Properties

Label 546.2.ch.a.137.6
Level $546$
Weight $2$
Character 546.137
Analytic conductor $4.360$
Analytic rank $0$
Dimension $152$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(137,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 8, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.137");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.ch (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(152\)
Relative dimension: \(38\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 137.6
Character \(\chi\) \(=\) 546.137
Dual form 546.2.ch.a.275.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.975072 + 1.43151i) q^{3} -1.00000i q^{4} +(-0.438011 - 0.117365i) q^{5} +(-0.322754 - 1.70171i) q^{6} +(2.35961 + 1.19677i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.09847 - 2.79166i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.975072 + 1.43151i) q^{3} -1.00000i q^{4} +(-0.438011 - 0.117365i) q^{5} +(-0.322754 - 1.70171i) q^{6} +(2.35961 + 1.19677i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.09847 - 2.79166i) q^{9} +(0.392710 - 0.226731i) q^{10} +(1.47365 - 5.49975i) q^{11} +(1.43151 + 0.975072i) q^{12} +(-0.258990 - 3.59624i) q^{13} +(-2.51474 + 0.822248i) q^{14} +(0.595101 - 0.512580i) q^{15} -1.00000 q^{16} -0.261719 q^{17} +(2.75074 + 1.19727i) q^{18} +(1.37379 - 0.368107i) q^{19} +(-0.117365 + 0.438011i) q^{20} +(-4.01398 + 2.21087i) q^{21} +(2.84688 + 4.93094i) q^{22} +4.08940 q^{23} +(-1.70171 + 0.322754i) q^{24} +(-4.15205 - 2.39719i) q^{25} +(2.72606 + 2.35979i) q^{26} +(5.06739 + 1.14959i) q^{27} +(1.19677 - 2.35961i) q^{28} +(4.54507 + 2.62410i) q^{29} +(-0.0583513 + 0.783249i) q^{30} +(-3.85724 + 1.03354i) q^{31} +(0.707107 - 0.707107i) q^{32} +(6.43606 + 7.47221i) q^{33} +(0.185063 - 0.185063i) q^{34} +(-0.893074 - 0.801133i) q^{35} +(-2.79166 + 1.09847i) q^{36} +(6.07241 - 6.07241i) q^{37} +(-0.711128 + 1.23171i) q^{38} +(5.40060 + 3.13584i) q^{39} +(-0.226731 - 0.392710i) q^{40} +(1.56697 + 5.84799i) q^{41} +(1.27499 - 4.40164i) q^{42} +(1.19950 - 0.692531i) q^{43} +(-5.49975 - 1.47365i) q^{44} +(0.153499 + 1.35170i) q^{45} +(-2.89164 + 2.89164i) q^{46} +(2.42896 - 9.06499i) q^{47} +(0.975072 - 1.43151i) q^{48} +(4.13548 + 5.64782i) q^{49} +(4.63101 - 1.24087i) q^{50} +(0.255195 - 0.374654i) q^{51} +(-3.59624 + 0.258990i) q^{52} +(3.14544 + 1.81602i) q^{53} +(-4.39607 + 2.77030i) q^{54} +(-1.29095 + 2.23600i) q^{55} +(0.822248 + 2.51474i) q^{56} +(-0.812597 + 2.32554i) q^{57} +(-5.06936 + 1.35833i) q^{58} +(4.19304 + 4.19304i) q^{59} +(-0.512580 - 0.595101i) q^{60} +(-4.77234 + 8.26593i) q^{61} +(1.99665 - 3.45831i) q^{62} +(0.749023 - 7.90183i) q^{63} +1.00000i q^{64} +(-0.308631 + 1.60559i) q^{65} +(-9.83463 - 0.732671i) q^{66} +(-0.426632 + 1.59221i) q^{67} +0.261719i q^{68} +(-3.98746 + 5.85404i) q^{69} +(1.19799 - 0.0650121i) q^{70} +(-5.85121 - 1.56783i) q^{71} +(1.19727 - 2.75074i) q^{72} +(2.54220 + 9.48763i) q^{73} +8.58769i q^{74} +(7.48015 - 3.60629i) q^{75} +(-0.368107 - 1.37379i) q^{76} +(10.0592 - 11.2136i) q^{77} +(-6.03618 + 1.60143i) q^{78} +(-8.38494 - 14.5231i) q^{79} +(0.438011 + 0.117365i) q^{80} +(-6.58673 + 6.13311i) q^{81} +(-5.24317 - 3.02714i) q^{82} +(-0.0952575 + 0.0952575i) q^{83} +(2.21087 + 4.01398i) q^{84} +(0.114636 + 0.0307165i) q^{85} +(-0.358481 + 1.33787i) q^{86} +(-8.18820 + 3.94765i) q^{87} +(4.93094 - 2.84688i) q^{88} +(-1.23138 - 1.23138i) q^{89} +(-1.06434 - 0.847255i) q^{90} +(3.69276 - 8.79565i) q^{91} -4.08940i q^{92} +(2.28155 - 6.52948i) q^{93} +(4.69238 + 8.12745i) q^{94} -0.644939 q^{95} +(0.322754 + 1.70171i) q^{96} +(0.458897 - 1.71263i) q^{97} +(-6.91783 - 1.06939i) q^{98} +(-16.9722 + 1.92737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.975072 + 1.43151i −0.562958 + 0.826485i
\(4\) 1.00000i 0.500000i
\(5\) −0.438011 0.117365i −0.195884 0.0524871i 0.159543 0.987191i \(-0.448998\pi\)
−0.355427 + 0.934704i \(0.615665\pi\)
\(6\) −0.322754 1.70171i −0.131764 0.694722i
\(7\) 2.35961 + 1.19677i 0.891847 + 0.452337i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.09847 2.79166i −0.366157 0.930553i
\(10\) 0.392710 0.226731i 0.124186 0.0716987i
\(11\) 1.47365 5.49975i 0.444324 1.65824i −0.273393 0.961902i \(-0.588146\pi\)
0.717716 0.696336i \(-0.245187\pi\)
\(12\) 1.43151 + 0.975072i 0.413243 + 0.281479i
\(13\) −0.258990 3.59624i −0.0718308 0.997417i
\(14\) −2.51474 + 0.822248i −0.672092 + 0.219755i
\(15\) 0.595101 0.512580i 0.153654 0.132348i
\(16\) −1.00000 −0.250000
\(17\) −0.261719 −0.0634761 −0.0317381 0.999496i \(-0.510104\pi\)
−0.0317381 + 0.999496i \(0.510104\pi\)
\(18\) 2.75074 + 1.19727i 0.648355 + 0.282198i
\(19\) 1.37379 0.368107i 0.315170 0.0844495i −0.0977665 0.995209i \(-0.531170\pi\)
0.412936 + 0.910760i \(0.364503\pi\)
\(20\) −0.117365 + 0.438011i −0.0262435 + 0.0979422i
\(21\) −4.01398 + 2.21087i −0.875922 + 0.482452i
\(22\) 2.84688 + 4.93094i 0.606957 + 1.05128i
\(23\) 4.08940 0.852699 0.426349 0.904559i \(-0.359799\pi\)
0.426349 + 0.904559i \(0.359799\pi\)
\(24\) −1.70171 + 0.322754i −0.347361 + 0.0658819i
\(25\) −4.15205 2.39719i −0.830410 0.479437i
\(26\) 2.72606 + 2.35979i 0.534624 + 0.462793i
\(27\) 5.06739 + 1.14959i 0.975220 + 0.221239i
\(28\) 1.19677 2.35961i 0.226169 0.445924i
\(29\) 4.54507 + 2.62410i 0.843998 + 0.487282i 0.858621 0.512611i \(-0.171322\pi\)
−0.0146233 + 0.999893i \(0.504655\pi\)
\(30\) −0.0583513 + 0.783249i −0.0106534 + 0.143001i
\(31\) −3.85724 + 1.03354i −0.692781 + 0.185630i −0.587995 0.808865i \(-0.700082\pi\)
−0.104786 + 0.994495i \(0.533416\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 6.43606 + 7.47221i 1.12037 + 1.30075i
\(34\) 0.185063 0.185063i 0.0317381 0.0317381i
\(35\) −0.893074 0.801133i −0.150957 0.135416i
\(36\) −2.79166 + 1.09847i −0.465277 + 0.183078i
\(37\) 6.07241 6.07241i 0.998299 0.998299i −0.00169975 0.999999i \(-0.500541\pi\)
0.999999 + 0.00169975i \(0.000541048\pi\)
\(38\) −0.711128 + 1.23171i −0.115360 + 0.199810i
\(39\) 5.40060 + 3.13584i 0.864788 + 0.502137i
\(40\) −0.226731 0.392710i −0.0358493 0.0620929i
\(41\) 1.56697 + 5.84799i 0.244719 + 0.913303i 0.973525 + 0.228583i \(0.0734091\pi\)
−0.728806 + 0.684721i \(0.759924\pi\)
\(42\) 1.27499 4.40164i 0.196735 0.679187i
\(43\) 1.19950 0.692531i 0.182922 0.105610i −0.405743 0.913987i \(-0.632987\pi\)
0.588665 + 0.808377i \(0.299654\pi\)
\(44\) −5.49975 1.47365i −0.829119 0.222162i
\(45\) 0.153499 + 1.35170i 0.0228823 + 0.201499i
\(46\) −2.89164 + 2.89164i −0.426349 + 0.426349i
\(47\) 2.42896 9.06499i 0.354300 1.32226i −0.527064 0.849826i \(-0.676707\pi\)
0.881363 0.472439i \(-0.156626\pi\)
\(48\) 0.975072 1.43151i 0.140740 0.206621i
\(49\) 4.13548 + 5.64782i 0.590782 + 0.806831i
\(50\) 4.63101 1.24087i 0.654923 0.175486i
\(51\) 0.255195 0.374654i 0.0357344 0.0524621i
\(52\) −3.59624 + 0.258990i −0.498708 + 0.0359154i
\(53\) 3.14544 + 1.81602i 0.432059 + 0.249450i 0.700224 0.713924i \(-0.253084\pi\)
−0.268164 + 0.963373i \(0.586417\pi\)
\(54\) −4.39607 + 2.77030i −0.598229 + 0.376990i
\(55\) −1.29095 + 2.23600i −0.174072 + 0.301502i
\(56\) 0.822248 + 2.51474i 0.109877 + 0.336046i
\(57\) −0.812597 + 2.32554i −0.107631 + 0.308025i
\(58\) −5.06936 + 1.35833i −0.665640 + 0.178358i
\(59\) 4.19304 + 4.19304i 0.545887 + 0.545887i 0.925249 0.379361i \(-0.123856\pi\)
−0.379361 + 0.925249i \(0.623856\pi\)
\(60\) −0.512580 0.595101i −0.0661738 0.0768272i
\(61\) −4.77234 + 8.26593i −0.611035 + 1.05834i 0.380031 + 0.924974i \(0.375913\pi\)
−0.991066 + 0.133370i \(0.957420\pi\)
\(62\) 1.99665 3.45831i 0.253575 0.439206i
\(63\) 0.749023 7.90183i 0.0943681 0.995537i
\(64\) 1.00000i 0.125000i
\(65\) −0.308631 + 1.60559i −0.0382809 + 0.199149i
\(66\) −9.83463 0.732671i −1.21056 0.0901856i
\(67\) −0.426632 + 1.59221i −0.0521214 + 0.194520i −0.987077 0.160244i \(-0.948772\pi\)
0.934956 + 0.354763i \(0.115439\pi\)
\(68\) 0.261719i 0.0317381i
\(69\) −3.98746 + 5.85404i −0.480034 + 0.704743i
\(70\) 1.19799 0.0650121i 0.143187 0.00777043i
\(71\) −5.85121 1.56783i −0.694411 0.186067i −0.105685 0.994400i \(-0.533704\pi\)
−0.588726 + 0.808333i \(0.700370\pi\)
\(72\) 1.19727 2.75074i 0.141099 0.324177i
\(73\) 2.54220 + 9.48763i 0.297542 + 1.11044i 0.939177 + 0.343433i \(0.111590\pi\)
−0.641635 + 0.767010i \(0.721744\pi\)
\(74\) 8.58769i 0.998299i
\(75\) 7.48015 3.60629i 0.863734 0.416418i
\(76\) −0.368107 1.37379i −0.0422248 0.157585i
\(77\) 10.0592 11.2136i 1.14635 1.27791i
\(78\) −6.03618 + 1.60143i −0.683462 + 0.181326i
\(79\) −8.38494 14.5231i −0.943379 1.63398i −0.758964 0.651132i \(-0.774294\pi\)
−0.184415 0.982848i \(-0.559039\pi\)
\(80\) 0.438011 + 0.117365i 0.0489711 + 0.0131218i
\(81\) −6.58673 + 6.13311i −0.731859 + 0.681456i
\(82\) −5.24317 3.02714i −0.579011 0.334292i
\(83\) −0.0952575 + 0.0952575i −0.0104559 + 0.0104559i −0.712315 0.701860i \(-0.752353\pi\)
0.701860 + 0.712315i \(0.252353\pi\)
\(84\) 2.21087 + 4.01398i 0.241226 + 0.437961i
\(85\) 0.114636 + 0.0307165i 0.0124340 + 0.00333168i
\(86\) −0.358481 + 1.33787i −0.0386559 + 0.144266i
\(87\) −8.18820 + 3.94765i −0.877867 + 0.423232i
\(88\) 4.93094 2.84688i 0.525640 0.303479i
\(89\) −1.23138 1.23138i −0.130527 0.130527i 0.638825 0.769352i \(-0.279421\pi\)
−0.769352 + 0.638825i \(0.779421\pi\)
\(90\) −1.06434 0.847255i −0.112191 0.0893085i
\(91\) 3.69276 8.79565i 0.387107 0.922035i
\(92\) 4.08940i 0.426349i
\(93\) 2.28155 6.52948i 0.236586 0.677075i
\(94\) 4.69238 + 8.12745i 0.483983 + 0.838282i
\(95\) −0.644939 −0.0661694
\(96\) 0.322754 + 1.70171i 0.0329409 + 0.173680i
\(97\) 0.458897 1.71263i 0.0465939 0.173891i −0.938708 0.344714i \(-0.887976\pi\)
0.985302 + 0.170823i \(0.0546426\pi\)
\(98\) −6.91783 1.06939i −0.698807 0.108024i
\(99\) −16.9722 + 1.92737i −1.70577 + 0.193708i
\(100\) −2.39719 + 4.15205i −0.239719 + 0.415205i
\(101\) −7.96445 13.7948i −0.792492 1.37264i −0.924419 0.381378i \(-0.875450\pi\)
0.131927 0.991259i \(-0.457884\pi\)
\(102\) 0.0844708 + 0.445371i 0.00836385 + 0.0440983i
\(103\) 12.1401 7.00907i 1.19620 0.690624i 0.236492 0.971634i \(-0.424002\pi\)
0.959705 + 0.281009i \(0.0906691\pi\)
\(104\) 2.35979 2.72606i 0.231397 0.267312i
\(105\) 2.01765 0.497286i 0.196902 0.0485302i
\(106\) −3.50828 + 0.940041i −0.340754 + 0.0913049i
\(107\) 15.2283i 1.47217i −0.676888 0.736086i \(-0.736672\pi\)
0.676888 0.736086i \(-0.263328\pi\)
\(108\) 1.14959 5.06739i 0.110620 0.487610i
\(109\) 5.85258 1.56819i 0.560575 0.150206i 0.0326046 0.999468i \(-0.489620\pi\)
0.527971 + 0.849263i \(0.322953\pi\)
\(110\) −0.668246 2.49393i −0.0637148 0.237787i
\(111\) 2.77171 + 14.6138i 0.263079 + 1.38708i
\(112\) −2.35961 1.19677i −0.222962 0.113084i
\(113\) 3.28411 1.89608i 0.308943 0.178368i −0.337510 0.941322i \(-0.609585\pi\)
0.646453 + 0.762954i \(0.276251\pi\)
\(114\) −1.06981 2.21900i −0.100197 0.207828i
\(115\) −1.79120 0.479951i −0.167030 0.0447556i
\(116\) 2.62410 4.54507i 0.243641 0.421999i
\(117\) −9.75498 + 4.67337i −0.901848 + 0.432053i
\(118\) −5.92985 −0.545887
\(119\) −0.617553 0.313218i −0.0566110 0.0287126i
\(120\) 0.783249 + 0.0583513i 0.0715005 + 0.00532672i
\(121\) −18.5493 10.7095i −1.68630 0.973588i
\(122\) −2.47034 9.21945i −0.223654 0.834690i
\(123\) −9.89939 3.45908i −0.892598 0.311895i
\(124\) 1.03354 + 3.85724i 0.0928150 + 0.346390i
\(125\) 3.14053 + 3.14053i 0.280897 + 0.280897i
\(126\) 5.05780 + 6.11708i 0.450585 + 0.544953i
\(127\) −7.49862 4.32933i −0.665395 0.384166i 0.128934 0.991653i \(-0.458844\pi\)
−0.794330 + 0.607487i \(0.792178\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −0.178229 + 2.39237i −0.0156922 + 0.210636i
\(130\) −0.917086 1.35356i −0.0804338 0.118715i
\(131\) 12.3406 7.12484i 1.07820 0.622500i 0.147791 0.989019i \(-0.452784\pi\)
0.930411 + 0.366519i \(0.119450\pi\)
\(132\) 7.47221 6.43606i 0.650373 0.560187i
\(133\) 3.68215 + 0.775530i 0.319283 + 0.0672470i
\(134\) −0.824190 1.42754i −0.0711991 0.123321i
\(135\) −2.08465 1.09827i −0.179418 0.0945237i
\(136\) −0.185063 0.185063i −0.0158690 0.0158690i
\(137\) 2.57796 + 2.57796i 0.220250 + 0.220250i 0.808604 0.588354i \(-0.200224\pi\)
−0.588354 + 0.808604i \(0.700224\pi\)
\(138\) −1.31987 6.95899i −0.112355 0.592388i
\(139\) 5.46197 + 9.46041i 0.463278 + 0.802421i 0.999122 0.0418959i \(-0.0133398\pi\)
−0.535844 + 0.844317i \(0.680006\pi\)
\(140\) −0.801133 + 0.893074i −0.0677081 + 0.0754785i
\(141\) 10.6083 + 12.3161i 0.893377 + 1.03720i
\(142\) 5.24605 3.02881i 0.440239 0.254172i
\(143\) −20.1601 3.87523i −1.68587 0.324063i
\(144\) 1.09847 + 2.79166i 0.0915391 + 0.232638i
\(145\) −1.68281 1.68281i −0.139750 0.139750i
\(146\) −8.50638 4.91116i −0.703993 0.406450i
\(147\) −12.1173 + 0.412969i −0.999420 + 0.0340611i
\(148\) −6.07241 6.07241i −0.499149 0.499149i
\(149\) 5.10625 + 19.0568i 0.418320 + 1.56119i 0.778091 + 0.628151i \(0.216188\pi\)
−0.359771 + 0.933041i \(0.617145\pi\)
\(150\) −2.73923 + 7.83930i −0.223658 + 0.640076i
\(151\) −0.508437 1.89751i −0.0413760 0.154417i 0.942147 0.335200i \(-0.108804\pi\)
−0.983523 + 0.180782i \(0.942137\pi\)
\(152\) 1.23171 + 0.711128i 0.0999049 + 0.0576801i
\(153\) 0.287490 + 0.730630i 0.0232422 + 0.0590679i
\(154\) 0.816305 + 15.0421i 0.0657798 + 1.21213i
\(155\) 1.81081 0.145448
\(156\) 3.13584 5.40060i 0.251068 0.432394i
\(157\) −7.93738 + 13.7480i −0.633472 + 1.09721i 0.353365 + 0.935486i \(0.385038\pi\)
−0.986837 + 0.161720i \(0.948296\pi\)
\(158\) 16.1985 + 4.34036i 1.28868 + 0.345301i
\(159\) −5.66669 + 2.73199i −0.449398 + 0.216661i
\(160\) −0.392710 + 0.226731i −0.0310464 + 0.0179247i
\(161\) 9.64937 + 4.89408i 0.760477 + 0.385707i
\(162\) 0.320759 8.99428i 0.0252012 0.706658i
\(163\) 2.70104 + 10.0804i 0.211562 + 0.789560i 0.987349 + 0.158565i \(0.0506867\pi\)
−0.775787 + 0.630995i \(0.782647\pi\)
\(164\) 5.84799 1.56697i 0.456652 0.122359i
\(165\) −1.94209 4.02828i −0.151191 0.313601i
\(166\) 0.134715i 0.0104559i
\(167\) −21.1909 + 5.67807i −1.63980 + 0.439382i −0.956731 0.290974i \(-0.906021\pi\)
−0.683067 + 0.730356i \(0.739354\pi\)
\(168\) −4.40164 1.27499i −0.339594 0.0983676i
\(169\) −12.8658 + 1.86278i −0.989681 + 0.143290i
\(170\) −0.102780 + 0.0593398i −0.00788283 + 0.00455115i
\(171\) −2.53670 3.43081i −0.193986 0.262361i
\(172\) −0.692531 1.19950i −0.0528050 0.0914610i
\(173\) 2.20153 3.81316i 0.167379 0.289909i −0.770118 0.637901i \(-0.779803\pi\)
0.937498 + 0.347992i \(0.113136\pi\)
\(174\) 2.99852 8.58134i 0.227317 0.650550i
\(175\) −6.92831 10.6255i −0.523731 0.803210i
\(176\) −1.47365 + 5.49975i −0.111081 + 0.414560i
\(177\) −10.0909 + 1.91388i −0.758479 + 0.143856i
\(178\) 1.74144 0.130527
\(179\) −10.1302 17.5460i −0.757164 1.31145i −0.944291 0.329111i \(-0.893251\pi\)
0.187127 0.982336i \(-0.440082\pi\)
\(180\) 1.35170 0.153499i 0.100750 0.0114412i
\(181\) 7.49322i 0.556967i −0.960441 0.278483i \(-0.910168\pi\)
0.960441 0.278483i \(-0.0898317\pi\)
\(182\) 3.60829 + 8.83064i 0.267464 + 0.654571i
\(183\) −7.17943 14.8916i −0.530719 1.10082i
\(184\) 2.89164 + 2.89164i 0.213175 + 0.213175i
\(185\) −3.37247 + 1.94710i −0.247949 + 0.143153i
\(186\) 3.00374 + 6.23034i 0.220245 + 0.456831i
\(187\) −0.385683 + 1.43939i −0.0282039 + 0.105259i
\(188\) −9.06499 2.42896i −0.661132 0.177150i
\(189\) 10.5812 + 8.77709i 0.769672 + 0.638440i
\(190\) 0.456041 0.456041i 0.0330847 0.0330847i
\(191\) 7.60377 + 4.39004i 0.550190 + 0.317652i 0.749199 0.662346i \(-0.230439\pi\)
−0.199009 + 0.979998i \(0.563772\pi\)
\(192\) −1.43151 0.975072i −0.103311 0.0703698i
\(193\) 12.1645 + 3.25947i 0.875621 + 0.234622i 0.668517 0.743697i \(-0.266929\pi\)
0.207104 + 0.978319i \(0.433596\pi\)
\(194\) 0.886520 + 1.53550i 0.0636485 + 0.110242i
\(195\) −1.99748 2.00737i −0.143043 0.143751i
\(196\) 5.64782 4.13548i 0.403415 0.295391i
\(197\) 3.55613 + 13.2717i 0.253364 + 0.945568i 0.968993 + 0.247087i \(0.0794734\pi\)
−0.715629 + 0.698480i \(0.753860\pi\)
\(198\) 10.6383 13.3640i 0.756031 0.949739i
\(199\) 18.2312i 1.29237i 0.763179 + 0.646187i \(0.223637\pi\)
−0.763179 + 0.646187i \(0.776363\pi\)
\(200\) −1.24087 4.63101i −0.0877431 0.327462i
\(201\) −1.86328 2.16325i −0.131426 0.152584i
\(202\) 15.3861 + 4.12270i 1.08256 + 0.290072i
\(203\) 7.58412 + 11.6312i 0.532301 + 0.816353i
\(204\) −0.374654 0.255195i −0.0262311 0.0178672i
\(205\) 2.74539i 0.191746i
\(206\) −3.62816 + 13.5405i −0.252786 + 0.943411i
\(207\) −4.49208 11.4162i −0.312221 0.793482i
\(208\) 0.258990 + 3.59624i 0.0179577 + 0.249354i
\(209\) 8.09799i 0.560150i
\(210\) −1.07506 + 1.77833i −0.0741859 + 0.122716i
\(211\) 6.97826 12.0867i 0.480403 0.832083i −0.519344 0.854565i \(-0.673824\pi\)
0.999747 + 0.0224824i \(0.00715696\pi\)
\(212\) 1.81602 3.14544i 0.124725 0.216030i
\(213\) 7.94972 6.84735i 0.544706 0.469173i
\(214\) 10.7680 + 10.7680i 0.736086 + 0.736086i
\(215\) −0.606672 + 0.162557i −0.0413747 + 0.0110863i
\(216\) 2.77030 + 4.39607i 0.188495 + 0.299115i
\(217\) −10.3385 2.17748i −0.701822 0.147817i
\(218\) −3.02952 + 5.24728i −0.205185 + 0.355390i
\(219\) −16.0605 5.61192i −1.08527 0.379218i
\(220\) 2.23600 + 1.29095i 0.150751 + 0.0870360i
\(221\) 0.0677825 + 0.941203i 0.00455954 + 0.0633122i
\(222\) −12.2934 8.37362i −0.825079 0.562000i
\(223\) 28.3691 7.60147i 1.89973 0.509032i 0.902869 0.429916i \(-0.141457\pi\)
0.996865 0.0791158i \(-0.0252097\pi\)
\(224\) 2.51474 0.822248i 0.168023 0.0549387i
\(225\) −2.13123 + 14.2243i −0.142082 + 0.948289i
\(226\) −0.981484 + 3.66295i −0.0652873 + 0.243656i
\(227\) 3.58283 3.58283i 0.237800 0.237800i −0.578138 0.815939i \(-0.696221\pi\)
0.815939 + 0.578138i \(0.196221\pi\)
\(228\) 2.32554 + 0.812597i 0.154012 + 0.0538156i
\(229\) 2.38859 + 0.640022i 0.157843 + 0.0422938i 0.336875 0.941549i \(-0.390630\pi\)
−0.179032 + 0.983843i \(0.557297\pi\)
\(230\) 1.60595 0.927194i 0.105893 0.0611373i
\(231\) 6.24403 + 25.3340i 0.410827 + 1.66685i
\(232\) 1.35833 + 5.06936i 0.0891789 + 0.332820i
\(233\) 8.16384 + 14.1402i 0.534831 + 0.926354i 0.999172 + 0.0406974i \(0.0129580\pi\)
−0.464341 + 0.885657i \(0.653709\pi\)
\(234\) 3.59324 10.2024i 0.234898 0.666951i
\(235\) −2.12782 + 3.68549i −0.138804 + 0.240415i
\(236\) 4.19304 4.19304i 0.272944 0.272944i
\(237\) 28.9660 + 2.15794i 1.88154 + 0.140173i
\(238\) 0.658154 0.215198i 0.0426618 0.0139492i
\(239\) −7.48384 + 7.48384i −0.484089 + 0.484089i −0.906435 0.422346i \(-0.861207\pi\)
0.422346 + 0.906435i \(0.361207\pi\)
\(240\) −0.595101 + 0.512580i −0.0384136 + 0.0330869i
\(241\) −4.03869 + 4.03869i −0.260155 + 0.260155i −0.825117 0.564962i \(-0.808891\pi\)
0.564962 + 0.825117i \(0.308891\pi\)
\(242\) 20.6891 5.54363i 1.32995 0.356358i
\(243\) −2.35710 15.4092i −0.151208 0.988502i
\(244\) 8.26593 + 4.77234i 0.529172 + 0.305518i
\(245\) −1.14853 2.95916i −0.0733768 0.189054i
\(246\) 9.44587 4.55399i 0.602247 0.290352i
\(247\) −1.67960 4.84515i −0.106870 0.308290i
\(248\) −3.45831 1.99665i −0.219603 0.126788i
\(249\) −0.0434796 0.229246i −0.00275541 0.0145278i
\(250\) −4.44138 −0.280897
\(251\) 10.3108 + 17.8587i 0.650809 + 1.12723i 0.982927 + 0.183996i \(0.0589034\pi\)
−0.332118 + 0.943238i \(0.607763\pi\)
\(252\) −7.90183 0.749023i −0.497769 0.0471840i
\(253\) 6.02636 22.4907i 0.378874 1.41398i
\(254\) 8.36363 2.24103i 0.524781 0.140615i
\(255\) −0.155749 + 0.134152i −0.00975339 + 0.00840091i
\(256\) 1.00000 0.0625000
\(257\) −11.2872 −0.704074 −0.352037 0.935986i \(-0.614511\pi\)
−0.352037 + 0.935986i \(0.614511\pi\)
\(258\) −1.56563 1.81769i −0.0974720 0.113164i
\(259\) 21.5958 7.06121i 1.34190 0.438762i
\(260\) 1.60559 + 0.308631i 0.0995743 + 0.0191405i
\(261\) 2.33296 15.5708i 0.144407 0.963807i
\(262\) −3.68809 + 13.7641i −0.227851 + 0.850351i
\(263\) −20.6695 + 11.9335i −1.27454 + 0.735853i −0.975838 0.218495i \(-0.929885\pi\)
−0.298697 + 0.954348i \(0.596552\pi\)
\(264\) −0.732671 + 9.83463i −0.0450928 + 0.605280i
\(265\) −1.16460 1.16460i −0.0715408 0.0715408i
\(266\) −3.15206 + 2.05529i −0.193265 + 0.126018i
\(267\) 2.96343 0.562057i 0.181359 0.0343973i
\(268\) 1.59221 + 0.426632i 0.0972598 + 0.0260607i
\(269\) 9.47216i 0.577528i 0.957400 + 0.288764i \(0.0932443\pi\)
−0.957400 + 0.288764i \(0.906756\pi\)
\(270\) 2.25066 0.697478i 0.136971 0.0424472i
\(271\) −3.24177 + 3.24177i −0.196924 + 0.196924i −0.798680 0.601756i \(-0.794468\pi\)
0.601756 + 0.798680i \(0.294468\pi\)
\(272\) 0.261719 0.0158690
\(273\) 8.99040 + 13.8626i 0.544124 + 0.839005i
\(274\) −3.64578 −0.220250
\(275\) −19.3026 + 19.3026i −1.16399 + 1.16399i
\(276\) 5.85404 + 3.98746i 0.352372 + 0.240017i
\(277\) 15.7090i 0.943860i −0.881636 0.471930i \(-0.843557\pi\)
0.881636 0.471930i \(-0.156443\pi\)
\(278\) −10.5517 2.82732i −0.632850 0.169572i
\(279\) 7.12237 + 9.63279i 0.426405 + 0.576700i
\(280\) −0.0650121 1.19799i −0.00388522 0.0715933i
\(281\) −20.7309 20.7309i −1.23670 1.23670i −0.961341 0.275361i \(-0.911203\pi\)
−0.275361 0.961341i \(-0.588797\pi\)
\(282\) −16.2100 1.20763i −0.965290 0.0719132i
\(283\) 24.3614 14.0650i 1.44813 0.836080i 0.449763 0.893148i \(-0.351508\pi\)
0.998370 + 0.0570679i \(0.0181751\pi\)
\(284\) −1.56783 + 5.85121i −0.0930334 + 0.347205i
\(285\) 0.628862 0.923240i 0.0372506 0.0546880i
\(286\) 16.9955 11.5151i 1.00497 0.680904i
\(287\) −3.30129 + 15.6743i −0.194869 + 0.925222i
\(288\) −2.75074 1.19727i −0.162089 0.0705496i
\(289\) −16.9315 −0.995971
\(290\) 2.37986 0.139750
\(291\) 2.00419 + 2.32685i 0.117488 + 0.136402i
\(292\) 9.48763 2.54220i 0.555222 0.148771i
\(293\) −5.34352 + 19.9423i −0.312172 + 1.16504i 0.614422 + 0.788977i \(0.289389\pi\)
−0.926594 + 0.376063i \(0.877277\pi\)
\(294\) 8.27623 8.86025i 0.482679 0.516740i
\(295\) −1.34448 2.32871i −0.0782787 0.135583i
\(296\) 8.58769 0.499149
\(297\) 13.7901 26.1753i 0.800180 1.51884i
\(298\) −17.0858 9.86451i −0.989756 0.571436i
\(299\) −1.05911 14.7065i −0.0612500 0.850496i
\(300\) −3.60629 7.48015i −0.208209 0.431867i
\(301\) 3.65915 0.198574i 0.210910 0.0114456i
\(302\) 1.70126 + 0.982225i 0.0978967 + 0.0565207i
\(303\) 27.5134 + 2.04972i 1.58060 + 0.117754i
\(304\) −1.37379 + 0.368107i −0.0787925 + 0.0211124i
\(305\) 3.06046 3.06046i 0.175242 0.175242i
\(306\) −0.719920 0.313347i −0.0411551 0.0179129i
\(307\) −23.1047 + 23.1047i −1.31865 + 1.31865i −0.403809 + 0.914843i \(0.632314\pi\)
−0.914843 + 0.403809i \(0.867686\pi\)
\(308\) −11.2136 10.0592i −0.638955 0.573176i
\(309\) −1.80385 + 24.2130i −0.102617 + 1.37743i
\(310\) −1.28044 + 1.28044i −0.0727241 + 0.0727241i
\(311\) −10.7534 + 18.6255i −0.609772 + 1.05616i 0.381506 + 0.924366i \(0.375405\pi\)
−0.991278 + 0.131789i \(0.957928\pi\)
\(312\) 1.60143 + 6.03618i 0.0906629 + 0.341731i
\(313\) −3.22152 5.57984i −0.182091 0.315391i 0.760501 0.649336i \(-0.224953\pi\)
−0.942592 + 0.333945i \(0.891620\pi\)
\(314\) −4.10869 15.3338i −0.231867 0.865339i
\(315\) −1.25548 + 3.37318i −0.0707381 + 0.190057i
\(316\) −14.5231 + 8.38494i −0.816990 + 0.471690i
\(317\) 10.8363 + 2.90357i 0.608626 + 0.163081i 0.549952 0.835196i \(-0.314646\pi\)
0.0586739 + 0.998277i \(0.481313\pi\)
\(318\) 2.07514 5.93876i 0.116368 0.333029i
\(319\) 21.1297 21.1297i 1.18304 1.18304i
\(320\) 0.117365 0.438011i 0.00656088 0.0244855i
\(321\) 21.7995 + 14.8487i 1.21673 + 0.828771i
\(322\) −10.2838 + 3.36250i −0.573092 + 0.187385i
\(323\) −0.359548 + 0.0963405i −0.0200058 + 0.00536053i
\(324\) 6.13311 + 6.58673i 0.340728 + 0.365929i
\(325\) −7.54551 + 15.5526i −0.418550 + 0.862703i
\(326\) −9.03787 5.21802i −0.500561 0.288999i
\(327\) −3.46179 + 9.90715i −0.191437 + 0.547867i
\(328\) −3.02714 + 5.24317i −0.167146 + 0.289506i
\(329\) 16.5801 18.4829i 0.914091 1.01900i
\(330\) 4.22169 + 1.47516i 0.232396 + 0.0812047i
\(331\) 9.91429 2.65653i 0.544939 0.146016i 0.0241608 0.999708i \(-0.492309\pi\)
0.520778 + 0.853692i \(0.325642\pi\)
\(332\) 0.0952575 + 0.0952575i 0.00522794 + 0.00522794i
\(333\) −23.6225 10.2818i −1.29450 0.563437i
\(334\) 10.9692 18.9992i 0.600208 1.03959i
\(335\) 0.373739 0.647335i 0.0204195 0.0353677i
\(336\) 4.01398 2.21087i 0.218981 0.120613i
\(337\) 31.9526i 1.74057i −0.492550 0.870284i \(-0.663935\pi\)
0.492550 0.870284i \(-0.336065\pi\)
\(338\) 7.78035 10.4147i 0.423195 0.566486i
\(339\) −0.487974 + 6.55006i −0.0265031 + 0.355751i
\(340\) 0.0307165 0.114636i 0.00166584 0.00621699i
\(341\) 22.7370i 1.23128i
\(342\) 4.21967 + 0.632232i 0.228173 + 0.0341872i
\(343\) 2.99895 + 18.2758i 0.161928 + 0.986803i
\(344\) 1.33787 + 0.358481i 0.0721330 + 0.0193280i
\(345\) 2.43361 2.09614i 0.131021 0.112853i
\(346\) 1.13960 + 4.25303i 0.0612650 + 0.228644i
\(347\) 5.72899i 0.307548i −0.988106 0.153774i \(-0.950857\pi\)
0.988106 0.153774i \(-0.0491428\pi\)
\(348\) 3.94765 + 8.18820i 0.211616 + 0.438934i
\(349\) 3.05898 + 11.4163i 0.163743 + 0.611098i 0.998197 + 0.0600203i \(0.0191166\pi\)
−0.834454 + 0.551078i \(0.814217\pi\)
\(350\) 12.4124 + 2.61428i 0.663470 + 0.139739i
\(351\) 2.82181 18.5213i 0.150617 0.988592i
\(352\) −2.84688 4.93094i −0.151739 0.262820i
\(353\) −5.03707 1.34968i −0.268096 0.0718361i 0.122267 0.992497i \(-0.460984\pi\)
−0.390363 + 0.920661i \(0.627650\pi\)
\(354\) 5.78203 8.48867i 0.307312 0.451168i
\(355\) 2.37889 + 1.37345i 0.126258 + 0.0728952i
\(356\) −1.23138 + 1.23138i −0.0652633 + 0.0652633i
\(357\) 1.05053 0.578627i 0.0556002 0.0306242i
\(358\) 19.5700 + 5.24376i 1.03431 + 0.277141i
\(359\) −5.52961 + 20.6368i −0.291842 + 1.08917i 0.651851 + 0.758347i \(0.273993\pi\)
−0.943693 + 0.330822i \(0.892674\pi\)
\(360\) −0.847255 + 1.06434i −0.0446542 + 0.0560954i
\(361\) −14.7027 + 8.48859i −0.773825 + 0.446768i
\(362\) 5.29851 + 5.29851i 0.278483 + 0.278483i
\(363\) 33.4177 16.1112i 1.75398 0.845617i
\(364\) −8.79565 3.69276i −0.461017 0.193553i
\(365\) 4.45405i 0.233136i
\(366\) 15.6065 + 5.45329i 0.815767 + 0.285048i
\(367\) −15.3314 26.5548i −0.800293 1.38615i −0.919423 0.393270i \(-0.871344\pi\)
0.119130 0.992879i \(-0.461990\pi\)
\(368\) −4.08940 −0.213175
\(369\) 14.6043 10.7983i 0.760272 0.562136i
\(370\) 1.00789 3.76150i 0.0523978 0.195551i
\(371\) 5.24863 + 8.04946i 0.272496 + 0.417907i
\(372\) −6.52948 2.28155i −0.338538 0.118293i
\(373\) −14.1624 + 24.5300i −0.733301 + 1.27011i 0.222164 + 0.975009i \(0.428688\pi\)
−0.955465 + 0.295105i \(0.904645\pi\)
\(374\) −0.745083 1.29052i −0.0385273 0.0667312i
\(375\) −7.55795 + 1.43347i −0.390291 + 0.0740242i
\(376\) 8.12745 4.69238i 0.419141 0.241991i
\(377\) 8.25975 17.0248i 0.425399 0.876819i
\(378\) −13.6884 + 1.27572i −0.704056 + 0.0656162i
\(379\) 9.43043 2.52688i 0.484408 0.129797i −0.00834614 0.999965i \(-0.502657\pi\)
0.492755 + 0.870168i \(0.335990\pi\)
\(380\) 0.644939i 0.0330847i
\(381\) 13.5092 6.51298i 0.692097 0.333670i
\(382\) −8.48091 + 2.27245i −0.433921 + 0.116269i
\(383\) −2.49550 9.31334i −0.127514 0.475889i 0.872403 0.488788i \(-0.162561\pi\)
−0.999917 + 0.0128986i \(0.995894\pi\)
\(384\) 1.70171 0.322754i 0.0868402 0.0164705i
\(385\) −5.72212 + 3.73109i −0.291626 + 0.190154i
\(386\) −10.9064 + 6.29682i −0.555122 + 0.320500i
\(387\) −3.25092 2.58787i −0.165254 0.131549i
\(388\) −1.71263 0.458897i −0.0869454 0.0232970i
\(389\) 0.282099 0.488611i 0.0143030 0.0247735i −0.858785 0.512336i \(-0.828780\pi\)
0.873088 + 0.487562i \(0.162114\pi\)
\(390\) 2.83186 + 0.00699187i 0.143397 + 0.000354047i
\(391\) −1.07027 −0.0541260
\(392\) −1.06939 + 6.91783i −0.0540122 + 0.349403i
\(393\) −1.83364 + 24.6130i −0.0924950 + 1.24156i
\(394\) −11.8991 6.86993i −0.599466 0.346102i
\(395\) 1.96819 + 7.34539i 0.0990304 + 0.369586i
\(396\) 1.92737 + 16.9722i 0.0968540 + 0.852885i
\(397\) 5.51630 + 20.5871i 0.276855 + 1.03324i 0.954588 + 0.297930i \(0.0962961\pi\)
−0.677733 + 0.735309i \(0.737037\pi\)
\(398\) −12.8914 12.8914i −0.646187 0.646187i
\(399\) −4.70054 + 4.51486i −0.235322 + 0.226026i
\(400\) 4.15205 + 2.39719i 0.207602 + 0.119859i
\(401\) −0.954975 0.954975i −0.0476892 0.0476892i 0.682860 0.730549i \(-0.260736\pi\)
−0.730549 + 0.682860i \(0.760736\pi\)
\(402\) 2.84719 + 0.212113i 0.142005 + 0.0105792i
\(403\) 4.71586 + 13.6039i 0.234914 + 0.677657i
\(404\) −13.7948 + 7.96445i −0.686318 + 0.396246i
\(405\) 3.60487 1.91332i 0.179127 0.0950735i
\(406\) −13.5873 2.86174i −0.674327 0.142026i
\(407\) −24.4481 42.3454i −1.21185 2.09898i
\(408\) 0.445371 0.0844708i 0.0220491 0.00418193i
\(409\) −1.29990 1.29990i −0.0642758 0.0642758i 0.674238 0.738514i \(-0.264472\pi\)
−0.738514 + 0.674238i \(0.764472\pi\)
\(410\) 1.94128 + 1.94128i 0.0958732 + 0.0958732i
\(411\) −6.20408 + 1.17669i −0.306025 + 0.0580419i
\(412\) −7.00907 12.1401i −0.345312 0.598098i
\(413\) 4.87581 + 14.9120i 0.239923 + 0.733773i
\(414\) 11.2489 + 4.89610i 0.552851 + 0.240630i
\(415\) 0.0529037 0.0305440i 0.00259694 0.00149934i
\(416\) −2.72606 2.35979i −0.133656 0.115698i
\(417\) −18.8685 1.40569i −0.923996 0.0688368i
\(418\) 5.72614 + 5.72614i 0.280075 + 0.280075i
\(419\) −4.78777 2.76422i −0.233898 0.135041i 0.378471 0.925613i \(-0.376450\pi\)
−0.612369 + 0.790572i \(0.709783\pi\)
\(420\) −0.497286 2.01765i −0.0242651 0.0984510i
\(421\) 21.4872 + 21.4872i 1.04722 + 1.04722i 0.998828 + 0.0483937i \(0.0154102\pi\)
0.0483937 + 0.998828i \(0.484590\pi\)
\(422\) 3.61221 + 13.4810i 0.175840 + 0.656243i
\(423\) −27.9745 + 3.17680i −1.36017 + 0.154461i
\(424\) 0.940041 + 3.50828i 0.0456524 + 0.170377i
\(425\) 1.08667 + 0.627389i 0.0527112 + 0.0304328i
\(426\) −0.779492 + 10.4631i −0.0377665 + 0.506939i
\(427\) −21.1533 + 13.7929i −1.02368 + 0.667487i
\(428\) −15.2283 −0.736086
\(429\) 25.2050 25.0808i 1.21691 1.21091i
\(430\) 0.314037 0.543927i 0.0151442 0.0262305i
\(431\) 11.9386 + 3.19895i 0.575064 + 0.154088i 0.534618 0.845094i \(-0.320456\pi\)
0.0404457 + 0.999182i \(0.487122\pi\)
\(432\) −5.06739 1.14959i −0.243805 0.0553098i
\(433\) −2.10458 + 1.21508i −0.101140 + 0.0583931i −0.549717 0.835351i \(-0.685264\pi\)
0.448577 + 0.893744i \(0.351931\pi\)
\(434\) 8.85012 5.77070i 0.424819 0.277003i
\(435\) 4.04983 0.768108i 0.194175 0.0368280i
\(436\) −1.56819 5.85258i −0.0751028 0.280288i
\(437\) 5.61799 1.50534i 0.268745 0.0720100i
\(438\) 15.3247 7.38827i 0.732244 0.353025i
\(439\) 10.9450i 0.522376i −0.965288 0.261188i \(-0.915886\pi\)
0.965288 0.261188i \(-0.0841142\pi\)
\(440\) −2.49393 + 0.668246i −0.118893 + 0.0318574i
\(441\) 11.2241 17.7488i 0.534480 0.845181i
\(442\) −0.713461 0.617602i −0.0339359 0.0293763i
\(443\) 19.2152 11.0939i 0.912943 0.527088i 0.0315659 0.999502i \(-0.489951\pi\)
0.881377 + 0.472414i \(0.156617\pi\)
\(444\) 14.6138 2.77171i 0.693540 0.131540i
\(445\) 0.394839 + 0.683881i 0.0187172 + 0.0324191i
\(446\) −14.6849 + 25.4350i −0.695351 + 1.20438i
\(447\) −32.2590 11.2721i −1.52580 0.533150i
\(448\) −1.19677 + 2.35961i −0.0565421 + 0.111481i
\(449\) −3.03074 + 11.3109i −0.143029 + 0.533793i 0.856806 + 0.515639i \(0.172445\pi\)
−0.999835 + 0.0181537i \(0.994221\pi\)
\(450\) −8.55112 11.5651i −0.403104 0.545186i
\(451\) 34.4717 1.62321
\(452\) −1.89608 3.28411i −0.0891841 0.154471i
\(453\) 3.21208 + 1.12238i 0.150917 + 0.0527338i
\(454\) 5.06688i 0.237800i
\(455\) −2.64977 + 3.41919i −0.124223 + 0.160294i
\(456\) −2.21900 + 1.06981i −0.103914 + 0.0500984i
\(457\) −0.922491 0.922491i −0.0431523 0.0431523i 0.685201 0.728354i \(-0.259714\pi\)
−0.728354 + 0.685201i \(0.759714\pi\)
\(458\) −2.14155 + 1.23643i −0.100068 + 0.0577744i
\(459\) −1.32623 0.300870i −0.0619032 0.0140434i
\(460\) −0.479951 + 1.79120i −0.0223778 + 0.0835152i
\(461\) −33.6775 9.02386i −1.56852 0.420283i −0.633170 0.774013i \(-0.718246\pi\)
−0.935348 + 0.353730i \(0.884913\pi\)
\(462\) −22.3290 13.4986i −1.03884 0.628013i
\(463\) −15.7649 + 15.7649i −0.732657 + 0.732657i −0.971145 0.238488i \(-0.923348\pi\)
0.238488 + 0.971145i \(0.423348\pi\)
\(464\) −4.54507 2.62410i −0.210999 0.121821i
\(465\) −1.76567 + 2.59221i −0.0818812 + 0.120211i
\(466\) −15.7713 4.22591i −0.730592 0.195762i
\(467\) −8.38248 14.5189i −0.387895 0.671854i 0.604271 0.796779i \(-0.293464\pi\)
−0.992166 + 0.124925i \(0.960131\pi\)
\(468\) 4.67337 + 9.75498i 0.216027 + 0.450924i
\(469\) −2.91220 + 3.24641i −0.134473 + 0.149905i
\(470\) −1.10144 4.11063i −0.0508056 0.189609i
\(471\) −11.9409 24.7677i −0.550207 1.14124i
\(472\) 5.92985i 0.272944i
\(473\) −2.04110 7.61750i −0.0938500 0.350253i
\(474\) −22.0080 + 18.9562i −1.01086 + 0.870685i
\(475\) −6.58648 1.76484i −0.302208 0.0809765i
\(476\) −0.313218 + 0.617553i −0.0143563 + 0.0283055i
\(477\) 1.61454 10.7758i 0.0739247 0.493392i
\(478\) 10.5837i 0.484089i
\(479\) −6.19234 + 23.1101i −0.282935 + 1.05593i 0.667400 + 0.744700i \(0.267407\pi\)
−0.950335 + 0.311229i \(0.899259\pi\)
\(480\) 0.0583513 0.783249i 0.00266336 0.0357503i
\(481\) −23.4105 20.2652i −1.06743 0.924011i
\(482\) 5.71157i 0.260155i
\(483\) −16.4148 + 9.04114i −0.746898 + 0.411386i
\(484\) −10.7095 + 18.5493i −0.486794 + 0.843152i
\(485\) −0.402003 + 0.696290i −0.0182540 + 0.0316169i
\(486\) 12.5627 + 9.22924i 0.569855 + 0.418647i
\(487\) 11.6115 + 11.6115i 0.526167 + 0.526167i 0.919427 0.393260i \(-0.128653\pi\)
−0.393260 + 0.919427i \(0.628653\pi\)
\(488\) −9.21945 + 2.47034i −0.417345 + 0.111827i
\(489\) −17.0640 5.96256i −0.771661 0.269636i
\(490\) 2.90458 + 1.28031i 0.131215 + 0.0578386i
\(491\) 18.2667 31.6388i 0.824363 1.42784i −0.0780426 0.996950i \(-0.524867\pi\)
0.902405 0.430888i \(-0.141800\pi\)
\(492\) −3.45908 + 9.89939i −0.155947 + 0.446299i
\(493\) −1.18953 0.686775i −0.0535737 0.0309308i
\(494\) 4.61370 + 2.23839i 0.207580 + 0.100710i
\(495\) 7.66021 + 1.14773i 0.344301 + 0.0515865i
\(496\) 3.85724 1.03354i 0.173195 0.0464075i
\(497\) −11.9302 10.7020i −0.535143 0.480051i
\(498\) 0.192846 + 0.131356i 0.00864163 + 0.00588622i
\(499\) −2.19212 + 8.18110i −0.0981327 + 0.366236i −0.997476 0.0710074i \(-0.977379\pi\)
0.899343 + 0.437244i \(0.144045\pi\)
\(500\) 3.14053 3.14053i 0.140449 0.140449i
\(501\) 12.5344 35.8716i 0.559994 1.60262i
\(502\) −19.9188 5.33724i −0.889022 0.238213i
\(503\) −1.38843 + 0.801610i −0.0619070 + 0.0357420i −0.530634 0.847601i \(-0.678046\pi\)
0.468727 + 0.883343i \(0.344713\pi\)
\(504\) 6.11708 5.05780i 0.272476 0.225292i
\(505\) 1.86949 + 6.97703i 0.0831912 + 0.310474i
\(506\) 11.6420 + 20.1646i 0.517552 + 0.896426i
\(507\) 9.87854 20.2340i 0.438721 0.898623i
\(508\) −4.32933 + 7.49862i −0.192083 + 0.332698i
\(509\) −9.49727 + 9.49727i −0.420959 + 0.420959i −0.885534 0.464575i \(-0.846207\pi\)
0.464575 + 0.885534i \(0.346207\pi\)
\(510\) 0.0152716 0.204991i 0.000676239 0.00907715i
\(511\) −5.35593 + 25.4295i −0.236932 + 1.12493i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 7.38472 0.286037i 0.326043 0.0126288i
\(514\) 7.98124 7.98124i 0.352037 0.352037i
\(515\) −6.14010 + 1.64523i −0.270565 + 0.0724977i
\(516\) 2.39237 + 0.178229i 0.105318 + 0.00784610i
\(517\) −46.2758 26.7173i −2.03521 1.17503i
\(518\) −10.2775 + 20.2636i −0.451568 + 0.890330i
\(519\) 3.31195 + 6.86963i 0.145378 + 0.301543i
\(520\) −1.35356 + 0.917086i −0.0593574 + 0.0402169i
\(521\) 4.73174 + 2.73187i 0.207301 + 0.119685i 0.600057 0.799958i \(-0.295145\pi\)
−0.392755 + 0.919643i \(0.628478\pi\)
\(522\) 9.36054 + 12.6599i 0.409700 + 0.554107i
\(523\) −12.0990 −0.529054 −0.264527 0.964378i \(-0.585216\pi\)
−0.264527 + 0.964378i \(0.585216\pi\)
\(524\) −7.12484 12.3406i −0.311250 0.539101i
\(525\) 21.9661 + 0.442611i 0.958680 + 0.0193171i
\(526\) 6.17725 23.0538i 0.269341 1.00519i
\(527\) 1.00951 0.270498i 0.0439751 0.0117831i
\(528\) −6.43606 7.47221i −0.280094 0.325186i
\(529\) −6.27681 −0.272905
\(530\) 1.64699 0.0715408
\(531\) 7.09961 16.3115i 0.308097 0.707857i
\(532\) 0.775530 3.68215i 0.0336235 0.159642i
\(533\) 20.6249 7.14975i 0.893366 0.309690i
\(534\) −1.69803 + 2.49290i −0.0734809 + 0.107878i
\(535\) −1.78726 + 6.67015i −0.0772700 + 0.288376i
\(536\) −1.42754 + 0.824190i −0.0616603 + 0.0355996i
\(537\) 34.9950 + 2.60709i 1.51014 + 0.112504i
\(538\) −6.69783 6.69783i −0.288764 0.288764i
\(539\) 37.1559 14.4212i 1.60042 0.621164i
\(540\) −1.09827 + 2.08465i −0.0472619 + 0.0897090i
\(541\) −13.4904 3.61474i −0.579998 0.155410i −0.0431198 0.999070i \(-0.513730\pi\)
−0.536878 + 0.843660i \(0.680396\pi\)
\(542\) 4.58456i 0.196924i
\(543\) 10.7267 + 7.30643i 0.460325 + 0.313549i
\(544\) −0.185063 + 0.185063i −0.00793452 + 0.00793452i
\(545\) −2.74754 −0.117692
\(546\) −16.1595 3.44519i −0.691564 0.147441i
\(547\) 13.7832 0.589326 0.294663 0.955601i \(-0.404793\pi\)
0.294663 + 0.955601i \(0.404793\pi\)
\(548\) 2.57796 2.57796i 0.110125 0.110125i
\(549\) 28.3179 + 4.24287i 1.20858 + 0.181081i
\(550\) 27.2980i 1.16399i
\(551\) 7.20993 + 1.93190i 0.307153 + 0.0823015i
\(552\) −6.95899 + 1.31987i −0.296194 + 0.0561774i
\(553\) −2.40427 44.3037i −0.102240 1.88399i
\(554\) 11.1079 + 11.1079i 0.471930 + 0.471930i
\(555\) 0.501103 6.72630i 0.0212706 0.285516i
\(556\) 9.46041 5.46197i 0.401211 0.231639i
\(557\) 2.17234 8.10728i 0.0920450 0.343517i −0.904510 0.426453i \(-0.859763\pi\)
0.996555 + 0.0829361i \(0.0264297\pi\)
\(558\) −11.8477 1.77514i −0.501552 0.0751475i
\(559\) −2.80116 4.13433i −0.118477 0.174863i
\(560\) 0.893074 + 0.801133i 0.0377393 + 0.0338540i
\(561\) −1.68444 1.95562i −0.0711170 0.0825663i
\(562\) 29.3179 1.23670
\(563\) 1.62164 0.0683438 0.0341719 0.999416i \(-0.489121\pi\)
0.0341719 + 0.999416i \(0.489121\pi\)
\(564\) 12.3161 10.6083i 0.518602 0.446688i
\(565\) −1.66101 + 0.445066i −0.0698791 + 0.0187241i
\(566\) −7.28060 + 27.1716i −0.306027 + 1.14211i
\(567\) −22.8820 + 6.58891i −0.960954 + 0.276708i
\(568\) −3.02881 5.24605i −0.127086 0.220119i
\(569\) −37.5849 −1.57564 −0.787820 0.615905i \(-0.788790\pi\)
−0.787820 + 0.615905i \(0.788790\pi\)
\(570\) 0.208157 + 1.09750i 0.00871872 + 0.0459693i
\(571\) 8.96101 + 5.17364i 0.375006 + 0.216510i 0.675643 0.737229i \(-0.263866\pi\)
−0.300637 + 0.953739i \(0.597199\pi\)
\(572\) −3.87523 + 20.1601i −0.162032 + 0.842935i
\(573\) −13.6986 + 6.60431i −0.572269 + 0.275899i
\(574\) −8.74901 13.4177i −0.365177 0.560046i
\(575\) −16.9794 9.80305i −0.708089 0.408815i
\(576\) 2.79166 1.09847i 0.116319 0.0457696i
\(577\) −31.4780 + 8.43451i −1.31045 + 0.351133i −0.845391 0.534148i \(-0.820633\pi\)
−0.465056 + 0.885281i \(0.653966\pi\)
\(578\) 11.9724 11.9724i 0.497985 0.497985i
\(579\) −16.5273 + 14.2355i −0.686850 + 0.591606i
\(580\) −1.68281 + 1.68281i −0.0698750 + 0.0698750i
\(581\) −0.338772 + 0.110769i −0.0140546 + 0.00459546i
\(582\) −3.06251 0.228154i −0.126945 0.00945729i
\(583\) 14.6230 14.6230i 0.605621 0.605621i
\(584\) −4.91116 + 8.50638i −0.203225 + 0.351996i
\(585\) 4.82127 0.902096i 0.199335 0.0372971i
\(586\) −10.3229 17.8798i −0.426435 0.738606i
\(587\) −9.43462 35.2105i −0.389409 1.45329i −0.831099 0.556125i \(-0.812288\pi\)
0.441690 0.897168i \(-0.354379\pi\)
\(588\) 0.412969 + 12.1173i 0.0170305 + 0.499710i
\(589\) −4.91860 + 2.83975i −0.202667 + 0.117010i
\(590\) 2.59734 + 0.695955i 0.106931 + 0.0286520i
\(591\) −22.4661 7.85018i −0.924131 0.322913i
\(592\) −6.07241 + 6.07241i −0.249575 + 0.249575i
\(593\) 6.30048 23.5137i 0.258730 0.965593i −0.707247 0.706966i \(-0.750063\pi\)
0.965977 0.258627i \(-0.0832700\pi\)
\(594\) 8.75768 + 28.2598i 0.359332 + 1.15951i
\(595\) 0.233734 + 0.209672i 0.00958217 + 0.00859570i
\(596\) 19.0568 5.10625i 0.780596 0.209160i
\(597\) −26.0982 17.7767i −1.06813 0.727552i
\(598\) 11.1479 + 9.65013i 0.455873 + 0.394623i
\(599\) 40.1828 + 23.1996i 1.64183 + 0.947909i 0.980184 + 0.198089i \(0.0634735\pi\)
0.661642 + 0.749820i \(0.269860\pi\)
\(600\) 7.83930 + 2.73923i 0.320038 + 0.111829i
\(601\) −17.8843 + 30.9765i −0.729515 + 1.26356i 0.227573 + 0.973761i \(0.426921\pi\)
−0.957088 + 0.289796i \(0.906413\pi\)
\(602\) −2.44699 + 2.72782i −0.0997320 + 0.111178i
\(603\) 4.91356 0.557985i 0.200095 0.0227229i
\(604\) −1.89751 + 0.508437i −0.0772087 + 0.0206880i
\(605\) 6.86790 + 6.86790i 0.279220 + 0.279220i
\(606\) −20.9043 + 18.0055i −0.849179 + 0.731425i
\(607\) −14.1838 + 24.5671i −0.575704 + 0.997148i 0.420261 + 0.907403i \(0.361938\pi\)
−0.995965 + 0.0897446i \(0.971395\pi\)
\(608\) 0.711128 1.23171i 0.0288400 0.0499524i
\(609\) −24.0454 0.484508i −0.974367 0.0196332i
\(610\) 4.32815i 0.175242i
\(611\) −33.2289 6.38737i −1.34430 0.258405i
\(612\) 0.730630 0.287490i 0.0295340 0.0116211i
\(613\) −4.83589 + 18.0478i −0.195320 + 0.728943i 0.796864 + 0.604159i \(0.206491\pi\)
−0.992184 + 0.124785i \(0.960176\pi\)
\(614\) 32.6749i 1.31865i
\(615\) 3.93007 + 2.67695i 0.158476 + 0.107945i
\(616\) 15.0421 0.816305i 0.606065 0.0328899i
\(617\) 43.9291 + 11.7708i 1.76852 + 0.473873i 0.988415 0.151778i \(-0.0485000\pi\)
0.780103 + 0.625651i \(0.215167\pi\)
\(618\) −15.8457 18.3967i −0.637407 0.740025i
\(619\) −7.55993 28.2140i −0.303859 1.13402i −0.933923 0.357474i \(-0.883638\pi\)
0.630064 0.776543i \(-0.283029\pi\)
\(620\) 1.81081i 0.0727241i
\(621\) 20.7226 + 4.70115i 0.831568 + 0.188650i
\(622\) −5.56639 20.7740i −0.223192 0.832963i
\(623\) −1.43190 4.37927i −0.0573677 0.175452i
\(624\) −5.40060 3.13584i −0.216197 0.125534i
\(625\) 10.9789 + 19.0161i 0.439157 + 0.760643i
\(626\) 6.22350 + 1.66758i 0.248741 + 0.0666500i
\(627\) 11.5924 + 7.89612i 0.462956 + 0.315341i
\(628\) 13.7480 + 7.93738i 0.548603 + 0.316736i
\(629\) −1.58927 + 1.58927i −0.0633682 + 0.0633682i
\(630\) −1.49744 3.27295i −0.0596595 0.130398i
\(631\) −6.48111 1.73661i −0.258009 0.0691332i 0.127496 0.991839i \(-0.459306\pi\)
−0.385505 + 0.922706i \(0.625973\pi\)
\(632\) 4.34036 16.1985i 0.172650 0.644340i
\(633\) 10.4980 + 21.7749i 0.417258 + 0.865474i
\(634\) −9.71554 + 5.60927i −0.385853 + 0.222772i
\(635\) 2.77637 + 2.77637i 0.110177 + 0.110177i
\(636\) 2.73199 + 5.66669i 0.108331 + 0.224699i
\(637\) 19.2398 16.3349i 0.762310 0.647212i
\(638\) 29.8820i 1.18304i
\(639\) 2.05054 + 18.0568i 0.0811180 + 0.714316i
\(640\) 0.226731 + 0.392710i 0.00896233 + 0.0155232i
\(641\) 16.8296 0.664730 0.332365 0.943151i \(-0.392153\pi\)
0.332365 + 0.943151i \(0.392153\pi\)
\(642\) −25.9142 + 4.91499i −1.02275 + 0.193979i
\(643\) −11.9656 + 44.6563i −0.471878 + 1.76107i 0.161135 + 0.986932i \(0.448485\pi\)
−0.633013 + 0.774141i \(0.718182\pi\)
\(644\) 4.89408 9.64937i 0.192854 0.380238i
\(645\) 0.358846 1.02697i 0.0141295 0.0404367i
\(646\) 0.186116 0.322362i 0.00732262 0.0126832i
\(647\) 7.82320 + 13.5502i 0.307562 + 0.532712i 0.977828 0.209408i \(-0.0671536\pi\)
−0.670267 + 0.742120i \(0.733820\pi\)
\(648\) −8.99428 0.320759i −0.353329 0.0126006i
\(649\) 29.2398 16.8816i 1.14776 0.662660i
\(650\) −5.66186 16.3328i −0.222077 0.640626i
\(651\) 13.1979 12.6765i 0.517265 0.496831i
\(652\) 10.0804 2.70104i 0.394780 0.105781i
\(653\) 45.3019i 1.77280i 0.462921 + 0.886399i \(0.346801\pi\)
−0.462921 + 0.886399i \(0.653199\pi\)
\(654\) −4.55756 9.45327i −0.178215 0.369652i
\(655\) −6.24151 + 1.67241i −0.243876 + 0.0653464i
\(656\) −1.56697 5.84799i −0.0611797 0.228326i
\(657\) 23.6937 17.5188i 0.924379 0.683475i
\(658\) 1.34548 + 24.7933i 0.0524522 + 0.966543i
\(659\) −9.16402 + 5.29085i −0.356980 + 0.206102i −0.667755 0.744381i \(-0.732745\pi\)
0.310775 + 0.950483i \(0.399411\pi\)
\(660\) −4.02828 + 1.94209i −0.156800 + 0.0755957i
\(661\) −22.0738 5.91465i −0.858570 0.230053i −0.197431 0.980317i \(-0.563260\pi\)
−0.661139 + 0.750264i \(0.729927\pi\)
\(662\) −5.13201 + 8.88891i −0.199461 + 0.345477i
\(663\) −1.41344 0.820709i −0.0548934 0.0318737i
\(664\) −0.134715 −0.00522794
\(665\) −1.52180 0.771845i −0.0590130 0.0299309i
\(666\) 23.9739 9.43332i 0.928970 0.365534i
\(667\) 18.5866 + 10.7310i 0.719676 + 0.415505i
\(668\) 5.67807 + 21.1909i 0.219691 + 0.819899i
\(669\) −16.7803 + 48.0227i −0.648763 + 1.85667i
\(670\) 0.193461 + 0.722008i 0.00747407 + 0.0278936i
\(671\) 38.4278 + 38.4278i 1.48349 + 1.48349i
\(672\) −1.27499 + 4.40164i −0.0491838 + 0.169797i
\(673\) 39.8433 + 23.0035i 1.53585 + 0.886721i 0.999075 + 0.0429919i \(0.0136890\pi\)
0.536770 + 0.843729i \(0.319644\pi\)
\(674\) 22.5939 + 22.5939i 0.870284 + 0.870284i
\(675\) −18.2843 16.9206i −0.703761 0.651276i
\(676\) 1.86278 + 12.8658i 0.0716452 + 0.494840i
\(677\) 20.8682 12.0482i 0.802028 0.463051i −0.0421516 0.999111i \(-0.513421\pi\)
0.844180 + 0.536060i \(0.180088\pi\)
\(678\) −4.28655 4.97664i −0.164624 0.191127i
\(679\) 3.13244 3.49193i 0.120212 0.134008i
\(680\) 0.0593398 + 0.102780i 0.00227558 + 0.00394142i
\(681\) 1.63536 + 8.62238i 0.0626670 + 0.330410i
\(682\) −16.0775 16.0775i −0.615638 0.615638i
\(683\) −7.97254 7.97254i −0.305061 0.305061i 0.537929 0.842990i \(-0.319207\pi\)
−0.842990 + 0.537929i \(0.819207\pi\)
\(684\) −3.43081 + 2.53670i −0.131180 + 0.0969932i
\(685\) −0.826612 1.43173i −0.0315832 0.0547038i
\(686\) −15.0435 10.8024i −0.574365 0.412437i
\(687\) −3.24525 + 2.79524i −0.123814 + 0.106645i
\(688\) −1.19950 + 0.692531i −0.0457305 + 0.0264025i
\(689\) 5.71620 11.7821i 0.217770 0.448861i
\(690\) −0.238622 + 3.20302i −0.00908418 + 0.121937i
\(691\) 4.53400 + 4.53400i 0.172482 + 0.172482i 0.788069 0.615587i \(-0.211081\pi\)
−0.615587 + 0.788069i \(0.711081\pi\)
\(692\) −3.81316 2.20153i −0.144955 0.0836896i
\(693\) −42.3543 15.7640i −1.60891 0.598825i
\(694\) 4.05101 + 4.05101i 0.153774 + 0.153774i
\(695\) −1.28208 4.78480i −0.0486322 0.181498i
\(696\) −8.58134 2.99852i −0.325275 0.113659i
\(697\) −0.410104 1.53053i −0.0155338 0.0579730i
\(698\) −10.2355 5.90949i −0.387421 0.223677i
\(699\) −28.2022 2.10104i −1.06671 0.0794686i
\(700\) −10.6255 + 6.92831i −0.401605 + 0.261866i
\(701\) −13.6748 −0.516492 −0.258246 0.966079i \(-0.583144\pi\)
−0.258246 + 0.966079i \(0.583144\pi\)
\(702\) 11.1012 + 15.0918i 0.418988 + 0.569605i
\(703\) 6.10695 10.5775i 0.230328 0.398940i
\(704\) 5.49975 + 1.47365i 0.207280 + 0.0555404i
\(705\) −3.20106 6.63962i −0.120559 0.250063i
\(706\) 4.51611 2.60738i 0.169966 0.0981299i
\(707\) −2.28370 42.0820i −0.0858874 1.58266i
\(708\) 1.91388 + 10.0909i 0.0719281 + 0.379240i
\(709\) 4.83553 + 18.0464i 0.181602 + 0.677748i 0.995332 + 0.0965055i \(0.0307665\pi\)
−0.813730 + 0.581242i \(0.802567\pi\)
\(710\) −2.65330 + 0.710950i −0.0995767 + 0.0266815i
\(711\) −31.3331 + 39.3611i −1.17508 + 1.47616i
\(712\) 1.74144i 0.0652633i
\(713\) −15.7738 + 4.22658i −0.590733 + 0.158287i
\(714\) −0.333689 + 1.15199i −0.0124880 + 0.0431122i
\(715\) 8.37552 + 4.06347i 0.313227 + 0.151965i
\(716\) −17.5460 + 10.1302i −0.655724 + 0.378582i
\(717\) −3.41595 18.0105i −0.127571 0.672615i
\(718\) −10.6824 18.5024i −0.398663 0.690505i
\(719\) 7.71621 13.3649i 0.287766 0.498425i −0.685510 0.728063i \(-0.740421\pi\)
0.973276 + 0.229638i \(0.0737541\pi\)
\(720\) −0.153499 1.35170i −0.00572059 0.0503748i
\(721\) 37.0340 2.00976i 1.37922 0.0748473i
\(722\) 4.39402 16.3987i 0.163528 0.610297i
\(723\) −1.84343 9.71945i −0.0685579 0.361470i
\(724\) −7.49322 −0.278483
\(725\) −12.5809 21.7907i −0.467243 0.809288i
\(726\) −12.2376 + 35.0222i −0.454179 + 1.29980i
\(727\) 4.06638i 0.150814i 0.997153 + 0.0754068i \(0.0240255\pi\)
−0.997153 + 0.0754068i \(0.975974\pi\)
\(728\) 8.83064 3.60829i 0.327285 0.133732i
\(729\) 24.3569 + 11.6509i 0.902106 + 0.431514i
\(730\) 3.14949 + 3.14949i 0.116568 + 0.116568i
\(731\) −0.313932 + 0.181248i −0.0116112 + 0.00670372i
\(732\) −14.8916 + 7.17943i −0.550408 + 0.265359i
\(733\) −9.47861 + 35.3747i −0.350100 + 1.30659i 0.536439 + 0.843939i \(0.319769\pi\)
−0.886539 + 0.462654i \(0.846897\pi\)
\(734\) 29.6180 + 7.93612i 1.09322 + 0.292928i
\(735\) 5.35598 + 1.24126i 0.197558 + 0.0457846i
\(736\) 2.89164 2.89164i 0.106587 0.106587i
\(737\) 8.12807 + 4.69274i 0.299401 + 0.172859i
\(738\) −2.69130 + 17.9624i −0.0990680 + 0.661204i
\(739\) 36.4971 + 9.77936i 1.34257 + 0.359740i 0.857386 0.514674i \(-0.172087\pi\)
0.485181 + 0.874414i \(0.338754\pi\)
\(740\) 1.94710 + 3.37247i 0.0715767 + 0.123974i
\(741\) 8.57364 + 2.32000i 0.314960 + 0.0852274i
\(742\) −9.40317 1.98048i −0.345201 0.0727059i
\(743\) 2.63477 + 9.83308i 0.0966602 + 0.360741i 0.997266 0.0738963i \(-0.0235434\pi\)
−0.900606 + 0.434637i \(0.856877\pi\)
\(744\) 6.23034 3.00374i 0.228415 0.110122i
\(745\) 8.94636i 0.327769i
\(746\) −7.33100 27.3596i −0.268407 1.00171i
\(747\) 0.370564 + 0.161289i 0.0135582 + 0.00590126i
\(748\) 1.43939 + 0.385683i 0.0526293 + 0.0141020i
\(749\) 18.2248 35.9327i 0.665918 1.31295i
\(750\) 4.33066 6.35790i 0.158133 0.232158i
\(751\) 1.11822i 0.0408043i −0.999792 0.0204022i \(-0.993505\pi\)
0.999792 0.0204022i \(-0.00649466\pi\)
\(752\) −2.42896 + 9.06499i −0.0885750 + 0.330566i
\(753\) −35.6188 2.65357i −1.29802 0.0967013i
\(754\) 6.19780 + 17.8788i 0.225710 + 0.651109i
\(755\) 0.890804i 0.0324197i
\(756\) 8.77709 10.5812i 0.319220 0.384836i
\(757\) 17.9794 31.1411i 0.653471 1.13184i −0.328804 0.944398i \(-0.606646\pi\)
0.982275 0.187446i \(-0.0600210\pi\)
\(758\) −4.88155 + 8.45509i −0.177306 + 0.307103i
\(759\) 26.3196 + 30.5569i 0.955342 + 1.10914i
\(760\) −0.456041 0.456041i −0.0165423 0.0165423i
\(761\) −46.9082 + 12.5690i −1.70042 + 0.455626i −0.973045 0.230614i \(-0.925926\pi\)
−0.727375 + 0.686240i \(0.759260\pi\)
\(762\) −4.94707 + 14.1578i −0.179214 + 0.512884i
\(763\) 15.6865 + 3.30388i 0.567891 + 0.119608i
\(764\) 4.39004 7.60377i 0.158826 0.275095i
\(765\) −0.0401737 0.353765i −0.00145248 0.0127904i
\(766\) 8.35011 + 4.82094i 0.301702 + 0.174188i
\(767\) 13.9932 16.1651i 0.505266 0.583689i
\(768\) −0.975072 + 1.43151i −0.0351849 + 0.0516553i
\(769\) 41.5055 11.1214i 1.49673 0.401046i 0.584724 0.811232i \(-0.301203\pi\)
0.912002 + 0.410186i \(0.134536\pi\)
\(770\) 1.40787 6.68443i 0.0507360 0.240890i
\(771\) 11.0058 16.1578i 0.396364 0.581907i
\(772\) 3.25947 12.1645i 0.117311 0.437811i
\(773\) 21.4904 21.4904i 0.772955 0.772955i −0.205667 0.978622i \(-0.565936\pi\)
0.978622 + 0.205667i \(0.0659365\pi\)
\(774\) 4.12865 0.468851i 0.148401 0.0168525i
\(775\) 18.4930 + 4.95520i 0.664290 + 0.177996i
\(776\) 1.53550 0.886520i 0.0551212 0.0318242i
\(777\) −10.9492 + 37.7999i −0.392801 + 1.35606i
\(778\) 0.146025 + 0.544974i 0.00523526 + 0.0195383i
\(779\) 4.30537 + 7.45713i 0.154256 + 0.267179i
\(780\) −2.00737 + 1.99748i −0.0718755 + 0.0715214i
\(781\) −17.2453 + 29.8698i −0.617086 + 1.06882i
\(782\) 0.756797 0.756797i 0.0270630 0.0270630i
\(783\) 20.0150 + 18.5223i 0.715277 + 0.661933i
\(784\) −4.13548 5.64782i −0.147696 0.201708i
\(785\) 5.09018 5.09018i 0.181676 0.181676i
\(786\) −16.1074 18.7006i −0.574532 0.667027i
\(787\) 28.6252 28.6252i 1.02038 1.02038i 0.0205919 0.999788i \(-0.493445\pi\)
0.999788 0.0205919i \(-0.00655507\pi\)
\(788\) 13.2717 3.55613i 0.472784 0.126682i
\(789\) 3.07120 41.2247i 0.109338 1.46764i
\(790\) −6.58569 3.80225i −0.234308 0.135278i
\(791\) 10.0184 0.543676i 0.356212 0.0193309i
\(792\) −13.3640 10.6383i −0.474870 0.378016i
\(793\) 30.9622 + 15.0217i 1.09950 + 0.533435i
\(794\) −18.4579 10.6567i −0.655047 0.378191i
\(795\) 2.80271 0.531573i 0.0994019 0.0188530i
\(796\) 18.2312 0.646187
\(797\) −10.9625 18.9877i −0.388313 0.672578i 0.603910 0.797053i \(-0.293609\pi\)
−0.992223 + 0.124475i \(0.960275\pi\)
\(798\) 0.131301 6.51627i 0.00464801 0.230674i
\(799\) −0.635704 + 2.37248i −0.0224896 + 0.0839323i
\(800\) −4.63101 + 1.24087i −0.163731 + 0.0438715i
\(801\) −2.08497 + 4.79025i −0.0736687 + 0.169255i
\(802\) 1.35054 0.0476892
\(803\) 55.9259 1.97358
\(804\) −2.16325 + 1.86328i −0.0762920 + 0.0657128i
\(805\) −3.65214 3.27615i −0.128721 0.115469i
\(806\) −12.9540 6.28478i −0.456286 0.221372i
\(807\) −13.5595 9.23604i −0.477318 0.325124i
\(808\) 4.12270 15.3861i 0.145036 0.541282i
\(809\) −36.3891 + 21.0092i −1.27937 + 0.738646i −0.976733 0.214460i \(-0.931201\pi\)
−0.302639 + 0.953105i \(0.597868\pi\)
\(810\) −1.19611 + 3.90195i −0.0420269 + 0.137100i
\(811\) −10.6439 10.6439i −0.373758 0.373758i 0.495086 0.868844i \(-0.335137\pi\)
−0.868844 + 0.495086i \(0.835137\pi\)
\(812\) 11.6312 7.58412i 0.408176 0.266151i
\(813\) −1.47968 7.80161i −0.0518948 0.273614i
\(814\) 47.2302 + 12.6553i 1.65542 + 0.443568i
\(815\) 4.73234i 0.165767i
\(816\) −0.255195 + 0.374654i −0.00893360 + 0.0131155i
\(817\) 1.39294 1.39294i 0.0487328 0.0487328i
\(818\) 1.83833 0.0642758
\(819\) −28.6109 0.647174i −0.999744 0.0226141i
\(820\) −2.74539 −0.0958732
\(821\) −19.2225 + 19.2225i −0.670870 + 0.670870i −0.957917 0.287047i \(-0.907327\pi\)
0.287047 + 0.957917i \(0.407327\pi\)
\(822\) 3.55490 5.21899i 0.123991 0.182033i
\(823\) 49.7026i 1.73252i −0.499590 0.866262i \(-0.666516\pi\)
0.499590 0.866262i \(-0.333484\pi\)
\(824\) 13.5405 + 3.62816i 0.471705 + 0.126393i
\(825\) −8.81054 46.4534i −0.306744 1.61730i
\(826\) −13.9921 7.09668i −0.486848 0.246925i
\(827\) 39.5130 + 39.5130i 1.37400 + 1.37400i 0.854419 + 0.519584i \(0.173913\pi\)
0.519584 + 0.854419i \(0.326087\pi\)
\(828\) −11.4162 + 4.49208i −0.396741 + 0.156111i
\(829\) 6.08826 3.51506i 0.211454 0.122083i −0.390533 0.920589i \(-0.627709\pi\)
0.601987 + 0.798506i \(0.294376\pi\)
\(830\) −0.0158107 + 0.0590064i −0.000548798 + 0.00204814i
\(831\) 22.4876 + 15.3174i 0.780087 + 0.531354i
\(832\) 3.59624 0.258990i 0.124677 0.00897885i
\(833\) −1.08233 1.47814i −0.0375006 0.0512145i
\(834\) 14.3360 12.3481i 0.496416 0.427579i
\(835\) 9.94823 0.344273
\(836\) −8.09799 −0.280075
\(837\) −20.7343 + 0.803115i −0.716682 + 0.0277597i
\(838\) 5.34006 1.43087i 0.184469 0.0494284i
\(839\) 5.88608 21.9672i 0.203210 0.758390i −0.786778 0.617237i \(-0.788252\pi\)
0.989988 0.141154i \(-0.0450812\pi\)
\(840\) 1.77833 + 1.07506i 0.0613580 + 0.0370930i
\(841\) −0.728243 1.26135i −0.0251118 0.0434950i
\(842\) −30.3875 −1.04722
\(843\) 49.8907 9.46247i 1.71833 0.325905i
\(844\) −12.0867 6.97826i −0.416041 0.240202i
\(845\) 5.85400 + 0.694080i 0.201384 + 0.0238771i
\(846\) 17.5346 22.0273i 0.602853 0.757314i
\(847\) −30.9524 47.4695i −1.06354 1.63107i
\(848\) −3.14544 1.81602i −0.108015 0.0623624i
\(849\) −3.61977 + 48.5881i −0.124230 + 1.66754i
\(850\) −1.21202 + 0.324760i −0.0415720 + 0.0111392i
\(851\) 24.8325 24.8325i 0.851248 0.851248i
\(852\) −6.84735 7.94972i −0.234586 0.272353i
\(853\) 23.4720 23.4720i 0.803667 0.803667i −0.179999 0.983667i \(-0.557610\pi\)
0.983667 + 0.179999i \(0.0576096\pi\)
\(854\) 5.20454 24.7107i 0.178096 0.845583i
\(855\) 0.708446 + 1.80045i 0.0242283 + 0.0615741i
\(856\) 10.7680 10.7680i 0.368043 0.368043i
\(857\) −10.2906 + 17.8238i −0.351519 + 0.608848i −0.986516 0.163666i \(-0.947668\pi\)
0.634997 + 0.772515i \(0.281001\pi\)
\(858\) −0.0877913 + 35.5574i −0.00299715 + 1.21391i
\(859\) −5.22372 9.04775i −0.178231 0.308705i 0.763044 0.646347i \(-0.223704\pi\)
−0.941275 + 0.337642i \(0.890371\pi\)
\(860\) 0.162557 + 0.606672i 0.00554316 + 0.0206874i
\(861\) −19.2189 20.0094i −0.654980 0.681918i
\(862\) −10.7039 + 6.17989i −0.364576 + 0.210488i
\(863\) 9.91870 + 2.65771i 0.337637 + 0.0904695i 0.423654 0.905824i \(-0.360747\pi\)
−0.0860172 + 0.996294i \(0.527414\pi\)
\(864\) 4.39607 2.77030i 0.149557 0.0942475i
\(865\) −1.41182 + 1.41182i −0.0480034 + 0.0480034i
\(866\) 0.628972 2.34736i 0.0213734 0.0797664i
\(867\) 16.5094 24.2377i 0.560690 0.823155i
\(868\) −2.17748 + 10.3385i −0.0739084 + 0.350911i
\(869\) −92.2302 + 24.7130i −3.12869 + 0.838331i
\(870\) −2.32053 + 3.40680i −0.0786734 + 0.115501i
\(871\) 5.83647 + 1.12190i 0.197761 + 0.0380142i
\(872\) 5.24728 + 3.02952i 0.177695 + 0.102592i
\(873\) −5.28515 + 0.600184i −0.178875 + 0.0203132i
\(874\) −2.90809 + 5.03695i −0.0983675 + 0.170377i
\(875\) 3.65191 + 11.1689i 0.123457 + 0.377578i
\(876\) −5.61192 + 16.0605i −0.189609 + 0.542634i
\(877\) −31.2419 + 8.37123i −1.05496 + 0.282676i −0.744301 0.667844i \(-0.767217\pi\)
−0.310662 + 0.950521i \(0.600551\pi\)
\(878\) 7.73928 + 7.73928i 0.261188 + 0.261188i
\(879\) −23.3374 27.0945i −0.787150 0.913874i
\(880\) 1.29095 2.23600i 0.0435180 0.0753754i
\(881\) 5.58224 9.66873i 0.188071 0.325748i −0.756536 0.653952i \(-0.773110\pi\)
0.944607 + 0.328204i \(0.106443\pi\)
\(882\) 4.61367 + 20.4869i 0.155350 + 0.689831i
\(883\) 33.9142i 1.14130i 0.821192 + 0.570652i \(0.193309\pi\)
−0.821192 + 0.570652i \(0.806691\pi\)
\(884\) 0.941203 0.0677825i 0.0316561 0.00227977i
\(885\) 4.64455 + 0.346015i 0.156125 + 0.0116312i
\(886\) −5.74263 + 21.4318i −0.192927 + 0.720015i
\(887\) 42.8082i 1.43736i 0.695341 + 0.718680i \(0.255253\pi\)
−0.695341 + 0.718680i \(0.744747\pi\)
\(888\) −8.37362 + 12.2934i −0.281000 + 0.412540i
\(889\) −12.5126 19.1897i −0.419658 0.643600i
\(890\) −0.762770 0.204384i −0.0255681 0.00685095i
\(891\) 24.0240 + 45.2635i 0.804835 + 1.51638i
\(892\) −7.60147 28.3691i −0.254516 0.949867i
\(893\) 13.3475i 0.446659i
\(894\) 30.7811 14.8400i 1.02947 0.496325i
\(895\) 2.37785 + 8.87425i 0.0794827 + 0.296633i
\(896\) −0.822248 2.51474i −0.0274694 0.0840115i
\(897\) 22.0852 + 12.8237i 0.737404 + 0.428171i
\(898\) −5.85494 10.1410i −0.195382 0.338411i
\(899\) −20.2435 5.42424i −0.675160 0.180909i
\(900\) 14.2243 + 2.13123i 0.474145 + 0.0710410i
\(901\) −0.823221 0.475287i −0.0274255 0.0158341i
\(902\) −24.3752 + 24.3752i −0.811604 + 0.811604i
\(903\) −3.28367 + 5.43175i −0.109274 + 0.180757i
\(904\) 3.66295 + 0.981484i 0.121828 + 0.0326437i
\(905\) −0.879439 + 3.28211i −0.0292335 + 0.109101i
\(906\) −3.06492 + 1.47764i −0.101825 + 0.0490914i
\(907\) −24.6753 + 14.2463i −0.819331 + 0.473041i −0.850186 0.526483i \(-0.823510\pi\)
0.0308547 + 0.999524i \(0.490177\pi\)
\(908\) −3.58283 3.58283i −0.118900 0.118900i
\(909\) −29.7618 + 37.3872i −0.987136 + 1.24006i
\(910\) −0.544065 4.29140i −0.0180356 0.142259i
\(911\) 11.8596i 0.392927i 0.980511 + 0.196464i \(0.0629458\pi\)
−0.980511 + 0.196464i \(0.937054\pi\)
\(912\) 0.812597 2.32554i 0.0269078 0.0770062i
\(913\) 0.383516 + 0.664270i 0.0126925 + 0.0219841i
\(914\) 1.30460 0.0431523
\(915\) 1.39693 + 7.36527i 0.0461810 + 0.243488i
\(916\) 0.640022 2.38859i 0.0211469 0.0789213i
\(917\) 37.6457 2.04295i 1.24317 0.0674642i
\(918\) 1.15053 0.725040i 0.0379733 0.0239299i
\(919\) −1.60787 + 2.78491i −0.0530387 + 0.0918657i −0.891326 0.453363i \(-0.850224\pi\)
0.838287 + 0.545229i \(0.183557\pi\)
\(920\) −0.927194 1.60595i −0.0305687 0.0529465i
\(921\) −10.5460 55.6034i −0.347501 1.83219i
\(922\) 30.1944 17.4328i 0.994400 0.574117i
\(923\) −4.12288 + 21.4484i −0.135706 + 0.705982i
\(924\) 25.3340 6.24403i 0.833426 0.205414i
\(925\) −39.7697 + 10.6562i −1.30762 + 0.350375i
\(926\) 22.2949i 0.732657i
\(927\) −32.9024 26.1917i −1.08066 0.860248i
\(928\) 5.06936 1.35833i 0.166410 0.0445894i
\(929\) −0.177628 0.662917i −0.00582779 0.0217496i 0.962951 0.269677i \(-0.0869171\pi\)
−0.968779 + 0.247928i \(0.920250\pi\)
\(930\) −0.584448 3.08149i −0.0191648 0.101046i
\(931\) 7.76029 + 6.23664i 0.254333 + 0.204398i
\(932\) 14.1402 8.16384i 0.463177 0.267415i
\(933\) −16.1773 33.5549i −0.529621 1.09854i
\(934\) 16.1937 + 4.33909i 0.529874 + 0.141979i
\(935\) 0.337867 0.585202i 0.0110494 0.0191382i
\(936\) −10.2024 3.59324i −0.333475 0.117449i
\(937\) 4.02803 0.131590 0.0657949 0.997833i \(-0.479042\pi\)
0.0657949 + 0.997833i \(0.479042\pi\)
\(938\) −0.236325 4.35479i −0.00771630 0.142189i
\(939\) 11.1288 + 0.829088i 0.363176 + 0.0270563i
\(940\) 3.68549 + 2.12782i 0.120207 + 0.0694018i
\(941\) −8.67568 32.3781i −0.282819 1.05550i −0.950418 0.310974i \(-0.899345\pi\)
0.667599 0.744521i \(-0.267322\pi\)
\(942\) 25.9569 + 9.06995i 0.845721 + 0.295515i
\(943\) 6.40795 + 23.9148i 0.208671 + 0.778772i
\(944\) −4.19304 4.19304i −0.136472 0.136472i
\(945\) −3.60458 5.08632i −0.117257 0.165458i
\(946\) 6.82966 + 3.94311i 0.222052 + 0.128202i
\(947\) 0.539541 + 0.539541i 0.0175327 + 0.0175327i 0.715819 0.698286i \(-0.246054\pi\)
−0.698286 + 0.715819i \(0.746054\pi\)
\(948\) 2.15794 28.9660i 0.0700866 0.940772i
\(949\) 33.4614 11.5996i 1.08620 0.376538i
\(950\) 5.90528 3.40941i 0.191592 0.110616i
\(951\) −14.7226 + 12.6811i −0.477415 + 0.411213i
\(952\) −0.215198 0.658154i −0.00697460 0.0213309i
\(953\) 21.5625 + 37.3474i 0.698479 + 1.20980i 0.968994 + 0.247086i \(0.0794729\pi\)
−0.270514 + 0.962716i \(0.587194\pi\)
\(954\) 6.47802 + 8.76132i 0.209734 + 0.283658i
\(955\) −2.81530 2.81530i −0.0911009 0.0911009i
\(956\) 7.48384 + 7.48384i 0.242045 + 0.242045i
\(957\) 9.64452 + 50.8505i 0.311763 + 1.64376i
\(958\) −11.9627 20.7200i −0.386497 0.669432i
\(959\) 2.99774 + 9.16819i 0.0968020 + 0.296056i
\(960\) 0.512580 + 0.595101i 0.0165434 + 0.0192068i
\(961\) −13.0367 + 7.52674i −0.420538 + 0.242798i
\(962\) 30.8834 2.22412i 0.995720 0.0717086i
\(963\) −42.5122 + 16.7278i −1.36994 + 0.539046i
\(964\) 4.03869 + 4.03869i 0.130077 + 0.130077i
\(965\) −4.94564 2.85537i −0.159206 0.0919176i
\(966\) 5.21394 18.0000i 0.167756 0.579142i
\(967\) −17.8213 17.8213i −0.573093 0.573093i 0.359898 0.932992i \(-0.382811\pi\)
−0.932992 + 0.359898i \(0.882811\pi\)
\(968\) −5.54363 20.6891i −0.178179 0.664973i
\(969\) 0.212672 0.608637i 0.00683201 0.0195522i
\(970\) −0.208092 0.776611i −0.00668144 0.0249355i
\(971\) −11.7375 6.77668i −0.376676 0.217474i 0.299695 0.954035i \(-0.403115\pi\)
−0.676371 + 0.736561i \(0.736448\pi\)
\(972\) −15.4092 + 2.35710i −0.494251 + 0.0756040i
\(973\) 1.56615 + 28.8596i 0.0502083 + 0.925195i
\(974\) −16.4211 −0.526167
\(975\) −14.9064 25.9664i −0.477385 0.831591i
\(976\) 4.77234 8.26593i 0.152759 0.264586i
\(977\) 43.7132 + 11.7129i 1.39851 + 0.374729i 0.877809 0.479010i \(-0.159004\pi\)
0.520700 + 0.853740i \(0.325671\pi\)
\(978\) 16.2822 7.84990i 0.520649 0.251012i
\(979\) −8.58695 + 4.95768i −0.274440 + 0.158448i
\(980\) −2.95916 + 1.14853i −0.0945270 + 0.0366884i
\(981\) −10.8067 14.6158i −0.345033 0.466646i
\(982\) 9.45552 + 35.2885i 0.301738 + 1.12610i
\(983\) 16.5406 4.43205i 0.527564 0.141360i 0.0148011 0.999890i \(-0.495288\pi\)
0.512763 + 0.858530i \(0.328622\pi\)
\(984\) −4.55399 9.44587i −0.145176 0.301123i
\(985\) 6.23050i 0.198520i
\(986\) 1.32675 0.355501i 0.0422523 0.0113215i
\(987\) 10.2918 + 41.7568i 0.327590 + 1.32913i
\(988\) −4.84515 + 1.67960i −0.154145 + 0.0534351i
\(989\) 4.90523 2.83204i 0.155977 0.0900535i
\(990\) −6.22816 + 4.60502i −0.197944 + 0.146357i
\(991\) 16.9016 + 29.2744i 0.536896 + 0.929931i 0.999069 + 0.0431410i \(0.0137365\pi\)
−0.462173 + 0.886790i \(0.652930\pi\)
\(992\) −1.99665 + 3.45831i −0.0633939 + 0.109801i
\(993\) −5.86429 + 16.7828i −0.186098 + 0.532585i
\(994\) 16.0034 0.868471i 0.507597 0.0275462i
\(995\) 2.13969 7.98545i 0.0678329 0.253156i
\(996\) −0.229246 + 0.0434796i −0.00726392 + 0.00137771i
\(997\) 21.0590 0.666946 0.333473 0.942760i \(-0.391779\pi\)
0.333473 + 0.942760i \(0.391779\pi\)
\(998\) −4.23485 7.33497i −0.134052 0.232185i
\(999\) 37.7521 23.7905i 1.19442 0.752698i
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 546.2.ch.a.137.6 yes 152
3.2 odd 2 inner 546.2.ch.a.137.38 yes 152
7.2 even 3 546.2.bw.a.527.26 yes 152
13.2 odd 12 546.2.bw.a.431.7 152
21.2 odd 6 546.2.bw.a.527.7 yes 152
39.2 even 12 546.2.bw.a.431.26 yes 152
91.2 odd 12 inner 546.2.ch.a.275.38 yes 152
273.2 even 12 inner 546.2.ch.a.275.6 yes 152
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bw.a.431.7 152 13.2 odd 12
546.2.bw.a.431.26 yes 152 39.2 even 12
546.2.bw.a.527.7 yes 152 21.2 odd 6
546.2.bw.a.527.26 yes 152 7.2 even 3
546.2.ch.a.137.6 yes 152 1.1 even 1 trivial
546.2.ch.a.137.38 yes 152 3.2 odd 2 inner
546.2.ch.a.275.6 yes 152 273.2 even 12 inner
546.2.ch.a.275.38 yes 152 91.2 odd 12 inner