\(164\) −1.28611 −0.100428
\(165\) −1.93238 −0.150436
\(166\) −24.8133 −1.92588
\(167\) −10.7819 −0.834325 −0.417162 0.908832i \(-0.636975\pi\)
−0.417162 + 0.908832i \(0.636975\pi\)
\(168\) 1.51365 0.116781
\(169\) −7.64358 −0.587968
\(170\) 5.59350 0.429002
\(171\) −20.7521 −1.58695
\(172\) 1.59002 0.121238
\(173\) 4.05113 0.308002 0.154001 0.988071i \(-0.450784\pi\)
0.154001 + 0.988071i \(0.450784\pi\)
\(174\) −5.76061 −0.436711
\(175\) −11.0592 −0.835999
\(176\) −4.65188 −0.350648
\(177\) −5.81720 −0.437248
\(178\) 14.6556 1.09848
\(179\) 6.86119 0.512829 0.256415 0.966567i \(-0.417459\pi\)
0.256415 + 0.966567i \(0.417459\pi\)
\(180\) −12.0706 −0.899693
\(181\) −13.2319 −0.983522 −0.491761 0.870730i \(-0.663647\pi\)
−0.491761 + 0.870730i \(0.663647\pi\)
\(182\) −13.0540 −0.967628
\(183\) 0.0972373 0.00718799
\(184\) 1.36802 0.100852
\(185\) −22.5754 −1.65978
\(186\) −3.11335 −0.228282
\(187\) −1.00000 −0.0731272
\(188\) −1.28133 −0.0934509
\(189\) −10.8565 −0.789695
\(190\) −45.1390 −3.27473
\(191\) 2.34918 0.169981 0.0849905 0.996382i \(-0.472914\pi\)
0.0849905 + 0.996382i \(0.472914\pi\)
\(192\) 2.91474 0.210354
\(193\) −18.2046 −1.31040 −0.655198 0.755457i \(-0.727415\pi\)
−0.655198 + 0.755457i \(0.727415\pi\)
\(194\) 26.4563 1.89945
\(195\) 4.47229 0.320267
\(196\) 2.96014 0.211438
\(197\) 24.9465 1.77736 0.888681 0.458526i \(-0.151622\pi\)
0.888681 + 0.458526i \(0.151622\pi\)
\(198\) 4.87238 0.346265
\(199\) −9.70404 −0.687901 −0.343951 0.938988i \(-0.611765\pi\)
−0.343951 + 0.938988i \(0.611765\pi\)
\(200\) 2.88587 0.204062
\(201\) 5.43808 0.383573
\(202\) 23.5724 1.65855
\(203\) 13.8268 0.970450
\(204\) 1.04078 0.0728693
\(205\) −2.38787 −0.166776
\(206\) −24.1725 −1.68418
\(207\) −4.52871 −0.314767
\(208\) 10.7663 0.746507
\(209\) 8.06990 0.558207
\(210\) −10.8993 −0.752124
\(211\) −16.9711 −1.16834 −0.584168 0.811633i \(-0.698579\pi\)
−0.584168 + 0.811633i \(0.698579\pi\)
\(212\) 17.9328 1.23163
\(213\) −1.11667 −0.0765127
\(214\) −8.14850 −0.557020
\(215\) 2.95213 0.201333
\(216\) 2.83298 0.192760
\(217\) 7.47275 0.507283
\(218\) −2.20927 −0.149631
\(219\) −8.49524 −0.574055
\(220\) 4.69394 0.316466
\(221\) 2.31439 0.155683
\(222\) −9.48432 −0.636546
\(223\) −28.1230 −1.88326 −0.941629 0.336653i \(-0.890705\pi\)
−0.941629 + 0.336653i \(0.890705\pi\)
\(224\) −21.6134 −1.44411
\(225\) −9.55342 −0.636895
\(226\) −13.3177 −0.885879
\(227\) −2.12293 −0.140904 −0.0704519 0.997515i \(-0.522444\pi\)
−0.0704519 + 0.997515i \(0.522444\pi\)
\(228\) −8.39901 −0.556238
\(229\) 26.4793 1.74980 0.874900 0.484304i \(-0.160927\pi\)
0.874900 + 0.484304i \(0.160927\pi\)
\(230\) −9.85065 −0.649533
\(231\) 1.94857 0.128206
\(232\) −3.60806 −0.236881
\(233\) 23.1464 1.51637 0.758184 0.652040i \(-0.226087\pi\)
0.758184 + 0.652040i \(0.226087\pi\)
\(234\) −11.2766 −0.737175
\(235\) −2.37900 −0.155189
\(236\) 14.1306 0.919822
\(237\) 6.60480 0.429028
\(238\) −5.64036 −0.365610
\(239\) −7.14075 −0.461897 −0.230948 0.972966i \(-0.574183\pi\)
−0.230948 + 0.972966i \(0.574183\pi\)
\(240\) 8.98919 0.580250
\(241\) −6.85523 −0.441584 −0.220792 0.975321i \(-0.570864\pi\)
−0.220792 + 0.975321i \(0.570864\pi\)
\(242\) −1.89473 −0.121798
\(243\) −14.4281 −0.925561
\(244\) −0.236199 −0.0151211
\(245\) 5.49597 0.351125
\(246\) −1.00319 −0.0639607
\(247\) −18.6769 −1.18838
\(248\) −1.94999 −0.123825
\(249\) −8.57221 −0.543241
\(250\) 7.18730 0.454565
\(251\) 4.30264 0.271581 0.135790 0.990738i \(-0.456643\pi\)
0.135790 + 0.990738i \(0.456643\pi\)
\(252\) 12.1718 0.766749
\(253\) 1.76109 0.110719
\(254\) 7.63001 0.478749
\(255\) 1.93238 0.121010
\(256\) 20.4331 1.27707
\(257\) 6.48342 0.404425 0.202212 0.979342i \(-0.435187\pi\)
0.202212 + 0.979342i \(0.435187\pi\)
\(258\) 1.24024 0.0772139
\(259\) 22.7645 1.41452
\(260\) −10.8636 −0.673734
\(261\) 11.9442 0.739325
\(262\) −9.95047 −0.614742
\(263\) −3.23554 −0.199512 −0.0997559 0.995012i \(-0.531806\pi\)
−0.0997559 + 0.995012i \(0.531806\pi\)
\(264\) −0.508473 −0.0312944
\(265\) 33.2952 2.04531
\(266\) 45.5172 2.79084
\(267\) 5.06304 0.309853
\(268\) −13.2097 −0.806908
\(269\) −2.61337 −0.159340 −0.0796699 0.996821i \(-0.525387\pi\)
−0.0796699 + 0.996821i \(0.525387\pi\)
\(270\) −20.3993 −1.24146
\(271\) 21.3015 1.29397 0.646986 0.762501i \(-0.276029\pi\)
0.646986 + 0.762501i \(0.276029\pi\)
\(272\) 4.65188 0.282061
\(273\) −4.50975 −0.272943
\(274\) −7.36098 −0.444693
\(275\) 3.71506 0.224027
\(276\) −1.83291 −0.110328
\(277\) −8.21199 −0.493411 −0.246705 0.969091i \(-0.579348\pi\)
−0.246705 + 0.969091i \(0.579348\pi\)
\(278\) −5.09726 −0.305713
\(279\) 6.45527 0.386467
\(280\) −6.82660 −0.407968
\(281\) 17.5590 1.04748 0.523741 0.851877i \(-0.324536\pi\)
0.523741 + 0.851877i \(0.324536\pi\)
\(282\) −0.999460 −0.0595170
\(283\) 3.39288 0.201686 0.100843 0.994902i \(-0.467846\pi\)
0.100843 + 0.994902i \(0.467846\pi\)
\(284\) 2.71250 0.160957
\(285\) −15.5941 −0.923716
\(286\) 4.38516 0.259300
\(287\) 2.40788 0.142132
\(288\) −18.6706 −1.10017
\(289\) 1.00000 0.0588235
\(290\) 25.9804 1.52562
\(291\) 9.13981 0.535785
\(292\) 20.6358 1.20762
\(293\) 10.0153 0.585099 0.292550 0.956250i \(-0.405496\pi\)
0.292550 + 0.956250i \(0.405496\pi\)
\(294\) 2.30895 0.134661
\(295\) 26.2357 1.52750
\(296\) −5.94034 −0.345275
\(297\) 3.64697 0.211619
\(298\) −21.1881 −1.22740
\(299\) −4.07585 −0.235713
\(300\) −3.86657 −0.223236
\(301\) −2.97686 −0.171583
\(302\) 28.5620 1.64356
\(303\) 8.14354 0.467834
\(304\) −37.5402 −2.15308
\(305\) −0.438542 −0.0251108
\(306\) −4.87238 −0.278535
\(307\) 15.9995 0.913141 0.456570 0.889687i \(-0.349078\pi\)
0.456570 + 0.889687i \(0.349078\pi\)
\(308\) −4.73327 −0.269703
\(309\) −8.35085 −0.475063
\(310\) 14.0412 0.797489
\(311\) −22.3221 −1.26577 −0.632884 0.774247i \(-0.718129\pi\)
−0.632884 + 0.774247i \(0.718129\pi\)
\(312\) 1.17681 0.0666236
\(313\) 1.76777 0.0999200 0.0499600 0.998751i \(-0.484091\pi\)
0.0499600 + 0.998751i \(0.484091\pi\)
\(314\) 3.42763 0.193432
\(315\) 22.5989 1.27330
\(316\) −16.0437 −0.902531
\(317\) −24.2100 −1.35977 −0.679884 0.733320i \(-0.737970\pi\)
−0.679884 + 0.733320i \(0.737970\pi\)
\(318\) 13.9879 0.784402
\(319\) −4.64475 −0.260056
\(320\) −13.1455 −0.734858
\(321\) −2.81505 −0.157121
\(322\) 9.93318 0.553555
\(323\) −8.06990 −0.449022
\(324\) 8.47068 0.470594
\(325\) −8.59812 −0.476938
\(326\) 45.2372 2.50546
\(327\) −0.763234 −0.0422070
\(328\) −0.628328 −0.0346936
\(329\) 2.39893 0.132258
\(330\) 3.66135 0.201550
\(331\) −6.08229 −0.334313 −0.167156 0.985930i \(-0.553458\pi\)
−0.167156 + 0.985930i \(0.553458\pi\)
\(332\) 20.8228 1.14280
\(333\) 19.6650 1.07763
\(334\) 20.4288 1.11781
\(335\) −24.5259 −1.33999
\(336\) −9.06450 −0.494509
\(337\) −16.8355 −0.917086 −0.458543 0.888672i \(-0.651629\pi\)
−0.458543 + 0.888672i \(0.651629\pi\)
\(338\) 14.4826 0.787748
\(339\) −4.60084 −0.249883
\(340\) −4.69394 −0.254565
\(341\) −2.51028 −0.135939
\(342\) 39.3196 2.12616
\(343\) 15.2960 0.825907
\(344\) 0.776803 0.0418824
\(345\) −3.40309 −0.183216
\(346\) −7.67581 −0.412654
\(347\) 15.2068 0.816344 0.408172 0.912905i \(-0.366166\pi\)
0.408172 + 0.912905i \(0.366166\pi\)
\(348\) 4.83418 0.259139
\(349\) 13.8219 0.739870 0.369935 0.929058i \(-0.379380\pi\)
0.369935 + 0.929058i \(0.379380\pi\)
\(350\) 20.9543 1.12005
\(351\) −8.44052 −0.450522
\(352\) 7.26047 0.386984
\(353\) 35.9828 1.91517 0.957586 0.288148i \(-0.0930395\pi\)
0.957586 + 0.288148i \(0.0930395\pi\)
\(354\) 11.0221 0.585816
\(355\) 5.03618 0.267293
\(356\) −12.2986 −0.651827
\(357\) −1.94857 −0.103129
\(358\) −13.0001 −0.687078
\(359\) −26.5807 −1.40287 −0.701437 0.712731i \(-0.747458\pi\)
−0.701437 + 0.712731i \(0.747458\pi\)
\(360\) −5.89711 −0.310805
\(361\) 46.1234 2.42755
\(362\) 25.0710 1.31770
\(363\) −0.654571 −0.0343561
\(364\) 10.9546 0.574179
\(365\) 38.3137 2.00543
\(366\) −0.184239 −0.00963032
\(367\) −11.7561 −0.613661 −0.306831 0.951764i \(-0.599269\pi\)
−0.306831 + 0.951764i \(0.599269\pi\)
\(368\) −8.19237 −0.427057
\(369\) 2.08002 0.108282
\(370\) 42.7744 2.22374
\(371\) −33.5742 −1.74308
\(372\) 2.61265 0.135460
\(373\) 31.2902 1.62015 0.810073 0.586329i \(-0.199427\pi\)
0.810073 + 0.586329i \(0.199427\pi\)
\(374\) 1.89473 0.0979744
\(375\) 2.48299 0.128221
\(376\) −0.625995 −0.0322832
\(377\) 10.7498 0.553642
\(378\) 20.5702 1.05802
\(379\) −22.7386 −1.16801 −0.584003 0.811752i \(-0.698514\pi\)
−0.584003 + 0.811752i \(0.698514\pi\)
\(380\) 37.8797 1.94319
\(381\) 2.63593 0.135043
\(382\) −4.45108 −0.227737
\(383\) −19.4061 −0.991606 −0.495803 0.868435i \(-0.665126\pi\)
−0.495803 + 0.868435i \(0.665126\pi\)
\(384\) 3.98232 0.203222
\(385\) −8.78807 −0.447882
\(386\) 34.4929 1.75564
\(387\) −2.57154 −0.130719
\(388\) −22.2015 −1.12711
\(389\) −33.6127 −1.70423 −0.852116 0.523353i \(-0.824681\pi\)
−0.852116 + 0.523353i \(0.824681\pi\)
\(390\) −8.47379 −0.429087
\(391\) −1.76109 −0.0890621
\(392\) 1.44617 0.0730428
\(393\) −3.43757 −0.173403
\(394\) −47.2669 −2.38127
\(395\) −29.7878 −1.49879
\(396\) −4.08879 −0.205470
\(397\) −1.48876 −0.0747186 −0.0373593 0.999302i \(-0.511895\pi\)
−0.0373593 + 0.999302i \(0.511895\pi\)
\(398\) 18.3866 0.921636
\(399\) 15.7248 0.787223
\(400\) −17.2820 −0.864101
\(401\) −30.0796 −1.50210 −0.751051 0.660244i \(-0.770453\pi\)
−0.751051 + 0.660244i \(0.770453\pi\)
\(402\) −10.3037 −0.513903
\(403\) 5.80977 0.289405
\(404\) −19.7815 −0.984165
\(405\) 15.7272 0.781490
\(406\) −26.1981 −1.30019
\(407\) −7.64717 −0.379056
\(408\) 0.508473 0.0251732
\(409\) −16.7006 −0.825792 −0.412896 0.910778i \(-0.635483\pi\)
−0.412896 + 0.910778i \(0.635483\pi\)
\(410\) 4.52438 0.223443
\(411\) −2.54299 −0.125436
\(412\) 20.2850 0.999373
\(413\) −26.4555 −1.30179
\(414\) 8.58070 0.421718
\(415\) 38.6608 1.89778
\(416\) −16.8036 −0.823863
\(417\) −1.76094 −0.0862338
\(418\) −15.2903 −0.747874
\(419\) −20.8018 −1.01623 −0.508116 0.861288i \(-0.669658\pi\)
−0.508116 + 0.861288i \(0.669658\pi\)
\(420\) 9.14647 0.446302
\(421\) −18.5118 −0.902210 −0.451105 0.892471i \(-0.648970\pi\)
−0.451105 + 0.892471i \(0.648970\pi\)
\(422\) 32.1557 1.56531
\(423\) 2.07230 0.100759
\(424\) 8.76108 0.425476
\(425\) −3.71506 −0.180207
\(426\) 2.11579 0.102510
\(427\) 0.442216 0.0214003
\(428\) 6.83804 0.330529
\(429\) 1.51494 0.0731418
\(430\) −5.59350 −0.269743
\(431\) 12.2863 0.591813 0.295906 0.955217i \(-0.404378\pi\)
0.295906 + 0.955217i \(0.404378\pi\)
\(432\) −16.9652 −0.816241
\(433\) 27.7426 1.33322 0.666612 0.745405i \(-0.267744\pi\)
0.666612 + 0.745405i \(0.267744\pi\)
\(434\) −14.1589 −0.679648
\(435\) 8.97543 0.430339
\(436\) 1.85397 0.0887892
\(437\) 14.2118 0.679844
\(438\) 16.0962 0.769107
\(439\) −9.60314 −0.458333 −0.229167 0.973387i \(-0.573600\pi\)
−0.229167 + 0.973387i \(0.573600\pi\)
\(440\) 2.29322 0.109325
\(441\) −4.78742 −0.227973
\(442\) −4.38516 −0.208581
\(443\) 12.9279 0.614223 0.307112 0.951674i \(-0.400638\pi\)
0.307112 + 0.951674i \(0.400638\pi\)
\(444\) 7.95903 0.377719
\(445\) −22.8344 −1.08245
\(446\) 53.2857 2.52315
\(447\) −7.31984 −0.346216
\(448\) 13.2557 0.626272
\(449\) −28.4481 −1.34255 −0.671273 0.741210i \(-0.734252\pi\)
−0.671273 + 0.741210i \(0.734252\pi\)
\(450\) 18.1012 0.853298
\(451\) −0.808864 −0.0380879
\(452\) 11.1759 0.525671
\(453\) 9.86726 0.463604
\(454\) 4.02239 0.188780
\(455\) 20.3391 0.953510
\(456\) −4.10333 −0.192156
\(457\) −0.348114 −0.0162841 −0.00814205 0.999967i \(-0.502592\pi\)
−0.00814205 + 0.999967i \(0.502592\pi\)
\(458\) −50.1712 −2.34435
\(459\) −3.64697 −0.170226
\(460\) 8.26645 0.385425
\(461\) −31.0780 −1.44744 −0.723722 0.690091i \(-0.757570\pi\)
−0.723722 + 0.690091i \(0.757570\pi\)
\(462\) −3.69202 −0.171768
\(463\) 5.12662 0.238254 0.119127 0.992879i \(-0.461990\pi\)
0.119127 + 0.992879i \(0.461990\pi\)
\(464\) 21.6068 1.00307
\(465\) 4.85081 0.224951
\(466\) −43.8562 −2.03160
\(467\) −12.2535 −0.567026 −0.283513 0.958968i \(-0.591500\pi\)
−0.283513 + 0.958968i \(0.591500\pi\)
\(468\) 9.46308 0.437431
\(469\) 24.7313 1.14199
\(470\) 4.50758 0.207919
\(471\) 1.18414 0.0545622
\(472\) 6.90348 0.317758
\(473\) 1.00000 0.0459800
\(474\) −12.5144 −0.574803
\(475\) 29.9802 1.37559
\(476\) 4.73327 0.216949
\(477\) −29.0028 −1.32794
\(478\) 13.5298 0.618840
\(479\) −37.7632 −1.72545 −0.862723 0.505677i \(-0.831243\pi\)
−0.862723 + 0.505677i \(0.831243\pi\)
\(480\) −14.0300 −0.640378
\(481\) 17.6985 0.806984
\(482\) 12.9889 0.591626
\(483\) 3.43160 0.156143
\(484\) 1.59002 0.0722736
\(485\) −41.2207 −1.87174
\(486\) 27.3374 1.24005
\(487\) 30.6830 1.39038 0.695190 0.718826i \(-0.255320\pi\)
0.695190 + 0.718826i \(0.255320\pi\)
\(488\) −0.115395 −0.00522368
\(489\) 15.6280 0.706724
\(490\) −10.4134 −0.470430
\(491\) −24.7737 −1.11802 −0.559012 0.829160i \(-0.688819\pi\)
−0.559012 + 0.829160i \(0.688819\pi\)
\(492\) 0.841851 0.0379536
\(493\) 4.64475 0.209189
\(494\) 35.3878 1.59217
\(495\) −7.59151 −0.341213
\(496\) 11.6775 0.524335
\(497\) −5.07838 −0.227796
\(498\) 16.2421 0.727824
\(499\) −15.7055 −0.703075 −0.351538 0.936174i \(-0.614341\pi\)
−0.351538 + 0.936174i \(0.614341\pi\)
\(500\) −6.03142 −0.269733
\(501\) 7.05749 0.315306
\(502\) −8.15237 −0.363858
\(503\) 20.8092 0.927838 0.463919 0.885878i \(-0.346443\pi\)
0.463919 + 0.885878i \(0.346443\pi\)
\(504\) 5.94651 0.264879
\(505\) −36.7275 −1.63435
\(506\) −3.33680 −0.148339
\(507\) 5.00327 0.222203
\(508\) −6.40294 −0.284084
\(509\) 32.3749 1.43499 0.717497 0.696562i \(-0.245288\pi\)
0.717497 + 0.696562i \(0.245288\pi\)
\(510\) −3.66135 −0.162127
\(511\) −38.6346 −1.70910
\(512\) −26.5476 −1.17325
\(513\) 29.4307 1.29940
\(514\) −12.2844 −0.541840
\(515\) 37.6625 1.65961
\(516\) −1.04078 −0.0458179
\(517\) −0.805861 −0.0354417
\(518\) −43.1328 −1.89515
\(519\) −2.65175 −0.116399
\(520\) −5.30742 −0.232746
\(521\) −4.44136 −0.194579 −0.0972897 0.995256i \(-0.531017\pi\)
−0.0972897 + 0.995256i \(0.531017\pi\)
\(522\) −22.6310 −0.990532
\(523\) −19.0302 −0.832133 −0.416067 0.909334i \(-0.636592\pi\)
−0.416067 + 0.909334i \(0.636592\pi\)
\(524\) 8.35022 0.364781
\(525\) 7.23905 0.315938
\(526\) 6.13049 0.267302
\(527\) 2.51028 0.109349
\(528\) 3.04499 0.132516
\(529\) −19.8986 −0.865155
\(530\) −63.0856 −2.74026
\(531\) −22.8533 −0.991751
\(532\) −38.1970 −1.65605
\(533\) 1.87203 0.0810866
\(534\) −9.59312 −0.415135
\(535\) 12.6959 0.548893
\(536\) −6.45357 −0.278752
\(537\) −4.49114 −0.193807
\(538\) 4.95164 0.213480
\(539\) 1.86170 0.0801890
\(540\) 17.1187 0.736670
\(541\) −10.6596 −0.458290 −0.229145 0.973392i \(-0.573593\pi\)
−0.229145 + 0.973392i \(0.573593\pi\)
\(542\) −40.3607 −1.73364
\(543\) 8.66125 0.371690
\(544\) −7.26047 −0.311290
\(545\) 3.44220 0.147448
\(546\) 8.54479 0.365683
\(547\) −7.27819 −0.311193 −0.155597 0.987821i \(-0.549730\pi\)
−0.155597 + 0.987821i \(0.549730\pi\)
\(548\) 6.17717 0.263876
\(549\) 0.382004 0.0163036
\(550\) −7.03906 −0.300146
\(551\) −37.4827 −1.59682
\(552\) −0.895467 −0.0381136
\(553\) 30.0373 1.27732
\(554\) 15.5595 0.661062
\(555\) 14.7772 0.627258
\(556\) 4.27751 0.181407
\(557\) 39.0784 1.65580 0.827901 0.560874i \(-0.189535\pi\)
0.827901 + 0.560874i \(0.189535\pi\)
\(558\) −12.2310 −0.517781
\(559\) −2.31439 −0.0978884
\(560\) 40.8810 1.72754
\(561\) 0.654571 0.0276360
\(562\) −33.2697 −1.40340
\(563\) 26.7746 1.12841 0.564207 0.825633i \(-0.309182\pi\)
0.564207 + 0.825633i \(0.309182\pi\)
\(564\) 0.838725 0.0353167
\(565\) 20.7499 0.872954
\(566\) −6.42861 −0.270215
\(567\) −15.8589 −0.666013
\(568\) 1.32519 0.0556036
\(569\) −8.22951 −0.344999 −0.172499 0.985010i \(-0.555184\pi\)
−0.172499 + 0.985010i \(0.555184\pi\)
\(570\) 29.5467 1.23758
\(571\) −7.11575 −0.297785 −0.148892 0.988853i \(-0.547571\pi\)
−0.148892 + 0.988853i \(0.547571\pi\)
\(572\) −3.67993 −0.153866
\(573\) −1.53771 −0.0642387
\(574\) −4.56229 −0.190426
\(575\) 6.54256 0.272843
\(576\) 11.4508 0.477117
\(577\) −35.1648 −1.46393 −0.731964 0.681343i \(-0.761396\pi\)
−0.731964 + 0.681343i \(0.761396\pi\)
\(578\) −1.89473 −0.0788106
\(579\) 11.9162 0.495221
\(580\) −21.8022 −0.905288
\(581\) −38.9847 −1.61736
\(582\) −17.3175 −0.717834
\(583\) 11.2784 0.467103
\(584\) 10.0816 0.417179
\(585\) 17.5697 0.726419
\(586\) −18.9763 −0.783904
\(587\) −23.2701 −0.960459 −0.480230 0.877143i \(-0.659447\pi\)
−0.480230 + 0.877143i \(0.659447\pi\)
\(588\) −1.93762 −0.0799062
\(589\) −20.2577 −0.834704
\(590\) −49.7097 −2.04651
\(591\) −16.3292 −0.671695
\(592\) 35.5737 1.46207
\(593\) −25.2457 −1.03671 −0.518357 0.855164i \(-0.673456\pi\)
−0.518357 + 0.855164i \(0.673456\pi\)
\(594\) −6.91004 −0.283522
\(595\) 8.78807 0.360276
\(596\) 17.7806 0.728323
\(597\) 6.35199 0.259970
\(598\) 7.72266 0.315803
\(599\) −43.3602 −1.77165 −0.885826 0.464018i \(-0.846407\pi\)
−0.885826 + 0.464018i \(0.846407\pi\)
\(600\) −1.88901 −0.0771185
\(601\) 22.6425 0.923608 0.461804 0.886982i \(-0.347202\pi\)
0.461804 + 0.886982i \(0.347202\pi\)
\(602\) 5.64036 0.229884
\(603\) 21.3639 0.870007
\(604\) −23.9686 −0.975267
\(605\) 2.95213 0.120021
\(606\) −15.4298 −0.626795
\(607\) −2.29332 −0.0930831 −0.0465416 0.998916i \(-0.514820\pi\)
−0.0465416 + 0.998916i \(0.514820\pi\)
\(608\) 58.5913 2.37619
\(609\) −9.05062 −0.366750
\(610\) 0.830920 0.0336430
\(611\) 1.86508 0.0754530
\(612\) 4.08879 0.165280
\(613\) −15.2958 −0.617790 −0.308895 0.951096i \(-0.599959\pi\)
−0.308895 + 0.951096i \(0.599959\pi\)
\(614\) −30.3148 −1.22341
\(615\) 1.56303 0.0630275
\(616\) −2.31243 −0.0931706
\(617\) 21.4378 0.863055 0.431528 0.902100i \(-0.357975\pi\)
0.431528 + 0.902100i \(0.357975\pi\)
\(618\) 15.8226 0.636480
\(619\) 7.96311 0.320064 0.160032 0.987112i \(-0.448840\pi\)
0.160032 + 0.987112i \(0.448840\pi\)
\(620\) −11.7831 −0.473221
\(621\) 6.42264 0.257732
\(622\) 42.2944 1.69585
\(623\) 23.0257 0.922505
\(624\) −7.04729 −0.282118
\(625\) −29.7736 −1.19094
\(626\) −3.34945 −0.133871
\(627\) −5.28233 −0.210956
\(628\) −2.87639 −0.114781
\(629\) 7.64717 0.304912
\(630\) −42.8188 −1.70594
\(631\) 25.4769 1.01422 0.507110 0.861881i \(-0.330714\pi\)
0.507110 + 0.861881i \(0.330714\pi\)
\(632\) −7.83816 −0.311785
\(633\) 11.1088 0.441534
\(634\) 45.8715 1.82179
\(635\) −11.8881 −0.471764
\(636\) −11.7383 −0.465455
\(637\) −4.30870 −0.170717
\(638\) 8.80058 0.348418
\(639\) −4.38691 −0.173544
\(640\) −17.9603 −0.709944
\(641\) 32.5634 1.28618 0.643088 0.765792i \(-0.277653\pi\)
0.643088 + 0.765792i \(0.277653\pi\)
\(642\) 5.33377 0.210507
\(643\) −34.4178 −1.35731 −0.678653 0.734459i \(-0.737436\pi\)
−0.678653 + 0.734459i \(0.737436\pi\)
\(644\) −8.33571 −0.328473
\(645\) −1.93238 −0.0760874
\(646\) 15.2903 0.601590
\(647\) −17.1473 −0.674128 −0.337064 0.941482i \(-0.609434\pi\)
−0.337064 + 0.941482i \(0.609434\pi\)
\(648\) 4.13835 0.162570
\(649\) 8.88704 0.348847
\(650\) 16.2911 0.638991
\(651\) −4.89145 −0.191711
\(652\) −37.9621 −1.48671
\(653\) −15.0431 −0.588682 −0.294341 0.955700i \(-0.595100\pi\)
−0.294341 + 0.955700i \(0.595100\pi\)
\(654\) 1.44613 0.0565480
\(655\) 15.5035 0.605773
\(656\) 3.76274 0.146910
\(657\) −33.3742 −1.30205
\(658\) −4.54535 −0.177196
\(659\) 46.9162 1.82760 0.913798 0.406170i \(-0.133136\pi\)
0.913798 + 0.406170i \(0.133136\pi\)
\(660\) −3.07252 −0.119598
\(661\) −7.78083 −0.302639 −0.151320 0.988485i \(-0.548352\pi\)
−0.151320 + 0.988485i \(0.548352\pi\)
\(662\) 11.5243 0.447905
\(663\) −1.51494 −0.0588352
\(664\) 10.1729 0.394787
\(665\) −70.9189 −2.75012
\(666\) −37.2599 −1.44379
\(667\) −8.17983 −0.316724
\(668\) −17.1434 −0.663297
\(669\) 18.4085 0.711715
\(670\) 46.4700 1.79529
\(671\) −0.148551 −0.00573475
\(672\) 14.1475 0.545752
\(673\) 14.4691 0.557744 0.278872 0.960328i \(-0.410040\pi\)
0.278872 + 0.960328i \(0.410040\pi\)
\(674\) 31.8987 1.22869
\(675\) 13.5487 0.521490
\(676\) −12.1535 −0.467440
\(677\) −36.5205 −1.40360 −0.701799 0.712375i \(-0.747619\pi\)
−0.701799 + 0.712375i \(0.747619\pi\)
\(678\) 8.71738 0.334789
\(679\) 41.5660 1.59516
\(680\) −2.29322 −0.0879411
\(681\) 1.38961 0.0532499
\(682\) 4.75631 0.182129
\(683\) 5.58282 0.213621 0.106810 0.994279i \(-0.465936\pi\)
0.106810 + 0.994279i \(0.465936\pi\)
\(684\) −32.9962 −1.26164
\(685\) 11.4689 0.438205
\(686\) −28.9819 −1.10653
\(687\) −17.3326 −0.661279
\(688\) −4.65188 −0.177351
\(689\) −26.1026 −0.994430
\(690\) 6.44796 0.245470
\(691\) −14.2933 −0.543743 −0.271872 0.962334i \(-0.587643\pi\)
−0.271872 + 0.962334i \(0.587643\pi\)
\(692\) 6.44137 0.244864
\(693\) 7.65510 0.290793
\(694\) −28.8129 −1.09372
\(695\) 7.94189 0.301253
\(696\) 2.36173 0.0895213
\(697\) 0.808864 0.0306379
\(698\) −26.1888 −0.991263
\(699\) −15.1509 −0.573061
\(700\) −17.5844 −0.664627
\(701\) 20.6862 0.781307 0.390653 0.920538i \(-0.372249\pi\)
0.390653 + 0.920538i \(0.372249\pi\)
\(702\) 15.9925 0.603600
\(703\) −61.7119 −2.32751
\(704\) −4.45290 −0.167825
\(705\) 1.55723 0.0586486
\(706\) −68.1779 −2.56591
\(707\) 37.0352 1.39285
\(708\) −9.24947 −0.347616
\(709\) −18.9119 −0.710251 −0.355125 0.934819i \(-0.615562\pi\)
−0.355125 + 0.934819i \(0.615562\pi\)
\(710\) −9.54223 −0.358114
\(711\) 25.9475 0.973107
\(712\) −6.00849 −0.225178
\(713\) −4.42082 −0.165561
\(714\) 3.69202 0.138170
\(715\) −6.83239 −0.255517
\(716\) 10.9094 0.407704
\(717\) 4.67413 0.174559
\(718\) 50.3633 1.87954
\(719\) −16.5230 −0.616204 −0.308102 0.951353i \(-0.599694\pi\)
−0.308102 + 0.951353i \(0.599694\pi\)
\(720\) 35.3147 1.31610
\(721\) −37.9780 −1.41437
\(722\) −87.3915 −3.25238
\(723\) 4.48724 0.166882
\(724\) −21.0390 −0.781910
\(725\) −17.2556 −0.640855
\(726\) 1.24024 0.0460296
\(727\) 3.86730 0.143430 0.0717151 0.997425i \(-0.477153\pi\)
0.0717151 + 0.997425i \(0.477153\pi\)
\(728\) 5.35188 0.198354
\(729\) −6.53801 −0.242149
\(730\) −72.5942 −2.68683
\(731\) −1.00000 −0.0369863
\(732\) 0.154609 0.00571452
\(733\) −49.5811 −1.83132 −0.915661 0.401952i \(-0.868332\pi\)
−0.915661 + 0.401952i \(0.868332\pi\)
\(734\) 22.2746 0.822171
\(735\) −3.59751 −0.132696
\(736\) 12.7863 0.471310
\(737\) −8.30785 −0.306024
\(738\) −3.94109 −0.145074
\(739\) 42.7314 1.57190 0.785950 0.618291i \(-0.212175\pi\)
0.785950 + 0.618291i \(0.212175\pi\)
\(740\) −35.8954 −1.31954
\(741\) 12.2254 0.449111
\(742\) 63.6141 2.33535
\(743\) −29.9767 −1.09974 −0.549869 0.835251i \(-0.685322\pi\)
−0.549869 + 0.835251i \(0.685322\pi\)
\(744\) 1.27641 0.0467954
\(745\) 33.0126 1.20949
\(746\) −59.2867 −2.17064
\(747\) −33.6766 −1.23216
\(748\) −1.59002 −0.0581369
\(749\) −12.8023 −0.467785
\(750\) −4.70460 −0.171788
\(751\) −13.7876 −0.503116 −0.251558 0.967842i \(-0.580943\pi\)
−0.251558 + 0.967842i \(0.580943\pi\)
\(752\) 3.74876 0.136703
\(753\) −2.81639 −0.102635
\(754\) −20.3680 −0.741759
\(755\) −44.5015 −1.61958
\(756\) −17.2621 −0.627816
\(757\) −8.49848 −0.308882 −0.154441 0.988002i \(-0.549358\pi\)
−0.154441 + 0.988002i \(0.549358\pi\)
\(758\) 43.0837 1.56487
\(759\) −1.15276 −0.0418425
\(760\) 18.5061 0.671286
\(761\) −26.0583 −0.944614 −0.472307 0.881434i \(-0.656579\pi\)
−0.472307 + 0.881434i \(0.656579\pi\)
\(762\) −4.99439 −0.180928
\(763\) −3.47104 −0.125660
\(764\) 3.73525 0.135137
\(765\) 7.59151 0.274471
\(766\) 36.7694 1.32853
\(767\) −20.5681 −0.742671
\(768\) −13.3749 −0.482626
\(769\) 13.6232 0.491266 0.245633 0.969363i \(-0.421004\pi\)
0.245633 + 0.969363i \(0.421004\pi\)
\(770\) 16.6511 0.600063
\(771\) −4.24386 −0.152839
\(772\) −28.9457 −1.04178
\(773\) 43.2246 1.55468 0.777340 0.629081i \(-0.216569\pi\)
0.777340 + 0.629081i \(0.216569\pi\)
\(774\) 4.87238 0.175134
\(775\) −9.32584 −0.334994
\(776\) −10.8465 −0.389368
\(777\) −14.9010 −0.534571
\(778\) 63.6872 2.28330
\(779\) −6.52746 −0.233870
\(780\) 7.11102 0.254615
\(781\) 1.70595 0.0610437
\(782\) 3.33680 0.119324
\(783\) −16.9393 −0.605360
\(784\) −8.66039 −0.309300
\(785\) −5.34048 −0.190610
\(786\) 6.51329 0.232321
\(787\) −26.4697 −0.943543 −0.471771 0.881721i \(-0.656385\pi\)
−0.471771 + 0.881721i \(0.656385\pi\)
\(788\) 39.6654 1.41302
\(789\) 2.11789 0.0753989
\(790\) 56.4399 2.00804
\(791\) −20.9237 −0.743962
\(792\) −1.99758 −0.0709808
\(793\) 0.343806 0.0122089
\(794\) 2.82080 0.100106
\(795\) −21.7941 −0.772957
\(796\) −15.4296 −0.546889
\(797\) −33.1969 −1.17589 −0.587947 0.808899i \(-0.700064\pi\)
−0.587947 + 0.808899i \(0.700064\pi\)
\(798\) −29.7942 −1.05470
\(799\) 0.805861 0.0285093
\(800\) 26.9731 0.953643
\(801\) 19.8906 0.702798
\(802\) 56.9928 2.01249
\(803\) 12.9783 0.457995
\(804\) 8.64666 0.304944
\(805\) −15.4766 −0.545478
\(806\) −11.0080 −0.387739
\(807\) 1.71064 0.0602172
\(808\) −9.66422 −0.339986
\(809\) 12.3123 0.432877 0.216439 0.976296i \(-0.430556\pi\)
0.216439 + 0.976296i \(0.430556\pi\)
\(810\) −29.7989 −1.04703
\(811\) 44.6830 1.56903 0.784517 0.620108i \(-0.212911\pi\)
0.784517 + 0.620108i \(0.212911\pi\)
\(812\) 21.9849 0.771518
\(813\) −13.9433 −0.489014
\(814\) 14.4894 0.507851
\(815\) −70.4827 −2.46890
\(816\) −3.04499 −0.106596
\(817\) 8.06990 0.282330
\(818\) 31.6432 1.10638
\(819\) −17.7169 −0.619079
\(820\) −3.79676 −0.132589
\(821\) 25.5553 0.891887 0.445944 0.895061i \(-0.352868\pi\)
0.445944 + 0.895061i \(0.352868\pi\)
\(822\) 4.81828 0.168057
\(823\) −16.4058 −0.571869 −0.285934 0.958249i \(-0.592304\pi\)
−0.285934 + 0.958249i \(0.592304\pi\)
\(824\) 9.91024 0.345240
\(825\) −2.43177 −0.0846635
\(826\) 50.1261 1.74411
\(827\) −6.95415 −0.241820 −0.120910 0.992663i \(-0.538581\pi\)
−0.120910 + 0.992663i \(0.538581\pi\)
\(828\) −7.20073 −0.250243
\(829\) −41.6877 −1.44787 −0.723937 0.689867i \(-0.757669\pi\)
−0.723937 + 0.689867i \(0.757669\pi\)
\(830\) −73.2519 −2.54261
\(831\) 5.37533 0.186468
\(832\) 10.3058 0.357288
\(833\) −1.86170 −0.0645040
\(834\) 3.33652 0.115534
\(835\) −31.8294 −1.10150
\(836\) 12.8313 0.443780
\(837\) −9.15491 −0.316440
\(838\) 39.4138 1.36153
\(839\) −49.7722 −1.71833 −0.859163 0.511701i \(-0.829015\pi\)
−0.859163 + 0.511701i \(0.829015\pi\)
\(840\) 4.46850 0.154178
\(841\) −7.42626 −0.256078
\(842\) 35.0750 1.20876
\(843\) −11.4936 −0.395862
\(844\) −26.9843 −0.928839
\(845\) −22.5648 −0.776254
\(846\) −3.92646 −0.134994
\(847\) −2.97686 −0.102286
\(848\) −52.4656 −1.80168
\(849\) −2.22088 −0.0762205
\(850\) 7.03906 0.241438
\(851\) −13.4673 −0.461655
\(852\) −1.77552 −0.0608284
\(853\) −7.24125 −0.247936 −0.123968 0.992286i \(-0.539562\pi\)
−0.123968 + 0.992286i \(0.539562\pi\)
\(854\) −0.837882 −0.0286717
\(855\) −61.2627 −2.09514
\(856\) 3.34072 0.114183
\(857\) −8.92241 −0.304784 −0.152392 0.988320i \(-0.548698\pi\)
−0.152392 + 0.988320i \(0.548698\pi\)
\(858\) −2.87040 −0.0979939
\(859\) −28.5188 −0.973048 −0.486524 0.873667i \(-0.661735\pi\)
−0.486524 + 0.873667i \(0.661735\pi\)
\(860\) 4.69394 0.160062
\(861\) −1.57613 −0.0537142
\(862\) −23.2794 −0.792898
\(863\) −22.0744 −0.751421 −0.375711 0.926737i \(-0.622601\pi\)
−0.375711 + 0.926737i \(0.622601\pi\)
\(864\) 26.4787 0.900823
\(865\) 11.9594 0.406633
\(866\) −52.5648 −1.78623
\(867\) −0.654571 −0.0222304
\(868\) 11.8818 0.403295
\(869\) −10.0903 −0.342289
\(870\) −17.0061 −0.576559
\(871\) 19.2276 0.651504
\(872\) 0.905757 0.0306728
\(873\) 35.9065 1.21525
\(874\) −26.9276 −0.910841
\(875\) 11.2921 0.381744
\(876\) −13.5076 −0.456379
\(877\) −15.6016 −0.526828 −0.263414 0.964683i \(-0.584849\pi\)
−0.263414 + 0.964683i \(0.584849\pi\)
\(878\) 18.1954 0.614065
\(879\) −6.55572 −0.221119
\(880\) −13.7329 −0.462937
\(881\) −3.51153 −0.118307 −0.0591533 0.998249i \(-0.518840\pi\)
−0.0591533 + 0.998249i \(0.518840\pi\)
\(882\) 9.07090 0.305433
\(883\) −11.8415 −0.398498 −0.199249 0.979949i \(-0.563850\pi\)
−0.199249 + 0.979949i \(0.563850\pi\)
\(884\) 3.67993 0.123770
\(885\) −17.1731 −0.577269
\(886\) −24.4949 −0.822924
\(887\) −37.9074 −1.27281 −0.636403 0.771357i \(-0.719578\pi\)
−0.636403 + 0.771357i \(0.719578\pi\)
\(888\) 3.88838 0.130485
\(889\) 11.9877 0.402054
\(890\) 43.2651 1.45025
\(891\) 5.32741 0.178475
\(892\) −44.7162 −1.49721
\(893\) −6.50322 −0.217622
\(894\) 13.8691 0.463854
\(895\) 20.2551 0.677053
\(896\) 18.1108 0.605039
\(897\) 2.66794 0.0890798
\(898\) 53.9015 1.79872
\(899\) 11.6596 0.388870
\(900\) −15.1901 −0.506338
\(901\) −11.2784 −0.375737
\(902\) 1.53258 0.0510294
\(903\) 1.94857 0.0648443
\(904\) 5.45998 0.181596
\(905\) −39.0624 −1.29848
\(906\) −18.6958 −0.621128
\(907\) −32.6679 −1.08472 −0.542359 0.840147i \(-0.682469\pi\)
−0.542359 + 0.840147i \(0.682469\pi\)
\(908\) −3.37550 −0.112020
\(909\) 31.9925 1.06113
\(910\) −38.5371 −1.27749
\(911\) 20.5666 0.681403 0.340701 0.940172i \(-0.389335\pi\)
0.340701 + 0.940172i \(0.389335\pi\)
\(912\) 24.5727 0.813685
\(913\) 13.0959 0.433411
\(914\) 0.659584 0.0218171
\(915\) 0.287057 0.00948981
\(916\) 42.1026 1.39111
\(917\) −15.6334 −0.516261
\(918\) 6.91004 0.228065
\(919\) 17.2439 0.568824 0.284412 0.958702i \(-0.408202\pi\)
0.284412 + 0.958702i \(0.408202\pi\)
\(920\) 4.03857 0.133148
\(921\) −10.4728 −0.345091
\(922\) 58.8845 1.93926
\(923\) −3.94824 −0.129958
\(924\) 3.09826 0.101925
\(925\) −28.4097 −0.934105
\(926\) −9.71358 −0.319208
\(927\) −32.8070 −1.07752
\(928\) −33.7231 −1.10701
\(929\) 38.6789 1.26901 0.634506 0.772918i \(-0.281203\pi\)
0.634506 + 0.772918i \(0.281203\pi\)
\(930\) −9.19100 −0.301385
\(931\) 15.0237 0.492383
\(932\) 36.8032 1.20553
\(933\) 14.6114 0.478355
\(934\) 23.2172 0.759690
\(935\) −2.95213 −0.0965449
\(936\) 4.62318 0.151113
\(937\) 13.1333 0.429047 0.214523 0.976719i \(-0.431180\pi\)
0.214523 + 0.976719i \(0.431180\pi\)
\(938\) −46.8593 −1.53001
\(939\) −1.15713 −0.0377615
\(940\) −3.78266 −0.123377
\(941\) 38.8873 1.26769 0.633845 0.773460i \(-0.281476\pi\)
0.633845 + 0.773460i \(0.281476\pi\)
\(942\) −2.24363 −0.0731014
\(943\) −1.42448 −0.0463875
\(944\) −41.3414 −1.34555
\(945\) −32.0498 −1.04258
\(946\) −1.89473 −0.0616031
\(947\) 12.7571 0.414549 0.207274 0.978283i \(-0.433541\pi\)
0.207274 + 0.978283i \(0.433541\pi\)
\(948\) 10.5018 0.341082
\(949\) −30.0369 −0.975040
\(950\) −56.8045 −1.84298
\(951\) 15.8472 0.513879
\(952\) 2.31243 0.0749464
\(953\) −6.74011 −0.218334 −0.109167 0.994023i \(-0.534818\pi\)
−0.109167 + 0.994023i \(0.534818\pi\)
\(954\) 54.9525 1.77915
\(955\) 6.93509 0.224414
\(956\) −11.3539 −0.367213
\(957\) 3.04032 0.0982797
\(958\) 71.5513 2.31172
\(959\) −11.5650 −0.373453
\(960\) 8.60470 0.277715
\(961\) −24.6985 −0.796726
\(962\) −33.5341 −1.08118
\(963\) −11.0592 −0.356376
\(964\) −10.9000 −0.351064
\(965\) −53.7424 −1.73003
\(966\) −6.50198 −0.209198
\(967\) −44.5197 −1.43166 −0.715829 0.698276i \(-0.753951\pi\)
−0.715829 + 0.698276i \(0.753951\pi\)
\(968\) 0.776803 0.0249674
\(969\) 5.28233 0.169693
\(970\) 78.1023 2.50771
\(971\) −36.6867 −1.17733 −0.588666 0.808376i \(-0.700347\pi\)
−0.588666 + 0.808376i \(0.700347\pi\)
\(972\) −22.9409 −0.735831
\(973\) −8.00842 −0.256738
\(974\) −58.1361 −1.86280
\(975\) 5.62808 0.180243
\(976\) 0.691041 0.0221197
\(977\) 37.5646 1.20180 0.600899 0.799325i \(-0.294809\pi\)
0.600899 + 0.799325i \(0.294809\pi\)
\(978\) −29.6110 −0.946855
\(979\) −7.73489 −0.247208
\(980\) 8.73871 0.279148
\(981\) −2.99843 −0.0957324
\(982\) 46.9397 1.49791
\(983\) 6.96919 0.222283 0.111141 0.993805i \(-0.464549\pi\)
0.111141 + 0.993805i \(0.464549\pi\)
\(984\) 0.411286 0.0131113
\(985\) 73.6452 2.34653
\(986\) −8.80058 −0.280268
\(987\) −1.57027 −0.0499824
\(988\) −29.6967 −0.944778
\(989\) 1.76109 0.0559994
\(990\) 14.3839 0.457150
\(991\) −1.47439 −0.0468356 −0.0234178 0.999726i \(-0.507455\pi\)
−0.0234178 + 0.999726i \(0.507455\pi\)
\(992\) −18.2258 −0.578669
\(993\) 3.98129 0.126342
\(994\) 9.62218 0.305197
\(995\) −28.6476 −0.908189
\(996\) −13.6300 −0.431882
\(997\) 5.43912 0.172259 0.0861293 0.996284i \(-0.472550\pi\)
0.0861293 + 0.996284i \(0.472550\pi\)
\(998\) 29.7578 0.941966
\(999\) −27.8890 −0.882368
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 8041.2.a.d.1.13 62
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.d.1.13 62 1.1 even 1 trivial