Properties

Label 1470.2.m.c.97.8
Level $1470$
Weight $2$
Character 1470.97
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(97,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.m (of order \(4\), degree \(2\), minimal)

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: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + 1250 x^{4} - 100000 x^{3} + 390625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.8
Root \(1.39977 - 1.74375i\) of defining polynomial
Character \(\chi\) \(=\) 1470.97
Dual form 1470.2.m.c.1273.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14668 + 0.625913i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14668 + 0.625913i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.07534 + 1.96052i) q^{10} +2.07328 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.326993 - 0.326993i) q^{13} +(1.07534 + 1.96052i) q^{15} -1.00000 q^{16} +(-1.26881 + 1.26881i) q^{17} +(-0.707107 + 0.707107i) q^{18} +4.37232 q^{19} +(-0.625913 + 2.14668i) q^{20} +(1.46603 + 1.46603i) q^{22} +(0.635591 - 0.635591i) q^{23} -1.00000 q^{24} +(4.21646 + 2.68727i) q^{25} -0.462438i q^{26} +(-0.707107 + 0.707107i) q^{27} -0.0288926i q^{29} +(-0.625913 + 2.14668i) q^{30} +8.03242i q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.46603 + 1.46603i) q^{33} -1.79437 q^{34} -1.00000 q^{36} +(-8.07760 - 8.07760i) q^{37} +(3.09170 + 3.09170i) q^{38} -0.462438i q^{39} +(-1.96052 + 1.07534i) q^{40} +10.6696i q^{41} +(2.50876 - 2.50876i) q^{43} +2.07328i q^{44} +(-0.625913 + 2.14668i) q^{45} +0.898861 q^{46} +(-0.525308 + 0.525308i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(1.08130 + 4.88168i) q^{50} -1.79437 q^{51} +(0.326993 - 0.326993i) q^{52} +(7.22526 - 7.22526i) q^{53} -1.00000 q^{54} +(4.45067 + 1.29769i) q^{55} +(3.09170 + 3.09170i) q^{57} +(0.0204302 - 0.0204302i) q^{58} -13.4242 q^{59} +(-1.96052 + 1.07534i) q^{60} -9.84270i q^{61} +(-5.67978 + 5.67978i) q^{62} -1.00000i q^{64} +(-0.497280 - 0.906619i) q^{65} +2.07328i q^{66} +(-3.33098 - 3.33098i) q^{67} +(-1.26881 - 1.26881i) q^{68} +0.898861 q^{69} +2.27478 q^{71} +(-0.707107 - 0.707107i) q^{72} +(8.14046 + 8.14046i) q^{73} -11.4235i q^{74} +(1.08130 + 4.88168i) q^{75} +4.37232i q^{76} +(0.326993 - 0.326993i) q^{78} -8.01313i q^{79} +(-2.14668 - 0.625913i) q^{80} -1.00000 q^{81} +(-7.54452 + 7.54452i) q^{82} +(4.26961 + 4.26961i) q^{83} +(-3.51790 + 1.92957i) q^{85} +3.54793 q^{86} +(0.0204302 - 0.0204302i) q^{87} +(-1.46603 + 1.46603i) q^{88} -0.0197698 q^{89} +(-1.96052 + 1.07534i) q^{90} +(0.635591 + 0.635591i) q^{92} +(-5.67978 + 5.67978i) q^{93} -0.742898 q^{94} +(9.38597 + 2.73669i) q^{95} -1.00000i q^{96} +(-5.65183 + 5.65183i) q^{97} +2.07328i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 2.14668 + 0.625913i 0.960024 + 0.279917i
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.07534 + 1.96052i 0.340054 + 0.619971i
\(11\) 2.07328 0.625117 0.312559 0.949898i \(-0.398814\pi\)
0.312559 + 0.949898i \(0.398814\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −0.326993 0.326993i −0.0906916 0.0906916i 0.660306 0.750997i \(-0.270427\pi\)
−0.750997 + 0.660306i \(0.770427\pi\)
\(14\) 0 0
\(15\) 1.07534 + 1.96052i 0.277653 + 0.506204i
\(16\) −1.00000 −0.250000
\(17\) −1.26881 + 1.26881i −0.307732 + 0.307732i −0.844029 0.536297i \(-0.819823\pi\)
0.536297 + 0.844029i \(0.319823\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) 4.37232 1.00308 0.501540 0.865135i \(-0.332767\pi\)
0.501540 + 0.865135i \(0.332767\pi\)
\(20\) −0.625913 + 2.14668i −0.139959 + 0.480012i
\(21\) 0 0
\(22\) 1.46603 + 1.46603i 0.312559 + 0.312559i
\(23\) 0.635591 0.635591i 0.132530 0.132530i −0.637730 0.770260i \(-0.720126\pi\)
0.770260 + 0.637730i \(0.220126\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.21646 + 2.68727i 0.843293 + 0.537454i
\(26\) 0.462438i 0.0906916i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 0.0288926i 0.00536522i −0.999996 0.00268261i \(-0.999146\pi\)
0.999996 0.00268261i \(-0.000853903\pi\)
\(30\) −0.625913 + 2.14668i −0.114276 + 0.391928i
\(31\) 8.03242i 1.44267i 0.692589 + 0.721333i \(0.256470\pi\)
−0.692589 + 0.721333i \(0.743530\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 1.46603 + 1.46603i 0.255203 + 0.255203i
\(34\) −1.79437 −0.307732
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −8.07760 8.07760i −1.32795 1.32795i −0.907157 0.420793i \(-0.861752\pi\)
−0.420793 0.907157i \(-0.638248\pi\)
\(38\) 3.09170 + 3.09170i 0.501540 + 0.501540i
\(39\) 0.462438i 0.0740494i
\(40\) −1.96052 + 1.07534i −0.309985 + 0.170027i
\(41\) 10.6696i 1.66631i 0.553042 + 0.833153i \(0.313467\pi\)
−0.553042 + 0.833153i \(0.686533\pi\)
\(42\) 0 0
\(43\) 2.50876 2.50876i 0.382583 0.382583i −0.489449 0.872032i \(-0.662802\pi\)
0.872032 + 0.489449i \(0.162802\pi\)
\(44\) 2.07328i 0.312559i
\(45\) −0.625913 + 2.14668i −0.0933057 + 0.320008i
\(46\) 0.898861 0.132530
\(47\) −0.525308 + 0.525308i −0.0766241 + 0.0766241i −0.744380 0.667756i \(-0.767255\pi\)
0.667756 + 0.744380i \(0.267255\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 0 0
\(50\) 1.08130 + 4.88168i 0.152919 + 0.690374i
\(51\) −1.79437 −0.251262
\(52\) 0.326993 0.326993i 0.0453458 0.0453458i
\(53\) 7.22526 7.22526i 0.992465 0.992465i −0.00750666 0.999972i \(-0.502389\pi\)
0.999972 + 0.00750666i \(0.00238947\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.45067 + 1.29769i 0.600128 + 0.174981i
\(56\) 0 0
\(57\) 3.09170 + 3.09170i 0.409505 + 0.409505i
\(58\) 0.0204302 0.0204302i 0.00268261 0.00268261i
\(59\) −13.4242 −1.74769 −0.873843 0.486208i \(-0.838380\pi\)
−0.873843 + 0.486208i \(0.838380\pi\)
\(60\) −1.96052 + 1.07534i −0.253102 + 0.138826i
\(61\) 9.84270i 1.26023i −0.776502 0.630114i \(-0.783008\pi\)
0.776502 0.630114i \(-0.216992\pi\)
\(62\) −5.67978 + 5.67978i −0.721333 + 0.721333i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.497280 0.906619i −0.0616800 0.112452i
\(66\) 2.07328i 0.255203i
\(67\) −3.33098 3.33098i −0.406944 0.406944i 0.473728 0.880671i \(-0.342908\pi\)
−0.880671 + 0.473728i \(0.842908\pi\)
\(68\) −1.26881 1.26881i −0.153866 0.153866i
\(69\) 0.898861 0.108210
\(70\) 0 0
\(71\) 2.27478 0.269966 0.134983 0.990848i \(-0.456902\pi\)
0.134983 + 0.990848i \(0.456902\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 8.14046 + 8.14046i 0.952768 + 0.952768i 0.998934 0.0461656i \(-0.0147002\pi\)
−0.0461656 + 0.998934i \(0.514700\pi\)
\(74\) 11.4235i 1.32795i
\(75\) 1.08130 + 4.88168i 0.124858 + 0.563688i
\(76\) 4.37232i 0.501540i
\(77\) 0 0
\(78\) 0.326993 0.326993i 0.0370247 0.0370247i
\(79\) 8.01313i 0.901547i −0.892638 0.450774i \(-0.851148\pi\)
0.892638 0.450774i \(-0.148852\pi\)
\(80\) −2.14668 0.625913i −0.240006 0.0699793i
\(81\) −1.00000 −0.111111
\(82\) −7.54452 + 7.54452i −0.833153 + 0.833153i
\(83\) 4.26961 + 4.26961i 0.468650 + 0.468650i 0.901477 0.432827i \(-0.142484\pi\)
−0.432827 + 0.901477i \(0.642484\pi\)
\(84\) 0 0
\(85\) −3.51790 + 1.92957i −0.381570 + 0.209291i
\(86\) 3.54793 0.382583
\(87\) 0.0204302 0.0204302i 0.00219034 0.00219034i
\(88\) −1.46603 + 1.46603i −0.156279 + 0.156279i
\(89\) −0.0197698 −0.00209560 −0.00104780 0.999999i \(-0.500334\pi\)
−0.00104780 + 0.999999i \(0.500334\pi\)
\(90\) −1.96052 + 1.07534i −0.206657 + 0.113351i
\(91\) 0 0
\(92\) 0.635591 + 0.635591i 0.0662649 + 0.0662649i
\(93\) −5.67978 + 5.67978i −0.588966 + 0.588966i
\(94\) −0.742898 −0.0766241
\(95\) 9.38597 + 2.73669i 0.962980 + 0.280779i
\(96\) 1.00000i 0.102062i
\(97\) −5.65183 + 5.65183i −0.573857 + 0.573857i −0.933204 0.359347i \(-0.882999\pi\)
0.359347 + 0.933204i \(0.382999\pi\)
\(98\) 0 0
\(99\) 2.07328i 0.208372i
\(100\) −2.68727 + 4.21646i −0.268727 + 0.421646i
\(101\) 4.18882i 0.416803i −0.978043 0.208402i \(-0.933174\pi\)
0.978043 0.208402i \(-0.0668261\pi\)
\(102\) −1.26881 1.26881i −0.125631 0.125631i
\(103\) −2.69132 2.69132i −0.265184 0.265184i 0.561972 0.827156i \(-0.310043\pi\)
−0.827156 + 0.561972i \(0.810043\pi\)
\(104\) 0.462438 0.0453458
\(105\) 0 0
\(106\) 10.2181 0.992465
\(107\) −12.1979 12.1979i −1.17922 1.17922i −0.979945 0.199271i \(-0.936143\pi\)
−0.199271 0.979945i \(-0.563857\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 12.6001i 1.20687i 0.797412 + 0.603435i \(0.206202\pi\)
−0.797412 + 0.603435i \(0.793798\pi\)
\(110\) 2.22949 + 4.06470i 0.212573 + 0.387554i
\(111\) 11.4235i 1.08427i
\(112\) 0 0
\(113\) 9.87937 9.87937i 0.929373 0.929373i −0.0682924 0.997665i \(-0.521755\pi\)
0.997665 + 0.0682924i \(0.0217551\pi\)
\(114\) 4.37232i 0.409505i
\(115\) 1.76223 0.966585i 0.164329 0.0901345i
\(116\) 0.0288926 0.00268261
\(117\) 0.326993 0.326993i 0.0302305 0.0302305i
\(118\) −9.49237 9.49237i −0.873843 0.873843i
\(119\) 0 0
\(120\) −2.14668 0.625913i −0.195964 0.0571378i
\(121\) −6.70151 −0.609228
\(122\) 6.95984 6.95984i 0.630114 0.630114i
\(123\) −7.54452 + 7.54452i −0.680267 + 0.680267i
\(124\) −8.03242 −0.721333
\(125\) 7.36940 + 8.40785i 0.659139 + 0.752021i
\(126\) 0 0
\(127\) −2.53710 2.53710i −0.225132 0.225132i 0.585524 0.810655i \(-0.300889\pi\)
−0.810655 + 0.585524i \(0.800889\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 3.54793 0.312378
\(130\) 0.289446 0.992706i 0.0253861 0.0870661i
\(131\) 19.7306i 1.72387i −0.507016 0.861937i \(-0.669251\pi\)
0.507016 0.861937i \(-0.330749\pi\)
\(132\) −1.46603 + 1.46603i −0.127602 + 0.127602i
\(133\) 0 0
\(134\) 4.71072i 0.406944i
\(135\) −1.96052 + 1.07534i −0.168735 + 0.0925509i
\(136\) 1.79437i 0.153866i
\(137\) 11.5948 + 11.5948i 0.990612 + 0.990612i 0.999956 0.00934474i \(-0.00297456\pi\)
−0.00934474 + 0.999956i \(0.502975\pi\)
\(138\) 0.635591 + 0.635591i 0.0541051 + 0.0541051i
\(139\) −6.98433 −0.592403 −0.296202 0.955125i \(-0.595720\pi\)
−0.296202 + 0.955125i \(0.595720\pi\)
\(140\) 0 0
\(141\) −0.742898 −0.0625633
\(142\) 1.60851 + 1.60851i 0.134983 + 0.134983i
\(143\) −0.677948 0.677948i −0.0566929 0.0566929i
\(144\) 1.00000i 0.0833333i
\(145\) 0.0180843 0.0620232i 0.00150182 0.00515075i
\(146\) 11.5123i 0.952768i
\(147\) 0 0
\(148\) 8.07760 8.07760i 0.663975 0.663975i
\(149\) 8.06301i 0.660547i 0.943885 + 0.330274i \(0.107141\pi\)
−0.943885 + 0.330274i \(0.892859\pi\)
\(150\) −2.68727 + 4.21646i −0.219415 + 0.344273i
\(151\) −20.7971 −1.69244 −0.846222 0.532831i \(-0.821128\pi\)
−0.846222 + 0.532831i \(0.821128\pi\)
\(152\) −3.09170 + 3.09170i −0.250770 + 0.250770i
\(153\) −1.26881 1.26881i −0.102577 0.102577i
\(154\) 0 0
\(155\) −5.02760 + 17.2430i −0.403826 + 1.38499i
\(156\) 0.462438 0.0370247
\(157\) 10.0893 10.0893i 0.805215 0.805215i −0.178690 0.983905i \(-0.557186\pi\)
0.983905 + 0.178690i \(0.0571861\pi\)
\(158\) 5.66614 5.66614i 0.450774 0.450774i
\(159\) 10.2181 0.810344
\(160\) −1.07534 1.96052i −0.0850134 0.154993i
\(161\) 0 0
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 8.54237 8.54237i 0.669090 0.669090i −0.288415 0.957505i \(-0.593128\pi\)
0.957505 + 0.288415i \(0.0931284\pi\)
\(164\) −10.6696 −0.833153
\(165\) 2.22949 + 4.06470i 0.173565 + 0.316437i
\(166\) 6.03813i 0.468650i
\(167\) 8.16680 8.16680i 0.631966 0.631966i −0.316595 0.948561i \(-0.602540\pi\)
0.948561 + 0.316595i \(0.102540\pi\)
\(168\) 0 0
\(169\) 12.7862i 0.983550i
\(170\) −3.85194 1.12312i −0.295430 0.0861395i
\(171\) 4.37232i 0.334360i
\(172\) 2.50876 + 2.50876i 0.191291 + 0.191291i
\(173\) 4.93408 + 4.93408i 0.375131 + 0.375131i 0.869342 0.494211i \(-0.164543\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(174\) 0.0288926 0.00219034
\(175\) 0 0
\(176\) −2.07328 −0.156279
\(177\) −9.49237 9.49237i −0.713490 0.713490i
\(178\) −0.0139794 0.0139794i −0.00104780 0.00104780i
\(179\) 6.45209i 0.482252i 0.970494 + 0.241126i \(0.0775167\pi\)
−0.970494 + 0.241126i \(0.922483\pi\)
\(180\) −2.14668 0.625913i −0.160004 0.0466528i
\(181\) 10.5123i 0.781370i 0.920524 + 0.390685i \(0.127762\pi\)
−0.920524 + 0.390685i \(0.872238\pi\)
\(182\) 0 0
\(183\) 6.95984 6.95984i 0.514486 0.514486i
\(184\) 0.898861i 0.0662649i
\(185\) −12.2841 22.3959i −0.903148 1.64658i
\(186\) −8.03242 −0.588966
\(187\) −2.63060 + 2.63060i −0.192369 + 0.192369i
\(188\) −0.525308 0.525308i −0.0383120 0.0383120i
\(189\) 0 0
\(190\) 4.70175 + 8.57202i 0.341101 + 0.621880i
\(191\) 24.8983 1.80158 0.900790 0.434254i \(-0.142988\pi\)
0.900790 + 0.434254i \(0.142988\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −8.94309 + 8.94309i −0.643738 + 0.643738i −0.951472 0.307734i \(-0.900429\pi\)
0.307734 + 0.951472i \(0.400429\pi\)
\(194\) −7.99290 −0.573857
\(195\) 0.289446 0.992706i 0.0207277 0.0710892i
\(196\) 0 0
\(197\) −2.46213 2.46213i −0.175419 0.175419i 0.613936 0.789356i \(-0.289585\pi\)
−0.789356 + 0.613936i \(0.789585\pi\)
\(198\) −1.46603 + 1.46603i −0.104186 + 0.104186i
\(199\) −7.59741 −0.538566 −0.269283 0.963061i \(-0.586787\pi\)
−0.269283 + 0.963061i \(0.586787\pi\)
\(200\) −4.88168 + 1.08130i −0.345187 + 0.0764597i
\(201\) 4.71072i 0.332268i
\(202\) 2.96194 2.96194i 0.208402 0.208402i
\(203\) 0 0
\(204\) 1.79437i 0.125631i
\(205\) −6.67823 + 22.9041i −0.466427 + 1.59969i
\(206\) 3.80611i 0.265184i
\(207\) 0.635591 + 0.635591i 0.0441766 + 0.0441766i
\(208\) 0.326993 + 0.326993i 0.0226729 + 0.0226729i
\(209\) 9.06504 0.627042
\(210\) 0 0
\(211\) −5.32272 −0.366431 −0.183216 0.983073i \(-0.558651\pi\)
−0.183216 + 0.983073i \(0.558651\pi\)
\(212\) 7.22526 + 7.22526i 0.496233 + 0.496233i
\(213\) 1.60851 + 1.60851i 0.110213 + 0.110213i
\(214\) 17.2504i 1.17922i
\(215\) 6.95578 3.81524i 0.474380 0.260197i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) −8.90962 + 8.90962i −0.603435 + 0.603435i
\(219\) 11.5123i 0.777932i
\(220\) −1.29769 + 4.45067i −0.0874905 + 0.300064i
\(221\) 0.829786 0.0558175
\(222\) 8.07760 8.07760i 0.542133 0.542133i
\(223\) −15.4987 15.4987i −1.03787 1.03787i −0.999254 0.0386189i \(-0.987704\pi\)
−0.0386189 0.999254i \(-0.512296\pi\)
\(224\) 0 0
\(225\) −2.68727 + 4.21646i −0.179151 + 0.281098i
\(226\) 13.9715 0.929373
\(227\) 6.80901 6.80901i 0.451930 0.451930i −0.444065 0.895995i \(-0.646464\pi\)
0.895995 + 0.444065i \(0.146464\pi\)
\(228\) −3.09170 + 3.09170i −0.204753 + 0.204753i
\(229\) 18.9728 1.25376 0.626880 0.779116i \(-0.284332\pi\)
0.626880 + 0.779116i \(0.284332\pi\)
\(230\) 1.92957 + 0.562609i 0.127232 + 0.0370973i
\(231\) 0 0
\(232\) 0.0204302 + 0.0204302i 0.00134131 + 0.00134131i
\(233\) 16.3943 16.3943i 1.07403 1.07403i 0.0769962 0.997031i \(-0.475467\pi\)
0.997031 0.0769962i \(-0.0245329\pi\)
\(234\) 0.462438 0.0302305
\(235\) −1.45647 + 0.798871i −0.0950094 + 0.0521126i
\(236\) 13.4242i 0.873843i
\(237\) 5.66614 5.66614i 0.368055 0.368055i
\(238\) 0 0
\(239\) 2.98741i 0.193239i −0.995321 0.0966197i \(-0.969197\pi\)
0.995321 0.0966197i \(-0.0308031\pi\)
\(240\) −1.07534 1.96052i −0.0694132 0.126551i
\(241\) 27.1053i 1.74601i 0.487715 + 0.873003i \(0.337830\pi\)
−0.487715 + 0.873003i \(0.662170\pi\)
\(242\) −4.73869 4.73869i −0.304614 0.304614i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 9.84270 0.630114
\(245\) 0 0
\(246\) −10.6696 −0.680267
\(247\) −1.42972 1.42972i −0.0909708 0.0909708i
\(248\) −5.67978 5.67978i −0.360666 0.360666i
\(249\) 6.03813i 0.382651i
\(250\) −0.734297 + 11.1562i −0.0464410 + 0.705580i
\(251\) 29.6570i 1.87194i −0.352086 0.935968i \(-0.614527\pi\)
0.352086 0.935968i \(-0.385473\pi\)
\(252\) 0 0
\(253\) 1.31776 1.31776i 0.0828467 0.0828467i
\(254\) 3.58801i 0.225132i
\(255\) −3.85194 1.12312i −0.241218 0.0703326i
\(256\) 1.00000 0.0625000
\(257\) −6.26264 + 6.26264i −0.390653 + 0.390653i −0.874920 0.484267i \(-0.839086\pi\)
0.484267 + 0.874920i \(0.339086\pi\)
\(258\) 2.50876 + 2.50876i 0.156189 + 0.156189i
\(259\) 0 0
\(260\) 0.906619 0.497280i 0.0562261 0.0308400i
\(261\) 0.0288926 0.00178841
\(262\) 13.9517 13.9517i 0.861937 0.861937i
\(263\) 19.4790 19.4790i 1.20113 1.20113i 0.227304 0.973824i \(-0.427009\pi\)
0.973824 0.227304i \(-0.0729912\pi\)
\(264\) −2.07328 −0.127602
\(265\) 20.0327 10.9879i 1.23060 0.674983i
\(266\) 0 0
\(267\) −0.0139794 0.0139794i −0.000855524 0.000855524i
\(268\) 3.33098 3.33098i 0.203472 0.203472i
\(269\) 2.19106 0.133591 0.0667957 0.997767i \(-0.478722\pi\)
0.0667957 + 0.997767i \(0.478722\pi\)
\(270\) −2.14668 0.625913i −0.130643 0.0380919i
\(271\) 7.28839i 0.442738i −0.975190 0.221369i \(-0.928947\pi\)
0.975190 0.221369i \(-0.0710526\pi\)
\(272\) 1.26881 1.26881i 0.0769331 0.0769331i
\(273\) 0 0
\(274\) 16.3975i 0.990612i
\(275\) 8.74191 + 5.57146i 0.527157 + 0.335972i
\(276\) 0.898861i 0.0541051i
\(277\) −16.6172 16.6172i −0.998433 0.998433i 0.00156542 0.999999i \(-0.499502\pi\)
−0.999999 + 0.00156542i \(0.999502\pi\)
\(278\) −4.93867 4.93867i −0.296202 0.296202i
\(279\) −8.03242 −0.480888
\(280\) 0 0
\(281\) 1.32521 0.0790557 0.0395278 0.999218i \(-0.487415\pi\)
0.0395278 + 0.999218i \(0.487415\pi\)
\(282\) −0.525308 0.525308i −0.0312817 0.0312817i
\(283\) −14.5224 14.5224i −0.863266 0.863266i 0.128450 0.991716i \(-0.459000\pi\)
−0.991716 + 0.128450i \(0.959000\pi\)
\(284\) 2.27478i 0.134983i
\(285\) 4.70175 + 8.57202i 0.278508 + 0.507763i
\(286\) 0.958763i 0.0566929i
\(287\) 0 0
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 13.7802i 0.810602i
\(290\) 0.0566445 0.0310695i 0.00332628 0.00182446i
\(291\) −7.99290 −0.468552
\(292\) −8.14046 + 8.14046i −0.476384 + 0.476384i
\(293\) 15.7254 + 15.7254i 0.918687 + 0.918687i 0.996934 0.0782467i \(-0.0249322\pi\)
−0.0782467 + 0.996934i \(0.524932\pi\)
\(294\) 0 0
\(295\) −28.8175 8.40241i −1.67782 0.489207i
\(296\) 11.4235 0.663975
\(297\) −1.46603 + 1.46603i −0.0850677 + 0.0850677i
\(298\) −5.70141 + 5.70141i −0.330274 + 0.330274i
\(299\) −0.415668 −0.0240387
\(300\) −4.88168 + 1.08130i −0.281844 + 0.0624291i
\(301\) 0 0
\(302\) −14.7058 14.7058i −0.846222 0.846222i
\(303\) 2.96194 2.96194i 0.170159 0.170159i
\(304\) −4.37232 −0.250770
\(305\) 6.16068 21.1291i 0.352760 1.20985i
\(306\) 1.79437i 0.102577i
\(307\) 12.0759 12.0759i 0.689205 0.689205i −0.272851 0.962056i \(-0.587967\pi\)
0.962056 + 0.272851i \(0.0879666\pi\)
\(308\) 0 0
\(309\) 3.80611i 0.216522i
\(310\) −15.7477 + 8.63761i −0.894410 + 0.490583i
\(311\) 20.2193i 1.14653i −0.819369 0.573267i \(-0.805676\pi\)
0.819369 0.573267i \(-0.194324\pi\)
\(312\) 0.326993 + 0.326993i 0.0185123 + 0.0185123i
\(313\) −8.65863 8.65863i −0.489415 0.489415i 0.418707 0.908121i \(-0.362484\pi\)
−0.908121 + 0.418707i \(0.862484\pi\)
\(314\) 14.2684 0.805215
\(315\) 0 0
\(316\) 8.01313 0.450774
\(317\) −11.3393 11.3393i −0.636876 0.636876i 0.312908 0.949784i \(-0.398697\pi\)
−0.949784 + 0.312908i \(0.898697\pi\)
\(318\) 7.22526 + 7.22526i 0.405172 + 0.405172i
\(319\) 0.0599025i 0.00335389i
\(320\) 0.625913 2.14668i 0.0349896 0.120003i
\(321\) 17.2504i 0.962825i
\(322\) 0 0
\(323\) −5.54766 + 5.54766i −0.308680 + 0.308680i
\(324\) 1.00000i 0.0555556i
\(325\) −0.500036 2.25747i −0.0277370 0.125222i
\(326\) 12.0807 0.669090
\(327\) −8.90962 + 8.90962i −0.492703 + 0.492703i
\(328\) −7.54452 7.54452i −0.416577 0.416577i
\(329\) 0 0
\(330\) −1.29769 + 4.45067i −0.0714357 + 0.245001i
\(331\) 21.7448 1.19520 0.597602 0.801793i \(-0.296120\pi\)
0.597602 + 0.801793i \(0.296120\pi\)
\(332\) −4.26961 + 4.26961i −0.234325 + 0.234325i
\(333\) 8.07760 8.07760i 0.442650 0.442650i
\(334\) 11.5496 0.631966
\(335\) −5.06564 9.23545i −0.276765 0.504586i
\(336\) 0 0
\(337\) −17.8706 17.8706i −0.973475 0.973475i 0.0261820 0.999657i \(-0.491665\pi\)
−0.999657 + 0.0261820i \(0.991665\pi\)
\(338\) 9.04117 9.04117i 0.491775 0.491775i
\(339\) 13.9715 0.758830
\(340\) −1.92957 3.51790i −0.104645 0.190785i
\(341\) 16.6534i 0.901835i
\(342\) −3.09170 + 3.09170i −0.167180 + 0.167180i
\(343\) 0 0
\(344\) 3.54793i 0.191291i
\(345\) 1.92957 + 0.562609i 0.103884 + 0.0302899i
\(346\) 6.97784i 0.375131i
\(347\) 14.1911 + 14.1911i 0.761818 + 0.761818i 0.976651 0.214833i \(-0.0689208\pi\)
−0.214833 + 0.976651i \(0.568921\pi\)
\(348\) 0.0204302 + 0.0204302i 0.00109517 + 0.00109517i
\(349\) −24.9858 −1.33746 −0.668730 0.743506i \(-0.733162\pi\)
−0.668730 + 0.743506i \(0.733162\pi\)
\(350\) 0 0
\(351\) 0.462438 0.0246831
\(352\) −1.46603 1.46603i −0.0781397 0.0781397i
\(353\) 19.1988 + 19.1988i 1.02185 + 1.02185i 0.999756 + 0.0220914i \(0.00703248\pi\)
0.0220914 + 0.999756i \(0.492968\pi\)
\(354\) 13.4242i 0.713490i
\(355\) 4.88322 + 1.42381i 0.259174 + 0.0755682i
\(356\) 0.0197698i 0.00104780i
\(357\) 0 0
\(358\) −4.56232 + 4.56232i −0.241126 + 0.241126i
\(359\) 16.7185i 0.882370i 0.897416 + 0.441185i \(0.145442\pi\)
−0.897416 + 0.441185i \(0.854558\pi\)
\(360\) −1.07534 1.96052i −0.0566756 0.103328i
\(361\) 0.117186 0.00616766
\(362\) −7.43329 + 7.43329i −0.390685 + 0.390685i
\(363\) −4.73869 4.73869i −0.248716 0.248716i
\(364\) 0 0
\(365\) 12.3797 + 22.5702i 0.647985 + 1.18138i
\(366\) 9.84270 0.514486
\(367\) 5.94533 5.94533i 0.310344 0.310344i −0.534699 0.845043i \(-0.679575\pi\)
0.845043 + 0.534699i \(0.179575\pi\)
\(368\) −0.635591 + 0.635591i −0.0331325 + 0.0331325i
\(369\) −10.6696 −0.555435
\(370\) 7.15009 24.5225i 0.371716 1.27486i
\(371\) 0 0
\(372\) −5.67978 5.67978i −0.294483 0.294483i
\(373\) −0.0162120 + 0.0162120i −0.000839423 + 0.000839423i −0.707526 0.706687i \(-0.750189\pi\)
0.706687 + 0.707526i \(0.250189\pi\)
\(374\) −3.72024 −0.192369
\(375\) −0.734297 + 11.1562i −0.0379189 + 0.576104i
\(376\) 0.742898i 0.0383120i
\(377\) −0.00944769 + 0.00944769i −0.000486581 + 0.000486581i
\(378\) 0 0
\(379\) 31.0300i 1.59391i 0.604041 + 0.796953i \(0.293556\pi\)
−0.604041 + 0.796953i \(0.706444\pi\)
\(380\) −2.73669 + 9.38597i −0.140389 + 0.481490i
\(381\) 3.58801i 0.183819i
\(382\) 17.6058 + 17.6058i 0.900790 + 0.900790i
\(383\) 3.47573 + 3.47573i 0.177602 + 0.177602i 0.790309 0.612708i \(-0.209920\pi\)
−0.612708 + 0.790309i \(0.709920\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −12.6474 −0.643738
\(387\) 2.50876 + 2.50876i 0.127528 + 0.127528i
\(388\) −5.65183 5.65183i −0.286928 0.286928i
\(389\) 11.0267i 0.559076i −0.960135 0.279538i \(-0.909819\pi\)
0.960135 0.279538i \(-0.0901814\pi\)
\(390\) 0.906619 0.497280i 0.0459084 0.0251808i
\(391\) 1.61289i 0.0815674i
\(392\) 0 0
\(393\) 13.9517 13.9517i 0.703768 0.703768i
\(394\) 3.48197i 0.175419i
\(395\) 5.01552 17.2016i 0.252358 0.865507i
\(396\) −2.07328 −0.104186
\(397\) −5.75974 + 5.75974i −0.289073 + 0.289073i −0.836714 0.547640i \(-0.815526\pi\)
0.547640 + 0.836714i \(0.315526\pi\)
\(398\) −5.37218 5.37218i −0.269283 0.269283i
\(399\) 0 0
\(400\) −4.21646 2.68727i −0.210823 0.134364i
\(401\) 11.7932 0.588926 0.294463 0.955663i \(-0.404859\pi\)
0.294463 + 0.955663i \(0.404859\pi\)
\(402\) 3.33098 3.33098i 0.166134 0.166134i
\(403\) 2.62655 2.62655i 0.130838 0.130838i
\(404\) 4.18882 0.208402
\(405\) −2.14668 0.625913i −0.106669 0.0311019i
\(406\) 0 0
\(407\) −16.7471 16.7471i −0.830124 0.830124i
\(408\) 1.26881 1.26881i 0.0628156 0.0628156i
\(409\) 6.26719 0.309892 0.154946 0.987923i \(-0.450480\pi\)
0.154946 + 0.987923i \(0.450480\pi\)
\(410\) −20.9179 + 11.4735i −1.03306 + 0.566633i
\(411\) 16.3975i 0.808831i
\(412\) 2.69132 2.69132i 0.132592 0.132592i
\(413\) 0 0
\(414\) 0.898861i 0.0441766i
\(415\) 6.49307 + 11.8379i 0.318732 + 0.581099i
\(416\) 0.462438i 0.0226729i
\(417\) −4.93867 4.93867i −0.241848 0.241848i
\(418\) 6.40995 + 6.40995i 0.313521 + 0.313521i
\(419\) −23.9790 −1.17145 −0.585726 0.810509i \(-0.699190\pi\)
−0.585726 + 0.810509i \(0.699190\pi\)
\(420\) 0 0
\(421\) −8.01218 −0.390490 −0.195245 0.980755i \(-0.562550\pi\)
−0.195245 + 0.980755i \(0.562550\pi\)
\(422\) −3.76373 3.76373i −0.183216 0.183216i
\(423\) −0.525308 0.525308i −0.0255414 0.0255414i
\(424\) 10.2181i 0.496233i
\(425\) −8.75955 + 1.94026i −0.424901 + 0.0941165i
\(426\) 2.27478i 0.110213i
\(427\) 0 0
\(428\) 12.1979 12.1979i 0.589608 0.589608i
\(429\) 0.958763i 0.0462895i
\(430\) 7.61626 + 2.22070i 0.367289 + 0.107091i
\(431\) −17.0950 −0.823437 −0.411719 0.911311i \(-0.635071\pi\)
−0.411719 + 0.911311i \(0.635071\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 3.28061 + 3.28061i 0.157656 + 0.157656i 0.781527 0.623871i \(-0.214441\pi\)
−0.623871 + 0.781527i \(0.714441\pi\)
\(434\) 0 0
\(435\) 0.0566445 0.0310695i 0.00271590 0.00148967i
\(436\) −12.6001 −0.603435
\(437\) 2.77901 2.77901i 0.132938 0.132938i
\(438\) −8.14046 + 8.14046i −0.388966 + 0.388966i
\(439\) 34.3470 1.63929 0.819647 0.572869i \(-0.194170\pi\)
0.819647 + 0.572869i \(0.194170\pi\)
\(440\) −4.06470 + 2.22949i −0.193777 + 0.106287i
\(441\) 0 0
\(442\) 0.586747 + 0.586747i 0.0279087 + 0.0279087i
\(443\) 19.9796 19.9796i 0.949258 0.949258i −0.0495155 0.998773i \(-0.515768\pi\)
0.998773 + 0.0495155i \(0.0157677\pi\)
\(444\) 11.4235 0.542133
\(445\) −0.0424395 0.0123742i −0.00201182 0.000586593i
\(446\) 21.9185i 1.03787i
\(447\) −5.70141 + 5.70141i −0.269667 + 0.269667i
\(448\) 0 0
\(449\) 10.0016i 0.472006i −0.971752 0.236003i \(-0.924163\pi\)
0.971752 0.236003i \(-0.0758375\pi\)
\(450\) −4.88168 + 1.08130i −0.230125 + 0.0509731i
\(451\) 22.1210i 1.04164i
\(452\) 9.87937 + 9.87937i 0.464686 + 0.464686i
\(453\) −14.7058 14.7058i −0.690937 0.690937i
\(454\) 9.62940 0.451930
\(455\) 0 0
\(456\) −4.37232 −0.204753
\(457\) −1.20959 1.20959i −0.0565823 0.0565823i 0.678249 0.734832i \(-0.262739\pi\)
−0.734832 + 0.678249i \(0.762739\pi\)
\(458\) 13.4158 + 13.4158i 0.626880 + 0.626880i
\(459\) 1.79437i 0.0837541i
\(460\) 0.966585 + 1.76223i 0.0450672 + 0.0821646i
\(461\) 8.80371i 0.410030i −0.978759 0.205015i \(-0.934276\pi\)
0.978759 0.205015i \(-0.0657243\pi\)
\(462\) 0 0
\(463\) −19.8709 + 19.8709i −0.923481 + 0.923481i −0.997274 0.0737924i \(-0.976490\pi\)
0.0737924 + 0.997274i \(0.476490\pi\)
\(464\) 0.0288926i 0.00134131i
\(465\) −15.7477 + 8.63761i −0.730283 + 0.400560i
\(466\) 23.1851 1.07403
\(467\) −19.3690 + 19.3690i −0.896291 + 0.896291i −0.995106 0.0988148i \(-0.968495\pi\)
0.0988148 + 0.995106i \(0.468495\pi\)
\(468\) 0.326993 + 0.326993i 0.0151153 + 0.0151153i
\(469\) 0 0
\(470\) −1.59476 0.464990i −0.0735610 0.0214484i
\(471\) 14.2684 0.657455
\(472\) 9.49237 9.49237i 0.436922 0.436922i
\(473\) 5.20137 5.20137i 0.239159 0.239159i
\(474\) 8.01313 0.368055
\(475\) 18.4357 + 11.7496i 0.845890 + 0.539109i
\(476\) 0 0
\(477\) 7.22526 + 7.22526i 0.330822 + 0.330822i
\(478\) 2.11242 2.11242i 0.0966197 0.0966197i
\(479\) 24.0136 1.09721 0.548605 0.836081i \(-0.315159\pi\)
0.548605 + 0.836081i \(0.315159\pi\)
\(480\) 0.625913 2.14668i 0.0285689 0.0979821i
\(481\) 5.28264i 0.240868i
\(482\) −19.1663 + 19.1663i −0.873003 + 0.873003i
\(483\) 0 0
\(484\) 6.70151i 0.304614i
\(485\) −15.6702 + 8.59512i −0.711549 + 0.390284i
\(486\) 1.00000i 0.0453609i
\(487\) −6.32464 6.32464i −0.286597 0.286597i 0.549136 0.835733i \(-0.314957\pi\)
−0.835733 + 0.549136i \(0.814957\pi\)
\(488\) 6.95984 + 6.95984i 0.315057 + 0.315057i
\(489\) 12.0807 0.546310
\(490\) 0 0
\(491\) 2.05148 0.0925818 0.0462909 0.998928i \(-0.485260\pi\)
0.0462909 + 0.998928i \(0.485260\pi\)
\(492\) −7.54452 7.54452i −0.340133 0.340133i
\(493\) 0.0366593 + 0.0366593i 0.00165105 + 0.00165105i
\(494\) 2.02193i 0.0909708i
\(495\) −1.29769 + 4.45067i −0.0583270 + 0.200043i
\(496\) 8.03242i 0.360666i
\(497\) 0 0
\(498\) −4.26961 + 4.26961i −0.191326 + 0.191326i
\(499\) 5.36056i 0.239971i 0.992776 + 0.119986i \(0.0382849\pi\)
−0.992776 + 0.119986i \(0.961715\pi\)
\(500\) −8.40785 + 7.36940i −0.376011 + 0.329570i
\(501\) 11.5496 0.515998
\(502\) 20.9707 20.9707i 0.935968 0.935968i
\(503\) −3.75049 3.75049i −0.167226 0.167226i 0.618533 0.785759i \(-0.287727\pi\)
−0.785759 + 0.618533i \(0.787727\pi\)
\(504\) 0 0
\(505\) 2.62184 8.99206i 0.116670 0.400141i
\(506\) 1.86359 0.0828467
\(507\) 9.04117 9.04117i 0.401533 0.401533i
\(508\) 2.53710 2.53710i 0.112566 0.112566i
\(509\) −9.76149 −0.432670 −0.216335 0.976319i \(-0.569410\pi\)
−0.216335 + 0.976319i \(0.569410\pi\)
\(510\) −1.92957 3.51790i −0.0854427 0.155775i
\(511\) 0 0
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −3.09170 + 3.09170i −0.136502 + 0.136502i
\(514\) −8.85671 −0.390653
\(515\) −4.09288 7.46195i −0.180354 0.328813i
\(516\) 3.54793i 0.156189i
\(517\) −1.08911 + 1.08911i −0.0478990 + 0.0478990i
\(518\) 0 0
\(519\) 6.97784i 0.306293i
\(520\) 0.992706 + 0.289446i 0.0435331 + 0.0126931i
\(521\) 23.1435i 1.01393i 0.861966 + 0.506967i \(0.169233\pi\)
−0.861966 + 0.506967i \(0.830767\pi\)
\(522\) 0.0204302 + 0.0204302i 0.000894204 + 0.000894204i
\(523\) −20.6002 20.6002i −0.900783 0.900783i 0.0947207 0.995504i \(-0.469804\pi\)
−0.995504 + 0.0947207i \(0.969804\pi\)
\(524\) 19.7306 0.861937
\(525\) 0 0
\(526\) 27.5475 1.20113
\(527\) −10.1916 10.1916i −0.443955 0.443955i
\(528\) −1.46603 1.46603i −0.0638008 0.0638008i
\(529\) 22.1920i 0.964872i
\(530\) 21.9349 + 6.39562i 0.952791 + 0.277808i
\(531\) 13.4242i 0.582562i
\(532\) 0 0
\(533\) 3.48888 3.48888i 0.151120 0.151120i
\(534\) 0.0197698i 0.000855524i
\(535\) −18.5501 33.8198i −0.801993 1.46216i
\(536\) 4.71072 0.203472
\(537\) −4.56232 + 4.56232i −0.196879 + 0.196879i
\(538\) 1.54931 + 1.54931i 0.0667957 + 0.0667957i
\(539\) 0 0
\(540\) −1.07534 1.96052i −0.0462754 0.0843673i
\(541\) −40.7258 −1.75094 −0.875469 0.483273i \(-0.839448\pi\)
−0.875469 + 0.483273i \(0.839448\pi\)
\(542\) 5.15367 5.15367i 0.221369 0.221369i
\(543\) −7.43329 + 7.43329i −0.318993 + 0.318993i
\(544\) 1.79437 0.0769331
\(545\) −7.88657 + 27.0484i −0.337824 + 1.15863i
\(546\) 0 0
\(547\) −24.2561 24.2561i −1.03711 1.03711i −0.999284 0.0378306i \(-0.987955\pi\)
−0.0378306 0.999284i \(-0.512045\pi\)
\(548\) −11.5948 + 11.5948i −0.495306 + 0.495306i
\(549\) 9.84270 0.420076
\(550\) 2.24184 + 10.1211i 0.0955925 + 0.431564i
\(551\) 0.126328i 0.00538174i
\(552\) −0.635591 + 0.635591i −0.0270525 + 0.0270525i
\(553\) 0 0
\(554\) 23.5003i 0.998433i
\(555\) 7.15009 24.5225i 0.303505 1.04092i
\(556\) 6.98433i 0.296202i
\(557\) −24.3133 24.3133i −1.03019 1.03019i −0.999530 0.0306577i \(-0.990240\pi\)
−0.0306577 0.999530i \(-0.509760\pi\)
\(558\) −5.67978 5.67978i −0.240444 0.240444i
\(559\) −1.64070 −0.0693941
\(560\) 0 0
\(561\) −3.72024 −0.157068
\(562\) 0.937068 + 0.937068i 0.0395278 + 0.0395278i
\(563\) −2.30717 2.30717i −0.0972357 0.0972357i 0.656816 0.754051i \(-0.271903\pi\)
−0.754051 + 0.656816i \(0.771903\pi\)
\(564\) 0.742898i 0.0312817i
\(565\) 27.3915 15.0242i 1.15237 0.632073i
\(566\) 20.5377i 0.863266i
\(567\) 0 0
\(568\) −1.60851 + 1.60851i −0.0674916 + 0.0674916i
\(569\) 11.4851i 0.481482i 0.970589 + 0.240741i \(0.0773905\pi\)
−0.970589 + 0.240741i \(0.922609\pi\)
\(570\) −2.73669 + 9.38597i −0.114628 + 0.393135i
\(571\) 2.24056 0.0937644 0.0468822 0.998900i \(-0.485071\pi\)
0.0468822 + 0.998900i \(0.485071\pi\)
\(572\) 0.677948 0.677948i 0.0283464 0.0283464i
\(573\) 17.6058 + 17.6058i 0.735492 + 0.735492i
\(574\) 0 0
\(575\) 4.38795 0.971941i 0.182990 0.0405328i
\(576\) 1.00000 0.0416667
\(577\) −5.15283 + 5.15283i −0.214515 + 0.214515i −0.806182 0.591667i \(-0.798470\pi\)
0.591667 + 0.806182i \(0.298470\pi\)
\(578\) −9.74409 + 9.74409i −0.405301 + 0.405301i
\(579\) −12.6474 −0.525610
\(580\) 0.0620232 + 0.0180843i 0.00257537 + 0.000750909i
\(581\) 0 0
\(582\) −5.65183 5.65183i −0.234276 0.234276i
\(583\) 14.9800 14.9800i 0.620407 0.620407i
\(584\) −11.5123 −0.476384
\(585\) 0.906619 0.497280i 0.0374841 0.0205600i
\(586\) 22.2391i 0.918687i
\(587\) −15.5725 + 15.5725i −0.642745 + 0.642745i −0.951229 0.308484i \(-0.900178\pi\)
0.308484 + 0.951229i \(0.400178\pi\)
\(588\) 0 0
\(589\) 35.1203i 1.44711i
\(590\) −14.4357 26.3185i −0.594307 1.08351i
\(591\) 3.48197i 0.143229i
\(592\) 8.07760 + 8.07760i 0.331987 + 0.331987i
\(593\) −11.1666 11.1666i −0.458557 0.458557i 0.439625 0.898182i \(-0.355112\pi\)
−0.898182 + 0.439625i \(0.855112\pi\)
\(594\) −2.07328 −0.0850677
\(595\) 0 0
\(596\) −8.06301 −0.330274
\(597\) −5.37218 5.37218i −0.219869 0.219869i
\(598\) −0.293921 0.293921i −0.0120193 0.0120193i
\(599\) 13.7247i 0.560776i 0.959887 + 0.280388i \(0.0904631\pi\)
−0.959887 + 0.280388i \(0.909537\pi\)
\(600\) −4.21646 2.68727i −0.172136 0.109707i
\(601\) 36.5565i 1.49117i 0.666411 + 0.745585i \(0.267830\pi\)
−0.666411 + 0.745585i \(0.732170\pi\)
\(602\) 0 0
\(603\) 3.33098 3.33098i 0.135648 0.135648i
\(604\) 20.7971i 0.846222i
\(605\) −14.3860 4.19457i −0.584874 0.170533i
\(606\) 4.18882 0.170159
\(607\) −22.5291 + 22.5291i −0.914430 + 0.914430i −0.996617 0.0821870i \(-0.973810\pi\)
0.0821870 + 0.996617i \(0.473810\pi\)
\(608\) −3.09170 3.09170i −0.125385 0.125385i
\(609\) 0 0
\(610\) 19.2968 10.5843i 0.781305 0.428545i
\(611\) 0.343544 0.0138983
\(612\) 1.26881 1.26881i 0.0512887 0.0512887i
\(613\) 2.84302 2.84302i 0.114828 0.114828i −0.647358 0.762186i \(-0.724126\pi\)
0.762186 + 0.647358i \(0.224126\pi\)
\(614\) 17.0778 0.689205
\(615\) −20.9179 + 11.4735i −0.843491 + 0.462654i
\(616\) 0 0
\(617\) 5.28987 + 5.28987i 0.212962 + 0.212962i 0.805525 0.592562i \(-0.201884\pi\)
−0.592562 + 0.805525i \(0.701884\pi\)
\(618\) 2.69132 2.69132i 0.108261 0.108261i
\(619\) −16.3515 −0.657222 −0.328611 0.944465i \(-0.606580\pi\)
−0.328611 + 0.944465i \(0.606580\pi\)
\(620\) −17.2430 5.02760i −0.692497 0.201913i
\(621\) 0.898861i 0.0360700i
\(622\) 14.2972 14.2972i 0.573267 0.573267i
\(623\) 0 0
\(624\) 0.462438i 0.0185123i
\(625\) 10.5571 + 22.6616i 0.422286 + 0.906463i
\(626\) 12.2452i 0.489415i
\(627\) 6.40995 + 6.40995i 0.255989 + 0.255989i
\(628\) 10.0893 + 10.0893i 0.402607 + 0.402607i
\(629\) 20.4979 0.817306
\(630\) 0 0
\(631\) 43.7268 1.74074 0.870368 0.492401i \(-0.163881\pi\)
0.870368 + 0.492401i \(0.163881\pi\)
\(632\) 5.66614 + 5.66614i 0.225387 + 0.225387i
\(633\) −3.76373 3.76373i −0.149595 0.149595i
\(634\) 16.0361i 0.636876i
\(635\) −3.85834 7.03436i −0.153114 0.279150i
\(636\) 10.2181i 0.405172i
\(637\) 0 0
\(638\) 0.0423574 0.0423574i 0.00167695 0.00167695i
\(639\) 2.27478i 0.0899888i
\(640\) 1.96052 1.07534i 0.0774963 0.0425067i
\(641\) −16.0222 −0.632838 −0.316419 0.948619i \(-0.602481\pi\)
−0.316419 + 0.948619i \(0.602481\pi\)
\(642\) 12.1979 12.1979i 0.481413 0.481413i
\(643\) 5.28588 + 5.28588i 0.208455 + 0.208455i 0.803610 0.595156i \(-0.202910\pi\)
−0.595156 + 0.803610i \(0.702910\pi\)
\(644\) 0 0
\(645\) 7.61626 + 2.22070i 0.299890 + 0.0874398i
\(646\) −7.84557 −0.308680
\(647\) −28.4692 + 28.4692i −1.11924 + 1.11924i −0.127388 + 0.991853i \(0.540659\pi\)
−0.991853 + 0.127388i \(0.959341\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −27.8322 −1.09251
\(650\) 1.24270 1.94985i 0.0487426 0.0764796i
\(651\) 0 0
\(652\) 8.54237 + 8.54237i 0.334545 + 0.334545i
\(653\) −5.75189 + 5.75189i −0.225089 + 0.225089i −0.810637 0.585548i \(-0.800879\pi\)
0.585548 + 0.810637i \(0.300879\pi\)
\(654\) −12.6001 −0.492703
\(655\) 12.3497 42.3553i 0.482542 1.65496i
\(656\) 10.6696i 0.416577i
\(657\) −8.14046 + 8.14046i −0.317589 + 0.317589i
\(658\) 0 0
\(659\) 15.0314i 0.585540i 0.956183 + 0.292770i \(0.0945770\pi\)
−0.956183 + 0.292770i \(0.905423\pi\)
\(660\) −4.06470 + 2.22949i −0.158218 + 0.0867827i
\(661\) 25.7580i 1.00187i 0.865485 + 0.500934i \(0.167010\pi\)
−0.865485 + 0.500934i \(0.832990\pi\)
\(662\) 15.3759 + 15.3759i 0.597602 + 0.597602i
\(663\) 0.586747 + 0.586747i 0.0227874 + 0.0227874i
\(664\) −6.03813 −0.234325
\(665\) 0 0
\(666\) 11.4235 0.442650
\(667\) −0.0183639 0.0183639i −0.000711052 0.000711052i
\(668\) 8.16680 + 8.16680i 0.315983 + 0.315983i
\(669\) 21.9185i 0.847420i
\(670\) 2.94850 10.1124i 0.113910 0.390676i
\(671\) 20.4067i 0.787791i
\(672\) 0 0
\(673\) 15.5407 15.5407i 0.599051 0.599051i −0.341009 0.940060i \(-0.610769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(674\) 25.2729i 0.973475i
\(675\) −4.88168 + 1.08130i −0.187896 + 0.0416194i
\(676\) 12.7862 0.491775
\(677\) 5.67922 5.67922i 0.218270 0.218270i −0.589499 0.807769i \(-0.700675\pi\)
0.807769 + 0.589499i \(0.200675\pi\)
\(678\) 9.87937 + 9.87937i 0.379415 + 0.379415i
\(679\) 0 0
\(680\) 1.12312 3.85194i 0.0430698 0.147715i
\(681\) 9.62940 0.368999
\(682\) −11.7758 + 11.7758i −0.450917 + 0.450917i
\(683\) −27.3490 + 27.3490i −1.04648 + 1.04648i −0.0476144 + 0.998866i \(0.515162\pi\)
−0.998866 + 0.0476144i \(0.984838\pi\)
\(684\) −4.37232 −0.167180
\(685\) 17.6330 + 32.1477i 0.673722 + 1.22830i
\(686\) 0 0
\(687\) 13.4158 + 13.4158i 0.511845 + 0.511845i
\(688\) −2.50876 + 2.50876i −0.0956457 + 0.0956457i
\(689\) −4.72522 −0.180016
\(690\) 0.966585 + 1.76223i 0.0367972 + 0.0670871i
\(691\) 25.5947i 0.973668i −0.873494 0.486834i \(-0.838152\pi\)
0.873494 0.486834i \(-0.161848\pi\)
\(692\) −4.93408 + 4.93408i −0.187566 + 0.187566i
\(693\) 0 0
\(694\) 20.0692i 0.761818i
\(695\) −14.9931 4.37159i −0.568721 0.165824i
\(696\) 0.0288926i 0.00109517i
\(697\) −13.5377 13.5377i −0.512776 0.512776i
\(698\) −17.6676 17.6676i −0.668730 0.668730i
\(699\) 23.1851 0.876940
\(700\) 0 0
\(701\) 41.0066 1.54880 0.774399 0.632698i \(-0.218052\pi\)
0.774399 + 0.632698i \(0.218052\pi\)
\(702\) 0.326993 + 0.326993i 0.0123416 + 0.0123416i
\(703\) −35.3179 35.3179i −1.33204 1.33204i
\(704\) 2.07328i 0.0781397i
\(705\) −1.59476 0.464990i −0.0600623 0.0175125i
\(706\) 27.1512i 1.02185i
\(707\) 0 0
\(708\) 9.49237 9.49237i 0.356745 0.356745i
\(709\) 15.5334i 0.583370i 0.956514 + 0.291685i \(0.0942159\pi\)
−0.956514 + 0.291685i \(0.905784\pi\)
\(710\) 2.44617 + 4.45975i 0.0918031 + 0.167371i
\(711\) 8.01313 0.300516
\(712\) 0.0139794 0.0139794i 0.000523899 0.000523899i
\(713\) 5.10533 + 5.10533i 0.191196 + 0.191196i
\(714\) 0 0
\(715\) −1.03100 1.87967i −0.0385572 0.0702958i
\(716\) −6.45209 −0.241126
\(717\) 2.11242 2.11242i 0.0788896 0.0788896i
\(718\) −11.8218 + 11.8218i −0.441185 + 0.441185i
\(719\) 0.379933 0.0141691 0.00708455 0.999975i \(-0.497745\pi\)
0.00708455 + 0.999975i \(0.497745\pi\)
\(720\) 0.625913 2.14668i 0.0233264 0.0800020i
\(721\) 0 0
\(722\) 0.0828627 + 0.0828627i 0.00308383 + 0.00308383i
\(723\) −19.1663 + 19.1663i −0.712804 + 0.712804i
\(724\) −10.5123 −0.390685
\(725\) 0.0776423 0.121825i 0.00288356 0.00452446i
\(726\) 6.70151i 0.248716i
\(727\) −27.3322 + 27.3322i −1.01369 + 1.01369i −0.0137898 + 0.999905i \(0.504390\pi\)
−0.999905 + 0.0137898i \(0.995610\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −7.20573 + 24.7133i −0.266696 + 0.914681i
\(731\) 6.36630i 0.235466i
\(732\) 6.95984 + 6.95984i 0.257243 + 0.257243i
\(733\) −6.42449 6.42449i −0.237294 0.237294i 0.578435 0.815729i \(-0.303664\pi\)
−0.815729 + 0.578435i \(0.803664\pi\)
\(734\) 8.40797 0.310344
\(735\) 0 0
\(736\) −0.898861 −0.0331325
\(737\) −6.90605 6.90605i −0.254388 0.254388i
\(738\) −7.54452 7.54452i −0.277718 0.277718i
\(739\) 3.73900i 0.137541i −0.997632 0.0687707i \(-0.978092\pi\)
0.997632 0.0687707i \(-0.0219077\pi\)
\(740\) 22.3959 12.2841i 0.823290 0.451574i
\(741\) 2.02193i 0.0742774i
\(742\) 0 0
\(743\) 1.84421 1.84421i 0.0676575 0.0676575i −0.672468 0.740126i \(-0.734766\pi\)
0.740126 + 0.672468i \(0.234766\pi\)
\(744\) 8.03242i 0.294483i
\(745\) −5.04675 + 17.3087i −0.184898 + 0.634141i
\(746\) −0.0229272 −0.000839423
\(747\) −4.26961 + 4.26961i −0.156217 + 0.156217i
\(748\) −2.63060 2.63060i −0.0961844 0.0961844i
\(749\) 0 0
\(750\) −8.40785 + 7.36940i −0.307011 + 0.269092i
\(751\) −18.9083 −0.689974 −0.344987 0.938607i \(-0.612117\pi\)
−0.344987 + 0.938607i \(0.612117\pi\)
\(752\) 0.525308 0.525308i 0.0191560 0.0191560i
\(753\) 20.9707 20.9707i 0.764214 0.764214i
\(754\) −0.0133610 −0.000486581
\(755\) −44.6447 13.0172i −1.62479 0.473744i
\(756\) 0 0
\(757\) 36.1051 + 36.1051i 1.31226 + 1.31226i 0.919744 + 0.392520i \(0.128396\pi\)
0.392520 + 0.919744i \(0.371604\pi\)
\(758\) −21.9416 + 21.9416i −0.796953 + 0.796953i
\(759\) 1.86359 0.0676440
\(760\) −8.57202 + 4.70175i −0.310940 + 0.170550i
\(761\) 24.5228i 0.888950i 0.895791 + 0.444475i \(0.146610\pi\)
−0.895791 + 0.444475i \(0.853390\pi\)
\(762\) 2.53710 2.53710i 0.0919096 0.0919096i
\(763\) 0 0
\(764\) 24.8983i 0.900790i
\(765\) −1.92957 3.51790i −0.0697637 0.127190i
\(766\) 4.91543i 0.177602i
\(767\) 4.38963 + 4.38963i 0.158500 + 0.158500i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) −41.6081 −1.50043 −0.750213 0.661196i \(-0.770049\pi\)
−0.750213 + 0.661196i \(0.770049\pi\)
\(770\) 0 0
\(771\) −8.85671 −0.318967
\(772\) −8.94309 8.94309i −0.321869 0.321869i
\(773\) 26.5458 + 26.5458i 0.954786 + 0.954786i 0.999021 0.0442349i \(-0.0140850\pi\)
−0.0442349 + 0.999021i \(0.514085\pi\)
\(774\) 3.54793i 0.127528i
\(775\) −21.5853 + 33.8684i −0.775366 + 1.21659i
\(776\) 7.99290i 0.286928i
\(777\) 0 0
\(778\) 7.79706 7.79706i 0.279538 0.279538i
\(779\) 46.6508i 1.67144i
\(780\) 0.992706 + 0.289446i 0.0355446 + 0.0103638i
\(781\) 4.71625 0.168761
\(782\) −1.14049 + 1.14049i −0.0407837 + 0.0407837i
\(783\) 0.0204302 + 0.0204302i 0.000730115 + 0.000730115i
\(784\) 0 0
\(785\) 27.9736 15.3435i 0.998419 0.547632i
\(786\) 19.7306 0.703768
\(787\) −3.71498 + 3.71498i −0.132425 + 0.132425i −0.770212 0.637788i \(-0.779850\pi\)
0.637788 + 0.770212i \(0.279850\pi\)
\(788\) 2.46213 2.46213i 0.0877096 0.0877096i
\(789\) 27.5475 0.980717
\(790\) 15.7099 8.61687i 0.558933 0.306574i
\(791\) 0 0
\(792\) −1.46603 1.46603i −0.0520931 0.0520931i
\(793\) −3.21850 + 3.21850i −0.114292 + 0.114292i
\(794\) −8.14551 −0.289073
\(795\) 21.9349 + 6.39562i 0.777950 + 0.226829i
\(796\) 7.59741i 0.269283i
\(797\) 0.406449 0.406449i 0.0143971 0.0143971i −0.699872 0.714269i \(-0.746759\pi\)
0.714269 + 0.699872i \(0.246759\pi\)
\(798\) 0 0
\(799\) 1.33304i 0.0471594i
\(800\) −1.08130 4.88168i −0.0382298 0.172593i
\(801\) 0.0197698i 0.000698532i
\(802\) 8.33908 + 8.33908i 0.294463 + 0.294463i
\(803\) 16.8774 + 16.8774i 0.595592 + 0.595592i
\(804\) 4.71072 0.166134
\(805\) 0 0
\(806\) 3.71450 0.130838
\(807\) 1.54931 + 1.54931i 0.0545385 + 0.0545385i
\(808\) 2.96194 + 2.96194i 0.104201 + 0.104201i
\(809\) 35.8295i 1.25970i 0.776718 + 0.629849i \(0.216883\pi\)
−0.776718 + 0.629849i \(0.783117\pi\)
\(810\) −1.07534 1.96052i −0.0377837 0.0688856i
\(811\) 30.6135i 1.07499i 0.843268 + 0.537493i \(0.180628\pi\)
−0.843268 + 0.537493i \(0.819372\pi\)
\(812\) 0 0
\(813\) 5.15367 5.15367i 0.180747 0.180747i
\(814\) 23.6840i 0.830124i
\(815\) 23.6845 12.9909i 0.829632 0.455053i
\(816\) 1.79437 0.0628156
\(817\) 10.9691 10.9691i 0.383761 0.383761i
\(818\) 4.43157 + 4.43157i 0.154946 + 0.154946i
\(819\) 0 0
\(820\) −22.9041 6.67823i −0.799847 0.233214i
\(821\) −26.8615 −0.937471 −0.468736 0.883338i \(-0.655290\pi\)
−0.468736 + 0.883338i \(0.655290\pi\)
\(822\) −11.5948 + 11.5948i −0.404415 + 0.404415i
\(823\) −3.80691 + 3.80691i −0.132701 + 0.132701i −0.770337 0.637637i \(-0.779912\pi\)
0.637637 + 0.770337i \(0.279912\pi\)
\(824\) 3.80611 0.132592
\(825\) 2.24184 + 10.1211i 0.0780510 + 0.352371i
\(826\) 0 0
\(827\) 5.30801 + 5.30801i 0.184578 + 0.184578i 0.793347 0.608770i \(-0.208337\pi\)
−0.608770 + 0.793347i \(0.708337\pi\)
\(828\) −0.635591 + 0.635591i −0.0220883 + 0.0220883i
\(829\) 42.2481 1.46734 0.733668 0.679508i \(-0.237807\pi\)
0.733668 + 0.679508i \(0.237807\pi\)
\(830\) −3.77935 + 12.9619i −0.131183 + 0.449915i
\(831\) 23.5003i 0.815217i
\(832\) −0.326993 + 0.326993i −0.0113364 + 0.0113364i
\(833\) 0 0
\(834\) 6.98433i 0.241848i
\(835\) 22.6432 12.4198i 0.783600 0.429804i
\(836\) 9.06504i 0.313521i
\(837\) −5.67978 5.67978i −0.196322 0.196322i
\(838\) −16.9557 16.9557i −0.585726 0.585726i
\(839\) −31.3254 −1.08147 −0.540736 0.841192i \(-0.681854\pi\)
−0.540736 + 0.841192i \(0.681854\pi\)
\(840\) 0 0
\(841\) 28.9992 0.999971
\(842\) −5.66547 5.66547i −0.195245 0.195245i
\(843\) 0.937068 + 0.937068i 0.0322743 + 0.0322743i
\(844\) 5.32272i 0.183216i
\(845\) 8.00302 27.4478i 0.275312 0.944232i
\(846\) 0.742898i 0.0255414i
\(847\) 0 0
\(848\) −7.22526 + 7.22526i −0.248116 + 0.248116i
\(849\) 20.5377i 0.704854i
\(850\) −7.56591 4.82197i −0.259509 0.165392i
\(851\) −10.2681 −0.351986
\(852\) −1.60851 + 1.60851i −0.0551067 + 0.0551067i
\(853\) −17.7771 17.7771i −0.608678 0.608678i 0.333923 0.942600i \(-0.391628\pi\)
−0.942600 + 0.333923i \(0.891628\pi\)
\(854\) 0 0
\(855\) −2.73669 + 9.38597i −0.0935930 + 0.320993i
\(856\) 17.2504 0.589608
\(857\) −30.2273 + 30.2273i −1.03255 + 1.03255i −0.0330932 + 0.999452i \(0.510536\pi\)
−0.999452 + 0.0330932i \(0.989464\pi\)
\(858\) 0.677948 0.677948i 0.0231448 0.0231448i
\(859\) −16.6575 −0.568348 −0.284174 0.958773i \(-0.591719\pi\)
−0.284174 + 0.958773i \(0.591719\pi\)
\(860\) 3.81524 + 6.95578i 0.130099 + 0.237190i
\(861\) 0 0
\(862\) −12.0880 12.0880i −0.411719 0.411719i
\(863\) −39.3141 + 39.3141i −1.33827 + 1.33827i −0.440528 + 0.897739i \(0.645209\pi\)
−0.897739 + 0.440528i \(0.854791\pi\)
\(864\) 1.00000 0.0340207
\(865\) 7.50358 + 13.6802i 0.255129 + 0.465141i
\(866\) 4.63948i 0.157656i
\(867\) −9.74409 + 9.74409i −0.330927 + 0.330927i
\(868\) 0 0
\(869\) 16.6134i 0.563573i
\(870\) 0.0620232 + 0.0180843i 0.00210278 + 0.000613114i
\(871\) 2.17841i 0.0738128i
\(872\) −8.90962 8.90962i −0.301718 0.301718i
\(873\) −5.65183 5.65183i −0.191286 0.191286i
\(874\) 3.93011 0.132938
\(875\) 0 0
\(876\) −11.5123 −0.388966
\(877\) 32.6886 + 32.6886i 1.10381 + 1.10381i 0.993946 + 0.109868i \(0.0350428\pi\)
0.109868 + 0.993946i \(0.464957\pi\)
\(878\) 24.2870 + 24.2870i 0.819647 + 0.819647i
\(879\) 22.2391i 0.750105i
\(880\) −4.45067 1.29769i −0.150032 0.0437452i
\(881\) 1.61071i 0.0542661i −0.999632 0.0271330i \(-0.991362\pi\)
0.999632 0.0271330i \(-0.00863778\pi\)
\(882\) 0 0
\(883\) −35.7890 + 35.7890i −1.20439 + 1.20439i −0.231579 + 0.972816i \(0.574389\pi\)
−0.972816 + 0.231579i \(0.925611\pi\)
\(884\) 0.829786i 0.0279087i
\(885\) −14.4357 26.3185i −0.485250 0.884686i
\(886\) 28.2554 0.949258
\(887\) 14.1627 14.1627i 0.475537 0.475537i −0.428164 0.903701i \(-0.640839\pi\)
0.903701 + 0.428164i \(0.140839\pi\)
\(888\) 8.07760 + 8.07760i 0.271067 + 0.271067i
\(889\) 0 0
\(890\) −0.0212594 0.0387591i −0.000712615 0.00129921i
\(891\) −2.07328 −0.0694575
\(892\) 15.4987 15.4987i 0.518936 0.518936i
\(893\) −2.29682 + 2.29682i −0.0768600 + 0.0768600i
\(894\) −8.06301 −0.269667
\(895\) −4.03845 + 13.8506i −0.134991 + 0.462974i
\(896\) 0 0
\(897\) −0.293921 0.293921i −0.00981375 0.00981375i
\(898\) 7.07222 7.07222i 0.236003 0.236003i
\(899\) 0.232078 0.00774022
\(900\) −4.21646 2.68727i −0.140549 0.0895757i
\(901\) 18.3350i 0.610827i
\(902\) −15.6419 + 15.6419i −0.520818 + 0.520818i
\(903\) 0 0
\(904\) 13.9715i 0.464686i
\(905\) −6.57976 + 22.5664i −0.218719 + 0.750134i
\(906\) 20.7971i 0.690937i
\(907\) −36.8528 36.8528i −1.22368 1.22368i −0.966315 0.257362i \(-0.917147\pi\)
−0.257362 0.966315i \(-0.582853\pi\)
\(908\) 6.80901 + 6.80901i 0.225965 + 0.225965i
\(909\) 4.18882 0.138934
\(910\) 0 0
\(911\) 14.6381 0.484981 0.242490 0.970154i \(-0.422036\pi\)
0.242490 + 0.970154i \(0.422036\pi\)
\(912\) −3.09170 3.09170i −0.102376 0.102376i
\(913\) 8.85209 + 8.85209i 0.292961 + 0.292961i
\(914\) 1.71062i 0.0565823i
\(915\) 19.2968 10.5843i 0.637933 0.349906i
\(916\) 18.9728i 0.626880i
\(917\) 0 0
\(918\) 1.26881 1.26881i 0.0418771 0.0418771i
\(919\) 49.3134i 1.62670i −0.581775 0.813350i \(-0.697642\pi\)
0.581775 0.813350i \(-0.302358\pi\)
\(920\) −0.562609 + 1.92957i −0.0185487 + 0.0636159i
\(921\) 17.0778 0.562734
\(922\) 6.22516 6.22516i 0.205015 0.205015i
\(923\) −0.743837 0.743837i −0.0244837 0.0244837i
\(924\) 0 0
\(925\) −12.3522 55.7656i −0.406138 1.83356i
\(926\) −28.1018 −0.923481
\(927\) 2.69132 2.69132i 0.0883947 0.0883947i
\(928\) −0.0204302 + 0.0204302i −0.000670653 + 0.000670653i
\(929\) −50.7683 −1.66566 −0.832828 0.553532i \(-0.813280\pi\)
−0.832828 + 0.553532i \(0.813280\pi\)
\(930\) −17.2430 5.02760i −0.565421 0.164861i
\(931\) 0 0
\(932\) 16.3943 + 16.3943i 0.537014 + 0.537014i
\(933\) 14.2972 14.2972i 0.468070 0.468070i
\(934\) −27.3919 −0.896291
\(935\) −7.29359 + 4.00053i −0.238526 + 0.130831i
\(936\) 0.462438i 0.0151153i
\(937\) 6.18012 6.18012i 0.201896 0.201896i −0.598916 0.800812i \(-0.704402\pi\)
0.800812 + 0.598916i \(0.204402\pi\)
\(938\) 0 0
\(939\) 12.2452i 0.399605i
\(940\) −0.798871 1.45647i −0.0260563 0.0475047i
\(941\) 11.7207i 0.382084i −0.981582 0.191042i \(-0.938813\pi\)
0.981582 0.191042i \(-0.0611867\pi\)
\(942\) 10.0893 + 10.0893i 0.328728 + 0.328728i
\(943\) 6.78148 + 6.78148i 0.220835 + 0.220835i
\(944\) 13.4242 0.436922
\(945\) 0 0
\(946\) 7.35584 0.239159
\(947\) −23.5131 23.5131i −0.764073 0.764073i 0.212983 0.977056i \(-0.431682\pi\)
−0.977056 + 0.212983i \(0.931682\pi\)
\(948\) 5.66614 + 5.66614i 0.184028 + 0.184028i
\(949\) 5.32375i 0.172816i
\(950\) 4.72780 + 21.3443i 0.153390 + 0.692499i
\(951\) 16.0361i 0.520007i
\(952\) 0 0
\(953\) −7.37438 + 7.37438i −0.238879 + 0.238879i −0.816386 0.577507i \(-0.804026\pi\)
0.577507 + 0.816386i \(0.304026\pi\)
\(954\) 10.2181i 0.330822i
\(955\) 53.4488 + 15.5842i 1.72956 + 0.504293i
\(956\) 2.98741 0.0966197
\(957\) 0.0423574 0.0423574i 0.00136922 0.00136922i
\(958\) 16.9802 + 16.9802i 0.548605 + 0.548605i
\(959\) 0 0
\(960\) 1.96052 1.07534i 0.0632755 0.0347066i
\(961\) −33.5198 −1.08128
\(962\) −3.73539 + 3.73539i −0.120434 + 0.120434i
\(963\) 12.1979 12.1979i 0.393072 0.393072i
\(964\) −27.1053 −0.873003
\(965\) −24.7956 + 13.6003i −0.798197 + 0.437811i
\(966\) 0 0
\(967\) −25.7706 25.7706i −0.828725 0.828725i 0.158615 0.987340i \(-0.449297\pi\)
−0.987340 + 0.158615i \(0.949297\pi\)
\(968\) 4.73869 4.73869i 0.152307 0.152307i
\(969\) −7.84557 −0.252036
\(970\) −17.1582 5.00286i −0.550916 0.160632i
\(971\) 54.9570i 1.76365i 0.471573 + 0.881827i \(0.343686\pi\)
−0.471573 + 0.881827i \(0.656314\pi\)
\(972\) 0.707107 0.707107i 0.0226805 0.0226805i
\(973\) 0 0
\(974\) 8.94440i 0.286597i
\(975\) 1.24270 1.94985i 0.0397981 0.0624453i
\(976\) 9.84270i 0.315057i
\(977\) 12.0469 + 12.0469i 0.385415 + 0.385415i 0.873048 0.487634i \(-0.162140\pi\)
−0.487634 + 0.873048i \(0.662140\pi\)
\(978\) 8.54237 + 8.54237i 0.273155 + 0.273155i
\(979\) −0.0409884 −0.00130999
\(980\) 0 0
\(981\) −12.6001 −0.402290
\(982\) 1.45061 + 1.45061i 0.0462909 + 0.0462909i
\(983\) 17.2157 + 17.2157i 0.549094 + 0.549094i 0.926179 0.377084i \(-0.123073\pi\)
−0.377084 + 0.926179i \(0.623073\pi\)
\(984\) 10.6696i 0.340133i
\(985\) −3.74432 6.82647i −0.119304 0.217510i
\(986\) 0.0518441i 0.00165105i
\(987\) 0 0
\(988\) 1.42972 1.42972i 0.0454854 0.0454854i
\(989\) 3.18909i 0.101407i
\(990\) −4.06470 + 2.22949i −0.129185 + 0.0708578i
\(991\) 52.6929 1.67384 0.836922 0.547322i \(-0.184353\pi\)
0.836922 + 0.547322i \(0.184353\pi\)
\(992\) 5.67978 5.67978i 0.180333 0.180333i
\(993\) 15.3759 + 15.3759i 0.487940 + 0.487940i
\(994\) 0 0
\(995\) −16.3092 4.75532i −0.517037 0.150754i
\(996\) −6.03813 −0.191326
\(997\) 10.7568 10.7568i 0.340670 0.340670i −0.515949 0.856619i \(-0.672561\pi\)
0.856619 + 0.515949i \(0.172561\pi\)
\(998\) −3.79048 + 3.79048i −0.119986 + 0.119986i
\(999\) 11.4235 0.361422
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 1470.2.m.c.97.8 16
5.3 odd 4 1470.2.m.f.1273.5 yes 16
7.6 odd 2 1470.2.m.f.97.5 yes 16
35.13 even 4 inner 1470.2.m.c.1273.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.m.c.97.8 16 1.1 even 1 trivial
1470.2.m.c.1273.8 yes 16 35.13 even 4 inner
1470.2.m.f.97.5 yes 16 7.6 odd 2
1470.2.m.f.1273.5 yes 16 5.3 odd 4