Properties

Label 69.2.e.a.64.1
Level $69$
Weight $2$
Character 69.64
Analytic conductor $0.551$
Analytic rank $0$
Dimension $10$
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] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 64.1
Root \(0.959493 + 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 69.64
Dual form 69.2.e.a.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.41153 - 0.708089i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.63158 + 2.33387i) q^{4} +(0.108660 - 0.755750i) q^{5} +(-2.11435 + 1.35881i) q^{6} +(-2.00357 - 4.38721i) q^{7} +(-3.81329 - 4.40077i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(-2.41153 - 0.708089i) q^{2} +(0.654861 - 0.755750i) q^{3} +(3.63158 + 2.33387i) q^{4} +(0.108660 - 0.755750i) q^{5} +(-2.11435 + 1.35881i) q^{6} +(-2.00357 - 4.38721i) q^{7} +(-3.81329 - 4.40077i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.797176 + 1.74557i) q^{10} +(3.23616 - 0.950224i) q^{11} +(4.14200 - 1.21620i) q^{12} +(-1.41718 + 3.10319i) q^{13} +(1.72514 + 11.9986i) q^{14} +(-0.500000 - 0.577031i) q^{15} +(2.49315 + 5.45923i) q^{16} +(0.774961 - 0.498037i) q^{17} +(-0.357685 + 2.48775i) q^{18} +(2.49611 + 1.60416i) q^{19} +(2.15843 - 2.49096i) q^{20} +(-4.62769 - 1.35881i) q^{21} -8.47695 q^{22} +(2.73939 + 3.93646i) q^{23} -5.82306 q^{24} +(4.23811 + 1.24442i) q^{25} +(5.61490 - 6.47994i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(2.96306 - 20.6086i) q^{28} +(-6.23737 + 4.00851i) q^{29} +(0.797176 + 1.74557i) q^{30} +(-0.311710 - 0.359733i) q^{31} +(-0.489262 - 3.40289i) q^{32} +(1.40111 - 3.06799i) q^{33} +(-2.22150 + 0.652290i) q^{34} +(-3.53334 + 1.03748i) q^{35} +(1.79329 - 3.92676i) q^{36} +(0.247817 + 1.72360i) q^{37} +(-4.88357 - 5.63594i) q^{38} +(1.41718 + 3.10319i) q^{39} +(-3.74024 + 2.40370i) q^{40} +(0.527961 - 3.67205i) q^{41} +(10.1977 + 6.55363i) q^{42} +(0.391457 - 0.451765i) q^{43} +(13.9701 + 4.10199i) q^{44} -0.763521 q^{45} +(-3.81876 - 11.4326i) q^{46} +5.02851 q^{47} +(5.75848 + 1.69084i) q^{48} +(-10.6493 + 12.2899i) q^{49} +(-9.33918 - 6.00192i) q^{50} +(0.131100 - 0.911821i) q^{51} +(-12.3890 + 7.96195i) q^{52} +(0.0367767 + 0.0805298i) q^{53} +(1.64589 + 1.89945i) q^{54} +(-0.366488 - 2.54898i) q^{55} +(-11.6669 + 25.5470i) q^{56} +(2.84695 - 0.835939i) q^{57} +(17.8800 - 5.25004i) q^{58} +(2.72548 - 5.96797i) q^{59} +(-0.469072 - 3.26247i) q^{60} +(3.85803 + 4.45240i) q^{61} +(0.496975 + 1.08822i) q^{62} +(-4.05742 + 2.60754i) q^{63} +(0.478549 - 3.32838i) q^{64} +(2.19124 + 1.40823i) q^{65} +(-5.55122 + 6.40645i) q^{66} +(9.60816 + 2.82121i) q^{67} +3.97669 q^{68} +(4.76890 + 0.507539i) q^{69} +9.25538 q^{70} +(-8.75112 - 2.56956i) q^{71} +(-3.81329 + 4.40077i) q^{72} +(-10.1506 - 6.52340i) q^{73} +(0.622847 - 4.33199i) q^{74} +(3.71585 - 2.38803i) q^{75} +(5.32094 + 11.6512i) q^{76} +(-10.6527 - 12.2939i) q^{77} +(-1.22023 - 8.48692i) q^{78} +(4.36916 - 9.56713i) q^{79} +(4.39672 - 1.29099i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.87333 + 8.48141i) q^{82} +(-0.420847 - 2.92705i) q^{83} +(-13.6345 - 15.7351i) q^{84} +(-0.292184 - 0.639793i) q^{85} +(-1.26390 + 0.812259i) q^{86} +(-1.05518 + 7.33891i) q^{87} +(-16.5222 - 10.6181i) q^{88} +(-6.39396 + 7.37902i) q^{89} +(1.84125 + 0.540641i) q^{90} +16.4537 q^{91} +(0.761114 + 20.6890i) q^{92} -0.475994 q^{93} +(-12.1264 - 3.56063i) q^{94} +(1.48357 - 1.71213i) q^{95} +(-2.89213 - 1.85866i) q^{96} +(-1.19327 + 8.29940i) q^{97} +(34.3834 - 22.0969i) q^{98} +(-1.40111 - 3.06799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{6}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41153 0.708089i −1.70521 0.500694i −0.723378 0.690452i \(-0.757411\pi\)
−0.981831 + 0.189758i \(0.939230\pi\)
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 3.63158 + 2.33387i 1.81579 + 1.16694i
\(5\) 0.108660 0.755750i 0.0485944 0.337981i −0.950992 0.309216i \(-0.899933\pi\)
0.999586 0.0287654i \(-0.00915756\pi\)
\(6\) −2.11435 + 1.35881i −0.863181 + 0.554733i
\(7\) −2.00357 4.38721i −0.757279 1.65821i −0.752827 0.658219i \(-0.771310\pi\)
−0.00445196 0.999990i \(-0.501417\pi\)
\(8\) −3.81329 4.40077i −1.34820 1.55591i
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) −0.797176 + 1.74557i −0.252089 + 0.551998i
\(11\) 3.23616 0.950224i 0.975740 0.286503i 0.245275 0.969453i \(-0.421122\pi\)
0.730465 + 0.682950i \(0.239303\pi\)
\(12\) 4.14200 1.21620i 1.19569 0.351087i
\(13\) −1.41718 + 3.10319i −0.393055 + 0.860669i 0.604873 + 0.796322i \(0.293224\pi\)
−0.997928 + 0.0643475i \(0.979503\pi\)
\(14\) 1.72514 + 11.9986i 0.461062 + 3.20676i
\(15\) −0.500000 0.577031i −0.129099 0.148989i
\(16\) 2.49315 + 5.45923i 0.623287 + 1.36481i
\(17\) 0.774961 0.498037i 0.187956 0.120792i −0.443279 0.896384i \(-0.646185\pi\)
0.631235 + 0.775592i \(0.282549\pi\)
\(18\) −0.357685 + 2.48775i −0.0843072 + 0.586369i
\(19\) 2.49611 + 1.60416i 0.572648 + 0.368018i 0.794687 0.607019i \(-0.207635\pi\)
−0.222039 + 0.975038i \(0.571271\pi\)
\(20\) 2.15843 2.49096i 0.482640 0.556996i
\(21\) −4.62769 1.35881i −1.00984 0.296517i
\(22\) −8.47695 −1.80729
\(23\) 2.73939 + 3.93646i 0.571203 + 0.820809i
\(24\) −5.82306 −1.18863
\(25\) 4.23811 + 1.24442i 0.847623 + 0.248885i
\(26\) 5.61490 6.47994i 1.10117 1.27082i
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 2.96306 20.6086i 0.559966 3.89465i
\(29\) −6.23737 + 4.00851i −1.15825 + 0.744362i −0.971265 0.238001i \(-0.923508\pi\)
−0.186985 + 0.982363i \(0.559872\pi\)
\(30\) 0.797176 + 1.74557i 0.145544 + 0.318696i
\(31\) −0.311710 0.359733i −0.0559848 0.0646099i 0.727066 0.686567i \(-0.240883\pi\)
−0.783051 + 0.621957i \(0.786338\pi\)
\(32\) −0.489262 3.40289i −0.0864901 0.601552i
\(33\) 1.40111 3.06799i 0.243901 0.534069i
\(34\) −2.22150 + 0.652290i −0.380983 + 0.111867i
\(35\) −3.53334 + 1.03748i −0.597243 + 0.175366i
\(36\) 1.79329 3.92676i 0.298882 0.654460i
\(37\) 0.247817 + 1.72360i 0.0407408 + 0.283358i 1.00000 0.000829807i \(0.000264136\pi\)
−0.959259 + 0.282529i \(0.908827\pi\)
\(38\) −4.88357 5.63594i −0.792219 0.914270i
\(39\) 1.41718 + 3.10319i 0.226930 + 0.496908i
\(40\) −3.74024 + 2.40370i −0.591383 + 0.380059i
\(41\) 0.527961 3.67205i 0.0824537 0.573478i −0.906152 0.422952i \(-0.860994\pi\)
0.988606 0.150526i \(-0.0480969\pi\)
\(42\) 10.1977 + 6.55363i 1.57353 + 1.01125i
\(43\) 0.391457 0.451765i 0.0596966 0.0688936i −0.725116 0.688627i \(-0.758214\pi\)
0.784812 + 0.619733i \(0.212759\pi\)
\(44\) 13.9701 + 4.10199i 2.10607 + 0.618398i
\(45\) −0.763521 −0.113819
\(46\) −3.81876 11.4326i −0.563046 1.68565i
\(47\) 5.02851 0.733484 0.366742 0.930323i \(-0.380473\pi\)
0.366742 + 0.930323i \(0.380473\pi\)
\(48\) 5.75848 + 1.69084i 0.831164 + 0.244052i
\(49\) −10.6493 + 12.2899i −1.52133 + 1.75570i
\(50\) −9.33918 6.00192i −1.32076 0.848800i
\(51\) 0.131100 0.911821i 0.0183577 0.127681i
\(52\) −12.3890 + 7.96195i −1.71805 + 1.10412i
\(53\) 0.0367767 + 0.0805298i 0.00505167 + 0.0110616i 0.912141 0.409877i \(-0.134428\pi\)
−0.907089 + 0.420938i \(0.861701\pi\)
\(54\) 1.64589 + 1.89945i 0.223977 + 0.258483i
\(55\) −0.366488 2.54898i −0.0494173 0.343705i
\(56\) −11.6669 + 25.5470i −1.55906 + 3.41386i
\(57\) 2.84695 0.835939i 0.377087 0.110723i
\(58\) 17.8800 5.25004i 2.34776 0.689363i
\(59\) 2.72548 5.96797i 0.354827 0.776963i −0.645090 0.764106i \(-0.723180\pi\)
0.999917 0.0128566i \(-0.00409251\pi\)
\(60\) −0.469072 3.26247i −0.0605569 0.421183i
\(61\) 3.85803 + 4.45240i 0.493970 + 0.570072i 0.946922 0.321463i \(-0.104175\pi\)
−0.452952 + 0.891535i \(0.649629\pi\)
\(62\) 0.496975 + 1.08822i 0.0631159 + 0.138205i
\(63\) −4.05742 + 2.60754i −0.511186 + 0.328519i
\(64\) 0.478549 3.32838i 0.0598186 0.416048i
\(65\) 2.19124 + 1.40823i 0.271790 + 0.174669i
\(66\) −5.55122 + 6.40645i −0.683308 + 0.788579i
\(67\) 9.60816 + 2.82121i 1.17382 + 0.344666i 0.809790 0.586720i \(-0.199581\pi\)
0.364034 + 0.931386i \(0.381399\pi\)
\(68\) 3.97669 0.482244
\(69\) 4.76890 + 0.507539i 0.574108 + 0.0611006i
\(70\) 9.25538 1.10623
\(71\) −8.75112 2.56956i −1.03857 0.304951i −0.282377 0.959303i \(-0.591123\pi\)
−0.756190 + 0.654353i \(0.772941\pi\)
\(72\) −3.81329 + 4.40077i −0.449401 + 0.518636i
\(73\) −10.1506 6.52340i −1.18804 0.763506i −0.211192 0.977445i \(-0.567734\pi\)
−0.976847 + 0.213939i \(0.931371\pi\)
\(74\) 0.622847 4.33199i 0.0724044 0.503584i
\(75\) 3.71585 2.38803i 0.429069 0.275746i
\(76\) 5.32094 + 11.6512i 0.610353 + 1.33649i
\(77\) −10.6527 12.2939i −1.21399 1.40102i
\(78\) −1.22023 8.48692i −0.138164 0.960954i
\(79\) 4.36916 9.56713i 0.491569 1.07639i −0.487549 0.873095i \(-0.662109\pi\)
0.979118 0.203291i \(-0.0651636\pi\)
\(80\) 4.39672 1.29099i 0.491568 0.144337i
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) −3.87333 + 8.48141i −0.427738 + 0.936615i
\(83\) −0.420847 2.92705i −0.0461939 0.321286i −0.999796 0.0202149i \(-0.993565\pi\)
0.953602 0.301071i \(-0.0973441\pi\)
\(84\) −13.6345 15.7351i −1.48765 1.71684i
\(85\) −0.292184 0.639793i −0.0316918 0.0693953i
\(86\) −1.26390 + 0.812259i −0.136290 + 0.0875882i
\(87\) −1.05518 + 7.33891i −0.113127 + 0.786813i
\(88\) −16.5222 10.6181i −1.76127 1.13190i
\(89\) −6.39396 + 7.37902i −0.677758 + 0.782175i −0.985569 0.169273i \(-0.945858\pi\)
0.307811 + 0.951448i \(0.400404\pi\)
\(90\) 1.84125 + 0.540641i 0.194085 + 0.0569885i
\(91\) 16.4537 1.72482
\(92\) 0.761114 + 20.6890i 0.0793516 + 2.15697i
\(93\) −0.475994 −0.0493583
\(94\) −12.1264 3.56063i −1.25074 0.367251i
\(95\) 1.48357 1.71213i 0.152211 0.175661i
\(96\) −2.89213 1.85866i −0.295177 0.189699i
\(97\) −1.19327 + 8.29940i −0.121159 + 0.842676i 0.835088 + 0.550116i \(0.185416\pi\)
−0.956247 + 0.292560i \(0.905493\pi\)
\(98\) 34.3834 22.0969i 3.47325 2.23212i
\(99\) −1.40111 3.06799i −0.140816 0.308345i
\(100\) 12.4867 + 14.4104i 1.24867 + 1.44104i
\(101\) 0.629480 + 4.37813i 0.0626356 + 0.435640i 0.996875 + 0.0789938i \(0.0251707\pi\)
−0.934240 + 0.356646i \(0.883920\pi\)
\(102\) −0.961802 + 2.10605i −0.0952326 + 0.208530i
\(103\) −15.5539 + 4.56703i −1.53257 + 0.450002i −0.935835 0.352438i \(-0.885353\pi\)
−0.596732 + 0.802440i \(0.703535\pi\)
\(104\) 19.0605 5.59668i 1.86904 0.548800i
\(105\) −1.52977 + 3.34973i −0.149290 + 0.326900i
\(106\) −0.0316659 0.220241i −0.00307567 0.0213917i
\(107\) 4.15860 + 4.79928i 0.402027 + 0.463964i 0.920278 0.391265i \(-0.127962\pi\)
−0.518251 + 0.855228i \(0.673417\pi\)
\(108\) −1.79329 3.92676i −0.172559 0.377852i
\(109\) −2.07028 + 1.33049i −0.198296 + 0.127437i −0.636021 0.771672i \(-0.719421\pi\)
0.437725 + 0.899109i \(0.355784\pi\)
\(110\) −0.921108 + 6.40645i −0.0878242 + 0.610831i
\(111\) 1.46490 + 0.941432i 0.139042 + 0.0893568i
\(112\) 18.9556 21.8759i 1.79113 2.06708i
\(113\) 8.87992 + 2.60738i 0.835352 + 0.245282i 0.671315 0.741172i \(-0.265730\pi\)
0.164038 + 0.986454i \(0.447548\pi\)
\(114\) −7.45741 −0.698451
\(115\) 3.27264 1.64256i 0.305175 0.153169i
\(116\) −32.0068 −2.97176
\(117\) 3.27329 + 0.961124i 0.302616 + 0.0888559i
\(118\) −10.7984 + 12.4620i −0.994075 + 1.14722i
\(119\) −3.73768 2.40206i −0.342633 0.220197i
\(120\) −0.632736 + 4.40077i −0.0577606 + 0.401734i
\(121\) 0.316044 0.203109i 0.0287313 0.0184645i
\(122\) −6.15105 13.4689i −0.556890 1.21942i
\(123\) −2.42941 2.80369i −0.219052 0.252800i
\(124\) −0.292429 2.03389i −0.0262609 0.182649i
\(125\) 2.98688 6.54035i 0.267154 0.584987i
\(126\) 11.6309 3.41515i 1.03617 0.304246i
\(127\) 1.28204 0.376440i 0.113762 0.0334037i −0.224356 0.974507i \(-0.572028\pi\)
0.338118 + 0.941104i \(0.390210\pi\)
\(128\) −6.36712 + 13.9420i −0.562779 + 1.23231i
\(129\) −0.0850717 0.591687i −0.00749015 0.0520951i
\(130\) −4.28709 4.94757i −0.376003 0.433931i
\(131\) −1.42534 3.12106i −0.124533 0.272688i 0.837089 0.547066i \(-0.184255\pi\)
−0.961622 + 0.274378i \(0.911528\pi\)
\(132\) 12.2485 7.87165i 1.06610 0.685139i
\(133\) 2.03662 14.1650i 0.176597 1.22826i
\(134\) −21.1727 13.6069i −1.82904 1.17545i
\(135\) −0.500000 + 0.577031i −0.0430331 + 0.0496629i
\(136\) −5.14690 1.51127i −0.441343 0.129590i
\(137\) −4.07129 −0.347833 −0.173917 0.984760i \(-0.555642\pi\)
−0.173917 + 0.984760i \(0.555642\pi\)
\(138\) −11.1410 4.60075i −0.948381 0.391642i
\(139\) 6.01342 0.510052 0.255026 0.966934i \(-0.417916\pi\)
0.255026 + 0.966934i \(0.417916\pi\)
\(140\) −15.2529 4.47867i −1.28911 0.378517i
\(141\) 3.29298 3.80030i 0.277319 0.320043i
\(142\) 19.2841 + 12.3931i 1.61829 + 1.04001i
\(143\) −1.63750 + 11.3891i −0.136935 + 0.952401i
\(144\) 5.04885 3.24470i 0.420738 0.270392i
\(145\) 2.35168 + 5.14945i 0.195296 + 0.427639i
\(146\) 19.8593 + 22.9189i 1.64357 + 1.89678i
\(147\) 2.31431 + 16.0964i 0.190881 + 1.32761i
\(148\) −3.12270 + 6.83777i −0.256685 + 0.562061i
\(149\) 14.5747 4.27953i 1.19401 0.350593i 0.376450 0.926437i \(-0.377145\pi\)
0.817560 + 0.575844i \(0.195326\pi\)
\(150\) −10.6518 + 3.12765i −0.869717 + 0.255372i
\(151\) −0.248740 + 0.544665i −0.0202422 + 0.0443242i −0.919483 0.393130i \(-0.871392\pi\)
0.899241 + 0.437454i \(0.144120\pi\)
\(152\) −2.45889 17.1019i −0.199442 1.38715i
\(153\) −0.603256 0.696195i −0.0487704 0.0562840i
\(154\) 16.9842 + 37.1901i 1.36862 + 2.99687i
\(155\) −0.305738 + 0.196486i −0.0245575 + 0.0157821i
\(156\) −2.09585 + 14.5770i −0.167803 + 1.16709i
\(157\) −2.89905 1.86310i −0.231369 0.148692i 0.419820 0.907607i \(-0.362093\pi\)
−0.651189 + 0.758915i \(0.725730\pi\)
\(158\) −17.3107 + 19.9777i −1.37717 + 1.58934i
\(159\) 0.0849440 + 0.0249418i 0.00673650 + 0.00197801i
\(160\) −2.62490 −0.207516
\(161\) 11.7815 19.9053i 0.928513 1.56875i
\(162\) 2.51334 0.197466
\(163\) −13.7358 4.03318i −1.07587 0.315903i −0.304643 0.952467i \(-0.598537\pi\)
−0.771224 + 0.636564i \(0.780355\pi\)
\(164\) 10.4874 12.1031i 0.818931 0.945096i
\(165\) −2.16639 1.39225i −0.168653 0.108387i
\(166\) −1.05773 + 7.35667i −0.0820958 + 0.570989i
\(167\) −19.1885 + 12.3317i −1.48485 + 0.954257i −0.488180 + 0.872743i \(0.662339\pi\)
−0.996672 + 0.0815140i \(0.974024\pi\)
\(168\) 11.6669 + 25.5470i 0.900122 + 1.97099i
\(169\) 0.891810 + 1.02920i 0.0686008 + 0.0791695i
\(170\) 0.251579 + 1.74977i 0.0192953 + 0.134201i
\(171\) 1.23259 2.69900i 0.0942588 0.206398i
\(172\) 2.47597 0.727010i 0.188791 0.0554340i
\(173\) 1.59528 0.468417i 0.121287 0.0356131i −0.220526 0.975381i \(-0.570777\pi\)
0.341813 + 0.939768i \(0.388959\pi\)
\(174\) 7.74118 16.9508i 0.586858 1.28504i
\(175\) −3.03182 21.0868i −0.229184 1.59401i
\(176\) 13.2557 + 15.2979i 0.999188 + 1.15312i
\(177\) −2.72548 5.96797i −0.204860 0.448580i
\(178\) 20.6442 13.2672i 1.54735 0.994421i
\(179\) −3.46892 + 24.1268i −0.259279 + 1.80333i 0.278712 + 0.960375i \(0.410092\pi\)
−0.537991 + 0.842950i \(0.680817\pi\)
\(180\) −2.77279 1.78196i −0.206671 0.132820i
\(181\) 6.93811 8.00700i 0.515705 0.595156i −0.436845 0.899537i \(-0.643904\pi\)
0.952550 + 0.304381i \(0.0984496\pi\)
\(182\) −39.6787 11.6507i −2.94118 0.863609i
\(183\) 5.89137 0.435503
\(184\) 6.87737 27.0663i 0.507007 1.99536i
\(185\) 1.32954 0.0977497
\(186\) 1.14787 + 0.337046i 0.0841662 + 0.0247134i
\(187\) 2.03465 2.34812i 0.148789 0.171711i
\(188\) 18.2614 + 11.7359i 1.33185 + 0.855929i
\(189\) −0.686393 + 4.77397i −0.0499277 + 0.347255i
\(190\) −4.79001 + 3.07835i −0.347504 + 0.223327i
\(191\) −7.13655 15.6269i −0.516383 1.13072i −0.970791 0.239927i \(-0.922877\pi\)
0.454408 0.890794i \(-0.349851\pi\)
\(192\) −2.20204 2.54129i −0.158919 0.183402i
\(193\) 2.01276 + 13.9991i 0.144882 + 1.00767i 0.924435 + 0.381339i \(0.124537\pi\)
−0.779554 + 0.626335i \(0.784554\pi\)
\(194\) 8.75432 19.1693i 0.628524 1.37628i
\(195\) 2.49922 0.733838i 0.178973 0.0525513i
\(196\) −67.3568 + 19.7777i −4.81120 + 1.41270i
\(197\) −1.27802 + 2.79847i −0.0910550 + 0.199383i −0.949680 0.313221i \(-0.898592\pi\)
0.858625 + 0.512604i \(0.171319\pi\)
\(198\) 1.20640 + 8.39066i 0.0857348 + 0.596299i
\(199\) −10.3265 11.9174i −0.732028 0.844805i 0.260671 0.965428i \(-0.416056\pi\)
−0.992698 + 0.120623i \(0.961511\pi\)
\(200\) −10.6847 23.3963i −0.755526 1.65437i
\(201\) 8.42414 5.41387i 0.594193 0.381865i
\(202\) 1.58209 11.0037i 0.111316 0.774218i
\(203\) 30.0832 + 19.3333i 2.11143 + 1.35693i
\(204\) 2.60418 3.00538i 0.182329 0.210419i
\(205\) −2.71778 0.798013i −0.189818 0.0557356i
\(206\) 40.7425 2.83866
\(207\) 3.50654 3.27173i 0.243721 0.227401i
\(208\) −20.4743 −1.41963
\(209\) 9.60214 + 2.81944i 0.664194 + 0.195025i
\(210\) 6.06099 6.99475i 0.418248 0.482684i
\(211\) −13.3259 8.56406i −0.917395 0.589574i −0.00549464 0.999985i \(-0.501749\pi\)
−0.911901 + 0.410411i \(0.865385\pi\)
\(212\) −0.0543888 + 0.378282i −0.00373544 + 0.0259805i
\(213\) −7.67271 + 4.93095i −0.525725 + 0.337863i
\(214\) −6.63027 14.5183i −0.453236 0.992448i
\(215\) −0.298886 0.344932i −0.0203838 0.0235242i
\(216\) 0.828708 + 5.76379i 0.0563864 + 0.392176i
\(217\) −0.953688 + 2.08829i −0.0647406 + 0.141762i
\(218\) 5.93463 1.74257i 0.401944 0.118021i
\(219\) −11.5773 + 3.39940i −0.782321 + 0.229710i
\(220\) 4.61807 10.1122i 0.311350 0.681762i
\(221\) 0.447245 + 3.11066i 0.0300850 + 0.209245i
\(222\) −2.86602 3.30757i −0.192355 0.221989i
\(223\) −6.99135 15.3089i −0.468176 1.02516i −0.985547 0.169401i \(-0.945817\pi\)
0.517372 0.855761i \(-0.326911\pi\)
\(224\) −13.9489 + 8.96442i −0.932001 + 0.598961i
\(225\) 0.628610 4.37208i 0.0419073 0.291472i
\(226\) −19.5679 12.5755i −1.30164 0.836513i
\(227\) 14.1033 16.2761i 0.936068 1.08028i −0.0605553 0.998165i \(-0.519287\pi\)
0.996623 0.0821148i \(-0.0261674\pi\)
\(228\) 12.2899 + 3.60863i 0.813917 + 0.238988i
\(229\) −0.566524 −0.0374370 −0.0187185 0.999825i \(-0.505959\pi\)
−0.0187185 + 0.999825i \(0.505959\pi\)
\(230\) −9.05515 + 1.64375i −0.597079 + 0.108386i
\(231\) −16.2671 −1.07030
\(232\) 41.4255 + 12.1636i 2.71972 + 0.798580i
\(233\) −5.27431 + 6.08688i −0.345532 + 0.398765i −0.901740 0.432278i \(-0.857710\pi\)
0.556209 + 0.831042i \(0.312255\pi\)
\(234\) −7.21307 4.63556i −0.471533 0.303036i
\(235\) 0.546400 3.80030i 0.0356432 0.247904i
\(236\) 23.8263 15.3122i 1.55096 0.996740i
\(237\) −4.36916 9.56713i −0.283808 0.621452i
\(238\) 7.31266 + 8.43926i 0.474009 + 0.547036i
\(239\) 0.983171 + 6.83811i 0.0635961 + 0.442320i 0.996596 + 0.0824432i \(0.0262723\pi\)
−0.933000 + 0.359877i \(0.882819\pi\)
\(240\) 1.90357 4.16824i 0.122875 0.269059i
\(241\) 0.317423 0.0932039i 0.0204470 0.00600379i −0.271493 0.962440i \(-0.587517\pi\)
0.291940 + 0.956437i \(0.405699\pi\)
\(242\) −0.905970 + 0.266017i −0.0582379 + 0.0171002i
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 3.61939 + 25.1734i 0.231707 + 1.61156i
\(245\) 8.13095 + 9.38361i 0.519467 + 0.599497i
\(246\) 3.87333 + 8.48141i 0.246955 + 0.540755i
\(247\) −8.51543 + 5.47254i −0.541824 + 0.348209i
\(248\) −0.394460 + 2.74353i −0.0250482 + 0.174214i
\(249\) −2.48772 1.59876i −0.157653 0.101317i
\(250\) −11.8341 + 13.6573i −0.748454 + 0.863762i
\(251\) −26.2161 7.69773i −1.65474 0.485877i −0.684704 0.728822i \(-0.740068\pi\)
−0.970040 + 0.242945i \(0.921886\pi\)
\(252\) −20.8205 −1.31157
\(253\) 12.6056 + 10.1360i 0.792510 + 0.637245i
\(254\) −3.35822 −0.210714
\(255\) −0.674863 0.198158i −0.0422616 0.0124091i
\(256\) 20.8226 24.0306i 1.30141 1.50191i
\(257\) 3.13015 + 2.01162i 0.195253 + 0.125482i 0.634615 0.772829i \(-0.281159\pi\)
−0.439361 + 0.898310i \(0.644795\pi\)
\(258\) −0.213814 + 1.48711i −0.0133115 + 0.0925833i
\(259\) 7.06528 4.54058i 0.439015 0.282138i
\(260\) 4.67104 + 10.2282i 0.289686 + 0.634323i
\(261\) 4.85538 + 5.60341i 0.300541 + 0.346842i
\(262\) 1.22726 + 8.53580i 0.0758205 + 0.527343i
\(263\) −7.67457 + 16.8050i −0.473234 + 1.03624i 0.511034 + 0.859560i \(0.329262\pi\)
−0.984269 + 0.176678i \(0.943465\pi\)
\(264\) −18.8444 + 5.53321i −1.15979 + 0.340545i
\(265\) 0.0648566 0.0190436i 0.00398411 0.00116984i
\(266\) −14.9415 + 32.7172i −0.916120 + 2.00602i
\(267\) 1.38954 + 9.66446i 0.0850385 + 0.591455i
\(268\) 28.3084 + 32.6697i 1.72921 + 1.99562i
\(269\) 3.10328 + 6.79523i 0.189210 + 0.414313i 0.980335 0.197343i \(-0.0632312\pi\)
−0.791124 + 0.611655i \(0.790504\pi\)
\(270\) 1.61435 1.03748i 0.0982464 0.0631392i
\(271\) −3.62528 + 25.2144i −0.220220 + 1.53166i 0.516985 + 0.855995i \(0.327054\pi\)
−0.737205 + 0.675669i \(0.763855\pi\)
\(272\) 4.65099 + 2.98901i 0.282008 + 0.181235i
\(273\) 10.7749 12.4349i 0.652127 0.752595i
\(274\) 9.81803 + 2.88283i 0.593129 + 0.174158i
\(275\) 14.8977 0.898366
\(276\) 16.1341 + 12.9732i 0.971158 + 0.780893i
\(277\) 31.4086 1.88716 0.943579 0.331146i \(-0.107435\pi\)
0.943579 + 0.331146i \(0.107435\pi\)
\(278\) −14.5015 4.25804i −0.869744 0.255380i
\(279\) −0.311710 + 0.359733i −0.0186616 + 0.0215366i
\(280\) 18.0394 + 11.5932i 1.07806 + 0.692827i
\(281\) 0.760027 5.28610i 0.0453394 0.315342i −0.954513 0.298169i \(-0.903624\pi\)
0.999853 0.0171736i \(-0.00546678\pi\)
\(282\) −10.6321 + 6.83281i −0.633130 + 0.406888i
\(283\) 7.16662 + 15.6927i 0.426011 + 0.932835i 0.993957 + 0.109769i \(0.0350111\pi\)
−0.567946 + 0.823066i \(0.692262\pi\)
\(284\) −25.7833 29.7556i −1.52996 1.76567i
\(285\) −0.322410 2.24241i −0.0190979 0.132829i
\(286\) 12.0133 26.3056i 0.710364 1.55548i
\(287\) −17.1679 + 5.04094i −1.01339 + 0.297557i
\(288\) −3.29862 + 0.968563i −0.194373 + 0.0570731i
\(289\) −6.70953 + 14.6918i −0.394678 + 0.864225i
\(290\) −2.02487 14.0833i −0.118904 0.826997i
\(291\) 5.49084 + 6.33676i 0.321879 + 0.371468i
\(292\) −21.6379 47.3804i −1.26626 2.77273i
\(293\) −27.6891 + 17.7947i −1.61762 + 1.03958i −0.660109 + 0.751170i \(0.729490\pi\)
−0.957507 + 0.288409i \(0.906874\pi\)
\(294\) 5.81664 40.4556i 0.339233 2.35942i
\(295\) −4.21414 2.70826i −0.245357 0.157681i
\(296\) 6.64019 7.66318i 0.385953 0.445414i
\(297\) −3.23616 0.950224i −0.187781 0.0551376i
\(298\) −38.1777 −2.21158
\(299\) −16.0978 + 2.92218i −0.930959 + 0.168994i
\(300\) 19.0677 1.10088
\(301\) −2.76630 0.812259i −0.159447 0.0468178i
\(302\) 0.985515 1.13735i 0.0567100 0.0654469i
\(303\) 3.72099 + 2.39133i 0.213765 + 0.137379i
\(304\) −2.53427 + 17.6263i −0.145351 + 1.01094i
\(305\) 3.78412 2.43190i 0.216678 0.139250i
\(306\) 0.961802 + 2.10605i 0.0549826 + 0.120395i
\(307\) −11.3883 13.1428i −0.649964 0.750098i 0.331140 0.943582i \(-0.392567\pi\)
−0.981104 + 0.193484i \(0.938021\pi\)
\(308\) −9.99378 69.5083i −0.569448 3.96060i
\(309\) −6.73409 + 14.7456i −0.383089 + 0.838847i
\(310\) 0.876426 0.257342i 0.0497777 0.0146160i
\(311\) 10.7262 3.14949i 0.608226 0.178591i 0.0369063 0.999319i \(-0.488250\pi\)
0.571320 + 0.820727i \(0.306432\pi\)
\(312\) 8.25231 18.0700i 0.467195 1.02301i
\(313\) −4.08868 28.4374i −0.231106 1.60737i −0.693336 0.720615i \(-0.743860\pi\)
0.462230 0.886760i \(-0.347049\pi\)
\(314\) 5.67189 + 6.54571i 0.320084 + 0.369396i
\(315\) 1.52977 + 3.34973i 0.0861927 + 0.188736i
\(316\) 38.1954 24.5467i 2.14866 1.38086i
\(317\) 2.68359 18.6648i 0.150726 1.04832i −0.764282 0.644882i \(-0.776906\pi\)
0.915007 0.403437i \(-0.132185\pi\)
\(318\) −0.187184 0.120296i −0.0104968 0.00674586i
\(319\) −16.3762 + 18.8991i −0.916889 + 1.05815i
\(320\) −2.46342 0.723326i −0.137710 0.0404352i
\(321\) 6.35036 0.354442
\(322\) −42.5062 + 39.6598i −2.36878 + 2.21015i
\(323\) 2.73332 0.152086
\(324\) −4.14200 1.21620i −0.230111 0.0675667i
\(325\) −9.86784 + 11.3881i −0.547369 + 0.631698i
\(326\) 30.2683 + 19.4523i 1.67641 + 1.07736i
\(327\) −0.350228 + 2.43589i −0.0193677 + 0.134705i
\(328\) −18.1731 + 11.6792i −1.00344 + 0.644874i
\(329\) −10.0750 22.0611i −0.555452 1.21627i
\(330\) 4.23847 + 4.89146i 0.233320 + 0.269266i
\(331\) 1.22889 + 8.54715i 0.0675462 + 0.469794i 0.995319 + 0.0966475i \(0.0308120\pi\)
−0.927773 + 0.373146i \(0.878279\pi\)
\(332\) 5.30303 11.6120i 0.291042 0.637293i
\(333\) 1.67079 0.490588i 0.0915588 0.0268841i
\(334\) 55.0056 16.1511i 3.00977 0.883750i
\(335\) 3.17616 6.95481i 0.173532 0.379982i
\(336\) −4.11944 28.6514i −0.224734 1.56306i
\(337\) 7.49057 + 8.64458i 0.408037 + 0.470900i 0.922156 0.386819i \(-0.126426\pi\)
−0.514118 + 0.857719i \(0.671881\pi\)
\(338\) −1.42186 3.11343i −0.0773389 0.169349i
\(339\) 7.78564 5.00352i 0.422858 0.271754i
\(340\) 0.432108 3.00538i 0.0234344 0.162990i
\(341\) −1.35057 0.867959i −0.0731375 0.0470026i
\(342\) −4.88357 + 5.63594i −0.264073 + 0.304757i
\(343\) 42.8612 + 12.5852i 2.31429 + 0.679536i
\(344\) −3.48086 −0.187675
\(345\) 0.901763 3.54894i 0.0485493 0.191069i
\(346\) −4.17875 −0.224651
\(347\) 26.7991 + 7.86893i 1.43865 + 0.422426i 0.905772 0.423764i \(-0.139292\pi\)
0.532880 + 0.846191i \(0.321110\pi\)
\(348\) −20.9600 + 24.1892i −1.12357 + 1.29667i
\(349\) −15.0280 9.65788i −0.804428 0.516975i 0.0726298 0.997359i \(-0.476861\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(350\) −7.61999 + 52.9982i −0.407306 + 2.83287i
\(351\) 2.86992 1.84438i 0.153185 0.0984459i
\(352\) −4.81684 10.5474i −0.256738 0.562178i
\(353\) −5.38350 6.21289i −0.286535 0.330679i 0.594174 0.804336i \(-0.297479\pi\)
−0.880709 + 0.473658i \(0.842933\pi\)
\(354\) 2.34672 + 16.3218i 0.124727 + 0.867494i
\(355\) −2.89284 + 6.33445i −0.153536 + 0.336198i
\(356\) −40.4418 + 11.8748i −2.14341 + 0.629363i
\(357\) −4.26302 + 1.25174i −0.225623 + 0.0662489i
\(358\) 25.4493 55.7263i 1.34504 2.94523i
\(359\) 0.690627 + 4.80342i 0.0364499 + 0.253515i 0.999897 0.0143857i \(-0.00457928\pi\)
−0.963447 + 0.267900i \(0.913670\pi\)
\(360\) 2.91153 + 3.36008i 0.153451 + 0.177092i
\(361\) −4.23561 9.27470i −0.222927 0.488142i
\(362\) −22.4011 + 14.3963i −1.17738 + 0.756654i
\(363\) 0.0534652 0.371859i 0.00280620 0.0195175i
\(364\) 59.7530 + 38.4010i 3.13191 + 2.01276i
\(365\) −6.03302 + 6.96248i −0.315783 + 0.364433i
\(366\) −14.2072 4.17161i −0.742623 0.218054i
\(367\) −10.9802 −0.573162 −0.286581 0.958056i \(-0.592519\pi\)
−0.286581 + 0.958056i \(0.592519\pi\)
\(368\) −14.6603 + 24.7692i −0.764223 + 1.29118i
\(369\) −3.70981 −0.193125
\(370\) −3.20622 0.941432i −0.166684 0.0489427i
\(371\) 0.279616 0.322694i 0.0145170 0.0167535i
\(372\) −1.72861 1.11091i −0.0896242 0.0575980i
\(373\) 2.17383 15.1193i 0.112557 0.782850i −0.852860 0.522140i \(-0.825134\pi\)
0.965417 0.260711i \(-0.0839569\pi\)
\(374\) −6.56930 + 4.22184i −0.339691 + 0.218306i
\(375\) −2.98688 6.54035i −0.154242 0.337742i
\(376\) −19.1752 22.1293i −0.988885 1.14123i
\(377\) −3.59971 25.0365i −0.185394 1.28945i
\(378\) 5.03565 11.0265i 0.259006 0.567144i
\(379\) −0.0700264 + 0.0205616i −0.00359701 + 0.00105618i −0.283531 0.958963i \(-0.591506\pi\)
0.279934 + 0.960019i \(0.409688\pi\)
\(380\) 9.38358 2.75527i 0.481368 0.141342i
\(381\) 0.555061 1.21541i 0.0284367 0.0622676i
\(382\) 6.14479 + 42.7380i 0.314395 + 2.18666i
\(383\) −17.3202 19.9885i −0.885019 1.02137i −0.999609 0.0279538i \(-0.991101\pi\)
0.114590 0.993413i \(-0.463445\pi\)
\(384\) 6.36712 + 13.9420i 0.324921 + 0.711477i
\(385\) −10.4486 + 6.71492i −0.532511 + 0.342224i
\(386\) 5.05875 35.1844i 0.257483 1.79084i
\(387\) −0.502877 0.323180i −0.0255627 0.0164281i
\(388\) −23.7032 + 27.3549i −1.20335 + 1.38874i
\(389\) 30.7724 + 9.03560i 1.56022 + 0.458123i 0.944137 0.329554i \(-0.106899\pi\)
0.616088 + 0.787678i \(0.288717\pi\)
\(390\) −6.54657 −0.331499
\(391\) 4.08343 + 1.68628i 0.206508 + 0.0852791i
\(392\) 94.6940 4.78277
\(393\) −3.29214 0.966659i −0.166066 0.0487615i
\(394\) 5.06354 5.84364i 0.255097 0.294398i
\(395\) −6.75560 4.34156i −0.339911 0.218448i
\(396\) 2.07208 14.4117i 0.104126 0.724213i
\(397\) 15.4067 9.90129i 0.773241 0.496932i −0.0935435 0.995615i \(-0.529819\pi\)
0.866784 + 0.498684i \(0.166183\pi\)
\(398\) 16.4641 + 36.0514i 0.825271 + 1.80709i
\(399\) −9.37150 10.8153i −0.469162 0.541442i
\(400\) 3.77265 + 26.2394i 0.188633 + 1.31197i
\(401\) 14.8518 32.5209i 0.741664 1.62402i −0.0391341 0.999234i \(-0.512460\pi\)
0.780798 0.624783i \(-0.214813\pi\)
\(402\) −24.1486 + 7.09066i −1.20442 + 0.353650i
\(403\) 1.55807 0.457490i 0.0776128 0.0227892i
\(404\) −7.93199 + 17.3686i −0.394631 + 0.864122i
\(405\) 0.108660 + 0.755750i 0.00539938 + 0.0375535i
\(406\) −58.8568 67.9244i −2.92101 3.37103i
\(407\) 2.43978 + 5.34238i 0.120936 + 0.264812i
\(408\) −4.51264 + 2.90010i −0.223409 + 0.143576i
\(409\) −1.57976 + 10.9875i −0.0781143 + 0.543297i 0.912759 + 0.408499i \(0.133948\pi\)
−0.990873 + 0.134798i \(0.956962\pi\)
\(410\) 5.98895 + 3.84886i 0.295773 + 0.190082i
\(411\) −2.66613 + 3.07687i −0.131510 + 0.151771i
\(412\) −67.1439 19.7152i −3.30794 0.971300i
\(413\) −31.6434 −1.55707
\(414\) −10.7728 + 5.40692i −0.529454 + 0.265736i
\(415\) −2.25785 −0.110833
\(416\) 11.2532 + 3.30423i 0.551732 + 0.162003i
\(417\) 3.93795 4.54464i 0.192842 0.222552i
\(418\) −21.1594 13.5983i −1.03494 0.665117i
\(419\) 5.42267 37.7155i 0.264915 1.84252i −0.229515 0.973305i \(-0.573714\pi\)
0.494429 0.869218i \(-0.335377\pi\)
\(420\) −13.3733 + 8.59450i −0.652551 + 0.419369i
\(421\) 16.1314 + 35.3228i 0.786197 + 1.72153i 0.687230 + 0.726440i \(0.258826\pi\)
0.0989662 + 0.995091i \(0.468446\pi\)
\(422\) 26.0718 + 30.0884i 1.26915 + 1.46468i
\(423\) −0.715632 4.97733i −0.0347952 0.242006i
\(424\) 0.214153 0.468930i 0.0104002 0.0227733i
\(425\) 3.90414 1.14636i 0.189379 0.0556066i
\(426\) 21.9945 6.45817i 1.06564 0.312900i
\(427\) 11.8038 25.8467i 0.571225 1.25081i
\(428\) 3.90136 + 27.1346i 0.188580 + 1.31160i
\(429\) 7.53494 + 8.69579i 0.363791 + 0.419837i
\(430\) 0.476529 + 1.04345i 0.0229803 + 0.0503197i
\(431\) 11.3809 7.31405i 0.548198 0.352305i −0.237040 0.971500i \(-0.576177\pi\)
0.785237 + 0.619195i \(0.212541\pi\)
\(432\) 0.854114 5.94049i 0.0410936 0.285812i
\(433\) −0.875146 0.562422i −0.0420569 0.0270283i 0.519443 0.854505i \(-0.326139\pi\)
−0.561500 + 0.827477i \(0.689776\pi\)
\(434\) 3.77854 4.36067i 0.181376 0.209319i
\(435\) 5.43172 + 1.59490i 0.260431 + 0.0764694i
\(436\) −10.6235 −0.508776
\(437\) 0.523141 + 14.2203i 0.0250252 + 0.680248i
\(438\) 30.3261 1.44903
\(439\) 38.7399 + 11.3751i 1.84895 + 0.542902i 0.999893 + 0.0146080i \(0.00465004\pi\)
0.849061 + 0.528294i \(0.177168\pi\)
\(440\) −9.81996 + 11.3328i −0.468148 + 0.540272i
\(441\) 13.6804 + 8.79184i 0.651446 + 0.418659i
\(442\) 1.12408 7.81813i 0.0534669 0.371871i
\(443\) −4.74472 + 3.04924i −0.225428 + 0.144874i −0.648480 0.761231i \(-0.724595\pi\)
0.423052 + 0.906105i \(0.360959\pi\)
\(444\) 3.12270 + 6.83777i 0.148197 + 0.324506i
\(445\) 4.88192 + 5.63404i 0.231425 + 0.267079i
\(446\) 6.01977 + 41.8684i 0.285044 + 1.98253i
\(447\) 6.31017 13.8174i 0.298461 0.653538i
\(448\) −15.5611 + 4.56915i −0.735193 + 0.215872i
\(449\) −19.6683 + 5.77512i −0.928203 + 0.272545i −0.710684 0.703511i \(-0.751614\pi\)
−0.217519 + 0.976056i \(0.569796\pi\)
\(450\) −4.61173 + 10.0983i −0.217399 + 0.476037i
\(451\) −1.78070 12.3850i −0.0838499 0.583189i
\(452\) 26.1628 + 30.1935i 1.23060 + 1.42018i
\(453\) 0.248740 + 0.544665i 0.0116868 + 0.0255906i
\(454\) −45.5354 + 29.2638i −2.13708 + 1.37342i
\(455\) 1.78787 12.4349i 0.0838167 0.582958i
\(456\) −14.5350 9.34109i −0.680665 0.437437i
\(457\) −6.82253 + 7.87362i −0.319144 + 0.368312i −0.892541 0.450965i \(-0.851080\pi\)
0.573397 + 0.819278i \(0.305625\pi\)
\(458\) 1.36619 + 0.401150i 0.0638379 + 0.0187445i
\(459\) −0.921198 −0.0429978
\(460\) 15.7184 + 1.67286i 0.732873 + 0.0779974i
\(461\) −17.5918 −0.819334 −0.409667 0.912235i \(-0.634355\pi\)
−0.409667 + 0.912235i \(0.634355\pi\)
\(462\) 39.2287 + 11.5186i 1.82508 + 0.535893i
\(463\) 3.41473 3.94081i 0.158696 0.183145i −0.670833 0.741608i \(-0.734063\pi\)
0.829529 + 0.558463i \(0.188609\pi\)
\(464\) −37.4341 24.0574i −1.73783 1.11684i
\(465\) −0.0517217 + 0.359733i −0.00239854 + 0.0166822i
\(466\) 17.0292 10.9440i 0.788863 0.506971i
\(467\) −0.104418 0.228644i −0.00483191 0.0105804i 0.907201 0.420698i \(-0.138215\pi\)
−0.912033 + 0.410118i \(0.865488\pi\)
\(468\) 9.64405 + 11.1298i 0.445796 + 0.514477i
\(469\) −6.87340 47.8055i −0.317384 2.20745i
\(470\) −4.00861 + 8.77762i −0.184903 + 0.404882i
\(471\) −3.30651 + 0.970880i −0.152356 + 0.0447358i
\(472\) −36.6567 + 10.7634i −1.68726 + 0.495425i
\(473\) 0.837541 1.83396i 0.0385102 0.0843255i
\(474\) 3.76198 + 26.1652i 0.172794 + 1.20181i
\(475\) 8.58257 + 9.90481i 0.393795 + 0.454464i
\(476\) −7.96757 17.4465i −0.365193 0.799661i
\(477\) 0.0744763 0.0478630i 0.00341003 0.00219150i
\(478\) 2.47104 17.1865i 0.113023 0.786091i
\(479\) −26.4674 17.0096i −1.20933 0.777188i −0.228783 0.973478i \(-0.573474\pi\)
−0.980546 + 0.196289i \(0.937111\pi\)
\(480\) −1.71894 + 1.98376i −0.0784586 + 0.0905460i
\(481\) −5.69986 1.67363i −0.259891 0.0763110i
\(482\) −0.831472 −0.0378725
\(483\) −7.32815 21.9390i −0.333442 0.998261i
\(484\) 1.62177 0.0737169
\(485\) 6.14260 + 1.80363i 0.278921 + 0.0818987i
\(486\) 1.64589 1.89945i 0.0746589 0.0861610i
\(487\) −3.08900 1.98518i −0.139976 0.0899570i 0.468779 0.883316i \(-0.344694\pi\)
−0.608755 + 0.793359i \(0.708331\pi\)
\(488\) 4.88222 33.9566i 0.221008 1.53714i
\(489\) −12.0431 + 7.73962i −0.544607 + 0.349998i
\(490\) −12.9636 28.3863i −0.585635 1.28236i
\(491\) −10.6670 12.3103i −0.481393 0.555558i 0.462152 0.886801i \(-0.347077\pi\)
−0.943545 + 0.331243i \(0.892532\pi\)
\(492\) −2.27914 15.8517i −0.102751 0.714652i
\(493\) −2.83733 + 6.21288i −0.127787 + 0.279814i
\(494\) 24.4103 7.16750i 1.09827 0.322481i
\(495\) −2.47088 + 0.725516i −0.111058 + 0.0326095i
\(496\) 1.18672 2.59856i 0.0532855 0.116679i
\(497\) 6.26029 + 43.5413i 0.280813 + 1.95309i
\(498\) 4.86714 + 5.61697i 0.218102 + 0.251703i
\(499\) 8.04026 + 17.6057i 0.359932 + 0.788140i 0.999807 + 0.0196614i \(0.00625883\pi\)
−0.639875 + 0.768479i \(0.721014\pi\)
\(500\) 26.1114 16.7808i 1.16774 0.750460i
\(501\) −3.24612 + 22.5773i −0.145026 + 1.00868i
\(502\) 57.7701 + 37.1266i 2.57841 + 1.65704i
\(503\) 23.3139 26.9057i 1.03952 1.19966i 0.0600201 0.998197i \(-0.480884\pi\)
0.979495 0.201467i \(-0.0645710\pi\)
\(504\) 26.9473 + 7.91245i 1.20033 + 0.352448i
\(505\) 3.37717 0.150282
\(506\) −23.2217 33.3692i −1.03233 1.48344i
\(507\) 1.36183 0.0604811
\(508\) 5.53438 + 1.62504i 0.245548 + 0.0720995i
\(509\) −0.922120 + 1.06418i −0.0408723 + 0.0471691i −0.775818 0.630957i \(-0.782662\pi\)
0.734945 + 0.678126i \(0.237208\pi\)
\(510\) 1.48714 + 0.955726i 0.0658516 + 0.0423203i
\(511\) −8.28205 + 57.6029i −0.366376 + 2.54820i
\(512\) −41.4422 + 26.6333i −1.83150 + 1.17704i
\(513\) −1.23259 2.69900i −0.0544203 0.119164i
\(514\) −6.12403 7.06751i −0.270120 0.311735i
\(515\) 1.76144 + 12.2511i 0.0776183 + 0.539847i
\(516\) 1.07198 2.34730i 0.0471912 0.103334i
\(517\) 16.2731 4.77821i 0.715690 0.210145i
\(518\) −20.2533 + 5.94690i −0.889878 + 0.261292i
\(519\) 0.690682 1.51238i 0.0303176 0.0663862i
\(520\) −2.15856 15.0131i −0.0946592 0.658370i
\(521\) 25.1455 + 29.0195i 1.10164 + 1.27137i 0.959558 + 0.281512i \(0.0908358\pi\)
0.142087 + 0.989854i \(0.454619\pi\)
\(522\) −7.74118 16.9508i −0.338822 0.741918i
\(523\) −3.95739 + 2.54326i −0.173044 + 0.111209i −0.624296 0.781188i \(-0.714614\pi\)
0.451252 + 0.892397i \(0.350978\pi\)
\(524\) 2.10792 14.6609i 0.0920851 0.640466i
\(525\) −17.9217 11.5176i −0.782169 0.502670i
\(526\) 30.4069 35.0914i 1.32580 1.53006i
\(527\) −0.420723 0.123536i −0.0183270 0.00538129i
\(528\) 20.2421 0.880922
\(529\) −7.99146 + 21.5670i −0.347455 + 0.937697i
\(530\) −0.169888 −0.00737947
\(531\) −6.29510 1.84841i −0.273184 0.0802140i
\(532\) 40.4555 46.6881i 1.75397 2.02419i
\(533\) 10.6468 + 6.84231i 0.461166 + 0.296373i
\(534\) 3.49238 24.2901i 0.151130 1.05113i
\(535\) 4.07893 2.62137i 0.176347 0.113332i
\(536\) −24.2232 53.0415i −1.04628 2.29104i
\(537\) 15.9622 + 18.4214i 0.688820 + 0.794940i
\(538\) −2.67202 18.5843i −0.115199 0.801226i
\(539\) −22.7846 + 49.8914i −0.981404 + 2.14897i
\(540\) −3.16250 + 0.928595i −0.136093 + 0.0399604i
\(541\) 2.33038 0.684262i 0.100191 0.0294187i −0.231253 0.972894i \(-0.574282\pi\)
0.331444 + 0.943475i \(0.392464\pi\)
\(542\) 26.5965 58.2382i 1.14242 2.50154i
\(543\) −1.50779 10.4869i −0.0647057 0.450038i
\(544\) −2.07392 2.39344i −0.0889188 0.102618i
\(545\) 0.780557 + 1.70918i 0.0334354 + 0.0732133i
\(546\) −34.7890 + 22.3576i −1.48883 + 0.956815i
\(547\) 2.31498 16.1010i 0.0989814 0.688431i −0.878552 0.477648i \(-0.841490\pi\)
0.977533 0.210783i \(-0.0676013\pi\)
\(548\) −14.7852 9.50186i −0.631592 0.405899i
\(549\) 3.85803 4.45240i 0.164657 0.190024i
\(550\) −35.9263 10.5489i −1.53190 0.449807i
\(551\) −21.9995 −0.937208
\(552\) −15.9516 22.9222i −0.678947 0.975636i
\(553\) −50.7269 −2.15713
\(554\) −75.7427 22.2401i −3.21800 0.944890i
\(555\) 0.870663 1.00480i 0.0369576 0.0426513i
\(556\) 21.8382 + 14.0346i 0.926146 + 0.595198i
\(557\) 4.29622 29.8809i 0.182037 1.26609i −0.669901 0.742450i \(-0.733663\pi\)
0.851938 0.523643i \(-0.175427\pi\)
\(558\) 1.00642 0.646787i 0.0426052 0.0273807i
\(559\) 0.847149 + 1.85500i 0.0358306 + 0.0784580i
\(560\) −14.4730 16.7027i −0.611596 0.705819i
\(561\) −0.442173 3.07538i −0.0186685 0.129843i
\(562\) −5.57586 + 12.2094i −0.235203 + 0.515024i
\(563\) 28.3538 8.32542i 1.19497 0.350875i 0.377042 0.926196i \(-0.376941\pi\)
0.817927 + 0.575321i \(0.195123\pi\)
\(564\) 20.8281 6.11568i 0.877021 0.257517i
\(565\) 2.93542 6.42768i 0.123494 0.270414i
\(566\) −6.17068 42.9180i −0.259373 1.80398i
\(567\) 3.15843 + 3.64502i 0.132642 + 0.153077i
\(568\) 22.0625 + 48.3102i 0.925723 + 2.02705i
\(569\) −17.6455 + 11.3400i −0.739736 + 0.475400i −0.855452 0.517883i \(-0.826720\pi\)
0.115715 + 0.993282i \(0.463084\pi\)
\(570\) −0.810326 + 5.63594i −0.0339408 + 0.236063i
\(571\) 4.34206 + 2.79047i 0.181709 + 0.116778i 0.628333 0.777944i \(-0.283737\pi\)
−0.446624 + 0.894722i \(0.647374\pi\)
\(572\) −32.5273 + 37.5385i −1.36004 + 1.56956i
\(573\) −16.4834 4.83998i −0.688606 0.202193i
\(574\) 44.9702 1.87702
\(575\) 6.71124 + 20.0921i 0.279878 + 0.837900i
\(576\) −3.36261 −0.140109
\(577\) −21.7407 6.38365i −0.905078 0.265755i −0.204110 0.978948i \(-0.565430\pi\)
−0.700968 + 0.713193i \(0.747248\pi\)
\(578\) 26.5834 30.6788i 1.10572 1.27607i
\(579\) 11.8979 + 7.64629i 0.494458 + 0.317769i
\(580\) −3.47788 + 24.1892i −0.144411 + 1.00440i
\(581\) −11.9984 + 7.71090i −0.497777 + 0.319902i
\(582\) −8.75432 19.1693i −0.362878 0.794593i
\(583\) 0.195537 + 0.225662i 0.00809831 + 0.00934595i
\(584\) 9.99923 + 69.5462i 0.413771 + 2.87784i
\(585\) 1.08205 2.36935i 0.0447371 0.0979605i
\(586\) 79.3734 23.3061i 3.27888 0.962767i
\(587\) −2.29196 + 0.672981i −0.0945995 + 0.0277769i −0.328690 0.944438i \(-0.606607\pi\)
0.234090 + 0.972215i \(0.424789\pi\)
\(588\) −29.1623 + 63.8565i −1.20263 + 2.63340i
\(589\) −0.200997 1.39796i −0.00828194 0.0576021i
\(590\) 8.24482 + 9.51503i 0.339434 + 0.391728i
\(591\) 1.27802 + 2.79847i 0.0525706 + 0.115114i
\(592\) −8.79170 + 5.65008i −0.361337 + 0.232217i
\(593\) −5.12798 + 35.6659i −0.210581 + 1.46462i 0.560642 + 0.828058i \(0.310554\pi\)
−0.771223 + 0.636565i \(0.780355\pi\)
\(594\) 7.13126 + 4.58298i 0.292599 + 0.188042i
\(595\) −2.22150 + 2.56374i −0.0910724 + 0.105103i
\(596\) 62.9172 + 18.4742i 2.57719 + 0.756731i
\(597\) −15.7690 −0.645384
\(598\) 40.8894 + 4.35174i 1.67209 + 0.177956i
\(599\) 13.8880 0.567450 0.283725 0.958906i \(-0.408430\pi\)
0.283725 + 0.958906i \(0.408430\pi\)
\(600\) −24.6788 7.24635i −1.00751 0.295831i
\(601\) −17.6880 + 20.4131i −0.721509 + 0.832666i −0.991488 0.130200i \(-0.958438\pi\)
0.269979 + 0.962866i \(0.412983\pi\)
\(602\) 6.09586 + 3.91757i 0.248449 + 0.159668i
\(603\) 1.42511 9.91187i 0.0580350 0.403642i
\(604\) −2.17450 + 1.39746i −0.0884791 + 0.0568620i
\(605\) −0.119158 0.260920i −0.00484448 0.0106079i
\(606\) −7.28000 8.40156i −0.295730 0.341290i
\(607\) −2.52692 17.5751i −0.102564 0.713351i −0.974607 0.223922i \(-0.928114\pi\)
0.872043 0.489430i \(-0.162795\pi\)
\(608\) 4.23751 9.27885i 0.171854 0.376307i
\(609\) 34.3114 10.0747i 1.39037 0.408249i
\(610\) −10.8475 + 3.18512i −0.439203 + 0.128962i
\(611\) −7.12630 + 15.6044i −0.288299 + 0.631287i
\(612\) −0.565941 3.93621i −0.0228768 0.159112i
\(613\) −1.90692 2.20070i −0.0770198 0.0888856i 0.715932 0.698170i \(-0.246002\pi\)
−0.792952 + 0.609285i \(0.791457\pi\)
\(614\) 18.1569 + 39.7581i 0.732754 + 1.60451i
\(615\) −2.38287 + 1.53138i −0.0960865 + 0.0617510i
\(616\) −13.4807 + 93.7604i −0.543153 + 3.77771i
\(617\) −4.67930 3.00721i −0.188382 0.121066i 0.443050 0.896497i \(-0.353896\pi\)
−0.631432 + 0.775431i \(0.717533\pi\)
\(618\) 26.6806 30.7911i 1.07325 1.23860i
\(619\) −30.9607 9.09087i −1.24441 0.365393i −0.407742 0.913097i \(-0.633684\pi\)
−0.836672 + 0.547704i \(0.815502\pi\)
\(620\) −1.56889 −0.0630079
\(621\) −0.176312 4.79259i −0.00707515 0.192320i
\(622\) −28.0966 −1.12657
\(623\) 45.1841 + 13.2672i 1.81026 + 0.531541i
\(624\) −13.4078 + 15.4734i −0.536741 + 0.619432i
\(625\) 13.9609 + 8.97214i 0.558437 + 0.358886i
\(626\) −10.2762 + 71.4727i −0.410720 + 2.85662i
\(627\) 8.41886 5.41047i 0.336217 0.216073i
\(628\) −6.17986 13.5320i −0.246603 0.539986i
\(629\) 1.05047 + 1.21230i 0.0418848 + 0.0483377i
\(630\) −1.31718 9.16118i −0.0524776 0.364990i
\(631\) −14.7279 + 32.2497i −0.586310 + 1.28384i 0.351337 + 0.936249i \(0.385727\pi\)
−0.937646 + 0.347590i \(0.887000\pi\)
\(632\) −58.7637 + 17.2546i −2.33749 + 0.686350i
\(633\) −15.1989 + 4.46281i −0.604103 + 0.177381i
\(634\) −19.6879 + 43.1105i −0.781906 + 1.71214i
\(635\) −0.145188 1.00980i −0.00576160 0.0400728i
\(636\) 0.250270 + 0.288827i 0.00992384 + 0.0114527i
\(637\) −23.0460 50.4637i −0.913116 1.99944i
\(638\) 52.8738 33.9800i 2.09330 1.34528i
\(639\) −1.29799 + 9.02773i −0.0513478 + 0.357132i
\(640\) 9.84484 + 6.32690i 0.389152 + 0.250093i
\(641\) 15.9578 18.4163i 0.630295 0.727399i −0.347333 0.937742i \(-0.612913\pi\)
0.977628 + 0.210343i \(0.0674580\pi\)
\(642\) −15.3141 4.49662i −0.604398 0.177467i
\(643\) 16.2231 0.639777 0.319888 0.947455i \(-0.396355\pi\)
0.319888 + 0.947455i \(0.396355\pi\)
\(644\) 89.2418 44.7910i 3.51662 1.76501i
\(645\) −0.456411 −0.0179712
\(646\) −6.59148 1.93543i −0.259338 0.0761486i
\(647\) 29.4336 33.9682i 1.15715 1.33543i 0.224577 0.974456i \(-0.427900\pi\)
0.932577 0.360971i \(-0.117555\pi\)
\(648\) 4.89867 + 3.14818i 0.192438 + 0.123672i
\(649\) 3.14920 21.9031i 0.123617 0.859773i
\(650\) 31.8604 20.4754i 1.24967 0.803112i
\(651\) 0.953688 + 2.08829i 0.0373780 + 0.0818464i
\(652\) −40.4695 46.7043i −1.58491 1.82908i
\(653\) 5.13339 + 35.7035i 0.200885 + 1.39719i 0.801665 + 0.597773i \(0.203948\pi\)
−0.600780 + 0.799414i \(0.705143\pi\)
\(654\) 2.56941 5.62623i 0.100472 0.220003i
\(655\) −2.51362 + 0.738065i −0.0982152 + 0.0288386i
\(656\) 21.3629 6.27270i 0.834079 0.244908i
\(657\) −5.01242 + 10.9757i −0.195553 + 0.428201i
\(658\) 8.67487 + 60.3350i 0.338182 + 2.35210i
\(659\) −7.11106 8.20660i −0.277007 0.319684i 0.600149 0.799888i \(-0.295108\pi\)
−0.877157 + 0.480204i \(0.840562\pi\)
\(660\) −4.61807 10.1122i −0.179758 0.393615i
\(661\) 37.5835 24.1535i 1.46183 0.939461i 0.463248 0.886228i \(-0.346684\pi\)
0.998582 0.0532330i \(-0.0169526\pi\)
\(662\) 3.08863 21.4819i 0.120043 0.834916i
\(663\) 2.64376 + 1.69904i 0.102675 + 0.0659853i
\(664\) −11.2765 + 13.0138i −0.437613 + 0.505032i
\(665\) −10.4839 3.07835i −0.406548 0.119373i
\(666\) −4.37654 −0.169587
\(667\) −32.8660 13.5723i −1.27257 0.525520i
\(668\) −98.4652 −3.80973
\(669\) −16.1481 4.74150i −0.624321 0.183317i
\(670\) −12.5840 + 14.5227i −0.486163 + 0.561062i
\(671\) 16.7160 + 10.7427i 0.645314 + 0.414718i
\(672\) −2.35974 + 16.4123i −0.0910289 + 0.633120i
\(673\) 9.46551 6.08312i 0.364869 0.234487i −0.345341 0.938477i \(-0.612237\pi\)
0.710209 + 0.703991i \(0.248600\pi\)
\(674\) −11.9426 26.1506i −0.460012 1.00729i
\(675\) −2.89254 3.33817i −0.111334 0.128486i
\(676\) 0.836646 + 5.81900i 0.0321787 + 0.223808i
\(677\) 4.92928 10.7936i 0.189447 0.414832i −0.790945 0.611887i \(-0.790411\pi\)
0.980392 + 0.197055i \(0.0631378\pi\)
\(678\) −22.3182 + 6.55322i −0.857126 + 0.251675i
\(679\) 38.8020 11.3933i 1.48908 0.437234i
\(680\) −1.70140 + 3.72555i −0.0652459 + 0.142868i
\(681\) −3.06494 21.3171i −0.117449 0.816873i
\(682\) 2.64235 + 3.04943i 0.101181 + 0.116769i
\(683\) −7.12926 15.6109i −0.272794 0.597335i 0.722805 0.691052i \(-0.242852\pi\)
−0.995599 + 0.0937170i \(0.970125\pi\)
\(684\) 10.7754 6.92492i 0.412007 0.264781i
\(685\) −0.442388 + 3.07687i −0.0169028 + 0.117561i
\(686\) −94.4496 60.6991i −3.60610 2.31750i
\(687\) −0.370995 + 0.428150i −0.0141543 + 0.0163350i
\(688\) 3.44225 + 1.01074i 0.131235 + 0.0385340i
\(689\) −0.302018 −0.0115060
\(690\) −4.68760 + 7.91986i −0.178454 + 0.301504i
\(691\) −21.3055 −0.810501 −0.405250 0.914206i \(-0.632816\pi\)
−0.405250 + 0.914206i \(0.632816\pi\)
\(692\) 6.88662 + 2.02209i 0.261790 + 0.0768685i
\(693\) −10.6527 + 12.2939i −0.404663 + 0.467006i
\(694\) −59.0550 37.9523i −2.24170 1.44065i
\(695\) 0.653420 4.54464i 0.0247857 0.172388i
\(696\) 36.3206 23.3418i 1.37673 0.884769i
\(697\) −1.41967 3.10864i −0.0537738 0.117748i
\(698\) 29.4017 + 33.9314i 1.11287 + 1.28432i
\(699\) 1.14622 + 7.97211i 0.0433539 + 0.301533i
\(700\) 38.2036 83.6541i 1.44396 3.16183i
\(701\) −37.6974 + 11.0689i −1.42381 + 0.418068i −0.900791 0.434253i \(-0.857012\pi\)
−0.523019 + 0.852321i \(0.675194\pi\)
\(702\) −8.22687 + 2.41563i −0.310503 + 0.0911720i
\(703\) −2.14635 + 4.69984i −0.0809510 + 0.177258i
\(704\) −1.61404 11.2259i −0.0608315 0.423093i
\(705\) −2.51426 2.90161i −0.0946924 0.109281i
\(706\) 8.58318 + 18.7946i 0.323032 + 0.707342i
\(707\) 17.9465 11.5335i 0.674949 0.433764i
\(708\) 4.03069 28.0340i 0.151483 1.05358i
\(709\) −16.0041 10.2852i −0.601047 0.386269i 0.204443 0.978878i \(-0.434462\pi\)
−0.805490 + 0.592609i \(0.798098\pi\)
\(710\) 11.4615 13.2273i 0.430144 0.496412i
\(711\) −10.0915 2.96315i −0.378463 0.111127i
\(712\) 56.8554 2.13075
\(713\) 0.562177 2.21248i 0.0210537 0.0828581i
\(714\) 11.1667 0.417905
\(715\) 8.42935 + 2.47508i 0.315240 + 0.0925627i
\(716\) −68.9066 + 79.5225i −2.57516 + 2.97189i
\(717\) 5.81174 + 3.73498i 0.217043 + 0.139485i
\(718\) 1.73578 12.0726i 0.0647787 0.450546i
\(719\) −3.40452 + 2.18795i −0.126967 + 0.0815968i −0.602583 0.798056i \(-0.705862\pi\)
0.475616 + 0.879653i \(0.342225\pi\)
\(720\) −1.90357 4.16824i −0.0709419 0.155341i
\(721\) 51.1998 + 59.0877i 1.90678 + 2.20054i
\(722\) 3.64699 + 25.3654i 0.135727 + 0.944002i
\(723\) 0.137429 0.300928i 0.00511105 0.0111916i
\(724\) 43.8836 12.8854i 1.63092 0.478881i
\(725\) −31.4230 + 9.22661i −1.16702 + 0.342668i
\(726\) −0.392242 + 0.858890i −0.0145575 + 0.0318764i
\(727\) −4.82536 33.5611i −0.178963 1.24471i −0.859169 0.511692i \(-0.829019\pi\)
0.680206 0.733021i \(-0.261890\pi\)
\(728\) −62.7430 72.4092i −2.32541 2.68366i
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 19.4789 12.5183i 0.720945 0.463323i
\(731\) 0.0783679 0.545061i 0.00289854 0.0201598i
\(732\) 21.3950 + 13.7497i 0.790781 + 0.508204i
\(733\) 26.8279 30.9611i 0.990912 1.14357i 0.00127246 0.999999i \(-0.499595\pi\)
0.989640 0.143574i \(-0.0458596\pi\)
\(734\) 26.4791 + 7.77497i 0.977362 + 0.286979i
\(735\) 12.4163 0.457982
\(736\) 12.0551 11.2478i 0.444356 0.414600i
\(737\) 33.7744 1.24410
\(738\) 8.94632 + 2.62688i 0.329318 + 0.0966966i
\(739\) −10.2508 + 11.8300i −0.377081 + 0.435174i −0.912290 0.409545i \(-0.865687\pi\)
0.535209 + 0.844720i \(0.320233\pi\)
\(740\) 4.82832 + 3.10298i 0.177493 + 0.114068i
\(741\) −1.44056 + 10.0193i −0.0529201 + 0.368068i
\(742\) −0.902799 + 0.580194i −0.0331428 + 0.0212996i
\(743\) 9.31220 + 20.3909i 0.341632 + 0.748069i 0.999989 0.00463635i \(-0.00147580\pi\)
−0.658358 + 0.752705i \(0.728749\pi\)
\(744\) 1.81511 + 2.09474i 0.0665450 + 0.0767970i
\(745\) −1.65056 11.4799i −0.0604717 0.420590i
\(746\) −15.9481 + 34.9215i −0.583902 + 1.27857i
\(747\) −2.83737 + 0.833126i −0.103814 + 0.0304825i
\(748\) 12.8692 3.77874i 0.470545 0.138164i
\(749\) 12.7234 27.8603i 0.464903 1.01799i
\(750\) 2.57179 + 17.8872i 0.0939086 + 0.653149i
\(751\) −25.9577 29.9568i −0.947211 1.09314i −0.995543 0.0943087i \(-0.969936\pi\)
0.0483318 0.998831i \(-0.484610\pi\)
\(752\) 12.5368 + 27.4518i 0.457171 + 1.00106i
\(753\) −22.9854 + 14.7718i −0.837636 + 0.538316i
\(754\) −9.04727 + 62.9252i −0.329482 + 2.29160i
\(755\) 0.384602 + 0.247169i 0.0139971 + 0.00899539i
\(756\) −13.6345 + 15.7351i −0.495883 + 0.572279i
\(757\) 37.0396 + 10.8758i 1.34623 + 0.395288i 0.873888 0.486128i \(-0.161591\pi\)
0.472340 + 0.881416i \(0.343409\pi\)
\(758\) 0.183430 0.00666248
\(759\) 15.9152 2.88904i 0.577686 0.104866i
\(760\) −13.1920 −0.478523
\(761\) −39.2329 11.5198i −1.42219 0.417593i −0.521946 0.852979i \(-0.674794\pi\)
−0.900244 + 0.435386i \(0.856612\pi\)
\(762\) −2.19917 + 2.53798i −0.0796675 + 0.0919412i
\(763\) 9.98506 + 6.41701i 0.361483 + 0.232311i
\(764\) 10.5542 73.4060i 0.381837 2.65573i
\(765\) −0.591699 + 0.380262i −0.0213929 + 0.0137484i
\(766\) 27.6144 + 60.4672i 0.997750 + 2.18477i
\(767\) 14.6572 + 16.9153i 0.529242 + 0.610778i
\(768\) −4.52519 31.4734i −0.163289 1.13570i
\(769\) 6.21928 13.6183i 0.224273 0.491089i −0.763728 0.645538i \(-0.776633\pi\)
0.988001 + 0.154449i \(0.0493603\pi\)
\(770\) 29.9519 8.79468i 1.07939 0.316938i
\(771\) 3.57009 1.04827i 0.128574 0.0377527i
\(772\) −25.3625 + 55.5362i −0.912817 + 1.99879i
\(773\) 4.82857 + 33.5834i 0.173672 + 1.20791i 0.871045 + 0.491204i \(0.163443\pi\)
−0.697373 + 0.716708i \(0.745648\pi\)
\(774\) 0.983863 + 1.13544i 0.0353642 + 0.0408125i
\(775\) −0.873403 1.91249i −0.0313736 0.0686985i
\(776\) 41.0741 26.3967i 1.47447 0.947586i
\(777\) 1.19523 8.31303i 0.0428788 0.298228i
\(778\) −67.8106 43.5792i −2.43113 1.56239i
\(779\) 7.20839 8.31893i 0.258267 0.298056i
\(780\) 10.7888 + 3.16788i 0.386301 + 0.113428i
\(781\) −30.7617 −1.10074
\(782\) −8.65326 6.95795i −0.309440 0.248816i
\(783\) 7.41437 0.264968
\(784\) −93.6437 27.4963i −3.34442 0.982010i
\(785\) −1.72305 + 1.98851i −0.0614984 + 0.0709729i
\(786\) 7.25461 + 4.66225i 0.258763 + 0.166297i
\(787\) −3.92180 + 27.2767i −0.139797 + 0.972311i 0.792307 + 0.610122i \(0.208880\pi\)
−0.932105 + 0.362189i \(0.882030\pi\)
\(788\) −11.1725 + 7.18012i −0.398003 + 0.255781i
\(789\) 7.67457 + 16.8050i 0.273222 + 0.598273i
\(790\) 13.2171 + 15.2534i 0.470244 + 0.542690i
\(791\) −6.35243 44.1821i −0.225866 1.57094i
\(792\) −8.15872 + 17.8651i −0.289908 + 0.634809i
\(793\) −19.2842 + 5.66234i −0.684800 + 0.201076i
\(794\) −44.1647 + 12.9679i −1.56735 + 0.460215i
\(795\) 0.0280798 0.0614862i 0.000995889 0.00218069i
\(796\) −9.68777 67.3799i −0.343374 2.38822i
\(797\) −0.630863 0.728055i −0.0223463 0.0257890i 0.744466 0.667660i \(-0.232704\pi\)
−0.766813 + 0.641871i \(0.778159\pi\)
\(798\) 14.9415 + 32.7172i 0.528922 + 1.15818i
\(799\) 3.89690 2.50439i 0.137862 0.0885988i
\(800\) 2.16109 15.0307i 0.0764059 0.531415i
\(801\) 8.21387 + 5.27873i 0.290223 + 0.186515i
\(802\) −58.8433 + 67.9088i −2.07783 + 2.39794i
\(803\) −39.0477 11.4654i −1.37796 0.404607i
\(804\) 43.2282 1.52454
\(805\) −13.7632 11.0668i −0.485089 0.390053i
\(806\) −4.08127 −0.143756
\(807\) 7.16771 + 2.10463i 0.252315 + 0.0740865i
\(808\) 16.8668 19.4653i 0.593370 0.684786i
\(809\) −11.3145 7.27141i −0.397798 0.255649i 0.326414 0.945227i \(-0.394160\pi\)
−0.724212 + 0.689578i \(0.757796\pi\)
\(810\) 0.273100 1.89945i 0.00959576 0.0667400i
\(811\) 20.0794 12.9043i 0.705085 0.453130i −0.138335 0.990385i \(-0.544175\pi\)
0.843420 + 0.537255i \(0.180539\pi\)
\(812\) 64.1280 + 140.421i 2.25045 + 4.92780i
\(813\) 16.6817 + 19.2517i 0.585053 + 0.675187i
\(814\) −2.10073 14.6109i −0.0736305 0.512111i
\(815\) −4.54061 + 9.94254i −0.159051 + 0.348272i
\(816\) 5.30470 1.55760i 0.185702 0.0545269i
\(817\) 1.70182 0.499700i 0.0595393 0.0174823i
\(818\) 11.5898 25.3780i 0.405227 0.887323i
\(819\) −2.34161 16.2863i −0.0818226 0.569088i
\(820\) −8.00737 9.24100i −0.279630 0.322710i
\(821\) 7.68700 + 16.8322i 0.268278 + 0.587447i 0.995044 0.0994386i \(-0.0317047\pi\)
−0.726766 + 0.686885i \(0.758977\pi\)
\(822\) 8.60814 5.53211i 0.300243 0.192955i
\(823\) 0.236016 1.64153i 0.00822701 0.0572201i −0.985294 0.170865i \(-0.945344\pi\)
0.993521 + 0.113645i \(0.0362528\pi\)
\(824\) 79.4099 + 51.0336i 2.76637 + 1.77784i
\(825\) 9.75593 11.2589i 0.339658 0.391986i
\(826\) 76.3090 + 22.4063i 2.65513 + 0.779616i
\(827\) −38.8604 −1.35131 −0.675654 0.737219i \(-0.736139\pi\)
−0.675654 + 0.737219i \(0.736139\pi\)
\(828\) 20.3701 3.69771i 0.707908 0.128504i
\(829\) −23.7245 −0.823986 −0.411993 0.911187i \(-0.635167\pi\)
−0.411993 + 0.911187i \(0.635167\pi\)
\(830\) 5.44487 + 1.59876i 0.188994 + 0.0554937i
\(831\) 20.5682 23.7370i 0.713505 0.823428i
\(832\) 9.65040 + 6.20194i 0.334567 + 0.215013i
\(833\) −2.13194 + 14.8279i −0.0738672 + 0.513758i
\(834\) −12.7145 + 8.17111i −0.440267 + 0.282942i
\(835\) 7.23466 + 15.8417i 0.250366 + 0.548224i
\(836\) 28.2907 + 32.6492i 0.978454 + 1.12920i
\(837\) 0.0677411 + 0.471149i 0.00234147 + 0.0162853i
\(838\) −39.7829 + 87.1123i −1.37428 + 3.00924i
\(839\) −12.0022 + 3.52417i −0.414363 + 0.121668i −0.482268 0.876024i \(-0.660187\pi\)
0.0679048 + 0.997692i \(0.478369\pi\)
\(840\) 20.5748 6.04132i 0.709900 0.208445i
\(841\) 10.7895 23.6258i 0.372053 0.814683i
\(842\) −13.8896 96.6046i −0.478669 3.32921i
\(843\) −3.49726 4.03605i −0.120452 0.139009i
\(844\) −28.4067 62.2021i −0.977800 2.14108i
\(845\) 0.874724 0.562151i 0.0300914 0.0193386i
\(846\) −1.79862 + 12.5097i −0.0618380 + 0.430093i
\(847\) −1.52430 0.979609i −0.0523756 0.0336597i
\(848\) −0.347941 + 0.401545i −0.0119483 + 0.0137891i
\(849\) 16.5529 + 4.86037i 0.568094 + 0.166807i
\(850\) −10.2267 −0.350772
\(851\) −6.10603 + 5.69714i −0.209312 + 0.195296i
\(852\) −39.3722 −1.34887
\(853\) 7.10728 + 2.08689i 0.243349 + 0.0714536i 0.401132 0.916020i \(-0.368617\pi\)
−0.157784 + 0.987474i \(0.550435\pi\)
\(854\) −46.7669 + 53.9719i −1.60033 + 1.84688i
\(855\) −1.90584 1.22481i −0.0651782 0.0418875i
\(856\) 5.26259 36.6021i 0.179872 1.25103i
\(857\) 30.3712 19.5184i 1.03746 0.666734i 0.0931019 0.995657i \(-0.470322\pi\)
0.944357 + 0.328922i \(0.106685\pi\)
\(858\) −12.0133 26.3056i −0.410129 0.898057i
\(859\) −15.8185 18.2555i −0.539721 0.622871i 0.418736 0.908108i \(-0.362473\pi\)
−0.958457 + 0.285237i \(0.907928\pi\)
\(860\) −0.280398 1.95021i −0.00956149 0.0665016i
\(861\) −7.43287 + 16.2757i −0.253312 + 0.554675i
\(862\) −32.6243 + 9.57936i −1.11119 + 0.326274i
\(863\) 51.9206 15.2453i 1.76740 0.518955i 0.773951 0.633245i \(-0.218277\pi\)
0.993447 + 0.114290i \(0.0364593\pi\)
\(864\) −1.42815 + 3.12721i −0.0485866 + 0.106390i
\(865\) −0.180662 1.25653i −0.00614270 0.0427234i
\(866\) 1.71220 + 1.97598i 0.0581828 + 0.0671465i
\(867\) 6.70953 + 14.6918i 0.227868 + 0.498961i
\(868\) −8.33719 + 5.35798i −0.282983 + 0.181862i
\(869\) 5.04841 35.1125i 0.171256 1.19111i
\(870\) −11.9694 7.69228i −0.405801 0.260793i
\(871\) −22.3712 + 25.8178i −0.758020 + 0.874802i
\(872\) 13.7497 + 4.03729i 0.465625 + 0.136720i
\(873\) 8.38474 0.283781
\(874\) 8.80764 34.6630i 0.297923 1.17249i
\(875\) −34.6783 −1.17234
\(876\) −49.9776 14.6747i −1.68859 0.495814i
\(877\) 5.97534 6.89591i 0.201773 0.232858i −0.645841 0.763472i \(-0.723493\pi\)
0.847614 + 0.530614i \(0.178038\pi\)
\(878\) −85.3679 54.8626i −2.88103 1.85152i
\(879\) −4.68417 + 32.5791i −0.157993 + 1.09887i
\(880\) 13.0018 8.35573i 0.438290 0.281672i
\(881\) 11.9030 + 26.0638i 0.401021 + 0.878113i 0.997166 + 0.0752364i \(0.0239711\pi\)
−0.596145 + 0.802877i \(0.703302\pi\)
\(882\) −26.7652 30.8887i −0.901232 1.04008i
\(883\) 6.00432 + 41.7610i 0.202061 + 1.40537i 0.798154 + 0.602453i \(0.205810\pi\)
−0.596093 + 0.802915i \(0.703281\pi\)
\(884\) −5.63567 + 12.3404i −0.189548 + 0.415053i
\(885\) −4.80644 + 1.41130i −0.161567 + 0.0474403i
\(886\) 13.6012 3.99366i 0.456940 0.134170i
\(887\) −10.7798 + 23.6045i −0.361951 + 0.792562i 0.637799 + 0.770203i \(0.279845\pi\)
−0.999750 + 0.0223595i \(0.992882\pi\)
\(888\) −1.44305 10.0366i −0.0484256 0.336807i
\(889\) −4.22017 4.87034i −0.141540 0.163346i
\(890\) −7.78350 17.0435i −0.260903 0.571299i
\(891\) −2.83737 + 1.82347i −0.0950554 + 0.0610884i
\(892\) 10.3395 71.9125i 0.346191 2.40781i
\(893\) 12.5517 + 8.06651i 0.420028 + 0.269936i
\(894\) −25.0011 + 28.8528i −0.836161 + 0.964982i
\(895\) 17.8569 + 5.24326i 0.596891 + 0.175263i
\(896\) 73.9236 2.46962
\(897\) −8.33337 + 14.0795i −0.278243 + 0.470101i
\(898\) 51.5199 1.71924
\(899\) 3.38624 + 0.994290i 0.112938 + 0.0331614i
\(900\) 12.4867 14.4104i 0.416224 0.480348i
\(901\) 0.0686074 + 0.0440913i 0.00228564 + 0.00146889i
\(902\) −4.47550 + 31.1278i −0.149018 + 1.03644i
\(903\) −2.42541 + 1.55871i −0.0807125 + 0.0518708i
\(904\) −22.3872 49.0212i −0.744588 1.63042i
\(905\) −5.29739 6.11351i −0.176091 0.203220i
\(906\) −0.214173 1.48961i −0.00711542 0.0494888i
\(907\) −6.99794 + 15.3233i −0.232363 + 0.508803i −0.989514 0.144436i \(-0.953863\pi\)
0.757151 + 0.653239i \(0.226590\pi\)
\(908\) 89.2034 26.1925i 2.96032 0.869228i
\(909\) 4.24398 1.24614i 0.140764 0.0413320i
\(910\) −13.1165 + 28.7212i −0.434809 + 0.952098i
\(911\) 0.482231 + 3.35399i 0.0159770 + 0.111123i 0.996249 0.0865292i \(-0.0275776\pi\)
−0.980272 + 0.197652i \(0.936668\pi\)
\(912\) 11.6614 + 13.4580i 0.386149 + 0.445640i
\(913\) −4.14328 9.07253i −0.137123 0.300257i
\(914\) 22.0279 14.1565i 0.728620 0.468256i
\(915\) 0.640159 4.45240i 0.0211630 0.147192i
\(916\) −2.05738 1.32220i −0.0679776 0.0436866i
\(917\) −10.8370 + 12.5065i −0.357868 + 0.413002i
\(918\) 2.22150 + 0.652290i 0.0733203 + 0.0215288i
\(919\) 29.9775 0.988867 0.494434 0.869215i \(-0.335376\pi\)
0.494434 + 0.869215i \(0.335376\pi\)
\(920\) −19.7081 8.13861i −0.649756 0.268322i
\(921\) −17.3904 −0.573033
\(922\) 42.4233 + 12.4566i 1.39714 + 0.410236i
\(923\) 20.3757 23.5148i 0.670675 0.774001i
\(924\) −59.0754 37.9654i −1.94344 1.24897i
\(925\) −1.09461 + 7.61321i −0.0359907 + 0.250321i
\(926\) −11.0252 + 7.08544i −0.362309 + 0.232842i
\(927\) 6.73409 + 14.7456i 0.221176 + 0.484309i
\(928\) 16.6922 + 19.2639i 0.547949 + 0.632367i
\(929\) −8.15732 56.7354i −0.267633 1.86143i −0.470741 0.882272i \(-0.656013\pi\)
0.203108 0.979156i \(-0.434896\pi\)
\(930\) 0.379451 0.830882i 0.0124427 0.0272457i
\(931\) −46.2967 + 13.5940i −1.51731 + 0.445524i
\(932\) −33.3601 + 9.79540i −1.09275 + 0.320859i
\(933\) 4.64393 10.1688i 0.152035 0.332911i
\(934\) 0.0899075 + 0.625320i 0.00294186 + 0.0204611i
\(935\) −1.55350 1.79284i −0.0508049 0.0586320i
\(936\) −8.25231 18.0700i −0.269735 0.590638i
\(937\) −21.1351 + 13.5827i −0.690453 + 0.443727i −0.838247 0.545291i \(-0.816419\pi\)
0.147794 + 0.989018i \(0.452783\pi\)
\(938\) −17.2752 + 120.151i −0.564054 + 3.92308i
\(939\) −24.1690 15.5325i −0.788727 0.506884i
\(940\) 10.8537 12.5258i 0.354009 0.408548i
\(941\) 12.2897 + 3.60857i 0.400632 + 0.117636i 0.475840 0.879532i \(-0.342144\pi\)
−0.0752086 + 0.997168i \(0.523962\pi\)
\(942\) 8.66122 0.282198
\(943\) 15.9012 7.98089i 0.517814 0.259893i
\(944\) 39.3755 1.28156
\(945\) 3.53334 + 1.03748i 0.114940 + 0.0337493i
\(946\) −3.31836 + 3.82959i −0.107889 + 0.124511i
\(947\) 10.1103 + 6.49749i 0.328541 + 0.211140i 0.694504 0.719489i \(-0.255624\pi\)
−0.365963 + 0.930629i \(0.619260\pi\)
\(948\) 6.46152 44.9408i 0.209860 1.45961i
\(949\) 34.6286 22.2544i 1.12409 0.722409i
\(950\) −13.6836 29.9630i −0.443956 0.972127i
\(951\) −12.3485 14.2510i −0.400428 0.462119i
\(952\) 3.68194 + 25.6085i 0.119332 + 0.829975i
\(953\) 10.7991 23.6467i 0.349817 0.765992i −0.650164 0.759794i \(-0.725300\pi\)
0.999981 0.00619817i \(-0.00197295\pi\)
\(954\) −0.213493 + 0.0626872i −0.00691209 + 0.00202957i
\(955\) −12.5855 + 3.69542i −0.407256 + 0.119581i
\(956\) −12.3888 + 27.1277i −0.400683 + 0.877373i
\(957\) 3.55888 + 24.7526i 0.115042 + 0.800136i
\(958\) 51.7827 + 59.7604i 1.67302 + 1.93077i
\(959\) 8.15711 + 17.8616i 0.263407 + 0.576781i
\(960\) −2.15985 + 1.38805i −0.0697089 + 0.0447992i
\(961\) 4.37952 30.4602i 0.141275 0.982587i
\(962\) 12.5603 + 8.07202i 0.404960 + 0.260252i
\(963\) 4.15860 4.79928i 0.134009 0.154655i
\(964\) 1.37027 + 0.402348i 0.0441335 + 0.0129588i
\(965\) 10.7985 0.347616
\(966\) 2.13725 + 58.0956i 0.0687648 + 1.86920i
\(967\) 36.2438 1.16552 0.582760 0.812644i \(-0.301973\pi\)
0.582760 + 0.812644i \(0.301973\pi\)
\(968\) −2.09901 0.616324i −0.0674647 0.0198094i
\(969\) 1.78994 2.06571i 0.0575013 0.0663600i
\(970\) −13.5359 8.69902i −0.434613 0.279309i
\(971\) 4.45032 30.9526i 0.142817 0.993317i −0.784790 0.619761i \(-0.787229\pi\)
0.927608 0.373556i \(-0.121862\pi\)
\(972\) −3.63158 + 2.33387i −0.116483 + 0.0748590i
\(973\) −12.0483 26.3821i −0.386251 0.845772i
\(974\) 6.04353 + 6.97460i 0.193647 + 0.223481i
\(975\) 2.14449 + 14.9152i 0.0686785 + 0.477670i
\(976\) −14.6881 + 32.1624i −0.470153 + 1.02949i
\(977\) −20.5363 + 6.02999i −0.657013 + 0.192917i −0.593212 0.805046i \(-0.702141\pi\)
−0.0638011 + 0.997963i \(0.520322\pi\)
\(978\) 34.5226 10.1367i 1.10391 0.324137i
\(979\) −13.6802 + 29.9554i −0.437220 + 0.957379i
\(980\) 7.62800 + 53.0539i 0.243668 + 1.69474i
\(981\) 1.61157 + 1.85986i 0.0514536 + 0.0593806i
\(982\) 17.0069 + 37.2399i 0.542712 + 1.18837i
\(983\) −46.3451 + 29.7842i −1.47818 + 0.949968i −0.480860 + 0.876798i \(0.659675\pi\)
−0.997319 + 0.0731704i \(0.976688\pi\)
\(984\) −3.07435 + 21.3826i −0.0980067 + 0.681651i
\(985\) 1.97607 + 1.26994i 0.0629629 + 0.0404638i
\(986\) 11.2416 12.9735i 0.358005 0.413159i
\(987\) −23.2704 6.83281i −0.740705 0.217491i
\(988\) −43.6967 −1.39018
\(989\) 2.85071 + 0.303392i 0.0906474 + 0.00964732i
\(990\) 6.47233 0.205704
\(991\) −33.8884 9.95053i −1.07650 0.316089i −0.305022 0.952345i \(-0.598664\pi\)
−0.771478 + 0.636256i \(0.780482\pi\)
\(992\) −1.07162 + 1.23672i −0.0340240 + 0.0392658i
\(993\) 7.26426 + 4.66846i 0.230524 + 0.148149i
\(994\) 15.7342 109.434i 0.499059 3.47103i
\(995\) −10.1287 + 6.50931i −0.321101 + 0.206359i
\(996\) −5.30303 11.6120i −0.168033 0.367941i
\(997\) 7.79466 + 8.99552i 0.246859 + 0.284891i 0.865634 0.500678i \(-0.166916\pi\)
−0.618774 + 0.785569i \(0.712370\pi\)
\(998\) −6.92292 48.1499i −0.219141 1.52416i
\(999\) 0.723373 1.58397i 0.0228865 0.0501145i
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 69.2.e.a.64.1 yes 10
3.2 odd 2 207.2.i.b.64.1 10
23.3 even 11 1587.2.a.o.1.5 5
23.9 even 11 inner 69.2.e.a.55.1 10
23.20 odd 22 1587.2.a.p.1.5 5
69.20 even 22 4761.2.a.bq.1.1 5
69.26 odd 22 4761.2.a.br.1.1 5
69.32 odd 22 207.2.i.b.55.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.a.55.1 10 23.9 even 11 inner
69.2.e.a.64.1 yes 10 1.1 even 1 trivial
207.2.i.b.55.1 10 69.32 odd 22
207.2.i.b.64.1 10 3.2 odd 2
1587.2.a.o.1.5 5 23.3 even 11
1587.2.a.p.1.5 5 23.20 odd 22
4761.2.a.bq.1.1 5 69.20 even 22
4761.2.a.br.1.1 5 69.26 odd 22