Properties

Label 882.2.bk.a.101.10
Level $882$
Weight $2$
Character 882.101
Analytic conductor $7.043$
Analytic rank $0$
Dimension $672$
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] = [882,2,Mod(5,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([35, 29]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.bk (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(56\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 101.10
Character \(\chi\) \(=\) 882.101
Dual form 882.2.bk.a.131.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.781831 + 0.623490i) q^{2} +(-0.545044 - 1.64406i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.101590 - 1.35563i) q^{5} +(1.45119 + 0.945547i) q^{6} +(-1.00823 - 2.44611i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-2.40585 + 1.79217i) q^{9} +O(q^{10})\) \(q+(-0.781831 + 0.623490i) q^{2} +(-0.545044 - 1.64406i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.101590 - 1.35563i) q^{5} +(1.45119 + 0.945547i) q^{6} +(-1.00823 - 2.44611i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-2.40585 + 1.79217i) q^{9} +(0.765792 + 1.12321i) q^{10} +(0.243376 + 0.0955179i) q^{11} +(-1.72412 + 0.165541i) q^{12} +(-3.81721 - 1.49815i) q^{13} +(2.31339 + 1.28382i) q^{14} +(-2.28410 + 0.571855i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-2.12404 - 0.655181i) q^{17} +(0.763575 - 2.90120i) q^{18} +(-4.04545 + 2.33564i) q^{19} +(-1.29903 - 0.400698i) q^{20} +(-3.47202 + 2.99083i) q^{21} +(-0.249833 + 0.0770633i) q^{22} +(4.58809 - 4.94478i) q^{23} +(1.24476 - 1.20440i) q^{24} +(3.11675 + 0.469775i) q^{25} +(3.91850 - 1.20870i) q^{26} +(4.25772 + 2.97856i) q^{27} +(-2.60914 + 0.438643i) q^{28} +(-1.30393 + 4.22723i) q^{29} +(1.42923 - 1.87121i) q^{30} +0.0715588i q^{31} +(0.974928 - 0.222521i) q^{32} +(0.0243866 - 0.452185i) q^{33} +(2.06914 - 0.812078i) q^{34} +(-3.41844 + 1.11829i) q^{35} +(1.21188 + 2.74433i) q^{36} +(-2.27262 + 2.10869i) q^{37} +(1.70661 - 4.34838i) q^{38} +(-0.382490 + 7.09227i) q^{39} +(1.26545 - 0.496654i) q^{40} +(7.67767 + 5.23455i) q^{41} +(0.849782 - 4.50310i) q^{42} +(-7.58131 + 5.16885i) q^{43} +(0.147279 - 0.216019i) q^{44} +(2.18510 + 3.44350i) q^{45} +(-0.504090 + 6.72661i) q^{46} +(-4.55308 - 5.70938i) q^{47} +(-0.222263 + 1.71773i) q^{48} +(-4.96693 + 4.93250i) q^{49} +(-2.72968 + 1.57598i) q^{50} +(0.0805415 + 3.84915i) q^{51} +(-2.30999 + 3.38814i) q^{52} +(4.57356 - 4.92913i) q^{53} +(-5.18592 + 0.325919i) q^{54} +(0.154211 - 0.320222i) q^{55} +(1.76642 - 1.96971i) q^{56} +(6.04488 + 5.37793i) q^{57} +(-1.61618 - 4.11797i) q^{58} +(-0.646025 - 0.311109i) q^{59} +(0.0492579 + 2.35408i) q^{60} +(-12.6192 + 2.88025i) q^{61} +(-0.0446162 - 0.0559469i) q^{62} +(6.80950 + 4.07807i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-2.41872 + 5.02251i) q^{65} +(0.262866 + 0.368737i) q^{66} +14.8240 q^{67} +(-1.11140 + 1.92500i) q^{68} +(-10.6302 - 4.84796i) q^{69} +(1.97540 - 3.00567i) q^{70} +(-3.23663 - 0.738740i) q^{71} +(-2.65855 - 1.39001i) q^{72} +(-10.1249 + 3.97371i) q^{73} +(0.462064 - 3.06560i) q^{74} +(-0.926430 - 5.38017i) q^{75} +(1.37689 + 4.46375i) q^{76} +(-0.0117318 - 0.691628i) q^{77} +(-4.12292 - 5.78344i) q^{78} +9.31765 q^{79} +(-0.679713 + 1.17730i) q^{80} +(2.57627 - 8.62339i) q^{81} +(-9.26634 + 0.694416i) q^{82} +(1.77087 + 4.51210i) q^{83} +(2.14325 + 4.05049i) q^{84} +(-1.10396 + 2.81285i) q^{85} +(2.70458 - 8.76804i) q^{86} +(7.66051 - 0.160292i) q^{87} +(0.0195381 + 0.260717i) q^{88} +(-14.8306 - 2.23535i) q^{89} +(-3.85537 - 1.32985i) q^{90} +(0.184006 + 10.8478i) q^{91} +(-3.79986 - 5.57337i) q^{92} +(0.117647 - 0.0390027i) q^{93} +(7.11948 + 1.62498i) q^{94} +(2.75528 + 5.72139i) q^{95} +(-0.897216 - 1.48155i) q^{96} +(-14.2836 - 8.24667i) q^{97} +(0.807940 - 6.95322i) q^{98} +(-0.756710 + 0.206368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.781831 + 0.623490i −0.552838 + 0.440874i
\(3\) −0.545044 1.64406i −0.314681 0.949197i
\(4\) 0.222521 0.974928i 0.111260 0.487464i
\(5\) 0.101590 1.35563i 0.0454325 0.606254i −0.927299 0.374321i \(-0.877876\pi\)
0.972732 0.231933i \(-0.0745051\pi\)
\(6\) 1.45119 + 0.945547i 0.592444 + 0.386018i
\(7\) −1.00823 2.44611i −0.381076 0.924544i
\(8\) 0.433884 + 0.900969i 0.153401 + 0.318541i
\(9\) −2.40585 + 1.79217i −0.801952 + 0.597389i
\(10\) 0.765792 + 1.12321i 0.242165 + 0.355191i
\(11\) 0.243376 + 0.0955179i 0.0733805 + 0.0287997i 0.401747 0.915751i \(-0.368403\pi\)
−0.328367 + 0.944550i \(0.606498\pi\)
\(12\) −1.72412 + 0.165541i −0.497711 + 0.0477876i
\(13\) −3.81721 1.49815i −1.05870 0.415511i −0.228833 0.973466i \(-0.573491\pi\)
−0.829871 + 0.557955i \(0.811586\pi\)
\(14\) 2.31339 + 1.28382i 0.618281 + 0.343117i
\(15\) −2.28410 + 0.571855i −0.589752 + 0.147652i
\(16\) −0.900969 0.433884i −0.225242 0.108471i
\(17\) −2.12404 0.655181i −0.515156 0.158905i 0.0262669 0.999655i \(-0.491638\pi\)
−0.541423 + 0.840750i \(0.682114\pi\)
\(18\) 0.763575 2.90120i 0.179976 0.683819i
\(19\) −4.04545 + 2.33564i −0.928090 + 0.535833i −0.886207 0.463289i \(-0.846669\pi\)
−0.0418831 + 0.999123i \(0.513336\pi\)
\(20\) −1.29903 0.400698i −0.290472 0.0895988i
\(21\) −3.47202 + 2.99083i −0.757657 + 0.652653i
\(22\) −0.249833 + 0.0770633i −0.0532646 + 0.0164299i
\(23\) 4.58809 4.94478i 0.956682 1.03106i −0.0428066 0.999083i \(-0.513630\pi\)
0.999489 0.0319747i \(-0.0101796\pi\)
\(24\) 1.24476 1.20440i 0.254085 0.245847i
\(25\) 3.11675 + 0.469775i 0.623351 + 0.0939550i
\(26\) 3.91850 1.20870i 0.768480 0.237045i
\(27\) 4.25772 + 2.97856i 0.819399 + 0.573223i
\(28\) −2.60914 + 0.438643i −0.493080 + 0.0828957i
\(29\) −1.30393 + 4.22723i −0.242133 + 0.784977i 0.750181 + 0.661233i \(0.229966\pi\)
−0.992314 + 0.123744i \(0.960510\pi\)
\(30\) 1.42923 1.87121i 0.260941 0.341634i
\(31\) 0.0715588i 0.0128523i 0.999979 + 0.00642617i \(0.00204553\pi\)
−0.999979 + 0.00642617i \(0.997954\pi\)
\(32\) 0.974928 0.222521i 0.172345 0.0393365i
\(33\) 0.0243866 0.452185i 0.00424516 0.0787153i
\(34\) 2.06914 0.812078i 0.354855 0.139270i
\(35\) −3.41844 + 1.11829i −0.577822 + 0.189025i
\(36\) 1.21188 + 2.74433i 0.201980 + 0.457388i
\(37\) −2.27262 + 2.10869i −0.373617 + 0.346666i −0.844525 0.535516i \(-0.820117\pi\)
0.470908 + 0.882183i \(0.343927\pi\)
\(38\) 1.70661 4.34838i 0.276849 0.705400i
\(39\) −0.382490 + 7.09227i −0.0612475 + 1.13567i
\(40\) 1.26545 0.496654i 0.200086 0.0785280i
\(41\) 7.67767 + 5.23455i 1.19905 + 0.817499i 0.987151 0.159792i \(-0.0510823\pi\)
0.211900 + 0.977291i \(0.432035\pi\)
\(42\) 0.849782 4.50310i 0.131124 0.694843i
\(43\) −7.58131 + 5.16885i −1.15614 + 0.788242i −0.980559 0.196223i \(-0.937132\pi\)
−0.175579 + 0.984465i \(0.556180\pi\)
\(44\) 0.147279 0.216019i 0.0222032 0.0325661i
\(45\) 2.18510 + 3.44350i 0.325735 + 0.513327i
\(46\) −0.504090 + 6.72661i −0.0743240 + 0.991785i
\(47\) −4.55308 5.70938i −0.664135 0.832799i 0.329652 0.944103i \(-0.393069\pi\)
−0.993786 + 0.111304i \(0.964497\pi\)
\(48\) −0.222263 + 1.71773i −0.0320808 + 0.247933i
\(49\) −4.96693 + 4.93250i −0.709562 + 0.704643i
\(50\) −2.72968 + 1.57598i −0.386035 + 0.222877i
\(51\) 0.0805415 + 3.84915i 0.0112781 + 0.538989i
\(52\) −2.30999 + 3.38814i −0.320338 + 0.469850i
\(53\) 4.57356 4.92913i 0.628227 0.677068i −0.336086 0.941831i \(-0.609103\pi\)
0.964313 + 0.264763i \(0.0852938\pi\)
\(54\) −5.18592 + 0.325919i −0.705714 + 0.0443519i
\(55\) 0.154211 0.320222i 0.0207938 0.0431788i
\(56\) 1.76642 1.96971i 0.236047 0.263214i
\(57\) 6.04488 + 5.37793i 0.800664 + 0.712324i
\(58\) −1.61618 4.11797i −0.212215 0.540716i
\(59\) −0.646025 0.311109i −0.0841053 0.0405030i 0.391358 0.920238i \(-0.372005\pi\)
−0.475464 + 0.879735i \(0.657720\pi\)
\(60\) 0.0492579 + 2.35408i 0.00635917 + 0.303911i
\(61\) −12.6192 + 2.88025i −1.61573 + 0.368779i −0.932426 0.361360i \(-0.882313\pi\)
−0.683299 + 0.730139i \(0.739455\pi\)
\(62\) −0.0446162 0.0559469i −0.00566626 0.00710526i
\(63\) 6.80950 + 4.07807i 0.857917 + 0.513788i
\(64\) −0.623490 + 0.781831i −0.0779362 + 0.0977289i
\(65\) −2.41872 + 5.02251i −0.300005 + 0.622966i
\(66\) 0.262866 + 0.368737i 0.0323566 + 0.0453884i
\(67\) 14.8240 1.81104 0.905522 0.424299i \(-0.139480\pi\)
0.905522 + 0.424299i \(0.139480\pi\)
\(68\) −1.11140 + 1.92500i −0.134777 + 0.233440i
\(69\) −10.6302 4.84796i −1.27973 0.583626i
\(70\) 1.97540 3.00567i 0.236106 0.359247i
\(71\) −3.23663 0.738740i −0.384118 0.0876724i 0.0261016 0.999659i \(-0.491691\pi\)
−0.410219 + 0.911987i \(0.634548\pi\)
\(72\) −2.65855 1.39001i −0.313313 0.163814i
\(73\) −10.1249 + 3.97371i −1.18502 + 0.465088i −0.874288 0.485408i \(-0.838671\pi\)
−0.310737 + 0.950496i \(0.600576\pi\)
\(74\) 0.462064 3.06560i 0.0537139 0.356368i
\(75\) −0.926430 5.38017i −0.106975 0.621249i
\(76\) 1.37689 + 4.46375i 0.157940 + 0.512027i
\(77\) −0.0117318 0.691628i −0.00133696 0.0788183i
\(78\) −4.12292 5.78344i −0.466828 0.654846i
\(79\) 9.31765 1.04832 0.524159 0.851620i \(-0.324380\pi\)
0.524159 + 0.851620i \(0.324380\pi\)
\(80\) −0.679713 + 1.17730i −0.0759943 + 0.131626i
\(81\) 2.57627 8.62339i 0.286253 0.958154i
\(82\) −9.26634 + 0.694416i −1.02330 + 0.0766854i
\(83\) 1.77087 + 4.51210i 0.194378 + 0.495267i 0.994520 0.104543i \(-0.0333379\pi\)
−0.800142 + 0.599810i \(0.795243\pi\)
\(84\) 2.14325 + 4.05049i 0.233848 + 0.441945i
\(85\) −1.10396 + 2.81285i −0.119741 + 0.305096i
\(86\) 2.70458 8.76804i 0.291642 0.945482i
\(87\) 7.66051 0.160292i 0.821293 0.0171851i
\(88\) 0.0195381 + 0.260717i 0.00208277 + 0.0277926i
\(89\) −14.8306 2.23535i −1.57204 0.236946i −0.695587 0.718442i \(-0.744856\pi\)
−0.876449 + 0.481495i \(0.840094\pi\)
\(90\) −3.85537 1.32985i −0.406391 0.140179i
\(91\) 0.184006 + 10.8478i 0.0192891 + 1.13716i
\(92\) −3.79986 5.57337i −0.396163 0.581064i
\(93\) 0.117647 0.0390027i 0.0121994 0.00404439i
\(94\) 7.11948 + 1.62498i 0.734318 + 0.167603i
\(95\) 2.75528 + 5.72139i 0.282686 + 0.587003i
\(96\) −0.897216 1.48155i −0.0915717 0.151211i
\(97\) −14.2836 8.24667i −1.45028 0.837322i −0.451787 0.892126i \(-0.649213\pi\)
−0.998497 + 0.0548035i \(0.982547\pi\)
\(98\) 0.807940 6.95322i 0.0816143 0.702381i
\(99\) −0.756710 + 0.206368i −0.0760522 + 0.0207407i
\(100\) 1.15154 2.93408i 0.115154 0.293408i
\(101\) 0.950168 + 0.647814i 0.0945453 + 0.0644599i 0.609670 0.792655i \(-0.291302\pi\)
−0.515125 + 0.857115i \(0.672254\pi\)
\(102\) −2.46288 2.95917i −0.243861 0.293002i
\(103\) −10.7944 0.808927i −1.06360 0.0797059i −0.468584 0.883419i \(-0.655236\pi\)
−0.595017 + 0.803713i \(0.702855\pi\)
\(104\) −0.306444 4.08921i −0.0300493 0.400980i
\(105\) 3.70173 + 5.01060i 0.361251 + 0.488984i
\(106\) −0.502494 + 6.70532i −0.0488066 + 0.651278i
\(107\) −2.56472 + 17.0158i −0.247941 + 1.64498i 0.424933 + 0.905225i \(0.360298\pi\)
−0.672874 + 0.739757i \(0.734940\pi\)
\(108\) 3.85131 3.48818i 0.370592 0.335651i
\(109\) −13.2456 + 1.99645i −1.26870 + 0.191226i −0.748681 0.662930i \(-0.769313\pi\)
−0.520017 + 0.854156i \(0.674074\pi\)
\(110\) 0.0790884 + 0.346509i 0.00754078 + 0.0330383i
\(111\) 4.70548 + 2.58700i 0.446625 + 0.245547i
\(112\) −0.152942 + 2.64133i −0.0144517 + 0.249582i
\(113\) 0.419253 2.78156i 0.0394400 0.261668i −0.960417 0.278566i \(-0.910141\pi\)
0.999857 + 0.0168981i \(0.00537909\pi\)
\(114\) −8.07916 0.435714i −0.756683 0.0408083i
\(115\) −6.23717 6.72207i −0.581619 0.626836i
\(116\) 3.83109 + 2.21188i 0.355708 + 0.205368i
\(117\) 11.8686 3.23676i 1.09725 0.299239i
\(118\) 0.699056 0.159555i 0.0643533 0.0146882i
\(119\) 0.538885 + 5.85622i 0.0493995 + 0.536839i
\(120\) −1.50626 1.80978i −0.137502 0.165210i
\(121\) −8.01346 7.43541i −0.728497 0.675946i
\(122\) 8.07029 10.1198i 0.730650 0.916206i
\(123\) 4.42124 15.4756i 0.398649 1.39539i
\(124\) 0.0697646 + 0.0159233i 0.00626505 + 0.00142996i
\(125\) 2.46598 10.8041i 0.220564 0.966352i
\(126\) −7.86652 + 1.05729i −0.700805 + 0.0941912i
\(127\) −1.56837 6.87146i −0.139170 0.609743i −0.995618 0.0935106i \(-0.970191\pi\)
0.856448 0.516233i \(-0.172666\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 12.6300 + 9.64686i 1.11201 + 0.849359i
\(130\) −1.24046 5.43480i −0.108795 0.476664i
\(131\) 12.9713 8.84371i 1.13331 0.772679i 0.156691 0.987648i \(-0.449917\pi\)
0.976621 + 0.214969i \(0.0689651\pi\)
\(132\) −0.435421 0.124396i −0.0378986 0.0108273i
\(133\) 9.79200 + 7.54076i 0.849074 + 0.653867i
\(134\) −11.5899 + 9.24263i −1.00121 + 0.798442i
\(135\) 4.47035 5.46929i 0.384746 0.470721i
\(136\) −0.331291 2.19797i −0.0284079 0.188474i
\(137\) 10.2190 0.765805i 0.873064 0.0654271i 0.369343 0.929293i \(-0.379583\pi\)
0.503722 + 0.863866i \(0.331964\pi\)
\(138\) 11.3337 2.83754i 0.964788 0.241548i
\(139\) 0.700410 1.02731i 0.0594080 0.0871355i −0.795385 0.606104i \(-0.792731\pi\)
0.854793 + 0.518969i \(0.173684\pi\)
\(140\) 0.329573 + 3.58157i 0.0278540 + 0.302698i
\(141\) −6.90493 + 10.5974i −0.581500 + 0.892461i
\(142\) 2.99110 1.44044i 0.251007 0.120879i
\(143\) −0.785916 0.729224i −0.0657216 0.0609808i
\(144\) 2.94519 0.570826i 0.245433 0.0475688i
\(145\) 5.59807 + 2.19708i 0.464895 + 0.182458i
\(146\) 5.43836 9.41952i 0.450082 0.779565i
\(147\) 10.8165 + 5.47750i 0.892131 + 0.451776i
\(148\) 1.55011 + 2.68487i 0.127418 + 0.220695i
\(149\) −1.69257 11.2295i −0.138661 0.919953i −0.944663 0.328041i \(-0.893611\pi\)
0.806003 0.591912i \(-0.201627\pi\)
\(150\) 4.07879 + 3.62877i 0.333032 + 0.296288i
\(151\) −0.734191 + 0.226468i −0.0597476 + 0.0184297i −0.324485 0.945891i \(-0.605191\pi\)
0.264737 + 0.964321i \(0.414715\pi\)
\(152\) −3.85960 2.63143i −0.313055 0.213437i
\(153\) 6.28433 2.23037i 0.508058 0.180315i
\(154\) 0.440395 + 0.533422i 0.0354881 + 0.0429844i
\(155\) 0.0970069 + 0.00726966i 0.00779178 + 0.000583913i
\(156\) 6.82934 + 1.95108i 0.546785 + 0.156211i
\(157\) −0.668483 + 1.38812i −0.0533508 + 0.110784i −0.925940 0.377671i \(-0.876725\pi\)
0.872589 + 0.488455i \(0.162439\pi\)
\(158\) −7.28483 + 5.80946i −0.579550 + 0.462176i
\(159\) −10.5966 4.83261i −0.840363 0.383251i
\(160\) −0.202612 1.34424i −0.0160179 0.106272i
\(161\) −16.7213 6.23748i −1.31783 0.491583i
\(162\) 3.36238 + 8.34832i 0.264174 + 0.655906i
\(163\) −0.306598 4.09126i −0.0240146 0.320452i −0.996255 0.0864671i \(-0.972442\pi\)
0.972240 0.233985i \(-0.0751768\pi\)
\(164\) 6.81175 6.32038i 0.531908 0.493539i
\(165\) −0.610516 0.0789966i −0.0475286 0.00614988i
\(166\) −4.19777 2.42358i −0.325810 0.188107i
\(167\) 8.76035 8.12841i 0.677896 0.628996i −0.264149 0.964482i \(-0.585091\pi\)
0.942045 + 0.335486i \(0.108901\pi\)
\(168\) −4.20110 1.83051i −0.324122 0.141227i
\(169\) 2.79700 + 2.59523i 0.215154 + 0.199633i
\(170\) −0.890670 2.88748i −0.0683113 0.221460i
\(171\) 5.54690 12.8693i 0.424182 0.984143i
\(172\) 3.35225 + 8.54140i 0.255607 + 0.651276i
\(173\) −1.22847 + 5.38228i −0.0933989 + 0.409207i −0.999916 0.0129619i \(-0.995874\pi\)
0.906517 + 0.422169i \(0.138731\pi\)
\(174\) −5.88929 + 4.90157i −0.446466 + 0.371587i
\(175\) −1.99329 8.09757i −0.150679 0.612119i
\(176\) −0.177830 0.191655i −0.0134045 0.0144466i
\(177\) −0.159370 + 1.23167i −0.0119790 + 0.0925780i
\(178\) 12.9887 7.49904i 0.973545 0.562077i
\(179\) −3.31092 + 10.7337i −0.247470 + 0.802276i 0.743564 + 0.668665i \(0.233134\pi\)
−0.991034 + 0.133612i \(0.957342\pi\)
\(180\) 3.84340 1.36406i 0.286470 0.101671i
\(181\) 1.49181 + 1.18967i 0.110885 + 0.0884278i 0.677363 0.735649i \(-0.263123\pi\)
−0.566478 + 0.824077i \(0.691694\pi\)
\(182\) −6.90736 8.36643i −0.512008 0.620161i
\(183\) 11.6133 + 19.1769i 0.858482 + 1.41759i
\(184\) 6.44579 + 1.98826i 0.475190 + 0.146577i
\(185\) 2.62771 + 3.29505i 0.193193 + 0.242257i
\(186\) −0.0676622 + 0.103845i −0.00496123 + 0.00761429i
\(187\) −0.454359 0.362339i −0.0332260 0.0264968i
\(188\) −6.57939 + 3.16847i −0.479851 + 0.231084i
\(189\) 2.99311 13.4179i 0.217716 0.976012i
\(190\) −5.72139 2.75528i −0.415074 0.199889i
\(191\) −4.75487 9.87360i −0.344051 0.714428i 0.655104 0.755539i \(-0.272625\pi\)
−0.999155 + 0.0411103i \(0.986910\pi\)
\(192\) 1.62521 + 0.598921i 0.117289 + 0.0432234i
\(193\) −4.99847 + 2.40714i −0.359798 + 0.173269i −0.605045 0.796191i \(-0.706845\pi\)
0.245248 + 0.969460i \(0.421131\pi\)
\(194\) 16.3091 2.45820i 1.17093 0.176489i
\(195\) 9.57561 + 1.23902i 0.685724 + 0.0887280i
\(196\) 3.70359 + 5.93999i 0.264542 + 0.424285i
\(197\) 13.2108i 0.941230i −0.882339 0.470615i \(-0.844032\pi\)
0.882339 0.470615i \(-0.155968\pi\)
\(198\) 0.462952 0.633146i 0.0329005 0.0449957i
\(199\) −11.2766 0.845064i −0.799377 0.0599050i −0.331224 0.943552i \(-0.607461\pi\)
−0.468153 + 0.883647i \(0.655081\pi\)
\(200\) 0.929056 + 3.01193i 0.0656942 + 0.212975i
\(201\) −8.07975 24.3716i −0.569901 1.71904i
\(202\) −1.14678 + 0.0859390i −0.0806869 + 0.00604665i
\(203\) 11.6549 1.07248i 0.818017 0.0752732i
\(204\) 3.77057 + 0.777995i 0.263993 + 0.0544705i
\(205\) 7.87606 9.87627i 0.550088 0.689789i
\(206\) 8.94374 6.09774i 0.623140 0.424850i
\(207\) −2.17639 + 20.1190i −0.151270 + 1.39837i
\(208\) 2.78917 + 3.00601i 0.193394 + 0.208429i
\(209\) −1.20766 + 0.182025i −0.0835355 + 0.0125910i
\(210\) −6.01818 1.60946i −0.415294 0.111063i
\(211\) 18.5721 + 2.79929i 1.27856 + 0.192711i 0.752985 0.658038i \(-0.228613\pi\)
0.525571 + 0.850750i \(0.323852\pi\)
\(212\) −3.78783 5.55573i −0.260149 0.381569i
\(213\) 0.549574 + 5.72386i 0.0376562 + 0.392192i
\(214\) −8.60401 14.9026i −0.588158 1.01872i
\(215\) 6.23684 + 10.8025i 0.425349 + 0.736726i
\(216\) −0.836229 + 5.12842i −0.0568982 + 0.348945i
\(217\) 0.175041 0.0721479i 0.0118825 0.00489772i
\(218\) 9.11106 9.81939i 0.617079 0.665053i
\(219\) 12.0515 + 14.4800i 0.814365 + 0.978468i
\(220\) −0.277879 0.221601i −0.0187346 0.0149403i
\(221\) 7.12637 + 5.68309i 0.479371 + 0.382286i
\(222\) −5.29186 + 0.911224i −0.355167 + 0.0611573i
\(223\) 17.4353 18.7908i 1.16755 1.25833i 0.207587 0.978217i \(-0.433439\pi\)
0.959968 0.280108i \(-0.0903704\pi\)
\(224\) −1.52727 2.16043i −0.102045 0.144350i
\(225\) −8.34037 + 4.45553i −0.556025 + 0.297036i
\(226\) 1.40649 + 2.43612i 0.0935584 + 0.162048i
\(227\) 3.59411 + 6.22518i 0.238550 + 0.413180i 0.960298 0.278975i \(-0.0899947\pi\)
−0.721749 + 0.692155i \(0.756661\pi\)
\(228\) 6.58821 4.69662i 0.436315 0.311041i
\(229\) 11.7586 + 17.2467i 0.777032 + 1.13970i 0.986800 + 0.161945i \(0.0517768\pi\)
−0.209768 + 0.977751i \(0.567271\pi\)
\(230\) 9.06755 + 1.36671i 0.597897 + 0.0901184i
\(231\) −1.13068 + 0.396255i −0.0743935 + 0.0260717i
\(232\) −4.37436 + 0.659328i −0.287190 + 0.0432870i
\(233\) −5.24892 5.65700i −0.343869 0.370602i 0.537311 0.843384i \(-0.319440\pi\)
−0.881179 + 0.472782i \(0.843250\pi\)
\(234\) −7.26114 + 9.93055i −0.474676 + 0.649180i
\(235\) −8.20233 + 5.59225i −0.535061 + 0.364798i
\(236\) −0.447063 + 0.560599i −0.0291013 + 0.0364919i
\(237\) −5.07853 15.3188i −0.329886 0.995061i
\(238\) −4.07261 4.24259i −0.263988 0.275006i
\(239\) −26.2803 + 1.96944i −1.69993 + 0.127392i −0.889047 0.457815i \(-0.848632\pi\)
−0.810884 + 0.585208i \(0.801013\pi\)
\(240\) 2.30602 + 0.475809i 0.148853 + 0.0307134i
\(241\) −2.68287 8.69764i −0.172819 0.560264i 0.827180 0.561937i \(-0.189944\pi\)
−0.999999 + 0.00167286i \(0.999468\pi\)
\(242\) 10.9011 + 0.816923i 0.700748 + 0.0525138i
\(243\) −15.5815 + 0.464582i −0.999556 + 0.0298029i
\(244\) 12.9437i 0.828638i
\(245\) 6.18203 + 7.23440i 0.394956 + 0.462189i
\(246\) 6.19222 + 14.8559i 0.394801 + 0.947178i
\(247\) 18.9415 2.85497i 1.20522 0.181657i
\(248\) −0.0644722 + 0.0310482i −0.00409399 + 0.00197156i
\(249\) 6.45296 5.37070i 0.408939 0.340355i
\(250\) 4.80830 + 9.98453i 0.304103 + 0.631477i
\(251\) 20.8602 + 10.0457i 1.31668 + 0.634081i 0.954551 0.298046i \(-0.0963350\pi\)
0.362131 + 0.932127i \(0.382049\pi\)
\(252\) 5.49108 5.73132i 0.345906 0.361039i
\(253\) 1.58894 0.765195i 0.0998960 0.0481074i
\(254\) 5.51048 + 4.39446i 0.345758 + 0.275733i
\(255\) 5.22619 + 0.281852i 0.327277 + 0.0176502i
\(256\) 0.623490 + 0.781831i 0.0389681 + 0.0488645i
\(257\) −15.1886 4.68505i −0.947436 0.292245i −0.217732 0.976009i \(-0.569866\pi\)
−0.729704 + 0.683763i \(0.760342\pi\)
\(258\) −15.8893 + 0.332475i −0.989223 + 0.0206990i
\(259\) 7.44942 + 3.43305i 0.462884 + 0.213319i
\(260\) 4.35837 + 3.47569i 0.270295 + 0.215553i
\(261\) −4.43884 12.5070i −0.274757 0.774161i
\(262\) −4.62744 + 15.0018i −0.285884 + 0.926814i
\(263\) −1.95709 + 1.12993i −0.120679 + 0.0696743i −0.559125 0.829084i \(-0.688863\pi\)
0.438445 + 0.898758i \(0.355529\pi\)
\(264\) 0.417986 0.174224i 0.0257252 0.0107228i
\(265\) −6.21743 6.70079i −0.381933 0.411626i
\(266\) −12.3573 + 0.209611i −0.757673 + 0.0128521i
\(267\) 4.40826 + 25.6007i 0.269781 + 1.56674i
\(268\) 3.29866 14.4524i 0.201498 0.882819i
\(269\) −0.399569 1.01809i −0.0243622 0.0620738i 0.918175 0.396175i \(-0.129663\pi\)
−0.942537 + 0.334101i \(0.891567\pi\)
\(270\) −0.0850143 + 7.06328i −0.00517381 + 0.429857i
\(271\) −6.95637 22.5520i −0.422569 1.36994i −0.877572 0.479446i \(-0.840838\pi\)
0.455002 0.890490i \(-0.349638\pi\)
\(272\) 1.62942 + 1.51189i 0.0987984 + 0.0916715i
\(273\) 17.7341 6.21505i 1.07332 0.376152i
\(274\) −7.51203 + 6.97015i −0.453818 + 0.421082i
\(275\) 0.713670 + 0.412037i 0.0430359 + 0.0248468i
\(276\) −7.09186 + 9.28492i −0.426880 + 0.558887i
\(277\) −4.49898 + 4.17444i −0.270317 + 0.250818i −0.803670 0.595075i \(-0.797122\pi\)
0.533353 + 0.845893i \(0.320932\pi\)
\(278\) 0.0929165 + 1.23988i 0.00557276 + 0.0743633i
\(279\) −0.128245 0.172160i −0.00767784 0.0103069i
\(280\) −2.49075 2.59470i −0.148851 0.155063i
\(281\) 1.51990 + 10.0839i 0.0906699 + 0.601555i 0.987311 + 0.158798i \(0.0507617\pi\)
−0.896641 + 0.442758i \(0.854000\pi\)
\(282\) −1.20888 12.5905i −0.0719875 0.749755i
\(283\) 5.08916 4.05847i 0.302519 0.241251i −0.460450 0.887685i \(-0.652312\pi\)
0.762969 + 0.646435i \(0.223741\pi\)
\(284\) −1.44044 + 2.99110i −0.0854742 + 0.177489i
\(285\) 7.90456 7.64825i 0.468226 0.453043i
\(286\) 1.06912 + 0.0801193i 0.0632183 + 0.00473755i
\(287\) 5.06341 24.0581i 0.298884 1.42010i
\(288\) −1.94674 + 2.28259i −0.114713 + 0.134503i
\(289\) −9.96376 6.79318i −0.586104 0.399599i
\(290\) −5.74661 + 1.77259i −0.337453 + 0.104090i
\(291\) −5.77279 + 27.9779i −0.338407 + 1.64010i
\(292\) 1.62109 + 10.7552i 0.0948672 + 0.629403i
\(293\) −6.45563 11.1815i −0.377142 0.653229i 0.613503 0.789692i \(-0.289760\pi\)
−0.990645 + 0.136463i \(0.956427\pi\)
\(294\) −11.8719 + 2.46151i −0.692381 + 0.143558i
\(295\) −0.487377 + 0.844162i −0.0283762 + 0.0491490i
\(296\) −2.88592 1.13264i −0.167740 0.0658333i
\(297\) 0.751720 + 1.13160i 0.0436192 + 0.0656619i
\(298\) 8.32476 + 7.72425i 0.482240 + 0.447454i
\(299\) −24.9217 + 12.0017i −1.44126 + 0.694074i
\(300\) −5.45143 0.293999i −0.314738 0.0169740i
\(301\) 20.2873 + 13.3333i 1.16934 + 0.768520i
\(302\) 0.432813 0.634820i 0.0249056 0.0365298i
\(303\) 0.547160 1.91522i 0.0314335 0.110026i
\(304\) 4.65822 0.349086i 0.267167 0.0200214i
\(305\) 2.62256 + 17.3995i 0.150167 + 0.996295i
\(306\) −3.52267 + 5.66199i −0.201378 + 0.323675i
\(307\) 17.7324 14.1411i 1.01204 0.807077i 0.0307360 0.999528i \(-0.490215\pi\)
0.981307 + 0.192450i \(0.0616435\pi\)
\(308\) −0.676898 0.142464i −0.0385699 0.00811765i
\(309\) 4.55349 + 18.1875i 0.259039 + 1.03465i
\(310\) −0.0803756 + 0.0547991i −0.00456503 + 0.00311238i
\(311\) −0.642256 2.81391i −0.0364190 0.159562i 0.953449 0.301556i \(-0.0975059\pi\)
−0.989868 + 0.141994i \(0.954649\pi\)
\(312\) −6.55587 + 2.73261i −0.371153 + 0.154704i
\(313\) 9.65857i 0.545935i −0.962023 0.272967i \(-0.911995\pi\)
0.962023 0.272967i \(-0.0880051\pi\)
\(314\) −0.342837 1.50207i −0.0193474 0.0847666i
\(315\) 6.22011 8.81685i 0.350464 0.496773i
\(316\) 2.07337 9.08404i 0.116636 0.511017i
\(317\) 7.88878 + 1.80056i 0.443078 + 0.101130i 0.438239 0.898859i \(-0.355602\pi\)
0.00483919 + 0.999988i \(0.498460\pi\)
\(318\) 11.2978 2.82856i 0.633550 0.158618i
\(319\) −0.721120 + 0.904256i −0.0403750 + 0.0506286i
\(320\) 0.996530 + 0.924645i 0.0557077 + 0.0516892i
\(321\) 29.3729 5.05781i 1.63943 0.282300i
\(322\) 16.9623 5.54893i 0.945271 0.309230i
\(323\) 10.1230 2.31050i 0.563258 0.128560i
\(324\) −7.83391 4.43056i −0.435217 0.246142i
\(325\) −11.1935 6.46258i −0.620905 0.358480i
\(326\) 2.79057 + 3.00752i 0.154555 + 0.166571i
\(327\) 10.5017 + 20.6884i 0.580746 + 1.14407i
\(328\) −1.38495 + 9.18853i −0.0764710 + 0.507352i
\(329\) −9.37522 + 16.8937i −0.516873 + 0.931381i
\(330\) 0.526574 0.318888i 0.0289870 0.0175542i
\(331\) −4.16454 18.2460i −0.228904 1.00289i −0.950536 0.310615i \(-0.899465\pi\)
0.721632 0.692277i \(-0.243392\pi\)
\(332\) 4.79303 0.722433i 0.263052 0.0396487i
\(333\) 1.68848 9.14612i 0.0925283 0.501204i
\(334\) −1.78113 + 11.8170i −0.0974592 + 0.646600i
\(335\) 1.50598 20.0958i 0.0822802 1.09795i
\(336\) 4.42586 1.18819i 0.241450 0.0648212i
\(337\) −1.24804 16.6539i −0.0679849 0.907196i −0.922060 0.387046i \(-0.873495\pi\)
0.854075 0.520149i \(-0.174124\pi\)
\(338\) −3.80488 0.285136i −0.206958 0.0155094i
\(339\) −4.80157 + 0.826797i −0.260785 + 0.0449055i
\(340\) 2.49667 + 1.70220i 0.135401 + 0.0923148i
\(341\) −0.00683514 + 0.0174156i −0.000370144 + 0.000943110i
\(342\) 3.68716 + 13.5201i 0.199379 + 0.731083i
\(343\) 17.0733 + 7.17657i 0.921870 + 0.387498i
\(344\) −7.94638 4.58784i −0.428440 0.247360i
\(345\) −7.65194 + 13.9181i −0.411967 + 0.749325i
\(346\) −2.39534 4.97397i −0.128774 0.267403i
\(347\) −32.5846 7.43722i −1.74923 0.399251i −0.776305 0.630358i \(-0.782908\pi\)
−0.972928 + 0.231107i \(0.925765\pi\)
\(348\) 1.54835 7.50411i 0.0830003 0.402263i
\(349\) −12.6480 18.5511i −0.677029 0.993020i −0.998930 0.0462464i \(-0.985274\pi\)
0.321901 0.946773i \(-0.395678\pi\)
\(350\) 6.60717 + 5.08814i 0.353168 + 0.271973i
\(351\) −11.7903 17.7485i −0.629321 0.947343i
\(352\) 0.258528 + 0.0389669i 0.0137796 + 0.00207694i
\(353\) −1.79802 23.9929i −0.0956991 1.27702i −0.813828 0.581105i \(-0.802620\pi\)
0.718129 0.695910i \(-0.244999\pi\)
\(354\) −0.643334 1.06232i −0.0341928 0.0564619i
\(355\) −1.33027 + 4.31261i −0.0706031 + 0.228890i
\(356\) −5.47941 + 13.9613i −0.290408 + 0.739948i
\(357\) 9.33426 4.07786i 0.494021 0.215823i
\(358\) −4.10379 10.4563i −0.216892 0.552632i
\(359\) −31.2427 + 2.34131i −1.64892 + 0.123570i −0.866500 0.499176i \(-0.833636\pi\)
−0.782424 + 0.622746i \(0.786017\pi\)
\(360\) −2.15441 + 3.46278i −0.113548 + 0.182505i
\(361\) 1.41045 2.44297i 0.0742341 0.128577i
\(362\) −1.90809 −0.100287
\(363\) −7.85655 + 17.2272i −0.412362 + 0.904195i
\(364\) 10.6168 + 2.23447i 0.556470 + 0.117118i
\(365\) 4.35828 + 14.1292i 0.228123 + 0.739556i
\(366\) −21.0362 7.75228i −1.09958 0.405218i
\(367\) −2.32700 + 15.4386i −0.121468 + 0.805889i 0.842273 + 0.539051i \(0.181217\pi\)
−0.963741 + 0.266838i \(0.914021\pi\)
\(368\) −6.27918 + 2.46440i −0.327325 + 0.128466i
\(369\) −27.8526 + 1.16611i −1.44995 + 0.0607053i
\(370\) −4.10886 0.937820i −0.213609 0.0487550i
\(371\) −16.6684 6.21774i −0.865381 0.322809i
\(372\) −0.0118459 0.123376i −0.000614182 0.00639675i
\(373\) −0.457877 + 0.793066i −0.0237080 + 0.0410634i −0.877636 0.479328i \(-0.840881\pi\)
0.853928 + 0.520391i \(0.174214\pi\)
\(374\) 0.581147 0.0300504
\(375\) −19.1067 + 1.83452i −0.986666 + 0.0947344i
\(376\) 3.16847 6.57939i 0.163401 0.339306i
\(377\) 11.3104 14.1828i 0.582514 0.730449i
\(378\) 6.02585 + 12.3567i 0.309936 + 0.635562i
\(379\) −9.91685 12.4353i −0.509394 0.638760i 0.458925 0.888475i \(-0.348235\pi\)
−0.968319 + 0.249715i \(0.919663\pi\)
\(380\) 6.19105 1.41307i 0.317594 0.0724888i
\(381\) −10.4423 + 6.32373i −0.534973 + 0.323975i
\(382\) 9.87360 + 4.75487i 0.505177 + 0.243280i
\(383\) −5.00770 12.7594i −0.255881 0.651975i 0.743987 0.668194i \(-0.232932\pi\)
−0.999868 + 0.0162189i \(0.994837\pi\)
\(384\) −1.64406 + 0.545044i −0.0838980 + 0.0278141i
\(385\) −0.938781 0.0543587i −0.0478447 0.00277038i
\(386\) 2.40714 4.99847i 0.122520 0.254415i
\(387\) 8.97608 26.0225i 0.456280 1.32280i
\(388\) −11.2183 + 12.0905i −0.569524 + 0.613801i
\(389\) 6.16023 9.03540i 0.312336 0.458113i −0.637686 0.770297i \(-0.720108\pi\)
0.950022 + 0.312184i \(0.101060\pi\)
\(390\) −8.25903 + 5.00159i −0.418212 + 0.253265i
\(391\) −12.9850 + 7.49690i −0.656681 + 0.379135i
\(392\) −6.59910 2.33492i −0.333305 0.117931i
\(393\) −21.6095 16.5054i −1.09006 0.832589i
\(394\) 8.23680 + 10.3286i 0.414964 + 0.520348i
\(395\) 0.946581 12.6312i 0.0476277 0.635547i
\(396\) 0.0328097 + 0.783659i 0.00164875 + 0.0393803i
\(397\) −19.1143 + 28.0355i −0.959318 + 1.40706i −0.0463975 + 0.998923i \(0.514774\pi\)
−0.912920 + 0.408138i \(0.866178\pi\)
\(398\) 9.34329 6.37015i 0.468337 0.319307i
\(399\) 7.06037 20.2087i 0.353461 1.01170i
\(400\) −2.60427 1.77556i −0.130214 0.0887781i
\(401\) −19.7631 + 7.75645i −0.986923 + 0.387339i −0.803246 0.595648i \(-0.796895\pi\)
−0.183678 + 0.982987i \(0.558800\pi\)
\(402\) 21.5124 + 14.0168i 1.07294 + 0.699096i
\(403\) 0.107205 0.273155i 0.00534028 0.0136068i
\(404\) 0.843004 0.782193i 0.0419410 0.0389156i
\(405\) −11.4284 4.36851i −0.567880 0.217073i
\(406\) −8.44352 + 8.10523i −0.419045 + 0.402256i
\(407\) −0.754518 + 0.296127i −0.0374001 + 0.0146785i
\(408\) −3.43302 + 1.74265i −0.169960 + 0.0862740i
\(409\) −6.04994 + 1.38086i −0.299150 + 0.0682791i −0.369462 0.929246i \(-0.620458\pi\)
0.0703114 + 0.997525i \(0.477601\pi\)
\(410\) 12.6322i 0.623861i
\(411\) −6.82881 16.3832i −0.336840 0.808122i
\(412\) −3.19062 + 10.3437i −0.157191 + 0.509599i
\(413\) −0.109665 + 1.89392i −0.00539624 + 0.0931937i
\(414\) −10.8424 17.0867i −0.532877 0.839764i
\(415\) 6.29662 1.94225i 0.309089 0.0953413i
\(416\) −4.05488 0.611174i −0.198807 0.0299653i
\(417\) −2.07072 0.591584i −0.101403 0.0289700i
\(418\) 0.830695 0.895276i 0.0406306 0.0437894i
\(419\) 15.5105 4.78436i 0.757739 0.233731i 0.108272 0.994121i \(-0.465468\pi\)
0.649467 + 0.760390i \(0.274992\pi\)
\(420\) 5.70868 2.49395i 0.278555 0.121692i
\(421\) −19.3756 5.97659i −0.944310 0.291281i −0.215895 0.976417i \(-0.569267\pi\)
−0.728416 + 0.685135i \(0.759743\pi\)
\(422\) −16.2656 + 9.39094i −0.791796 + 0.457144i
\(423\) 21.1862 + 5.57606i 1.03011 + 0.271117i
\(424\) 6.42539 + 1.98197i 0.312044 + 0.0962530i
\(425\) −6.31233 3.03986i −0.306193 0.147455i
\(426\) −3.99844 4.13244i −0.193725 0.200217i
\(427\) 19.7685 + 27.9641i 0.956667 + 1.35328i
\(428\) 16.0185 + 6.28680i 0.774283 + 0.303884i
\(429\) −0.770528 + 1.68955i −0.0372014 + 0.0815723i
\(430\) −11.6114 4.55714i −0.559952 0.219765i
\(431\) 10.6877 + 15.6759i 0.514806 + 0.755082i 0.992341 0.123531i \(-0.0394218\pi\)
−0.477535 + 0.878613i \(0.658469\pi\)
\(432\) −2.54373 4.53094i −0.122385 0.217995i
\(433\) −2.47401 5.13734i −0.118893 0.246885i 0.833026 0.553234i \(-0.186607\pi\)
−0.951919 + 0.306350i \(0.900892\pi\)
\(434\) −0.0918689 + 0.165544i −0.00440985 + 0.00794635i
\(435\) 0.560936 10.4011i 0.0268948 0.498693i
\(436\) −1.00103 + 13.3578i −0.0479404 + 0.639721i
\(437\) −7.01164 + 30.7200i −0.335412 + 1.46954i
\(438\) −18.4504 3.80693i −0.881593 0.181902i
\(439\) 10.8652 8.66470i 0.518567 0.413543i −0.328921 0.944357i \(-0.606685\pi\)
0.847488 + 0.530814i \(0.178114\pi\)
\(440\) 0.355420 0.0169440
\(441\) 3.10985 20.7685i 0.148088 0.988974i
\(442\) −9.11497 −0.433555
\(443\) −20.4106 + 16.2769i −0.969739 + 0.773341i −0.973976 0.226650i \(-0.927223\pi\)
0.00423744 + 0.999991i \(0.498651\pi\)
\(444\) 3.56921 4.01185i 0.169387 0.190394i
\(445\) −4.53693 + 19.8776i −0.215071 + 0.942288i
\(446\) −1.91561 + 25.5620i −0.0907065 + 1.21039i
\(447\) −17.5394 + 8.90323i −0.829583 + 0.421108i
\(448\) 2.54107 + 0.736858i 0.120054 + 0.0348133i
\(449\) 13.2619 + 27.5385i 0.625866 + 1.29962i 0.937024 + 0.349266i \(0.113569\pi\)
−0.311157 + 0.950358i \(0.600717\pi\)
\(450\) 3.74279 8.68361i 0.176437 0.409349i
\(451\) 1.36856 + 2.00732i 0.0644432 + 0.0945208i
\(452\) −2.61853 1.02770i −0.123165 0.0483389i
\(453\) 0.772493 + 1.08362i 0.0362949 + 0.0509128i
\(454\) −6.69133 2.62615i −0.314040 0.123251i
\(455\) 14.7243 + 0.852586i 0.690284 + 0.0399699i
\(456\) −2.22257 + 7.77964i −0.104081 + 0.364315i
\(457\) 12.4838 + 6.01187i 0.583966 + 0.281223i 0.702450 0.711733i \(-0.252089\pi\)
−0.118484 + 0.992956i \(0.537804\pi\)
\(458\) −19.9464 6.15266i −0.932035 0.287495i
\(459\) −7.09210 9.11616i −0.331031 0.425506i
\(460\) −7.94143 + 4.58499i −0.370271 + 0.213776i
\(461\) 21.2125 + 6.54318i 0.987964 + 0.304746i 0.746297 0.665613i \(-0.231830\pi\)
0.241666 + 0.970359i \(0.422306\pi\)
\(462\) 0.636942 1.01477i 0.0296332 0.0472116i
\(463\) 17.2538 5.32210i 0.801854 0.247339i 0.133370 0.991066i \(-0.457420\pi\)
0.668483 + 0.743727i \(0.266944\pi\)
\(464\) 3.00892 3.24285i 0.139686 0.150545i
\(465\) −0.0409212 0.163447i −0.00189768 0.00757968i
\(466\) 7.63085 + 1.15017i 0.353492 + 0.0532804i
\(467\) −7.10264 + 2.19087i −0.328671 + 0.101382i −0.454699 0.890645i \(-0.650253\pi\)
0.126028 + 0.992027i \(0.459777\pi\)
\(468\) −0.514602 12.2913i −0.0237875 0.568164i
\(469\) −14.9461 36.2613i −0.690146 1.67439i
\(470\) 2.92613 9.48627i 0.134972 0.437569i
\(471\) 2.64650 + 0.342439i 0.121944 + 0.0157788i
\(472\) 0.717034i 0.0330041i
\(473\) −2.33882 + 0.533821i −0.107539 + 0.0245451i
\(474\) 13.5216 + 8.81028i 0.621070 + 0.404670i
\(475\) −13.7059 + 5.37917i −0.628870 + 0.246813i
\(476\) 5.82931 + 0.777759i 0.267186 + 0.0356485i
\(477\) −2.16950 + 20.0554i −0.0993348 + 0.918272i
\(478\) 19.3188 17.9253i 0.883623 0.819882i
\(479\) −9.38412 + 23.9103i −0.428771 + 1.09249i 0.539366 + 0.842071i \(0.318664\pi\)
−0.968137 + 0.250420i \(0.919431\pi\)
\(480\) −2.09958 + 1.06578i −0.0958323 + 0.0486459i
\(481\) 11.8342 4.64459i 0.539594 0.211775i
\(482\) 7.52044 + 5.12735i 0.342547 + 0.233544i
\(483\) −1.14092 + 30.8906i −0.0519137 + 1.40557i
\(484\) −9.03215 + 6.15801i −0.410552 + 0.279910i
\(485\) −12.6305 + 18.5255i −0.573520 + 0.841199i
\(486\) 11.8925 10.0782i 0.539453 0.457154i
\(487\) 0.524642 7.00086i 0.0237738 0.317239i −0.972621 0.232398i \(-0.925343\pi\)
0.996395 0.0848409i \(-0.0270382\pi\)
\(488\) −8.07029 10.1198i −0.365325 0.458103i
\(489\) −6.55916 + 2.73398i −0.296616 + 0.123635i
\(490\) −9.34388 1.80164i −0.422114 0.0813899i
\(491\) 10.7222 6.19047i 0.483887 0.279372i −0.238148 0.971229i \(-0.576540\pi\)
0.722035 + 0.691857i \(0.243207\pi\)
\(492\) −14.1038 7.75403i −0.635847 0.349579i
\(493\) 5.53920 8.12451i 0.249473 0.365910i
\(494\) −13.0290 + 14.0419i −0.586202 + 0.631776i
\(495\) 0.202883 + 1.04678i 0.00911891 + 0.0470493i
\(496\) 0.0310482 0.0644722i 0.00139410 0.00289489i
\(497\) 1.45624 + 8.66199i 0.0653212 + 0.388543i
\(498\) −1.69654 + 8.22234i −0.0760240 + 0.368452i
\(499\) −13.9038 35.4262i −0.622418 1.58589i −0.798816 0.601576i \(-0.794540\pi\)
0.176398 0.984319i \(-0.443556\pi\)
\(500\) −9.98453 4.80830i −0.446522 0.215034i
\(501\) −18.1384 9.97218i −0.810362 0.445524i
\(502\) −22.5726 + 5.15204i −1.00746 + 0.229947i
\(503\) 4.23205 + 5.30683i 0.188698 + 0.236620i 0.867177 0.498000i \(-0.165932\pi\)
−0.678479 + 0.734620i \(0.737361\pi\)
\(504\) −0.719680 + 7.90456i −0.0320571 + 0.352097i
\(505\) 0.974721 1.22226i 0.0433745 0.0543899i
\(506\) −0.765195 + 1.58894i −0.0340170 + 0.0706371i
\(507\) 2.74223 6.01294i 0.121787 0.267044i
\(508\) −7.04817 −0.312712
\(509\) 2.56856 4.44887i 0.113849 0.197193i −0.803470 0.595345i \(-0.797015\pi\)
0.917319 + 0.398153i \(0.130349\pi\)
\(510\) −4.26173 + 3.03812i −0.188713 + 0.134530i
\(511\) 19.9284 + 20.7601i 0.881579 + 0.918373i
\(512\) −0.974928 0.222521i −0.0430861 0.00983413i
\(513\) −24.1812 2.10508i −1.06763 0.0929416i
\(514\) 14.7960 5.80699i 0.652622 0.256135i
\(515\) −2.19320 + 14.5510i −0.0966441 + 0.641192i
\(516\) 12.2154 10.1667i 0.537755 0.447566i
\(517\) −0.562760 1.82442i −0.0247502 0.0802381i
\(518\) −7.96466 + 1.96057i −0.349947 + 0.0861427i
\(519\) 9.51835 0.913902i 0.417809 0.0401158i
\(520\) −5.57457 −0.244461
\(521\) 9.74630 16.8811i 0.426993 0.739574i −0.569611 0.821914i \(-0.692906\pi\)
0.996604 + 0.0823407i \(0.0262396\pi\)
\(522\) 11.2684 + 7.01076i 0.493204 + 0.306853i
\(523\) −28.8636 + 2.16302i −1.26212 + 0.0945825i −0.688921 0.724837i \(-0.741915\pi\)
−0.573195 + 0.819419i \(0.694296\pi\)
\(524\) −5.73559 14.6140i −0.250560 0.638417i
\(525\) −12.2265 + 7.69062i −0.533606 + 0.335646i
\(526\) 0.825617 2.10364i 0.0359986 0.0917230i
\(527\) 0.0468839 0.151994i 0.00204229 0.00662096i
\(528\) −0.218167 + 0.396824i −0.00949451 + 0.0172695i
\(529\) −1.68153 22.4385i −0.0731101 0.975586i
\(530\) 9.03885 + 1.36239i 0.392623 + 0.0591784i
\(531\) 2.11180 0.409301i 0.0916444 0.0177622i
\(532\) 9.53062 7.86852i 0.413205 0.341144i
\(533\) −21.4652 31.4837i −0.929761 1.36371i
\(534\) −19.4083 17.2669i −0.839878 0.747212i
\(535\) 22.8065 + 5.20544i 0.986012 + 0.225051i
\(536\) 6.43191 + 13.3560i 0.277816 + 0.576891i
\(537\) 19.4515 0.407012i 0.839393 0.0175639i
\(538\) 0.947163 + 0.546845i 0.0408351 + 0.0235761i
\(539\) −1.67997 + 0.726019i −0.0723615 + 0.0312719i
\(540\) −4.33741 5.57530i −0.186653 0.239923i
\(541\) −8.71297 + 22.2003i −0.374600 + 0.954465i 0.611934 + 0.790909i \(0.290392\pi\)
−0.986534 + 0.163556i \(0.947703\pi\)
\(542\) 19.4996 + 13.2946i 0.837582 + 0.571053i
\(543\) 1.14280 3.10104i 0.0490421 0.133078i
\(544\) −2.21658 0.166110i −0.0950351 0.00712190i
\(545\) 1.36082 + 18.1589i 0.0582912 + 0.777842i
\(546\) −9.99009 + 15.9162i −0.427536 + 0.681149i
\(547\) −0.964819 + 12.8746i −0.0412527 + 0.550479i 0.937840 + 0.347067i \(0.112822\pi\)
−0.979093 + 0.203412i \(0.934797\pi\)
\(548\) 1.52733 10.1332i 0.0652442 0.432867i
\(549\) 25.1981 29.5452i 1.07543 1.26096i
\(550\) −0.814871 + 0.122822i −0.0347462 + 0.00523715i
\(551\) −4.59832 20.1466i −0.195895 0.858272i
\(552\) −0.244418 11.6809i −0.0104031 0.497174i
\(553\) −9.39436 22.7920i −0.399489 0.969216i
\(554\) 0.914721 6.06878i 0.0388628 0.257838i
\(555\) 3.98503 6.11606i 0.169155 0.259612i
\(556\) −0.845700 0.911448i −0.0358657 0.0386540i
\(557\) 37.5416 + 21.6747i 1.59069 + 0.918385i 0.993189 + 0.116517i \(0.0371729\pi\)
0.597501 + 0.801868i \(0.296160\pi\)
\(558\) 0.207606 + 0.0546405i 0.00878867 + 0.00231312i
\(559\) 36.6831 8.37269i 1.55153 0.354127i
\(560\) 3.56511 + 0.475665i 0.150654 + 0.0201005i
\(561\) −0.348061 + 0.944483i −0.0146951 + 0.0398761i
\(562\) −7.47552 6.93627i −0.315336 0.292589i
\(563\) 0.455169 0.570764i 0.0191831 0.0240548i −0.772147 0.635443i \(-0.780817\pi\)
0.791331 + 0.611389i \(0.209389\pi\)
\(564\) 8.79520 + 9.08995i 0.370345 + 0.382756i
\(565\) −3.72817 0.850930i −0.156845 0.0357989i
\(566\) −1.44845 + 6.34608i −0.0608829 + 0.266745i
\(567\) −23.6913 + 2.39253i −0.994939 + 0.100477i
\(568\) −0.738740 3.23663i −0.0309969 0.135806i
\(569\) 42.2251i 1.77017i 0.465432 + 0.885084i \(0.345899\pi\)
−0.465432 + 0.885084i \(0.654101\pi\)
\(570\) −1.41143 + 10.9081i −0.0591182 + 0.456888i
\(571\) −4.19348 18.3728i −0.175492 0.768880i −0.983676 0.179950i \(-0.942406\pi\)
0.808184 0.588930i \(-0.200451\pi\)
\(572\) −0.885824 + 0.603944i −0.0370381 + 0.0252522i
\(573\) −13.6412 + 13.1988i −0.569867 + 0.551389i
\(574\) 11.0412 + 21.9664i 0.460853 + 0.916858i
\(575\) 16.6229 13.2563i 0.693222 0.552826i
\(576\) 0.0988530 2.99837i 0.00411887 0.124932i
\(577\) 3.42876 + 22.7484i 0.142741 + 0.947026i 0.939456 + 0.342670i \(0.111331\pi\)
−0.796714 + 0.604356i \(0.793430\pi\)
\(578\) 12.0255 0.901184i 0.500193 0.0374843i
\(579\) 6.68186 + 6.90578i 0.277688 + 0.286994i
\(580\) 3.38769 4.96882i 0.140666 0.206319i
\(581\) 9.25166 8.88099i 0.383823 0.368446i
\(582\) −12.9306 25.4733i −0.535991 1.05590i
\(583\) 1.58391 0.762773i 0.0655990 0.0315908i
\(584\) −7.97320 7.39805i −0.329933 0.306133i
\(585\) −3.18211 16.4182i −0.131564 0.678808i
\(586\) 12.0188 + 4.71702i 0.496490 + 0.194858i
\(587\) −15.3478 + 26.5831i −0.633470 + 1.09720i 0.353367 + 0.935485i \(0.385037\pi\)
−0.986837 + 0.161717i \(0.948297\pi\)
\(588\) 7.74707 9.32647i 0.319484 0.384617i
\(589\) −0.167136 0.289487i −0.00688670 0.0119281i
\(590\) −0.145280 0.963867i −0.00598107 0.0396818i
\(591\) −21.7193 + 7.20046i −0.893413 + 0.296187i
\(592\) 2.96249 0.913807i 0.121758 0.0375572i
\(593\) 10.5256 + 7.17623i 0.432235 + 0.294693i 0.759825 0.650127i \(-0.225284\pi\)
−0.327591 + 0.944820i \(0.606237\pi\)
\(594\) −1.29326 0.416027i −0.0530630 0.0170698i
\(595\) 7.99359 0.135592i 0.327705 0.00555871i
\(596\) −11.3245 0.848657i −0.463872 0.0347624i
\(597\) 4.75691 + 19.0000i 0.194687 + 0.777618i
\(598\) 12.0017 24.9217i 0.490784 1.01912i
\(599\) 8.32837 6.64166i 0.340288 0.271371i −0.438403 0.898779i \(-0.644456\pi\)
0.778691 + 0.627408i \(0.215884\pi\)
\(600\) 4.44541 3.16905i 0.181483 0.129376i
\(601\) −5.64304 37.4391i −0.230185 1.52717i −0.743360 0.668891i \(-0.766769\pi\)
0.513176 0.858284i \(-0.328469\pi\)
\(602\) −24.1744 + 2.22451i −0.985277 + 0.0906643i
\(603\) −35.6645 + 26.5672i −1.45237 + 1.08190i
\(604\) 0.0574170 + 0.766177i 0.00233627 + 0.0311753i
\(605\) −10.8937 + 10.1079i −0.442893 + 0.410944i
\(606\) 0.766332 + 1.83853i 0.0311301 + 0.0746851i
\(607\) 37.1312 + 21.4377i 1.50711 + 0.870131i 0.999966 + 0.00827008i \(0.00263248\pi\)
0.507145 + 0.861861i \(0.330701\pi\)
\(608\) −3.42429 + 3.17728i −0.138873 + 0.128856i
\(609\) −8.11567 18.5769i −0.328864 0.752772i
\(610\) −12.8988 11.9684i −0.522259 0.484585i
\(611\) 8.82659 + 28.6151i 0.357086 + 1.15764i
\(612\) −0.776056 6.62308i −0.0313702 0.267722i
\(613\) 3.73514 + 9.51697i 0.150861 + 0.384387i 0.986247 0.165276i \(-0.0528515\pi\)
−0.835387 + 0.549663i \(0.814756\pi\)
\(614\) −5.04691 + 22.1120i −0.203677 + 0.892366i
\(615\) −20.5300 7.56571i −0.827848 0.305079i
\(616\) 0.618045 0.310656i 0.0249018 0.0125167i
\(617\) −15.4211 16.6200i −0.620832 0.669098i 0.341843 0.939757i \(-0.388949\pi\)
−0.962675 + 0.270659i \(0.912758\pi\)
\(618\) −14.8998 11.3805i −0.599357 0.457791i
\(619\) −40.2015 + 23.2104i −1.61584 + 0.932903i −0.627854 + 0.778331i \(0.716067\pi\)
−0.987982 + 0.154572i \(0.950600\pi\)
\(620\) 0.0286735 0.0929571i 0.00115155 0.00373325i
\(621\) 34.2631 7.38764i 1.37493 0.296456i
\(622\) 2.25658 + 1.79956i 0.0904805 + 0.0721558i
\(623\) 9.48474 + 38.5310i 0.379998 + 1.54371i
\(624\) 3.42183 6.22396i 0.136983 0.249158i
\(625\) 0.663776 + 0.204748i 0.0265511 + 0.00818992i
\(626\) 6.02202 + 7.55138i 0.240688 + 0.301814i
\(627\) 0.957487 + 1.88625i 0.0382384 + 0.0753296i
\(628\) 1.20457 + 0.960609i 0.0480674 + 0.0383325i
\(629\) 6.20872 2.98996i 0.247558 0.119218i
\(630\) 0.634134 + 10.7715i 0.0252645 + 0.429145i
\(631\) 27.3876 + 13.1892i 1.09028 + 0.525053i 0.890591 0.454806i \(-0.150291\pi\)
0.199693 + 0.979859i \(0.436006\pi\)
\(632\) 4.04278 + 8.39491i 0.160813 + 0.333932i
\(633\) −5.52040 32.0593i −0.219416 1.27424i
\(634\) −7.29033 + 3.51084i −0.289536 + 0.139433i
\(635\) −9.47446 + 1.42804i −0.375982 + 0.0566702i
\(636\) −7.06941 + 9.25553i −0.280320 + 0.367006i
\(637\) 26.3494 11.3872i 1.04400 0.451178i
\(638\) 1.15659i 0.0457897i
\(639\) 9.11081 4.02329i 0.360418 0.159159i
\(640\) −1.35563 0.101590i −0.0535858 0.00401570i
\(641\) 6.25480 + 20.2776i 0.247050 + 0.800915i 0.991138 + 0.132834i \(0.0424078\pi\)
−0.744089 + 0.668081i \(0.767116\pi\)
\(642\) −19.8112 + 22.2681i −0.781884 + 0.878850i
\(643\) 27.9902 2.09758i 1.10383 0.0827204i 0.489672 0.871907i \(-0.337116\pi\)
0.614154 + 0.789186i \(0.289497\pi\)
\(644\) −9.80195 + 14.9141i −0.386251 + 0.587699i
\(645\) 14.3606 16.1416i 0.565449 0.635574i
\(646\) −6.47389 + 8.11800i −0.254712 + 0.319398i
\(647\) 23.1587 15.7894i 0.910464 0.620744i −0.0148732 0.999889i \(-0.504734\pi\)
0.925337 + 0.379146i \(0.123782\pi\)
\(648\) 8.88721 1.42041i 0.349122 0.0557988i
\(649\) −0.127510 0.137423i −0.00500521 0.00539434i
\(650\) 12.7808 1.92640i 0.501304 0.0755595i
\(651\) −0.214020 0.248453i −0.00838811 0.00973766i
\(652\) −4.05691 0.611481i −0.158881 0.0239474i
\(653\) 8.29626 + 12.1684i 0.324658 + 0.476185i 0.953519 0.301332i \(-0.0974312\pi\)
−0.628862 + 0.777517i \(0.716479\pi\)
\(654\) −21.1096 9.62712i −0.825449 0.376450i
\(655\) −10.6710 18.4827i −0.416951 0.722180i
\(656\) −4.64616 8.04738i −0.181402 0.314198i
\(657\) 17.2374 27.7056i 0.672494 1.08090i
\(658\) −3.20322 19.0534i −0.124875 0.742779i
\(659\) 13.6146 14.6730i 0.530348 0.571580i −0.409873 0.912142i \(-0.634427\pi\)
0.940222 + 0.340563i \(0.110618\pi\)
\(660\) −0.212869 + 0.577631i −0.00828590 + 0.0224842i
\(661\) −11.0821 8.83767i −0.431043 0.343745i 0.383811 0.923412i \(-0.374611\pi\)
−0.814854 + 0.579666i \(0.803183\pi\)
\(662\) 14.6322 + 11.6688i 0.568696 + 0.453520i
\(663\) 5.45915 14.8137i 0.212016 0.575316i
\(664\) −3.29691 + 3.55323i −0.127945 + 0.137892i
\(665\) 11.2172 12.5082i 0.434985 0.485048i
\(666\) 4.38240 + 8.20348i 0.169815 + 0.317878i
\(667\) 14.9202 + 25.8425i 0.577712 + 1.00063i
\(668\) −5.97526 10.3494i −0.231190 0.400432i
\(669\) −40.3962 18.4229i −1.56181 0.712269i
\(670\) 11.3521 + 16.6505i 0.438571 + 0.643266i
\(671\) −3.34632 0.504377i −0.129183 0.0194713i
\(672\) −2.71945 + 3.68844i −0.104905 + 0.142285i
\(673\) −8.66537 + 1.30609i −0.334025 + 0.0503462i −0.313914 0.949452i \(-0.601640\pi\)
−0.0201116 + 0.999798i \(0.506402\pi\)
\(674\) 11.3593 + 12.2424i 0.437544 + 0.471560i
\(675\) 11.8710 + 11.2836i 0.456916 + 0.434306i
\(676\) 3.15256 2.14938i 0.121252 0.0826683i
\(677\) 8.33640 10.4535i 0.320394 0.401761i −0.595387 0.803439i \(-0.703001\pi\)
0.915781 + 0.401678i \(0.131573\pi\)
\(678\) 3.23852 3.64014i 0.124374 0.139799i
\(679\) −5.77104 + 43.2540i −0.221472 + 1.65993i
\(680\) −3.01328 + 0.225814i −0.115554 + 0.00865957i
\(681\) 8.27562 9.30192i 0.317122 0.356451i
\(682\) −0.00551455 0.0178777i −0.000211163 0.000684574i
\(683\) −23.7313 1.77841i −0.908053 0.0680492i −0.387491 0.921873i \(-0.626658\pi\)
−0.520562 + 0.853824i \(0.674277\pi\)
\(684\) −11.3124 8.27153i −0.432540 0.316270i
\(685\) 13.9309i 0.532271i
\(686\) −17.8229 + 5.03415i −0.680483 + 0.192205i
\(687\) 21.9457 28.7321i 0.837280 1.09620i
\(688\) 9.07320 1.36756i 0.345913 0.0521379i
\(689\) −24.8428 + 11.9637i −0.946436 + 0.455780i
\(690\) −2.69526 15.6525i −0.102607 0.595881i
\(691\) 10.3947 + 21.5848i 0.395433 + 0.821125i 0.999704 + 0.0243456i \(0.00775022\pi\)
−0.604271 + 0.796779i \(0.706535\pi\)
\(692\) 4.97397 + 2.39534i 0.189082 + 0.0910572i
\(693\) 1.26774 + 1.64293i 0.0481574 + 0.0624098i
\(694\) 30.1127 14.5015i 1.14306 0.550470i
\(695\) −1.32150 1.05386i −0.0501272 0.0399751i
\(696\) 3.46819 + 6.83233i 0.131461 + 0.258979i
\(697\) −12.8781 16.1487i −0.487794 0.611675i
\(698\) 21.4550 + 6.61800i 0.812084 + 0.250495i
\(699\) −6.43954 + 11.7128i −0.243566 + 0.443021i
\(700\) −8.33810 + 0.141435i −0.315151 + 0.00534575i
\(701\) 3.55240 + 2.83295i 0.134172 + 0.106999i 0.688276 0.725448i \(-0.258368\pi\)
−0.554104 + 0.832447i \(0.686939\pi\)
\(702\) 20.2840 + 6.52516i 0.765572 + 0.246276i
\(703\) 4.26865 13.8386i 0.160995 0.521934i
\(704\) −0.226421 + 0.130724i −0.00853356 + 0.00492686i
\(705\) 13.6646 + 10.4371i 0.514639 + 0.393083i
\(706\) 16.3651 + 17.6374i 0.615909 + 0.663792i
\(707\) 0.626635 2.97737i 0.0235670 0.111975i
\(708\) 1.16533 + 0.429447i 0.0437957 + 0.0161396i
\(709\) −3.40715 + 14.9277i −0.127958 + 0.560622i 0.869782 + 0.493436i \(0.164259\pi\)
−0.997740 + 0.0671860i \(0.978598\pi\)
\(710\) −1.64883 4.20114i −0.0618794 0.157666i
\(711\) −22.4169 + 16.6988i −0.840700 + 0.626254i
\(712\) −4.42076 14.3318i −0.165675 0.537105i
\(713\) 0.353842 + 0.328318i 0.0132515 + 0.0122956i
\(714\) −4.75531 + 9.00801i −0.177963 + 0.337116i
\(715\) −1.06840 + 0.991327i −0.0399557 + 0.0370735i
\(716\) 9.72786 + 5.61638i 0.363547 + 0.209894i
\(717\) 17.5618 + 42.1329i 0.655857 + 1.57348i
\(718\) 22.9667 21.3100i 0.857110 0.795282i
\(719\) −0.298774 3.98687i −0.0111424 0.148685i 0.988858 0.148865i \(-0.0475619\pi\)
−1.00000 0.000179592i \(0.999943\pi\)
\(720\) −0.474624 4.05057i −0.0176882 0.150956i
\(721\) 8.90452 + 27.2199i 0.331622 + 1.01372i
\(722\) 0.420433 + 2.78939i 0.0156469 + 0.103810i
\(723\) −12.8371 + 9.15138i −0.477419 + 0.340344i
\(724\) 1.49181 1.18967i 0.0554425 0.0442139i
\(725\) −6.04987 + 12.5627i −0.224686 + 0.466566i
\(726\) −4.59850 18.3673i −0.170666 0.681673i
\(727\) −0.981321 0.0735398i −0.0363952 0.00272744i 0.0565201 0.998401i \(-0.482000\pi\)
−0.0929152 + 0.995674i \(0.529619\pi\)
\(728\) −9.69370 + 4.87247i −0.359273 + 0.180586i
\(729\) 9.25642 + 25.3637i 0.342830 + 0.939397i
\(730\) −12.2169 8.32931i −0.452166 0.308282i
\(731\) 19.4896 6.01173i 0.720847 0.222352i
\(732\) 21.2803 7.05491i 0.786541 0.260757i
\(733\) 4.53888 + 30.1135i 0.167647 + 1.11227i 0.901443 + 0.432898i \(0.142509\pi\)
−0.733796 + 0.679370i \(0.762253\pi\)
\(734\) −7.80650 13.5213i −0.288143 0.499079i
\(735\) 8.52429 14.1067i 0.314423 0.520333i
\(736\) 3.37274 5.84175i 0.124321 0.215330i
\(737\) 3.60781 + 1.41596i 0.132895 + 0.0521576i
\(738\) 21.0489 18.2775i 0.774822 0.672804i
\(739\) −5.74894 5.33424i −0.211478 0.196223i 0.567320 0.823497i \(-0.307980\pi\)
−0.778799 + 0.627274i \(0.784171\pi\)
\(740\) 3.79716 1.82861i 0.139586 0.0672212i
\(741\) −15.0177 29.5848i −0.551688 1.08683i
\(742\) 16.9086 5.53137i 0.620734 0.203063i
\(743\) 27.7435 40.6922i 1.01781 1.49285i 0.154619 0.987974i \(-0.450585\pi\)
0.863190 0.504879i \(-0.168463\pi\)
\(744\) 0.0861852 + 0.0890734i 0.00315970 + 0.00326559i
\(745\) −15.3949 + 1.15369i −0.564025 + 0.0422678i
\(746\) −0.136486 0.905526i −0.00499711 0.0331537i
\(747\) −12.3469 7.68177i −0.451749 0.281061i
\(748\) −0.454359 + 0.362339i −0.0166130 + 0.0132484i
\(749\) 44.2085 10.8823i 1.61534 0.397631i
\(750\) 13.7944 13.3471i 0.503701 0.487368i
\(751\) −2.83468 + 1.93265i −0.103439 + 0.0705235i −0.613935 0.789357i \(-0.710414\pi\)
0.510496 + 0.859880i \(0.329462\pi\)
\(752\) 1.62498 + 7.11948i 0.0592568 + 0.259621i
\(753\) 5.14606 39.7707i 0.187533 1.44933i
\(754\) 18.1404i 0.660636i
\(755\) 0.232419 + 1.01829i 0.00845860 + 0.0370595i
\(756\) −12.4155 5.90384i −0.451547 0.214720i
\(757\) 4.01408 17.5868i 0.145894 0.639205i −0.848106 0.529827i \(-0.822257\pi\)
0.994000 0.109378i \(-0.0348859\pi\)
\(758\) 15.5066 + 3.53928i 0.563225 + 0.128552i
\(759\) −2.12407 2.19525i −0.0770988 0.0796825i
\(760\) −3.95933 + 4.96484i −0.143620 + 0.180094i
\(761\) −8.43889 7.83015i −0.305910 0.283843i 0.512247 0.858838i \(-0.328813\pi\)
−0.818157 + 0.574996i \(0.805004\pi\)
\(762\) 4.22130 11.4547i 0.152922 0.414961i
\(763\) 18.2382 + 30.3873i 0.660267 + 1.10010i
\(764\) −10.6841 + 2.43858i −0.386537 + 0.0882246i
\(765\) −2.38512 8.74579i −0.0862343 0.316205i
\(766\) 11.8705 + 6.85346i 0.428900 + 0.247625i
\(767\) 1.99993 + 2.15541i 0.0722132 + 0.0778273i
\(768\) 0.945547 1.45119i 0.0341195 0.0523652i
\(769\) −7.44515 + 49.3954i −0.268479 + 1.78124i 0.295389 + 0.955377i \(0.404551\pi\)
−0.563868 + 0.825865i \(0.690687\pi\)
\(770\) 0.767860 0.542821i 0.0276718 0.0195619i
\(771\) 0.575935 + 27.5244i 0.0207418 + 0.991268i
\(772\) 1.23452 + 5.40878i 0.0444313 + 0.194666i
\(773\) 26.5276 3.99840i 0.954133 0.143812i 0.346517 0.938044i \(-0.387364\pi\)
0.607616 + 0.794231i \(0.292126\pi\)
\(774\) 9.20696 + 25.9417i 0.330937 + 0.932454i
\(775\) −0.0336165 + 0.223031i −0.00120754 + 0.00801151i
\(776\) 1.23255 16.4472i 0.0442459 0.590421i
\(777\) 1.58387 14.1184i 0.0568210 0.506496i
\(778\) 0.817217 + 10.9050i 0.0292986 + 0.390963i
\(779\) −43.2857 3.24381i −1.55087 0.116222i
\(780\) 3.33873 9.05982i 0.119546 0.324394i
\(781\) −0.717154 0.488948i −0.0256618 0.0174959i
\(782\) 5.47785 13.9573i 0.195888 0.499113i
\(783\) −18.1428 + 14.1146i −0.648371 + 0.504413i
\(784\) 6.61518 2.28896i 0.236257 0.0817485i
\(785\) 1.81386 + 1.04723i 0.0647394 + 0.0373773i
\(786\) 27.1860 0.568853i 0.969692 0.0202903i
\(787\) −0.805661 1.67297i −0.0287187 0.0596350i 0.886116 0.463464i \(-0.153394\pi\)
−0.914835 + 0.403829i \(0.867679\pi\)
\(788\) −12.8796 2.93968i −0.458816 0.104722i
\(789\) 2.92437 + 2.60171i 0.104110 + 0.0926234i
\(790\) 7.13539 + 10.4657i 0.253866 + 0.372353i
\(791\) −7.22673 + 1.77892i −0.256953 + 0.0632512i
\(792\) −0.514255 0.592233i −0.0182733 0.0210441i
\(793\) 52.4853 + 7.91088i 1.86381 + 0.280924i
\(794\) −2.53570 33.8366i −0.0899887 1.20082i
\(795\) −7.62772 + 13.8740i −0.270527 + 0.492061i
\(796\) −3.33316 + 10.8058i −0.118141 + 0.383002i
\(797\) 0.919081 2.34178i 0.0325555 0.0829501i −0.913672 0.406453i \(-0.866765\pi\)
0.946227 + 0.323503i \(0.104861\pi\)
\(798\) 7.07987 + 20.2018i 0.250625 + 0.715137i
\(799\) 5.93026 + 15.1101i 0.209798 + 0.534556i
\(800\) 3.14315 0.235546i 0.111127 0.00832781i
\(801\) 39.6863 21.2009i 1.40225 0.749098i
\(802\) 10.6154 18.3863i 0.374841 0.649244i
\(803\) −2.84370 −0.100352
\(804\) −25.5584 + 2.45399i −0.901377 + 0.0865454i
\(805\) −10.1544 + 22.0342i −0.357896 + 0.776604i
\(806\) 0.0864928 + 0.280403i 0.00304658 + 0.00987676i
\(807\) −1.45601 + 1.21182i −0.0512540 + 0.0426580i
\(808\) −0.171397 + 1.13715i −0.00602974 + 0.0400047i
\(809\) −12.4186 + 4.87394i −0.436614 + 0.171359i −0.573459 0.819234i \(-0.694399\pi\)
0.136845 + 0.990592i \(0.456304\pi\)
\(810\) 11.6588 3.71003i 0.409648 0.130357i
\(811\) −11.4661 2.61705i −0.402628 0.0918972i 0.0164114 0.999865i \(-0.494776\pi\)
−0.419039 + 0.907968i \(0.637633\pi\)
\(812\) 1.54788 11.6014i 0.0543199 0.407129i
\(813\) −33.2853 + 23.7285i −1.16737 + 0.832195i
\(814\) 0.405274 0.701956i 0.0142049 0.0246035i
\(815\) −5.57737 −0.195367
\(816\) 1.59752 3.50291i 0.0559244 0.122626i
\(817\) 18.5972 38.6175i 0.650635 1.35106i
\(818\) 3.86908 4.85167i 0.135279 0.169635i
\(819\) −19.8838 25.7685i −0.694796 0.900424i
\(820\) −7.87606 9.87627i −0.275044 0.344894i
\(821\) −34.1376 + 7.79169i −1.19141 + 0.271932i −0.771856 0.635798i \(-0.780671\pi\)
−0.419556 + 0.907730i \(0.637814\pi\)
\(822\) 15.5537 + 8.55118i 0.542498 + 0.298257i
\(823\) −11.2659 5.42538i −0.392705 0.189117i 0.227102 0.973871i \(-0.427075\pi\)
−0.619807 + 0.784754i \(0.712789\pi\)
\(824\) −3.95469 10.0764i −0.137768 0.351027i
\(825\) 0.288432 1.39789i 0.0100419 0.0486684i
\(826\) −1.09510 1.54910i −0.0381034 0.0539001i
\(827\) 20.9946 43.5956i 0.730052 1.51597i −0.122010 0.992529i \(-0.538934\pi\)
0.852063 0.523440i \(-0.175352\pi\)
\(828\) 19.1303 + 6.59873i 0.664825 + 0.229322i
\(829\) 4.91748 5.29978i 0.170791 0.184069i −0.641856 0.766825i \(-0.721835\pi\)
0.812647 + 0.582756i \(0.198026\pi\)
\(830\) −3.71192 + 5.44439i −0.128843 + 0.188978i
\(831\) 9.31516 + 5.12133i 0.323139 + 0.177657i
\(832\) 3.55129 2.05034i 0.123119 0.0710827i
\(833\) 13.7817 7.22261i 0.477506 0.250249i
\(834\) 1.98780 0.828551i 0.0688318 0.0286904i
\(835\) −10.1291 12.7015i −0.350533 0.439554i
\(836\) −0.0912679 + 1.21789i −0.00315657 + 0.0421214i
\(837\) −0.213142 + 0.304677i −0.00736726 + 0.0105312i
\(838\) −9.14361 + 13.4112i −0.315861 + 0.463283i
\(839\) 22.9301 15.6335i 0.791635 0.539727i −0.0986551 0.995122i \(-0.531454\pi\)
0.890290 + 0.455394i \(0.150502\pi\)
\(840\) −2.90827 + 5.50916i −0.100345 + 0.190084i
\(841\) 7.79168 + 5.31228i 0.268679 + 0.183182i
\(842\) 18.8748 7.40782i 0.650469 0.255290i
\(843\) 15.7501 7.99498i 0.542463 0.275362i
\(844\) 6.86179 17.4836i 0.236193 0.601809i
\(845\) 3.80231 3.52803i 0.130803 0.121368i
\(846\) −20.0407 + 8.84985i −0.689012 + 0.304264i
\(847\) −10.1084 + 27.0985i −0.347329 + 0.931114i
\(848\) −6.25931 + 2.45660i −0.214946 + 0.0843599i
\(849\) −9.44617 6.15483i −0.324192 0.211233i
\(850\) 6.83050 1.55902i 0.234284 0.0534739i
\(851\) 20.9125i 0.716870i
\(852\) 5.70264 + 0.737883i 0.195369 + 0.0252795i
\(853\) 7.89288 25.5881i 0.270247 0.876119i −0.714125 0.700018i \(-0.753175\pi\)
0.984372 0.176101i \(-0.0563486\pi\)
\(854\) −32.8910 9.53770i −1.12551 0.326373i
\(855\) −16.8825 8.82692i −0.577369 0.301874i
\(856\) −16.4435 + 5.07215i −0.562028 + 0.173363i
\(857\) −51.8408 7.81374i −1.77085 0.266912i −0.819068 0.573696i \(-0.805509\pi\)
−0.951779 + 0.306784i \(0.900747\pi\)
\(858\) −0.450995 1.80136i −0.0153967 0.0614974i
\(859\) 0.450103 0.485096i 0.0153573 0.0165513i −0.725326 0.688405i \(-0.758311\pi\)
0.740684 + 0.671854i \(0.234502\pi\)
\(860\) 11.9195 3.67668i 0.406452 0.125374i
\(861\) −42.3127 + 4.78817i −1.44201 + 0.163180i
\(862\) −18.1297 5.59228i −0.617501 0.190474i
\(863\) 11.0206 6.36275i 0.375146 0.216591i −0.300558 0.953763i \(-0.597173\pi\)
0.675704 + 0.737173i \(0.263840\pi\)
\(864\) 4.81376 + 1.95644i 0.163768 + 0.0665596i
\(865\) 7.17156 + 2.21213i 0.243840 + 0.0752148i
\(866\) 5.13734 + 2.47401i 0.174574 + 0.0840703i
\(867\) −5.73769 + 20.0836i −0.194862 + 0.682074i
\(868\) −0.0313887 0.186707i −0.00106540 0.00633723i
\(869\) 2.26769 + 0.890002i 0.0769261 + 0.0301913i
\(870\) 6.04640 + 8.48162i 0.204992 + 0.287554i
\(871\) −56.5865 22.2086i −1.91736 0.752508i
\(872\) −7.54579 11.0676i −0.255533 0.374798i
\(873\) 49.1438 5.75840i 1.66327 0.194892i
\(874\) −13.6717 28.3895i −0.462452 0.960291i
\(875\) −28.9144 + 4.86104i −0.977486 + 0.164333i
\(876\) 16.7987 8.52724i 0.567574 0.288109i
\(877\) 2.44338 32.6046i 0.0825069 1.10098i −0.790237 0.612801i \(-0.790043\pi\)
0.872744 0.488178i \(-0.162338\pi\)
\(878\) −3.09239 + 13.5487i −0.104363 + 0.457245i
\(879\) −14.8644 + 16.7078i −0.501364 + 0.563541i
\(880\) −0.277879 + 0.221601i −0.00936729 + 0.00747016i
\(881\) 18.4170 0.620486 0.310243 0.950657i \(-0.399590\pi\)
0.310243 + 0.950657i \(0.399590\pi\)
\(882\) 10.5175 + 18.1764i 0.354144 + 0.612031i
\(883\) −35.7330 −1.20251 −0.601256 0.799056i \(-0.705333\pi\)
−0.601256 + 0.799056i \(0.705333\pi\)
\(884\) 7.12637 5.68309i 0.239686 0.191143i
\(885\) 1.65349 + 0.341171i 0.0555816 + 0.0114683i
\(886\) 5.80917 25.4517i 0.195163 0.855065i
\(887\) 0.161046 2.14901i 0.00540740 0.0721567i −0.993847 0.110760i \(-0.964672\pi\)
0.999255 + 0.0386028i \(0.0122907\pi\)
\(888\) −0.289173 + 5.36195i −0.00970402 + 0.179935i
\(889\) −15.2271 + 10.7644i −0.510700 + 0.361027i
\(890\) −8.84636 18.3697i −0.296531 0.615752i
\(891\) 1.45069 1.85264i 0.0485999 0.0620658i
\(892\) −14.4400 21.1795i −0.483485 0.709143i
\(893\) 31.7543 + 12.4627i 1.06262 + 0.417047i
\(894\) 8.16175 17.8964i 0.272970 0.598546i
\(895\) 14.2146 + 5.57880i 0.475140 + 0.186479i
\(896\) −2.44611 + 1.00823i −0.0817189 + 0.0336827i
\(897\) 33.3148 + 34.4313i 1.11235 + 1.14963i
\(898\) −27.5385 13.2619i −0.918973 0.442554i
\(899\) −0.302495 0.0933074i −0.0100888 0.00311198i
\(900\) 2.48792 + 9.12271i 0.0829306 + 0.304090i
\(901\) −12.9439 + 7.47317i −0.431224 + 0.248968i
\(902\) −2.32153 0.716097i −0.0772984 0.0238434i
\(903\) 10.8633 40.6208i 0.361508 1.35177i
\(904\) 2.68801 0.829141i 0.0894019 0.0275768i
\(905\) 1.76431 1.90147i 0.0586475 0.0632070i
\(906\) −1.27958 0.365565i −0.0425113 0.0121451i
\(907\) −24.1310 3.63716i −0.801255 0.120770i −0.264366 0.964422i \(-0.585163\pi\)
−0.536889 + 0.843653i \(0.680401\pi\)
\(908\) 6.86887 2.11877i 0.227951 0.0703137i
\(909\) −3.44696 + 0.144315i −0.114328 + 0.00478662i
\(910\) −12.0435 + 8.51385i −0.399237 + 0.282231i
\(911\) −13.6109 + 44.1254i −0.450949 + 1.46194i 0.389995 + 0.920817i \(0.372477\pi\)
−0.840943 + 0.541123i \(0.817999\pi\)
\(912\) −3.11285 7.46812i −0.103077 0.247294i
\(913\) 1.26728i 0.0419410i
\(914\) −13.5085 + 3.08324i −0.446823 + 0.101984i
\(915\) 27.1764 13.7952i 0.898426 0.456054i
\(916\) 19.4309 7.62605i 0.642014 0.251972i
\(917\) −34.7108 22.8128i −1.14625 0.753346i
\(918\) 11.2287 + 2.70545i 0.370601 + 0.0892931i
\(919\) 37.0513 34.3786i 1.22221 1.13405i 0.235446 0.971888i \(-0.424345\pi\)
0.986765 0.162158i \(-0.0518455\pi\)
\(920\) 3.35017 8.53609i 0.110452 0.281427i
\(921\) −32.9138 21.4456i −1.08455 0.706656i
\(922\) −20.6642 + 8.11010i −0.680539 + 0.267092i
\(923\) 11.2482 + 7.66888i 0.370238 + 0.252424i
\(924\) 0.134720 + 1.19051i 0.00443196 + 0.0391649i
\(925\) −8.07382 + 5.50464i −0.265466 + 0.180991i
\(926\) −10.1713 + 14.9186i −0.334250 + 0.490255i
\(927\) 27.4194 17.3992i 0.900573 0.571464i
\(928\) −0.330588 + 4.41140i −0.0108521 + 0.144811i
\(929\) −29.8644 37.4488i −0.979820 1.22866i −0.973503 0.228676i \(-0.926560\pi\)
−0.00631784 0.999980i \(-0.502011\pi\)
\(930\) 0.133901 + 0.102274i 0.00439079 + 0.00335370i
\(931\) 8.57293 31.5552i 0.280966 1.03418i
\(932\) −6.68316 + 3.85852i −0.218914 + 0.126390i
\(933\) −4.27617 + 2.58961i −0.139995 + 0.0847800i
\(934\) 4.18708 6.14132i 0.137005 0.200950i
\(935\) −0.537354 + 0.579130i −0.0175734 + 0.0189396i
\(936\) 8.06581 + 9.28885i 0.263639 + 0.303615i
\(937\) −4.81653 + 10.0016i −0.157349 + 0.326739i −0.964708 0.263322i \(-0.915182\pi\)
0.807359 + 0.590061i \(0.200896\pi\)
\(938\) 34.2938 + 19.0315i 1.11973 + 0.621399i
\(939\) −15.8793 + 5.26435i −0.518200 + 0.171795i
\(940\) 3.62685 + 9.24108i 0.118295 + 0.301411i
\(941\) 8.72154 + 4.20007i 0.284314 + 0.136918i 0.570606 0.821224i \(-0.306708\pi\)
−0.286292 + 0.958142i \(0.592423\pi\)
\(942\) −2.28263 + 1.38234i −0.0743720 + 0.0450390i
\(943\) 61.1095 13.9479i 1.99000 0.454205i
\(944\) 0.447063 + 0.560599i 0.0145507 + 0.0182460i
\(945\) −17.8856 5.42066i −0.581820 0.176334i
\(946\) 1.49573 1.87559i 0.0486305 0.0609807i
\(947\) 15.9535 33.1279i 0.518421 1.07651i −0.463303 0.886200i \(-0.653336\pi\)
0.981724 0.190312i \(-0.0609498\pi\)
\(948\) −16.0648 + 1.54245i −0.521759 + 0.0500966i
\(949\) 44.6019 1.44784
\(950\) 7.36185 12.7511i 0.238850 0.413700i
\(951\) −1.33950 13.9510i −0.0434363 0.452392i
\(952\) −5.04246 + 3.02644i −0.163427 + 0.0980874i
\(953\) 43.0769 + 9.83201i 1.39540 + 0.318490i 0.853122 0.521712i \(-0.174706\pi\)
0.542274 + 0.840202i \(0.317563\pi\)
\(954\) −10.8081 17.0326i −0.349926 0.551450i
\(955\) −13.8679 + 5.44277i −0.448756 + 0.176124i
\(956\) −3.92786 + 26.0596i −0.127036 + 0.842829i
\(957\) 1.87969 + 0.692704i 0.0607618 + 0.0223919i
\(958\) −7.57106 24.5448i −0.244610 0.793005i
\(959\) −12.1763 24.2246i −0.393194 0.782253i
\(960\) 0.977018 2.14233i 0.0315331 0.0691433i
\(961\) 30.9949 0.999835
\(962\) −6.35651 + 11.0098i −0.204942 + 0.354970i
\(963\) −24.3249 45.5340i −0.783857 1.46731i
\(964\) −9.07657 + 0.680195i −0.292337 + 0.0219076i
\(965\) 2.75538 + 7.02059i 0.0886988 + 0.226001i
\(966\) −18.3679 24.8626i −0.590979 0.799940i
\(967\) −14.8930 + 37.9467i −0.478926 + 1.22028i 0.463568 + 0.886061i \(0.346569\pi\)
−0.942494 + 0.334223i \(0.891526\pi\)
\(968\) 3.22216 10.4460i 0.103564 0.335747i
\(969\) −9.31607 15.3834i −0.299275 0.494187i
\(970\) −1.67556 22.3588i −0.0537990 0.717897i
\(971\) −0.889209 0.134027i −0.0285361 0.00430112i 0.134759 0.990878i \(-0.456974\pi\)
−0.163295 + 0.986577i \(0.552212\pi\)
\(972\) −3.01428 + 15.2943i −0.0966832 + 0.490563i
\(973\) −3.21910 0.677511i −0.103200 0.0217200i
\(974\) 3.95478 + 5.80060i 0.126719 + 0.185863i
\(975\) −4.52390 + 21.9252i −0.144881 + 0.702168i
\(976\) 12.6192 + 2.88025i 0.403931 + 0.0921947i
\(977\) −23.3712 48.5309i −0.747712 1.55264i −0.831100 0.556123i \(-0.812288\pi\)
0.0833883 0.996517i \(-0.473426\pi\)
\(978\) 3.42355 6.22708i 0.109473 0.199120i
\(979\) −3.39588 1.96061i −0.108533 0.0626614i
\(980\) 8.42865 4.41723i 0.269243 0.141103i
\(981\) 28.2890 28.5415i 0.903199 0.911260i
\(982\) −4.52327 + 11.5251i −0.144343 + 0.367781i
\(983\) −6.87746 4.68897i −0.219357 0.149555i 0.448656 0.893704i \(-0.351903\pi\)
−0.668013 + 0.744149i \(0.732855\pi\)
\(984\) 15.8613 2.73122i 0.505641 0.0870680i
\(985\) −17.9089 1.34209i −0.570625 0.0427624i
\(986\) 0.734830 + 9.80563i 0.0234018 + 0.312275i
\(987\) 32.8842 + 6.20559i 1.04672 + 0.197526i
\(988\) 1.43149 19.1019i 0.0455417 0.607711i
\(989\) −9.22487 + 61.2030i −0.293334 + 1.94614i
\(990\) −0.811277 0.691911i −0.0257841 0.0219904i
\(991\) 28.7890 4.33924i 0.914513 0.137841i 0.325107 0.945677i \(-0.394600\pi\)
0.589406 + 0.807837i \(0.299362\pi\)
\(992\) 0.0159233 + 0.0697646i 0.000505566 + 0.00221503i
\(993\) −27.7277 + 16.7916i −0.879911 + 0.532866i
\(994\) −6.53920 5.86427i −0.207411 0.186003i
\(995\) −2.29118 + 15.2010i −0.0726354 + 0.481904i
\(996\) −3.80013 7.48626i −0.120412 0.237211i
\(997\) 9.09346 + 9.80042i 0.287993 + 0.310382i 0.860433 0.509564i \(-0.170193\pi\)
−0.572440 + 0.819947i \(0.694003\pi\)
\(998\) 32.9583 + 19.0285i 1.04328 + 0.602336i
\(999\) −15.9570 + 2.20907i −0.504859 + 0.0698919i
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 882.2.bk.a.101.10 yes 672
9.5 odd 6 882.2.bc.a.689.38 yes 672
49.33 odd 42 882.2.bc.a.425.38 672
441.131 even 42 inner 882.2.bk.a.131.10 yes 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.bc.a.425.38 672 49.33 odd 42
882.2.bc.a.689.38 yes 672 9.5 odd 6
882.2.bk.a.101.10 yes 672 1.1 even 1 trivial
882.2.bk.a.131.10 yes 672 441.131 even 42 inner