Properties

Label 507.2.q.b.16.8
Level $507$
Weight $2$
Character 507.16
Analytic conductor $4.048$
Analytic rank $0$
Dimension $384$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(16,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.q (of order \(39\), degree \(24\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(384\)
Relative dimension: \(16\) over \(\Q(\zeta_{39})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label 16.8
Character \(\chi\) \(=\) 507.16
Dual form 507.2.q.b.412.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.488381 - 0.0394262i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.73714 - 0.282313i) q^{4} +(-1.47540 - 1.30709i) q^{5} +(0.391703 + 0.294346i) q^{6} +(-2.51230 + 2.61558i) q^{7} +(1.78872 + 0.440880i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\) \(q+(-0.488381 - 0.0394262i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.73714 - 0.282313i) q^{4} +(-1.47540 - 1.30709i) q^{5} +(0.391703 + 0.294346i) q^{6} +(-2.51230 + 2.61558i) q^{7} +(1.78872 + 0.440880i) q^{8} +(0.428693 + 0.903450i) q^{9} +(0.669022 + 0.696526i) q^{10} +(1.12753 - 2.37622i) q^{11} +(1.31733 + 1.16705i) q^{12} +(-2.54884 + 2.55018i) q^{13} +(1.33008 - 1.17835i) q^{14} +(0.548397 + 1.89329i) q^{15} +(2.48252 + 0.828787i) q^{16} +(-0.712142 + 0.741418i) q^{17} +(-0.173746 - 0.458130i) q^{18} +(3.84634 - 6.66206i) q^{19} +(2.19396 + 2.68711i) q^{20} +(3.52131 - 0.867924i) q^{21} +(-0.644349 + 1.11605i) q^{22} +(3.63512 + 6.29621i) q^{23} +(-1.27617 - 1.32864i) q^{24} +(-0.134366 - 1.10660i) q^{25} +(1.34535 - 1.14497i) q^{26} +(0.120537 - 0.992709i) q^{27} +(5.10262 - 3.83437i) q^{28} +(6.59247 + 0.532199i) q^{29} +(-0.193182 - 0.946266i) q^{30} +(-0.336720 + 2.77314i) q^{31} +(-4.56941 - 1.94684i) q^{32} +(-2.22298 + 1.40573i) q^{33} +(0.377028 - 0.334018i) q^{34} +(7.12542 - 0.575223i) q^{35} +(-0.489643 - 1.69044i) q^{36} +(7.28723 - 3.10480i) q^{37} +(-2.14114 + 3.10198i) q^{38} +(3.51724 - 0.793125i) q^{39} +(-2.06280 - 2.98848i) q^{40} +(7.57116 + 4.78771i) q^{41} +(-1.75396 + 0.285046i) q^{42} +(-5.85918 - 2.49636i) q^{43} +(-2.62951 + 3.80950i) q^{44} +(0.548397 - 1.89329i) q^{45} +(-1.52709 - 3.21827i) q^{46} +(-4.17499 + 11.0086i) q^{47} +(-1.65524 - 2.02730i) q^{48} +(-0.247752 - 6.14790i) q^{49} +(0.0219927 + 0.545742i) q^{50} +(0.998158 - 0.246024i) q^{51} +(5.14763 - 3.71046i) q^{52} +(-3.80665 - 0.938255i) q^{53} +(-0.0980066 + 0.480068i) q^{54} +(-4.76947 + 2.03208i) q^{55} +(-5.64695 + 3.57092i) q^{56} +(-6.81153 + 3.57497i) q^{57} +(-3.19866 - 0.519832i) q^{58} +(10.9870 - 3.66801i) q^{59} +(-0.418143 - 3.44372i) q^{60} +(-3.85089 + 13.2948i) q^{61} +(0.273782 - 1.34107i) q^{62} +(-3.44005 - 1.14846i) q^{63} +(-2.47999 - 1.30160i) q^{64} +(7.09385 - 0.430982i) q^{65} +(1.14109 - 0.598888i) q^{66} +(-4.83779 + 0.786217i) q^{67} +(1.44640 - 1.08690i) q^{68} +(0.292743 - 7.26434i) q^{69} -3.50260 q^{70} +(0.197565 - 4.90252i) q^{71} +(0.368498 + 1.80502i) q^{72} +(4.61330 + 6.68351i) q^{73} +(-3.68136 + 1.22902i) q^{74} +(-0.477877 + 1.00710i) q^{75} +(-8.56241 + 10.4870i) q^{76} +(3.38249 + 8.91890i) q^{77} +(-1.74902 + 0.248676i) q^{78} +(-0.149270 + 0.393593i) q^{79} +(-2.57940 - 4.46766i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-3.50885 - 2.63673i) q^{82} +(5.21576 + 2.73744i) q^{83} +(-6.36202 + 0.513596i) q^{84} +(2.01979 - 0.163054i) q^{85} +(2.76309 + 1.45018i) q^{86} +(-5.28745 - 3.97326i) q^{87} +(3.06446 - 3.75328i) q^{88} +(2.64964 + 4.58930i) q^{89} +(-0.342472 + 0.903024i) q^{90} +(-0.266775 - 13.0735i) q^{91} +(-4.53721 - 11.9636i) q^{92} +(1.76674 - 2.16387i) q^{93} +(2.47301 - 5.21177i) q^{94} +(-14.3828 + 4.80167i) q^{95} +(2.82150 + 4.08765i) q^{96} +(0.729973 + 3.57564i) q^{97} +(-0.121391 + 3.01228i) q^{98} +2.63016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{39}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.488381 0.0394262i −0.345338 0.0278785i −0.0934188 0.995627i \(-0.529780\pi\)
−0.251919 + 0.967748i \(0.581062\pi\)
\(3\) −0.845190 0.534466i −0.487971 0.308574i
\(4\) −1.73714 0.282313i −0.868569 0.141156i
\(5\) −1.47540 1.30709i −0.659817 0.584547i 0.265329 0.964158i \(-0.414519\pi\)
−0.925146 + 0.379611i \(0.876058\pi\)
\(6\) 0.391703 + 0.294346i 0.159912 + 0.120166i
\(7\) −2.51230 + 2.61558i −0.949559 + 0.988596i −0.999949 0.0101340i \(-0.996774\pi\)
0.0503897 + 0.998730i \(0.483954\pi\)
\(8\) 1.78872 + 0.440880i 0.632408 + 0.155875i
\(9\) 0.428693 + 0.903450i 0.142898 + 0.301150i
\(10\) 0.669022 + 0.696526i 0.211563 + 0.220261i
\(11\) 1.12753 2.37622i 0.339963 0.716456i −0.659413 0.751781i \(-0.729195\pi\)
0.999376 + 0.0353246i \(0.0112465\pi\)
\(12\) 1.31733 + 1.16705i 0.380279 + 0.336898i
\(13\) −2.54884 + 2.55018i −0.706920 + 0.707294i
\(14\) 1.33008 1.17835i 0.355479 0.314927i
\(15\) 0.548397 + 1.89329i 0.141595 + 0.488844i
\(16\) 2.48252 + 0.828787i 0.620630 + 0.207197i
\(17\) −0.712142 + 0.741418i −0.172720 + 0.179820i −0.801936 0.597410i \(-0.796197\pi\)
0.629216 + 0.777230i \(0.283376\pi\)
\(18\) −0.173746 0.458130i −0.0409523 0.107982i
\(19\) 3.84634 6.66206i 0.882411 1.52838i 0.0337587 0.999430i \(-0.489252\pi\)
0.848652 0.528951i \(-0.177414\pi\)
\(20\) 2.19396 + 2.68711i 0.490584 + 0.600857i
\(21\) 3.52131 0.867924i 0.768412 0.189397i
\(22\) −0.644349 + 1.11605i −0.137376 + 0.237942i
\(23\) 3.63512 + 6.29621i 0.757975 + 1.31285i 0.943882 + 0.330284i \(0.107144\pi\)
−0.185907 + 0.982567i \(0.559522\pi\)
\(24\) −1.27617 1.32864i −0.260498 0.271207i
\(25\) −0.134366 1.10660i −0.0268732 0.221321i
\(26\) 1.34535 1.14497i 0.263844 0.224547i
\(27\) 0.120537 0.992709i 0.0231973 0.191047i
\(28\) 5.10262 3.83437i 0.964304 0.724628i
\(29\) 6.59247 + 0.532199i 1.22419 + 0.0988269i 0.675603 0.737266i \(-0.263883\pi\)
0.548588 + 0.836093i \(0.315165\pi\)
\(30\) −0.193182 0.946266i −0.0352700 0.172764i
\(31\) −0.336720 + 2.77314i −0.0604768 + 0.498071i 0.930726 + 0.365718i \(0.119176\pi\)
−0.991203 + 0.132353i \(0.957747\pi\)
\(32\) −4.56941 1.94684i −0.807765 0.344157i
\(33\) −2.22298 + 1.40573i −0.386971 + 0.244706i
\(34\) 0.377028 0.334018i 0.0646598 0.0572836i
\(35\) 7.12542 0.575223i 1.20442 0.0972305i
\(36\) −0.489643 1.69044i −0.0816072 0.281741i
\(37\) 7.28723 3.10480i 1.19801 0.510426i 0.301510 0.953463i \(-0.402509\pi\)
0.896503 + 0.443037i \(0.146099\pi\)
\(38\) −2.14114 + 3.10198i −0.347339 + 0.503207i
\(39\) 3.51724 0.793125i 0.563209 0.127002i
\(40\) −2.06280 2.98848i −0.326158 0.472521i
\(41\) 7.57116 + 4.78771i 1.18242 + 0.747715i 0.973156 0.230145i \(-0.0739200\pi\)
0.209261 + 0.977860i \(0.432894\pi\)
\(42\) −1.75396 + 0.285046i −0.270642 + 0.0439836i
\(43\) −5.85918 2.49636i −0.893517 0.380692i −0.104112 0.994566i \(-0.533200\pi\)
−0.789404 + 0.613874i \(0.789610\pi\)
\(44\) −2.62951 + 3.80950i −0.396413 + 0.574304i
\(45\) 0.548397 1.89329i 0.0817502 0.282234i
\(46\) −1.52709 3.21827i −0.225157 0.474508i
\(47\) −4.17499 + 11.0086i −0.608985 + 1.60576i 0.174712 + 0.984620i \(0.444100\pi\)
−0.783698 + 0.621143i \(0.786669\pi\)
\(48\) −1.65524 2.02730i −0.238914 0.292616i
\(49\) −0.247752 6.14790i −0.0353931 0.878271i
\(50\) 0.0219927 + 0.545742i 0.00311023 + 0.0771796i
\(51\) 0.998158 0.246024i 0.139770 0.0344502i
\(52\) 5.14763 3.71046i 0.713848 0.514548i
\(53\) −3.80665 0.938255i −0.522884 0.128879i −0.0309651 0.999520i \(-0.509858\pi\)
−0.491919 + 0.870641i \(0.663704\pi\)
\(54\) −0.0980066 + 0.480068i −0.0133370 + 0.0653290i
\(55\) −4.76947 + 2.03208i −0.643115 + 0.274006i
\(56\) −5.64695 + 3.57092i −0.754606 + 0.477184i
\(57\) −6.81153 + 3.57497i −0.902209 + 0.473516i
\(58\) −3.19866 0.519832i −0.420004 0.0682573i
\(59\) 10.9870 3.66801i 1.43039 0.477534i 0.507183 0.861838i \(-0.330687\pi\)
0.923207 + 0.384304i \(0.125559\pi\)
\(60\) −0.418143 3.44372i −0.0539820 0.444582i
\(61\) −3.85089 + 13.2948i −0.493055 + 1.70222i 0.198672 + 0.980066i \(0.436337\pi\)
−0.691728 + 0.722159i \(0.743150\pi\)
\(62\) 0.273782 1.34107i 0.0347704 0.170317i
\(63\) −3.44005 1.14846i −0.433405 0.144692i
\(64\) −2.47999 1.30160i −0.309999 0.162700i
\(65\) 7.09385 0.430982i 0.879884 0.0534568i
\(66\) 1.14109 0.598888i 0.140458 0.0737180i
\(67\) −4.83779 + 0.786217i −0.591030 + 0.0960517i −0.448568 0.893749i \(-0.648066\pi\)
−0.142462 + 0.989800i \(0.545502\pi\)
\(68\) 1.44640 1.08690i 0.175402 0.131806i
\(69\) 0.292743 7.26434i 0.0352421 0.874524i
\(70\) −3.50260 −0.418641
\(71\) 0.197565 4.90252i 0.0234466 0.581822i −0.944179 0.329432i \(-0.893143\pi\)
0.967626 0.252389i \(-0.0812163\pi\)
\(72\) 0.368498 + 1.80502i 0.0434279 + 0.212724i
\(73\) 4.61330 + 6.68351i 0.539945 + 0.782246i 0.994076 0.108689i \(-0.0346653\pi\)
−0.454130 + 0.890935i \(0.650050\pi\)
\(74\) −3.68136 + 1.22902i −0.427949 + 0.142870i
\(75\) −0.477877 + 1.00710i −0.0551805 + 0.116290i
\(76\) −8.56241 + 10.4870i −0.982176 + 1.20295i
\(77\) 3.38249 + 8.91890i 0.385471 + 1.01640i
\(78\) −1.74902 + 0.248676i −0.198038 + 0.0281570i
\(79\) −0.149270 + 0.393593i −0.0167942 + 0.0442826i −0.943151 0.332364i \(-0.892154\pi\)
0.926357 + 0.376647i \(0.122923\pi\)
\(80\) −2.57940 4.46766i −0.288386 0.499499i
\(81\) −0.632445 + 0.774605i −0.0702717 + 0.0860672i
\(82\) −3.50885 2.63673i −0.387488 0.291178i
\(83\) 5.21576 + 2.73744i 0.572504 + 0.300473i 0.726021 0.687673i \(-0.241368\pi\)
−0.153517 + 0.988146i \(0.549060\pi\)
\(84\) −6.36202 + 0.513596i −0.694154 + 0.0560379i
\(85\) 2.01979 0.163054i 0.219077 0.0176857i
\(86\) 2.76309 + 1.45018i 0.297952 + 0.156377i
\(87\) −5.28745 3.97326i −0.566874 0.425978i
\(88\) 3.06446 3.75328i 0.326672 0.400101i
\(89\) 2.64964 + 4.58930i 0.280861 + 0.486465i 0.971597 0.236642i \(-0.0760467\pi\)
−0.690736 + 0.723107i \(0.742713\pi\)
\(90\) −0.342472 + 0.903024i −0.0360997 + 0.0951871i
\(91\) −0.266775 13.0735i −0.0279656 1.37047i
\(92\) −4.53721 11.9636i −0.473037 1.24729i
\(93\) 1.76674 2.16387i 0.183203 0.224382i
\(94\) 2.47301 5.21177i 0.255072 0.537553i
\(95\) −14.3828 + 4.80167i −1.47564 + 0.492641i
\(96\) 2.82150 + 4.08765i 0.287968 + 0.417194i
\(97\) 0.729973 + 3.57564i 0.0741175 + 0.363052i 0.999887 0.0150369i \(-0.00478659\pi\)
−0.925769 + 0.378089i \(0.876581\pi\)
\(98\) −0.121391 + 3.01228i −0.0122623 + 0.304287i
\(99\) 2.63016 0.264341
\(100\) −0.0789957 + 1.96026i −0.00789957 + 0.196026i
\(101\) −0.956123 + 0.718480i −0.0951378 + 0.0714914i −0.647247 0.762281i \(-0.724080\pi\)
0.552109 + 0.833772i \(0.313823\pi\)
\(102\) −0.497181 + 0.0807998i −0.0492283 + 0.00800038i
\(103\) 7.56105 3.96835i 0.745013 0.391013i −0.0490917 0.998794i \(-0.515633\pi\)
0.794104 + 0.607781i \(0.207940\pi\)
\(104\) −5.68348 + 3.43784i −0.557311 + 0.337108i
\(105\) −6.32977 3.32212i −0.617722 0.324206i
\(106\) 1.82211 + 0.608308i 0.176978 + 0.0590841i
\(107\) 2.49431 12.2180i 0.241134 1.18115i −0.661231 0.750182i \(-0.729966\pi\)
0.902365 0.430972i \(-0.141829\pi\)
\(108\) −0.489643 + 1.69044i −0.0471159 + 0.162663i
\(109\) −1.66164 13.6848i −0.159156 1.31077i −0.825193 0.564850i \(-0.808934\pi\)
0.666037 0.745919i \(-0.267989\pi\)
\(110\) 2.40944 0.804388i 0.229731 0.0766954i
\(111\) −7.81850 1.27063i −0.742100 0.120603i
\(112\) −8.40458 + 4.41106i −0.794158 + 0.416806i
\(113\) 2.97058 1.87848i 0.279449 0.176713i −0.387388 0.921917i \(-0.626622\pi\)
0.666836 + 0.745204i \(0.267648\pi\)
\(114\) 3.46757 1.47739i 0.324768 0.138371i
\(115\) 2.86645 14.0408i 0.267298 1.30931i
\(116\) −11.3018 2.78564i −1.04934 0.258640i
\(117\) −3.39663 1.20950i −0.314019 0.111818i
\(118\) −5.51048 + 1.35821i −0.507280 + 0.125033i
\(119\) −0.150125 3.72533i −0.0137620 0.341500i
\(120\) 0.146217 + 3.62834i 0.0133477 + 0.331220i
\(121\) 2.58182 + 3.16215i 0.234711 + 0.287468i
\(122\) 2.40486 6.34110i 0.217726 0.574097i
\(123\) −3.84020 8.09306i −0.346259 0.729726i
\(124\) 1.36782 4.72227i 0.122834 0.424072i
\(125\) −6.84677 + 9.91926i −0.612394 + 0.887205i
\(126\) 1.63478 + 0.696513i 0.145637 + 0.0620503i
\(127\) −13.9632 + 2.26924i −1.23903 + 0.201362i −0.744396 0.667738i \(-0.767262\pi\)
−0.494635 + 0.869101i \(0.664698\pi\)
\(128\) 9.55575 + 6.04269i 0.844617 + 0.534103i
\(129\) 3.61790 + 5.24143i 0.318538 + 0.461482i
\(130\) −3.48150 0.0692000i −0.305347 0.00606924i
\(131\) −4.17925 + 6.05469i −0.365143 + 0.529001i −0.961893 0.273426i \(-0.911843\pi\)
0.596750 + 0.802427i \(0.296458\pi\)
\(132\) 4.25848 1.81437i 0.370653 0.157921i
\(133\) 7.76198 + 26.7975i 0.673049 + 2.32364i
\(134\) 2.39368 0.193238i 0.206783 0.0166932i
\(135\) −1.47540 + 1.30709i −0.126982 + 0.112496i
\(136\) −1.60070 + 1.01222i −0.137259 + 0.0867972i
\(137\) 15.0539 + 6.41389i 1.28615 + 0.547975i 0.923374 0.383903i \(-0.125420\pi\)
0.362772 + 0.931878i \(0.381830\pi\)
\(138\) −0.429376 + 3.53623i −0.0365509 + 0.301024i
\(139\) 0.233780 + 1.14513i 0.0198290 + 0.0971287i 0.988501 0.151216i \(-0.0483187\pi\)
−0.968672 + 0.248344i \(0.920114\pi\)
\(140\) −12.5402 1.01235i −1.05984 0.0855594i
\(141\) 9.41236 7.07293i 0.792663 0.595648i
\(142\) −0.289774 + 2.38651i −0.0243173 + 0.200271i
\(143\) 3.18590 + 8.93199i 0.266419 + 0.746930i
\(144\) 0.315470 + 2.59813i 0.0262892 + 0.216511i
\(145\) −9.03087 9.40214i −0.749973 0.780805i
\(146\) −1.98954 3.44599i −0.164656 0.285192i
\(147\) −3.07644 + 5.32855i −0.253741 + 0.439492i
\(148\) −13.5355 + 3.33619i −1.11261 + 0.274233i
\(149\) 5.77308 + 7.07074i 0.472949 + 0.579258i 0.954895 0.296943i \(-0.0959672\pi\)
−0.481946 + 0.876201i \(0.660070\pi\)
\(150\) 0.273093 0.473010i 0.0222979 0.0386211i
\(151\) 0.124706 + 0.328822i 0.0101484 + 0.0267591i 0.939995 0.341189i \(-0.110830\pi\)
−0.929846 + 0.367948i \(0.880060\pi\)
\(152\) 9.81720 10.2208i 0.796280 0.829015i
\(153\) −0.975124 0.325544i −0.0788341 0.0263187i
\(154\) −1.30031 4.48918i −0.104782 0.361749i
\(155\) 4.12153 3.65136i 0.331049 0.293284i
\(156\) −6.33384 + 0.384808i −0.507113 + 0.0308093i
\(157\) −0.870628 0.771309i −0.0694837 0.0615572i 0.627666 0.778483i \(-0.284010\pi\)
−0.697150 + 0.716925i \(0.745549\pi\)
\(158\) 0.0884185 0.186338i 0.00703420 0.0148243i
\(159\) 2.71588 + 2.82753i 0.215383 + 0.224238i
\(160\) 4.19699 + 8.84498i 0.331802 + 0.699257i
\(161\) −25.6007 6.31001i −2.01762 0.497299i
\(162\) 0.339414 0.353368i 0.0266669 0.0277632i
\(163\) −10.0318 7.53841i −0.785751 0.590454i 0.130319 0.991472i \(-0.458400\pi\)
−0.916070 + 0.401018i \(0.868656\pi\)
\(164\) −11.8005 10.4544i −0.921466 0.816348i
\(165\) 5.11719 + 0.831624i 0.398373 + 0.0647418i
\(166\) −2.43935 1.54255i −0.189330 0.119725i
\(167\) 4.01824 + 0.324386i 0.310940 + 0.0251017i 0.234952 0.972007i \(-0.424507\pi\)
0.0759885 + 0.997109i \(0.475789\pi\)
\(168\) 6.68128 0.515472
\(169\) −0.00687730 13.0000i −0.000529023 1.00000i
\(170\) −0.992856 −0.0761485
\(171\) 7.66774 + 0.619004i 0.586367 + 0.0473364i
\(172\) 9.47345 + 5.99065i 0.722344 + 0.456783i
\(173\) 14.4549 + 2.34915i 1.09899 + 0.178603i 0.682748 0.730654i \(-0.260784\pi\)
0.416237 + 0.909256i \(0.363349\pi\)
\(174\) 2.42564 + 2.14893i 0.183887 + 0.162910i
\(175\) 3.23198 + 2.42867i 0.244314 + 0.183590i
\(176\) 4.76849 4.96452i 0.359438 0.374215i
\(177\) −11.2466 2.77203i −0.845343 0.208358i
\(178\) −1.11309 2.34579i −0.0834299 0.175825i
\(179\) −8.41302 8.75888i −0.628819 0.654670i 0.328230 0.944598i \(-0.393548\pi\)
−0.957048 + 0.289928i \(0.906369\pi\)
\(180\) −1.48714 + 3.13408i −0.110845 + 0.233601i
\(181\) 15.6802 + 13.8914i 1.16550 + 1.03254i 0.998918 + 0.0465154i \(0.0148117\pi\)
0.166582 + 0.986028i \(0.446727\pi\)
\(182\) −0.385151 + 6.39537i −0.0285493 + 0.474056i
\(183\) 10.3603 9.17847i 0.765859 0.678492i
\(184\) 3.72634 + 12.8648i 0.274709 + 0.948407i
\(185\) −14.8098 4.94424i −1.08884 0.363507i
\(186\) −0.948157 + 0.987136i −0.0695222 + 0.0723803i
\(187\) 0.958809 + 2.52817i 0.0701151 + 0.184878i
\(188\) 10.3604 17.9447i 0.755609 1.30875i
\(189\) 2.29368 + 2.80925i 0.166841 + 0.204343i
\(190\) 7.21358 1.77799i 0.523328 0.128989i
\(191\) −10.3629 + 17.9490i −0.749832 + 1.29875i 0.198071 + 0.980188i \(0.436532\pi\)
−0.947903 + 0.318560i \(0.896801\pi\)
\(192\) 1.40040 + 2.42557i 0.101065 + 0.175050i
\(193\) 13.3334 + 13.8815i 0.959759 + 0.999215i 1.00000 2.47590e-5i \(7.88104e-6\pi\)
−0.0402412 + 0.999190i \(0.512813\pi\)
\(194\) −0.215531 1.77506i −0.0154742 0.127442i
\(195\) −6.22600 3.42716i −0.445853 0.245424i
\(196\) −1.30525 + 10.7497i −0.0932320 + 0.767835i
\(197\) 17.7855 13.3649i 1.26716 0.952210i 0.267227 0.963634i \(-0.413893\pi\)
0.999935 + 0.0114231i \(0.00363617\pi\)
\(198\) −1.28452 0.103697i −0.0912868 0.00736943i
\(199\) −2.90194 14.2146i −0.205713 1.00765i −0.943184 0.332270i \(-0.892185\pi\)
0.737471 0.675378i \(-0.236020\pi\)
\(200\) 0.247536 2.03864i 0.0175035 0.144154i
\(201\) 4.50906 + 1.92113i 0.318044 + 0.135506i
\(202\) 0.495279 0.313196i 0.0348477 0.0220364i
\(203\) −17.9543 + 15.9061i −1.26014 + 1.11639i
\(204\) −1.80339 + 0.145585i −0.126263 + 0.0101930i
\(205\) −4.91251 16.9599i −0.343104 1.18453i
\(206\) −3.84913 + 1.63996i −0.268182 + 0.114262i
\(207\) −4.12997 + 5.98329i −0.287053 + 0.415867i
\(208\) −8.44109 + 4.21844i −0.585284 + 0.292496i
\(209\) −11.4936 16.6514i −0.795031 1.15180i
\(210\) 2.96036 + 1.87202i 0.204284 + 0.129182i
\(211\) −8.75199 + 1.42234i −0.602512 + 0.0979177i −0.454013 0.890995i \(-0.650008\pi\)
−0.148499 + 0.988913i \(0.547444\pi\)
\(212\) 6.34780 + 2.70454i 0.435969 + 0.185749i
\(213\) −2.78721 + 4.03797i −0.190976 + 0.276677i
\(214\) −1.69988 + 5.86868i −0.116202 + 0.401175i
\(215\) 5.38165 + 11.3416i 0.367025 + 0.773489i
\(216\) 0.653272 1.72254i 0.0444495 0.117204i
\(217\) −6.40743 7.84767i −0.434964 0.532735i
\(218\) 0.271972 + 6.74893i 0.0184203 + 0.457095i
\(219\) −0.327003 8.11449i −0.0220968 0.548326i
\(220\) 8.85891 2.18353i 0.597268 0.147213i
\(221\) −0.0756206 3.70585i −0.00508679 0.249282i
\(222\) 3.76831 + 0.928806i 0.252913 + 0.0623374i
\(223\) 4.60842 22.5735i 0.308602 1.51163i −0.469181 0.883102i \(-0.655451\pi\)
0.777783 0.628533i \(-0.216344\pi\)
\(224\) 16.5718 7.06060i 1.10725 0.471756i
\(225\) 0.942160 0.595786i 0.0628107 0.0397191i
\(226\) −1.52484 + 0.800296i −0.101431 + 0.0532349i
\(227\) 5.35877 + 0.870884i 0.355674 + 0.0578026i 0.335623 0.941996i \(-0.391053\pi\)
0.0200506 + 0.999799i \(0.493617\pi\)
\(228\) 12.8418 4.28723i 0.850471 0.283929i
\(229\) 0.619453 + 5.10166i 0.0409346 + 0.337127i 0.998760 + 0.0497772i \(0.0158511\pi\)
−0.957826 + 0.287350i \(0.907226\pi\)
\(230\) −1.95350 + 6.74426i −0.128810 + 0.444703i
\(231\) 1.90800 9.34599i 0.125537 0.614921i
\(232\) 11.5575 + 3.85844i 0.758784 + 0.253319i
\(233\) −8.56662 4.49611i −0.561218 0.294550i 0.160160 0.987091i \(-0.448799\pi\)
−0.721379 + 0.692541i \(0.756491\pi\)
\(234\) 1.61117 + 0.724614i 0.105325 + 0.0473695i
\(235\) 20.5489 10.7849i 1.34046 0.703529i
\(236\) −20.1215 + 3.27007i −1.30980 + 0.212863i
\(237\) 0.336523 0.252881i 0.0218595 0.0164264i
\(238\) −0.0735570 + 1.82530i −0.00476799 + 0.118316i
\(239\) 7.39887 0.478593 0.239297 0.970947i \(-0.423083\pi\)
0.239297 + 0.970947i \(0.423083\pi\)
\(240\) −0.207724 + 5.15462i −0.0134085 + 0.332729i
\(241\) 2.52891 + 12.3874i 0.162902 + 0.797945i 0.976331 + 0.216281i \(0.0693928\pi\)
−0.813430 + 0.581663i \(0.802402\pi\)
\(242\) −1.13624 1.64613i −0.0730403 0.105817i
\(243\) 0.948536 0.316668i 0.0608486 0.0203143i
\(244\) 10.4428 22.0078i 0.668532 1.40890i
\(245\) −7.67030 + 9.39441i −0.490037 + 0.600187i
\(246\) 1.55640 + 4.10390i 0.0992327 + 0.261655i
\(247\) 7.18578 + 26.7894i 0.457221 + 1.70457i
\(248\) −1.82492 + 4.81192i −0.115883 + 0.305557i
\(249\) −2.94524 5.10130i −0.186647 0.323282i
\(250\) 3.73491 4.57444i 0.236217 0.289313i
\(251\) 22.7492 + 17.0949i 1.43591 + 1.07902i 0.982193 + 0.187876i \(0.0601602\pi\)
0.453721 + 0.891144i \(0.350096\pi\)
\(252\) 5.65162 + 2.96620i 0.356018 + 0.186853i
\(253\) 19.0599 1.53867i 1.19828 0.0967354i
\(254\) 6.90882 0.557738i 0.433498 0.0349956i
\(255\) −1.79425 0.941696i −0.112360 0.0589713i
\(256\) 0.0495633 + 0.0372444i 0.00309771 + 0.00232778i
\(257\) 16.2978 19.9611i 1.01663 1.24514i 0.0474238 0.998875i \(-0.484899\pi\)
0.969202 0.246266i \(-0.0792037\pi\)
\(258\) −1.56026 2.70246i −0.0971378 0.168248i
\(259\) −10.1868 + 26.8605i −0.632980 + 1.66903i
\(260\) −12.4447 1.25401i −0.771786 0.0777702i
\(261\) 2.34533 + 6.18412i 0.145172 + 0.382788i
\(262\) 2.27978 2.79222i 0.140845 0.172504i
\(263\) −1.22766 + 2.58725i −0.0757010 + 0.159536i −0.937773 0.347250i \(-0.887116\pi\)
0.862072 + 0.506787i \(0.169167\pi\)
\(264\) −4.59605 + 1.53439i −0.282867 + 0.0944350i
\(265\) 4.38994 + 6.35992i 0.269672 + 0.390687i
\(266\) −2.73428 13.3934i −0.167650 0.821203i
\(267\) 0.213380 5.29497i 0.0130587 0.324047i
\(268\) 8.62587 0.526909
\(269\) −0.398287 + 9.88338i −0.0242840 + 0.602600i 0.940537 + 0.339692i \(0.110323\pi\)
−0.964821 + 0.262909i \(0.915318\pi\)
\(270\) 0.772089 0.580187i 0.0469878 0.0353091i
\(271\) 22.9111 3.72342i 1.39175 0.226182i 0.582112 0.813109i \(-0.302227\pi\)
0.809640 + 0.586927i \(0.199662\pi\)
\(272\) −2.38238 + 1.25037i −0.144453 + 0.0758149i
\(273\) −6.76186 + 11.1922i −0.409247 + 0.677381i
\(274\) −7.09919 3.72594i −0.428878 0.225092i
\(275\) −2.78103 0.928445i −0.167702 0.0559873i
\(276\) −2.55935 + 12.5365i −0.154055 + 0.754610i
\(277\) −4.99326 + 17.2387i −0.300016 + 1.03577i 0.658934 + 0.752200i \(0.271007\pi\)
−0.958950 + 0.283574i \(0.908480\pi\)
\(278\) −0.0690256 0.568477i −0.00413988 0.0340950i
\(279\) −2.64975 + 0.884615i −0.158636 + 0.0529605i
\(280\) 12.9990 + 2.11254i 0.776838 + 0.126248i
\(281\) 20.2344 10.6198i 1.20708 0.633526i 0.263499 0.964660i \(-0.415123\pi\)
0.943584 + 0.331134i \(0.107431\pi\)
\(282\) −4.87568 + 3.08319i −0.290342 + 0.183601i
\(283\) −12.7289 + 5.42327i −0.756653 + 0.322380i −0.735616 0.677399i \(-0.763107\pi\)
−0.0210374 + 0.999779i \(0.506697\pi\)
\(284\) −1.72724 + 8.46057i −0.102493 + 0.502043i
\(285\) 14.7225 + 3.62877i 0.872086 + 0.214950i
\(286\) −1.20378 4.48782i −0.0711811 0.265371i
\(287\) −31.5436 + 7.77481i −1.86196 + 0.458933i
\(288\) −0.199995 4.96283i −0.0117848 0.292438i
\(289\) 0.641966 + 15.9302i 0.0377627 + 0.937072i
\(290\) 4.03982 + 4.94788i 0.237226 + 0.290550i
\(291\) 1.29409 3.41224i 0.0758611 0.200029i
\(292\) −6.12710 12.9126i −0.358561 0.755652i
\(293\) −0.685460 + 2.36648i −0.0400450 + 0.138251i −0.978050 0.208370i \(-0.933184\pi\)
0.938005 + 0.346622i \(0.112671\pi\)
\(294\) 1.71256 2.48107i 0.0998786 0.144699i
\(295\) −21.0046 8.94923i −1.22294 0.521045i
\(296\) 14.4037 2.34082i 0.837196 0.136058i
\(297\) −2.22298 1.40573i −0.128990 0.0815686i
\(298\) −2.54069 3.68083i −0.147178 0.213225i
\(299\) −25.3218 6.77778i −1.46440 0.391969i
\(300\) 1.11446 1.61457i 0.0643432 0.0932172i
\(301\) 21.2494 9.05354i 1.22480 0.521837i
\(302\) −0.0479397 0.165507i −0.00275862 0.00952386i
\(303\) 1.19211 0.0962369i 0.0684848 0.00552867i
\(304\) 15.0700 13.3509i 0.864326 0.765726i
\(305\) 23.0590 14.5816i 1.32036 0.834943i
\(306\) 0.463398 + 0.197435i 0.0264907 + 0.0112866i
\(307\) −1.16380 + 9.58474i −0.0664214 + 0.547030i 0.921075 + 0.389386i \(0.127313\pi\)
−0.987496 + 0.157644i \(0.949610\pi\)
\(308\) −3.35794 16.4483i −0.191336 0.937228i
\(309\) −8.51147 0.687117i −0.484201 0.0390887i
\(310\) −2.15684 + 1.62076i −0.122500 + 0.0920529i
\(311\) 0.0585148 0.481912i 0.00331807 0.0273267i −0.990956 0.134189i \(-0.957157\pi\)
0.994274 + 0.106862i \(0.0340803\pi\)
\(312\) 6.64103 + 0.132000i 0.375974 + 0.00747306i
\(313\) 3.72142 + 30.6486i 0.210347 + 1.73236i 0.590149 + 0.807294i \(0.299069\pi\)
−0.379802 + 0.925068i \(0.624008\pi\)
\(314\) 0.394789 + 0.411019i 0.0222792 + 0.0231951i
\(315\) 3.57430 + 6.19087i 0.201389 + 0.348816i
\(316\) 0.370419 0.641584i 0.0208377 0.0360919i
\(317\) 11.9977 2.95717i 0.673858 0.166091i 0.112484 0.993653i \(-0.464119\pi\)
0.561374 + 0.827562i \(0.310273\pi\)
\(318\) −1.21491 1.48799i −0.0681285 0.0834423i
\(319\) 8.69782 15.0651i 0.486984 0.843482i
\(320\) 1.95767 + 5.16194i 0.109437 + 0.288561i
\(321\) −8.63825 + 8.99337i −0.482140 + 0.501961i
\(322\) 12.2541 + 4.09103i 0.682896 + 0.227984i
\(323\) 2.20023 + 7.59608i 0.122424 + 0.422657i
\(324\) 1.31733 1.16705i 0.0731848 0.0648361i
\(325\) 3.16452 + 2.47789i 0.175536 + 0.137449i
\(326\) 4.60213 + 4.07713i 0.254889 + 0.225812i
\(327\) −5.90967 + 12.4544i −0.326806 + 0.688728i
\(328\) 11.4319 + 11.9019i 0.631220 + 0.657170i
\(329\) −18.3049 38.5768i −1.00918 2.12681i
\(330\) −2.46635 0.607901i −0.135768 0.0334638i
\(331\) −14.0288 + 14.6056i −0.771094 + 0.802794i −0.984724 0.174121i \(-0.944292\pi\)
0.213630 + 0.976915i \(0.431471\pi\)
\(332\) −8.28768 6.22779i −0.454845 0.341794i
\(333\) 5.92901 + 5.25265i 0.324908 + 0.287843i
\(334\) −1.94964 0.316848i −0.106680 0.0173371i
\(335\) 8.16531 + 5.16343i 0.446118 + 0.282108i
\(336\) 9.46103 + 0.763773i 0.516142 + 0.0416673i
\(337\) 12.0869 0.658414 0.329207 0.944258i \(-0.393219\pi\)
0.329207 + 0.944258i \(0.393219\pi\)
\(338\) −0.509182 + 6.34923i −0.0276958 + 0.345352i
\(339\) −3.51469 −0.190892
\(340\) −3.55469 0.286964i −0.192780 0.0155628i
\(341\) 6.20992 + 3.92692i 0.336286 + 0.212654i
\(342\) −3.72037 0.604620i −0.201175 0.0326941i
\(343\) −2.29959 2.03726i −0.124166 0.110002i
\(344\) −9.37984 7.04849i −0.505727 0.380029i
\(345\) −9.92704 + 10.3351i −0.534454 + 0.556425i
\(346\) −6.96688 1.71718i −0.374542 0.0923163i
\(347\) −7.48521 15.7747i −0.401827 0.846833i −0.999000 0.0447197i \(-0.985761\pi\)
0.597173 0.802113i \(-0.296291\pi\)
\(348\) 8.06333 + 8.39482i 0.432240 + 0.450009i
\(349\) 9.84297 20.7436i 0.526882 1.11038i −0.449290 0.893386i \(-0.648323\pi\)
0.976173 0.216995i \(-0.0696256\pi\)
\(350\) −1.48268 1.31354i −0.0792528 0.0702118i
\(351\) 2.22436 + 2.83764i 0.118728 + 0.151462i
\(352\) −9.77826 + 8.66278i −0.521183 + 0.461728i
\(353\) −8.35915 28.8591i −0.444913 1.53602i −0.799308 0.600922i \(-0.794800\pi\)
0.354395 0.935096i \(-0.384687\pi\)
\(354\) 5.38332 + 1.79721i 0.286120 + 0.0955209i
\(355\) −6.69950 + 6.97492i −0.355572 + 0.370190i
\(356\) −3.30717 8.72028i −0.175279 0.462174i
\(357\) −1.86417 + 3.22884i −0.0986626 + 0.170889i
\(358\) 3.76343 + 4.60937i 0.198904 + 0.243613i
\(359\) −14.5219 + 3.57933i −0.766437 + 0.188910i −0.603105 0.797661i \(-0.706070\pi\)
−0.163332 + 0.986571i \(0.552224\pi\)
\(360\) 1.81564 3.14478i 0.0956926 0.165744i
\(361\) −20.0887 34.7946i −1.05730 1.83130i
\(362\) −7.11023 7.40253i −0.373705 0.389068i
\(363\) −0.492064 4.05251i −0.0258267 0.212702i
\(364\) −3.22739 + 22.7858i −0.169161 + 1.19430i
\(365\) 1.92949 15.8908i 0.100994 0.831763i
\(366\) −5.42167 + 4.07412i −0.283395 + 0.212958i
\(367\) −21.7026 1.75201i −1.13286 0.0914543i −0.500221 0.865897i \(-0.666748\pi\)
−0.632643 + 0.774443i \(0.718030\pi\)
\(368\) 3.80604 + 18.6432i 0.198403 + 0.971844i
\(369\) −1.07976 + 8.89263i −0.0562101 + 0.462932i
\(370\) 7.03789 + 2.99857i 0.365883 + 0.155888i
\(371\) 12.0175 7.59942i 0.623918 0.394542i
\(372\) −3.67996 + 3.26016i −0.190797 + 0.169032i
\(373\) −16.5427 + 1.33547i −0.856550 + 0.0691479i −0.500935 0.865485i \(-0.667011\pi\)
−0.355615 + 0.934633i \(0.615729\pi\)
\(374\) −0.368588 1.27251i −0.0190592 0.0658001i
\(375\) 11.0883 4.72429i 0.572599 0.243962i
\(376\) −12.3213 + 17.8505i −0.635425 + 0.920572i
\(377\) −18.1603 + 15.4555i −0.935305 + 0.796000i
\(378\) −1.00943 1.46242i −0.0519197 0.0752186i
\(379\) 13.6753 + 8.64771i 0.702451 + 0.444203i 0.837358 0.546655i \(-0.184099\pi\)
−0.134907 + 0.990858i \(0.543074\pi\)
\(380\) 26.3404 4.28074i 1.35124 0.219597i
\(381\) 13.0144 + 5.54490i 0.666746 + 0.284074i
\(382\) 5.76870 8.35741i 0.295152 0.427602i
\(383\) −8.04130 + 27.7618i −0.410891 + 1.41856i 0.442255 + 0.896889i \(0.354179\pi\)
−0.853146 + 0.521672i \(0.825309\pi\)
\(384\) −4.84681 10.2144i −0.247338 0.521253i
\(385\) 6.66726 17.5801i 0.339795 0.895966i
\(386\) −5.96448 7.30517i −0.303584 0.371823i
\(387\) −0.256446 6.36365i −0.0130359 0.323483i
\(388\) −0.258615 6.41747i −0.0131292 0.325798i
\(389\) −9.47735 + 2.33596i −0.480521 + 0.118438i −0.472133 0.881527i \(-0.656516\pi\)
−0.00838735 + 0.999965i \(0.502670\pi\)
\(390\) 2.90554 + 1.91923i 0.147128 + 0.0971839i
\(391\) −7.25685 1.78865i −0.366994 0.0904560i
\(392\) 2.26733 11.1061i 0.114517 0.560942i
\(393\) 6.76829 2.88370i 0.341415 0.145463i
\(394\) −9.21302 + 5.82596i −0.464145 + 0.293508i
\(395\) 0.734692 0.385596i 0.0369664 0.0194014i
\(396\) −4.56895 0.742526i −0.229598 0.0373133i
\(397\) 6.25210 2.08726i 0.313784 0.104756i −0.155414 0.987849i \(-0.549671\pi\)
0.469198 + 0.883093i \(0.344543\pi\)
\(398\) 0.856823 + 7.05657i 0.0429486 + 0.353714i
\(399\) 7.76198 26.7975i 0.388585 1.34155i
\(400\) 0.583572 2.85853i 0.0291786 0.142926i
\(401\) −17.2413 5.75598i −0.860988 0.287440i −0.148318 0.988940i \(-0.547386\pi\)
−0.712670 + 0.701500i \(0.752514\pi\)
\(402\) −2.12640 1.11602i −0.106055 0.0556620i
\(403\) −6.21378 7.92698i −0.309530 0.394871i
\(404\) 1.86375 0.978173i 0.0927252 0.0486659i
\(405\) 1.94558 0.316188i 0.0966768 0.0157115i
\(406\) 9.39564 7.06036i 0.466298 0.350400i
\(407\) 0.838888 20.8168i 0.0415821 1.03185i
\(408\) 1.89389 0.0937616
\(409\) 0.925723 22.9716i 0.0457741 1.13587i −0.799200 0.601065i \(-0.794743\pi\)
0.844974 0.534807i \(-0.179616\pi\)
\(410\) 1.73051 + 8.47660i 0.0854638 + 0.418629i
\(411\) −9.29544 13.4668i −0.458510 0.664267i
\(412\) −14.2549 + 4.75899i −0.702289 + 0.234459i
\(413\) −18.0087 + 37.9526i −0.886151 + 1.86752i
\(414\) 2.25290 2.75930i 0.110724 0.135612i
\(415\) −4.11723 10.8563i −0.202107 0.532912i
\(416\) 16.6115 6.69065i 0.814445 0.328036i
\(417\) 0.414444 1.09280i 0.0202954 0.0535146i
\(418\) 4.95677 + 8.58538i 0.242444 + 0.419925i
\(419\) −8.03229 + 9.83777i −0.392403 + 0.480607i −0.932590 0.360939i \(-0.882456\pi\)
0.540186 + 0.841545i \(0.318354\pi\)
\(420\) 10.0578 + 7.55796i 0.490771 + 0.368791i
\(421\) −13.0864 6.86828i −0.637793 0.334739i 0.114641 0.993407i \(-0.463428\pi\)
−0.752434 + 0.658667i \(0.771120\pi\)
\(422\) 4.33038 0.349585i 0.210800 0.0170175i
\(423\) −11.7355 + 0.947385i −0.570598 + 0.0460634i
\(424\) −6.39538 3.35655i −0.310587 0.163009i
\(425\) 0.916144 + 0.688437i 0.0444395 + 0.0333941i
\(426\) 1.52042 1.86218i 0.0736646 0.0902228i
\(427\) −25.0990 43.4728i −1.21463 2.10379i
\(428\) −7.78225 + 20.5201i −0.376169 + 0.991877i
\(429\) 2.08115 9.25198i 0.100479 0.446690i
\(430\) −2.18114 5.75119i −0.105184 0.277347i
\(431\) 7.51934 9.20952i 0.362194 0.443607i −0.561073 0.827766i \(-0.689611\pi\)
0.923267 + 0.384160i \(0.125509\pi\)
\(432\) 1.12198 2.36452i 0.0539812 0.113763i
\(433\) −37.5803 + 12.5461i −1.80599 + 0.602929i −0.806054 + 0.591842i \(0.798401\pi\)
−0.999939 + 0.0110865i \(0.996471\pi\)
\(434\) 2.81986 + 4.08528i 0.135358 + 0.196100i
\(435\) 2.60769 + 12.7733i 0.125029 + 0.612432i
\(436\) −0.976901 + 24.2415i −0.0467851 + 1.16096i
\(437\) 55.9276 2.67538
\(438\) −0.160222 + 3.97586i −0.00765568 + 0.189974i
\(439\) 1.22156 0.917945i 0.0583020 0.0438111i −0.571192 0.820817i \(-0.693519\pi\)
0.629494 + 0.777006i \(0.283262\pi\)
\(440\) −9.42715 + 1.53206i −0.449422 + 0.0730382i
\(441\) 5.44811 2.85939i 0.259434 0.136161i
\(442\) −0.109176 + 1.81285i −0.00519296 + 0.0862283i
\(443\) −19.1042 10.0267i −0.907670 0.476382i −0.0547950 0.998498i \(-0.517451\pi\)
−0.852875 + 0.522116i \(0.825143\pi\)
\(444\) 13.2231 + 4.41452i 0.627541 + 0.209504i
\(445\) 2.08936 10.2343i 0.0990450 0.485154i
\(446\) −3.14065 + 10.8428i −0.148714 + 0.513421i
\(447\) −1.10028 9.06164i −0.0520416 0.428601i
\(448\) 9.63491 3.21661i 0.455207 0.151970i
\(449\) 15.4764 + 2.51516i 0.730376 + 0.118698i 0.514216 0.857660i \(-0.328083\pi\)
0.216159 + 0.976358i \(0.430647\pi\)
\(450\) −0.483623 + 0.253825i −0.0227982 + 0.0119654i
\(451\) 19.9133 12.5924i 0.937683 0.592955i
\(452\) −5.69063 + 2.42455i −0.267665 + 0.114041i
\(453\) 0.0703440 0.344568i 0.00330505 0.0161892i
\(454\) −2.58278 0.636599i −0.121216 0.0298771i
\(455\) −16.6946 + 19.6373i −0.782655 + 0.920610i
\(456\) −13.7601 + 3.39155i −0.644374 + 0.158824i
\(457\) 1.38387 + 34.3404i 0.0647348 + 1.60638i 0.626730 + 0.779236i \(0.284393\pi\)
−0.561995 + 0.827140i \(0.689966\pi\)
\(458\) −0.101390 2.51598i −0.00473766 0.117564i
\(459\) 0.650173 + 0.796318i 0.0303475 + 0.0371689i
\(460\) −8.94333 + 23.5816i −0.416985 + 1.09950i
\(461\) −8.65170 18.2331i −0.402950 0.849198i −0.998932 0.0462010i \(-0.985289\pi\)
0.595982 0.802997i \(-0.296763\pi\)
\(462\) −1.30031 + 4.48918i −0.0604958 + 0.208856i
\(463\) −6.13647 + 8.89021i −0.285186 + 0.413163i −0.939227 0.343296i \(-0.888457\pi\)
0.654042 + 0.756459i \(0.273072\pi\)
\(464\) 15.9249 + 6.78495i 0.739293 + 0.314983i
\(465\) −5.43500 + 0.883274i −0.252042 + 0.0409609i
\(466\) 4.00651 + 2.53357i 0.185598 + 0.117365i
\(467\) 10.9327 + 15.8388i 0.505905 + 0.732930i 0.989842 0.142173i \(-0.0454089\pi\)
−0.483937 + 0.875103i \(0.660794\pi\)
\(468\) 5.55896 + 3.05998i 0.256963 + 0.141448i
\(469\) 10.0975 14.6288i 0.466261 0.675496i
\(470\) −10.4609 + 4.45697i −0.482525 + 0.205585i
\(471\) 0.323608 + 1.11722i 0.0149111 + 0.0514790i
\(472\) 21.2699 1.71708i 0.979025 0.0790351i
\(473\) −12.5383 + 11.1080i −0.576511 + 0.510744i
\(474\) −0.174322 + 0.110234i −0.00800687 + 0.00506324i
\(475\) −7.88908 3.36122i −0.361976 0.154223i
\(476\) −0.790917 + 6.51379i −0.0362516 + 0.298559i
\(477\) −0.784216 3.84134i −0.0359068 0.175883i
\(478\) −3.61347 0.291709i −0.165276 0.0133425i
\(479\) 17.3475 13.0358i 0.792626 0.595620i −0.125415 0.992104i \(-0.540026\pi\)
0.918041 + 0.396484i \(0.129770\pi\)
\(480\) 1.18008 9.71884i 0.0538631 0.443602i
\(481\) −10.6561 + 26.4974i −0.485878 + 1.20818i
\(482\) −0.746684 6.14950i −0.0340105 0.280102i
\(483\) 18.2650 + 19.0159i 0.831086 + 0.865252i
\(484\) −3.59226 6.22198i −0.163285 0.282817i
\(485\) 3.59668 6.22963i 0.163317 0.282873i
\(486\) −0.475732 + 0.117258i −0.0215797 + 0.00531891i
\(487\) −14.6770 17.9761i −0.665080 0.814576i 0.326345 0.945251i \(-0.394183\pi\)
−0.991425 + 0.130675i \(0.958285\pi\)
\(488\) −12.7496 + 22.0829i −0.577146 + 0.999646i
\(489\) 4.44976 + 11.7330i 0.201225 + 0.530587i
\(490\) 4.11642 4.28564i 0.185961 0.193606i
\(491\) 2.94313 + 0.982560i 0.132821 + 0.0443423i 0.382302 0.924038i \(-0.375132\pi\)
−0.249480 + 0.968380i \(0.580260\pi\)
\(492\) 4.38619 + 15.1429i 0.197745 + 0.682695i
\(493\) −5.08936 + 4.50878i −0.229213 + 0.203065i
\(494\) −2.45320 13.3667i −0.110375 0.601398i
\(495\) −3.88052 3.43784i −0.174416 0.154520i
\(496\) −3.13426 + 6.60531i −0.140732 + 0.296587i
\(497\) 12.3266 + 12.8333i 0.552922 + 0.575653i
\(498\) 1.23727 + 2.60750i 0.0554436 + 0.116845i
\(499\) −27.6167 6.80690i −1.23629 0.304719i −0.433597 0.901107i \(-0.642756\pi\)
−0.802696 + 0.596388i \(0.796602\pi\)
\(500\) 14.6941 15.2982i 0.657141 0.684156i
\(501\) −3.22280 2.42178i −0.143984 0.108197i
\(502\) −10.4363 9.24573i −0.465794 0.412657i
\(503\) −7.30956 1.18792i −0.325917 0.0529667i −0.00474863 0.999989i \(-0.501512\pi\)
−0.321169 + 0.947022i \(0.604076\pi\)
\(504\) −5.64695 3.57092i −0.251535 0.159061i
\(505\) 2.34977 + 0.189693i 0.104564 + 0.00844125i
\(506\) −9.36914 −0.416509
\(507\) −6.94224 + 10.9911i −0.308316 + 0.488134i
\(508\) 24.8966 1.10461
\(509\) −29.6806 2.39606i −1.31557 0.106204i −0.597327 0.801998i \(-0.703771\pi\)
−0.718241 + 0.695794i \(0.755053\pi\)
\(510\) 0.839152 + 0.530647i 0.0371583 + 0.0234975i
\(511\) −29.0712 4.72453i −1.28604 0.209001i
\(512\) −16.9481 15.0147i −0.749008 0.663563i
\(513\) −6.14986 4.62132i −0.271523 0.204036i
\(514\) −8.74651 + 9.10608i −0.385792 + 0.401652i
\(515\) −16.3425 4.02807i −0.720137 0.177498i
\(516\) −4.80507 10.1265i −0.211531 0.445793i
\(517\) 21.4513 + 22.3331i 0.943426 + 0.982210i
\(518\) 6.03407 12.7165i 0.265122 0.558733i
\(519\) −10.9616 9.71113i −0.481161 0.426271i
\(520\) 12.8789 + 2.35663i 0.564778 + 0.103345i
\(521\) −7.93980 + 7.03405i −0.347849 + 0.308167i −0.818897 0.573940i \(-0.805414\pi\)
0.471048 + 0.882107i \(0.343876\pi\)
\(522\) −0.901598 3.11268i −0.0394619 0.136238i
\(523\) 17.8274 + 5.95166i 0.779538 + 0.260248i 0.678467 0.734631i \(-0.262645\pi\)
0.101071 + 0.994879i \(0.467773\pi\)
\(524\) 8.96925 9.33798i 0.391824 0.407932i
\(525\) −1.43359 3.78007i −0.0625671 0.164976i
\(526\) 0.701573 1.21516i 0.0305901 0.0529835i
\(527\) −1.81626 2.22452i −0.0791177 0.0969016i
\(528\) −6.68364 + 1.64737i −0.290868 + 0.0716926i
\(529\) −14.9282 + 25.8564i −0.649052 + 1.12419i
\(530\) −1.89321 3.27914i −0.0822360 0.142437i
\(531\) 8.02392 + 8.35379i 0.348209 + 0.362524i
\(532\) −5.91838 48.7422i −0.256594 2.11324i
\(533\) −31.5072 + 7.10477i −1.36473 + 0.307742i
\(534\) −0.312972 + 2.57755i −0.0135436 + 0.111542i
\(535\) −19.6500 + 14.7660i −0.849545 + 0.638391i
\(536\) −9.00008 0.726561i −0.388744 0.0313827i
\(537\) 2.42928 + 11.8994i 0.104831 + 0.513497i
\(538\) 0.584180 4.81115i 0.0251858 0.207424i
\(539\) −14.8881 6.34321i −0.641275 0.273222i
\(540\) 2.93197 1.85407i 0.126172 0.0797864i
\(541\) 16.3863 14.5170i 0.704502 0.624135i −0.232852 0.972512i \(-0.574806\pi\)
0.937354 + 0.348378i \(0.113267\pi\)
\(542\) −11.3362 + 0.915150i −0.486930 + 0.0393090i
\(543\) −5.82825 20.1214i −0.250114 0.863494i
\(544\) 4.69749 2.00141i 0.201403 0.0858099i
\(545\) −15.4357 + 22.3624i −0.661192 + 0.957902i
\(546\) 3.74363 5.19945i 0.160213 0.222516i
\(547\) −16.4047 23.7663i −0.701413 1.01617i −0.998125 0.0612052i \(-0.980506\pi\)
0.296712 0.954967i \(-0.404110\pi\)
\(548\) −24.3401 15.3917i −1.03976 0.657502i
\(549\) −13.6620 + 2.22030i −0.583082 + 0.0947600i
\(550\) 1.32160 + 0.563080i 0.0563531 + 0.0240098i
\(551\) 28.9024 41.8724i 1.23129 1.78382i
\(552\) 3.72634 12.8648i 0.158603 0.547563i
\(553\) −0.654462 1.37925i −0.0278305 0.0586516i
\(554\) 3.11827 8.22220i 0.132483 0.349328i
\(555\) 9.87457 + 12.0941i 0.419152 + 0.513368i
\(556\) −0.0828237 2.05525i −0.00351251 0.0871620i
\(557\) 1.05510 + 26.1821i 0.0447062 + 1.10937i 0.853438 + 0.521195i \(0.174513\pi\)
−0.808732 + 0.588178i \(0.799846\pi\)
\(558\) 1.32896 0.327560i 0.0562595 0.0138667i
\(559\) 21.3003 8.57917i 0.900905 0.362860i
\(560\) 18.1657 + 4.47745i 0.767642 + 0.189207i
\(561\) 0.540846 2.64924i 0.0228345 0.111851i
\(562\) −10.3008 + 4.38876i −0.434513 + 0.185129i
\(563\) 19.2969 12.2026i 0.813267 0.514279i −0.0619098 0.998082i \(-0.519719\pi\)
0.875177 + 0.483803i \(0.160745\pi\)
\(564\) −18.3473 + 9.62943i −0.772563 + 0.405472i
\(565\) −6.83812 1.11130i −0.287682 0.0467528i
\(566\) 6.43036 2.14677i 0.270288 0.0902355i
\(567\) −0.437149 3.60025i −0.0183585 0.151196i
\(568\) 2.51481 8.68213i 0.105519 0.364294i
\(569\) −2.48092 + 12.1523i −0.104005 + 0.509452i 0.894097 + 0.447874i \(0.147819\pi\)
−0.998102 + 0.0615784i \(0.980387\pi\)
\(570\) −7.04712 2.35268i −0.295172 0.0985427i
\(571\) 12.0968 + 6.34889i 0.506235 + 0.265693i 0.698448 0.715660i \(-0.253874\pi\)
−0.192213 + 0.981353i \(0.561566\pi\)
\(572\) −3.01274 16.4155i −0.125969 0.686367i
\(573\) 18.3518 9.63175i 0.766656 0.402372i
\(574\) 15.7119 2.55343i 0.655800 0.106578i
\(575\) 6.47898 4.86863i 0.270192 0.203036i
\(576\) 0.112777 2.79854i 0.00469905 0.116606i
\(577\) 13.5273 0.563150 0.281575 0.959539i \(-0.409143\pi\)
0.281575 + 0.959539i \(0.409143\pi\)
\(578\) 0.314544 7.80533i 0.0130833 0.324659i
\(579\) −3.85005 18.8588i −0.160003 0.783744i
\(580\) 13.0335 + 18.8823i 0.541188 + 0.784047i
\(581\) −20.2635 + 6.76495i −0.840672 + 0.280658i
\(582\) −0.766543 + 1.61546i −0.0317742 + 0.0669628i
\(583\) −6.52160 + 7.98751i −0.270097 + 0.330809i
\(584\) 5.30527 + 13.9888i 0.219534 + 0.578863i
\(585\) 3.43045 + 6.22419i 0.141832 + 0.257338i
\(586\) 0.428067 1.12872i 0.0176833 0.0466270i
\(587\) 16.6704 + 28.8740i 0.688060 + 1.19176i 0.972464 + 0.233051i \(0.0748710\pi\)
−0.284404 + 0.958705i \(0.591796\pi\)
\(588\) 6.84853 8.38792i 0.282428 0.345912i
\(589\) 17.1797 + 12.9097i 0.707877 + 0.531935i
\(590\) 9.90543 + 5.19877i 0.407800 + 0.214030i
\(591\) −22.1752 + 1.79017i −0.912165 + 0.0736376i
\(592\) 20.6639 1.66816i 0.849281 0.0685611i
\(593\) 28.5431 + 14.9806i 1.17212 + 0.615179i 0.934425 0.356160i \(-0.115914\pi\)
0.237700 + 0.971339i \(0.423607\pi\)
\(594\) 1.03024 + 0.774175i 0.0422713 + 0.0317648i
\(595\) −4.64783 + 5.69256i −0.190542 + 0.233372i
\(596\) −8.03249 13.9127i −0.329023 0.569885i
\(597\) −5.14454 + 13.5651i −0.210552 + 0.555181i
\(598\) 12.0995 + 4.30849i 0.494784 + 0.176187i
\(599\) −5.00934 13.2085i −0.204676 0.539686i 0.792894 0.609360i \(-0.208574\pi\)
−0.997570 + 0.0696734i \(0.977804\pi\)
\(600\) −1.29880 + 1.59074i −0.0530233 + 0.0649418i
\(601\) 7.98130 16.8202i 0.325564 0.686112i −0.673002 0.739640i \(-0.734996\pi\)
0.998566 + 0.0535287i \(0.0170469\pi\)
\(602\) −10.7348 + 3.58379i −0.437517 + 0.146065i
\(603\) −2.78423 4.03366i −0.113383 0.164263i
\(604\) −0.123800 0.606415i −0.00503737 0.0246747i
\(605\) 0.324004 8.04009i 0.0131727 0.326876i
\(606\) −0.585998 −0.0238045
\(607\) −0.100174 + 2.48578i −0.00406592 + 0.100895i 0.995882 + 0.0906620i \(0.0288983\pi\)
−0.999948 + 0.0102328i \(0.996743\pi\)
\(608\) −30.5455 + 22.9534i −1.23878 + 0.930885i
\(609\) 23.6760 3.84773i 0.959401 0.155918i
\(610\) −11.8365 + 6.21227i −0.479246 + 0.251528i
\(611\) −17.4325 38.7060i −0.705242 1.56588i
\(612\) 1.60202 + 0.840806i 0.0647579 + 0.0339876i
\(613\) −4.26569 1.42410i −0.172290 0.0575188i 0.229214 0.973376i \(-0.426384\pi\)
−0.401504 + 0.915857i \(0.631512\pi\)
\(614\) 0.946267 4.63512i 0.0381882 0.187058i
\(615\) −4.91251 + 16.9599i −0.198091 + 0.683891i
\(616\) 2.11817 + 17.4447i 0.0853434 + 0.702866i
\(617\) 19.8298 6.62017i 0.798319 0.266518i 0.111895 0.993720i \(-0.464308\pi\)
0.686424 + 0.727202i \(0.259180\pi\)
\(618\) 4.12975 + 0.671150i 0.166123 + 0.0269976i
\(619\) −12.4168 + 6.51684i −0.499073 + 0.261934i −0.695424 0.718600i \(-0.744783\pi\)
0.196350 + 0.980534i \(0.437091\pi\)
\(620\) −8.19050 + 5.17936i −0.328938 + 0.208008i
\(621\) 6.68847 2.84969i 0.268399 0.114354i
\(622\) −0.0475775 + 0.233050i −0.00190768 + 0.00934445i
\(623\) −18.6604 4.59936i −0.747611 0.184270i
\(624\) 9.38894 + 0.946091i 0.375858 + 0.0378739i
\(625\) 17.6553 4.35165i 0.706213 0.174066i
\(626\) −0.609111 15.1149i −0.0243450 0.604114i
\(627\) 0.814699 + 20.2165i 0.0325359 + 0.807371i
\(628\) 1.29465 + 1.58566i 0.0516622 + 0.0632748i
\(629\) −2.88759 + 7.61394i −0.115136 + 0.303588i
\(630\) −1.50154 3.16443i −0.0598227 0.126074i
\(631\) −1.39234 + 4.80690i −0.0554280 + 0.191360i −0.983455 0.181154i \(-0.942017\pi\)
0.928027 + 0.372514i \(0.121504\pi\)
\(632\) −0.440529 + 0.638217i −0.0175233 + 0.0253869i
\(633\) 8.15728 + 3.47549i 0.324223 + 0.138138i
\(634\) −5.97604 + 0.971202i −0.237339 + 0.0385713i
\(635\) 23.5673 + 14.9031i 0.935240 + 0.591410i
\(636\) −3.91961 5.67854i −0.155423 0.225169i
\(637\) 16.3097 + 15.0382i 0.646216 + 0.595834i
\(638\) −4.84181 + 7.01457i −0.191689 + 0.277710i
\(639\) 4.51387 1.92318i 0.178566 0.0760799i
\(640\) −6.20019 21.4055i −0.245084 0.846128i
\(641\) −27.2676 + 2.20127i −1.07700 + 0.0869448i −0.606215 0.795301i \(-0.707313\pi\)
−0.470789 + 0.882246i \(0.656031\pi\)
\(642\) 4.57333 4.05162i 0.180495 0.159905i
\(643\) −13.2578 + 8.38373i −0.522837 + 0.330622i −0.769676 0.638434i \(-0.779582\pi\)
0.246839 + 0.969056i \(0.420608\pi\)
\(644\) 42.6906 + 18.1888i 1.68225 + 0.716738i
\(645\) 1.51317 12.4621i 0.0595811 0.490695i
\(646\) −0.775067 3.79653i −0.0304946 0.149372i
\(647\) 34.1776 + 2.75910i 1.34366 + 0.108472i 0.731272 0.682085i \(-0.238927\pi\)
0.612388 + 0.790557i \(0.290209\pi\)
\(648\) −1.47278 + 1.10672i −0.0578561 + 0.0434760i
\(649\) 3.67221 30.2433i 0.144147 1.18715i
\(650\) −1.44780 1.33492i −0.0567873 0.0523599i
\(651\) 1.22118 + 10.0573i 0.0478618 + 0.394178i
\(652\) 15.2984 + 15.9274i 0.599133 + 0.623764i
\(653\) −3.39141 5.87409i −0.132716 0.229871i 0.792007 0.610513i \(-0.209036\pi\)
−0.924723 + 0.380642i \(0.875703\pi\)
\(654\) 3.37720 5.84949i 0.132059 0.228733i
\(655\) 14.0801 3.47042i 0.550153 0.135601i
\(656\) 14.8276 + 18.1605i 0.578919 + 0.709047i
\(657\) −4.06054 + 7.03306i −0.158417 + 0.274386i
\(658\) 7.41884 + 19.5619i 0.289216 + 0.762601i
\(659\) −7.51926 + 7.82837i −0.292909 + 0.304950i −0.851355 0.524591i \(-0.824218\pi\)
0.558446 + 0.829541i \(0.311398\pi\)
\(660\) −8.65449 2.88929i −0.336875 0.112466i
\(661\) 1.80914 + 6.24586i 0.0703672 + 0.242936i 0.987990 0.154516i \(-0.0493818\pi\)
−0.917623 + 0.397452i \(0.869895\pi\)
\(662\) 7.42725 6.57997i 0.288668 0.255738i
\(663\) −1.91673 + 3.17256i −0.0744398 + 0.123212i
\(664\) 8.12265 + 7.19604i 0.315220 + 0.279260i
\(665\) 23.5746 49.6825i 0.914185 1.92660i
\(666\) −2.68853 2.79905i −0.104178 0.108461i
\(667\) 20.6136 + 43.4422i 0.798161 + 1.68209i
\(668\) −6.88866 1.69790i −0.266530 0.0656938i
\(669\) −15.9598 + 16.6159i −0.617040 + 0.642407i
\(670\) −3.78421 2.84365i −0.146197 0.109860i
\(671\) 27.2493 + 24.1408i 1.05195 + 0.931945i
\(672\) −17.7800 2.88953i −0.685878 0.111466i
\(673\) 7.56710 + 4.78514i 0.291690 + 0.184454i 0.672293 0.740285i \(-0.265309\pi\)
−0.380603 + 0.924738i \(0.624284\pi\)
\(674\) −5.90300 0.476539i −0.227375 0.0183556i
\(675\) −1.11473 −0.0429060
\(676\) −3.65812 + 22.5847i −0.140697 + 0.868644i
\(677\) 23.4989 0.903136 0.451568 0.892237i \(-0.350865\pi\)
0.451568 + 0.892237i \(0.350865\pi\)
\(678\) 1.71651 + 0.138571i 0.0659221 + 0.00532178i
\(679\) −11.1863 7.07378i −0.429290 0.271467i
\(680\) 3.68472 + 0.598826i 0.141303 + 0.0229639i
\(681\) −4.06372 3.60014i −0.155722 0.137958i
\(682\) −2.87799 2.16267i −0.110204 0.0828127i
\(683\) 19.1761 19.9644i 0.733753 0.763918i −0.244875 0.969555i \(-0.578747\pi\)
0.978628 + 0.205637i \(0.0659266\pi\)
\(684\) −13.1452 3.23999i −0.502618 0.123884i
\(685\) −13.8270 29.1398i −0.528303 1.11338i
\(686\) 1.04276 + 1.08562i 0.0398126 + 0.0414493i
\(687\) 2.20311 4.64295i 0.0840537 0.177139i
\(688\) −12.4766 11.0533i −0.475665 0.421402i
\(689\) 12.0952 7.31620i 0.460792 0.278725i
\(690\) 5.25565 4.65610i 0.200079 0.177255i
\(691\) 1.10422 + 3.81220i 0.0420064 + 0.145023i 0.978780 0.204912i \(-0.0656909\pi\)
−0.936774 + 0.349935i \(0.886204\pi\)
\(692\) −24.4470 8.16160i −0.929334 0.310257i
\(693\) −6.60773 + 6.87938i −0.251007 + 0.261326i
\(694\) 3.03370 + 7.99920i 0.115158 + 0.303646i
\(695\) 1.15187 1.99509i 0.0436928 0.0756781i
\(696\) −7.70604 9.43818i −0.292097 0.357753i
\(697\) −8.94144 + 2.20387i −0.338681 + 0.0834774i
\(698\) −5.62497 + 9.74273i −0.212908 + 0.368768i
\(699\) 4.83741 + 8.37864i 0.182968 + 0.316909i
\(700\) −4.92875 5.13137i −0.186289 0.193948i
\(701\) 1.33175 + 10.9679i 0.0502995 + 0.414254i 0.996010 + 0.0892431i \(0.0284448\pi\)
−0.945710 + 0.325011i \(0.894632\pi\)
\(702\) −0.974459 1.47355i −0.0367786 0.0556155i
\(703\) 7.34483 60.4901i 0.277015 2.28143i
\(704\) −5.88914 + 4.42540i −0.221955 + 0.166789i
\(705\) −23.1319 1.86740i −0.871197 0.0703303i
\(706\) 2.94465 + 14.4238i 0.110823 + 0.542848i
\(707\) 0.522825 4.30585i 0.0196628 0.161938i
\(708\) 18.7542 + 7.99044i 0.704828 + 0.300299i
\(709\) 14.5229 9.18371i 0.545418 0.344901i −0.233171 0.972436i \(-0.574910\pi\)
0.778589 + 0.627534i \(0.215936\pi\)
\(710\) 3.54690 3.14228i 0.133113 0.117928i
\(711\) −0.419582 + 0.0338722i −0.0157356 + 0.00127031i
\(712\) 2.71612 + 9.37715i 0.101791 + 0.351424i
\(713\) −18.6843 + 7.96064i −0.699733 + 0.298128i
\(714\) 1.03773 1.50341i 0.0388360 0.0562637i
\(715\) 6.97441 17.3425i 0.260828 0.648572i
\(716\) 12.1418 + 17.5905i 0.453762 + 0.657388i
\(717\) −6.25345 3.95444i −0.233539 0.147681i
\(718\) 7.23335 1.17553i 0.269946 0.0438705i
\(719\) 6.96903 + 2.96923i 0.259901 + 0.110733i 0.517987 0.855389i \(-0.326682\pi\)
−0.258086 + 0.966122i \(0.583092\pi\)
\(720\) 2.93054 4.24561i 0.109215 0.158225i
\(721\) −8.61609 + 29.7462i −0.320880 + 1.10781i
\(722\) 8.43911 + 17.7851i 0.314071 + 0.661891i
\(723\) 4.48325 11.8214i 0.166734 0.439641i
\(724\) −23.3170 28.5581i −0.866568 1.06135i
\(725\) −0.296870 7.36676i −0.0110255 0.273595i
\(726\) 0.0805397 + 1.99857i 0.00298911 + 0.0741740i
\(727\) 27.6081 6.80479i 1.02393 0.252376i 0.308620 0.951185i \(-0.400133\pi\)
0.715308 + 0.698810i \(0.246287\pi\)
\(728\) 5.28666 23.5024i 0.195937 0.871059i
\(729\) −0.970942 0.239316i −0.0359608 0.00886354i
\(730\) −1.56884 + 7.68470i −0.0580655 + 0.284423i
\(731\) 6.02342 2.56634i 0.222784 0.0949194i
\(732\) −20.5886 + 13.0194i −0.760975 + 0.481211i
\(733\) 3.28648 1.72488i 0.121389 0.0637099i −0.402936 0.915228i \(-0.632010\pi\)
0.524325 + 0.851518i \(0.324318\pi\)
\(734\) 10.5301 + 1.71130i 0.388671 + 0.0631652i
\(735\) 11.5039 3.84055i 0.424326 0.141661i
\(736\) −4.35261 35.8470i −0.160439 1.32134i
\(737\) −3.58652 + 12.3821i −0.132111 + 0.456101i
\(738\) 0.877937 4.30042i 0.0323173 0.158301i
\(739\) 7.56338 + 2.52503i 0.278224 + 0.0928847i 0.452356 0.891838i \(-0.350584\pi\)
−0.174132 + 0.984722i \(0.555712\pi\)
\(740\) 24.3308 + 12.7698i 0.894420 + 0.469428i
\(741\) 8.24465 26.4827i 0.302875 0.972865i
\(742\) −6.16875 + 3.23761i −0.226462 + 0.118856i
\(743\) 23.8812 3.88107i 0.876115 0.142383i 0.294309 0.955710i \(-0.404910\pi\)
0.581806 + 0.813328i \(0.302346\pi\)
\(744\) 4.11421 3.09163i 0.150834 0.113345i
\(745\) 0.724491 17.9781i 0.0265433 0.658665i
\(746\) 8.13181 0.297727
\(747\) −0.237185 + 5.88570i −0.00867816 + 0.215346i
\(748\) −0.951850 4.66247i −0.0348031 0.170477i
\(749\) 25.6906 + 37.2192i 0.938713 + 1.35996i
\(750\) −5.60159 + 1.87009i −0.204541 + 0.0682859i
\(751\) −16.5770 + 34.9354i −0.604905 + 1.27481i 0.337811 + 0.941214i \(0.390313\pi\)
−0.942716 + 0.333596i \(0.891738\pi\)
\(752\) −19.4882 + 23.8688i −0.710663 + 0.870404i
\(753\) −10.0907 26.6071i −0.367727 0.969616i
\(754\) 9.47852 6.83220i 0.345187 0.248814i
\(755\) 0.245808 0.648143i 0.00894588 0.0235883i
\(756\) −3.19136 5.52760i −0.116069 0.201037i
\(757\) −27.1243 + 33.2212i −0.985850 + 1.20745i −0.00760970 + 0.999971i \(0.502422\pi\)
−0.978240 + 0.207476i \(0.933475\pi\)
\(758\) −6.33779 4.76254i −0.230199 0.172983i
\(759\) −16.9316 8.88637i −0.614577 0.322555i
\(760\) −27.8437 + 2.24778i −1.01000 + 0.0815354i
\(761\) −35.2427 + 2.84509i −1.27755 + 0.103134i −0.700545 0.713608i \(-0.747060\pi\)
−0.577002 + 0.816742i \(0.695778\pi\)
\(762\) −6.13736 3.22113i −0.222333 0.116689i
\(763\) 39.9683 + 30.0342i 1.44695 + 1.08731i
\(764\) 23.0690 28.2544i 0.834608 1.02221i
\(765\) 1.01318 + 1.75488i 0.0366316 + 0.0634478i
\(766\) 5.02176 13.2413i 0.181444 0.478428i
\(767\) −18.6500 + 37.3681i −0.673414 + 1.34928i
\(768\) −0.0219846 0.0579685i −0.000793299 0.00209176i
\(769\) 11.0888 13.5813i 0.399873 0.489755i −0.534943 0.844888i \(-0.679667\pi\)
0.934816 + 0.355133i \(0.115564\pi\)
\(770\) −3.94928 + 8.32293i −0.142322 + 0.299938i
\(771\) −24.4432 + 8.16035i −0.880302 + 0.293888i
\(772\) −19.2430 27.8783i −0.692572 1.00336i
\(773\) 5.23911 + 25.6628i 0.188438 + 0.923028i 0.958507 + 0.285068i \(0.0920163\pi\)
−0.770070 + 0.637960i \(0.779779\pi\)
\(774\) −0.125651 + 3.11800i −0.00451643 + 0.112074i
\(775\) 3.11401 0.111859
\(776\) −0.270712 + 6.71766i −0.00971801 + 0.241150i
\(777\) 22.9658 17.2577i 0.823895 0.619117i
\(778\) 4.72066 0.767182i 0.169244 0.0275048i
\(779\) 61.0173 32.0243i 2.18617 1.14739i
\(780\) 9.84789 + 7.71113i 0.352611 + 0.276103i
\(781\) −11.4267 5.99718i −0.408879 0.214596i
\(782\) 3.47359 + 1.15965i 0.124215 + 0.0414691i
\(783\) 1.32295 6.48026i 0.0472785 0.231585i
\(784\) 4.48024 15.4676i 0.160009 0.552414i
\(785\) 0.276353 + 2.27597i 0.00986347 + 0.0812330i
\(786\) −3.41920 + 1.14150i −0.121959 + 0.0407158i
\(787\) −18.8683 3.06639i −0.672581 0.109305i −0.185477 0.982649i \(-0.559383\pi\)
−0.487105 + 0.873344i \(0.661947\pi\)
\(788\) −34.6689 + 18.1956i −1.23503 + 0.648193i
\(789\) 2.42040 1.53057i 0.0861687 0.0544898i
\(790\) −0.374012 + 0.159352i −0.0133068 + 0.00566948i
\(791\) −2.54967 + 12.4891i −0.0906557 + 0.444061i
\(792\) 4.70461 + 1.15958i 0.167171 + 0.0412040i
\(793\) −24.0889 43.7067i −0.855422 1.55207i
\(794\) −3.13570 + 0.772881i −0.111282 + 0.0274285i
\(795\) −0.311170 7.72161i −0.0110361 0.273857i
\(796\) 1.02810 + 25.5120i 0.0364400 + 0.904250i
\(797\) −11.6345 14.2497i −0.412116 0.504750i 0.526280 0.850311i \(-0.323586\pi\)
−0.938396 + 0.345561i \(0.887689\pi\)
\(798\) −4.84733 + 12.7814i −0.171594 + 0.452455i
\(799\) −5.18875 10.9351i −0.183565 0.386855i
\(800\) −1.54041 + 5.31812i −0.0544618 + 0.188024i
\(801\) −3.01033 + 4.36121i −0.106365 + 0.154096i
\(802\) 8.19338 + 3.49087i 0.289318 + 0.123267i
\(803\) 21.0831 3.42634i 0.744006 0.120913i
\(804\) −7.29050 4.61023i −0.257116 0.162590i
\(805\) 29.5235 + 42.7721i 1.04057 + 1.50752i
\(806\) 2.72216 + 4.11637i 0.0958840 + 0.144993i
\(807\) 5.61896 8.14046i 0.197797 0.286558i
\(808\) −2.02700 + 0.863624i −0.0713096 + 0.0303822i
\(809\) 12.4436 + 42.9604i 0.437495 + 1.51041i 0.812264 + 0.583290i \(0.198235\pi\)
−0.374769 + 0.927118i \(0.622278\pi\)
\(810\) −0.962652 + 0.0777133i −0.0338242 + 0.00273057i
\(811\) −20.8682 + 18.4876i −0.732781 + 0.649187i −0.944638 0.328113i \(-0.893587\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(812\) 35.6795 22.5624i 1.25211 0.791784i
\(813\) −21.3543 9.09822i −0.748928 0.319088i
\(814\) −1.23042 + 10.1335i −0.0431263 + 0.355177i
\(815\) 4.94752 + 24.2346i 0.173304 + 0.848900i
\(816\) 2.68185 + 0.216501i 0.0938834 + 0.00757905i
\(817\) −39.1673 + 29.4323i −1.37029 + 1.02971i
\(818\) −1.35779 + 11.1824i −0.0474740 + 0.390983i
\(819\) 11.6969 5.84553i 0.408723 0.204259i
\(820\) 3.74570 + 30.8486i 0.130806 + 1.07728i
\(821\) −1.93328 2.01275i −0.0674718 0.0702456i 0.686611 0.727025i \(-0.259098\pi\)
−0.754083 + 0.656780i \(0.771918\pi\)
\(822\) 4.00878 + 6.94340i 0.139822 + 0.242179i
\(823\) 20.7243 35.8956i 0.722405 1.25124i −0.237629 0.971356i \(-0.576370\pi\)
0.960033 0.279885i \(-0.0902965\pi\)
\(824\) 15.2742 3.76475i 0.532101 0.131151i
\(825\) 1.85428 + 2.27108i 0.0645577 + 0.0790688i
\(826\) 10.2914 17.8253i 0.358085 0.620222i
\(827\) 0.547731 + 1.44425i 0.0190465 + 0.0502214i 0.944202 0.329366i \(-0.106835\pi\)
−0.925156 + 0.379588i \(0.876066\pi\)
\(828\) 8.86348 9.22786i 0.308027 0.320690i
\(829\) 6.20679 + 2.07213i 0.215571 + 0.0719681i 0.422402 0.906408i \(-0.361187\pi\)
−0.206831 + 0.978377i \(0.566315\pi\)
\(830\) 1.58276 + 5.46432i 0.0549384 + 0.189669i
\(831\) 13.4338 11.9013i 0.466012 0.412851i
\(832\) 9.64041 3.00687i 0.334221 0.104244i
\(833\) 4.73460 + 4.19449i 0.164044 + 0.145330i
\(834\) −0.245492 + 0.517363i −0.00850069 + 0.0179148i
\(835\) −5.50449 5.73078i −0.190491 0.198322i
\(836\) 15.2651 + 32.1706i 0.527956 + 1.11264i
\(837\) 2.71233 + 0.668530i 0.0937520 + 0.0231078i
\(838\) 4.31069 4.48790i 0.148910 0.155032i
\(839\) −32.8405 24.6780i −1.13378 0.851979i −0.143304 0.989679i \(-0.545773\pi\)
−0.990474 + 0.137699i \(0.956029\pi\)
\(840\) −9.85753 8.73301i −0.340117 0.301318i
\(841\) 14.5530 + 2.36509i 0.501827 + 0.0815549i
\(842\) 6.12037 + 3.87029i 0.210922 + 0.133379i
\(843\) −22.7778 1.83882i −0.784511 0.0633322i
\(844\) 15.6050 0.537145
\(845\) −16.9820 + 19.1891i −0.584198 + 0.660126i
\(846\) 5.76873 0.198333
\(847\) −14.7572 1.19132i −0.507062 0.0409343i
\(848\) −8.67247 5.48414i −0.297814 0.188326i
\(849\) 13.6569 + 2.21946i 0.468703 + 0.0761716i
\(850\) −0.420285 0.372340i −0.0144157 0.0127712i
\(851\) 46.0384 + 34.5956i 1.57818 + 1.18592i
\(852\) 5.98173 6.22764i 0.204931 0.213356i
\(853\) −19.2251 4.73857i −0.658256 0.162246i −0.103981 0.994579i \(-0.533158\pi\)
−0.554275 + 0.832334i \(0.687004\pi\)
\(854\) 10.5439 + 22.2208i 0.360806 + 0.760382i
\(855\) −10.5039 10.9357i −0.359224 0.373992i
\(856\) 9.84828 20.7548i 0.336607 0.709385i
\(857\) −25.4943 22.5859i −0.870868 0.771521i 0.103937 0.994584i \(-0.466856\pi\)
−0.974804 + 0.223063i \(0.928395\pi\)
\(858\) −1.38116 + 4.43644i −0.0471522 + 0.151458i
\(859\) −9.33061 + 8.26620i −0.318356 + 0.282039i −0.807133 0.590370i \(-0.798982\pi\)
0.488776 + 0.872409i \(0.337443\pi\)
\(860\) −6.14680 21.2212i −0.209604 0.723637i
\(861\) 30.8157 + 10.2878i 1.05020 + 0.350608i
\(862\) −4.03540 + 4.20130i −0.137446 + 0.143097i
\(863\) 9.66966 + 25.4968i 0.329159 + 0.867921i 0.992791 + 0.119861i \(0.0382450\pi\)
−0.663632 + 0.748059i \(0.730986\pi\)
\(864\) −2.48343 + 4.30143i −0.0844880 + 0.146338i
\(865\) −18.2562 22.3597i −0.620728 0.760254i
\(866\) 18.8481 4.64565i 0.640486 0.157866i
\(867\) 7.97158 13.8072i 0.270729 0.468916i
\(868\) 8.91509 + 15.4414i 0.302598 + 0.524115i
\(869\) 0.766955 + 0.798485i 0.0260172 + 0.0270867i
\(870\) −0.769942 6.34104i −0.0261035 0.214982i
\(871\) 10.3257 14.3412i 0.349874 0.485933i
\(872\) 3.06116 25.2109i 0.103664 0.853749i
\(873\) −2.91748 + 2.19235i −0.0987419 + 0.0741997i
\(874\) −27.3140 2.20501i −0.923910 0.0745857i
\(875\) −8.74348 42.8284i −0.295583 1.44786i
\(876\) −1.72277 + 14.1883i −0.0582071 + 0.479379i
\(877\) −3.40837 1.45217i −0.115093 0.0490364i 0.333653 0.942696i \(-0.391719\pi\)
−0.448745 + 0.893660i \(0.648129\pi\)
\(878\) −0.632780 + 0.400146i −0.0213553 + 0.0135043i
\(879\) 1.84415 1.63377i 0.0622015 0.0551057i
\(880\) −13.5245 + 1.09181i −0.455910 + 0.0368048i
\(881\) 16.0354 + 55.3607i 0.540247 + 1.86515i 0.500123 + 0.865954i \(0.333288\pi\)
0.0401235 + 0.999195i \(0.487225\pi\)
\(882\) −2.77349 + 1.18167i −0.0933882 + 0.0397890i
\(883\) 22.3679 32.4055i 0.752740 1.09053i −0.240061 0.970758i \(-0.577167\pi\)
0.992801 0.119775i \(-0.0382172\pi\)
\(884\) −0.914843 + 6.45892i −0.0307695 + 0.217237i
\(885\) 12.9698 + 18.7901i 0.435976 + 0.631621i
\(886\) 8.93484 + 5.65005i 0.300172 + 0.189817i
\(887\) 4.73945 0.770236i 0.159135 0.0258620i −0.0803216 0.996769i \(-0.525595\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(888\) −13.4249 5.71983i −0.450511 0.191945i
\(889\) 29.1443 42.2228i 0.977467 1.41611i
\(890\) −1.42390 + 4.91589i −0.0477294 + 0.164781i
\(891\) 1.12753 + 2.37622i 0.0377736 + 0.0796062i
\(892\) −14.3782 + 37.9123i −0.481419 + 1.26940i
\(893\) 57.2812 + 70.1567i 1.91684 + 2.34770i
\(894\) 0.180091 + 4.46891i 0.00602315 + 0.149463i
\(895\) 0.963918 + 23.9194i 0.0322202 + 0.799536i
\(896\) −39.8120 + 9.81278i −1.33003 + 0.327822i
\(897\) 17.7793 + 19.2622i 0.593632 + 0.643145i
\(898\) −7.45921 1.83853i −0.248917 0.0613526i
\(899\) −3.69568 + 18.1027i −0.123258 + 0.603757i
\(900\) −1.80486 + 0.768979i −0.0601620 + 0.0256326i
\(901\) 3.40651 2.15415i 0.113487 0.0717651i
\(902\) −10.2218 + 5.36480i −0.340348 + 0.178628i
\(903\) −22.7986 3.70514i −0.758690 0.123299i
\(904\) 6.14172 2.05041i 0.204271 0.0681955i
\(905\) −4.97718 40.9908i −0.165447 1.36258i
\(906\) −0.0479397 + 0.165507i −0.00159269 + 0.00549860i
\(907\) 8.04917 39.4274i 0.267268 1.30917i −0.595414 0.803419i \(-0.703012\pi\)
0.862682 0.505747i \(-0.168783\pi\)
\(908\) −9.06306 3.02569i −0.300768 0.100411i
\(909\) −1.05899 0.555803i −0.0351246 0.0184348i
\(910\) 8.92755 8.93228i 0.295945 0.296102i
\(911\) 1.43207 0.751608i 0.0474466 0.0249019i −0.440833 0.897589i \(-0.645317\pi\)
0.488280 + 0.872687i \(0.337625\pi\)
\(912\) −19.8726 + 3.22962i −0.658049 + 0.106943i
\(913\) 12.3857 9.30722i 0.409906 0.308024i
\(914\) 0.678055 16.8258i 0.0224281 0.556547i
\(915\) −27.2827 −0.901937
\(916\) 0.364185 9.03717i 0.0120330 0.298596i
\(917\) −5.33700 26.1423i −0.176243 0.863296i
\(918\) −0.286137 0.414540i −0.00944391 0.0136819i
\(919\) 34.1737 11.4089i 1.12729 0.376344i 0.308948 0.951079i \(-0.400023\pi\)
0.818339 + 0.574735i \(0.194895\pi\)
\(920\) 11.3176 23.8513i 0.373130 0.786355i
\(921\) 6.10634 7.47891i 0.201211 0.246439i
\(922\) 3.50647 + 9.24579i 0.115479 + 0.304494i
\(923\) 11.9988 + 12.9995i 0.394944 + 0.427885i
\(924\) −5.95295 + 15.6966i −0.195838 + 0.516381i
\(925\) −4.41494 7.64690i −0.145162 0.251428i
\(926\) 3.34744 4.09987i 0.110004 0.134730i
\(927\) 6.82657 + 5.12984i 0.224214 + 0.168486i
\(928\) −29.0876 15.2663i −0.954847 0.501142i
\(929\) −17.3028 + 1.39683i −0.567686 + 0.0458284i −0.360978 0.932574i \(-0.617557\pi\)
−0.206708 + 0.978403i \(0.566275\pi\)
\(930\) 2.68918 0.217093i 0.0881816 0.00711876i
\(931\) −41.9106 21.9964i −1.37356 0.720902i
\(932\) 13.6121 + 10.2288i 0.445879 + 0.335057i
\(933\) −0.307022 + 0.376033i −0.0100514 + 0.0123108i
\(934\) −4.71486 8.16638i −0.154275 0.267212i
\(935\) 1.88992 4.98330i 0.0618069 0.162971i
\(936\) −5.54238 3.66097i −0.181158 0.119662i
\(937\) 7.11946 + 18.7725i 0.232583 + 0.613270i 0.999598 0.0283589i \(-0.00902814\pi\)
−0.767015 + 0.641629i \(0.778259\pi\)
\(938\) −5.50821 + 6.74634i −0.179849 + 0.220276i
\(939\) 13.2353 27.8929i 0.431919 0.910249i
\(940\) −38.7410 + 12.9336i −1.26359 + 0.421849i
\(941\) 6.52087 + 9.44712i 0.212574 + 0.307967i 0.914737 0.404049i \(-0.132398\pi\)
−0.702163 + 0.712016i \(0.747782\pi\)
\(942\) −0.113996 0.558390i −0.00371419 0.0181933i
\(943\) −2.62237 + 65.0735i −0.0853963 + 2.11909i
\(944\) 30.3155 0.986686
\(945\) 0.287845 7.14280i 0.00936360 0.232355i
\(946\) 6.56141 4.93058i 0.213330 0.160307i
\(947\) −7.73135 + 1.25647i −0.251235 + 0.0408297i −0.284724 0.958609i \(-0.591902\pi\)
0.0334894 + 0.999439i \(0.489338\pi\)
\(948\) −0.655979 + 0.344284i −0.0213052 + 0.0111818i
\(949\) −28.8027 5.27042i −0.934976 0.171085i
\(950\) 3.72036 + 1.95259i 0.120704 + 0.0633505i
\(951\) −11.7208 3.91299i −0.380075 0.126888i
\(952\) 1.37389 6.72975i 0.0445280 0.218113i
\(953\) 11.8847 41.0308i 0.384984 1.32912i −0.501018 0.865437i \(-0.667041\pi\)
0.886002 0.463682i \(-0.153472\pi\)
\(954\) 0.231547 + 1.90696i 0.00749660 + 0.0617401i
\(955\) 38.7503 12.9368i 1.25393 0.418624i
\(956\) −12.8529 2.08879i −0.415691 0.0675564i
\(957\) −15.4031 + 8.08416i −0.497911 + 0.261324i
\(958\) −8.98613 + 5.68249i −0.290329 + 0.183593i
\(959\) −54.5960 + 23.2612i −1.76300 + 0.751143i
\(960\) 1.10428 5.40913i 0.0356405 0.174579i
\(961\) 22.5223 + 5.55124i 0.726525 + 0.179072i
\(962\) 6.24895 12.5207i 0.201474 0.403684i
\(963\) 12.1076 2.98426i 0.390162 0.0961664i
\(964\) −0.895944 22.2326i −0.0288564 0.716065i
\(965\) −1.52767 37.9087i −0.0491773 1.22032i
\(966\) −8.17056 10.0071i −0.262883 0.321974i
\(967\) −19.4219 + 51.2113i −0.624565 + 1.64684i 0.130699 + 0.991422i \(0.458278\pi\)
−0.755264 + 0.655421i \(0.772491\pi\)
\(968\) 3.22402 + 6.79448i 0.103624 + 0.218383i
\(969\) 2.20023 7.59608i 0.0706816 0.244021i
\(970\) −2.00216 + 2.90063i −0.0642855 + 0.0931336i
\(971\) 41.5829 + 17.7168i 1.33446 + 0.568560i 0.937086 0.349098i \(-0.113512\pi\)
0.397372 + 0.917657i \(0.369922\pi\)
\(972\) −1.73714 + 0.282313i −0.0557188 + 0.00905518i
\(973\) −3.58250 2.26544i −0.114850 0.0726266i
\(974\) 6.45926 + 9.35786i 0.206968 + 0.299845i
\(975\) −1.35027 3.78562i −0.0432433 0.121237i
\(976\) −20.5784 + 29.8130i −0.658700 + 0.954292i
\(977\) −0.429292 + 0.182904i −0.0137343 + 0.00585162i −0.398823 0.917028i \(-0.630581\pi\)
0.385089 + 0.922880i \(0.374171\pi\)
\(978\) −1.71059 5.90564i −0.0546986 0.188841i
\(979\) 13.8927 1.12154i 0.444013 0.0358444i
\(980\) 15.9765 14.1540i 0.510352 0.452132i
\(981\) 11.6512 7.36779i 0.371995 0.235236i
\(982\) −1.39863 0.595900i −0.0446320 0.0190159i
\(983\) 1.62114 13.3513i 0.0517063 0.425839i −0.943753 0.330651i \(-0.892732\pi\)
0.995459 0.0951882i \(-0.0303453\pi\)
\(984\) −3.30098 16.1693i −0.105231 0.515458i
\(985\) −43.7097 3.52861i −1.39271 0.112431i
\(986\) 2.66331 2.00135i 0.0848171 0.0637359i
\(987\) −5.14684 + 42.3880i −0.163826 + 1.34923i
\(988\) −4.91973 48.5655i −0.156517 1.54507i
\(989\) −5.58119 45.9652i −0.177471 1.46161i
\(990\) 1.75963 + 1.83197i 0.0559248 + 0.0582239i
\(991\) 8.32741 + 14.4235i 0.264529 + 0.458177i 0.967440 0.253100i \(-0.0814503\pi\)
−0.702911 + 0.711278i \(0.748117\pi\)
\(992\) 6.93748 12.0161i 0.220265 0.381511i
\(993\) 19.6632 4.84654i 0.623992 0.153800i
\(994\) −5.51410 6.75354i −0.174897 0.214209i
\(995\) −14.2982 + 24.7653i −0.453285 + 0.785112i
\(996\) 3.67612 + 9.69314i 0.116482 + 0.307139i
\(997\) −0.362524 + 0.377428i −0.0114813 + 0.0119532i −0.726918 0.686724i \(-0.759048\pi\)
0.715437 + 0.698677i \(0.246228\pi\)
\(998\) 13.2191 + 4.41319i 0.418443 + 0.139697i
\(999\) −2.20378 7.60834i −0.0697246 0.240717i
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 507.2.q.b.16.8 384
169.74 even 39 inner 507.2.q.b.412.8 yes 384
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.q.b.16.8 384 1.1 even 1 trivial
507.2.q.b.412.8 yes 384 169.74 even 39 inner