Properties

Label 392.2.z.a.53.6
Level $392$
Weight $2$
Character 392.53
Analytic conductor $3.130$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,2,Mod(37,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 21, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 392.z (of order \(42\), degree \(12\), 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: \(3.13013575923\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 53.6
Character \(\chi\) \(=\) 392.53
Dual form 392.2.z.a.37.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37066 - 0.348278i) q^{2} +(1.48945 - 1.60524i) q^{3} +(1.75740 + 0.954740i) q^{4} +(-1.25029 - 4.05335i) q^{5} +(-2.60059 + 1.68150i) q^{6} +(2.55536 + 0.685667i) q^{7} +(-2.07629 - 1.92069i) q^{8} +(-0.134159 - 1.79023i) q^{9} +O(q^{10})\) \(q+(-1.37066 - 0.348278i) q^{2} +(1.48945 - 1.60524i) q^{3} +(1.75740 + 0.954740i) q^{4} +(-1.25029 - 4.05335i) q^{5} +(-2.60059 + 1.68150i) q^{6} +(2.55536 + 0.685667i) q^{7} +(-2.07629 - 1.92069i) q^{8} +(-0.134159 - 1.79023i) q^{9} +(0.302031 + 5.99121i) q^{10} +(5.31750 + 0.398492i) q^{11} +(4.15015 - 1.39903i) q^{12} +(-1.33482 - 2.77179i) q^{13} +(-3.26372 - 1.82979i) q^{14} +(-8.36885 - 4.03023i) q^{15} +(2.17694 + 3.35573i) q^{16} +(0.221290 - 0.0333541i) q^{17} +(-0.439612 + 2.50052i) q^{18} +(-4.52324 + 2.61149i) q^{19} +(1.67262 - 8.31708i) q^{20} +(4.90673 - 3.08071i) q^{21} +(-7.14969 - 2.39817i) q^{22} +(2.76583 + 0.416882i) q^{23} +(-6.17568 + 0.472179i) q^{24} +(-10.7352 + 7.31915i) q^{25} +(0.864232 + 4.26406i) q^{26} +(2.06260 + 1.64487i) q^{27} +(3.83617 + 3.64470i) q^{28} +(-1.75874 + 1.40254i) q^{29} +(10.0672 + 8.43875i) q^{30} +(-0.285976 + 0.495326i) q^{31} +(-1.81512 - 5.35774i) q^{32} +(8.55981 - 7.94235i) q^{33} +(-0.314929 - 0.0313534i) q^{34} +(-0.415701 - 11.2151i) q^{35} +(1.47343 - 3.27425i) q^{36} +(2.64765 + 1.03913i) q^{37} +(7.10934 - 2.00412i) q^{38} +(-6.43754 - 1.98572i) q^{39} +(-5.18925 + 10.8173i) q^{40} +(-0.686642 + 3.00838i) q^{41} +(-7.79839 + 2.51369i) q^{42} +(-7.43650 + 1.69733i) q^{43} +(8.96455 + 5.77714i) q^{44} +(-7.08870 + 2.78211i) q^{45} +(-3.64582 - 1.53468i) q^{46} +(-9.37630 - 6.39265i) q^{47} +(8.62920 + 1.50366i) q^{48} +(6.05972 + 3.50425i) q^{49} +(17.2634 - 6.29321i) q^{50} +(0.276058 - 0.404903i) q^{51} +(0.300513 - 6.14556i) q^{52} +(-0.164186 + 0.0644382i) q^{53} +(-2.25425 - 2.97291i) q^{54} +(-5.03321 - 22.0519i) q^{55} +(-3.98870 - 6.33169i) q^{56} +(-2.54505 + 11.1506i) q^{57} +(2.89910 - 1.30988i) q^{58} +(2.49119 - 8.07623i) q^{59} +(-10.8596 - 15.0728i) q^{60} +(-1.03222 - 0.405116i) q^{61} +(0.564487 - 0.579323i) q^{62} +(0.884677 - 4.66668i) q^{63} +(0.621921 + 7.97579i) q^{64} +(-9.56611 + 8.87605i) q^{65} +(-14.4987 + 7.90504i) q^{66} +(11.4437 + 6.60700i) q^{67} +(0.420740 + 0.152658i) q^{68} +(4.78875 - 3.81890i) q^{69} +(-3.33617 + 15.5168i) q^{70} +(-0.725683 + 0.909977i) q^{71} +(-3.15992 + 3.97471i) q^{72} +(6.74083 - 4.59582i) q^{73} +(-3.26712 - 2.34641i) q^{74} +(-4.24054 + 28.1341i) q^{75} +(-10.4425 + 0.270933i) q^{76} +(13.3149 + 4.66432i) q^{77} +(8.13208 + 4.96379i) q^{78} +(4.67829 + 8.10303i) q^{79} +(10.8801 - 13.0196i) q^{80} +(11.0381 - 1.66373i) q^{81} +(1.98890 - 3.88431i) q^{82} +(1.51482 - 3.14556i) q^{83} +(11.5644 - 0.729394i) q^{84} +(-0.411873 - 0.855263i) q^{85} +(10.7840 + 0.263508i) q^{86} +(-0.368119 + 4.91221i) q^{87} +(-10.2753 - 11.0406i) q^{88} +(0.794611 + 10.6034i) q^{89} +(10.6851 - 1.34448i) q^{90} +(-1.51043 - 7.99816i) q^{91} +(4.46267 + 3.37328i) q^{92} +(0.369171 + 1.19682i) q^{93} +(10.6253 + 12.0277i) q^{94} +(16.2407 + 15.0691i) q^{95} +(-11.3040 - 5.06636i) q^{96} +8.28730 q^{97} +(-7.08535 - 6.91359i) q^{98} -9.57303i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37066 0.348278i −0.969201 0.246270i
\(3\) 1.48945 1.60524i 0.859933 0.926787i −0.138040 0.990427i \(-0.544080\pi\)
0.997973 + 0.0636398i \(0.0202709\pi\)
\(4\) 1.75740 + 0.954740i 0.878702 + 0.477370i
\(5\) −1.25029 4.05335i −0.559148 1.81271i −0.582290 0.812981i \(-0.697843\pi\)
0.0231418 0.999732i \(-0.492633\pi\)
\(6\) −2.60059 + 1.68150i −1.06169 + 0.686468i
\(7\) 2.55536 + 0.685667i 0.965835 + 0.259158i
\(8\) −2.07629 1.92069i −0.734078 0.679065i
\(9\) −0.134159 1.79023i −0.0447198 0.596744i
\(10\) 0.302031 + 5.99121i 0.0955105 + 1.89459i
\(11\) 5.31750 + 0.398492i 1.60329 + 0.120150i 0.846091 0.533038i \(-0.178950\pi\)
0.757196 + 0.653188i \(0.226569\pi\)
\(12\) 4.15015 1.39903i 1.19804 0.403864i
\(13\) −1.33482 2.77179i −0.370213 0.768756i 0.629755 0.776794i \(-0.283155\pi\)
−0.999968 + 0.00803866i \(0.997441\pi\)
\(14\) −3.26372 1.82979i −0.872266 0.489032i
\(15\) −8.36885 4.03023i −2.16083 1.04060i
\(16\) 2.17694 + 3.35573i 0.544236 + 0.838932i
\(17\) 0.221290 0.0333541i 0.0536707 0.00808955i −0.122152 0.992511i \(-0.538980\pi\)
0.175823 + 0.984422i \(0.443741\pi\)
\(18\) −0.439612 + 2.50052i −0.103618 + 0.589379i
\(19\) −4.52324 + 2.61149i −1.03770 + 0.599118i −0.919182 0.393834i \(-0.871148\pi\)
−0.118521 + 0.992952i \(0.537815\pi\)
\(20\) 1.67262 8.31708i 0.374010 1.85976i
\(21\) 4.90673 3.08071i 1.07074 0.672265i
\(22\) −7.14969 2.39817i −1.52432 0.511291i
\(23\) 2.76583 + 0.416882i 0.576716 + 0.0869259i 0.430922 0.902389i \(-0.358188\pi\)
0.145794 + 0.989315i \(0.453426\pi\)
\(24\) −6.17568 + 0.472179i −1.26061 + 0.0963831i
\(25\) −10.7352 + 7.31915i −2.14704 + 1.46383i
\(26\) 0.864232 + 4.26406i 0.169490 + 0.836251i
\(27\) 2.06260 + 1.64487i 0.396947 + 0.316555i
\(28\) 3.83617 + 3.64470i 0.724968 + 0.688783i
\(29\) −1.75874 + 1.40254i −0.326589 + 0.260446i −0.773033 0.634365i \(-0.781261\pi\)
0.446444 + 0.894811i \(0.352690\pi\)
\(30\) 10.0672 + 8.43875i 1.83801 + 1.54070i
\(31\) −0.285976 + 0.495326i −0.0513629 + 0.0889631i −0.890564 0.454858i \(-0.849690\pi\)
0.839201 + 0.543822i \(0.183023\pi\)
\(32\) −1.81512 5.35774i −0.320870 0.947123i
\(33\) 8.55981 7.94235i 1.49007 1.38258i
\(34\) −0.314929 0.0313534i −0.0540099 0.00537706i
\(35\) −0.415701 11.2151i −0.0702664 1.89569i
\(36\) 1.47343 3.27425i 0.245572 0.545709i
\(37\) 2.64765 + 1.03913i 0.435271 + 0.170831i 0.572851 0.819659i \(-0.305837\pi\)
−0.137580 + 0.990491i \(0.543932\pi\)
\(38\) 7.10934 2.00412i 1.15329 0.325111i
\(39\) −6.43754 1.98572i −1.03083 0.317969i
\(40\) −5.18925 + 10.8173i −0.820493 + 1.71037i
\(41\) −0.686642 + 3.00838i −0.107235 + 0.469829i 0.892585 + 0.450879i \(0.148889\pi\)
−0.999820 + 0.0189500i \(0.993968\pi\)
\(42\) −7.79839 + 2.51369i −1.20332 + 0.387870i
\(43\) −7.43650 + 1.69733i −1.13406 + 0.258841i −0.748041 0.663652i \(-0.769006\pi\)
−0.386014 + 0.922493i \(0.626148\pi\)
\(44\) 8.96455 + 5.77714i 1.35146 + 0.870937i
\(45\) −7.08870 + 2.78211i −1.05672 + 0.414733i
\(46\) −3.64582 1.53468i −0.537546 0.226276i
\(47\) −9.37630 6.39265i −1.36767 0.932464i −0.999997 0.00251019i \(-0.999201\pi\)
−0.367677 0.929954i \(-0.619847\pi\)
\(48\) 8.62920 + 1.50366i 1.24552 + 0.217035i
\(49\) 6.05972 + 3.50425i 0.865675 + 0.500607i
\(50\) 17.2634 6.29321i 2.44142 0.889994i
\(51\) 0.276058 0.404903i 0.0386559 0.0566977i
\(52\) 0.300513 6.14556i 0.0416736 0.852236i
\(53\) −0.164186 + 0.0644382i −0.0225527 + 0.00885127i −0.376591 0.926380i \(-0.622904\pi\)
0.354038 + 0.935231i \(0.384808\pi\)
\(54\) −2.25425 2.97291i −0.306764 0.404562i
\(55\) −5.03321 22.0519i −0.678678 2.97348i
\(56\) −3.98870 6.33169i −0.533013 0.846107i
\(57\) −2.54505 + 11.1506i −0.337100 + 1.47693i
\(58\) 2.89910 1.30988i 0.380670 0.171996i
\(59\) 2.49119 8.07623i 0.324325 1.05143i −0.635798 0.771856i \(-0.719329\pi\)
0.960123 0.279579i \(-0.0901950\pi\)
\(60\) −10.8596 15.0728i −1.40197 1.94589i
\(61\) −1.03222 0.405116i −0.132162 0.0518698i 0.298338 0.954460i \(-0.403568\pi\)
−0.430500 + 0.902590i \(0.641663\pi\)
\(62\) 0.564487 0.579323i 0.0716899 0.0735740i
\(63\) 0.884677 4.66668i 0.111459 0.587946i
\(64\) 0.621921 + 7.97579i 0.0777401 + 0.996974i
\(65\) −9.56611 + 8.87605i −1.18653 + 1.10094i
\(66\) −14.4987 + 7.90504i −1.78467 + 0.973043i
\(67\) 11.4437 + 6.60700i 1.39807 + 0.807174i 0.994190 0.107640i \(-0.0343295\pi\)
0.403876 + 0.914814i \(0.367663\pi\)
\(68\) 0.420740 + 0.152658i 0.0510222 + 0.0185125i
\(69\) 4.78875 3.81890i 0.576498 0.459742i
\(70\) −3.33617 + 15.5168i −0.398749 + 1.85461i
\(71\) −0.725683 + 0.909977i −0.0861227 + 0.107994i −0.823026 0.568004i \(-0.807716\pi\)
0.736903 + 0.675998i \(0.236287\pi\)
\(72\) −3.15992 + 3.97471i −0.372401 + 0.468424i
\(73\) 6.74083 4.59582i 0.788955 0.537900i −0.100493 0.994938i \(-0.532042\pi\)
0.889447 + 0.457038i \(0.151090\pi\)
\(74\) −3.26712 2.34641i −0.379795 0.272764i
\(75\) −4.24054 + 28.1341i −0.489655 + 3.24865i
\(76\) −10.4425 + 0.270933i −1.19783 + 0.0310782i
\(77\) 13.3149 + 4.66432i 1.51737 + 0.531549i
\(78\) 8.13208 + 4.96379i 0.920776 + 0.562039i
\(79\) 4.67829 + 8.10303i 0.526348 + 0.911662i 0.999529 + 0.0306965i \(0.00977252\pi\)
−0.473180 + 0.880966i \(0.656894\pi\)
\(80\) 10.8801 13.0196i 1.21644 1.45563i
\(81\) 11.0381 1.66373i 1.22646 0.184859i
\(82\) 1.98890 3.88431i 0.219638 0.428950i
\(83\) 1.51482 3.14556i 0.166273 0.345270i −0.801138 0.598479i \(-0.795772\pi\)
0.967411 + 0.253209i \(0.0814862\pi\)
\(84\) 11.5644 0.729394i 1.26178 0.0795834i
\(85\) −0.411873 0.855263i −0.0446739 0.0927663i
\(86\) 10.7840 + 0.263508i 1.16287 + 0.0284148i
\(87\) −0.368119 + 4.91221i −0.0394665 + 0.526644i
\(88\) −10.2753 11.0406i −1.09535 1.17694i
\(89\) 0.794611 + 10.6034i 0.0842286 + 1.12395i 0.865885 + 0.500243i \(0.166756\pi\)
−0.781656 + 0.623710i \(0.785625\pi\)
\(90\) 10.6851 1.34448i 1.12631 0.141721i
\(91\) −1.51043 7.99816i −0.158336 0.838435i
\(92\) 4.46267 + 3.37328i 0.465266 + 0.351689i
\(93\) 0.369171 + 1.19682i 0.0382812 + 0.124105i
\(94\) 10.6253 + 12.0277i 1.09591 + 1.24056i
\(95\) 16.2407 + 15.0691i 1.66626 + 1.54606i
\(96\) −11.3040 5.06636i −1.15371 0.517084i
\(97\) 8.28730 0.841448 0.420724 0.907189i \(-0.361776\pi\)
0.420724 + 0.907189i \(0.361776\pi\)
\(98\) −7.08535 6.91359i −0.715729 0.698378i
\(99\) 9.57303i 0.962126i
\(100\) −25.8540 + 2.61336i −2.58540 + 0.261336i
\(101\) −11.9832 + 12.9148i −1.19237 + 1.28507i −0.243317 + 0.969947i \(0.578236\pi\)
−0.949051 + 0.315121i \(0.897955\pi\)
\(102\) −0.519400 + 0.458838i −0.0514282 + 0.0454317i
\(103\) 8.22729 2.53778i 0.810659 0.250055i 0.138405 0.990376i \(-0.455803\pi\)
0.672254 + 0.740321i \(0.265326\pi\)
\(104\) −2.55226 + 8.31880i −0.250270 + 0.815725i
\(105\) −18.6220 16.0369i −1.81732 1.56504i
\(106\) 0.247485 0.0311404i 0.0240379 0.00302462i
\(107\) 2.16913 0.162554i 0.209698 0.0157147i 0.0305329 0.999534i \(-0.490280\pi\)
0.179165 + 0.983819i \(0.442661\pi\)
\(108\) 2.05440 + 4.85994i 0.197685 + 0.467648i
\(109\) −1.63739 0.122705i −0.156833 0.0117530i −0.00391801 0.999992i \(-0.501247\pi\)
−0.152915 + 0.988239i \(0.548866\pi\)
\(110\) −0.781397 + 31.9786i −0.0745033 + 3.04904i
\(111\) 5.61158 2.70240i 0.532628 0.256500i
\(112\) 3.26196 + 10.0678i 0.308226 + 0.951313i
\(113\) −11.4471 5.51263i −1.07685 0.518585i −0.190543 0.981679i \(-0.561025\pi\)
−0.886309 + 0.463094i \(0.846739\pi\)
\(114\) 7.37189 14.3972i 0.690440 1.34842i
\(115\) −1.76833 11.7321i −0.164898 1.09402i
\(116\) −4.42988 + 0.785704i −0.411304 + 0.0729508i
\(117\) −4.78307 + 2.76151i −0.442195 + 0.255301i
\(118\) −6.22733 + 10.2021i −0.573273 + 0.939181i
\(119\) 0.588345 + 0.0664994i 0.0539335 + 0.00609599i
\(120\) 9.63532 + 24.4419i 0.879580 + 2.23123i
\(121\) 17.2399 + 2.59850i 1.56726 + 0.236227i
\(122\) 1.27373 + 0.914775i 0.115318 + 0.0828199i
\(123\) 3.80645 + 5.58304i 0.343216 + 0.503406i
\(124\) −0.975483 + 0.597454i −0.0876010 + 0.0536530i
\(125\) 26.5074 + 21.1389i 2.37089 + 1.89072i
\(126\) −2.83789 + 6.08830i −0.252819 + 0.542389i
\(127\) 2.61957 + 3.28484i 0.232450 + 0.291483i 0.884352 0.466820i \(-0.154600\pi\)
−0.651903 + 0.758303i \(0.726029\pi\)
\(128\) 1.92535 11.1487i 0.170179 0.985413i
\(129\) −8.35164 + 14.4655i −0.735321 + 1.27361i
\(130\) 16.2032 8.83436i 1.42111 0.774825i
\(131\) −1.27724 1.37653i −0.111593 0.120268i 0.674785 0.738014i \(-0.264236\pi\)
−0.786378 + 0.617746i \(0.788046\pi\)
\(132\) 22.6259 5.78552i 1.96933 0.503565i
\(133\) −13.3491 + 3.57187i −1.15752 + 0.309720i
\(134\) −13.3843 13.0415i −1.15622 1.12661i
\(135\) 4.08837 10.4170i 0.351871 0.896553i
\(136\) −0.523524 0.355776i −0.0448918 0.0305075i
\(137\) 8.46929 + 2.61243i 0.723580 + 0.223195i 0.634603 0.772839i \(-0.281164\pi\)
0.0889777 + 0.996034i \(0.471640\pi\)
\(138\) −7.89378 + 3.56659i −0.671964 + 0.303609i
\(139\) −8.82260 2.01370i −0.748323 0.170800i −0.168680 0.985671i \(-0.553951\pi\)
−0.579642 + 0.814871i \(0.696808\pi\)
\(140\) 9.97690 20.1063i 0.843202 1.69929i
\(141\) −24.2272 + 5.52971i −2.04030 + 0.465686i
\(142\) 1.31159 0.994528i 0.110066 0.0834589i
\(143\) −5.99339 15.2709i −0.501192 1.27702i
\(144\) 5.71548 4.34744i 0.476290 0.362287i
\(145\) 7.88394 + 5.37518i 0.654726 + 0.446384i
\(146\) −10.8400 + 3.95161i −0.897124 + 0.327038i
\(147\) 14.6508 4.50793i 1.20838 0.371808i
\(148\) 3.66090 + 4.35398i 0.300924 + 0.357895i
\(149\) −3.39654 + 4.98181i −0.278255 + 0.408126i −0.939770 0.341806i \(-0.888961\pi\)
0.661515 + 0.749932i \(0.269914\pi\)
\(150\) 15.6108 37.0854i 1.27462 3.02801i
\(151\) 1.34353 + 3.42325i 0.109335 + 0.278580i 0.975061 0.221938i \(-0.0712382\pi\)
−0.865726 + 0.500518i \(0.833143\pi\)
\(152\) 14.4074 + 3.26552i 1.16859 + 0.264869i
\(153\) −0.0893997 0.391686i −0.00722754 0.0316659i
\(154\) −16.6257 11.0305i −1.33974 0.888861i
\(155\) 2.36528 + 0.539860i 0.189984 + 0.0433626i
\(156\) −9.41751 9.63588i −0.754005 0.771488i
\(157\) 0.796574 2.58243i 0.0635735 0.206100i −0.918213 0.396086i \(-0.870368\pi\)
0.981787 + 0.189986i \(0.0608443\pi\)
\(158\) −3.59022 12.7358i −0.285623 1.01321i
\(159\) −0.141107 + 0.359535i −0.0111905 + 0.0285130i
\(160\) −19.4474 + 14.0560i −1.53745 + 1.11123i
\(161\) 6.78185 + 2.96172i 0.534485 + 0.233416i
\(162\) −15.7090 1.56394i −1.23421 0.122874i
\(163\) −2.34540 2.52774i −0.183706 0.197988i 0.634484 0.772936i \(-0.281213\pi\)
−0.818190 + 0.574948i \(0.805022\pi\)
\(164\) −4.07892 + 4.63137i −0.318510 + 0.361649i
\(165\) −42.8954 24.7657i −3.33940 1.92800i
\(166\) −3.17183 + 3.78390i −0.246182 + 0.293688i
\(167\) 6.51007 + 8.16337i 0.503765 + 0.631701i 0.967074 0.254496i \(-0.0819095\pi\)
−0.463309 + 0.886197i \(0.653338\pi\)
\(168\) −16.1048 3.02787i −1.24252 0.233606i
\(169\) 2.20431 2.76412i 0.169562 0.212625i
\(170\) 0.266667 + 1.31572i 0.0204525 + 0.100911i
\(171\) 5.28202 + 7.74730i 0.403926 + 0.592451i
\(172\) −14.6895 4.11702i −1.12006 0.313920i
\(173\) 0.296646 1.96812i 0.0225536 0.149633i −0.974720 0.223432i \(-0.928274\pi\)
0.997273 + 0.0737985i \(0.0235122\pi\)
\(174\) 2.21538 6.60475i 0.167948 0.500705i
\(175\) −32.4509 + 11.3423i −2.45305 + 0.857396i
\(176\) 10.2387 + 18.7116i 0.771769 + 1.41044i
\(177\) −9.25381 16.0281i −0.695559 1.20474i
\(178\) 2.60377 14.8103i 0.195161 1.11008i
\(179\) −3.59473 23.8495i −0.268683 1.78260i −0.562564 0.826754i \(-0.690185\pi\)
0.293881 0.955842i \(-0.405053\pi\)
\(180\) −15.1139 1.87857i −1.12652 0.140021i
\(181\) 5.28659 10.9777i 0.392949 0.815968i −0.606827 0.794834i \(-0.707558\pi\)
0.999777 0.0211341i \(-0.00672771\pi\)
\(182\) −0.715301 + 11.4888i −0.0530216 + 0.851605i
\(183\) −2.18775 + 1.05356i −0.161723 + 0.0778816i
\(184\) −4.94195 6.17786i −0.364326 0.455438i
\(185\) 0.901604 12.0311i 0.0662872 0.884542i
\(186\) −0.0891798 1.76901i −0.00653898 0.129710i
\(187\) 1.19000 0.0891782i 0.0870214 0.00652136i
\(188\) −10.3746 20.1864i −0.756648 1.47224i
\(189\) 4.14285 + 5.61748i 0.301348 + 0.408612i
\(190\) −17.0121 26.3109i −1.23419 1.90879i
\(191\) −15.3923 + 4.74791i −1.11375 + 0.343546i −0.796405 0.604764i \(-0.793268\pi\)
−0.317345 + 0.948310i \(0.602791\pi\)
\(192\) 13.7294 + 10.8812i 0.990833 + 0.785282i
\(193\) −6.07004 5.63217i −0.436931 0.405412i 0.430800 0.902448i \(-0.358232\pi\)
−0.867730 + 0.497035i \(0.834422\pi\)
\(194\) −11.3591 2.88629i −0.815533 0.207223i
\(195\) 28.5763i 2.04639i
\(196\) 7.30374 + 11.9438i 0.521696 + 0.853132i
\(197\) 12.7093i 0.905500i −0.891637 0.452750i \(-0.850443\pi\)
0.891637 0.452750i \(-0.149557\pi\)
\(198\) −3.33408 + 13.1213i −0.236943 + 0.932494i
\(199\) 11.4815 + 10.6533i 0.813901 + 0.755190i 0.972686 0.232123i \(-0.0745672\pi\)
−0.158785 + 0.987313i \(0.550758\pi\)
\(200\) 36.3472 + 5.42236i 2.57013 + 0.383419i
\(201\) 27.6506 8.52907i 1.95032 0.601594i
\(202\) 20.9227 13.5283i 1.47212 0.951845i
\(203\) −5.45588 + 2.37810i −0.382928 + 0.166910i
\(204\) 0.871723 0.448014i 0.0610328 0.0313673i
\(205\) 13.0525 0.978150i 0.911626 0.0683170i
\(206\) −12.1606 + 0.613046i −0.847272 + 0.0427130i
\(207\) 0.375254 5.00741i 0.0260819 0.348039i
\(208\) 6.39554 10.5133i 0.443451 0.728968i
\(209\) −25.0930 + 12.0841i −1.73572 + 0.835878i
\(210\) 19.9391 + 28.4668i 1.37593 + 1.96439i
\(211\) 4.17863 8.67702i 0.287669 0.597351i −0.706188 0.708025i \(-0.749587\pi\)
0.993857 + 0.110674i \(0.0353009\pi\)
\(212\) −0.350063 0.0435108i −0.0240424 0.00298833i
\(213\) 0.379868 + 2.52026i 0.0260281 + 0.172685i
\(214\) −3.02975 0.532654i −0.207109 0.0364115i
\(215\) 16.1777 + 28.0206i 1.10331 + 1.91099i
\(216\) −1.12327 7.37682i −0.0764286 0.501929i
\(217\) −1.07040 + 1.06965i −0.0726635 + 0.0726126i
\(218\) 2.20156 + 0.738454i 0.149109 + 0.0500144i
\(219\) 2.66270 17.6659i 0.179929 1.19375i
\(220\) 12.2085 43.5596i 0.823095 2.93679i
\(221\) −0.387833 0.568847i −0.0260885 0.0382648i
\(222\) −8.63275 + 1.74967i −0.579392 + 0.117430i
\(223\) −0.0356433 + 0.0446953i −0.00238685 + 0.00299302i −0.783023 0.621992i \(-0.786324\pi\)
0.780637 + 0.624985i \(0.214895\pi\)
\(224\) −0.964654 14.9355i −0.0644537 0.997921i
\(225\) 14.5432 + 18.2366i 0.969548 + 1.21577i
\(226\) 13.7701 + 11.5427i 0.915975 + 0.767809i
\(227\) −3.40537 1.96609i −0.226022 0.130494i 0.382713 0.923867i \(-0.374990\pi\)
−0.608736 + 0.793373i \(0.708323\pi\)
\(228\) −15.1186 + 17.1662i −1.00125 + 1.13686i
\(229\) −5.79349 6.24390i −0.382845 0.412608i 0.512000 0.858985i \(-0.328905\pi\)
−0.894845 + 0.446377i \(0.852714\pi\)
\(230\) −1.66226 + 16.6966i −0.109606 + 1.10094i
\(231\) 27.3192 14.4264i 1.79747 0.949185i
\(232\) 6.34549 + 0.465898i 0.416602 + 0.0305877i
\(233\) −7.33306 + 18.6843i −0.480405 + 1.22405i 0.461189 + 0.887302i \(0.347423\pi\)
−0.941594 + 0.336750i \(0.890672\pi\)
\(234\) 7.51772 2.11924i 0.491449 0.138539i
\(235\) −14.1885 + 45.9981i −0.925558 + 3.00059i
\(236\) 12.0887 11.8148i 0.786908 0.769075i
\(237\) 19.9754 + 4.55925i 1.29754 + 0.296155i
\(238\) −0.783259 0.296055i −0.0507711 0.0191904i
\(239\) −3.58273 15.6970i −0.231747 1.01535i −0.948190 0.317705i \(-0.897088\pi\)
0.716442 0.697647i \(-0.245769\pi\)
\(240\) −4.69417 36.8572i −0.303007 2.37912i
\(241\) 1.95698 + 4.98630i 0.126060 + 0.321196i 0.979946 0.199265i \(-0.0638555\pi\)
−0.853886 + 0.520461i \(0.825760\pi\)
\(242\) −22.7250 9.56593i −1.46082 0.614921i
\(243\) 9.31165 13.6577i 0.597342 0.876141i
\(244\) −1.42725 1.69745i −0.0913701 0.108668i
\(245\) 6.62752 28.9435i 0.423417 1.84913i
\(246\) −3.27289 8.97814i −0.208672 0.572425i
\(247\) 13.2762 + 9.05158i 0.844746 + 0.575938i
\(248\) 1.54513 0.479166i 0.0981161 0.0304271i
\(249\) −2.79314 7.11679i −0.177008 0.451009i
\(250\) −28.9703 38.2062i −1.83224 2.41637i
\(251\) −2.99498 + 0.683586i −0.189042 + 0.0431475i −0.315994 0.948761i \(-0.602338\pi\)
0.126952 + 0.991909i \(0.459481\pi\)
\(252\) 6.01020 7.35661i 0.378607 0.463423i
\(253\) 14.5412 + 3.31893i 0.914197 + 0.208659i
\(254\) −2.44650 5.41473i −0.153507 0.339751i
\(255\) −1.98637 0.612713i −0.124391 0.0383696i
\(256\) −6.52184 + 14.6105i −0.407615 + 0.913154i
\(257\) 7.48033 19.0596i 0.466610 1.18890i −0.483042 0.875597i \(-0.660468\pi\)
0.949652 0.313306i \(-0.101437\pi\)
\(258\) 16.4852 16.9185i 1.02633 1.05330i
\(259\) 6.05320 + 4.47075i 0.376128 + 0.277799i
\(260\) −25.2858 + 6.46567i −1.56816 + 0.400984i
\(261\) 2.74683 + 2.96038i 0.170025 + 0.183243i
\(262\) 1.27124 + 2.33159i 0.0785373 + 0.144046i
\(263\) 3.10576 5.37934i 0.191510 0.331704i −0.754241 0.656598i \(-0.771995\pi\)
0.945751 + 0.324893i \(0.105328\pi\)
\(264\) −33.0274 + 0.0498521i −2.03269 + 0.00306819i
\(265\) 0.466471 + 0.584936i 0.0286551 + 0.0359324i
\(266\) 19.5411 0.246607i 1.19814 0.0151205i
\(267\) 18.2045 + 14.5176i 1.11410 + 0.888462i
\(268\) 13.8032 + 22.5369i 0.843163 + 1.37666i
\(269\) 1.39484 + 2.04585i 0.0850446 + 0.124738i 0.866404 0.499344i \(-0.166426\pi\)
−0.781359 + 0.624082i \(0.785473\pi\)
\(270\) −9.23177 + 12.8543i −0.561828 + 0.782285i
\(271\) −14.2636 2.14989i −0.866451 0.130596i −0.299249 0.954175i \(-0.596736\pi\)
−0.567202 + 0.823579i \(0.691974\pi\)
\(272\) 0.593663 + 0.669979i 0.0359961 + 0.0406234i
\(273\) −15.0887 9.48822i −0.913208 0.574253i
\(274\) −10.6986 6.53042i −0.646329 0.394517i
\(275\) −60.0012 + 34.6417i −3.61821 + 2.08897i
\(276\) 12.0618 2.13935i 0.726038 0.128773i
\(277\) 4.14017 + 27.4682i 0.248759 + 1.65041i 0.669197 + 0.743085i \(0.266638\pi\)
−0.420438 + 0.907321i \(0.638124\pi\)
\(278\) 11.3914 + 5.83281i 0.683213 + 0.349829i
\(279\) 0.925115 + 0.445512i 0.0553852 + 0.0266721i
\(280\) −20.6775 + 24.0841i −1.23572 + 1.43930i
\(281\) −3.27702 + 1.57813i −0.195491 + 0.0941433i −0.529068 0.848579i \(-0.677458\pi\)
0.333578 + 0.942723i \(0.391744\pi\)
\(282\) 35.1331 + 0.858478i 2.09215 + 0.0511216i
\(283\) −12.7239 0.953522i −0.756356 0.0566810i −0.309030 0.951052i \(-0.600004\pi\)
−0.447325 + 0.894371i \(0.647623\pi\)
\(284\) −2.14411 + 0.906360i −0.127230 + 0.0537826i
\(285\) 48.3792 3.62552i 2.86574 0.214757i
\(286\) 2.89636 + 23.0185i 0.171265 + 1.36112i
\(287\) −3.81736 + 7.21667i −0.225332 + 0.425987i
\(288\) −9.34809 + 3.96827i −0.550841 + 0.233833i
\(289\) −16.1969 + 4.99608i −0.952758 + 0.293887i
\(290\) −8.93413 10.1133i −0.524630 0.593875i
\(291\) 12.3435 13.3031i 0.723589 0.779843i
\(292\) 16.2342 1.64098i 0.950034 0.0960309i
\(293\) 18.5947i 1.08631i 0.839631 + 0.543157i \(0.182771\pi\)
−0.839631 + 0.543157i \(0.817229\pi\)
\(294\) −21.6512 + 1.07627i −1.26273 + 0.0627696i
\(295\) −35.8505 −2.08730
\(296\) −3.50144 7.24283i −0.203517 0.420981i
\(297\) 10.3124 + 9.56851i 0.598387 + 0.555222i
\(298\) 6.39055 5.64541i 0.370195 0.327030i
\(299\) −2.53639 8.22276i −0.146683 0.475534i
\(300\) −34.3131 + 45.3944i −1.98107 + 2.62085i
\(301\) −20.1667 0.761664i −1.16239 0.0439016i
\(302\) −0.649272 5.16003i −0.0373614 0.296926i
\(303\) 2.88306 + 38.4717i 0.165627 + 2.21014i
\(304\) −18.6103 9.49369i −1.06737 0.544501i
\(305\) −0.351502 + 4.69046i −0.0201269 + 0.268575i
\(306\) −0.0138791 + 0.568003i −0.000793418 + 0.0324706i
\(307\) 3.29713 + 6.84656i 0.188177 + 0.390754i 0.973618 0.228182i \(-0.0732782\pi\)
−0.785441 + 0.618936i \(0.787564\pi\)
\(308\) 18.9464 + 20.9094i 1.07957 + 1.19142i
\(309\) 8.18035 16.9867i 0.465364 0.966338i
\(310\) −3.05397 1.56374i −0.173454 0.0888144i
\(311\) −21.3964 + 3.22499i −1.21328 + 0.182872i −0.724338 0.689445i \(-0.757855\pi\)
−0.488940 + 0.872317i \(0.662616\pi\)
\(312\) 9.55222 + 16.4874i 0.540788 + 0.933416i
\(313\) −9.20174 15.9379i −0.520113 0.900863i −0.999727 0.0233828i \(-0.992556\pi\)
0.479613 0.877480i \(-0.340777\pi\)
\(314\) −1.99123 + 3.26220i −0.112372 + 0.184096i
\(315\) −20.0218 + 2.24881i −1.12810 + 0.126706i
\(316\) 0.485356 + 18.7068i 0.0273034 + 1.05234i
\(317\) 4.14265 27.4847i 0.232675 1.54370i −0.501754 0.865010i \(-0.667312\pi\)
0.734429 0.678685i \(-0.237450\pi\)
\(318\) 0.318628 0.443655i 0.0178678 0.0248790i
\(319\) −9.91098 + 6.75719i −0.554908 + 0.378330i
\(320\) 31.5511 12.4929i 1.76376 0.698376i
\(321\) 2.96986 3.72409i 0.165762 0.207859i
\(322\) −8.26409 6.42148i −0.460540 0.357855i
\(323\) −0.913843 + 0.728765i −0.0508476 + 0.0405496i
\(324\) 20.9869 + 7.61471i 1.16594 + 0.423039i
\(325\) 34.6168 + 19.9860i 1.92019 + 1.10862i
\(326\) 2.33439 + 4.28152i 0.129290 + 0.237132i
\(327\) −2.63577 + 2.44564i −0.145759 + 0.135244i
\(328\) 7.20381 4.92742i 0.397764 0.272071i
\(329\) −19.5766 22.7645i −1.07929 1.25505i
\(330\) 50.1695 + 48.8848i 2.76174 + 2.69102i
\(331\) 0.311745 + 0.122351i 0.0171350 + 0.00672501i 0.373893 0.927472i \(-0.378023\pi\)
−0.356758 + 0.934197i \(0.616118\pi\)
\(332\) 5.66534 4.08176i 0.310926 0.224016i
\(333\) 1.50507 4.87932i 0.0824774 0.267385i
\(334\) −6.07996 13.4565i −0.332681 0.736307i
\(335\) 12.4726 54.6459i 0.681449 2.98562i
\(336\) 21.0197 + 9.75914i 1.14672 + 0.532405i
\(337\) −2.43821 10.6825i −0.132818 0.581914i −0.996908 0.0785765i \(-0.974963\pi\)
0.864090 0.503337i \(-0.167895\pi\)
\(338\) −3.98404 + 3.02095i −0.216703 + 0.164318i
\(339\) −25.8989 + 10.1646i −1.40664 + 0.552065i
\(340\) 0.0927263 1.89627i 0.00502879 0.102840i
\(341\) −1.71806 + 2.51994i −0.0930383 + 0.136462i
\(342\) −4.54162 12.4585i −0.245583 0.673679i
\(343\) 13.0820 + 13.1096i 0.706363 + 0.707850i
\(344\) 18.7003 + 10.7590i 1.00825 + 0.580089i
\(345\) −21.4667 14.6358i −1.15573 0.787962i
\(346\) −1.09205 + 2.59430i −0.0587090 + 0.139470i
\(347\) −19.8577 + 7.79357i −1.06602 + 0.418381i −0.832530 0.553979i \(-0.813109\pi\)
−0.233486 + 0.972360i \(0.575013\pi\)
\(348\) −5.33682 + 8.28129i −0.286084 + 0.443924i
\(349\) −17.4528 + 3.98349i −0.934228 + 0.213231i −0.662431 0.749123i \(-0.730475\pi\)
−0.271797 + 0.962355i \(0.587618\pi\)
\(350\) 48.4293 4.24446i 2.58865 0.226876i
\(351\) 1.80602 7.91269i 0.0963982 0.422348i
\(352\) −7.51687 29.2131i −0.400651 1.55706i
\(353\) 24.7205 + 7.62528i 1.31574 + 0.405853i 0.871650 0.490129i \(-0.163050\pi\)
0.444092 + 0.895981i \(0.353526\pi\)
\(354\) 7.10158 + 25.1919i 0.377445 + 1.33893i
\(355\) 4.59577 + 1.80371i 0.243918 + 0.0957309i
\(356\) −8.72699 + 19.3930i −0.462530 + 1.02783i
\(357\) 0.983056 0.845388i 0.0520288 0.0447427i
\(358\) −3.37911 + 33.9415i −0.178591 + 1.79386i
\(359\) 18.7605 17.4072i 0.990141 0.918716i −0.00655193 0.999979i \(-0.502086\pi\)
0.996693 + 0.0812621i \(0.0258951\pi\)
\(360\) 20.0617 + 7.83873i 1.05735 + 0.413137i
\(361\) 4.13979 7.17033i 0.217884 0.377386i
\(362\) −11.0694 + 13.2055i −0.581795 + 0.694066i
\(363\) 29.8491 23.8039i 1.56667 1.24938i
\(364\) 4.98172 15.4981i 0.261113 0.812319i
\(365\) −27.0565 21.5768i −1.41620 1.12938i
\(366\) 3.36558 0.682130i 0.175922 0.0356555i
\(367\) −18.8898 + 12.8788i −0.986038 + 0.672270i −0.945062 0.326890i \(-0.893999\pi\)
−0.0409763 + 0.999160i \(0.513047\pi\)
\(368\) 4.62211 + 10.1889i 0.240944 + 0.531134i
\(369\) 5.47781 + 0.825647i 0.285164 + 0.0429815i
\(370\) −5.42595 + 16.1765i −0.282082 + 0.840974i
\(371\) −0.463737 + 0.0520860i −0.0240760 + 0.00270417i
\(372\) −0.493872 + 2.45576i −0.0256061 + 0.127325i
\(373\) 5.16668 2.98298i 0.267521 0.154453i −0.360240 0.932860i \(-0.617305\pi\)
0.627760 + 0.778407i \(0.283972\pi\)
\(374\) −1.66214 0.292218i −0.0859473 0.0151102i
\(375\) 73.4145 11.0654i 3.79111 0.571417i
\(376\) 7.18958 + 31.2819i 0.370774 + 1.61324i
\(377\) 6.23516 + 3.00269i 0.321127 + 0.154647i
\(378\) −3.72198 9.14251i −0.191438 0.470240i
\(379\) −9.01901 18.7282i −0.463275 0.962001i −0.993467 0.114123i \(-0.963594\pi\)
0.530191 0.847878i \(-0.322120\pi\)
\(380\) 14.1543 + 41.9882i 0.726101 + 2.15395i
\(381\) 9.17468 + 0.687547i 0.470033 + 0.0352241i
\(382\) 22.7512 1.14694i 1.16405 0.0586826i
\(383\) 1.43648 + 19.1685i 0.0734005 + 0.979462i 0.905365 + 0.424634i \(0.139597\pi\)
−0.831965 + 0.554828i \(0.812784\pi\)
\(384\) −15.0286 19.6960i −0.766926 1.00511i
\(385\) 2.25861 59.8017i 0.115110 3.04778i
\(386\) 6.35838 + 9.83384i 0.323633 + 0.500529i
\(387\) 4.03630 + 13.0854i 0.205177 + 0.665166i
\(388\) 14.5641 + 7.91222i 0.739383 + 0.401682i
\(389\) −21.2153 + 22.8646i −1.07566 + 1.15928i −0.0890742 + 0.996025i \(0.528391\pi\)
−0.986583 + 0.163258i \(0.947800\pi\)
\(390\) 9.95251 39.1684i 0.503965 1.98337i
\(391\) 0.625955 0.0316559
\(392\) −5.85115 18.9147i −0.295528 0.955334i
\(393\) −4.11204 −0.207425
\(394\) −4.42637 + 17.4201i −0.222997 + 0.877612i
\(395\) 26.9952 29.0939i 1.35828 1.46387i
\(396\) 9.13976 16.8237i 0.459290 0.845422i
\(397\) 8.82692 + 28.6162i 0.443011 + 1.43621i 0.851940 + 0.523639i \(0.175426\pi\)
−0.408929 + 0.912566i \(0.634098\pi\)
\(398\) −12.0269 18.6007i −0.602854 0.932371i
\(399\) −14.1491 + 26.7487i −0.708340 + 1.33911i
\(400\) −47.9311 20.0911i −2.39655 1.00456i
\(401\) −0.246569 3.29024i −0.0123131 0.164307i −0.999971 0.00767734i \(-0.997556\pi\)
0.987657 0.156629i \(-0.0500628\pi\)
\(402\) −40.8699 + 2.06035i −2.03841 + 0.102761i
\(403\) 1.75466 + 0.131494i 0.0874061 + 0.00655018i
\(404\) −33.3895 + 11.2557i −1.66119 + 0.559991i
\(405\) −20.5446 42.6613i −1.02087 2.11986i
\(406\) 8.30638 1.35940i 0.412239 0.0674658i
\(407\) 13.6648 + 6.58062i 0.677339 + 0.326189i
\(408\) −1.35087 + 0.310473i −0.0668779 + 0.0153707i
\(409\) 21.1766 3.19186i 1.04712 0.157827i 0.397121 0.917766i \(-0.370009\pi\)
0.649994 + 0.759939i \(0.274771\pi\)
\(410\) −18.2312 3.20519i −0.900374 0.158293i
\(411\) 16.8081 9.70418i 0.829084 0.478672i
\(412\) 16.8816 + 3.39501i 0.831696 + 0.167260i
\(413\) 11.9035 18.9295i 0.585732 0.931462i
\(414\) −2.25832 + 6.73275i −0.110990 + 0.330897i
\(415\) −14.6440 2.20723i −0.718847 0.108349i
\(416\) −12.4277 + 12.1827i −0.609316 + 0.597308i
\(417\) −16.3733 + 11.1631i −0.801802 + 0.546659i
\(418\) 38.6025 7.82389i 1.88811 0.382679i
\(419\) 1.15528 + 0.921309i 0.0564393 + 0.0450089i 0.651303 0.758818i \(-0.274223\pi\)
−0.594864 + 0.803826i \(0.702794\pi\)
\(420\) −17.4154 45.9626i −0.849783 2.24274i
\(421\) 4.24042 3.38163i 0.206666 0.164810i −0.514687 0.857378i \(-0.672092\pi\)
0.721353 + 0.692568i \(0.243521\pi\)
\(422\) −8.74949 + 10.4379i −0.425919 + 0.508109i
\(423\) −10.1864 + 17.6434i −0.495281 + 0.857851i
\(424\) 0.464662 + 0.181558i 0.0225660 + 0.00881722i
\(425\) −2.13147 + 1.97772i −0.103392 + 0.0959334i
\(426\) 0.357082 3.58671i 0.0173007 0.173777i
\(427\) −2.35992 1.74298i −0.114204 0.0843485i
\(428\) 3.96723 + 1.78528i 0.191763 + 0.0862948i
\(429\) −33.4403 13.1244i −1.61451 0.633650i
\(430\) −12.4151 44.0410i −0.598710 2.12384i
\(431\) 24.0894 + 7.43060i 1.16035 + 0.357920i 0.814383 0.580328i \(-0.197076\pi\)
0.345964 + 0.938248i \(0.387552\pi\)
\(432\) −1.02957 + 10.5023i −0.0495352 + 0.505292i
\(433\) 1.92796 8.44695i 0.0926519 0.405934i −0.907240 0.420612i \(-0.861815\pi\)
0.999892 + 0.0146781i \(0.00467235\pi\)
\(434\) 1.83969 1.09333i 0.0883079 0.0524814i
\(435\) 20.3712 4.64959i 0.976723 0.222931i
\(436\) −2.76040 1.77892i −0.132199 0.0851950i
\(437\) −13.5992 + 5.33729i −0.650538 + 0.255317i
\(438\) −9.80230 + 23.2865i −0.468372 + 1.11267i
\(439\) −3.82294 2.60644i −0.182459 0.124398i 0.468646 0.883386i \(-0.344742\pi\)
−0.651105 + 0.758988i \(0.725694\pi\)
\(440\) −31.9045 + 55.4533i −1.52099 + 2.64363i
\(441\) 5.46045 11.3184i 0.260022 0.538974i
\(442\) 0.333470 + 0.914768i 0.0158615 + 0.0435111i
\(443\) 2.27688 3.33956i 0.108178 0.158667i −0.768332 0.640051i \(-0.778913\pi\)
0.876510 + 0.481384i \(0.159866\pi\)
\(444\) 12.4419 + 0.608399i 0.590467 + 0.0288734i
\(445\) 41.9856 16.4781i 1.99031 0.781138i
\(446\) 0.0644212 0.0488482i 0.00305043 0.00231303i
\(447\) 2.93804 + 12.8724i 0.138965 + 0.608844i
\(448\) −3.87950 + 20.8074i −0.183289 + 0.983059i
\(449\) −1.13083 + 4.95447i −0.0533669 + 0.233816i −0.994577 0.104007i \(-0.966833\pi\)
0.941210 + 0.337823i \(0.109691\pi\)
\(450\) −13.5824 30.0613i −0.640279 1.41710i
\(451\) −4.85003 + 15.7234i −0.228379 + 0.740387i
\(452\) −14.8541 20.6169i −0.698676 0.969738i
\(453\) 7.49626 + 2.94206i 0.352205 + 0.138230i
\(454\) 3.98285 + 3.88086i 0.186925 + 0.182138i
\(455\) −30.5309 + 16.1223i −1.43131 + 0.755827i
\(456\) 26.7010 18.2635i 1.25039 0.855268i
\(457\) −11.1203 + 10.3182i −0.520188 + 0.482664i −0.896014 0.444027i \(-0.853550\pi\)
0.375826 + 0.926690i \(0.377359\pi\)
\(458\) 5.76628 + 10.5760i 0.269441 + 0.494184i
\(459\) 0.511295 + 0.295196i 0.0238652 + 0.0137786i
\(460\) 8.09344 22.3064i 0.377359 1.04004i
\(461\) −32.2613 + 25.7275i −1.50256 + 1.19825i −0.578685 + 0.815551i \(0.696434\pi\)
−0.923873 + 0.382699i \(0.874995\pi\)
\(462\) −42.4697 + 10.2589i −1.97587 + 0.477289i
\(463\) 13.3679 16.7629i 0.621261 0.779037i −0.367260 0.930118i \(-0.619704\pi\)
0.988521 + 0.151081i \(0.0482756\pi\)
\(464\) −8.53523 2.84858i −0.396238 0.132242i
\(465\) 4.38957 2.99276i 0.203561 0.138786i
\(466\) 16.5585 23.0559i 0.767056 1.06804i
\(467\) −3.91908 + 26.0014i −0.181353 + 1.20320i 0.694093 + 0.719885i \(0.255806\pi\)
−0.875446 + 0.483315i \(0.839432\pi\)
\(468\) −11.0423 + 0.286497i −0.510431 + 0.0132433i
\(469\) 24.7125 + 24.7298i 1.14112 + 1.14192i
\(470\) 35.4678 58.1061i 1.63601 2.68023i
\(471\) −2.95897 5.12508i −0.136342 0.236151i
\(472\) −20.6843 + 11.9838i −0.952073 + 0.551597i
\(473\) −40.2200 + 6.06219i −1.84932 + 0.278740i
\(474\) −25.7915 13.2062i −1.18464 0.606579i
\(475\) 29.4441 61.1412i 1.35099 2.80535i
\(476\) 0.970470 + 0.678583i 0.0444814 + 0.0311028i
\(477\) 0.137387 + 0.285286i 0.00629050 + 0.0130624i
\(478\) −0.556212 + 22.7629i −0.0254406 + 1.04115i
\(479\) −0.603884 + 8.05828i −0.0275922 + 0.368192i 0.966267 + 0.257542i \(0.0829124\pi\)
−0.993859 + 0.110650i \(0.964707\pi\)
\(480\) −6.40245 + 52.1535i −0.292231 + 2.38047i
\(481\) −0.653906 8.72577i −0.0298156 0.397861i
\(482\) −0.945728 7.51608i −0.0430767 0.342348i
\(483\) 14.8555 6.47518i 0.675948 0.294631i
\(484\) 27.8166 + 21.0262i 1.26439 + 0.955738i
\(485\) −10.3616 33.5914i −0.470494 1.52530i
\(486\) −17.5198 + 15.4770i −0.794712 + 0.702049i
\(487\) −20.7316 19.2361i −0.939438 0.871671i 0.0524709 0.998622i \(-0.483290\pi\)
−0.991909 + 0.126951i \(0.959481\pi\)
\(488\) 1.36508 + 2.82371i 0.0617943 + 0.127823i
\(489\) −7.55099 −0.341468
\(490\) −19.1645 + 37.3634i −0.865762 + 1.68791i
\(491\) 23.0675i 1.04102i 0.853854 + 0.520512i \(0.174259\pi\)
−0.853854 + 0.520512i \(0.825741\pi\)
\(492\) 1.35913 + 13.4458i 0.0612741 + 0.606185i
\(493\) −0.342410 + 0.369030i −0.0154214 + 0.0166203i
\(494\) −15.0447 17.0304i −0.676893 0.766235i
\(495\) −38.8029 + 11.9691i −1.74406 + 0.537971i
\(496\) −2.28473 + 0.118636i −0.102588 + 0.00532693i
\(497\) −2.47832 + 1.82774i −0.111168 + 0.0819855i
\(498\) 1.34981 + 10.7275i 0.0604864 + 0.480710i
\(499\) 32.1618 2.41019i 1.43976 0.107895i 0.668166 0.744013i \(-0.267080\pi\)
0.771592 + 0.636118i \(0.219461\pi\)
\(500\) 26.4020 + 62.4573i 1.18073 + 2.79318i
\(501\) 22.8006 + 1.70867i 1.01866 + 0.0763377i
\(502\) 4.34318 + 0.106125i 0.193845 + 0.00473661i
\(503\) 4.47760 2.15630i 0.199646 0.0961446i −0.331389 0.943494i \(-0.607517\pi\)
0.531036 + 0.847350i \(0.321803\pi\)
\(504\) −10.8001 + 7.99017i −0.481073 + 0.355910i
\(505\) 67.3306 + 32.4247i 2.99617 + 1.44288i
\(506\) −18.7751 9.61350i −0.834654 0.427372i
\(507\) −1.15388 7.65547i −0.0512454 0.339991i
\(508\) 1.46748 + 8.27381i 0.0651090 + 0.367091i
\(509\) −6.05578 + 3.49630i −0.268418 + 0.154971i −0.628168 0.778078i \(-0.716195\pi\)
0.359751 + 0.933048i \(0.382862\pi\)
\(510\) 2.50923 + 1.53163i 0.111111 + 0.0678216i
\(511\) 20.3764 7.12201i 0.901401 0.315059i
\(512\) 14.0277 17.7545i 0.619943 0.784647i
\(513\) −13.6252 2.05367i −0.601567 0.0906716i
\(514\) −16.8910 + 23.5189i −0.745030 + 1.03737i
\(515\) −20.5730 30.1751i −0.906556 1.32967i
\(516\) −28.4880 + 17.4480i −1.25411 + 0.768107i
\(517\) −47.3111 37.7293i −2.08074 1.65933i
\(518\) −6.73981 8.23606i −0.296130 0.361872i
\(519\) −2.71746 3.40759i −0.119283 0.149577i
\(520\) 36.9101 0.0557128i 1.61861 0.00244317i
\(521\) −12.6756 + 21.9548i −0.555329 + 0.961858i 0.442549 + 0.896745i \(0.354074\pi\)
−0.997878 + 0.0651139i \(0.979259\pi\)
\(522\) −2.73393 5.01433i −0.119661 0.219471i
\(523\) −26.5299 28.5924i −1.16007 1.25026i −0.962891 0.269892i \(-0.913012\pi\)
−0.197180 0.980367i \(-0.563178\pi\)
\(524\) −0.930390 3.63855i −0.0406443 0.158951i
\(525\) −30.1267 + 68.9852i −1.31484 + 3.01076i
\(526\) −6.13045 + 6.29157i −0.267300 + 0.274325i
\(527\) −0.0467625 + 0.119149i −0.00203701 + 0.00519021i
\(528\) 45.2866 + 11.4344i 1.97085 + 0.497618i
\(529\) −14.5021 4.47332i −0.630528 0.194492i
\(530\) −0.435652 0.964209i −0.0189235 0.0418826i
\(531\) −14.7925 3.37630i −0.641942 0.146519i
\(532\) −26.8700 6.46771i −1.16496 0.280411i
\(533\) 9.25512 2.11242i 0.400884 0.0914991i
\(534\) −19.8959 26.2389i −0.860982 1.13547i
\(535\) −3.37093 8.58900i −0.145738 0.371335i
\(536\) −11.0703 35.6977i −0.478165 1.54191i
\(537\) −43.6384 29.7522i −1.88314 1.28390i
\(538\) −1.19932 3.28995i −0.0517063 0.141840i
\(539\) 30.8262 + 21.0486i 1.32778 + 0.906627i
\(540\) 17.1305 14.4036i 0.737177 0.619830i
\(541\) −7.99284 + 11.7233i −0.343639 + 0.504026i −0.958687 0.284464i \(-0.908184\pi\)
0.615048 + 0.788490i \(0.289137\pi\)
\(542\) 18.8017 + 7.91445i 0.807603 + 0.339955i
\(543\) −9.74780 24.8370i −0.418318 1.06586i
\(544\) −0.580369 1.12507i −0.0248831 0.0482370i
\(545\) 1.54985 + 6.79033i 0.0663882 + 0.290866i
\(546\) 17.3769 + 18.2602i 0.743662 + 0.781463i
\(547\) 36.0960 + 8.23869i 1.54336 + 0.352261i 0.907669 0.419687i \(-0.137860\pi\)
0.635686 + 0.771947i \(0.280717\pi\)
\(548\) 12.3898 + 12.6771i 0.529265 + 0.541537i
\(549\) −0.586771 + 1.90226i −0.0250428 + 0.0811867i
\(550\) 94.3061 26.5848i 4.02122 1.13358i
\(551\) 4.29244 10.9370i 0.182864 0.465931i
\(552\) −17.2777 1.26856i −0.735390 0.0539937i
\(553\) 6.39873 + 23.9139i 0.272102 + 1.01692i
\(554\) 3.89183 39.0915i 0.165348 1.66084i
\(555\) −17.9699 19.3669i −0.762779 0.822080i
\(556\) −13.5823 11.9622i −0.576018 0.507309i
\(557\) 17.4819 + 10.0932i 0.740732 + 0.427662i 0.822335 0.569003i \(-0.192671\pi\)
−0.0816033 + 0.996665i \(0.526004\pi\)
\(558\) −1.11285 0.932841i −0.0471109 0.0394903i
\(559\) 14.6311 + 18.3468i 0.618828 + 0.775985i
\(560\) 36.7297 25.8095i 1.55211 1.09065i
\(561\) 1.62929 2.04306i 0.0687887 0.0862583i
\(562\) 5.04130 1.02176i 0.212654 0.0431004i
\(563\) 22.9749 + 33.6979i 0.968275 + 1.42020i 0.906546 + 0.422106i \(0.138709\pi\)
0.0617288 + 0.998093i \(0.480339\pi\)
\(564\) −47.8565 13.4128i −2.01512 0.564780i
\(565\) −8.03240 + 53.2915i −0.337926 + 2.24199i
\(566\) 17.1080 + 5.73840i 0.719102 + 0.241203i
\(567\) 29.3472 + 3.31705i 1.23247 + 0.139303i
\(568\) 3.25451 0.495563i 0.136556 0.0207934i
\(569\) −13.9899 24.2312i −0.586487 1.01583i −0.994688 0.102934i \(-0.967177\pi\)
0.408201 0.912892i \(-0.366156\pi\)
\(570\) −67.5741 11.8801i −2.83037 0.497602i
\(571\) −3.95580 26.2450i −0.165545 1.09832i −0.905092 0.425215i \(-0.860198\pi\)
0.739547 0.673105i \(-0.235040\pi\)
\(572\) 4.04693 32.5593i 0.169211 1.36137i
\(573\) −15.3045 + 31.7802i −0.639356 + 1.32764i
\(574\) 7.74570 8.56208i 0.323299 0.357375i
\(575\) −32.7430 + 15.7682i −1.36548 + 0.657580i
\(576\) 14.1951 2.18341i 0.591462 0.0909755i
\(577\) −2.82710 + 37.7250i −0.117694 + 1.57051i 0.555797 + 0.831318i \(0.312413\pi\)
−0.673490 + 0.739196i \(0.735206\pi\)
\(578\) 23.9404 1.20689i 0.995789 0.0502001i
\(579\) −18.0820 + 1.35506i −0.751462 + 0.0563143i
\(580\) 8.72338 + 16.9735i 0.362218 + 0.704785i
\(581\) 6.02772 6.99937i 0.250072 0.290383i
\(582\) −21.5519 + 13.9351i −0.893355 + 0.577627i
\(583\) −0.898737 + 0.277224i −0.0372219 + 0.0114814i
\(584\) −22.8230 3.40479i −0.944423 0.140891i
\(585\) 17.1736 + 15.9348i 0.710040 + 0.658821i
\(586\) 6.47613 25.4870i 0.267526 1.05286i
\(587\) 3.75673i 0.155057i 0.996990 + 0.0775284i \(0.0247028\pi\)
−0.996990 + 0.0775284i \(0.975297\pi\)
\(588\) 30.0513 + 6.06545i 1.23929 + 0.250135i
\(589\) 2.98730i 0.123090i
\(590\) 49.1387 + 12.4859i 2.02301 + 0.514038i
\(591\) −20.4015 18.9298i −0.839206 0.778669i
\(592\) 2.27676 + 11.1469i 0.0935742 + 0.458135i
\(593\) −36.9315 + 11.3918i −1.51659 + 0.467807i −0.937656 0.347565i \(-0.887009\pi\)
−0.578937 + 0.815372i \(0.696532\pi\)
\(594\) −10.8023 16.7067i −0.443223 0.685486i
\(595\) −0.466058 2.46791i −0.0191065 0.101174i
\(596\) −10.7254 + 5.51224i −0.439331 + 0.225790i
\(597\) 34.2021 2.56310i 1.39980 0.104901i
\(598\) 0.612709 + 12.1540i 0.0250555 + 0.497012i
\(599\) 0.329715 4.39974i 0.0134718 0.179769i −0.986409 0.164310i \(-0.947460\pi\)
0.999881 0.0154584i \(-0.00492075\pi\)
\(600\) 62.8414 50.2697i 2.56549 2.05225i
\(601\) 18.3873 8.85488i 0.750035 0.361198i −0.0194935 0.999810i \(-0.506205\pi\)
0.769529 + 0.638612i \(0.220491\pi\)
\(602\) 27.3764 + 8.06761i 1.11578 + 0.328811i
\(603\) 10.2928 21.3732i 0.419155 0.870384i
\(604\) −0.907194 + 7.29876i −0.0369132 + 0.296982i
\(605\) −11.0223 73.1282i −0.448120 2.97309i
\(606\) 9.44718 53.7357i 0.383765 2.18286i
\(607\) −17.5353 30.3720i −0.711735 1.23276i −0.964205 0.265157i \(-0.914576\pi\)
0.252470 0.967605i \(-0.418757\pi\)
\(608\) 22.2019 + 19.4942i 0.900406 + 0.790593i
\(609\) −4.30882 + 12.3001i −0.174602 + 0.498424i
\(610\) 2.11537 6.30660i 0.0856490 0.255347i
\(611\) −5.20338 + 34.5222i −0.210506 + 1.39662i
\(612\) 0.216846 0.773704i 0.00876550 0.0312751i
\(613\) 18.3983 + 26.9853i 0.743098 + 1.08993i 0.992586 + 0.121547i \(0.0387856\pi\)
−0.249487 + 0.968378i \(0.580262\pi\)
\(614\) −2.13473 10.5326i −0.0861506 0.425061i
\(615\) 17.8708 22.4093i 0.720622 0.903631i
\(616\) −18.6868 35.2582i −0.752913 1.42059i
\(617\) −11.6431 14.5999i −0.468732 0.587771i 0.490128 0.871650i \(-0.336950\pi\)
−0.958860 + 0.283879i \(0.908378\pi\)
\(618\) −17.1285 + 20.4339i −0.689011 + 0.821971i
\(619\) −29.0361 16.7640i −1.16706 0.673801i −0.214072 0.976818i \(-0.568673\pi\)
−0.952985 + 0.303017i \(0.902006\pi\)
\(620\) 3.64133 + 3.20698i 0.146239 + 0.128796i
\(621\) 5.01908 + 5.40929i 0.201409 + 0.217067i
\(622\) 30.4503 + 3.03154i 1.22095 + 0.121554i
\(623\) −5.23985 + 27.6402i −0.209930 + 1.10738i
\(624\) −7.35062 25.9254i −0.294260 1.03785i
\(625\) 28.8074 73.4000i 1.15229 2.93600i
\(626\) 7.06162 + 25.0502i 0.282239 + 1.00121i
\(627\) −17.9767 + 58.2790i −0.717920 + 2.32744i
\(628\) 3.86545 3.77785i 0.154248 0.150753i
\(629\) 0.620557 + 0.141638i 0.0247432 + 0.00564748i
\(630\) 28.2262 + 3.89080i 1.12456 + 0.155013i
\(631\) 0.229259 + 1.00445i 0.00912664 + 0.0399864i 0.979286 0.202481i \(-0.0649004\pi\)
−0.970160 + 0.242467i \(0.922043\pi\)
\(632\) 5.84993 25.8097i 0.232698 1.02666i
\(633\) −7.70487 19.6317i −0.306241 0.780289i
\(634\) −15.2505 + 36.2293i −0.605674 + 1.43885i
\(635\) 10.0394 14.7251i 0.398401 0.584346i
\(636\) −0.591245 + 0.497128i −0.0234444 + 0.0197124i
\(637\) 1.62438 21.4738i 0.0643602 0.850824i
\(638\) 15.9379 5.81002i 0.630989 0.230021i
\(639\) 1.72643 + 1.17706i 0.0682965 + 0.0465637i
\(640\) −47.5968 + 6.13499i −1.88143 + 0.242507i
\(641\) 9.72746 + 24.7852i 0.384212 + 0.978956i 0.983900 + 0.178722i \(0.0571961\pi\)
−0.599688 + 0.800234i \(0.704709\pi\)
\(642\) −5.36769 + 4.07012i −0.211846 + 0.160635i
\(643\) −14.0884 + 3.21558i −0.555590 + 0.126810i −0.491092 0.871108i \(-0.663402\pi\)
−0.0644988 + 0.997918i \(0.520545\pi\)
\(644\) 9.09078 + 11.6798i 0.358227 + 0.460250i
\(645\) 69.0756 + 15.7661i 2.71985 + 0.620788i
\(646\) 1.50638 0.680616i 0.0592677 0.0267785i
\(647\) 45.7011 + 14.0969i 1.79670 + 0.554207i 0.998818 0.0486105i \(-0.0154793\pi\)
0.797879 + 0.602818i \(0.205955\pi\)
\(648\) −26.1139 17.7464i −1.02585 0.697146i
\(649\) 16.4652 41.9526i 0.646315 1.64678i
\(650\) −40.4870 39.4502i −1.58803 1.54736i
\(651\) 0.122743 + 3.31144i 0.00481068 + 0.129786i
\(652\) −1.70848 6.68152i −0.0669094 0.261668i
\(653\) −19.6072 21.1316i −0.767290 0.826942i 0.221670 0.975122i \(-0.428849\pi\)
−0.988960 + 0.148180i \(0.952659\pi\)
\(654\) 4.46451 2.43415i 0.174576 0.0951830i
\(655\) −3.98265 + 6.89816i −0.155615 + 0.269533i
\(656\) −11.5901 + 4.24488i −0.452516 + 0.165735i
\(657\) −9.13194 11.4511i −0.356271 0.446749i
\(658\) 18.9044 + 38.0205i 0.736970 + 1.48219i
\(659\) −3.24594 2.58855i −0.126444 0.100836i 0.558226 0.829689i \(-0.311482\pi\)
−0.684670 + 0.728853i \(0.740054\pi\)
\(660\) −51.7398 84.4772i −2.01397 3.28827i
\(661\) 9.98470 + 14.6449i 0.388360 + 0.569619i 0.969779 0.243985i \(-0.0784547\pi\)
−0.581419 + 0.813604i \(0.697502\pi\)
\(662\) −0.384683 0.276275i −0.0149511 0.0107377i
\(663\) −1.49079 0.224701i −0.0578976 0.00872666i
\(664\) −9.18683 + 3.62158i −0.356518 + 0.140544i
\(665\) 31.1683 + 49.6428i 1.20866 + 1.92506i
\(666\) −3.76230 + 6.16370i −0.145786 + 0.238838i
\(667\) −5.44906 + 3.14602i −0.210988 + 0.121814i
\(668\) 3.64693 + 20.5618i 0.141104 + 0.795559i
\(669\) 0.0186580 + 0.123788i 0.000721359 + 0.00478590i
\(670\) −36.1276 + 70.5568i −1.39573 + 2.72585i
\(671\) −5.32739 2.56554i −0.205662 0.0990415i
\(672\) −25.4119 20.6971i −0.980286 0.798410i
\(673\) −39.6299 + 19.0848i −1.52762 + 0.735663i −0.993930 0.110017i \(-0.964910\pi\)
−0.533691 + 0.845680i \(0.679195\pi\)
\(674\) −0.378529 + 15.4912i −0.0145804 + 0.596701i
\(675\) −34.1815 2.56155i −1.31565 0.0985941i
\(676\) 6.51289 2.75313i 0.250496 0.105890i
\(677\) −42.5061 + 3.18539i −1.63364 + 0.122424i −0.859688 0.510819i \(-0.829342\pi\)
−0.773952 + 0.633244i \(0.781723\pi\)
\(678\) 39.0387 4.91213i 1.49927 0.188649i
\(679\) 21.1770 + 5.68233i 0.812700 + 0.218068i
\(680\) −0.787527 + 2.56685i −0.0302003 + 0.0984341i
\(681\) −8.22817 + 2.53806i −0.315304 + 0.0972585i
\(682\) 3.23251 2.85561i 0.123779 0.109347i
\(683\) −9.47791 + 10.2148i −0.362662 + 0.390857i −0.887853 0.460128i \(-0.847804\pi\)
0.525190 + 0.850985i \(0.323994\pi\)
\(684\) 1.88599 + 18.6581i 0.0721126 + 0.713410i
\(685\) 37.5953i 1.43644i
\(686\) −13.3652 22.5249i −0.510286 0.860005i
\(687\) −18.6521 −0.711621
\(688\) −21.8846 21.2599i −0.834343 0.810525i
\(689\) 0.397768 + 0.369075i 0.0151538 + 0.0140606i
\(690\) 24.3262 + 27.5370i 0.926082 + 1.04832i
\(691\) −1.75809 5.69959i −0.0668809 0.216823i 0.915963 0.401263i \(-0.131429\pi\)
−0.982844 + 0.184441i \(0.940953\pi\)
\(692\) 2.40037 3.17556i 0.0912482 0.120717i
\(693\) 6.56391 24.4625i 0.249342 0.929255i
\(694\) 29.9324 3.76632i 1.13622 0.142967i
\(695\) 2.86860 + 38.2788i 0.108812 + 1.45200i
\(696\) 10.1991 9.49211i 0.386598 0.359798i
\(697\) −0.0516053 + 0.688625i −0.00195469 + 0.0260835i
\(698\) 25.3092 + 0.618430i 0.957967 + 0.0234079i
\(699\) 19.0707 + 39.6007i 0.721319 + 1.49783i
\(700\) −67.8582 11.0492i −2.56480 0.417619i
\(701\) −19.0068 + 39.4681i −0.717878 + 1.49069i 0.147229 + 0.989102i \(0.452965\pi\)
−0.865107 + 0.501587i \(0.832750\pi\)
\(702\) −5.23125 + 10.2166i −0.197441 + 0.385600i
\(703\) −14.6896 + 2.21411i −0.554030 + 0.0835066i
\(704\) 0.128781 + 42.6591i 0.00485362 + 1.60778i
\(705\) 52.7050 + 91.2878i 1.98499 + 3.43810i
\(706\) −31.2277 19.0613i −1.17527 0.717380i
\(707\) −39.4765 + 24.7854i −1.48467 + 0.932152i
\(708\) −0.960051 37.0028i −0.0360809 1.39065i
\(709\) −4.08529 + 27.1041i −0.153426 + 1.01792i 0.771077 + 0.636742i \(0.219718\pi\)
−0.924503 + 0.381175i \(0.875520\pi\)
\(710\) −5.67104 4.07287i −0.212830 0.152852i
\(711\) 13.8787 9.46232i 0.520491 0.354865i
\(712\) 18.7159 23.5418i 0.701407 0.882266i
\(713\) −0.997455 + 1.25077i −0.0373550 + 0.0468417i
\(714\) −1.64186 + 0.816361i −0.0614452 + 0.0305516i
\(715\) −54.4048 + 43.3864i −2.03463 + 1.62256i
\(716\) 16.4527 45.3453i 0.614865 1.69463i
\(717\) −30.5337 17.6286i −1.14030 0.658354i
\(718\) −31.7768 + 17.3254i −1.18590 + 0.646579i
\(719\) 9.54847 8.85969i 0.356098 0.330411i −0.481756 0.876306i \(-0.660001\pi\)
0.837854 + 0.545895i \(0.183810\pi\)
\(720\) −24.7677 17.7313i −0.923038 0.660806i
\(721\) 22.7637 0.843770i 0.847766 0.0314236i
\(722\) −8.17151 + 8.38627i −0.304112 + 0.312105i
\(723\) 10.9190 + 4.28540i 0.406083 + 0.159376i
\(724\) 19.7716 14.2450i 0.734804 0.529411i
\(725\) 8.61498 27.9291i 0.319952 1.03726i
\(726\) −49.2033 + 22.2312i −1.82611 + 0.825076i
\(727\) −1.75124 + 7.67268i −0.0649499 + 0.284564i −0.996965 0.0778564i \(-0.975192\pi\)
0.932015 + 0.362421i \(0.118050\pi\)
\(728\) −12.2259 + 19.5075i −0.453121 + 0.722997i
\(729\) −0.602787 2.64098i −0.0223254 0.0978142i
\(730\) 29.5704 + 38.9976i 1.09445 + 1.44337i
\(731\) −1.58901 + 0.623640i −0.0587716 + 0.0230662i
\(732\) −4.85063 0.237192i −0.179285 0.00876687i
\(733\) 14.6498 21.4873i 0.541102 0.793651i −0.454156 0.890922i \(-0.650059\pi\)
0.995258 + 0.0972714i \(0.0310115\pi\)
\(734\) 30.3768 11.0736i 1.12123 0.408733i
\(735\) −36.5900 53.7486i −1.34964 1.98255i
\(736\) −2.78676 15.5753i −0.102721 0.574113i
\(737\) 58.2189 + 39.6929i 2.14452 + 1.46211i
\(738\) −7.22065 3.03948i −0.265796 0.111885i
\(739\) 32.0043 12.5607i 1.17730 0.462054i 0.305627 0.952151i \(-0.401134\pi\)
0.871668 + 0.490097i \(0.163039\pi\)
\(740\) 13.0710 20.2827i 0.480500 0.745605i
\(741\) 34.3042 7.82971i 1.26020 0.287632i
\(742\) 0.653765 + 0.0901173i 0.0240005 + 0.00330831i
\(743\) 9.38887 41.1353i 0.344444 1.50911i −0.445137 0.895463i \(-0.646845\pi\)
0.789581 0.613646i \(-0.210298\pi\)
\(744\) 1.53222 3.19401i 0.0561738 0.117098i
\(745\) 24.4397 + 7.53865i 0.895401 + 0.276195i
\(746\) −8.12066 + 2.28921i −0.297318 + 0.0838139i
\(747\) −5.83451 2.28988i −0.213474 0.0837822i
\(748\) 2.17645 + 0.979419i 0.0795791 + 0.0358111i
\(749\) 5.65436 + 1.07192i 0.206606 + 0.0391670i
\(750\) −104.480 10.4017i −3.81507 0.379817i
\(751\) 9.55944 8.86986i 0.348829 0.323666i −0.486225 0.873833i \(-0.661627\pi\)
0.835054 + 0.550167i \(0.185436\pi\)
\(752\) 1.04034 45.3807i 0.0379374 1.65487i
\(753\) −3.36355 + 5.82584i −0.122575 + 0.212305i
\(754\) −7.50049 6.28723i −0.273152 0.228967i
\(755\) 12.1958 9.72585i 0.443852 0.353960i
\(756\) 1.91743 + 13.8275i 0.0697362 + 0.502903i
\(757\) −18.8694 15.0479i −0.685821 0.546924i 0.217409 0.976081i \(-0.430239\pi\)
−0.903230 + 0.429157i \(0.858811\pi\)
\(758\) 5.83936 + 28.8110i 0.212095 + 1.04646i
\(759\) 26.9860 18.3988i 0.979530 0.667832i
\(760\) −4.77716 62.4811i −0.173286 2.26643i
\(761\) 28.3854 + 4.27841i 1.02897 + 0.155092i 0.641765 0.766901i \(-0.278202\pi\)
0.387205 + 0.921994i \(0.373440\pi\)
\(762\) −12.3359 4.13773i −0.446882 0.149894i
\(763\) −4.09998 1.43626i −0.148429 0.0519961i
\(764\) −31.5836 6.35168i −1.14265 0.229796i
\(765\) −1.47586 + 0.852090i −0.0533600 + 0.0308074i
\(766\) 4.70703 26.7737i 0.170072 0.967372i
\(767\) −25.7109 + 3.87529i −0.928366 + 0.139929i
\(768\) 13.7394 + 32.2306i 0.495778 + 1.16302i
\(769\) −7.13222 3.43470i −0.257195 0.123858i 0.300844 0.953673i \(-0.402732\pi\)
−0.558039 + 0.829815i \(0.688446\pi\)
\(770\) −23.9234 + 81.1811i −0.862140 + 2.92556i
\(771\) −19.4537 40.3960i −0.700607 1.45482i
\(772\) −5.29025 15.6933i −0.190400 0.564814i
\(773\) 6.40220 + 0.479778i 0.230271 + 0.0172564i 0.189366 0.981907i \(-0.439357\pi\)
0.0409052 + 0.999163i \(0.486976\pi\)
\(774\) −0.975040 19.3413i −0.0350471 0.695209i
\(775\) −0.555343 7.41054i −0.0199485 0.266194i
\(776\) −17.2068 15.9173i −0.617688 0.571398i
\(777\) 16.1926 3.05792i 0.580905 0.109702i
\(778\) 37.0421 23.9508i 1.32803 0.858677i
\(779\) −4.75051 15.4008i −0.170205 0.551790i
\(780\) −27.2830 + 50.2202i −0.976887 + 1.79817i
\(781\) −4.22144 + 4.54963i −0.151055 + 0.162798i
\(782\) −0.857970 0.218006i −0.0306809 0.00779589i
\(783\) −5.93457 −0.212084
\(784\) 1.43236 + 27.9633i 0.0511558 + 0.998691i
\(785\) −11.4634 −0.409148
\(786\) 5.63620 + 1.43213i 0.201037 + 0.0510826i
\(787\) −6.86894 + 7.40296i −0.244851 + 0.263887i −0.843505 0.537121i \(-0.819512\pi\)
0.598654 + 0.801008i \(0.295702\pi\)
\(788\) 12.1341 22.3354i 0.432259 0.795665i
\(789\) −4.00927 12.9977i −0.142734 0.462732i
\(790\) −47.1339 + 30.4759i −1.67695 + 1.08429i
\(791\) −25.4716 21.9356i −0.905666 0.779942i
\(792\) −18.3868 + 19.8763i −0.653346 + 0.706275i
\(793\) 0.254934 + 3.40185i 0.00905296 + 0.120803i
\(794\) −2.13230 42.2972i −0.0756725 1.50107i
\(795\) 1.63375 + 0.122433i 0.0579431 + 0.00434223i
\(796\) 10.0065 + 29.6839i 0.354672 + 1.05212i
\(797\) −10.0066 20.7789i −0.354452 0.736028i 0.645155 0.764052i \(-0.276793\pi\)
−0.999607 + 0.0280238i \(0.991079\pi\)
\(798\) 28.7095 31.7355i 1.01631 1.12342i
\(799\) −2.28810 1.10189i −0.0809471 0.0389821i
\(800\) 58.6998 + 44.2314i 2.07535 + 1.56382i
\(801\) 18.8759 2.84508i 0.666946 0.100526i
\(802\) −0.807956 + 4.59567i −0.0285299 + 0.162279i
\(803\) 37.6758 21.7521i 1.32955 0.767616i
\(804\) 56.7363 + 11.4101i 2.00093 + 0.402402i
\(805\) 3.52559 31.1922i 0.124261 1.09938i
\(806\) −2.35925 0.791345i −0.0831010 0.0278739i
\(807\) 5.36161 + 0.808133i 0.188738 + 0.0284476i
\(808\) 49.6857 3.79885i 1.74794 0.133643i
\(809\) 6.17703 4.21143i 0.217173 0.148066i −0.449848 0.893105i \(-0.648522\pi\)
0.667020 + 0.745039i \(0.267569\pi\)
\(810\) 13.3016 + 65.6293i 0.467371 + 2.30598i
\(811\) −1.79517 1.43160i −0.0630368 0.0502702i 0.591465 0.806331i \(-0.298550\pi\)
−0.654501 + 0.756061i \(0.727121\pi\)
\(812\) −11.8587 1.02966i −0.416157 0.0361341i
\(813\) −24.6959 + 19.6943i −0.866124 + 0.690711i
\(814\) −16.4379 13.7789i −0.576147 0.482951i
\(815\) −7.31339 + 12.6672i −0.256177 + 0.443711i
\(816\) 1.95971 + 0.0449258i 0.0686035 + 0.00157272i
\(817\) 29.2045 27.0978i 1.02174 0.948032i
\(818\) −30.1375 3.00040i −1.05373 0.104906i
\(819\) −14.1159 + 3.77705i −0.493250 + 0.131981i
\(820\) 23.8724 + 10.7427i 0.833661 + 0.375153i
\(821\) 30.8018 + 12.0888i 1.07499 + 0.421903i 0.835780 0.549065i \(-0.185016\pi\)
0.239211 + 0.970968i \(0.423111\pi\)
\(822\) −26.4180 + 7.44721i −0.921432 + 0.259751i
\(823\) −3.09524 0.954756i −0.107893 0.0332807i 0.240338 0.970689i \(-0.422742\pi\)
−0.348232 + 0.937408i \(0.613218\pi\)
\(824\) −21.9565 10.5329i −0.764890 0.366930i
\(825\) −33.7603 + 147.913i −1.17538 + 5.14968i
\(826\) −22.9083 + 21.8002i −0.797083 + 0.758526i
\(827\) 18.2213 4.15890i 0.633618 0.144619i 0.106365 0.994327i \(-0.466079\pi\)
0.527254 + 0.849708i \(0.323222\pi\)
\(828\) 5.44025 8.44178i 0.189062 0.293372i
\(829\) 5.67262 2.22634i 0.197018 0.0773239i −0.264780 0.964309i \(-0.585299\pi\)
0.461799 + 0.886985i \(0.347204\pi\)
\(830\) 19.3032 + 8.12555i 0.670024 + 0.282042i
\(831\) 50.2597 + 34.2665i 1.74349 + 1.18869i
\(832\) 21.2770 12.3701i 0.737649 0.428856i
\(833\) 1.45784 + 0.573338i 0.0505110 + 0.0198650i
\(834\) 26.3300 9.59834i 0.911733 0.332363i
\(835\) 24.9495 36.5942i 0.863414 1.26640i
\(836\) −55.6358 2.72054i −1.92420 0.0940920i
\(837\) −1.40460 + 0.551265i −0.0485501 + 0.0190545i
\(838\) −1.26263 1.66516i −0.0436168 0.0575220i
\(839\) 4.05587 + 17.7699i 0.140024 + 0.613486i 0.995427 + 0.0955232i \(0.0304524\pi\)
−0.855403 + 0.517963i \(0.826690\pi\)
\(840\) 7.86275 + 69.0643i 0.271291 + 2.38295i
\(841\) −5.32709 + 23.3395i −0.183693 + 0.804810i
\(842\) −6.98992 + 3.15820i −0.240888 + 0.108839i
\(843\) −2.34767 + 7.61095i −0.0808579 + 0.262135i
\(844\) 15.6278 11.2595i 0.537933 0.387569i
\(845\) −13.9600 5.47889i −0.480238 0.188480i
\(846\) 20.1069 20.6353i 0.691289 0.709458i
\(847\) 42.2724 + 18.4609i 1.45250 + 0.634324i
\(848\) −0.573661 0.410685i −0.0196996 0.0141030i
\(849\) −20.4822 + 19.0047i −0.702946 + 0.652239i
\(850\) 3.61031 1.96843i 0.123833 0.0675165i
\(851\) 6.88976 + 3.97781i 0.236178 + 0.136357i
\(852\) −1.73861 + 4.79179i −0.0595638 + 0.164164i
\(853\) −27.7153 + 22.1022i −0.948954 + 0.756766i −0.970023 0.243012i \(-0.921864\pi\)
0.0210692 + 0.999778i \(0.493293\pi\)
\(854\) 2.62760 + 3.21093i 0.0899146 + 0.109876i
\(855\) 24.7984 31.0963i 0.848089 1.06347i
\(856\) −4.81595 3.82871i −0.164606 0.130863i
\(857\) 42.1498 28.7373i 1.43981 0.981647i 0.443461 0.896294i \(-0.353751\pi\)
0.996351 0.0853528i \(-0.0272018\pi\)
\(858\) 41.2643 + 29.6355i 1.40874 + 1.01174i
\(859\) 6.80077 45.1202i 0.232039 1.53948i −0.504695 0.863298i \(-0.668395\pi\)
0.736734 0.676183i \(-0.236367\pi\)
\(860\) 1.67838 + 64.6890i 0.0572323 + 2.20588i
\(861\) 5.89875 + 16.8766i 0.201029 + 0.575154i
\(862\) −30.4304 18.5746i −1.03647 0.632655i
\(863\) −20.5628 35.6159i −0.699967 1.21238i −0.968477 0.249102i \(-0.919865\pi\)
0.268510 0.963277i \(-0.413469\pi\)
\(864\) 5.06891 14.0365i 0.172448 0.477531i
\(865\) −8.34836 + 1.25831i −0.283853 + 0.0427839i
\(866\) −5.58446 + 10.9064i −0.189768 + 0.370615i
\(867\) −16.1045 + 33.4413i −0.546937 + 1.13573i
\(868\) −2.90237 + 0.857855i −0.0985127 + 0.0291175i
\(869\) 21.6478 + 44.9521i 0.734352 + 1.52490i
\(870\) −29.5413 0.721840i −1.00154 0.0244727i
\(871\) 3.03795 40.5386i 0.102937 1.37360i
\(872\) 3.16401 + 3.39968i 0.107147 + 0.115128i
\(873\) −1.11182 14.8362i −0.0376294 0.502130i
\(874\) 20.4987 2.57930i 0.693379 0.0872461i
\(875\) 53.2417 + 72.1928i 1.79990 + 2.44056i
\(876\) 21.5458 28.5039i 0.727965 0.963059i
\(877\) −12.8867 41.7776i −0.435152 1.41073i −0.862231 0.506515i \(-0.830933\pi\)
0.427079 0.904215i \(-0.359543\pi\)
\(878\) 4.33218 + 4.90398i 0.146204 + 0.165501i
\(879\) 29.8490 + 27.6958i 1.00678 + 0.934157i
\(880\) 63.0433 64.8959i 2.12519 2.18764i
\(881\) 8.84863 0.298118 0.149059 0.988828i \(-0.452376\pi\)
0.149059 + 0.988828i \(0.452376\pi\)
\(882\) −11.4264 + 13.6120i −0.384746 + 0.458338i
\(883\) 17.1873i 0.578398i 0.957269 + 0.289199i \(0.0933889\pi\)
−0.957269 + 0.289199i \(0.906611\pi\)
\(884\) −0.138479 1.36997i −0.00465755 0.0460772i
\(885\) −53.3974 + 57.5487i −1.79493 + 1.93448i
\(886\) −4.28391 + 3.78441i −0.143921 + 0.127140i
\(887\) 16.5632 5.10908i 0.556139 0.171546i −0.00392994 0.999992i \(-0.501251\pi\)
0.560069 + 0.828446i \(0.310775\pi\)
\(888\) −16.8417 5.16715i −0.565171 0.173398i
\(889\) 4.44165 + 10.1901i 0.148968 + 0.341765i
\(890\) −63.2869 + 7.96322i −2.12138 + 0.266928i
\(891\) 59.3584 4.44829i 1.98858 0.149023i
\(892\) −0.105312 + 0.0445177i −0.00352611 + 0.00149056i
\(893\) 59.1056 + 4.42935i 1.97789 + 0.148223i
\(894\) 0.456126 18.6669i 0.0152551 0.624315i
\(895\) −92.1759 + 44.3896i −3.08110 + 1.48378i
\(896\) 12.5642 27.1687i 0.419742 0.907644i
\(897\) −16.9773 8.17585i −0.566857 0.272984i
\(898\) 3.27551 6.39704i 0.109305 0.213472i
\(899\) −0.191760 1.27224i −0.00639554 0.0424316i
\(900\) 8.14709 + 45.9341i 0.271570 + 1.53114i
\(901\) −0.0341834 + 0.0197358i −0.00113881 + 0.000657494i
\(902\) 12.1239 19.8623i 0.403680 0.661341i
\(903\) −31.2599 + 31.2380i −1.04027 + 1.03954i
\(904\) 13.1794 + 33.4321i 0.438340 + 1.11193i
\(905\) −51.1064 7.70304i −1.69883 0.256058i
\(906\) −9.25015 6.64334i −0.307316 0.220710i
\(907\) 27.0470 + 39.6706i 0.898080 + 1.31724i 0.947928 + 0.318485i \(0.103174\pi\)
−0.0498474 + 0.998757i \(0.515874\pi\)
\(908\) −4.10751 6.70646i −0.136313 0.222562i
\(909\) 24.7281 + 19.7200i 0.820180 + 0.654071i
\(910\) 47.4624 11.4650i 1.57336 0.380060i
\(911\) −11.1576 13.9912i −0.369669 0.463550i 0.561852 0.827238i \(-0.310089\pi\)
−0.931521 + 0.363688i \(0.881518\pi\)
\(912\) −42.9587 + 15.7337i −1.42251 + 0.520994i
\(913\) 9.30854 16.1229i 0.308068 0.533589i
\(914\) 18.8358 10.2697i 0.623032 0.339692i
\(915\) 7.00578 + 7.55044i 0.231604 + 0.249610i
\(916\) −4.22021 16.5043i −0.139440 0.545319i
\(917\) −2.31995 4.39330i −0.0766117 0.145079i
\(918\) −0.598000 0.582686i −0.0197369 0.0192315i
\(919\) −9.34828 + 23.8190i −0.308371 + 0.785717i 0.689727 + 0.724070i \(0.257731\pi\)
−0.998098 + 0.0616473i \(0.980365\pi\)
\(920\) −18.8622 + 27.7556i −0.621867 + 0.915075i
\(921\) 15.9013 + 4.90490i 0.523965 + 0.161622i
\(922\) 53.1795 24.0277i 1.75137 0.791311i
\(923\) 3.49092 + 0.796780i 0.114905 + 0.0262263i
\(924\) 61.7843 + 0.729759i 2.03255 + 0.0240073i
\(925\) −36.0286 + 8.22330i −1.18461 + 0.270381i
\(926\) −24.1610 + 18.3204i −0.793980 + 0.602046i
\(927\) −5.64699 14.3883i −0.185471 0.472574i
\(928\) 10.7068 + 6.87706i 0.351467 + 0.225751i
\(929\) −18.1437 12.3702i −0.595275 0.405852i 0.227863 0.973693i \(-0.426826\pi\)
−0.823138 + 0.567841i \(0.807779\pi\)
\(930\) −7.05891 + 2.57326i −0.231471 + 0.0843804i
\(931\) −36.5609 0.0256286i −1.19823 0.000839943i
\(932\) −30.7258 + 25.8348i −1.00646 + 0.846246i
\(933\) −26.6919 + 39.1498i −0.873854 + 1.28171i
\(934\) 14.4274 34.2741i 0.472080 1.12148i
\(935\) −1.84932 4.71199i −0.0604792 0.154099i
\(936\) 15.2350 + 3.45310i 0.497972 + 0.112868i
\(937\) −11.1566 48.8802i −0.364470 1.59685i −0.741704 0.670728i \(-0.765982\pi\)
0.377234 0.926118i \(-0.376875\pi\)
\(938\) −25.2595 42.5029i −0.824751 1.38777i
\(939\) −39.2897 8.96761i −1.28217 0.292647i
\(940\) −68.8512 + 67.2909i −2.24568 + 2.19479i
\(941\) −6.77382 + 21.9602i −0.220820 + 0.715882i 0.775591 + 0.631236i \(0.217452\pi\)
−0.996411 + 0.0846458i \(0.973024\pi\)
\(942\) 2.27078 + 8.05528i 0.0739860 + 0.262455i
\(943\) −3.15327 + 8.03441i −0.102685 + 0.261636i
\(944\) 32.5248 9.22174i 1.05859 0.300142i
\(945\) 17.5898 23.8159i 0.572198 0.774732i
\(946\) 57.2391 + 5.69855i 1.86101 + 0.185276i
\(947\) −2.63383 2.83859i −0.0855879 0.0922418i 0.688806 0.724946i \(-0.258135\pi\)
−0.774393 + 0.632704i \(0.781945\pi\)
\(948\) 30.7519 + 27.0837i 0.998776 + 0.879639i
\(949\) −21.7364 12.5495i −0.705595 0.407375i
\(950\) −61.6519 + 73.5490i −2.00025 + 2.38624i
\(951\) −37.9494 47.5870i −1.23059 1.54311i
\(952\) −1.09385 1.26810i −0.0354518 0.0410993i
\(953\) 35.8191 44.9157i 1.16029 1.45496i 0.293736 0.955886i \(-0.405101\pi\)
0.866558 0.499077i \(-0.166327\pi\)
\(954\) −0.0889510 0.438878i −0.00287990 0.0142092i
\(955\) 38.4898 + 56.4542i 1.24550 + 1.82682i
\(956\) 8.69021 31.0065i 0.281061 1.00282i
\(957\) −3.91495 + 25.9740i −0.126552 + 0.839620i
\(958\) 3.63424 10.8348i 0.117417 0.350057i
\(959\) 19.8508 + 12.4828i 0.641017 + 0.403091i
\(960\) 26.9395 69.2547i 0.869468 2.23519i
\(961\) 15.3364 + 26.5635i 0.494724 + 0.856887i
\(962\) −2.14271 + 12.1878i −0.0690839 + 0.392950i
\(963\) −0.582018 3.86144i −0.0187553 0.124433i
\(964\) −1.32142 + 10.6313i −0.0425599 + 0.342413i
\(965\) −15.2398 + 31.6458i −0.490588 + 1.01872i
\(966\) −22.6169 + 3.70142i −0.727688 + 0.119091i
\(967\) 39.5221 19.0328i 1.27095 0.612055i 0.327898 0.944713i \(-0.393660\pi\)
0.943048 + 0.332658i \(0.107945\pi\)
\(968\) −30.8040 38.5077i −0.990079 1.23768i
\(969\) −0.191276 + 2.55240i −0.00614466 + 0.0819948i
\(970\) 2.50302 + 49.6509i 0.0803671 + 1.59420i
\(971\) −9.21437 + 0.690522i −0.295703 + 0.0221599i −0.221756 0.975102i \(-0.571179\pi\)
−0.0739475 + 0.997262i \(0.523560\pi\)
\(972\) 29.4039 15.1119i 0.943129 0.484713i
\(973\) −21.1642 11.1951i −0.678492 0.358898i
\(974\) 21.7164 + 33.5865i 0.695838 + 1.07618i
\(975\) 83.6422 25.8002i 2.67869 0.826267i
\(976\) −0.887623 4.34576i −0.0284121 0.139105i
\(977\) −39.8939 37.0162i −1.27632 1.18425i −0.972857 0.231409i \(-0.925667\pi\)
−0.303463 0.952843i \(-0.598143\pi\)
\(978\) 10.3498 + 2.62984i 0.330951 + 0.0840931i
\(979\) 56.7000i 1.81214i
\(980\) 39.2808 44.5379i 1.25478 1.42271i
\(981\) 2.94777i 0.0941150i
\(982\) 8.03392 31.6177i 0.256373 1.00896i
\(983\) −34.0586 31.6018i −1.08630 1.00794i −0.999932 0.0116769i \(-0.996283\pi\)
−0.0863692 0.996263i \(-0.527526\pi\)
\(984\) 2.81999 18.9030i 0.0898981 0.602605i
\(985\) −51.5153 + 15.8904i −1.64141 + 0.506309i
\(986\) 0.597851 0.386560i 0.0190395 0.0123106i
\(987\) −65.7009 2.48141i −2.09128 0.0789842i
\(988\) 14.6898 + 28.5826i 0.467345 + 0.909335i
\(989\) −21.2757 + 1.59439i −0.676528 + 0.0506987i
\(990\) 57.3540 2.89135i 1.82283 0.0918931i
\(991\) 4.28621 57.1954i 0.136156 1.81687i −0.343211 0.939258i \(-0.611514\pi\)
0.479366 0.877615i \(-0.340866\pi\)
\(992\) 3.17290 + 0.633113i 0.100740 + 0.0201013i
\(993\) 0.660730 0.318191i 0.0209676 0.0100975i
\(994\) 4.03349 1.64206i 0.127935 0.0520831i
\(995\) 28.8262 59.8582i 0.913852 1.89763i
\(996\) 1.88602 15.1738i 0.0597608 0.480800i
\(997\) −1.70343 11.3015i −0.0539481 0.357922i −0.999476 0.0323800i \(-0.989691\pi\)
0.945528 0.325542i \(-0.105547\pi\)
\(998\) −44.9222 7.89769i −1.42199 0.249997i
\(999\) 3.75182 + 6.49833i 0.118702 + 0.205598i
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 392.2.z.a.53.6 yes 648
8.5 even 2 inner 392.2.z.a.53.15 yes 648
49.37 even 21 inner 392.2.z.a.37.15 yes 648
392.37 even 42 inner 392.2.z.a.37.6 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.z.a.37.6 648 392.37 even 42 inner
392.2.z.a.37.15 yes 648 49.37 even 21 inner
392.2.z.a.53.6 yes 648 1.1 even 1 trivial
392.2.z.a.53.15 yes 648 8.5 even 2 inner