Properties

Label 4017.2.a.e.1.8
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $16$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} - 2118 x^{6} - 710 x^{5} + 1113 x^{4} + 243 x^{3} - 183 x^{2} - 10 x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(0.256478\) of defining polynomial
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.256478 q^{2} +1.00000 q^{3} -1.93422 q^{4} -0.330746 q^{5} -0.256478 q^{6} +1.25226 q^{7} +1.00904 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.256478 q^{2} +1.00000 q^{3} -1.93422 q^{4} -0.330746 q^{5} -0.256478 q^{6} +1.25226 q^{7} +1.00904 q^{8} +1.00000 q^{9} +0.0848290 q^{10} -0.708671 q^{11} -1.93422 q^{12} -1.00000 q^{13} -0.321176 q^{14} -0.330746 q^{15} +3.60964 q^{16} -5.11986 q^{17} -0.256478 q^{18} +4.61143 q^{19} +0.639735 q^{20} +1.25226 q^{21} +0.181758 q^{22} +4.94053 q^{23} +1.00904 q^{24} -4.89061 q^{25} +0.256478 q^{26} +1.00000 q^{27} -2.42214 q^{28} -5.42929 q^{29} +0.0848290 q^{30} -7.69609 q^{31} -2.94387 q^{32} -0.708671 q^{33} +1.31313 q^{34} -0.414179 q^{35} -1.93422 q^{36} -10.3326 q^{37} -1.18273 q^{38} -1.00000 q^{39} -0.333736 q^{40} +8.14897 q^{41} -0.321176 q^{42} +6.55836 q^{43} +1.37073 q^{44} -0.330746 q^{45} -1.26714 q^{46} -6.08641 q^{47} +3.60964 q^{48} -5.43185 q^{49} +1.25433 q^{50} -5.11986 q^{51} +1.93422 q^{52} +6.75068 q^{53} -0.256478 q^{54} +0.234390 q^{55} +1.26358 q^{56} +4.61143 q^{57} +1.39249 q^{58} +13.2817 q^{59} +0.639735 q^{60} +0.799420 q^{61} +1.97388 q^{62} +1.25226 q^{63} -6.46425 q^{64} +0.330746 q^{65} +0.181758 q^{66} -2.78601 q^{67} +9.90293 q^{68} +4.94053 q^{69} +0.106228 q^{70} -4.43224 q^{71} +1.00904 q^{72} +14.2243 q^{73} +2.65009 q^{74} -4.89061 q^{75} -8.91952 q^{76} -0.887438 q^{77} +0.256478 q^{78} -0.500065 q^{79} -1.19387 q^{80} +1.00000 q^{81} -2.09003 q^{82} -5.34068 q^{83} -2.42214 q^{84} +1.69337 q^{85} -1.68207 q^{86} -5.42929 q^{87} -0.715077 q^{88} -10.3891 q^{89} +0.0848290 q^{90} -1.25226 q^{91} -9.55607 q^{92} -7.69609 q^{93} +1.56103 q^{94} -1.52521 q^{95} -2.94387 q^{96} -9.27613 q^{97} +1.39315 q^{98} -0.708671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.256478 −0.181357 −0.0906786 0.995880i \(-0.528904\pi\)
−0.0906786 + 0.995880i \(0.528904\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.93422 −0.967110
\(5\) −0.330746 −0.147914 −0.0739570 0.997261i \(-0.523563\pi\)
−0.0739570 + 0.997261i \(0.523563\pi\)
\(6\) −0.256478 −0.104707
\(7\) 1.25226 0.473308 0.236654 0.971594i \(-0.423949\pi\)
0.236654 + 0.971594i \(0.423949\pi\)
\(8\) 1.00904 0.356750
\(9\) 1.00000 0.333333
\(10\) 0.0848290 0.0268253
\(11\) −0.708671 −0.213672 −0.106836 0.994277i \(-0.534072\pi\)
−0.106836 + 0.994277i \(0.534072\pi\)
\(12\) −1.93422 −0.558361
\(13\) −1.00000 −0.277350
\(14\) −0.321176 −0.0858379
\(15\) −0.330746 −0.0853982
\(16\) 3.60964 0.902410
\(17\) −5.11986 −1.24175 −0.620874 0.783910i \(-0.713222\pi\)
−0.620874 + 0.783910i \(0.713222\pi\)
\(18\) −0.256478 −0.0604524
\(19\) 4.61143 1.05794 0.528968 0.848642i \(-0.322579\pi\)
0.528968 + 0.848642i \(0.322579\pi\)
\(20\) 0.639735 0.143049
\(21\) 1.25226 0.273265
\(22\) 0.181758 0.0387510
\(23\) 4.94053 1.03017 0.515086 0.857138i \(-0.327760\pi\)
0.515086 + 0.857138i \(0.327760\pi\)
\(24\) 1.00904 0.205969
\(25\) −4.89061 −0.978121
\(26\) 0.256478 0.0502994
\(27\) 1.00000 0.192450
\(28\) −2.42214 −0.457741
\(29\) −5.42929 −1.00819 −0.504097 0.863647i \(-0.668175\pi\)
−0.504097 + 0.863647i \(0.668175\pi\)
\(30\) 0.0848290 0.0154876
\(31\) −7.69609 −1.38226 −0.691130 0.722731i \(-0.742887\pi\)
−0.691130 + 0.722731i \(0.742887\pi\)
\(32\) −2.94387 −0.520408
\(33\) −0.708671 −0.123364
\(34\) 1.31313 0.225200
\(35\) −0.414179 −0.0700089
\(36\) −1.93422 −0.322370
\(37\) −10.3326 −1.69868 −0.849338 0.527850i \(-0.822998\pi\)
−0.849338 + 0.527850i \(0.822998\pi\)
\(38\) −1.18273 −0.191864
\(39\) −1.00000 −0.160128
\(40\) −0.333736 −0.0527683
\(41\) 8.14897 1.27265 0.636327 0.771419i \(-0.280453\pi\)
0.636327 + 0.771419i \(0.280453\pi\)
\(42\) −0.321176 −0.0495585
\(43\) 6.55836 1.00014 0.500070 0.865985i \(-0.333308\pi\)
0.500070 + 0.865985i \(0.333308\pi\)
\(44\) 1.37073 0.206645
\(45\) −0.330746 −0.0493047
\(46\) −1.26714 −0.186829
\(47\) −6.08641 −0.887794 −0.443897 0.896078i \(-0.646404\pi\)
−0.443897 + 0.896078i \(0.646404\pi\)
\(48\) 3.60964 0.521007
\(49\) −5.43185 −0.775979
\(50\) 1.25433 0.177389
\(51\) −5.11986 −0.716924
\(52\) 1.93422 0.268228
\(53\) 6.75068 0.927277 0.463638 0.886025i \(-0.346544\pi\)
0.463638 + 0.886025i \(0.346544\pi\)
\(54\) −0.256478 −0.0349022
\(55\) 0.234390 0.0316051
\(56\) 1.26358 0.168853
\(57\) 4.61143 0.610799
\(58\) 1.39249 0.182843
\(59\) 13.2817 1.72912 0.864562 0.502526i \(-0.167596\pi\)
0.864562 + 0.502526i \(0.167596\pi\)
\(60\) 0.639735 0.0825894
\(61\) 0.799420 0.102355 0.0511776 0.998690i \(-0.483703\pi\)
0.0511776 + 0.998690i \(0.483703\pi\)
\(62\) 1.97388 0.250683
\(63\) 1.25226 0.157769
\(64\) −6.46425 −0.808031
\(65\) 0.330746 0.0410240
\(66\) 0.181758 0.0223729
\(67\) −2.78601 −0.340365 −0.170183 0.985413i \(-0.554436\pi\)
−0.170183 + 0.985413i \(0.554436\pi\)
\(68\) 9.90293 1.20091
\(69\) 4.94053 0.594770
\(70\) 0.106228 0.0126966
\(71\) −4.43224 −0.526011 −0.263005 0.964794i \(-0.584714\pi\)
−0.263005 + 0.964794i \(0.584714\pi\)
\(72\) 1.00904 0.118917
\(73\) 14.2243 1.66483 0.832414 0.554155i \(-0.186958\pi\)
0.832414 + 0.554155i \(0.186958\pi\)
\(74\) 2.65009 0.308067
\(75\) −4.89061 −0.564719
\(76\) −8.91952 −1.02314
\(77\) −0.887438 −0.101133
\(78\) 0.256478 0.0290404
\(79\) −0.500065 −0.0562617 −0.0281309 0.999604i \(-0.508956\pi\)
−0.0281309 + 0.999604i \(0.508956\pi\)
\(80\) −1.19387 −0.133479
\(81\) 1.00000 0.111111
\(82\) −2.09003 −0.230805
\(83\) −5.34068 −0.586215 −0.293108 0.956079i \(-0.594689\pi\)
−0.293108 + 0.956079i \(0.594689\pi\)
\(84\) −2.42214 −0.264277
\(85\) 1.69337 0.183672
\(86\) −1.68207 −0.181383
\(87\) −5.42929 −0.582081
\(88\) −0.715077 −0.0762275
\(89\) −10.3891 −1.10125 −0.550624 0.834754i \(-0.685610\pi\)
−0.550624 + 0.834754i \(0.685610\pi\)
\(90\) 0.0848290 0.00894176
\(91\) −1.25226 −0.131272
\(92\) −9.55607 −0.996289
\(93\) −7.69609 −0.798048
\(94\) 1.56103 0.161008
\(95\) −1.52521 −0.156483
\(96\) −2.94387 −0.300458
\(97\) −9.27613 −0.941848 −0.470924 0.882174i \(-0.656079\pi\)
−0.470924 + 0.882174i \(0.656079\pi\)
\(98\) 1.39315 0.140729
\(99\) −0.708671 −0.0712241
\(100\) 9.45951 0.945951
\(101\) −12.4389 −1.23772 −0.618858 0.785503i \(-0.712404\pi\)
−0.618858 + 0.785503i \(0.712404\pi\)
\(102\) 1.31313 0.130019
\(103\) 1.00000 0.0985329
\(104\) −1.00904 −0.0989445
\(105\) −0.414179 −0.0404197
\(106\) −1.73140 −0.168168
\(107\) 9.17964 0.887429 0.443715 0.896168i \(-0.353660\pi\)
0.443715 + 0.896168i \(0.353660\pi\)
\(108\) −1.93422 −0.186120
\(109\) −14.3027 −1.36995 −0.684975 0.728567i \(-0.740187\pi\)
−0.684975 + 0.728567i \(0.740187\pi\)
\(110\) −0.0601158 −0.00573182
\(111\) −10.3326 −0.980731
\(112\) 4.52020 0.427118
\(113\) −9.63960 −0.906817 −0.453409 0.891303i \(-0.649792\pi\)
−0.453409 + 0.891303i \(0.649792\pi\)
\(114\) −1.18273 −0.110773
\(115\) −1.63406 −0.152377
\(116\) 10.5014 0.975034
\(117\) −1.00000 −0.0924500
\(118\) −3.40645 −0.313589
\(119\) −6.41138 −0.587730
\(120\) −0.333736 −0.0304658
\(121\) −10.4978 −0.954344
\(122\) −0.205034 −0.0185629
\(123\) 8.14897 0.734768
\(124\) 14.8859 1.33680
\(125\) 3.27128 0.292592
\(126\) −0.321176 −0.0286126
\(127\) −6.11083 −0.542248 −0.271124 0.962544i \(-0.587395\pi\)
−0.271124 + 0.962544i \(0.587395\pi\)
\(128\) 7.54568 0.666950
\(129\) 6.55836 0.577431
\(130\) −0.0848290 −0.00743999
\(131\) −13.1424 −1.14826 −0.574128 0.818766i \(-0.694659\pi\)
−0.574128 + 0.818766i \(0.694659\pi\)
\(132\) 1.37073 0.119306
\(133\) 5.77470 0.500730
\(134\) 0.714550 0.0617277
\(135\) −0.330746 −0.0284661
\(136\) −5.16614 −0.442993
\(137\) −6.50977 −0.556167 −0.278084 0.960557i \(-0.589699\pi\)
−0.278084 + 0.960557i \(0.589699\pi\)
\(138\) −1.26714 −0.107866
\(139\) 2.15233 0.182559 0.0912793 0.995825i \(-0.470904\pi\)
0.0912793 + 0.995825i \(0.470904\pi\)
\(140\) 0.801112 0.0677063
\(141\) −6.08641 −0.512568
\(142\) 1.13677 0.0953958
\(143\) 0.708671 0.0592620
\(144\) 3.60964 0.300803
\(145\) 1.79572 0.149126
\(146\) −3.64822 −0.301929
\(147\) −5.43185 −0.448012
\(148\) 19.9856 1.64281
\(149\) −14.2020 −1.16348 −0.581738 0.813376i \(-0.697627\pi\)
−0.581738 + 0.813376i \(0.697627\pi\)
\(150\) 1.25433 0.102416
\(151\) 18.8801 1.53644 0.768219 0.640187i \(-0.221143\pi\)
0.768219 + 0.640187i \(0.221143\pi\)
\(152\) 4.65312 0.377418
\(153\) −5.11986 −0.413916
\(154\) 0.227608 0.0183412
\(155\) 2.54545 0.204456
\(156\) 1.93422 0.154861
\(157\) −10.2255 −0.816081 −0.408040 0.912964i \(-0.633788\pi\)
−0.408040 + 0.912964i \(0.633788\pi\)
\(158\) 0.128256 0.0102035
\(159\) 6.75068 0.535363
\(160\) 0.973674 0.0769757
\(161\) 6.18681 0.487589
\(162\) −0.256478 −0.0201508
\(163\) −18.7160 −1.46595 −0.732976 0.680255i \(-0.761869\pi\)
−0.732976 + 0.680255i \(0.761869\pi\)
\(164\) −15.7619 −1.23080
\(165\) 0.234390 0.0182472
\(166\) 1.36977 0.106314
\(167\) −5.05071 −0.390836 −0.195418 0.980720i \(-0.562606\pi\)
−0.195418 + 0.980720i \(0.562606\pi\)
\(168\) 1.26358 0.0974871
\(169\) 1.00000 0.0769231
\(170\) −0.434312 −0.0333102
\(171\) 4.61143 0.352645
\(172\) −12.6853 −0.967245
\(173\) −18.0644 −1.37341 −0.686704 0.726937i \(-0.740943\pi\)
−0.686704 + 0.726937i \(0.740943\pi\)
\(174\) 1.39249 0.105565
\(175\) −6.12429 −0.462953
\(176\) −2.55805 −0.192820
\(177\) 13.2817 0.998310
\(178\) 2.66459 0.199719
\(179\) 25.0335 1.87109 0.935545 0.353208i \(-0.114909\pi\)
0.935545 + 0.353208i \(0.114909\pi\)
\(180\) 0.639735 0.0476830
\(181\) −3.97181 −0.295223 −0.147611 0.989045i \(-0.547158\pi\)
−0.147611 + 0.989045i \(0.547158\pi\)
\(182\) 0.321176 0.0238071
\(183\) 0.799420 0.0590948
\(184\) 4.98519 0.367513
\(185\) 3.41748 0.251258
\(186\) 1.97388 0.144732
\(187\) 3.62830 0.265327
\(188\) 11.7724 0.858594
\(189\) 1.25226 0.0910882
\(190\) 0.391183 0.0283794
\(191\) 18.8856 1.36651 0.683256 0.730179i \(-0.260564\pi\)
0.683256 + 0.730179i \(0.260564\pi\)
\(192\) −6.46425 −0.466517
\(193\) −15.7494 −1.13367 −0.566835 0.823831i \(-0.691832\pi\)
−0.566835 + 0.823831i \(0.691832\pi\)
\(194\) 2.37912 0.170811
\(195\) 0.330746 0.0236852
\(196\) 10.5064 0.750457
\(197\) −21.1867 −1.50949 −0.754743 0.656020i \(-0.772239\pi\)
−0.754743 + 0.656020i \(0.772239\pi\)
\(198\) 0.181758 0.0129170
\(199\) 0.295285 0.0209322 0.0104661 0.999945i \(-0.496668\pi\)
0.0104661 + 0.999945i \(0.496668\pi\)
\(200\) −4.93482 −0.348944
\(201\) −2.78601 −0.196510
\(202\) 3.19030 0.224469
\(203\) −6.79886 −0.477187
\(204\) 9.90293 0.693344
\(205\) −2.69524 −0.188244
\(206\) −0.256478 −0.0178697
\(207\) 4.94053 0.343391
\(208\) −3.60964 −0.250284
\(209\) −3.26799 −0.226052
\(210\) 0.106228 0.00733040
\(211\) 0.815219 0.0561220 0.0280610 0.999606i \(-0.491067\pi\)
0.0280610 + 0.999606i \(0.491067\pi\)
\(212\) −13.0573 −0.896778
\(213\) −4.43224 −0.303692
\(214\) −2.35437 −0.160942
\(215\) −2.16915 −0.147935
\(216\) 1.00904 0.0686565
\(217\) −9.63748 −0.654235
\(218\) 3.66832 0.248450
\(219\) 14.2243 0.961189
\(220\) −0.453362 −0.0305656
\(221\) 5.11986 0.344399
\(222\) 2.65009 0.177863
\(223\) −7.97500 −0.534045 −0.267023 0.963690i \(-0.586040\pi\)
−0.267023 + 0.963690i \(0.586040\pi\)
\(224\) −3.68648 −0.246314
\(225\) −4.89061 −0.326040
\(226\) 2.47234 0.164458
\(227\) 6.13888 0.407452 0.203726 0.979028i \(-0.434695\pi\)
0.203726 + 0.979028i \(0.434695\pi\)
\(228\) −8.91952 −0.590710
\(229\) −0.550057 −0.0363488 −0.0181744 0.999835i \(-0.505785\pi\)
−0.0181744 + 0.999835i \(0.505785\pi\)
\(230\) 0.419100 0.0276347
\(231\) −0.887438 −0.0583891
\(232\) −5.47837 −0.359673
\(233\) −6.24861 −0.409360 −0.204680 0.978829i \(-0.565615\pi\)
−0.204680 + 0.978829i \(0.565615\pi\)
\(234\) 0.256478 0.0167665
\(235\) 2.01305 0.131317
\(236\) −25.6896 −1.67225
\(237\) −0.500065 −0.0324827
\(238\) 1.64438 0.106589
\(239\) 14.1237 0.913589 0.456795 0.889572i \(-0.348997\pi\)
0.456795 + 0.889572i \(0.348997\pi\)
\(240\) −1.19387 −0.0770642
\(241\) −6.98081 −0.449674 −0.224837 0.974396i \(-0.572185\pi\)
−0.224837 + 0.974396i \(0.572185\pi\)
\(242\) 2.69245 0.173077
\(243\) 1.00000 0.0641500
\(244\) −1.54625 −0.0989887
\(245\) 1.79656 0.114778
\(246\) −2.09003 −0.133255
\(247\) −4.61143 −0.293418
\(248\) −7.76567 −0.493120
\(249\) −5.34068 −0.338452
\(250\) −0.839010 −0.0530637
\(251\) −10.4449 −0.659279 −0.329640 0.944107i \(-0.606927\pi\)
−0.329640 + 0.944107i \(0.606927\pi\)
\(252\) −2.42214 −0.152580
\(253\) −3.50121 −0.220119
\(254\) 1.56729 0.0983406
\(255\) 1.69337 0.106043
\(256\) 10.9932 0.687074
\(257\) 21.9346 1.36824 0.684121 0.729368i \(-0.260186\pi\)
0.684121 + 0.729368i \(0.260186\pi\)
\(258\) −1.68207 −0.104721
\(259\) −12.9391 −0.803997
\(260\) −0.639735 −0.0396747
\(261\) −5.42929 −0.336065
\(262\) 3.37073 0.208244
\(263\) 19.0663 1.17568 0.587840 0.808977i \(-0.299978\pi\)
0.587840 + 0.808977i \(0.299978\pi\)
\(264\) −0.715077 −0.0440100
\(265\) −2.23276 −0.137157
\(266\) −1.48108 −0.0908109
\(267\) −10.3891 −0.635806
\(268\) 5.38875 0.329171
\(269\) −11.3506 −0.692059 −0.346030 0.938224i \(-0.612470\pi\)
−0.346030 + 0.938224i \(0.612470\pi\)
\(270\) 0.0848290 0.00516253
\(271\) −12.7824 −0.776478 −0.388239 0.921559i \(-0.626917\pi\)
−0.388239 + 0.921559i \(0.626917\pi\)
\(272\) −18.4809 −1.12057
\(273\) −1.25226 −0.0757900
\(274\) 1.66961 0.100865
\(275\) 3.46583 0.208998
\(276\) −9.55607 −0.575208
\(277\) −32.0113 −1.92337 −0.961686 0.274154i \(-0.911602\pi\)
−0.961686 + 0.274154i \(0.911602\pi\)
\(278\) −0.552026 −0.0331083
\(279\) −7.69609 −0.460753
\(280\) −0.417923 −0.0249757
\(281\) −1.68742 −0.100663 −0.0503314 0.998733i \(-0.516028\pi\)
−0.0503314 + 0.998733i \(0.516028\pi\)
\(282\) 1.56103 0.0929579
\(283\) −27.5741 −1.63911 −0.819554 0.573002i \(-0.805779\pi\)
−0.819554 + 0.573002i \(0.805779\pi\)
\(284\) 8.57293 0.508710
\(285\) −1.52521 −0.0903458
\(286\) −0.181758 −0.0107476
\(287\) 10.2046 0.602358
\(288\) −2.94387 −0.173469
\(289\) 9.21296 0.541939
\(290\) −0.460561 −0.0270451
\(291\) −9.27613 −0.543776
\(292\) −27.5129 −1.61007
\(293\) −20.4622 −1.19541 −0.597706 0.801716i \(-0.703921\pi\)
−0.597706 + 0.801716i \(0.703921\pi\)
\(294\) 1.39315 0.0812502
\(295\) −4.39285 −0.255762
\(296\) −10.4260 −0.606002
\(297\) −0.708671 −0.0411213
\(298\) 3.64251 0.211005
\(299\) −4.94053 −0.285718
\(300\) 9.45951 0.546145
\(301\) 8.21275 0.473375
\(302\) −4.84232 −0.278644
\(303\) −12.4389 −0.714596
\(304\) 16.6456 0.954692
\(305\) −0.264405 −0.0151398
\(306\) 1.31313 0.0750667
\(307\) −3.25494 −0.185769 −0.0928847 0.995677i \(-0.529609\pi\)
−0.0928847 + 0.995677i \(0.529609\pi\)
\(308\) 1.71650 0.0978066
\(309\) 1.00000 0.0568880
\(310\) −0.652852 −0.0370795
\(311\) −27.2162 −1.54329 −0.771643 0.636055i \(-0.780565\pi\)
−0.771643 + 0.636055i \(0.780565\pi\)
\(312\) −1.00904 −0.0571256
\(313\) 11.9023 0.672758 0.336379 0.941727i \(-0.390798\pi\)
0.336379 + 0.941727i \(0.390798\pi\)
\(314\) 2.62261 0.148002
\(315\) −0.414179 −0.0233363
\(316\) 0.967235 0.0544112
\(317\) 20.6928 1.16222 0.581111 0.813824i \(-0.302618\pi\)
0.581111 + 0.813824i \(0.302618\pi\)
\(318\) −1.73140 −0.0970920
\(319\) 3.84758 0.215423
\(320\) 2.13802 0.119519
\(321\) 9.17964 0.512357
\(322\) −1.58678 −0.0884278
\(323\) −23.6099 −1.31369
\(324\) −1.93422 −0.107457
\(325\) 4.89061 0.271282
\(326\) 4.80024 0.265861
\(327\) −14.3027 −0.790941
\(328\) 8.22263 0.454019
\(329\) −7.62174 −0.420200
\(330\) −0.0601158 −0.00330927
\(331\) 25.4281 1.39765 0.698826 0.715292i \(-0.253706\pi\)
0.698826 + 0.715292i \(0.253706\pi\)
\(332\) 10.3300 0.566934
\(333\) −10.3326 −0.566225
\(334\) 1.29540 0.0708809
\(335\) 0.921461 0.0503448
\(336\) 4.52020 0.246597
\(337\) −11.8426 −0.645110 −0.322555 0.946551i \(-0.604542\pi\)
−0.322555 + 0.946551i \(0.604542\pi\)
\(338\) −0.256478 −0.0139506
\(339\) −9.63960 −0.523551
\(340\) −3.27535 −0.177631
\(341\) 5.45400 0.295351
\(342\) −1.18273 −0.0639547
\(343\) −15.5679 −0.840586
\(344\) 6.61765 0.356800
\(345\) −1.63406 −0.0879749
\(346\) 4.63311 0.249077
\(347\) 22.8076 1.22438 0.612189 0.790712i \(-0.290289\pi\)
0.612189 + 0.790712i \(0.290289\pi\)
\(348\) 10.5014 0.562936
\(349\) −1.31325 −0.0702967 −0.0351484 0.999382i \(-0.511190\pi\)
−0.0351484 + 0.999382i \(0.511190\pi\)
\(350\) 1.57075 0.0839599
\(351\) −1.00000 −0.0533761
\(352\) 2.08624 0.111197
\(353\) 22.2826 1.18598 0.592992 0.805209i \(-0.297947\pi\)
0.592992 + 0.805209i \(0.297947\pi\)
\(354\) −3.40645 −0.181051
\(355\) 1.46595 0.0778043
\(356\) 20.0949 1.06503
\(357\) −6.41138 −0.339326
\(358\) −6.42053 −0.339336
\(359\) −5.68425 −0.300003 −0.150002 0.988686i \(-0.547928\pi\)
−0.150002 + 0.988686i \(0.547928\pi\)
\(360\) −0.333736 −0.0175894
\(361\) 2.26531 0.119227
\(362\) 1.01868 0.0535407
\(363\) −10.4978 −0.550991
\(364\) 2.42214 0.126955
\(365\) −4.70463 −0.246251
\(366\) −0.205034 −0.0107173
\(367\) 25.9656 1.35539 0.677697 0.735341i \(-0.262978\pi\)
0.677697 + 0.735341i \(0.262978\pi\)
\(368\) 17.8336 0.929638
\(369\) 8.14897 0.424218
\(370\) −0.876507 −0.0455674
\(371\) 8.45358 0.438888
\(372\) 14.8859 0.771800
\(373\) −34.2715 −1.77451 −0.887256 0.461278i \(-0.847391\pi\)
−0.887256 + 0.461278i \(0.847391\pi\)
\(374\) −0.930578 −0.0481190
\(375\) 3.27128 0.168928
\(376\) −6.14143 −0.316720
\(377\) 5.42929 0.279623
\(378\) −0.321176 −0.0165195
\(379\) −28.4091 −1.45928 −0.729640 0.683832i \(-0.760312\pi\)
−0.729640 + 0.683832i \(0.760312\pi\)
\(380\) 2.95009 0.151337
\(381\) −6.11083 −0.313067
\(382\) −4.84373 −0.247827
\(383\) 27.4522 1.40274 0.701370 0.712798i \(-0.252572\pi\)
0.701370 + 0.712798i \(0.252572\pi\)
\(384\) 7.54568 0.385064
\(385\) 0.293516 0.0149590
\(386\) 4.03938 0.205599
\(387\) 6.55836 0.333380
\(388\) 17.9421 0.910870
\(389\) 27.9248 1.41584 0.707921 0.706292i \(-0.249633\pi\)
0.707921 + 0.706292i \(0.249633\pi\)
\(390\) −0.0848290 −0.00429548
\(391\) −25.2948 −1.27921
\(392\) −5.48096 −0.276830
\(393\) −13.1424 −0.662946
\(394\) 5.43391 0.273756
\(395\) 0.165394 0.00832190
\(396\) 1.37073 0.0688815
\(397\) 13.3500 0.670018 0.335009 0.942215i \(-0.391261\pi\)
0.335009 + 0.942215i \(0.391261\pi\)
\(398\) −0.0757339 −0.00379620
\(399\) 5.77470 0.289096
\(400\) −17.6533 −0.882667
\(401\) 15.1361 0.755863 0.377931 0.925834i \(-0.376636\pi\)
0.377931 + 0.925834i \(0.376636\pi\)
\(402\) 0.714550 0.0356385
\(403\) 7.69609 0.383370
\(404\) 24.0595 1.19701
\(405\) −0.330746 −0.0164349
\(406\) 1.74376 0.0865413
\(407\) 7.32244 0.362960
\(408\) −5.16614 −0.255762
\(409\) −0.521617 −0.0257923 −0.0128962 0.999917i \(-0.504105\pi\)
−0.0128962 + 0.999917i \(0.504105\pi\)
\(410\) 0.691269 0.0341393
\(411\) −6.50977 −0.321103
\(412\) −1.93422 −0.0952921
\(413\) 16.6320 0.818409
\(414\) −1.26714 −0.0622764
\(415\) 1.76641 0.0867095
\(416\) 2.94387 0.144335
\(417\) 2.15233 0.105400
\(418\) 0.838167 0.0409961
\(419\) 38.7591 1.89351 0.946753 0.321961i \(-0.104342\pi\)
0.946753 + 0.321961i \(0.104342\pi\)
\(420\) 0.801112 0.0390903
\(421\) −20.4436 −0.996358 −0.498179 0.867074i \(-0.665998\pi\)
−0.498179 + 0.867074i \(0.665998\pi\)
\(422\) −0.209086 −0.0101781
\(423\) −6.08641 −0.295931
\(424\) 6.81170 0.330805
\(425\) 25.0392 1.21458
\(426\) 1.13677 0.0550768
\(427\) 1.00108 0.0484456
\(428\) −17.7554 −0.858241
\(429\) 0.708671 0.0342150
\(430\) 0.556339 0.0268290
\(431\) −0.0783003 −0.00377159 −0.00188580 0.999998i \(-0.500600\pi\)
−0.00188580 + 0.999998i \(0.500600\pi\)
\(432\) 3.60964 0.173669
\(433\) −19.2156 −0.923441 −0.461721 0.887025i \(-0.652768\pi\)
−0.461721 + 0.887025i \(0.652768\pi\)
\(434\) 2.47180 0.118650
\(435\) 1.79572 0.0860980
\(436\) 27.6645 1.32489
\(437\) 22.7829 1.08986
\(438\) −3.64822 −0.174319
\(439\) −31.7739 −1.51648 −0.758242 0.651973i \(-0.773941\pi\)
−0.758242 + 0.651973i \(0.773941\pi\)
\(440\) 0.236509 0.0112751
\(441\) −5.43185 −0.258660
\(442\) −1.31313 −0.0624593
\(443\) 22.2621 1.05770 0.528852 0.848714i \(-0.322622\pi\)
0.528852 + 0.848714i \(0.322622\pi\)
\(444\) 19.9856 0.948474
\(445\) 3.43617 0.162890
\(446\) 2.04541 0.0968530
\(447\) −14.2020 −0.671733
\(448\) −8.09489 −0.382448
\(449\) −35.2282 −1.66252 −0.831262 0.555882i \(-0.812381\pi\)
−0.831262 + 0.555882i \(0.812381\pi\)
\(450\) 1.25433 0.0591298
\(451\) −5.77494 −0.271931
\(452\) 18.6451 0.876992
\(453\) 18.8801 0.887063
\(454\) −1.57449 −0.0738943
\(455\) 0.414179 0.0194170
\(456\) 4.65312 0.217902
\(457\) 17.2978 0.809157 0.404579 0.914503i \(-0.367418\pi\)
0.404579 + 0.914503i \(0.367418\pi\)
\(458\) 0.141077 0.00659212
\(459\) −5.11986 −0.238975
\(460\) 3.16063 0.147365
\(461\) 5.45741 0.254177 0.127089 0.991891i \(-0.459437\pi\)
0.127089 + 0.991891i \(0.459437\pi\)
\(462\) 0.227608 0.0105893
\(463\) 30.2868 1.40755 0.703773 0.710425i \(-0.251497\pi\)
0.703773 + 0.710425i \(0.251497\pi\)
\(464\) −19.5978 −0.909805
\(465\) 2.54545 0.118042
\(466\) 1.60263 0.0742404
\(467\) −16.6959 −0.772594 −0.386297 0.922374i \(-0.626246\pi\)
−0.386297 + 0.922374i \(0.626246\pi\)
\(468\) 1.93422 0.0894093
\(469\) −3.48880 −0.161098
\(470\) −0.516304 −0.0238153
\(471\) −10.2255 −0.471165
\(472\) 13.4017 0.616864
\(473\) −4.64772 −0.213702
\(474\) 0.128256 0.00589097
\(475\) −22.5527 −1.03479
\(476\) 12.4010 0.568399
\(477\) 6.75068 0.309092
\(478\) −3.62243 −0.165686
\(479\) 21.5906 0.986499 0.493250 0.869888i \(-0.335809\pi\)
0.493250 + 0.869888i \(0.335809\pi\)
\(480\) 0.973674 0.0444419
\(481\) 10.3326 0.471128
\(482\) 1.79042 0.0815516
\(483\) 6.18681 0.281510
\(484\) 20.3050 0.922955
\(485\) 3.06804 0.139313
\(486\) −0.256478 −0.0116341
\(487\) −19.7281 −0.893968 −0.446984 0.894542i \(-0.647502\pi\)
−0.446984 + 0.894542i \(0.647502\pi\)
\(488\) 0.806647 0.0365152
\(489\) −18.7160 −0.846367
\(490\) −0.460779 −0.0208159
\(491\) −8.40069 −0.379118 −0.189559 0.981869i \(-0.560706\pi\)
−0.189559 + 0.981869i \(0.560706\pi\)
\(492\) −15.7619 −0.710601
\(493\) 27.7972 1.25192
\(494\) 1.18273 0.0532136
\(495\) 0.234390 0.0105350
\(496\) −27.7801 −1.24737
\(497\) −5.55031 −0.248965
\(498\) 1.36977 0.0613806
\(499\) −9.62383 −0.430822 −0.215411 0.976524i \(-0.569109\pi\)
−0.215411 + 0.976524i \(0.569109\pi\)
\(500\) −6.32737 −0.282968
\(501\) −5.05071 −0.225649
\(502\) 2.67890 0.119565
\(503\) −36.2219 −1.61506 −0.807528 0.589830i \(-0.799195\pi\)
−0.807528 + 0.589830i \(0.799195\pi\)
\(504\) 1.26358 0.0562842
\(505\) 4.11411 0.183076
\(506\) 0.897983 0.0399202
\(507\) 1.00000 0.0444116
\(508\) 11.8197 0.524413
\(509\) 10.5162 0.466123 0.233062 0.972462i \(-0.425126\pi\)
0.233062 + 0.972462i \(0.425126\pi\)
\(510\) −0.434312 −0.0192317
\(511\) 17.8125 0.787977
\(512\) −17.9109 −0.791556
\(513\) 4.61143 0.203600
\(514\) −5.62574 −0.248141
\(515\) −0.330746 −0.0145744
\(516\) −12.6853 −0.558439
\(517\) 4.31326 0.189697
\(518\) 3.31860 0.145811
\(519\) −18.0644 −0.792937
\(520\) 0.333736 0.0146353
\(521\) −0.119135 −0.00521938 −0.00260969 0.999997i \(-0.500831\pi\)
−0.00260969 + 0.999997i \(0.500831\pi\)
\(522\) 1.39249 0.0609478
\(523\) 0.0576810 0.00252221 0.00126111 0.999999i \(-0.499599\pi\)
0.00126111 + 0.999999i \(0.499599\pi\)
\(524\) 25.4203 1.11049
\(525\) −6.12429 −0.267286
\(526\) −4.89009 −0.213218
\(527\) 39.4029 1.71642
\(528\) −2.55805 −0.111325
\(529\) 1.40886 0.0612547
\(530\) 0.572653 0.0248745
\(531\) 13.2817 0.576375
\(532\) −11.1695 −0.484260
\(533\) −8.14897 −0.352971
\(534\) 2.66459 0.115308
\(535\) −3.03613 −0.131263
\(536\) −2.81120 −0.121425
\(537\) 25.0335 1.08027
\(538\) 2.91118 0.125510
\(539\) 3.84940 0.165805
\(540\) 0.639735 0.0275298
\(541\) −13.9639 −0.600356 −0.300178 0.953883i \(-0.597046\pi\)
−0.300178 + 0.953883i \(0.597046\pi\)
\(542\) 3.27841 0.140820
\(543\) −3.97181 −0.170447
\(544\) 15.0722 0.646216
\(545\) 4.73055 0.202635
\(546\) 0.321176 0.0137451
\(547\) 34.6906 1.48326 0.741630 0.670809i \(-0.234053\pi\)
0.741630 + 0.670809i \(0.234053\pi\)
\(548\) 12.5913 0.537875
\(549\) 0.799420 0.0341184
\(550\) −0.888909 −0.0379032
\(551\) −25.0368 −1.06660
\(552\) 4.98519 0.212184
\(553\) −0.626210 −0.0266291
\(554\) 8.21018 0.348817
\(555\) 3.41748 0.145064
\(556\) −4.16308 −0.176554
\(557\) −7.20735 −0.305385 −0.152693 0.988274i \(-0.548794\pi\)
−0.152693 + 0.988274i \(0.548794\pi\)
\(558\) 1.97388 0.0835609
\(559\) −6.55836 −0.277389
\(560\) −1.49504 −0.0631768
\(561\) 3.62830 0.153187
\(562\) 0.432785 0.0182559
\(563\) −24.3619 −1.02673 −0.513366 0.858170i \(-0.671602\pi\)
−0.513366 + 0.858170i \(0.671602\pi\)
\(564\) 11.7724 0.495709
\(565\) 3.18826 0.134131
\(566\) 7.07214 0.297264
\(567\) 1.25226 0.0525898
\(568\) −4.47231 −0.187654
\(569\) −8.76301 −0.367364 −0.183682 0.982986i \(-0.558802\pi\)
−0.183682 + 0.982986i \(0.558802\pi\)
\(570\) 0.391183 0.0163849
\(571\) 17.5523 0.734540 0.367270 0.930114i \(-0.380293\pi\)
0.367270 + 0.930114i \(0.380293\pi\)
\(572\) −1.37073 −0.0573129
\(573\) 18.8856 0.788956
\(574\) −2.61725 −0.109242
\(575\) −24.1622 −1.00763
\(576\) −6.46425 −0.269344
\(577\) 9.00167 0.374744 0.187372 0.982289i \(-0.440003\pi\)
0.187372 + 0.982289i \(0.440003\pi\)
\(578\) −2.36292 −0.0982846
\(579\) −15.7494 −0.654525
\(580\) −3.47331 −0.144221
\(581\) −6.68789 −0.277461
\(582\) 2.37912 0.0986178
\(583\) −4.78401 −0.198133
\(584\) 14.3529 0.593926
\(585\) 0.330746 0.0136747
\(586\) 5.24809 0.216797
\(587\) −21.7448 −0.897505 −0.448752 0.893656i \(-0.648131\pi\)
−0.448752 + 0.893656i \(0.648131\pi\)
\(588\) 10.5064 0.433276
\(589\) −35.4900 −1.46234
\(590\) 1.12667 0.0463842
\(591\) −21.1867 −0.871503
\(592\) −37.2971 −1.53290
\(593\) 43.0547 1.76805 0.884023 0.467443i \(-0.154825\pi\)
0.884023 + 0.467443i \(0.154825\pi\)
\(594\) 0.181758 0.00745764
\(595\) 2.12054 0.0869335
\(596\) 27.4698 1.12521
\(597\) 0.295285 0.0120852
\(598\) 1.26714 0.0518171
\(599\) −6.37811 −0.260603 −0.130301 0.991474i \(-0.541594\pi\)
−0.130301 + 0.991474i \(0.541594\pi\)
\(600\) −4.93482 −0.201463
\(601\) −7.98434 −0.325688 −0.162844 0.986652i \(-0.552067\pi\)
−0.162844 + 0.986652i \(0.552067\pi\)
\(602\) −2.10639 −0.0858500
\(603\) −2.78601 −0.113455
\(604\) −36.5182 −1.48590
\(605\) 3.47210 0.141161
\(606\) 3.19030 0.129597
\(607\) 42.7106 1.73357 0.866786 0.498681i \(-0.166182\pi\)
0.866786 + 0.498681i \(0.166182\pi\)
\(608\) −13.5755 −0.550558
\(609\) −6.79886 −0.275504
\(610\) 0.0678140 0.00274571
\(611\) 6.08641 0.246230
\(612\) 9.90293 0.400302
\(613\) 44.1711 1.78405 0.892027 0.451983i \(-0.149283\pi\)
0.892027 + 0.451983i \(0.149283\pi\)
\(614\) 0.834821 0.0336906
\(615\) −2.69524 −0.108682
\(616\) −0.895460 −0.0360791
\(617\) 11.8923 0.478766 0.239383 0.970925i \(-0.423055\pi\)
0.239383 + 0.970925i \(0.423055\pi\)
\(618\) −0.256478 −0.0103171
\(619\) −3.87155 −0.155611 −0.0778054 0.996969i \(-0.524791\pi\)
−0.0778054 + 0.996969i \(0.524791\pi\)
\(620\) −4.92346 −0.197731
\(621\) 4.94053 0.198257
\(622\) 6.98034 0.279886
\(623\) −13.0099 −0.521230
\(624\) −3.60964 −0.144501
\(625\) 23.3711 0.934843
\(626\) −3.05268 −0.122010
\(627\) −3.26799 −0.130511
\(628\) 19.7783 0.789240
\(629\) 52.9017 2.10933
\(630\) 0.106228 0.00423221
\(631\) −6.83787 −0.272211 −0.136106 0.990694i \(-0.543459\pi\)
−0.136106 + 0.990694i \(0.543459\pi\)
\(632\) −0.504586 −0.0200713
\(633\) 0.815219 0.0324020
\(634\) −5.30724 −0.210778
\(635\) 2.02113 0.0802061
\(636\) −13.0573 −0.517755
\(637\) 5.43185 0.215218
\(638\) −0.986820 −0.0390686
\(639\) −4.43224 −0.175337
\(640\) −2.49570 −0.0986513
\(641\) 30.7090 1.21293 0.606467 0.795108i \(-0.292586\pi\)
0.606467 + 0.795108i \(0.292586\pi\)
\(642\) −2.35437 −0.0929197
\(643\) 6.11570 0.241180 0.120590 0.992702i \(-0.461521\pi\)
0.120590 + 0.992702i \(0.461521\pi\)
\(644\) −11.9667 −0.471552
\(645\) −2.16915 −0.0854102
\(646\) 6.05541 0.238247
\(647\) 5.89149 0.231618 0.115809 0.993271i \(-0.463054\pi\)
0.115809 + 0.993271i \(0.463054\pi\)
\(648\) 1.00904 0.0396388
\(649\) −9.41232 −0.369466
\(650\) −1.25433 −0.0491990
\(651\) −9.63748 −0.377723
\(652\) 36.2009 1.41774
\(653\) −3.45013 −0.135014 −0.0675070 0.997719i \(-0.521505\pi\)
−0.0675070 + 0.997719i \(0.521505\pi\)
\(654\) 3.66832 0.143443
\(655\) 4.34679 0.169843
\(656\) 29.4149 1.14846
\(657\) 14.2243 0.554943
\(658\) 1.95481 0.0762064
\(659\) 8.74597 0.340695 0.170347 0.985384i \(-0.445511\pi\)
0.170347 + 0.985384i \(0.445511\pi\)
\(660\) −0.453362 −0.0176471
\(661\) 33.0513 1.28555 0.642773 0.766057i \(-0.277784\pi\)
0.642773 + 0.766057i \(0.277784\pi\)
\(662\) −6.52173 −0.253474
\(663\) 5.11986 0.198839
\(664\) −5.38896 −0.209132
\(665\) −1.90996 −0.0740649
\(666\) 2.65009 0.102689
\(667\) −26.8236 −1.03861
\(668\) 9.76918 0.377981
\(669\) −7.97500 −0.308331
\(670\) −0.236334 −0.00913039
\(671\) −0.566526 −0.0218705
\(672\) −3.68648 −0.142209
\(673\) −12.3192 −0.474869 −0.237434 0.971404i \(-0.576306\pi\)
−0.237434 + 0.971404i \(0.576306\pi\)
\(674\) 3.03738 0.116995
\(675\) −4.89061 −0.188240
\(676\) −1.93422 −0.0743930
\(677\) −15.8012 −0.607290 −0.303645 0.952785i \(-0.598204\pi\)
−0.303645 + 0.952785i \(0.598204\pi\)
\(678\) 2.47234 0.0949498
\(679\) −11.6161 −0.445785
\(680\) 1.70868 0.0655249
\(681\) 6.13888 0.235242
\(682\) −1.39883 −0.0535640
\(683\) −6.68038 −0.255618 −0.127809 0.991799i \(-0.540794\pi\)
−0.127809 + 0.991799i \(0.540794\pi\)
\(684\) −8.91952 −0.341046
\(685\) 2.15308 0.0822650
\(686\) 3.99281 0.152446
\(687\) −0.550057 −0.0209860
\(688\) 23.6733 0.902537
\(689\) −6.75068 −0.257180
\(690\) 0.419100 0.0159549
\(691\) −26.5969 −1.01179 −0.505896 0.862594i \(-0.668838\pi\)
−0.505896 + 0.862594i \(0.668838\pi\)
\(692\) 34.9404 1.32824
\(693\) −0.887438 −0.0337110
\(694\) −5.84965 −0.222050
\(695\) −0.711875 −0.0270030
\(696\) −5.47837 −0.207657
\(697\) −41.7216 −1.58032
\(698\) 0.336820 0.0127488
\(699\) −6.24861 −0.236344
\(700\) 11.8457 0.447726
\(701\) −32.8829 −1.24197 −0.620984 0.783823i \(-0.713267\pi\)
−0.620984 + 0.783823i \(0.713267\pi\)
\(702\) 0.256478 0.00968013
\(703\) −47.6483 −1.79709
\(704\) 4.58102 0.172654
\(705\) 2.01305 0.0758160
\(706\) −5.71499 −0.215087
\(707\) −15.5767 −0.585821
\(708\) −25.6896 −0.965475
\(709\) 10.1394 0.380793 0.190396 0.981707i \(-0.439023\pi\)
0.190396 + 0.981707i \(0.439023\pi\)
\(710\) −0.375983 −0.0141104
\(711\) −0.500065 −0.0187539
\(712\) −10.4831 −0.392870
\(713\) −38.0228 −1.42396
\(714\) 1.64438 0.0615392
\(715\) −0.234390 −0.00876569
\(716\) −48.4202 −1.80955
\(717\) 14.1237 0.527461
\(718\) 1.45788 0.0544077
\(719\) 42.3890 1.58084 0.790422 0.612563i \(-0.209862\pi\)
0.790422 + 0.612563i \(0.209862\pi\)
\(720\) −1.19387 −0.0444931
\(721\) 1.25226 0.0466365
\(722\) −0.581002 −0.0216227
\(723\) −6.98081 −0.259619
\(724\) 7.68236 0.285513
\(725\) 26.5525 0.986136
\(726\) 2.69245 0.0999262
\(727\) −35.7924 −1.32747 −0.663733 0.747970i \(-0.731029\pi\)
−0.663733 + 0.747970i \(0.731029\pi\)
\(728\) −1.26358 −0.0468313
\(729\) 1.00000 0.0370370
\(730\) 1.20663 0.0446595
\(731\) −33.5779 −1.24192
\(732\) −1.54625 −0.0571512
\(733\) 6.61836 0.244455 0.122227 0.992502i \(-0.460996\pi\)
0.122227 + 0.992502i \(0.460996\pi\)
\(734\) −6.65960 −0.245810
\(735\) 1.79656 0.0662672
\(736\) −14.5443 −0.536110
\(737\) 1.97436 0.0727267
\(738\) −2.09003 −0.0769351
\(739\) 33.1978 1.22120 0.610600 0.791939i \(-0.290928\pi\)
0.610600 + 0.791939i \(0.290928\pi\)
\(740\) −6.61015 −0.242994
\(741\) −4.61143 −0.169405
\(742\) −2.16815 −0.0795955
\(743\) 23.5188 0.862821 0.431411 0.902156i \(-0.358016\pi\)
0.431411 + 0.902156i \(0.358016\pi\)
\(744\) −7.76567 −0.284703
\(745\) 4.69726 0.172094
\(746\) 8.78988 0.321820
\(747\) −5.34068 −0.195405
\(748\) −7.01792 −0.256601
\(749\) 11.4953 0.420028
\(750\) −0.839010 −0.0306363
\(751\) 37.5255 1.36932 0.684662 0.728861i \(-0.259950\pi\)
0.684662 + 0.728861i \(0.259950\pi\)
\(752\) −21.9698 −0.801155
\(753\) −10.4449 −0.380635
\(754\) −1.39249 −0.0507116
\(755\) −6.24451 −0.227261
\(756\) −2.42214 −0.0880923
\(757\) −31.6614 −1.15075 −0.575376 0.817889i \(-0.695144\pi\)
−0.575376 + 0.817889i \(0.695144\pi\)
\(758\) 7.28631 0.264651
\(759\) −3.50121 −0.127086
\(760\) −1.53900 −0.0558254
\(761\) −6.36049 −0.230568 −0.115284 0.993333i \(-0.536778\pi\)
−0.115284 + 0.993333i \(0.536778\pi\)
\(762\) 1.56729 0.0567770
\(763\) −17.9106 −0.648408
\(764\) −36.5288 −1.32157
\(765\) 1.69337 0.0612240
\(766\) −7.04087 −0.254397
\(767\) −13.2817 −0.479573
\(768\) 10.9932 0.396683
\(769\) 37.3675 1.34750 0.673752 0.738957i \(-0.264681\pi\)
0.673752 + 0.738957i \(0.264681\pi\)
\(770\) −0.0752804 −0.00271292
\(771\) 21.9346 0.789955
\(772\) 30.4629 1.09638
\(773\) −0.839820 −0.0302062 −0.0151031 0.999886i \(-0.504808\pi\)
−0.0151031 + 0.999886i \(0.504808\pi\)
\(774\) −1.68207 −0.0604609
\(775\) 37.6386 1.35202
\(776\) −9.35998 −0.336004
\(777\) −12.9391 −0.464188
\(778\) −7.16208 −0.256773
\(779\) 37.5784 1.34639
\(780\) −0.639735 −0.0229062
\(781\) 3.14100 0.112394
\(782\) 6.48756 0.231995
\(783\) −5.42929 −0.194027
\(784\) −19.6070 −0.700252
\(785\) 3.38203 0.120710
\(786\) 3.37073 0.120230
\(787\) 34.0547 1.21392 0.606959 0.794733i \(-0.292389\pi\)
0.606959 + 0.794733i \(0.292389\pi\)
\(788\) 40.9796 1.45984
\(789\) 19.0663 0.678779
\(790\) −0.0424200 −0.00150924
\(791\) −12.0712 −0.429204
\(792\) −0.715077 −0.0254092
\(793\) −0.799420 −0.0283882
\(794\) −3.42398 −0.121513
\(795\) −2.23276 −0.0791878
\(796\) −0.571145 −0.0202437
\(797\) 12.6514 0.448135 0.224067 0.974574i \(-0.428066\pi\)
0.224067 + 0.974574i \(0.428066\pi\)
\(798\) −1.48108 −0.0524297
\(799\) 31.1616 1.10242
\(800\) 14.3973 0.509022
\(801\) −10.3891 −0.367082
\(802\) −3.88208 −0.137081
\(803\) −10.0803 −0.355728
\(804\) 5.38875 0.190047
\(805\) −2.04626 −0.0721213
\(806\) −1.97388 −0.0695269
\(807\) −11.3506 −0.399560
\(808\) −12.5513 −0.441555
\(809\) −20.2253 −0.711084 −0.355542 0.934660i \(-0.615704\pi\)
−0.355542 + 0.934660i \(0.615704\pi\)
\(810\) 0.0848290 0.00298059
\(811\) −4.53408 −0.159213 −0.0796066 0.996826i \(-0.525366\pi\)
−0.0796066 + 0.996826i \(0.525366\pi\)
\(812\) 13.1505 0.461492
\(813\) −12.7824 −0.448300
\(814\) −1.87804 −0.0658254
\(815\) 6.19024 0.216835
\(816\) −18.4809 −0.646960
\(817\) 30.2434 1.05808
\(818\) 0.133783 0.00467762
\(819\) −1.25226 −0.0437574
\(820\) 5.21318 0.182052
\(821\) 52.6392 1.83712 0.918561 0.395279i \(-0.129352\pi\)
0.918561 + 0.395279i \(0.129352\pi\)
\(822\) 1.66961 0.0582344
\(823\) −46.9477 −1.63649 −0.818247 0.574867i \(-0.805054\pi\)
−0.818247 + 0.574867i \(0.805054\pi\)
\(824\) 1.00904 0.0351516
\(825\) 3.46583 0.120665
\(826\) −4.26575 −0.148424
\(827\) 36.9321 1.28425 0.642127 0.766598i \(-0.278052\pi\)
0.642127 + 0.766598i \(0.278052\pi\)
\(828\) −9.55607 −0.332096
\(829\) −36.0868 −1.25335 −0.626674 0.779282i \(-0.715584\pi\)
−0.626674 + 0.779282i \(0.715584\pi\)
\(830\) −0.453044 −0.0157254
\(831\) −32.0113 −1.11046
\(832\) 6.46425 0.224107
\(833\) 27.8103 0.963571
\(834\) −0.552026 −0.0191151
\(835\) 1.67050 0.0578101
\(836\) 6.32101 0.218617
\(837\) −7.69609 −0.266016
\(838\) −9.94085 −0.343401
\(839\) 13.7228 0.473764 0.236882 0.971538i \(-0.423874\pi\)
0.236882 + 0.971538i \(0.423874\pi\)
\(840\) −0.417923 −0.0144197
\(841\) 0.477214 0.0164557
\(842\) 5.24332 0.180697
\(843\) −1.68742 −0.0581177
\(844\) −1.57681 −0.0542761
\(845\) −0.330746 −0.0113780
\(846\) 1.56103 0.0536693
\(847\) −13.1459 −0.451699
\(848\) 24.3675 0.836784
\(849\) −27.5741 −0.946339
\(850\) −6.42201 −0.220273
\(851\) −51.0487 −1.74993
\(852\) 8.57293 0.293704
\(853\) 19.2984 0.660766 0.330383 0.943847i \(-0.392822\pi\)
0.330383 + 0.943847i \(0.392822\pi\)
\(854\) −0.256755 −0.00878596
\(855\) −1.52521 −0.0521612
\(856\) 9.26262 0.316590
\(857\) 22.9235 0.783053 0.391527 0.920167i \(-0.371947\pi\)
0.391527 + 0.920167i \(0.371947\pi\)
\(858\) −0.181758 −0.00620513
\(859\) 21.4588 0.732164 0.366082 0.930583i \(-0.380699\pi\)
0.366082 + 0.930583i \(0.380699\pi\)
\(860\) 4.19561 0.143069
\(861\) 10.2046 0.347772
\(862\) 0.0200823 0.000684006 0
\(863\) 0.740930 0.0252216 0.0126108 0.999920i \(-0.495986\pi\)
0.0126108 + 0.999920i \(0.495986\pi\)
\(864\) −2.94387 −0.100153
\(865\) 5.97471 0.203146
\(866\) 4.92837 0.167473
\(867\) 9.21296 0.312889
\(868\) 18.6410 0.632717
\(869\) 0.354382 0.0120216
\(870\) −0.460561 −0.0156145
\(871\) 2.78601 0.0944004
\(872\) −14.4320 −0.488729
\(873\) −9.27613 −0.313949
\(874\) −5.84332 −0.197653
\(875\) 4.09648 0.138486
\(876\) −27.5129 −0.929575
\(877\) −50.6246 −1.70947 −0.854735 0.519064i \(-0.826281\pi\)
−0.854735 + 0.519064i \(0.826281\pi\)
\(878\) 8.14929 0.275025
\(879\) −20.4622 −0.690171
\(880\) 0.846064 0.0285208
\(881\) −2.82396 −0.0951417 −0.0475708 0.998868i \(-0.515148\pi\)
−0.0475708 + 0.998868i \(0.515148\pi\)
\(882\) 1.39315 0.0469098
\(883\) 8.04046 0.270583 0.135291 0.990806i \(-0.456803\pi\)
0.135291 + 0.990806i \(0.456803\pi\)
\(884\) −9.90293 −0.333072
\(885\) −4.39285 −0.147664
\(886\) −5.70974 −0.191822
\(887\) 35.8445 1.20354 0.601770 0.798670i \(-0.294463\pi\)
0.601770 + 0.798670i \(0.294463\pi\)
\(888\) −10.4260 −0.349875
\(889\) −7.65232 −0.256651
\(890\) −0.881301 −0.0295413
\(891\) −0.708671 −0.0237414
\(892\) 15.4254 0.516480
\(893\) −28.0671 −0.939228
\(894\) 3.64251 0.121824
\(895\) −8.27972 −0.276760
\(896\) 9.44913 0.315673
\(897\) −4.94053 −0.164960
\(898\) 9.03526 0.301511
\(899\) 41.7843 1.39359
\(900\) 9.45951 0.315317
\(901\) −34.5625 −1.15144
\(902\) 1.48114 0.0493167
\(903\) 8.21275 0.273303
\(904\) −9.72674 −0.323507
\(905\) 1.31366 0.0436676
\(906\) −4.84232 −0.160875
\(907\) 38.8272 1.28924 0.644618 0.764504i \(-0.277016\pi\)
0.644618 + 0.764504i \(0.277016\pi\)
\(908\) −11.8739 −0.394050
\(909\) −12.4389 −0.412572
\(910\) −0.106228 −0.00352141
\(911\) 10.4250 0.345397 0.172699 0.984975i \(-0.444751\pi\)
0.172699 + 0.984975i \(0.444751\pi\)
\(912\) 16.6456 0.551192
\(913\) 3.78478 0.125258
\(914\) −4.43650 −0.146747
\(915\) −0.264405 −0.00874095
\(916\) 1.06393 0.0351533
\(917\) −16.4576 −0.543479
\(918\) 1.31313 0.0433398
\(919\) 25.0699 0.826979 0.413490 0.910509i \(-0.364310\pi\)
0.413490 + 0.910509i \(0.364310\pi\)
\(920\) −1.64883 −0.0543604
\(921\) −3.25494 −0.107254
\(922\) −1.39971 −0.0460968
\(923\) 4.43224 0.145889
\(924\) 1.71650 0.0564687
\(925\) 50.5329 1.66151
\(926\) −7.76789 −0.255269
\(927\) 1.00000 0.0328443
\(928\) 15.9831 0.524673
\(929\) 2.55448 0.0838097 0.0419048 0.999122i \(-0.486657\pi\)
0.0419048 + 0.999122i \(0.486657\pi\)
\(930\) −0.652852 −0.0214079
\(931\) −25.0486 −0.820936
\(932\) 12.0862 0.395896
\(933\) −27.2162 −0.891017
\(934\) 4.28213 0.140116
\(935\) −1.20004 −0.0392456
\(936\) −1.00904 −0.0329815
\(937\) −47.3948 −1.54832 −0.774161 0.632989i \(-0.781828\pi\)
−0.774161 + 0.632989i \(0.781828\pi\)
\(938\) 0.894800 0.0292162
\(939\) 11.9023 0.388417
\(940\) −3.89369 −0.126998
\(941\) 15.2103 0.495842 0.247921 0.968780i \(-0.420253\pi\)
0.247921 + 0.968780i \(0.420253\pi\)
\(942\) 2.62261 0.0854491
\(943\) 40.2602 1.31105
\(944\) 47.9420 1.56038
\(945\) −0.414179 −0.0134732
\(946\) 1.19204 0.0387565
\(947\) −16.6182 −0.540018 −0.270009 0.962858i \(-0.587027\pi\)
−0.270009 + 0.962858i \(0.587027\pi\)
\(948\) 0.967235 0.0314143
\(949\) −14.2243 −0.461740
\(950\) 5.78427 0.187666
\(951\) 20.6928 0.671010
\(952\) −6.46934 −0.209672
\(953\) −37.9356 −1.22886 −0.614428 0.788973i \(-0.710613\pi\)
−0.614428 + 0.788973i \(0.710613\pi\)
\(954\) −1.73140 −0.0560561
\(955\) −6.24632 −0.202126
\(956\) −27.3184 −0.883541
\(957\) 3.84758 0.124375
\(958\) −5.53751 −0.178909
\(959\) −8.15190 −0.263239
\(960\) 2.13802 0.0690044
\(961\) 28.2299 0.910640
\(962\) −2.65009 −0.0854424
\(963\) 9.17964 0.295810
\(964\) 13.5024 0.434884
\(965\) 5.20906 0.167686
\(966\) −1.58678 −0.0510538
\(967\) −27.6609 −0.889516 −0.444758 0.895651i \(-0.646710\pi\)
−0.444758 + 0.895651i \(0.646710\pi\)
\(968\) −10.5927 −0.340462
\(969\) −23.6099 −0.758459
\(970\) −0.786884 −0.0252653
\(971\) −45.4523 −1.45863 −0.729316 0.684177i \(-0.760162\pi\)
−0.729316 + 0.684177i \(0.760162\pi\)
\(972\) −1.93422 −0.0620401
\(973\) 2.69527 0.0864065
\(974\) 5.05983 0.162127
\(975\) 4.89061 0.156625
\(976\) 2.88562 0.0923664
\(977\) 6.57078 0.210218 0.105109 0.994461i \(-0.466481\pi\)
0.105109 + 0.994461i \(0.466481\pi\)
\(978\) 4.80024 0.153495
\(979\) 7.36249 0.235306
\(980\) −3.47495 −0.111003
\(981\) −14.3027 −0.456650
\(982\) 2.15459 0.0687558
\(983\) 15.1444 0.483032 0.241516 0.970397i \(-0.422355\pi\)
0.241516 + 0.970397i \(0.422355\pi\)
\(984\) 8.22263 0.262128
\(985\) 7.00740 0.223274
\(986\) −7.12937 −0.227045
\(987\) −7.62174 −0.242603
\(988\) 8.91952 0.283768
\(989\) 32.4018 1.03032
\(990\) −0.0601158 −0.00191061
\(991\) −4.66382 −0.148151 −0.0740756 0.997253i \(-0.523601\pi\)
−0.0740756 + 0.997253i \(0.523601\pi\)
\(992\) 22.6563 0.719339
\(993\) 25.4281 0.806935
\(994\) 1.42353 0.0451516
\(995\) −0.0976641 −0.00309616
\(996\) 10.3300 0.327320
\(997\) −41.9785 −1.32947 −0.664736 0.747078i \(-0.731456\pi\)
−0.664736 + 0.747078i \(0.731456\pi\)
\(998\) 2.46830 0.0781326
\(999\) −10.3326 −0.326910
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 4017.2.a.e.1.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.e.1.8 16 1.1 even 1 trivial