Properties

Label 162.2.g.a.31.3
Level $162$
Weight $2$
Character 162.31
Analytic conductor $1.294$
Analytic rank $0$
Dimension $72$
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] = [162,2,Mod(7,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\), degree \(18\), 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(4\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 31.3
Character \(\chi\) \(=\) 162.31
Dual form 162.2.g.a.115.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +O(q^{10})\) \(q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +(2.29243 - 0.834375i) q^{10} +(-1.56143 + 1.02697i) q^{11} +(-1.72346 - 0.172300i) q^{12} +(4.35581 - 0.509122i) q^{13} +(0.414704 + 0.557045i) q^{14} +(-3.49099 + 2.38058i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-3.09677 - 2.59850i) q^{17} +(2.96641 - 0.447666i) q^{18} +(6.05044 - 5.07693i) q^{19} +(-1.67412 - 1.77446i) q^{20} +(-0.934225 - 0.757666i) q^{21} +(1.56143 + 1.02697i) q^{22} +(2.63822 + 0.625269i) q^{23} +(0.524419 + 1.65075i) q^{24} +(-0.944964 - 0.110450i) q^{25} +(-2.19273 - 3.79792i) q^{26} +(-4.78758 + 2.01967i) q^{27} +(0.347231 - 0.601422i) q^{28} +(0.986496 - 1.32509i) q^{29} +(3.56860 + 2.26258i) q^{30} +(-2.29559 - 7.66782i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-3.05986 - 1.05613i) q^{33} +(-1.15942 + 3.87272i) q^{34} +(-0.294190 - 1.66844i) q^{35} +(-1.58599 - 2.54650i) q^{36} +(-1.07416 + 6.09184i) q^{37} +(-7.05817 - 3.54475i) q^{38} +(5.30420 + 5.43713i) q^{39} +(-0.966256 + 2.24003i) q^{40} +(-2.57993 + 5.98096i) q^{41} +(-0.325674 + 1.15792i) q^{42} +(-3.81384 - 1.91538i) q^{43} +(0.324528 - 1.84049i) q^{44} +(-6.95709 - 2.27189i) q^{45} +(-0.470813 - 2.67011i) q^{46} +(0.986899 - 3.29647i) q^{47} +(1.30804 - 1.13536i) q^{48} +(-5.82445 + 2.92515i) q^{49} +(0.272864 + 0.911429i) q^{50} +(0.290247 - 6.99588i) q^{51} +(-2.61882 + 3.51768i) q^{52} +(5.32106 - 9.21634i) q^{53} +(3.75076 + 3.59608i) q^{54} +(-2.27961 - 3.94840i) q^{55} +(-0.689767 - 0.0806222i) q^{56} +(13.3624 + 2.93198i) q^{57} +(-1.60745 - 0.380973i) q^{58} +(-5.75027 - 3.78201i) q^{59} +(0.664091 - 4.17291i) q^{60} +(7.31570 + 7.75419i) q^{61} +(-6.13147 + 5.14492i) q^{62} +(0.0515617 - 2.08275i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.622066 + 10.6805i) q^{65} +(0.242194 + 3.22792i) q^{66} +(-6.33676 - 8.51174i) q^{67} +(4.01521 - 0.469311i) q^{68} +(1.93184 + 4.28036i) q^{69} +(-1.41546 + 0.930964i) q^{70} +(7.97798 - 2.90375i) q^{71} +(-1.71005 + 2.46490i) q^{72} +(2.86854 + 1.04406i) q^{73} +(6.01908 - 1.42655i) q^{74} +(-0.847669 - 1.41313i) q^{75} +(-0.459245 + 7.88493i) q^{76} +(0.890651 - 0.944035i) q^{77} +(2.89158 - 7.02394i) q^{78} +(3.88894 + 9.01558i) q^{79} +2.43955 q^{80} +(-7.83297 - 4.43222i) q^{81} +6.51367 q^{82} +(2.85728 + 6.62392i) q^{83} +(1.19221 - 0.159589i) q^{84} +(6.76771 - 7.17335i) q^{85} +(-0.248150 + 4.26057i) q^{86} +(2.86092 - 0.0478192i) q^{87} +(-1.81850 + 0.430993i) q^{88} +(17.4051 + 6.33493i) q^{89} +(0.669479 + 7.28796i) q^{90} +(-2.86187 + 1.04164i) q^{91} +(-2.26526 + 1.48989i) q^{92} +(8.09168 - 11.2570i) q^{93} +(-3.41776 + 0.399479i) q^{94} +(11.5062 + 15.4555i) q^{95} +(-1.56059 - 0.751367i) q^{96} +(-0.260900 - 4.47948i) q^{97} +(4.99286 + 4.18951i) q^{98} +(-1.78661 - 5.31436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 9 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{10}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.396080 0.918216i −0.280071 0.649277i
\(3\) 1.05738 + 1.37184i 0.610481 + 0.792031i
\(4\) −0.686242 + 0.727374i −0.343121 + 0.363687i
\(5\) −0.141847 + 2.43542i −0.0634360 + 1.08915i 0.804975 + 0.593309i \(0.202179\pi\)
−0.868411 + 0.495845i \(0.834858\pi\)
\(6\) 0.840836 1.51426i 0.343270 0.618196i
\(7\) −0.675743 + 0.160154i −0.255407 + 0.0605326i −0.356325 0.934362i \(-0.615970\pi\)
0.100918 + 0.994895i \(0.467822\pi\)
\(8\) 0.939693 + 0.342020i 0.332232 + 0.120922i
\(9\) −0.763881 + 2.90112i −0.254627 + 0.967039i
\(10\) 2.29243 0.834375i 0.724929 0.263852i
\(11\) −1.56143 + 1.02697i −0.470788 + 0.309642i −0.762642 0.646821i \(-0.776098\pi\)
0.291854 + 0.956463i \(0.405728\pi\)
\(12\) −1.72346 0.172300i −0.497520 0.0497387i
\(13\) 4.35581 0.509122i 1.20809 0.141205i 0.511886 0.859053i \(-0.328947\pi\)
0.696199 + 0.717849i \(0.254873\pi\)
\(14\) 0.414704 + 0.557045i 0.110834 + 0.148876i
\(15\) −3.49099 + 2.38058i −0.901370 + 0.614664i
\(16\) −0.0581448 0.998308i −0.0145362 0.249577i
\(17\) −3.09677 2.59850i −0.751077 0.630228i 0.184711 0.982793i \(-0.440865\pi\)
−0.935787 + 0.352565i \(0.885310\pi\)
\(18\) 2.96641 0.447666i 0.699190 0.105516i
\(19\) 6.05044 5.07693i 1.38807 1.16473i 0.421951 0.906619i \(-0.361345\pi\)
0.966116 0.258108i \(-0.0830991\pi\)
\(20\) −1.67412 1.77446i −0.374345 0.396782i
\(21\) −0.934225 0.757666i −0.203865 0.165336i
\(22\) 1.56143 + 1.02697i 0.332897 + 0.218950i
\(23\) 2.63822 + 0.625269i 0.550107 + 0.130378i 0.496264 0.868172i \(-0.334705\pi\)
0.0538429 + 0.998549i \(0.482853\pi\)
\(24\) 0.524419 + 1.65075i 0.107047 + 0.336959i
\(25\) −0.944964 0.110450i −0.188993 0.0220901i
\(26\) −2.19273 3.79792i −0.430030 0.744834i
\(27\) −4.78758 + 2.01967i −0.921370 + 0.388686i
\(28\) 0.347231 0.601422i 0.0656205 0.113658i
\(29\) 0.986496 1.32509i 0.183188 0.246064i −0.701038 0.713124i \(-0.747280\pi\)
0.884225 + 0.467060i \(0.154687\pi\)
\(30\) 3.56860 + 2.26258i 0.651534 + 0.413089i
\(31\) −2.29559 7.66782i −0.412301 1.37718i −0.872174 0.489196i \(-0.837290\pi\)
0.459873 0.887985i \(-0.347895\pi\)
\(32\) −0.893633 + 0.448799i −0.157973 + 0.0793372i
\(33\) −3.05986 1.05613i −0.532653 0.183848i
\(34\) −1.15942 + 3.87272i −0.198838 + 0.664165i
\(35\) −0.294190 1.66844i −0.0497273 0.282017i
\(36\) −1.58599 2.54650i −0.264332 0.424416i
\(37\) −1.07416 + 6.09184i −0.176590 + 1.00149i 0.759702 + 0.650271i \(0.225345\pi\)
−0.936292 + 0.351222i \(0.885766\pi\)
\(38\) −7.05817 3.54475i −1.14499 0.575034i
\(39\) 5.30420 + 5.43713i 0.849351 + 0.870638i
\(40\) −0.966256 + 2.24003i −0.152778 + 0.354180i
\(41\) −2.57993 + 5.98096i −0.402918 + 0.934069i 0.589110 + 0.808053i \(0.299478\pi\)
−0.992028 + 0.126016i \(0.959781\pi\)
\(42\) −0.325674 + 1.15792i −0.0502525 + 0.178670i
\(43\) −3.81384 1.91538i −0.581605 0.292093i 0.133569 0.991040i \(-0.457356\pi\)
−0.715174 + 0.698946i \(0.753653\pi\)
\(44\) 0.324528 1.84049i 0.0489244 0.277464i
\(45\) −6.95709 2.27189i −1.03710 0.338673i
\(46\) −0.470813 2.67011i −0.0694176 0.393687i
\(47\) 0.986899 3.29647i 0.143954 0.480840i −0.855354 0.518044i \(-0.826660\pi\)
0.999308 + 0.0372047i \(0.0118454\pi\)
\(48\) 1.30804 1.13536i 0.188799 0.163875i
\(49\) −5.82445 + 2.92515i −0.832064 + 0.417878i
\(50\) 0.272864 + 0.911429i 0.0385888 + 0.128895i
\(51\) 0.290247 6.99588i 0.0406427 0.979619i
\(52\) −2.61882 + 3.51768i −0.363165 + 0.487815i
\(53\) 5.32106 9.21634i 0.730903 1.26596i −0.225594 0.974221i \(-0.572432\pi\)
0.956497 0.291741i \(-0.0942344\pi\)
\(54\) 3.75076 + 3.59608i 0.510414 + 0.489365i
\(55\) −2.27961 3.94840i −0.307383 0.532403i
\(56\) −0.689767 0.0806222i −0.0921740 0.0107736i
\(57\) 13.3624 + 2.93198i 1.76989 + 0.388350i
\(58\) −1.60745 0.380973i −0.211069 0.0500243i
\(59\) −5.75027 3.78201i −0.748621 0.492376i 0.116965 0.993136i \(-0.462683\pi\)
−0.865586 + 0.500760i \(0.833054\pi\)
\(60\) 0.664091 4.17291i 0.0857337 0.538720i
\(61\) 7.31570 + 7.75419i 0.936680 + 0.992822i 0.999987 0.00517165i \(-0.00164619\pi\)
−0.0633069 + 0.997994i \(0.520165\pi\)
\(62\) −6.13147 + 5.14492i −0.778698 + 0.653405i
\(63\) 0.0515617 2.08275i 0.00649616 0.262402i
\(64\) 0.766044 + 0.642788i 0.0957556 + 0.0803485i
\(65\) 0.622066 + 10.6805i 0.0771578 + 1.32475i
\(66\) 0.242194 + 3.22792i 0.0298121 + 0.397330i
\(67\) −6.33676 8.51174i −0.774158 1.03987i −0.997871 0.0652194i \(-0.979225\pi\)
0.223713 0.974655i \(-0.428182\pi\)
\(68\) 4.01521 0.469311i 0.486916 0.0569123i
\(69\) 1.93184 + 4.28036i 0.232566 + 0.515295i
\(70\) −1.41546 + 0.930964i −0.169180 + 0.111272i
\(71\) 7.97798 2.90375i 0.946812 0.344612i 0.177960 0.984038i \(-0.443050\pi\)
0.768852 + 0.639426i \(0.220828\pi\)
\(72\) −1.71005 + 2.46490i −0.201532 + 0.290491i
\(73\) 2.86854 + 1.04406i 0.335737 + 0.122198i 0.504387 0.863478i \(-0.331719\pi\)
−0.168650 + 0.985676i \(0.553941\pi\)
\(74\) 6.01908 1.42655i 0.699704 0.165833i
\(75\) −0.847669 1.41313i −0.0978804 0.163174i
\(76\) −0.459245 + 7.88493i −0.0526790 + 0.904464i
\(77\) 0.890651 0.944035i 0.101499 0.107583i
\(78\) 2.89158 7.02394i 0.327407 0.795304i
\(79\) 3.88894 + 9.01558i 0.437540 + 1.01433i 0.984213 + 0.176986i \(0.0566348\pi\)
−0.546673 + 0.837346i \(0.684106\pi\)
\(80\) 2.43955 0.272750
\(81\) −7.83297 4.43222i −0.870330 0.492469i
\(82\) 6.51367 0.719315
\(83\) 2.85728 + 6.62392i 0.313627 + 0.727070i 1.00000 0.000180023i \(-5.73031e-5\pi\)
−0.686373 + 0.727250i \(0.740798\pi\)
\(84\) 1.19221 0.159589i 0.130081 0.0174125i
\(85\) 6.76771 7.17335i 0.734061 0.778059i
\(86\) −0.248150 + 4.26057i −0.0267587 + 0.459429i
\(87\) 2.86092 0.0478192i 0.306723 0.00512676i
\(88\) −1.81850 + 0.430993i −0.193853 + 0.0459441i
\(89\) 17.4051 + 6.33493i 1.84493 + 0.671501i 0.987655 + 0.156648i \(0.0500688\pi\)
0.857279 + 0.514853i \(0.172153\pi\)
\(90\) 0.669479 + 7.28796i 0.0705692 + 0.768219i
\(91\) −2.86187 + 1.04164i −0.300006 + 0.109193i
\(92\) −2.26526 + 1.48989i −0.236170 + 0.155331i
\(93\) 8.09168 11.2570i 0.839068 1.16730i
\(94\) −3.41776 + 0.399479i −0.352515 + 0.0412031i
\(95\) 11.5062 + 15.4555i 1.18051 + 1.58570i
\(96\) −1.56059 0.751367i −0.159277 0.0766861i
\(97\) −0.260900 4.47948i −0.0264904 0.454822i −0.985307 0.170795i \(-0.945366\pi\)
0.958816 0.284027i \(-0.0916706\pi\)
\(98\) 4.99286 + 4.18951i 0.504355 + 0.423204i
\(99\) −1.78661 5.31436i −0.179561 0.534114i
\(100\) 0.728813 0.611546i 0.0728813 0.0611546i
\(101\) −4.70033 4.98206i −0.467701 0.495734i 0.449988 0.893035i \(-0.351428\pi\)
−0.917688 + 0.397301i \(0.869947\pi\)
\(102\) −6.53869 + 2.50442i −0.647426 + 0.247974i
\(103\) −8.80772 5.79293i −0.867851 0.570794i 0.0356581 0.999364i \(-0.488647\pi\)
−0.903509 + 0.428570i \(0.859018\pi\)
\(104\) 4.26726 + 1.01136i 0.418439 + 0.0991718i
\(105\) 1.97775 2.16776i 0.193009 0.211552i
\(106\) −10.5702 1.23547i −1.02666 0.120000i
\(107\) −7.99271 13.8438i −0.772685 1.33833i −0.936087 0.351770i \(-0.885580\pi\)
0.163402 0.986560i \(-0.447753\pi\)
\(108\) 1.81638 4.86834i 0.174781 0.468456i
\(109\) 2.49832 4.32722i 0.239296 0.414473i −0.721216 0.692710i \(-0.756417\pi\)
0.960513 + 0.278237i \(0.0897500\pi\)
\(110\) −2.72258 + 3.65706i −0.259588 + 0.348687i
\(111\) −9.49282 + 4.96784i −0.901019 + 0.471527i
\(112\) 0.199174 + 0.665288i 0.0188202 + 0.0628638i
\(113\) −8.68926 + 4.36391i −0.817417 + 0.410522i −0.807818 0.589432i \(-0.799352\pi\)
−0.00959849 + 0.999954i \(0.503055\pi\)
\(114\) −2.60037 13.4308i −0.243547 1.25791i
\(115\) −1.89702 + 6.33648i −0.176898 + 0.590880i
\(116\) 0.286864 + 1.62689i 0.0266346 + 0.151053i
\(117\) −1.85030 + 13.0256i −0.171060 + 1.20422i
\(118\) −1.19514 + 6.77797i −0.110021 + 0.623962i
\(119\) 2.50878 + 1.25996i 0.229980 + 0.115500i
\(120\) −4.09467 + 1.04303i −0.373790 + 0.0952148i
\(121\) −2.97348 + 6.89331i −0.270317 + 0.626665i
\(122\) 4.22242 9.78867i 0.382280 0.886225i
\(123\) −10.9329 + 2.78491i −0.985786 + 0.251107i
\(124\) 7.15270 + 3.59222i 0.642331 + 0.322591i
\(125\) −1.71508 + 9.72671i −0.153402 + 0.869984i
\(126\) −1.93284 + 0.777590i −0.172191 + 0.0692732i
\(127\) 0.799789 + 4.53583i 0.0709698 + 0.402490i 0.999511 + 0.0312611i \(0.00995234\pi\)
−0.928541 + 0.371229i \(0.878937\pi\)
\(128\) 0.286803 0.957990i 0.0253501 0.0846751i
\(129\) −1.40510 7.25727i −0.123712 0.638967i
\(130\) 9.56058 4.80150i 0.838518 0.421120i
\(131\) −0.842729 2.81491i −0.0736296 0.245940i 0.913250 0.407401i \(-0.133565\pi\)
−0.986879 + 0.161461i \(0.948380\pi\)
\(132\) 2.86800 1.50090i 0.249628 0.130637i
\(133\) −3.27546 + 4.39970i −0.284018 + 0.381503i
\(134\) −5.30576 + 9.18984i −0.458347 + 0.793881i
\(135\) −4.23965 11.9463i −0.364891 1.02817i
\(136\) −2.02127 3.50095i −0.173323 0.300204i
\(137\) −22.4321 2.62193i −1.91650 0.224007i −0.927708 0.373307i \(-0.878224\pi\)
−0.988792 + 0.149300i \(0.952298\pi\)
\(138\) 3.16513 3.46921i 0.269434 0.295319i
\(139\) −9.55124 2.26369i −0.810126 0.192003i −0.195379 0.980728i \(-0.562594\pi\)
−0.614747 + 0.788725i \(0.710742\pi\)
\(140\) 1.41546 + 0.930964i 0.119628 + 0.0786809i
\(141\) 5.56576 2.13177i 0.468721 0.179527i
\(142\) −5.82619 6.17540i −0.488923 0.518228i
\(143\) −6.27843 + 5.26823i −0.525029 + 0.440552i
\(144\) 2.94063 + 0.593904i 0.245052 + 0.0494920i
\(145\) 3.08723 + 2.59049i 0.256380 + 0.215129i
\(146\) −0.177495 3.04747i −0.0146896 0.252210i
\(147\) −10.1715 4.89720i −0.838932 0.403914i
\(148\) −3.69392 4.96179i −0.303638 0.407857i
\(149\) 8.85502 1.03500i 0.725431 0.0847908i 0.254641 0.967036i \(-0.418043\pi\)
0.470791 + 0.882245i \(0.343969\pi\)
\(150\) −0.961811 + 1.33805i −0.0785316 + 0.109252i
\(151\) 11.4929 7.55897i 0.935275 0.615140i 0.0122686 0.999925i \(-0.496095\pi\)
0.923006 + 0.384785i \(0.125724\pi\)
\(152\) 7.42197 2.70138i 0.602001 0.219111i
\(153\) 9.90411 6.99915i 0.800700 0.565848i
\(154\) −1.21960 0.443897i −0.0982779 0.0357702i
\(155\) 19.0000 4.50308i 1.52612 0.361696i
\(156\) −7.59479 + 0.126944i −0.608070 + 0.0101637i
\(157\) −1.03391 + 17.7515i −0.0825149 + 1.41673i 0.662192 + 0.749334i \(0.269626\pi\)
−0.744707 + 0.667392i \(0.767411\pi\)
\(158\) 6.73792 7.14178i 0.536040 0.568170i
\(159\) 18.2697 2.44557i 1.44888 0.193947i
\(160\) −0.966256 2.24003i −0.0763892 0.177090i
\(161\) −1.88290 −0.148393
\(162\) −0.967254 + 8.94787i −0.0759946 + 0.703011i
\(163\) −21.3005 −1.66839 −0.834193 0.551472i \(-0.814066\pi\)
−0.834193 + 0.551472i \(0.814066\pi\)
\(164\) −2.57993 5.98096i −0.201459 0.467035i
\(165\) 3.00615 7.30224i 0.234028 0.568478i
\(166\) 4.95048 5.24720i 0.384232 0.407262i
\(167\) 0.529121 9.08466i 0.0409446 0.702992i −0.913910 0.405917i \(-0.866952\pi\)
0.954854 0.297074i \(-0.0960109\pi\)
\(168\) −0.618747 1.03150i −0.0477374 0.0795817i
\(169\) 6.06432 1.43727i 0.466486 0.110559i
\(170\) −9.26724 3.37300i −0.710765 0.258697i
\(171\) 10.1069 + 21.4312i 0.772897 + 1.63889i
\(172\) 4.01041 1.45967i 0.305791 0.111299i
\(173\) −8.41308 + 5.53337i −0.639635 + 0.420694i −0.827473 0.561506i \(-0.810222\pi\)
0.187838 + 0.982200i \(0.439852\pi\)
\(174\) −1.17706 2.60800i −0.0892327 0.197712i
\(175\) 0.656242 0.0767037i 0.0496073 0.00579826i
\(176\) 1.11602 + 1.49907i 0.0841230 + 0.112997i
\(177\) −0.891930 11.8875i −0.0670415 0.893517i
\(178\) −1.07696 18.4907i −0.0807218 1.38594i
\(179\) 9.72888 + 8.16350i 0.727171 + 0.610169i 0.929359 0.369178i \(-0.120361\pi\)
−0.202188 + 0.979347i \(0.564805\pi\)
\(180\) 6.42676 3.50134i 0.479022 0.260974i
\(181\) −2.29087 + 1.92227i −0.170279 + 0.142881i −0.723945 0.689858i \(-0.757673\pi\)
0.553666 + 0.832739i \(0.313229\pi\)
\(182\) 2.08998 + 2.21525i 0.154919 + 0.164205i
\(183\) −2.90200 + 18.2351i −0.214522 + 1.34798i
\(184\) 2.26526 + 1.48989i 0.166997 + 0.109836i
\(185\) −14.6838 3.48013i −1.07958 0.255865i
\(186\) −13.5413 2.97124i −0.992897 0.217862i
\(187\) 7.50395 + 0.877086i 0.548743 + 0.0641389i
\(188\) 1.72052 + 2.98002i 0.125481 + 0.217340i
\(189\) 2.91172 2.13153i 0.211796 0.155046i
\(190\) 9.63414 16.6868i 0.698934 1.21059i
\(191\) 5.32394 7.15129i 0.385227 0.517449i −0.566638 0.823967i \(-0.691756\pi\)
0.951865 + 0.306517i \(0.0991637\pi\)
\(192\) −0.0717982 + 1.73056i −0.00518159 + 0.124893i
\(193\) −0.525396 1.75494i −0.0378188 0.126324i 0.936996 0.349341i \(-0.113595\pi\)
−0.974814 + 0.223017i \(0.928409\pi\)
\(194\) −4.00979 + 2.01379i −0.287886 + 0.144582i
\(195\) −13.9941 + 12.1467i −1.00214 + 0.869844i
\(196\) 1.86930 6.24391i 0.133522 0.445994i
\(197\) −2.56216 14.5308i −0.182547 1.03527i −0.929067 0.369911i \(-0.879388\pi\)
0.746520 0.665362i \(-0.231723\pi\)
\(198\) −4.17210 + 3.74540i −0.296498 + 0.266174i
\(199\) −4.46744 + 25.3361i −0.316688 + 1.79603i 0.245903 + 0.969294i \(0.420916\pi\)
−0.562591 + 0.826735i \(0.690196\pi\)
\(200\) −0.850200 0.426986i −0.0601182 0.0301925i
\(201\) 4.97635 17.6932i 0.351005 1.24798i
\(202\) −2.71290 + 6.28922i −0.190879 + 0.442508i
\(203\) −0.454399 + 1.05341i −0.0318925 + 0.0739352i
\(204\) 4.88944 + 5.01198i 0.342329 + 0.350909i
\(205\) −14.2002 7.13161i −0.991785 0.498093i
\(206\) −1.83060 + 10.3819i −0.127544 + 0.723338i
\(207\) −3.82927 + 7.17615i −0.266152 + 0.498777i
\(208\) −0.761528 4.31884i −0.0528025 0.299458i
\(209\) −4.23349 + 14.1409i −0.292837 + 0.978143i
\(210\) −2.77382 0.957400i −0.191412 0.0660669i
\(211\) 11.2716 5.66079i 0.775966 0.389705i −0.0163104 0.999867i \(-0.505192\pi\)
0.792277 + 0.610162i \(0.208896\pi\)
\(212\) 3.05219 + 10.1950i 0.209625 + 0.700198i
\(213\) 12.4193 + 7.87413i 0.850954 + 0.539526i
\(214\) −9.54583 + 12.8223i −0.652540 + 0.876513i
\(215\) 5.20575 9.01662i 0.355029 0.614928i
\(216\) −5.18962 + 0.260422i −0.353109 + 0.0177195i
\(217\) 2.77926 + 4.81383i 0.188669 + 0.326784i
\(218\) −4.96286 0.580076i −0.336128 0.0392877i
\(219\) 1.60086 + 5.03914i 0.108176 + 0.340514i
\(220\) 4.43633 + 1.05143i 0.299097 + 0.0708874i
\(221\) −14.8119 9.74194i −0.996356 0.655314i
\(222\) 8.32147 + 6.74880i 0.558500 + 0.452950i
\(223\) 8.54564 + 9.05785i 0.572258 + 0.606558i 0.947260 0.320466i \(-0.103839\pi\)
−0.375002 + 0.927024i \(0.622358\pi\)
\(224\) 0.531989 0.446392i 0.0355450 0.0298258i
\(225\) 1.04227 2.65708i 0.0694847 0.177139i
\(226\) 7.44865 + 6.25016i 0.495477 + 0.415754i
\(227\) 0.712321 + 12.2301i 0.0472784 + 0.811738i 0.935719 + 0.352747i \(0.114752\pi\)
−0.888441 + 0.458992i \(0.848211\pi\)
\(228\) −11.3024 + 7.70738i −0.748523 + 0.510434i
\(229\) −7.98067 10.7199i −0.527378 0.708391i 0.455997 0.889982i \(-0.349283\pi\)
−0.983374 + 0.181590i \(0.941876\pi\)
\(230\) 6.56963 0.767880i 0.433189 0.0506325i
\(231\) 2.23682 + 0.223622i 0.147172 + 0.0147133i
\(232\) 1.38021 0.907779i 0.0906153 0.0595986i
\(233\) −5.09727 + 1.85525i −0.333933 + 0.121542i −0.503545 0.863969i \(-0.667971\pi\)
0.169611 + 0.985511i \(0.445749\pi\)
\(234\) 12.6932 3.46021i 0.829781 0.226201i
\(235\) 7.88831 + 2.87111i 0.514576 + 0.187291i
\(236\) 6.69701 1.58722i 0.435938 0.103319i
\(237\) −8.25582 + 14.8679i −0.536273 + 0.965776i
\(238\) 0.163236 2.80265i 0.0105810 0.181669i
\(239\) 1.31200 1.39064i 0.0848662 0.0899529i −0.683549 0.729905i \(-0.739564\pi\)
0.768415 + 0.639952i \(0.221046\pi\)
\(240\) 2.57954 + 3.34667i 0.166508 + 0.216026i
\(241\) 2.53579 + 5.87863i 0.163345 + 0.378676i 0.980156 0.198230i \(-0.0635193\pi\)
−0.816811 + 0.576906i \(0.804260\pi\)
\(242\) 7.50729 0.482587
\(243\) −2.20216 15.4321i −0.141269 0.989971i
\(244\) −10.6605 −0.682471
\(245\) −6.29779 14.5999i −0.402351 0.932754i
\(246\) 6.88745 + 8.93571i 0.439128 + 0.569720i
\(247\) 23.7698 25.1945i 1.51244 1.60309i
\(248\) 0.465395 7.99053i 0.0295526 0.507399i
\(249\) −6.06571 + 10.9238i −0.384399 + 0.692265i
\(250\) 9.61053 2.27774i 0.607824 0.144057i
\(251\) −9.84637 3.58379i −0.621497 0.226207i 0.0120290 0.999928i \(-0.496171\pi\)
−0.633526 + 0.773721i \(0.718393\pi\)
\(252\) 1.47955 + 1.46677i 0.0932031 + 0.0923981i
\(253\) −4.76152 + 1.73305i −0.299354 + 0.108956i
\(254\) 3.84809 2.53093i 0.241451 0.158805i
\(255\) 16.9967 + 1.69922i 1.06438 + 0.106409i
\(256\) −0.993238 + 0.116093i −0.0620774 + 0.00725581i
\(257\) −11.4029 15.3168i −0.711295 0.955435i 0.288703 0.957419i \(-0.406776\pi\)
−0.999998 + 0.00198350i \(0.999369\pi\)
\(258\) −6.10721 + 4.16464i −0.380218 + 0.259279i
\(259\) −0.249780 4.28855i −0.0155206 0.266478i
\(260\) −8.19557 6.87690i −0.508268 0.426487i
\(261\) 3.09069 + 3.87415i 0.191309 + 0.239804i
\(262\) −2.25091 + 1.88874i −0.139062 + 0.116687i
\(263\) −6.90162 7.31529i −0.425572 0.451080i 0.478737 0.877958i \(-0.341095\pi\)
−0.904309 + 0.426878i \(0.859613\pi\)
\(264\) −2.51411 2.03897i −0.154733 0.125490i
\(265\) 21.6909 + 14.2663i 1.33246 + 0.876374i
\(266\) 5.33722 + 1.26494i 0.327246 + 0.0775587i
\(267\) 9.71333 + 30.5754i 0.594446 + 1.87118i
\(268\) 10.5398 + 1.23192i 0.643818 + 0.0752516i
\(269\) −3.94610 6.83484i −0.240598 0.416728i 0.720287 0.693676i \(-0.244010\pi\)
−0.960885 + 0.276949i \(0.910677\pi\)
\(270\) −9.29001 + 8.62458i −0.565372 + 0.524875i
\(271\) −3.22186 + 5.58042i −0.195714 + 0.338986i −0.947134 0.320837i \(-0.896036\pi\)
0.751421 + 0.659824i \(0.229369\pi\)
\(272\) −2.41404 + 3.24262i −0.146373 + 0.196613i
\(273\) −4.45505 2.82462i −0.269632 0.170954i
\(274\) 6.47738 + 21.6360i 0.391313 + 1.30708i
\(275\) 1.58892 0.797986i 0.0958156 0.0481204i
\(276\) −4.43913 1.53219i −0.267204 0.0922271i
\(277\) 3.97545 13.2789i 0.238862 0.797854i −0.751546 0.659680i \(-0.770692\pi\)
0.990408 0.138173i \(-0.0441231\pi\)
\(278\) 1.70450 + 9.66670i 0.102229 + 0.579770i
\(279\) 23.9988 0.802487i 1.43677 0.0480436i
\(280\) 0.294190 1.66844i 0.0175812 0.0997082i
\(281\) 18.2744 + 9.17775i 1.09016 + 0.547498i 0.900723 0.434395i \(-0.143038\pi\)
0.189436 + 0.981893i \(0.439334\pi\)
\(282\) −4.16191 4.26622i −0.247838 0.254050i
\(283\) −11.0299 + 25.5703i −0.655662 + 1.52000i 0.187459 + 0.982272i \(0.439975\pi\)
−0.843121 + 0.537724i \(0.819284\pi\)
\(284\) −3.36271 + 7.79565i −0.199540 + 0.462587i
\(285\) −9.03601 + 32.1271i −0.535247 + 1.90304i
\(286\) 7.32413 + 3.67832i 0.433085 + 0.217504i
\(287\) 0.785498 4.45478i 0.0463665 0.262957i
\(288\) −0.619390 2.93536i −0.0364979 0.172968i
\(289\) −0.114230 0.647833i −0.00671944 0.0381078i
\(290\) 1.15584 3.86079i 0.0678735 0.226713i
\(291\) 5.86925 5.09444i 0.344062 0.298641i
\(292\) −2.72793 + 1.37002i −0.159640 + 0.0801743i
\(293\) −8.85324 29.5719i −0.517212 1.72761i −0.672837 0.739791i \(-0.734924\pi\)
0.155625 0.987816i \(-0.450261\pi\)
\(294\) −0.467960 + 11.2793i −0.0272920 + 0.657823i
\(295\) 10.0264 13.4679i 0.583762 0.784129i
\(296\) −3.09291 + 5.35708i −0.179772 + 0.311374i
\(297\) 5.40132 8.07025i 0.313416 0.468284i
\(298\) −4.45765 7.72088i −0.258225 0.447258i
\(299\) 11.8099 + 1.38038i 0.682986 + 0.0798296i
\(300\) 1.60958 + 0.353174i 0.0929290 + 0.0203905i
\(301\) 2.88393 + 0.683505i 0.166227 + 0.0393966i
\(302\) −11.4929 7.55897i −0.661339 0.434970i
\(303\) 1.86453 11.7160i 0.107115 0.673069i
\(304\) −5.42014 5.74501i −0.310866 0.329499i
\(305\) −19.9224 + 16.7169i −1.14076 + 0.957207i
\(306\) −10.3496 6.32189i −0.591644 0.361399i
\(307\) −22.0435 18.4967i −1.25809 1.05566i −0.995883 0.0906508i \(-0.971105\pi\)
−0.262207 0.965012i \(-0.584450\pi\)
\(308\) 0.0754643 + 1.29567i 0.00429998 + 0.0738277i
\(309\) −1.36617 18.2081i −0.0777189 1.03582i
\(310\) −11.6603 15.6625i −0.662261 0.889571i
\(311\) −12.5663 + 1.46879i −0.712569 + 0.0832873i −0.464651 0.885494i \(-0.653820\pi\)
−0.247918 + 0.968781i \(0.579746\pi\)
\(312\) 3.12470 + 6.92338i 0.176902 + 0.391959i
\(313\) 5.31511 3.49580i 0.300428 0.197594i −0.390341 0.920670i \(-0.627643\pi\)
0.690768 + 0.723076i \(0.257272\pi\)
\(314\) 16.7093 6.08167i 0.942958 0.343209i
\(315\) 5.06506 + 0.421006i 0.285384 + 0.0237210i
\(316\) −9.22645 3.35815i −0.519029 0.188911i
\(317\) 18.6880 4.42915i 1.04963 0.248766i 0.330615 0.943766i \(-0.392744\pi\)
0.719010 + 0.695000i \(0.244596\pi\)
\(318\) −9.48184 15.8069i −0.531715 0.886408i
\(319\) −0.179514 + 3.08213i −0.0100508 + 0.172566i
\(320\) −1.67412 + 1.77446i −0.0935861 + 0.0991955i
\(321\) 10.5401 25.6029i 0.588290 1.42901i
\(322\) 0.745778 + 1.72891i 0.0415606 + 0.0963483i
\(323\) −31.9292 −1.77659
\(324\) 8.59919 2.65592i 0.477733 0.147551i
\(325\) −4.17232 −0.231439
\(326\) 8.43671 + 19.5585i 0.467266 + 1.08324i
\(327\) 8.57794 1.14824i 0.474361 0.0634977i
\(328\) −4.46995 + 4.73787i −0.246812 + 0.261605i
\(329\) −0.138947 + 2.38562i −0.00766038 + 0.131524i
\(330\) −7.89571 + 0.131974i −0.434644 + 0.00726492i
\(331\) 5.03636 1.19364i 0.276823 0.0656083i −0.0898592 0.995954i \(-0.528642\pi\)
0.366682 + 0.930346i \(0.380494\pi\)
\(332\) −6.77885 2.46730i −0.372038 0.135411i
\(333\) −16.8526 7.76970i −0.923518 0.425777i
\(334\) −8.55125 + 3.11240i −0.467904 + 0.170303i
\(335\) 21.6285 14.2253i 1.18169 0.777211i
\(336\) −0.702064 + 0.976699i −0.0383007 + 0.0532833i
\(337\) 26.2604 3.06940i 1.43049 0.167201i 0.634696 0.772762i \(-0.281125\pi\)
0.795799 + 0.605561i \(0.207051\pi\)
\(338\) −3.72168 4.99908i −0.202433 0.271914i
\(339\) −15.1745 7.30593i −0.824163 0.396804i
\(340\) 0.573423 + 9.84530i 0.0310983 + 0.533936i
\(341\) 11.4590 + 9.61524i 0.620539 + 0.520694i
\(342\) 15.6753 17.7688i 0.847625 0.960828i
\(343\) 7.19128 6.03420i 0.388293 0.325816i
\(344\) −2.92874 3.10428i −0.157907 0.167372i
\(345\) −10.6985 + 4.09769i −0.575988 + 0.220612i
\(346\) 8.41308 + 5.53337i 0.452290 + 0.297476i
\(347\) −3.41862 0.810228i −0.183521 0.0434953i 0.137828 0.990456i \(-0.455988\pi\)
−0.321349 + 0.946961i \(0.604136\pi\)
\(348\) −1.92850 + 2.11377i −0.103378 + 0.113310i
\(349\) −22.8121 2.66635i −1.22110 0.142726i −0.518982 0.854785i \(-0.673689\pi\)
−0.702120 + 0.712059i \(0.747763\pi\)
\(350\) −0.330355 0.572192i −0.0176582 0.0305849i
\(351\) −19.8255 + 11.2348i −1.05821 + 0.599668i
\(352\) 0.934440 1.61850i 0.0498058 0.0862662i
\(353\) 6.39081 8.58435i 0.340149 0.456899i −0.598829 0.800877i \(-0.704367\pi\)
0.938978 + 0.343978i \(0.111775\pi\)
\(354\) −10.5620 + 5.52737i −0.561364 + 0.293777i
\(355\) 5.94020 + 19.8416i 0.315273 + 1.05308i
\(356\) −16.5519 + 8.31270i −0.877251 + 0.440572i
\(357\) 0.924285 + 4.77390i 0.0489184 + 0.252662i
\(358\) 3.64244 12.1666i 0.192509 0.643025i
\(359\) 5.49988 + 31.1914i 0.290273 + 1.64622i 0.685818 + 0.727773i \(0.259444\pi\)
−0.395546 + 0.918446i \(0.629444\pi\)
\(360\) −5.76049 4.51434i −0.303605 0.237927i
\(361\) 7.53339 42.7240i 0.396494 2.24863i
\(362\) 2.67243 + 1.34214i 0.140460 + 0.0705415i
\(363\) −12.6006 + 3.20973i −0.661361 + 0.168467i
\(364\) 1.20628 2.79647i 0.0632261 0.146575i
\(365\) −2.94962 + 6.83799i −0.154390 + 0.357917i
\(366\) 17.8932 4.55790i 0.935292 0.238245i
\(367\) −11.4005 5.72555i −0.595102 0.298872i 0.125639 0.992076i \(-0.459902\pi\)
−0.720741 + 0.693205i \(0.756198\pi\)
\(368\) 0.470813 2.67011i 0.0245428 0.139189i
\(369\) −15.3807 12.0534i −0.800688 0.627477i
\(370\) 2.62046 + 14.8613i 0.136231 + 0.772605i
\(371\) −2.11963 + 7.08007i −0.110046 + 0.367579i
\(372\) 2.63520 + 13.6107i 0.136629 + 0.705682i
\(373\) −21.4099 + 10.7525i −1.10856 + 0.556742i −0.906319 0.422593i \(-0.861120\pi\)
−0.202244 + 0.979335i \(0.564824\pi\)
\(374\) −2.16681 7.23764i −0.112043 0.374250i
\(375\) −15.1570 + 7.93205i −0.782703 + 0.409609i
\(376\) 2.05484 2.76013i 0.105970 0.142343i
\(377\) 3.62236 6.27411i 0.186561 0.323133i
\(378\) −3.11048 1.82933i −0.159986 0.0940905i
\(379\) 0.540044 + 0.935384i 0.0277402 + 0.0480475i 0.879562 0.475784i \(-0.157836\pi\)
−0.851822 + 0.523831i \(0.824502\pi\)
\(380\) −19.1380 2.23691i −0.981758 0.114751i
\(381\) −5.37674 + 5.89329i −0.275459 + 0.301923i
\(382\) −8.67514 2.05605i −0.443859 0.105196i
\(383\) 31.4543 + 20.6878i 1.60724 + 1.05710i 0.953938 + 0.300003i \(0.0969877\pi\)
0.653303 + 0.757096i \(0.273383\pi\)
\(384\) 1.61747 0.619514i 0.0825411 0.0316145i
\(385\) 2.17279 + 2.30302i 0.110735 + 0.117373i
\(386\) −1.40332 + 1.17753i −0.0714271 + 0.0599344i
\(387\) 8.47007 9.60128i 0.430558 0.488060i
\(388\) 3.43730 + 2.88423i 0.174502 + 0.146425i
\(389\) 1.28739 + 22.1036i 0.0652733 + 1.12070i 0.858849 + 0.512228i \(0.171180\pi\)
−0.793576 + 0.608471i \(0.791783\pi\)
\(390\) 16.6961 + 8.03854i 0.845439 + 0.407047i
\(391\) −6.54520 8.79172i −0.331005 0.444617i
\(392\) −6.47365 + 0.756661i −0.326969 + 0.0382172i
\(393\) 2.97052 4.13253i 0.149843 0.208458i
\(394\) −12.3276 + 8.10796i −0.621053 + 0.408473i
\(395\) −22.5084 + 8.19238i −1.13252 + 0.412203i
\(396\) 5.09157 + 2.34741i 0.255861 + 0.117962i
\(397\) 23.9869 + 8.73052i 1.20387 + 0.438172i 0.864573 0.502508i \(-0.167589\pi\)
0.339296 + 0.940680i \(0.389811\pi\)
\(398\) 25.0335 5.93305i 1.25482 0.297397i
\(399\) −9.49909 + 0.158774i −0.475549 + 0.00794864i
\(400\) −0.0553188 + 0.949788i −0.00276594 + 0.0474894i
\(401\) 4.28696 4.54392i 0.214081 0.226912i −0.611430 0.791298i \(-0.709406\pi\)
0.825511 + 0.564386i \(0.190887\pi\)
\(402\) −18.2172 + 2.43854i −0.908591 + 0.121623i
\(403\) −13.9030 32.2308i −0.692559 1.60553i
\(404\) 6.84939 0.340770
\(405\) 11.9054 18.4479i 0.591584 0.916683i
\(406\) 1.14724 0.0569366
\(407\) −4.57890 10.6151i −0.226968 0.526171i
\(408\) 2.66547 6.47470i 0.131961 0.320546i
\(409\) 9.66974 10.2493i 0.478138 0.506797i −0.442739 0.896651i \(-0.645993\pi\)
0.920877 + 0.389854i \(0.127475\pi\)
\(410\) −0.923946 + 15.8635i −0.0456304 + 0.783444i
\(411\) −20.1224 33.5455i −0.992565 1.65468i
\(412\) 10.2578 2.43115i 0.505368 0.119774i
\(413\) 4.49141 + 1.63474i 0.221008 + 0.0804403i
\(414\) 8.10595 + 0.673765i 0.398386 + 0.0331137i
\(415\) −16.5373 + 6.01910i −0.811786 + 0.295466i
\(416\) −3.66400 + 2.40985i −0.179643 + 0.118153i
\(417\) −6.99391 15.4963i −0.342493 0.758859i
\(418\) 14.6612 1.71364i 0.717101 0.0838171i
\(419\) 14.8608 + 19.9615i 0.725995 + 0.975181i 0.999910 + 0.0134268i \(0.00427400\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(420\) 0.219554 + 2.92617i 0.0107131 + 0.142783i
\(421\) −0.276523 4.74771i −0.0134769 0.231389i −0.998320 0.0579415i \(-0.981546\pi\)
0.984843 0.173448i \(-0.0554907\pi\)
\(422\) −9.66227 8.10760i −0.470352 0.394672i
\(423\) 8.80958 + 5.38122i 0.428336 + 0.261644i
\(424\) 8.15233 6.84062i 0.395912 0.332210i
\(425\) 2.63933 + 2.79753i 0.128026 + 0.135700i
\(426\) 2.31113 14.5223i 0.111975 0.703610i
\(427\) −6.18540 4.06820i −0.299333 0.196874i
\(428\) 15.5545 + 3.68649i 0.751857 + 0.178193i
\(429\) −13.8659 3.04246i −0.669451 0.146891i
\(430\) −10.3411 1.20870i −0.498692 0.0582887i
\(431\) 9.13866 + 15.8286i 0.440194 + 0.762438i 0.997704 0.0677322i \(-0.0215763\pi\)
−0.557510 + 0.830171i \(0.688243\pi\)
\(432\) 2.29463 + 4.66205i 0.110400 + 0.224303i
\(433\) −16.0854 + 27.8607i −0.773015 + 1.33890i 0.162889 + 0.986644i \(0.447919\pi\)
−0.935904 + 0.352256i \(0.885415\pi\)
\(434\) 3.31932 4.45862i 0.159333 0.214021i
\(435\) −0.289353 + 6.97432i −0.0138734 + 0.334393i
\(436\) 1.43306 + 4.78674i 0.0686309 + 0.229243i
\(437\) 19.1368 9.61089i 0.915439 0.459751i
\(438\) 3.99295 3.46583i 0.190791 0.165604i
\(439\) −7.21221 + 24.0905i −0.344220 + 1.14978i 0.594211 + 0.804309i \(0.297464\pi\)
−0.938431 + 0.345466i \(0.887721\pi\)
\(440\) −0.791701 4.48996i −0.0377429 0.214050i
\(441\) −4.03701 19.1319i −0.192239 0.911042i
\(442\) −3.07851 + 17.4591i −0.146430 + 0.830445i
\(443\) −5.57999 2.80237i −0.265113 0.133145i 0.311278 0.950319i \(-0.399243\pi\)
−0.576391 + 0.817174i \(0.695539\pi\)
\(444\) 2.90089 10.3140i 0.137670 0.489479i
\(445\) −17.8971 + 41.4901i −0.848402 + 1.96682i
\(446\) 4.93231 11.4344i 0.233551 0.541433i
\(447\) 10.7830 + 11.0533i 0.510019 + 0.522801i
\(448\) −0.620594 0.311674i −0.0293203 0.0147252i
\(449\) 1.31051 7.43224i 0.0618466 0.350749i −0.938143 0.346247i \(-0.887456\pi\)
0.999990 0.00450206i \(-0.00143305\pi\)
\(450\) −2.85260 + 0.0953869i −0.134473 + 0.00449658i
\(451\) −2.11387 11.9883i −0.0995381 0.564509i
\(452\) 2.78874 9.31503i 0.131171 0.438142i
\(453\) 22.5220 + 7.77361i 1.05818 + 0.365236i
\(454\) 10.9477 5.49815i 0.513802 0.258041i
\(455\) −2.13088 7.11762i −0.0998970 0.333679i
\(456\) 11.5537 + 7.32535i 0.541052 + 0.343041i
\(457\) −5.43504 + 7.30053i −0.254240 + 0.341504i −0.910858 0.412719i \(-0.864579\pi\)
0.656618 + 0.754223i \(0.271986\pi\)
\(458\) −6.68221 + 11.5739i −0.312239 + 0.540814i
\(459\) 20.0741 + 6.18606i 0.936981 + 0.288741i
\(460\) −3.30718 5.72820i −0.154198 0.267079i
\(461\) 19.3563 + 2.26243i 0.901515 + 0.105372i 0.554207 0.832379i \(-0.313022\pi\)
0.347308 + 0.937751i \(0.387096\pi\)
\(462\) −0.680626 2.14246i −0.0316656 0.0996762i
\(463\) −9.69976 2.29889i −0.450786 0.106838i −0.00104939 0.999999i \(-0.500334\pi\)
−0.449737 + 0.893161i \(0.648482\pi\)
\(464\) −1.38021 0.907779i −0.0640747 0.0421426i
\(465\) 26.2678 + 21.3034i 1.21814 + 0.987923i
\(466\) 3.72245 + 3.94557i 0.172439 + 0.182775i
\(467\) 11.9126 9.99582i 0.551247 0.462551i −0.324116 0.946017i \(-0.605067\pi\)
0.875363 + 0.483466i \(0.160622\pi\)
\(468\) −8.20475 10.2846i −0.379265 0.475406i
\(469\) 5.64521 + 4.73689i 0.260672 + 0.218729i
\(470\) −0.488100 8.38036i −0.0225144 0.386557i
\(471\) −25.4455 + 17.3518i −1.17247 + 0.799529i
\(472\) −4.10996 5.52064i −0.189176 0.254108i
\(473\) 7.92207 0.925957i 0.364257 0.0425755i
\(474\) 16.9219 + 1.69174i 0.777250 + 0.0777043i
\(475\) −6.27820 + 4.12924i −0.288064 + 0.189462i
\(476\) −2.63809 + 0.960186i −0.120917 + 0.0440101i
\(477\) 22.6730 + 22.4772i 1.03813 + 1.02916i
\(478\) −1.79656 0.653895i −0.0821729 0.0299085i
\(479\) −18.9679 + 4.49547i −0.866665 + 0.205403i −0.639817 0.768527i \(-0.720990\pi\)
−0.226847 + 0.973930i \(0.572842\pi\)
\(480\) 2.05126 3.69412i 0.0936268 0.168613i
\(481\) −1.57734 + 27.0818i −0.0719203 + 1.23482i
\(482\) 4.39347 4.65681i 0.200117 0.212112i
\(483\) −1.99095 2.58303i −0.0905911 0.117532i
\(484\) −2.97348 6.89331i −0.135158 0.313332i
\(485\) 10.9464 0.497052
\(486\) −13.2978 + 8.13441i −0.603200 + 0.368985i
\(487\) 8.28387 0.375378 0.187689 0.982229i \(-0.439900\pi\)
0.187689 + 0.982229i \(0.439900\pi\)
\(488\) 4.22242 + 9.78867i 0.191140 + 0.443112i
\(489\) −22.5228 29.2209i −1.01852 1.32141i
\(490\) −10.9114 + 11.5655i −0.492929 + 0.522474i
\(491\) −0.250629 + 4.30314i −0.0113108 + 0.194198i 0.987919 + 0.154968i \(0.0495275\pi\)
−0.999230 + 0.0392299i \(0.987510\pi\)
\(492\) 5.47693 9.86342i 0.246919 0.444677i
\(493\) −6.49820 + 1.54010i −0.292664 + 0.0693627i
\(494\) −32.5488 11.8468i −1.46444 0.533012i
\(495\) 13.1961 3.59731i 0.593122 0.161687i
\(496\) −7.52137 + 2.73755i −0.337719 + 0.122920i
\(497\) −4.92602 + 3.23989i −0.220962 + 0.145329i
\(498\) 12.4329 + 1.24296i 0.557130 + 0.0556982i
\(499\) 20.6040 2.40826i 0.922362 0.107809i 0.358362 0.933583i \(-0.383336\pi\)
0.564001 + 0.825774i \(0.309261\pi\)
\(500\) −5.89799 7.92238i −0.263766 0.354300i
\(501\) 13.0222 8.88010i 0.581787 0.396733i
\(502\) 0.609258 + 10.4606i 0.0271925 + 0.466878i
\(503\) 10.7596 + 9.02839i 0.479747 + 0.402556i 0.850335 0.526242i \(-0.176399\pi\)
−0.370588 + 0.928798i \(0.620844\pi\)
\(504\) 0.760794 1.93951i 0.0338885 0.0863926i
\(505\) 12.8002 10.7406i 0.569599 0.477951i
\(506\) 3.47726 + 3.68568i 0.154583 + 0.163848i
\(507\) 8.38401 + 6.79952i 0.372347 + 0.301977i
\(508\) −3.84809 2.53093i −0.170732 0.112292i
\(509\) 12.8694 + 3.05011i 0.570428 + 0.135194i 0.505700 0.862709i \(-0.331234\pi\)
0.0647272 + 0.997903i \(0.479382\pi\)
\(510\) −5.17181 16.2797i −0.229012 0.720877i
\(511\) −2.10560 0.246110i −0.0931464 0.0108873i
\(512\) 0.500000 + 0.866025i 0.0220971 + 0.0382733i
\(513\) −18.7133 + 36.5261i −0.826211 + 1.61267i
\(514\) −9.54766 + 16.5370i −0.421129 + 0.729417i
\(515\) 15.3576 20.6288i 0.676736 0.909014i
\(516\) 6.24298 + 3.95821i 0.274832 + 0.174250i
\(517\) 1.84440 + 6.16071i 0.0811164 + 0.270948i
\(518\) −3.83889 + 1.92796i −0.168671 + 0.0847097i
\(519\) −16.4867 5.69049i −0.723688 0.249785i
\(520\) −3.06838 + 10.2491i −0.134557 + 0.449453i
\(521\) 2.42643 + 13.7610i 0.106304 + 0.602878i 0.990692 + 0.136126i \(0.0434651\pi\)
−0.884388 + 0.466753i \(0.845424\pi\)
\(522\) 2.33315 4.37239i 0.102119 0.191374i
\(523\) −1.99108 + 11.2920i −0.0870639 + 0.493764i 0.909828 + 0.414985i \(0.136213\pi\)
−0.996892 + 0.0787788i \(0.974898\pi\)
\(524\) 2.62581 + 1.31873i 0.114709 + 0.0576090i
\(525\) 0.799125 + 0.819153i 0.0348767 + 0.0357508i
\(526\) −3.98343 + 9.23462i −0.173686 + 0.402649i
\(527\) −12.8159 + 29.7106i −0.558269 + 1.29421i
\(528\) −0.876426 + 3.11609i −0.0381416 + 0.135610i
\(529\) −13.9843 7.02319i −0.608014 0.305356i
\(530\) 4.50825 25.5675i 0.195826 1.11058i
\(531\) 15.3646 13.7932i 0.666766 0.598574i
\(532\) −0.952472 5.40174i −0.0412949 0.234195i
\(533\) −8.19268 + 27.3654i −0.354864 + 1.18533i
\(534\) 24.2276 21.0292i 1.04843 0.910024i
\(535\) 34.8492 17.5019i 1.50666 0.756674i
\(536\) −3.04342 10.1657i −0.131456 0.439092i
\(537\) −0.911847 + 21.9784i −0.0393491 + 0.948438i
\(538\) −4.71289 + 6.33051i −0.203187 + 0.272928i
\(539\) 6.09042 10.5489i 0.262333 0.454374i
\(540\) 11.5988 + 5.11421i 0.499134 + 0.220081i
\(541\) −13.0207 22.5525i −0.559802 0.969606i −0.997513 0.0704897i \(-0.977544\pi\)
0.437710 0.899116i \(-0.355790\pi\)
\(542\) 6.40014 + 0.748069i 0.274910 + 0.0321323i
\(543\) −5.05937 1.11013i −0.217118 0.0476402i
\(544\) 3.93358 + 0.932275i 0.168651 + 0.0399710i
\(545\) 10.1842 + 6.69828i 0.436245 + 0.286923i
\(546\) −0.829053 + 5.20948i −0.0354802 + 0.222945i
\(547\) 17.6538 + 18.7119i 0.754822 + 0.800065i 0.984903 0.173107i \(-0.0553806\pi\)
−0.230081 + 0.973171i \(0.573899\pi\)
\(548\) 17.3009 14.5172i 0.739059 0.620144i
\(549\) −28.0842 + 15.3004i −1.19860 + 0.653007i
\(550\) −1.36206 1.14291i −0.0580786 0.0487337i
\(551\) −0.758665 13.0258i −0.0323202 0.554916i
\(552\) 0.351367 + 4.68295i 0.0149552 + 0.199320i
\(553\) −4.07181 5.46939i −0.173151 0.232582i
\(554\) −13.7675 + 1.60919i −0.584926 + 0.0683681i
\(555\) −10.7523 23.8237i −0.456408 1.01126i
\(556\) 8.20100 5.39389i 0.347800 0.228752i
\(557\) 1.13016 0.411346i 0.0478866 0.0174293i −0.317966 0.948102i \(-0.603000\pi\)
0.365852 + 0.930673i \(0.380777\pi\)
\(558\) −10.2423 21.7182i −0.433591 0.919406i
\(559\) −17.5875 6.40134i −0.743874 0.270748i
\(560\) −1.64851 + 0.390704i −0.0696622 + 0.0165102i
\(561\) 6.73133 + 11.2216i 0.284197 + 0.473777i
\(562\) 1.18904 20.4150i 0.0501565 0.861153i
\(563\) 2.95231 3.12926i 0.124425 0.131883i −0.662166 0.749357i \(-0.730363\pi\)
0.786591 + 0.617474i \(0.211844\pi\)
\(564\) −2.26886 + 5.51129i −0.0955363 + 0.232067i
\(565\) −9.39541 21.7810i −0.395268 0.916334i
\(566\) 27.8478 1.17053
\(567\) 6.00292 + 1.74056i 0.252099 + 0.0730966i
\(568\) 8.48999 0.356232
\(569\) −0.154573 0.358340i −0.00648003 0.0150224i 0.914945 0.403578i \(-0.132234\pi\)
−0.921425 + 0.388555i \(0.872974\pi\)
\(570\) 33.0786 4.42788i 1.38551 0.185463i
\(571\) −8.72547 + 9.24845i −0.365149 + 0.387036i −0.883733 0.467991i \(-0.844978\pi\)
0.518584 + 0.855027i \(0.326459\pi\)
\(572\) 0.476550 8.18205i 0.0199256 0.342108i
\(573\) 15.4399 0.258072i 0.645010 0.0107811i
\(574\) −4.40157 + 1.04319i −0.183718 + 0.0435420i
\(575\) −2.42396 0.882250i −0.101086 0.0367924i
\(576\) −2.44997 + 1.73137i −0.102082 + 0.0721405i
\(577\) 38.3069 13.9426i 1.59474 0.580436i 0.616395 0.787437i \(-0.288593\pi\)
0.978341 + 0.207001i \(0.0663703\pi\)
\(578\) −0.549607 + 0.361482i −0.0228606 + 0.0150357i
\(579\) 1.85196 2.57641i 0.0769646 0.107072i
\(580\) −4.00284 + 0.467865i −0.166209 + 0.0194270i
\(581\) −2.99164 4.01847i −0.124114 0.166714i
\(582\) −7.00249 3.37144i −0.290262 0.139751i
\(583\) 1.15643 + 19.8552i 0.0478946 + 0.822318i
\(584\) 2.33845 + 1.96219i 0.0967658 + 0.0811961i
\(585\) −31.4604 6.35391i −1.30073 0.262702i
\(586\) −23.6468 + 19.8420i −0.976839 + 0.819666i
\(587\) −23.3798 24.7811i −0.964987 1.02283i −0.999725 0.0234303i \(-0.992541\pi\)
0.0347382 0.999396i \(-0.488940\pi\)
\(588\) 10.5422 4.03782i 0.434753 0.166517i
\(589\) −52.8183 34.7391i −2.17634 1.43140i
\(590\) −16.3377 3.87210i −0.672612 0.159412i
\(591\) 17.2247 18.8795i 0.708528 0.776597i
\(592\) 6.14399 + 0.718130i 0.252517 + 0.0295150i
\(593\) 19.6691 + 34.0678i 0.807712 + 1.39900i 0.914445 + 0.404711i \(0.132628\pi\)
−0.106732 + 0.994288i \(0.534039\pi\)
\(594\) −9.54959 1.76311i −0.391824 0.0723415i
\(595\) −3.42439 + 5.93122i −0.140386 + 0.243156i
\(596\) −5.32385 + 7.15117i −0.218073 + 0.292923i
\(597\) −39.4809 + 20.6614i −1.61584 + 0.845614i
\(598\) −3.41018 11.3908i −0.139453 0.465805i
\(599\) 7.65216 3.84306i 0.312659 0.157023i −0.285549 0.958364i \(-0.592176\pi\)
0.598208 + 0.801341i \(0.295880\pi\)
\(600\) −0.313231 1.61782i −0.0127876 0.0660474i
\(601\) 1.76835 5.90669i 0.0721324 0.240939i −0.914318 0.404996i \(-0.867273\pi\)
0.986451 + 0.164057i \(0.0524581\pi\)
\(602\) −0.514663 2.91880i −0.0209761 0.118961i
\(603\) 29.5341 11.8817i 1.20272 0.483861i
\(604\) −2.38868 + 13.5469i −0.0971940 + 0.551215i
\(605\) −16.3663 8.21948i −0.665386 0.334169i
\(606\) −11.4964 + 2.92845i −0.467008 + 0.118960i
\(607\) 5.15898 11.9599i 0.209397 0.485436i −0.780857 0.624709i \(-0.785217\pi\)
0.990254 + 0.139273i \(0.0444767\pi\)
\(608\) −3.12835 + 7.25234i −0.126872 + 0.294121i
\(609\) −1.92559 + 0.490501i −0.0780288 + 0.0198761i
\(610\) 23.2406 + 11.6719i 0.940985 + 0.472580i
\(611\) 2.62044 14.8613i 0.106012 0.601222i
\(612\) −1.70562 + 12.0071i −0.0689455 + 0.485358i
\(613\) 1.57852 + 8.95223i 0.0637558 + 0.361577i 0.999949 + 0.0100916i \(0.00321230\pi\)
−0.936193 + 0.351486i \(0.885677\pi\)
\(614\) −8.25298 + 27.5669i −0.333063 + 1.11251i
\(615\) −5.23164 27.0212i −0.210960 1.08960i
\(616\) 1.15982 0.582482i 0.0467303 0.0234689i
\(617\) 3.53554 + 11.8095i 0.142335 + 0.475434i 0.999195 0.0401163i \(-0.0127729\pi\)
−0.856860 + 0.515550i \(0.827588\pi\)
\(618\) −16.1779 + 8.46631i −0.650769 + 0.340565i
\(619\) 18.3546 24.6545i 0.737733 0.990947i −0.261933 0.965086i \(-0.584360\pi\)
0.999666 0.0258608i \(-0.00823267\pi\)
\(620\) −9.76316 + 16.9103i −0.392098 + 0.679134i
\(621\) −13.8935 + 2.33481i −0.557528 + 0.0936927i
\(622\) 6.32592 + 10.9568i 0.253646 + 0.439328i
\(623\) −12.7759 1.49329i −0.511856 0.0598274i
\(624\) 5.11952 5.61136i 0.204945 0.224634i
\(625\) −28.0741 6.65369i −1.12297 0.266148i
\(626\) −5.31511 3.49580i −0.212434 0.139720i
\(627\) −23.8754 + 9.14463i −0.953491 + 0.365201i
\(628\) −12.2025 12.9339i −0.486932 0.516118i
\(629\) 19.1561 16.0738i 0.763802 0.640906i
\(630\) −1.61959 4.81757i −0.0645261 0.191937i
\(631\) −14.1277 11.8545i −0.562415 0.471922i 0.316704 0.948524i \(-0.397424\pi\)
−0.879119 + 0.476602i \(0.841868\pi\)
\(632\) 0.570900 + 9.80197i 0.0227092 + 0.389902i
\(633\) 19.6840 + 9.47713i 0.782371 + 0.376682i
\(634\) −11.4689 15.4054i −0.455487 0.611825i
\(635\) −11.1601 + 1.30443i −0.442875 + 0.0517647i
\(636\) −10.7586 + 14.9672i −0.426606 + 0.593487i
\(637\) −23.8810 + 15.7068i −0.946198 + 0.622324i
\(638\) 2.90117 1.05594i 0.114858 0.0418050i
\(639\) 2.32988 + 25.3632i 0.0921688 + 1.00335i
\(640\) 2.29243 + 0.834375i 0.0906161 + 0.0329816i
\(641\) −45.1789 + 10.7076i −1.78446 + 0.422924i −0.984248 0.176796i \(-0.943427\pi\)
−0.800210 + 0.599720i \(0.795279\pi\)
\(642\) −27.6837 + 0.462723i −1.09259 + 0.0182622i
\(643\) 0.394719 6.77706i 0.0155662 0.267261i −0.981541 0.191252i \(-0.938745\pi\)
0.997107 0.0760090i \(-0.0242178\pi\)
\(644\) 1.29212 1.36957i 0.0509168 0.0539686i
\(645\) 17.8738 2.39258i 0.703781 0.0942076i
\(646\) 12.6465 + 29.3179i 0.497570 + 1.15350i
\(647\) −39.2378 −1.54260 −0.771298 0.636474i \(-0.780392\pi\)
−0.771298 + 0.636474i \(0.780392\pi\)
\(648\) −5.84468 6.84396i −0.229601 0.268856i
\(649\) 12.8626 0.504902
\(650\) 1.65257 + 3.83109i 0.0648192 + 0.150268i
\(651\) −3.66504 + 8.90276i −0.143644 + 0.348927i
\(652\) 14.6173 15.4934i 0.572458 0.606770i
\(653\) −0.545832 + 9.37158i −0.0213601 + 0.366738i 0.970643 + 0.240525i \(0.0773195\pi\)
−0.992003 + 0.126214i \(0.959718\pi\)
\(654\) −4.45188 7.42161i −0.174082 0.290208i
\(655\) 6.97503 1.65311i 0.272537 0.0645925i
\(656\) 6.12085 + 2.22781i 0.238979 + 0.0869813i
\(657\) −5.22017 + 7.52442i −0.203658 + 0.293556i
\(658\) 2.24555 0.817314i 0.0875407 0.0318622i
\(659\) 1.56937 1.03219i 0.0611340 0.0402085i −0.518574 0.855033i \(-0.673537\pi\)
0.579708 + 0.814824i \(0.303167\pi\)
\(660\) 3.24851 + 7.19769i 0.126448 + 0.280170i
\(661\) 32.4822 3.79662i 1.26341 0.147671i 0.542118 0.840302i \(-0.317623\pi\)
0.721292 + 0.692631i \(0.243549\pi\)
\(662\) −3.09082 4.15169i −0.120128 0.161360i
\(663\) −2.29749 30.6205i −0.0892270 1.18920i
\(664\) 0.419451 + 7.20170i 0.0162779 + 0.279480i
\(665\) −10.2505 8.60120i −0.397498 0.333540i
\(666\) −0.459278 + 18.5518i −0.0177967 + 0.718867i
\(667\) 3.43113 2.87906i 0.132854 0.111478i
\(668\) 6.24483 + 6.61914i 0.241620 + 0.256102i
\(669\) −3.38989 + 21.3008i −0.131061 + 0.823538i
\(670\) −21.6285 14.2253i −0.835583 0.549571i
\(671\) −19.3862 4.59462i −0.748397 0.177373i
\(672\) 1.17489 + 0.257796i 0.0453225 + 0.00994469i
\(673\) 30.3981 + 3.55302i 1.17176 + 0.136959i 0.679625 0.733560i \(-0.262143\pi\)
0.492135 + 0.870519i \(0.336217\pi\)
\(674\) −13.2196 22.8970i −0.509199 0.881959i
\(675\) 4.74717 1.37973i 0.182719 0.0531057i
\(676\) −3.11616 + 5.39734i −0.119852 + 0.207590i
\(677\) −11.1166 + 14.9322i −0.427245 + 0.573889i −0.962665 0.270697i \(-0.912746\pi\)
0.535420 + 0.844586i \(0.320153\pi\)
\(678\) −0.698131 + 16.8272i −0.0268116 + 0.646243i
\(679\) 0.893708 + 2.98519i 0.0342974 + 0.114561i
\(680\) 8.81299 4.42605i 0.337963 0.169731i
\(681\) −16.0245 + 13.9091i −0.614060 + 0.532996i
\(682\) 4.29019 14.3302i 0.164280 0.548733i
\(683\) −5.67430 32.1806i −0.217121 1.23135i −0.877188 0.480148i \(-0.840583\pi\)
0.660067 0.751207i \(-0.270528\pi\)
\(684\) −22.5243 7.35548i −0.861238 0.281244i
\(685\) 9.56743 54.2596i 0.365553 2.07315i
\(686\) −8.38902 4.21313i −0.320294 0.160858i
\(687\) 6.26735 22.2832i 0.239114 0.850159i
\(688\) −1.69039 + 3.91876i −0.0644454 + 0.149401i
\(689\) 18.4853 42.8537i 0.704234 1.63260i
\(690\) 8.00002 + 8.20053i 0.304556 + 0.312189i
\(691\) 19.4419 + 9.76411i 0.739606 + 0.371444i 0.778371 0.627804i \(-0.216046\pi\)
−0.0387652 + 0.999248i \(0.512342\pi\)
\(692\) 1.74858 9.91668i 0.0664710 0.376976i
\(693\) 2.05840 + 3.30501i 0.0781923 + 0.125547i
\(694\) 0.610082 + 3.45995i 0.0231584 + 0.131338i
\(695\) 6.86784 22.9402i 0.260512 0.870171i
\(696\) 2.70474 + 0.933556i 0.102523 + 0.0353864i
\(697\) 23.5310 11.8177i 0.891299 0.447627i
\(698\) 6.58711 + 22.0025i 0.249326 + 0.832806i
\(699\) −7.93488 5.03092i −0.300125 0.190287i
\(700\) −0.394549 + 0.529971i −0.0149125 + 0.0200310i
\(701\) 15.0925 26.1410i 0.570036 0.987332i −0.426525 0.904476i \(-0.640263\pi\)
0.996562 0.0828560i \(-0.0264042\pi\)
\(702\) 18.1684 + 13.7543i 0.685724 + 0.519121i
\(703\) 24.4287 + 42.3118i 0.921346 + 1.59582i
\(704\) −1.85624 0.216964i −0.0699598 0.00817713i
\(705\) 4.40227 + 13.8573i 0.165799 + 0.521898i
\(706\) −10.4136 2.46806i −0.391920 0.0928867i
\(707\) 3.97412 + 2.61382i 0.149462 + 0.0983027i
\(708\) 9.25871 + 7.50891i 0.347964 + 0.282202i
\(709\) −19.3256 20.4840i −0.725789 0.769291i 0.254455 0.967085i \(-0.418104\pi\)
−0.980244 + 0.197793i \(0.936623\pi\)
\(710\) 15.8661 13.3133i 0.595445 0.499638i
\(711\) −29.1260 + 4.39545i −1.09231 + 0.164842i
\(712\) 14.1887 + 11.9058i 0.531745 + 0.446187i
\(713\) −1.26183 21.6647i −0.0472558 0.811351i
\(714\) 4.01738 2.73954i 0.150347 0.102525i
\(715\) −11.9398 16.0379i −0.446523 0.599784i
\(716\) −12.6143 + 1.47440i −0.471418 + 0.0551008i
\(717\) 3.29502 + 0.329414i 0.123055 + 0.0123022i
\(718\) 26.4621 17.4044i 0.987555 0.649525i
\(719\) −3.87526 + 1.41048i −0.144523 + 0.0526020i −0.413269 0.910609i \(-0.635613\pi\)
0.268746 + 0.963211i \(0.413391\pi\)
\(720\) −1.86353 + 7.07742i −0.0694495 + 0.263760i
\(721\) 6.87952 + 2.50394i 0.256207 + 0.0932516i
\(722\) −42.2137 + 10.0048i −1.57103 + 0.372341i
\(723\) −5.38322 + 9.69466i −0.200204 + 0.360548i
\(724\) 0.173883 2.98546i 0.00646232 0.110954i
\(725\) −1.07856 + 1.14321i −0.0400567 + 0.0424577i
\(726\) 7.93808 + 10.2988i 0.294610 + 0.382224i
\(727\) 15.8886 + 36.8340i 0.589277 + 1.36610i 0.908288 + 0.418346i \(0.137390\pi\)
−0.319011 + 0.947751i \(0.603351\pi\)
\(728\) −3.04554 −0.112875
\(729\) 18.8419 19.3387i 0.697846 0.716248i
\(730\) 7.44704 0.275627
\(731\) 6.83347 + 15.8418i 0.252745 + 0.585928i
\(732\) −11.2723 14.6245i −0.416635 0.540538i
\(733\) 3.92057 4.15556i 0.144809 0.153489i −0.650909 0.759156i \(-0.725612\pi\)
0.795718 + 0.605667i \(0.207094\pi\)
\(734\) −0.741783 + 12.7359i −0.0273797 + 0.470091i
\(735\) 13.3695 24.0772i 0.493143 0.888103i
\(736\) −2.63822 + 0.625269i −0.0972461 + 0.0230477i
\(737\) 18.6357 + 6.78282i 0.686453 + 0.249848i
\(738\) −4.97567 + 18.8969i −0.183157 + 0.695606i
\(739\) 11.1409 4.05496i 0.409825 0.149164i −0.128877 0.991661i \(-0.541137\pi\)
0.538702 + 0.842496i \(0.318915\pi\)
\(740\) 12.6080 8.29243i 0.463480 0.304836i
\(741\) 59.6967 + 5.96807i 2.19301 + 0.219243i
\(742\) 7.34058 0.857991i 0.269481 0.0314978i
\(743\) −0.164744 0.221290i −0.00604388 0.00811834i 0.799091 0.601210i \(-0.205315\pi\)
−0.805135 + 0.593092i \(0.797907\pi\)
\(744\) 11.4538 7.81060i 0.419917 0.286351i
\(745\) 1.26461 + 21.7125i 0.0463317 + 0.795485i
\(746\) 18.3531 + 15.4001i 0.671956 + 0.563838i
\(747\) −21.3994 + 3.22942i −0.782963 + 0.118158i
\(748\) −5.78749 + 4.85628i −0.211612 + 0.177563i
\(749\) 7.61816 + 8.07478i 0.278362 + 0.295046i
\(750\) 13.2867 + 10.7757i 0.485162 + 0.393471i
\(751\) −8.35010 5.49195i −0.304700 0.200404i 0.387946 0.921682i \(-0.373185\pi\)
−0.692646 + 0.721278i \(0.743555\pi\)
\(752\) −3.34828 0.793556i −0.122099 0.0289380i
\(753\) −5.49501 17.2971i −0.200249 0.630340i
\(754\) −7.19573 0.841060i −0.262053 0.0306296i
\(755\) 16.7790 + 29.0622i 0.610652 + 1.05768i
\(756\) −0.447722 + 3.58065i −0.0162835 + 0.130227i
\(757\) 13.4452 23.2877i 0.488672 0.846405i −0.511243 0.859436i \(-0.670815\pi\)
0.999915 + 0.0130311i \(0.00414804\pi\)
\(758\) 0.644984 0.866364i 0.0234269 0.0314678i
\(759\) −7.41221 4.69953i −0.269046 0.170582i
\(760\) 5.52620 + 18.4588i 0.200456 + 0.669571i
\(761\) 2.86608 1.43940i 0.103895 0.0521782i −0.396093 0.918211i \(-0.629634\pi\)
0.499988 + 0.866032i \(0.333338\pi\)
\(762\) 7.54094 + 2.60280i 0.273179 + 0.0942894i
\(763\) −0.995203 + 3.32421i −0.0360288 + 0.120344i
\(764\) 1.54815 + 8.78001i 0.0560102 + 0.317650i
\(765\) 15.6410 + 25.1135i 0.565502 + 0.907980i
\(766\) 6.53748 37.0759i 0.236209 1.33961i
\(767\) −26.9726 13.5461i −0.973924 0.489123i
\(768\) −1.20949 1.23981i −0.0436439 0.0447377i
\(769\) −2.25508 + 5.22786i −0.0813202 + 0.188521i −0.954025 0.299727i \(-0.903105\pi\)
0.872705 + 0.488248i \(0.162364\pi\)
\(770\) 1.25407 2.90727i 0.0451936 0.104771i
\(771\) 8.95490 31.8387i 0.322503 1.14664i
\(772\) 1.63705 + 0.822157i 0.0589187 + 0.0295901i
\(773\) −2.56872 + 14.5679i −0.0923903 + 0.523971i 0.903126 + 0.429377i \(0.141267\pi\)
−0.995516 + 0.0945948i \(0.969844\pi\)
\(774\) −12.1709 3.97449i −0.437473 0.142860i
\(775\) 1.32234 + 7.49936i 0.0474999 + 0.269385i
\(776\) 1.28691 4.29857i 0.0461973 0.154310i
\(777\) 5.61909 4.87730i 0.201584 0.174972i
\(778\) 19.7860 9.93691i 0.709363 0.356255i
\(779\) 14.7551 + 49.2856i 0.528658 + 1.76584i
\(780\) 0.768137 18.5145i 0.0275037 0.662926i
\(781\) −9.47498 + 12.7271i −0.339042 + 0.455412i
\(782\) −5.48028 + 9.49213i −0.195974 + 0.339438i
\(783\) −2.04667 + 8.33639i −0.0731421 + 0.297918i
\(784\) 3.25886 + 5.64451i 0.116388 + 0.201590i
\(785\) −43.0858 5.03601i −1.53780 0.179743i
\(786\) −4.97112 1.09076i −0.177314 0.0389063i
\(787\) −9.68719 2.29591i −0.345311 0.0818402i 0.0543010 0.998525i \(-0.482707\pi\)
−0.399612 + 0.916684i \(0.630855\pi\)
\(788\) 12.3276 + 8.10796i 0.439151 + 0.288834i
\(789\) 2.73774 17.2030i 0.0974661 0.612442i
\(790\) 16.4375 + 17.4227i 0.584820 + 0.619873i
\(791\) 5.17281 4.34050i 0.183924 0.154330i
\(792\) 0.138759 5.60492i 0.00493057 0.199162i
\(793\) 35.8137 + 30.0512i 1.27178 + 1.06715i
\(794\) −1.48422 25.4831i −0.0526731 0.904363i
\(795\) 3.36450 + 44.8414i 0.119326 + 1.59036i
\(796\) −15.3631 20.6362i −0.544530 0.731431i
\(797\) 8.08677 0.945208i 0.286448 0.0334810i 0.0283444 0.999598i \(-0.490976\pi\)
0.258104 + 0.966117i \(0.416902\pi\)
\(798\) 3.90819 + 8.65933i 0.138348 + 0.306537i
\(799\) −11.6221 + 7.64396i −0.411159 + 0.270424i
\(800\) 0.894021 0.325397i 0.0316084 0.0115045i
\(801\) −31.6738 + 45.6550i −1.11914 + 1.61314i
\(802\) −5.87028 2.13661i −0.207287 0.0754462i
\(803\) −5.55122 + 1.31566i −0.195898 + 0.0464288i
\(804\) 9.45457 + 15.7615i 0.333437 + 0.555864i
\(805\) 0.267084 4.58565i 0.00941346 0.161623i
\(806\) −24.0882 + 25.5320i −0.848469 + 0.899325i
\(807\) 5.20376 12.6405i 0.183181 0.444965i
\(808\) −2.71290 6.28922i −0.0954396 0.221254i
\(809\) −0.180076 −0.00633114 −0.00316557 0.999995i \(-0.501008\pi\)
−0.00316557 + 0.999995i \(0.501008\pi\)
\(810\) −21.6546 3.62490i −0.760866 0.127366i
\(811\) 26.2915 0.923220 0.461610 0.887083i \(-0.347272\pi\)
0.461610 + 0.887083i \(0.347272\pi\)
\(812\) −0.454399 1.05341i −0.0159463 0.0369676i
\(813\) −11.0622 + 1.48077i −0.387967 + 0.0519330i
\(814\) −7.93334 + 8.40885i −0.278063 + 0.294730i
\(815\) 3.02142 51.8758i 0.105836 1.81713i
\(816\) −7.00092 + 0.117018i −0.245081 + 0.00409644i
\(817\) −32.7997 + 7.77367i −1.14752 + 0.271966i
\(818\) −13.2411 4.81936i −0.462964 0.168505i
\(819\) −0.835780 9.09832i −0.0292045 0.317921i
\(820\) 14.9321 5.43484i 0.521452 0.189793i
\(821\) 30.1923 19.8578i 1.05372 0.693041i 0.100380 0.994949i \(-0.467994\pi\)
0.953337 + 0.301908i \(0.0976237\pi\)
\(822\) −22.8320 + 31.7634i −0.796357 + 1.10788i
\(823\) 14.7440 1.72333i 0.513945 0.0600716i 0.144832 0.989456i \(-0.453736\pi\)
0.369113 + 0.929385i \(0.379662\pi\)
\(824\) −6.29525 8.45599i −0.219305 0.294578i
\(825\) 2.77481 + 1.33597i 0.0966064 + 0.0465124i
\(826\) −0.277912 4.77157i −0.00966981 0.166024i
\(827\) −21.8426 18.3281i −0.759541 0.637330i 0.178466 0.983946i \(-0.442886\pi\)
−0.938007 + 0.346616i \(0.887331\pi\)
\(828\) −2.59194 7.70988i −0.0900762 0.267937i
\(829\) −9.42545 + 7.90889i −0.327359 + 0.274687i −0.791623 0.611010i \(-0.790764\pi\)
0.464264 + 0.885697i \(0.346319\pi\)
\(830\) 12.0769 + 12.8008i 0.419197 + 0.444323i
\(831\) 22.4201 8.58724i 0.777746 0.297888i
\(832\) 3.66400 + 2.40985i 0.127026 + 0.0835466i
\(833\) 25.6380 + 6.07631i 0.888303 + 0.210532i
\(834\) −11.4588 + 12.5597i −0.396787 + 0.434907i
\(835\) 22.0499 + 2.57726i 0.763069 + 0.0891899i
\(836\) −7.38048 12.7834i −0.255259 0.442122i
\(837\) 26.4768 + 32.0739i 0.915172 + 1.10864i
\(838\) 12.4429 21.5517i 0.429832 0.744491i
\(839\) −8.14892 + 10.9459i −0.281332 + 0.377895i −0.920218 0.391407i \(-0.871988\pi\)
0.638885 + 0.769302i \(0.279396\pi\)
\(840\) 2.59990 1.36060i 0.0897050 0.0469450i
\(841\) 7.53459 + 25.1673i 0.259814 + 0.867838i
\(842\) −4.24990 + 2.13438i −0.146461 + 0.0735556i
\(843\) 6.73266 + 34.7739i 0.231885 + 1.19768i
\(844\) −3.61750 + 12.0833i −0.124520 + 0.415925i
\(845\) 2.64015 + 14.9730i 0.0908240 + 0.515088i
\(846\) 1.45183 10.2205i 0.0499149 0.351388i
\(847\) 0.905320 5.13432i 0.0311072 0.176417i
\(848\) −9.51014 4.77617i −0.326580 0.164014i
\(849\) −46.7412 + 11.9063i −1.60415 + 0.408623i
\(850\) 1.52335 3.53152i 0.0522505 0.121130i
\(851\) −6.64290 + 15.4000i −0.227716 + 0.527905i
\(852\) −14.2500 + 3.62989i −0.488199 + 0.124358i
\(853\) 28.4119 + 14.2690i 0.972806 + 0.488561i 0.862897 0.505380i \(-0.168648\pi\)
0.109909 + 0.993942i \(0.464944\pi\)
\(854\) −1.28558 + 7.29087i −0.0439915 + 0.249488i
\(855\) −53.6277 + 21.5747i −1.83403 + 0.737839i
\(856\) −2.77584 15.7426i −0.0948763 0.538070i
\(857\) −8.06448 + 26.9372i −0.275477 + 0.920159i 0.702542 + 0.711643i \(0.252048\pi\)
−0.978019 + 0.208516i \(0.933137\pi\)
\(858\) 2.69836 + 13.9369i 0.0921204 + 0.475799i
\(859\) −18.1968 + 9.13876i −0.620866 + 0.311811i −0.731282 0.682075i \(-0.761078\pi\)
0.110416 + 0.993885i \(0.464782\pi\)
\(860\) 2.98605 + 9.97410i 0.101823 + 0.340114i
\(861\) 6.94181 3.63283i 0.236576 0.123807i
\(862\) 10.9145 14.6607i 0.371748 0.499344i
\(863\) −6.85376 + 11.8711i −0.233305 + 0.404096i −0.958779 0.284154i \(-0.908287\pi\)
0.725474 + 0.688250i \(0.241621\pi\)
\(864\) 3.37191 3.95351i 0.114715 0.134501i
\(865\) −12.2827 21.2743i −0.417625 0.723348i
\(866\) 31.9533 + 3.73480i 1.08582 + 0.126914i
\(867\) 0.767937 0.841714i 0.0260805 0.0285861i
\(868\) −5.40870 1.28188i −0.183583 0.0435100i
\(869\) −15.3310 10.0834i −0.520069 0.342055i
\(870\) 6.51854 2.49670i 0.220999 0.0846461i
\(871\) −31.9352 33.8494i −1.08208 1.14694i
\(872\) 3.82766 3.21178i 0.129621 0.108765i
\(873\) 13.1948 + 2.66489i 0.446576 + 0.0901928i
\(874\) −16.4046 13.7651i −0.554893 0.465611i
\(875\) −0.398818 6.84744i −0.0134825 0.231486i
\(876\) −4.76391 2.29365i −0.160958 0.0774951i
\(877\) 0.525309 + 0.705612i 0.0177384 + 0.0238268i 0.810904 0.585179i \(-0.198976\pi\)
−0.793166 + 0.609006i \(0.791568\pi\)
\(878\) 24.9769 2.91938i 0.842929 0.0985242i
\(879\) 31.2066 43.4140i 1.05257 1.46432i
\(880\) −3.80918 + 2.50533i −0.128407 + 0.0844548i
\(881\) −35.9119 + 13.0709i −1.20990 + 0.440369i −0.866670 0.498881i \(-0.833744\pi\)
−0.343233 + 0.939250i \(0.611522\pi\)
\(882\) −15.9682 + 11.2846i −0.537678 + 0.379972i
\(883\) 9.75210 + 3.54947i 0.328184 + 0.119449i 0.500857 0.865530i \(-0.333018\pi\)
−0.172673 + 0.984979i \(0.555240\pi\)
\(884\) 17.2506 4.08846i 0.580200 0.137510i
\(885\) 29.0775 0.486020i 0.977430 0.0163374i
\(886\) −0.363066 + 6.23360i −0.0121974 + 0.209422i
\(887\) −7.32785 + 7.76707i −0.246045 + 0.260793i −0.838613 0.544728i \(-0.816633\pi\)
0.592567 + 0.805521i \(0.298114\pi\)
\(888\) −10.6194 + 1.42151i −0.356365 + 0.0477028i
\(889\) −1.26688 2.93697i −0.0424899 0.0985027i
\(890\) 45.1855 1.51462
\(891\) 16.7824 1.12361i 0.562230 0.0376425i
\(892\) −12.4528 −0.416951
\(893\) −10.7648 24.9555i −0.360229 0.835105i
\(894\) 5.87835 14.2791i 0.196601 0.477565i
\(895\) −21.2616 + 22.5360i −0.710696 + 0.753294i
\(896\) −0.0403794 + 0.693288i −0.00134898 + 0.0231611i
\(897\) 10.5940 + 17.6609i 0.353722 + 0.589680i
\(898\) −7.34347 + 1.74043i −0.245055 + 0.0580791i
\(899\) −12.4252 4.52239i −0.414403 0.150830i
\(900\) 1.21744 + 2.58152i 0.0405814 + 0.0860507i
\(901\) −40.4267 + 14.7141i −1.34681 + 0.490199i
\(902\) −10.1706 + 6.68933i −0.338645 + 0.222730i
\(903\) 2.11176 + 4.67902i 0.0702751 + 0.155708i
\(904\) −9.65778 + 1.12883i −0.321213 + 0.0375444i
\(905\) −4.35658 5.85191i −0.144818 0.194524i
\(906\) −1.78267 23.7591i −0.0592252 0.789342i
\(907\) −1.69416 29.0877i −0.0562538 0.965840i −0.901859 0.432031i \(-0.857797\pi\)
0.845605 0.533809i \(-0.179240\pi\)
\(908\) −9.38466 7.87466i −0.311441 0.261330i
\(909\) 18.0441 9.83052i 0.598483 0.326058i
\(910\) −5.69152 + 4.77575i −0.188672 + 0.158315i
\(911\) −16.3190 17.2971i −0.540672 0.573079i 0.398220 0.917290i \(-0.369628\pi\)
−0.938892 + 0.344211i \(0.888147\pi\)
\(912\) 2.15006 13.5102i 0.0711957 0.447369i
\(913\) −11.2640 7.40844i −0.372783 0.245184i
\(914\) 8.85617 + 2.09895i 0.292936 + 0.0694271i
\(915\) −43.9985 9.65418i −1.45455 0.319157i
\(916\) 13.2740 + 1.55151i 0.438587 + 0.0512635i
\(917\) 1.02029 + 1.76719i 0.0336929 + 0.0583578i
\(918\) −2.27082 20.8826i −0.0749483 0.689228i
\(919\) 5.59461 9.69014i 0.184549 0.319648i −0.758875 0.651236i \(-0.774251\pi\)
0.943424 + 0.331588i \(0.107584\pi\)
\(920\) −3.94982 + 5.30553i −0.130222 + 0.174918i
\(921\) 2.06605 49.7982i 0.0680785 1.64091i
\(922\) −5.58925 18.6694i −0.184072 0.614844i
\(923\) 33.2722 16.7099i 1.09517 0.550015i
\(924\) −1.69766 + 1.47355i −0.0558488 + 0.0484761i
\(925\) 1.68789 5.63793i 0.0554974 0.185374i
\(926\) 1.73101 + 9.81702i 0.0568844 + 0.322607i
\(927\) 23.5340 21.1271i 0.772959 0.693906i
\(928\) −0.286864 + 1.62689i −0.00941676 + 0.0534051i
\(929\) 27.4141 + 13.7679i 0.899426 + 0.451709i 0.837541 0.546374i \(-0.183992\pi\)
0.0618851 + 0.998083i \(0.480289\pi\)
\(930\) 9.15702 32.5573i 0.300271 1.06760i
\(931\) −20.3897 + 47.2687i −0.668247 + 1.54917i
\(932\) 2.14850 4.98077i 0.0703763 0.163151i
\(933\) −15.3023 15.6858i −0.500976 0.513531i
\(934\) −13.8966 6.97916i −0.454712 0.228365i
\(935\) −3.20049 + 18.1509i −0.104667 + 0.593597i
\(936\) −6.19375 + 11.6073i −0.202449 + 0.379395i
\(937\) 0.516383 + 2.92855i 0.0168695 + 0.0956716i 0.992080 0.125607i \(-0.0400880\pi\)
−0.975211 + 0.221279i \(0.928977\pi\)
\(938\) 2.11354 7.05971i 0.0690095 0.230508i
\(939\) 10.4158 + 3.59507i 0.339906 + 0.117321i
\(940\) −7.50165 + 3.76747i −0.244677 + 0.122881i
\(941\) 3.91004 + 13.0605i 0.127464 + 0.425759i 0.997770 0.0667532i \(-0.0212640\pi\)
−0.870306 + 0.492512i \(0.836079\pi\)
\(942\) 26.0112 + 16.4917i 0.847489 + 0.537330i
\(943\) −10.5461 + 14.1659i −0.343430 + 0.461306i
\(944\) −3.44126 + 5.96044i −0.112004 + 0.193996i
\(945\) 4.77816 + 7.39361i 0.155433 + 0.240514i
\(946\) −3.98800 6.90742i −0.129661 0.224579i
\(947\) 29.2273 + 3.41618i 0.949760 + 0.111011i 0.576844 0.816854i \(-0.304284\pi\)
0.372916 + 0.927865i \(0.378358\pi\)
\(948\) −5.14905 16.2081i −0.167233 0.526413i
\(949\) 13.0264 + 3.08730i 0.422853 + 0.100218i
\(950\) 6.27820 + 4.12924i 0.203692 + 0.133970i
\(951\) 25.8365 + 20.9537i 0.837806 + 0.679469i
\(952\) 1.92655 + 2.04203i 0.0624399 + 0.0661824i
\(953\) 31.1156 26.1091i 1.00793 0.845756i 0.0198693 0.999803i \(-0.493675\pi\)
0.988064 + 0.154047i \(0.0492306\pi\)
\(954\) 11.6586 29.7215i 0.377461 0.962270i
\(955\) 16.6612 + 13.9804i 0.539145 + 0.452396i
\(956\) 0.111165 + 1.90863i 0.00359533 + 0.0617294i
\(957\) −4.41801 + 3.01273i −0.142814 + 0.0973878i
\(958\) 11.6406 + 15.6361i 0.376091 + 0.505178i
\(959\) 15.5782 1.82083i 0.503047 0.0587978i
\(960\) −4.20446 0.420334i −0.135698 0.0135662i
\(961\) −27.6255 + 18.1696i −0.891146 + 0.586116i
\(962\) 25.4917 9.27822i 0.821886 0.299142i
\(963\) 46.2679 12.6128i 1.49096 0.406442i
\(964\) −6.01612 2.18969i −0.193766 0.0705252i
\(965\) 4.34856 1.03063i 0.139985 0.0331770i
\(966\) −1.58321 + 2.85120i −0.0509389 + 0.0917360i
\(967\) 1.91687 32.9114i 0.0616424 1.05836i −0.815694 0.578483i \(-0.803645\pi\)
0.877337 0.479875i \(-0.159318\pi\)
\(968\) −5.15181 + 5.46060i −0.165586 + 0.175510i
\(969\) −33.7614 43.8017i −1.08457 1.40711i
\(970\) −4.33566 10.0512i −0.139210 0.322724i
\(971\) −24.2831 −0.779283 −0.389642 0.920967i \(-0.627401\pi\)
−0.389642 + 0.920967i \(0.627401\pi\)
\(972\) 12.7361 + 8.98837i 0.408512 + 0.288302i
\(973\) 6.81673 0.218534
\(974\) −3.28107 7.60638i −0.105132 0.243724i
\(975\) −4.41174 5.72375i −0.141289 0.183307i
\(976\) 7.31570 7.75419i 0.234170 0.248206i
\(977\) −1.56211 + 26.8204i −0.0499762 + 0.858059i 0.876429 + 0.481531i \(0.159919\pi\)
−0.926405 + 0.376528i \(0.877118\pi\)
\(978\) −17.9103 + 32.2546i −0.572707 + 1.03139i
\(979\) −33.6825 + 7.98290i −1.07650 + 0.255134i
\(980\) 14.9414 + 5.43822i 0.477285 + 0.173718i
\(981\) 10.6454 + 10.5534i 0.339880 + 0.336945i
\(982\) 4.05048 1.47426i 0.129256 0.0470454i
\(983\) −52.0526 + 34.2356i −1.66022 + 1.09194i −0.767868 + 0.640608i \(0.778682\pi\)
−0.892354 + 0.451337i \(0.850947\pi\)
\(984\) −11.2261 1.12231i −0.357873 0.0357778i
\(985\) 35.7520 4.17880i 1.13915 0.133148i
\(986\) 3.98795 + 5.35675i 0.127002 + 0.170594i
\(987\) −3.41961 + 2.33191i −0.108847 + 0.0742254i
\(988\) 2.01400 + 34.5791i 0.0640740 + 1.10011i
\(989\) −8.86412 7.43788i −0.281863 0.236511i
\(990\) −8.52983 10.6921i −0.271096 0.339817i
\(991\) −20.5688 + 17.2593i −0.653390 + 0.548259i −0.908098 0.418759i \(-0.862465\pi\)
0.254707 + 0.967018i \(0.418021\pi\)
\(992\) 5.49273 + 5.82195i 0.174394 + 0.184847i
\(993\) 6.96284 + 5.64693i 0.220959 + 0.179200i
\(994\) 4.92602 + 3.23989i 0.156244 + 0.102763i
\(995\) −61.0704 14.4740i −1.93606 0.458855i
\(996\) −3.78311 11.9084i −0.119872 0.377331i
\(997\) −48.5136 5.67042i −1.53644 0.179584i −0.694634 0.719363i \(-0.744434\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(998\) −10.3721 17.9651i −0.328324 0.568674i
\(999\) −7.16092 31.3346i −0.226561 0.991384i
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 162.2.g.a.31.3 72
3.2 odd 2 486.2.g.a.145.3 72
81.34 even 27 inner 162.2.g.a.115.3 yes 72
81.47 odd 54 486.2.g.a.181.3 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.2.g.a.31.3 72 1.1 even 1 trivial
162.2.g.a.115.3 yes 72 81.34 even 27 inner
486.2.g.a.145.3 72 3.2 odd 2
486.2.g.a.181.3 72 81.47 odd 54