Properties

Label 8038.2.a.c.1.10
Level $8038$
Weight $2$
Character 8038.1
Self dual yes
Analytic conductor $64.184$
Analytic rank $1$
Dimension $84$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8038,2,Mod(1,8038)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8038, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8038.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8038 = 2 \cdot 4019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8038.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: \(64.1837531447\)
Analytic rank: \(1\)
Dimension: \(84\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 8038.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.71506 q^{3} +1.00000 q^{4} -2.98033 q^{5} +2.71506 q^{6} +3.18004 q^{7} -1.00000 q^{8} +4.37153 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.71506 q^{3} +1.00000 q^{4} -2.98033 q^{5} +2.71506 q^{6} +3.18004 q^{7} -1.00000 q^{8} +4.37153 q^{9} +2.98033 q^{10} -4.66208 q^{11} -2.71506 q^{12} -0.206957 q^{13} -3.18004 q^{14} +8.09177 q^{15} +1.00000 q^{16} -3.33338 q^{17} -4.37153 q^{18} -4.88581 q^{19} -2.98033 q^{20} -8.63399 q^{21} +4.66208 q^{22} +7.91913 q^{23} +2.71506 q^{24} +3.88237 q^{25} +0.206957 q^{26} -3.72379 q^{27} +3.18004 q^{28} -1.80448 q^{29} -8.09177 q^{30} +5.19137 q^{31} -1.00000 q^{32} +12.6578 q^{33} +3.33338 q^{34} -9.47758 q^{35} +4.37153 q^{36} -0.280897 q^{37} +4.88581 q^{38} +0.561900 q^{39} +2.98033 q^{40} +5.18280 q^{41} +8.63399 q^{42} -0.889927 q^{43} -4.66208 q^{44} -13.0286 q^{45} -7.91913 q^{46} -11.9910 q^{47} -2.71506 q^{48} +3.11267 q^{49} -3.88237 q^{50} +9.05031 q^{51} -0.206957 q^{52} -6.17248 q^{53} +3.72379 q^{54} +13.8946 q^{55} -3.18004 q^{56} +13.2652 q^{57} +1.80448 q^{58} -10.4000 q^{59} +8.09177 q^{60} +6.51902 q^{61} -5.19137 q^{62} +13.9017 q^{63} +1.00000 q^{64} +0.616800 q^{65} -12.6578 q^{66} +4.53232 q^{67} -3.33338 q^{68} -21.5009 q^{69} +9.47758 q^{70} +1.72059 q^{71} -4.37153 q^{72} +11.0021 q^{73} +0.280897 q^{74} -10.5409 q^{75} -4.88581 q^{76} -14.8256 q^{77} -0.561900 q^{78} +5.85921 q^{79} -2.98033 q^{80} -3.00429 q^{81} -5.18280 q^{82} +8.19014 q^{83} -8.63399 q^{84} +9.93456 q^{85} +0.889927 q^{86} +4.89927 q^{87} +4.66208 q^{88} -9.24870 q^{89} +13.0286 q^{90} -0.658131 q^{91} +7.91913 q^{92} -14.0949 q^{93} +11.9910 q^{94} +14.5613 q^{95} +2.71506 q^{96} +8.00436 q^{97} -3.11267 q^{98} -20.3805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 84 q^{2} - 19 q^{3} + 84 q^{4} - 32 q^{5} + 19 q^{6} + q^{7} - 84 q^{8} + 77 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 84 q^{2} - 19 q^{3} + 84 q^{4} - 32 q^{5} + 19 q^{6} + q^{7} - 84 q^{8} + 77 q^{9} + 32 q^{10} - 6 q^{11} - 19 q^{12} - 29 q^{13} - q^{14} - 4 q^{15} + 84 q^{16} - 36 q^{17} - 77 q^{18} + 33 q^{19} - 32 q^{20} - 21 q^{21} + 6 q^{22} - 62 q^{23} + 19 q^{24} + 82 q^{25} + 29 q^{26} - 82 q^{27} + q^{28} - 51 q^{29} + 4 q^{30} + 39 q^{31} - 84 q^{32} - 32 q^{33} + 36 q^{34} - 34 q^{35} + 77 q^{36} - 32 q^{37} - 33 q^{38} + 29 q^{39} + 32 q^{40} - 38 q^{41} + 21 q^{42} - 6 q^{44} - 91 q^{45} + 62 q^{46} - 58 q^{47} - 19 q^{48} + 83 q^{49} - 82 q^{50} - q^{51} - 29 q^{52} - 106 q^{53} + 82 q^{54} + 32 q^{55} - q^{56} - 44 q^{57} + 51 q^{58} - 42 q^{59} - 4 q^{60} - 41 q^{61} - 39 q^{62} - 9 q^{63} + 84 q^{64} - 49 q^{65} + 32 q^{66} - 16 q^{67} - 36 q^{68} - 45 q^{69} + 34 q^{70} - 62 q^{71} - 77 q^{72} - 16 q^{73} + 32 q^{74} - 80 q^{75} + 33 q^{76} - 134 q^{77} - 29 q^{78} + 53 q^{79} - 32 q^{80} + 56 q^{81} + 38 q^{82} - 90 q^{83} - 21 q^{84} - 60 q^{85} - 3 q^{87} + 6 q^{88} - 54 q^{89} + 91 q^{90} + 33 q^{91} - 62 q^{92} - 69 q^{93} + 58 q^{94} - 47 q^{95} + 19 q^{96} - 31 q^{97} - 83 q^{98} + 23 q^{99}+O(q^{100}) \) 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
\(3\) −2.71506 −1.56754 −0.783769 0.621052i \(-0.786706\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.98033 −1.33284 −0.666422 0.745575i \(-0.732175\pi\)
−0.666422 + 0.745575i \(0.732175\pi\)
\(6\) 2.71506 1.10842
\(7\) 3.18004 1.20194 0.600971 0.799271i \(-0.294781\pi\)
0.600971 + 0.799271i \(0.294781\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.37153 1.45718
\(10\) 2.98033 0.942463
\(11\) −4.66208 −1.40567 −0.702836 0.711352i \(-0.748083\pi\)
−0.702836 + 0.711352i \(0.748083\pi\)
\(12\) −2.71506 −0.783769
\(13\) −0.206957 −0.0573995 −0.0286998 0.999588i \(-0.509137\pi\)
−0.0286998 + 0.999588i \(0.509137\pi\)
\(14\) −3.18004 −0.849902
\(15\) 8.09177 2.08929
\(16\) 1.00000 0.250000
\(17\) −3.33338 −0.808463 −0.404231 0.914657i \(-0.632461\pi\)
−0.404231 + 0.914657i \(0.632461\pi\)
\(18\) −4.37153 −1.03038
\(19\) −4.88581 −1.12088 −0.560440 0.828195i \(-0.689368\pi\)
−0.560440 + 0.828195i \(0.689368\pi\)
\(20\) −2.98033 −0.666422
\(21\) −8.63399 −1.88409
\(22\) 4.66208 0.993960
\(23\) 7.91913 1.65125 0.825626 0.564217i \(-0.190822\pi\)
0.825626 + 0.564217i \(0.190822\pi\)
\(24\) 2.71506 0.554209
\(25\) 3.88237 0.776474
\(26\) 0.206957 0.0405876
\(27\) −3.72379 −0.716644
\(28\) 3.18004 0.600971
\(29\) −1.80448 −0.335084 −0.167542 0.985865i \(-0.553583\pi\)
−0.167542 + 0.985865i \(0.553583\pi\)
\(30\) −8.09177 −1.47735
\(31\) 5.19137 0.932398 0.466199 0.884680i \(-0.345623\pi\)
0.466199 + 0.884680i \(0.345623\pi\)
\(32\) −1.00000 −0.176777
\(33\) 12.6578 2.20344
\(34\) 3.33338 0.571669
\(35\) −9.47758 −1.60200
\(36\) 4.37153 0.728589
\(37\) −0.280897 −0.0461791 −0.0230896 0.999733i \(-0.507350\pi\)
−0.0230896 + 0.999733i \(0.507350\pi\)
\(38\) 4.88581 0.792582
\(39\) 0.561900 0.0899759
\(40\) 2.98033 0.471232
\(41\) 5.18280 0.809418 0.404709 0.914446i \(-0.367373\pi\)
0.404709 + 0.914446i \(0.367373\pi\)
\(42\) 8.63399 1.33225
\(43\) −0.889927 −0.135713 −0.0678563 0.997695i \(-0.521616\pi\)
−0.0678563 + 0.997695i \(0.521616\pi\)
\(44\) −4.66208 −0.702836
\(45\) −13.0286 −1.94219
\(46\) −7.91913 −1.16761
\(47\) −11.9910 −1.74906 −0.874530 0.484971i \(-0.838830\pi\)
−0.874530 + 0.484971i \(0.838830\pi\)
\(48\) −2.71506 −0.391885
\(49\) 3.11267 0.444667
\(50\) −3.88237 −0.549050
\(51\) 9.05031 1.26730
\(52\) −0.206957 −0.0286998
\(53\) −6.17248 −0.847855 −0.423928 0.905696i \(-0.639349\pi\)
−0.423928 + 0.905696i \(0.639349\pi\)
\(54\) 3.72379 0.506744
\(55\) 13.8946 1.87354
\(56\) −3.18004 −0.424951
\(57\) 13.2652 1.75702
\(58\) 1.80448 0.236940
\(59\) −10.4000 −1.35396 −0.676981 0.736001i \(-0.736712\pi\)
−0.676981 + 0.736001i \(0.736712\pi\)
\(60\) 8.09177 1.04464
\(61\) 6.51902 0.834675 0.417337 0.908752i \(-0.362963\pi\)
0.417337 + 0.908752i \(0.362963\pi\)
\(62\) −5.19137 −0.659305
\(63\) 13.9017 1.75144
\(64\) 1.00000 0.125000
\(65\) 0.616800 0.0765046
\(66\) −12.6578 −1.55807
\(67\) 4.53232 0.553711 0.276856 0.960912i \(-0.410708\pi\)
0.276856 + 0.960912i \(0.410708\pi\)
\(68\) −3.33338 −0.404231
\(69\) −21.5009 −2.58840
\(70\) 9.47758 1.13279
\(71\) 1.72059 0.204197 0.102098 0.994774i \(-0.467444\pi\)
0.102098 + 0.994774i \(0.467444\pi\)
\(72\) −4.37153 −0.515190
\(73\) 11.0021 1.28770 0.643848 0.765153i \(-0.277337\pi\)
0.643848 + 0.765153i \(0.277337\pi\)
\(74\) 0.280897 0.0326536
\(75\) −10.5409 −1.21715
\(76\) −4.88581 −0.560440
\(77\) −14.8256 −1.68954
\(78\) −0.561900 −0.0636226
\(79\) 5.85921 0.659212 0.329606 0.944118i \(-0.393084\pi\)
0.329606 + 0.944118i \(0.393084\pi\)
\(80\) −2.98033 −0.333211
\(81\) −3.00429 −0.333810
\(82\) −5.18280 −0.572345
\(83\) 8.19014 0.898984 0.449492 0.893284i \(-0.351605\pi\)
0.449492 + 0.893284i \(0.351605\pi\)
\(84\) −8.63399 −0.942046
\(85\) 9.93456 1.07755
\(86\) 0.889927 0.0959633
\(87\) 4.89927 0.525257
\(88\) 4.66208 0.496980
\(89\) −9.24870 −0.980360 −0.490180 0.871621i \(-0.663069\pi\)
−0.490180 + 0.871621i \(0.663069\pi\)
\(90\) 13.0286 1.37334
\(91\) −0.658131 −0.0689909
\(92\) 7.91913 0.825626
\(93\) −14.0949 −1.46157
\(94\) 11.9910 1.23677
\(95\) 14.5613 1.49396
\(96\) 2.71506 0.277104
\(97\) 8.00436 0.812719 0.406360 0.913713i \(-0.366798\pi\)
0.406360 + 0.913713i \(0.366798\pi\)
\(98\) −3.11267 −0.314427
\(99\) −20.3805 −2.04831
\(100\) 3.88237 0.388237
\(101\) 1.16145 0.115569 0.0577844 0.998329i \(-0.481596\pi\)
0.0577844 + 0.998329i \(0.481596\pi\)
\(102\) −9.05031 −0.896114
\(103\) −14.4312 −1.42195 −0.710973 0.703220i \(-0.751745\pi\)
−0.710973 + 0.703220i \(0.751745\pi\)
\(104\) 0.206957 0.0202938
\(105\) 25.7322 2.51120
\(106\) 6.17248 0.599524
\(107\) −6.01878 −0.581857 −0.290929 0.956745i \(-0.593964\pi\)
−0.290929 + 0.956745i \(0.593964\pi\)
\(108\) −3.72379 −0.358322
\(109\) 2.77808 0.266092 0.133046 0.991110i \(-0.457524\pi\)
0.133046 + 0.991110i \(0.457524\pi\)
\(110\) −13.8946 −1.32479
\(111\) 0.762650 0.0723875
\(112\) 3.18004 0.300486
\(113\) 9.98211 0.939037 0.469519 0.882923i \(-0.344427\pi\)
0.469519 + 0.882923i \(0.344427\pi\)
\(114\) −13.2652 −1.24240
\(115\) −23.6016 −2.20086
\(116\) −1.80448 −0.167542
\(117\) −0.904719 −0.0836413
\(118\) 10.4000 0.957396
\(119\) −10.6003 −0.971726
\(120\) −8.09177 −0.738674
\(121\) 10.7350 0.975912
\(122\) −6.51902 −0.590204
\(123\) −14.0716 −1.26879
\(124\) 5.19137 0.466199
\(125\) 3.33091 0.297925
\(126\) −13.9017 −1.23846
\(127\) 18.2806 1.62214 0.811071 0.584948i \(-0.198885\pi\)
0.811071 + 0.584948i \(0.198885\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.41620 0.212735
\(130\) −0.616800 −0.0540969
\(131\) −11.4382 −0.999357 −0.499679 0.866211i \(-0.666549\pi\)
−0.499679 + 0.866211i \(0.666549\pi\)
\(132\) 12.6578 1.10172
\(133\) −15.5371 −1.34723
\(134\) −4.53232 −0.391533
\(135\) 11.0981 0.955175
\(136\) 3.33338 0.285835
\(137\) 17.7954 1.52037 0.760184 0.649708i \(-0.225109\pi\)
0.760184 + 0.649708i \(0.225109\pi\)
\(138\) 21.5009 1.83028
\(139\) 8.20329 0.695794 0.347897 0.937533i \(-0.386896\pi\)
0.347897 + 0.937533i \(0.386896\pi\)
\(140\) −9.47758 −0.801001
\(141\) 32.5561 2.74172
\(142\) −1.72059 −0.144389
\(143\) 0.964850 0.0806848
\(144\) 4.37153 0.364294
\(145\) 5.37795 0.446614
\(146\) −11.0021 −0.910539
\(147\) −8.45107 −0.697032
\(148\) −0.280897 −0.0230896
\(149\) 0.563397 0.0461553 0.0230777 0.999734i \(-0.492654\pi\)
0.0230777 + 0.999734i \(0.492654\pi\)
\(150\) 10.5409 0.860657
\(151\) −11.8749 −0.966368 −0.483184 0.875519i \(-0.660520\pi\)
−0.483184 + 0.875519i \(0.660520\pi\)
\(152\) 4.88581 0.396291
\(153\) −14.5720 −1.17807
\(154\) 14.8256 1.19468
\(155\) −15.4720 −1.24274
\(156\) 0.561900 0.0449880
\(157\) −18.7754 −1.49844 −0.749219 0.662322i \(-0.769571\pi\)
−0.749219 + 0.662322i \(0.769571\pi\)
\(158\) −5.85921 −0.466134
\(159\) 16.7586 1.32905
\(160\) 2.98033 0.235616
\(161\) 25.1832 1.98471
\(162\) 3.00429 0.236040
\(163\) 5.27573 0.413227 0.206614 0.978423i \(-0.433756\pi\)
0.206614 + 0.978423i \(0.433756\pi\)
\(164\) 5.18280 0.404709
\(165\) −37.7245 −2.93685
\(166\) −8.19014 −0.635678
\(167\) 9.39964 0.727366 0.363683 0.931523i \(-0.381519\pi\)
0.363683 + 0.931523i \(0.381519\pi\)
\(168\) 8.63399 0.666127
\(169\) −12.9572 −0.996705
\(170\) −9.93456 −0.761946
\(171\) −21.3585 −1.63332
\(172\) −0.889927 −0.0678563
\(173\) −3.38774 −0.257565 −0.128782 0.991673i \(-0.541107\pi\)
−0.128782 + 0.991673i \(0.541107\pi\)
\(174\) −4.89927 −0.371413
\(175\) 12.3461 0.933277
\(176\) −4.66208 −0.351418
\(177\) 28.2365 2.12239
\(178\) 9.24870 0.693219
\(179\) 12.7495 0.952943 0.476472 0.879190i \(-0.341916\pi\)
0.476472 + 0.879190i \(0.341916\pi\)
\(180\) −13.0286 −0.971096
\(181\) 8.33225 0.619331 0.309666 0.950846i \(-0.399783\pi\)
0.309666 + 0.950846i \(0.399783\pi\)
\(182\) 0.658131 0.0487839
\(183\) −17.6995 −1.30838
\(184\) −7.91913 −0.583806
\(185\) 0.837164 0.0615496
\(186\) 14.0949 1.03349
\(187\) 15.5405 1.13643
\(188\) −11.9910 −0.874530
\(189\) −11.8418 −0.861365
\(190\) −14.5613 −1.05639
\(191\) 15.5119 1.12240 0.561201 0.827679i \(-0.310339\pi\)
0.561201 + 0.827679i \(0.310339\pi\)
\(192\) −2.71506 −0.195942
\(193\) 20.2688 1.45898 0.729491 0.683990i \(-0.239757\pi\)
0.729491 + 0.683990i \(0.239757\pi\)
\(194\) −8.00436 −0.574679
\(195\) −1.67465 −0.119924
\(196\) 3.11267 0.222333
\(197\) 19.8796 1.41636 0.708181 0.706030i \(-0.249516\pi\)
0.708181 + 0.706030i \(0.249516\pi\)
\(198\) 20.3805 1.44838
\(199\) −1.66224 −0.117833 −0.0589164 0.998263i \(-0.518765\pi\)
−0.0589164 + 0.998263i \(0.518765\pi\)
\(200\) −3.88237 −0.274525
\(201\) −12.3055 −0.867964
\(202\) −1.16145 −0.0817194
\(203\) −5.73832 −0.402751
\(204\) 9.05031 0.633648
\(205\) −15.4465 −1.07883
\(206\) 14.4312 1.00547
\(207\) 34.6187 2.40617
\(208\) −0.206957 −0.0143499
\(209\) 22.7780 1.57559
\(210\) −25.7322 −1.77569
\(211\) 3.03770 0.209124 0.104562 0.994518i \(-0.466656\pi\)
0.104562 + 0.994518i \(0.466656\pi\)
\(212\) −6.17248 −0.423928
\(213\) −4.67151 −0.320086
\(214\) 6.01878 0.411435
\(215\) 2.65228 0.180884
\(216\) 3.72379 0.253372
\(217\) 16.5088 1.12069
\(218\) −2.77808 −0.188155
\(219\) −29.8713 −2.01851
\(220\) 13.8946 0.936771
\(221\) 0.689865 0.0464054
\(222\) −0.762650 −0.0511857
\(223\) −10.3577 −0.693602 −0.346801 0.937939i \(-0.612732\pi\)
−0.346801 + 0.937939i \(0.612732\pi\)
\(224\) −3.18004 −0.212475
\(225\) 16.9719 1.13146
\(226\) −9.98211 −0.664000
\(227\) 6.77101 0.449408 0.224704 0.974427i \(-0.427859\pi\)
0.224704 + 0.974427i \(0.427859\pi\)
\(228\) 13.2652 0.878512
\(229\) 7.30024 0.482413 0.241207 0.970474i \(-0.422457\pi\)
0.241207 + 0.970474i \(0.422457\pi\)
\(230\) 23.6016 1.55625
\(231\) 40.2524 2.64841
\(232\) 1.80448 0.118470
\(233\) −25.5717 −1.67526 −0.837628 0.546241i \(-0.816058\pi\)
−0.837628 + 0.546241i \(0.816058\pi\)
\(234\) 0.904719 0.0591433
\(235\) 35.7370 2.33122
\(236\) −10.4000 −0.676981
\(237\) −15.9081 −1.03334
\(238\) 10.6003 0.687114
\(239\) 19.1259 1.23715 0.618575 0.785726i \(-0.287710\pi\)
0.618575 + 0.785726i \(0.287710\pi\)
\(240\) 8.09177 0.522321
\(241\) −6.79789 −0.437891 −0.218945 0.975737i \(-0.570262\pi\)
−0.218945 + 0.975737i \(0.570262\pi\)
\(242\) −10.7350 −0.690074
\(243\) 19.3282 1.23990
\(244\) 6.51902 0.417337
\(245\) −9.27678 −0.592671
\(246\) 14.0716 0.897173
\(247\) 1.01115 0.0643380
\(248\) −5.19137 −0.329652
\(249\) −22.2367 −1.40919
\(250\) −3.33091 −0.210665
\(251\) 13.4974 0.851948 0.425974 0.904735i \(-0.359932\pi\)
0.425974 + 0.904735i \(0.359932\pi\)
\(252\) 13.9017 0.875722
\(253\) −36.9197 −2.32112
\(254\) −18.2806 −1.14703
\(255\) −26.9729 −1.68911
\(256\) 1.00000 0.0625000
\(257\) −18.4986 −1.15391 −0.576955 0.816776i \(-0.695759\pi\)
−0.576955 + 0.816776i \(0.695759\pi\)
\(258\) −2.41620 −0.150426
\(259\) −0.893263 −0.0555046
\(260\) 0.616800 0.0382523
\(261\) −7.88835 −0.488276
\(262\) 11.4382 0.706652
\(263\) 20.5832 1.26922 0.634609 0.772834i \(-0.281161\pi\)
0.634609 + 0.772834i \(0.281161\pi\)
\(264\) −12.6578 −0.779035
\(265\) 18.3960 1.13006
\(266\) 15.5371 0.952639
\(267\) 25.1108 1.53675
\(268\) 4.53232 0.276856
\(269\) 30.4811 1.85847 0.929234 0.369491i \(-0.120468\pi\)
0.929234 + 0.369491i \(0.120468\pi\)
\(270\) −11.0981 −0.675411
\(271\) −2.74238 −0.166588 −0.0832938 0.996525i \(-0.526544\pi\)
−0.0832938 + 0.996525i \(0.526544\pi\)
\(272\) −3.33338 −0.202116
\(273\) 1.78686 0.108146
\(274\) −17.7954 −1.07506
\(275\) −18.0999 −1.09147
\(276\) −21.5009 −1.29420
\(277\) 7.80451 0.468928 0.234464 0.972125i \(-0.424667\pi\)
0.234464 + 0.972125i \(0.424667\pi\)
\(278\) −8.20329 −0.492001
\(279\) 22.6943 1.35867
\(280\) 9.47758 0.566394
\(281\) −13.6091 −0.811853 −0.405927 0.913906i \(-0.633051\pi\)
−0.405927 + 0.913906i \(0.633051\pi\)
\(282\) −32.5561 −1.93869
\(283\) 8.78731 0.522351 0.261176 0.965291i \(-0.415890\pi\)
0.261176 + 0.965291i \(0.415890\pi\)
\(284\) 1.72059 0.102098
\(285\) −39.5348 −2.34184
\(286\) −0.964850 −0.0570528
\(287\) 16.4815 0.972874
\(288\) −4.37153 −0.257595
\(289\) −5.88860 −0.346388
\(290\) −5.37795 −0.315804
\(291\) −21.7323 −1.27397
\(292\) 11.0021 0.643848
\(293\) −3.65314 −0.213419 −0.106709 0.994290i \(-0.534031\pi\)
−0.106709 + 0.994290i \(0.534031\pi\)
\(294\) 8.45107 0.492876
\(295\) 30.9954 1.80462
\(296\) 0.280897 0.0163268
\(297\) 17.3606 1.00737
\(298\) −0.563397 −0.0326367
\(299\) −1.63892 −0.0947811
\(300\) −10.5409 −0.608577
\(301\) −2.83001 −0.163119
\(302\) 11.8749 0.683325
\(303\) −3.15341 −0.181158
\(304\) −4.88581 −0.280220
\(305\) −19.4288 −1.11249
\(306\) 14.5720 0.833024
\(307\) −12.2995 −0.701968 −0.350984 0.936381i \(-0.614153\pi\)
−0.350984 + 0.936381i \(0.614153\pi\)
\(308\) −14.8256 −0.844768
\(309\) 39.1815 2.22895
\(310\) 15.4720 0.878751
\(311\) 31.9397 1.81113 0.905566 0.424206i \(-0.139447\pi\)
0.905566 + 0.424206i \(0.139447\pi\)
\(312\) −0.561900 −0.0318113
\(313\) 26.3933 1.49184 0.745918 0.666038i \(-0.232011\pi\)
0.745918 + 0.666038i \(0.232011\pi\)
\(314\) 18.7754 1.05956
\(315\) −41.4315 −2.33440
\(316\) 5.85921 0.329606
\(317\) 19.1032 1.07294 0.536470 0.843919i \(-0.319757\pi\)
0.536470 + 0.843919i \(0.319757\pi\)
\(318\) −16.7586 −0.939778
\(319\) 8.41264 0.471018
\(320\) −2.98033 −0.166606
\(321\) 16.3413 0.912084
\(322\) −25.1832 −1.40340
\(323\) 16.2862 0.906190
\(324\) −3.00429 −0.166905
\(325\) −0.803483 −0.0445692
\(326\) −5.27573 −0.292196
\(327\) −7.54264 −0.417109
\(328\) −5.18280 −0.286172
\(329\) −38.1317 −2.10227
\(330\) 37.7245 2.07667
\(331\) 33.7805 1.85674 0.928371 0.371655i \(-0.121209\pi\)
0.928371 + 0.371655i \(0.121209\pi\)
\(332\) 8.19014 0.449492
\(333\) −1.22795 −0.0672912
\(334\) −9.39964 −0.514326
\(335\) −13.5078 −0.738011
\(336\) −8.63399 −0.471023
\(337\) −34.1726 −1.86150 −0.930751 0.365653i \(-0.880846\pi\)
−0.930751 + 0.365653i \(0.880846\pi\)
\(338\) 12.9572 0.704777
\(339\) −27.1020 −1.47198
\(340\) 9.93456 0.538777
\(341\) −24.2026 −1.31065
\(342\) 21.3585 1.15493
\(343\) −12.3619 −0.667479
\(344\) 0.889927 0.0479817
\(345\) 64.0798 3.44994
\(346\) 3.38774 0.182126
\(347\) −25.1976 −1.35268 −0.676338 0.736591i \(-0.736434\pi\)
−0.676338 + 0.736591i \(0.736434\pi\)
\(348\) 4.89927 0.262628
\(349\) 9.19423 0.492156 0.246078 0.969250i \(-0.420858\pi\)
0.246078 + 0.969250i \(0.420858\pi\)
\(350\) −12.3461 −0.659927
\(351\) 0.770664 0.0411350
\(352\) 4.66208 0.248490
\(353\) −6.61158 −0.351899 −0.175949 0.984399i \(-0.556300\pi\)
−0.175949 + 0.984399i \(0.556300\pi\)
\(354\) −28.2365 −1.50075
\(355\) −5.12793 −0.272162
\(356\) −9.24870 −0.490180
\(357\) 28.7804 1.52322
\(358\) −12.7495 −0.673832
\(359\) −3.95873 −0.208934 −0.104467 0.994528i \(-0.533314\pi\)
−0.104467 + 0.994528i \(0.533314\pi\)
\(360\) 13.0286 0.686668
\(361\) 4.87110 0.256374
\(362\) −8.33225 −0.437933
\(363\) −29.1462 −1.52978
\(364\) −0.658131 −0.0344955
\(365\) −32.7898 −1.71630
\(366\) 17.6995 0.925168
\(367\) −21.0053 −1.09647 −0.548233 0.836325i \(-0.684699\pi\)
−0.548233 + 0.836325i \(0.684699\pi\)
\(368\) 7.91913 0.412813
\(369\) 22.6568 1.17947
\(370\) −0.837164 −0.0435221
\(371\) −19.6287 −1.01907
\(372\) −14.0949 −0.730785
\(373\) −12.4902 −0.646716 −0.323358 0.946277i \(-0.604812\pi\)
−0.323358 + 0.946277i \(0.604812\pi\)
\(374\) −15.5405 −0.803579
\(375\) −9.04360 −0.467009
\(376\) 11.9910 0.618386
\(377\) 0.373450 0.0192336
\(378\) 11.8418 0.609077
\(379\) 14.1273 0.725672 0.362836 0.931853i \(-0.381809\pi\)
0.362836 + 0.931853i \(0.381809\pi\)
\(380\) 14.5613 0.746980
\(381\) −49.6329 −2.54277
\(382\) −15.5119 −0.793658
\(383\) −34.1908 −1.74707 −0.873534 0.486763i \(-0.838177\pi\)
−0.873534 + 0.486763i \(0.838177\pi\)
\(384\) 2.71506 0.138552
\(385\) 44.1853 2.25189
\(386\) −20.2688 −1.03166
\(387\) −3.89035 −0.197757
\(388\) 8.00436 0.406360
\(389\) −16.7005 −0.846750 −0.423375 0.905954i \(-0.639155\pi\)
−0.423375 + 0.905954i \(0.639155\pi\)
\(390\) 1.67465 0.0847990
\(391\) −26.3974 −1.33498
\(392\) −3.11267 −0.157213
\(393\) 31.0553 1.56653
\(394\) −19.8796 −1.00152
\(395\) −17.4624 −0.878628
\(396\) −20.3805 −1.02416
\(397\) 3.64414 0.182894 0.0914472 0.995810i \(-0.470851\pi\)
0.0914472 + 0.995810i \(0.470851\pi\)
\(398\) 1.66224 0.0833204
\(399\) 42.1840 2.11184
\(400\) 3.88237 0.194119
\(401\) −19.8567 −0.991597 −0.495799 0.868438i \(-0.665125\pi\)
−0.495799 + 0.868438i \(0.665125\pi\)
\(402\) 12.3055 0.613743
\(403\) −1.07439 −0.0535192
\(404\) 1.16145 0.0577844
\(405\) 8.95379 0.444917
\(406\) 5.73832 0.284788
\(407\) 1.30956 0.0649126
\(408\) −9.05031 −0.448057
\(409\) −18.5685 −0.918152 −0.459076 0.888397i \(-0.651819\pi\)
−0.459076 + 0.888397i \(0.651819\pi\)
\(410\) 15.4465 0.762847
\(411\) −48.3156 −2.38323
\(412\) −14.4312 −0.710973
\(413\) −33.0724 −1.62738
\(414\) −34.6187 −1.70142
\(415\) −24.4093 −1.19821
\(416\) 0.206957 0.0101469
\(417\) −22.2724 −1.09068
\(418\) −22.7780 −1.11411
\(419\) −14.9158 −0.728684 −0.364342 0.931265i \(-0.618706\pi\)
−0.364342 + 0.931265i \(0.618706\pi\)
\(420\) 25.7322 1.25560
\(421\) −25.5757 −1.24648 −0.623242 0.782029i \(-0.714185\pi\)
−0.623242 + 0.782029i \(0.714185\pi\)
\(422\) −3.03770 −0.147873
\(423\) −52.4188 −2.54869
\(424\) 6.17248 0.299762
\(425\) −12.9414 −0.627750
\(426\) 4.67151 0.226335
\(427\) 20.7307 1.00323
\(428\) −6.01878 −0.290929
\(429\) −2.61962 −0.126477
\(430\) −2.65228 −0.127904
\(431\) −2.65323 −0.127802 −0.0639009 0.997956i \(-0.520354\pi\)
−0.0639009 + 0.997956i \(0.520354\pi\)
\(432\) −3.72379 −0.179161
\(433\) −12.7148 −0.611035 −0.305517 0.952187i \(-0.598829\pi\)
−0.305517 + 0.952187i \(0.598829\pi\)
\(434\) −16.5088 −0.792447
\(435\) −14.6014 −0.700085
\(436\) 2.77808 0.133046
\(437\) −38.6913 −1.85086
\(438\) 29.8713 1.42730
\(439\) −10.0130 −0.477896 −0.238948 0.971032i \(-0.576803\pi\)
−0.238948 + 0.971032i \(0.576803\pi\)
\(440\) −13.8946 −0.662397
\(441\) 13.6071 0.647958
\(442\) −0.689865 −0.0328135
\(443\) 15.6462 0.743376 0.371688 0.928358i \(-0.378779\pi\)
0.371688 + 0.928358i \(0.378779\pi\)
\(444\) 0.762650 0.0361938
\(445\) 27.5642 1.30667
\(446\) 10.3577 0.490451
\(447\) −1.52966 −0.0723502
\(448\) 3.18004 0.150243
\(449\) 1.71080 0.0807377 0.0403689 0.999185i \(-0.487147\pi\)
0.0403689 + 0.999185i \(0.487147\pi\)
\(450\) −16.9719 −0.800064
\(451\) −24.1627 −1.13778
\(452\) 9.98211 0.469519
\(453\) 32.2411 1.51482
\(454\) −6.77101 −0.317779
\(455\) 1.96145 0.0919542
\(456\) −13.2652 −0.621202
\(457\) −28.2034 −1.31930 −0.659649 0.751574i \(-0.729295\pi\)
−0.659649 + 0.751574i \(0.729295\pi\)
\(458\) −7.30024 −0.341118
\(459\) 12.4128 0.579380
\(460\) −23.6016 −1.10043
\(461\) 19.2700 0.897495 0.448748 0.893659i \(-0.351870\pi\)
0.448748 + 0.893659i \(0.351870\pi\)
\(462\) −40.2524 −1.87271
\(463\) −32.2347 −1.49807 −0.749037 0.662528i \(-0.769484\pi\)
−0.749037 + 0.662528i \(0.769484\pi\)
\(464\) −1.80448 −0.0837709
\(465\) 42.0074 1.94805
\(466\) 25.5717 1.18458
\(467\) −32.8624 −1.52069 −0.760346 0.649518i \(-0.774971\pi\)
−0.760346 + 0.649518i \(0.774971\pi\)
\(468\) −0.904719 −0.0418206
\(469\) 14.4130 0.665529
\(470\) −35.7370 −1.64842
\(471\) 50.9762 2.34886
\(472\) 10.4000 0.478698
\(473\) 4.14892 0.190767
\(474\) 15.9081 0.730682
\(475\) −18.9685 −0.870335
\(476\) −10.6003 −0.485863
\(477\) −26.9832 −1.23548
\(478\) −19.1259 −0.874797
\(479\) −4.90869 −0.224284 −0.112142 0.993692i \(-0.535771\pi\)
−0.112142 + 0.993692i \(0.535771\pi\)
\(480\) −8.09177 −0.369337
\(481\) 0.0581335 0.00265066
\(482\) 6.79789 0.309636
\(483\) −68.3737 −3.11111
\(484\) 10.7350 0.487956
\(485\) −23.8556 −1.08323
\(486\) −19.3282 −0.876745
\(487\) 7.40585 0.335591 0.167795 0.985822i \(-0.446335\pi\)
0.167795 + 0.985822i \(0.446335\pi\)
\(488\) −6.51902 −0.295102
\(489\) −14.3239 −0.647750
\(490\) 9.27678 0.419082
\(491\) −19.5284 −0.881305 −0.440652 0.897678i \(-0.645253\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(492\) −14.0716 −0.634397
\(493\) 6.01501 0.270903
\(494\) −1.01115 −0.0454938
\(495\) 60.7405 2.73008
\(496\) 5.19137 0.233099
\(497\) 5.47156 0.245433
\(498\) 22.2367 0.996450
\(499\) 33.7657 1.51156 0.755780 0.654825i \(-0.227258\pi\)
0.755780 + 0.654825i \(0.227258\pi\)
\(500\) 3.33091 0.148963
\(501\) −25.5206 −1.14017
\(502\) −13.4974 −0.602418
\(503\) −10.8833 −0.485262 −0.242631 0.970119i \(-0.578010\pi\)
−0.242631 + 0.970119i \(0.578010\pi\)
\(504\) −13.9017 −0.619229
\(505\) −3.46151 −0.154035
\(506\) 36.9197 1.64128
\(507\) 35.1795 1.56237
\(508\) 18.2806 0.811071
\(509\) 21.2484 0.941821 0.470910 0.882181i \(-0.343926\pi\)
0.470910 + 0.882181i \(0.343926\pi\)
\(510\) 26.9729 1.19438
\(511\) 34.9871 1.54774
\(512\) −1.00000 −0.0441942
\(513\) 18.1937 0.803273
\(514\) 18.4986 0.815938
\(515\) 43.0097 1.89523
\(516\) 2.41620 0.106367
\(517\) 55.9028 2.45860
\(518\) 0.893263 0.0392477
\(519\) 9.19790 0.403743
\(520\) −0.616800 −0.0270485
\(521\) −5.68808 −0.249199 −0.124600 0.992207i \(-0.539765\pi\)
−0.124600 + 0.992207i \(0.539765\pi\)
\(522\) 7.88835 0.345264
\(523\) 32.8650 1.43709 0.718543 0.695483i \(-0.244810\pi\)
0.718543 + 0.695483i \(0.244810\pi\)
\(524\) −11.4382 −0.499679
\(525\) −33.5204 −1.46295
\(526\) −20.5832 −0.897472
\(527\) −17.3048 −0.753809
\(528\) 12.6578 0.550861
\(529\) 39.7126 1.72664
\(530\) −18.3960 −0.799073
\(531\) −45.4639 −1.97296
\(532\) −15.5371 −0.673617
\(533\) −1.07262 −0.0464602
\(534\) −25.1108 −1.08665
\(535\) 17.9380 0.775525
\(536\) −4.53232 −0.195766
\(537\) −34.6156 −1.49378
\(538\) −30.4811 −1.31414
\(539\) −14.5115 −0.625055
\(540\) 11.0981 0.477588
\(541\) −21.9527 −0.943818 −0.471909 0.881647i \(-0.656435\pi\)
−0.471909 + 0.881647i \(0.656435\pi\)
\(542\) 2.74238 0.117795
\(543\) −22.6225 −0.970826
\(544\) 3.33338 0.142917
\(545\) −8.27959 −0.354659
\(546\) −1.78686 −0.0764707
\(547\) 15.5043 0.662917 0.331458 0.943470i \(-0.392459\pi\)
0.331458 + 0.943470i \(0.392459\pi\)
\(548\) 17.7954 0.760184
\(549\) 28.4981 1.21627
\(550\) 18.0999 0.771784
\(551\) 8.81634 0.375589
\(552\) 21.5009 0.915139
\(553\) 18.6325 0.792336
\(554\) −7.80451 −0.331582
\(555\) −2.27295 −0.0964813
\(556\) 8.20329 0.347897
\(557\) 17.1437 0.726404 0.363202 0.931710i \(-0.381684\pi\)
0.363202 + 0.931710i \(0.381684\pi\)
\(558\) −22.6943 −0.960725
\(559\) 0.184177 0.00778984
\(560\) −9.47758 −0.400501
\(561\) −42.1933 −1.78140
\(562\) 13.6091 0.574067
\(563\) 26.8191 1.13029 0.565146 0.824991i \(-0.308820\pi\)
0.565146 + 0.824991i \(0.308820\pi\)
\(564\) 32.5561 1.37086
\(565\) −29.7500 −1.25159
\(566\) −8.78731 −0.369358
\(567\) −9.55378 −0.401221
\(568\) −1.72059 −0.0721945
\(569\) −38.3653 −1.60836 −0.804179 0.594387i \(-0.797395\pi\)
−0.804179 + 0.594387i \(0.797395\pi\)
\(570\) 39.5348 1.65593
\(571\) 14.9750 0.626683 0.313341 0.949641i \(-0.398552\pi\)
0.313341 + 0.949641i \(0.398552\pi\)
\(572\) 0.964850 0.0403424
\(573\) −42.1157 −1.75941
\(574\) −16.4815 −0.687926
\(575\) 30.7450 1.28215
\(576\) 4.37153 0.182147
\(577\) −37.3763 −1.55600 −0.777998 0.628266i \(-0.783765\pi\)
−0.777998 + 0.628266i \(0.783765\pi\)
\(578\) 5.88860 0.244933
\(579\) −55.0310 −2.28701
\(580\) 5.37795 0.223307
\(581\) 26.0450 1.08053
\(582\) 21.7323 0.900832
\(583\) 28.7766 1.19181
\(584\) −11.0021 −0.455269
\(585\) 2.69636 0.111481
\(586\) 3.65314 0.150910
\(587\) −45.1867 −1.86506 −0.932528 0.361097i \(-0.882402\pi\)
−0.932528 + 0.361097i \(0.882402\pi\)
\(588\) −8.45107 −0.348516
\(589\) −25.3640 −1.04511
\(590\) −30.9954 −1.27606
\(591\) −53.9742 −2.22020
\(592\) −0.280897 −0.0115448
\(593\) −16.1582 −0.663536 −0.331768 0.943361i \(-0.607645\pi\)
−0.331768 + 0.943361i \(0.607645\pi\)
\(594\) −17.3606 −0.712315
\(595\) 31.5923 1.29516
\(596\) 0.563397 0.0230777
\(597\) 4.51307 0.184707
\(598\) 1.63892 0.0670203
\(599\) 11.3198 0.462516 0.231258 0.972892i \(-0.425716\pi\)
0.231258 + 0.972892i \(0.425716\pi\)
\(600\) 10.5409 0.430329
\(601\) 3.30959 0.135001 0.0675005 0.997719i \(-0.478498\pi\)
0.0675005 + 0.997719i \(0.478498\pi\)
\(602\) 2.83001 0.115342
\(603\) 19.8132 0.806856
\(604\) −11.8749 −0.483184
\(605\) −31.9940 −1.30074
\(606\) 3.15341 0.128098
\(607\) −40.5505 −1.64590 −0.822948 0.568117i \(-0.807672\pi\)
−0.822948 + 0.568117i \(0.807672\pi\)
\(608\) 4.88581 0.198146
\(609\) 15.5799 0.631328
\(610\) 19.4288 0.786650
\(611\) 2.48161 0.100395
\(612\) −14.5720 −0.589037
\(613\) 30.2864 1.22325 0.611627 0.791146i \(-0.290515\pi\)
0.611627 + 0.791146i \(0.290515\pi\)
\(614\) 12.2995 0.496366
\(615\) 41.9380 1.69110
\(616\) 14.8256 0.597341
\(617\) −38.4514 −1.54799 −0.773997 0.633189i \(-0.781746\pi\)
−0.773997 + 0.633189i \(0.781746\pi\)
\(618\) −39.1815 −1.57611
\(619\) −42.1015 −1.69220 −0.846102 0.533021i \(-0.821057\pi\)
−0.846102 + 0.533021i \(0.821057\pi\)
\(620\) −15.4720 −0.621371
\(621\) −29.4892 −1.18336
\(622\) −31.9397 −1.28066
\(623\) −29.4113 −1.17834
\(624\) 0.561900 0.0224940
\(625\) −29.3391 −1.17356
\(626\) −26.3933 −1.05489
\(627\) −61.8437 −2.46980
\(628\) −18.7754 −0.749219
\(629\) 0.936334 0.0373341
\(630\) 41.4315 1.65067
\(631\) 31.5677 1.25669 0.628345 0.777935i \(-0.283733\pi\)
0.628345 + 0.777935i \(0.283733\pi\)
\(632\) −5.85921 −0.233067
\(633\) −8.24752 −0.327810
\(634\) −19.1032 −0.758684
\(635\) −54.4823 −2.16206
\(636\) 16.7586 0.664523
\(637\) −0.644188 −0.0255236
\(638\) −8.41264 −0.333060
\(639\) 7.52163 0.297551
\(640\) 2.98033 0.117808
\(641\) −8.82845 −0.348703 −0.174351 0.984683i \(-0.555783\pi\)
−0.174351 + 0.984683i \(0.555783\pi\)
\(642\) −16.3413 −0.644941
\(643\) −24.2926 −0.958006 −0.479003 0.877813i \(-0.659002\pi\)
−0.479003 + 0.877813i \(0.659002\pi\)
\(644\) 25.1832 0.992356
\(645\) −7.20108 −0.283542
\(646\) −16.2862 −0.640773
\(647\) −11.9308 −0.469047 −0.234524 0.972110i \(-0.575353\pi\)
−0.234524 + 0.972110i \(0.575353\pi\)
\(648\) 3.00429 0.118020
\(649\) 48.4856 1.90323
\(650\) 0.803483 0.0315152
\(651\) −44.8223 −1.75672
\(652\) 5.27573 0.206614
\(653\) −22.6933 −0.888056 −0.444028 0.896013i \(-0.646451\pi\)
−0.444028 + 0.896013i \(0.646451\pi\)
\(654\) 7.54264 0.294941
\(655\) 34.0895 1.33199
\(656\) 5.18280 0.202354
\(657\) 48.0960 1.87640
\(658\) 38.1317 1.48653
\(659\) 1.43771 0.0560053 0.0280026 0.999608i \(-0.491085\pi\)
0.0280026 + 0.999608i \(0.491085\pi\)
\(660\) −37.7245 −1.46842
\(661\) −0.449770 −0.0174940 −0.00874701 0.999962i \(-0.502784\pi\)
−0.00874701 + 0.999962i \(0.502784\pi\)
\(662\) −33.7805 −1.31291
\(663\) −1.87302 −0.0727422
\(664\) −8.19014 −0.317839
\(665\) 46.3056 1.79565
\(666\) 1.22795 0.0475820
\(667\) −14.2899 −0.553308
\(668\) 9.39964 0.363683
\(669\) 28.1217 1.08725
\(670\) 13.5078 0.521852
\(671\) −30.3922 −1.17328
\(672\) 8.63399 0.333064
\(673\) −6.07289 −0.234093 −0.117046 0.993126i \(-0.537343\pi\)
−0.117046 + 0.993126i \(0.537343\pi\)
\(674\) 34.1726 1.31628
\(675\) −14.4571 −0.556456
\(676\) −12.9572 −0.498353
\(677\) 31.6368 1.21590 0.607950 0.793976i \(-0.291992\pi\)
0.607950 + 0.793976i \(0.291992\pi\)
\(678\) 27.1020 1.04085
\(679\) 25.4542 0.976842
\(680\) −9.93456 −0.380973
\(681\) −18.3837 −0.704464
\(682\) 24.2026 0.926766
\(683\) −4.71850 −0.180548 −0.0902742 0.995917i \(-0.528774\pi\)
−0.0902742 + 0.995917i \(0.528774\pi\)
\(684\) −21.3585 −0.816661
\(685\) −53.0363 −2.02641
\(686\) 12.3619 0.471979
\(687\) −19.8206 −0.756201
\(688\) −0.889927 −0.0339282
\(689\) 1.27744 0.0486665
\(690\) −64.0798 −2.43947
\(691\) −1.92218 −0.0731232 −0.0365616 0.999331i \(-0.511641\pi\)
−0.0365616 + 0.999331i \(0.511641\pi\)
\(692\) −3.38774 −0.128782
\(693\) −64.8107 −2.46196
\(694\) 25.1976 0.956487
\(695\) −24.4485 −0.927386
\(696\) −4.89927 −0.185706
\(697\) −17.2762 −0.654384
\(698\) −9.19423 −0.348007
\(699\) 69.4285 2.62603
\(700\) 12.3461 0.466639
\(701\) −4.67864 −0.176710 −0.0883549 0.996089i \(-0.528161\pi\)
−0.0883549 + 0.996089i \(0.528161\pi\)
\(702\) −0.770664 −0.0290868
\(703\) 1.37241 0.0517613
\(704\) −4.66208 −0.175709
\(705\) −97.0280 −3.65429
\(706\) 6.61158 0.248830
\(707\) 3.69346 0.138907
\(708\) 28.2365 1.06119
\(709\) 20.9711 0.787587 0.393794 0.919199i \(-0.371162\pi\)
0.393794 + 0.919199i \(0.371162\pi\)
\(710\) 5.12793 0.192448
\(711\) 25.6137 0.960590
\(712\) 9.24870 0.346610
\(713\) 41.1111 1.53962
\(714\) −28.7804 −1.07708
\(715\) −2.87557 −0.107540
\(716\) 12.7495 0.476472
\(717\) −51.9278 −1.93928
\(718\) 3.95873 0.147738
\(719\) −33.4944 −1.24913 −0.624565 0.780973i \(-0.714724\pi\)
−0.624565 + 0.780973i \(0.714724\pi\)
\(720\) −13.0286 −0.485548
\(721\) −45.8917 −1.70910
\(722\) −4.87110 −0.181284
\(723\) 18.4567 0.686411
\(724\) 8.33225 0.309666
\(725\) −7.00566 −0.260184
\(726\) 29.1462 1.08172
\(727\) 16.2573 0.602950 0.301475 0.953474i \(-0.402521\pi\)
0.301475 + 0.953474i \(0.402521\pi\)
\(728\) 0.658131 0.0243920
\(729\) −43.4643 −1.60979
\(730\) 32.7898 1.21361
\(731\) 2.96646 0.109719
\(732\) −17.6995 −0.654192
\(733\) −11.0712 −0.408925 −0.204462 0.978874i \(-0.565545\pi\)
−0.204462 + 0.978874i \(0.565545\pi\)
\(734\) 21.0053 0.775319
\(735\) 25.1870 0.929035
\(736\) −7.91913 −0.291903
\(737\) −21.1301 −0.778336
\(738\) −22.6568 −0.834008
\(739\) 0.171298 0.00630131 0.00315065 0.999995i \(-0.498997\pi\)
0.00315065 + 0.999995i \(0.498997\pi\)
\(740\) 0.837164 0.0307748
\(741\) −2.74533 −0.100852
\(742\) 19.6287 0.720594
\(743\) −38.9687 −1.42962 −0.714811 0.699318i \(-0.753487\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(744\) 14.0949 0.516743
\(745\) −1.67911 −0.0615179
\(746\) 12.4902 0.457297
\(747\) 35.8035 1.30998
\(748\) 15.5405 0.568216
\(749\) −19.1400 −0.699359
\(750\) 9.04360 0.330226
\(751\) 12.3065 0.449070 0.224535 0.974466i \(-0.427914\pi\)
0.224535 + 0.974466i \(0.427914\pi\)
\(752\) −11.9910 −0.437265
\(753\) −36.6462 −1.33546
\(754\) −0.373450 −0.0136002
\(755\) 35.3912 1.28802
\(756\) −11.8418 −0.430683
\(757\) −2.40537 −0.0874246 −0.0437123 0.999044i \(-0.513918\pi\)
−0.0437123 + 0.999044i \(0.513918\pi\)
\(758\) −14.1273 −0.513127
\(759\) 100.239 3.63844
\(760\) −14.5613 −0.528195
\(761\) −15.1862 −0.550501 −0.275251 0.961373i \(-0.588761\pi\)
−0.275251 + 0.961373i \(0.588761\pi\)
\(762\) 49.6329 1.79801
\(763\) 8.83441 0.319827
\(764\) 15.5119 0.561201
\(765\) 43.4293 1.57019
\(766\) 34.1908 1.23536
\(767\) 2.15235 0.0777167
\(768\) −2.71506 −0.0979712
\(769\) 15.8385 0.571151 0.285576 0.958356i \(-0.407815\pi\)
0.285576 + 0.958356i \(0.407815\pi\)
\(770\) −44.1853 −1.59233
\(771\) 50.2247 1.80880
\(772\) 20.2688 0.729491
\(773\) 24.4928 0.880944 0.440472 0.897766i \(-0.354811\pi\)
0.440472 + 0.897766i \(0.354811\pi\)
\(774\) 3.89035 0.139836
\(775\) 20.1548 0.723983
\(776\) −8.00436 −0.287340
\(777\) 2.42526 0.0870057
\(778\) 16.7005 0.598743
\(779\) −25.3222 −0.907261
\(780\) −1.67465 −0.0599620
\(781\) −8.02155 −0.287034
\(782\) 26.3974 0.943971
\(783\) 6.71951 0.240136
\(784\) 3.11267 0.111167
\(785\) 55.9568 1.99719
\(786\) −31.0553 −1.10770
\(787\) −43.5080 −1.55089 −0.775446 0.631413i \(-0.782475\pi\)
−0.775446 + 0.631413i \(0.782475\pi\)
\(788\) 19.8796 0.708181
\(789\) −55.8847 −1.98955
\(790\) 17.4624 0.621284
\(791\) 31.7435 1.12867
\(792\) 20.3805 0.724188
\(793\) −1.34916 −0.0479099
\(794\) −3.64414 −0.129326
\(795\) −49.9463 −1.77141
\(796\) −1.66224 −0.0589164
\(797\) 0.437157 0.0154849 0.00774245 0.999970i \(-0.497535\pi\)
0.00774245 + 0.999970i \(0.497535\pi\)
\(798\) −42.1840 −1.49330
\(799\) 39.9704 1.41405
\(800\) −3.88237 −0.137263
\(801\) −40.4310 −1.42856
\(802\) 19.8567 0.701165
\(803\) −51.2926 −1.81008
\(804\) −12.3055 −0.433982
\(805\) −75.0542 −2.64531
\(806\) 1.07439 0.0378438
\(807\) −82.7580 −2.91322
\(808\) −1.16145 −0.0408597
\(809\) −20.4158 −0.717783 −0.358891 0.933379i \(-0.616845\pi\)
−0.358891 + 0.933379i \(0.616845\pi\)
\(810\) −8.95379 −0.314604
\(811\) −7.47920 −0.262630 −0.131315 0.991341i \(-0.541920\pi\)
−0.131315 + 0.991341i \(0.541920\pi\)
\(812\) −5.73832 −0.201376
\(813\) 7.44571 0.261133
\(814\) −1.30956 −0.0459002
\(815\) −15.7234 −0.550768
\(816\) 9.05031 0.316824
\(817\) 4.34801 0.152118
\(818\) 18.5685 0.649231
\(819\) −2.87704 −0.100532
\(820\) −15.4465 −0.539414
\(821\) −34.6098 −1.20789 −0.603945 0.797026i \(-0.706405\pi\)
−0.603945 + 0.797026i \(0.706405\pi\)
\(822\) 48.3156 1.68520
\(823\) 8.69650 0.303141 0.151570 0.988446i \(-0.451567\pi\)
0.151570 + 0.988446i \(0.451567\pi\)
\(824\) 14.4312 0.502734
\(825\) 49.1424 1.71092
\(826\) 33.0724 1.15073
\(827\) −23.8248 −0.828470 −0.414235 0.910170i \(-0.635951\pi\)
−0.414235 + 0.910170i \(0.635951\pi\)
\(828\) 34.6187 1.20308
\(829\) −21.9911 −0.763781 −0.381890 0.924208i \(-0.624727\pi\)
−0.381890 + 0.924208i \(0.624727\pi\)
\(830\) 24.4093 0.847260
\(831\) −21.1897 −0.735062
\(832\) −0.206957 −0.00717494
\(833\) −10.3757 −0.359496
\(834\) 22.2724 0.771231
\(835\) −28.0140 −0.969466
\(836\) 22.7780 0.787795
\(837\) −19.3316 −0.668197
\(838\) 14.9158 0.515257
\(839\) 57.0136 1.96833 0.984165 0.177257i \(-0.0567225\pi\)
0.984165 + 0.177257i \(0.0567225\pi\)
\(840\) −25.7322 −0.887844
\(841\) −25.7438 −0.887719
\(842\) 25.5757 0.881398
\(843\) 36.9496 1.27261
\(844\) 3.03770 0.104562
\(845\) 38.6166 1.32845
\(846\) 52.4188 1.80220
\(847\) 34.1379 1.17299
\(848\) −6.17248 −0.211964
\(849\) −23.8580 −0.818806
\(850\) 12.9414 0.443886
\(851\) −2.22446 −0.0762534
\(852\) −4.67151 −0.160043
\(853\) 54.1597 1.85439 0.927196 0.374575i \(-0.122211\pi\)
0.927196 + 0.374575i \(0.122211\pi\)
\(854\) −20.7307 −0.709392
\(855\) 63.6553 2.17697
\(856\) 6.01878 0.205718
\(857\) −54.2068 −1.85167 −0.925835 0.377929i \(-0.876636\pi\)
−0.925835 + 0.377929i \(0.876636\pi\)
\(858\) 2.61962 0.0894325
\(859\) 30.7914 1.05059 0.525295 0.850920i \(-0.323955\pi\)
0.525295 + 0.850920i \(0.323955\pi\)
\(860\) 2.65228 0.0904419
\(861\) −44.7483 −1.52502
\(862\) 2.65323 0.0903695
\(863\) 6.74771 0.229695 0.114847 0.993383i \(-0.463362\pi\)
0.114847 + 0.993383i \(0.463362\pi\)
\(864\) 3.72379 0.126686
\(865\) 10.0966 0.343294
\(866\) 12.7148 0.432067
\(867\) 15.9879 0.542977
\(868\) 16.5088 0.560345
\(869\) −27.3161 −0.926636
\(870\) 14.6014 0.495035
\(871\) −0.937995 −0.0317827
\(872\) −2.77808 −0.0940776
\(873\) 34.9913 1.18428
\(874\) 38.6913 1.30875
\(875\) 10.5924 0.358089
\(876\) −29.8713 −1.00926
\(877\) −3.33844 −0.112731 −0.0563655 0.998410i \(-0.517951\pi\)
−0.0563655 + 0.998410i \(0.517951\pi\)
\(878\) 10.0130 0.337923
\(879\) 9.91847 0.334542
\(880\) 13.8946 0.468385
\(881\) 10.0319 0.337985 0.168992 0.985617i \(-0.445949\pi\)
0.168992 + 0.985617i \(0.445949\pi\)
\(882\) −13.6071 −0.458176
\(883\) −3.32455 −0.111880 −0.0559400 0.998434i \(-0.517816\pi\)
−0.0559400 + 0.998434i \(0.517816\pi\)
\(884\) 0.689865 0.0232027
\(885\) −84.1542 −2.82881
\(886\) −15.6462 −0.525646
\(887\) 43.8304 1.47168 0.735841 0.677155i \(-0.236787\pi\)
0.735841 + 0.677155i \(0.236787\pi\)
\(888\) −0.762650 −0.0255929
\(889\) 58.1331 1.94972
\(890\) −27.5642 −0.923954
\(891\) 14.0063 0.469228
\(892\) −10.3577 −0.346801
\(893\) 58.5855 1.96049
\(894\) 1.52966 0.0511594
\(895\) −37.9978 −1.27012
\(896\) −3.18004 −0.106238
\(897\) 4.44976 0.148573
\(898\) −1.71080 −0.0570902
\(899\) −9.36773 −0.312431
\(900\) 16.9719 0.565730
\(901\) 20.5752 0.685459
\(902\) 24.1627 0.804529
\(903\) 7.68363 0.255695
\(904\) −9.98211 −0.332000
\(905\) −24.8329 −0.825472
\(906\) −32.2411 −1.07114
\(907\) −12.2466 −0.406641 −0.203321 0.979112i \(-0.565173\pi\)
−0.203321 + 0.979112i \(0.565173\pi\)
\(908\) 6.77101 0.224704
\(909\) 5.07732 0.168404
\(910\) −1.96145 −0.0650214
\(911\) 33.0019 1.09340 0.546701 0.837328i \(-0.315883\pi\)
0.546701 + 0.837328i \(0.315883\pi\)
\(912\) 13.2652 0.439256
\(913\) −38.1831 −1.26368
\(914\) 28.2034 0.932884
\(915\) 52.7504 1.74387
\(916\) 7.30024 0.241207
\(917\) −36.3738 −1.20117
\(918\) −12.4128 −0.409683
\(919\) 20.4217 0.673649 0.336825 0.941567i \(-0.390647\pi\)
0.336825 + 0.941567i \(0.390647\pi\)
\(920\) 23.6016 0.778123
\(921\) 33.3938 1.10036
\(922\) −19.2700 −0.634625
\(923\) −0.356088 −0.0117208
\(924\) 40.2524 1.32421
\(925\) −1.09054 −0.0358569
\(926\) 32.2347 1.05930
\(927\) −63.0864 −2.07203
\(928\) 1.80448 0.0592350
\(929\) −3.02829 −0.0993551 −0.0496775 0.998765i \(-0.515819\pi\)
−0.0496775 + 0.998765i \(0.515819\pi\)
\(930\) −42.0074 −1.37748
\(931\) −15.2079 −0.498418
\(932\) −25.5717 −0.837628
\(933\) −86.7180 −2.83902
\(934\) 32.8624 1.07529
\(935\) −46.3158 −1.51469
\(936\) 0.904719 0.0295717
\(937\) −5.39320 −0.176188 −0.0880941 0.996112i \(-0.528078\pi\)
−0.0880941 + 0.996112i \(0.528078\pi\)
\(938\) −14.4130 −0.470600
\(939\) −71.6592 −2.33851
\(940\) 35.7370 1.16561
\(941\) −12.8638 −0.419347 −0.209674 0.977771i \(-0.567240\pi\)
−0.209674 + 0.977771i \(0.567240\pi\)
\(942\) −50.9762 −1.66090
\(943\) 41.0433 1.33655
\(944\) −10.4000 −0.338490
\(945\) 35.2925 1.14807
\(946\) −4.14892 −0.134893
\(947\) 10.8217 0.351657 0.175828 0.984421i \(-0.443740\pi\)
0.175828 + 0.984421i \(0.443740\pi\)
\(948\) −15.9081 −0.516671
\(949\) −2.27696 −0.0739131
\(950\) 18.9685 0.615420
\(951\) −51.8662 −1.68188
\(952\) 10.6003 0.343557
\(953\) −10.2430 −0.331803 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(954\) 26.9832 0.873613
\(955\) −46.2306 −1.49599
\(956\) 19.1259 0.618575
\(957\) −22.8408 −0.738338
\(958\) 4.90869 0.158593
\(959\) 56.5902 1.82739
\(960\) 8.09177 0.261161
\(961\) −4.04966 −0.130634
\(962\) −0.0581335 −0.00187430
\(963\) −26.3113 −0.847870
\(964\) −6.79789 −0.218945
\(965\) −60.4078 −1.94460
\(966\) 68.3737 2.19989
\(967\) −10.7481 −0.345635 −0.172818 0.984954i \(-0.555287\pi\)
−0.172818 + 0.984954i \(0.555287\pi\)
\(968\) −10.7350 −0.345037
\(969\) −44.2180 −1.42049
\(970\) 23.8556 0.765958
\(971\) −30.7645 −0.987280 −0.493640 0.869666i \(-0.664334\pi\)
−0.493640 + 0.869666i \(0.664334\pi\)
\(972\) 19.3282 0.619952
\(973\) 26.0868 0.836305
\(974\) −7.40585 −0.237299
\(975\) 2.18150 0.0698640
\(976\) 6.51902 0.208669
\(977\) 27.7488 0.887764 0.443882 0.896085i \(-0.353601\pi\)
0.443882 + 0.896085i \(0.353601\pi\)
\(978\) 14.3239 0.458028
\(979\) 43.1182 1.37806
\(980\) −9.27678 −0.296336
\(981\) 12.1445 0.387743
\(982\) 19.5284 0.623177
\(983\) 18.6357 0.594388 0.297194 0.954817i \(-0.403949\pi\)
0.297194 + 0.954817i \(0.403949\pi\)
\(984\) 14.0716 0.448586
\(985\) −59.2478 −1.88779
\(986\) −6.01501 −0.191557
\(987\) 103.530 3.29539
\(988\) 1.01115 0.0321690
\(989\) −7.04745 −0.224096
\(990\) −60.7405 −1.93046
\(991\) 12.5523 0.398736 0.199368 0.979925i \(-0.436111\pi\)
0.199368 + 0.979925i \(0.436111\pi\)
\(992\) −5.19137 −0.164826
\(993\) −91.7159 −2.91052
\(994\) −5.47156 −0.173547
\(995\) 4.95401 0.157053
\(996\) −22.2367 −0.704597
\(997\) −18.7170 −0.592774 −0.296387 0.955068i \(-0.595782\pi\)
−0.296387 + 0.955068i \(0.595782\pi\)
\(998\) −33.7657 −1.06883
\(999\) 1.04600 0.0330940
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 8038.2.a.c.1.10 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8038.2.a.c.1.10 84 1.1 even 1 trivial