Properties

Label 475.2.bi.a.117.30
Level $475$
Weight $2$
Character 475.117
Analytic conductor $3.793$
Analytic rank $0$
Dimension $2304$
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] = [475,2,Mod(2,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(180))
 
chi = DirichletCharacter(H, H._module([9, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.bi (of order \(180\), degree \(48\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(2304\)
Relative dimension: \(48\) over \(\Q(\zeta_{180})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{180}]$

Embedding invariants

Embedding label 117.30
Character \(\chi\) \(=\) 475.117
Dual form 475.2.bi.a.203.30

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.278268 + 0.655558i) q^{2} +(0.198697 - 0.0386228i) q^{3} +(1.03699 - 1.07384i) q^{4} +(1.59924 - 1.56283i) q^{5} +(0.0806105 + 0.119510i) q^{6} +(0.712034 - 2.65735i) q^{7} +(2.32227 + 0.891434i) q^{8} +(-2.74356 + 1.10847i) q^{9} +O(q^{10})\) \(q+(0.278268 + 0.655558i) q^{2} +(0.198697 - 0.0386228i) q^{3} +(1.03699 - 1.07384i) q^{4} +(1.59924 - 1.56283i) q^{5} +(0.0806105 + 0.119510i) q^{6} +(0.712034 - 2.65735i) q^{7} +(2.32227 + 0.891434i) q^{8} +(-2.74356 + 1.10847i) q^{9} +(1.46954 + 0.613507i) q^{10} +(1.11267 + 0.236504i) q^{11} +(0.164573 - 0.253420i) q^{12} +(-3.11217 + 0.382127i) q^{13} +(1.94018 - 0.272675i) q^{14} +(0.257403 - 0.372297i) q^{15} +(-0.0423716 - 1.21336i) q^{16} +(0.178571 - 0.297192i) q^{17} +(-1.49011 - 1.49011i) q^{18} +(-0.204998 - 4.35408i) q^{19} +(-0.0198305 - 3.33797i) q^{20} +(0.0388449 - 0.555508i) q^{21} +(0.154577 + 0.795229i) q^{22} +(-1.01491 + 3.31961i) q^{23} +(0.495857 + 0.0874330i) q^{24} +(0.115115 - 4.99867i) q^{25} +(-1.11653 - 1.93388i) q^{26} +(-1.01161 + 0.656945i) q^{27} +(-2.11518 - 3.52026i) q^{28} +(-2.00512 + 8.04208i) q^{29} +(0.315689 + 0.0651441i) q^{30} +(3.42584 + 0.360071i) q^{31} +(5.29249 - 2.46793i) q^{32} +(0.230218 + 0.00401847i) q^{33} +(0.244517 + 0.0343646i) q^{34} +(-3.01427 - 5.36251i) q^{35} +(-1.65474 + 4.09562i) q^{36} +(3.38790 + 6.64914i) q^{37} +(2.79731 - 1.34599i) q^{38} +(-0.603621 + 0.196128i) q^{39} +(5.10701 - 2.20370i) q^{40} +(9.26939 - 0.323694i) q^{41} +(0.374977 - 0.129115i) q^{42} +(4.28651 + 6.12178i) q^{43} +(1.40779 - 0.949568i) q^{44} +(-2.65525 + 6.06043i) q^{45} +(-2.45861 + 0.258411i) q^{46} +(-8.86632 + 5.32742i) q^{47} +(-0.0552826 - 0.239455i) q^{48} +(-0.492320 - 0.284241i) q^{49} +(3.30896 - 1.31551i) q^{50} +(0.0240031 - 0.0659480i) q^{51} +(-2.81696 + 3.73823i) q^{52} +(-0.0693819 - 3.97489i) q^{53} +(-0.712164 - 0.480360i) q^{54} +(2.14903 - 1.36068i) q^{55} +(4.02238 - 5.53633i) q^{56} +(-0.208899 - 0.857224i) q^{57} +(-5.83001 + 0.923384i) q^{58} +(5.08648 - 3.17839i) q^{59} +(-0.132862 - 0.662478i) q^{60} +(2.97069 - 1.57954i) q^{61} +(0.717256 + 2.34604i) q^{62} +(0.992083 + 8.07987i) q^{63} +(1.28610 + 1.15801i) q^{64} +(-4.37990 + 5.47492i) q^{65} +(0.0614279 + 0.152039i) q^{66} +(-5.61695 + 6.46156i) q^{67} +(-0.133959 - 0.499942i) q^{68} +(-0.0734463 + 0.698795i) q^{69} +(2.67667 - 3.46825i) q^{70} +(9.54401 - 4.65493i) q^{71} +(-7.35941 + 0.128459i) q^{72} +(-14.6563 - 1.79956i) q^{73} +(-3.41615 + 4.07121i) q^{74} +(-0.170190 - 0.997668i) q^{75} +(-4.88815 - 4.29501i) q^{76} +(1.42073 - 2.78834i) q^{77} +(-0.296542 - 0.341133i) q^{78} +(-3.44064 + 5.10096i) q^{79} +(-1.96404 - 1.87423i) q^{80} +(6.21001 - 5.99694i) q^{81} +(2.79158 + 5.98655i) q^{82} +(0.0247818 + 0.0306029i) q^{83} +(-0.556243 - 0.617771i) q^{84} +(-0.178884 - 0.754356i) q^{85} +(-2.82038 + 4.51356i) q^{86} +(-0.0878030 + 1.67538i) q^{87} +(2.37308 + 1.54109i) q^{88} +(0.147884 - 4.23486i) q^{89} +(-4.71184 - 0.0542473i) q^{90} +(-1.20053 + 8.54221i) q^{91} +(2.51227 + 4.53225i) q^{92} +(0.694612 - 0.0607707i) q^{93} +(-5.95965 - 4.32994i) q^{94} +(-7.13253 - 6.64282i) q^{95} +(0.956284 - 0.694781i) q^{96} +(-7.57187 + 6.58212i) q^{97} +(0.0493398 - 0.401840i) q^{98} +(-3.31482 + 0.584493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2304 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 30 q^{7} - 72 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2304 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 30 q^{7} - 72 q^{8} - 60 q^{9} - 48 q^{10} - 18 q^{11} - 72 q^{12} - 48 q^{13} - 60 q^{14} - 66 q^{15} - 36 q^{16} - 30 q^{17} - 60 q^{19} - 36 q^{20} - 36 q^{21} - 156 q^{22} - 120 q^{23} - 72 q^{25} - 48 q^{26} - 72 q^{27} - 60 q^{28} - 24 q^{30} - 54 q^{31} - 78 q^{32} - 90 q^{33} - 60 q^{34} - 30 q^{35} - 36 q^{36} - 204 q^{38} - 120 q^{39} + 36 q^{40} - 36 q^{41} - 84 q^{42} + 132 q^{43} - 60 q^{44} - 42 q^{45} - 54 q^{46} + 84 q^{47} - 120 q^{48} - 216 q^{50} - 96 q^{51} - 30 q^{53} - 60 q^{54} - 78 q^{55} - 234 q^{57} - 240 q^{58} + 60 q^{59} - 144 q^{60} - 36 q^{61} + 180 q^{62} + 66 q^{63} - 30 q^{64} + 288 q^{65} - 108 q^{66} - 168 q^{67} - 48 q^{68} - 90 q^{69} - 96 q^{70} - 36 q^{71} - 528 q^{72} - 66 q^{73} - 96 q^{76} - 288 q^{77} + 168 q^{78} - 60 q^{79} - 420 q^{80} - 36 q^{81} - 120 q^{82} + 90 q^{83} + 990 q^{84} + 96 q^{85} - 36 q^{86} + 216 q^{87} + 108 q^{88} - 60 q^{89} - 240 q^{90} - 36 q^{91} + 312 q^{92} + 30 q^{93} - 36 q^{95} - 72 q^{96} + 12 q^{97} - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.278268 + 0.655558i 0.196765 + 0.463550i 0.989230 0.146368i \(-0.0467582\pi\)
−0.792465 + 0.609917i \(0.791203\pi\)
\(3\) 0.198697 0.0386228i 0.114718 0.0222989i −0.133124 0.991099i \(-0.542501\pi\)
0.247842 + 0.968800i \(0.420279\pi\)
\(4\) 1.03699 1.07384i 0.518497 0.536919i
\(5\) 1.59924 1.56283i 0.715200 0.698920i
\(6\) 0.0806105 + 0.119510i 0.0329091 + 0.0487898i
\(7\) 0.712034 2.65735i 0.269123 1.00438i −0.690554 0.723280i \(-0.742633\pi\)
0.959678 0.281102i \(-0.0907000\pi\)
\(8\) 2.32227 + 0.891434i 0.821045 + 0.315170i
\(9\) −2.74356 + 1.10847i −0.914521 + 0.369490i
\(10\) 1.46954 + 0.613507i 0.464711 + 0.194008i
\(11\) 1.11267 + 0.236504i 0.335481 + 0.0713087i 0.372572 0.928003i \(-0.378476\pi\)
−0.0370912 + 0.999312i \(0.511809\pi\)
\(12\) 0.164573 0.253420i 0.0475081 0.0731560i
\(13\) −3.11217 + 0.382127i −0.863162 + 0.105983i −0.541326 0.840813i \(-0.682078\pi\)
−0.321836 + 0.946796i \(0.604300\pi\)
\(14\) 1.94018 0.272675i 0.518535 0.0728754i
\(15\) 0.257403 0.372297i 0.0664611 0.0961267i
\(16\) −0.0423716 1.21336i −0.0105929 0.303341i
\(17\) 0.178571 0.297192i 0.0433098 0.0720796i −0.834754 0.550622i \(-0.814390\pi\)
0.878064 + 0.478543i \(0.158835\pi\)
\(18\) −1.49011 1.49011i −0.351223 0.351223i
\(19\) −0.204998 4.35408i −0.0470298 0.998893i
\(20\) −0.0198305 3.33797i −0.00443423 0.746392i
\(21\) 0.0388449 0.555508i 0.00847665 0.121222i
\(22\) 0.154577 + 0.795229i 0.0329559 + 0.169543i
\(23\) −1.01491 + 3.31961i −0.211622 + 0.692186i 0.785670 + 0.618646i \(0.212319\pi\)
−0.997292 + 0.0735399i \(0.976570\pi\)
\(24\) 0.495857 + 0.0874330i 0.101216 + 0.0178472i
\(25\) 0.115115 4.99867i 0.0230229 0.999735i
\(26\) −1.11653 1.93388i −0.218969 0.379265i
\(27\) −1.01161 + 0.656945i −0.194684 + 0.126429i
\(28\) −2.11518 3.52026i −0.399732 0.665266i
\(29\) −2.00512 + 8.04208i −0.372341 + 1.49338i 0.433450 + 0.901177i \(0.357296\pi\)
−0.805791 + 0.592200i \(0.798260\pi\)
\(30\) 0.315689 + 0.0651441i 0.0576367 + 0.0118936i
\(31\) 3.42584 + 0.360071i 0.615300 + 0.0646706i 0.407051 0.913405i \(-0.366557\pi\)
0.208249 + 0.978076i \(0.433224\pi\)
\(32\) 5.29249 2.46793i 0.935589 0.436272i
\(33\) 0.230218 + 0.00401847i 0.0400758 + 0.000699525i
\(34\) 0.244517 + 0.0343646i 0.0419343 + 0.00589349i
\(35\) −3.01427 5.36251i −0.509505 0.906430i
\(36\) −1.65474 + 4.09562i −0.275790 + 0.682603i
\(37\) 3.38790 + 6.64914i 0.556968 + 1.09311i 0.982167 + 0.188011i \(0.0602042\pi\)
−0.425199 + 0.905100i \(0.639796\pi\)
\(38\) 2.79731 1.34599i 0.453783 0.218348i
\(39\) −0.603621 + 0.196128i −0.0966567 + 0.0314057i
\(40\) 5.10701 2.20370i 0.807490 0.348435i
\(41\) 9.26939 0.323694i 1.44764 0.0505526i 0.699754 0.714384i \(-0.253293\pi\)
0.747882 + 0.663831i \(0.231071\pi\)
\(42\) 0.374977 0.129115i 0.0578602 0.0199229i
\(43\) 4.28651 + 6.12178i 0.653687 + 0.933562i 0.999990 0.00456068i \(-0.00145171\pi\)
−0.346302 + 0.938123i \(0.612563\pi\)
\(44\) 1.40779 0.949568i 0.212233 0.143153i
\(45\) −2.65525 + 6.06043i −0.395822 + 0.903436i
\(46\) −2.45861 + 0.258411i −0.362503 + 0.0381006i
\(47\) −8.86632 + 5.32742i −1.29329 + 0.777085i −0.984725 0.174120i \(-0.944292\pi\)
−0.308562 + 0.951204i \(0.599848\pi\)
\(48\) −0.0552826 0.239455i −0.00797935 0.0345624i
\(49\) −0.492320 0.284241i −0.0703315 0.0406059i
\(50\) 3.30896 1.31551i 0.467957 0.186041i
\(51\) 0.0240031 0.0659480i 0.00336111 0.00923457i
\(52\) −2.81696 + 3.73823i −0.390642 + 0.518400i
\(53\) −0.0693819 3.97489i −0.00953034 0.545993i −0.966622 0.256207i \(-0.917527\pi\)
0.957092 0.289786i \(-0.0935840\pi\)
\(54\) −0.712164 0.480360i −0.0969132 0.0653688i
\(55\) 2.14903 1.36068i 0.289775 0.183474i
\(56\) 4.02238 5.53633i 0.537513 0.739824i
\(57\) −0.208899 0.857224i −0.0276694 0.113542i
\(58\) −5.83001 + 0.923384i −0.765518 + 0.121246i
\(59\) 5.08648 3.17839i 0.662203 0.413791i −0.156760 0.987637i \(-0.550105\pi\)
0.818963 + 0.573846i \(0.194549\pi\)
\(60\) −0.132862 0.662478i −0.0171524 0.0855255i
\(61\) 2.97069 1.57954i 0.380358 0.202240i −0.268273 0.963343i \(-0.586453\pi\)
0.648631 + 0.761103i \(0.275342\pi\)
\(62\) 0.717256 + 2.34604i 0.0910915 + 0.297947i
\(63\) 0.992083 + 8.07987i 0.124991 + 1.01797i
\(64\) 1.28610 + 1.15801i 0.160762 + 0.144751i
\(65\) −4.37990 + 5.47492i −0.543260 + 0.679080i
\(66\) 0.0614279 + 0.152039i 0.00756125 + 0.0187148i
\(67\) −5.61695 + 6.46156i −0.686220 + 0.789406i −0.986380 0.164483i \(-0.947404\pi\)
0.300160 + 0.953889i \(0.402960\pi\)
\(68\) −0.133959 0.499942i −0.0162449 0.0606268i
\(69\) −0.0734463 + 0.698795i −0.00884189 + 0.0841250i
\(70\) 2.67667 3.46825i 0.319923 0.414535i
\(71\) 9.54401 4.65493i 1.13267 0.552438i 0.225933 0.974143i \(-0.427457\pi\)
0.906733 + 0.421705i \(0.138568\pi\)
\(72\) −7.35941 + 0.128459i −0.867315 + 0.0151390i
\(73\) −14.6563 1.79956i −1.71538 0.210623i −0.796360 0.604823i \(-0.793244\pi\)
−0.919025 + 0.394200i \(0.871022\pi\)
\(74\) −3.41615 + 4.07121i −0.397120 + 0.473269i
\(75\) −0.170190 0.997668i −0.0196518 0.115201i
\(76\) −4.88815 4.29501i −0.560710 0.492672i
\(77\) 1.42073 2.78834i 0.161907 0.317761i
\(78\) −0.296542 0.341133i −0.0335768 0.0386257i
\(79\) −3.44064 + 5.10096i −0.387102 + 0.573903i −0.971344 0.237677i \(-0.923614\pi\)
0.584242 + 0.811579i \(0.301392\pi\)
\(80\) −1.96404 1.87423i −0.219587 0.209546i
\(81\) 6.21001 5.99694i 0.690001 0.666326i
\(82\) 2.79158 + 5.98655i 0.308278 + 0.661104i
\(83\) 0.0247818 + 0.0306029i 0.00272015 + 0.00335911i 0.778504 0.627639i \(-0.215979\pi\)
−0.775784 + 0.630998i \(0.782645\pi\)
\(84\) −0.556243 0.617771i −0.0606911 0.0674043i
\(85\) −0.178884 0.754356i −0.0194027 0.0818214i
\(86\) −2.82038 + 4.51356i −0.304130 + 0.486709i
\(87\) −0.0878030 + 1.67538i −0.00941347 + 0.179620i
\(88\) 2.37308 + 1.54109i 0.252971 + 0.164281i
\(89\) 0.147884 4.23486i 0.0156757 0.448894i −0.966023 0.258455i \(-0.916787\pi\)
0.981699 0.190439i \(-0.0609911\pi\)
\(90\) −4.71184 0.0542473i −0.496672 0.00571817i
\(91\) −1.20053 + 8.54221i −0.125850 + 0.895467i
\(92\) 2.51227 + 4.53225i 0.261922 + 0.472520i
\(93\) 0.694612 0.0607707i 0.0720279 0.00630163i
\(94\) −5.95965 4.32994i −0.614691 0.446599i
\(95\) −7.13253 6.64282i −0.731782 0.681539i
\(96\) 0.956284 0.694781i 0.0976003 0.0709108i
\(97\) −7.57187 + 6.58212i −0.768807 + 0.668313i −0.948985 0.315321i \(-0.897888\pi\)
0.180179 + 0.983634i \(0.442332\pi\)
\(98\) 0.0493398 0.401840i 0.00498407 0.0405920i
\(99\) −3.31482 + 0.584493i −0.333152 + 0.0587438i
\(100\) −5.24839 5.30721i −0.524839 0.530721i
\(101\) 6.23583 + 2.26966i 0.620488 + 0.225839i 0.633086 0.774081i \(-0.281788\pi\)
−0.0125978 + 0.999921i \(0.504010\pi\)
\(102\) 0.0499121 0.00261578i 0.00494203 0.000259001i
\(103\) 0.359826 0.444349i 0.0354547 0.0437830i −0.759110 0.650962i \(-0.774366\pi\)
0.794565 + 0.607179i \(0.207699\pi\)
\(104\) −7.56794 1.88690i −0.742097 0.185026i
\(105\) −0.806043 0.949096i −0.0786617 0.0926223i
\(106\) 2.58646 1.15157i 0.251220 0.111850i
\(107\) 5.33997 + 1.43084i 0.516234 + 0.138324i 0.507524 0.861638i \(-0.330561\pi\)
0.00870990 + 0.999962i \(0.497228\pi\)
\(108\) −0.343577 + 1.76755i −0.0330607 + 0.170082i
\(109\) −17.1608 9.12458i −1.64371 0.873976i −0.993450 0.114265i \(-0.963549\pi\)
−0.650260 0.759712i \(-0.725340\pi\)
\(110\) 1.49001 + 1.03018i 0.142067 + 0.0982239i
\(111\) 0.929975 + 1.19031i 0.0882693 + 0.112980i
\(112\) −3.25449 0.751359i −0.307521 0.0709968i
\(113\) −5.92136 + 3.01708i −0.557035 + 0.283823i −0.709758 0.704446i \(-0.751196\pi\)
0.152723 + 0.988269i \(0.451196\pi\)
\(114\) 0.503831 0.375484i 0.0471881 0.0351673i
\(115\) 3.56491 + 6.89496i 0.332430 + 0.642959i
\(116\) 6.55660 + 10.4928i 0.608765 + 0.974228i
\(117\) 8.11487 4.49814i 0.750220 0.415854i
\(118\) 3.49902 + 2.45004i 0.322111 + 0.225545i
\(119\) −0.662593 0.686135i −0.0607398 0.0628979i
\(120\) 0.929636 0.635115i 0.0848638 0.0579778i
\(121\) −8.86691 3.94780i −0.806083 0.358891i
\(122\) 1.86213 + 1.50792i 0.168589 + 0.136521i
\(123\) 1.82930 0.422327i 0.164942 0.0380799i
\(124\) 3.93923 3.30541i 0.353754 0.296835i
\(125\) −7.62799 8.17397i −0.682268 0.731102i
\(126\) −5.02076 + 2.89874i −0.447285 + 0.258240i
\(127\) 11.5907 + 12.4295i 1.02851 + 1.10294i 0.994628 + 0.103516i \(0.0330094\pi\)
0.0338825 + 0.999426i \(0.489213\pi\)
\(128\) 3.40113 9.87759i 0.300620 0.873064i
\(129\) 1.08816 + 1.05082i 0.0958070 + 0.0925197i
\(130\) −4.80791 1.34779i −0.421682 0.118209i
\(131\) 3.48880 + 13.9928i 0.304818 + 1.22256i 0.905942 + 0.423401i \(0.139164\pi\)
−0.601125 + 0.799155i \(0.705280\pi\)
\(132\) 0.243049 0.243049i 0.0211547 0.0211547i
\(133\) −11.7163 2.55550i −1.01593 0.221590i
\(134\) −5.79895 1.88419i −0.500953 0.162770i
\(135\) −0.591104 + 2.63158i −0.0508741 + 0.226490i
\(136\) 0.679616 0.530974i 0.0582766 0.0455307i
\(137\) −4.27789 5.67695i −0.365485 0.485015i 0.578184 0.815906i \(-0.303762\pi\)
−0.943669 + 0.330892i \(0.892650\pi\)
\(138\) −0.478538 + 0.146304i −0.0407359 + 0.0124542i
\(139\) −6.77276 0.236510i −0.574458 0.0200605i −0.253802 0.967256i \(-0.581681\pi\)
−0.320656 + 0.947196i \(0.603903\pi\)
\(140\) −8.88425 2.32405i −0.750856 0.196418i
\(141\) −1.55595 + 1.40099i −0.131035 + 0.117984i
\(142\) 5.70737 + 4.96134i 0.478952 + 0.416346i
\(143\) −3.55318 0.310863i −0.297132 0.0259957i
\(144\) 1.46123 + 3.28197i 0.121769 + 0.273497i
\(145\) 9.36177 + 15.9949i 0.777452 + 1.32830i
\(146\) −2.89865 10.1088i −0.239894 0.836610i
\(147\) −0.108801 0.0374631i −0.00897374 0.00308991i
\(148\) 10.6533 + 3.25705i 0.875698 + 0.267728i
\(149\) −5.38539 14.7962i −0.441189 1.21216i −0.938711 0.344705i \(-0.887979\pi\)
0.497523 0.867451i \(-0.334243\pi\)
\(150\) 0.606671 0.389188i 0.0495345 0.0317771i
\(151\) 4.26977i 0.347469i 0.984793 + 0.173735i \(0.0555835\pi\)
−0.984793 + 0.173735i \(0.944417\pi\)
\(152\) 3.40531 10.2941i 0.276207 0.834959i
\(153\) −0.160492 + 1.01330i −0.0129750 + 0.0819208i
\(154\) 2.22326 + 0.155466i 0.179156 + 0.0125278i
\(155\) 6.04147 4.77818i 0.485262 0.383793i
\(156\) −0.415341 + 0.851575i −0.0332539 + 0.0681805i
\(157\) 11.5491 8.08676i 0.921718 0.645394i −0.0133316 0.999911i \(-0.504244\pi\)
0.935049 + 0.354517i \(0.115355\pi\)
\(158\) −4.30140 0.836107i −0.342201 0.0665171i
\(159\) −0.167307 0.787119i −0.0132683 0.0624226i
\(160\) 4.60699 12.2181i 0.364214 0.965924i
\(161\) 8.09870 + 5.06063i 0.638267 + 0.398833i
\(162\) 5.65939 + 2.40227i 0.444644 + 0.188740i
\(163\) −23.8368 1.24923i −1.86704 0.0978476i −0.914934 0.403604i \(-0.867757\pi\)
−0.952110 + 0.305757i \(0.901091\pi\)
\(164\) 9.26470 10.2895i 0.723452 0.803474i
\(165\) 0.374453 0.353365i 0.0291511 0.0275094i
\(166\) −0.0131660 + 0.0247617i −0.00102188 + 0.00192188i
\(167\) −2.07434 6.02433i −0.160518 0.466177i 0.836079 0.548609i \(-0.184842\pi\)
−0.996597 + 0.0824320i \(0.973731\pi\)
\(168\) 0.585407 1.25541i 0.0451651 0.0968569i
\(169\) −3.07424 + 0.766494i −0.236480 + 0.0589611i
\(170\) 0.444747 0.327182i 0.0341105 0.0250937i
\(171\) 5.38879 + 11.7184i 0.412091 + 0.896132i
\(172\) 11.0189 + 1.74522i 0.840182 + 0.133072i
\(173\) −11.9536 + 5.07402i −0.908818 + 0.385770i −0.794212 0.607641i \(-0.792116\pi\)
−0.114606 + 0.993411i \(0.536560\pi\)
\(174\) −1.12274 + 0.408645i −0.0851149 + 0.0309793i
\(175\) −13.2012 3.86512i −0.997920 0.292176i
\(176\) 0.239820 1.36009i 0.0180771 0.102520i
\(177\) 0.887910 0.827990i 0.0667394 0.0622355i
\(178\) 2.81735 1.08148i 0.211169 0.0810602i
\(179\) 1.75904 + 16.7361i 0.131477 + 1.25092i 0.838963 + 0.544189i \(0.183163\pi\)
−0.707486 + 0.706727i \(0.750171\pi\)
\(180\) 3.75445 + 9.13594i 0.279840 + 0.680953i
\(181\) −0.495554 7.08676i −0.0368343 0.526754i −0.980585 0.196096i \(-0.937174\pi\)
0.943750 0.330659i \(-0.107271\pi\)
\(182\) −5.93399 + 1.59001i −0.439856 + 0.117859i
\(183\) 0.529260 0.428587i 0.0391241 0.0316820i
\(184\) −5.31609 + 6.80429i −0.391908 + 0.501619i
\(185\) 15.8095 + 5.33882i 1.16234 + 0.392518i
\(186\) 0.233127 + 0.438448i 0.0170937 + 0.0321486i
\(187\) 0.268977 0.288442i 0.0196695 0.0210930i
\(188\) −3.47353 + 15.0455i −0.253333 + 1.09731i
\(189\) 1.02543 + 3.15596i 0.0745892 + 0.229562i
\(190\) 2.37000 6.52427i 0.171938 0.473320i
\(191\) 1.49616 4.60472i 0.108259 0.333186i −0.882223 0.470832i \(-0.843954\pi\)
0.990481 + 0.137646i \(0.0439538\pi\)
\(192\) 0.300269 + 0.180420i 0.0216700 + 0.0130207i
\(193\) 14.9152 + 6.95508i 1.07362 + 0.500638i 0.877320 0.479906i \(-0.159329\pi\)
0.196301 + 0.980544i \(0.437107\pi\)
\(194\) −6.42197 3.13221i −0.461071 0.224879i
\(195\) −0.658817 + 1.25701i −0.0471789 + 0.0900166i
\(196\) −0.815762 + 0.233916i −0.0582687 + 0.0167083i
\(197\) −0.381354 0.993460i −0.0271703 0.0707811i 0.919324 0.393501i \(-0.128736\pi\)
−0.946495 + 0.322720i \(0.895403\pi\)
\(198\) −1.30558 2.01042i −0.0927835 0.142874i
\(199\) 10.4501 + 12.4539i 0.740786 + 0.882834i 0.996472 0.0839254i \(-0.0267457\pi\)
−0.255686 + 0.966760i \(0.582301\pi\)
\(200\) 4.72332 11.5056i 0.333989 0.813571i
\(201\) −0.866508 + 1.50084i −0.0611188 + 0.105861i
\(202\) 0.247340 + 4.71952i 0.0174028 + 0.332065i
\(203\) 19.9429 + 11.0545i 1.39972 + 0.775875i
\(204\) −0.0459264 0.0941631i −0.00321549 0.00659273i
\(205\) 14.3181 15.0042i 1.00002 1.04794i
\(206\) 0.391425 + 0.112239i 0.0272718 + 0.00782008i
\(207\) −0.895232 10.2325i −0.0622229 0.711211i
\(208\) 0.595526 + 3.76000i 0.0412923 + 0.260709i
\(209\) 0.801663 4.89311i 0.0554522 0.338464i
\(210\) 0.397892 0.792511i 0.0274572 0.0546885i
\(211\) −3.52737 1.42515i −0.242834 0.0981113i 0.249964 0.968255i \(-0.419581\pi\)
−0.492798 + 0.870144i \(0.664026\pi\)
\(212\) −4.34033 4.04743i −0.298095 0.277978i
\(213\) 1.71658 1.29354i 0.117618 0.0886317i
\(214\) 0.547943 + 3.89882i 0.0374566 + 0.266518i
\(215\) 16.4225 + 3.09107i 1.12000 + 0.210809i
\(216\) −2.93484 + 0.623820i −0.199691 + 0.0424456i
\(217\) 3.39615 8.84727i 0.230546 0.600592i
\(218\) 1.20638 13.7890i 0.0817065 0.933910i
\(219\) −2.98166 + 0.208498i −0.201482 + 0.0140890i
\(220\) 0.767379 3.71873i 0.0517366 0.250717i
\(221\) −0.442178 + 0.993149i −0.0297441 + 0.0668064i
\(222\) −0.521538 + 0.940879i −0.0350033 + 0.0631477i
\(223\) −1.16589 0.878564i −0.0780740 0.0588330i 0.562059 0.827097i \(-0.310010\pi\)
−0.640133 + 0.768264i \(0.721121\pi\)
\(224\) −2.78971 15.8212i −0.186395 1.05710i
\(225\) 5.22506 + 13.8418i 0.348338 + 0.922785i
\(226\) −3.62560 3.04224i −0.241171 0.202367i
\(227\) 0.430092 + 0.219143i 0.0285462 + 0.0145450i 0.468205 0.883620i \(-0.344901\pi\)
−0.439659 + 0.898165i \(0.644901\pi\)
\(228\) −1.13715 0.664612i −0.0753094 0.0440150i
\(229\) −14.0307 19.3116i −0.927174 1.27614i −0.960952 0.276715i \(-0.910754\pi\)
0.0337784 0.999429i \(-0.489246\pi\)
\(230\) −3.52805 + 4.25566i −0.232633 + 0.280610i
\(231\) 0.174601 0.608907i 0.0114879 0.0400631i
\(232\) −11.8254 + 16.8884i −0.776376 + 1.10878i
\(233\) −0.0627007 + 3.59212i −0.00410766 + 0.235327i 0.990846 + 0.134995i \(0.0431018\pi\)
−0.994954 + 0.100333i \(0.968009\pi\)
\(234\) 5.20690 + 4.06808i 0.340386 + 0.265939i
\(235\) −5.85348 + 22.3764i −0.381839 + 1.45967i
\(236\) 1.86157 8.75802i 0.121178 0.570098i
\(237\) −0.486632 + 1.14643i −0.0316101 + 0.0744688i
\(238\) 0.265423 0.625298i 0.0172048 0.0405320i
\(239\) 3.91446 18.4161i 0.253205 1.19124i −0.649291 0.760540i \(-0.724934\pi\)
0.902496 0.430697i \(-0.141732\pi\)
\(240\) −0.462638 0.296548i −0.0298631 0.0191421i
\(241\) −17.5669 13.7248i −1.13158 0.884090i −0.137264 0.990534i \(-0.543831\pi\)
−0.994319 + 0.106445i \(0.966053\pi\)
\(242\) 0.120638 6.91133i 0.00775488 0.444277i
\(243\) 3.07784 4.39561i 0.197444 0.281979i
\(244\) 1.38441 4.82801i 0.0886278 0.309082i
\(245\) −1.23156 + 0.314845i −0.0786814 + 0.0201147i
\(246\) 0.785895 + 1.08169i 0.0501069 + 0.0689662i
\(247\) 2.30180 + 13.4723i 0.146460 + 0.857222i
\(248\) 7.63474 + 3.89010i 0.484807 + 0.247021i
\(249\) 0.00610604 + 0.00512357i 0.000386954 + 0.000324693i
\(250\) 3.23589 7.27515i 0.204655 0.460121i
\(251\) 1.93933 + 10.9985i 0.122409 + 0.694217i 0.982813 + 0.184604i \(0.0591002\pi\)
−0.860404 + 0.509613i \(0.829789\pi\)
\(252\) 9.70525 + 7.31343i 0.611373 + 0.460703i
\(253\) −1.91435 + 3.45358i −0.120354 + 0.217125i
\(254\) −4.92295 + 11.0571i −0.308894 + 0.693786i
\(255\) −0.0646790 0.142979i −0.00405036 0.00895371i
\(256\) 10.8746 0.760423i 0.679660 0.0475264i
\(257\) −0.413235 + 4.72330i −0.0257769 + 0.294631i 0.972354 + 0.233513i \(0.0750222\pi\)
−0.998131 + 0.0611180i \(0.980533\pi\)
\(258\) −0.386076 + 1.00576i −0.0240360 + 0.0626160i
\(259\) 20.0814 4.26843i 1.24780 0.265227i
\(260\) 1.33724 + 10.3808i 0.0829323 + 0.643787i
\(261\) −3.41326 24.2866i −0.211275 1.50330i
\(262\) −8.20228 + 6.18086i −0.506738 + 0.381855i
\(263\) 12.8288 + 11.9631i 0.791060 + 0.737676i 0.969185 0.246332i \(-0.0792254\pi\)
−0.178125 + 0.984008i \(0.557003\pi\)
\(264\) 0.531045 + 0.214556i 0.0326835 + 0.0132050i
\(265\) −6.32304 6.24835i −0.388421 0.383833i
\(266\) −1.58498 8.39180i −0.0971814 0.514534i
\(267\) −0.134178 0.847165i −0.00821155 0.0518457i
\(268\) 1.11393 + 12.7323i 0.0680442 + 0.777749i
\(269\) 29.0934 + 8.34240i 1.77386 + 0.508645i 0.993211 0.116328i \(-0.0371124\pi\)
0.780646 + 0.624973i \(0.214890\pi\)
\(270\) −1.88964 + 0.344782i −0.115000 + 0.0209828i
\(271\) 3.04295 + 6.23898i 0.184846 + 0.378991i 0.971014 0.239022i \(-0.0768268\pi\)
−0.786168 + 0.618013i \(0.787938\pi\)
\(272\) −0.368168 0.204079i −0.0223234 0.0123741i
\(273\) 0.0913824 + 1.74368i 0.00553071 + 0.105532i
\(274\) 2.53117 4.38412i 0.152914 0.264854i
\(275\) 1.31029 5.53463i 0.0790136 0.333750i
\(276\) 0.674229 + 0.803514i 0.0405838 + 0.0483659i
\(277\) −12.5538 19.3312i −0.754287 1.16150i −0.982204 0.187819i \(-0.939858\pi\)
0.227917 0.973681i \(-0.426808\pi\)
\(278\) −1.72960 4.50575i −0.103734 0.270237i
\(279\) −9.79815 + 2.80957i −0.586600 + 0.168205i
\(280\) −2.21962 15.1402i −0.132648 0.904801i
\(281\) −17.2349 8.40604i −1.02815 0.501462i −0.154487 0.987995i \(-0.549373\pi\)
−0.873662 + 0.486533i \(0.838261\pi\)
\(282\) −1.35140 0.630168i −0.0804747 0.0375260i
\(283\) −20.5968 12.3758i −1.22435 0.735664i −0.251670 0.967813i \(-0.580980\pi\)
−0.972680 + 0.232149i \(0.925424\pi\)
\(284\) 4.89844 15.0758i 0.290669 0.894587i
\(285\) −1.67378 1.04443i −0.0991460 0.0618667i
\(286\) −0.784948 2.41582i −0.0464150 0.142851i
\(287\) 5.73995 24.8625i 0.338819 1.46759i
\(288\) −11.7847 + 12.6375i −0.694417 + 0.744671i
\(289\) 7.92458 + 14.9040i 0.466152 + 0.876704i
\(290\) −7.88048 + 10.5880i −0.462758 + 0.621751i
\(291\) −1.25029 + 1.60030i −0.0732932 + 0.0938110i
\(292\) −17.1309 + 13.8723i −1.00251 + 0.811815i
\(293\) 2.18221 0.584722i 0.127486 0.0341598i −0.194512 0.980900i \(-0.562312\pi\)
0.321998 + 0.946740i \(0.395646\pi\)
\(294\) −0.00571652 0.0817501i −0.000333394 0.00476776i
\(295\) 3.16720 13.0323i 0.184402 0.758770i
\(296\) 1.94035 + 18.4612i 0.112780 + 1.07303i
\(297\) −1.28095 + 0.491710i −0.0743282 + 0.0285319i
\(298\) 8.20122 7.64776i 0.475084 0.443023i
\(299\) 1.89005 10.7190i 0.109305 0.619897i
\(300\) −1.24782 0.851818i −0.0720429 0.0491798i
\(301\) 19.3198 7.03184i 1.11358 0.405309i
\(302\) −2.79908 + 1.18814i −0.161069 + 0.0683698i
\(303\) 1.32670 + 0.210129i 0.0762170 + 0.0120716i
\(304\) −5.27439 + 0.433226i −0.302507 + 0.0248472i
\(305\) 2.28227 7.16875i 0.130683 0.410481i
\(306\) −0.708940 + 0.176759i −0.0405274 + 0.0101046i
\(307\) 3.48652 7.47686i 0.198986 0.426727i −0.781342 0.624104i \(-0.785464\pi\)
0.980328 + 0.197376i \(0.0632421\pi\)
\(308\) −1.52094 4.41712i −0.0866634 0.251689i
\(309\) 0.0543345 0.102188i 0.00309098 0.00581329i
\(310\) 4.81352 + 2.63092i 0.273390 + 0.149426i
\(311\) 20.7650 23.0619i 1.17748 1.30772i 0.235567 0.971858i \(-0.424305\pi\)
0.941911 0.335863i \(-0.109028\pi\)
\(312\) −1.57660 0.0826263i −0.0892576 0.00467779i
\(313\) 25.7519 + 10.9311i 1.45559 + 0.617859i 0.967028 0.254672i \(-0.0819674\pi\)
0.488558 + 0.872531i \(0.337523\pi\)
\(314\) 8.51509 + 5.32082i 0.480534 + 0.300271i
\(315\) 14.2140 + 11.3712i 0.800871 + 0.640692i
\(316\) 1.90968 + 8.98435i 0.107428 + 0.505409i
\(317\) 12.3280 + 2.39632i 0.692408 + 0.134591i 0.524752 0.851255i \(-0.324158\pi\)
0.167656 + 0.985846i \(0.446380\pi\)
\(318\) 0.469446 0.328710i 0.0263252 0.0184331i
\(319\) −4.13301 + 8.47393i −0.231404 + 0.474449i
\(320\) 3.86654 0.158026i 0.216146 0.00883392i
\(321\) 1.11630 + 0.0780592i 0.0623057 + 0.00435684i
\(322\) −1.06393 + 6.71738i −0.0592904 + 0.374345i
\(323\) −1.33060 0.716587i −0.0740367 0.0398720i
\(324\) 12.8873i 0.715962i
\(325\) 1.55187 + 15.6007i 0.0860824 + 0.865373i
\(326\) −5.81408 15.9740i −0.322012 0.884720i
\(327\) −3.76223 1.15023i −0.208052 0.0636077i
\(328\) 21.8146 + 7.51135i 1.20451 + 0.414745i
\(329\) 7.84369 + 27.3542i 0.432437 + 1.50809i
\(330\) 0.335850 + 0.147145i 0.0184879 + 0.00810009i
\(331\) 4.01960 + 9.02818i 0.220937 + 0.496234i 0.989675 0.143331i \(-0.0457813\pi\)
−0.768737 + 0.639565i \(0.779115\pi\)
\(332\) 0.0585611 + 0.00512343i 0.00321396 + 0.000281185i
\(333\) −16.6653 14.4869i −0.913253 0.793879i
\(334\) 3.37208 3.03623i 0.184512 0.166135i
\(335\) 1.11550 + 19.1119i 0.0609464 + 1.04420i
\(336\) −0.675678 0.0235952i −0.0368613 0.00128722i
\(337\) −5.30769 + 1.62272i −0.289128 + 0.0883953i −0.433576 0.901117i \(-0.642748\pi\)
0.144448 + 0.989512i \(0.453859\pi\)
\(338\) −1.35794 1.80205i −0.0738624 0.0980187i
\(339\) −1.06003 + 0.828185i −0.0575728 + 0.0449808i
\(340\) −0.995557 0.590170i −0.0539917 0.0320065i
\(341\) 3.72666 + 1.21086i 0.201810 + 0.0655720i
\(342\) −6.18260 + 6.79354i −0.334317 + 0.367352i
\(343\) 12.5113 12.5113i 0.675547 0.675547i
\(344\) 4.49726 + 18.0375i 0.242476 + 0.972519i
\(345\) 0.974640 + 1.23232i 0.0524729 + 0.0663460i
\(346\) −6.65263 6.42437i −0.357647 0.345376i
\(347\) 7.32225 21.2653i 0.393079 1.14158i −0.557252 0.830343i \(-0.688144\pi\)
0.950331 0.311240i \(-0.100744\pi\)
\(348\) 1.70804 + 1.83164i 0.0915604 + 0.0981865i
\(349\) 5.45864 3.15155i 0.292194 0.168698i −0.346737 0.937963i \(-0.612710\pi\)
0.638931 + 0.769264i \(0.279377\pi\)
\(350\) −1.13967 9.72973i −0.0609179 0.520076i
\(351\) 2.89726 2.43109i 0.154644 0.129762i
\(352\) 6.47245 1.49428i 0.344983 0.0796455i
\(353\) −19.7895 16.0252i −1.05329 0.852936i −0.0638604 0.997959i \(-0.520341\pi\)
−0.989428 + 0.145022i \(0.953675\pi\)
\(354\) 0.789873 + 0.351674i 0.0419813 + 0.0186913i
\(355\) 7.98827 22.3600i 0.423973 1.18675i
\(356\) −4.39419 4.55032i −0.232892 0.241167i
\(357\) −0.158156 0.110742i −0.00837049 0.00586108i
\(358\) −10.4820 + 5.81028i −0.553992 + 0.307083i
\(359\) −3.58539 5.73782i −0.189230 0.302831i 0.739807 0.672820i \(-0.234917\pi\)
−0.929036 + 0.369989i \(0.879361\pi\)
\(360\) −11.5687 + 11.7070i −0.609723 + 0.617011i
\(361\) −18.9160 + 1.78516i −0.995576 + 0.0939556i
\(362\) 4.50789 2.29688i 0.236929 0.120721i
\(363\) −1.91430 0.441952i −0.100475 0.0231965i
\(364\) 7.92801 + 10.1474i 0.415541 + 0.531868i
\(365\) −26.2512 + 20.0273i −1.37405 + 1.04828i
\(366\) 0.428240 + 0.227699i 0.0223845 + 0.0119020i
\(367\) −2.01350 + 10.3586i −0.105104 + 0.540712i 0.891111 + 0.453785i \(0.149927\pi\)
−0.996215 + 0.0869265i \(0.972295\pi\)
\(368\) 4.07089 + 1.09079i 0.212210 + 0.0568614i
\(369\) −25.0724 + 11.1629i −1.30521 + 0.581119i
\(370\) 0.899383 + 11.8497i 0.0467567 + 0.616037i
\(371\) −10.6121 2.64588i −0.550951 0.137367i
\(372\) 0.655050 0.808919i 0.0339628 0.0419405i
\(373\) 0.485488 0.0254433i 0.0251376 0.00131741i −0.0397630 0.999209i \(-0.512660\pi\)
0.0649006 + 0.997892i \(0.479327\pi\)
\(374\) 0.263938 + 0.0960657i 0.0136479 + 0.00496744i
\(375\) −1.83136 1.32953i −0.0945711 0.0686566i
\(376\) −25.3390 + 4.46795i −1.30676 + 0.230417i
\(377\) 3.16717 25.7946i 0.163118 1.32849i
\(378\) −1.78357 + 1.55043i −0.0917369 + 0.0797456i
\(379\) −0.0643462 + 0.0467503i −0.00330524 + 0.00240140i −0.589437 0.807815i \(-0.700650\pi\)
0.586131 + 0.810216i \(0.300650\pi\)
\(380\) −14.5297 + 0.770621i −0.745357 + 0.0395320i
\(381\) 2.78311 + 2.02204i 0.142583 + 0.103592i
\(382\) 3.43500 0.300523i 0.175750 0.0153761i
\(383\) −18.2577 32.9377i −0.932924 1.68304i −0.704799 0.709407i \(-0.748963\pi\)
−0.228124 0.973632i \(-0.573259\pi\)
\(384\) 0.294294 2.09401i 0.0150181 0.106859i
\(385\) −2.08562 6.67957i −0.106293 0.340422i
\(386\) −0.409033 + 11.7132i −0.0208192 + 0.596185i
\(387\) −18.5461 12.0440i −0.942753 0.612231i
\(388\) −0.783841 + 14.9566i −0.0397935 + 0.759305i
\(389\) −10.9930 + 17.5925i −0.557369 + 0.891976i −0.999989 0.00473283i \(-0.998493\pi\)
0.442620 + 0.896709i \(0.354049\pi\)
\(390\) −1.00737 0.0821064i −0.0510103 0.00415762i
\(391\) 0.805327 + 0.894406i 0.0407271 + 0.0452321i
\(392\) −0.889916 1.09896i −0.0449476 0.0555056i
\(393\) 1.23365 + 2.64558i 0.0622297 + 0.133452i
\(394\) 0.545153 0.526448i 0.0274644 0.0265221i
\(395\) 2.46954 + 13.5348i 0.124256 + 0.681009i
\(396\) −2.80980 + 4.16570i −0.141198 + 0.209334i
\(397\) 7.23132 + 8.31868i 0.362930 + 0.417503i 0.906730 0.421712i \(-0.138571\pi\)
−0.543800 + 0.839215i \(0.683015\pi\)
\(398\) −5.25635 + 10.3162i −0.263477 + 0.517102i
\(399\) −2.42669 0.0552554i −0.121486 0.00276623i
\(400\) −6.07008 + 0.0721259i −0.303504 + 0.00360630i
\(401\) 0.780488 0.930149i 0.0389757 0.0464494i −0.746204 0.665717i \(-0.768126\pi\)
0.785180 + 0.619267i \(0.212570\pi\)
\(402\) −1.22501 0.150412i −0.0610978 0.00750187i
\(403\) −10.7994 + 0.188505i −0.537957 + 0.00939008i
\(404\) 8.90376 4.34265i 0.442978 0.216055i
\(405\) 0.559072 19.2957i 0.0277805 0.958812i
\(406\) −1.69742 + 16.1498i −0.0842414 + 0.801504i
\(407\) 2.19705 + 8.19952i 0.108904 + 0.406435i
\(408\) 0.114530 0.131752i 0.00567008 0.00652268i
\(409\) −8.92808 22.0978i −0.441465 1.09266i −0.969859 0.243666i \(-0.921650\pi\)
0.528394 0.848999i \(-0.322794\pi\)
\(410\) 13.8204 + 5.21115i 0.682539 + 0.257360i
\(411\) −1.06926 0.962769i −0.0527429 0.0474899i
\(412\) −0.104021 0.847181i −0.00512474 0.0417376i
\(413\) −4.82433 15.7797i −0.237390 0.776466i
\(414\) 6.45892 3.43427i 0.317438 0.168785i
\(415\) 0.0874592 + 0.0102116i 0.00429320 + 0.000501268i
\(416\) −15.5281 + 9.70303i −0.761327 + 0.475730i
\(417\) −1.35486 + 0.214589i −0.0663479 + 0.0105085i
\(418\) 3.43080 0.836059i 0.167806 0.0408930i
\(419\) −20.6237 + 28.3861i −1.00754 + 1.38675i −0.0869498 + 0.996213i \(0.527712\pi\)
−0.920586 + 0.390541i \(0.872288\pi\)
\(420\) −1.85504 0.118647i −0.0905165 0.00578938i
\(421\) 7.86962 + 5.30812i 0.383542 + 0.258702i 0.735797 0.677202i \(-0.236808\pi\)
−0.352256 + 0.935904i \(0.614585\pi\)
\(422\) −0.0472852 2.70897i −0.00230181 0.131871i
\(423\) 18.4200 24.4442i 0.895612 1.18852i
\(424\) 3.38223 9.29260i 0.164256 0.451288i
\(425\) −1.46501 0.926828i −0.0710634 0.0449578i
\(426\) 1.32566 + 0.765369i 0.0642284 + 0.0370823i
\(427\) −2.08216 9.01883i −0.100763 0.436452i
\(428\) 7.07400 4.25049i 0.341935 0.205455i
\(429\) −0.718013 + 0.0754662i −0.0346660 + 0.00364354i
\(430\) 2.54347 + 11.6260i 0.122657 + 0.560657i
\(431\) −24.1522 + 16.2909i −1.16337 + 0.784705i −0.980129 0.198363i \(-0.936438\pi\)
−0.183244 + 0.983068i \(0.558660\pi\)
\(432\) 0.839976 + 1.19961i 0.0404134 + 0.0577162i
\(433\) 5.39974 1.85928i 0.259495 0.0893513i −0.192741 0.981250i \(-0.561738\pi\)
0.452236 + 0.891898i \(0.350627\pi\)
\(434\) 6.74494 0.235539i 0.323768 0.0113062i
\(435\) 2.47792 + 2.81655i 0.118807 + 0.135043i
\(436\) −27.5940 + 8.96583i −1.32151 + 0.429385i
\(437\) 14.6619 + 3.73846i 0.701373 + 0.178835i
\(438\) −0.966383 1.89663i −0.0461756 0.0906246i
\(439\) 7.73896 19.1546i 0.369360 0.914199i −0.621998 0.783019i \(-0.713679\pi\)
0.991359 0.131180i \(-0.0418767\pi\)
\(440\) 6.20358 1.24415i 0.295744 0.0593123i
\(441\) 1.66579 + 0.234111i 0.0793231 + 0.0111481i
\(442\) −0.774111 0.0135122i −0.0368207 0.000642708i
\(443\) −8.05726 + 3.75716i −0.382812 + 0.178508i −0.604492 0.796611i \(-0.706624\pi\)
0.221680 + 0.975119i \(0.428846\pi\)
\(444\) 2.24258 + 0.235705i 0.106428 + 0.0111861i
\(445\) −6.38187 7.00366i −0.302530 0.332005i
\(446\) 0.251519 1.00879i 0.0119098 0.0477675i
\(447\) −1.64153 2.73197i −0.0776419 0.129218i
\(448\) 3.99297 2.59306i 0.188650 0.122511i
\(449\) 4.17997 + 7.23993i 0.197265 + 0.341673i 0.947641 0.319338i \(-0.103461\pi\)
−0.750376 + 0.661012i \(0.770127\pi\)
\(450\) −7.62013 + 7.27706i −0.359216 + 0.343044i
\(451\) 10.3903 + 1.83209i 0.489259 + 0.0862696i
\(452\) −2.90055 + 9.48727i −0.136430 + 0.446244i
\(453\) 0.164911 + 0.848391i 0.00774817 + 0.0398609i
\(454\) −0.0239801 + 0.342931i −0.00112544 + 0.0160945i
\(455\) 11.4301 + 15.5372i 0.535852 + 0.728397i
\(456\) 0.279040 2.17692i 0.0130672 0.101944i
\(457\) −15.4506 15.4506i −0.722751 0.722751i 0.246414 0.969165i \(-0.420748\pi\)
−0.969165 + 0.246414i \(0.920748\pi\)
\(458\) 8.75558 14.5717i 0.409121 0.680892i
\(459\) 0.0145952 + 0.417952i 0.000681246 + 0.0195083i
\(460\) 11.1009 + 3.32189i 0.517580 + 0.154884i
\(461\) −0.785125 + 0.110342i −0.0365669 + 0.00513915i −0.157433 0.987530i \(-0.550322\pi\)
0.120866 + 0.992669i \(0.461433\pi\)
\(462\) 0.447760 0.0549780i 0.0208317 0.00255781i
\(463\) −11.7364 + 18.0725i −0.545437 + 0.839899i −0.998673 0.0514910i \(-0.983603\pi\)
0.453236 + 0.891390i \(0.350269\pi\)
\(464\) 9.84292 + 2.09218i 0.456946 + 0.0971269i
\(465\) 1.01587 1.18275i 0.0471101 0.0548486i
\(466\) −2.37229 + 0.958468i −0.109894 + 0.0444002i
\(467\) −1.38038 0.529878i −0.0638763 0.0245198i 0.326220 0.945294i \(-0.394225\pi\)
−0.390096 + 0.920774i \(0.627558\pi\)
\(468\) 3.58478 13.3786i 0.165707 0.618426i
\(469\) 13.1712 + 19.5270i 0.608187 + 0.901675i
\(470\) −16.2979 + 2.38933i −0.751764 + 0.110212i
\(471\) 1.98244 2.05287i 0.0913459 0.0945914i
\(472\) 14.6455 2.84679i 0.674113 0.131034i
\(473\) 3.32163 + 7.82527i 0.152729 + 0.359806i
\(474\) −0.886968 −0.0407398
\(475\) −21.7882 + 0.523502i −0.999711 + 0.0240199i
\(476\) −1.42390 −0.0652644
\(477\) 4.59640 + 10.8284i 0.210455 + 0.495800i
\(478\) 13.1621 2.55845i 0.602020 0.117021i
\(479\) −2.27075 + 2.35143i −0.103753 + 0.107439i −0.769208 0.638999i \(-0.779349\pi\)
0.665455 + 0.746438i \(0.268238\pi\)
\(480\) 0.443499 2.60563i 0.0202428 0.118930i
\(481\) −13.0846 19.3987i −0.596605 0.884503i
\(482\) 4.10908 15.3353i 0.187163 0.698503i
\(483\) 1.80464 + 0.692738i 0.0821141 + 0.0315207i
\(484\) −13.4342 + 5.42778i −0.610647 + 0.246717i
\(485\) −1.82245 + 22.3599i −0.0827534 + 1.01531i
\(486\) 3.73804 + 0.794546i 0.169561 + 0.0360413i
\(487\) −7.87984 + 12.1339i −0.357070 + 0.549839i −0.970865 0.239626i \(-0.922975\pi\)
0.613796 + 0.789465i \(0.289642\pi\)
\(488\) 8.30679 1.01995i 0.376031 0.0461707i
\(489\) −4.78455 + 0.672425i −0.216365 + 0.0304081i
\(490\) −0.549102 0.719747i −0.0248059 0.0325149i
\(491\) 0.316180 + 9.05422i 0.0142690 + 0.408611i 0.985419 + 0.170143i \(0.0544230\pi\)
−0.971150 + 0.238468i \(0.923355\pi\)
\(492\) 1.44346 2.40232i 0.0650762 0.108305i
\(493\) 2.03199 + 2.03199i 0.0915160 + 0.0915160i
\(494\) −8.19137 + 5.25788i −0.368547 + 0.236563i
\(495\) −4.38772 + 6.11526i −0.197214 + 0.274860i
\(496\) 0.291738 4.17205i 0.0130994 0.187330i
\(497\) −5.57409 28.6762i −0.250032 1.28630i
\(498\) −0.00165969 + 0.00542859i −7.43723e−5 + 0.000243261i
\(499\) 39.4133 + 6.94962i 1.76438 + 0.311108i 0.959369 0.282153i \(-0.0910486\pi\)
0.805010 + 0.593261i \(0.202160\pi\)
\(500\) −16.6877 0.285122i −0.746296 0.0127511i
\(501\) −0.644843 1.11690i −0.0288094 0.0498994i
\(502\) −6.67048 + 4.33186i −0.297718 + 0.193340i
\(503\) −7.21831 12.0133i −0.321849 0.535646i 0.653328 0.757075i \(-0.273372\pi\)
−0.975176 + 0.221429i \(0.928928\pi\)
\(504\) −4.89879 + 19.6480i −0.218209 + 0.875190i
\(505\) 13.5197 6.11584i 0.601617 0.272151i
\(506\) −2.79673 0.293948i −0.124330 0.0130676i
\(507\) −0.581238 + 0.271036i −0.0258137 + 0.0120371i
\(508\) 25.3668 + 0.442779i 1.12547 + 0.0196451i
\(509\) 22.1495 + 3.11291i 0.981761 + 0.137977i 0.611751 0.791050i \(-0.290465\pi\)
0.370010 + 0.929028i \(0.379354\pi\)
\(510\) 0.0757332 0.0821874i 0.00335352 0.00363932i
\(511\) −15.2178 + 37.6654i −0.673196 + 1.66622i
\(512\) −5.96090 11.6989i −0.263437 0.517024i
\(513\) 3.06777 + 4.26994i 0.135445 + 0.188522i
\(514\) −3.21139 + 1.04344i −0.141648 + 0.0460243i
\(515\) −0.118995 1.27297i −0.00524353 0.0560936i
\(516\) 2.25682 0.0788100i 0.0993512 0.00346942i
\(517\) −11.1252 + 3.83072i −0.489286 + 0.168475i
\(518\) 8.38620 + 11.9767i 0.368469 + 0.526228i
\(519\) −2.17918 + 1.46987i −0.0956553 + 0.0645203i
\(520\) −15.0518 + 8.80982i −0.660066 + 0.386336i
\(521\) −12.3130 + 1.29415i −0.539443 + 0.0566978i −0.370332 0.928899i \(-0.620756\pi\)
−0.169111 + 0.985597i \(0.554090\pi\)
\(522\) 14.9715 8.99576i 0.655283 0.393734i
\(523\) 0.0508992 + 0.220469i 0.00222567 + 0.00964042i 0.975471 0.220128i \(-0.0706475\pi\)
−0.973245 + 0.229769i \(0.926203\pi\)
\(524\) 18.6439 + 10.7640i 0.814461 + 0.470229i
\(525\) −2.77233 0.258120i −0.120994 0.0112653i
\(526\) −4.27265 + 11.7390i −0.186296 + 0.511845i
\(527\) 0.718766 0.953834i 0.0313099 0.0415497i
\(528\) −0.00487883 0.279508i −0.000212324 0.0121640i
\(529\) 9.07811 + 6.12326i 0.394700 + 0.266229i
\(530\) 2.33666 5.88384i 0.101498 0.255578i
\(531\) −10.4319 + 14.3583i −0.452707 + 0.623098i
\(532\) −14.8939 + 9.93132i −0.645731 + 0.430577i
\(533\) −28.7243 + 4.54948i −1.24419 + 0.197060i
\(534\) 0.518029 0.323700i 0.0224173 0.0140079i
\(535\) 10.7760 6.05722i 0.465888 0.261876i
\(536\) −18.8041 + 9.99833i −0.812214 + 0.431862i
\(537\) 0.995911 + 3.25748i 0.0429767 + 0.140571i
\(538\) 2.62684 + 21.3939i 0.113251 + 0.922355i
\(539\) −0.480563 0.432701i −0.0206993 0.0186378i
\(540\) 2.21292 + 3.36368i 0.0952289 + 0.144750i
\(541\) −6.44499 15.9519i −0.277092 0.685826i 0.722895 0.690958i \(-0.242811\pi\)
−0.999987 + 0.00513178i \(0.998366\pi\)
\(542\) −3.24326 + 3.73094i −0.139310 + 0.160258i
\(543\) −0.372175 1.38898i −0.0159716 0.0596067i
\(544\) 0.211636 2.01358i 0.00907383 0.0863317i
\(545\) −41.7044 + 12.2271i −1.78642 + 0.523753i
\(546\) −1.11766 + 0.545117i −0.0478312 + 0.0233289i
\(547\) −27.2710 + 0.476017i −1.16602 + 0.0203530i −0.597191 0.802099i \(-0.703716\pi\)
−0.568834 + 0.822452i \(0.692605\pi\)
\(548\) −10.5323 1.29320i −0.449916 0.0552427i
\(549\) −6.39939 + 7.62650i −0.273119 + 0.325491i
\(550\) 3.99288 0.681137i 0.170257 0.0290438i
\(551\) 35.4269 + 7.08182i 1.50924 + 0.301696i
\(552\) −0.793491 + 1.55731i −0.0337732 + 0.0662837i
\(553\) 11.1052 + 12.7750i 0.472240 + 0.543250i
\(554\) 9.17940 13.6090i 0.389995 0.578192i
\(555\) 3.34751 + 0.450199i 0.142094 + 0.0191099i
\(556\) −7.27728 + 7.02759i −0.308625 + 0.298036i
\(557\) −5.74085 12.3113i −0.243248 0.521646i 0.746342 0.665562i \(-0.231808\pi\)
−0.989590 + 0.143916i \(0.954030\pi\)
\(558\) −4.56835 5.64144i −0.193394 0.238821i
\(559\) −15.6797 17.4140i −0.663180 0.736536i
\(560\) −6.37895 + 3.88463i −0.269560 + 0.164155i
\(561\) 0.0423044 0.0677012i 0.00178609 0.00285835i
\(562\) 0.714718 13.6376i 0.0301486 0.575269i
\(563\) 31.3198 + 20.3393i 1.31997 + 0.857200i 0.996042 0.0888804i \(-0.0283289\pi\)
0.323931 + 0.946081i \(0.394996\pi\)
\(564\) −0.109080 + 3.12365i −0.00459311 + 0.131529i
\(565\) −4.75446 + 14.0791i −0.200022 + 0.592313i
\(566\) 2.38163 16.9462i 0.100107 0.712300i
\(567\) −11.5142 20.7722i −0.483551 0.872349i
\(568\) 26.3133 2.30212i 1.10408 0.0965946i
\(569\) −34.6887 25.2028i −1.45423 1.05656i −0.984821 0.173574i \(-0.944468\pi\)
−0.469405 0.882983i \(-0.655532\pi\)
\(570\) 0.218927 1.38789i 0.00916983 0.0581323i
\(571\) 18.6138 13.5237i 0.778964 0.565951i −0.125704 0.992068i \(-0.540119\pi\)
0.904668 + 0.426117i \(0.140119\pi\)
\(572\) −4.01844 + 3.49318i −0.168019 + 0.146057i
\(573\) 0.119436 0.972730i 0.00498952 0.0406364i
\(574\) 17.8960 3.15556i 0.746967 0.131710i
\(575\) 16.4768 + 5.45532i 0.687130 + 0.227503i
\(576\) −4.81210 1.75146i −0.200504 0.0729775i
\(577\) 10.5491 0.552855i 0.439165 0.0230157i 0.168527 0.985697i \(-0.446099\pi\)
0.270638 + 0.962681i \(0.412765\pi\)
\(578\) −7.56526 + 9.34232i −0.314674 + 0.388589i
\(579\) 3.23223 + 0.805887i 0.134327 + 0.0334915i
\(580\) 26.8840 + 6.53353i 1.11630 + 0.271290i
\(581\) 0.0989681 0.0440634i 0.00410589 0.00182806i
\(582\) −1.39700 0.374326i −0.0579076 0.0155163i
\(583\) 0.862879 4.43913i 0.0357368 0.183850i
\(584\) −32.4315 17.2442i −1.34203 0.713568i
\(585\) 5.94775 19.8758i 0.245909 0.821762i
\(586\) 0.990559 + 1.26786i 0.0409196 + 0.0523747i
\(587\) 15.7548 + 3.63729i 0.650272 + 0.150127i 0.537193 0.843459i \(-0.319485\pi\)
0.113078 + 0.993586i \(0.463929\pi\)
\(588\) −0.153055 + 0.0779854i −0.00631188 + 0.00321606i
\(589\) 0.865483 14.9902i 0.0356616 0.617660i
\(590\) 9.42477 1.55019i 0.388011 0.0638202i
\(591\) −0.114144 0.182669i −0.00469526 0.00751398i
\(592\) 7.92426 4.39249i 0.325685 0.180530i
\(593\) 1.24329 + 0.870563i 0.0510559 + 0.0357497i 0.598826 0.800879i \(-0.295634\pi\)
−0.547770 + 0.836629i \(0.684523\pi\)
\(594\) −0.678792 0.702910i −0.0278512 0.0288407i
\(595\) −2.13196 0.0617710i −0.0874017 0.00253237i
\(596\) −21.4734 9.56056i −0.879584 0.391616i
\(597\) 2.55740 + 2.07094i 0.104668 + 0.0847581i
\(598\) 7.55288 1.74372i 0.308860 0.0713060i
\(599\) −12.0346 + 10.0982i −0.491721 + 0.412603i −0.854643 0.519217i \(-0.826224\pi\)
0.362922 + 0.931820i \(0.381779\pi\)
\(600\) 0.494129 2.46856i 0.0201728 0.100779i
\(601\) 16.1073 9.29954i 0.657030 0.379336i −0.134115 0.990966i \(-0.542819\pi\)
0.791144 + 0.611630i \(0.209486\pi\)
\(602\) 9.98587 + 10.7085i 0.406994 + 0.436447i
\(603\) 8.24800 23.9539i 0.335885 0.975480i
\(604\) 4.58504 + 4.42772i 0.186563 + 0.180162i
\(605\) −20.3500 + 7.54402i −0.827347 + 0.306708i
\(606\) 0.231427 + 0.928203i 0.00940108 + 0.0377057i
\(607\) −21.7410 + 21.7410i −0.882441 + 0.882441i −0.993782 0.111341i \(-0.964485\pi\)
0.111341 + 0.993782i \(0.464485\pi\)
\(608\) −11.8305 22.5380i −0.479790 0.914036i
\(609\) 4.38955 + 1.42625i 0.177874 + 0.0577946i
\(610\) 5.33462 0.498670i 0.215992 0.0201906i
\(611\) 25.5578 19.9679i 1.03396 0.807816i
\(612\) 0.921696 + 1.22313i 0.0372574 + 0.0494422i
\(613\) 12.6455 3.86613i 0.510749 0.156152i −0.0263796 0.999652i \(-0.508398\pi\)
0.537129 + 0.843500i \(0.319509\pi\)
\(614\) 5.87171 + 0.205045i 0.236963 + 0.00827492i
\(615\) 2.26546 3.53429i 0.0913520 0.142516i
\(616\) 5.78493 5.20878i 0.233082 0.209868i
\(617\) −20.6272 17.9309i −0.830418 0.721871i 0.132640 0.991164i \(-0.457655\pi\)
−0.963058 + 0.269293i \(0.913210\pi\)
\(618\) 0.0821099 + 0.00718369i 0.00330294 + 0.000288970i
\(619\) 7.00022 + 15.7227i 0.281362 + 0.631950i 0.997842 0.0656574i \(-0.0209144\pi\)
−0.716480 + 0.697608i \(0.754248\pi\)
\(620\) 1.13397 11.4425i 0.0455412 0.459542i
\(621\) −1.15411 4.02487i −0.0463130 0.161513i
\(622\) 20.8967 + 7.19530i 0.837880 + 0.288505i
\(623\) −11.1482 3.40834i −0.446643 0.136552i
\(624\) 0.263551 + 0.724101i 0.0105505 + 0.0289872i
\(625\) −24.9735 1.15084i −0.998940 0.0460336i
\(626\) 19.9237i 0.796310i
\(627\) −0.0296975 1.00321i −0.00118601 0.0400643i
\(628\) 3.29246 20.7878i 0.131383 0.829522i
\(629\) 2.58105 + 0.180485i 0.102913 + 0.00719639i
\(630\) −3.49914 + 12.4824i −0.139409 + 0.497309i
\(631\) −4.02921 + 8.26111i −0.160400 + 0.328870i −0.963825 0.266538i \(-0.914120\pi\)
0.803424 + 0.595407i \(0.203009\pi\)
\(632\) −12.5373 + 8.77868i −0.498705 + 0.349197i
\(633\) −0.755921 0.146936i −0.0300451 0.00584018i
\(634\) 1.85956 + 8.74853i 0.0738525 + 0.347448i
\(635\) 37.9616 + 1.76341i 1.50646 + 0.0699787i
\(636\) −1.01873 0.636576i −0.0403954 0.0252419i
\(637\) 1.64080 + 0.696480i 0.0650110 + 0.0275955i
\(638\) −6.70524 0.351407i −0.265463 0.0139123i
\(639\) −21.0247 + 23.3503i −0.831726 + 0.923725i
\(640\) −9.99780 21.1120i −0.395198 0.834525i
\(641\) 12.4173 23.3536i 0.490455 0.922412i −0.507691 0.861539i \(-0.669501\pi\)
0.998146 0.0608722i \(-0.0193882\pi\)
\(642\) 0.259458 + 0.753520i 0.0102400 + 0.0297391i
\(643\) 19.7530 42.3604i 0.778981 1.67053i 0.0377423 0.999288i \(-0.487983\pi\)
0.741238 0.671242i \(-0.234239\pi\)
\(644\) 13.8326 3.44885i 0.545080 0.135904i
\(645\) 3.38248 0.0200949i 0.133185 0.000791237i
\(646\) 0.0995006 1.07169i 0.00391480 0.0421651i
\(647\) 33.4907 + 5.30441i 1.31666 + 0.208538i 0.774946 0.632028i \(-0.217777\pi\)
0.541710 + 0.840566i \(0.317777\pi\)
\(648\) 19.7672 8.39067i 0.776528 0.329616i
\(649\) 6.41125 2.33350i 0.251664 0.0915981i
\(650\) −9.79536 + 5.35853i −0.384205 + 0.210179i
\(651\) 0.333099 1.88910i 0.0130552 0.0740395i
\(652\) −26.0601 + 24.3014i −1.02059 + 0.951717i
\(653\) 41.1214 15.7850i 1.60920 0.617715i 0.622848 0.782343i \(-0.285976\pi\)
0.986356 + 0.164627i \(0.0526422\pi\)
\(654\) −0.292866 2.78643i −0.0114520 0.108958i
\(655\) 27.4478 + 16.9254i 1.07247 + 0.661330i
\(656\) −0.785517 11.2334i −0.0306693 0.438591i
\(657\) 42.2051 11.3088i 1.64658 0.441199i
\(658\) −15.7496 + 12.7538i −0.613984 + 0.497195i
\(659\) 20.4509 26.1759i 0.796652 1.01967i −0.202532 0.979276i \(-0.564917\pi\)
0.999184 0.0403927i \(-0.0128609\pi\)
\(660\) 0.00884817 0.768539i 0.000344415 0.0299153i
\(661\) −2.50277 4.70703i −0.0973466 0.183082i 0.829516 0.558483i \(-0.188616\pi\)
−0.926863 + 0.375400i \(0.877505\pi\)
\(662\) −4.79997 + 5.14734i −0.186556 + 0.200057i
\(663\) −0.0495014 + 0.214414i −0.00192247 + 0.00832715i
\(664\) 0.0302694 + 0.0931595i 0.00117468 + 0.00361529i
\(665\) −22.7309 + 14.2237i −0.881465 + 0.551571i
\(666\) 4.85961 14.9563i 0.188306 0.579546i
\(667\) −24.6616 14.8182i −0.954899 0.573761i
\(668\) −8.62024 4.01968i −0.333527 0.155526i
\(669\) −0.265592 0.129538i −0.0102684 0.00500823i
\(670\) −12.2186 + 6.04951i −0.472045 + 0.233713i
\(671\) 3.67895 1.05492i 0.142024 0.0407248i
\(672\) −1.16537 3.03589i −0.0449550 0.117112i
\(673\) −10.5048 16.1759i −0.404930 0.623537i 0.576104 0.817377i \(-0.304572\pi\)
−0.981033 + 0.193840i \(0.937906\pi\)
\(674\) −2.54075 3.02795i −0.0978660 0.116632i
\(675\) 3.16740 + 5.13232i 0.121913 + 0.197543i
\(676\) −2.36487 + 4.09608i −0.0909567 + 0.157542i
\(677\) −0.323438 6.17156i −0.0124307 0.237192i −0.997778 0.0666306i \(-0.978775\pi\)
0.985347 0.170562i \(-0.0545582\pi\)
\(678\) −0.837896 0.464453i −0.0321792 0.0178372i
\(679\) 12.0996 + 24.8078i 0.464338 + 0.952035i
\(680\) 0.257043 1.91128i 0.00985716 0.0732942i
\(681\) 0.0939219 + 0.0269317i 0.00359909 + 0.00103202i
\(682\) 0.243217 + 2.77999i 0.00931328 + 0.106451i
\(683\) −0.127021 0.801977i −0.00486031 0.0306868i 0.985139 0.171759i \(-0.0549450\pi\)
−0.989999 + 0.141072i \(0.954945\pi\)
\(684\) 18.1719 + 6.36526i 0.694818 + 0.243382i
\(685\) −15.7135 2.39317i −0.600381 0.0914382i
\(686\) 11.6834 + 4.72040i 0.446074 + 0.180226i
\(687\) −3.53372 3.29525i −0.134820 0.125722i
\(688\) 7.24631 5.46049i 0.276263 0.208179i
\(689\) 1.73484 + 12.3440i 0.0660921 + 0.470270i
\(690\) −0.536648 + 0.981849i −0.0204298 + 0.0373784i
\(691\) −10.3963 + 2.20980i −0.395493 + 0.0840647i −0.401365 0.915918i \(-0.631464\pi\)
0.00587198 + 0.999983i \(0.498131\pi\)
\(692\) −6.94716 + 18.0980i −0.264092 + 0.687982i
\(693\) −0.807067 + 9.22482i −0.0306579 + 0.350422i
\(694\) 15.9782 1.11731i 0.606525 0.0424124i
\(695\) −11.2009 + 10.2064i −0.424873 + 0.387153i
\(696\) −1.69739 + 3.81241i −0.0643396 + 0.144509i
\(697\) 1.55904 2.81259i 0.0590530 0.106534i
\(698\) 3.58499 + 2.70148i 0.135694 + 0.102253i
\(699\) 0.126279 + 0.716165i 0.00477632 + 0.0270878i
\(700\) −17.8401 + 10.1679i −0.674293 + 0.384310i
\(701\) −0.288577 0.242145i −0.0108994 0.00914569i 0.637322 0.770598i \(-0.280042\pi\)
−0.648221 + 0.761452i \(0.724487\pi\)
\(702\) 2.39994 + 1.22283i 0.0905797 + 0.0461527i
\(703\) 28.2563 16.1143i 1.06571 0.607761i
\(704\) 1.15712 + 1.59264i 0.0436106 + 0.0600249i
\(705\) −0.298831 + 4.67220i −0.0112546 + 0.175965i
\(706\) 4.99868 17.4325i 0.188128 0.656080i
\(707\) 10.4714 14.9547i 0.393817 0.562429i
\(708\) 0.0316302 1.81209i 0.00118873 0.0681026i
\(709\) −1.95892 1.53047i −0.0735687 0.0574781i 0.578206 0.815891i \(-0.303753\pi\)
−0.651775 + 0.758413i \(0.725975\pi\)
\(710\) 16.8812 0.985301i 0.633539 0.0369777i
\(711\) 3.78535 17.8087i 0.141962 0.667877i
\(712\) 4.11853 9.70264i 0.154348 0.363622i
\(713\) −4.67220 + 11.0070i −0.174975 + 0.412216i
\(714\) 0.0285881 0.134496i 0.00106988 0.00503339i
\(715\) −6.16821 + 5.05588i −0.230678 + 0.189079i
\(716\) 19.7960 + 15.4663i 0.739811 + 0.578004i
\(717\) 0.0665109 3.81041i 0.00248390 0.142302i
\(718\) 2.76378 3.94708i 0.103143 0.147304i
\(719\) −1.32606 + 4.62453i −0.0494537 + 0.172466i −0.982113 0.188293i \(-0.939704\pi\)
0.932659 + 0.360759i \(0.117482\pi\)
\(720\) 7.46601 + 2.96499i 0.278242 + 0.110499i
\(721\) −0.924580 1.27257i −0.0344331 0.0473932i
\(722\) −6.43398 11.9038i −0.239448 0.443012i
\(723\) −4.02058 2.04859i −0.149527 0.0761878i
\(724\) −8.12391 6.81677i −0.301923 0.253343i
\(725\) 39.9689 + 10.9487i 1.48441 + 0.406624i
\(726\) −0.242964 1.37792i −0.00901725 0.0511394i
\(727\) −9.42822 7.10467i −0.349673 0.263498i 0.412380 0.911012i \(-0.364698\pi\)
−0.762053 + 0.647514i \(0.775809\pi\)
\(728\) −10.4028 + 18.7671i −0.385552 + 0.695555i
\(729\) −10.0922 + 22.6674i −0.373785 + 0.839535i
\(730\) −20.4340 11.6362i −0.756295 0.430677i
\(731\) 2.58479 0.180746i 0.0956018 0.00668513i
\(732\) 0.0886069 1.01278i 0.00327500 0.0374335i
\(733\) 7.32473 19.0816i 0.270545 0.704794i −0.729244 0.684254i \(-0.760128\pi\)
0.999789 0.0205401i \(-0.00653856\pi\)
\(734\) −7.35093 + 1.56249i −0.271328 + 0.0576725i
\(735\) −0.232547 + 0.110125i −0.00857762 + 0.00406202i
\(736\) 2.82118 + 20.0737i 0.103990 + 0.739927i
\(737\) −7.77797 + 5.86112i −0.286505 + 0.215897i
\(738\) −14.2948 13.3301i −0.526198 0.490688i
\(739\) 40.4947 + 16.3609i 1.48962 + 0.601846i 0.967915 0.251279i \(-0.0808513\pi\)
0.521706 + 0.853125i \(0.325296\pi\)
\(740\) 22.1274 11.4406i 0.813420 0.420564i
\(741\) 0.977699 + 2.58801i 0.0359167 + 0.0950728i
\(742\) −1.21847 7.69309i −0.0447313 0.282422i
\(743\) 0.0853243 + 0.975262i 0.00313025 + 0.0357789i 0.997599 0.0692522i \(-0.0220613\pi\)
−0.994469 + 0.105031i \(0.966506\pi\)
\(744\) 1.66725 + 0.478075i 0.0611243 + 0.0175271i
\(745\) −31.7366 15.2462i −1.16274 0.558579i
\(746\) 0.151775 + 0.311186i 0.00555689 + 0.0113933i
\(747\) −0.101913 0.0564912i −0.00372880 0.00206690i
\(748\) −0.0308131 0.587950i −0.00112664 0.0214976i
\(749\) 7.60447 13.1713i 0.277861 0.481270i
\(750\) 0.361975 1.57053i 0.0132174 0.0573476i
\(751\) −20.3086 24.2029i −0.741073 0.883176i 0.255422 0.966830i \(-0.417786\pi\)
−0.996495 + 0.0836533i \(0.973341\pi\)
\(752\) 6.83978 + 10.5323i 0.249421 + 0.384075i
\(753\) 0.810129 + 2.11046i 0.0295228 + 0.0769094i
\(754\) 17.7912 5.10154i 0.647916 0.185787i
\(755\) 6.67293 + 6.82838i 0.242853 + 0.248510i
\(756\) 4.45235 + 2.17156i 0.161930 + 0.0789788i
\(757\) −18.3208 8.54315i −0.665882 0.310506i 0.0601273 0.998191i \(-0.480849\pi\)
−0.726009 + 0.687685i \(0.758627\pi\)
\(758\) −0.0485530 0.0291736i −0.00176353 0.00105963i
\(759\) −0.246989 + 0.760154i −0.00896513 + 0.0275918i
\(760\) −10.6420 21.7846i −0.386026 0.790210i
\(761\) 12.7215 + 39.1526i 0.461153 + 1.41928i 0.863758 + 0.503908i \(0.168105\pi\)
−0.402605 + 0.915374i \(0.631895\pi\)
\(762\) −0.551119 + 2.38716i −0.0199649 + 0.0864776i
\(763\) −36.4663 + 39.1053i −1.32017 + 1.41571i
\(764\) −3.39321 6.38170i −0.122762 0.230882i
\(765\) 1.32696 + 1.87134i 0.0479764 + 0.0676583i
\(766\) 16.5121 21.1345i 0.596605 0.763620i
\(767\) −14.6155 + 11.8354i −0.527734 + 0.427350i
\(768\) 2.13137 0.571099i 0.0769093 0.0206078i
\(769\) −1.99399 28.5153i −0.0719050 1.02829i −0.890815 0.454367i \(-0.849866\pi\)
0.818910 0.573922i \(-0.194579\pi\)
\(770\) 3.79849 3.22596i 0.136888 0.116255i
\(771\) 0.100318 + 0.954465i 0.00361288 + 0.0343742i
\(772\) 22.9356 8.80415i 0.825470 0.316868i
\(773\) 21.6825 20.2193i 0.779867 0.727238i −0.187044 0.982352i \(-0.559891\pi\)
0.966911 + 0.255114i \(0.0821129\pi\)
\(774\) 2.73475 15.5095i 0.0982986 0.557479i
\(775\) 2.19424 17.0832i 0.0788195 0.613648i
\(776\) −23.4514 + 8.53562i −0.841857 + 0.306411i
\(777\) 3.82525 1.62372i 0.137230 0.0582507i
\(778\) −14.5919 2.31114i −0.523146 0.0828582i
\(779\) −3.30960 40.2933i −0.118579 1.44366i
\(780\) 0.666640 + 2.01098i 0.0238695 + 0.0720045i
\(781\) 11.7202 2.92217i 0.419382 0.104564i
\(782\) −0.362239 + 0.776824i −0.0129536 + 0.0277792i
\(783\) −3.25482 9.45267i −0.116318 0.337811i
\(784\) −0.324027 + 0.609407i −0.0115724 + 0.0217645i
\(785\) 5.83148 30.9819i 0.208135 1.10579i
\(786\) −1.39105 + 1.54491i −0.0496170 + 0.0551052i
\(787\) 30.0564 + 1.57519i 1.07139 + 0.0561494i 0.579866 0.814712i \(-0.303105\pi\)
0.491529 + 0.870861i \(0.336438\pi\)
\(788\) −1.46228 0.620699i −0.0520914 0.0221115i
\(789\) 3.01110 + 1.88154i 0.107198 + 0.0669848i
\(790\) −8.18564 + 5.38523i −0.291232 + 0.191598i
\(791\) 3.80123 + 17.8834i 0.135156 + 0.635859i
\(792\) −8.21894 1.59760i −0.292047 0.0567683i
\(793\) −8.64171 + 6.05099i −0.306876 + 0.214877i
\(794\) −3.44114 + 7.05538i −0.122121 + 0.250386i
\(795\) −1.49770 0.997316i −0.0531179 0.0353711i
\(796\) 24.2101 + 1.69294i 0.858105 + 0.0600046i
\(797\) −4.53799 + 28.6518i −0.160744 + 1.01490i 0.766991 + 0.641658i \(0.221753\pi\)
−0.927735 + 0.373240i \(0.878247\pi\)
\(798\) −0.639046 1.60621i −0.0226220 0.0568592i
\(799\) 3.58632i 0.126875i
\(800\) −11.7271 26.7395i −0.414617 0.945385i
\(801\) 4.28849 + 11.7825i 0.151526 + 0.416315i
\(802\) 0.826952 + 0.252825i 0.0292007 + 0.00892754i
\(803\) −15.8819 5.46858i −0.560460 0.192982i
\(804\) 0.713092 + 2.48685i 0.0251488 + 0.0877043i
\(805\) 20.8606 4.56376i 0.735241 0.160851i
\(806\) −3.12871 7.02719i −0.110204 0.247522i
\(807\) 6.10298 + 0.533942i 0.214835 + 0.0187956i
\(808\) 12.4580 + 10.8296i 0.438271 + 0.380983i
\(809\) −40.1400 + 36.1422i −1.41125 + 1.27069i −0.495694 + 0.868497i \(0.665086\pi\)
−0.915554 + 0.402196i \(0.868247\pi\)
\(810\) 12.8050 5.00288i 0.449923 0.175783i
\(811\) −18.1257 0.632963i −0.636479 0.0222263i −0.285157 0.958481i \(-0.592046\pi\)
−0.351322 + 0.936255i \(0.614268\pi\)
\(812\) 32.5514 9.95196i 1.14233 0.349245i
\(813\) 0.845592 + 1.12214i 0.0296562 + 0.0393551i
\(814\) −4.76389 + 3.72196i −0.166974 + 0.130455i
\(815\) −40.0730 + 35.2551i −1.40370 + 1.23493i
\(816\) −0.0810359 0.0263302i −0.00283682 0.000921740i
\(817\) 25.7760 19.9188i 0.901787 0.696869i
\(818\) 12.0020 12.0020i 0.419640 0.419640i
\(819\) −6.17507 24.7668i −0.215774 0.865424i
\(820\) −1.26430 30.9345i −0.0441512 1.08028i
\(821\) 19.3331 + 18.6697i 0.674729 + 0.651578i 0.950888 0.309534i \(-0.100173\pi\)
−0.276160 + 0.961112i \(0.589062\pi\)
\(822\) 0.333610 0.968872i 0.0116360 0.0337933i
\(823\) 12.5098 + 13.4151i 0.436064 + 0.467621i 0.911004 0.412397i \(-0.135308\pi\)
−0.474941 + 0.880018i \(0.657530\pi\)
\(824\) 1.23172 0.711134i 0.0429090 0.0247735i
\(825\) 0.0465884 1.15032i 0.00162200 0.0400490i
\(826\) 9.00203 7.55360i 0.313221 0.262823i
\(827\) −28.8828 + 6.66812i −1.00435 + 0.231873i −0.694950 0.719058i \(-0.744574\pi\)
−0.309403 + 0.950931i \(0.600129\pi\)
\(828\) −11.9164 9.64974i −0.414125 0.335352i
\(829\) 15.0352 + 6.69411i 0.522195 + 0.232496i 0.650868 0.759191i \(-0.274405\pi\)
−0.128673 + 0.991687i \(0.541072\pi\)
\(830\) 0.0176428 + 0.0601761i 0.000612390 + 0.00208874i
\(831\) −3.24103 3.35619i −0.112430 0.116425i
\(832\) −4.44506 3.11246i −0.154105 0.107905i
\(833\) −0.172388 + 0.0955563i −0.00597290 + 0.00331083i
\(834\) −0.517691 0.828478i −0.0179262 0.0286878i
\(835\) −12.7324 6.39248i −0.440622 0.221221i
\(836\) −4.42309 5.93498i −0.152976 0.205266i
\(837\) −3.70215 + 1.88634i −0.127965 + 0.0652015i
\(838\) −24.3477 5.62111i −0.841077 0.194178i
\(839\) 20.7977 + 26.6198i 0.718017 + 0.919019i 0.999174 0.0406425i \(-0.0129405\pi\)
−0.281157 + 0.959662i \(0.590718\pi\)
\(840\) −1.02579 2.92259i −0.0353931 0.100839i
\(841\) −35.0491 18.6359i −1.20859 0.642619i
\(842\) −1.28992 + 6.63607i −0.0444536 + 0.228694i
\(843\) −3.74919 1.00459i −0.129129 0.0346000i
\(844\) −5.18823 + 2.30995i −0.178586 + 0.0795118i
\(845\) −3.71853 + 6.03032i −0.127921 + 0.207449i
\(846\) 21.1503 + 5.27336i 0.727162 + 0.181302i
\(847\) −16.8042 + 20.7515i −0.577400 + 0.713029i
\(848\) −4.82004 + 0.252608i −0.165521 + 0.00867458i
\(849\) −4.57050 1.66353i −0.156859 0.0570921i
\(850\) 0.199925 1.21831i 0.00685737 0.0417875i
\(851\) −25.5109 + 4.49826i −0.874503 + 0.154199i
\(852\) 0.391034 3.18472i 0.0133966 0.109107i
\(853\) 17.1033 14.8677i 0.585607 0.509060i −0.311868 0.950125i \(-0.600955\pi\)
0.897475 + 0.441065i \(0.145399\pi\)
\(854\) 5.33297 3.87463i 0.182491 0.132587i
\(855\) 26.9319 + 10.3188i 0.921052 + 0.352895i
\(856\) 11.1253 + 8.08302i 0.380256 + 0.276272i
\(857\) 31.3445 2.74229i 1.07071 0.0936749i 0.461854 0.886956i \(-0.347185\pi\)
0.608855 + 0.793281i \(0.291629\pi\)
\(858\) −0.249273 0.449700i −0.00851003 0.0153525i
\(859\) 2.87704 20.4712i 0.0981634 0.698469i −0.877561 0.479466i \(-0.840831\pi\)
0.975724 0.219003i \(-0.0702806\pi\)
\(860\) 20.3493 14.4296i 0.693905 0.492047i
\(861\) 0.180254 5.16179i 0.00614303 0.175913i
\(862\) −17.4004 11.3000i −0.592661 0.384878i
\(863\) −1.20727 + 23.0361i −0.0410960 + 0.784158i 0.897894 + 0.440212i \(0.145097\pi\)
−0.938990 + 0.343945i \(0.888237\pi\)
\(864\) −3.73263 + 5.97345i −0.126986 + 0.203221i
\(865\) −11.1869 + 26.7961i −0.380364 + 0.911093i
\(866\) 2.72144 + 3.02247i 0.0924783 + 0.102708i
\(867\) 2.15022 + 2.65531i 0.0730254 + 0.0901789i
\(868\) −5.97875 12.8215i −0.202932 0.435189i
\(869\) −5.03468 + 4.86193i −0.170790 + 0.164930i
\(870\) −1.15689 + 2.40818i −0.0392222 + 0.0816449i
\(871\) 15.0118 22.2559i 0.508655 0.754112i
\(872\) −31.7181 36.4875i −1.07411 1.23562i
\(873\) 13.4778 26.4517i 0.456154 0.895253i
\(874\) 1.62915 + 10.6520i 0.0551068 + 0.360310i
\(875\) −27.1525 + 14.4501i −0.917920 + 0.488502i
\(876\) −2.86807 + 3.41803i −0.0969030 + 0.115484i
\(877\) −14.7625 1.81261i −0.498494 0.0612074i −0.131283 0.991345i \(-0.541910\pi\)
−0.367211 + 0.930138i \(0.619687\pi\)
\(878\) 14.7105 0.256772i 0.496454 0.00866564i
\(879\) 0.411016 0.200466i 0.0138632 0.00676154i
\(880\) −1.74206 2.54990i −0.0587248 0.0859571i
\(881\) −0.103247 + 0.982331i −0.00347848 + 0.0330956i −0.996123 0.0879662i \(-0.971963\pi\)
0.992645 + 0.121062i \(0.0386299\pi\)
\(882\) 0.310061 + 1.15717i 0.0104403 + 0.0389638i
\(883\) −20.4238 + 23.4949i −0.687315 + 0.790666i −0.986541 0.163517i \(-0.947716\pi\)
0.299225 + 0.954182i \(0.403272\pi\)
\(884\) 0.607945 + 1.50472i 0.0204474 + 0.0506091i
\(885\) 0.125970 2.71181i 0.00423443 0.0911564i
\(886\) −4.70512 4.23650i −0.158071 0.142328i
\(887\) 6.36207 + 51.8149i 0.213618 + 1.73978i 0.584766 + 0.811202i \(0.301186\pi\)
−0.371149 + 0.928573i \(0.621036\pi\)
\(888\) 1.09856 + 3.59324i 0.0368653 + 0.120581i
\(889\) 41.2825 21.9503i 1.38457 0.736190i
\(890\) 2.81544 6.13258i 0.0943736 0.205565i
\(891\) 8.32796 5.20389i 0.278997 0.174337i
\(892\) −2.15246 + 0.340916i −0.0720696 + 0.0114147i
\(893\) 25.0136 + 37.5125i 0.837048 + 1.25531i
\(894\) 1.33418 1.83634i 0.0446217 0.0614164i
\(895\) 28.9689 + 24.0159i 0.968322 + 0.802764i
\(896\) −23.8265 16.0711i −0.795986 0.536899i
\(897\) −0.0384506 2.20284i −0.00128383 0.0735506i
\(898\) −3.58304 + 4.75486i −0.119568 + 0.158672i
\(899\) −9.76494 + 26.8289i −0.325679 + 0.894795i
\(900\) 20.2822 + 8.74296i 0.676073 + 0.291432i
\(901\) −1.19369 0.689179i −0.0397677 0.0229599i
\(902\) 1.69024 + 7.32125i 0.0562790 + 0.243771i
\(903\) 3.56720 2.14339i 0.118709 0.0713276i
\(904\) −16.4405 + 1.72797i −0.546803 + 0.0574713i
\(905\) −11.8679 10.5589i −0.394503 0.350991i
\(906\) −0.510281 + 0.344189i −0.0169529 + 0.0114349i
\(907\) 9.18206 + 13.1133i 0.304885 + 0.435421i 0.942134 0.335237i \(-0.108816\pi\)
−0.637248 + 0.770658i \(0.719927\pi\)
\(908\) 0.681326 0.234599i 0.0226106 0.00778545i
\(909\) −19.6242 + 0.685294i −0.650895 + 0.0227298i
\(910\) −7.00494 + 11.8166i −0.232211 + 0.391717i
\(911\) 29.6497 9.63376i 0.982338 0.319181i 0.226551 0.973999i \(-0.427255\pi\)
0.755786 + 0.654818i \(0.227255\pi\)
\(912\) −1.03127 + 0.289792i −0.0341488 + 0.00959598i
\(913\) 0.0203361 + 0.0399118i 0.000673026 + 0.00132089i
\(914\) 5.82938 14.4282i 0.192819 0.477243i
\(915\) 0.176604 1.51256i 0.00583834 0.0500036i
\(916\) −35.2872 4.95929i −1.16592 0.163860i
\(917\) 39.6679 + 0.692405i 1.30995 + 0.0228652i
\(918\) −0.269931 + 0.125871i −0.00890904 + 0.00415435i
\(919\) −7.01819 0.737641i −0.231509 0.0243325i −0.0119363 0.999929i \(-0.503800\pi\)
−0.219572 + 0.975596i \(0.570466\pi\)
\(920\) 2.13227 + 19.1898i 0.0702988 + 0.632670i
\(921\) 0.403984 1.62029i 0.0133117 0.0533904i
\(922\) −0.290811 0.483991i −0.00957735 0.0159394i
\(923\) −27.9239 + 18.1340i −0.919125 + 0.596887i
\(924\) −0.472807 0.818926i −0.0155542 0.0269407i
\(925\) 33.6269 16.1696i 1.10564 0.531654i
\(926\) −15.1134 2.66491i −0.496658 0.0875742i
\(927\) −0.494659 + 1.61796i −0.0162467 + 0.0531406i
\(928\) 9.23523 + 47.5111i 0.303161 + 1.55963i
\(929\) −2.52504 + 36.1098i −0.0828439 + 1.18472i 0.761225 + 0.648488i \(0.224598\pi\)
−0.844069 + 0.536235i \(0.819846\pi\)
\(930\) 1.05805 + 0.336844i 0.0346947 + 0.0110456i
\(931\) −1.13668 + 2.20187i −0.0372533 + 0.0721633i
\(932\) 3.79233 + 3.79233i 0.124222 + 0.124222i
\(933\) 3.23524 5.38434i 0.105917 0.176275i
\(934\) −0.0367495 1.05237i −0.00120248 0.0344345i
\(935\) −0.0206292 0.881652i −0.000674648 0.0288331i
\(936\) 22.8547 3.21202i 0.747029 0.104988i
\(937\) −41.7502 + 5.12628i −1.36392 + 0.167468i −0.770507 0.637431i \(-0.779997\pi\)
−0.593412 + 0.804899i \(0.702219\pi\)
\(938\) −9.13600 + 14.0682i −0.298301 + 0.459343i
\(939\) 5.53902 + 1.17736i 0.180759 + 0.0384215i
\(940\) 17.9586 + 29.4898i 0.585744 + 0.961852i
\(941\) −7.26277 + 2.93435i −0.236760 + 0.0956571i −0.489921 0.871767i \(-0.662974\pi\)
0.253161 + 0.967424i \(0.418530\pi\)
\(942\) 1.89743 + 0.728354i 0.0618215 + 0.0237311i
\(943\) −8.33302 + 31.0993i −0.271361 + 1.01273i
\(944\) −4.07206 6.03707i −0.132534 0.196490i
\(945\) 6.57214 + 3.44454i 0.213792 + 0.112051i
\(946\) −4.20562 + 4.35504i −0.136736 + 0.141595i
\(947\) −33.0089 + 6.41627i −1.07264 + 0.208501i −0.696134 0.717912i \(-0.745098\pi\)
−0.376510 + 0.926413i \(0.622876\pi\)
\(948\) 0.726449 + 1.71141i 0.0235940 + 0.0555839i
\(949\) 46.3005 1.50298
\(950\) −6.40615 14.1378i −0.207843 0.458690i
\(951\) 2.54209 0.0824328
\(952\) −0.927073 2.18405i −0.0300466 0.0707854i
\(953\) −33.9838 + 6.60578i −1.10084 + 0.213982i −0.708412 0.705799i \(-0.750588\pi\)
−0.392431 + 0.919781i \(0.628366\pi\)
\(954\) −5.81965 + 6.02642i −0.188418 + 0.195113i
\(955\) −4.80368 9.70228i −0.155443 0.313958i
\(956\) −15.7166 23.3008i −0.508312 0.753603i
\(957\) −0.493930 + 1.84337i −0.0159665 + 0.0595878i
\(958\) −2.17337 0.834280i −0.0702185 0.0269544i
\(959\) −18.1316 + 7.32565i −0.585501 + 0.236558i
\(960\) 0.762166 0.180736i 0.0245988 0.00583322i
\(961\) −18.7158 3.97817i −0.603736 0.128328i
\(962\) 9.07594 13.9757i 0.292620 0.450595i
\(963\) −16.2366 + 1.99360i −0.523216 + 0.0642429i
\(964\) −32.9549 + 4.63151i −1.06141 + 0.149171i
\(965\) 34.7226 12.1872i 1.11776 0.392318i
\(966\) 0.0480445 + 1.37582i 0.00154581 + 0.0442661i
\(967\) 1.38442 2.30406i 0.0445199 0.0740935i −0.834106 0.551604i \(-0.814016\pi\)
0.878626 + 0.477510i \(0.158461\pi\)
\(968\) −17.0721 17.0721i −0.548719 0.548719i
\(969\) −0.292063 0.0909922i −0.00938242 0.00292309i
\(970\) −15.1654 + 5.02733i −0.486931 + 0.161418i
\(971\) −2.76897 + 39.5982i −0.0888606 + 1.27077i 0.724610 + 0.689160i \(0.242020\pi\)
−0.813470 + 0.581607i \(0.802424\pi\)
\(972\) −1.52847 7.86332i −0.0490258 0.252216i
\(973\) −5.45092 + 17.8292i −0.174749 + 0.571577i
\(974\) −10.1472 1.78922i −0.325137 0.0573303i
\(975\) 0.910896 + 3.03988i 0.0291720 + 0.0973541i
\(976\) −2.04243 3.53759i −0.0653766 0.113236i
\(977\) −24.6439 + 16.0039i −0.788428 + 0.512011i −0.874935 0.484240i \(-0.839096\pi\)
0.0865074 + 0.996251i \(0.472429\pi\)
\(978\) −1.77220 2.94944i −0.0566688 0.0943127i
\(979\) 1.16611 4.67700i 0.0372690 0.149478i
\(980\) −0.939025 + 1.64899i −0.0299960 + 0.0526749i
\(981\) 57.1962 + 6.01156i 1.82613 + 0.191934i
\(982\) −5.84759 + 2.72677i −0.186604 + 0.0870148i
\(983\) −39.2916 0.685838i −1.25321 0.0218748i −0.613004 0.790080i \(-0.710039\pi\)
−0.640204 + 0.768205i \(0.721150\pi\)
\(984\) 4.62460 + 0.649945i 0.147427 + 0.0207195i
\(985\) −2.16249 0.992786i −0.0689025 0.0316328i
\(986\) −0.766648 + 1.89752i −0.0244151 + 0.0604294i
\(987\) 2.61501 + 5.13225i 0.0832368 + 0.163361i
\(988\) 16.8540 + 11.4989i 0.536198 + 0.365830i
\(989\) −24.6723 + 8.01652i −0.784534 + 0.254910i
\(990\) −5.22987 1.17473i −0.166216 0.0373354i
\(991\) −25.7903 + 0.900618i −0.819257 + 0.0286091i −0.441462 0.897280i \(-0.645540\pi\)
−0.377795 + 0.925889i \(0.623318\pi\)
\(992\) 19.0199 6.54907i 0.603882 0.207933i
\(993\) 1.14738 + 1.63862i 0.0364109 + 0.0520002i
\(994\) 17.2478 11.6338i 0.547068 0.369002i
\(995\) 36.1755 + 3.58505i 1.14684 + 0.113654i
\(996\) 0.0118338 0.00124378i 0.000374968 3.94108e-5i
\(997\) 24.8907 14.9558i 0.788296 0.473656i −0.0632106 0.998000i \(-0.520134\pi\)
0.851506 + 0.524344i \(0.175690\pi\)
\(998\) 6.41157 + 27.7715i 0.202955 + 0.879093i
\(999\) −7.79534 4.50064i −0.246634 0.142394i
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 475.2.bi.a.117.30 yes 2304
19.13 odd 18 inner 475.2.bi.a.317.19 yes 2304
25.3 odd 20 inner 475.2.bi.a.3.19 2304
475.203 even 180 inner 475.2.bi.a.203.30 yes 2304
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.bi.a.3.19 2304 25.3 odd 20 inner
475.2.bi.a.117.30 yes 2304 1.1 even 1 trivial
475.2.bi.a.203.30 yes 2304 475.203 even 180 inner
475.2.bi.a.317.19 yes 2304 19.13 odd 18 inner