Properties

Label 88.2.o.a.53.10
Level $88$
Weight $2$
Character 88.53
Analytic conductor $0.703$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [88,2,Mod(5,88)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(88, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("88.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 88.o (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.702683537787\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 53.10
Character \(\chi\) \(=\) 88.53
Dual form 88.2.o.a.5.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40939 + 0.116729i) q^{2} +(0.317655 + 0.437215i) q^{3} +(1.97275 + 0.329033i) q^{4} +(-2.75892 + 0.896426i) q^{5} +(0.396664 + 0.653285i) q^{6} +(-2.10709 - 1.53089i) q^{7} +(2.74196 + 0.694011i) q^{8} +(0.836799 - 2.57540i) q^{9} +O(q^{10})\) \(q+(1.40939 + 0.116729i) q^{2} +(0.317655 + 0.437215i) q^{3} +(1.97275 + 0.329033i) q^{4} +(-2.75892 + 0.896426i) q^{5} +(0.396664 + 0.653285i) q^{6} +(-2.10709 - 1.53089i) q^{7} +(2.74196 + 0.694011i) q^{8} +(0.836799 - 2.57540i) q^{9} +(-3.99302 + 0.941367i) q^{10} +(-2.98171 - 1.45237i) q^{11} +(0.482796 + 0.967034i) q^{12} +(2.48923 + 0.808799i) q^{13} +(-2.79101 - 2.40358i) q^{14} +(-1.26831 - 0.921484i) q^{15} +(3.78348 + 1.29820i) q^{16} +(2.12944 + 6.55375i) q^{17} +(1.48000 - 3.53206i) q^{18} +(-0.940841 - 1.29496i) q^{19} +(-5.73760 + 0.860650i) q^{20} -1.40755i q^{21} +(-4.03286 - 2.39501i) q^{22} -4.01642 q^{23} +(0.567566 + 1.41928i) q^{24} +(2.76295 - 2.00740i) q^{25} +(3.41387 + 1.43048i) q^{26} +(2.93375 - 0.953233i) q^{27} +(-3.65305 - 3.71336i) q^{28} +(-1.17414 + 1.61606i) q^{29} +(-1.67998 - 1.44678i) q^{30} +(-1.60087 + 4.92697i) q^{31} +(5.18085 + 2.27130i) q^{32} +(-0.312158 - 1.76500i) q^{33} +(2.23620 + 9.48535i) q^{34} +(7.18561 + 2.33475i) q^{35} +(2.49819 - 4.80529i) q^{36} +(5.04873 - 6.94898i) q^{37} +(-1.17485 - 1.93492i) q^{38} +(0.437097 + 1.34525i) q^{39} +(-8.18697 + 0.543246i) q^{40} +(-3.03285 + 2.20349i) q^{41} +(0.164301 - 1.98378i) q^{42} +2.47162i q^{43} +(-5.40429 - 3.84625i) q^{44} +7.85545i q^{45} +(-5.66069 - 0.468832i) q^{46} +(9.58423 - 6.96335i) q^{47} +(0.634249 + 2.06657i) q^{48} +(-0.0669162 - 0.205947i) q^{49} +(4.12839 - 2.50669i) q^{50} +(-2.18897 + 3.01286i) q^{51} +(4.64450 + 2.41459i) q^{52} +(-1.23048 - 0.399807i) q^{53} +(4.24606 - 1.00102i) q^{54} +(9.52824 + 1.33409i) q^{55} +(-4.71510 - 5.65999i) q^{56} +(0.267311 - 0.822700i) q^{57} +(-1.84346 + 2.14060i) q^{58} +(-0.206617 + 0.284384i) q^{59} +(-2.19887 - 2.23517i) q^{60} +(2.93056 - 0.952198i) q^{61} +(-2.83136 + 6.75714i) q^{62} +(-5.70587 + 4.14556i) q^{63} +(7.03670 + 3.80590i) q^{64} -7.59259 q^{65} +(-0.233924 - 2.52401i) q^{66} -10.3946i q^{67} +(2.04446 + 13.6296i) q^{68} +(-1.27583 - 1.75604i) q^{69} +(9.85479 + 4.12933i) q^{70} +(1.07237 + 3.30042i) q^{71} +(4.08183 - 6.48090i) q^{72} +(-1.07956 - 0.784343i) q^{73} +(7.92676 - 9.20447i) q^{74} +(1.75533 + 0.570342i) q^{75} +(-1.42996 - 2.86419i) q^{76} +(4.05931 + 7.62496i) q^{77} +(0.459010 + 1.94699i) q^{78} +(1.33582 - 4.11124i) q^{79} +(-11.6020 - 0.190011i) q^{80} +(-5.22362 - 3.79518i) q^{81} +(-4.53167 + 2.75156i) q^{82} +(-15.2001 + 4.93882i) q^{83} +(0.463129 - 2.77674i) q^{84} +(-11.7499 - 16.1724i) q^{85} +(-0.288510 + 3.48348i) q^{86} -1.07954 q^{87} +(-7.16778 - 6.05169i) q^{88} -13.1240 q^{89} +(-0.916958 + 11.0714i) q^{90} +(-4.00684 - 5.51494i) q^{91} +(-7.92338 - 1.32153i) q^{92} +(-2.66267 + 0.865153i) q^{93} +(14.3207 - 8.69531i) q^{94} +(3.75654 + 2.72928i) q^{95} +(0.652675 + 2.98663i) q^{96} +(2.66143 - 8.19103i) q^{97} +(-0.0702709 - 0.298070i) q^{98} +(-6.23554 + 6.46377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 5 q^{2} - q^{4} - 7 q^{6} - 10 q^{7} - 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 5 q^{2} - q^{4} - 7 q^{6} - 10 q^{7} - 5 q^{8} - 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} - 6 q^{17} - 20 q^{18} + 8 q^{20} - 35 q^{22} - 8 q^{23} + 25 q^{24} - 4 q^{25} - 10 q^{26} + 32 q^{28} - 28 q^{30} - 6 q^{31} + 20 q^{32} - 10 q^{33} + 10 q^{34} + 18 q^{36} + 12 q^{38} - 34 q^{39} + 10 q^{40} - 14 q^{41} + 40 q^{42} + 26 q^{44} + 18 q^{46} - 6 q^{47} + 18 q^{48} - 4 q^{49} + 61 q^{50} + 20 q^{52} + 108 q^{54} - 2 q^{55} - 32 q^{56} - 26 q^{57} + 4 q^{58} - 46 q^{60} + 48 q^{62} + 60 q^{63} - 49 q^{64} - 36 q^{65} + 50 q^{66} - 42 q^{68} - 8 q^{70} + 22 q^{71} - 101 q^{72} - 6 q^{73} + 54 q^{74} - 134 q^{76} - 12 q^{78} + 74 q^{79} - 44 q^{80} - 4 q^{81} - 31 q^{82} - 28 q^{84} - 15 q^{86} + 68 q^{87} - 73 q^{88} - 16 q^{89} - 84 q^{90} - 4 q^{92} - 100 q^{94} + 66 q^{95} - 30 q^{96} + 10 q^{97} - 144 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/88\mathbb{Z}\right)^\times\).

\(n\) \(23\) \(45\) \(57\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40939 + 0.116729i 0.996588 + 0.0825398i
\(3\) 0.317655 + 0.437215i 0.183398 + 0.252426i 0.890810 0.454375i \(-0.150137\pi\)
−0.707412 + 0.706801i \(0.750137\pi\)
\(4\) 1.97275 + 0.329033i 0.986374 + 0.164516i
\(5\) −2.75892 + 0.896426i −1.23382 + 0.400894i −0.852098 0.523382i \(-0.824670\pi\)
−0.381726 + 0.924275i \(0.624670\pi\)
\(6\) 0.396664 + 0.653285i 0.161937 + 0.266702i
\(7\) −2.10709 1.53089i −0.796405 0.578622i 0.113452 0.993543i \(-0.463809\pi\)
−0.909857 + 0.414921i \(0.863809\pi\)
\(8\) 2.74196 + 0.694011i 0.969429 + 0.245370i
\(9\) 0.836799 2.57540i 0.278933 0.858468i
\(10\) −3.99302 + 0.941367i −1.26270 + 0.297686i
\(11\) −2.98171 1.45237i −0.899020 0.437907i
\(12\) 0.482796 + 0.967034i 0.139371 + 0.279159i
\(13\) 2.48923 + 0.808799i 0.690387 + 0.224320i 0.633137 0.774040i \(-0.281767\pi\)
0.0572498 + 0.998360i \(0.481767\pi\)
\(14\) −2.79101 2.40358i −0.745928 0.642383i
\(15\) −1.26831 0.921484i −0.327477 0.237926i
\(16\) 3.78348 + 1.29820i 0.945869 + 0.324549i
\(17\) 2.12944 + 6.55375i 0.516466 + 1.58952i 0.780599 + 0.625032i \(0.214914\pi\)
−0.264133 + 0.964486i \(0.585086\pi\)
\(18\) 1.48000 3.53206i 0.348839 0.832515i
\(19\) −0.940841 1.29496i −0.215844 0.297084i 0.687341 0.726334i \(-0.258778\pi\)
−0.903185 + 0.429251i \(0.858778\pi\)
\(20\) −5.73760 + 0.860650i −1.28297 + 0.192447i
\(21\) 1.40755i 0.307152i
\(22\) −4.03286 2.39501i −0.859808 0.510618i
\(23\) −4.01642 −0.837480 −0.418740 0.908106i \(-0.637528\pi\)
−0.418740 + 0.908106i \(0.637528\pi\)
\(24\) 0.567566 + 1.41928i 0.115854 + 0.289710i
\(25\) 2.76295 2.00740i 0.552590 0.401480i
\(26\) 3.41387 + 1.43048i 0.669516 + 0.280539i
\(27\) 2.93375 0.953233i 0.564600 0.183450i
\(28\) −3.65305 3.71336i −0.690361 0.701760i
\(29\) −1.17414 + 1.61606i −0.218032 + 0.300095i −0.903997 0.427540i \(-0.859380\pi\)
0.685965 + 0.727635i \(0.259380\pi\)
\(30\) −1.67998 1.44678i −0.306722 0.264144i
\(31\) −1.60087 + 4.92697i −0.287525 + 0.884910i 0.698106 + 0.715994i \(0.254026\pi\)
−0.985631 + 0.168915i \(0.945974\pi\)
\(32\) 5.18085 + 2.27130i 0.915853 + 0.401514i
\(33\) −0.312158 1.76500i −0.0543397 0.307248i
\(34\) 2.23620 + 9.48535i 0.383505 + 1.62672i
\(35\) 7.18561 + 2.33475i 1.21459 + 0.394644i
\(36\) 2.49819 4.80529i 0.416364 0.800881i
\(37\) 5.04873 6.94898i 0.830006 1.14240i −0.157916 0.987453i \(-0.550478\pi\)
0.987922 0.154952i \(-0.0495224\pi\)
\(38\) −1.17485 1.93492i −0.190586 0.313886i
\(39\) 0.437097 + 1.34525i 0.0699915 + 0.215412i
\(40\) −8.18697 + 0.543246i −1.29447 + 0.0858947i
\(41\) −3.03285 + 2.20349i −0.473651 + 0.344128i −0.798863 0.601513i \(-0.794565\pi\)
0.325211 + 0.945641i \(0.394565\pi\)
\(42\) 0.164301 1.98378i 0.0253522 0.306104i
\(43\) 2.47162i 0.376919i 0.982081 + 0.188460i \(0.0603494\pi\)
−0.982081 + 0.188460i \(0.939651\pi\)
\(44\) −5.40429 3.84625i −0.814728 0.579844i
\(45\) 7.85545i 1.17102i
\(46\) −5.66069 0.468832i −0.834623 0.0691255i
\(47\) 9.58423 6.96335i 1.39800 1.01571i 0.403071 0.915169i \(-0.367943\pi\)
0.994933 0.100541i \(-0.0320572\pi\)
\(48\) 0.634249 + 2.06657i 0.0915460 + 0.298284i
\(49\) −0.0669162 0.205947i −0.00955945 0.0294210i
\(50\) 4.12839 2.50669i 0.583843 0.354500i
\(51\) −2.18897 + 3.01286i −0.306517 + 0.421884i
\(52\) 4.64450 + 2.41459i 0.644076 + 0.334844i
\(53\) −1.23048 0.399807i −0.169019 0.0549177i 0.223285 0.974753i \(-0.428322\pi\)
−0.392304 + 0.919836i \(0.628322\pi\)
\(54\) 4.24606 1.00102i 0.577815 0.136222i
\(55\) 9.52824 + 1.33409i 1.28479 + 0.179888i
\(56\) −4.71510 5.65999i −0.630082 0.756347i
\(57\) 0.267311 0.822700i 0.0354062 0.108969i
\(58\) −1.84346 + 2.14060i −0.242058 + 0.281075i
\(59\) −0.206617 + 0.284384i −0.0268993 + 0.0370237i −0.822255 0.569120i \(-0.807284\pi\)
0.795356 + 0.606143i \(0.207284\pi\)
\(60\) −2.19887 2.23517i −0.283873 0.288560i
\(61\) 2.93056 0.952198i 0.375220 0.121916i −0.115335 0.993327i \(-0.536794\pi\)
0.490555 + 0.871410i \(0.336794\pi\)
\(62\) −2.83136 + 6.75714i −0.359584 + 0.858158i
\(63\) −5.70587 + 4.14556i −0.718872 + 0.522291i
\(64\) 7.03670 + 3.80590i 0.879587 + 0.475738i
\(65\) −7.59259 −0.941745
\(66\) −0.233924 2.52401i −0.0287941 0.310684i
\(67\) 10.3946i 1.26990i −0.772553 0.634950i \(-0.781021\pi\)
0.772553 0.634950i \(-0.218979\pi\)
\(68\) 2.04446 + 13.6296i 0.247927 + 1.65283i
\(69\) −1.27583 1.75604i −0.153592 0.211402i
\(70\) 9.85479 + 4.12933i 1.17787 + 0.493550i
\(71\) 1.07237 + 3.30042i 0.127267 + 0.391688i 0.994307 0.106550i \(-0.0339806\pi\)
−0.867040 + 0.498238i \(0.833981\pi\)
\(72\) 4.08183 6.48090i 0.481048 0.763782i
\(73\) −1.07956 0.784343i −0.126352 0.0918004i 0.522814 0.852447i \(-0.324882\pi\)
−0.649167 + 0.760646i \(0.724882\pi\)
\(74\) 7.92676 9.20447i 0.921467 1.07000i
\(75\) 1.75533 + 0.570342i 0.202688 + 0.0658574i
\(76\) −1.42996 2.86419i −0.164028 0.328545i
\(77\) 4.05931 + 7.62496i 0.462602 + 0.868944i
\(78\) 0.459010 + 1.94699i 0.0519726 + 0.220454i
\(79\) 1.33582 4.11124i 0.150292 0.462551i −0.847362 0.531016i \(-0.821810\pi\)
0.997653 + 0.0684655i \(0.0218103\pi\)
\(80\) −11.6020 0.190011i −1.29715 0.0212439i
\(81\) −5.22362 3.79518i −0.580402 0.421687i
\(82\) −4.53167 + 2.75156i −0.500439 + 0.303859i
\(83\) −15.2001 + 4.93882i −1.66843 + 0.542106i −0.982613 0.185666i \(-0.940556\pi\)
−0.685819 + 0.727772i \(0.740556\pi\)
\(84\) 0.463129 2.77674i 0.0505315 0.302967i
\(85\) −11.7499 16.1724i −1.27446 1.75414i
\(86\) −0.288510 + 3.48348i −0.0311108 + 0.375633i
\(87\) −1.07954 −0.115739
\(88\) −7.16778 6.05169i −0.764088 0.645113i
\(89\) −13.1240 −1.39114 −0.695571 0.718457i \(-0.744849\pi\)
−0.695571 + 0.718457i \(0.744849\pi\)
\(90\) −0.916958 + 11.0714i −0.0966558 + 1.16703i
\(91\) −4.00684 5.51494i −0.420031 0.578123i
\(92\) −7.92338 1.32153i −0.826069 0.137779i
\(93\) −2.66267 + 0.865153i −0.276106 + 0.0897122i
\(94\) 14.3207 8.69531i 1.47707 0.896853i
\(95\) 3.75654 + 2.72928i 0.385412 + 0.280019i
\(96\) 0.652675 + 2.98663i 0.0666133 + 0.304822i
\(97\) 2.66143 8.19103i 0.270227 0.831673i −0.720216 0.693750i \(-0.755957\pi\)
0.990443 0.137923i \(-0.0440427\pi\)
\(98\) −0.0702709 0.298070i −0.00709843 0.0301096i
\(99\) −6.23554 + 6.46377i −0.626695 + 0.649633i
\(100\) 6.11111 3.05100i 0.611111 0.305100i
\(101\) −8.27982 2.69028i −0.823873 0.267692i −0.133410 0.991061i \(-0.542593\pi\)
−0.690462 + 0.723368i \(0.742593\pi\)
\(102\) −3.43679 + 3.99077i −0.340293 + 0.395145i
\(103\) −1.00931 0.733309i −0.0994506 0.0722551i 0.536949 0.843615i \(-0.319577\pi\)
−0.636399 + 0.771360i \(0.719577\pi\)
\(104\) 6.26404 + 3.94524i 0.614240 + 0.386863i
\(105\) 1.26176 + 3.88330i 0.123135 + 0.378971i
\(106\) −1.68755 0.707116i −0.163910 0.0686811i
\(107\) 11.0372 + 15.1915i 1.06701 + 1.46861i 0.873067 + 0.487601i \(0.162128\pi\)
0.193943 + 0.981013i \(0.437872\pi\)
\(108\) 6.10119 0.915189i 0.587087 0.0880641i
\(109\) 12.1780i 1.16644i 0.812313 + 0.583221i \(0.198208\pi\)
−0.812313 + 0.583221i \(0.801792\pi\)
\(110\) 13.2733 + 2.99247i 1.26556 + 0.285321i
\(111\) 4.64195 0.440594
\(112\) −5.98472 8.52751i −0.565503 0.805774i
\(113\) 4.29474 3.12031i 0.404015 0.293534i −0.367159 0.930158i \(-0.619670\pi\)
0.771174 + 0.636624i \(0.219670\pi\)
\(114\) 0.472778 1.12830i 0.0442797 0.105675i
\(115\) 11.0810 3.60042i 1.03330 0.335741i
\(116\) −2.84802 + 2.80176i −0.264432 + 0.260137i
\(117\) 4.16596 5.73396i 0.385143 0.530104i
\(118\) −0.324400 + 0.376690i −0.0298634 + 0.0346771i
\(119\) 5.54615 17.0693i 0.508415 1.56474i
\(120\) −2.83815 3.40690i −0.259086 0.311006i
\(121\) 6.78123 + 8.66112i 0.616475 + 0.787374i
\(122\) 4.24145 0.999934i 0.384003 0.0905298i
\(123\) −1.92680 0.626055i −0.173734 0.0564495i
\(124\) −4.77925 + 9.19293i −0.429189 + 0.825550i
\(125\) 2.70225 3.71933i 0.241697 0.332667i
\(126\) −8.52569 + 5.17666i −0.759529 + 0.461173i
\(127\) 3.06303 + 9.42703i 0.271800 + 0.836514i 0.990048 + 0.140727i \(0.0449440\pi\)
−0.718249 + 0.695787i \(0.755056\pi\)
\(128\) 9.47318 + 6.18538i 0.837318 + 0.546716i
\(129\) −1.08063 + 0.785124i −0.0951442 + 0.0691263i
\(130\) −10.7009 0.886275i −0.938532 0.0777315i
\(131\) 11.4291i 0.998568i −0.866438 0.499284i \(-0.833596\pi\)
0.866438 0.499284i \(-0.166404\pi\)
\(132\) −0.0350652 3.58462i −0.00305204 0.312001i
\(133\) 4.16892i 0.361491i
\(134\) 1.21335 14.6500i 0.104817 1.26557i
\(135\) −7.23946 + 5.25978i −0.623074 + 0.452689i
\(136\) 1.29047 + 19.4480i 0.110657 + 1.66765i
\(137\) 0.362610 + 1.11600i 0.0309799 + 0.0953463i 0.965351 0.260955i \(-0.0840375\pi\)
−0.934371 + 0.356302i \(0.884038\pi\)
\(138\) −1.59317 2.62386i −0.135619 0.223358i
\(139\) −4.25643 + 5.85848i −0.361026 + 0.496909i −0.950434 0.310926i \(-0.899361\pi\)
0.589408 + 0.807835i \(0.299361\pi\)
\(140\) 13.4072 + 6.97017i 1.13312 + 0.589087i
\(141\) 6.08896 + 1.97842i 0.512783 + 0.166613i
\(142\) 1.12613 + 4.77675i 0.0945029 + 0.400856i
\(143\) −6.24748 6.02689i −0.522441 0.503994i
\(144\) 6.50939 8.65764i 0.542449 0.721470i
\(145\) 1.79067 5.51111i 0.148707 0.457673i
\(146\) −1.42996 1.23146i −0.118344 0.101916i
\(147\) 0.0687867 0.0946768i 0.00567343 0.00780881i
\(148\) 12.2463 12.0474i 1.00664 0.990289i
\(149\) 11.6889 3.79794i 0.957589 0.311139i 0.211793 0.977315i \(-0.432070\pi\)
0.745795 + 0.666175i \(0.232070\pi\)
\(150\) 2.40737 + 1.00873i 0.196561 + 0.0823625i
\(151\) −11.6953 + 8.49716i −0.951753 + 0.691489i −0.951221 0.308511i \(-0.900169\pi\)
−0.000531993 1.00000i \(0.500169\pi\)
\(152\) −1.68104 4.20368i −0.136350 0.340963i
\(153\) 18.6605 1.50861
\(154\) 4.83110 + 11.2204i 0.389301 + 0.904162i
\(155\) 15.0281i 1.20709i
\(156\) 0.419652 + 2.79765i 0.0335991 + 0.223991i
\(157\) 10.4310 + 14.3570i 0.832482 + 1.14581i 0.987456 + 0.157894i \(0.0504706\pi\)
−0.154974 + 0.987919i \(0.549529\pi\)
\(158\) 2.36259 5.63840i 0.187958 0.448567i
\(159\) −0.216067 0.664984i −0.0171352 0.0527367i
\(160\) −16.3296 1.62209i −1.29097 0.128238i
\(161\) 8.46295 + 6.14869i 0.666974 + 0.484585i
\(162\) −6.91910 5.95863i −0.543616 0.468154i
\(163\) 5.48140 + 1.78101i 0.429336 + 0.139500i 0.515710 0.856763i \(-0.327528\pi\)
−0.0863742 + 0.996263i \(0.527528\pi\)
\(164\) −6.70807 + 3.34903i −0.523812 + 0.261516i
\(165\) 2.44341 + 4.58967i 0.190219 + 0.357305i
\(166\) −21.9994 + 5.18642i −1.70748 + 0.402545i
\(167\) −0.730775 + 2.24909i −0.0565491 + 0.174040i −0.975342 0.220701i \(-0.929166\pi\)
0.918793 + 0.394741i \(0.129166\pi\)
\(168\) 0.976853 3.85944i 0.0753659 0.297762i
\(169\) −4.97513 3.61464i −0.382702 0.278050i
\(170\) −14.6724 24.1647i −1.12532 1.85335i
\(171\) −4.12233 + 1.33943i −0.315243 + 0.102429i
\(172\) −0.813245 + 4.87589i −0.0620093 + 0.371783i
\(173\) −1.45606 2.00409i −0.110702 0.152368i 0.750071 0.661357i \(-0.230019\pi\)
−0.860773 + 0.508989i \(0.830019\pi\)
\(174\) −1.52149 0.126013i −0.115344 0.00955304i
\(175\) −8.89490 −0.672391
\(176\) −9.39577 9.36587i −0.708233 0.705979i
\(177\) −0.189970 −0.0142790
\(178\) −18.4968 1.53195i −1.38640 0.114825i
\(179\) 12.0304 + 16.5584i 0.899195 + 1.23764i 0.970724 + 0.240197i \(0.0772119\pi\)
−0.0715297 + 0.997438i \(0.522788\pi\)
\(180\) −2.58470 + 15.4968i −0.192652 + 1.15507i
\(181\) −16.4003 + 5.32879i −1.21903 + 0.396086i −0.846727 0.532027i \(-0.821430\pi\)
−0.372299 + 0.928113i \(0.621430\pi\)
\(182\) −5.00344 8.24041i −0.370880 0.610820i
\(183\) 1.34722 + 0.978815i 0.0995896 + 0.0723561i
\(184\) −11.0129 2.78744i −0.811878 0.205493i
\(185\) −7.69977 + 23.6975i −0.566098 + 1.74227i
\(186\) −3.85372 + 0.908526i −0.282568 + 0.0666164i
\(187\) 3.16910 22.6342i 0.231748 1.65517i
\(188\) 21.1985 10.5834i 1.54606 0.771875i
\(189\) −7.64097 2.48270i −0.555798 0.180590i
\(190\) 4.97583 + 4.28511i 0.360985 + 0.310875i
\(191\) −16.4049 11.9189i −1.18702 0.862419i −0.194072 0.980987i \(-0.562170\pi\)
−0.992946 + 0.118568i \(0.962170\pi\)
\(192\) 0.571245 + 4.28551i 0.0412261 + 0.309280i
\(193\) 0.797696 + 2.45506i 0.0574194 + 0.176719i 0.975653 0.219321i \(-0.0703842\pi\)
−0.918233 + 0.396040i \(0.870384\pi\)
\(194\) 4.70711 11.2337i 0.337951 0.806531i
\(195\) −2.41183 3.31959i −0.172714 0.237721i
\(196\) −0.0642456 0.428299i −0.00458897 0.0305928i
\(197\) 21.0439i 1.49931i −0.661826 0.749657i \(-0.730218\pi\)
0.661826 0.749657i \(-0.269782\pi\)
\(198\) −9.54280 + 8.38209i −0.678177 + 0.595689i
\(199\) 7.98438 0.565998 0.282999 0.959120i \(-0.408671\pi\)
0.282999 + 0.959120i \(0.408671\pi\)
\(200\) 8.96907 3.58670i 0.634209 0.253618i
\(201\) 4.54467 3.30189i 0.320556 0.232898i
\(202\) −11.3554 4.75814i −0.798966 0.334781i
\(203\) 4.94803 1.60771i 0.347284 0.112839i
\(204\) −5.30962 + 5.22337i −0.371747 + 0.365709i
\(205\) 6.39211 8.79798i 0.446444 0.614477i
\(206\) −1.33692 1.15133i −0.0931473 0.0802171i
\(207\) −3.36093 + 10.3439i −0.233601 + 0.718950i
\(208\) 8.36794 + 6.29158i 0.580213 + 0.436242i
\(209\) 0.924559 + 5.22764i 0.0639531 + 0.361604i
\(210\) 1.32502 + 5.62036i 0.0914349 + 0.387842i
\(211\) 8.96458 + 2.91277i 0.617147 + 0.200523i 0.600873 0.799344i \(-0.294820\pi\)
0.0162737 + 0.999868i \(0.494820\pi\)
\(212\) −2.29588 1.19359i −0.157681 0.0819759i
\(213\) −1.10235 + 1.51725i −0.0755316 + 0.103960i
\(214\) 13.7825 + 22.6990i 0.942150 + 1.55167i
\(215\) −2.21563 6.81900i −0.151105 0.465052i
\(216\) 8.70578 0.577671i 0.592353 0.0393056i
\(217\) 10.9158 7.93081i 0.741014 0.538378i
\(218\) −1.42153 + 17.1635i −0.0962779 + 1.16246i
\(219\) 0.721148i 0.0487307i
\(220\) 18.3579 + 5.76692i 1.23769 + 0.388806i
\(221\) 18.0361i 1.21324i
\(222\) 6.54231 + 0.541850i 0.439091 + 0.0363666i
\(223\) −11.7366 + 8.52716i −0.785943 + 0.571021i −0.906757 0.421654i \(-0.861450\pi\)
0.120814 + 0.992675i \(0.461450\pi\)
\(224\) −7.43939 12.7172i −0.497065 0.849701i
\(225\) −2.85783 8.79551i −0.190522 0.586367i
\(226\) 6.41719 3.89641i 0.426865 0.259185i
\(227\) 1.60136 2.20409i 0.106286 0.146291i −0.752560 0.658523i \(-0.771181\pi\)
0.858847 + 0.512233i \(0.171181\pi\)
\(228\) 0.798033 1.53503i 0.0528510 0.101660i
\(229\) −13.2781 4.31433i −0.877444 0.285099i −0.164549 0.986369i \(-0.552617\pi\)
−0.712896 + 0.701270i \(0.752617\pi\)
\(230\) 16.0376 3.78092i 1.05749 0.249307i
\(231\) −2.04428 + 4.19690i −0.134504 + 0.276136i
\(232\) −4.34101 + 3.61632i −0.285001 + 0.237423i
\(233\) 3.84177 11.8238i 0.251683 0.774600i −0.742782 0.669533i \(-0.766494\pi\)
0.994465 0.105067i \(-0.0335057\pi\)
\(234\) 6.54078 7.59508i 0.427584 0.496506i
\(235\) −20.2000 + 27.8029i −1.31770 + 1.81366i
\(236\) −0.501176 + 0.493035i −0.0326238 + 0.0320938i
\(237\) 2.22183 0.721915i 0.144323 0.0468934i
\(238\) 9.80916 23.4099i 0.635833 1.51744i
\(239\) 14.4442 10.4943i 0.934320 0.678823i −0.0127269 0.999919i \(-0.504051\pi\)
0.947047 + 0.321096i \(0.104051\pi\)
\(240\) −3.60237 5.13294i −0.232532 0.331330i
\(241\) 0.714420 0.0460198 0.0230099 0.999735i \(-0.492675\pi\)
0.0230099 + 0.999735i \(0.492675\pi\)
\(242\) 8.54638 + 12.9984i 0.549382 + 0.835571i
\(243\) 12.7436i 0.817501i
\(244\) 6.09457 0.914196i 0.390165 0.0585254i
\(245\) 0.369232 + 0.508204i 0.0235894 + 0.0324680i
\(246\) −2.64253 1.10727i −0.168482 0.0705968i
\(247\) −1.29461 3.98439i −0.0823739 0.253521i
\(248\) −7.80889 + 12.3985i −0.495865 + 0.787307i
\(249\) −6.98773 5.07688i −0.442829 0.321734i
\(250\) 4.24268 4.92655i 0.268331 0.311583i
\(251\) −1.43791 0.467205i −0.0907600 0.0294897i 0.263285 0.964718i \(-0.415194\pi\)
−0.354045 + 0.935228i \(0.615194\pi\)
\(252\) −12.6203 + 6.30073i −0.795002 + 0.396908i
\(253\) 11.9758 + 5.83333i 0.752912 + 0.366738i
\(254\) 3.21659 + 13.6439i 0.201827 + 0.856094i
\(255\) 3.33838 10.2745i 0.209057 0.643412i
\(256\) 12.6294 + 9.82339i 0.789335 + 0.613962i
\(257\) 14.9092 + 10.8321i 0.930007 + 0.675690i 0.945995 0.324182i \(-0.105089\pi\)
−0.0159873 + 0.999872i \(0.505089\pi\)
\(258\) −1.61467 + 0.980403i −0.100525 + 0.0610373i
\(259\) −21.2762 + 6.91307i −1.32204 + 0.429557i
\(260\) −14.9783 2.49821i −0.928913 0.154932i
\(261\) 3.17949 + 4.37620i 0.196806 + 0.270880i
\(262\) 1.33411 16.1081i 0.0824216 0.995161i
\(263\) 11.2903 0.696191 0.348096 0.937459i \(-0.386828\pi\)
0.348096 + 0.937459i \(0.386828\pi\)
\(264\) 0.369008 5.05621i 0.0227109 0.311188i
\(265\) 3.75319 0.230556
\(266\) −0.486633 + 5.87562i −0.0298374 + 0.360257i
\(267\) −4.16891 5.73801i −0.255133 0.351161i
\(268\) 3.42016 20.5059i 0.208919 1.25260i
\(269\) −16.7217 + 5.43320i −1.01954 + 0.331268i −0.770646 0.637263i \(-0.780066\pi\)
−0.248892 + 0.968531i \(0.580066\pi\)
\(270\) −10.8172 + 6.56801i −0.658312 + 0.399716i
\(271\) −5.28024 3.83632i −0.320752 0.233040i 0.415744 0.909481i \(-0.363521\pi\)
−0.736496 + 0.676442i \(0.763521\pi\)
\(272\) −0.451369 + 27.5604i −0.0273683 + 1.67109i
\(273\) 1.13842 3.50370i 0.0689004 0.212054i
\(274\) 0.380789 + 1.61520i 0.0230043 + 0.0975780i
\(275\) −11.1538 + 1.97266i −0.672601 + 0.118956i
\(276\) −1.93911 3.88401i −0.116721 0.233790i
\(277\) 0.243758 + 0.0792018i 0.0146460 + 0.00475877i 0.316331 0.948649i \(-0.397549\pi\)
−0.301685 + 0.953408i \(0.597549\pi\)
\(278\) −6.68282 + 7.76002i −0.400809 + 0.465415i
\(279\) 11.3493 + 8.24576i 0.679466 + 0.493661i
\(280\) 18.0823 + 11.3887i 1.08063 + 0.680604i
\(281\) −8.02159 24.6879i −0.478528 1.47276i −0.841140 0.540818i \(-0.818115\pi\)
0.362612 0.931940i \(-0.381885\pi\)
\(282\) 8.35077 + 3.49912i 0.497281 + 0.208370i
\(283\) 5.53179 + 7.61385i 0.328831 + 0.452597i 0.941138 0.338024i \(-0.109758\pi\)
−0.612307 + 0.790620i \(0.709758\pi\)
\(284\) 1.02957 + 6.86374i 0.0610939 + 0.407288i
\(285\) 2.50938i 0.148643i
\(286\) −8.10161 9.22349i −0.479058 0.545396i
\(287\) 9.76379 0.576339
\(288\) 10.1849 11.4421i 0.600148 0.674235i
\(289\) −24.6639 + 17.9194i −1.45082 + 1.05408i
\(290\) 3.16705 7.55827i 0.185976 0.443837i
\(291\) 4.42665 1.43831i 0.259495 0.0843151i
\(292\) −1.87162 1.90252i −0.109528 0.111337i
\(293\) 1.12821 1.55285i 0.0659107 0.0907182i −0.774789 0.632220i \(-0.782144\pi\)
0.840700 + 0.541502i \(0.182144\pi\)
\(294\) 0.107999 0.125407i 0.00629861 0.00731388i
\(295\) 0.315110 0.969810i 0.0183464 0.0564645i
\(296\) 18.6661 15.5499i 1.08494 0.903822i
\(297\) −10.1320 1.41863i −0.587921 0.0823172i
\(298\) 16.9175 3.98834i 0.980002 0.231039i
\(299\) −9.99777 3.24847i −0.578186 0.187864i
\(300\) 3.27517 + 1.70270i 0.189092 + 0.0983056i
\(301\) 3.78379 5.20793i 0.218094 0.300180i
\(302\) −17.4751 + 10.6106i −1.00558 + 0.610572i
\(303\) −1.45390 4.47464i −0.0835243 0.257061i
\(304\) −1.87854 6.12084i −0.107742 0.351054i
\(305\) −7.23160 + 5.25407i −0.414080 + 0.300847i
\(306\) 26.2998 + 2.17822i 1.50346 + 0.124520i
\(307\) 10.2272i 0.583696i 0.956465 + 0.291848i \(0.0942702\pi\)
−0.956465 + 0.291848i \(0.905730\pi\)
\(308\) 5.49915 + 16.3778i 0.313343 + 0.933210i
\(309\) 0.674226i 0.0383554i
\(310\) 1.75422 21.1805i 0.0996330 1.20297i
\(311\) 12.1023 8.79286i 0.686261 0.498598i −0.189168 0.981945i \(-0.560579\pi\)
0.875429 + 0.483347i \(0.160579\pi\)
\(312\) 0.264886 + 3.99196i 0.0149962 + 0.226000i
\(313\) −1.50236 4.62380i −0.0849186 0.261353i 0.899577 0.436762i \(-0.143875\pi\)
−0.984496 + 0.175410i \(0.943875\pi\)
\(314\) 13.0254 + 21.4522i 0.735066 + 1.21062i
\(315\) 12.0258 16.5521i 0.677579 0.932607i
\(316\) 3.98798 7.67092i 0.224341 0.431523i
\(317\) −10.1662 3.30321i −0.570992 0.185527i 0.00926917 0.999957i \(-0.497049\pi\)
−0.580261 + 0.814431i \(0.697049\pi\)
\(318\) −0.226899 0.962442i −0.0127238 0.0539711i
\(319\) 5.84807 3.11335i 0.327429 0.174314i
\(320\) −22.8254 4.19229i −1.27598 0.234356i
\(321\) −3.13589 + 9.65129i −0.175028 + 0.538682i
\(322\) 11.2098 + 9.65376i 0.624700 + 0.537983i
\(323\) 6.48336 8.92358i 0.360744 0.496521i
\(324\) −9.05615 9.20568i −0.503119 0.511427i
\(325\) 8.50120 2.76221i 0.471561 0.153220i
\(326\) 7.51752 + 3.14998i 0.416357 + 0.174461i
\(327\) −5.32441 + 3.86841i −0.294440 + 0.213924i
\(328\) −9.84520 + 3.93706i −0.543610 + 0.217388i
\(329\) −30.8550 −1.70109
\(330\) 2.90797 + 6.75384i 0.160078 + 0.371787i
\(331\) 21.3447i 1.17321i 0.809874 + 0.586604i \(0.199536\pi\)
−0.809874 + 0.586604i \(0.800464\pi\)
\(332\) −31.6111 + 4.74172i −1.73488 + 0.260236i
\(333\) −13.6716 18.8174i −0.749201 1.03119i
\(334\) −1.29248 + 3.08454i −0.0707213 + 0.168779i
\(335\) 9.31798 + 28.6778i 0.509095 + 1.56683i
\(336\) 1.82727 5.32542i 0.0996859 0.290525i
\(337\) −6.33981 4.60614i −0.345351 0.250913i 0.401565 0.915831i \(-0.368466\pi\)
−0.746916 + 0.664918i \(0.768466\pi\)
\(338\) −6.58996 5.67518i −0.358446 0.308689i
\(339\) 2.72849 + 0.886541i 0.148191 + 0.0481503i
\(340\) −17.8584 35.7701i −0.968507 1.93991i
\(341\) 11.9291 12.3657i 0.645998 0.669643i
\(342\) −5.96631 + 1.40658i −0.322621 + 0.0760589i
\(343\) −5.80814 + 17.8756i −0.313610 + 0.965193i
\(344\) −1.71533 + 6.77709i −0.0924847 + 0.365396i
\(345\) 5.09408 + 3.70106i 0.274256 + 0.199259i
\(346\) −1.81822 2.99451i −0.0977479 0.160986i
\(347\) 25.9390 8.42811i 1.39248 0.452444i 0.485729 0.874109i \(-0.338554\pi\)
0.906752 + 0.421665i \(0.138554\pi\)
\(348\) −2.12966 0.355203i −0.114162 0.0190409i
\(349\) −4.40503 6.06300i −0.235796 0.324545i 0.674678 0.738112i \(-0.264283\pi\)
−0.910474 + 0.413567i \(0.864283\pi\)
\(350\) −12.5364 1.03829i −0.670097 0.0554990i
\(351\) 8.07373 0.430944
\(352\) −12.1490 14.2969i −0.647545 0.762027i
\(353\) 18.1327 0.965105 0.482552 0.875867i \(-0.339710\pi\)
0.482552 + 0.875867i \(0.339710\pi\)
\(354\) −0.267742 0.0221750i −0.0142303 0.00117859i
\(355\) −5.91716 8.14428i −0.314050 0.432253i
\(356\) −25.8904 4.31823i −1.37219 0.228866i
\(357\) 9.22471 2.99729i 0.488224 0.158633i
\(358\) 15.0227 + 24.7415i 0.793972 + 1.30763i
\(359\) 3.89757 + 2.83175i 0.205706 + 0.149454i 0.685869 0.727725i \(-0.259422\pi\)
−0.480163 + 0.877179i \(0.659422\pi\)
\(360\) −5.45177 + 21.5393i −0.287334 + 1.13522i
\(361\) 5.07959 15.6334i 0.267347 0.822809i
\(362\) −23.7364 + 5.59594i −1.24756 + 0.294116i
\(363\) −1.63268 + 5.71610i −0.0856933 + 0.300018i
\(364\) −6.08989 12.1980i −0.319197 0.639348i
\(365\) 3.68151 + 1.19619i 0.192699 + 0.0626117i
\(366\) 1.78450 + 1.53679i 0.0932775 + 0.0803293i
\(367\) 6.83396 + 4.96517i 0.356730 + 0.259180i 0.751687 0.659520i \(-0.229240\pi\)
−0.394957 + 0.918700i \(0.629240\pi\)
\(368\) −15.1960 5.21410i −0.792147 0.271804i
\(369\) 3.13700 + 9.65469i 0.163306 + 0.502603i
\(370\) −13.6181 + 32.5001i −0.707973 + 1.68960i
\(371\) 1.98067 + 2.72616i 0.102831 + 0.141535i
\(372\) −5.53744 + 0.830625i −0.287103 + 0.0430659i
\(373\) 27.7651i 1.43762i 0.695207 + 0.718810i \(0.255313\pi\)
−0.695207 + 0.718810i \(0.744687\pi\)
\(374\) 7.10856 31.5304i 0.367575 1.63040i
\(375\) 2.48453 0.128301
\(376\) 31.1122 12.4417i 1.60449 0.641630i
\(377\) −4.22976 + 3.07310i −0.217844 + 0.158273i
\(378\) −10.4793 4.39101i −0.538996 0.225849i
\(379\) 14.5832 4.73836i 0.749087 0.243393i 0.0904987 0.995897i \(-0.471154\pi\)
0.658588 + 0.752503i \(0.271154\pi\)
\(380\) 6.51268 + 6.62021i 0.334093 + 0.339610i
\(381\) −3.14865 + 4.33375i −0.161310 + 0.222025i
\(382\) −21.7296 18.7132i −1.11178 0.957452i
\(383\) −3.66763 + 11.2878i −0.187407 + 0.576780i −0.999982 0.00607729i \(-0.998066\pi\)
0.812574 + 0.582858i \(0.198066\pi\)
\(384\) 0.304863 + 6.10663i 0.0155575 + 0.311628i
\(385\) −18.0345 17.3977i −0.919124 0.886671i
\(386\) 0.837687 + 3.55324i 0.0426371 + 0.180855i
\(387\) 6.36543 + 2.06825i 0.323573 + 0.105135i
\(388\) 7.94544 15.2831i 0.403369 0.775884i
\(389\) −2.66981 + 3.67468i −0.135365 + 0.186314i −0.871318 0.490719i \(-0.836734\pi\)
0.735953 + 0.677032i \(0.236734\pi\)
\(390\) −3.01171 4.96013i −0.152504 0.251166i
\(391\) −8.55273 26.3226i −0.432530 1.33119i
\(392\) −0.0405521 0.611138i −0.00204819 0.0308672i
\(393\) 4.99699 3.63052i 0.252065 0.183136i
\(394\) 2.45643 29.6590i 0.123753 1.49420i
\(395\) 12.5400i 0.630958i
\(396\) −14.4279 + 10.6997i −0.725031 + 0.537680i
\(397\) 10.8631i 0.545204i −0.962127 0.272602i \(-0.912116\pi\)
0.962127 0.272602i \(-0.0878841\pi\)
\(398\) 11.2531 + 0.932008i 0.564066 + 0.0467173i
\(399\) −1.82271 + 1.32428i −0.0912497 + 0.0662968i
\(400\) 13.0596 4.00810i 0.652978 0.200405i
\(401\) 0.717382 + 2.20787i 0.0358243 + 0.110256i 0.967370 0.253369i \(-0.0815388\pi\)
−0.931545 + 0.363625i \(0.881539\pi\)
\(402\) 6.79062 4.12315i 0.338685 0.205644i
\(403\) −7.96985 + 10.9696i −0.397006 + 0.546432i
\(404\) −15.4488 8.03157i −0.768607 0.399586i
\(405\) 17.8136 + 5.78800i 0.885166 + 0.287608i
\(406\) 7.16136 1.68831i 0.355412 0.0837895i
\(407\) −25.1464 + 13.3872i −1.24646 + 0.663580i
\(408\) −8.09303 + 6.74197i −0.400664 + 0.333777i
\(409\) −7.79638 + 23.9948i −0.385506 + 1.18647i 0.550606 + 0.834765i \(0.314397\pi\)
−0.936112 + 0.351701i \(0.885603\pi\)
\(410\) 10.0359 11.6536i 0.495640 0.575531i
\(411\) −0.372746 + 0.513042i −0.0183862 + 0.0253065i
\(412\) −1.74984 1.77873i −0.0862083 0.0876318i
\(413\) 0.870723 0.282915i 0.0428455 0.0139213i
\(414\) −5.94429 + 14.1862i −0.292146 + 0.697215i
\(415\) 37.5086 27.2516i 1.84123 1.33773i
\(416\) 11.0593 + 9.84405i 0.542225 + 0.482644i
\(417\) −3.91349 −0.191644
\(418\) 0.692845 + 7.47570i 0.0338882 + 0.365648i
\(419\) 16.7174i 0.816696i −0.912826 0.408348i \(-0.866105\pi\)
0.912826 0.408348i \(-0.133895\pi\)
\(420\) 1.21140 + 8.07594i 0.0591105 + 0.394065i
\(421\) 5.58527 + 7.68747i 0.272209 + 0.374664i 0.923134 0.384478i \(-0.125619\pi\)
−0.650925 + 0.759142i \(0.725619\pi\)
\(422\) 12.2946 + 5.15164i 0.598490 + 0.250778i
\(423\) −9.91336 30.5102i −0.482004 1.48346i
\(424\) −3.09646 1.95022i −0.150377 0.0947111i
\(425\) 19.0396 + 13.8331i 0.923555 + 0.671002i
\(426\) −1.73074 + 2.00972i −0.0838548 + 0.0973713i
\(427\) −7.63267 2.48001i −0.369371 0.120016i
\(428\) 16.7752 + 33.6005i 0.810860 + 1.62414i
\(429\) 0.650501 4.64596i 0.0314065 0.224309i
\(430\) −2.32670 9.86925i −0.112204 0.475937i
\(431\) −9.62842 + 29.6332i −0.463785 + 1.42738i 0.396720 + 0.917940i \(0.370148\pi\)
−0.860505 + 0.509443i \(0.829852\pi\)
\(432\) 12.3372 + 0.202052i 0.593576 + 0.00972126i
\(433\) 4.03731 + 2.93328i 0.194021 + 0.140964i 0.680555 0.732697i \(-0.261739\pi\)
−0.486534 + 0.873662i \(0.661739\pi\)
\(434\) 16.3104 9.90340i 0.782924 0.475378i
\(435\) 2.97835 0.967726i 0.142801 0.0463989i
\(436\) −4.00696 + 24.0242i −0.191899 + 1.15055i
\(437\) 3.77881 + 5.20109i 0.180765 + 0.248802i
\(438\) 0.0841788 1.01638i 0.00402222 0.0485644i
\(439\) 22.9729 1.09644 0.548219 0.836335i \(-0.315306\pi\)
0.548219 + 0.836335i \(0.315306\pi\)
\(440\) 25.2002 + 10.2707i 1.20137 + 0.489638i
\(441\) −0.586391 −0.0279234
\(442\) −2.10533 + 25.4198i −0.100140 + 1.20910i
\(443\) −16.7191 23.0119i −0.794350 1.09333i −0.993553 0.113371i \(-0.963835\pi\)
0.199203 0.979958i \(-0.436165\pi\)
\(444\) 9.15740 + 1.52735i 0.434591 + 0.0724850i
\(445\) 36.2080 11.7647i 1.71643 0.557701i
\(446\) −17.5368 + 10.6481i −0.830393 + 0.504201i
\(447\) 5.37354 + 3.90411i 0.254160 + 0.184658i
\(448\) −9.00053 18.7918i −0.425235 0.887829i
\(449\) 3.51971 10.8326i 0.166106 0.511220i −0.833010 0.553257i \(-0.813385\pi\)
0.999116 + 0.0420368i \(0.0133847\pi\)
\(450\) −3.00111 12.7299i −0.141473 0.600092i
\(451\) 12.2434 2.16536i 0.576518 0.101963i
\(452\) 9.49913 4.74248i 0.446801 0.223068i
\(453\) −7.43017 2.41421i −0.349100 0.113429i
\(454\) 2.51422 2.91949i 0.117998 0.137018i
\(455\) 15.9983 + 11.6234i 0.750011 + 0.544915i
\(456\) 1.30392 2.07029i 0.0610616 0.0969503i
\(457\) 4.30346 + 13.2447i 0.201307 + 0.619560i 0.999845 + 0.0176152i \(0.00560737\pi\)
−0.798538 + 0.601945i \(0.794393\pi\)
\(458\) −18.2104 7.63051i −0.850918 0.356550i
\(459\) 12.4945 + 17.1972i 0.583193 + 0.802697i
\(460\) 23.0446 3.45673i 1.07446 0.161171i
\(461\) 12.8159i 0.596895i −0.954426 0.298447i \(-0.903531\pi\)
0.954426 0.298447i \(-0.0964687\pi\)
\(462\) −3.37109 + 5.67643i −0.156837 + 0.264092i
\(463\) −38.2137 −1.77594 −0.887970 0.459902i \(-0.847884\pi\)
−0.887970 + 0.459902i \(0.847884\pi\)
\(464\) −6.54029 + 4.59007i −0.303625 + 0.213089i
\(465\) 6.57053 4.77377i 0.304701 0.221378i
\(466\) 6.79472 16.2158i 0.314759 0.751183i
\(467\) −31.0499 + 10.0887i −1.43682 + 0.466851i −0.920904 0.389789i \(-0.872548\pi\)
−0.515915 + 0.856640i \(0.672548\pi\)
\(468\) 10.1051 9.94092i 0.467106 0.459519i
\(469\) −15.9130 + 21.9023i −0.734793 + 1.01136i
\(470\) −31.7150 + 36.8271i −1.46290 + 1.69871i
\(471\) −2.96364 + 9.12115i −0.136557 + 0.420280i
\(472\) −0.763903 + 0.636376i −0.0351615 + 0.0292916i
\(473\) 3.58972 7.36967i 0.165055 0.338858i
\(474\) 3.21568 0.758107i 0.147701 0.0348210i
\(475\) −5.19900 1.68926i −0.238546 0.0775084i
\(476\) 16.5575 31.8486i 0.758913 1.45978i
\(477\) −2.05933 + 2.83442i −0.0942901 + 0.129779i
\(478\) 21.5825 13.1046i 0.987162 0.599388i
\(479\) −8.04318 24.7544i −0.367502 1.13106i −0.948399 0.317079i \(-0.897298\pi\)
0.580897 0.813977i \(-0.302702\pi\)
\(480\) −4.47797 7.65480i −0.204391 0.349392i
\(481\) 18.1877 13.2142i 0.829290 0.602514i
\(482\) 1.00689 + 0.0833934i 0.0458628 + 0.00379847i
\(483\) 5.65329i 0.257234i
\(484\) 10.5279 + 19.3175i 0.478539 + 0.878066i
\(485\) 24.9841i 1.13447i
\(486\) 1.48754 17.9606i 0.0674764 0.814711i
\(487\) −4.51476 + 3.28017i −0.204583 + 0.148638i −0.685360 0.728205i \(-0.740355\pi\)
0.480776 + 0.876843i \(0.340355\pi\)
\(488\) 8.69632 0.577044i 0.393664 0.0261216i
\(489\) 0.962508 + 2.96230i 0.0435261 + 0.133960i
\(490\) 0.461069 + 0.759357i 0.0208290 + 0.0343043i
\(491\) −14.3870 + 19.8019i −0.649274 + 0.893649i −0.999067 0.0431777i \(-0.986252\pi\)
0.349793 + 0.936827i \(0.386252\pi\)
\(492\) −3.59510 1.86903i −0.162080 0.0842624i
\(493\) −13.0915 4.25370i −0.589613 0.191577i
\(494\) −1.35951 5.76667i −0.0611673 0.259455i
\(495\) 11.4090 23.4227i 0.512798 1.05277i
\(496\) −12.4530 + 16.5628i −0.559157 + 0.743692i
\(497\) 2.79300 8.59596i 0.125283 0.385582i
\(498\) −9.25580 7.97097i −0.414762 0.357188i
\(499\) 12.3320 16.9736i 0.552057 0.759842i −0.438232 0.898862i \(-0.644395\pi\)
0.990290 + 0.139020i \(0.0443952\pi\)
\(500\) 6.55465 6.44818i 0.293133 0.288371i
\(501\) −1.21547 + 0.394931i −0.0543033 + 0.0176442i
\(502\) −1.97203 0.826318i −0.0880162 0.0368804i
\(503\) −19.7116 + 14.3213i −0.878898 + 0.638557i −0.932960 0.359981i \(-0.882783\pi\)
0.0540618 + 0.998538i \(0.482783\pi\)
\(504\) −18.5223 + 7.40702i −0.825050 + 0.329935i
\(505\) 25.2550 1.12383
\(506\) 16.1976 + 9.61935i 0.720072 + 0.427632i
\(507\) 3.32341i 0.147598i
\(508\) 2.94078 + 19.6050i 0.130476 + 0.869831i
\(509\) −17.7289 24.4017i −0.785818 1.08159i −0.994616 0.103627i \(-0.966955\pi\)
0.208798 0.977959i \(-0.433045\pi\)
\(510\) 5.90440 14.0910i 0.261451 0.623961i
\(511\) 1.07398 + 3.30536i 0.0475100 + 0.146221i
\(512\) 16.6530 + 15.3192i 0.735966 + 0.677019i
\(513\) −3.99459 2.90224i −0.176365 0.128137i
\(514\) 19.7484 + 17.0070i 0.871063 + 0.750147i
\(515\) 3.44197 + 1.11836i 0.151671 + 0.0492810i
\(516\) −2.39014 + 1.19329i −0.105220 + 0.0525316i
\(517\) −38.6908 + 6.84284i −1.70162 + 0.300948i
\(518\) −30.7934 + 7.25965i −1.35299 + 0.318971i
\(519\) 0.413694 1.27322i 0.0181592 0.0558882i
\(520\) −20.8186 5.26935i −0.912956 0.231076i
\(521\) 19.7953 + 14.3821i 0.867246 + 0.630091i 0.929847 0.367947i \(-0.119939\pi\)
−0.0626003 + 0.998039i \(0.519939\pi\)
\(522\) 3.97031 + 6.53890i 0.173776 + 0.286200i
\(523\) 15.6714 5.09195i 0.685263 0.222655i 0.0543647 0.998521i \(-0.482687\pi\)
0.630898 + 0.775866i \(0.282687\pi\)
\(524\) 3.76056 22.5468i 0.164281 0.984962i
\(525\) −2.82551 3.88898i −0.123315 0.169729i
\(526\) 15.9124 + 1.31791i 0.693816 + 0.0574635i
\(527\) −35.6991 −1.55508
\(528\) 1.11028 7.08309i 0.0483188 0.308252i
\(529\) −6.86841 −0.298626
\(530\) 5.28970 + 0.438105i 0.229770 + 0.0190301i
\(531\) 0.559507 + 0.770095i 0.0242805 + 0.0334193i
\(532\) −1.37171 + 8.22423i −0.0594712 + 0.356565i
\(533\) −9.33163 + 3.03203i −0.404198 + 0.131332i
\(534\) −5.20582 8.57372i −0.225278 0.371021i
\(535\) −44.0688 32.0179i −1.90526 1.38425i
\(536\) 7.21396 28.5015i 0.311596 1.23108i
\(537\) −3.41807 + 10.5197i −0.147501 + 0.453960i
\(538\) −24.2015 + 5.70558i −1.04340 + 0.245985i
\(539\) −0.0995866 + 0.711261i −0.00428950 + 0.0306362i
\(540\) −16.0123 + 7.99420i −0.689059 + 0.344016i
\(541\) −13.9748 4.54069i −0.600824 0.195220i −0.00721621 0.999974i \(-0.502297\pi\)
−0.593608 + 0.804754i \(0.702297\pi\)
\(542\) −6.99410 6.02322i −0.300422 0.258719i
\(543\) −7.53947 5.47775i −0.323550 0.235073i
\(544\) −3.85325 + 38.7906i −0.165207 + 1.66313i
\(545\) −10.9167 33.5981i −0.467620 1.43919i
\(546\) 2.01346 4.80519i 0.0861682 0.205643i
\(547\) −13.1684 18.1248i −0.563041 0.774959i 0.428669 0.903462i \(-0.358983\pi\)
−0.991709 + 0.128503i \(0.958983\pi\)
\(548\) 0.348139 + 2.32090i 0.0148717 + 0.0991438i
\(549\) 8.34418i 0.356121i
\(550\) −15.9503 + 1.47827i −0.680125 + 0.0630337i
\(551\) 3.19741 0.136214
\(552\) −2.27958 5.70043i −0.0970254 0.242626i
\(553\) −9.10856 + 6.61776i −0.387335 + 0.281416i
\(554\) 0.334304 + 0.140080i 0.0142032 + 0.00595141i
\(555\) −12.8067 + 4.16117i −0.543616 + 0.176632i
\(556\) −10.3245 + 10.1568i −0.437856 + 0.430744i
\(557\) 2.36764 3.25878i 0.100320 0.138079i −0.755906 0.654681i \(-0.772803\pi\)
0.856226 + 0.516602i \(0.172803\pi\)
\(558\) 15.0331 + 12.9463i 0.636401 + 0.548059i
\(559\) −1.99905 + 6.15243i −0.0845506 + 0.260220i
\(560\) 24.1556 + 18.1618i 1.02076 + 0.767476i
\(561\) 10.9027 5.80428i 0.460311 0.245057i
\(562\) −8.42374 35.7312i −0.355334 1.50723i
\(563\) −2.31640 0.752644i −0.0976246 0.0317202i 0.259797 0.965663i \(-0.416344\pi\)
−0.357422 + 0.933943i \(0.616344\pi\)
\(564\) 11.3610 + 5.90640i 0.478385 + 0.248704i
\(565\) −9.05170 + 12.4586i −0.380808 + 0.524137i
\(566\) 6.90768 + 11.3766i 0.290351 + 0.478194i
\(567\) 5.19663 + 15.9936i 0.218238 + 0.671667i
\(568\) 0.649871 + 9.79386i 0.0272680 + 0.410941i
\(569\) 3.09710 2.25018i 0.129837 0.0943324i −0.520971 0.853574i \(-0.674430\pi\)
0.650808 + 0.759242i \(0.274430\pi\)
\(570\) −0.292918 + 3.53670i −0.0122690 + 0.148136i
\(571\) 42.5296i 1.77981i −0.456149 0.889903i \(-0.650772\pi\)
0.456149 0.889903i \(-0.349228\pi\)
\(572\) −10.3417 13.9452i −0.432407 0.583077i
\(573\) 10.9586i 0.457800i
\(574\) 13.7610 + 1.13972i 0.574372 + 0.0475709i
\(575\) −11.0972 + 8.06256i −0.462784 + 0.336232i
\(576\) 15.6900 14.9375i 0.653751 0.622398i
\(577\) 5.51240 + 16.9654i 0.229484 + 0.706280i 0.997805 + 0.0662151i \(0.0210924\pi\)
−0.768321 + 0.640064i \(0.778908\pi\)
\(578\) −36.8527 + 22.3763i −1.53287 + 0.930733i
\(579\) −0.819994 + 1.12863i −0.0340778 + 0.0469041i
\(580\) 5.34587 10.2828i 0.221975 0.426972i
\(581\) 39.5889 + 12.8632i 1.64242 + 0.533655i
\(582\) 6.40677 1.51041i 0.265569 0.0626087i
\(583\) 3.08827 + 2.97922i 0.127903 + 0.123387i
\(584\) −2.41576 2.89986i −0.0999647 0.119997i
\(585\) −6.35347 + 19.5540i −0.262684 + 0.808458i
\(586\) 1.77135 2.05687i 0.0731736 0.0849684i
\(587\) 0.341798 0.470445i 0.0141075 0.0194173i −0.801905 0.597452i \(-0.796180\pi\)
0.816012 + 0.578034i \(0.196180\pi\)
\(588\) 0.166851 0.164140i 0.00688080 0.00676904i
\(589\) 7.88638 2.56244i 0.324952 0.105583i
\(590\) 0.557317 1.33006i 0.0229444 0.0547575i
\(591\) 9.20070 6.68470i 0.378466 0.274972i
\(592\) 28.1229 19.7370i 1.15584 0.811187i
\(593\) 8.33594 0.342316 0.171158 0.985244i \(-0.445249\pi\)
0.171158 + 0.985244i \(0.445249\pi\)
\(594\) −14.1144 3.18210i −0.579120 0.130563i
\(595\) 52.0645i 2.13443i
\(596\) 24.3088 3.64637i 0.995728 0.149361i
\(597\) 2.53628 + 3.49089i 0.103803 + 0.142873i
\(598\) −13.7115 5.74538i −0.560707 0.234946i
\(599\) −2.22501 6.84789i −0.0909116 0.279797i 0.895255 0.445554i \(-0.146993\pi\)
−0.986167 + 0.165757i \(0.946993\pi\)
\(600\) 4.41723 + 2.78208i 0.180333 + 0.113578i
\(601\) −19.4703 14.1460i −0.794209 0.577027i 0.115001 0.993365i \(-0.463313\pi\)
−0.909210 + 0.416339i \(0.863313\pi\)
\(602\) 5.94074 6.89832i 0.242126 0.281155i
\(603\) −26.7702 8.69818i −1.09017 0.354217i
\(604\) −25.8678 + 12.9146i −1.05255 + 0.525488i
\(605\) −26.4729 17.8164i −1.07628 0.724341i
\(606\) −1.52679 6.47621i −0.0620215 0.263078i
\(607\) 7.27210 22.3812i 0.295165 0.908426i −0.688000 0.725710i \(-0.741511\pi\)
0.983166 0.182716i \(-0.0584888\pi\)
\(608\) −1.93311 8.84591i −0.0783981 0.358749i
\(609\) 2.27468 + 1.65265i 0.0921748 + 0.0669689i
\(610\) −10.8054 + 6.56088i −0.437499 + 0.265642i
\(611\) 29.4893 9.58164i 1.19301 0.387632i
\(612\) 36.8124 + 6.13990i 1.48805 + 0.248191i
\(613\) 24.2131 + 33.3265i 0.977957 + 1.34604i 0.937923 + 0.346845i \(0.112747\pi\)
0.0400347 + 0.999198i \(0.487253\pi\)
\(614\) −1.19381 + 14.4141i −0.0481782 + 0.581704i
\(615\) 5.87709 0.236987
\(616\) 5.83867 + 23.7245i 0.235247 + 0.955889i
\(617\) 14.6295 0.588961 0.294481 0.955657i \(-0.404853\pi\)
0.294481 + 0.955657i \(0.404853\pi\)
\(618\) 0.0787016 0.950246i 0.00316584 0.0382245i
\(619\) 12.0503 + 16.5858i 0.484341 + 0.666638i 0.979332 0.202260i \(-0.0648287\pi\)
−0.494991 + 0.868898i \(0.664829\pi\)
\(620\) 4.94475 29.6468i 0.198586 1.19064i
\(621\) −11.7832 + 3.82858i −0.472842 + 0.153636i
\(622\) 18.0833 10.9799i 0.725073 0.440252i
\(623\) 27.6535 + 20.0914i 1.10791 + 0.804946i
\(624\) −0.0926495 + 5.65714i −0.00370895 + 0.226467i
\(625\) −9.39795 + 28.9239i −0.375918 + 1.15696i
\(626\) −1.57768 6.69210i −0.0630569 0.267470i
\(627\) −1.99191 + 2.06482i −0.0795493 + 0.0824609i
\(628\) 15.8538 + 31.7549i 0.632634 + 1.26716i
\(629\) 56.2929 + 18.2907i 2.24454 + 0.729296i
\(630\) 18.8812 21.9246i 0.752244 0.873498i
\(631\) 27.5103 + 19.9874i 1.09517 + 0.795687i 0.980265 0.197690i \(-0.0633438\pi\)
0.114904 + 0.993377i \(0.463344\pi\)
\(632\) 6.51602 10.3458i 0.259193 0.411533i
\(633\) 1.57414 + 4.84470i 0.0625664 + 0.192560i
\(634\) −13.9426 5.84219i −0.553730 0.232023i
\(635\) −16.9013 23.2626i −0.670706 0.923148i
\(636\) −0.207443 1.38294i −0.00822567 0.0548371i
\(637\) 0.566770i 0.0224562i
\(638\) 8.60562 3.70528i 0.340700 0.146693i
\(639\) 9.39727 0.371750
\(640\) −31.6804 8.57294i −1.25228 0.338875i
\(641\) 23.4076 17.0066i 0.924544 0.671721i −0.0201069 0.999798i \(-0.506401\pi\)
0.944651 + 0.328077i \(0.106401\pi\)
\(642\) −5.54627 + 13.2364i −0.218894 + 0.522397i
\(643\) 16.0204 5.20536i 0.631784 0.205279i 0.0244190 0.999702i \(-0.492226\pi\)
0.607365 + 0.794423i \(0.292226\pi\)
\(644\) 14.6722 + 14.9144i 0.578164 + 0.587710i
\(645\) 2.27756 3.13480i 0.0896789 0.123432i
\(646\) 10.1792 11.8200i 0.400496 0.465051i
\(647\) 8.40795 25.8770i 0.330551 1.01733i −0.638322 0.769770i \(-0.720371\pi\)
0.968872 0.247560i \(-0.0796289\pi\)
\(648\) −11.6891 14.0315i −0.459189 0.551209i
\(649\) 1.02911 0.547867i 0.0403959 0.0215057i
\(650\) 12.3039 2.90068i 0.482599 0.113774i
\(651\) 6.93493 + 2.25330i 0.271802 + 0.0883137i
\(652\) 10.2274 + 5.31705i 0.400536 + 0.208232i
\(653\) −10.3083 + 14.1881i −0.403394 + 0.555224i −0.961592 0.274484i \(-0.911493\pi\)
0.558198 + 0.829708i \(0.311493\pi\)
\(654\) −7.95571 + 4.83058i −0.311093 + 0.188890i
\(655\) 10.2454 + 31.5320i 0.400320 + 1.23206i
\(656\) −14.3353 + 4.39963i −0.559699 + 0.171777i
\(657\) −2.92337 + 2.12395i −0.114052 + 0.0828633i
\(658\) −43.4866 3.60167i −1.69529 0.140408i
\(659\) 0.0398060i 0.00155062i 1.00000 0.000775311i \(0.000246789\pi\)
−1.00000 0.000775311i \(0.999753\pi\)
\(660\) 3.31009 + 9.85822i 0.128845 + 0.383731i
\(661\) 33.5882i 1.30643i −0.757173 0.653214i \(-0.773420\pi\)
0.757173 0.653214i \(-0.226580\pi\)
\(662\) −2.49154 + 30.0829i −0.0968364 + 1.16921i
\(663\) −7.88563 + 5.72925i −0.306253 + 0.222506i
\(664\) −45.1058 + 2.99299i −1.75044 + 0.116151i
\(665\) −3.73713 11.5017i −0.144920 0.446016i
\(666\) −17.0721 28.1169i −0.661531 1.08951i
\(667\) 4.71583 6.49078i 0.182598 0.251324i
\(668\) −2.18166 + 4.19645i −0.0844110 + 0.162365i
\(669\) −7.45640 2.42273i −0.288281 0.0936682i
\(670\) 9.78512 + 41.5058i 0.378032 + 1.60351i
\(671\) −10.1210 1.41709i −0.390719 0.0547061i
\(672\) 3.19697 7.29228i 0.123326 0.281306i
\(673\) −1.54864 + 4.76623i −0.0596958 + 0.183725i −0.976458 0.215710i \(-0.930794\pi\)
0.916762 + 0.399435i \(0.130794\pi\)
\(674\) −8.39758 7.23188i −0.323463 0.278562i
\(675\) 6.19228 8.52295i 0.238341 0.328048i
\(676\) −8.62535 8.76776i −0.331744 0.337222i
\(677\) −14.1747 + 4.60563i −0.544776 + 0.177009i −0.568460 0.822711i \(-0.692461\pi\)
0.0236836 + 0.999720i \(0.492461\pi\)
\(678\) 3.74202 + 1.56797i 0.143711 + 0.0602177i
\(679\) −18.1474 + 13.1849i −0.696435 + 0.505989i
\(680\) −20.9940 52.4986i −0.805083 2.01323i
\(681\) 1.47234 0.0564203
\(682\) 18.2562 16.0357i 0.699066 0.614037i
\(683\) 31.7556i 1.21510i 0.794283 + 0.607548i \(0.207847\pi\)
−0.794283 + 0.607548i \(0.792153\pi\)
\(684\) −8.57304 + 1.28597i −0.327798 + 0.0491703i
\(685\) −2.00082 2.75390i −0.0764475 0.105221i
\(686\) −10.2725 + 24.5157i −0.392207 + 0.936014i
\(687\) −2.33158 7.17587i −0.0889554 0.273776i
\(688\) −3.20866 + 9.35133i −0.122329 + 0.356516i
\(689\) −2.73958 1.99042i −0.104370 0.0758289i
\(690\) 6.74751 + 5.81086i 0.256873 + 0.221216i
\(691\) 10.9968 + 3.57308i 0.418338 + 0.135926i 0.510620 0.859807i \(-0.329416\pi\)
−0.0922814 + 0.995733i \(0.529416\pi\)
\(692\) −2.21303 4.43266i −0.0841266 0.168505i
\(693\) 23.0342 4.07381i 0.874996 0.154751i
\(694\) 37.5420 8.85064i 1.42507 0.335966i
\(695\) 6.49145 19.9786i 0.246235 0.757832i
\(696\) −2.96005 0.749211i −0.112200 0.0283988i
\(697\) −20.8994 15.1843i −0.791623 0.575148i
\(698\) −5.50067 9.05932i −0.208203 0.342900i
\(699\) 6.38988 2.07620i 0.241687 0.0785290i
\(700\) −17.5474 2.92671i −0.663230 0.110619i
\(701\) 6.32315 + 8.70306i 0.238822 + 0.328710i 0.911557 0.411173i \(-0.134881\pi\)
−0.672735 + 0.739883i \(0.734881\pi\)
\(702\) 11.3790 + 0.942438i 0.429474 + 0.0355700i
\(703\) −13.7487 −0.518541
\(704\) −15.4538 21.5680i −0.582438 0.812875i
\(705\) −18.5724 −0.699479
\(706\) 25.5560 + 2.11661i 0.961811 + 0.0796595i
\(707\) 13.3278 + 18.3442i 0.501244 + 0.689903i
\(708\) −0.374763 0.0625064i −0.0140845 0.00234913i
\(709\) 27.2305 8.84772i 1.02266 0.332283i 0.250777 0.968045i \(-0.419314\pi\)
0.771885 + 0.635762i \(0.219314\pi\)
\(710\) −7.38891 12.1691i −0.277301 0.456700i
\(711\) −9.47029 6.88057i −0.355163 0.258041i
\(712\) −35.9855 9.10822i −1.34861 0.341345i
\(713\) 6.42975 19.7887i 0.240796 0.741094i
\(714\) 13.3511 3.14755i 0.499651 0.117794i
\(715\) 22.6389 + 11.0273i 0.846648 + 0.412397i
\(716\) 18.2847 + 36.6240i 0.683331 + 1.36870i
\(717\) 9.17657 + 2.98165i 0.342705 + 0.111352i
\(718\) 5.16264 + 4.44599i 0.192668 + 0.165923i
\(719\) −2.53670 1.84302i −0.0946028 0.0687329i 0.539478 0.841999i \(-0.318621\pi\)
−0.634081 + 0.773267i \(0.718621\pi\)
\(720\) −10.1979 + 29.7209i −0.380054 + 1.10763i
\(721\) 1.00410 + 3.09030i 0.0373946 + 0.115089i
\(722\) 8.98398 21.4406i 0.334349 0.797935i
\(723\) 0.226939 + 0.312355i 0.00843996 + 0.0116166i
\(724\) −34.1071 + 5.11612i −1.26758 + 0.190139i
\(725\) 6.82207i 0.253365i
\(726\) −2.96831 + 7.86562i −0.110164 + 0.291921i
\(727\) 43.0374 1.59617 0.798084 0.602546i \(-0.205847\pi\)
0.798084 + 0.602546i \(0.205847\pi\)
\(728\) −7.15917 17.9026i −0.265336 0.663513i
\(729\) −10.0992 + 7.33748i −0.374043 + 0.271758i
\(730\) 5.04904 + 2.11564i 0.186873 + 0.0783034i
\(731\) −16.1984 + 5.26318i −0.599120 + 0.194666i
\(732\) 2.33567 + 2.37424i 0.0863289 + 0.0877543i
\(733\) 16.1331 22.2052i 0.595888 0.820169i −0.399436 0.916761i \(-0.630794\pi\)
0.995324 + 0.0965916i \(0.0307941\pi\)
\(734\) 9.05213 + 7.79557i 0.334120 + 0.287740i
\(735\) −0.104906 + 0.322867i −0.00386952 + 0.0119091i
\(736\) −20.8084 9.12250i −0.767009 0.336260i
\(737\) −15.0968 + 30.9937i −0.556098 + 1.14167i
\(738\) 3.29427 + 13.9734i 0.121264 + 0.514367i
\(739\) −38.2425 12.4258i −1.40677 0.457089i −0.495399 0.868666i \(-0.664978\pi\)
−0.911375 + 0.411577i \(0.864978\pi\)
\(740\) −22.9869 + 44.2156i −0.845017 + 1.62540i
\(741\) 1.33080 1.83168i 0.0488880 0.0672886i
\(742\) 2.47331 + 4.07342i 0.0907981 + 0.149540i
\(743\) 10.3306 + 31.7944i 0.378994 + 1.16642i 0.940744 + 0.339117i \(0.110128\pi\)
−0.561750 + 0.827307i \(0.689872\pi\)
\(744\) −7.90136 + 0.524294i −0.289678 + 0.0192216i
\(745\) −28.8440 + 20.9564i −1.05676 + 0.767783i
\(746\) −3.24098 + 39.1317i −0.118661 + 1.43271i
\(747\) 43.2793i 1.58351i
\(748\) 13.6992 43.6088i 0.500893 1.59449i
\(749\) 48.9066i 1.78701i
\(750\) 3.50167 + 0.290017i 0.127863 + 0.0105899i
\(751\) 19.7735 14.3663i 0.721545 0.524233i −0.165333 0.986238i \(-0.552870\pi\)
0.886877 + 0.462005i \(0.152870\pi\)
\(752\) 45.3015 13.9034i 1.65198 0.507006i
\(753\) −0.252490 0.777085i −0.00920126 0.0283186i
\(754\) −6.32010 + 3.83746i −0.230164 + 0.139752i
\(755\) 24.6494 33.9269i 0.897082 1.23473i
\(756\) −14.2568 7.41187i −0.518515 0.269567i
\(757\) −48.1159 15.6338i −1.74880 0.568221i −0.752858 0.658183i \(-0.771325\pi\)
−0.995945 + 0.0899623i \(0.971325\pi\)
\(758\) 21.1064 4.97591i 0.766621 0.180733i
\(759\) 1.25376 + 7.08898i 0.0455084 + 0.257314i
\(760\) 8.40612 + 10.0907i 0.304922 + 0.366027i
\(761\) 7.06297 21.7376i 0.256032 0.787987i −0.737592 0.675247i \(-0.764037\pi\)
0.993624 0.112740i \(-0.0359628\pi\)
\(762\) −4.94354 + 5.74039i −0.179086 + 0.207952i
\(763\) 18.6432 25.6602i 0.674929 0.928961i
\(764\) −28.4411 28.9107i −1.02896 1.04595i
\(765\) −51.4827 + 16.7277i −1.86136 + 0.604792i
\(766\) −6.48673 + 15.4808i −0.234375 + 0.559344i
\(767\) −0.744327 + 0.540785i −0.0268761 + 0.0195266i
\(768\) −0.283150 + 8.64220i −0.0102173 + 0.311848i
\(769\) 10.5112 0.379044 0.189522 0.981877i \(-0.439306\pi\)
0.189522 + 0.981877i \(0.439306\pi\)
\(770\) −23.3868 26.6253i −0.842802 0.959510i
\(771\) 9.95938i 0.358678i
\(772\) 0.765860 + 5.10568i 0.0275639 + 0.183757i
\(773\) 19.8566 + 27.3303i 0.714193 + 0.983003i 0.999697 + 0.0246252i \(0.00783924\pi\)
−0.285503 + 0.958378i \(0.592161\pi\)
\(774\) 8.72993 + 3.65800i 0.313791 + 0.131484i
\(775\) 5.46728 + 16.8266i 0.196391 + 0.604428i
\(776\) 12.9822 20.6124i 0.466034 0.739943i
\(777\) −9.78101 7.10632i −0.350892 0.254938i
\(778\) −4.19174 + 4.86740i −0.150281 + 0.174505i
\(779\) 5.70686 + 1.85427i 0.204469 + 0.0664362i
\(780\) −3.66567 7.34229i −0.131252 0.262896i
\(781\) 1.59594 11.3984i 0.0571070 0.407866i
\(782\) −8.98151 38.0971i −0.321178 1.36235i
\(783\) −1.90414 + 5.86035i −0.0680485 + 0.209432i
\(784\) 0.0141839 0.866065i 0.000506569 0.0309309i
\(785\) −41.6481 30.2592i −1.48649 1.08000i
\(786\) 7.46648 4.53352i 0.266321 0.161705i
\(787\) −26.9776 + 8.76555i −0.961647 + 0.312458i −0.747439 0.664330i \(-0.768717\pi\)
−0.214208 + 0.976788i \(0.568717\pi\)
\(788\) 6.92412 41.5143i 0.246662 1.47889i
\(789\) 3.58643 + 4.93630i 0.127680 + 0.175737i
\(790\) −1.46378 + 17.6738i −0.0520791 + 0.628805i
\(791\) −13.8263 −0.491605
\(792\) −21.5835 + 13.3959i −0.766937 + 0.476001i
\(793\) 8.06497 0.286395
\(794\) 1.26804 15.3103i 0.0450010 0.543343i
\(795\) 1.19222 + 1.64095i 0.0422836 + 0.0581984i
\(796\) 15.7512 + 2.62712i 0.558285 + 0.0931158i
\(797\) 22.9290 7.45008i 0.812186 0.263895i 0.126663 0.991946i \(-0.459573\pi\)
0.685524 + 0.728050i \(0.259573\pi\)
\(798\) −2.72349 + 1.65366i −0.0964105 + 0.0585389i
\(799\) 66.0452 + 47.9846i 2.33651 + 1.69757i
\(800\) 18.8739 4.12454i 0.667291 0.145824i
\(801\) −10.9822 + 33.7996i −0.388036 + 1.19425i
\(802\) 0.753347 + 3.19549i 0.0266016 + 0.112837i
\(803\) 2.07977 + 3.90660i 0.0733934 + 0.137861i
\(804\) 10.0519 5.01846i 0.354504 0.176987i
\(805\) −28.8604 9.37732i −1.01720 0.330507i
\(806\) −12.5131 + 14.5300i −0.440754 + 0.511799i
\(807\) −7.68720 5.58508i −0.270602 0.196604i
\(808\) −20.8359 13.1229i −0.733003 0.461663i
\(809\) −7.00409 21.5564i −0.246251 0.757882i −0.995428 0.0955125i \(-0.969551\pi\)
0.749178 0.662369i \(-0.230449\pi\)
\(810\) 24.4307 + 10.2369i 0.858406 + 0.359688i
\(811\) −29.5211 40.6323i −1.03663 1.42679i −0.899854 0.436192i \(-0.856327\pi\)
−0.136773 0.990602i \(-0.543673\pi\)
\(812\) 10.2902 1.54355i 0.361116 0.0541680i
\(813\) 3.52723i 0.123705i
\(814\) −37.0037 + 15.9325i −1.29698 + 0.558433i
\(815\) −16.7193 −0.585650
\(816\) −12.1932 + 8.55736i −0.426847 + 0.299567i
\(817\) 3.20065 2.32541i 0.111976 0.0813557i
\(818\) −13.7890 + 32.9079i −0.482122 + 1.15060i
\(819\) −17.5561 + 5.70433i −0.613461 + 0.199325i
\(820\) 15.5048 15.2530i 0.541453 0.532658i
\(821\) −13.4554 + 18.5197i −0.469596 + 0.646343i −0.976464 0.215680i \(-0.930803\pi\)
0.506868 + 0.862024i \(0.330803\pi\)
\(822\) −0.585231 + 0.679564i −0.0204123 + 0.0237025i
\(823\) 7.75502 23.8675i 0.270323 0.831968i −0.720096 0.693874i \(-0.755902\pi\)
0.990419 0.138094i \(-0.0440976\pi\)
\(824\) −2.25857 2.71118i −0.0786811 0.0944484i
\(825\) −4.40555 4.24999i −0.153381 0.147966i
\(826\) 1.26021 0.297098i 0.0438483 0.0103374i
\(827\) 12.5706 + 4.08442i 0.437121 + 0.142029i 0.519307 0.854588i \(-0.326190\pi\)
−0.0821857 + 0.996617i \(0.526190\pi\)
\(828\) −10.0338 + 19.3000i −0.348697 + 0.670722i
\(829\) 17.6423 24.2826i 0.612744 0.843370i −0.384056 0.923310i \(-0.625473\pi\)
0.996800 + 0.0799400i \(0.0254729\pi\)
\(830\) 56.0452 34.0297i 1.94536 1.18119i
\(831\) 0.0428028 + 0.131733i 0.00148481 + 0.00456978i
\(832\) 14.4377 + 15.1650i 0.500538 + 0.525753i
\(833\) 1.20723 0.877104i 0.0418280 0.0303899i
\(834\) −5.51563 0.456817i −0.190991 0.0158183i
\(835\) 6.86015i 0.237405i
\(836\) 0.103857 + 10.6170i 0.00359198 + 0.367198i
\(837\) 15.9805i 0.552366i
\(838\) 1.95140 23.5612i 0.0674100 0.813910i
\(839\) 2.19656 1.59589i 0.0758336 0.0550963i −0.549223 0.835676i \(-0.685076\pi\)
0.625056 + 0.780580i \(0.285076\pi\)
\(840\) 0.764644 + 11.5235i 0.0263827 + 0.397600i
\(841\) 7.72843 + 23.7857i 0.266498 + 0.820196i
\(842\) 6.97446 + 11.4866i 0.240356 + 0.395854i
\(843\) 8.24583 11.3494i 0.284001 0.390894i
\(844\) 16.7265 + 8.69580i 0.575748 + 0.299322i
\(845\) 16.9662 + 5.51266i 0.583656 + 0.189641i
\(846\) −10.4103 44.1579i −0.357915 1.51818i
\(847\) −1.02943 28.6311i −0.0353718 0.983775i
\(848\) −4.13646 3.11006i −0.142047 0.106800i
\(849\) −1.57169 + 4.83716i −0.0539402 + 0.166011i
\(850\) 25.2194 + 21.7186i 0.865019 + 0.744942i
\(851\) −20.2778 + 27.9100i −0.695114 + 0.956742i
\(852\) −2.67388 + 2.63045i −0.0916056 + 0.0901177i
\(853\) −14.2235 + 4.62150i −0.487004 + 0.158237i −0.542219 0.840237i \(-0.682416\pi\)
0.0552150 + 0.998474i \(0.482416\pi\)
\(854\) −10.4679 4.38624i −0.358204 0.150094i
\(855\) 10.1725 7.39073i 0.347891 0.252758i
\(856\) 19.7206 + 49.3143i 0.674037 + 1.68553i
\(857\) −13.6354 −0.465776 −0.232888 0.972504i \(-0.574818\pi\)
−0.232888 + 0.972504i \(0.574818\pi\)
\(858\) 1.45913 6.47203i 0.0498137 0.220952i
\(859\) 5.59465i 0.190887i 0.995435 + 0.0954434i \(0.0304269\pi\)
−0.995435 + 0.0954434i \(0.969573\pi\)
\(860\) −2.12720 14.1812i −0.0725370 0.483575i
\(861\) 3.10152 + 4.26888i 0.105699 + 0.145483i
\(862\) −17.0292 + 40.6408i −0.580018 + 1.38423i
\(863\) −1.37818 4.24160i −0.0469138 0.144386i 0.924856 0.380318i \(-0.124186\pi\)
−0.971769 + 0.235933i \(0.924186\pi\)
\(864\) 17.3644 + 1.72488i 0.590748 + 0.0586817i
\(865\) 5.81366 + 4.22387i 0.197670 + 0.143616i
\(866\) 5.34774 + 4.60540i 0.181724 + 0.156498i
\(867\) −15.6692 5.09124i −0.532154 0.172907i
\(868\) 24.1437 12.0538i 0.819490 0.409134i
\(869\) −9.95410 + 10.3184i −0.337670 + 0.350029i
\(870\) 4.31062 1.01624i 0.146144 0.0344538i
\(871\) 8.40712 25.8745i 0.284865 0.876723i
\(872\) −8.45168 + 33.3916i −0.286210 + 1.13078i
\(873\) −18.8681 13.7085i −0.638589 0.463962i
\(874\) 4.71869 + 7.77144i 0.159612 + 0.262873i
\(875\) −11.3878 + 3.70012i −0.384978 + 0.125087i
\(876\) 0.237281 1.42264i 0.00801699 0.0480667i
\(877\) 21.8420 + 30.0630i 0.737553 + 1.01515i 0.998756 + 0.0498707i \(0.0158809\pi\)
−0.261203 + 0.965284i \(0.584119\pi\)
\(878\) 32.3778 + 2.68160i 1.09270 + 0.0904998i
\(879\) 1.03731 0.0349876
\(880\) 34.3180 + 17.4170i 1.15686 + 0.587128i
\(881\) −30.4894 −1.02721 −0.513607 0.858025i \(-0.671691\pi\)
−0.513607 + 0.858025i \(0.671691\pi\)
\(882\) −0.826453 0.0684488i −0.0278281 0.00230479i
\(883\) −18.2464 25.1141i −0.614042 0.845156i 0.382861 0.923806i \(-0.374939\pi\)
−0.996902 + 0.0786504i \(0.974939\pi\)
\(884\) −5.93445 + 35.5806i −0.199597 + 1.19671i
\(885\) 0.524112 0.170294i 0.0176178 0.00572438i
\(886\) −20.8776 34.3843i −0.701396 1.15516i
\(887\) −27.0640 19.6632i −0.908720 0.660224i 0.0319705 0.999489i \(-0.489822\pi\)
−0.940691 + 0.339265i \(0.889822\pi\)
\(888\) 12.7280 + 3.22157i 0.427125 + 0.108109i
\(889\) 7.97768 24.5528i 0.267563 0.823473i
\(890\) 52.4045 12.3545i 1.75660 0.414124i
\(891\) 10.0633 + 18.9028i 0.337134 + 0.633267i
\(892\) −25.9591 + 12.9602i −0.869176 + 0.433940i
\(893\) −18.0345 5.85976i −0.603501 0.196089i
\(894\) 7.11768 + 6.12965i 0.238051 + 0.205006i
\(895\) −48.0343 34.8989i −1.60561 1.16654i
\(896\) −10.4917 27.5356i −0.350503 0.919898i
\(897\) −1.75556 5.40306i −0.0586165 0.180403i
\(898\) 6.22512 14.8564i 0.207735 0.495766i
\(899\) −6.08265 8.37205i −0.202868 0.279223i
\(900\) −2.74378 18.2916i −0.0914593 0.609721i
\(901\) 8.91562i 0.297023i
\(902\) 17.5084 1.62268i 0.582967 0.0540292i
\(903\) 3.47892 0.115771
\(904\) 13.9415 5.57517i 0.463689 0.185427i
\(905\) 40.4702 29.4034i 1.34528 0.977400i
\(906\) −10.1902 4.26987i −0.338546 0.141857i
\(907\) −33.3966 + 10.8512i −1.10892 + 0.360309i −0.805528 0.592558i \(-0.798118\pi\)
−0.303389 + 0.952867i \(0.598118\pi\)
\(908\) 3.88431 3.82121i 0.128905 0.126811i
\(909\) −13.8571 + 19.0726i −0.459611 + 0.632600i
\(910\) 21.1910 + 18.2494i 0.702474 + 0.604961i
\(911\) −6.57828 + 20.2459i −0.217948 + 0.670775i 0.780983 + 0.624552i \(0.214718\pi\)
−0.998931 + 0.0462229i \(0.985282\pi\)
\(912\) 2.07939 2.76564i 0.0688556 0.0915795i
\(913\) 52.4955 + 7.35011i 1.73735 + 0.243253i
\(914\) 4.51921 + 19.1692i 0.149482 + 0.634062i
\(915\) −4.59431 1.49278i −0.151883 0.0493499i
\(916\) −24.7749 12.8800i −0.818585 0.425568i
\(917\) −17.4968 + 24.0822i −0.577794 + 0.795265i
\(918\) 15.6022 + 25.6960i 0.514949 + 0.848095i
\(919\) −1.35893 4.18235i −0.0448269 0.137963i 0.926138 0.377185i \(-0.123108\pi\)
−0.970965 + 0.239222i \(0.923108\pi\)
\(920\) 32.8823 2.18190i 1.08410 0.0719352i
\(921\) −4.47148 + 3.24872i −0.147340 + 0.107049i
\(922\) 1.49598 18.0625i 0.0492676 0.594858i
\(923\) 9.08282i 0.298965i
\(924\) −5.41377 + 7.60679i −0.178100 + 0.250245i
\(925\) 29.3345i 0.964513i
\(926\) −53.8579 4.46064i −1.76988 0.146586i
\(927\) −2.73316 + 1.98576i −0.0897687 + 0.0652208i
\(928\) −9.75360 + 5.70575i −0.320178 + 0.187300i
\(929\) 6.11559 + 18.8219i 0.200646 + 0.617525i 0.999864 + 0.0164841i \(0.00524728\pi\)
−0.799218 + 0.601041i \(0.794753\pi\)
\(930\) 9.81766 5.96112i 0.321934 0.195473i
\(931\) −0.203735 + 0.280417i −0.00667714 + 0.00919029i
\(932\) 11.4693 22.0612i 0.375688 0.722640i
\(933\) 7.68874 + 2.49822i 0.251718 + 0.0817882i
\(934\) −44.9390 + 10.5945i −1.47045 + 0.346663i
\(935\) 11.5466 + 65.2866i 0.377613 + 2.13510i
\(936\) 15.4023 12.8311i 0.503441 0.419396i
\(937\) 14.3550 44.1802i 0.468958 1.44330i −0.384979 0.922925i \(-0.625791\pi\)
0.853936 0.520377i \(-0.174209\pi\)
\(938\) −24.9842 + 29.0114i −0.815762 + 0.947255i
\(939\) 1.54436 2.12563i 0.0503983 0.0693673i
\(940\) −48.9975 + 48.2016i −1.59812 + 1.57216i
\(941\) −44.8387 + 14.5690i −1.46170 + 0.474935i −0.928588 0.371111i \(-0.878977\pi\)
−0.533110 + 0.846046i \(0.678977\pi\)
\(942\) −5.24162 + 12.5093i −0.170781 + 0.407575i
\(943\) 12.1812 8.85015i 0.396674 0.288200i
\(944\) −1.15092 + 0.807731i −0.0374592 + 0.0262894i
\(945\) 23.3063 0.758155
\(946\) 5.91956 9.96770i 0.192461 0.324078i
\(947\) 5.18884i 0.168615i −0.996440 0.0843074i \(-0.973132\pi\)
0.996440 0.0843074i \(-0.0268678\pi\)
\(948\) 4.62064 0.693104i 0.150071 0.0225110i
\(949\) −2.05288 2.82555i −0.0666394 0.0917212i
\(950\) −7.13022 2.98769i −0.231335 0.0969335i
\(951\) −1.78514 5.49410i −0.0578872 0.178158i
\(952\) 27.0536 42.9542i 0.876813 1.39216i
\(953\) 14.1293 + 10.2655i 0.457692 + 0.332533i 0.792625 0.609709i \(-0.208714\pi\)
−0.334933 + 0.942242i \(0.608714\pi\)
\(954\) −3.23325 + 3.75442i −0.104680 + 0.121554i
\(955\) 55.9442 + 18.1774i 1.81031 + 0.588206i
\(956\) 31.9478 15.9501i 1.03327 0.515863i
\(957\) 3.21887 + 1.56789i 0.104051 + 0.0506827i
\(958\) −8.44641 35.8274i −0.272891 1.15753i
\(959\) 0.944421 2.90663i 0.0304969 0.0938599i
\(960\) −5.41766 11.3113i −0.174854 0.365070i
\(961\) 3.36730 + 2.44648i 0.108623 + 0.0789189i
\(962\) 27.1761 16.5009i 0.876192 0.532009i
\(963\) 48.3601 15.7131i 1.55838 0.506349i
\(964\) 1.40937 + 0.235067i 0.0453928 + 0.00757101i
\(965\) −4.40155 6.05822i −0.141691 0.195021i
\(966\) −0.659902 + 7.96768i −0.0212320 + 0.256356i
\(967\) 22.0455 0.708936 0.354468 0.935068i \(-0.384662\pi\)
0.354468 + 0.935068i \(0.384662\pi\)
\(968\) 12.5829 + 28.4547i 0.404431 + 0.914568i
\(969\) 5.96100 0.191495
\(970\) −2.91637 + 35.2123i −0.0936390 + 1.13060i
\(971\) 15.1513 + 20.8540i 0.486228 + 0.669236i 0.979687 0.200534i \(-0.0642675\pi\)
−0.493459 + 0.869769i \(0.664268\pi\)
\(972\) 4.19305 25.1399i 0.134492 0.806362i
\(973\) 17.9374 5.82821i 0.575046 0.186844i
\(974\) −6.74594 + 4.09602i −0.216154 + 0.131245i
\(975\) 3.90813 + 2.83942i 0.125160 + 0.0909342i
\(976\) 12.3239 + 0.201833i 0.394477 + 0.00646052i
\(977\) 9.06120 27.8875i 0.289893 0.892200i −0.694996 0.719014i \(-0.744594\pi\)
0.984889 0.173186i \(-0.0554062\pi\)
\(978\) 1.01076 + 4.28738i 0.0323206 + 0.137095i
\(979\) 39.1320 + 19.0610i 1.25067 + 0.609191i
\(980\) 0.561186 + 1.12405i 0.0179264 + 0.0359064i
\(981\) 31.3633 + 10.1906i 1.00135 + 0.325359i
\(982\) −22.5883 + 26.2292i −0.720820 + 0.837009i
\(983\) 23.2947 + 16.9246i 0.742984 + 0.539810i 0.893644 0.448776i \(-0.148140\pi\)
−0.150660 + 0.988586i \(0.548140\pi\)
\(984\) −4.84872 3.05384i −0.154572 0.0973529i
\(985\) 18.8643 + 58.0583i 0.601066 + 1.84989i
\(986\) −17.9545 7.52327i −0.571789 0.239590i
\(987\) −9.80124 13.4902i −0.311977 0.429399i
\(988\) −1.24294 8.28617i −0.0395432 0.263618i
\(989\) 9.92707i 0.315662i
\(990\) 18.8139 31.6799i 0.597944 1.00685i
\(991\) −50.7188 −1.61113 −0.805567 0.592504i \(-0.798139\pi\)
−0.805567 + 0.592504i \(0.798139\pi\)
\(992\) −19.4845 + 21.8898i −0.618634 + 0.695002i
\(993\) −9.33220 + 6.78024i −0.296148 + 0.215164i
\(994\) 4.93981 11.7890i 0.156681 0.373925i
\(995\) −22.0282 + 7.15740i −0.698342 + 0.226905i
\(996\) −12.1146 12.3146i −0.383865 0.390203i
\(997\) 7.80937 10.7487i 0.247325 0.340414i −0.667247 0.744837i \(-0.732527\pi\)
0.914572 + 0.404422i \(0.132527\pi\)
\(998\) 19.3619 22.4829i 0.612891 0.711682i
\(999\) 8.18770 25.1992i 0.259047 0.797266i
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 88.2.o.a.53.10 yes 40
3.2 odd 2 792.2.br.b.757.1 40
4.3 odd 2 352.2.w.a.273.4 40
8.3 odd 2 352.2.w.a.273.7 40
8.5 even 2 inner 88.2.o.a.53.3 yes 40
11.2 odd 10 968.2.o.d.245.9 40
11.3 even 5 968.2.o.j.565.6 40
11.4 even 5 968.2.c.h.485.12 20
11.5 even 5 inner 88.2.o.a.5.3 40
11.6 odd 10 968.2.o.i.269.8 40
11.7 odd 10 968.2.c.i.485.9 20
11.8 odd 10 968.2.o.d.565.5 40
11.9 even 5 968.2.o.j.245.2 40
11.10 odd 2 968.2.o.i.493.1 40
24.5 odd 2 792.2.br.b.757.8 40
33.5 odd 10 792.2.br.b.181.8 40
44.7 even 10 3872.2.c.i.1937.12 20
44.15 odd 10 3872.2.c.h.1937.12 20
44.27 odd 10 352.2.w.a.49.7 40
88.5 even 10 inner 88.2.o.a.5.10 yes 40
88.13 odd 10 968.2.o.d.245.5 40
88.21 odd 2 968.2.o.i.493.8 40
88.27 odd 10 352.2.w.a.49.4 40
88.29 odd 10 968.2.c.i.485.10 20
88.37 even 10 968.2.c.h.485.11 20
88.51 even 10 3872.2.c.i.1937.9 20
88.53 even 10 968.2.o.j.245.6 40
88.59 odd 10 3872.2.c.h.1937.9 20
88.61 odd 10 968.2.o.i.269.1 40
88.69 even 10 968.2.o.j.565.2 40
88.85 odd 10 968.2.o.d.565.9 40
264.5 odd 10 792.2.br.b.181.1 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.o.a.5.3 40 11.5 even 5 inner
88.2.o.a.5.10 yes 40 88.5 even 10 inner
88.2.o.a.53.3 yes 40 8.5 even 2 inner
88.2.o.a.53.10 yes 40 1.1 even 1 trivial
352.2.w.a.49.4 40 88.27 odd 10
352.2.w.a.49.7 40 44.27 odd 10
352.2.w.a.273.4 40 4.3 odd 2
352.2.w.a.273.7 40 8.3 odd 2
792.2.br.b.181.1 40 264.5 odd 10
792.2.br.b.181.8 40 33.5 odd 10
792.2.br.b.757.1 40 3.2 odd 2
792.2.br.b.757.8 40 24.5 odd 2
968.2.c.h.485.11 20 88.37 even 10
968.2.c.h.485.12 20 11.4 even 5
968.2.c.i.485.9 20 11.7 odd 10
968.2.c.i.485.10 20 88.29 odd 10
968.2.o.d.245.5 40 88.13 odd 10
968.2.o.d.245.9 40 11.2 odd 10
968.2.o.d.565.5 40 11.8 odd 10
968.2.o.d.565.9 40 88.85 odd 10
968.2.o.i.269.1 40 88.61 odd 10
968.2.o.i.269.8 40 11.6 odd 10
968.2.o.i.493.1 40 11.10 odd 2
968.2.o.i.493.8 40 88.21 odd 2
968.2.o.j.245.2 40 11.9 even 5
968.2.o.j.245.6 40 88.53 even 10
968.2.o.j.565.2 40 88.69 even 10
968.2.o.j.565.6 40 11.3 even 5
3872.2.c.h.1937.9 20 88.59 odd 10
3872.2.c.h.1937.12 20 44.15 odd 10
3872.2.c.i.1937.9 20 88.51 even 10
3872.2.c.i.1937.12 20 44.7 even 10