Properties

Label 475.2.n.b.39.5
Level $475$
Weight $2$
Character 475.39
Analytic conductor $3.793$
Analytic rank $0$
Dimension $96$
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] = [475,2,Mod(39,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.39");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.n (of order \(10\), degree \(4\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 39.5
Character \(\chi\) \(=\) 475.39
Dual form 475.2.n.b.134.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.09699 - 1.50988i) q^{2} +(-2.32300 - 0.754787i) q^{3} +(-0.458306 + 1.41052i) q^{4} +(-0.339804 - 2.21010i) q^{5} +(1.40867 + 4.33543i) q^{6} +1.57904i q^{7} +(-0.917463 + 0.298102i) q^{8} +(2.39956 + 1.74338i) q^{9} +O(q^{10})\) \(q+(-1.09699 - 1.50988i) q^{2} +(-2.32300 - 0.754787i) q^{3} +(-0.458306 + 1.41052i) q^{4} +(-0.339804 - 2.21010i) q^{5} +(1.40867 + 4.33543i) q^{6} +1.57904i q^{7} +(-0.917463 + 0.298102i) q^{8} +(2.39956 + 1.74338i) q^{9} +(-2.96421 + 2.93752i) q^{10} +(0.575073 - 0.417815i) q^{11} +(2.12929 - 2.93071i) q^{12} +(-2.92977 + 4.03248i) q^{13} +(2.38416 - 1.73219i) q^{14} +(-0.878789 + 5.39053i) q^{15} +(3.85626 + 2.80174i) q^{16} +(-0.705512 + 0.229235i) q^{17} -5.53551i q^{18} +(0.309017 + 0.951057i) q^{19} +(3.27312 + 0.533600i) q^{20} +(1.19184 - 3.66812i) q^{21} +(-1.26170 - 0.409950i) q^{22} +(-0.216662 - 0.298210i) q^{23} +2.35627 q^{24} +(-4.76907 + 1.50200i) q^{25} +9.30247 q^{26} +(0.0487863 + 0.0671486i) q^{27} +(-2.22728 - 0.723686i) q^{28} +(0.695032 - 2.13909i) q^{29} +(9.10305 - 4.58649i) q^{30} +(0.289000 + 0.889451i) q^{31} -6.96660i q^{32} +(-1.65125 + 0.536525i) q^{33} +(1.12005 + 0.813767i) q^{34} +(3.48984 - 0.536566i) q^{35} +(-3.55881 + 2.58563i) q^{36} +(3.32764 - 4.58011i) q^{37} +(1.09699 - 1.50988i) q^{38} +(9.84951 - 7.15609i) q^{39} +(0.970592 + 1.92639i) q^{40} +(-3.01068 - 2.18739i) q^{41} +(-6.84584 + 2.22435i) q^{42} -1.75667i q^{43} +(0.325777 + 1.00264i) q^{44} +(3.03766 - 5.89567i) q^{45} +(-0.212584 + 0.654265i) q^{46} +(12.9339 + 4.20249i) q^{47} +(-6.84337 - 9.41909i) q^{48} +4.50662 q^{49} +(7.49945 + 5.55302i) q^{50} +1.81192 q^{51} +(-4.34517 - 5.98061i) q^{52} +(-9.93925 - 3.22946i) q^{53} +(0.0478680 - 0.147322i) q^{54} +(-1.11882 - 1.12899i) q^{55} +(-0.470716 - 1.44871i) q^{56} -2.44254i q^{57} +(-3.99220 + 1.29714i) q^{58} +(6.19938 + 4.50411i) q^{59} +(-7.20070 - 3.71006i) q^{60} +(-10.4321 + 7.57939i) q^{61} +(1.02593 - 1.41207i) q^{62} +(-2.75288 + 3.78901i) q^{63} +(-2.80618 + 2.03881i) q^{64} +(9.90773 + 5.10482i) q^{65} +(2.62149 + 1.90463i) q^{66} +(-6.89610 + 2.24068i) q^{67} -1.10020i q^{68} +(0.278220 + 0.856274i) q^{69} +(-4.63847 - 4.68062i) q^{70} +(-3.83012 + 11.7879i) q^{71} +(-2.72121 - 0.884176i) q^{72} +(3.88381 + 5.34561i) q^{73} -10.5658 q^{74} +(12.2122 + 0.110484i) q^{75} -1.48311 q^{76} +(0.659749 + 0.908066i) q^{77} +(-21.6096 - 7.02139i) q^{78} +(-2.85625 + 8.79062i) q^{79} +(4.88174 - 9.47477i) q^{80} +(-2.81230 - 8.65536i) q^{81} +6.94530i q^{82} +(7.75155 - 2.51863i) q^{83} +(4.62772 + 3.36224i) q^{84} +(0.746367 + 1.48135i) q^{85} +(-2.65235 + 1.92705i) q^{86} +(-3.22911 + 4.44449i) q^{87} +(-0.403057 + 0.554760i) q^{88} +(-10.9490 + 7.95488i) q^{89} +(-12.2340 + 1.88099i) q^{90} +(-6.36747 - 4.62624i) q^{91} +(0.519928 - 0.168935i) q^{92} -2.28433i q^{93} +(-7.84314 - 24.1387i) q^{94} +(1.99692 - 1.00613i) q^{95} +(-5.25830 + 16.1834i) q^{96} +(2.30248 + 0.748120i) q^{97} +(-4.94371 - 6.80443i) q^{98} +2.10833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09699 1.50988i −0.775688 1.06764i −0.995745 0.0921562i \(-0.970624\pi\)
0.220056 0.975487i \(-0.429376\pi\)
\(3\) −2.32300 0.754787i −1.34118 0.435777i −0.451466 0.892289i \(-0.649099\pi\)
−0.889717 + 0.456512i \(0.849099\pi\)
\(4\) −0.458306 + 1.41052i −0.229153 + 0.705260i
\(5\) −0.339804 2.21010i −0.151965 0.988386i
\(6\) 1.40867 + 4.33543i 0.575086 + 1.76993i
\(7\) 1.57904i 0.596823i 0.954437 + 0.298411i \(0.0964567\pi\)
−0.954437 + 0.298411i \(0.903543\pi\)
\(8\) −0.917463 + 0.298102i −0.324372 + 0.105395i
\(9\) 2.39956 + 1.74338i 0.799853 + 0.581127i
\(10\) −2.96421 + 2.93752i −0.937366 + 0.928924i
\(11\) 0.575073 0.417815i 0.173391 0.125976i −0.497705 0.867346i \(-0.665824\pi\)
0.671096 + 0.741370i \(0.265824\pi\)
\(12\) 2.12929 2.93071i 0.614672 0.846024i
\(13\) −2.92977 + 4.03248i −0.812572 + 1.11841i 0.178350 + 0.983967i \(0.442924\pi\)
−0.990921 + 0.134442i \(0.957076\pi\)
\(14\) 2.38416 1.73219i 0.637194 0.462948i
\(15\) −0.878789 + 5.39053i −0.226902 + 1.39183i
\(16\) 3.85626 + 2.80174i 0.964066 + 0.700435i
\(17\) −0.705512 + 0.229235i −0.171112 + 0.0555976i −0.393320 0.919402i \(-0.628674\pi\)
0.222208 + 0.974999i \(0.428674\pi\)
\(18\) 5.53551i 1.30473i
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i
\(20\) 3.27312 + 0.533600i 0.731893 + 0.119317i
\(21\) 1.19184 3.66812i 0.260081 0.800448i
\(22\) −1.26170 0.409950i −0.268995 0.0874017i
\(23\) −0.216662 0.298210i −0.0451771 0.0621810i 0.785831 0.618442i \(-0.212236\pi\)
−0.831008 + 0.556261i \(0.812236\pi\)
\(24\) 2.35627 0.480971
\(25\) −4.76907 + 1.50200i −0.953813 + 0.300400i
\(26\) 9.30247 1.82436
\(27\) 0.0487863 + 0.0671486i 0.00938893 + 0.0129227i
\(28\) −2.22728 0.723686i −0.420915 0.136764i
\(29\) 0.695032 2.13909i 0.129064 0.397219i −0.865555 0.500813i \(-0.833034\pi\)
0.994620 + 0.103594i \(0.0330344\pi\)
\(30\) 9.10305 4.58649i 1.66198 0.837375i
\(31\) 0.289000 + 0.889451i 0.0519059 + 0.159750i 0.973649 0.228050i \(-0.0732350\pi\)
−0.921743 + 0.387800i \(0.873235\pi\)
\(32\) 6.96660i 1.23153i
\(33\) −1.65125 + 0.536525i −0.287447 + 0.0933970i
\(34\) 1.12005 + 0.813767i 0.192088 + 0.139560i
\(35\) 3.48984 0.536566i 0.589891 0.0906963i
\(36\) −3.55881 + 2.58563i −0.593135 + 0.430938i
\(37\) 3.32764 4.58011i 0.547061 0.752965i −0.442549 0.896744i \(-0.645926\pi\)
0.989610 + 0.143780i \(0.0459257\pi\)
\(38\) 1.09699 1.50988i 0.177955 0.244934i
\(39\) 9.84951 7.15609i 1.57718 1.14589i
\(40\) 0.970592 + 1.92639i 0.153464 + 0.304588i
\(41\) −3.01068 2.18739i −0.470190 0.341613i 0.327326 0.944912i \(-0.393853\pi\)
−0.797515 + 0.603299i \(0.793853\pi\)
\(42\) −6.84584 + 2.22435i −1.05634 + 0.343224i
\(43\) 1.75667i 0.267890i −0.990989 0.133945i \(-0.957236\pi\)
0.990989 0.133945i \(-0.0427645\pi\)
\(44\) 0.325777 + 1.00264i 0.0491128 + 0.151154i
\(45\) 3.03766 5.89567i 0.452828 0.878875i
\(46\) −0.212584 + 0.654265i −0.0313438 + 0.0964662i
\(47\) 12.9339 + 4.20249i 1.88661 + 0.612996i 0.982680 + 0.185312i \(0.0593295\pi\)
0.903928 + 0.427684i \(0.140671\pi\)
\(48\) −6.84337 9.41909i −0.987756 1.35953i
\(49\) 4.50662 0.643803
\(50\) 7.49945 + 5.55302i 1.06058 + 0.785315i
\(51\) 1.81192 0.253720
\(52\) −4.34517 5.98061i −0.602566 0.829361i
\(53\) −9.93925 3.22946i −1.36526 0.443600i −0.467465 0.884012i \(-0.654833\pi\)
−0.897796 + 0.440411i \(0.854833\pi\)
\(54\) 0.0478680 0.147322i 0.00651401 0.0200481i
\(55\) −1.11882 1.12899i −0.150862 0.152233i
\(56\) −0.470716 1.44871i −0.0629021 0.193593i
\(57\) 2.44254i 0.323523i
\(58\) −3.99220 + 1.29714i −0.524202 + 0.170323i
\(59\) 6.19938 + 4.50411i 0.807090 + 0.586386i 0.912986 0.407992i \(-0.133771\pi\)
−0.105895 + 0.994377i \(0.533771\pi\)
\(60\) −7.20070 3.71006i −0.929607 0.478967i
\(61\) −10.4321 + 7.57939i −1.33570 + 0.970441i −0.336107 + 0.941824i \(0.609110\pi\)
−0.999590 + 0.0286174i \(0.990890\pi\)
\(62\) 1.02593 1.41207i 0.130293 0.179333i
\(63\) −2.75288 + 3.78901i −0.346830 + 0.477371i
\(64\) −2.80618 + 2.03881i −0.350772 + 0.254851i
\(65\) 9.90773 + 5.10482i 1.22890 + 0.633175i
\(66\) 2.62149 + 1.90463i 0.322684 + 0.234443i
\(67\) −6.89610 + 2.24068i −0.842493 + 0.273743i −0.698298 0.715807i \(-0.746059\pi\)
−0.144195 + 0.989549i \(0.546059\pi\)
\(68\) 1.10020i 0.133419i
\(69\) 0.278220 + 0.856274i 0.0334938 + 0.103083i
\(70\) −4.63847 4.68062i −0.554403 0.559441i
\(71\) −3.83012 + 11.7879i −0.454551 + 1.39896i 0.417110 + 0.908856i \(0.363043\pi\)
−0.871661 + 0.490109i \(0.836957\pi\)
\(72\) −2.72121 0.884176i −0.320698 0.104201i
\(73\) 3.88381 + 5.34561i 0.454566 + 0.625656i 0.973371 0.229236i \(-0.0736228\pi\)
−0.518805 + 0.854893i \(0.673623\pi\)
\(74\) −10.5658 −1.22825
\(75\) 12.2122 + 0.110484i 1.41015 + 0.0127576i
\(76\) −1.48311 −0.170124
\(77\) 0.659749 + 0.908066i 0.0751853 + 0.103484i
\(78\) −21.6096 7.02139i −2.44681 0.795016i
\(79\) −2.85625 + 8.79062i −0.321353 + 0.989022i 0.651707 + 0.758471i \(0.274053\pi\)
−0.973060 + 0.230552i \(0.925947\pi\)
\(80\) 4.88174 9.47477i 0.545796 1.05931i
\(81\) −2.81230 8.65536i −0.312478 0.961707i
\(82\) 6.94530i 0.766980i
\(83\) 7.75155 2.51863i 0.850844 0.276456i 0.149044 0.988831i \(-0.452380\pi\)
0.701799 + 0.712375i \(0.252380\pi\)
\(84\) 4.62772 + 3.36224i 0.504926 + 0.366850i
\(85\) 0.746367 + 1.48135i 0.0809549 + 0.160675i
\(86\) −2.65235 + 1.92705i −0.286011 + 0.207799i
\(87\) −3.22911 + 4.44449i −0.346197 + 0.476500i
\(88\) −0.403057 + 0.554760i −0.0429660 + 0.0591376i
\(89\) −10.9490 + 7.95488i −1.16059 + 0.843215i −0.989852 0.142102i \(-0.954614\pi\)
−0.170734 + 0.985317i \(0.554614\pi\)
\(90\) −12.2340 + 1.88099i −1.28958 + 0.198274i
\(91\) −6.36747 4.62624i −0.667492 0.484961i
\(92\) 0.519928 0.168935i 0.0542063 0.0176127i
\(93\) 2.28433i 0.236873i
\(94\) −7.84314 24.1387i −0.808959 2.48972i
\(95\) 1.99692 1.00613i 0.204880 0.103227i
\(96\) −5.25830 + 16.1834i −0.536673 + 1.65171i
\(97\) 2.30248 + 0.748120i 0.233781 + 0.0759600i 0.423565 0.905866i \(-0.360779\pi\)
−0.189784 + 0.981826i \(0.560779\pi\)
\(98\) −4.94371 6.80443i −0.499390 0.687352i
\(99\) 2.10833 0.211896
\(100\) 0.0670860 7.41524i 0.00670860 0.741524i
\(101\) 8.77553 0.873198 0.436599 0.899656i \(-0.356183\pi\)
0.436599 + 0.899656i \(0.356183\pi\)
\(102\) −1.98766 2.73578i −0.196808 0.270883i
\(103\) 9.59211 + 3.11666i 0.945138 + 0.307094i 0.740739 0.671793i \(-0.234476\pi\)
0.204400 + 0.978887i \(0.434476\pi\)
\(104\) 1.48586 4.57302i 0.145701 0.448422i
\(105\) −8.51189 1.38765i −0.830675 0.135421i
\(106\) 6.02717 + 18.5497i 0.585410 + 1.80171i
\(107\) 2.24001i 0.216550i −0.994121 0.108275i \(-0.965467\pi\)
0.994121 0.108275i \(-0.0345328\pi\)
\(108\) −0.117074 + 0.0380395i −0.0112654 + 0.00366035i
\(109\) −0.677401 0.492161i −0.0648832 0.0471404i 0.554871 0.831936i \(-0.312768\pi\)
−0.619754 + 0.784796i \(0.712768\pi\)
\(110\) −0.477300 + 2.92778i −0.0455088 + 0.279153i
\(111\) −11.1871 + 8.12791i −1.06183 + 0.771467i
\(112\) −4.42407 + 6.08921i −0.418036 + 0.575377i
\(113\) −8.04188 + 11.0687i −0.756516 + 1.04126i 0.240980 + 0.970530i \(0.422531\pi\)
−0.997496 + 0.0707251i \(0.977469\pi\)
\(114\) −3.68794 + 2.67944i −0.345407 + 0.250953i
\(115\) −0.585450 + 0.580177i −0.0545935 + 0.0541018i
\(116\) 2.69869 + 1.96071i 0.250567 + 0.182048i
\(117\) −14.0603 + 4.56847i −1.29988 + 0.422355i
\(118\) 14.3013i 1.31654i
\(119\) −0.361972 1.11403i −0.0331819 0.102123i
\(120\) −0.800670 5.20758i −0.0730908 0.475385i
\(121\) −3.24305 + 9.98107i −0.294822 + 0.907370i
\(122\) 22.8879 + 7.43672i 2.07217 + 0.673289i
\(123\) 5.34279 + 7.35372i 0.481743 + 0.663063i
\(124\) −1.38704 −0.124560
\(125\) 4.94012 + 10.0297i 0.441858 + 0.897085i
\(126\) 8.74081 0.778694
\(127\) 5.99644 + 8.25339i 0.532098 + 0.732370i 0.987448 0.157942i \(-0.0504861\pi\)
−0.455351 + 0.890312i \(0.650486\pi\)
\(128\) −7.09458 2.30517i −0.627078 0.203750i
\(129\) −1.32591 + 4.08074i −0.116740 + 0.359289i
\(130\) −3.16102 20.5594i −0.277240 1.80318i
\(131\) 2.29959 + 7.07741i 0.200916 + 0.618356i 0.999856 + 0.0169459i \(0.00539431\pi\)
−0.798940 + 0.601410i \(0.794606\pi\)
\(132\) 2.57502i 0.224127i
\(133\) −1.50176 + 0.487952i −0.130219 + 0.0423108i
\(134\) 10.9481 + 7.95426i 0.945771 + 0.687143i
\(135\) 0.131827 0.130640i 0.0113459 0.0112437i
\(136\) 0.578946 0.420629i 0.0496442 0.0360686i
\(137\) 1.60511 2.20925i 0.137134 0.188749i −0.734927 0.678147i \(-0.762783\pi\)
0.872061 + 0.489398i \(0.162783\pi\)
\(138\) 0.987663 1.35940i 0.0840754 0.115720i
\(139\) −9.93926 + 7.22129i −0.843037 + 0.612502i −0.923217 0.384278i \(-0.874450\pi\)
0.0801807 + 0.996780i \(0.474450\pi\)
\(140\) −0.842578 + 5.16841i −0.0712108 + 0.436810i
\(141\) −26.8735 19.5247i −2.26316 1.64428i
\(142\) 21.9998 7.14818i 1.84619 0.599862i
\(143\) 3.54307i 0.296287i
\(144\) 4.36883 + 13.4459i 0.364069 + 1.12049i
\(145\) −4.96377 0.809217i −0.412219 0.0672018i
\(146\) 3.81071 11.7282i 0.315376 0.970629i
\(147\) −10.4689 3.40154i −0.863457 0.280554i
\(148\) 4.93526 + 6.79280i 0.405676 + 0.558364i
\(149\) 6.94397 0.568873 0.284436 0.958695i \(-0.408194\pi\)
0.284436 + 0.958695i \(0.408194\pi\)
\(150\) −13.2298 18.5601i −1.08021 1.51543i
\(151\) −4.39870 −0.357962 −0.178981 0.983853i \(-0.557280\pi\)
−0.178981 + 0.983853i \(0.557280\pi\)
\(152\) −0.567023 0.780441i −0.0459917 0.0633021i
\(153\) −2.09256 0.679914i −0.169174 0.0549678i
\(154\) 0.647330 1.99228i 0.0521633 0.160542i
\(155\) 1.86757 0.940958i 0.150007 0.0755795i
\(156\) 5.57972 + 17.1726i 0.446735 + 1.37491i
\(157\) 14.5764i 1.16332i −0.813431 0.581661i \(-0.802403\pi\)
0.813431 0.581661i \(-0.197597\pi\)
\(158\) 16.4060 5.33064i 1.30519 0.424083i
\(159\) 20.6513 + 15.0040i 1.63775 + 1.18990i
\(160\) −15.3969 + 2.36728i −1.21723 + 0.187150i
\(161\) 0.470886 0.342119i 0.0371110 0.0269627i
\(162\) −9.98346 + 13.7411i −0.784375 + 1.07960i
\(163\) −7.90999 + 10.8872i −0.619559 + 0.852749i −0.997321 0.0731534i \(-0.976694\pi\)
0.377762 + 0.925903i \(0.376694\pi\)
\(164\) 4.46517 3.24414i 0.348671 0.253324i
\(165\) 1.74688 + 3.46712i 0.135994 + 0.269915i
\(166\) −12.3062 8.94097i −0.955146 0.693954i
\(167\) 13.3363 4.33324i 1.03200 0.335316i 0.256417 0.966566i \(-0.417458\pi\)
0.775579 + 0.631250i \(0.217458\pi\)
\(168\) 3.72065i 0.287054i
\(169\) −3.66014 11.2647i −0.281549 0.866519i
\(170\) 1.41791 2.75195i 0.108748 0.211065i
\(171\) −0.916550 + 2.82085i −0.0700904 + 0.215716i
\(172\) 2.47782 + 0.805092i 0.188932 + 0.0613877i
\(173\) 3.78326 + 5.20721i 0.287636 + 0.395897i 0.928245 0.371971i \(-0.121318\pi\)
−0.640608 + 0.767868i \(0.721318\pi\)
\(174\) 10.2529 0.777273
\(175\) −2.37173 7.53057i −0.179286 0.569257i
\(176\) 3.38824 0.255398
\(177\) −11.0015 15.1423i −0.826923 1.13816i
\(178\) 24.0218 + 7.80514i 1.80051 + 0.585020i
\(179\) 3.51229 10.8097i 0.262521 0.807957i −0.729733 0.683732i \(-0.760356\pi\)
0.992254 0.124225i \(-0.0396443\pi\)
\(180\) 6.92379 + 6.98671i 0.516069 + 0.520759i
\(181\) −2.68276 8.25667i −0.199408 0.613714i −0.999897 0.0143664i \(-0.995427\pi\)
0.800489 0.599347i \(-0.204573\pi\)
\(182\) 14.6890i 1.08882i
\(183\) 29.9546 9.73285i 2.21431 0.719473i
\(184\) 0.287676 + 0.209009i 0.0212078 + 0.0154083i
\(185\) −11.2532 5.79807i −0.827354 0.426283i
\(186\) −3.44905 + 2.50588i −0.252896 + 0.183740i
\(187\) −0.309943 + 0.426600i −0.0226653 + 0.0311961i
\(188\) −11.8554 + 16.3176i −0.864644 + 1.19008i
\(189\) −0.106031 + 0.0770357i −0.00771259 + 0.00560352i
\(190\) −3.70973 1.91139i −0.269132 0.138667i
\(191\) −7.44314 5.40776i −0.538567 0.391292i 0.284986 0.958532i \(-0.408011\pi\)
−0.823553 + 0.567240i \(0.808011\pi\)
\(192\) 8.05760 2.61807i 0.581507 0.188943i
\(193\) 21.4959i 1.54731i 0.633608 + 0.773654i \(0.281573\pi\)
−0.633608 + 0.773654i \(0.718427\pi\)
\(194\) −1.39622 4.29713i −0.100243 0.308516i
\(195\) −19.1626 19.3367i −1.37226 1.38473i
\(196\) −2.06541 + 6.35668i −0.147529 + 0.454049i
\(197\) −6.83153 2.21970i −0.486726 0.158147i 0.0553657 0.998466i \(-0.482368\pi\)
−0.542092 + 0.840319i \(0.682368\pi\)
\(198\) −2.31282 3.18332i −0.164365 0.226229i
\(199\) 14.2342 1.00903 0.504516 0.863402i \(-0.331671\pi\)
0.504516 + 0.863402i \(0.331671\pi\)
\(200\) 3.92769 2.79970i 0.277730 0.197969i
\(201\) 17.7109 1.24923
\(202\) −9.62666 13.2500i −0.677329 0.932264i
\(203\) 3.37772 + 1.09749i 0.237069 + 0.0770284i
\(204\) −0.830416 + 2.55576i −0.0581407 + 0.178939i
\(205\) −3.81130 + 7.39719i −0.266193 + 0.516642i
\(206\) −5.81666 17.9018i −0.405266 1.24728i
\(207\) 1.09330i 0.0759894i
\(208\) −22.5959 + 7.34186i −1.56675 + 0.509067i
\(209\) 0.575073 + 0.417815i 0.0397786 + 0.0289009i
\(210\) 7.24227 + 14.3741i 0.499764 + 0.991909i
\(211\) 6.80211 4.94202i 0.468277 0.340223i −0.328493 0.944507i \(-0.606541\pi\)
0.796769 + 0.604284i \(0.206541\pi\)
\(212\) 9.11044 12.5394i 0.625707 0.861212i
\(213\) 17.7947 24.4923i 1.21927 1.67818i
\(214\) −3.38214 + 2.45727i −0.231199 + 0.167976i
\(215\) −3.88241 + 0.596924i −0.264778 + 0.0407099i
\(216\) −0.0647767 0.0470631i −0.00440750 0.00320224i
\(217\) −1.40448 + 0.456344i −0.0953425 + 0.0309786i
\(218\) 1.56269i 0.105838i
\(219\) −4.98729 15.3493i −0.337010 1.03721i
\(220\) 2.10523 1.06070i 0.141935 0.0715125i
\(221\) 1.14260 3.51657i 0.0768597 0.236550i
\(222\) 24.5443 + 7.97491i 1.64730 + 0.535241i
\(223\) 1.16785 + 1.60740i 0.0782048 + 0.107640i 0.846327 0.532663i \(-0.178809\pi\)
−0.768122 + 0.640303i \(0.778809\pi\)
\(224\) 11.0006 0.735007
\(225\) −14.0622 4.71016i −0.937481 0.314011i
\(226\) 25.5342 1.69851
\(227\) −9.21392 12.6819i −0.611549 0.841726i 0.385154 0.922852i \(-0.374148\pi\)
−0.996704 + 0.0811265i \(0.974148\pi\)
\(228\) 3.44526 + 1.11943i 0.228168 + 0.0741362i
\(229\) 8.25569 25.4084i 0.545551 1.67903i −0.174124 0.984724i \(-0.555709\pi\)
0.719675 0.694311i \(-0.244291\pi\)
\(230\) 1.51823 + 0.247509i 0.100109 + 0.0163202i
\(231\) −0.847197 2.60740i −0.0557415 0.171555i
\(232\) 2.16972i 0.142449i
\(233\) −19.0808 + 6.19974i −1.25003 + 0.406159i −0.857931 0.513765i \(-0.828250\pi\)
−0.392097 + 0.919924i \(0.628250\pi\)
\(234\) 22.3218 + 16.2178i 1.45922 + 1.06019i
\(235\) 4.89291 30.0133i 0.319178 1.95785i
\(236\) −9.19436 + 6.68009i −0.598502 + 0.434837i
\(237\) 13.2701 18.2647i 0.861986 1.18642i
\(238\) −1.28497 + 1.76862i −0.0832925 + 0.114642i
\(239\) −18.9980 + 13.8028i −1.22888 + 0.892831i −0.996805 0.0798678i \(-0.974550\pi\)
−0.232071 + 0.972699i \(0.574550\pi\)
\(240\) −18.4917 + 18.3252i −1.19363 + 1.18288i
\(241\) −8.81784 6.40654i −0.568007 0.412681i 0.266373 0.963870i \(-0.414175\pi\)
−0.834381 + 0.551188i \(0.814175\pi\)
\(242\) 18.6278 6.05253i 1.19744 0.389071i
\(243\) 21.9801i 1.41002i
\(244\) −5.90978 18.1884i −0.378335 1.16439i
\(245\) −1.53137 9.96007i −0.0978356 0.636325i
\(246\) 5.24222 16.1339i 0.334232 1.02866i
\(247\) −4.74047 1.54027i −0.301629 0.0980051i
\(248\) −0.530294 0.729887i −0.0336737 0.0463479i
\(249\) −19.9079 −1.26161
\(250\) 9.72436 18.4615i 0.615023 1.16761i
\(251\) 2.20070 0.138907 0.0694534 0.997585i \(-0.477874\pi\)
0.0694534 + 0.997585i \(0.477874\pi\)
\(252\) −4.08282 5.61952i −0.257193 0.353996i
\(253\) −0.249193 0.0809677i −0.0156666 0.00509040i
\(254\) 5.88356 18.1078i 0.369168 1.13618i
\(255\) −0.615700 4.00453i −0.0385566 0.250773i
\(256\) 6.44588 + 19.8384i 0.402868 + 1.23990i
\(257\) 1.76868i 0.110327i −0.998477 0.0551636i \(-0.982432\pi\)
0.998477 0.0551636i \(-0.0175680\pi\)
\(258\) 7.61592 2.47456i 0.474146 0.154059i
\(259\) 7.23219 + 5.25449i 0.449386 + 0.326498i
\(260\) −11.7412 + 11.6355i −0.728160 + 0.721602i
\(261\) 5.39702 3.92116i 0.334067 0.242714i
\(262\) 8.16339 11.2359i 0.504336 0.694159i
\(263\) −13.9802 + 19.2421i −0.862058 + 1.18652i 0.119017 + 0.992892i \(0.462026\pi\)
−0.981075 + 0.193629i \(0.937974\pi\)
\(264\) 1.35503 0.984484i 0.0833961 0.0605908i
\(265\) −3.76002 + 23.0641i −0.230976 + 1.41682i
\(266\) 2.38416 + 1.73219i 0.146182 + 0.106208i
\(267\) 31.4386 10.2150i 1.92401 0.625149i
\(268\) 10.7540i 0.656906i
\(269\) 9.24399 + 28.4501i 0.563616 + 1.73463i 0.672028 + 0.740526i \(0.265424\pi\)
−0.108412 + 0.994106i \(0.534576\pi\)
\(270\) −0.341863 0.0557321i −0.0208051 0.00339175i
\(271\) −6.11475 + 18.8193i −0.371445 + 1.14319i 0.574401 + 0.818574i \(0.305235\pi\)
−0.945846 + 0.324615i \(0.894765\pi\)
\(272\) −3.36290 1.09267i −0.203905 0.0662529i
\(273\) 11.2998 + 15.5528i 0.683894 + 0.941299i
\(274\) −5.09648 −0.307890
\(275\) −2.11500 + 2.85635i −0.127539 + 0.172244i
\(276\) −1.33530 −0.0803757
\(277\) 5.47019 + 7.52907i 0.328672 + 0.452378i 0.941090 0.338156i \(-0.109803\pi\)
−0.612418 + 0.790534i \(0.709803\pi\)
\(278\) 21.8065 + 7.08536i 1.30787 + 0.424952i
\(279\) −0.857180 + 2.63813i −0.0513180 + 0.157941i
\(280\) −3.04185 + 1.53261i −0.181785 + 0.0915909i
\(281\) −2.77965 8.55489i −0.165820 0.510342i 0.833276 0.552858i \(-0.186463\pi\)
−0.999096 + 0.0425157i \(0.986463\pi\)
\(282\) 61.9941i 3.69169i
\(283\) 25.6854 8.34570i 1.52684 0.496100i 0.579130 0.815235i \(-0.303392\pi\)
0.947709 + 0.319135i \(0.103392\pi\)
\(284\) −14.8717 10.8049i −0.882472 0.641154i
\(285\) −5.39826 + 0.829987i −0.319765 + 0.0491642i
\(286\) 5.34960 3.88671i 0.316329 0.229826i
\(287\) 3.45398 4.75400i 0.203882 0.280620i
\(288\) 12.1455 16.7168i 0.715678 0.985046i
\(289\) −13.3081 + 9.66889i −0.782829 + 0.568758i
\(290\) 4.22338 + 8.38238i 0.248006 + 0.492230i
\(291\) −4.78397 3.47576i −0.280441 0.203753i
\(292\) −9.32007 + 3.02827i −0.545416 + 0.177216i
\(293\) 3.14290i 0.183610i 0.995777 + 0.0918052i \(0.0292637\pi\)
−0.995777 + 0.0918052i \(0.970736\pi\)
\(294\) 6.34832 + 19.5381i 0.370242 + 1.13949i
\(295\) 7.84795 15.2318i 0.456926 0.886827i
\(296\) −1.68765 + 5.19405i −0.0980927 + 0.301898i
\(297\) 0.0561114 + 0.0182317i 0.00325591 + 0.00105791i
\(298\) −7.61746 10.4845i −0.441268 0.607353i
\(299\) 1.83729 0.106253
\(300\) −5.75277 + 17.1750i −0.332137 + 0.991596i
\(301\) 2.77386 0.159883
\(302\) 4.82533 + 6.64150i 0.277667 + 0.382175i
\(303\) −20.3855 6.62366i −1.17112 0.380519i
\(304\) −1.47296 + 4.53331i −0.0844802 + 0.260003i
\(305\) 20.2961 + 20.4805i 1.16215 + 1.17271i
\(306\) 1.26893 + 3.90537i 0.0725399 + 0.223255i
\(307\) 21.3849i 1.22050i 0.792209 + 0.610249i \(0.208931\pi\)
−0.792209 + 0.610249i \(0.791069\pi\)
\(308\) −1.58321 + 0.514417i −0.0902119 + 0.0293116i
\(309\) −19.9300 14.4800i −1.13378 0.823739i
\(310\) −3.46943 1.78758i −0.197051 0.101528i
\(311\) 17.2160 12.5082i 0.976231 0.709273i 0.0193679 0.999812i \(-0.493835\pi\)
0.956863 + 0.290539i \(0.0938346\pi\)
\(312\) −6.90332 + 9.50160i −0.390824 + 0.537922i
\(313\) −8.21463 + 11.3065i −0.464318 + 0.639079i −0.975397 0.220454i \(-0.929246\pi\)
0.511079 + 0.859534i \(0.329246\pi\)
\(314\) −22.0085 + 15.9901i −1.24201 + 0.902376i
\(315\) 9.30953 + 4.79661i 0.524532 + 0.270258i
\(316\) −11.0903 8.05759i −0.623879 0.453275i
\(317\) 5.43815 1.76696i 0.305437 0.0992425i −0.152288 0.988336i \(-0.548664\pi\)
0.457725 + 0.889094i \(0.348664\pi\)
\(318\) 47.6402i 2.67153i
\(319\) −0.494049 1.52053i −0.0276614 0.0851332i
\(320\) 5.45951 + 5.50913i 0.305196 + 0.307970i
\(321\) −1.69073 + 5.20355i −0.0943676 + 0.290434i
\(322\) −1.03311 0.335679i −0.0575732 0.0187067i
\(323\) −0.436030 0.600144i −0.0242614 0.0333929i
\(324\) 13.4975 0.749859
\(325\) 7.91547 23.6317i 0.439071 1.31085i
\(326\) 25.1155 1.39102
\(327\) 1.20212 + 1.65458i 0.0664776 + 0.0914986i
\(328\) 3.41425 + 1.10936i 0.188521 + 0.0612541i
\(329\) −6.63592 + 20.4233i −0.365850 + 1.12597i
\(330\) 3.31862 6.44096i 0.182684 0.354563i
\(331\) −4.87711 15.0102i −0.268070 0.825036i −0.990970 0.134083i \(-0.957191\pi\)
0.722900 0.690953i \(-0.242809\pi\)
\(332\) 12.0880i 0.663417i
\(333\) 15.9697 5.18889i 0.875137 0.284349i
\(334\) −21.1725 15.3827i −1.15851 0.841704i
\(335\) 7.29545 + 14.4797i 0.398593 + 0.791109i
\(336\) 14.8732 10.8060i 0.811398 0.589515i
\(337\) 3.96048 5.45113i 0.215741 0.296942i −0.687406 0.726273i \(-0.741251\pi\)
0.903147 + 0.429331i \(0.141251\pi\)
\(338\) −12.9932 + 17.8837i −0.706739 + 0.972742i
\(339\) 27.0358 19.6426i 1.46838 1.06684i
\(340\) −2.43155 + 0.373852i −0.131869 + 0.0202750i
\(341\) 0.537822 + 0.390751i 0.0291247 + 0.0211603i
\(342\) 5.26458 1.71057i 0.284676 0.0924968i
\(343\) 18.1695i 0.981059i
\(344\) 0.523666 + 1.61168i 0.0282342 + 0.0868959i
\(345\) 1.79791 0.905860i 0.0967961 0.0487698i
\(346\) 3.71205 11.4245i 0.199561 0.614186i
\(347\) −20.9025 6.79165i −1.12211 0.364595i −0.311535 0.950235i \(-0.600843\pi\)
−0.810571 + 0.585640i \(0.800843\pi\)
\(348\) −4.78913 6.59167i −0.256724 0.353351i
\(349\) −21.4653 −1.14901 −0.574504 0.818502i \(-0.694805\pi\)
−0.574504 + 0.818502i \(0.694805\pi\)
\(350\) −8.76846 + 11.8420i −0.468694 + 0.632980i
\(351\) −0.413708 −0.0220821
\(352\) −2.91075 4.00631i −0.155144 0.213537i
\(353\) −25.8143 8.38757i −1.37396 0.446425i −0.473278 0.880913i \(-0.656929\pi\)
−0.900678 + 0.434488i \(0.856929\pi\)
\(354\) −10.7944 + 33.2218i −0.573716 + 1.76572i
\(355\) 27.3539 + 4.45936i 1.45179 + 0.236678i
\(356\) −6.20255 19.0895i −0.328735 1.01174i
\(357\) 2.86111i 0.151426i
\(358\) −20.1743 + 6.55502i −1.06624 + 0.346444i
\(359\) −15.0863 10.9609i −0.796226 0.578492i 0.113579 0.993529i \(-0.463769\pi\)
−0.909805 + 0.415037i \(0.863769\pi\)
\(360\) −1.02943 + 6.31459i −0.0542560 + 0.332808i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) −9.52360 + 13.1081i −0.500549 + 0.688947i
\(363\) 15.0672 20.7382i 0.790822 1.08847i
\(364\) 9.44365 6.86121i 0.494982 0.359625i
\(365\) 10.4946 10.4001i 0.549312 0.544365i
\(366\) −47.5553 34.5509i −2.48576 1.80601i
\(367\) −18.1973 + 5.91265i −0.949889 + 0.308638i −0.742671 0.669657i \(-0.766441\pi\)
−0.207219 + 0.978295i \(0.566441\pi\)
\(368\) 1.75701i 0.0915903i
\(369\) −3.41086 10.4975i −0.177562 0.546480i
\(370\) 3.59030 + 23.3514i 0.186651 + 1.21398i
\(371\) 5.09946 15.6945i 0.264751 0.814819i
\(372\) 3.22209 + 1.04692i 0.167057 + 0.0542803i
\(373\) 0.602349 + 0.829062i 0.0311885 + 0.0429272i 0.824326 0.566115i \(-0.191554\pi\)
−0.793138 + 0.609042i \(0.791554\pi\)
\(374\) 0.984117 0.0508875
\(375\) −3.90558 27.0277i −0.201684 1.39571i
\(376\) −13.1192 −0.676570
\(377\) 6.58955 + 9.06974i 0.339379 + 0.467115i
\(378\) 0.232629 + 0.0755857i 0.0119651 + 0.00388771i
\(379\) 1.38662 4.26759i 0.0712261 0.219211i −0.909107 0.416564i \(-0.863234\pi\)
0.980333 + 0.197352i \(0.0632343\pi\)
\(380\) 0.503967 + 3.27782i 0.0258530 + 0.168148i
\(381\) −7.70015 23.6986i −0.394491 1.21412i
\(382\) 17.1705i 0.878518i
\(383\) 19.4009 6.30374i 0.991340 0.322106i 0.231940 0.972730i \(-0.425493\pi\)
0.759400 + 0.650624i \(0.225493\pi\)
\(384\) 14.7408 + 10.7098i 0.752237 + 0.546532i
\(385\) 1.78273 1.76667i 0.0908563 0.0900380i
\(386\) 32.4561 23.5808i 1.65197 1.20023i
\(387\) 3.06255 4.21523i 0.155678 0.214272i
\(388\) −2.11048 + 2.90482i −0.107143 + 0.147470i
\(389\) −27.4960 + 19.9770i −1.39410 + 1.01287i −0.398699 + 0.917082i \(0.630538\pi\)
−0.995401 + 0.0957917i \(0.969462\pi\)
\(390\) −8.17491 + 50.1453i −0.413953 + 2.53920i
\(391\) 0.221218 + 0.160724i 0.0111875 + 0.00812816i
\(392\) −4.13466 + 1.34343i −0.208832 + 0.0678535i
\(393\) 18.1765i 0.916883i
\(394\) 4.14264 + 12.7497i 0.208703 + 0.642323i
\(395\) 20.3987 + 3.32549i 1.02637 + 0.167324i
\(396\) −0.966262 + 2.97385i −0.0485565 + 0.149442i
\(397\) −10.6784 3.46963i −0.535934 0.174136i 0.0285304 0.999593i \(-0.490917\pi\)
−0.564464 + 0.825457i \(0.690917\pi\)
\(398\) −15.6147 21.4918i −0.782695 1.07729i
\(399\) 3.85688 0.193086
\(400\) −22.5990 7.56957i −1.12995 0.378478i
\(401\) 33.3706 1.66645 0.833224 0.552936i \(-0.186493\pi\)
0.833224 + 0.552936i \(0.186493\pi\)
\(402\) −19.4286 26.7412i −0.969011 1.33373i
\(403\) −4.43340 1.44050i −0.220843 0.0717563i
\(404\) −4.02188 + 12.3781i −0.200096 + 0.615832i
\(405\) −18.1736 + 9.15659i −0.903052 + 0.454994i
\(406\) −2.04825 6.30386i −0.101653 0.312855i
\(407\) 4.02423i 0.199474i
\(408\) −1.66237 + 0.540138i −0.0822998 + 0.0267408i
\(409\) 10.3604 + 7.52724i 0.512287 + 0.372198i 0.813690 0.581299i \(-0.197455\pi\)
−0.301404 + 0.953497i \(0.597455\pi\)
\(410\) 15.3498 2.36004i 0.758072 0.116554i
\(411\) −5.39618 + 3.92056i −0.266174 + 0.193387i
\(412\) −8.79224 + 12.1015i −0.433163 + 0.596197i
\(413\) −7.11219 + 9.78910i −0.349968 + 0.481690i
\(414\) −1.65074 + 1.19933i −0.0811295 + 0.0589441i
\(415\) −8.20044 16.2759i −0.402544 0.798950i
\(416\) 28.0927 + 20.4105i 1.37736 + 1.00071i
\(417\) 28.5394 9.27301i 1.39758 0.454101i
\(418\) 1.32663i 0.0648875i
\(419\) 6.59085 + 20.2845i 0.321984 + 0.990965i 0.972784 + 0.231715i \(0.0744338\pi\)
−0.650800 + 0.759250i \(0.725566\pi\)
\(420\) 5.85836 11.3702i 0.285858 0.554810i
\(421\) −1.07170 + 3.29834i −0.0522312 + 0.160751i −0.973770 0.227536i \(-0.926933\pi\)
0.921538 + 0.388287i \(0.126933\pi\)
\(422\) −14.9237 4.84900i −0.726473 0.236046i
\(423\) 23.7092 + 32.6329i 1.15278 + 1.58667i
\(424\) 10.0816 0.489606
\(425\) 3.02032 2.15292i 0.146507 0.104432i
\(426\) −56.5009 −2.73748
\(427\) −11.9682 16.4728i −0.579181 0.797175i
\(428\) 3.15959 + 1.02661i 0.152724 + 0.0496232i
\(429\) 2.67427 8.23055i 0.129115 0.397375i
\(430\) 5.16024 + 5.20714i 0.248849 + 0.251111i
\(431\) −3.31377 10.1987i −0.159619 0.491256i 0.838981 0.544161i \(-0.183152\pi\)
−0.998600 + 0.0529049i \(0.983152\pi\)
\(432\) 0.395629i 0.0190347i
\(433\) 26.8359 8.71951i 1.28965 0.419033i 0.417682 0.908593i \(-0.362843\pi\)
0.871969 + 0.489560i \(0.162843\pi\)
\(434\) 2.22972 + 1.61999i 0.107030 + 0.0777620i
\(435\) 10.9200 + 5.62640i 0.523576 + 0.269765i
\(436\) 1.00466 0.729928i 0.0481145 0.0349572i
\(437\) 0.216662 0.298210i 0.0103643 0.0142653i
\(438\) −17.7045 + 24.3682i −0.845955 + 1.16436i
\(439\) −15.8021 + 11.4809i −0.754194 + 0.547954i −0.897124 0.441779i \(-0.854348\pi\)
0.142930 + 0.989733i \(0.454348\pi\)
\(440\) 1.36304 + 0.702285i 0.0649801 + 0.0334801i
\(441\) 10.8139 + 7.85676i 0.514948 + 0.374131i
\(442\) −6.56300 + 2.13245i −0.312170 + 0.101430i
\(443\) 33.6627i 1.59937i −0.600423 0.799683i \(-0.705001\pi\)
0.600423 0.799683i \(-0.294999\pi\)
\(444\) −6.33747 19.5047i −0.300763 0.925653i
\(445\) 21.3016 + 21.4951i 1.00979 + 1.01897i
\(446\) 1.14586 3.52661i 0.0542583 0.166990i
\(447\) −16.1308 5.24122i −0.762962 0.247901i
\(448\) −3.21936 4.43108i −0.152101 0.209349i
\(449\) −31.3512 −1.47956 −0.739778 0.672851i \(-0.765069\pi\)
−0.739778 + 0.672851i \(0.765069\pi\)
\(450\) 8.31435 + 26.3992i 0.391942 + 1.24447i
\(451\) −2.64529 −0.124562
\(452\) −11.9270 16.4161i −0.560998 0.772148i
\(453\) 10.2182 + 3.32009i 0.480092 + 0.155991i
\(454\) −9.04049 + 27.8238i −0.424291 + 1.30583i
\(455\) −8.06074 + 15.6447i −0.377893 + 0.733437i
\(456\) 0.728127 + 2.24094i 0.0340977 + 0.104942i
\(457\) 17.2006i 0.804611i 0.915505 + 0.402306i \(0.131791\pi\)
−0.915505 + 0.402306i \(0.868209\pi\)
\(458\) −47.4199 + 15.4077i −2.21579 + 0.719953i
\(459\) −0.0498121 0.0361906i −0.00232503 0.00168923i
\(460\) −0.550037 1.09169i −0.0256456 0.0509002i
\(461\) −32.0798 + 23.3073i −1.49411 + 1.08553i −0.521449 + 0.853282i \(0.674608\pi\)
−0.972656 + 0.232249i \(0.925392\pi\)
\(462\) −3.00749 + 4.13946i −0.139921 + 0.192585i
\(463\) −8.38871 + 11.5461i −0.389857 + 0.536591i −0.958162 0.286226i \(-0.907599\pi\)
0.568306 + 0.822818i \(0.307599\pi\)
\(464\) 8.67340 6.30159i 0.402652 0.292544i
\(465\) −5.04858 + 0.776224i −0.234122 + 0.0359965i
\(466\) 30.2923 + 22.0087i 1.40326 + 1.01953i
\(467\) −11.4433 + 3.71815i −0.529532 + 0.172055i −0.561567 0.827431i \(-0.689801\pi\)
0.0320348 + 0.999487i \(0.489801\pi\)
\(468\) 21.9261i 1.01354i
\(469\) −3.53813 10.8893i −0.163376 0.502819i
\(470\) −50.6838 + 25.5366i −2.33787 + 1.17791i
\(471\) −11.0021 + 33.8609i −0.506949 + 1.56023i
\(472\) −7.03039 2.28431i −0.323600 0.105144i
\(473\) −0.733963 1.01021i −0.0337477 0.0464497i
\(474\) −42.1346 −1.93531
\(475\) −2.90221 4.07151i −0.133163 0.186814i
\(476\) 1.73726 0.0796273
\(477\) −18.2196 25.0772i −0.834220 1.14821i
\(478\) 41.6811 + 13.5430i 1.90645 + 0.619443i
\(479\) −6.57331 + 20.2306i −0.300342 + 0.924359i 0.681032 + 0.732254i \(0.261531\pi\)
−0.981374 + 0.192105i \(0.938469\pi\)
\(480\) 37.5537 + 6.12218i 1.71408 + 0.279438i
\(481\) 8.71997 + 26.8373i 0.397596 + 1.22368i
\(482\) 20.3418i 0.926541i
\(483\) −1.35209 + 0.439322i −0.0615224 + 0.0199898i
\(484\) −12.5922 9.14877i −0.572373 0.415853i
\(485\) 0.871026 5.34291i 0.0395513 0.242609i
\(486\) 33.1872 24.1119i 1.50540 1.09374i
\(487\) 12.6283 17.3814i 0.572243 0.787625i −0.420575 0.907258i \(-0.638172\pi\)
0.992818 + 0.119633i \(0.0381717\pi\)
\(488\) 7.31167 10.0636i 0.330984 0.455560i
\(489\) 26.5924 19.3205i 1.20255 0.873703i
\(490\) −13.3586 + 13.2383i −0.603479 + 0.598044i
\(491\) −1.41936 1.03123i −0.0640550 0.0465387i 0.555297 0.831652i \(-0.312605\pi\)
−0.619352 + 0.785113i \(0.712605\pi\)
\(492\) −12.8212 + 4.16586i −0.578025 + 0.187812i
\(493\) 1.66848i 0.0751444i
\(494\) 2.87462 + 8.84717i 0.129335 + 0.398053i
\(495\) −0.716421 4.65962i −0.0322007 0.209435i
\(496\) −1.37755 + 4.23966i −0.0618538 + 0.190366i
\(497\) −18.6136 6.04792i −0.834934 0.271286i
\(498\) 21.8387 + 30.0584i 0.978616 + 1.34695i
\(499\) 25.8999 1.15944 0.579720 0.814816i \(-0.303162\pi\)
0.579720 + 0.814816i \(0.303162\pi\)
\(500\) −16.4112 + 2.37147i −0.733932 + 0.106055i
\(501\) −34.2509 −1.53022
\(502\) −2.41414 3.32278i −0.107748 0.148303i
\(503\) −32.4817 10.5539i −1.44829 0.470577i −0.523817 0.851831i \(-0.675493\pi\)
−0.924471 + 0.381253i \(0.875493\pi\)
\(504\) 1.39615 4.29692i 0.0621896 0.191400i
\(505\) −2.98196 19.3948i −0.132696 0.863057i
\(506\) 0.151111 + 0.465071i 0.00671769 + 0.0206749i
\(507\) 28.9306i 1.28485i
\(508\) −14.3898 + 4.67552i −0.638443 + 0.207443i
\(509\) −17.8532 12.9711i −0.791330 0.574935i 0.117028 0.993129i \(-0.462663\pi\)
−0.908358 + 0.418194i \(0.862663\pi\)
\(510\) −5.37093 + 5.32256i −0.237829 + 0.235687i
\(511\) −8.44096 + 6.13271i −0.373406 + 0.271295i
\(512\) 14.1131 19.4250i 0.623715 0.858470i
\(513\) −0.0487863 + 0.0671486i −0.00215397 + 0.00296468i
\(514\) −2.67049 + 1.94022i −0.117790 + 0.0855795i
\(515\) 3.62869 22.2586i 0.159899 0.980829i
\(516\) −5.14829 3.74045i −0.226641 0.164664i
\(517\) 9.19382 2.98725i 0.404344 0.131379i
\(518\) 16.6838i 0.733045i
\(519\) −4.85817 14.9519i −0.213250 0.656316i
\(520\) −10.6117 1.72997i −0.465355 0.0758644i
\(521\) 12.0680 37.1415i 0.528709 1.62720i −0.228153 0.973625i \(-0.573269\pi\)
0.756863 0.653574i \(-0.226731\pi\)
\(522\) −11.8409 3.84736i −0.518264 0.168394i
\(523\) −5.66916 7.80293i −0.247895 0.341198i 0.666878 0.745167i \(-0.267630\pi\)
−0.914773 + 0.403969i \(0.867630\pi\)
\(524\) −11.0368 −0.482143
\(525\) −0.174460 + 19.2836i −0.00761405 + 0.841607i
\(526\) 44.3894 1.93547
\(527\) −0.407786 0.561269i −0.0177634 0.0244493i
\(528\) −7.87088 2.55740i −0.342536 0.111297i
\(529\) 7.06540 21.7451i 0.307191 0.945438i
\(530\) 38.9486 19.6239i 1.69182 0.852408i
\(531\) 7.02339 + 21.6158i 0.304789 + 0.938045i
\(532\) 2.34190i 0.101534i
\(533\) 17.6412 5.73198i 0.764125 0.248279i
\(534\) −49.9112 36.2626i −2.15987 1.56924i
\(535\) −4.95065 + 0.761167i −0.214035 + 0.0329081i
\(536\) 5.65897 4.11148i 0.244430 0.177589i
\(537\) −16.3181 + 22.4599i −0.704178 + 0.969217i
\(538\) 32.8155 45.1667i 1.41478 1.94727i
\(539\) 2.59164 1.88293i 0.111630 0.0811037i
\(540\) 0.123853 + 0.245818i 0.00532979 + 0.0105783i
\(541\) 33.1938 + 24.1167i 1.42711 + 1.03686i 0.990545 + 0.137185i \(0.0438054\pi\)
0.436566 + 0.899672i \(0.356195\pi\)
\(542\) 35.1226 11.4120i 1.50864 0.490188i
\(543\) 21.2051i 0.909999i
\(544\) 1.59699 + 4.91502i 0.0684702 + 0.210730i
\(545\) −0.857539 + 1.66436i −0.0367329 + 0.0712934i
\(546\) 11.0871 34.1225i 0.474483 1.46031i
\(547\) −1.57414 0.511470i −0.0673055 0.0218689i 0.275171 0.961395i \(-0.411266\pi\)
−0.342476 + 0.939527i \(0.611266\pi\)
\(548\) 2.38056 + 3.27656i 0.101692 + 0.139968i
\(549\) −38.2463 −1.63231
\(550\) 6.63287 + 0.0600078i 0.282826 + 0.00255874i
\(551\) 2.24917 0.0958179
\(552\) −0.510514 0.702662i −0.0217289 0.0299073i
\(553\) −13.8808 4.51014i −0.590271 0.191791i
\(554\) 5.36722 16.5186i 0.228031 0.701808i
\(555\) 21.7649 + 21.9627i 0.923869 + 0.932265i
\(556\) −5.63056 17.3291i −0.238789 0.734917i
\(557\) 42.4409i 1.79828i −0.437661 0.899140i \(-0.644193\pi\)
0.437661 0.899140i \(-0.355807\pi\)
\(558\) 4.92356 1.59976i 0.208431 0.0677233i
\(559\) 7.08374 + 5.14664i 0.299610 + 0.217680i
\(560\) 14.9611 + 7.70849i 0.632221 + 0.325743i
\(561\) 1.04199 0.757050i 0.0439928 0.0319627i
\(562\) −9.86758 + 13.5816i −0.416239 + 0.572903i
\(563\) 6.29897 8.66979i 0.265470 0.365388i −0.655384 0.755296i \(-0.727493\pi\)
0.920854 + 0.389908i \(0.127493\pi\)
\(564\) 39.8563 28.9573i 1.67825 1.21932i
\(565\) 27.1956 + 14.0121i 1.14413 + 0.589495i
\(566\) −40.7776 29.6266i −1.71401 1.24530i
\(567\) 13.6672 4.44074i 0.573969 0.186494i
\(568\) 11.9567i 0.501692i
\(569\) −12.7060 39.1051i −0.532664 1.63937i −0.748643 0.662973i \(-0.769294\pi\)
0.215979 0.976398i \(-0.430706\pi\)
\(570\) 7.17501 + 7.24022i 0.300528 + 0.303259i
\(571\) −3.66515 + 11.2802i −0.153382 + 0.472061i −0.997993 0.0633191i \(-0.979831\pi\)
0.844612 + 0.535380i \(0.179831\pi\)
\(572\) −4.99758 1.62381i −0.208959 0.0678950i
\(573\) 13.2087 + 18.1802i 0.551801 + 0.759489i
\(574\) −10.9669 −0.457751
\(575\) 1.48119 + 1.09675i 0.0617698 + 0.0457378i
\(576\) −10.2880 −0.428667
\(577\) −1.82526 2.51225i −0.0759864 0.104586i 0.769332 0.638849i \(-0.220589\pi\)
−0.845318 + 0.534263i \(0.820589\pi\)
\(578\) 29.1977 + 9.48689i 1.21446 + 0.394603i
\(579\) 16.2248 49.9349i 0.674281 2.07522i
\(580\) 3.41634 6.63063i 0.141856 0.275322i
\(581\) 3.97703 + 12.2400i 0.164995 + 0.507803i
\(582\) 11.0361i 0.457460i
\(583\) −7.06511 + 2.29559i −0.292607 + 0.0950738i
\(584\) −5.15679 3.74663i −0.213390 0.155037i
\(585\) 14.8745 + 29.5223i 0.614986 + 1.22060i
\(586\) 4.74539 3.44773i 0.196030 0.142424i
\(587\) −25.8043 + 35.5166i −1.06506 + 1.46593i −0.190076 + 0.981769i \(0.560873\pi\)
−0.874981 + 0.484157i \(0.839127\pi\)
\(588\) 9.59588 13.2076i 0.395728 0.544672i
\(589\) −0.756612 + 0.549711i −0.0311757 + 0.0226504i
\(590\) −31.6072 + 4.85963i −1.30125 + 0.200068i
\(591\) 14.1942 + 10.3127i 0.583872 + 0.424208i
\(592\) 25.6645 8.33891i 1.05481 0.342727i
\(593\) 0.915667i 0.0376019i 0.999823 + 0.0188010i \(0.00598489\pi\)
−0.999823 + 0.0188010i \(0.994015\pi\)
\(594\) −0.0340260 0.104721i −0.00139610 0.00429676i
\(595\) −2.33913 + 1.17855i −0.0958948 + 0.0483157i
\(596\) −3.18246 + 9.79462i −0.130359 + 0.401203i
\(597\) −33.0659 10.7438i −1.35330 0.439713i
\(598\) −2.01549 2.77409i −0.0824196 0.113441i
\(599\) 37.0015 1.51184 0.755919 0.654665i \(-0.227190\pi\)
0.755919 + 0.654665i \(0.227190\pi\)
\(600\) −11.2372 + 3.53912i −0.458757 + 0.144484i
\(601\) 27.8575 1.13633 0.568166 0.822914i \(-0.307653\pi\)
0.568166 + 0.822914i \(0.307653\pi\)
\(602\) −3.04289 4.18818i −0.124019 0.170698i
\(603\) −20.4540 6.64590i −0.832950 0.270642i
\(604\) 2.01595 6.20446i 0.0820280 0.252456i
\(605\) 23.1612 + 3.77584i 0.941635 + 0.153510i
\(606\) 12.3618 + 38.0457i 0.502164 + 1.54550i
\(607\) 5.29957i 0.215103i 0.994200 + 0.107552i \(0.0343011\pi\)
−0.994200 + 0.107552i \(0.965699\pi\)
\(608\) 6.62563 2.15280i 0.268705 0.0873075i
\(609\) −7.01805 5.09892i −0.284386 0.206618i
\(610\) 8.65848 53.1115i 0.350572 2.15042i
\(611\) −54.8399 + 39.8435i −2.21858 + 1.61190i
\(612\) 1.91807 2.63999i 0.0775332 0.106715i
\(613\) 26.1853 36.0410i 1.05762 1.45568i 0.175602 0.984461i \(-0.443813\pi\)
0.882014 0.471223i \(-0.156187\pi\)
\(614\) 32.2885 23.4590i 1.30306 0.946727i
\(615\) 14.4369 14.3069i 0.582154 0.576911i
\(616\) −0.875991 0.636445i −0.0352947 0.0256431i
\(617\) 1.08419 0.352276i 0.0436480 0.0141821i −0.287112 0.957897i \(-0.592695\pi\)
0.330760 + 0.943715i \(0.392695\pi\)
\(618\) 45.9763i 1.84944i
\(619\) −0.945273 2.90925i −0.0379937 0.116933i 0.930261 0.366899i \(-0.119580\pi\)
−0.968255 + 0.249966i \(0.919580\pi\)
\(620\) 0.471322 + 3.06549i 0.0189288 + 0.123113i
\(621\) 0.00945422 0.0290971i 0.000379385 0.00116763i
\(622\) −37.7716 12.2727i −1.51450 0.492092i
\(623\) −12.5611 17.2889i −0.503250 0.692664i
\(624\) 58.0318 2.32313
\(625\) 20.4880 14.3263i 0.819519 0.573052i
\(626\) 26.0827 1.04248
\(627\) −1.02053 1.40464i −0.0407561 0.0560960i
\(628\) 20.5603 + 6.68045i 0.820446 + 0.266579i
\(629\) −1.29777 + 3.99413i −0.0517455 + 0.159256i
\(630\) −2.97017 19.3181i −0.118334 0.769650i
\(631\) −13.5059 41.5667i −0.537660 1.65475i −0.737831 0.674985i \(-0.764150\pi\)
0.200172 0.979761i \(-0.435850\pi\)
\(632\) 8.91652i 0.354680i
\(633\) −19.5315 + 6.34616i −0.776306 + 0.252237i
\(634\) −8.63348 6.27259i −0.342879 0.249116i
\(635\) 16.2032 16.0573i 0.643004 0.637213i
\(636\) −30.6281 + 22.2526i −1.21448 + 0.882374i
\(637\) −13.2034 + 18.1729i −0.523136 + 0.720035i
\(638\) −1.75384 + 2.41395i −0.0694352 + 0.0955694i
\(639\) −29.7414 + 21.6084i −1.17655 + 0.854814i
\(640\) −2.68388 + 16.4630i −0.106090 + 0.650758i
\(641\) 6.56530 + 4.76997i 0.259314 + 0.188402i 0.709844 0.704358i \(-0.248765\pi\)
−0.450531 + 0.892761i \(0.648765\pi\)
\(642\) 9.71142 3.15543i 0.383279 0.124535i
\(643\) 35.4679i 1.39872i 0.714771 + 0.699359i \(0.246531\pi\)
−0.714771 + 0.699359i \(0.753469\pi\)
\(644\) 0.266756 + 0.820990i 0.0105117 + 0.0323515i
\(645\) 9.46938 + 1.54374i 0.372857 + 0.0607848i
\(646\) −0.427823 + 1.31670i −0.0168325 + 0.0518050i
\(647\) 45.6697 + 14.8390i 1.79546 + 0.583381i 0.999751 0.0222980i \(-0.00709825\pi\)
0.795709 + 0.605679i \(0.207098\pi\)
\(648\) 5.16036 + 7.10263i 0.202718 + 0.279017i
\(649\) 5.44698 0.213813
\(650\) −44.3641 + 13.9723i −1.74010 + 0.548040i
\(651\) 3.60705 0.141371
\(652\) −11.7314 16.1469i −0.459437 0.632360i
\(653\) −24.6089 7.99592i −0.963021 0.312904i −0.215025 0.976608i \(-0.568983\pi\)
−0.747995 + 0.663704i \(0.768983\pi\)
\(654\) 1.17950 3.63011i 0.0461219 0.141949i
\(655\) 14.8604 7.48726i 0.580642 0.292551i
\(656\) −5.48149 16.8703i −0.214016 0.658674i
\(657\) 19.5981i 0.764594i
\(658\) 38.1161 12.3847i 1.48592 0.482805i
\(659\) 5.96551 + 4.33420i 0.232383 + 0.168836i 0.697883 0.716212i \(-0.254125\pi\)
−0.465500 + 0.885048i \(0.654125\pi\)
\(660\) −5.69105 + 0.875004i −0.221524 + 0.0340595i
\(661\) 17.5746 12.7687i 0.683572 0.496644i −0.190968 0.981596i \(-0.561163\pi\)
0.874541 + 0.484952i \(0.161163\pi\)
\(662\) −17.3134 + 23.8299i −0.672905 + 0.926174i
\(663\) −5.30852 + 7.30655i −0.206166 + 0.283763i
\(664\) −6.36096 + 4.62150i −0.246853 + 0.179349i
\(665\) 1.58873 + 3.15323i 0.0616081 + 0.122277i
\(666\) −25.3532 18.4202i −0.982417 0.713768i
\(667\) −0.788484 + 0.256194i −0.0305302 + 0.00991987i
\(668\) 20.7971i 0.804665i
\(669\) −1.49966 4.61547i −0.0579801 0.178444i
\(670\) 13.8595 26.8993i 0.535438 1.03921i
\(671\) −2.83246 + 8.71740i −0.109346 + 0.336532i
\(672\) −25.5543 8.30310i −0.985779 0.320299i
\(673\) 20.0390 + 27.5813i 0.772446 + 1.06318i 0.996076 + 0.0885063i \(0.0282093\pi\)
−0.223630 + 0.974674i \(0.571791\pi\)
\(674\) −12.5751 −0.484376
\(675\) −0.333522 0.246959i −0.0128373 0.00950545i
\(676\) 17.5666 0.675639
\(677\) −16.0452 22.0843i −0.616667 0.848770i 0.380438 0.924807i \(-0.375773\pi\)
−0.997105 + 0.0760367i \(0.975773\pi\)
\(678\) −59.3159 19.2729i −2.27801 0.740171i
\(679\) −1.18131 + 3.63571i −0.0453347 + 0.139526i
\(680\) −1.12636 1.13659i −0.0431939 0.0435864i
\(681\) 11.8318 + 36.4145i 0.453395 + 1.39541i
\(682\) 1.24069i 0.0475086i
\(683\) −46.2000 + 15.0113i −1.76779 + 0.574391i −0.997959 0.0638523i \(-0.979661\pi\)
−0.769835 + 0.638243i \(0.779661\pi\)
\(684\) −3.55881 2.58563i −0.136074 0.0988639i
\(685\) −5.42808 2.79674i −0.207396 0.106858i
\(686\) 27.4336 19.9317i 1.04742 0.760996i
\(687\) −38.3559 + 52.7924i −1.46337 + 2.01415i
\(688\) 4.92173 6.77418i 0.187639 0.258263i
\(689\) 42.1424 30.6183i 1.60550 1.16646i
\(690\) −3.34002 1.72090i −0.127152 0.0655136i
\(691\) −20.1101 14.6108i −0.765023 0.555822i 0.135424 0.990788i \(-0.456760\pi\)
−0.900447 + 0.434966i \(0.856760\pi\)
\(692\) −9.07878 + 2.94987i −0.345123 + 0.112137i
\(693\) 3.32915i 0.126464i
\(694\) 12.6753 + 39.0106i 0.481148 + 1.48082i
\(695\) 19.3372 + 19.5129i 0.733500 + 0.740166i
\(696\) 1.63768 5.04026i 0.0620761 0.191051i
\(697\) 2.62550 + 0.853075i 0.0994478 + 0.0323125i
\(698\) 23.5471 + 32.4099i 0.891273 + 1.22673i
\(699\) 49.0042 1.85351
\(700\) 11.7090 + 0.105932i 0.442559 + 0.00400384i
\(701\) 36.5974 1.38226 0.691132 0.722728i \(-0.257112\pi\)
0.691132 + 0.722728i \(0.257112\pi\)
\(702\) 0.453833 + 0.624648i 0.0171288 + 0.0235758i
\(703\) 5.38424 + 1.74944i 0.203070 + 0.0659815i
\(704\) −0.761912 + 2.34492i −0.0287156 + 0.0883777i
\(705\) −34.0199 + 66.0277i −1.28126 + 2.48675i
\(706\) 15.6538 + 48.1774i 0.589138 + 1.81318i
\(707\) 13.8570i 0.521144i
\(708\) 26.4005 8.57805i 0.992192 0.322383i
\(709\) 12.8729 + 9.35272i 0.483452 + 0.351249i 0.802661 0.596436i \(-0.203417\pi\)
−0.319208 + 0.947685i \(0.603417\pi\)
\(710\) −23.2738 46.1928i −0.873451 1.73359i
\(711\) −22.1791 + 16.1141i −0.831783 + 0.604326i
\(712\) 7.67389 10.5622i 0.287591 0.395835i
\(713\) 0.202627 0.278893i 0.00758846 0.0104446i
\(714\) 4.31992 3.13861i 0.161669 0.117459i
\(715\) 7.83054 1.20395i 0.292846 0.0450253i
\(716\) 13.6376 + 9.90832i 0.509662 + 0.370291i
\(717\) 54.5504 17.7245i 2.03722 0.661934i
\(718\) 34.8024i 1.29882i
\(719\) −13.4436 41.3752i −0.501362 1.54303i −0.806802 0.590823i \(-0.798803\pi\)
0.305439 0.952212i \(-0.401197\pi\)
\(720\) 28.2322 14.2245i 1.05215 0.530117i
\(721\) −4.92135 + 15.1464i −0.183281 + 0.564080i
\(722\) 1.77497 + 0.576721i 0.0660574 + 0.0214633i
\(723\) 15.6483 + 21.5380i 0.581965 + 0.801006i
\(724\) 12.8757 0.478523
\(725\) −0.101738 + 11.2454i −0.00377844 + 0.417643i
\(726\) −47.8406 −1.77553
\(727\) 23.6438 + 32.5429i 0.876900 + 1.20695i 0.977270 + 0.211999i \(0.0679972\pi\)
−0.100370 + 0.994950i \(0.532003\pi\)
\(728\) 7.22101 + 2.34625i 0.267628 + 0.0869577i
\(729\) 8.15339 25.0935i 0.301977 0.929391i
\(730\) −27.2153 4.43676i −1.00728 0.164212i
\(731\) 0.402690 + 1.23935i 0.0148940 + 0.0458390i
\(732\) 46.7123i 1.72653i
\(733\) 39.8808 12.9581i 1.47303 0.478617i 0.541009 0.841017i \(-0.318043\pi\)
0.932023 + 0.362400i \(0.118043\pi\)
\(734\) 28.8896 + 20.9895i 1.06633 + 0.774736i
\(735\) −3.96037 + 24.2931i −0.146080 + 0.896063i
\(736\) −2.07751 + 1.50940i −0.0765780 + 0.0556372i
\(737\) −3.02957 + 4.16985i −0.111596 + 0.153598i
\(738\) −12.1083 + 16.6657i −0.445713 + 0.613471i
\(739\) −36.7229 + 26.6807i −1.35087 + 0.981467i −0.351906 + 0.936035i \(0.614466\pi\)
−0.998967 + 0.0454314i \(0.985534\pi\)
\(740\) 13.3357 13.2156i 0.490231 0.485816i
\(741\) 9.84951 + 7.15609i 0.361831 + 0.262885i
\(742\) −29.2908 + 9.51717i −1.07530 + 0.349386i
\(743\) 12.1979i 0.447497i −0.974647 0.223749i \(-0.928171\pi\)
0.974647 0.223749i \(-0.0718295\pi\)
\(744\) 0.680961 + 2.09578i 0.0249653 + 0.0768352i
\(745\) −2.35959 15.3469i −0.0864488 0.562266i
\(746\) 0.591011 1.81894i 0.0216384 0.0665963i
\(747\) 22.9913 + 7.47031i 0.841206 + 0.273324i
\(748\) −0.459680 0.632695i −0.0168075 0.0231336i
\(749\) 3.53708 0.129242
\(750\) −36.5241 + 35.5461i −1.33367 + 1.29796i
\(751\) 3.84449 0.140288 0.0701438 0.997537i \(-0.477654\pi\)
0.0701438 + 0.997537i \(0.477654\pi\)
\(752\) 38.1024 + 52.4434i 1.38945 + 1.91242i
\(753\) −5.11221 1.66106i −0.186299 0.0605324i
\(754\) 6.46551 19.8988i 0.235460 0.724672i
\(755\) 1.49470 + 9.72157i 0.0543977 + 0.353804i
\(756\) −0.0600660 0.184864i −0.00218458 0.00672345i
\(757\) 15.1935i 0.552218i 0.961126 + 0.276109i \(0.0890452\pi\)
−0.961126 + 0.276109i \(0.910955\pi\)
\(758\) −7.96464 + 2.58787i −0.289289 + 0.0939956i
\(759\) 0.517761 + 0.376175i 0.0187935 + 0.0136543i
\(760\) −1.53217 + 1.51837i −0.0555778 + 0.0550772i
\(761\) −0.935508 + 0.679686i −0.0339121 + 0.0246386i −0.604612 0.796520i \(-0.706672\pi\)
0.570700 + 0.821159i \(0.306672\pi\)
\(762\) −27.3350 + 37.6234i −0.990243 + 1.36295i
\(763\) 0.777144 1.06965i 0.0281345 0.0387238i
\(764\) 11.0390 8.02030i 0.399377 0.290164i
\(765\) −0.791616 + 4.85580i −0.0286209 + 0.175562i
\(766\) −30.8004 22.3778i −1.11286 0.808544i
\(767\) −36.3255 + 11.8029i −1.31164 + 0.426177i
\(768\) 50.9498i 1.83849i
\(769\) 15.4079 + 47.4205i 0.555621 + 1.71003i 0.694297 + 0.719689i \(0.255715\pi\)
−0.138676 + 0.990338i \(0.544285\pi\)
\(770\) −4.62309 0.753678i −0.166605 0.0271607i
\(771\) −1.33498 + 4.10864i −0.0480780 + 0.147969i
\(772\) −30.3204 9.85169i −1.09125 0.354570i
\(773\) −28.8184 39.6651i −1.03653 1.42666i −0.899933 0.436028i \(-0.856385\pi\)
−0.136592 0.990627i \(-0.543615\pi\)
\(774\) −9.72406 −0.349524
\(775\) −2.71422 3.80777i −0.0974976 0.136779i
\(776\) −2.33545 −0.0838378
\(777\) −12.8343 17.6649i −0.460429 0.633726i
\(778\) 60.3255 + 19.6010i 2.16278 + 0.702728i
\(779\) 1.14998 3.53927i 0.0412022 0.126807i
\(780\) 36.0572 18.1671i 1.29105 0.650485i
\(781\) 2.72256 + 8.37918i 0.0974208 + 0.299830i
\(782\) 0.510323i 0.0182491i
\(783\) 0.177545 0.0576878i 0.00634493 0.00206159i
\(784\) 17.3787 + 12.6264i 0.620668 + 0.450942i
\(785\) −32.2153 + 4.95312i −1.14981 + 0.176785i
\(786\) −27.4443 + 19.9394i −0.978905 + 0.711216i
\(787\) −5.82424 + 8.01638i −0.207612 + 0.285753i −0.900107 0.435670i \(-0.856512\pi\)
0.692495 + 0.721423i \(0.256512\pi\)
\(788\) 6.26186 8.61871i 0.223070 0.307029i
\(789\) 46.9998 34.1473i 1.67324 1.21568i
\(790\) −17.3561 34.4475i −0.617501 1.22559i
\(791\) −17.4780 12.6985i −0.621445 0.451506i
\(792\) −1.93432 + 0.628498i −0.0687330 + 0.0223327i
\(793\) 64.2732i 2.28241i
\(794\) 6.47539 + 19.9292i 0.229803 + 0.707261i
\(795\) 26.1430 50.7398i 0.927197 1.79956i
\(796\) −6.52360 + 20.0776i −0.231223 + 0.711631i
\(797\) 29.8393 + 9.69538i 1.05696 + 0.343428i 0.785397 0.618992i \(-0.212459\pi\)
0.271566 + 0.962420i \(0.412459\pi\)
\(798\) −4.23096 5.82342i −0.149774 0.206147i
\(799\) −10.0884 −0.356902
\(800\) 10.4639 + 33.2242i 0.369953 + 1.17465i
\(801\) −40.1411 −1.41831
\(802\) −36.6072 50.3854i −1.29264 1.77917i
\(803\) 4.46695 + 1.45140i 0.157635 + 0.0512188i
\(804\) −8.11699 + 24.9815i −0.286264 + 0.881031i
\(805\) −0.916126 0.924451i −0.0322892 0.0325826i
\(806\) 2.68841 + 8.27409i 0.0946954 + 0.291442i
\(807\) 73.0667i 2.57207i
\(808\) −8.05123 + 2.61600i −0.283241 + 0.0920306i
\(809\) −33.4947 24.3353i −1.17761 0.855585i −0.185711 0.982604i \(-0.559459\pi\)
−0.991900 + 0.127020i \(0.959459\pi\)
\(810\) 33.7615 + 17.3952i 1.18626 + 0.611204i
\(811\) −18.7639 + 13.6328i −0.658891 + 0.478713i −0.866288 0.499544i \(-0.833501\pi\)
0.207397 + 0.978257i \(0.433501\pi\)
\(812\) −3.09605 + 4.26135i −0.108650 + 0.149544i
\(813\) 28.4091 39.1018i 0.996350 1.37136i
\(814\) −6.07609 + 4.41454i −0.212967 + 0.154730i
\(815\) 26.7496 + 13.7824i 0.936997 + 0.482775i
\(816\) 6.98726 + 5.07654i 0.244603 + 0.177715i
\(817\) 1.67069 0.542841i 0.0584501 0.0189916i
\(818\) 23.9002i 0.835649i
\(819\) −7.21382 22.2019i −0.252071 0.775796i
\(820\) −8.68714 8.76609i −0.303368 0.306125i
\(821\) 6.89781 21.2293i 0.240735 0.740907i −0.755574 0.655064i \(-0.772642\pi\)
0.996309 0.0858428i \(-0.0273583\pi\)
\(822\) 11.8391 + 3.84676i 0.412936 + 0.134171i
\(823\) −1.01857 1.40194i −0.0355051 0.0488685i 0.790895 0.611951i \(-0.209615\pi\)
−0.826400 + 0.563083i \(0.809615\pi\)
\(824\) −9.72949 −0.338943
\(825\) 7.06908 5.03891i 0.246114 0.175432i
\(826\) 22.5823 0.785739
\(827\) 25.2382 + 34.7373i 0.877617 + 1.20794i 0.977075 + 0.212894i \(0.0682888\pi\)
−0.0994588 + 0.995042i \(0.531711\pi\)
\(828\) 1.54212 + 0.501064i 0.0535923 + 0.0174132i
\(829\) 4.44809 13.6898i 0.154489 0.475467i −0.843620 0.536940i \(-0.819580\pi\)
0.998109 + 0.0614735i \(0.0195800\pi\)
\(830\) −15.5787 + 30.2361i −0.540745 + 1.04951i
\(831\) −7.02438 21.6188i −0.243673 0.749949i
\(832\) 17.2891i 0.599391i
\(833\) −3.17947 + 1.03307i −0.110162 + 0.0357939i
\(834\) −45.3085 32.9186i −1.56891 1.13988i
\(835\) −14.1086 28.0022i −0.488249 0.969054i
\(836\) −0.852896 + 0.619665i −0.0294980 + 0.0214316i
\(837\) −0.0456261 + 0.0627990i −0.00157707 + 0.00217065i
\(838\) 23.3971 32.2033i 0.808238 1.11244i
\(839\) −19.6285 + 14.2610i −0.677652 + 0.492343i −0.872578 0.488475i \(-0.837553\pi\)
0.194926 + 0.980818i \(0.437553\pi\)
\(840\) 8.22300 1.26429i 0.283721 0.0436223i
\(841\) 19.3689 + 14.0723i 0.667892 + 0.485252i
\(842\) 6.15572 2.00011i 0.212140 0.0689285i
\(843\) 21.9710i 0.756723i
\(844\) 3.85338 + 11.8595i 0.132639 + 0.408220i
\(845\) −23.6525 + 11.9171i −0.813669 + 0.409960i
\(846\) 23.2629 71.5959i 0.799795 2.46152i
\(847\) −15.7606 5.12092i −0.541539 0.175957i
\(848\) −29.2803 40.3008i −1.00549 1.38394i
\(849\) −65.9664 −2.26396
\(850\) −6.56389 2.19858i −0.225140 0.0754108i
\(851\) −2.08680 −0.0715347
\(852\) 26.3915 + 36.3248i 0.904157 + 1.24447i
\(853\) −30.8855 10.0353i −1.05750 0.343603i −0.271893 0.962328i \(-0.587650\pi\)
−0.785608 + 0.618725i \(0.787650\pi\)
\(854\) −11.7429 + 36.1410i −0.401834 + 1.23672i
\(855\) 6.54581 + 1.06713i 0.223862 + 0.0364950i
\(856\) 0.667752 + 2.05513i 0.0228233 + 0.0702429i
\(857\) 4.24327i 0.144947i 0.997370 + 0.0724736i \(0.0230893\pi\)
−0.997370 + 0.0724736i \(0.976911\pi\)
\(858\) −15.3607 + 4.99101i −0.524407 + 0.170390i
\(859\) −37.2437 27.0591i −1.27074 0.923245i −0.271505 0.962437i \(-0.587522\pi\)
−0.999232 + 0.0391923i \(0.987522\pi\)
\(860\) 0.937359 5.74980i 0.0319637 0.196066i
\(861\) −11.6119 + 8.43651i −0.395731 + 0.287515i
\(862\) −11.7637 + 16.1913i −0.400672 + 0.551478i
\(863\) −7.89742 + 10.8699i −0.268831 + 0.370015i −0.921995 0.387202i \(-0.873441\pi\)
0.653163 + 0.757217i \(0.273441\pi\)
\(864\) 0.467797 0.339875i 0.0159148 0.0115628i
\(865\) 10.2229 10.1308i 0.347589 0.344458i
\(866\) −42.6041 30.9537i −1.44775 1.05185i
\(867\) 38.2126 12.4160i 1.29777 0.421671i
\(868\) 2.19020i 0.0743401i
\(869\) 2.03030 + 6.24863i 0.0688733 + 0.211970i
\(870\) −3.48399 22.6600i −0.118118 0.768246i
\(871\) 11.1685 34.3731i 0.378430 1.16469i
\(872\) 0.768204 + 0.249605i 0.0260147 + 0.00845268i
\(873\) 4.22067 + 5.80925i 0.142848 + 0.196613i
\(874\) −0.687935 −0.0232698
\(875\) −15.8374 + 7.80067i −0.535401 + 0.263711i
\(876\) 23.9362 0.808729
\(877\) 29.8521 + 41.0879i 1.00803 + 1.38744i 0.920263 + 0.391300i \(0.127974\pi\)
0.0877709 + 0.996141i \(0.472026\pi\)
\(878\) 34.6695 + 11.2648i 1.17004 + 0.380169i
\(879\) 2.37222 7.30095i 0.0800131 0.246255i
\(880\) −1.15134 7.48835i −0.0388117 0.252432i
\(881\) 2.23657 + 6.88344i 0.0753518 + 0.231909i 0.981637 0.190757i \(-0.0610943\pi\)
−0.906285 + 0.422666i \(0.861094\pi\)
\(882\) 24.9464i 0.839990i
\(883\) 11.8282 3.84320i 0.398049 0.129334i −0.103150 0.994666i \(-0.532892\pi\)
0.501200 + 0.865332i \(0.332892\pi\)
\(884\) 4.43653 + 3.22333i 0.149217 + 0.108412i
\(885\) −29.7275 + 29.4598i −0.999279 + 0.990280i
\(886\) −50.8266 + 36.9277i −1.70755 + 1.24061i
\(887\) −12.7792 + 17.5890i −0.429083 + 0.590582i −0.967742 0.251942i \(-0.918931\pi\)
0.538660 + 0.842524i \(0.318931\pi\)
\(888\) 7.84081 10.7920i 0.263120 0.362154i
\(889\) −13.0325 + 9.46864i −0.437095 + 0.317568i
\(890\) 9.08743 55.7427i 0.304611 1.86850i
\(891\) −5.23362 3.80245i −0.175333 0.127387i
\(892\) −2.80251 + 0.910590i −0.0938349 + 0.0304888i
\(893\) 13.5995i 0.455091i
\(894\) 9.78174 + 30.1051i 0.327150 + 1.00687i
\(895\) −25.0840 4.08932i −0.838467 0.136691i
\(896\) 3.63996 11.2027i 0.121603 0.374255i
\(897\) −4.26803 1.38677i −0.142505 0.0463028i
\(898\) 34.3919 + 47.3364i 1.14767 + 1.57964i
\(899\) 2.10348 0.0701549
\(900\) 13.0886 17.6764i 0.436286 0.589212i
\(901\) 7.75256 0.258275
\(902\) 2.90185 + 3.99405i 0.0966210 + 0.132987i
\(903\) −6.44367 2.09367i −0.214432 0.0696731i
\(904\) 4.07853 12.5524i 0.135650 0.417487i
\(905\) −17.3364 + 8.73481i −0.576283 + 0.290355i
\(906\) −6.19631 19.0703i −0.205859 0.633568i
\(907\) 15.1334i 0.502495i −0.967923 0.251247i \(-0.919159\pi\)
0.967923 0.251247i \(-0.0808408\pi\)
\(908\) 22.1108 7.18425i 0.733774 0.238418i
\(909\) 21.0574 + 15.2991i 0.698430 + 0.507439i
\(910\) 32.4642 4.99139i 1.07618 0.165463i
\(911\) 10.4323 7.57952i 0.345638 0.251121i −0.401399 0.915903i \(-0.631476\pi\)
0.747037 + 0.664783i \(0.231476\pi\)
\(912\) 6.84337 9.41909i 0.226607 0.311897i
\(913\) 3.40539 4.68711i 0.112702 0.155121i
\(914\) 25.9708 18.8689i 0.859038 0.624128i
\(915\) −31.6893 62.8954i −1.04762 2.07926i
\(916\) 32.0555 + 23.2896i 1.05914 + 0.769512i
\(917\) −11.1755 + 3.63116i −0.369049 + 0.119911i
\(918\) 0.114911i 0.00379262i
\(919\) 5.12350 + 15.7685i 0.169009 + 0.520155i 0.999309 0.0371607i \(-0.0118314\pi\)
−0.830301 + 0.557316i \(0.811831\pi\)
\(920\) 0.364177 0.706815i 0.0120065 0.0233030i
\(921\) 16.1410 49.6770i 0.531865 1.63691i
\(922\) 70.3824 + 22.8686i 2.31792 + 0.753138i
\(923\) −36.3131 49.9806i −1.19526 1.64513i
\(924\) 4.06607 0.133764
\(925\) −8.99041 + 26.8409i −0.295603 + 0.882525i
\(926\) 26.6355 0.875295
\(927\) 17.5833 + 24.2013i 0.577511 + 0.794876i
\(928\) −14.9022 4.84201i −0.489188 0.158947i
\(929\) 7.23826 22.2771i 0.237480 0.730887i −0.759303 0.650737i \(-0.774460\pi\)
0.996783 0.0801502i \(-0.0255400\pi\)
\(930\) 6.71024 + 6.77122i 0.220037 + 0.222037i
\(931\) 1.39262 + 4.28605i 0.0456413 + 0.140470i
\(932\) 29.7553i 0.974667i
\(933\) −49.4338 + 16.0620i −1.61839 + 0.525847i
\(934\) 18.1671 + 13.1992i 0.594446 + 0.431890i
\(935\) 1.04815 + 0.540044i 0.0342781 + 0.0176613i
\(936\) 11.5379 8.38281i 0.377130 0.274001i
\(937\) −6.74346 + 9.28157i −0.220299 + 0.303216i −0.904834 0.425764i \(-0.860005\pi\)
0.684535 + 0.728980i \(0.260005\pi\)
\(938\) −12.5601 + 17.2875i −0.410103 + 0.564458i
\(939\) 27.6165 20.0646i 0.901232 0.654783i
\(940\) 40.0919 + 20.6568i 1.30765 + 0.673751i
\(941\) 19.7548 + 14.3527i 0.643988 + 0.467884i 0.861218 0.508236i \(-0.169702\pi\)
−0.217230 + 0.976120i \(0.569702\pi\)
\(942\) 63.1949 20.5333i 2.05900 0.669010i
\(943\) 1.37174i 0.0446699i
\(944\) 11.2871 + 34.7381i 0.367364 + 1.13063i
\(945\) 0.206286 + 0.208161i 0.00671049 + 0.00677147i
\(946\) −0.720148 + 2.21639i −0.0234140 + 0.0720609i
\(947\) −13.7884 4.48012i −0.448063 0.145584i 0.0762898 0.997086i \(-0.475693\pi\)
−0.524353 + 0.851501i \(0.675693\pi\)
\(948\) 19.6810 + 27.0886i 0.639210 + 0.879796i
\(949\) −32.9348 −1.06911
\(950\) −2.96378 + 8.84838i −0.0961576 + 0.287079i
\(951\) −13.9665 −0.452894
\(952\) 0.664191 + 0.914181i 0.0215266 + 0.0296288i
\(953\) 29.3662 + 9.54164i 0.951263 + 0.309084i 0.743229 0.669037i \(-0.233293\pi\)
0.208034 + 0.978122i \(0.433293\pi\)
\(954\) −17.8767 + 55.0188i −0.578779 + 1.78130i
\(955\) −9.42247 + 18.2877i −0.304904 + 0.591775i
\(956\) −10.7623 33.1230i −0.348078 1.07127i
\(957\) 3.90508i 0.126233i
\(958\) 37.7565 12.2678i 1.21986 0.396356i
\(959\) 3.48850 + 2.53454i 0.112650 + 0.0818447i
\(960\) −8.52421 16.9185i −0.275118 0.546041i
\(961\) 24.3719 17.7072i 0.786191 0.571201i
\(962\) 30.9553 42.6063i 0.998038 1.37368i
\(963\) 3.90520 5.37505i 0.125843 0.173208i
\(964\) 13.0778 9.50160i 0.421208 0.306026i
\(965\) 47.5080 7.30440i 1.52934 0.235137i
\(966\) 2.14655 + 1.55956i 0.0690643 + 0.0501781i
\(967\) 35.1873 11.4330i 1.13155 0.367662i 0.317383 0.948297i \(-0.397196\pi\)
0.814164 + 0.580636i \(0.197196\pi\)
\(968\) 10.1240i 0.325398i
\(969\) 0.559916 + 1.72324i 0.0179871 + 0.0553585i
\(970\) −9.02264 + 4.54597i −0.289699 + 0.145962i
\(971\) −9.63458 + 29.6522i −0.309188 + 0.951584i 0.668893 + 0.743359i \(0.266769\pi\)
−0.978081 + 0.208225i \(0.933231\pi\)
\(972\) −31.0033 10.0736i −0.994433 0.323111i
\(973\) −11.4027 15.6945i −0.365555 0.503143i
\(974\) −40.0968 −1.28478
\(975\) −36.2245 + 48.9218i −1.16011 + 1.56675i
\(976\) −61.4645 −1.96743
\(977\) −7.78955 10.7214i −0.249210 0.343008i 0.666024 0.745930i \(-0.267995\pi\)
−0.915234 + 0.402922i \(0.867995\pi\)
\(978\) −58.3431 18.9568i −1.86561 0.606173i
\(979\) −2.97278 + 9.14927i −0.0950104 + 0.292412i
\(980\) 14.7507 + 2.40473i 0.471194 + 0.0768163i
\(981\) −0.767440 2.36194i −0.0245025 0.0754109i
\(982\) 3.27431i 0.104487i
\(983\) −45.6279 + 14.8254i −1.45530 + 0.472857i −0.926632 0.375969i \(-0.877310\pi\)
−0.528672 + 0.848826i \(0.677310\pi\)
\(984\) −7.09397 5.15407i −0.226148 0.164306i
\(985\) −2.58437 + 15.8526i −0.0823448 + 0.505106i
\(986\) 2.51919 1.83030i 0.0802275 0.0582887i
\(987\) 30.8304 42.4344i 0.981343 1.35070i
\(988\) 4.34517 5.98061i 0.138238 0.190269i
\(989\) −0.523856 + 0.380604i −0.0166576 + 0.0121025i
\(990\) −6.24955 + 6.19326i −0.198624 + 0.196835i
\(991\) −47.7999 34.7287i −1.51842 1.10319i −0.962266 0.272111i \(-0.912278\pi\)
−0.556150 0.831082i \(-0.687722\pi\)
\(992\) 6.19645 2.01335i 0.196738 0.0639239i
\(993\) 38.5498i 1.22334i
\(994\) 11.2873 + 34.7387i 0.358011 + 1.10185i
\(995\) −4.83683 31.4589i −0.153338 0.997314i
\(996\) 9.12390 28.0805i 0.289102 0.889764i
\(997\) −9.03586 2.93593i −0.286169 0.0929818i 0.162415 0.986722i \(-0.448072\pi\)
−0.448584 + 0.893741i \(0.648072\pi\)
\(998\) −28.4119 39.1057i −0.899364 1.23787i
\(999\) 0.469891 0.0148667
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 475.2.n.b.39.5 96
25.9 even 10 inner 475.2.n.b.134.5 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.n.b.39.5 96 1.1 even 1 trivial
475.2.n.b.134.5 yes 96 25.9 even 10 inner