Properties

Label 345.2.m.c.151.1
Level $345$
Weight $2$
Character 345.151
Analytic conductor $2.755$
Analytic rank $0$
Dimension $50$
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] = [345,2,Mod(16,345)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(345, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("345.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.m (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.75483886973\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 151.1
Character \(\chi\) \(=\) 345.151
Dual form 345.2.m.c.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71238 - 1.97619i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.688461 + 4.78835i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.372136 - 2.58826i) q^{6} +(-3.22191 - 0.946039i) q^{7} +(6.24206 - 4.01153i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-1.71238 - 1.97619i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.688461 + 4.78835i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.372136 - 2.58826i) q^{6} +(-3.22191 - 0.946039i) q^{7} +(6.24206 - 4.01153i) q^{8} +(0.415415 + 0.909632i) q^{9} +(2.50896 - 0.736696i) q^{10} +(2.97536 - 3.43375i) q^{11} +(-3.16795 + 3.65601i) q^{12} +(-4.24933 + 1.24772i) q^{13} +(3.64759 + 7.98710i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-9.33308 - 2.74044i) q^{16} +(-0.923869 - 6.42565i) q^{17} +(1.08626 - 2.37858i) q^{18} +(1.07871 - 7.50260i) q^{19} +(-4.06964 - 2.61540i) q^{20} +(-2.19898 - 2.53776i) q^{21} -11.8807 q^{22} +(-3.08438 - 3.67241i) q^{23} +7.41995 q^{24} +(-0.654861 - 0.755750i) q^{25} +(9.74221 + 6.26094i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(6.74813 - 14.7763i) q^{28} +(0.103326 + 0.718648i) q^{29} +(2.50896 + 0.736696i) q^{30} +(-2.89757 + 1.86215i) q^{31} +(4.40143 + 9.63779i) q^{32} +(4.35946 - 1.28005i) q^{33} +(-11.1163 + 12.8289i) q^{34} +(2.19898 - 2.53776i) q^{35} +(-4.64163 + 1.36291i) q^{36} +(1.61577 + 3.53805i) q^{37} +(-16.6737 + 10.7156i) q^{38} +(-4.24933 - 1.24772i) q^{39} +(1.05597 + 7.34443i) q^{40} +(0.199578 - 0.437015i) q^{41} +(-1.24961 + 8.69121i) q^{42} +(2.82894 + 1.81805i) q^{43} +(14.3936 + 16.6111i) q^{44} -1.00000 q^{45} +(-1.97576 + 12.3839i) q^{46} +10.8226 q^{47} +(-6.36989 - 7.35125i) q^{48} +(3.59696 + 2.31162i) q^{49} +(-0.372136 + 2.58826i) q^{50} +(2.69676 - 5.90508i) q^{51} +(-3.04901 - 21.2063i) q^{52} +(-10.9100 - 3.20346i) q^{53} +(2.19978 - 1.41371i) q^{54} +(1.88744 + 4.13292i) q^{55} +(-23.9064 + 7.01956i) q^{56} +(4.96368 - 5.72839i) q^{57} +(1.24325 - 1.43479i) q^{58} +(-5.83162 + 1.71232i) q^{59} +(-2.00961 - 4.40043i) q^{60} +(-1.15240 + 0.740602i) q^{61} +(8.64172 + 2.53744i) q^{62} +(-0.477884 - 3.32375i) q^{63} +(3.42765 - 7.50550i) q^{64} +(0.630274 - 4.38365i) q^{65} +(-9.99470 - 6.42320i) q^{66} +(5.68458 + 6.56035i) q^{67} +31.4043 q^{68} +(-0.609290 - 4.75697i) q^{69} -8.78059 q^{70} +(-3.41996 - 3.94685i) q^{71} +(6.24206 + 4.01153i) q^{72} +(0.691195 - 4.80736i) q^{73} +(4.22505 - 9.25157i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(35.1824 + 10.3305i) q^{76} +(-12.8348 + 8.24844i) q^{77} +(4.81075 + 10.5341i) q^{78} +(-4.55729 + 1.33814i) q^{79} +(6.36989 - 7.35125i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-1.20538 + 0.353932i) q^{82} +(0.0538928 + 0.118009i) q^{83} +(13.6656 - 8.78233i) q^{84} +(6.22876 + 1.82893i) q^{85} +(-1.25141 - 8.70372i) q^{86} +(-0.301607 + 0.660428i) q^{87} +(4.79780 - 33.3695i) q^{88} +(-1.88276 - 1.20997i) q^{89} +(1.71238 + 1.97619i) q^{90} +14.8714 q^{91} +(19.7083 - 12.2408i) q^{92} -3.44435 q^{93} +(-18.5325 - 21.3876i) q^{94} +(6.37649 + 4.09792i) q^{95} +(-1.50786 + 10.4874i) q^{96} +(2.93361 - 6.42370i) q^{97} +(-1.59115 - 11.0667i) q^{98} +(4.35946 + 1.28005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/345\mathbb{Z}\right)^\times\).

\(n\) \(116\) \(166\) \(277\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71238 1.97619i −1.21084 1.39738i −0.893498 0.449067i \(-0.851756\pi\)
−0.317338 0.948312i \(-0.602789\pi\)
\(3\) 0.841254 + 0.540641i 0.485698 + 0.312139i
\(4\) −0.688461 + 4.78835i −0.344230 + 2.39417i
\(5\) −0.415415 + 0.909632i −0.185779 + 0.406800i
\(6\) −0.372136 2.58826i −0.151924 1.05665i
\(7\) −3.22191 0.946039i −1.21777 0.357569i −0.391147 0.920328i \(-0.627922\pi\)
−0.826621 + 0.562759i \(0.809740\pi\)
\(8\) 6.24206 4.01153i 2.20690 1.41829i
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 2.50896 0.736696i 0.793402 0.232964i
\(11\) 2.97536 3.43375i 0.897106 1.03532i −0.102072 0.994777i \(-0.532547\pi\)
0.999178 0.0405385i \(-0.0129074\pi\)
\(12\) −3.16795 + 3.65601i −0.914508 + 1.05540i
\(13\) −4.24933 + 1.24772i −1.17855 + 0.346055i −0.811616 0.584191i \(-0.801412\pi\)
−0.366937 + 0.930246i \(0.619594\pi\)
\(14\) 3.64759 + 7.98710i 0.974859 + 2.13464i
\(15\) −0.841254 + 0.540641i −0.217211 + 0.139593i
\(16\) −9.33308 2.74044i −2.33327 0.685110i
\(17\) −0.923869 6.42565i −0.224071 1.55845i −0.722409 0.691466i \(-0.756965\pi\)
0.498338 0.866983i \(-0.333944\pi\)
\(18\) 1.08626 2.37858i 0.256034 0.560636i
\(19\) 1.07871 7.50260i 0.247473 1.72121i −0.365244 0.930912i \(-0.619015\pi\)
0.612717 0.790302i \(-0.290076\pi\)
\(20\) −4.06964 2.61540i −0.909999 0.584821i
\(21\) −2.19898 2.53776i −0.479856 0.553784i
\(22\) −11.8807 −2.53298
\(23\) −3.08438 3.67241i −0.643138 0.765751i
\(24\) 7.41995 1.51459
\(25\) −0.654861 0.755750i −0.130972 0.151150i
\(26\) 9.74221 + 6.26094i 1.91061 + 1.22787i
\(27\) −0.142315 + 0.989821i −0.0273885 + 0.190491i
\(28\) 6.74813 14.7763i 1.27528 2.79246i
\(29\) 0.103326 + 0.718648i 0.0191872 + 0.133450i 0.997163 0.0752663i \(-0.0239807\pi\)
−0.977976 + 0.208716i \(0.933072\pi\)
\(30\) 2.50896 + 0.736696i 0.458071 + 0.134502i
\(31\) −2.89757 + 1.86215i −0.520419 + 0.334453i −0.774338 0.632773i \(-0.781917\pi\)
0.253919 + 0.967226i \(0.418280\pi\)
\(32\) 4.40143 + 9.63779i 0.778071 + 1.70374i
\(33\) 4.35946 1.28005i 0.758885 0.222829i
\(34\) −11.1163 + 12.8289i −1.90643 + 2.20014i
\(35\) 2.19898 2.53776i 0.371695 0.428959i
\(36\) −4.64163 + 1.36291i −0.773606 + 0.227151i
\(37\) 1.61577 + 3.53805i 0.265631 + 0.581652i 0.994704 0.102785i \(-0.0327754\pi\)
−0.729072 + 0.684437i \(0.760048\pi\)
\(38\) −16.6737 + 10.7156i −2.70484 + 1.73829i
\(39\) −4.24933 1.24772i −0.680438 0.199795i
\(40\) 1.05597 + 7.34443i 0.166963 + 1.16126i
\(41\) 0.199578 0.437015i 0.0311689 0.0682503i −0.893407 0.449248i \(-0.851692\pi\)
0.924576 + 0.380997i \(0.124419\pi\)
\(42\) −1.24961 + 8.69121i −0.192819 + 1.34108i
\(43\) 2.82894 + 1.81805i 0.431409 + 0.277250i 0.738271 0.674504i \(-0.235643\pi\)
−0.306862 + 0.951754i \(0.599279\pi\)
\(44\) 14.3936 + 16.6111i 2.16992 + 2.50422i
\(45\) −1.00000 −0.149071
\(46\) −1.97576 + 12.3839i −0.291310 + 1.82591i
\(47\) 10.8226 1.57864 0.789321 0.613981i \(-0.210433\pi\)
0.789321 + 0.613981i \(0.210433\pi\)
\(48\) −6.36989 7.35125i −0.919415 1.06106i
\(49\) 3.59696 + 2.31162i 0.513851 + 0.330232i
\(50\) −0.372136 + 2.58826i −0.0526280 + 0.366036i
\(51\) 2.69676 5.90508i 0.377622 0.826877i
\(52\) −3.04901 21.2063i −0.422821 2.94079i
\(53\) −10.9100 3.20346i −1.49860 0.440029i −0.573326 0.819327i \(-0.694347\pi\)
−0.925274 + 0.379298i \(0.876165\pi\)
\(54\) 2.19978 1.41371i 0.299352 0.192382i
\(55\) 1.88744 + 4.13292i 0.254502 + 0.557283i
\(56\) −23.9064 + 7.01956i −3.19463 + 0.938029i
\(57\) 4.96368 5.72839i 0.657455 0.758744i
\(58\) 1.24325 1.43479i 0.163247 0.188397i
\(59\) −5.83162 + 1.71232i −0.759213 + 0.222925i −0.638352 0.769744i \(-0.720384\pi\)
−0.120861 + 0.992669i \(0.538565\pi\)
\(60\) −2.00961 4.40043i −0.259439 0.568093i
\(61\) −1.15240 + 0.740602i −0.147550 + 0.0948244i −0.612333 0.790600i \(-0.709769\pi\)
0.464783 + 0.885425i \(0.346132\pi\)
\(62\) 8.64172 + 2.53744i 1.09750 + 0.322255i
\(63\) −0.477884 3.32375i −0.0602077 0.418754i
\(64\) 3.42765 7.50550i 0.428456 0.938188i
\(65\) 0.630274 4.38365i 0.0781759 0.543725i
\(66\) −9.99470 6.42320i −1.23026 0.790641i
\(67\) 5.68458 + 6.56035i 0.694482 + 0.801474i 0.987996 0.154480i \(-0.0493703\pi\)
−0.293514 + 0.955955i \(0.594825\pi\)
\(68\) 31.4043 3.80833
\(69\) −0.609290 4.75697i −0.0733499 0.572672i
\(70\) −8.78059 −1.04948
\(71\) −3.41996 3.94685i −0.405875 0.468405i 0.515607 0.856825i \(-0.327566\pi\)
−0.921482 + 0.388420i \(0.873021\pi\)
\(72\) 6.24206 + 4.01153i 0.735634 + 0.472763i
\(73\) 0.691195 4.80736i 0.0808982 0.562659i −0.908550 0.417775i \(-0.862810\pi\)
0.989449 0.144884i \(-0.0462810\pi\)
\(74\) 4.22505 9.25157i 0.491152 1.07547i
\(75\) −0.142315 0.989821i −0.0164331 0.114295i
\(76\) 35.1824 + 10.3305i 4.03570 + 1.18499i
\(77\) −12.8348 + 8.24844i −1.46266 + 0.939997i
\(78\) 4.81075 + 10.5341i 0.544710 + 1.19275i
\(79\) −4.55729 + 1.33814i −0.512735 + 0.150552i −0.527857 0.849333i \(-0.677004\pi\)
0.0151225 + 0.999886i \(0.495186\pi\)
\(80\) 6.36989 7.35125i 0.712176 0.821894i
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) −1.20538 + 0.353932i −0.133112 + 0.0390852i
\(83\) 0.0538928 + 0.118009i 0.00591550 + 0.0129531i 0.912567 0.408928i \(-0.134097\pi\)
−0.906651 + 0.421881i \(0.861370\pi\)
\(84\) 13.6656 8.78233i 1.49104 0.958231i
\(85\) 6.22876 + 1.82893i 0.675604 + 0.198375i
\(86\) −1.25141 8.70372i −0.134943 0.938546i
\(87\) −0.301607 + 0.660428i −0.0323357 + 0.0708053i
\(88\) 4.79780 33.3695i 0.511448 3.55720i
\(89\) −1.88276 1.20997i −0.199572 0.128257i 0.437038 0.899443i \(-0.356027\pi\)
−0.636610 + 0.771186i \(0.719664\pi\)
\(90\) 1.71238 + 1.97619i 0.180501 + 0.208309i
\(91\) 14.8714 1.55894
\(92\) 19.7083 12.2408i 2.05473 1.27619i
\(93\) −3.44435 −0.357162
\(94\) −18.5325 21.3876i −1.91148 2.20596i
\(95\) 6.37649 + 4.09792i 0.654214 + 0.420438i
\(96\) −1.50786 + 10.4874i −0.153896 + 1.07037i
\(97\) 2.93361 6.42370i 0.297863 0.652228i −0.700233 0.713914i \(-0.746921\pi\)
0.998096 + 0.0616863i \(0.0196478\pi\)
\(98\) −1.59115 11.0667i −0.160730 1.11790i
\(99\) 4.35946 + 1.28005i 0.438142 + 0.128650i
\(100\) 4.06964 2.61540i 0.406964 0.261540i
\(101\) −3.92121 8.58626i −0.390175 0.854365i −0.998173 0.0604259i \(-0.980754\pi\)
0.607997 0.793939i \(-0.291973\pi\)
\(102\) −16.2875 + 4.78243i −1.61270 + 0.473531i
\(103\) 9.65374 11.1410i 0.951211 1.09776i −0.0439041 0.999036i \(-0.513980\pi\)
0.995115 0.0987204i \(-0.0314749\pi\)
\(104\) −21.5194 + 24.8347i −2.11015 + 2.43524i
\(105\) 3.22191 0.946039i 0.314426 0.0923239i
\(106\) 12.3514 + 27.0458i 1.19967 + 2.62692i
\(107\) −9.15159 + 5.88137i −0.884717 + 0.568573i −0.902221 0.431274i \(-0.858064\pi\)
0.0175039 + 0.999847i \(0.494428\pi\)
\(108\) −4.64163 1.36291i −0.446641 0.131146i
\(109\) 1.00558 + 6.99397i 0.0963172 + 0.669901i 0.979585 + 0.201031i \(0.0644293\pi\)
−0.883268 + 0.468869i \(0.844662\pi\)
\(110\) 4.93543 10.8071i 0.470575 1.03041i
\(111\) −0.553539 + 3.84995i −0.0525396 + 0.365421i
\(112\) 27.4778 + 17.6589i 2.59641 + 1.66861i
\(113\) −3.38846 3.91049i −0.318759 0.367868i 0.573646 0.819104i \(-0.305529\pi\)
−0.892405 + 0.451236i \(0.850983\pi\)
\(114\) −19.8201 −1.85632
\(115\) 4.62184 1.28008i 0.430989 0.119368i
\(116\) −3.51228 −0.326107
\(117\) −2.90020 3.34701i −0.268124 0.309431i
\(118\) 13.3698 + 8.59227i 1.23079 + 0.790983i
\(119\) −3.10229 + 21.5769i −0.284386 + 1.97795i
\(120\) −3.08236 + 6.74943i −0.281380 + 0.616135i
\(121\) −1.37241 9.54530i −0.124764 0.867754i
\(122\) 3.43692 + 1.00917i 0.311164 + 0.0913661i
\(123\) 0.404164 0.259740i 0.0364422 0.0234200i
\(124\) −6.92179 15.1566i −0.621595 1.36110i
\(125\) 0.959493 0.281733i 0.0858197 0.0251989i
\(126\) −5.75006 + 6.63592i −0.512256 + 0.591175i
\(127\) −5.38458 + 6.21413i −0.477804 + 0.551415i −0.942566 0.334021i \(-0.891594\pi\)
0.464762 + 0.885436i \(0.346140\pi\)
\(128\) −0.369601 + 0.108525i −0.0326684 + 0.00959232i
\(129\) 1.39694 + 3.05888i 0.122994 + 0.269319i
\(130\) −9.74221 + 6.26094i −0.854449 + 0.549121i
\(131\) 15.6290 + 4.58909i 1.36551 + 0.400950i 0.880703 0.473670i \(-0.157071\pi\)
0.484809 + 0.874620i \(0.338889\pi\)
\(132\) 3.12803 + 21.7559i 0.272260 + 1.89361i
\(133\) −10.5733 + 23.1522i −0.916818 + 2.00755i
\(134\) 3.23036 22.4676i 0.279061 1.94091i
\(135\) −0.841254 0.540641i −0.0724036 0.0465310i
\(136\) −31.5435 36.4032i −2.70483 3.12155i
\(137\) −0.756822 −0.0646596 −0.0323298 0.999477i \(-0.510293\pi\)
−0.0323298 + 0.999477i \(0.510293\pi\)
\(138\) −8.35736 + 9.34982i −0.711425 + 0.795910i
\(139\) −18.5056 −1.56962 −0.784810 0.619736i \(-0.787240\pi\)
−0.784810 + 0.619736i \(0.787240\pi\)
\(140\) 10.6378 + 12.2766i 0.899054 + 1.03756i
\(141\) 9.10457 + 5.85115i 0.766743 + 0.492756i
\(142\) −1.94345 + 13.5170i −0.163091 + 1.13432i
\(143\) −8.35897 + 18.3036i −0.699012 + 1.53062i
\(144\) −1.38431 9.62809i −0.115359 0.802341i
\(145\) −0.696629 0.204549i −0.0578519 0.0169868i
\(146\) −10.6839 + 6.86611i −0.884203 + 0.568243i
\(147\) 1.77619 + 3.88932i 0.146498 + 0.320786i
\(148\) −18.0538 + 5.30108i −1.48401 + 0.435746i
\(149\) 12.7972 14.7687i 1.04838 1.20990i 0.0712104 0.997461i \(-0.477314\pi\)
0.977174 0.212439i \(-0.0681407\pi\)
\(150\) −1.71238 + 1.97619i −0.139815 + 0.161356i
\(151\) −3.87449 + 1.13765i −0.315302 + 0.0925810i −0.435555 0.900162i \(-0.643448\pi\)
0.120253 + 0.992743i \(0.461630\pi\)
\(152\) −23.3635 51.1589i −1.89503 4.14954i
\(153\) 5.46119 3.50969i 0.441511 0.283742i
\(154\) 38.2786 + 11.2396i 3.08458 + 0.905715i
\(155\) −0.490182 3.40929i −0.0393723 0.273841i
\(156\) 8.90001 19.4883i 0.712571 1.56031i
\(157\) −1.31099 + 9.11812i −0.104628 + 0.727705i 0.868206 + 0.496203i \(0.165273\pi\)
−0.972835 + 0.231502i \(0.925636\pi\)
\(158\) 10.4482 + 6.71467i 0.831217 + 0.534191i
\(159\) −7.44614 8.59330i −0.590517 0.681493i
\(160\) −10.5953 −0.837629
\(161\) 6.46336 + 14.7501i 0.509384 + 1.16247i
\(162\) 2.61488 0.205444
\(163\) 10.4016 + 12.0041i 0.814717 + 0.940233i 0.999091 0.0426227i \(-0.0135713\pi\)
−0.184374 + 0.982856i \(0.559026\pi\)
\(164\) 1.95518 + 1.25652i 0.152674 + 0.0981176i
\(165\) −0.646608 + 4.49726i −0.0503384 + 0.350111i
\(166\) 0.140923 0.308579i 0.0109378 0.0239503i
\(167\) −0.185381 1.28935i −0.0143452 0.0997732i 0.981391 0.192021i \(-0.0615040\pi\)
−0.995736 + 0.0922474i \(0.970595\pi\)
\(168\) −23.9064 7.01956i −1.84442 0.541571i
\(169\) 5.56375 3.57561i 0.427981 0.275047i
\(170\) −7.05170 15.4411i −0.540841 1.18428i
\(171\) 7.27271 2.13546i 0.556158 0.163303i
\(172\) −10.6531 + 12.2943i −0.812288 + 0.937430i
\(173\) 8.36790 9.65708i 0.636200 0.734214i −0.342498 0.939518i \(-0.611273\pi\)
0.978698 + 0.205305i \(0.0658185\pi\)
\(174\) 1.82160 0.534870i 0.138095 0.0405484i
\(175\) 1.39494 + 3.05448i 0.105447 + 0.230897i
\(176\) −37.1793 + 23.8937i −2.80250 + 1.80105i
\(177\) −5.83162 1.71232i −0.438332 0.128706i
\(178\) 0.832854 + 5.79263i 0.0624251 + 0.434176i
\(179\) 0.0461786 0.101117i 0.00345155 0.00755783i −0.907898 0.419190i \(-0.862314\pi\)
0.911350 + 0.411633i \(0.135041\pi\)
\(180\) 0.688461 4.78835i 0.0513148 0.356903i
\(181\) 3.80972 + 2.44836i 0.283175 + 0.181985i 0.674516 0.738260i \(-0.264352\pi\)
−0.391341 + 0.920246i \(0.627989\pi\)
\(182\) −25.4655 29.3887i −1.88763 2.17844i
\(183\) −1.36986 −0.101263
\(184\) −33.9849 10.5503i −2.50540 0.777781i
\(185\) −3.88954 −0.285965
\(186\) 5.89804 + 6.80670i 0.432465 + 0.499091i
\(187\) −24.8129 15.9463i −1.81450 1.16611i
\(188\) −7.45095 + 51.8225i −0.543416 + 3.77954i
\(189\) 1.39494 3.05448i 0.101467 0.222181i
\(190\) −2.82070 19.6184i −0.204635 1.42327i
\(191\) 11.0462 + 3.24347i 0.799278 + 0.234689i 0.655771 0.754960i \(-0.272344\pi\)
0.143507 + 0.989649i \(0.454162\pi\)
\(192\) 6.94130 4.46090i 0.500945 0.321938i
\(193\) 1.81295 + 3.96980i 0.130499 + 0.285752i 0.963590 0.267382i \(-0.0861587\pi\)
−0.833092 + 0.553135i \(0.813431\pi\)
\(194\) −17.7179 + 5.20245i −1.27207 + 0.373514i
\(195\) 2.90020 3.34701i 0.207688 0.239684i
\(196\) −13.5452 + 15.6320i −0.967516 + 1.11657i
\(197\) 5.55720 1.63174i 0.395934 0.116257i −0.0777036 0.996977i \(-0.524759\pi\)
0.473638 + 0.880720i \(0.342941\pi\)
\(198\) −4.93543 10.8071i −0.350746 0.768026i
\(199\) 11.8347 7.60572i 0.838942 0.539155i −0.0491660 0.998791i \(-0.515656\pi\)
0.888108 + 0.459636i \(0.152020\pi\)
\(200\) −7.11939 2.09044i −0.503417 0.147817i
\(201\) 1.23538 + 8.59223i 0.0871367 + 0.606049i
\(202\) −10.2535 + 22.4520i −0.721434 + 1.57972i
\(203\) 0.346962 2.41317i 0.0243520 0.169372i
\(204\) 26.4190 + 16.9784i 1.84970 + 1.18873i
\(205\) 0.314615 + 0.363085i 0.0219737 + 0.0253590i
\(206\) −38.5477 −2.68574
\(207\) 2.05925 4.33122i 0.143127 0.301041i
\(208\) 43.0787 2.98697
\(209\) −22.5525 26.0270i −1.55999 1.80032i
\(210\) −7.38670 4.74714i −0.509731 0.327584i
\(211\) 2.90082 20.1757i 0.199701 1.38895i −0.605452 0.795882i \(-0.707007\pi\)
0.805152 0.593068i \(-0.202083\pi\)
\(212\) 22.8504 50.0353i 1.56937 3.43644i
\(213\) −0.743229 5.16927i −0.0509252 0.354193i
\(214\) 27.2937 + 8.01416i 1.86576 + 0.547837i
\(215\) −2.82894 + 1.81805i −0.192932 + 0.123990i
\(216\) 3.08236 + 6.74943i 0.209728 + 0.459240i
\(217\) 11.0974 3.25849i 0.753340 0.221200i
\(218\) 12.0995 13.9636i 0.819481 0.945732i
\(219\) 3.18053 3.67052i 0.214920 0.248031i
\(220\) −21.0893 + 6.19237i −1.42184 + 0.417490i
\(221\) 11.9432 + 26.1520i 0.803388 + 1.75917i
\(222\) 8.55611 5.49868i 0.574249 0.369047i
\(223\) 1.44121 + 0.423176i 0.0965102 + 0.0283380i 0.329631 0.944110i \(-0.393076\pi\)
−0.233121 + 0.972448i \(0.574894\pi\)
\(224\) −5.06330 35.2160i −0.338306 2.35297i
\(225\) 0.415415 0.909632i 0.0276943 0.0606421i
\(226\) −1.92555 + 13.3925i −0.128086 + 0.890855i
\(227\) 12.6259 + 8.11414i 0.838007 + 0.538555i 0.887813 0.460204i \(-0.152224\pi\)
−0.0498057 + 0.998759i \(0.515860\pi\)
\(228\) 24.0122 + 27.7116i 1.59025 + 1.83525i
\(229\) 1.31445 0.0868616 0.0434308 0.999056i \(-0.486171\pi\)
0.0434308 + 0.999056i \(0.486171\pi\)
\(230\) −10.4440 6.94167i −0.688659 0.457720i
\(231\) −15.2568 −1.00382
\(232\) 3.52785 + 4.07135i 0.231614 + 0.267297i
\(233\) −14.0181 9.00891i −0.918359 0.590193i −0.00617763 0.999981i \(-0.501966\pi\)
−0.912181 + 0.409788i \(0.865603\pi\)
\(234\) −1.64809 + 11.4627i −0.107739 + 0.749341i
\(235\) −4.49588 + 9.84460i −0.293279 + 0.642191i
\(236\) −4.18434 29.1027i −0.272377 1.89443i
\(237\) −4.55729 1.33814i −0.296028 0.0869215i
\(238\) 47.9524 30.8171i 3.10829 1.99758i
\(239\) 11.4371 + 25.0437i 0.739803 + 1.61994i 0.783878 + 0.620915i \(0.213239\pi\)
−0.0440752 + 0.999028i \(0.514034\pi\)
\(240\) 9.33308 2.74044i 0.602448 0.176895i
\(241\) −5.76839 + 6.65708i −0.371575 + 0.428820i −0.910484 0.413543i \(-0.864291\pi\)
0.538910 + 0.842364i \(0.318836\pi\)
\(242\) −16.5133 + 19.0573i −1.06151 + 1.22505i
\(243\) −0.959493 + 0.281733i −0.0615515 + 0.0180732i
\(244\) −2.75288 6.02797i −0.176235 0.385901i
\(245\) −3.59696 + 2.31162i −0.229801 + 0.147684i
\(246\) −1.20538 0.353932i −0.0768523 0.0225659i
\(247\) 4.77732 + 33.2270i 0.303973 + 2.11418i
\(248\) −10.6167 + 23.2474i −0.674162 + 1.47621i
\(249\) −0.0184628 + 0.128412i −0.00117004 + 0.00813777i
\(250\) −2.19978 1.41371i −0.139126 0.0894109i
\(251\) 7.68932 + 8.87395i 0.485345 + 0.560119i 0.944616 0.328178i \(-0.106435\pi\)
−0.459270 + 0.888297i \(0.651889\pi\)
\(252\) 16.2443 1.02329
\(253\) −21.7873 0.335763i −1.36976 0.0211092i
\(254\) 21.5008 1.34908
\(255\) 4.25118 + 4.90612i 0.266219 + 0.307233i
\(256\) −13.0352 8.37724i −0.814703 0.523578i
\(257\) −1.87292 + 13.0265i −0.116830 + 0.812568i 0.844181 + 0.536058i \(0.180087\pi\)
−0.961011 + 0.276510i \(0.910822\pi\)
\(258\) 3.65283 7.99859i 0.227416 0.497971i
\(259\) −1.85875 12.9279i −0.115497 0.803299i
\(260\) 20.5565 + 6.03594i 1.27486 + 0.374333i
\(261\) −0.610782 + 0.392526i −0.0378065 + 0.0242968i
\(262\) −17.6939 38.7442i −1.09313 2.39362i
\(263\) −20.4860 + 6.01522i −1.26322 + 0.370914i −0.843691 0.536829i \(-0.819622\pi\)
−0.419527 + 0.907743i \(0.637804\pi\)
\(264\) 22.0771 25.4783i 1.35875 1.56808i
\(265\) 7.44614 8.59330i 0.457413 0.527882i
\(266\) 63.8587 18.7506i 3.91543 1.14967i
\(267\) −0.929714 2.03579i −0.0568976 0.124588i
\(268\) −35.3269 + 22.7032i −2.15793 + 1.38682i
\(269\) −13.9019 4.08195i −0.847611 0.248881i −0.171045 0.985263i \(-0.554714\pi\)
−0.676566 + 0.736382i \(0.736533\pi\)
\(270\) 0.372136 + 2.58826i 0.0226475 + 0.157517i
\(271\) 10.6768 23.3790i 0.648571 1.42017i −0.244228 0.969718i \(-0.578535\pi\)
0.892799 0.450455i \(-0.148738\pi\)
\(272\) −8.98656 + 62.5029i −0.544890 + 3.78979i
\(273\) 12.5106 + 8.04007i 0.757176 + 0.486607i
\(274\) 1.29597 + 1.49563i 0.0782923 + 0.0903541i
\(275\) −4.54351 −0.273984
\(276\) 23.1975 + 0.357495i 1.39633 + 0.0215187i
\(277\) −3.56368 −0.214121 −0.107060 0.994253i \(-0.534144\pi\)
−0.107060 + 0.994253i \(0.534144\pi\)
\(278\) 31.6886 + 36.5706i 1.90055 + 2.19336i
\(279\) −2.89757 1.86215i −0.173473 0.111484i
\(280\) 3.54587 24.6621i 0.211906 1.47384i
\(281\) 1.24465 2.72541i 0.0742497 0.162584i −0.868867 0.495045i \(-0.835152\pi\)
0.943117 + 0.332461i \(0.107879\pi\)
\(282\) −4.02749 28.0118i −0.239833 1.66808i
\(283\) 28.7283 + 8.43538i 1.70772 + 0.501431i 0.982369 0.186951i \(-0.0598604\pi\)
0.725349 + 0.688382i \(0.241679\pi\)
\(284\) 21.2534 13.6587i 1.26116 0.810497i
\(285\) 3.14874 + 6.89478i 0.186515 + 0.408412i
\(286\) 50.4852 14.8238i 2.98525 0.876548i
\(287\) −1.05646 + 1.21922i −0.0623607 + 0.0719681i
\(288\) −6.93842 + 8.00737i −0.408850 + 0.471839i
\(289\) −24.1240 + 7.08346i −1.41906 + 0.416674i
\(290\) 0.788666 + 1.72694i 0.0463121 + 0.101409i
\(291\) 5.94082 3.81793i 0.348257 0.223811i
\(292\) 22.5435 + 6.61936i 1.31926 + 0.387369i
\(293\) −1.25273 8.71291i −0.0731851 0.509013i −0.993135 0.116977i \(-0.962680\pi\)
0.919950 0.392037i \(-0.128229\pi\)
\(294\) 4.64453 10.1701i 0.270875 0.593133i
\(295\) 0.864964 6.01596i 0.0503601 0.350262i
\(296\) 24.2787 + 15.6030i 1.41117 + 0.906906i
\(297\) 2.97536 + 3.43375i 0.172648 + 0.199247i
\(298\) −51.0995 −2.96011
\(299\) 17.6887 + 11.7569i 1.02296 + 0.679917i
\(300\) 4.83759 0.279298
\(301\) −7.39464 8.53387i −0.426220 0.491884i
\(302\) 8.88283 + 5.70865i 0.511150 + 0.328496i
\(303\) 1.34335 9.34319i 0.0771733 0.536752i
\(304\) −30.6281 + 67.0662i −1.75664 + 3.84651i
\(305\) −0.194951 1.35592i −0.0111629 0.0776396i
\(306\) −16.2875 4.78243i −0.931092 0.273393i
\(307\) −7.33231 + 4.71219i −0.418477 + 0.268939i −0.732890 0.680348i \(-0.761829\pi\)
0.314413 + 0.949286i \(0.398192\pi\)
\(308\) −30.6602 67.1364i −1.74702 3.82545i
\(309\) 14.1445 4.15321i 0.804654 0.236268i
\(310\) −5.89804 + 6.80670i −0.334986 + 0.386594i
\(311\) 16.4972 19.0387i 0.935468 1.07959i −0.0612088 0.998125i \(-0.519496\pi\)
0.996676 0.0814622i \(-0.0259590\pi\)
\(312\) −31.5299 + 9.25800i −1.78503 + 0.524131i
\(313\) −2.92536 6.40564i −0.165351 0.362068i 0.808760 0.588139i \(-0.200139\pi\)
−0.974111 + 0.226071i \(0.927412\pi\)
\(314\) 20.2641 13.0229i 1.14357 0.734926i
\(315\) 3.22191 + 0.946039i 0.181534 + 0.0533033i
\(316\) −3.26997 22.7431i −0.183950 1.27940i
\(317\) 3.66526 8.02580i 0.205861 0.450774i −0.778336 0.627848i \(-0.783936\pi\)
0.984197 + 0.177074i \(0.0566633\pi\)
\(318\) −4.23140 + 29.4300i −0.237285 + 1.65035i
\(319\) 2.77509 + 1.78344i 0.155375 + 0.0998537i
\(320\) 5.40335 + 6.23580i 0.302056 + 0.348592i
\(321\) −10.8785 −0.607179
\(322\) 18.0814 38.0307i 1.00764 2.11937i
\(323\) −49.2056 −2.73787
\(324\) −3.16795 3.65601i −0.175997 0.203111i
\(325\) 3.72568 + 2.39435i 0.206664 + 0.132815i
\(326\) 5.91090 41.1112i 0.327374 2.27694i
\(327\) −2.93528 + 6.42736i −0.162321 + 0.355434i
\(328\) −0.507320 3.52849i −0.0280121 0.194828i
\(329\) −34.8695 10.2386i −1.92242 0.564474i
\(330\) 9.99470 6.42320i 0.550190 0.353586i
\(331\) −8.72090 19.0961i −0.479344 1.04962i −0.982643 0.185504i \(-0.940608\pi\)
0.503300 0.864112i \(-0.332119\pi\)
\(332\) −0.602170 + 0.176813i −0.0330484 + 0.00970388i
\(333\) −2.54711 + 2.93952i −0.139581 + 0.161085i
\(334\) −2.23057 + 2.57421i −0.122051 + 0.140855i
\(335\) −8.32896 + 2.44560i −0.455060 + 0.133618i
\(336\) 13.5687 + 29.7112i 0.740232 + 1.62088i
\(337\) −4.82059 + 3.09801i −0.262594 + 0.168759i −0.665313 0.746565i \(-0.731702\pi\)
0.402718 + 0.915324i \(0.368065\pi\)
\(338\) −16.5934 4.87225i −0.902560 0.265015i
\(339\) −0.736382 5.12165i −0.0399948 0.278170i
\(340\) −13.0458 + 28.5664i −0.707509 + 1.54923i
\(341\) −2.22714 + 15.4901i −0.120607 + 0.838837i
\(342\) −16.6737 10.7156i −0.901613 0.579431i
\(343\) 5.99065 + 6.91358i 0.323465 + 0.373298i
\(344\) 24.9515 1.34530
\(345\) 4.58020 + 1.42189i 0.246590 + 0.0765518i
\(346\) −33.4133 −1.79631
\(347\) −6.48284 7.48160i −0.348017 0.401633i 0.554572 0.832135i \(-0.312882\pi\)
−0.902589 + 0.430502i \(0.858336\pi\)
\(348\) −2.95471 1.89888i −0.158389 0.101791i
\(349\) −0.493785 + 3.43435i −0.0264317 + 0.183837i −0.998760 0.0497816i \(-0.984147\pi\)
0.972328 + 0.233618i \(0.0750566\pi\)
\(350\) 3.64759 7.98710i 0.194972 0.426929i
\(351\) −0.630274 4.38365i −0.0336415 0.233982i
\(352\) 46.1897 + 13.5625i 2.46192 + 0.722884i
\(353\) −4.17004 + 2.67992i −0.221949 + 0.142638i −0.646891 0.762583i \(-0.723931\pi\)
0.424942 + 0.905221i \(0.360295\pi\)
\(354\) 6.60209 + 14.4566i 0.350897 + 0.768358i
\(355\) 5.01089 1.47133i 0.265950 0.0780900i
\(356\) 7.08998 8.18228i 0.375768 0.433660i
\(357\) −14.2752 + 16.4744i −0.755522 + 0.871918i
\(358\) −0.278902 + 0.0818930i −0.0147404 + 0.00432818i
\(359\) −4.04165 8.84999i −0.213310 0.467084i 0.772486 0.635032i \(-0.219013\pi\)
−0.985796 + 0.167948i \(0.946286\pi\)
\(360\) −6.24206 + 4.01153i −0.328985 + 0.211426i
\(361\) −36.8950 10.8333i −1.94184 0.570176i
\(362\) −1.68527 11.7213i −0.0885756 0.616057i
\(363\) 4.00604 8.77199i 0.210262 0.460410i
\(364\) −10.2384 + 71.2093i −0.536636 + 3.73238i
\(365\) 4.08580 + 2.62578i 0.213861 + 0.137440i
\(366\) 2.34572 + 2.70711i 0.122613 + 0.141503i
\(367\) 22.2404 1.16094 0.580470 0.814282i \(-0.302869\pi\)
0.580470 + 0.814282i \(0.302869\pi\)
\(368\) 18.7227 + 42.7275i 0.975990 + 2.22732i
\(369\) 0.480431 0.0250102
\(370\) 6.66037 + 7.68648i 0.346256 + 0.399601i
\(371\) 32.1204 + 20.6425i 1.66761 + 1.07171i
\(372\) 2.37130 16.4927i 0.122946 0.855109i
\(373\) 3.71722 8.13958i 0.192470 0.421452i −0.788652 0.614840i \(-0.789221\pi\)
0.981122 + 0.193389i \(0.0619478\pi\)
\(374\) 10.9762 + 76.3413i 0.567567 + 3.94752i
\(375\) 0.959493 + 0.281733i 0.0495480 + 0.0145486i
\(376\) 67.5555 43.4153i 3.48391 2.23897i
\(377\) −1.33574 2.92486i −0.0687940 0.150638i
\(378\) −8.42491 + 2.47378i −0.433331 + 0.127237i
\(379\) −6.10544 + 7.04606i −0.313615 + 0.361932i −0.890571 0.454844i \(-0.849695\pi\)
0.576956 + 0.816775i \(0.304241\pi\)
\(380\) −24.0122 + 27.7116i −1.23180 + 1.42158i
\(381\) −7.88941 + 2.31654i −0.404187 + 0.118680i
\(382\) −12.5057 27.3836i −0.639845 1.40107i
\(383\) 29.2354 18.7884i 1.49386 0.960044i 0.498189 0.867068i \(-0.333998\pi\)
0.995668 0.0929757i \(-0.0296379\pi\)
\(384\) −0.369601 0.108525i −0.0188611 0.00553813i
\(385\) −2.17127 15.1015i −0.110658 0.769644i
\(386\) 4.74064 10.3805i 0.241292 0.528356i
\(387\) −0.478571 + 3.32854i −0.0243271 + 0.169199i
\(388\) 28.7393 + 18.4696i 1.45901 + 0.937652i
\(389\) −23.0115 26.5567i −1.16673 1.34648i −0.926741 0.375701i \(-0.877402\pi\)
−0.239988 0.970776i \(-0.577143\pi\)
\(390\) −11.5806 −0.586406
\(391\) −20.7481 + 23.2120i −1.04927 + 1.17388i
\(392\) 31.7256 1.60238
\(393\) 10.6669 + 12.3103i 0.538074 + 0.620970i
\(394\) −12.7407 8.18794i −0.641866 0.412502i
\(395\) 0.675950 4.70134i 0.0340107 0.236550i
\(396\) −9.13066 + 19.9934i −0.458833 + 1.00470i
\(397\) 4.07797 + 28.3629i 0.204668 + 1.42349i 0.790202 + 0.612847i \(0.209976\pi\)
−0.585534 + 0.810648i \(0.699115\pi\)
\(398\) −35.2959 10.3638i −1.76923 0.519491i
\(399\) −21.4118 + 13.7605i −1.07193 + 0.688889i
\(400\) 4.04078 + 8.84808i 0.202039 + 0.442404i
\(401\) −20.3676 + 5.98046i −1.01711 + 0.298650i −0.747458 0.664309i \(-0.768726\pi\)
−0.269649 + 0.962959i \(0.586908\pi\)
\(402\) 14.8645 17.1545i 0.741373 0.855590i
\(403\) 9.98930 11.5283i 0.497603 0.574264i
\(404\) 43.8136 12.8648i 2.17981 0.640050i
\(405\) −0.415415 0.909632i −0.0206421 0.0452000i
\(406\) −5.36303 + 3.44661i −0.266163 + 0.171052i
\(407\) 16.9563 + 4.97882i 0.840493 + 0.246791i
\(408\) −6.85506 47.6780i −0.339376 2.36041i
\(409\) 11.4827 25.1435i 0.567781 1.24327i −0.380189 0.924909i \(-0.624141\pi\)
0.947970 0.318358i \(-0.103132\pi\)
\(410\) 0.178786 1.24348i 0.00882959 0.0614112i
\(411\) −0.636679 0.409169i −0.0314051 0.0201828i
\(412\) 46.7008 + 53.8956i 2.30078 + 2.65525i
\(413\) 20.4089 1.00426
\(414\) −12.0856 + 3.34724i −0.593972 + 0.164508i
\(415\) −0.129732 −0.00636831
\(416\) −30.7284 35.4625i −1.50658 1.73869i
\(417\) −15.5679 10.0049i −0.762362 0.489940i
\(418\) −12.8159 + 89.1362i −0.626844 + 4.35980i
\(419\) 0.351352 0.769353i 0.0171646 0.0375853i −0.900856 0.434119i \(-0.857060\pi\)
0.918020 + 0.396534i \(0.129787\pi\)
\(420\) 2.31180 + 16.0790i 0.112805 + 0.784573i
\(421\) 11.3957 + 3.34609i 0.555394 + 0.163079i 0.547372 0.836889i \(-0.315628\pi\)
0.00802228 + 0.999968i \(0.497446\pi\)
\(422\) −44.8383 + 28.8158i −2.18270 + 1.40273i
\(423\) 4.49588 + 9.84460i 0.218597 + 0.478661i
\(424\) −80.9515 + 23.7695i −3.93135 + 1.15435i
\(425\) −4.25118 + 4.90612i −0.206212 + 0.237982i
\(426\) −8.94279 + 10.3205i −0.433280 + 0.500031i
\(427\) 4.41357 1.29594i 0.213588 0.0627150i
\(428\) −21.8615 47.8701i −1.05672 2.31389i
\(429\) −16.9277 + 10.8788i −0.817276 + 0.525231i
\(430\) 8.43703 + 2.47734i 0.406870 + 0.119468i
\(431\) −1.09964 7.64818i −0.0529679 0.368400i −0.999015 0.0443710i \(-0.985872\pi\)
0.946047 0.324029i \(-0.105037\pi\)
\(432\) 4.04078 8.84808i 0.194412 0.425703i
\(433\) 5.56534 38.7078i 0.267453 1.86018i −0.204920 0.978779i \(-0.565694\pi\)
0.472374 0.881398i \(-0.343397\pi\)
\(434\) −25.4424 16.3508i −1.22127 0.784864i
\(435\) −0.475454 0.548703i −0.0227963 0.0263083i
\(436\) −34.1819 −1.63701
\(437\) −30.8798 + 19.1794i −1.47718 + 0.917474i
\(438\) −12.6999 −0.606827
\(439\) 18.9321 + 21.8488i 0.903581 + 1.04279i 0.998879 + 0.0473388i \(0.0150740\pi\)
−0.0952984 + 0.995449i \(0.530381\pi\)
\(440\) 28.3608 + 18.2264i 1.35205 + 0.868910i
\(441\) −0.608497 + 4.23219i −0.0289761 + 0.201533i
\(442\) 31.2301 68.3843i 1.48546 3.25271i
\(443\) −1.29179 8.98459i −0.0613747 0.426871i −0.997223 0.0744685i \(-0.976274\pi\)
0.935849 0.352402i \(-0.114635\pi\)
\(444\) −18.0538 5.30108i −0.856796 0.251578i
\(445\) 1.88276 1.20997i 0.0892512 0.0573583i
\(446\) −1.63162 3.57274i −0.0772592 0.169174i
\(447\) 18.7502 5.50556i 0.886856 0.260404i
\(448\) −18.1441 + 20.9394i −0.857227 + 0.989293i
\(449\) −7.38292 + 8.52034i −0.348421 + 0.402100i −0.902727 0.430213i \(-0.858438\pi\)
0.554306 + 0.832313i \(0.312984\pi\)
\(450\) −2.50896 + 0.736696i −0.118273 + 0.0347282i
\(451\) −0.906785 1.98558i −0.0426988 0.0934974i
\(452\) 21.0576 13.5329i 0.990466 0.636534i
\(453\) −3.87449 1.13765i −0.182040 0.0534516i
\(454\) −5.58516 38.8456i −0.262125 1.82312i
\(455\) −6.17779 + 13.5275i −0.289619 + 0.634178i
\(456\) 8.00398 55.6689i 0.374821 2.60694i
\(457\) −11.0119 7.07692i −0.515115 0.331044i 0.257122 0.966379i \(-0.417226\pi\)
−0.772237 + 0.635335i \(0.780862\pi\)
\(458\) −2.25085 2.59762i −0.105175 0.121379i
\(459\) 6.49172 0.303008
\(460\) 2.94749 + 23.0123i 0.137428 + 1.07295i
\(461\) 0.794029 0.0369816 0.0184908 0.999829i \(-0.494114\pi\)
0.0184908 + 0.999829i \(0.494114\pi\)
\(462\) 26.1254 + 30.1504i 1.21547 + 1.40272i
\(463\) −35.1181 22.5691i −1.63208 1.04887i −0.947412 0.320017i \(-0.896311\pi\)
−0.684667 0.728856i \(-0.740052\pi\)
\(464\) 1.00506 6.99036i 0.0466588 0.324519i
\(465\) 1.43083 3.13309i 0.0663533 0.145294i
\(466\) 6.20105 + 43.1292i 0.287258 + 1.99792i
\(467\) 36.9722 + 10.8560i 1.71087 + 0.502357i 0.983039 0.183398i \(-0.0587097\pi\)
0.727832 + 0.685755i \(0.240528\pi\)
\(468\) 18.0233 11.5829i 0.833129 0.535419i
\(469\) −12.1089 26.5147i −0.559135 1.22434i
\(470\) 27.1535 7.97299i 1.25250 0.367766i
\(471\) −6.03250 + 6.96188i −0.277963 + 0.320786i
\(472\) −29.5323 + 34.0821i −1.35934 + 1.56876i
\(473\) 14.6598 4.30452i 0.674060 0.197922i
\(474\) 5.15939 + 11.2975i 0.236979 + 0.518911i
\(475\) −6.37649 + 4.09792i −0.292573 + 0.188026i
\(476\) −101.182 29.7097i −4.63767 1.36174i
\(477\) −1.61820 11.2548i −0.0740923 0.515323i
\(478\) 29.9066 65.4863i 1.36789 2.99527i
\(479\) 0.364903 2.53796i 0.0166729 0.115962i −0.979785 0.200052i \(-0.935889\pi\)
0.996458 + 0.0840893i \(0.0267981\pi\)
\(480\) −8.91330 5.72823i −0.406835 0.261457i
\(481\) −11.2804 13.0183i −0.514344 0.593585i
\(482\) 23.0334 1.04914
\(483\) −2.53720 + 15.9030i −0.115447 + 0.723609i
\(484\) 46.6511 2.12050
\(485\) 4.62454 + 5.33700i 0.209990 + 0.242341i
\(486\) 2.19978 + 1.41371i 0.0997839 + 0.0641272i
\(487\) 2.55695 17.7840i 0.115866 0.805869i −0.846163 0.532924i \(-0.821093\pi\)
0.962030 0.272945i \(-0.0879977\pi\)
\(488\) −4.22240 + 9.24577i −0.191139 + 0.418536i
\(489\) 2.26049 + 15.7220i 0.102223 + 0.710974i
\(490\) 10.7276 + 3.14990i 0.484623 + 0.142298i
\(491\) −12.5103 + 8.03986i −0.564580 + 0.362834i −0.791584 0.611060i \(-0.790743\pi\)
0.227004 + 0.973894i \(0.427107\pi\)
\(492\) 0.965477 + 2.11410i 0.0435271 + 0.0953110i
\(493\) 4.52232 1.32787i 0.203675 0.0598044i
\(494\) 57.4823 66.3381i 2.58625 2.98469i
\(495\) −2.97536 + 3.43375i −0.133733 + 0.154336i
\(496\) 32.1464 9.43902i 1.44341 0.423825i
\(497\) 7.28495 + 15.9518i 0.326775 + 0.715537i
\(498\) 0.285382 0.183404i 0.0127883 0.00821853i
\(499\) 35.3172 + 10.3701i 1.58101 + 0.464228i 0.950183 0.311693i \(-0.100896\pi\)
0.630831 + 0.775920i \(0.282714\pi\)
\(500\) 0.688461 + 4.78835i 0.0307889 + 0.214142i
\(501\) 0.541125 1.18490i 0.0241757 0.0529373i
\(502\) 4.36959 30.3912i 0.195024 1.35642i
\(503\) −1.60313 1.03027i −0.0714802 0.0459375i 0.504413 0.863463i \(-0.331709\pi\)
−0.575893 + 0.817525i \(0.695345\pi\)
\(504\) −16.3163 18.8300i −0.726786 0.838756i
\(505\) 9.43927 0.420042
\(506\) 36.6446 + 43.6309i 1.62905 + 1.93963i
\(507\) 6.61365 0.293722
\(508\) −26.0484 30.0614i −1.15571 1.33376i
\(509\) 1.09149 + 0.701457i 0.0483793 + 0.0310915i 0.564607 0.825360i \(-0.309028\pi\)
−0.516228 + 0.856451i \(0.672664\pi\)
\(510\) 2.41580 16.8023i 0.106974 0.744018i
\(511\) −6.77492 + 14.8350i −0.299705 + 0.656262i
\(512\) 5.87590 + 40.8678i 0.259680 + 1.80612i
\(513\) 7.27271 + 2.13546i 0.321098 + 0.0942829i
\(514\) 28.9499 18.6050i 1.27693 0.820631i
\(515\) 6.12391 + 13.4095i 0.269852 + 0.590893i
\(516\) −15.6087 + 4.58313i −0.687135 + 0.201761i
\(517\) 32.2012 37.1622i 1.41621 1.63439i
\(518\) −22.3651 + 25.8107i −0.982665 + 1.13406i
\(519\) 12.2605 3.60002i 0.538178 0.158023i
\(520\) −13.6509 29.8914i −0.598633 1.31082i
\(521\) −14.1235 + 9.07665i −0.618763 + 0.397655i −0.812134 0.583471i \(-0.801694\pi\)
0.193371 + 0.981126i \(0.438058\pi\)
\(522\) 1.82160 + 0.534870i 0.0797293 + 0.0234106i
\(523\) 1.25097 + 8.70067i 0.0547010 + 0.380454i 0.998721 + 0.0505649i \(0.0161022\pi\)
−0.944020 + 0.329889i \(0.892989\pi\)
\(524\) −32.7341 + 71.6777i −1.43000 + 3.13125i
\(525\) −0.477884 + 3.32375i −0.0208566 + 0.145060i
\(526\) 46.9670 + 30.1839i 2.04786 + 1.31608i
\(527\) 14.6425 + 16.8984i 0.637838 + 0.736105i
\(528\) −44.1951 −1.92335
\(529\) −3.97321 + 22.6542i −0.172748 + 0.984966i
\(530\) −29.7326 −1.29150
\(531\) −3.98013 4.59331i −0.172723 0.199333i
\(532\) −103.582 66.5679i −4.49083 2.88608i
\(533\) −0.302803 + 2.10604i −0.0131159 + 0.0912228i
\(534\) −2.43109 + 5.32334i −0.105204 + 0.230364i
\(535\) −1.54817 10.7678i −0.0669334 0.465532i
\(536\) 61.8005 + 18.1463i 2.66938 + 0.783799i
\(537\) 0.0935158 0.0600990i 0.00403551 0.00259346i
\(538\) 15.7385 + 34.4626i 0.678537 + 1.48579i
\(539\) 18.6398 5.47314i 0.802873 0.235745i
\(540\) 3.16795 3.65601i 0.136327 0.157329i
\(541\) −1.24363 + 1.43522i −0.0534677 + 0.0617050i −0.781853 0.623462i \(-0.785725\pi\)
0.728386 + 0.685167i \(0.240271\pi\)
\(542\) −64.4842 + 18.9343i −2.76983 + 0.813297i
\(543\) 1.88126 + 4.11938i 0.0807326 + 0.176780i
\(544\) 57.8627 37.1861i 2.48084 1.59434i
\(545\) −6.77967 1.99069i −0.290409 0.0852718i
\(546\) −5.53417 38.4910i −0.236841 1.64726i
\(547\) 9.17260 20.0852i 0.392192 0.858781i −0.605811 0.795609i \(-0.707151\pi\)
0.998003 0.0631718i \(-0.0201216\pi\)
\(548\) 0.521042 3.62393i 0.0222578 0.154807i
\(549\) −1.15240 0.740602i −0.0491832 0.0316081i
\(550\) 7.78022 + 8.97885i 0.331750 + 0.382859i
\(551\) 5.50319 0.234444
\(552\) −22.8859 27.2491i −0.974091 1.15980i
\(553\) 15.9491 0.678225
\(554\) 6.10238 + 7.04252i 0.259265 + 0.299208i
\(555\) −3.27209 2.10284i −0.138892 0.0892607i
\(556\) 12.7403 88.6111i 0.540311 3.75795i
\(557\) 14.1141 30.9056i 0.598034 1.30951i −0.332429 0.943128i \(-0.607868\pi\)
0.930464 0.366385i \(-0.119405\pi\)
\(558\) 1.28177 + 8.91488i 0.0542615 + 0.377397i
\(559\) −14.2895 4.19578i −0.604382 0.177463i
\(560\) −27.4778 + 17.6589i −1.16115 + 0.746225i
\(561\) −12.2527 26.8298i −0.517311 1.13275i
\(562\) −7.51725 + 2.20726i −0.317096 + 0.0931077i
\(563\) −17.7579 + 20.4937i −0.748407 + 0.863708i −0.994413 0.105560i \(-0.966336\pi\)
0.246006 + 0.969268i \(0.420882\pi\)
\(564\) −34.2855 + 39.5676i −1.44368 + 1.66610i
\(565\) 4.96472 1.45777i 0.208867 0.0613290i
\(566\) −32.5238 71.2172i −1.36708 2.99348i
\(567\) 2.82487 1.81544i 0.118633 0.0762411i
\(568\) −37.1805 10.9172i −1.56006 0.458075i
\(569\) 5.10942 + 35.5368i 0.214198 + 1.48978i 0.758931 + 0.651171i \(0.225722\pi\)
−0.544733 + 0.838609i \(0.683369\pi\)
\(570\) 8.23358 18.0290i 0.344867 0.755152i
\(571\) 5.04869 35.1144i 0.211281 1.46949i −0.557606 0.830106i \(-0.688280\pi\)
0.768887 0.639385i \(-0.220811\pi\)
\(572\) −81.8891 52.6269i −3.42396 2.20044i
\(573\) 7.53914 + 8.70063i 0.314952 + 0.363474i
\(574\) 4.21846 0.176075
\(575\) −0.755584 + 4.73594i −0.0315100 + 0.197502i
\(576\) 8.25114 0.343798
\(577\) 29.1366 + 33.6254i 1.21297 + 1.39984i 0.891560 + 0.452903i \(0.149612\pi\)
0.321411 + 0.946940i \(0.395843\pi\)
\(578\) 55.3078 + 35.5442i 2.30050 + 1.47844i
\(579\) −0.621088 + 4.31976i −0.0258115 + 0.179523i
\(580\) 1.45905 3.19488i 0.0605838 0.132660i
\(581\) −0.0619970 0.431199i −0.00257207 0.0178891i
\(582\) −17.7179 5.20245i −0.734432 0.215649i
\(583\) −43.4610 + 27.9307i −1.79997 + 1.15677i
\(584\) −14.9704 32.7806i −0.619480 1.35647i
\(585\) 4.24933 1.24772i 0.175688 0.0515868i
\(586\) −15.0732 + 17.3954i −0.622670 + 0.718599i
\(587\) 29.7011 34.2769i 1.22590 1.41476i 0.346922 0.937894i \(-0.387227\pi\)
0.878975 0.476867i \(-0.158228\pi\)
\(588\) −19.8463 + 5.82739i −0.818447 + 0.240318i
\(589\) 10.8454 + 23.7480i 0.446875 + 0.978520i
\(590\) −13.3698 + 8.59227i −0.550428 + 0.353738i
\(591\) 5.55720 + 1.63174i 0.228593 + 0.0671209i
\(592\) −5.38433 37.4488i −0.221294 1.53914i
\(593\) 1.53648 3.36443i 0.0630958 0.138161i −0.875457 0.483296i \(-0.839440\pi\)
0.938553 + 0.345135i \(0.112167\pi\)
\(594\) 1.69080 11.7598i 0.0693745 0.482510i
\(595\) −18.3383 11.7853i −0.751797 0.483150i
\(596\) 61.9074 + 71.4450i 2.53583 + 2.92650i
\(597\) 14.0680 0.575764
\(598\) −7.05593 55.0885i −0.288539 2.25274i
\(599\) −15.2093 −0.621433 −0.310717 0.950503i \(-0.600569\pi\)
−0.310717 + 0.950503i \(0.600569\pi\)
\(600\) −4.85904 5.60763i −0.198369 0.228930i
\(601\) 15.5364 + 9.98462i 0.633742 + 0.407281i 0.817693 0.575654i \(-0.195253\pi\)
−0.183952 + 0.982935i \(0.558889\pi\)
\(602\) −4.20213 + 29.2265i −0.171266 + 1.19118i
\(603\) −3.60605 + 7.89614i −0.146850 + 0.321556i
\(604\) −2.78005 19.3357i −0.113119 0.786757i
\(605\) 9.25283 + 2.71687i 0.376181 + 0.110457i
\(606\) −20.7643 + 13.3444i −0.843491 + 0.542079i
\(607\) 13.4419 + 29.4338i 0.545592 + 1.19468i 0.958810 + 0.284047i \(0.0916773\pi\)
−0.413218 + 0.910632i \(0.635595\pi\)
\(608\) 77.0563 22.6258i 3.12505 0.917597i
\(609\) 1.59654 1.84251i 0.0646952 0.0746622i
\(610\) −2.34572 + 2.70711i −0.0949756 + 0.109608i
\(611\) −45.9890 + 13.5036i −1.86051 + 0.546296i
\(612\) 13.0458 + 28.5664i 0.527346 + 1.15473i
\(613\) 26.3364 16.9254i 1.06372 0.683609i 0.112976 0.993598i \(-0.463962\pi\)
0.950740 + 0.309989i \(0.100325\pi\)
\(614\) 21.8679 + 6.42099i 0.882516 + 0.259130i
\(615\) 0.0683724 + 0.475541i 0.00275704 + 0.0191757i
\(616\) −47.0269 + 102.975i −1.89477 + 4.14896i
\(617\) −2.12999 + 14.8144i −0.0857503 + 0.596407i 0.900958 + 0.433906i \(0.142865\pi\)
−0.986708 + 0.162501i \(0.948044\pi\)
\(618\) −32.4284 20.8404i −1.30446 0.838326i
\(619\) −10.4119 12.0159i −0.418488 0.482961i 0.506887 0.862012i \(-0.330796\pi\)
−0.925376 + 0.379051i \(0.876251\pi\)
\(620\) 16.6623 0.669176
\(621\) 4.07398 2.53035i 0.163483 0.101539i
\(622\) −65.8736 −2.64129
\(623\) 4.92140 + 5.67959i 0.197172 + 0.227548i
\(624\) 36.2401 + 23.2901i 1.45076 + 0.932350i
\(625\) −0.142315 + 0.989821i −0.00569259 + 0.0395929i
\(626\) −7.64946 + 16.7500i −0.305734 + 0.669464i
\(627\) −4.90113 34.0881i −0.195732 1.36135i
\(628\) −42.7582 12.5549i −1.70624 0.500996i
\(629\) 21.2415 13.6511i 0.846954 0.544304i
\(630\) −3.64759 7.98710i −0.145323 0.318214i
\(631\) 9.95478 2.92299i 0.396294 0.116362i −0.0775127 0.996991i \(-0.524698\pi\)
0.473806 + 0.880629i \(0.342880\pi\)
\(632\) −23.0789 + 26.6344i −0.918028 + 1.05946i
\(633\) 13.3481 15.4045i 0.530540 0.612276i
\(634\) −22.1368 + 6.49996i −0.879166 + 0.258147i
\(635\) −3.41574 7.47943i −0.135550 0.296812i
\(636\) 46.2741 29.7386i 1.83489 1.17921i
\(637\) −18.1689 5.33488i −0.719879 0.211376i
\(638\) −1.22759 8.53806i −0.0486007 0.338025i
\(639\) 2.16948 4.75049i 0.0858231 0.187926i
\(640\) 0.0548203 0.381284i 0.00216696 0.0150716i
\(641\) −23.6870 15.2227i −0.935581 0.601261i −0.0184423 0.999830i \(-0.505871\pi\)
−0.917138 + 0.398569i \(0.869507\pi\)
\(642\) 18.6282 + 21.4980i 0.735195 + 0.848460i
\(643\) −4.58049 −0.180637 −0.0903184 0.995913i \(-0.528788\pi\)
−0.0903184 + 0.995913i \(0.528788\pi\)
\(644\) −75.0786 + 20.7939i −2.95851 + 0.819396i
\(645\) −3.36276 −0.132409
\(646\) 84.2588 + 97.2398i 3.31512 + 3.82585i
\(647\) −28.8202 18.5216i −1.13304 0.728159i −0.166846 0.985983i \(-0.553358\pi\)
−0.966192 + 0.257823i \(0.916995\pi\)
\(648\) −1.05597 + 7.34443i −0.0414824 + 0.288516i
\(649\) −11.4715 + 25.1191i −0.450297 + 0.986012i
\(650\) −1.64809 11.4627i −0.0646434 0.449605i
\(651\) 11.0974 + 3.25849i 0.434941 + 0.127710i
\(652\) −64.6409 + 41.5422i −2.53153 + 1.62692i
\(653\) −11.3567 24.8677i −0.444422 0.973148i −0.990765 0.135587i \(-0.956708\pi\)
0.546344 0.837561i \(-0.316019\pi\)
\(654\) 17.7280 5.20541i 0.693220 0.203548i
\(655\) −10.6669 + 12.3103i −0.416790 + 0.481002i
\(656\) −3.06029 + 3.53177i −0.119484 + 0.137892i
\(657\) 4.66006 1.36832i 0.181806 0.0533832i
\(658\) 39.4765 + 86.4414i 1.53895 + 3.36984i
\(659\) 20.2184 12.9936i 0.787598 0.506158i −0.0839493 0.996470i \(-0.526753\pi\)
0.871547 + 0.490312i \(0.163117\pi\)
\(660\) −21.0893 6.19237i −0.820900 0.241038i
\(661\) −0.806668 5.61050i −0.0313757 0.218223i 0.968101 0.250559i \(-0.0806144\pi\)
−0.999477 + 0.0323360i \(0.989705\pi\)
\(662\) −22.8041 + 49.9340i −0.886306 + 1.94074i
\(663\) −4.09156 + 28.4575i −0.158903 + 1.10520i
\(664\) 0.809798 + 0.520425i 0.0314262 + 0.0201964i
\(665\) −16.6677 19.2356i −0.646346 0.745923i
\(666\) 10.1707 0.394106
\(667\) 2.32048 2.59604i 0.0898492 0.100519i
\(668\) 6.30150 0.243812
\(669\) 0.983633 + 1.13517i 0.0380294 + 0.0438883i
\(670\) 19.0953 + 12.2718i 0.737718 + 0.474102i
\(671\) −0.885763 + 6.16062i −0.0341945 + 0.237828i
\(672\) 14.7797 32.3631i 0.570140 1.24843i
\(673\) 7.20771 + 50.1307i 0.277837 + 1.93240i 0.353875 + 0.935293i \(0.384864\pi\)
−0.0760377 + 0.997105i \(0.524227\pi\)
\(674\) 14.3770 + 4.22145i 0.553780 + 0.162604i
\(675\) 0.841254 0.540641i 0.0323799 0.0208093i
\(676\) 13.2908 + 29.1029i 0.511186 + 1.11934i
\(677\) −13.8716 + 4.07306i −0.533128 + 0.156541i −0.537206 0.843451i \(-0.680520\pi\)
0.00407769 + 0.999992i \(0.498702\pi\)
\(678\) −8.86040 + 10.2254i −0.340282 + 0.392706i
\(679\) −15.5289 + 17.9213i −0.595944 + 0.687756i
\(680\) 46.2171 13.5706i 1.77235 0.520408i
\(681\) 6.23471 + 13.6521i 0.238914 + 0.523150i
\(682\) 34.4252 22.1237i 1.31821 0.847162i
\(683\) 8.33337 + 2.44690i 0.318867 + 0.0936279i 0.437250 0.899340i \(-0.355953\pi\)
−0.118382 + 0.992968i \(0.537771\pi\)
\(684\) 5.21836 + 36.2945i 0.199529 + 1.38775i
\(685\) 0.314395 0.688429i 0.0120124 0.0263035i
\(686\) 3.40429 23.6774i 0.129977 0.904006i
\(687\) 1.10579 + 0.710648i 0.0421885 + 0.0271129i
\(688\) −21.4204 24.7205i −0.816647 0.942460i
\(689\) 50.3572 1.91845
\(690\) −5.03312 11.4862i −0.191608 0.437271i
\(691\) 44.7625 1.70284 0.851422 0.524481i \(-0.175741\pi\)
0.851422 + 0.524481i \(0.175741\pi\)
\(692\) 40.4805 + 46.7170i 1.53884 + 1.77591i
\(693\) −12.8348 8.24844i −0.487555 0.313332i
\(694\) −3.68399 + 25.6227i −0.139842 + 0.972624i
\(695\) 7.68749 16.8332i 0.291603 0.638521i
\(696\) 0.766674 + 5.33234i 0.0290607 + 0.202122i
\(697\) −2.99249 0.878674i −0.113349 0.0332822i
\(698\) 7.63249 4.90510i 0.288894 0.185661i
\(699\) −6.92222 15.1576i −0.261822 0.573311i
\(700\) −15.5863 + 4.57655i −0.589106 + 0.172977i
\(701\) 9.51336 10.9790i 0.359315 0.414671i −0.547095 0.837070i \(-0.684266\pi\)
0.906410 + 0.422399i \(0.138812\pi\)
\(702\) −7.58367 + 8.75203i −0.286227 + 0.330324i
\(703\) 28.2875 8.30596i 1.06688 0.313265i
\(704\) −15.5735 34.1013i −0.586950 1.28524i
\(705\) −9.10457 + 5.85115i −0.342898 + 0.220367i
\(706\) 12.4368 + 3.65176i 0.468063 + 0.137436i
\(707\) 4.51087 + 31.3738i 0.169649 + 1.17993i
\(708\) 12.2140 26.7450i 0.459031 1.00514i
\(709\) −0.430639 + 2.99516i −0.0161730 + 0.112486i −0.996309 0.0858422i \(-0.972642\pi\)
0.980136 + 0.198328i \(0.0635510\pi\)
\(710\) −11.4882 7.38300i −0.431144 0.277079i
\(711\) −3.11038 3.58957i −0.116648 0.134619i
\(712\) −16.6061 −0.622341
\(713\) 15.7758 + 4.89747i 0.590808 + 0.183412i
\(714\) 57.0011 2.13321
\(715\) −13.1771 15.2072i −0.492795 0.568716i
\(716\) 0.452391 + 0.290734i 0.0169067 + 0.0108652i
\(717\) −3.91817 + 27.2515i −0.146327 + 1.01772i
\(718\) −10.5684 + 23.1416i −0.394410 + 0.863638i
\(719\) −4.54982 31.6447i −0.169680 1.18015i −0.879547 0.475813i \(-0.842154\pi\)
0.709867 0.704336i \(-0.248755\pi\)
\(720\) 9.33308 + 2.74044i 0.347823 + 0.102130i
\(721\) −41.6433 + 26.7625i −1.55088 + 0.996689i
\(722\) 41.7695 + 91.4624i 1.55450 + 3.40388i
\(723\) −8.45177 + 2.48166i −0.314325 + 0.0922941i
\(724\) −14.3465 + 16.5567i −0.533182 + 0.615325i
\(725\) 0.475454 0.548703i 0.0176579 0.0203783i
\(726\) −24.1950 + 7.10430i −0.897961 + 0.263665i
\(727\) −6.88509 15.0762i −0.255354 0.559147i 0.737926 0.674881i \(-0.235805\pi\)
−0.993280 + 0.115734i \(0.963078\pi\)
\(728\) 92.8280 59.6570i 3.44044 2.21103i
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) −1.80739 12.5707i −0.0668945 0.465261i
\(731\) 9.06857 19.8574i 0.335413 0.734452i
\(732\) 0.943095 6.55937i 0.0348578 0.242441i
\(733\) −5.08804 3.26989i −0.187931 0.120776i 0.443292 0.896377i \(-0.353810\pi\)
−0.631223 + 0.775601i \(0.717447\pi\)
\(734\) −38.0841 43.9514i −1.40571 1.62227i
\(735\) −4.27571 −0.157712
\(736\) 21.8182 45.8905i 0.804231 1.69155i
\(737\) 39.4403 1.45280
\(738\) −0.822681 0.949424i −0.0302833 0.0349488i
\(739\) −37.5059 24.1036i −1.37968 0.886665i −0.380406 0.924820i \(-0.624216\pi\)
−0.999272 + 0.0381548i \(0.987852\pi\)
\(740\) 2.67780 18.6245i 0.0984377 0.684649i
\(741\) −13.9449 + 30.5351i −0.512280 + 1.12174i
\(742\) −14.2087 98.8240i −0.521619 3.62794i
\(743\) −41.6727 12.2362i −1.52882 0.448903i −0.594134 0.804366i \(-0.702505\pi\)
−0.934691 + 0.355462i \(0.884323\pi\)
\(744\) −21.4998 + 13.8171i −0.788222 + 0.506559i
\(745\) 8.11796 + 17.7759i 0.297419 + 0.651257i
\(746\) −22.4507 + 6.59212i −0.821978 + 0.241355i
\(747\) −0.0849567 + 0.0980452i −0.00310840 + 0.00358729i
\(748\) 93.4392 107.835i 3.41648 3.94282i
\(749\) 35.0496 10.2915i 1.28069 0.376043i
\(750\) −1.08626 2.37858i −0.0396646 0.0868534i
\(751\) −17.2615 + 11.0933i −0.629881 + 0.404800i −0.816266 0.577677i \(-0.803959\pi\)
0.186384 + 0.982477i \(0.440323\pi\)
\(752\) −101.008 29.6587i −3.68340 1.08154i
\(753\) 1.67105 + 11.6224i 0.0608964 + 0.423544i
\(754\) −3.49279 + 7.64814i −0.127200 + 0.278529i
\(755\) 0.574676 3.99696i 0.0209146 0.145464i
\(756\) 13.6656 + 8.78233i 0.497012 + 0.319410i
\(757\) −13.0239 15.0304i −0.473363 0.546290i 0.467981 0.883738i \(-0.344981\pi\)
−0.941344 + 0.337449i \(0.890436\pi\)
\(758\) 24.3792 0.885493
\(759\) −18.1471 12.0616i −0.658699 0.437807i
\(760\) 56.2414 2.04009
\(761\) −10.8312 12.4999i −0.392631 0.453120i 0.524676 0.851302i \(-0.324187\pi\)
−0.917306 + 0.398182i \(0.869641\pi\)
\(762\) 18.0876 + 11.6242i 0.655245 + 0.421100i
\(763\) 3.37667 23.4853i 0.122244 0.850224i
\(764\) −23.1358 + 50.6603i −0.837023 + 1.83282i
\(765\) 0.923869 + 6.42565i 0.0334025 + 0.232320i
\(766\) −87.1917 25.6018i −3.15036 0.925030i
\(767\) 22.6440 14.5524i 0.817629 0.525458i
\(768\) −6.43686 14.0948i −0.232270 0.508601i
\(769\) 19.3738 5.68867i 0.698638 0.205139i 0.0869209 0.996215i \(-0.472297\pi\)
0.611717 + 0.791077i \(0.290479\pi\)
\(770\) −26.1254 + 30.1504i −0.941495 + 1.08654i
\(771\) −8.61823 + 9.94597i −0.310378 + 0.358195i
\(772\) −20.2569 + 5.94797i −0.729063 + 0.214072i
\(773\) 21.1971 + 46.4152i 0.762407 + 1.66944i 0.742693 + 0.669632i \(0.233548\pi\)
0.0197132 + 0.999806i \(0.493725\pi\)
\(774\) 7.39733 4.75397i 0.265891 0.170878i
\(775\) 3.30483 + 0.970385i 0.118713 + 0.0348573i
\(776\) −7.45712 51.8654i −0.267695 1.86186i
\(777\) 5.42566 11.8805i 0.194644 0.426212i
\(778\) −13.0767 + 90.9503i −0.468822 + 3.26073i
\(779\) −3.06346 1.96877i −0.109760 0.0705384i
\(780\) 14.0300 + 16.1915i 0.502354 + 0.579747i
\(781\) −23.7281 −0.849060
\(782\) 81.3999 + 1.25445i 2.91086 + 0.0448590i
\(783\) −0.726038 −0.0259465
\(784\) −27.2358 31.4318i −0.972708 1.12256i
\(785\) −7.74953 4.98032i −0.276592 0.177755i
\(786\) 6.06165 42.1597i 0.216212 1.50379i
\(787\) −7.95983 + 17.4296i −0.283737 + 0.621298i −0.996812 0.0797906i \(-0.974575\pi\)
0.713074 + 0.701088i \(0.247302\pi\)
\(788\) 3.98743 + 27.7332i 0.142046 + 0.987955i
\(789\) −20.4860 6.01522i −0.729319 0.214147i
\(790\) −10.4482 + 6.71467i −0.371731 + 0.238897i
\(791\) 7.21784 + 15.8049i 0.256637 + 0.561956i
\(792\) 32.3470 9.49794i 1.14940 0.337495i
\(793\) 3.97287 4.58494i 0.141081 0.162816i
\(794\) 49.0676 56.6270i 1.74134 2.00962i
\(795\) 10.9100 3.20346i 0.386937 0.113615i
\(796\) 28.2711 + 61.9051i 1.00204 + 2.19417i
\(797\) 20.9816 13.4841i 0.743207 0.477630i −0.113433 0.993546i \(-0.536185\pi\)
0.856639 + 0.515916i \(0.172548\pi\)
\(798\) 63.8587 + 18.7506i 2.26057 + 0.663764i
\(799\) −9.99868 69.5424i −0.353728 2.46023i
\(800\) 4.40143 9.63779i 0.155614 0.340747i
\(801\) 0.318506 2.21526i 0.0112539 0.0782723i
\(802\) 46.6956 + 30.0094i 1.64888 + 1.05967i
\(803\) −14.4507 16.6771i −0.509956 0.588520i
\(804\) −41.9931 −1.48098
\(805\) −16.1022 0.248150i −0.567527 0.00874612i
\(806\) −39.8876 −1.40498
\(807\) −9.48811 10.9499i −0.333997 0.385454i
\(808\) −58.9205 37.8659i −2.07282 1.33212i
\(809\) −4.53881 + 31.5681i −0.159576 + 1.10988i 0.739840 + 0.672783i \(0.234901\pi\)
−0.899416 + 0.437094i \(0.856008\pi\)
\(810\) −1.08626 + 2.37858i −0.0381673 + 0.0835747i
\(811\) −5.13286 35.6998i −0.180239 1.25359i −0.856197 0.516650i \(-0.827179\pi\)
0.675957 0.736941i \(-0.263730\pi\)
\(812\) 11.3162 + 3.32275i 0.397122 + 0.116606i
\(813\) 21.6216 13.8953i 0.758301 0.487331i
\(814\) −19.1965 42.0346i −0.672838 1.47331i
\(815\) −15.2403 + 4.47495i −0.533844 + 0.156751i
\(816\) −41.3516 + 47.7223i −1.44759 + 1.67061i
\(817\) 16.6917 19.2632i 0.583968 0.673935i
\(818\) −69.3511 + 20.3633i −2.42481 + 0.711987i
\(819\) 6.17779 + 13.5275i 0.215870 + 0.472688i
\(820\) −1.95518 + 1.25652i −0.0682778 + 0.0438795i
\(821\) 23.0051 + 6.75490i 0.802883 + 0.235748i 0.657330 0.753603i \(-0.271686\pi\)
0.145553 + 0.989350i \(0.453504\pi\)
\(822\) 0.281641 + 1.95885i 0.00982335 + 0.0683229i
\(823\) −20.8794 + 45.7196i −0.727812 + 1.59369i 0.0748107 + 0.997198i \(0.476165\pi\)
−0.802622 + 0.596488i \(0.796563\pi\)
\(824\) 15.5667 108.269i 0.542293 3.77173i
\(825\) −3.82224 2.45641i −0.133073 0.0855211i
\(826\) −34.9478 40.3319i −1.21599 1.40333i
\(827\) 22.6627 0.788061 0.394030 0.919097i \(-0.371080\pi\)
0.394030 + 0.919097i \(0.371080\pi\)
\(828\) 19.3217 + 12.8423i 0.671476 + 0.446300i
\(829\) 0.357249 0.0124078 0.00620388 0.999981i \(-0.498025\pi\)
0.00620388 + 0.999981i \(0.498025\pi\)
\(830\) 0.222151 + 0.256376i 0.00771099 + 0.00889895i
\(831\) −2.99796 1.92667i −0.103998 0.0668355i
\(832\) −5.20048 + 36.1701i −0.180294 + 1.25397i
\(833\) 11.5306 25.2484i 0.399510 0.874806i
\(834\) 6.88658 + 47.8972i 0.238463 + 1.65855i
\(835\) 1.24985 + 0.366988i 0.0432527 + 0.0127002i
\(836\) 140.153 90.0707i 4.84729 3.11516i
\(837\) −1.43083 3.13309i −0.0494568 0.108295i
\(838\) −2.12204 + 0.623086i −0.0733046 + 0.0215242i
\(839\) 2.46412 2.84375i 0.0850709 0.0981771i −0.711618 0.702566i \(-0.752037\pi\)
0.796689 + 0.604389i \(0.206583\pi\)
\(840\) 16.3163 18.8300i 0.562966 0.649698i
\(841\) 27.3195 8.02173i 0.942052 0.276612i
\(842\) −12.9013 28.2500i −0.444609 0.973558i
\(843\) 2.52053 1.61985i 0.0868118 0.0557905i
\(844\) 94.6110 + 27.7803i 3.25665 + 0.956238i
\(845\) 0.941220 + 6.54633i 0.0323790 + 0.225201i
\(846\) 11.7562 25.7424i 0.404186 0.885043i
\(847\) −4.60845 + 32.0525i −0.158348 + 1.10134i
\(848\) 93.0448 + 59.7963i 3.19517 + 2.05341i
\(849\) 19.6072 + 22.6280i 0.672919 + 0.776590i
\(850\) 16.9751 0.582240
\(851\) 8.00951 16.8465i 0.274563 0.577490i
\(852\) 25.2640 0.865530
\(853\) −30.1104 34.7493i −1.03096 1.18979i −0.981588 0.191012i \(-0.938823\pi\)
−0.0493728 0.998780i \(-0.515722\pi\)
\(854\) −10.1187 6.50292i −0.346256 0.222525i
\(855\) −1.07871 + 7.50260i −0.0368911 + 0.256583i
\(856\) −33.5315 + 73.4237i −1.14608 + 2.50957i
\(857\) −6.34036 44.0982i −0.216583 1.50636i −0.750524 0.660843i \(-0.770199\pi\)
0.533942 0.845521i \(-0.320710\pi\)
\(858\) 50.4852 + 14.8238i 1.72353 + 0.506075i
\(859\) 10.1776 6.54075i 0.347255 0.223167i −0.355373 0.934725i \(-0.615646\pi\)
0.702628 + 0.711557i \(0.252010\pi\)
\(860\) −6.75783 14.7976i −0.230440 0.504594i
\(861\) −1.54791 + 0.454506i −0.0527525 + 0.0154895i
\(862\) −13.2313 + 15.2697i −0.450659 + 0.520088i
\(863\) −16.1653 + 18.6557i −0.550273 + 0.635049i −0.960947 0.276733i \(-0.910748\pi\)
0.410674 + 0.911782i \(0.365294\pi\)
\(864\) −10.1661 + 2.98503i −0.345857 + 0.101553i
\(865\) 5.30823 + 11.6234i 0.180485 + 0.395208i
\(866\) −86.0240 + 55.2843i −2.92322 + 1.87864i
\(867\) −24.1240 7.08346i −0.819295 0.240567i
\(868\) 7.96266 + 55.3815i 0.270270 + 1.87977i
\(869\) −8.96474 + 19.6300i −0.304108 + 0.665904i
\(870\) −0.270185 + 1.87918i −0.00916013 + 0.0637101i
\(871\) −32.3411 20.7844i −1.09584 0.704252i
\(872\) 34.3334 + 39.6229i 1.16268 + 1.34180i
\(873\) 7.06187 0.239008
\(874\) 90.7801 + 28.1820i 3.07068 + 0.953270i
\(875\) −3.35793 −0.113519
\(876\) 15.3861 + 17.7565i 0.519848 + 0.599936i
\(877\) 20.8903 + 13.4254i 0.705416 + 0.453343i 0.843536 0.537072i \(-0.180470\pi\)
−0.138120 + 0.990415i \(0.544106\pi\)
\(878\) 10.7585 74.8270i 0.363082 2.52529i
\(879\) 3.65669 8.00704i 0.123337 0.270071i
\(880\) −6.28962 43.7453i −0.212023 1.47465i
\(881\) 37.6745 + 11.0622i 1.26928 + 0.372696i 0.845942 0.533274i \(-0.179039\pi\)
0.423342 + 0.905970i \(0.360857\pi\)
\(882\) 9.40560 6.04462i 0.316703 0.203533i
\(883\) 5.02867 + 11.0113i 0.169228 + 0.370558i 0.975177 0.221427i \(-0.0710716\pi\)
−0.805949 + 0.591985i \(0.798344\pi\)
\(884\) −133.447 + 39.1837i −4.48832 + 1.31789i
\(885\) 3.98013 4.59331i 0.133790 0.154402i
\(886\) −15.5433 + 17.9379i −0.522186 + 0.602634i
\(887\) −18.9571 + 5.56632i −0.636518 + 0.186899i −0.584042 0.811724i \(-0.698530\pi\)
−0.0524763 + 0.998622i \(0.516711\pi\)
\(888\) 11.9890 + 26.2522i 0.402323 + 0.880965i
\(889\) 23.2274 14.9274i 0.779024 0.500648i
\(890\) −5.61514 1.64875i −0.188220 0.0552664i
\(891\) 0.646608 + 4.49726i 0.0216622 + 0.150664i
\(892\) −3.01853 + 6.60966i −0.101068 + 0.221308i
\(893\) 11.6745 81.1978i 0.390672 2.71718i
\(894\) −42.9876 27.6265i −1.43772 0.923967i
\(895\) 0.0727959 + 0.0840110i 0.00243330 + 0.00280818i
\(896\) 1.29349 0.0432125
\(897\) 8.52443 + 19.4537i 0.284622 + 0.649541i
\(898\) 29.4802 0.983767
\(899\) −1.63763 1.88992i −0.0546180 0.0630325i
\(900\) 4.06964 + 2.61540i 0.135655 + 0.0871799i
\(901\) −10.5049 + 73.0632i −0.349969 + 2.43409i
\(902\) −2.37113 + 5.19205i −0.0789501 + 0.172877i
\(903\) −1.60701 11.1770i −0.0534779 0.371947i
\(904\) −36.8380 10.8166i −1.22521 0.359755i
\(905\) −3.80972 + 2.44836i −0.126639 + 0.0813863i
\(906\) 4.38639 + 9.60485i 0.145728 + 0.319100i
\(907\) 18.3791 5.39660i 0.610269 0.179191i 0.0380278 0.999277i \(-0.487892\pi\)
0.572241 + 0.820086i \(0.306074\pi\)
\(908\) −47.5458 + 54.8707i −1.57786 + 1.82095i
\(909\) 6.18141 7.13372i 0.205024 0.236611i
\(910\) 37.3116 10.9557i 1.23687 0.363178i
\(911\) 7.36503 + 16.1272i 0.244014 + 0.534317i 0.991522 0.129936i \(-0.0414771\pi\)
−0.747508 + 0.664253i \(0.768750\pi\)
\(912\) −62.0247 + 39.8609i −2.05384 + 1.31993i
\(913\) 0.565564 + 0.166064i 0.0187174 + 0.00549593i
\(914\) 4.87121 + 33.8800i 0.161125 + 1.12065i
\(915\) 0.569061 1.24607i 0.0188126 0.0411938i
\(916\) −0.904950 + 6.29407i −0.0299004 + 0.207962i
\(917\) −46.0138 29.5713i −1.51951 0.976530i
\(918\) −11.1163 12.8289i −0.366893 0.423417i
\(919\) 9.04286 0.298296 0.149148 0.988815i \(-0.452347\pi\)
0.149148 + 0.988815i \(0.452347\pi\)
\(920\) 23.7147 26.5310i 0.781852 0.874700i
\(921\) −8.71593 −0.287200
\(922\) −1.35968 1.56916i −0.0447787 0.0516774i
\(923\) 19.4571 + 12.5043i 0.640439 + 0.411585i
\(924\) 10.5037 73.0548i 0.345546 2.40333i
\(925\) 1.61577 3.53805i 0.0531263 0.116330i
\(926\) 15.5348 + 108.047i 0.510506 + 3.55065i
\(927\) 14.1445 + 4.15321i 0.464567 + 0.136409i
\(928\) −6.47140 + 4.15892i −0.212434 + 0.136523i
\(929\) 0.713917 + 1.56326i 0.0234229 + 0.0512889i 0.920982 0.389605i \(-0.127389\pi\)
−0.897559 + 0.440894i \(0.854661\pi\)
\(930\) −8.64172 + 2.53744i −0.283373 + 0.0832059i
\(931\) 21.2233 24.4929i 0.695564 0.802724i
\(932\) 52.7887 60.9215i 1.72915 1.99555i
\(933\) 24.1714 7.09736i 0.791336 0.232357i
\(934\) −41.8570 91.6539i −1.36960 2.99901i
\(935\) 24.8129 15.9463i 0.811470 0.521500i
\(936\) −31.5299 9.25800i −1.03059 0.302607i
\(937\) 6.23427 + 43.3603i 0.203665 + 1.41652i 0.793291 + 0.608843i \(0.208366\pi\)
−0.589626 + 0.807676i \(0.700725\pi\)
\(938\) −31.6632 + 69.3327i −1.03384 + 2.26379i
\(939\) 1.00218 6.97034i 0.0327050 0.227468i
\(940\) −44.0442 28.3055i −1.43656 0.923223i
\(941\) −27.9470 32.2526i −0.911048 1.05141i −0.998473 0.0552340i \(-0.982410\pi\)
0.0874258 0.996171i \(-0.472136\pi\)
\(942\) 24.0879 0.784828
\(943\) −2.22047 + 0.614988i −0.0723086 + 0.0200268i
\(944\) 59.1195 1.92418
\(945\) 2.19898 + 2.53776i 0.0715328 + 0.0825532i
\(946\) −33.6098 21.5997i −1.09275 0.702267i
\(947\) −0.866591 + 6.02727i −0.0281604 + 0.195860i −0.999045 0.0436866i \(-0.986090\pi\)
0.970885 + 0.239547i \(0.0769988\pi\)
\(948\) 9.54499 20.9006i 0.310007 0.678821i
\(949\) 3.06111 + 21.2905i 0.0993680 + 0.691119i
\(950\) 19.0173 + 5.58397i 0.617002 + 0.181168i
\(951\) 7.42248 4.77014i 0.240691 0.154682i
\(952\) 67.1917 + 147.129i 2.17769 + 4.76848i
\(953\) −48.0173 + 14.0991i −1.55543 + 0.456716i −0.942719 0.333589i \(-0.891740\pi\)
−0.612714 + 0.790305i \(0.709922\pi\)
\(954\) −19.4707 + 22.4704i −0.630389 + 0.727507i
\(955\) −7.53914 + 8.70063i −0.243961 + 0.281546i
\(956\) −127.792 + 37.5231i −4.13309 + 1.21358i
\(957\) 1.37035 + 3.00066i 0.0442973 + 0.0969975i
\(958\) −5.64035 + 3.62483i −0.182231 + 0.117113i
\(959\) 2.43841 + 0.715983i 0.0787405 + 0.0231203i
\(960\) 1.17426 + 8.16716i 0.0378991 + 0.263594i
\(961\) −7.94958 + 17.4071i −0.256438 + 0.561521i
\(962\) −6.41031 + 44.5847i −0.206677 + 1.43747i
\(963\) −9.15159 5.88137i −0.294906 0.189524i
\(964\) −27.9051 32.2042i −0.898763 1.03723i
\(965\) −4.36418 −0.140488
\(966\) 35.7720 22.2179i 1.15094 0.714850i
\(967\) −38.7437 −1.24591 −0.622956 0.782257i \(-0.714068\pi\)
−0.622956 + 0.782257i \(0.714068\pi\)
\(968\) −46.8579 54.0769i −1.50607 1.73810i
\(969\) −41.3944 26.6026i −1.32978 0.854598i
\(970\) 2.62798 18.2780i 0.0843792 0.586870i
\(971\) −10.6638 + 23.3505i −0.342218 + 0.749354i −0.999993 0.00386144i \(-0.998771\pi\)
0.657774 + 0.753215i \(0.271498\pi\)
\(972\) −0.688461 4.78835i −0.0220824 0.153586i
\(973\) 59.6233 + 17.5070i 1.91143 + 0.561248i
\(974\) −39.5230 + 25.3999i −1.26640 + 0.813866i
\(975\) 1.83976 + 4.02851i 0.0589195 + 0.129016i
\(976\) 12.7850 3.75402i 0.409238 0.120163i
\(977\) 32.4951 37.5014i 1.03961 1.19977i 0.0601397 0.998190i \(-0.480845\pi\)
0.979471 0.201585i \(-0.0646092\pi\)
\(978\) 27.1989 31.3893i 0.869726 1.00372i
\(979\) −9.75664 + 2.86481i −0.311824 + 0.0915597i
\(980\) −8.59250 18.8149i −0.274477 0.601022i
\(981\) −5.94420 + 3.82011i −0.189784 + 0.121967i
\(982\) 37.3107 + 10.9554i 1.19063 + 0.349601i
\(983\) 1.48433 + 10.3237i 0.0473427 + 0.329276i 0.999705 + 0.0243054i \(0.00773742\pi\)
−0.952362 + 0.304970i \(0.901353\pi\)
\(984\) 1.48086 3.24263i 0.0472081 0.103371i
\(985\) −0.824260 + 5.73286i −0.0262631 + 0.182664i
\(986\) −10.3681 6.66316i −0.330187 0.212198i
\(987\) −23.7987 27.4652i −0.757521 0.874226i
\(988\) −162.391 −5.16636
\(989\) −2.04890 15.9966i −0.0651511 0.508661i
\(990\) 11.8807 0.377594
\(991\) 9.78359 + 11.2909i 0.310786 + 0.358666i 0.889557 0.456824i \(-0.151013\pi\)
−0.578771 + 0.815490i \(0.696468\pi\)
\(992\) −30.7005 19.7300i −0.974742 0.626429i
\(993\) 2.98765 20.7795i 0.0948101 0.659418i
\(994\) 19.0493 41.7121i 0.604206 1.32303i
\(995\) 2.00208 + 13.9248i 0.0634702 + 0.441445i
\(996\) −0.602170 0.176813i −0.0190805 0.00560254i
\(997\) −26.6800 + 17.1462i −0.844964 + 0.543025i −0.890000 0.455960i \(-0.849296\pi\)
0.0450363 + 0.998985i \(0.485660\pi\)
\(998\) −39.9832 87.5511i −1.26565 2.77138i
\(999\) −3.73199 + 1.09581i −0.118075 + 0.0346699i
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 345.2.m.c.151.1 yes 50
23.4 even 11 7935.2.a.bv.1.23 25
23.16 even 11 inner 345.2.m.c.16.1 50
23.19 odd 22 7935.2.a.bw.1.23 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
345.2.m.c.16.1 50 23.16 even 11 inner
345.2.m.c.151.1 yes 50 1.1 even 1 trivial
7935.2.a.bv.1.23 25 23.4 even 11
7935.2.a.bw.1.23 25 23.19 odd 22