Properties

Label 8038.2.a.a.1.8
Level $8038$
Weight $2$
Character 8038.1
Self dual yes
Analytic conductor $64.184$
Analytic rank $1$
Dimension $75$
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] = [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: \(75\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.93359 q^{3} +1.00000 q^{4} +2.13721 q^{5} -2.93359 q^{6} +0.512181 q^{7} +1.00000 q^{8} +5.60596 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.93359 q^{3} +1.00000 q^{4} +2.13721 q^{5} -2.93359 q^{6} +0.512181 q^{7} +1.00000 q^{8} +5.60596 q^{9} +2.13721 q^{10} -3.75894 q^{11} -2.93359 q^{12} +0.496248 q^{13} +0.512181 q^{14} -6.26969 q^{15} +1.00000 q^{16} +0.791674 q^{17} +5.60596 q^{18} -7.88651 q^{19} +2.13721 q^{20} -1.50253 q^{21} -3.75894 q^{22} +3.47552 q^{23} -2.93359 q^{24} -0.432347 q^{25} +0.496248 q^{26} -7.64481 q^{27} +0.512181 q^{28} +10.6545 q^{29} -6.26969 q^{30} -4.77695 q^{31} +1.00000 q^{32} +11.0272 q^{33} +0.791674 q^{34} +1.09464 q^{35} +5.60596 q^{36} +8.16170 q^{37} -7.88651 q^{38} -1.45579 q^{39} +2.13721 q^{40} -9.76999 q^{41} -1.50253 q^{42} +3.17097 q^{43} -3.75894 q^{44} +11.9811 q^{45} +3.47552 q^{46} +6.28598 q^{47} -2.93359 q^{48} -6.73767 q^{49} -0.432347 q^{50} -2.32245 q^{51} +0.496248 q^{52} -4.96994 q^{53} -7.64481 q^{54} -8.03362 q^{55} +0.512181 q^{56} +23.1358 q^{57} +10.6545 q^{58} -11.5166 q^{59} -6.26969 q^{60} -0.835492 q^{61} -4.77695 q^{62} +2.87126 q^{63} +1.00000 q^{64} +1.06058 q^{65} +11.0272 q^{66} +9.34626 q^{67} +0.791674 q^{68} -10.1958 q^{69} +1.09464 q^{70} -12.0889 q^{71} +5.60596 q^{72} -9.29368 q^{73} +8.16170 q^{74} +1.26833 q^{75} -7.88651 q^{76} -1.92525 q^{77} -1.45579 q^{78} -6.52746 q^{79} +2.13721 q^{80} +5.60887 q^{81} -9.76999 q^{82} -10.9223 q^{83} -1.50253 q^{84} +1.69197 q^{85} +3.17097 q^{86} -31.2559 q^{87} -3.75894 q^{88} -3.10941 q^{89} +11.9811 q^{90} +0.254168 q^{91} +3.47552 q^{92} +14.0136 q^{93} +6.28598 q^{94} -16.8551 q^{95} -2.93359 q^{96} -8.79117 q^{97} -6.73767 q^{98} -21.0724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9} - 29 q^{10} - 30 q^{11} - 30 q^{12} - 23 q^{13} - 31 q^{14} - 22 q^{15} + 75 q^{16} - 48 q^{17} + 55 q^{18} - 58 q^{19} - 29 q^{20} - 5 q^{21} - 30 q^{22} - 79 q^{23} - 30 q^{24} + 42 q^{25} - 23 q^{26} - 108 q^{27} - 31 q^{28} - 39 q^{29} - 22 q^{30} - 95 q^{31} + 75 q^{32} - 44 q^{33} - 48 q^{34} - 60 q^{35} + 55 q^{36} - 16 q^{37} - 58 q^{38} - 57 q^{39} - 29 q^{40} - 85 q^{41} - 5 q^{42} - 55 q^{43} - 30 q^{44} - 48 q^{45} - 79 q^{46} - 88 q^{47} - 30 q^{48} + 26 q^{49} + 42 q^{50} - 39 q^{51} - 23 q^{52} - 79 q^{53} - 108 q^{54} - 78 q^{55} - 31 q^{56} - 40 q^{57} - 39 q^{58} - 74 q^{59} - 22 q^{60} - 21 q^{61} - 95 q^{62} - 97 q^{63} + 75 q^{64} - 63 q^{65} - 44 q^{66} - 59 q^{67} - 48 q^{68} + 3 q^{69} - 60 q^{70} - 72 q^{71} + 55 q^{72} - 91 q^{73} - 16 q^{74} - 95 q^{75} - 58 q^{76} - 60 q^{77} - 57 q^{78} - 64 q^{79} - 29 q^{80} + 47 q^{81} - 85 q^{82} - 105 q^{83} - 5 q^{84} + 14 q^{85} - 55 q^{86} - 75 q^{87} - 30 q^{88} - 78 q^{89} - 48 q^{90} - 89 q^{91} - 79 q^{92} + 27 q^{93} - 88 q^{94} - 53 q^{95} - 30 q^{96} - 79 q^{97} + 26 q^{98} - 57 q^{99}+O(q^{100}) \) 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
\(3\) −2.93359 −1.69371 −0.846855 0.531824i \(-0.821507\pi\)
−0.846855 + 0.531824i \(0.821507\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.13721 0.955788 0.477894 0.878418i \(-0.341400\pi\)
0.477894 + 0.878418i \(0.341400\pi\)
\(6\) −2.93359 −1.19763
\(7\) 0.512181 0.193586 0.0967930 0.995305i \(-0.469142\pi\)
0.0967930 + 0.995305i \(0.469142\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.60596 1.86865
\(10\) 2.13721 0.675844
\(11\) −3.75894 −1.13336 −0.566681 0.823937i \(-0.691773\pi\)
−0.566681 + 0.823937i \(0.691773\pi\)
\(12\) −2.93359 −0.846855
\(13\) 0.496248 0.137634 0.0688171 0.997629i \(-0.478077\pi\)
0.0688171 + 0.997629i \(0.478077\pi\)
\(14\) 0.512181 0.136886
\(15\) −6.26969 −1.61883
\(16\) 1.00000 0.250000
\(17\) 0.791674 0.192009 0.0960046 0.995381i \(-0.469394\pi\)
0.0960046 + 0.995381i \(0.469394\pi\)
\(18\) 5.60596 1.32134
\(19\) −7.88651 −1.80929 −0.904644 0.426168i \(-0.859863\pi\)
−0.904644 + 0.426168i \(0.859863\pi\)
\(20\) 2.13721 0.477894
\(21\) −1.50253 −0.327879
\(22\) −3.75894 −0.801408
\(23\) 3.47552 0.724697 0.362348 0.932043i \(-0.381975\pi\)
0.362348 + 0.932043i \(0.381975\pi\)
\(24\) −2.93359 −0.598817
\(25\) −0.432347 −0.0864694
\(26\) 0.496248 0.0973221
\(27\) −7.64481 −1.47124
\(28\) 0.512181 0.0967930
\(29\) 10.6545 1.97849 0.989245 0.146270i \(-0.0467267\pi\)
0.989245 + 0.146270i \(0.0467267\pi\)
\(30\) −6.26969 −1.14468
\(31\) −4.77695 −0.857965 −0.428982 0.903313i \(-0.641128\pi\)
−0.428982 + 0.903313i \(0.641128\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.0272 1.91959
\(34\) 0.791674 0.135771
\(35\) 1.09464 0.185027
\(36\) 5.60596 0.934326
\(37\) 8.16170 1.34178 0.670888 0.741559i \(-0.265913\pi\)
0.670888 + 0.741559i \(0.265913\pi\)
\(38\) −7.88651 −1.27936
\(39\) −1.45579 −0.233113
\(40\) 2.13721 0.337922
\(41\) −9.76999 −1.52582 −0.762908 0.646507i \(-0.776229\pi\)
−0.762908 + 0.646507i \(0.776229\pi\)
\(42\) −1.50253 −0.231845
\(43\) 3.17097 0.483568 0.241784 0.970330i \(-0.422268\pi\)
0.241784 + 0.970330i \(0.422268\pi\)
\(44\) −3.75894 −0.566681
\(45\) 11.9811 1.78603
\(46\) 3.47552 0.512438
\(47\) 6.28598 0.916905 0.458453 0.888719i \(-0.348404\pi\)
0.458453 + 0.888719i \(0.348404\pi\)
\(48\) −2.93359 −0.423427
\(49\) −6.73767 −0.962524
\(50\) −0.432347 −0.0611431
\(51\) −2.32245 −0.325208
\(52\) 0.496248 0.0688171
\(53\) −4.96994 −0.682673 −0.341337 0.939941i \(-0.610880\pi\)
−0.341337 + 0.939941i \(0.610880\pi\)
\(54\) −7.64481 −1.04033
\(55\) −8.03362 −1.08325
\(56\) 0.512181 0.0684430
\(57\) 23.1358 3.06441
\(58\) 10.6545 1.39900
\(59\) −11.5166 −1.49933 −0.749665 0.661817i \(-0.769786\pi\)
−0.749665 + 0.661817i \(0.769786\pi\)
\(60\) −6.26969 −0.809414
\(61\) −0.835492 −0.106974 −0.0534869 0.998569i \(-0.517034\pi\)
−0.0534869 + 0.998569i \(0.517034\pi\)
\(62\) −4.77695 −0.606673
\(63\) 2.87126 0.361745
\(64\) 1.00000 0.125000
\(65\) 1.06058 0.131549
\(66\) 11.0272 1.35735
\(67\) 9.34626 1.14183 0.570914 0.821010i \(-0.306589\pi\)
0.570914 + 0.821010i \(0.306589\pi\)
\(68\) 0.791674 0.0960046
\(69\) −10.1958 −1.22743
\(70\) 1.09464 0.130834
\(71\) −12.0889 −1.43469 −0.717345 0.696718i \(-0.754643\pi\)
−0.717345 + 0.696718i \(0.754643\pi\)
\(72\) 5.60596 0.660668
\(73\) −9.29368 −1.08774 −0.543871 0.839169i \(-0.683042\pi\)
−0.543871 + 0.839169i \(0.683042\pi\)
\(74\) 8.16170 0.948779
\(75\) 1.26833 0.146454
\(76\) −7.88651 −0.904644
\(77\) −1.92525 −0.219403
\(78\) −1.45579 −0.164835
\(79\) −6.52746 −0.734396 −0.367198 0.930143i \(-0.619683\pi\)
−0.367198 + 0.930143i \(0.619683\pi\)
\(80\) 2.13721 0.238947
\(81\) 5.60887 0.623208
\(82\) −9.76999 −1.07892
\(83\) −10.9223 −1.19887 −0.599437 0.800422i \(-0.704609\pi\)
−0.599437 + 0.800422i \(0.704609\pi\)
\(84\) −1.50253 −0.163939
\(85\) 1.69197 0.183520
\(86\) 3.17097 0.341934
\(87\) −31.2559 −3.35099
\(88\) −3.75894 −0.400704
\(89\) −3.10941 −0.329596 −0.164798 0.986327i \(-0.552697\pi\)
−0.164798 + 0.986327i \(0.552697\pi\)
\(90\) 11.9811 1.26292
\(91\) 0.254168 0.0266441
\(92\) 3.47552 0.362348
\(93\) 14.0136 1.45314
\(94\) 6.28598 0.648350
\(95\) −16.8551 −1.72930
\(96\) −2.93359 −0.299408
\(97\) −8.79117 −0.892608 −0.446304 0.894881i \(-0.647260\pi\)
−0.446304 + 0.894881i \(0.647260\pi\)
\(98\) −6.73767 −0.680608
\(99\) −21.0724 −2.11786
\(100\) −0.432347 −0.0432347
\(101\) 15.3006 1.52247 0.761233 0.648478i \(-0.224594\pi\)
0.761233 + 0.648478i \(0.224594\pi\)
\(102\) −2.32245 −0.229957
\(103\) 7.60134 0.748982 0.374491 0.927230i \(-0.377817\pi\)
0.374491 + 0.927230i \(0.377817\pi\)
\(104\) 0.496248 0.0486611
\(105\) −3.21121 −0.313382
\(106\) −4.96994 −0.482723
\(107\) −9.87990 −0.955126 −0.477563 0.878597i \(-0.658480\pi\)
−0.477563 + 0.878597i \(0.658480\pi\)
\(108\) −7.64481 −0.735622
\(109\) 0.372892 0.0357166 0.0178583 0.999841i \(-0.494315\pi\)
0.0178583 + 0.999841i \(0.494315\pi\)
\(110\) −8.03362 −0.765976
\(111\) −23.9431 −2.27258
\(112\) 0.512181 0.0483965
\(113\) 14.0372 1.32051 0.660256 0.751041i \(-0.270448\pi\)
0.660256 + 0.751041i \(0.270448\pi\)
\(114\) 23.1358 2.16686
\(115\) 7.42791 0.692656
\(116\) 10.6545 0.989245
\(117\) 2.78194 0.257191
\(118\) −11.5166 −1.06019
\(119\) 0.405480 0.0371703
\(120\) −6.26969 −0.572342
\(121\) 3.12960 0.284509
\(122\) −0.835492 −0.0756419
\(123\) 28.6612 2.58429
\(124\) −4.77695 −0.428982
\(125\) −11.6100 −1.03843
\(126\) 2.87126 0.255792
\(127\) 17.0192 1.51021 0.755103 0.655606i \(-0.227587\pi\)
0.755103 + 0.655606i \(0.227587\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.30232 −0.819023
\(130\) 1.06058 0.0930193
\(131\) 0.145300 0.0126949 0.00634745 0.999980i \(-0.497980\pi\)
0.00634745 + 0.999980i \(0.497980\pi\)
\(132\) 11.0272 0.959793
\(133\) −4.03932 −0.350253
\(134\) 9.34626 0.807394
\(135\) −16.3385 −1.40620
\(136\) 0.791674 0.0678855
\(137\) 16.7232 1.42876 0.714381 0.699757i \(-0.246708\pi\)
0.714381 + 0.699757i \(0.246708\pi\)
\(138\) −10.1958 −0.867921
\(139\) −11.3603 −0.963570 −0.481785 0.876290i \(-0.660011\pi\)
−0.481785 + 0.876290i \(0.660011\pi\)
\(140\) 1.09464 0.0925136
\(141\) −18.4405 −1.55297
\(142\) −12.0889 −1.01448
\(143\) −1.86536 −0.155989
\(144\) 5.60596 0.467163
\(145\) 22.7709 1.89102
\(146\) −9.29368 −0.769150
\(147\) 19.7656 1.63024
\(148\) 8.16170 0.670888
\(149\) 10.3572 0.848492 0.424246 0.905547i \(-0.360539\pi\)
0.424246 + 0.905547i \(0.360539\pi\)
\(150\) 1.26833 0.103559
\(151\) 14.6775 1.19443 0.597217 0.802079i \(-0.296273\pi\)
0.597217 + 0.802079i \(0.296273\pi\)
\(152\) −7.88651 −0.639680
\(153\) 4.43809 0.358798
\(154\) −1.92525 −0.155141
\(155\) −10.2093 −0.820033
\(156\) −1.45579 −0.116556
\(157\) −16.7771 −1.33895 −0.669477 0.742833i \(-0.733482\pi\)
−0.669477 + 0.742833i \(0.733482\pi\)
\(158\) −6.52746 −0.519296
\(159\) 14.5798 1.15625
\(160\) 2.13721 0.168961
\(161\) 1.78010 0.140291
\(162\) 5.60887 0.440675
\(163\) −14.4114 −1.12879 −0.564395 0.825505i \(-0.690890\pi\)
−0.564395 + 0.825505i \(0.690890\pi\)
\(164\) −9.76999 −0.762908
\(165\) 23.5674 1.83472
\(166\) −10.9223 −0.847732
\(167\) 24.2361 1.87545 0.937724 0.347381i \(-0.112929\pi\)
0.937724 + 0.347381i \(0.112929\pi\)
\(168\) −1.50253 −0.115923
\(169\) −12.7537 −0.981057
\(170\) 1.69197 0.129768
\(171\) −44.2114 −3.38093
\(172\) 3.17097 0.241784
\(173\) 15.7039 1.19394 0.596972 0.802262i \(-0.296370\pi\)
0.596972 + 0.802262i \(0.296370\pi\)
\(174\) −31.2559 −2.36951
\(175\) −0.221440 −0.0167393
\(176\) −3.75894 −0.283340
\(177\) 33.7849 2.53943
\(178\) −3.10941 −0.233060
\(179\) −17.5159 −1.30920 −0.654600 0.755975i \(-0.727163\pi\)
−0.654600 + 0.755975i \(0.727163\pi\)
\(180\) 11.9811 0.893017
\(181\) −10.6523 −0.791779 −0.395890 0.918298i \(-0.629564\pi\)
−0.395890 + 0.918298i \(0.629564\pi\)
\(182\) 0.254168 0.0188402
\(183\) 2.45099 0.181183
\(184\) 3.47552 0.256219
\(185\) 17.4432 1.28245
\(186\) 14.0136 1.02753
\(187\) −2.97585 −0.217616
\(188\) 6.28598 0.458453
\(189\) −3.91552 −0.284812
\(190\) −16.8551 −1.22280
\(191\) −0.526669 −0.0381085 −0.0190542 0.999818i \(-0.506066\pi\)
−0.0190542 + 0.999818i \(0.506066\pi\)
\(192\) −2.93359 −0.211714
\(193\) −4.91514 −0.353800 −0.176900 0.984229i \(-0.556607\pi\)
−0.176900 + 0.984229i \(0.556607\pi\)
\(194\) −8.79117 −0.631169
\(195\) −3.11132 −0.222806
\(196\) −6.73767 −0.481262
\(197\) 13.1721 0.938476 0.469238 0.883072i \(-0.344529\pi\)
0.469238 + 0.883072i \(0.344529\pi\)
\(198\) −21.0724 −1.49755
\(199\) −2.33670 −0.165644 −0.0828220 0.996564i \(-0.526393\pi\)
−0.0828220 + 0.996564i \(0.526393\pi\)
\(200\) −0.432347 −0.0305716
\(201\) −27.4181 −1.93392
\(202\) 15.3006 1.07655
\(203\) 5.45702 0.383008
\(204\) −2.32245 −0.162604
\(205\) −20.8805 −1.45836
\(206\) 7.60134 0.529610
\(207\) 19.4836 1.35421
\(208\) 0.496248 0.0344086
\(209\) 29.6449 2.05058
\(210\) −3.21121 −0.221595
\(211\) 10.6670 0.734349 0.367174 0.930152i \(-0.380325\pi\)
0.367174 + 0.930152i \(0.380325\pi\)
\(212\) −4.96994 −0.341337
\(213\) 35.4639 2.42995
\(214\) −9.87990 −0.675376
\(215\) 6.77701 0.462188
\(216\) −7.64481 −0.520163
\(217\) −2.44666 −0.166090
\(218\) 0.372892 0.0252554
\(219\) 27.2638 1.84232
\(220\) −8.03362 −0.541627
\(221\) 0.392866 0.0264270
\(222\) −23.9431 −1.60696
\(223\) −6.24952 −0.418499 −0.209250 0.977862i \(-0.567102\pi\)
−0.209250 + 0.977862i \(0.567102\pi\)
\(224\) 0.512181 0.0342215
\(225\) −2.42372 −0.161581
\(226\) 14.0372 0.933743
\(227\) −2.71972 −0.180514 −0.0902571 0.995918i \(-0.528769\pi\)
−0.0902571 + 0.995918i \(0.528769\pi\)
\(228\) 23.1358 1.53220
\(229\) −15.5315 −1.02635 −0.513177 0.858283i \(-0.671531\pi\)
−0.513177 + 0.858283i \(0.671531\pi\)
\(230\) 7.42791 0.489782
\(231\) 5.64791 0.371605
\(232\) 10.6545 0.699502
\(233\) −26.5727 −1.74084 −0.870419 0.492312i \(-0.836152\pi\)
−0.870419 + 0.492312i \(0.836152\pi\)
\(234\) 2.78194 0.181861
\(235\) 13.4344 0.876367
\(236\) −11.5166 −0.749665
\(237\) 19.1489 1.24385
\(238\) 0.405480 0.0262834
\(239\) −13.8726 −0.897343 −0.448672 0.893697i \(-0.648103\pi\)
−0.448672 + 0.893697i \(0.648103\pi\)
\(240\) −6.26969 −0.404707
\(241\) −1.51488 −0.0975818 −0.0487909 0.998809i \(-0.515537\pi\)
−0.0487909 + 0.998809i \(0.515537\pi\)
\(242\) 3.12960 0.201178
\(243\) 6.48029 0.415711
\(244\) −0.835492 −0.0534869
\(245\) −14.3998 −0.919969
\(246\) 28.6612 1.82737
\(247\) −3.91366 −0.249020
\(248\) −4.77695 −0.303336
\(249\) 32.0414 2.03054
\(250\) −11.6100 −0.734284
\(251\) −14.9268 −0.942169 −0.471084 0.882088i \(-0.656137\pi\)
−0.471084 + 0.882088i \(0.656137\pi\)
\(252\) 2.87126 0.180872
\(253\) −13.0643 −0.821344
\(254\) 17.0192 1.06788
\(255\) −4.96355 −0.310830
\(256\) 1.00000 0.0625000
\(257\) −28.1086 −1.75337 −0.876683 0.481069i \(-0.840249\pi\)
−0.876683 + 0.481069i \(0.840249\pi\)
\(258\) −9.30232 −0.579137
\(259\) 4.18027 0.259749
\(260\) 1.06058 0.0657746
\(261\) 59.7286 3.69711
\(262\) 0.145300 0.00897665
\(263\) −13.2633 −0.817848 −0.408924 0.912568i \(-0.634096\pi\)
−0.408924 + 0.912568i \(0.634096\pi\)
\(264\) 11.0272 0.678676
\(265\) −10.6218 −0.652491
\(266\) −4.03932 −0.247666
\(267\) 9.12173 0.558241
\(268\) 9.34626 0.570914
\(269\) 24.8275 1.51376 0.756881 0.653553i \(-0.226722\pi\)
0.756881 + 0.653553i \(0.226722\pi\)
\(270\) −16.3385 −0.994332
\(271\) −11.7641 −0.714618 −0.357309 0.933986i \(-0.616306\pi\)
−0.357309 + 0.933986i \(0.616306\pi\)
\(272\) 0.791674 0.0480023
\(273\) −0.745626 −0.0451273
\(274\) 16.7232 1.01029
\(275\) 1.62516 0.0980011
\(276\) −10.1958 −0.613713
\(277\) −24.8395 −1.49246 −0.746229 0.665689i \(-0.768138\pi\)
−0.746229 + 0.665689i \(0.768138\pi\)
\(278\) −11.3603 −0.681347
\(279\) −26.7793 −1.60324
\(280\) 1.09464 0.0654170
\(281\) 18.8372 1.12373 0.561865 0.827229i \(-0.310084\pi\)
0.561865 + 0.827229i \(0.310084\pi\)
\(282\) −18.4405 −1.09812
\(283\) −12.0030 −0.713505 −0.356752 0.934199i \(-0.616116\pi\)
−0.356752 + 0.934199i \(0.616116\pi\)
\(284\) −12.0889 −0.717345
\(285\) 49.4460 2.92893
\(286\) −1.86536 −0.110301
\(287\) −5.00400 −0.295377
\(288\) 5.60596 0.330334
\(289\) −16.3733 −0.963132
\(290\) 22.7709 1.33715
\(291\) 25.7897 1.51182
\(292\) −9.29368 −0.543871
\(293\) −26.5703 −1.55226 −0.776128 0.630575i \(-0.782819\pi\)
−0.776128 + 0.630575i \(0.782819\pi\)
\(294\) 19.7656 1.15275
\(295\) −24.6133 −1.43304
\(296\) 8.16170 0.474389
\(297\) 28.7363 1.66745
\(298\) 10.3572 0.599975
\(299\) 1.72472 0.0997431
\(300\) 1.26833 0.0732270
\(301\) 1.62411 0.0936120
\(302\) 14.6775 0.844593
\(303\) −44.8857 −2.57862
\(304\) −7.88651 −0.452322
\(305\) −1.78562 −0.102244
\(306\) 4.43809 0.253709
\(307\) −3.01042 −0.171814 −0.0859070 0.996303i \(-0.527379\pi\)
−0.0859070 + 0.996303i \(0.527379\pi\)
\(308\) −1.92525 −0.109702
\(309\) −22.2992 −1.26856
\(310\) −10.2093 −0.579851
\(311\) −32.6484 −1.85132 −0.925659 0.378358i \(-0.876489\pi\)
−0.925659 + 0.378358i \(0.876489\pi\)
\(312\) −1.45579 −0.0824177
\(313\) 14.7984 0.836457 0.418228 0.908342i \(-0.362651\pi\)
0.418228 + 0.908342i \(0.362651\pi\)
\(314\) −16.7771 −0.946784
\(315\) 6.13648 0.345751
\(316\) −6.52746 −0.367198
\(317\) −20.5053 −1.15169 −0.575845 0.817559i \(-0.695327\pi\)
−0.575845 + 0.817559i \(0.695327\pi\)
\(318\) 14.5798 0.817592
\(319\) −40.0496 −2.24234
\(320\) 2.13721 0.119473
\(321\) 28.9836 1.61771
\(322\) 1.78010 0.0992009
\(323\) −6.24354 −0.347400
\(324\) 5.60887 0.311604
\(325\) −0.214551 −0.0119012
\(326\) −14.4114 −0.798174
\(327\) −1.09391 −0.0604935
\(328\) −9.76999 −0.539458
\(329\) 3.21956 0.177500
\(330\) 23.5674 1.29734
\(331\) 4.60693 0.253220 0.126610 0.991953i \(-0.459590\pi\)
0.126610 + 0.991953i \(0.459590\pi\)
\(332\) −10.9223 −0.599437
\(333\) 45.7541 2.50731
\(334\) 24.2361 1.32614
\(335\) 19.9749 1.09135
\(336\) −1.50253 −0.0819696
\(337\) −26.8660 −1.46348 −0.731741 0.681582i \(-0.761292\pi\)
−0.731741 + 0.681582i \(0.761292\pi\)
\(338\) −12.7537 −0.693712
\(339\) −41.1795 −2.23656
\(340\) 1.69197 0.0917600
\(341\) 17.9562 0.972385
\(342\) −44.2114 −2.39068
\(343\) −7.03617 −0.379917
\(344\) 3.17097 0.170967
\(345\) −21.7905 −1.17316
\(346\) 15.7039 0.844246
\(347\) 7.82858 0.420260 0.210130 0.977673i \(-0.432611\pi\)
0.210130 + 0.977673i \(0.432611\pi\)
\(348\) −31.2559 −1.67549
\(349\) 7.56079 0.404720 0.202360 0.979311i \(-0.435139\pi\)
0.202360 + 0.979311i \(0.435139\pi\)
\(350\) −0.221440 −0.0118365
\(351\) −3.79372 −0.202494
\(352\) −3.75894 −0.200352
\(353\) 8.62179 0.458892 0.229446 0.973321i \(-0.426309\pi\)
0.229446 + 0.973321i \(0.426309\pi\)
\(354\) 33.7849 1.79565
\(355\) −25.8365 −1.37126
\(356\) −3.10941 −0.164798
\(357\) −1.18951 −0.0629557
\(358\) −17.5159 −0.925745
\(359\) −8.31771 −0.438992 −0.219496 0.975613i \(-0.570441\pi\)
−0.219496 + 0.975613i \(0.570441\pi\)
\(360\) 11.9811 0.631459
\(361\) 43.1970 2.27352
\(362\) −10.6523 −0.559872
\(363\) −9.18096 −0.481876
\(364\) 0.254168 0.0133220
\(365\) −19.8625 −1.03965
\(366\) 2.45099 0.128115
\(367\) −3.19579 −0.166819 −0.0834095 0.996515i \(-0.526581\pi\)
−0.0834095 + 0.996515i \(0.526581\pi\)
\(368\) 3.47552 0.181174
\(369\) −54.7702 −2.85122
\(370\) 17.4432 0.906831
\(371\) −2.54550 −0.132156
\(372\) 14.0136 0.726572
\(373\) −34.9203 −1.80810 −0.904051 0.427424i \(-0.859421\pi\)
−0.904051 + 0.427424i \(0.859421\pi\)
\(374\) −2.97585 −0.153878
\(375\) 34.0591 1.75881
\(376\) 6.28598 0.324175
\(377\) 5.28727 0.272308
\(378\) −3.91552 −0.201393
\(379\) −24.9331 −1.28072 −0.640362 0.768073i \(-0.721216\pi\)
−0.640362 + 0.768073i \(0.721216\pi\)
\(380\) −16.8551 −0.864648
\(381\) −49.9273 −2.55785
\(382\) −0.526669 −0.0269468
\(383\) −3.63985 −0.185988 −0.0929939 0.995667i \(-0.529644\pi\)
−0.0929939 + 0.995667i \(0.529644\pi\)
\(384\) −2.93359 −0.149704
\(385\) −4.11467 −0.209703
\(386\) −4.91514 −0.250174
\(387\) 17.7763 0.903620
\(388\) −8.79117 −0.446304
\(389\) 29.1880 1.47989 0.739945 0.672668i \(-0.234852\pi\)
0.739945 + 0.672668i \(0.234852\pi\)
\(390\) −3.11132 −0.157548
\(391\) 2.75148 0.139148
\(392\) −6.73767 −0.340304
\(393\) −0.426250 −0.0215015
\(394\) 13.1721 0.663603
\(395\) −13.9505 −0.701927
\(396\) −21.0724 −1.05893
\(397\) 32.9156 1.65199 0.825993 0.563681i \(-0.190615\pi\)
0.825993 + 0.563681i \(0.190615\pi\)
\(398\) −2.33670 −0.117128
\(399\) 11.8497 0.593227
\(400\) −0.432347 −0.0216174
\(401\) 3.99011 0.199257 0.0996284 0.995025i \(-0.468235\pi\)
0.0996284 + 0.995025i \(0.468235\pi\)
\(402\) −27.4181 −1.36749
\(403\) −2.37055 −0.118085
\(404\) 15.3006 0.761233
\(405\) 11.9873 0.595655
\(406\) 5.45702 0.270828
\(407\) −30.6793 −1.52072
\(408\) −2.32245 −0.114978
\(409\) −16.0808 −0.795145 −0.397573 0.917571i \(-0.630147\pi\)
−0.397573 + 0.917571i \(0.630147\pi\)
\(410\) −20.8805 −1.03121
\(411\) −49.0591 −2.41991
\(412\) 7.60134 0.374491
\(413\) −5.89857 −0.290250
\(414\) 19.4836 0.957568
\(415\) −23.3431 −1.14587
\(416\) 0.496248 0.0243305
\(417\) 33.3265 1.63201
\(418\) 29.6449 1.44998
\(419\) 4.85887 0.237371 0.118686 0.992932i \(-0.462132\pi\)
0.118686 + 0.992932i \(0.462132\pi\)
\(420\) −3.21121 −0.156691
\(421\) 20.6219 1.00505 0.502524 0.864563i \(-0.332405\pi\)
0.502524 + 0.864563i \(0.332405\pi\)
\(422\) 10.6670 0.519263
\(423\) 35.2389 1.71338
\(424\) −4.96994 −0.241361
\(425\) −0.342278 −0.0166029
\(426\) 35.4639 1.71823
\(427\) −0.427923 −0.0207086
\(428\) −9.87990 −0.477563
\(429\) 5.47221 0.264201
\(430\) 6.77701 0.326816
\(431\) 3.55708 0.171338 0.0856692 0.996324i \(-0.472697\pi\)
0.0856692 + 0.996324i \(0.472697\pi\)
\(432\) −7.64481 −0.367811
\(433\) −37.0515 −1.78058 −0.890291 0.455392i \(-0.849499\pi\)
−0.890291 + 0.455392i \(0.849499\pi\)
\(434\) −2.44666 −0.117443
\(435\) −66.8004 −3.20283
\(436\) 0.372892 0.0178583
\(437\) −27.4097 −1.31119
\(438\) 27.2638 1.30272
\(439\) 39.8988 1.90427 0.952133 0.305685i \(-0.0988855\pi\)
0.952133 + 0.305685i \(0.0988855\pi\)
\(440\) −8.03362 −0.382988
\(441\) −37.7711 −1.79862
\(442\) 0.392866 0.0186867
\(443\) 20.2233 0.960839 0.480420 0.877039i \(-0.340484\pi\)
0.480420 + 0.877039i \(0.340484\pi\)
\(444\) −23.9431 −1.13629
\(445\) −6.64544 −0.315024
\(446\) −6.24952 −0.295924
\(447\) −30.3837 −1.43710
\(448\) 0.512181 0.0241983
\(449\) 15.6372 0.737967 0.368984 0.929436i \(-0.379706\pi\)
0.368984 + 0.929436i \(0.379706\pi\)
\(450\) −2.42372 −0.114255
\(451\) 36.7248 1.72930
\(452\) 14.0372 0.660256
\(453\) −43.0577 −2.02303
\(454\) −2.71972 −0.127643
\(455\) 0.543210 0.0254661
\(456\) 23.1358 1.08343
\(457\) −6.84392 −0.320145 −0.160073 0.987105i \(-0.551173\pi\)
−0.160073 + 0.987105i \(0.551173\pi\)
\(458\) −15.5315 −0.725741
\(459\) −6.05220 −0.282492
\(460\) 7.42791 0.346328
\(461\) −23.9589 −1.11588 −0.557938 0.829883i \(-0.688407\pi\)
−0.557938 + 0.829883i \(0.688407\pi\)
\(462\) 5.64791 0.262764
\(463\) −23.6330 −1.09832 −0.549160 0.835717i \(-0.685052\pi\)
−0.549160 + 0.835717i \(0.685052\pi\)
\(464\) 10.6545 0.494622
\(465\) 29.9500 1.38890
\(466\) −26.5727 −1.23096
\(467\) 35.4564 1.64073 0.820364 0.571842i \(-0.193771\pi\)
0.820364 + 0.571842i \(0.193771\pi\)
\(468\) 2.78194 0.128595
\(469\) 4.78697 0.221042
\(470\) 13.4344 0.619685
\(471\) 49.2170 2.26780
\(472\) −11.5166 −0.530094
\(473\) −11.9195 −0.548057
\(474\) 19.1489 0.879537
\(475\) 3.40971 0.156448
\(476\) 0.405480 0.0185852
\(477\) −27.8612 −1.27568
\(478\) −13.8726 −0.634517
\(479\) 13.4062 0.612545 0.306272 0.951944i \(-0.400918\pi\)
0.306272 + 0.951944i \(0.400918\pi\)
\(480\) −6.26969 −0.286171
\(481\) 4.05022 0.184674
\(482\) −1.51488 −0.0690008
\(483\) −5.22207 −0.237613
\(484\) 3.12960 0.142254
\(485\) −18.7886 −0.853144
\(486\) 6.48029 0.293952
\(487\) 12.6732 0.574276 0.287138 0.957889i \(-0.407296\pi\)
0.287138 + 0.957889i \(0.407296\pi\)
\(488\) −0.835492 −0.0378209
\(489\) 42.2772 1.91184
\(490\) −14.3998 −0.650516
\(491\) −26.4360 −1.19304 −0.596519 0.802599i \(-0.703450\pi\)
−0.596519 + 0.802599i \(0.703450\pi\)
\(492\) 28.6612 1.29215
\(493\) 8.43489 0.379888
\(494\) −3.91366 −0.176084
\(495\) −45.0361 −2.02422
\(496\) −4.77695 −0.214491
\(497\) −6.19171 −0.277736
\(498\) 32.0414 1.43581
\(499\) 29.2330 1.30865 0.654325 0.756213i \(-0.272953\pi\)
0.654325 + 0.756213i \(0.272953\pi\)
\(500\) −11.6100 −0.519217
\(501\) −71.0989 −3.17646
\(502\) −14.9268 −0.666214
\(503\) −13.0045 −0.579840 −0.289920 0.957051i \(-0.593629\pi\)
−0.289920 + 0.957051i \(0.593629\pi\)
\(504\) 2.87126 0.127896
\(505\) 32.7006 1.45516
\(506\) −13.0643 −0.580778
\(507\) 37.4143 1.66163
\(508\) 17.0192 0.755103
\(509\) −21.6487 −0.959563 −0.479781 0.877388i \(-0.659284\pi\)
−0.479781 + 0.877388i \(0.659284\pi\)
\(510\) −4.96355 −0.219790
\(511\) −4.76004 −0.210572
\(512\) 1.00000 0.0441942
\(513\) 60.2908 2.66190
\(514\) −28.1086 −1.23982
\(515\) 16.2456 0.715868
\(516\) −9.30232 −0.409512
\(517\) −23.6286 −1.03919
\(518\) 4.18027 0.183670
\(519\) −46.0688 −2.02219
\(520\) 1.06058 0.0465097
\(521\) −26.3267 −1.15339 −0.576697 0.816958i \(-0.695659\pi\)
−0.576697 + 0.816958i \(0.695659\pi\)
\(522\) 59.7286 2.61425
\(523\) −44.4467 −1.94352 −0.971759 0.235976i \(-0.924171\pi\)
−0.971759 + 0.235976i \(0.924171\pi\)
\(524\) 0.145300 0.00634745
\(525\) 0.649614 0.0283515
\(526\) −13.2633 −0.578306
\(527\) −3.78178 −0.164737
\(528\) 11.0272 0.479896
\(529\) −10.9207 −0.474815
\(530\) −10.6218 −0.461381
\(531\) −64.5614 −2.80173
\(532\) −4.03932 −0.175127
\(533\) −4.84834 −0.210005
\(534\) 9.12173 0.394736
\(535\) −21.1154 −0.912898
\(536\) 9.34626 0.403697
\(537\) 51.3845 2.21741
\(538\) 24.8275 1.07039
\(539\) 25.3265 1.09089
\(540\) −16.3385 −0.703099
\(541\) −5.15523 −0.221640 −0.110820 0.993840i \(-0.535348\pi\)
−0.110820 + 0.993840i \(0.535348\pi\)
\(542\) −11.7641 −0.505311
\(543\) 31.2495 1.34104
\(544\) 0.791674 0.0339427
\(545\) 0.796948 0.0341375
\(546\) −0.745626 −0.0319098
\(547\) −22.7363 −0.972136 −0.486068 0.873921i \(-0.661569\pi\)
−0.486068 + 0.873921i \(0.661569\pi\)
\(548\) 16.7232 0.714381
\(549\) −4.68373 −0.199897
\(550\) 1.62516 0.0692973
\(551\) −84.0267 −3.57966
\(552\) −10.1958 −0.433961
\(553\) −3.34324 −0.142169
\(554\) −24.8395 −1.05533
\(555\) −51.1713 −2.17210
\(556\) −11.3603 −0.481785
\(557\) 37.6512 1.59533 0.797667 0.603098i \(-0.206067\pi\)
0.797667 + 0.603098i \(0.206067\pi\)
\(558\) −26.7793 −1.13366
\(559\) 1.57358 0.0665555
\(560\) 1.09464 0.0462568
\(561\) 8.72993 0.368578
\(562\) 18.8372 0.794598
\(563\) 41.6686 1.75612 0.878062 0.478548i \(-0.158837\pi\)
0.878062 + 0.478548i \(0.158837\pi\)
\(564\) −18.4405 −0.776485
\(565\) 30.0005 1.26213
\(566\) −12.0030 −0.504524
\(567\) 2.87275 0.120644
\(568\) −12.0889 −0.507239
\(569\) −27.5309 −1.15415 −0.577077 0.816690i \(-0.695807\pi\)
−0.577077 + 0.816690i \(0.695807\pi\)
\(570\) 49.4460 2.07106
\(571\) −24.4727 −1.02415 −0.512075 0.858941i \(-0.671123\pi\)
−0.512075 + 0.858941i \(0.671123\pi\)
\(572\) −1.86536 −0.0779947
\(573\) 1.54503 0.0645447
\(574\) −5.00400 −0.208863
\(575\) −1.50263 −0.0626641
\(576\) 5.60596 0.233581
\(577\) 30.4840 1.26907 0.634533 0.772896i \(-0.281192\pi\)
0.634533 + 0.772896i \(0.281192\pi\)
\(578\) −16.3733 −0.681038
\(579\) 14.4190 0.599234
\(580\) 22.7709 0.945508
\(581\) −5.59417 −0.232085
\(582\) 25.7897 1.06902
\(583\) 18.6817 0.773716
\(584\) −9.29368 −0.384575
\(585\) 5.94558 0.245820
\(586\) −26.5703 −1.09761
\(587\) 6.36677 0.262785 0.131392 0.991330i \(-0.458055\pi\)
0.131392 + 0.991330i \(0.458055\pi\)
\(588\) 19.7656 0.815118
\(589\) 37.6734 1.55231
\(590\) −24.6133 −1.01331
\(591\) −38.6417 −1.58951
\(592\) 8.16170 0.335444
\(593\) −34.2163 −1.40510 −0.702548 0.711636i \(-0.747955\pi\)
−0.702548 + 0.711636i \(0.747955\pi\)
\(594\) 28.7363 1.17907
\(595\) 0.866595 0.0355269
\(596\) 10.3572 0.424246
\(597\) 6.85491 0.280553
\(598\) 1.72472 0.0705290
\(599\) −10.1414 −0.414366 −0.207183 0.978302i \(-0.566430\pi\)
−0.207183 + 0.978302i \(0.566430\pi\)
\(600\) 1.26833 0.0517793
\(601\) −36.1932 −1.47635 −0.738176 0.674608i \(-0.764313\pi\)
−0.738176 + 0.674608i \(0.764313\pi\)
\(602\) 1.62411 0.0661937
\(603\) 52.3947 2.13368
\(604\) 14.6775 0.597217
\(605\) 6.68860 0.271930
\(606\) −44.8857 −1.82336
\(607\) 32.6689 1.32599 0.662996 0.748623i \(-0.269285\pi\)
0.662996 + 0.748623i \(0.269285\pi\)
\(608\) −7.88651 −0.319840
\(609\) −16.0087 −0.648704
\(610\) −1.78562 −0.0722976
\(611\) 3.11940 0.126198
\(612\) 4.43809 0.179399
\(613\) −3.25737 −0.131564 −0.0657819 0.997834i \(-0.520954\pi\)
−0.0657819 + 0.997834i \(0.520954\pi\)
\(614\) −3.01042 −0.121491
\(615\) 61.2548 2.47003
\(616\) −1.92525 −0.0775707
\(617\) −4.15597 −0.167313 −0.0836566 0.996495i \(-0.526660\pi\)
−0.0836566 + 0.996495i \(0.526660\pi\)
\(618\) −22.2992 −0.897006
\(619\) 5.87241 0.236032 0.118016 0.993012i \(-0.462347\pi\)
0.118016 + 0.993012i \(0.462347\pi\)
\(620\) −10.2093 −0.410016
\(621\) −26.5697 −1.06621
\(622\) −32.6484 −1.30908
\(623\) −1.59258 −0.0638053
\(624\) −1.45579 −0.0582781
\(625\) −22.6513 −0.906054
\(626\) 14.7984 0.591464
\(627\) −86.9659 −3.47308
\(628\) −16.7771 −0.669477
\(629\) 6.46141 0.257633
\(630\) 6.13648 0.244483
\(631\) −14.6696 −0.583986 −0.291993 0.956420i \(-0.594318\pi\)
−0.291993 + 0.956420i \(0.594318\pi\)
\(632\) −6.52746 −0.259648
\(633\) −31.2927 −1.24377
\(634\) −20.5053 −0.814368
\(635\) 36.3735 1.44344
\(636\) 14.5798 0.578125
\(637\) −3.34355 −0.132476
\(638\) −40.0496 −1.58558
\(639\) −67.7699 −2.68094
\(640\) 2.13721 0.0844805
\(641\) 50.1773 1.98188 0.990941 0.134297i \(-0.0428775\pi\)
0.990941 + 0.134297i \(0.0428775\pi\)
\(642\) 28.9836 1.14389
\(643\) −8.40217 −0.331349 −0.165675 0.986180i \(-0.552980\pi\)
−0.165675 + 0.986180i \(0.552980\pi\)
\(644\) 1.78010 0.0701456
\(645\) −19.8810 −0.782813
\(646\) −6.24354 −0.245649
\(647\) −30.0993 −1.18332 −0.591662 0.806186i \(-0.701528\pi\)
−0.591662 + 0.806186i \(0.701528\pi\)
\(648\) 5.60887 0.220337
\(649\) 43.2901 1.69928
\(650\) −0.214551 −0.00841539
\(651\) 7.17750 0.281308
\(652\) −14.4114 −0.564395
\(653\) −16.1370 −0.631490 −0.315745 0.948844i \(-0.602254\pi\)
−0.315745 + 0.948844i \(0.602254\pi\)
\(654\) −1.09391 −0.0427754
\(655\) 0.310536 0.0121336
\(656\) −9.76999 −0.381454
\(657\) −52.0999 −2.03261
\(658\) 3.21956 0.125511
\(659\) 6.97166 0.271577 0.135789 0.990738i \(-0.456643\pi\)
0.135789 + 0.990738i \(0.456643\pi\)
\(660\) 23.5674 0.917358
\(661\) −0.204648 −0.00795990 −0.00397995 0.999992i \(-0.501267\pi\)
−0.00397995 + 0.999992i \(0.501267\pi\)
\(662\) 4.60693 0.179053
\(663\) −1.15251 −0.0447597
\(664\) −10.9223 −0.423866
\(665\) −8.63285 −0.334768
\(666\) 45.7541 1.77294
\(667\) 37.0299 1.43381
\(668\) 24.2361 0.937724
\(669\) 18.3335 0.708816
\(670\) 19.9749 0.771697
\(671\) 3.14056 0.121240
\(672\) −1.50253 −0.0579613
\(673\) −42.2927 −1.63026 −0.815131 0.579276i \(-0.803335\pi\)
−0.815131 + 0.579276i \(0.803335\pi\)
\(674\) −26.8660 −1.03484
\(675\) 3.30521 0.127218
\(676\) −12.7537 −0.490528
\(677\) 43.7485 1.68139 0.840695 0.541508i \(-0.182147\pi\)
0.840695 + 0.541508i \(0.182147\pi\)
\(678\) −41.1795 −1.58149
\(679\) −4.50267 −0.172797
\(680\) 1.69197 0.0648841
\(681\) 7.97855 0.305739
\(682\) 17.9562 0.687580
\(683\) −4.95345 −0.189538 −0.0947692 0.995499i \(-0.530211\pi\)
−0.0947692 + 0.995499i \(0.530211\pi\)
\(684\) −44.2114 −1.69047
\(685\) 35.7410 1.36559
\(686\) −7.03617 −0.268642
\(687\) 45.5632 1.73834
\(688\) 3.17097 0.120892
\(689\) −2.46632 −0.0939592
\(690\) −21.7905 −0.829549
\(691\) 11.0630 0.420855 0.210428 0.977609i \(-0.432514\pi\)
0.210428 + 0.977609i \(0.432514\pi\)
\(692\) 15.7039 0.596972
\(693\) −10.7929 −0.409988
\(694\) 7.82858 0.297169
\(695\) −24.2794 −0.920968
\(696\) −31.2559 −1.18475
\(697\) −7.73465 −0.292971
\(698\) 7.56079 0.286180
\(699\) 77.9535 2.94847
\(700\) −0.221440 −0.00836964
\(701\) −32.0270 −1.20964 −0.604821 0.796361i \(-0.706755\pi\)
−0.604821 + 0.796361i \(0.706755\pi\)
\(702\) −3.79372 −0.143185
\(703\) −64.3673 −2.42766
\(704\) −3.75894 −0.141670
\(705\) −39.4112 −1.48431
\(706\) 8.62179 0.324485
\(707\) 7.83667 0.294728
\(708\) 33.7849 1.26972
\(709\) 19.8478 0.745401 0.372701 0.927952i \(-0.378432\pi\)
0.372701 + 0.927952i \(0.378432\pi\)
\(710\) −25.8365 −0.969627
\(711\) −36.5926 −1.37233
\(712\) −3.10941 −0.116530
\(713\) −16.6024 −0.621764
\(714\) −1.18951 −0.0445164
\(715\) −3.98667 −0.149093
\(716\) −17.5159 −0.654600
\(717\) 40.6965 1.51984
\(718\) −8.31771 −0.310414
\(719\) −22.3077 −0.831938 −0.415969 0.909379i \(-0.636558\pi\)
−0.415969 + 0.909379i \(0.636558\pi\)
\(720\) 11.9811 0.446509
\(721\) 3.89326 0.144993
\(722\) 43.1970 1.60762
\(723\) 4.44403 0.165275
\(724\) −10.6523 −0.395890
\(725\) −4.60644 −0.171079
\(726\) −9.18096 −0.340737
\(727\) 48.1921 1.78735 0.893674 0.448718i \(-0.148119\pi\)
0.893674 + 0.448718i \(0.148119\pi\)
\(728\) 0.254168 0.00942011
\(729\) −35.8371 −1.32730
\(730\) −19.8625 −0.735145
\(731\) 2.51037 0.0928494
\(732\) 2.45099 0.0905913
\(733\) 34.7110 1.28208 0.641041 0.767507i \(-0.278503\pi\)
0.641041 + 0.767507i \(0.278503\pi\)
\(734\) −3.19579 −0.117959
\(735\) 42.2431 1.55816
\(736\) 3.47552 0.128110
\(737\) −35.1320 −1.29410
\(738\) −54.7702 −2.01612
\(739\) 43.7162 1.60813 0.804063 0.594545i \(-0.202668\pi\)
0.804063 + 0.594545i \(0.202668\pi\)
\(740\) 17.4432 0.641226
\(741\) 11.4811 0.421768
\(742\) −2.54550 −0.0934484
\(743\) −24.6376 −0.903868 −0.451934 0.892051i \(-0.649266\pi\)
−0.451934 + 0.892051i \(0.649266\pi\)
\(744\) 14.0136 0.513764
\(745\) 22.1354 0.810979
\(746\) −34.9203 −1.27852
\(747\) −61.2297 −2.24028
\(748\) −2.97585 −0.108808
\(749\) −5.06029 −0.184899
\(750\) 34.0591 1.24366
\(751\) 2.94149 0.107337 0.0536683 0.998559i \(-0.482909\pi\)
0.0536683 + 0.998559i \(0.482909\pi\)
\(752\) 6.28598 0.229226
\(753\) 43.7890 1.59576
\(754\) 5.28727 0.192551
\(755\) 31.3688 1.14163
\(756\) −3.91552 −0.142406
\(757\) −6.24680 −0.227044 −0.113522 0.993535i \(-0.536213\pi\)
−0.113522 + 0.993535i \(0.536213\pi\)
\(758\) −24.9331 −0.905609
\(759\) 38.3252 1.39112
\(760\) −16.8551 −0.611399
\(761\) 9.98552 0.361975 0.180987 0.983485i \(-0.442071\pi\)
0.180987 + 0.983485i \(0.442071\pi\)
\(762\) −49.9273 −1.80867
\(763\) 0.190988 0.00691423
\(764\) −0.526669 −0.0190542
\(765\) 9.48512 0.342935
\(766\) −3.63985 −0.131513
\(767\) −5.71507 −0.206359
\(768\) −2.93359 −0.105857
\(769\) 33.6538 1.21359 0.606793 0.794860i \(-0.292456\pi\)
0.606793 + 0.794860i \(0.292456\pi\)
\(770\) −4.11467 −0.148282
\(771\) 82.4591 2.96969
\(772\) −4.91514 −0.176900
\(773\) −23.5186 −0.845905 −0.422953 0.906152i \(-0.639006\pi\)
−0.422953 + 0.906152i \(0.639006\pi\)
\(774\) 17.7763 0.638956
\(775\) 2.06530 0.0741877
\(776\) −8.79117 −0.315585
\(777\) −12.2632 −0.439939
\(778\) 29.1880 1.04644
\(779\) 77.0511 2.76064
\(780\) −3.11132 −0.111403
\(781\) 45.4414 1.62602
\(782\) 2.75148 0.0983928
\(783\) −81.4515 −2.91084
\(784\) −6.73767 −0.240631
\(785\) −35.8560 −1.27976
\(786\) −0.426250 −0.0152038
\(787\) 18.8879 0.673280 0.336640 0.941634i \(-0.390710\pi\)
0.336640 + 0.941634i \(0.390710\pi\)
\(788\) 13.1721 0.469238
\(789\) 38.9090 1.38520
\(790\) −13.9505 −0.496337
\(791\) 7.18960 0.255633
\(792\) −21.0724 −0.748776
\(793\) −0.414611 −0.0147233
\(794\) 32.9156 1.16813
\(795\) 31.1600 1.10513
\(796\) −2.33670 −0.0828220
\(797\) −22.3235 −0.790739 −0.395369 0.918522i \(-0.629383\pi\)
−0.395369 + 0.918522i \(0.629383\pi\)
\(798\) 11.8497 0.419475
\(799\) 4.97645 0.176054
\(800\) −0.432347 −0.0152858
\(801\) −17.4312 −0.615901
\(802\) 3.99011 0.140896
\(803\) 34.9343 1.23281
\(804\) −27.4181 −0.966962
\(805\) 3.80443 0.134089
\(806\) −2.37055 −0.0834990
\(807\) −72.8338 −2.56387
\(808\) 15.3006 0.538273
\(809\) −4.10546 −0.144340 −0.0721702 0.997392i \(-0.522992\pi\)
−0.0721702 + 0.997392i \(0.522992\pi\)
\(810\) 11.9873 0.421191
\(811\) 38.9482 1.36766 0.683828 0.729643i \(-0.260314\pi\)
0.683828 + 0.729643i \(0.260314\pi\)
\(812\) 5.45702 0.191504
\(813\) 34.5111 1.21036
\(814\) −30.6793 −1.07531
\(815\) −30.8002 −1.07888
\(816\) −2.32245 −0.0813019
\(817\) −25.0078 −0.874913
\(818\) −16.0808 −0.562253
\(819\) 1.42486 0.0497885
\(820\) −20.8805 −0.729179
\(821\) −22.7832 −0.795139 −0.397570 0.917572i \(-0.630146\pi\)
−0.397570 + 0.917572i \(0.630146\pi\)
\(822\) −49.0591 −1.71113
\(823\) −8.16719 −0.284690 −0.142345 0.989817i \(-0.545464\pi\)
−0.142345 + 0.989817i \(0.545464\pi\)
\(824\) 7.60134 0.264805
\(825\) −4.76757 −0.165985
\(826\) −5.89857 −0.205237
\(827\) 34.8373 1.21141 0.605706 0.795689i \(-0.292891\pi\)
0.605706 + 0.795689i \(0.292891\pi\)
\(828\) 19.4836 0.677103
\(829\) −31.1862 −1.08314 −0.541570 0.840655i \(-0.682170\pi\)
−0.541570 + 0.840655i \(0.682170\pi\)
\(830\) −23.3431 −0.810252
\(831\) 72.8688 2.52779
\(832\) 0.496248 0.0172043
\(833\) −5.33404 −0.184814
\(834\) 33.3265 1.15400
\(835\) 51.7976 1.79253
\(836\) 29.6449 1.02529
\(837\) 36.5188 1.26228
\(838\) 4.85887 0.167847
\(839\) −23.8689 −0.824047 −0.412023 0.911173i \(-0.635178\pi\)
−0.412023 + 0.911173i \(0.635178\pi\)
\(840\) −3.21121 −0.110797
\(841\) 84.5182 2.91442
\(842\) 20.6219 0.710676
\(843\) −55.2605 −1.90327
\(844\) 10.6670 0.367174
\(845\) −27.2574 −0.937682
\(846\) 35.2389 1.21154
\(847\) 1.60292 0.0550770
\(848\) −4.96994 −0.170668
\(849\) 35.2119 1.20847
\(850\) −0.342278 −0.0117400
\(851\) 28.3662 0.972380
\(852\) 35.4639 1.21497
\(853\) 23.8896 0.817963 0.408982 0.912543i \(-0.365884\pi\)
0.408982 + 0.912543i \(0.365884\pi\)
\(854\) −0.427923 −0.0146432
\(855\) −94.4889 −3.23145
\(856\) −9.87990 −0.337688
\(857\) −12.1322 −0.414428 −0.207214 0.978296i \(-0.566440\pi\)
−0.207214 + 0.978296i \(0.566440\pi\)
\(858\) 5.47221 0.186818
\(859\) 46.9899 1.60327 0.801637 0.597811i \(-0.203963\pi\)
0.801637 + 0.597811i \(0.203963\pi\)
\(860\) 6.77701 0.231094
\(861\) 14.6797 0.500283
\(862\) 3.55708 0.121154
\(863\) 18.7609 0.638627 0.319313 0.947649i \(-0.396548\pi\)
0.319313 + 0.947649i \(0.396548\pi\)
\(864\) −7.64481 −0.260082
\(865\) 33.5625 1.14116
\(866\) −37.0515 −1.25906
\(867\) 48.0324 1.63127
\(868\) −2.44666 −0.0830450
\(869\) 24.5363 0.832336
\(870\) −66.8004 −2.26474
\(871\) 4.63806 0.157155
\(872\) 0.372892 0.0126277
\(873\) −49.2829 −1.66797
\(874\) −27.4097 −0.927148
\(875\) −5.94644 −0.201026
\(876\) 27.2638 0.921160
\(877\) −38.7335 −1.30794 −0.653969 0.756521i \(-0.726897\pi\)
−0.653969 + 0.756521i \(0.726897\pi\)
\(878\) 39.8988 1.34652
\(879\) 77.9465 2.62907
\(880\) −8.03362 −0.270813
\(881\) 34.0835 1.14830 0.574152 0.818749i \(-0.305332\pi\)
0.574152 + 0.818749i \(0.305332\pi\)
\(882\) −37.7711 −1.27182
\(883\) −27.1482 −0.913608 −0.456804 0.889567i \(-0.651006\pi\)
−0.456804 + 0.889567i \(0.651006\pi\)
\(884\) 0.392866 0.0132135
\(885\) 72.2054 2.42716
\(886\) 20.2233 0.679416
\(887\) −28.5311 −0.957980 −0.478990 0.877820i \(-0.658997\pi\)
−0.478990 + 0.877820i \(0.658997\pi\)
\(888\) −23.9431 −0.803478
\(889\) 8.71688 0.292355
\(890\) −6.64544 −0.222756
\(891\) −21.0834 −0.706320
\(892\) −6.24952 −0.209250
\(893\) −49.5745 −1.65895
\(894\) −30.3837 −1.01618
\(895\) −37.4351 −1.25132
\(896\) 0.512181 0.0171108
\(897\) −5.05962 −0.168936
\(898\) 15.6372 0.521822
\(899\) −50.8959 −1.69747
\(900\) −2.42372 −0.0807906
\(901\) −3.93457 −0.131080
\(902\) 36.7248 1.22280
\(903\) −4.76447 −0.158551
\(904\) 14.0372 0.466871
\(905\) −22.7662 −0.756773
\(906\) −43.0577 −1.43050
\(907\) −9.10965 −0.302481 −0.151241 0.988497i \(-0.548327\pi\)
−0.151241 + 0.988497i \(0.548327\pi\)
\(908\) −2.71972 −0.0902571
\(909\) 85.7745 2.84496
\(910\) 0.543210 0.0180072
\(911\) −50.9909 −1.68940 −0.844702 0.535238i \(-0.820222\pi\)
−0.844702 + 0.535238i \(0.820222\pi\)
\(912\) 23.1358 0.766102
\(913\) 41.0561 1.35876
\(914\) −6.84392 −0.226377
\(915\) 5.23828 0.173172
\(916\) −15.5315 −0.513177
\(917\) 0.0744197 0.00245755
\(918\) −6.05220 −0.199752
\(919\) −32.8564 −1.08383 −0.541917 0.840432i \(-0.682301\pi\)
−0.541917 + 0.840432i \(0.682301\pi\)
\(920\) 7.42791 0.244891
\(921\) 8.83135 0.291003
\(922\) −23.9589 −0.789044
\(923\) −5.99909 −0.197463
\(924\) 5.64791 0.185803
\(925\) −3.52869 −0.116023
\(926\) −23.6330 −0.776630
\(927\) 42.6128 1.39959
\(928\) 10.6545 0.349751
\(929\) −34.4575 −1.13051 −0.565256 0.824915i \(-0.691223\pi\)
−0.565256 + 0.824915i \(0.691223\pi\)
\(930\) 29.9500 0.982098
\(931\) 53.1367 1.74148
\(932\) −26.5727 −0.870419
\(933\) 95.7769 3.13560
\(934\) 35.4564 1.16017
\(935\) −6.36001 −0.207995
\(936\) 2.78194 0.0909306
\(937\) −8.79159 −0.287209 −0.143604 0.989635i \(-0.545869\pi\)
−0.143604 + 0.989635i \(0.545869\pi\)
\(938\) 4.78697 0.156300
\(939\) −43.4125 −1.41671
\(940\) 13.4344 0.438183
\(941\) −29.5580 −0.963563 −0.481782 0.876291i \(-0.660010\pi\)
−0.481782 + 0.876291i \(0.660010\pi\)
\(942\) 49.2170 1.60358
\(943\) −33.9558 −1.10575
\(944\) −11.5166 −0.374833
\(945\) −8.36828 −0.272220
\(946\) −11.9195 −0.387535
\(947\) 26.3146 0.855109 0.427555 0.903990i \(-0.359375\pi\)
0.427555 + 0.903990i \(0.359375\pi\)
\(948\) 19.1489 0.621927
\(949\) −4.61196 −0.149711
\(950\) 3.40971 0.110626
\(951\) 60.1541 1.95063
\(952\) 0.405480 0.0131417
\(953\) −21.4241 −0.693996 −0.346998 0.937866i \(-0.612799\pi\)
−0.346998 + 0.937866i \(0.612799\pi\)
\(954\) −27.8612 −0.902041
\(955\) −1.12560 −0.0364236
\(956\) −13.8726 −0.448672
\(957\) 117.489 3.79788
\(958\) 13.4062 0.433134
\(959\) 8.56532 0.276588
\(960\) −6.26969 −0.202353
\(961\) −8.18078 −0.263896
\(962\) 4.05022 0.130584
\(963\) −55.3863 −1.78480
\(964\) −1.51488 −0.0487909
\(965\) −10.5047 −0.338158
\(966\) −5.22207 −0.168017
\(967\) 18.1263 0.582902 0.291451 0.956586i \(-0.405862\pi\)
0.291451 + 0.956586i \(0.405862\pi\)
\(968\) 3.12960 0.100589
\(969\) 18.3160 0.588395
\(970\) −18.7886 −0.603264
\(971\) 14.1363 0.453654 0.226827 0.973935i \(-0.427165\pi\)
0.226827 + 0.973935i \(0.427165\pi\)
\(972\) 6.48029 0.207855
\(973\) −5.81854 −0.186534
\(974\) 12.6732 0.406075
\(975\) 0.629405 0.0201571
\(976\) −0.835492 −0.0267434
\(977\) −40.4882 −1.29533 −0.647666 0.761924i \(-0.724255\pi\)
−0.647666 + 0.761924i \(0.724255\pi\)
\(978\) 42.2772 1.35188
\(979\) 11.6881 0.373552
\(980\) −14.3998 −0.459985
\(981\) 2.09042 0.0667419
\(982\) −26.4360 −0.843606
\(983\) 18.4960 0.589932 0.294966 0.955508i \(-0.404692\pi\)
0.294966 + 0.955508i \(0.404692\pi\)
\(984\) 28.6612 0.913685
\(985\) 28.1516 0.896984
\(986\) 8.43489 0.268621
\(987\) −9.44487 −0.300634
\(988\) −3.91366 −0.124510
\(989\) 11.0208 0.350440
\(990\) −45.0361 −1.43134
\(991\) −25.3351 −0.804796 −0.402398 0.915465i \(-0.631823\pi\)
−0.402398 + 0.915465i \(0.631823\pi\)
\(992\) −4.77695 −0.151668
\(993\) −13.5149 −0.428881
\(994\) −6.19171 −0.196389
\(995\) −4.99400 −0.158320
\(996\) 32.0414 1.01527
\(997\) 56.5943 1.79236 0.896180 0.443692i \(-0.146331\pi\)
0.896180 + 0.443692i \(0.146331\pi\)
\(998\) 29.2330 0.925356
\(999\) −62.3946 −1.97408
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.a.1.8 75
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8038.2.a.a.1.8 75 1.1 even 1 trivial