Properties

Label 462.2.bf.a.5.8
Level $462$
Weight $2$
Character 462.5
Analytic conductor $3.689$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(5,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 25, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.bf (of order \(30\), degree \(8\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(32\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 462.5
Dual form 462.2.bf.a.185.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.207912 + 0.978148i) q^{2} +(-0.442840 - 1.67448i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.833125 - 0.925279i) q^{5} +(1.72996 - 0.0850182i) q^{6} +(0.162919 - 2.64073i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.60779 + 1.48306i) q^{9} +O(q^{10})\) \(q+(-0.207912 + 0.978148i) q^{2} +(-0.442840 - 1.67448i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.833125 - 0.925279i) q^{5} +(1.72996 - 0.0850182i) q^{6} +(0.162919 - 2.64073i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.60779 + 1.48306i) q^{9} +(1.07828 - 0.622543i) q^{10} +(-2.68990 + 1.94022i) q^{11} +(-0.276519 + 1.70984i) q^{12} +(-0.204850 + 0.0665599i) q^{13} +(2.54915 + 0.708397i) q^{14} +(-1.18042 + 1.80480i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-6.51226 + 1.38422i) q^{17} +(-0.908458 - 2.85914i) q^{18} +(3.39194 + 7.61841i) q^{19} +(0.384753 + 1.18415i) q^{20} +(-4.49400 + 0.896617i) q^{21} +(-1.33856 - 3.03451i) q^{22} +(-4.30279 - 2.48421i) q^{23} +(-1.61498 - 0.625971i) q^{24} +(0.360598 - 3.43086i) q^{25} +(-0.0225146 - 0.214212i) q^{26} +(3.63818 + 3.70994i) q^{27} +(-1.22292 + 2.34616i) q^{28} +(-1.56875 - 2.15920i) q^{29} +(-1.51994 - 1.52987i) q^{30} +(-1.39914 - 1.25979i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.44005 + 3.64499i) q^{33} -6.65775i q^{34} +(-2.57914 + 2.04931i) q^{35} +(2.98554 - 0.294157i) q^{36} +(-0.731234 - 6.95723i) q^{37} +(-8.15716 + 1.73386i) q^{38} +(0.202169 + 0.313543i) q^{39} +(-1.23827 + 0.130147i) q^{40} +(3.94677 + 2.86750i) q^{41} +(0.0573328 - 4.58222i) q^{42} -10.6893 q^{43} +(3.24650 - 0.678394i) q^{44} +(3.54485 + 1.17736i) q^{45} +(3.32453 - 3.69226i) q^{46} +(-1.78386 + 0.794224i) q^{47} +(0.948066 - 1.44954i) q^{48} +(-6.94692 - 0.860448i) q^{49} +(3.28092 + 1.06603i) q^{50} +(5.20175 + 10.2917i) q^{51} +(0.214212 + 0.0225146i) q^{52} +(-7.31540 - 6.58681i) q^{53} +(-4.38529 + 2.78734i) q^{54} +(4.03626 + 0.872467i) q^{55} +(-2.04063 - 1.68399i) q^{56} +(11.2548 - 9.05348i) q^{57} +(2.43817 - 1.08554i) q^{58} +(0.946432 + 0.421379i) q^{59} +(1.81245 - 1.16865i) q^{60} +(9.04006 - 8.13971i) q^{61} +(1.52315 - 1.10664i) q^{62} +(3.49149 + 7.12808i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.232252 + 0.134091i) q^{65} +(-4.48847 + 3.58519i) q^{66} +(1.73671 + 3.00806i) q^{67} +(6.51226 + 1.38422i) q^{68} +(-2.25433 + 8.30505i) q^{69} +(-1.46830 - 2.94886i) q^{70} +(10.6592 + 3.46339i) q^{71} +(-0.333001 + 2.98146i) q^{72} +(-0.132143 + 0.296798i) q^{73} +(6.95723 + 0.731234i) q^{74} +(-5.90461 + 0.915508i) q^{75} -8.33939i q^{76} +(4.68535 + 7.41940i) q^{77} +(-0.348724 + 0.132562i) q^{78} +(-5.64611 - 1.20012i) q^{79} +(0.130147 - 1.23827i) q^{80} +(4.60109 - 7.73498i) q^{81} +(-3.62542 + 3.26434i) q^{82} +(5.21538 - 16.0513i) q^{83} +(4.47016 + 1.00878i) q^{84} +(6.70632 + 4.87243i) q^{85} +(2.22243 - 10.4557i) q^{86} +(-2.92083 + 3.58302i) q^{87} +(-0.0114167 + 3.31661i) q^{88} +(-5.27577 + 9.13790i) q^{89} +(-1.88865 + 3.22260i) q^{90} +(0.142393 + 0.551798i) q^{91} +(2.92037 + 4.01954i) q^{92} +(-1.48990 + 2.90071i) q^{93} +(-0.405984 - 1.91000i) q^{94} +(4.22325 - 9.48558i) q^{95} +(1.22075 + 1.22872i) q^{96} +(6.47039 - 2.10236i) q^{97} +(2.28599 - 6.61621i) q^{98} +(4.13724 - 9.04894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207912 + 0.978148i −0.147016 + 0.691655i
\(3\) −0.442840 1.67448i −0.255674 0.966763i
\(4\) −0.913545 0.406737i −0.456773 0.203368i
\(5\) −0.833125 0.925279i −0.372585 0.413797i 0.527470 0.849573i \(-0.323141\pi\)
−0.900055 + 0.435776i \(0.856474\pi\)
\(6\) 1.72996 0.0850182i 0.706254 0.0347086i
\(7\) 0.162919 2.64073i 0.0615774 0.998102i
\(8\) 0.587785 0.809017i 0.207813 0.286031i
\(9\) −2.60779 + 1.48306i −0.869262 + 0.494352i
\(10\) 1.07828 0.622543i 0.340981 0.196865i
\(11\) −2.68990 + 1.94022i −0.811036 + 0.584997i
\(12\) −0.276519 + 1.70984i −0.0798242 + 0.493587i
\(13\) −0.204850 + 0.0665599i −0.0568152 + 0.0184604i −0.337287 0.941402i \(-0.609509\pi\)
0.280471 + 0.959862i \(0.409509\pi\)
\(14\) 2.54915 + 0.708397i 0.681289 + 0.189327i
\(15\) −1.18042 + 1.80480i −0.304784 + 0.465998i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) −6.51226 + 1.38422i −1.57945 + 0.335723i −0.912405 0.409289i \(-0.865777\pi\)
−0.667050 + 0.745013i \(0.732443\pi\)
\(18\) −0.908458 2.85914i −0.214126 0.673907i
\(19\) 3.39194 + 7.61841i 0.778164 + 1.74778i 0.655311 + 0.755359i \(0.272538\pi\)
0.122853 + 0.992425i \(0.460796\pi\)
\(20\) 0.384753 + 1.18415i 0.0860333 + 0.264783i
\(21\) −4.49400 + 0.896617i −0.980672 + 0.195658i
\(22\) −1.33856 3.03451i −0.285381 0.646960i
\(23\) −4.30279 2.48421i −0.897193 0.517995i −0.0209045 0.999781i \(-0.506655\pi\)
−0.876288 + 0.481787i \(0.839988\pi\)
\(24\) −1.61498 0.625971i −0.329656 0.127776i
\(25\) 0.360598 3.43086i 0.0721197 0.686173i
\(26\) −0.0225146 0.214212i −0.00441548 0.0420105i
\(27\) 3.63818 + 3.70994i 0.700169 + 0.713978i
\(28\) −1.22292 + 2.34616i −0.231109 + 0.443383i
\(29\) −1.56875 2.15920i −0.291309 0.400953i 0.638130 0.769929i \(-0.279708\pi\)
−0.929439 + 0.368976i \(0.879708\pi\)
\(30\) −1.51994 1.52987i −0.277502 0.279314i
\(31\) −1.39914 1.25979i −0.251292 0.226264i 0.533851 0.845578i \(-0.320744\pi\)
−0.785143 + 0.619314i \(0.787411\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 4.44005 + 3.64499i 0.772914 + 0.634511i
\(34\) 6.65775i 1.14179i
\(35\) −2.57914 + 2.04931i −0.435955 + 0.346397i
\(36\) 2.98554 0.294157i 0.497591 0.0490261i
\(37\) −0.731234 6.95723i −0.120214 1.14376i −0.873757 0.486362i \(-0.838323\pi\)
0.753543 0.657399i \(-0.228343\pi\)
\(38\) −8.15716 + 1.73386i −1.32327 + 0.281269i
\(39\) 0.202169 + 0.313543i 0.0323730 + 0.0502070i
\(40\) −1.23827 + 0.130147i −0.195787 + 0.0205780i
\(41\) 3.94677 + 2.86750i 0.616382 + 0.447828i 0.851656 0.524101i \(-0.175599\pi\)
−0.235274 + 0.971929i \(0.575599\pi\)
\(42\) 0.0573328 4.58222i 0.00884665 0.707051i
\(43\) −10.6893 −1.63010 −0.815052 0.579388i \(-0.803292\pi\)
−0.815052 + 0.579388i \(0.803292\pi\)
\(44\) 3.24650 0.678394i 0.489429 0.102272i
\(45\) 3.54485 + 1.17736i 0.528435 + 0.175510i
\(46\) 3.32453 3.69226i 0.490175 0.544394i
\(47\) −1.78386 + 0.794224i −0.260202 + 0.115849i −0.532692 0.846309i \(-0.678820\pi\)
0.272490 + 0.962159i \(0.412153\pi\)
\(48\) 0.948066 1.44954i 0.136841 0.209223i
\(49\) −6.94692 0.860448i −0.992416 0.122921i
\(50\) 3.28092 + 1.06603i 0.463992 + 0.150760i
\(51\) 5.20175 + 10.2917i 0.728390 + 1.44112i
\(52\) 0.214212 + 0.0225146i 0.0297059 + 0.00312222i
\(53\) −7.31540 6.58681i −1.00485 0.904768i −0.00938746 0.999956i \(-0.502988\pi\)
−0.995459 + 0.0951878i \(0.969655\pi\)
\(54\) −4.38529 + 2.78734i −0.596762 + 0.379309i
\(55\) 4.03626 + 0.872467i 0.544250 + 0.117643i
\(56\) −2.04063 1.68399i −0.272691 0.225032i
\(57\) 11.2548 9.05348i 1.49074 1.19916i
\(58\) 2.43817 1.08554i 0.320148 0.142539i
\(59\) 0.946432 + 0.421379i 0.123215 + 0.0548588i 0.467418 0.884036i \(-0.345184\pi\)
−0.344203 + 0.938895i \(0.611851\pi\)
\(60\) 1.81245 1.16865i 0.233986 0.150872i
\(61\) 9.04006 8.13971i 1.15746 1.04218i 0.158969 0.987284i \(-0.449183\pi\)
0.998492 0.0548991i \(-0.0174837\pi\)
\(62\) 1.52315 1.10664i 0.193441 0.140543i
\(63\) 3.49149 + 7.12808i 0.439887 + 0.898053i
\(64\) −0.309017 0.951057i −0.0386271 0.118882i
\(65\) 0.232252 + 0.134091i 0.0288074 + 0.0166319i
\(66\) −4.48847 + 3.58519i −0.552493 + 0.441307i
\(67\) 1.73671 + 3.00806i 0.212172 + 0.367494i 0.952394 0.304869i \(-0.0986128\pi\)
−0.740222 + 0.672363i \(0.765279\pi\)
\(68\) 6.51226 + 1.38422i 0.789727 + 0.167862i
\(69\) −2.25433 + 8.30505i −0.271389 + 0.999811i
\(70\) −1.46830 2.94886i −0.175495 0.352456i
\(71\) 10.6592 + 3.46339i 1.26502 + 0.411028i 0.863279 0.504727i \(-0.168407\pi\)
0.401736 + 0.915755i \(0.368407\pi\)
\(72\) −0.333001 + 2.98146i −0.0392445 + 0.351369i
\(73\) −0.132143 + 0.296798i −0.0154662 + 0.0347376i −0.921113 0.389294i \(-0.872719\pi\)
0.905647 + 0.424032i \(0.139386\pi\)
\(74\) 6.95723 + 0.731234i 0.808761 + 0.0850042i
\(75\) −5.90461 + 0.915508i −0.681806 + 0.105714i
\(76\) 8.33939i 0.956594i
\(77\) 4.68535 + 7.41940i 0.533945 + 0.845519i
\(78\) −0.348724 + 0.132562i −0.0394853 + 0.0150097i
\(79\) −5.64611 1.20012i −0.635238 0.135024i −0.120973 0.992656i \(-0.538602\pi\)
−0.514264 + 0.857632i \(0.671935\pi\)
\(80\) 0.130147 1.23827i 0.0145509 0.138442i
\(81\) 4.60109 7.73498i 0.511232 0.859443i
\(82\) −3.62542 + 3.26434i −0.400360 + 0.360486i
\(83\) 5.21538 16.0513i 0.572462 1.76186i −0.0722018 0.997390i \(-0.523003\pi\)
0.644664 0.764466i \(-0.276997\pi\)
\(84\) 4.47016 + 1.00878i 0.487735 + 0.110067i
\(85\) 6.70632 + 4.87243i 0.727402 + 0.528489i
\(86\) 2.22243 10.4557i 0.239651 1.12747i
\(87\) −2.92083 + 3.58302i −0.313146 + 0.384140i
\(88\) −0.0114167 + 3.31661i −0.00121702 + 0.353551i
\(89\) −5.27577 + 9.13790i −0.559231 + 0.968616i 0.438330 + 0.898814i \(0.355570\pi\)
−0.997561 + 0.0698018i \(0.977763\pi\)
\(90\) −1.88865 + 3.22260i −0.199081 + 0.339692i
\(91\) 0.142393 + 0.551798i 0.0149268 + 0.0578442i
\(92\) 2.92037 + 4.01954i 0.304470 + 0.419066i
\(93\) −1.48990 + 2.90071i −0.154495 + 0.300790i
\(94\) −0.405984 1.91000i −0.0418740 0.197002i
\(95\) 4.22325 9.48558i 0.433297 0.973200i
\(96\) 1.22075 + 1.22872i 0.124592 + 0.125406i
\(97\) 6.47039 2.10236i 0.656968 0.213462i 0.0384841 0.999259i \(-0.487747\pi\)
0.618484 + 0.785797i \(0.287747\pi\)
\(98\) 2.28599 6.61621i 0.230920 0.668338i
\(99\) 4.13724 9.04894i 0.415808 0.909452i
\(100\) −1.72488 + 2.98758i −0.172488 + 0.298758i
\(101\) 1.92643 2.13952i 0.191687 0.212890i −0.639638 0.768676i \(-0.720916\pi\)
0.831326 + 0.555786i \(0.187582\pi\)
\(102\) −11.1483 + 2.94832i −1.10384 + 0.291927i
\(103\) −13.0804 + 1.37480i −1.28885 + 0.135463i −0.724038 0.689760i \(-0.757716\pi\)
−0.564807 + 0.825223i \(0.691049\pi\)
\(104\) −0.0665599 + 0.204850i −0.00652673 + 0.0200872i
\(105\) 4.57369 + 3.41121i 0.446346 + 0.332900i
\(106\) 7.96383 5.78606i 0.773516 0.561992i
\(107\) −0.556187 1.24922i −0.0537687 0.120766i 0.884663 0.466230i \(-0.154388\pi\)
−0.938432 + 0.345464i \(0.887722\pi\)
\(108\) −1.81468 4.86898i −0.174618 0.468518i
\(109\) −2.79218 4.83619i −0.267442 0.463223i 0.700758 0.713399i \(-0.252845\pi\)
−0.968201 + 0.250175i \(0.919512\pi\)
\(110\) −1.69259 + 3.76667i −0.161382 + 0.359138i
\(111\) −11.3259 + 4.30538i −1.07501 + 0.408648i
\(112\) 2.07146 1.64592i 0.195734 0.155525i
\(113\) −3.18542 + 4.38435i −0.299659 + 0.412445i −0.932121 0.362146i \(-0.882044\pi\)
0.632462 + 0.774591i \(0.282044\pi\)
\(114\) 6.51563 + 12.8912i 0.610245 + 1.20737i
\(115\) 1.28617 + 6.05094i 0.119936 + 0.564253i
\(116\) 0.554898 + 2.61059i 0.0515210 + 0.242387i
\(117\) 0.435493 0.477378i 0.0402614 0.0441336i
\(118\) −0.608945 + 0.838141i −0.0560579 + 0.0771571i
\(119\) 2.59439 + 17.4226i 0.237828 + 1.59713i
\(120\) 0.766282 + 2.01582i 0.0699517 + 0.184018i
\(121\) 3.47113 10.4380i 0.315557 0.948907i
\(122\) 6.08230 + 10.5349i 0.550666 + 0.953781i
\(123\) 3.05379 7.87864i 0.275351 0.710393i
\(124\) 0.765772 + 1.71995i 0.0687684 + 0.154456i
\(125\) −8.51141 + 6.18390i −0.761283 + 0.553105i
\(126\) −7.69823 + 1.93319i −0.685813 + 0.172222i
\(127\) −5.29258 + 16.2889i −0.469641 + 1.44541i 0.383410 + 0.923578i \(0.374750\pi\)
−0.853051 + 0.521828i \(0.825250\pi\)
\(128\) 0.994522 0.104528i 0.0879041 0.00923910i
\(129\) 4.73365 + 17.8991i 0.416775 + 1.57592i
\(130\) −0.179449 + 0.199298i −0.0157387 + 0.0174796i
\(131\) 3.37630 5.84793i 0.294989 0.510936i −0.679993 0.733218i \(-0.738017\pi\)
0.974982 + 0.222282i \(0.0713506\pi\)
\(132\) −2.57364 5.13579i −0.224007 0.447013i
\(133\) 20.6708 7.71601i 1.79238 0.669063i
\(134\) −3.30341 + 1.07334i −0.285371 + 0.0927228i
\(135\) 0.401665 6.45717i 0.0345698 0.555745i
\(136\) −2.70795 + 6.08215i −0.232205 + 0.521540i
\(137\) −3.00850 14.1539i −0.257034 1.20925i −0.897414 0.441190i \(-0.854556\pi\)
0.640380 0.768058i \(-0.278777\pi\)
\(138\) −7.65486 3.93178i −0.651625 0.334696i
\(139\) 6.95523 + 9.57306i 0.589935 + 0.811976i 0.994741 0.102427i \(-0.0326608\pi\)
−0.404805 + 0.914403i \(0.632661\pi\)
\(140\) 3.18970 0.823109i 0.269579 0.0695654i
\(141\) 2.11988 + 2.63532i 0.178526 + 0.221934i
\(142\) −5.60388 + 9.70620i −0.470267 + 0.814526i
\(143\) 0.421886 0.576493i 0.0352799 0.0482088i
\(144\) −2.84707 0.945604i −0.237256 0.0788004i
\(145\) −0.690896 + 3.25041i −0.0573758 + 0.269932i
\(146\) −0.262838 0.190963i −0.0217526 0.0158042i
\(147\) 1.63557 + 12.0135i 0.134899 + 0.990859i
\(148\) −2.16174 + 6.65316i −0.177694 + 0.546887i
\(149\) 16.2178 14.6025i 1.32861 1.19629i 0.364372 0.931253i \(-0.381284\pi\)
0.964239 0.265033i \(-0.0853830\pi\)
\(150\) 0.332136 5.96592i 0.0271188 0.487116i
\(151\) 0.440960 4.19545i 0.0358848 0.341421i −0.961819 0.273688i \(-0.911757\pi\)
0.997703 0.0677336i \(-0.0215768\pi\)
\(152\) 8.15716 + 1.73386i 0.661633 + 0.140634i
\(153\) 14.9297 13.2678i 1.20699 1.07264i
\(154\) −8.23141 + 3.04038i −0.663306 + 0.245001i
\(155\) 2.34415i 0.188287i
\(156\) −0.0571614 0.368665i −0.00457658 0.0295168i
\(157\) −2.83860 0.298349i −0.226545 0.0238109i −0.00942440 0.999956i \(-0.503000\pi\)
−0.217121 + 0.976145i \(0.569667\pi\)
\(158\) 2.34779 5.27321i 0.186780 0.419514i
\(159\) −7.78995 + 15.1664i −0.617784 + 1.20277i
\(160\) 1.18415 + 0.384753i 0.0936150 + 0.0304174i
\(161\) −7.26115 + 10.9578i −0.572258 + 0.863594i
\(162\) 6.60933 + 6.10874i 0.519278 + 0.479948i
\(163\) −0.987361 0.209870i −0.0773361 0.0164383i 0.169081 0.985602i \(-0.445920\pi\)
−0.246417 + 0.969164i \(0.579253\pi\)
\(164\) −2.43924 4.22489i −0.190473 0.329908i
\(165\) −0.326488 7.14502i −0.0254171 0.556239i
\(166\) 14.6162 + 8.43865i 1.13444 + 0.654967i
\(167\) 0.962885 + 2.96346i 0.0745103 + 0.229319i 0.981375 0.192103i \(-0.0615309\pi\)
−0.906864 + 0.421423i \(0.861531\pi\)
\(168\) −1.91613 + 4.16274i −0.147833 + 0.321163i
\(169\) −10.4797 + 7.61394i −0.806130 + 0.585688i
\(170\) −6.16027 + 5.54674i −0.472471 + 0.425415i
\(171\) −20.1440 14.8368i −1.54045 1.13460i
\(172\) 9.76517 + 4.34773i 0.744587 + 0.331512i
\(173\) 17.7918 7.92143i 1.35269 0.602255i 0.402927 0.915232i \(-0.367993\pi\)
0.949761 + 0.312977i \(0.101326\pi\)
\(174\) −2.89745 3.60196i −0.219655 0.273064i
\(175\) −9.00124 1.51119i −0.680430 0.114236i
\(176\) −3.24176 0.700728i −0.244357 0.0528194i
\(177\) 0.286474 1.77139i 0.0215327 0.133146i
\(178\) −7.84132 7.06036i −0.587732 0.529196i
\(179\) −6.46479 0.679477i −0.483201 0.0507865i −0.140204 0.990123i \(-0.544776\pi\)
−0.342998 + 0.939336i \(0.611442\pi\)
\(180\) −2.75951 2.51739i −0.205682 0.187635i
\(181\) −14.9647 4.86233i −1.11232 0.361414i −0.305487 0.952196i \(-0.598819\pi\)
−0.806831 + 0.590782i \(0.798819\pi\)
\(182\) −0.569345 + 0.0245559i −0.0422027 + 0.00182020i
\(183\) −17.6331 11.5328i −1.30348 0.852532i
\(184\) −4.53889 + 2.02084i −0.334611 + 0.148978i
\(185\) −5.82817 + 6.47284i −0.428495 + 0.475892i
\(186\) −2.52756 2.06043i −0.185329 0.151078i
\(187\) 14.8316 16.3586i 1.08460 1.19626i
\(188\) 1.95267 0.142413
\(189\) 10.3897 9.00304i 0.755737 0.654875i
\(190\) 8.40023 + 6.10313i 0.609417 + 0.442767i
\(191\) −5.71136 + 0.600288i −0.413260 + 0.0434353i −0.308877 0.951102i \(-0.599953\pi\)
−0.104382 + 0.994537i \(0.533287\pi\)
\(192\) −1.45568 + 0.938609i −0.105055 + 0.0677383i
\(193\) 4.75503 1.01071i 0.342275 0.0727528i −0.0335673 0.999436i \(-0.510687\pi\)
0.375842 + 0.926684i \(0.377353\pi\)
\(194\) 0.711146 + 6.76610i 0.0510573 + 0.485777i
\(195\) 0.121682 0.448283i 0.00871385 0.0321022i
\(196\) 5.99635 + 3.61162i 0.428310 + 0.257973i
\(197\) 2.29054i 0.163194i −0.996665 0.0815972i \(-0.973998\pi\)
0.996665 0.0815972i \(-0.0260021\pi\)
\(198\) 7.99102 + 5.92821i 0.567897 + 0.421299i
\(199\) −1.65742 + 0.956915i −0.117492 + 0.0678339i −0.557594 0.830114i \(-0.688275\pi\)
0.440102 + 0.897948i \(0.354942\pi\)
\(200\) −2.56367 2.30834i −0.181279 0.163224i
\(201\) 4.26787 4.24018i 0.301032 0.299079i
\(202\) 1.69224 + 2.32917i 0.119066 + 0.163880i
\(203\) −5.95743 + 3.79087i −0.418130 + 0.266067i
\(204\) −0.566030 11.5177i −0.0396300 0.806397i
\(205\) −0.634919 6.04085i −0.0443447 0.421911i
\(206\) 1.37480 13.0804i 0.0957869 0.911351i
\(207\) 14.9050 + 0.0970279i 1.03597 + 0.00674391i
\(208\) −0.186535 0.107696i −0.0129339 0.00746738i
\(209\) −23.9053 13.9117i −1.65357 0.962292i
\(210\) −4.28759 + 3.76451i −0.295872 + 0.259776i
\(211\) −6.62961 20.4038i −0.456401 1.40466i −0.869482 0.493964i \(-0.835547\pi\)
0.413081 0.910694i \(-0.364453\pi\)
\(212\) 4.00385 + 8.99279i 0.274985 + 0.617627i
\(213\) 1.07906 19.3824i 0.0739359 1.32806i
\(214\) 1.33756 0.284306i 0.0914335 0.0194348i
\(215\) 8.90553 + 9.89059i 0.607352 + 0.674533i
\(216\) 5.13987 0.762706i 0.349724 0.0518956i
\(217\) −3.55470 + 3.48950i −0.241309 + 0.236882i
\(218\) 5.31104 1.72566i 0.359709 0.116877i
\(219\) 0.555501 + 0.0898372i 0.0375373 + 0.00607063i
\(220\) −3.33245 2.43873i −0.224673 0.164419i
\(221\) 1.24190 0.717014i 0.0835395 0.0482315i
\(222\) −1.85650 11.9736i −0.124600 0.803614i
\(223\) −1.67382 + 2.30382i −0.112088 + 0.154275i −0.861375 0.507970i \(-0.830396\pi\)
0.749287 + 0.662245i \(0.230396\pi\)
\(224\) 1.17927 + 2.36840i 0.0787935 + 0.158245i
\(225\) 4.14780 + 9.48174i 0.276520 + 0.632116i
\(226\) −3.62626 4.02737i −0.241215 0.267897i
\(227\) −13.6525 6.07850i −0.906151 0.403444i −0.0998858 0.994999i \(-0.531848\pi\)
−0.806265 + 0.591555i \(0.798514\pi\)
\(228\) −13.9642 + 3.69302i −0.924800 + 0.244576i
\(229\) 2.78564 13.1054i 0.184080 0.866029i −0.785041 0.619444i \(-0.787358\pi\)
0.969121 0.246585i \(-0.0793085\pi\)
\(230\) −6.18612 −0.407901
\(231\) 10.3488 11.1311i 0.680901 0.732376i
\(232\) −2.66891 −0.175223
\(233\) 0.0833526 0.392143i 0.00546061 0.0256901i −0.975333 0.220739i \(-0.929153\pi\)
0.980794 + 0.195049i \(0.0624865\pi\)
\(234\) 0.376402 + 0.525229i 0.0246062 + 0.0343353i
\(235\) 2.22105 + 0.988877i 0.144886 + 0.0645072i
\(236\) −0.693219 0.769897i −0.0451247 0.0501160i
\(237\) 0.490747 + 9.98578i 0.0318774 + 0.648646i
\(238\) −17.5813 1.08467i −1.13963 0.0703088i
\(239\) −12.3299 + 16.9706i −0.797552 + 1.09774i 0.195574 + 0.980689i \(0.437343\pi\)
−0.993126 + 0.117047i \(0.962657\pi\)
\(240\) −2.13109 + 0.330424i −0.137561 + 0.0213288i
\(241\) −19.9062 + 11.4929i −1.28227 + 0.740321i −0.977264 0.212028i \(-0.931993\pi\)
−0.305011 + 0.952349i \(0.598660\pi\)
\(242\) 9.48819 + 5.56545i 0.609924 + 0.357761i
\(243\) −14.9896 4.27909i −0.961586 0.274504i
\(244\) −11.5692 + 3.75907i −0.740644 + 0.240650i
\(245\) 4.99149 + 7.14470i 0.318895 + 0.456458i
\(246\) 7.07156 + 4.62512i 0.450866 + 0.294887i
\(247\) −1.20192 1.33487i −0.0764763 0.0849355i
\(248\) −1.84158 + 0.391440i −0.116940 + 0.0248565i
\(249\) −29.1872 1.62491i −1.84966 0.102975i
\(250\) −4.27915 9.61112i −0.270637 0.607860i
\(251\) −0.212998 0.655540i −0.0134443 0.0413773i 0.944109 0.329633i \(-0.106925\pi\)
−0.957554 + 0.288255i \(0.906925\pi\)
\(252\) −0.290388 7.93194i −0.0182927 0.499665i
\(253\) 16.3940 1.66604i 1.03068 0.104743i
\(254\) −14.8326 8.56358i −0.930677 0.537327i
\(255\) 5.18897 13.3873i 0.324946 0.838346i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) −2.82123 26.8422i −0.175983 1.67437i −0.624830 0.780761i \(-0.714832\pi\)
0.448847 0.893609i \(-0.351835\pi\)
\(258\) −18.4921 + 0.908786i −1.15127 + 0.0565786i
\(259\) −18.4913 + 0.797530i −1.14899 + 0.0495561i
\(260\) −0.157633 0.216964i −0.00977600 0.0134555i
\(261\) 7.29316 + 3.30418i 0.451435 + 0.204524i
\(262\) 5.01817 + 4.51838i 0.310023 + 0.279146i
\(263\) −0.504228 + 0.291116i −0.0310920 + 0.0179510i −0.515465 0.856910i \(-0.672381\pi\)
0.484373 + 0.874861i \(0.339048\pi\)
\(264\) 5.55865 1.44961i 0.342112 0.0892172i
\(265\) 12.2564i 0.752906i
\(266\) 3.24970 + 21.8233i 0.199252 + 1.33807i
\(267\) 17.6376 + 4.78756i 1.07940 + 0.292994i
\(268\) −0.363071 3.45439i −0.0221781 0.211010i
\(269\) 1.36254 0.289617i 0.0830756 0.0176583i −0.166186 0.986094i \(-0.553145\pi\)
0.249262 + 0.968436i \(0.419812\pi\)
\(270\) 6.23256 + 1.73541i 0.379301 + 0.105614i
\(271\) 11.7335 1.23324i 0.712757 0.0749138i 0.258792 0.965933i \(-0.416676\pi\)
0.453965 + 0.891019i \(0.350009\pi\)
\(272\) −5.38623 3.91333i −0.326588 0.237280i
\(273\) 0.860919 0.482792i 0.0521052 0.0292199i
\(274\) 14.4701 0.874171
\(275\) 5.68664 + 9.92832i 0.342917 + 0.598700i
\(276\) 5.43740 6.67012i 0.327293 0.401494i
\(277\) 14.9416 16.5943i 0.897752 0.997055i −0.102245 0.994759i \(-0.532603\pi\)
0.999997 0.00229533i \(-0.000730626\pi\)
\(278\) −10.8099 + 4.81289i −0.648337 + 0.288658i
\(279\) 5.51698 + 1.21026i 0.330293 + 0.0724563i
\(280\) 0.141947 + 3.29113i 0.00848293 + 0.196683i
\(281\) 16.1806 + 5.25739i 0.965252 + 0.313629i 0.748898 0.662686i \(-0.230583\pi\)
0.216354 + 0.976315i \(0.430583\pi\)
\(282\) −3.01848 + 1.52564i −0.179748 + 0.0908504i
\(283\) 18.7456 + 1.97024i 1.11431 + 0.117119i 0.643741 0.765243i \(-0.277381\pi\)
0.470571 + 0.882362i \(0.344048\pi\)
\(284\) −8.32899 7.49945i −0.494234 0.445011i
\(285\) −17.7537 2.87117i −1.05164 0.170073i
\(286\) 0.476180 + 0.532527i 0.0281571 + 0.0314890i
\(287\) 8.21529 9.95519i 0.484933 0.587636i
\(288\) 1.51688 2.58826i 0.0893831 0.152514i
\(289\) 24.9632 11.1143i 1.46842 0.653783i
\(290\) −3.03573 1.35160i −0.178264 0.0793684i
\(291\) −6.38570 9.90354i −0.374337 0.580556i
\(292\) 0.241437 0.217391i 0.0141290 0.0127219i
\(293\) 0.419491 0.304778i 0.0245069 0.0178053i −0.575464 0.817827i \(-0.695179\pi\)
0.599971 + 0.800022i \(0.295179\pi\)
\(294\) −12.0911 0.897929i −0.705165 0.0523683i
\(295\) −0.398603 1.22678i −0.0232076 0.0714256i
\(296\) −6.05832 3.49777i −0.352133 0.203304i
\(297\) −16.9844 2.92050i −0.985536 0.169465i
\(298\) 10.9116 + 18.8994i 0.632091 + 1.09481i
\(299\) 1.04678 + 0.222499i 0.0605366 + 0.0128675i
\(300\) 5.76650 + 1.56526i 0.332929 + 0.0903705i
\(301\) −1.74149 + 28.2276i −0.100378 + 1.62701i
\(302\) 4.01209 + 1.30361i 0.230870 + 0.0750142i
\(303\) −4.43570 2.27832i −0.254824 0.130886i
\(304\) −3.39194 + 7.61841i −0.194541 + 0.436946i
\(305\) −15.0630 1.58319i −0.862505 0.0906529i
\(306\) 9.87381 + 17.3620i 0.564448 + 0.992518i
\(307\) 27.2975i 1.55795i 0.627054 + 0.778976i \(0.284261\pi\)
−0.627054 + 0.778976i \(0.715739\pi\)
\(308\) −1.26254 8.68366i −0.0719399 0.494798i
\(309\) 8.09458 + 21.2940i 0.460485 + 1.21137i
\(310\) −2.29293 0.487376i −0.130229 0.0276811i
\(311\) −0.848541 + 8.07333i −0.0481163 + 0.457796i 0.943764 + 0.330620i \(0.107258\pi\)
−0.991880 + 0.127176i \(0.959409\pi\)
\(312\) 0.372494 + 0.0207375i 0.0210883 + 0.00117403i
\(313\) −0.900388 + 0.810713i −0.0508929 + 0.0458242i −0.694185 0.719797i \(-0.744235\pi\)
0.643292 + 0.765621i \(0.277568\pi\)
\(314\) 0.882009 2.71454i 0.0497746 0.153191i
\(315\) 3.68661 9.16918i 0.207717 0.516625i
\(316\) 4.66985 + 3.39284i 0.262700 + 0.190862i
\(317\) −2.36285 + 11.1163i −0.132711 + 0.624356i 0.860638 + 0.509217i \(0.170065\pi\)
−0.993349 + 0.115139i \(0.963269\pi\)
\(318\) −13.2154 10.7730i −0.741081 0.604120i
\(319\) 8.40908 + 2.76431i 0.470818 + 0.154772i
\(320\) −0.622543 + 1.07828i −0.0348012 + 0.0602775i
\(321\) −1.84549 + 1.48453i −0.103005 + 0.0828584i
\(322\) −9.20864 9.38072i −0.513178 0.522767i
\(323\) −32.6348 44.9179i −1.81585 2.49930i
\(324\) −7.34941 + 5.19483i −0.408300 + 0.288601i
\(325\) 0.154489 + 0.726814i 0.00856952 + 0.0403164i
\(326\) 0.410568 0.922150i 0.0227392 0.0510732i
\(327\) −6.86164 + 6.81711i −0.379449 + 0.376987i
\(328\) 4.63971 1.50753i 0.256185 0.0832396i
\(329\) 1.80671 + 4.84008i 0.0996070 + 0.266842i
\(330\) 7.05676 + 1.16618i 0.388462 + 0.0641960i
\(331\) 2.83035 4.90232i 0.155570 0.269456i −0.777696 0.628640i \(-0.783612\pi\)
0.933267 + 0.359185i \(0.116945\pi\)
\(332\) −11.2931 + 12.5423i −0.619791 + 0.688347i
\(333\) 12.2249 + 17.0585i 0.669918 + 0.934800i
\(334\) −3.09889 + 0.325707i −0.169564 + 0.0178219i
\(335\) 1.33641 4.11303i 0.0730156 0.224719i
\(336\) −3.67339 2.73974i −0.200400 0.149465i
\(337\) −15.8834 + 11.5400i −0.865225 + 0.628623i −0.929301 0.369322i \(-0.879590\pi\)
0.0640762 + 0.997945i \(0.479590\pi\)
\(338\) −5.26871 11.8337i −0.286580 0.643669i
\(339\) 8.75215 + 3.39236i 0.475352 + 0.184248i
\(340\) −4.14473 7.17889i −0.224780 0.389330i
\(341\) 6.20779 + 0.674078i 0.336171 + 0.0365034i
\(342\) 18.7007 16.6190i 1.01122 0.898655i
\(343\) −3.40399 + 18.2047i −0.183798 + 0.982964i
\(344\) −6.28302 + 8.64783i −0.338758 + 0.466260i
\(345\) 9.56263 4.83326i 0.514835 0.260214i
\(346\) 4.04920 + 19.0500i 0.217686 + 1.02413i
\(347\) 3.77056 + 17.7391i 0.202414 + 0.952284i 0.955643 + 0.294526i \(0.0951618\pi\)
−0.753229 + 0.657758i \(0.771505\pi\)
\(348\) 4.12566 2.08524i 0.221158 0.111781i
\(349\) −10.8399 + 14.9199i −0.580248 + 0.798643i −0.993723 0.111873i \(-0.964315\pi\)
0.413474 + 0.910516i \(0.364315\pi\)
\(350\) 3.34963 8.49034i 0.179045 0.453828i
\(351\) −0.992215 0.517824i −0.0529605 0.0276394i
\(352\) 1.35941 3.02523i 0.0724570 0.161245i
\(353\) 0.434790 + 0.753078i 0.0231415 + 0.0400823i 0.877364 0.479825i \(-0.159300\pi\)
−0.854223 + 0.519907i \(0.825967\pi\)
\(354\) 1.67312 + 0.648506i 0.0889252 + 0.0344677i
\(355\) −5.67585 12.7482i −0.301243 0.676603i
\(356\) 8.53638 6.20204i 0.452427 0.328708i
\(357\) 28.0250 12.0597i 1.48324 0.638267i
\(358\) 2.00874 6.18225i 0.106165 0.326742i
\(359\) 14.7539 1.55070i 0.778683 0.0818429i 0.293156 0.956065i \(-0.405294\pi\)
0.485527 + 0.874222i \(0.338628\pi\)
\(360\) 3.03611 2.17581i 0.160017 0.114675i
\(361\) −33.8215 + 37.5626i −1.78008 + 1.97698i
\(362\) 7.86741 13.6268i 0.413502 0.716207i
\(363\) −19.0154 1.19000i −0.998048 0.0624585i
\(364\) 0.0943542 0.562009i 0.00494550 0.0294573i
\(365\) 0.384713 0.125001i 0.0201368 0.00654284i
\(366\) 14.9469 14.8500i 0.781289 0.776220i
\(367\) 4.05474 9.10710i 0.211656 0.475387i −0.776253 0.630421i \(-0.782882\pi\)
0.987909 + 0.155035i \(0.0495489\pi\)
\(368\) −1.03299 4.85986i −0.0538486 0.253338i
\(369\) −14.5450 1.62454i −0.757182 0.0845700i
\(370\) −5.11964 7.04659i −0.266158 0.366335i
\(371\) −18.5858 + 18.2449i −0.964927 + 0.947227i
\(372\) 2.54092 2.04394i 0.131740 0.105973i
\(373\) 6.04989 10.4787i 0.313251 0.542567i −0.665813 0.746119i \(-0.731915\pi\)
0.979064 + 0.203551i \(0.0652484\pi\)
\(374\) 12.9175 + 17.9087i 0.667946 + 0.926036i
\(375\) 14.1240 + 11.5137i 0.729361 + 0.594566i
\(376\) −0.405984 + 1.91000i −0.0209370 + 0.0985009i
\(377\) 0.465074 + 0.337896i 0.0239525 + 0.0174025i
\(378\) 6.64617 + 12.0345i 0.341842 + 0.618986i
\(379\) −9.75382 + 30.0192i −0.501020 + 1.54198i 0.306340 + 0.951922i \(0.400896\pi\)
−0.807360 + 0.590059i \(0.799104\pi\)
\(380\) −7.71627 + 6.94776i −0.395836 + 0.356412i
\(381\) 29.6192 + 1.64897i 1.51744 + 0.0844791i
\(382\) 0.600288 5.71136i 0.0307134 0.292219i
\(383\) 3.40809 + 0.724412i 0.174145 + 0.0370157i 0.294159 0.955757i \(-0.404961\pi\)
−0.120014 + 0.992772i \(0.538294\pi\)
\(384\) −0.615445 1.61902i −0.0314068 0.0826203i
\(385\) 2.96153 10.5165i 0.150934 0.535973i
\(386\) 4.86126i 0.247432i
\(387\) 27.8754 15.8528i 1.41699 0.805845i
\(388\) −6.76610 0.711146i −0.343497 0.0361029i
\(389\) −12.8187 + 28.7912i −0.649933 + 1.45977i 0.224425 + 0.974491i \(0.427950\pi\)
−0.874358 + 0.485282i \(0.838717\pi\)
\(390\) 0.413188 + 0.212227i 0.0209226 + 0.0107465i
\(391\) 31.4596 + 10.2218i 1.59098 + 0.516940i
\(392\) −4.77941 + 5.11441i −0.241397 + 0.258317i
\(393\) −11.2874 3.06387i −0.569375 0.154552i
\(394\) 2.24049 + 0.476231i 0.112874 + 0.0239922i
\(395\) 3.59347 + 6.22408i 0.180807 + 0.313167i
\(396\) −7.46009 + 6.58385i −0.374884 + 0.330851i
\(397\) 13.2441 + 7.64646i 0.664700 + 0.383765i 0.794066 0.607832i \(-0.207961\pi\)
−0.129365 + 0.991597i \(0.541294\pi\)
\(398\) −0.591406 1.82016i −0.0296445 0.0912364i
\(399\) −22.0742 31.1959i −1.10509 1.56175i
\(400\) 2.79092 2.02772i 0.139546 0.101386i
\(401\) 3.35548 3.02129i 0.167565 0.150876i −0.581082 0.813845i \(-0.697371\pi\)
0.748647 + 0.662969i \(0.230704\pi\)
\(402\) 3.26018 + 5.05619i 0.162603 + 0.252180i
\(403\) 0.370464 + 0.164941i 0.0184541 + 0.00821631i
\(404\) −2.63011 + 1.17100i −0.130853 + 0.0582594i
\(405\) −10.9903 + 2.18691i −0.546112 + 0.108669i
\(406\) −2.46941 6.61541i −0.122555 0.328317i
\(407\) 15.4655 + 17.2955i 0.766595 + 0.857306i
\(408\) 11.3837 + 1.84099i 0.563575 + 0.0911428i
\(409\) 5.07406 + 4.56870i 0.250896 + 0.225908i 0.784976 0.619526i \(-0.212675\pi\)
−0.534080 + 0.845434i \(0.679342\pi\)
\(410\) 6.04085 + 0.634919i 0.298336 + 0.0313564i
\(411\) −22.3682 + 11.3056i −1.10334 + 0.557664i
\(412\) 12.5087 + 4.06432i 0.616258 + 0.200234i
\(413\) 1.26694 2.43062i 0.0623420 0.119603i
\(414\) −3.19383 + 14.5591i −0.156968 + 0.715540i
\(415\) −19.1970 + 8.54704i −0.942342 + 0.419558i
\(416\) 0.144126 0.160068i 0.00706634 0.00784796i
\(417\) 12.9499 15.8857i 0.634158 0.777928i
\(418\) 18.5779 20.4905i 0.908674 1.00223i
\(419\) 8.85188 0.432443 0.216221 0.976344i \(-0.430627\pi\)
0.216221 + 0.976344i \(0.430627\pi\)
\(420\) −2.79081 4.97659i −0.136177 0.242833i
\(421\) −15.8202 11.4940i −0.771029 0.560185i 0.131244 0.991350i \(-0.458103\pi\)
−0.902273 + 0.431165i \(0.858103\pi\)
\(422\) 21.3363 2.24254i 1.03864 0.109165i
\(423\) 3.47404 4.71672i 0.168913 0.229335i
\(424\) −9.62872 + 2.04665i −0.467612 + 0.0993940i
\(425\) 2.40077 + 22.8418i 0.116455 + 1.10799i
\(426\) 18.7345 + 5.08530i 0.907689 + 0.246384i
\(427\) −20.0220 25.1985i −0.968931 1.21944i
\(428\) 1.36744i 0.0660976i
\(429\) −1.15216 0.451147i −0.0556266 0.0217816i
\(430\) −11.5260 + 6.65455i −0.555834 + 0.320911i
\(431\) −1.62355 1.46185i −0.0782035 0.0704147i 0.629102 0.777323i \(-0.283423\pi\)
−0.707305 + 0.706908i \(0.750089\pi\)
\(432\) −0.322600 + 5.18613i −0.0155211 + 0.249518i
\(433\) 4.22156 + 5.81048i 0.202875 + 0.279234i 0.898316 0.439349i \(-0.144791\pi\)
−0.695441 + 0.718583i \(0.744791\pi\)
\(434\) −2.67418 4.20253i −0.128365 0.201728i
\(435\) 5.74871 0.282518i 0.275630 0.0135457i
\(436\) 0.583724 + 5.55376i 0.0279553 + 0.265977i
\(437\) 4.33100 41.2067i 0.207180 1.97118i
\(438\) −0.203369 + 0.524684i −0.00971736 + 0.0250704i
\(439\) 7.63565 + 4.40844i 0.364430 + 0.210404i 0.671022 0.741437i \(-0.265856\pi\)
−0.306593 + 0.951841i \(0.599189\pi\)
\(440\) 3.07830 2.75258i 0.146752 0.131224i
\(441\) 19.3922 8.05880i 0.923436 0.383752i
\(442\) 0.443139 + 1.36384i 0.0210780 + 0.0648713i
\(443\) 10.9306 + 24.5505i 0.519329 + 1.16643i 0.962818 + 0.270151i \(0.0870738\pi\)
−0.443489 + 0.896280i \(0.646260\pi\)
\(444\) 12.0979 + 0.673517i 0.574142 + 0.0319637i
\(445\) 12.8505 2.73146i 0.609172 0.129483i
\(446\) −1.90547 2.11624i −0.0902266 0.100207i
\(447\) −31.6336 20.6898i −1.49622 0.978593i
\(448\) −2.56183 + 0.661086i −0.121035 + 0.0312334i
\(449\) 10.0356 3.26077i 0.473611 0.153885i −0.0624794 0.998046i \(-0.519901\pi\)
0.536090 + 0.844161i \(0.319901\pi\)
\(450\) −10.1369 + 2.08579i −0.477859 + 0.0983253i
\(451\) −16.1800 0.0556959i −0.761886 0.00262262i
\(452\) 4.69330 2.70968i 0.220754 0.127453i
\(453\) −7.22049 + 1.11953i −0.339248 + 0.0526003i
\(454\) 8.78419 12.0904i 0.412263 0.567431i
\(455\) 0.391936 0.591470i 0.0183743 0.0277285i
\(456\) −0.709001 14.4268i −0.0332020 0.675599i
\(457\) −7.42520 8.24652i −0.347336 0.385756i 0.544010 0.839078i \(-0.316905\pi\)
−0.891346 + 0.453323i \(0.850239\pi\)
\(458\) 12.2398 + 5.44953i 0.571930 + 0.254640i
\(459\) −28.8282 19.1240i −1.34558 0.892632i
\(460\) 1.28617 6.05094i 0.0599678 0.282126i
\(461\) 9.70109 0.451825 0.225912 0.974148i \(-0.427464\pi\)
0.225912 + 0.974148i \(0.427464\pi\)
\(462\) 8.73627 + 12.4369i 0.406448 + 0.578619i
\(463\) −5.13050 −0.238435 −0.119217 0.992868i \(-0.538039\pi\)
−0.119217 + 0.992868i \(0.538039\pi\)
\(464\) 0.554898 2.61059i 0.0257605 0.121194i
\(465\) 3.92524 1.03808i 0.182029 0.0481400i
\(466\) 0.366244 + 0.163062i 0.0169659 + 0.00755371i
\(467\) 3.21033 + 3.56543i 0.148556 + 0.164989i 0.812830 0.582501i \(-0.197926\pi\)
−0.664274 + 0.747489i \(0.731259\pi\)
\(468\) −0.592010 + 0.258975i −0.0273657 + 0.0119711i
\(469\) 8.22643 4.09610i 0.379861 0.189141i
\(470\) −1.42905 + 1.96692i −0.0659172 + 0.0907272i
\(471\) 0.757467 + 4.88532i 0.0349022 + 0.225103i
\(472\) 0.897201 0.517999i 0.0412970 0.0238429i
\(473\) 28.7532 20.7396i 1.32207 0.953606i
\(474\) −9.86960 1.59614i −0.453326 0.0733131i
\(475\) 27.3609 8.89008i 1.25540 0.407905i
\(476\) 4.71633 16.9716i 0.216173 0.777892i
\(477\) 28.8456 + 6.32785i 1.32075 + 0.289733i
\(478\) −14.0362 15.5888i −0.642002 0.713015i
\(479\) 23.9567 5.09216i 1.09461 0.232667i 0.374987 0.927030i \(-0.377647\pi\)
0.719625 + 0.694363i \(0.244314\pi\)
\(480\) 0.119874 2.15322i 0.00547148 0.0982805i
\(481\) 0.612866 + 1.37652i 0.0279443 + 0.0627638i
\(482\) −7.10299 21.8608i −0.323532 0.995730i
\(483\) 21.5641 + 7.30612i 0.981202 + 0.332440i
\(484\) −7.41654 + 8.12373i −0.337115 + 0.369260i
\(485\) −7.33591 4.23539i −0.333106 0.192319i
\(486\) 7.30210 13.7724i 0.331230 0.624729i
\(487\) −2.57533 + 24.5026i −0.116699 + 1.11032i 0.766799 + 0.641887i \(0.221848\pi\)
−0.883499 + 0.468434i \(0.844819\pi\)
\(488\) −1.27155 12.0980i −0.0575602 0.547649i
\(489\) 0.0858190 + 1.74626i 0.00388087 + 0.0789685i
\(490\) −8.02636 + 3.39695i −0.362594 + 0.153459i
\(491\) −10.8273 14.9025i −0.488630 0.672541i 0.491505 0.870875i \(-0.336447\pi\)
−0.980135 + 0.198334i \(0.936447\pi\)
\(492\) −5.99431 + 5.95541i −0.270244 + 0.268491i
\(493\) 13.2049 + 11.8897i 0.594719 + 0.535487i
\(494\) 1.55559 0.898120i 0.0699893 0.0404083i
\(495\) −11.8196 + 3.71080i −0.531253 + 0.166788i
\(496\) 1.88272i 0.0845367i
\(497\) 10.8825 27.5838i 0.488145 1.23730i
\(498\) 7.65776 28.2115i 0.343152 1.26419i
\(499\) −2.80675 26.7044i −0.125647 1.19545i −0.857680 0.514184i \(-0.828095\pi\)
0.732032 0.681270i \(-0.238572\pi\)
\(500\) 10.2908 2.18737i 0.460217 0.0978222i
\(501\) 4.53585 2.92467i 0.202647 0.130665i
\(502\) 0.685500 0.0720489i 0.0305953 0.00321570i
\(503\) 2.55198 + 1.85413i 0.113787 + 0.0826713i 0.643224 0.765678i \(-0.277597\pi\)
−0.529436 + 0.848350i \(0.677597\pi\)
\(504\) 7.81898 + 1.36510i 0.348285 + 0.0608064i
\(505\) −3.58462 −0.159513
\(506\) −1.77887 + 16.3821i −0.0790802 + 0.728274i
\(507\) 17.3902 + 14.1763i 0.772327 + 0.629592i
\(508\) 11.4603 12.7280i 0.508469 0.564712i
\(509\) −22.0862 + 9.83342i −0.978955 + 0.435859i −0.832903 0.553418i \(-0.813323\pi\)
−0.146051 + 0.989277i \(0.546656\pi\)
\(510\) 12.0159 + 7.85896i 0.532074 + 0.348000i
\(511\) 0.762235 + 0.397308i 0.0337193 + 0.0175759i
\(512\) −0.951057 0.309017i −0.0420312 0.0136568i
\(513\) −15.9233 + 40.3011i −0.703033 + 1.77933i
\(514\) 26.8422 + 2.82123i 1.18396 + 0.124439i
\(515\) 12.1696 + 10.9576i 0.536259 + 0.482849i
\(516\) 2.95580 18.2770i 0.130122 0.804598i
\(517\) 3.25743 5.59745i 0.143262 0.246176i
\(518\) 3.06445 18.2530i 0.134644 0.801992i
\(519\) −21.1432 26.2842i −0.928085 1.15375i
\(520\) 0.244996 0.109079i 0.0107438 0.00478345i
\(521\) −24.6068 10.9556i −1.07804 0.479975i −0.210630 0.977566i \(-0.567552\pi\)
−0.867412 + 0.497590i \(0.834218\pi\)
\(522\) −4.74831 + 6.44681i −0.207828 + 0.282169i
\(523\) −9.31632 + 8.38845i −0.407374 + 0.366801i −0.847193 0.531285i \(-0.821709\pi\)
0.439819 + 0.898086i \(0.355043\pi\)
\(524\) −5.46298 + 3.96908i −0.238651 + 0.173390i
\(525\) 1.45564 + 15.7416i 0.0635293 + 0.687021i
\(526\) −0.179920 0.553736i −0.00784487 0.0241440i
\(527\) 10.8554 + 6.26734i 0.472867 + 0.273010i
\(528\) 0.262222 + 5.73857i 0.0114117 + 0.249739i
\(529\) 0.842645 + 1.45950i 0.0366367 + 0.0634567i
\(530\) −11.9886 2.54825i −0.520751 0.110689i
\(531\) −3.09302 + 0.304746i −0.134226 + 0.0132249i
\(532\) −22.0221 1.35864i −0.954779 0.0589046i
\(533\) −0.999357 0.324711i −0.0432870 0.0140648i
\(534\) −8.35000 + 16.2568i −0.361340 + 0.703499i
\(535\) −0.692501 + 1.55538i −0.0299394 + 0.0672451i
\(536\) 3.45439 + 0.363071i 0.149207 + 0.0156823i
\(537\) 1.72510 + 11.1261i 0.0744434 + 0.480126i
\(538\) 1.39298i 0.0600556i
\(539\) 20.3560 11.1640i 0.876793 0.480867i
\(540\) −2.99331 + 5.73555i −0.128812 + 0.246819i
\(541\) −40.0469 8.51222i −1.72175 0.365969i −0.762163 0.647385i \(-0.775862\pi\)
−0.959586 + 0.281416i \(0.909196\pi\)
\(542\) −1.23324 + 11.7335i −0.0529720 + 0.503995i
\(543\) −1.51492 + 27.2114i −0.0650113 + 1.16775i
\(544\) 4.94767 4.45490i 0.212130 0.191002i
\(545\) −2.14860 + 6.61270i −0.0920357 + 0.283257i
\(546\) 0.293247 + 0.942484i 0.0125498 + 0.0403346i
\(547\) −2.93640 2.13342i −0.125551 0.0912185i 0.523237 0.852187i \(-0.324724\pi\)
−0.648789 + 0.760969i \(0.724724\pi\)
\(548\) −3.00850 + 14.1539i −0.128517 + 0.604624i
\(549\) −11.5029 + 34.6335i −0.490932 + 1.47812i
\(550\) −10.8937 + 3.49816i −0.464508 + 0.149162i
\(551\) 11.1286 19.2752i 0.474092 0.821152i
\(552\) 5.39387 + 6.70538i 0.229578 + 0.285400i
\(553\) −4.08905 + 14.7143i −0.173884 + 0.625718i
\(554\) 13.1251 + 18.0652i 0.557634 + 0.767517i
\(555\) 13.4196 + 6.89274i 0.569630 + 0.292580i
\(556\) −2.46021 11.5744i −0.104336 0.490863i
\(557\) −5.37049 + 12.0623i −0.227555 + 0.511097i −0.990852 0.134951i \(-0.956912\pi\)
0.763297 + 0.646047i \(0.223579\pi\)
\(558\) −2.33086 + 5.14479i −0.0986730 + 0.217796i
\(559\) 2.18971 0.711479i 0.0926147 0.0300924i
\(560\) −3.24872 0.545419i −0.137284 0.0230482i
\(561\) −33.9602 17.5911i −1.43380 0.742696i
\(562\) −8.50663 + 14.7339i −0.358830 + 0.621513i
\(563\) 22.6207 25.1229i 0.953350 1.05880i −0.0448600 0.998993i \(-0.514284\pi\)
0.998210 0.0598090i \(-0.0190492\pi\)
\(564\) −0.864722 3.26972i −0.0364114 0.137680i
\(565\) 6.71060 0.705313i 0.282317 0.0296727i
\(566\) −5.82462 + 17.9264i −0.244827 + 0.753501i
\(567\) −19.6764 13.4104i −0.826331 0.563185i
\(568\) 9.06726 6.58775i 0.380454 0.276416i
\(569\) −5.28791 11.8768i −0.221681 0.497903i 0.768130 0.640294i \(-0.221188\pi\)
−0.989810 + 0.142391i \(0.954521\pi\)
\(570\) 6.49962 16.7688i 0.272239 0.702366i
\(571\) −7.43968 12.8859i −0.311341 0.539258i 0.667312 0.744778i \(-0.267445\pi\)
−0.978653 + 0.205520i \(0.934111\pi\)
\(572\) −0.619893 + 0.355056i −0.0259190 + 0.0148456i
\(573\) 3.53439 + 9.29775i 0.147651 + 0.388419i
\(574\) 8.02959 + 10.1056i 0.335149 + 0.421798i
\(575\) −10.0746 + 13.8665i −0.420139 + 0.578272i
\(576\) 2.21632 + 2.02186i 0.0923467 + 0.0842443i
\(577\) 5.65674 + 26.6129i 0.235493 + 1.10791i 0.923915 + 0.382598i \(0.124971\pi\)
−0.688422 + 0.725311i \(0.741696\pi\)
\(578\) 5.68131 + 26.7285i 0.236311 + 1.11176i
\(579\) −3.79814 7.51464i −0.157845 0.312298i
\(580\) 1.95322 2.68838i 0.0811033 0.111629i
\(581\) −41.5374 16.3875i −1.72326 0.679866i
\(582\) 11.0148 4.18710i 0.456578 0.173561i
\(583\) 32.4575 + 3.52443i 1.34425 + 0.145967i
\(584\) 0.162443 + 0.281359i 0.00672194 + 0.0116427i
\(585\) −0.804528 0.00523729i −0.0332632 0.000216535i
\(586\) 0.210901 + 0.473691i 0.00871224 + 0.0195680i
\(587\) 8.89587 6.46323i 0.367172 0.266766i −0.388865 0.921295i \(-0.627133\pi\)
0.756037 + 0.654529i \(0.227133\pi\)
\(588\) 3.39218 11.6402i 0.139891 0.480032i
\(589\) 4.85180 14.9323i 0.199915 0.615275i
\(590\) 1.28284 0.134832i 0.0528137 0.00555095i
\(591\) −3.83548 + 1.01434i −0.157770 + 0.0417245i
\(592\) 4.68094 5.19871i 0.192385 0.213666i
\(593\) −6.99855 + 12.1218i −0.287396 + 0.497784i −0.973187 0.230014i \(-0.926123\pi\)
0.685791 + 0.727798i \(0.259456\pi\)
\(594\) 6.38794 16.0061i 0.262100 0.656737i
\(595\) 13.9593 16.9158i 0.572277 0.693479i
\(596\) −20.7551 + 6.74373i −0.850160 + 0.276234i
\(597\) 2.33631 + 2.35157i 0.0956188 + 0.0962433i
\(598\) −0.435274 + 0.977641i −0.0177997 + 0.0399787i
\(599\) 3.55618 + 16.7305i 0.145302 + 0.683590i 0.989138 + 0.146990i \(0.0469584\pi\)
−0.843837 + 0.536600i \(0.819708\pi\)
\(600\) −2.72998 + 5.31505i −0.111451 + 0.216986i
\(601\) −2.03136 2.79593i −0.0828610 0.114048i 0.765574 0.643347i \(-0.222455\pi\)
−0.848435 + 0.529299i \(0.822455\pi\)
\(602\) −27.2487 7.57228i −1.11057 0.308623i
\(603\) −8.99009 5.26875i −0.366105 0.214560i
\(604\) −2.10928 + 3.65338i −0.0858255 + 0.148654i
\(605\) −12.5499 + 5.48437i −0.510227 + 0.222971i
\(606\) 3.15076 3.86508i 0.127991 0.157008i
\(607\) −8.88071 + 41.7805i −0.360457 + 1.69582i 0.307444 + 0.951566i \(0.400526\pi\)
−0.667901 + 0.744250i \(0.732807\pi\)
\(608\) −6.74671 4.90177i −0.273615 0.198793i
\(609\) 8.98593 + 8.29687i 0.364128 + 0.336206i
\(610\) 4.68036 14.4047i 0.189502 0.583228i
\(611\) 0.312560 0.281430i 0.0126448 0.0113854i
\(612\) −19.0355 + 6.04828i −0.769463 + 0.244487i
\(613\) 3.03912 28.9153i 0.122749 1.16788i −0.743666 0.668552i \(-0.766915\pi\)
0.866415 0.499325i \(-0.166419\pi\)
\(614\) −26.7010 5.67548i −1.07757 0.229044i
\(615\) −9.83413 + 3.73829i −0.396550 + 0.150742i
\(616\) 8.75640 + 0.570485i 0.352805 + 0.0229855i
\(617\) 19.3142i 0.777559i −0.921331 0.388780i \(-0.872897\pi\)
0.921331 0.388780i \(-0.127103\pi\)
\(618\) −22.5116 + 3.49042i −0.905551 + 0.140405i
\(619\) 1.84086 + 0.193482i 0.0739903 + 0.00777669i 0.141451 0.989945i \(-0.454823\pi\)
−0.0674610 + 0.997722i \(0.521490\pi\)
\(620\) 0.953452 2.14149i 0.0382915 0.0860042i
\(621\) −6.43804 25.0011i −0.258350 1.00326i
\(622\) −7.72048 2.50854i −0.309563 0.100583i
\(623\) 23.2712 + 15.4206i 0.932342 + 0.617814i
\(624\) −0.0977301 + 0.360042i −0.00391234 + 0.0144132i
\(625\) −4.05898 0.862763i −0.162359 0.0345105i
\(626\) −0.605796 1.04927i −0.0242125 0.0419372i
\(627\) −12.7086 + 46.1897i −0.507534 + 1.84464i
\(628\) 2.47184 + 1.42712i 0.0986373 + 0.0569483i
\(629\) 14.3923 + 44.2951i 0.573860 + 1.76616i
\(630\) 8.20233 + 5.51243i 0.326789 + 0.219620i
\(631\) 19.7537 14.3519i 0.786381 0.571339i −0.120506 0.992713i \(-0.538452\pi\)
0.906887 + 0.421373i \(0.138452\pi\)
\(632\) −4.28962 + 3.86239i −0.170632 + 0.153638i
\(633\) −31.2300 + 20.1368i −1.24128 + 0.800366i
\(634\) −10.3822 4.62244i −0.412328 0.183580i
\(635\) 19.4812 8.67357i 0.773086 0.344200i
\(636\) 13.2852 10.6867i 0.526793 0.423757i
\(637\) 1.48035 0.286123i 0.0586535 0.0113366i
\(638\) −4.45225 + 7.65059i −0.176266 + 0.302890i
\(639\) −32.9333 + 6.77643i −1.30282 + 0.268071i
\(640\) −0.925279 0.833125i −0.0365749 0.0329322i
\(641\) −14.0941 1.48135i −0.556684 0.0585099i −0.177991 0.984032i \(-0.556960\pi\)
−0.378693 + 0.925522i \(0.623626\pi\)
\(642\) −1.06839 2.11381i −0.0421660 0.0834256i
\(643\) −23.2718 7.56146i −0.917749 0.298195i −0.188206 0.982130i \(-0.560267\pi\)
−0.729543 + 0.683935i \(0.760267\pi\)
\(644\) 11.0903 7.05705i 0.437020 0.278087i
\(645\) 12.6179 19.2921i 0.496830 0.759626i
\(646\) 50.7215 22.5827i 1.99561 0.888503i
\(647\) −19.3511 + 21.4915i −0.760768 + 0.844919i −0.991770 0.128035i \(-0.959133\pi\)
0.231001 + 0.972953i \(0.425800\pi\)
\(648\) −3.55328 8.26887i −0.139586 0.324832i
\(649\) −3.36337 + 0.702815i −0.132024 + 0.0275879i
\(650\) −0.743052 −0.0291449
\(651\) 7.41727 + 4.40700i 0.290706 + 0.172724i
\(652\) 0.816637 + 0.593322i 0.0319820 + 0.0232363i
\(653\) −36.0759 + 3.79173i −1.41176 + 0.148382i −0.779512 0.626387i \(-0.784533\pi\)
−0.632245 + 0.774768i \(0.717866\pi\)
\(654\) −5.24153 8.12905i −0.204960 0.317871i
\(655\) −8.22385 + 1.74803i −0.321333 + 0.0683013i
\(656\) 0.509940 + 4.85175i 0.0199098 + 0.189429i
\(657\) −0.0955674 0.969961i −0.00372844 0.0378418i
\(658\) −5.10995 + 0.760919i −0.199206 + 0.0296637i
\(659\) 10.2870i 0.400726i −0.979722 0.200363i \(-0.935788\pi\)
0.979722 0.200363i \(-0.0642122\pi\)
\(660\) −2.60788 + 6.66009i −0.101512 + 0.259244i
\(661\) 6.68898 3.86189i 0.260171 0.150210i −0.364241 0.931305i \(-0.618672\pi\)
0.624413 + 0.781095i \(0.285338\pi\)
\(662\) 4.20673 + 3.78775i 0.163499 + 0.147215i
\(663\) −1.75059 1.76202i −0.0679873 0.0684314i
\(664\) −9.92023 13.6540i −0.384980 0.529879i
\(665\) −24.3608 12.6978i −0.944672 0.492401i
\(666\) −19.2274 + 8.41105i −0.745047 + 0.325922i
\(667\) 1.38608 + 13.1877i 0.0536692 + 0.510628i
\(668\) 0.325707 3.09889i 0.0126020 0.119900i
\(669\) 4.59895 + 1.78257i 0.177805 + 0.0689180i
\(670\) 3.74530 + 2.16235i 0.144693 + 0.0835388i
\(671\) −8.52408 + 39.4347i −0.329068 + 1.52236i
\(672\) 3.44361 3.02350i 0.132840 0.116634i
\(673\) 2.25596 + 6.94312i 0.0869607 + 0.267638i 0.985075 0.172124i \(-0.0550630\pi\)
−0.898115 + 0.439762i \(0.855063\pi\)
\(674\) −7.98546 17.9356i −0.307588 0.690855i
\(675\) 14.0402 11.1443i 0.540408 0.428945i
\(676\) 12.6705 2.69321i 0.487328 0.103585i
\(677\) 7.32120 + 8.13101i 0.281377 + 0.312500i 0.867221 0.497923i \(-0.165904\pi\)
−0.585845 + 0.810423i \(0.699237\pi\)
\(678\) −5.13791 + 7.85559i −0.197320 + 0.301692i
\(679\) −4.49761 17.4291i −0.172602 0.668866i
\(680\) 7.88375 2.56159i 0.302328 0.0982323i
\(681\) −4.13246 + 25.5527i −0.158356 + 0.979183i
\(682\) −1.95002 + 5.93199i −0.0746701 + 0.227148i
\(683\) 19.5151 11.2670i 0.746723 0.431121i −0.0777857 0.996970i \(-0.524785\pi\)
0.824509 + 0.565849i \(0.191452\pi\)
\(684\) 12.3678 + 21.7473i 0.472894 + 0.831531i
\(685\) −10.5898 + 14.5757i −0.404617 + 0.556908i
\(686\) −17.0992 7.11459i −0.652850 0.271636i
\(687\) −23.1783 + 1.13909i −0.884309 + 0.0434590i
\(688\) −7.15254 7.94370i −0.272688 0.302851i
\(689\) 1.93698 + 0.862398i 0.0737930 + 0.0328547i
\(690\) 2.73946 + 10.3586i 0.104290 + 0.394343i
\(691\) 2.66061 12.5172i 0.101214 0.476176i −0.898122 0.439747i \(-0.855068\pi\)
0.999336 0.0364294i \(-0.0115984\pi\)
\(692\) −19.4756 −0.740350
\(693\) −23.2218 12.3996i −0.882122 0.471021i
\(694\) −18.1354 −0.688410
\(695\) 3.06317 14.4111i 0.116193 0.546644i
\(696\) 1.18190 + 4.46905i 0.0447998 + 0.169399i
\(697\) −29.6717 13.2107i −1.12389 0.500390i
\(698\) −12.3401 13.7051i −0.467080 0.518745i
\(699\) −0.693548 + 0.0340841i −0.0262324 + 0.00128918i
\(700\) 7.60838 + 5.04168i 0.287570 + 0.190557i
\(701\) 19.0798 26.2611i 0.720634 0.991868i −0.278868 0.960329i \(-0.589959\pi\)
0.999503 0.0315386i \(-0.0100407\pi\)
\(702\) 0.712802 0.862871i 0.0269030 0.0325670i
\(703\) 50.5227 29.1693i 1.90550 1.10014i
\(704\) 2.67648 + 1.95869i 0.100874 + 0.0738208i
\(705\) 0.672286 4.15703i 0.0253198 0.156563i
\(706\) −0.827019 + 0.268715i −0.0311253 + 0.0101132i
\(707\) −5.33605 5.43576i −0.200683 0.204433i
\(708\) −0.982195 + 1.50172i −0.0369131 + 0.0564382i
\(709\) −19.3274 21.4653i −0.725856 0.806145i 0.261409 0.965228i \(-0.415813\pi\)
−0.987265 + 0.159083i \(0.949146\pi\)
\(710\) 13.6497 2.90133i 0.512263 0.108885i
\(711\) 16.5037 5.24385i 0.618937 0.196660i
\(712\) 4.29170 + 9.63931i 0.160838 + 0.361249i
\(713\) 2.89060 + 8.89635i 0.108254 + 0.333171i
\(714\) 5.96945 + 29.9199i 0.223401 + 1.11973i
\(715\) −0.884901 + 0.0899282i −0.0330934 + 0.00336312i
\(716\) 5.62952 + 3.25020i 0.210385 + 0.121466i
\(717\) 33.8771 + 13.1309i 1.26516 + 0.490382i
\(718\) −1.55070 + 14.7539i −0.0578716 + 0.550612i
\(719\) −0.620032 5.89921i −0.0231233 0.220003i −0.999981 0.00611464i \(-0.998054\pi\)
0.976858 0.213889i \(-0.0686130\pi\)
\(720\) 1.49702 + 3.42214i 0.0557907 + 0.127536i
\(721\) 1.49945 + 34.7657i 0.0558423 + 1.29474i
\(722\) −29.7099 40.8921i −1.10569 1.52185i
\(723\) 28.0599 + 28.2432i 1.04356 + 1.05037i
\(724\) 11.6933 + 10.5287i 0.434576 + 0.391294i
\(725\) −7.97359 + 4.60356i −0.296132 + 0.170972i
\(726\) 5.11751 18.3524i 0.189928 0.681122i
\(727\) 35.2401i 1.30698i −0.756934 0.653491i \(-0.773304\pi\)
0.756934 0.653491i \(-0.226696\pi\)
\(728\) 0.530110 + 0.209141i 0.0196472 + 0.00775127i
\(729\) −0.527250 + 26.9949i −0.0195278 + 0.999809i
\(730\) 0.0422829 + 0.402295i 0.00156496 + 0.0148896i
\(731\) 69.6115 14.7964i 2.57468 0.547264i
\(732\) 11.4178 + 17.7078i 0.422014 + 0.654499i
\(733\) 44.3796 4.66448i 1.63920 0.172287i 0.760391 0.649466i \(-0.225007\pi\)
0.878806 + 0.477179i \(0.158341\pi\)
\(734\) 8.06506 + 5.85961i 0.297687 + 0.216282i
\(735\) 9.75324 11.5221i 0.359754 0.425000i
\(736\) 4.96843 0.183139
\(737\) −10.5079 4.72181i −0.387062 0.173930i
\(738\) 4.61311 13.8894i 0.169811 0.511276i
\(739\) −0.170323 + 0.189162i −0.00626542 + 0.00695845i −0.746269 0.665644i \(-0.768157\pi\)
0.740004 + 0.672602i \(0.234824\pi\)
\(740\) 7.95703 3.54270i 0.292506 0.130232i
\(741\) −1.70295 + 2.60373i −0.0625596 + 0.0956503i
\(742\) −13.9820 21.9730i −0.513294 0.806654i
\(743\) 0.346996 + 0.112746i 0.0127301 + 0.00413625i 0.315375 0.948967i \(-0.397870\pi\)
−0.302645 + 0.953103i \(0.597870\pi\)
\(744\) 1.47098 + 2.91035i 0.0539289 + 0.106699i
\(745\) −27.0229 2.84022i −0.990041 0.104057i
\(746\) 8.99189 + 8.09633i 0.329216 + 0.296428i
\(747\) 10.2044 + 49.5930i 0.373358 + 1.81451i
\(748\) −20.2030 + 8.91176i −0.738696 + 0.325846i
\(749\) −3.38946 + 1.26522i −0.123848 + 0.0462301i
\(750\) −14.1987 + 11.4215i −0.518462 + 0.417056i
\(751\) 8.84640 3.93867i 0.322810 0.143724i −0.238933 0.971036i \(-0.576798\pi\)
0.561743 + 0.827312i \(0.310131\pi\)
\(752\) −1.78386 0.794224i −0.0650505 0.0289624i
\(753\) −1.00337 + 0.646961i −0.0365647 + 0.0235766i
\(754\) −0.427206 + 0.384658i −0.0155579 + 0.0140084i
\(755\) −4.24934 + 3.08733i −0.154649 + 0.112359i
\(756\) −13.1533 + 3.99883i −0.478381 + 0.145436i
\(757\) −8.36370 25.7408i −0.303984 0.935566i −0.980054 0.198729i \(-0.936319\pi\)
0.676071 0.736837i \(-0.263681\pi\)
\(758\) −27.3352 15.7820i −0.992861 0.573228i
\(759\) −10.0497 26.7136i −0.364780 0.969644i
\(760\) −5.19163 8.99217i −0.188320 0.326180i
\(761\) −36.1344 7.68061i −1.30987 0.278422i −0.500509 0.865731i \(-0.666854\pi\)
−0.809362 + 0.587310i \(0.800187\pi\)
\(762\) −7.77112 + 28.6292i −0.281518 + 1.03712i
\(763\) −13.2260 + 6.58548i −0.478813 + 0.238411i
\(764\) 5.46175 + 1.77463i 0.197599 + 0.0642039i
\(765\) −24.7147 2.76040i −0.893563 0.0998024i
\(766\) −1.41716 + 3.18300i −0.0512042 + 0.115007i
\(767\) −0.221924 0.0233251i −0.00801320 0.000842221i
\(768\) 1.71160 0.265383i 0.0617620 0.00957618i
\(769\) 40.4284i 1.45788i −0.684575 0.728942i \(-0.740012\pi\)
0.684575 0.728942i \(-0.259988\pi\)
\(770\) 9.67100 + 5.08333i 0.348518 + 0.183190i
\(771\) −43.6974 + 16.6109i −1.57372 + 0.598226i
\(772\) −4.75503 1.01071i −0.171137 0.0363764i
\(773\) 2.53023 24.0735i 0.0910061 0.865865i −0.849842 0.527037i \(-0.823303\pi\)
0.940848 0.338828i \(-0.110030\pi\)
\(774\) 9.71079 + 30.5623i 0.349047 + 1.09854i
\(775\) −4.82668 + 4.34596i −0.173380 + 0.156112i
\(776\) 2.10236 6.47039i 0.0754702 0.232273i
\(777\) 9.52413 + 30.6102i 0.341676 + 1.09813i
\(778\) −25.4969 18.5246i −0.914109 0.664139i
\(779\) −8.45858 + 39.7945i −0.303060 + 1.42579i
\(780\) −0.293496 + 0.360034i −0.0105088 + 0.0128913i
\(781\) −35.3919 + 11.3650i −1.26642 + 0.406671i
\(782\) −16.5393 + 28.6469i −0.591443 + 1.02441i
\(783\) 2.30309 13.6755i 0.0823056 0.488722i
\(784\) −4.00896 5.73832i −0.143177 0.204940i
\(785\) 2.08886 + 2.87506i 0.0745545 + 0.102615i
\(786\) 5.34370 10.4038i 0.190604 0.371090i
\(787\) −5.05016 23.7591i −0.180019 0.846922i −0.971743 0.236043i \(-0.924149\pi\)
0.791724 0.610879i \(-0.209184\pi\)
\(788\) −0.931648 + 2.09252i −0.0331886 + 0.0745428i
\(789\) 0.710761 + 0.715403i 0.0253038 + 0.0254690i
\(790\) −6.83519 + 2.22089i −0.243185 + 0.0790157i
\(791\) 11.0589 + 9.12613i 0.393210 + 0.324488i
\(792\) −4.88894 8.66593i −0.173721 0.307930i
\(793\) −1.31008 + 2.26913i −0.0465223 + 0.0805790i
\(794\) −10.2330 + 11.3649i −0.363154 + 0.403324i
\(795\) 20.5232 5.42763i 0.727882 0.192498i
\(796\) 1.90334 0.200050i 0.0674623 0.00709057i
\(797\) 2.76765 8.51795i 0.0980352 0.301721i −0.889998 0.455965i \(-0.849294\pi\)
0.988033 + 0.154244i \(0.0492941\pi\)
\(798\) 35.1037 15.1058i 1.24266 0.534740i
\(799\) 10.5175 7.64145i 0.372084 0.270335i
\(800\) 1.40314 + 3.15151i 0.0496086 + 0.111423i
\(801\) 0.206060 31.6540i 0.00728077 1.11844i
\(802\) 2.25762 + 3.91032i 0.0797195 + 0.138078i
\(803\) −0.220401 1.05474i −0.00777777 0.0372211i
\(804\) −5.62353 + 2.13770i −0.198327 + 0.0753907i
\(805\) 16.1884 2.41061i 0.570568 0.0849628i
\(806\) −0.238361 + 0.328076i −0.00839590 + 0.0115560i
\(807\) −1.08835 2.15330i −0.0383116 0.0757996i
\(808\) −0.598580 2.81610i −0.0210580 0.0990700i
\(809\) 4.53880 + 21.3534i 0.159576 + 0.750744i 0.983042 + 0.183379i \(0.0587037\pi\)
−0.823467 + 0.567365i \(0.807963\pi\)
\(810\) 0.145888 11.2048i 0.00512597 0.393697i
\(811\) −9.30208 + 12.8032i −0.326640 + 0.449582i −0.940480 0.339849i \(-0.889624\pi\)
0.613840 + 0.789431i \(0.289624\pi\)
\(812\) 6.98427 1.04002i 0.245100 0.0364976i
\(813\) −7.26108 19.1014i −0.254657 0.669914i
\(814\) −20.1330 + 11.5316i −0.705661 + 0.404181i
\(815\) 0.628407 + 1.08843i 0.0220121 + 0.0381261i
\(816\) −4.16756 + 10.7521i −0.145894 + 0.376400i
\(817\) −36.2575 81.4356i −1.26849 2.84907i
\(818\) −5.52382 + 4.01329i −0.193136 + 0.140321i
\(819\) −1.18968 1.22779i −0.0415707 0.0429026i
\(820\) −1.87701 + 5.77684i −0.0655479 + 0.201736i
\(821\) 39.0590 4.10527i 1.36317 0.143275i 0.605464 0.795872i \(-0.292987\pi\)
0.757705 + 0.652598i \(0.226321\pi\)
\(822\) −6.40794 24.2299i −0.223502 0.845116i
\(823\) 26.2782 29.1849i 0.916000 1.01732i −0.0837828 0.996484i \(-0.526700\pi\)
0.999783 0.0208371i \(-0.00663315\pi\)
\(824\) −6.57620 + 11.3903i −0.229093 + 0.396800i
\(825\) 14.1065 13.9188i 0.491126 0.484592i
\(826\) 2.11410 + 1.74461i 0.0735588 + 0.0607027i
\(827\) −41.3663 + 13.4407i −1.43845 + 0.467380i −0.921413 0.388584i \(-0.872964\pi\)
−0.517035 + 0.855964i \(0.672964\pi\)
\(828\) −13.5769 6.15104i −0.471830 0.213763i
\(829\) −11.0800 + 24.8862i −0.384826 + 0.864333i 0.612446 + 0.790513i \(0.290186\pi\)
−0.997272 + 0.0738203i \(0.976481\pi\)
\(830\) −4.36899 20.5545i −0.151650 0.713457i
\(831\) −34.4036 17.6708i −1.19345 0.612993i
\(832\) 0.126604 + 0.174256i 0.00438922 + 0.00604124i
\(833\) 46.4312 4.01262i 1.60874 0.139029i
\(834\) 12.8462 + 15.9697i 0.444827 + 0.552986i
\(835\) 1.93982 3.35987i 0.0671302 0.116273i
\(836\) 16.1802 + 22.4321i 0.559605 + 0.775832i
\(837\) −0.416581 9.77404i −0.0143991 0.337840i
\(838\) −1.84041 + 8.65845i −0.0635759 + 0.299101i
\(839\) 37.4246 + 27.1906i 1.29204 + 0.938723i 0.999844 0.0176356i \(-0.00561386\pi\)
0.292197 + 0.956358i \(0.405614\pi\)
\(840\) 5.44808 1.69513i 0.187977 0.0584875i
\(841\) 6.76034 20.8062i 0.233115 0.717454i
\(842\) 14.5321 13.0847i 0.500808 0.450930i
\(843\) 1.63800 29.4223i 0.0564157 1.01336i
\(844\) −2.24254 + 21.3363i −0.0771914 + 0.734427i
\(845\) 15.7759 + 3.35327i 0.542708 + 0.115356i
\(846\) 3.89136 + 4.37878i 0.133788 + 0.150546i
\(847\) −26.9984 10.8669i −0.927675 0.373390i
\(848\) 9.84384i 0.338039i
\(849\) −5.00217 32.2617i −0.171674 1.10722i
\(850\) −22.8418 2.40077i −0.783468 0.0823458i
\(851\) −14.1369 + 31.7520i −0.484607 + 1.08844i
\(852\) −8.86930 + 17.2678i −0.303857 + 0.591585i
\(853\) 39.4910 + 12.8314i 1.35215 + 0.439339i 0.893413 0.449236i \(-0.148304\pi\)
0.458732 + 0.888574i \(0.348304\pi\)
\(854\) 28.8106 14.3454i 0.985879 0.490889i
\(855\) 3.05431 + 30.9997i 0.104455 + 1.06017i
\(856\) −1.33756 0.284306i −0.0457167 0.00971739i
\(857\) −15.7192 27.2265i −0.536958 0.930038i −0.999066 0.0432146i \(-0.986240\pi\)
0.462108 0.886824i \(-0.347093\pi\)
\(858\) 0.680835 1.03318i 0.0232433 0.0352722i
\(859\) 7.59837 + 4.38692i 0.259253 + 0.149680i 0.623994 0.781429i \(-0.285509\pi\)
−0.364741 + 0.931109i \(0.618842\pi\)
\(860\) −4.11274 12.6577i −0.140243 0.431624i
\(861\) −20.3079 9.34781i −0.692090 0.318572i
\(862\) 1.76746 1.28413i 0.0601998 0.0437377i
\(863\) −8.19366 + 7.37760i −0.278915 + 0.251137i −0.796701 0.604374i \(-0.793423\pi\)
0.517785 + 0.855511i \(0.326757\pi\)
\(864\) −5.00573 1.39381i −0.170298 0.0474183i
\(865\) −22.1523 9.86286i −0.753202 0.335347i
\(866\) −6.56122 + 2.92124i −0.222959 + 0.0992679i
\(867\) −29.6654 36.8785i −1.00749 1.25246i
\(868\) 4.66669 1.74199i 0.158398 0.0591268i
\(869\) 17.5160 7.72648i 0.594189 0.262103i
\(870\) −0.918880 + 5.68183i −0.0311529 + 0.192632i
\(871\) −0.555981 0.500608i −0.0188387 0.0169624i
\(872\) −5.55376 0.583724i −0.188074 0.0197674i
\(873\) −13.7555 + 15.0784i −0.465552 + 0.510328i
\(874\) 39.4058 + 12.8037i 1.33292 + 0.433092i
\(875\) 14.9433 + 23.4838i 0.505177 + 0.793897i
\(876\) −0.470936 0.308013i −0.0159114 0.0104068i
\(877\) −19.2218 + 8.55811i −0.649075 + 0.288987i −0.704743 0.709462i \(-0.748938\pi\)
0.0556681 + 0.998449i \(0.482271\pi\)
\(878\) −5.89965 + 6.55222i −0.199104 + 0.221127i
\(879\) −0.696113 0.567463i −0.0234793 0.0191400i
\(880\) 2.05242 + 3.58332i 0.0691870 + 0.120794i
\(881\) −1.33960 −0.0451322 −0.0225661 0.999745i \(-0.507184\pi\)
−0.0225661 + 0.999745i \(0.507184\pi\)
\(882\) 3.85084 + 20.6439i 0.129664 + 0.695117i
\(883\) 37.3688 + 27.1500i 1.25756 + 0.913670i 0.998635 0.0522280i \(-0.0166322\pi\)
0.258924 + 0.965898i \(0.416632\pi\)
\(884\) −1.42617 + 0.149897i −0.0479673 + 0.00504157i
\(885\) −1.87770 + 1.21072i −0.0631181 + 0.0406979i
\(886\) −26.2866 + 5.58740i −0.883117 + 0.187712i
\(887\) −4.77460 45.4273i −0.160316 1.52530i −0.718467 0.695561i \(-0.755156\pi\)
0.558151 0.829739i \(-0.311511\pi\)
\(888\) −3.17410 + 11.6935i −0.106516 + 0.392409i
\(889\) 42.1523 + 16.6301i 1.41374 + 0.557754i
\(890\) 13.1376i 0.440373i
\(891\) 2.63105 + 29.7334i 0.0881436 + 0.996108i
\(892\) 2.46616 1.42384i 0.0825732 0.0476737i
\(893\) −12.1015 10.8962i −0.404960 0.364627i
\(894\) 26.8147 26.6407i 0.896816 0.890997i
\(895\) 4.75728 + 6.54783i 0.159018 + 0.218870i
\(896\) −0.114005 2.64329i −0.00380865 0.0883063i
\(897\) −0.0909832 1.85134i −0.00303784 0.0618144i
\(898\) 1.10299 + 10.4943i 0.0368074 + 0.350199i
\(899\) −0.525237 + 4.99729i −0.0175176 + 0.166669i
\(900\) 0.0673700 10.3491i 0.00224567 0.344969i
\(901\) 56.7574 + 32.7689i 1.89086 + 1.09169i
\(902\) 3.41849 15.8148i 0.113823 0.526576i
\(903\) 48.0378 9.58421i 1.59860 0.318943i
\(904\) 1.67467 + 5.15412i 0.0556988 + 0.171423i
\(905\) 7.96846 + 17.8975i 0.264881 + 0.594932i
\(906\) 0.406154 7.29547i 0.0134936 0.242376i
\(907\) 48.2593 10.2578i 1.60242 0.340606i 0.681947 0.731401i \(-0.261133\pi\)
0.920478 + 0.390795i \(0.127800\pi\)
\(908\) 9.99987 + 11.1060i 0.331857 + 0.368565i
\(909\) −1.85070 + 8.43643i −0.0613838 + 0.279819i
\(910\) 0.497057 + 0.506345i 0.0164773 + 0.0167852i
\(911\) 9.09751 2.95596i 0.301414 0.0979353i −0.154406 0.988008i \(-0.549346\pi\)
0.455819 + 0.890072i \(0.349346\pi\)
\(912\) 14.2590 + 2.30600i 0.472162 + 0.0763593i
\(913\) 17.1141 + 53.2953i 0.566394 + 1.76382i
\(914\) 9.61010 5.54839i 0.317874 0.183525i
\(915\) 4.01948 + 25.9238i 0.132880 + 0.857015i
\(916\) −7.87525 + 10.8394i −0.260206 + 0.358142i
\(917\) −14.8927 9.86865i −0.491802 0.325891i
\(918\) 24.6998 24.2221i 0.815215 0.799448i
\(919\) −12.6511 14.0504i −0.417320 0.463481i 0.497428 0.867505i \(-0.334278\pi\)
−0.914748 + 0.404024i \(0.867611\pi\)
\(920\) 5.65130 + 2.51612i 0.186318 + 0.0829541i
\(921\) 45.7092 12.0884i 1.50617 0.398327i
\(922\) −2.01697 + 9.48909i −0.0664253 + 0.312507i
\(923\) −2.41406 −0.0794599
\(924\) −13.9815 + 5.95957i −0.459959 + 0.196056i
\(925\) −24.1330 −0.793487
\(926\) 1.06669 5.01839i 0.0350536 0.164914i
\(927\) 32.0719 22.9841i 1.05338 0.754896i
\(928\) 2.43817 + 1.08554i 0.0800369 + 0.0356347i
\(929\) −11.1147 12.3442i −0.364662 0.404999i 0.532692 0.846309i \(-0.321180\pi\)
−0.897354 + 0.441311i \(0.854514\pi\)
\(930\) 0.199296 + 4.05529i 0.00653516 + 0.132978i
\(931\) −17.0082 55.8431i −0.557423 1.83018i
\(932\) −0.235645 + 0.324338i −0.00771882 + 0.0106240i
\(933\) 13.8944 2.15432i 0.454883 0.0705294i
\(934\) −4.15499 + 2.39888i −0.135955 + 0.0784938i
\(935\) −27.4929 0.0946380i −0.899113 0.00309499i
\(936\) −0.130230 0.632917i −0.00425671 0.0206876i
\(937\) −37.0688 + 12.0444i −1.21098 + 0.393472i −0.843791 0.536672i \(-0.819681\pi\)
−0.367193 + 0.930145i \(0.619681\pi\)
\(938\) 2.29622 + 8.89829i 0.0749744 + 0.290539i
\(939\) 1.75625 + 1.14867i 0.0573131 + 0.0374854i
\(940\) −1.62682 1.80677i −0.0530611 0.0589303i
\(941\) 12.0773 2.56710i 0.393707 0.0836851i −0.00680405 0.999977i \(-0.502166\pi\)
0.400511 + 0.916292i \(0.368832\pi\)
\(942\) −4.93605 0.274800i −0.160825 0.00895347i
\(943\) −9.85864 22.1429i −0.321041 0.721071i
\(944\) 0.320141 + 0.985294i 0.0104197 + 0.0320686i
\(945\) −16.9862 2.11268i −0.552562 0.0687256i
\(946\) 14.3082 + 32.4368i 0.465201 + 1.05461i
\(947\) −39.1579 22.6078i −1.27246 0.734656i −0.297010 0.954874i \(-0.595990\pi\)
−0.975451 + 0.220219i \(0.929323\pi\)
\(948\) 3.61326 9.32207i 0.117353 0.302767i
\(949\) 0.00731468 0.0695946i 0.000237445 0.00225913i
\(950\) 3.00717 + 28.6113i 0.0975655 + 0.928274i
\(951\) 19.6605 0.966206i 0.637535 0.0313314i
\(952\) 15.6202 + 8.14186i 0.506252 + 0.263879i
\(953\) −4.83619 6.65644i −0.156659 0.215623i 0.723471 0.690354i \(-0.242545\pi\)
−0.880131 + 0.474731i \(0.842545\pi\)
\(954\) −12.1869 + 26.8996i −0.394566 + 0.870907i
\(955\) 5.31371 + 4.78449i 0.171948 + 0.154822i
\(956\) 18.1664 10.4884i 0.587545 0.339219i
\(957\) 0.904920 15.3050i 0.0292519 0.494741i
\(958\) 24.4919i 0.791299i
\(959\) −37.8668 + 5.63871i −1.22278 + 0.182084i
\(960\) 2.08124 + 0.564934i 0.0671718 + 0.0182332i
\(961\) −2.86987 27.3050i −0.0925763 0.880805i
\(962\) −1.47386 + 0.313279i −0.0475192 + 0.0101005i
\(963\) 3.30308 + 2.43283i 0.106440 + 0.0783970i
\(964\) 22.8598 2.40267i 0.736266 0.0773847i
\(965\) −4.89673 3.55768i −0.157631 0.114526i
\(966\) −11.6299 + 19.5739i −0.374186 + 0.629779i
\(967\) −36.8891 −1.18628 −0.593138 0.805101i \(-0.702111\pi\)
−0.593138 + 0.805101i \(0.702111\pi\)
\(968\) −6.40422 8.94349i −0.205839 0.287455i
\(969\) −60.7623 + 74.5378i −1.95196 + 2.39450i
\(970\) 5.66806 6.29501i 0.181990 0.202121i
\(971\) 44.0091 19.5941i 1.41232 0.628805i 0.448117 0.893975i \(-0.352095\pi\)
0.964202 + 0.265170i \(0.0854282\pi\)
\(972\) 11.9533 + 10.0060i 0.383401 + 0.320942i
\(973\) 26.4130 16.8073i 0.846762 0.538816i
\(974\) −23.4318 7.61344i −0.750802 0.243950i
\(975\) 1.14862 0.580552i 0.0367854 0.0185925i
\(976\) 12.0980 + 1.27155i 0.387246 + 0.0407012i
\(977\) 9.87653 + 8.89286i 0.315978 + 0.284508i 0.811824 0.583903i \(-0.198475\pi\)
−0.495845 + 0.868411i \(0.665142\pi\)
\(978\) −1.72594 0.279124i −0.0551895 0.00892539i
\(979\) −3.53820 34.8162i −0.113081 1.11273i
\(980\) −1.65395 8.55723i −0.0528334 0.273351i
\(981\) 14.4537 + 8.47080i 0.461473 + 0.270452i
\(982\) 16.8280 7.49230i 0.537003 0.239089i
\(983\) 33.9407 + 15.1114i 1.08254 + 0.481979i 0.868927 0.494940i \(-0.164810\pi\)
0.213614 + 0.976918i \(0.431476\pi\)
\(984\) −4.57899 7.10152i −0.145973 0.226388i
\(985\) −2.11939 + 1.90831i −0.0675295 + 0.0608038i
\(986\) −14.3754 + 10.4443i −0.457805 + 0.332615i
\(987\) 7.30454 5.16868i 0.232506 0.164521i
\(988\) 0.555069 + 1.70833i 0.0176591 + 0.0543491i
\(989\) 45.9938 + 26.5545i 1.46252 + 0.844385i
\(990\) −1.17227 12.3329i −0.0372572 0.391964i
\(991\) −28.5200 49.3982i −0.905969 1.56918i −0.819611 0.572920i \(-0.805810\pi\)
−0.0863581 0.996264i \(-0.527523\pi\)
\(992\) 1.84158 + 0.391440i 0.0584702 + 0.0124282i
\(993\) −9.46224 2.56844i −0.300275 0.0815069i
\(994\) 24.7185 + 16.3797i 0.784023 + 0.519531i
\(995\) 2.26625 + 0.736351i 0.0718451 + 0.0233439i
\(996\) 26.0029 + 13.3559i 0.823933 + 0.423198i
\(997\) −22.2199 + 49.9068i −0.703712 + 1.58056i 0.106423 + 0.994321i \(0.466060\pi\)
−0.810135 + 0.586243i \(0.800606\pi\)
\(998\) 26.7044 + 2.80675i 0.845314 + 0.0888460i
\(999\) 23.1505 28.0245i 0.732450 0.886656i
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 462.2.bf.a.5.8 256
3.2 odd 2 inner 462.2.bf.a.5.22 yes 256
7.3 odd 6 inner 462.2.bf.a.269.13 yes 256
11.9 even 5 inner 462.2.bf.a.383.17 yes 256
21.17 even 6 inner 462.2.bf.a.269.17 yes 256
33.20 odd 10 inner 462.2.bf.a.383.13 yes 256
77.31 odd 30 inner 462.2.bf.a.185.22 yes 256
231.185 even 30 inner 462.2.bf.a.185.8 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.bf.a.5.8 256 1.1 even 1 trivial
462.2.bf.a.5.22 yes 256 3.2 odd 2 inner
462.2.bf.a.185.8 yes 256 231.185 even 30 inner
462.2.bf.a.185.22 yes 256 77.31 odd 30 inner
462.2.bf.a.269.13 yes 256 7.3 odd 6 inner
462.2.bf.a.269.17 yes 256 21.17 even 6 inner
462.2.bf.a.383.13 yes 256 33.20 odd 10 inner
462.2.bf.a.383.17 yes 256 11.9 even 5 inner