Properties

Label 8015.2.a.i.1.8
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $1$
Dimension $44$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, 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("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(1\)
Dimension: \(44\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.87978 q^{2} +3.08968 q^{3} +1.53356 q^{4} +1.00000 q^{5} -5.80791 q^{6} -1.00000 q^{7} +0.876807 q^{8} +6.54615 q^{9} +O(q^{10})\) \(q-1.87978 q^{2} +3.08968 q^{3} +1.53356 q^{4} +1.00000 q^{5} -5.80791 q^{6} -1.00000 q^{7} +0.876807 q^{8} +6.54615 q^{9} -1.87978 q^{10} -4.11760 q^{11} +4.73821 q^{12} +0.273088 q^{13} +1.87978 q^{14} +3.08968 q^{15} -4.71532 q^{16} +4.88218 q^{17} -12.3053 q^{18} -2.85217 q^{19} +1.53356 q^{20} -3.08968 q^{21} +7.74017 q^{22} -7.60448 q^{23} +2.70906 q^{24} +1.00000 q^{25} -0.513344 q^{26} +10.9565 q^{27} -1.53356 q^{28} +0.390236 q^{29} -5.80791 q^{30} +3.68320 q^{31} +7.11012 q^{32} -12.7221 q^{33} -9.17741 q^{34} -1.00000 q^{35} +10.0389 q^{36} -10.8320 q^{37} +5.36144 q^{38} +0.843755 q^{39} +0.876807 q^{40} -11.3586 q^{41} +5.80791 q^{42} +0.586083 q^{43} -6.31458 q^{44} +6.54615 q^{45} +14.2947 q^{46} +1.17774 q^{47} -14.5688 q^{48} +1.00000 q^{49} -1.87978 q^{50} +15.0844 q^{51} +0.418796 q^{52} -5.64463 q^{53} -20.5957 q^{54} -4.11760 q^{55} -0.876807 q^{56} -8.81231 q^{57} -0.733556 q^{58} -9.44277 q^{59} +4.73821 q^{60} -7.72166 q^{61} -6.92359 q^{62} -6.54615 q^{63} -3.93481 q^{64} +0.273088 q^{65} +23.9147 q^{66} +10.3534 q^{67} +7.48711 q^{68} -23.4954 q^{69} +1.87978 q^{70} +11.7403 q^{71} +5.73971 q^{72} -11.6305 q^{73} +20.3618 q^{74} +3.08968 q^{75} -4.37397 q^{76} +4.11760 q^{77} -1.58607 q^{78} -2.29928 q^{79} -4.71532 q^{80} +14.2136 q^{81} +21.3515 q^{82} -0.722398 q^{83} -4.73821 q^{84} +4.88218 q^{85} -1.10171 q^{86} +1.20571 q^{87} -3.61034 q^{88} +7.10098 q^{89} -12.3053 q^{90} -0.273088 q^{91} -11.6619 q^{92} +11.3799 q^{93} -2.21389 q^{94} -2.85217 q^{95} +21.9680 q^{96} -15.4305 q^{97} -1.87978 q^{98} -26.9544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87978 −1.32920 −0.664601 0.747198i \(-0.731399\pi\)
−0.664601 + 0.747198i \(0.731399\pi\)
\(3\) 3.08968 1.78383 0.891915 0.452203i \(-0.149362\pi\)
0.891915 + 0.452203i \(0.149362\pi\)
\(4\) 1.53356 0.766779
\(5\) 1.00000 0.447214
\(6\) −5.80791 −2.37107
\(7\) −1.00000 −0.377964
\(8\) 0.876807 0.309998
\(9\) 6.54615 2.18205
\(10\) −1.87978 −0.594437
\(11\) −4.11760 −1.24150 −0.620752 0.784007i \(-0.713173\pi\)
−0.620752 + 0.784007i \(0.713173\pi\)
\(12\) 4.73821 1.36780
\(13\) 0.273088 0.0757409 0.0378705 0.999283i \(-0.487943\pi\)
0.0378705 + 0.999283i \(0.487943\pi\)
\(14\) 1.87978 0.502391
\(15\) 3.08968 0.797753
\(16\) −4.71532 −1.17883
\(17\) 4.88218 1.18410 0.592052 0.805900i \(-0.298318\pi\)
0.592052 + 0.805900i \(0.298318\pi\)
\(18\) −12.3053 −2.90038
\(19\) −2.85217 −0.654333 −0.327167 0.944967i \(-0.606094\pi\)
−0.327167 + 0.944967i \(0.606094\pi\)
\(20\) 1.53356 0.342914
\(21\) −3.08968 −0.674224
\(22\) 7.74017 1.65021
\(23\) −7.60448 −1.58564 −0.792822 0.609453i \(-0.791389\pi\)
−0.792822 + 0.609453i \(0.791389\pi\)
\(24\) 2.70906 0.552984
\(25\) 1.00000 0.200000
\(26\) −0.513344 −0.100675
\(27\) 10.9565 2.10857
\(28\) −1.53356 −0.289815
\(29\) 0.390236 0.0724650 0.0362325 0.999343i \(-0.488464\pi\)
0.0362325 + 0.999343i \(0.488464\pi\)
\(30\) −5.80791 −1.06038
\(31\) 3.68320 0.661522 0.330761 0.943715i \(-0.392695\pi\)
0.330761 + 0.943715i \(0.392695\pi\)
\(32\) 7.11012 1.25690
\(33\) −12.7221 −2.21463
\(34\) −9.17741 −1.57391
\(35\) −1.00000 −0.169031
\(36\) 10.0389 1.67315
\(37\) −10.8320 −1.78077 −0.890386 0.455205i \(-0.849566\pi\)
−0.890386 + 0.455205i \(0.849566\pi\)
\(38\) 5.36144 0.869741
\(39\) 0.843755 0.135109
\(40\) 0.876807 0.138635
\(41\) −11.3586 −1.77391 −0.886954 0.461858i \(-0.847183\pi\)
−0.886954 + 0.461858i \(0.847183\pi\)
\(42\) 5.80791 0.896181
\(43\) 0.586083 0.0893769 0.0446884 0.999001i \(-0.485770\pi\)
0.0446884 + 0.999001i \(0.485770\pi\)
\(44\) −6.31458 −0.951958
\(45\) 6.54615 0.975842
\(46\) 14.2947 2.10764
\(47\) 1.17774 0.171791 0.0858956 0.996304i \(-0.472625\pi\)
0.0858956 + 0.996304i \(0.472625\pi\)
\(48\) −14.5688 −2.10283
\(49\) 1.00000 0.142857
\(50\) −1.87978 −0.265840
\(51\) 15.0844 2.11224
\(52\) 0.418796 0.0580765
\(53\) −5.64463 −0.775349 −0.387674 0.921796i \(-0.626722\pi\)
−0.387674 + 0.921796i \(0.626722\pi\)
\(54\) −20.5957 −2.80272
\(55\) −4.11760 −0.555217
\(56\) −0.876807 −0.117168
\(57\) −8.81231 −1.16722
\(58\) −0.733556 −0.0963207
\(59\) −9.44277 −1.22934 −0.614672 0.788783i \(-0.710711\pi\)
−0.614672 + 0.788783i \(0.710711\pi\)
\(60\) 4.73821 0.611700
\(61\) −7.72166 −0.988657 −0.494329 0.869275i \(-0.664586\pi\)
−0.494329 + 0.869275i \(0.664586\pi\)
\(62\) −6.92359 −0.879296
\(63\) −6.54615 −0.824737
\(64\) −3.93481 −0.491851
\(65\) 0.273088 0.0338724
\(66\) 23.9147 2.94369
\(67\) 10.3534 1.26487 0.632435 0.774613i \(-0.282056\pi\)
0.632435 + 0.774613i \(0.282056\pi\)
\(68\) 7.48711 0.907945
\(69\) −23.4954 −2.82852
\(70\) 1.87978 0.224676
\(71\) 11.7403 1.39332 0.696661 0.717401i \(-0.254668\pi\)
0.696661 + 0.717401i \(0.254668\pi\)
\(72\) 5.73971 0.676431
\(73\) −11.6305 −1.36125 −0.680624 0.732633i \(-0.738291\pi\)
−0.680624 + 0.732633i \(0.738291\pi\)
\(74\) 20.3618 2.36701
\(75\) 3.08968 0.356766
\(76\) −4.37397 −0.501729
\(77\) 4.11760 0.469244
\(78\) −1.58607 −0.179587
\(79\) −2.29928 −0.258690 −0.129345 0.991600i \(-0.541287\pi\)
−0.129345 + 0.991600i \(0.541287\pi\)
\(80\) −4.71532 −0.527188
\(81\) 14.2136 1.57929
\(82\) 21.3515 2.35788
\(83\) −0.722398 −0.0792934 −0.0396467 0.999214i \(-0.512623\pi\)
−0.0396467 + 0.999214i \(0.512623\pi\)
\(84\) −4.73821 −0.516981
\(85\) 4.88218 0.529547
\(86\) −1.10171 −0.118800
\(87\) 1.20571 0.129265
\(88\) −3.61034 −0.384864
\(89\) 7.10098 0.752702 0.376351 0.926477i \(-0.377179\pi\)
0.376351 + 0.926477i \(0.377179\pi\)
\(90\) −12.3053 −1.29709
\(91\) −0.273088 −0.0286274
\(92\) −11.6619 −1.21584
\(93\) 11.3799 1.18004
\(94\) −2.21389 −0.228345
\(95\) −2.85217 −0.292627
\(96\) 21.9680 2.24210
\(97\) −15.4305 −1.56673 −0.783363 0.621565i \(-0.786497\pi\)
−0.783363 + 0.621565i \(0.786497\pi\)
\(98\) −1.87978 −0.189886
\(99\) −26.9544 −2.70902
\(100\) 1.53356 0.153356
\(101\) −11.1085 −1.10534 −0.552668 0.833402i \(-0.686390\pi\)
−0.552668 + 0.833402i \(0.686390\pi\)
\(102\) −28.3553 −2.80759
\(103\) −18.9383 −1.86605 −0.933023 0.359818i \(-0.882839\pi\)
−0.933023 + 0.359818i \(0.882839\pi\)
\(104\) 0.239445 0.0234795
\(105\) −3.08968 −0.301522
\(106\) 10.6106 1.03060
\(107\) −10.9789 −1.06137 −0.530686 0.847569i \(-0.678066\pi\)
−0.530686 + 0.847569i \(0.678066\pi\)
\(108\) 16.8024 1.61681
\(109\) 7.35037 0.704038 0.352019 0.935993i \(-0.385495\pi\)
0.352019 + 0.935993i \(0.385495\pi\)
\(110\) 7.74017 0.737996
\(111\) −33.4675 −3.17660
\(112\) 4.71532 0.445556
\(113\) 17.3099 1.62838 0.814190 0.580599i \(-0.197181\pi\)
0.814190 + 0.580599i \(0.197181\pi\)
\(114\) 16.5652 1.55147
\(115\) −7.60448 −0.709122
\(116\) 0.598450 0.0555646
\(117\) 1.78767 0.165270
\(118\) 17.7503 1.63405
\(119\) −4.88218 −0.447549
\(120\) 2.70906 0.247302
\(121\) 5.95464 0.541331
\(122\) 14.5150 1.31413
\(123\) −35.0943 −3.16435
\(124\) 5.64839 0.507241
\(125\) 1.00000 0.0894427
\(126\) 12.3053 1.09624
\(127\) 15.6918 1.39242 0.696210 0.717838i \(-0.254868\pi\)
0.696210 + 0.717838i \(0.254868\pi\)
\(128\) −6.82369 −0.603135
\(129\) 1.81081 0.159433
\(130\) −0.513344 −0.0450232
\(131\) 14.8642 1.29869 0.649345 0.760494i \(-0.275043\pi\)
0.649345 + 0.760494i \(0.275043\pi\)
\(132\) −19.5101 −1.69813
\(133\) 2.85217 0.247315
\(134\) −19.4621 −1.68127
\(135\) 10.9565 0.942983
\(136\) 4.28073 0.367070
\(137\) −20.1741 −1.72359 −0.861797 0.507254i \(-0.830661\pi\)
−0.861797 + 0.507254i \(0.830661\pi\)
\(138\) 44.1662 3.75967
\(139\) −6.10706 −0.517994 −0.258997 0.965878i \(-0.583392\pi\)
−0.258997 + 0.965878i \(0.583392\pi\)
\(140\) −1.53356 −0.129609
\(141\) 3.63885 0.306446
\(142\) −22.0692 −1.85201
\(143\) −1.12447 −0.0940326
\(144\) −30.8672 −2.57226
\(145\) 0.390236 0.0324073
\(146\) 21.8627 1.80937
\(147\) 3.08968 0.254833
\(148\) −16.6115 −1.36546
\(149\) 10.6447 0.872047 0.436023 0.899935i \(-0.356387\pi\)
0.436023 + 0.899935i \(0.356387\pi\)
\(150\) −5.80791 −0.474214
\(151\) 9.46042 0.769878 0.384939 0.922942i \(-0.374222\pi\)
0.384939 + 0.922942i \(0.374222\pi\)
\(152\) −2.50081 −0.202842
\(153\) 31.9595 2.58377
\(154\) −7.74017 −0.623720
\(155\) 3.68320 0.295842
\(156\) 1.29395 0.103599
\(157\) 23.5609 1.88037 0.940183 0.340671i \(-0.110654\pi\)
0.940183 + 0.340671i \(0.110654\pi\)
\(158\) 4.32214 0.343851
\(159\) −17.4401 −1.38309
\(160\) 7.11012 0.562105
\(161\) 7.60448 0.599317
\(162\) −26.7184 −2.09920
\(163\) −12.8723 −1.00824 −0.504119 0.863634i \(-0.668183\pi\)
−0.504119 + 0.863634i \(0.668183\pi\)
\(164\) −17.4190 −1.36019
\(165\) −12.7221 −0.990413
\(166\) 1.35795 0.105397
\(167\) −11.6269 −0.899719 −0.449859 0.893099i \(-0.648526\pi\)
−0.449859 + 0.893099i \(0.648526\pi\)
\(168\) −2.70906 −0.209008
\(169\) −12.9254 −0.994263
\(170\) −9.17741 −0.703875
\(171\) −18.6707 −1.42779
\(172\) 0.898793 0.0685323
\(173\) 1.76293 0.134033 0.0670167 0.997752i \(-0.478652\pi\)
0.0670167 + 0.997752i \(0.478652\pi\)
\(174\) −2.26646 −0.171820
\(175\) −1.00000 −0.0755929
\(176\) 19.4158 1.46352
\(177\) −29.1752 −2.19294
\(178\) −13.3482 −1.00049
\(179\) −11.3007 −0.844650 −0.422325 0.906444i \(-0.638786\pi\)
−0.422325 + 0.906444i \(0.638786\pi\)
\(180\) 10.0389 0.748255
\(181\) 0.438301 0.0325786 0.0162893 0.999867i \(-0.494815\pi\)
0.0162893 + 0.999867i \(0.494815\pi\)
\(182\) 0.513344 0.0380516
\(183\) −23.8575 −1.76360
\(184\) −6.66767 −0.491547
\(185\) −10.8320 −0.796386
\(186\) −21.3917 −1.56851
\(187\) −20.1029 −1.47007
\(188\) 1.80613 0.131726
\(189\) −10.9565 −0.796966
\(190\) 5.36144 0.388960
\(191\) 13.0163 0.941828 0.470914 0.882179i \(-0.343924\pi\)
0.470914 + 0.882179i \(0.343924\pi\)
\(192\) −12.1573 −0.877378
\(193\) 10.3764 0.746910 0.373455 0.927648i \(-0.378173\pi\)
0.373455 + 0.927648i \(0.378173\pi\)
\(194\) 29.0058 2.08250
\(195\) 0.843755 0.0604225
\(196\) 1.53356 0.109540
\(197\) −4.03627 −0.287573 −0.143786 0.989609i \(-0.545928\pi\)
−0.143786 + 0.989609i \(0.545928\pi\)
\(198\) 50.6683 3.60084
\(199\) −8.14506 −0.577388 −0.288694 0.957421i \(-0.593221\pi\)
−0.288694 + 0.957421i \(0.593221\pi\)
\(200\) 0.876807 0.0619997
\(201\) 31.9888 2.25631
\(202\) 20.8815 1.46921
\(203\) −0.390236 −0.0273892
\(204\) 23.1328 1.61962
\(205\) −11.3586 −0.793316
\(206\) 35.5997 2.48035
\(207\) −49.7801 −3.45995
\(208\) −1.28770 −0.0892856
\(209\) 11.7441 0.812357
\(210\) 5.80791 0.400784
\(211\) 7.51833 0.517583 0.258792 0.965933i \(-0.416676\pi\)
0.258792 + 0.965933i \(0.416676\pi\)
\(212\) −8.65636 −0.594521
\(213\) 36.2739 2.48545
\(214\) 20.6379 1.41078
\(215\) 0.586083 0.0399706
\(216\) 9.60672 0.653655
\(217\) −3.68320 −0.250032
\(218\) −13.8171 −0.935809
\(219\) −35.9346 −2.42823
\(220\) −6.31458 −0.425729
\(221\) 1.33326 0.0896850
\(222\) 62.9114 4.22234
\(223\) 15.8612 1.06214 0.531071 0.847327i \(-0.321790\pi\)
0.531071 + 0.847327i \(0.321790\pi\)
\(224\) −7.11012 −0.475065
\(225\) 6.54615 0.436410
\(226\) −32.5388 −2.16445
\(227\) −19.5954 −1.30059 −0.650297 0.759680i \(-0.725356\pi\)
−0.650297 + 0.759680i \(0.725356\pi\)
\(228\) −13.5142 −0.894999
\(229\) 1.00000 0.0660819
\(230\) 14.2947 0.942566
\(231\) 12.7221 0.837052
\(232\) 0.342162 0.0224640
\(233\) 6.27293 0.410953 0.205477 0.978662i \(-0.434126\pi\)
0.205477 + 0.978662i \(0.434126\pi\)
\(234\) −3.36042 −0.219678
\(235\) 1.17774 0.0768273
\(236\) −14.4810 −0.942634
\(237\) −7.10406 −0.461458
\(238\) 9.17741 0.594883
\(239\) 4.46549 0.288849 0.144424 0.989516i \(-0.453867\pi\)
0.144424 + 0.989516i \(0.453867\pi\)
\(240\) −14.5688 −0.940414
\(241\) 9.26330 0.596702 0.298351 0.954456i \(-0.403563\pi\)
0.298351 + 0.954456i \(0.403563\pi\)
\(242\) −11.1934 −0.719538
\(243\) 11.0461 0.708609
\(244\) −11.8416 −0.758081
\(245\) 1.00000 0.0638877
\(246\) 65.9695 4.20606
\(247\) −0.778893 −0.0495598
\(248\) 3.22945 0.205071
\(249\) −2.23198 −0.141446
\(250\) −1.87978 −0.118887
\(251\) −7.16465 −0.452229 −0.226114 0.974101i \(-0.572602\pi\)
−0.226114 + 0.974101i \(0.572602\pi\)
\(252\) −10.0389 −0.632391
\(253\) 31.3122 1.96858
\(254\) −29.4970 −1.85081
\(255\) 15.0844 0.944622
\(256\) 20.6966 1.29354
\(257\) −15.3430 −0.957067 −0.478534 0.878069i \(-0.658831\pi\)
−0.478534 + 0.878069i \(0.658831\pi\)
\(258\) −3.40392 −0.211919
\(259\) 10.8320 0.673069
\(260\) 0.418796 0.0259726
\(261\) 2.55454 0.158122
\(262\) −27.9413 −1.72622
\(263\) 4.44327 0.273984 0.136992 0.990572i \(-0.456257\pi\)
0.136992 + 0.990572i \(0.456257\pi\)
\(264\) −11.1548 −0.686532
\(265\) −5.64463 −0.346747
\(266\) −5.36144 −0.328731
\(267\) 21.9398 1.34269
\(268\) 15.8775 0.969875
\(269\) −5.07697 −0.309548 −0.154774 0.987950i \(-0.549465\pi\)
−0.154774 + 0.987950i \(0.549465\pi\)
\(270\) −20.5957 −1.25342
\(271\) −29.7934 −1.80982 −0.904911 0.425601i \(-0.860063\pi\)
−0.904911 + 0.425601i \(0.860063\pi\)
\(272\) −23.0210 −1.39586
\(273\) −0.843755 −0.0510664
\(274\) 37.9229 2.29100
\(275\) −4.11760 −0.248301
\(276\) −36.0316 −2.16885
\(277\) 9.02010 0.541965 0.270983 0.962584i \(-0.412651\pi\)
0.270983 + 0.962584i \(0.412651\pi\)
\(278\) 11.4799 0.688519
\(279\) 24.1108 1.44347
\(280\) −0.876807 −0.0523993
\(281\) −11.1578 −0.665616 −0.332808 0.942995i \(-0.607996\pi\)
−0.332808 + 0.942995i \(0.607996\pi\)
\(282\) −6.84022 −0.407329
\(283\) 11.6501 0.692529 0.346264 0.938137i \(-0.387450\pi\)
0.346264 + 0.938137i \(0.387450\pi\)
\(284\) 18.0045 1.06837
\(285\) −8.81231 −0.521996
\(286\) 2.11374 0.124988
\(287\) 11.3586 0.670474
\(288\) 46.5439 2.74263
\(289\) 6.83570 0.402100
\(290\) −0.733556 −0.0430759
\(291\) −47.6752 −2.79477
\(292\) −17.8361 −1.04378
\(293\) 8.75204 0.511299 0.255650 0.966769i \(-0.417711\pi\)
0.255650 + 0.966769i \(0.417711\pi\)
\(294\) −5.80791 −0.338724
\(295\) −9.44277 −0.549779
\(296\) −9.49760 −0.552037
\(297\) −45.1144 −2.61780
\(298\) −20.0096 −1.15913
\(299\) −2.07669 −0.120098
\(300\) 4.73821 0.273561
\(301\) −0.586083 −0.0337813
\(302\) −17.7835 −1.02332
\(303\) −34.3217 −1.97173
\(304\) 13.4489 0.771347
\(305\) −7.72166 −0.442141
\(306\) −60.0767 −3.43435
\(307\) 5.16995 0.295065 0.147532 0.989057i \(-0.452867\pi\)
0.147532 + 0.989057i \(0.452867\pi\)
\(308\) 6.31458 0.359806
\(309\) −58.5133 −3.32871
\(310\) −6.92359 −0.393233
\(311\) 1.16283 0.0659379 0.0329689 0.999456i \(-0.489504\pi\)
0.0329689 + 0.999456i \(0.489504\pi\)
\(312\) 0.739811 0.0418835
\(313\) −16.9049 −0.955523 −0.477761 0.878490i \(-0.658552\pi\)
−0.477761 + 0.878490i \(0.658552\pi\)
\(314\) −44.2892 −2.49939
\(315\) −6.54615 −0.368834
\(316\) −3.52608 −0.198358
\(317\) −2.24685 −0.126196 −0.0630979 0.998007i \(-0.520098\pi\)
−0.0630979 + 0.998007i \(0.520098\pi\)
\(318\) 32.7835 1.83841
\(319\) −1.60684 −0.0899656
\(320\) −3.93481 −0.219962
\(321\) −33.9214 −1.89331
\(322\) −14.2947 −0.796614
\(323\) −13.9248 −0.774798
\(324\) 21.7974 1.21097
\(325\) 0.273088 0.0151482
\(326\) 24.1971 1.34015
\(327\) 22.7103 1.25588
\(328\) −9.95926 −0.549908
\(329\) −1.17774 −0.0649309
\(330\) 23.9147 1.31646
\(331\) −0.994093 −0.0546403 −0.0273202 0.999627i \(-0.508697\pi\)
−0.0273202 + 0.999627i \(0.508697\pi\)
\(332\) −1.10784 −0.0608005
\(333\) −70.9080 −3.88573
\(334\) 21.8560 1.19591
\(335\) 10.3534 0.565667
\(336\) 14.5688 0.794795
\(337\) 2.49224 0.135761 0.0678804 0.997693i \(-0.478376\pi\)
0.0678804 + 0.997693i \(0.478376\pi\)
\(338\) 24.2969 1.32158
\(339\) 53.4822 2.90475
\(340\) 7.48711 0.406045
\(341\) −15.1659 −0.821282
\(342\) 35.0968 1.89782
\(343\) −1.00000 −0.0539949
\(344\) 0.513882 0.0277067
\(345\) −23.4954 −1.26495
\(346\) −3.31392 −0.178158
\(347\) 21.5213 1.15533 0.577663 0.816275i \(-0.303965\pi\)
0.577663 + 0.816275i \(0.303965\pi\)
\(348\) 1.84902 0.0991179
\(349\) −14.5825 −0.780583 −0.390292 0.920691i \(-0.627626\pi\)
−0.390292 + 0.920691i \(0.627626\pi\)
\(350\) 1.87978 0.100478
\(351\) 2.99208 0.159705
\(352\) −29.2767 −1.56045
\(353\) −6.56600 −0.349473 −0.174737 0.984615i \(-0.555907\pi\)
−0.174737 + 0.984615i \(0.555907\pi\)
\(354\) 54.8428 2.91486
\(355\) 11.7403 0.623112
\(356\) 10.8898 0.577156
\(357\) −15.0844 −0.798351
\(358\) 21.2427 1.12271
\(359\) 1.24490 0.0657034 0.0328517 0.999460i \(-0.489541\pi\)
0.0328517 + 0.999460i \(0.489541\pi\)
\(360\) 5.73971 0.302509
\(361\) −10.8651 −0.571848
\(362\) −0.823907 −0.0433036
\(363\) 18.3980 0.965642
\(364\) −0.418796 −0.0219509
\(365\) −11.6305 −0.608769
\(366\) 44.8467 2.34418
\(367\) −15.7248 −0.820827 −0.410414 0.911899i \(-0.634616\pi\)
−0.410414 + 0.911899i \(0.634616\pi\)
\(368\) 35.8575 1.86920
\(369\) −74.3547 −3.87075
\(370\) 20.3618 1.05856
\(371\) 5.64463 0.293054
\(372\) 17.4518 0.904831
\(373\) −28.3215 −1.46643 −0.733215 0.679997i \(-0.761981\pi\)
−0.733215 + 0.679997i \(0.761981\pi\)
\(374\) 37.7889 1.95402
\(375\) 3.08968 0.159551
\(376\) 1.03265 0.0532549
\(377\) 0.106569 0.00548857
\(378\) 20.5957 1.05933
\(379\) 26.5688 1.36475 0.682374 0.731004i \(-0.260948\pi\)
0.682374 + 0.731004i \(0.260948\pi\)
\(380\) −4.37397 −0.224380
\(381\) 48.4826 2.48384
\(382\) −24.4678 −1.25188
\(383\) −2.67497 −0.136685 −0.0683423 0.997662i \(-0.521771\pi\)
−0.0683423 + 0.997662i \(0.521771\pi\)
\(384\) −21.0831 −1.07589
\(385\) 4.11760 0.209852
\(386\) −19.5053 −0.992795
\(387\) 3.83659 0.195025
\(388\) −23.6635 −1.20133
\(389\) −15.7293 −0.797509 −0.398754 0.917058i \(-0.630557\pi\)
−0.398754 + 0.917058i \(0.630557\pi\)
\(390\) −1.58607 −0.0803138
\(391\) −37.1265 −1.87757
\(392\) 0.876807 0.0442855
\(393\) 45.9256 2.31664
\(394\) 7.58729 0.382242
\(395\) −2.29928 −0.115689
\(396\) −41.3362 −2.07722
\(397\) 1.32960 0.0667305 0.0333652 0.999443i \(-0.489378\pi\)
0.0333652 + 0.999443i \(0.489378\pi\)
\(398\) 15.3109 0.767466
\(399\) 8.81231 0.441167
\(400\) −4.71532 −0.235766
\(401\) −13.1006 −0.654212 −0.327106 0.944988i \(-0.606073\pi\)
−0.327106 + 0.944988i \(0.606073\pi\)
\(402\) −60.1317 −2.99910
\(403\) 1.00584 0.0501043
\(404\) −17.0355 −0.847547
\(405\) 14.2136 0.706280
\(406\) 0.733556 0.0364058
\(407\) 44.6019 2.21084
\(408\) 13.2261 0.654790
\(409\) −7.20693 −0.356360 −0.178180 0.983998i \(-0.557021\pi\)
−0.178180 + 0.983998i \(0.557021\pi\)
\(410\) 21.3515 1.05448
\(411\) −62.3317 −3.07460
\(412\) −29.0430 −1.43084
\(413\) 9.44277 0.464648
\(414\) 93.5754 4.59898
\(415\) −0.722398 −0.0354611
\(416\) 1.94169 0.0951991
\(417\) −18.8689 −0.924014
\(418\) −22.0763 −1.07979
\(419\) 17.1308 0.836894 0.418447 0.908241i \(-0.362575\pi\)
0.418447 + 0.908241i \(0.362575\pi\)
\(420\) −4.73821 −0.231201
\(421\) −40.3820 −1.96810 −0.984050 0.177891i \(-0.943073\pi\)
−0.984050 + 0.177891i \(0.943073\pi\)
\(422\) −14.1328 −0.687973
\(423\) 7.70966 0.374857
\(424\) −4.94925 −0.240357
\(425\) 4.88218 0.236821
\(426\) −68.1869 −3.30366
\(427\) 7.72166 0.373677
\(428\) −16.8368 −0.813837
\(429\) −3.47425 −0.167738
\(430\) −1.10171 −0.0531290
\(431\) 3.59873 0.173345 0.0866725 0.996237i \(-0.472377\pi\)
0.0866725 + 0.996237i \(0.472377\pi\)
\(432\) −51.6633 −2.48565
\(433\) 28.1791 1.35420 0.677100 0.735891i \(-0.263236\pi\)
0.677100 + 0.735891i \(0.263236\pi\)
\(434\) 6.92359 0.332343
\(435\) 1.20571 0.0578092
\(436\) 11.2722 0.539841
\(437\) 21.6893 1.03754
\(438\) 67.5490 3.22762
\(439\) 25.4740 1.21581 0.607904 0.794010i \(-0.292011\pi\)
0.607904 + 0.794010i \(0.292011\pi\)
\(440\) −3.61034 −0.172116
\(441\) 6.54615 0.311721
\(442\) −2.50624 −0.119210
\(443\) 19.4683 0.924968 0.462484 0.886628i \(-0.346958\pi\)
0.462484 + 0.886628i \(0.346958\pi\)
\(444\) −51.3244 −2.43575
\(445\) 7.10098 0.336619
\(446\) −29.8154 −1.41180
\(447\) 32.8887 1.55558
\(448\) 3.93481 0.185902
\(449\) 4.41952 0.208570 0.104285 0.994547i \(-0.466745\pi\)
0.104285 + 0.994547i \(0.466745\pi\)
\(450\) −12.3053 −0.580077
\(451\) 46.7700 2.20231
\(452\) 26.5457 1.24861
\(453\) 29.2297 1.37333
\(454\) 36.8350 1.72875
\(455\) −0.273088 −0.0128026
\(456\) −7.72670 −0.361836
\(457\) −11.2328 −0.525450 −0.262725 0.964871i \(-0.584621\pi\)
−0.262725 + 0.964871i \(0.584621\pi\)
\(458\) −1.87978 −0.0878362
\(459\) 53.4915 2.49677
\(460\) −11.6619 −0.543739
\(461\) 29.6531 1.38108 0.690542 0.723292i \(-0.257372\pi\)
0.690542 + 0.723292i \(0.257372\pi\)
\(462\) −23.9147 −1.11261
\(463\) −30.8834 −1.43527 −0.717637 0.696418i \(-0.754776\pi\)
−0.717637 + 0.696418i \(0.754776\pi\)
\(464\) −1.84009 −0.0854239
\(465\) 11.3799 0.527731
\(466\) −11.7917 −0.546240
\(467\) −28.8611 −1.33553 −0.667766 0.744371i \(-0.732749\pi\)
−0.667766 + 0.744371i \(0.732749\pi\)
\(468\) 2.74150 0.126726
\(469\) −10.3534 −0.478076
\(470\) −2.21389 −0.102119
\(471\) 72.7958 3.35425
\(472\) −8.27949 −0.381094
\(473\) −2.41326 −0.110962
\(474\) 13.3540 0.613371
\(475\) −2.85217 −0.130867
\(476\) −7.48711 −0.343171
\(477\) −36.9506 −1.69185
\(478\) −8.39412 −0.383938
\(479\) −2.78355 −0.127184 −0.0635919 0.997976i \(-0.520256\pi\)
−0.0635919 + 0.997976i \(0.520256\pi\)
\(480\) 21.9680 1.00270
\(481\) −2.95809 −0.134877
\(482\) −17.4129 −0.793137
\(483\) 23.4954 1.06908
\(484\) 9.13178 0.415081
\(485\) −15.4305 −0.700661
\(486\) −20.7642 −0.941885
\(487\) 35.3405 1.60143 0.800715 0.599046i \(-0.204453\pi\)
0.800715 + 0.599046i \(0.204453\pi\)
\(488\) −6.77041 −0.306482
\(489\) −39.7714 −1.79852
\(490\) −1.87978 −0.0849196
\(491\) 0.205490 0.00927361 0.00463681 0.999989i \(-0.498524\pi\)
0.00463681 + 0.999989i \(0.498524\pi\)
\(492\) −53.8192 −2.42636
\(493\) 1.90520 0.0858061
\(494\) 1.46414 0.0658750
\(495\) −26.9544 −1.21151
\(496\) −17.3674 −0.779821
\(497\) −11.7403 −0.526626
\(498\) 4.19562 0.188010
\(499\) −13.9276 −0.623487 −0.311743 0.950166i \(-0.600913\pi\)
−0.311743 + 0.950166i \(0.600913\pi\)
\(500\) 1.53356 0.0685828
\(501\) −35.9235 −1.60495
\(502\) 13.4679 0.601103
\(503\) 40.5982 1.81018 0.905091 0.425217i \(-0.139802\pi\)
0.905091 + 0.425217i \(0.139802\pi\)
\(504\) −5.73971 −0.255667
\(505\) −11.1085 −0.494321
\(506\) −58.8600 −2.61664
\(507\) −39.9355 −1.77360
\(508\) 24.0642 1.06768
\(509\) −12.4269 −0.550813 −0.275406 0.961328i \(-0.588812\pi\)
−0.275406 + 0.961328i \(0.588812\pi\)
\(510\) −28.3553 −1.25559
\(511\) 11.6305 0.514503
\(512\) −25.2576 −1.11624
\(513\) −31.2498 −1.37971
\(514\) 28.8413 1.27214
\(515\) −18.9383 −0.834521
\(516\) 2.77699 0.122250
\(517\) −4.84947 −0.213279
\(518\) −20.3618 −0.894645
\(519\) 5.44691 0.239093
\(520\) 0.239445 0.0105004
\(521\) 44.7863 1.96212 0.981062 0.193693i \(-0.0620467\pi\)
0.981062 + 0.193693i \(0.0620467\pi\)
\(522\) −4.80197 −0.210176
\(523\) −29.8999 −1.30743 −0.653715 0.756741i \(-0.726790\pi\)
−0.653715 + 0.756741i \(0.726790\pi\)
\(524\) 22.7951 0.995807
\(525\) −3.08968 −0.134845
\(526\) −8.35236 −0.364180
\(527\) 17.9820 0.783310
\(528\) 59.9887 2.61067
\(529\) 34.8281 1.51427
\(530\) 10.6106 0.460896
\(531\) −61.8137 −2.68249
\(532\) 4.37397 0.189636
\(533\) −3.10188 −0.134357
\(534\) −41.2419 −1.78471
\(535\) −10.9789 −0.474660
\(536\) 9.07794 0.392107
\(537\) −34.9154 −1.50671
\(538\) 9.54356 0.411452
\(539\) −4.11760 −0.177358
\(540\) 16.8024 0.723060
\(541\) 26.7008 1.14796 0.573979 0.818870i \(-0.305399\pi\)
0.573979 + 0.818870i \(0.305399\pi\)
\(542\) 56.0050 2.40562
\(543\) 1.35421 0.0581147
\(544\) 34.7129 1.48830
\(545\) 7.35037 0.314855
\(546\) 1.58607 0.0678775
\(547\) −42.0148 −1.79642 −0.898212 0.439563i \(-0.855133\pi\)
−0.898212 + 0.439563i \(0.855133\pi\)
\(548\) −30.9382 −1.32161
\(549\) −50.5471 −2.15730
\(550\) 7.74017 0.330042
\(551\) −1.11302 −0.0474163
\(552\) −20.6010 −0.876836
\(553\) 2.29928 0.0977755
\(554\) −16.9558 −0.720381
\(555\) −33.4675 −1.42062
\(556\) −9.36553 −0.397187
\(557\) 6.64563 0.281585 0.140792 0.990039i \(-0.455035\pi\)
0.140792 + 0.990039i \(0.455035\pi\)
\(558\) −45.3228 −1.91867
\(559\) 0.160052 0.00676949
\(560\) 4.71532 0.199258
\(561\) −62.1115 −2.62235
\(562\) 20.9741 0.884738
\(563\) 36.2031 1.52578 0.762890 0.646529i \(-0.223780\pi\)
0.762890 + 0.646529i \(0.223780\pi\)
\(564\) 5.58038 0.234976
\(565\) 17.3099 0.728234
\(566\) −21.8996 −0.920511
\(567\) −14.2136 −0.596915
\(568\) 10.2940 0.431927
\(569\) 14.9868 0.628281 0.314141 0.949376i \(-0.398284\pi\)
0.314141 + 0.949376i \(0.398284\pi\)
\(570\) 16.5652 0.693839
\(571\) 18.4057 0.770256 0.385128 0.922863i \(-0.374157\pi\)
0.385128 + 0.922863i \(0.374157\pi\)
\(572\) −1.72443 −0.0721022
\(573\) 40.2163 1.68006
\(574\) −21.3515 −0.891196
\(575\) −7.60448 −0.317129
\(576\) −25.7578 −1.07324
\(577\) −8.86999 −0.369262 −0.184631 0.982808i \(-0.559109\pi\)
−0.184631 + 0.982808i \(0.559109\pi\)
\(578\) −12.8496 −0.534472
\(579\) 32.0598 1.33236
\(580\) 0.598450 0.0248493
\(581\) 0.722398 0.0299701
\(582\) 89.6188 3.71482
\(583\) 23.2423 0.962598
\(584\) −10.1977 −0.421984
\(585\) 1.78767 0.0739112
\(586\) −16.4519 −0.679620
\(587\) 23.6884 0.977724 0.488862 0.872361i \(-0.337412\pi\)
0.488862 + 0.872361i \(0.337412\pi\)
\(588\) 4.73821 0.195400
\(589\) −10.5051 −0.432856
\(590\) 17.7503 0.730768
\(591\) −12.4708 −0.512981
\(592\) 51.0764 2.09923
\(593\) 18.9734 0.779142 0.389571 0.920996i \(-0.372623\pi\)
0.389571 + 0.920996i \(0.372623\pi\)
\(594\) 84.8050 3.47959
\(595\) −4.88218 −0.200150
\(596\) 16.3242 0.668667
\(597\) −25.1657 −1.02996
\(598\) 3.90371 0.159635
\(599\) −34.3412 −1.40314 −0.701572 0.712599i \(-0.747518\pi\)
−0.701572 + 0.712599i \(0.747518\pi\)
\(600\) 2.70906 0.110597
\(601\) −10.3442 −0.421948 −0.210974 0.977492i \(-0.567664\pi\)
−0.210974 + 0.977492i \(0.567664\pi\)
\(602\) 1.10171 0.0449022
\(603\) 67.7749 2.76001
\(604\) 14.5081 0.590326
\(605\) 5.95464 0.242091
\(606\) 64.5171 2.62083
\(607\) −27.2104 −1.10444 −0.552219 0.833699i \(-0.686219\pi\)
−0.552219 + 0.833699i \(0.686219\pi\)
\(608\) −20.2793 −0.822434
\(609\) −1.20571 −0.0488577
\(610\) 14.5150 0.587695
\(611\) 0.321626 0.0130116
\(612\) 49.0117 1.98118
\(613\) 32.3076 1.30489 0.652445 0.757836i \(-0.273743\pi\)
0.652445 + 0.757836i \(0.273743\pi\)
\(614\) −9.71835 −0.392201
\(615\) −35.0943 −1.41514
\(616\) 3.61034 0.145465
\(617\) −8.43779 −0.339693 −0.169846 0.985471i \(-0.554327\pi\)
−0.169846 + 0.985471i \(0.554327\pi\)
\(618\) 109.992 4.42452
\(619\) −29.4777 −1.18481 −0.592405 0.805641i \(-0.701821\pi\)
−0.592405 + 0.805641i \(0.701821\pi\)
\(620\) 5.64839 0.226845
\(621\) −83.3183 −3.34345
\(622\) −2.18585 −0.0876448
\(623\) −7.10098 −0.284495
\(624\) −3.97857 −0.159270
\(625\) 1.00000 0.0400000
\(626\) 31.7775 1.27008
\(627\) 36.2856 1.44911
\(628\) 36.1320 1.44182
\(629\) −52.8839 −2.10862
\(630\) 12.3053 0.490255
\(631\) 42.2443 1.68172 0.840859 0.541254i \(-0.182050\pi\)
0.840859 + 0.541254i \(0.182050\pi\)
\(632\) −2.01603 −0.0801933
\(633\) 23.2293 0.923281
\(634\) 4.22358 0.167740
\(635\) 15.6918 0.622709
\(636\) −26.7454 −1.06052
\(637\) 0.273088 0.0108201
\(638\) 3.02049 0.119582
\(639\) 76.8540 3.04030
\(640\) −6.82369 −0.269730
\(641\) −5.62034 −0.221990 −0.110995 0.993821i \(-0.535404\pi\)
−0.110995 + 0.993821i \(0.535404\pi\)
\(642\) 63.7646 2.51659
\(643\) −25.1007 −0.989875 −0.494937 0.868929i \(-0.664809\pi\)
−0.494937 + 0.868929i \(0.664809\pi\)
\(644\) 11.6619 0.459544
\(645\) 1.81081 0.0713007
\(646\) 26.1755 1.02986
\(647\) 10.2646 0.403544 0.201772 0.979432i \(-0.435330\pi\)
0.201772 + 0.979432i \(0.435330\pi\)
\(648\) 12.4626 0.489577
\(649\) 38.8815 1.52623
\(650\) −0.513344 −0.0201350
\(651\) −11.3799 −0.446014
\(652\) −19.7404 −0.773095
\(653\) 38.0884 1.49052 0.745258 0.666777i \(-0.232327\pi\)
0.745258 + 0.666777i \(0.232327\pi\)
\(654\) −42.6903 −1.66932
\(655\) 14.8642 0.580791
\(656\) 53.5592 2.09113
\(657\) −76.1350 −2.97031
\(658\) 2.21389 0.0863064
\(659\) 27.7386 1.08054 0.540271 0.841491i \(-0.318322\pi\)
0.540271 + 0.841491i \(0.318322\pi\)
\(660\) −19.5101 −0.759428
\(661\) −21.5170 −0.836913 −0.418456 0.908237i \(-0.637429\pi\)
−0.418456 + 0.908237i \(0.637429\pi\)
\(662\) 1.86867 0.0726280
\(663\) 4.11936 0.159983
\(664\) −0.633404 −0.0245808
\(665\) 2.85217 0.110602
\(666\) 133.291 5.16493
\(667\) −2.96754 −0.114904
\(668\) −17.8306 −0.689885
\(669\) 49.0060 1.89468
\(670\) −19.4621 −0.751886
\(671\) 31.7947 1.22742
\(672\) −21.9680 −0.847435
\(673\) −25.3568 −0.977431 −0.488716 0.872443i \(-0.662534\pi\)
−0.488716 + 0.872443i \(0.662534\pi\)
\(674\) −4.68485 −0.180454
\(675\) 10.9565 0.421715
\(676\) −19.8219 −0.762380
\(677\) 39.3176 1.51110 0.755550 0.655091i \(-0.227370\pi\)
0.755550 + 0.655091i \(0.227370\pi\)
\(678\) −100.534 −3.86100
\(679\) 15.4305 0.592167
\(680\) 4.28073 0.164159
\(681\) −60.5437 −2.32004
\(682\) 28.5086 1.09165
\(683\) −27.4837 −1.05163 −0.525817 0.850598i \(-0.676240\pi\)
−0.525817 + 0.850598i \(0.676240\pi\)
\(684\) −28.6327 −1.09480
\(685\) −20.1741 −0.770814
\(686\) 1.87978 0.0717702
\(687\) 3.08968 0.117879
\(688\) −2.76357 −0.105360
\(689\) −1.54148 −0.0587256
\(690\) 44.1662 1.68138
\(691\) −18.1517 −0.690523 −0.345261 0.938507i \(-0.612210\pi\)
−0.345261 + 0.938507i \(0.612210\pi\)
\(692\) 2.70356 0.102774
\(693\) 26.9544 1.02391
\(694\) −40.4553 −1.53566
\(695\) −6.10706 −0.231654
\(696\) 1.05717 0.0400720
\(697\) −55.4545 −2.10049
\(698\) 27.4118 1.03755
\(699\) 19.3814 0.733071
\(700\) −1.53356 −0.0579630
\(701\) 50.6862 1.91439 0.957196 0.289441i \(-0.0934695\pi\)
0.957196 + 0.289441i \(0.0934695\pi\)
\(702\) −5.62444 −0.212281
\(703\) 30.8948 1.16522
\(704\) 16.2020 0.610634
\(705\) 3.63885 0.137047
\(706\) 12.3426 0.464520
\(707\) 11.1085 0.417777
\(708\) −44.7418 −1.68150
\(709\) 9.07369 0.340770 0.170385 0.985378i \(-0.445499\pi\)
0.170385 + 0.985378i \(0.445499\pi\)
\(710\) −22.0692 −0.828242
\(711\) −15.0514 −0.564473
\(712\) 6.22619 0.233336
\(713\) −28.0088 −1.04894
\(714\) 28.3553 1.06117
\(715\) −1.12447 −0.0420527
\(716\) −17.3302 −0.647660
\(717\) 13.7970 0.515257
\(718\) −2.34013 −0.0873330
\(719\) −25.6189 −0.955425 −0.477713 0.878516i \(-0.658534\pi\)
−0.477713 + 0.878516i \(0.658534\pi\)
\(720\) −30.8672 −1.15035
\(721\) 18.9383 0.705299
\(722\) 20.4240 0.760102
\(723\) 28.6207 1.06441
\(724\) 0.672159 0.0249806
\(725\) 0.390236 0.0144930
\(726\) −34.5840 −1.28353
\(727\) 17.6612 0.655016 0.327508 0.944848i \(-0.393791\pi\)
0.327508 + 0.944848i \(0.393791\pi\)
\(728\) −0.239445 −0.00887444
\(729\) −8.51178 −0.315251
\(730\) 21.8627 0.809177
\(731\) 2.86137 0.105831
\(732\) −36.5868 −1.35229
\(733\) −24.3988 −0.901190 −0.450595 0.892729i \(-0.648788\pi\)
−0.450595 + 0.892729i \(0.648788\pi\)
\(734\) 29.5591 1.09105
\(735\) 3.08968 0.113965
\(736\) −54.0688 −1.99300
\(737\) −42.6312 −1.57034
\(738\) 139.770 5.14501
\(739\) −28.3385 −1.04245 −0.521224 0.853420i \(-0.674525\pi\)
−0.521224 + 0.853420i \(0.674525\pi\)
\(740\) −16.6115 −0.610652
\(741\) −2.40653 −0.0884062
\(742\) −10.6106 −0.389529
\(743\) −20.3300 −0.745837 −0.372918 0.927864i \(-0.621643\pi\)
−0.372918 + 0.927864i \(0.621643\pi\)
\(744\) 9.97800 0.365811
\(745\) 10.6447 0.389991
\(746\) 53.2380 1.94918
\(747\) −4.72892 −0.173022
\(748\) −30.8289 −1.12722
\(749\) 10.9789 0.401161
\(750\) −5.80791 −0.212075
\(751\) 30.1256 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(752\) −5.55342 −0.202512
\(753\) −22.1365 −0.806699
\(754\) −0.200325 −0.00729542
\(755\) 9.46042 0.344300
\(756\) −16.8024 −0.611097
\(757\) −3.23180 −0.117462 −0.0587309 0.998274i \(-0.518705\pi\)
−0.0587309 + 0.998274i \(0.518705\pi\)
\(758\) −49.9434 −1.81403
\(759\) 96.7449 3.51162
\(760\) −2.50081 −0.0907138
\(761\) 25.0613 0.908471 0.454235 0.890882i \(-0.349913\pi\)
0.454235 + 0.890882i \(0.349913\pi\)
\(762\) −91.1365 −3.30153
\(763\) −7.35037 −0.266101
\(764\) 19.9613 0.722174
\(765\) 31.9595 1.15550
\(766\) 5.02834 0.181681
\(767\) −2.57870 −0.0931116
\(768\) 63.9460 2.30745
\(769\) −36.6145 −1.32035 −0.660176 0.751111i \(-0.729518\pi\)
−0.660176 + 0.751111i \(0.729518\pi\)
\(770\) −7.74017 −0.278936
\(771\) −47.4049 −1.70724
\(772\) 15.9128 0.572715
\(773\) −32.8600 −1.18189 −0.590947 0.806711i \(-0.701246\pi\)
−0.590947 + 0.806711i \(0.701246\pi\)
\(774\) −7.21193 −0.259227
\(775\) 3.68320 0.132304
\(776\) −13.5295 −0.485682
\(777\) 33.4675 1.20064
\(778\) 29.5676 1.06005
\(779\) 32.3965 1.16073
\(780\) 1.29395 0.0463307
\(781\) −48.3420 −1.72981
\(782\) 69.7894 2.49567
\(783\) 4.27561 0.152798
\(784\) −4.71532 −0.168404
\(785\) 23.5609 0.840925
\(786\) −86.3299 −3.07928
\(787\) −15.6961 −0.559504 −0.279752 0.960072i \(-0.590252\pi\)
−0.279752 + 0.960072i \(0.590252\pi\)
\(788\) −6.18986 −0.220505
\(789\) 13.7283 0.488741
\(790\) 4.32214 0.153775
\(791\) −17.3099 −0.615470
\(792\) −23.6338 −0.839792
\(793\) −2.10869 −0.0748818
\(794\) −2.49934 −0.0886983
\(795\) −17.4401 −0.618537
\(796\) −12.4909 −0.442729
\(797\) 41.4649 1.46876 0.734381 0.678738i \(-0.237473\pi\)
0.734381 + 0.678738i \(0.237473\pi\)
\(798\) −16.5652 −0.586401
\(799\) 5.74994 0.203418
\(800\) 7.11012 0.251381
\(801\) 46.4840 1.64243
\(802\) 24.6262 0.869580
\(803\) 47.8898 1.68999
\(804\) 49.0566 1.73009
\(805\) 7.60448 0.268023
\(806\) −1.89075 −0.0665987
\(807\) −15.6862 −0.552181
\(808\) −9.74000 −0.342652
\(809\) 1.49560 0.0525826 0.0262913 0.999654i \(-0.491630\pi\)
0.0262913 + 0.999654i \(0.491630\pi\)
\(810\) −26.7184 −0.938789
\(811\) 24.9790 0.877132 0.438566 0.898699i \(-0.355487\pi\)
0.438566 + 0.898699i \(0.355487\pi\)
\(812\) −0.598450 −0.0210015
\(813\) −92.0523 −3.22841
\(814\) −83.8416 −2.93865
\(815\) −12.8723 −0.450898
\(816\) −71.1277 −2.48997
\(817\) −1.67161 −0.0584823
\(818\) 13.5474 0.473674
\(819\) −1.78767 −0.0624663
\(820\) −17.4190 −0.608297
\(821\) −47.4480 −1.65595 −0.827974 0.560766i \(-0.810507\pi\)
−0.827974 + 0.560766i \(0.810507\pi\)
\(822\) 117.170 4.08676
\(823\) −9.52464 −0.332008 −0.166004 0.986125i \(-0.553086\pi\)
−0.166004 + 0.986125i \(0.553086\pi\)
\(824\) −16.6052 −0.578471
\(825\) −12.7221 −0.442926
\(826\) −17.7503 −0.617611
\(827\) 46.1669 1.60538 0.802691 0.596396i \(-0.203401\pi\)
0.802691 + 0.596396i \(0.203401\pi\)
\(828\) −76.3406 −2.65302
\(829\) 7.82929 0.271922 0.135961 0.990714i \(-0.456588\pi\)
0.135961 + 0.990714i \(0.456588\pi\)
\(830\) 1.35795 0.0471350
\(831\) 27.8693 0.966774
\(832\) −1.07455 −0.0372532
\(833\) 4.88218 0.169158
\(834\) 35.4693 1.22820
\(835\) −11.6269 −0.402366
\(836\) 18.0103 0.622898
\(837\) 40.3549 1.39487
\(838\) −32.2020 −1.11240
\(839\) 33.9127 1.17080 0.585399 0.810745i \(-0.300938\pi\)
0.585399 + 0.810745i \(0.300938\pi\)
\(840\) −2.70906 −0.0934714
\(841\) −28.8477 −0.994749
\(842\) 75.9092 2.61600
\(843\) −34.4739 −1.18735
\(844\) 11.5298 0.396872
\(845\) −12.9254 −0.444648
\(846\) −14.4924 −0.498260
\(847\) −5.95464 −0.204604
\(848\) 26.6162 0.914004
\(849\) 35.9952 1.23535
\(850\) −9.17741 −0.314782
\(851\) 82.3719 2.82367
\(852\) 55.6282 1.90579
\(853\) 7.84264 0.268527 0.134263 0.990946i \(-0.457133\pi\)
0.134263 + 0.990946i \(0.457133\pi\)
\(854\) −14.5150 −0.496693
\(855\) −18.6707 −0.638526
\(856\) −9.62640 −0.329023
\(857\) 21.8165 0.745236 0.372618 0.927985i \(-0.378460\pi\)
0.372618 + 0.927985i \(0.378460\pi\)
\(858\) 6.53080 0.222958
\(859\) −41.9910 −1.43271 −0.716357 0.697734i \(-0.754192\pi\)
−0.716357 + 0.697734i \(0.754192\pi\)
\(860\) 0.898793 0.0306486
\(861\) 35.0943 1.19601
\(862\) −6.76481 −0.230410
\(863\) 39.2439 1.33588 0.667939 0.744216i \(-0.267177\pi\)
0.667939 + 0.744216i \(0.267177\pi\)
\(864\) 77.9019 2.65028
\(865\) 1.76293 0.0599416
\(866\) −52.9704 −1.80001
\(867\) 21.1202 0.717278
\(868\) −5.64839 −0.191719
\(869\) 9.46753 0.321164
\(870\) −2.26646 −0.0768401
\(871\) 2.82739 0.0958024
\(872\) 6.44486 0.218251
\(873\) −101.010 −3.41867
\(874\) −40.7710 −1.37910
\(875\) −1.00000 −0.0338062
\(876\) −55.1078 −1.86192
\(877\) 14.8513 0.501492 0.250746 0.968053i \(-0.419324\pi\)
0.250746 + 0.968053i \(0.419324\pi\)
\(878\) −47.8854 −1.61605
\(879\) 27.0410 0.912071
\(880\) 19.4158 0.654506
\(881\) −54.3354 −1.83061 −0.915303 0.402765i \(-0.868049\pi\)
−0.915303 + 0.402765i \(0.868049\pi\)
\(882\) −12.3053 −0.414341
\(883\) −44.8923 −1.51074 −0.755372 0.655296i \(-0.772544\pi\)
−0.755372 + 0.655296i \(0.772544\pi\)
\(884\) 2.04464 0.0687686
\(885\) −29.1752 −0.980712
\(886\) −36.5961 −1.22947
\(887\) −12.2076 −0.409892 −0.204946 0.978773i \(-0.565702\pi\)
−0.204946 + 0.978773i \(0.565702\pi\)
\(888\) −29.3446 −0.984739
\(889\) −15.6918 −0.526285
\(890\) −13.3482 −0.447434
\(891\) −58.5260 −1.96069
\(892\) 24.3240 0.814428
\(893\) −3.35912 −0.112409
\(894\) −61.8234 −2.06768
\(895\) −11.3007 −0.377739
\(896\) 6.82369 0.227964
\(897\) −6.41632 −0.214235
\(898\) −8.30770 −0.277232
\(899\) 1.43732 0.0479372
\(900\) 10.0389 0.334630
\(901\) −27.5581 −0.918093
\(902\) −87.9171 −2.92732
\(903\) −1.81081 −0.0602601
\(904\) 15.1775 0.504795
\(905\) 0.438301 0.0145696
\(906\) −54.9453 −1.82544
\(907\) 12.1831 0.404532 0.202266 0.979331i \(-0.435169\pi\)
0.202266 + 0.979331i \(0.435169\pi\)
\(908\) −30.0507 −0.997268
\(909\) −72.7178 −2.41190
\(910\) 0.513344 0.0170172
\(911\) 8.19262 0.271434 0.135717 0.990748i \(-0.456666\pi\)
0.135717 + 0.990748i \(0.456666\pi\)
\(912\) 41.5528 1.37595
\(913\) 2.97454 0.0984431
\(914\) 21.1152 0.698429
\(915\) −23.8575 −0.788704
\(916\) 1.53356 0.0506702
\(917\) −14.8642 −0.490858
\(918\) −100.552 −3.31871
\(919\) 12.8789 0.424837 0.212419 0.977179i \(-0.431866\pi\)
0.212419 + 0.977179i \(0.431866\pi\)
\(920\) −6.66767 −0.219826
\(921\) 15.9735 0.526345
\(922\) −55.7412 −1.83574
\(923\) 3.20614 0.105531
\(924\) 19.5101 0.641834
\(925\) −10.8320 −0.356155
\(926\) 58.0539 1.90777
\(927\) −123.973 −4.07180
\(928\) 2.77463 0.0910816
\(929\) −58.4248 −1.91686 −0.958428 0.285335i \(-0.907895\pi\)
−0.958428 + 0.285335i \(0.907895\pi\)
\(930\) −21.3917 −0.701461
\(931\) −2.85217 −0.0934762
\(932\) 9.61990 0.315110
\(933\) 3.59277 0.117622
\(934\) 54.2524 1.77519
\(935\) −20.1029 −0.657434
\(936\) 1.56744 0.0512335
\(937\) 43.9779 1.43669 0.718347 0.695684i \(-0.244899\pi\)
0.718347 + 0.695684i \(0.244899\pi\)
\(938\) 19.4621 0.635460
\(939\) −52.2309 −1.70449
\(940\) 1.80613 0.0589096
\(941\) −24.3846 −0.794915 −0.397457 0.917621i \(-0.630107\pi\)
−0.397457 + 0.917621i \(0.630107\pi\)
\(942\) −136.840 −4.45848
\(943\) 86.3759 2.81279
\(944\) 44.5256 1.44919
\(945\) −10.9565 −0.356414
\(946\) 4.53638 0.147491
\(947\) 21.3477 0.693707 0.346854 0.937919i \(-0.387250\pi\)
0.346854 + 0.937919i \(0.387250\pi\)
\(948\) −10.8945 −0.353836
\(949\) −3.17615 −0.103102
\(950\) 5.36144 0.173948
\(951\) −6.94207 −0.225112
\(952\) −4.28073 −0.138739
\(953\) −50.6737 −1.64148 −0.820741 0.571300i \(-0.806439\pi\)
−0.820741 + 0.571300i \(0.806439\pi\)
\(954\) 69.4588 2.24881
\(955\) 13.0163 0.421198
\(956\) 6.84809 0.221483
\(957\) −4.96462 −0.160483
\(958\) 5.23246 0.169053
\(959\) 20.1741 0.651457
\(960\) −12.1573 −0.392375
\(961\) −17.4341 −0.562389
\(962\) 5.56055 0.179279
\(963\) −71.8696 −2.31597
\(964\) 14.2058 0.457538
\(965\) 10.3764 0.334028
\(966\) −44.1662 −1.42102
\(967\) −4.17101 −0.134131 −0.0670654 0.997749i \(-0.521364\pi\)
−0.0670654 + 0.997749i \(0.521364\pi\)
\(968\) 5.22107 0.167812
\(969\) −43.0233 −1.38211
\(970\) 29.0058 0.931320
\(971\) 24.7362 0.793823 0.396911 0.917857i \(-0.370082\pi\)
0.396911 + 0.917857i \(0.370082\pi\)
\(972\) 16.9399 0.543347
\(973\) 6.10706 0.195783
\(974\) −66.4321 −2.12862
\(975\) 0.843755 0.0270218
\(976\) 36.4101 1.16546
\(977\) −20.3057 −0.649637 −0.324818 0.945776i \(-0.605303\pi\)
−0.324818 + 0.945776i \(0.605303\pi\)
\(978\) 74.7613 2.39060
\(979\) −29.2390 −0.934482
\(980\) 1.53356 0.0489877
\(981\) 48.1166 1.53625
\(982\) −0.386274 −0.0123265
\(983\) 58.4313 1.86367 0.931834 0.362884i \(-0.118208\pi\)
0.931834 + 0.362884i \(0.118208\pi\)
\(984\) −30.7710 −0.980943
\(985\) −4.03627 −0.128606
\(986\) −3.58136 −0.114054
\(987\) −3.63885 −0.115826
\(988\) −1.19448 −0.0380014
\(989\) −4.45686 −0.141720
\(990\) 50.6683 1.61034
\(991\) −0.405886 −0.0128934 −0.00644670 0.999979i \(-0.502052\pi\)
−0.00644670 + 0.999979i \(0.502052\pi\)
\(992\) 26.1880 0.831469
\(993\) −3.07143 −0.0974690
\(994\) 22.0692 0.699993
\(995\) −8.14506 −0.258216
\(996\) −3.42287 −0.108458
\(997\) −60.8518 −1.92720 −0.963598 0.267355i \(-0.913850\pi\)
−0.963598 + 0.267355i \(0.913850\pi\)
\(998\) 26.1808 0.828740
\(999\) −118.681 −3.75489
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 8015.2.a.i.1.8 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.i.1.8 44 1.1 even 1 trivial