Properties

Label 432.2.bj.a.11.21
Level $432$
Weight $2$
Character 432.11
Analytic conductor $3.450$
Analytic rank $0$
Dimension $840$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(11,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 9, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.bj (of order \(36\), degree \(12\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(70\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 11.21
Character \(\chi\) \(=\) 432.11
Dual form 432.2.bj.a.275.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.859031 - 1.12342i) q^{2} +(-0.160747 + 1.72458i) q^{3} +(-0.524131 + 1.93010i) q^{4} +(2.32382 - 1.08362i) q^{5} +(2.07550 - 1.30088i) q^{6} +(0.387383 - 2.19696i) q^{7} +(2.61855 - 1.06920i) q^{8} +(-2.94832 - 0.554439i) q^{9} +O(q^{10})\) \(q+(-0.859031 - 1.12342i) q^{2} +(-0.160747 + 1.72458i) q^{3} +(-0.524131 + 1.93010i) q^{4} +(2.32382 - 1.08362i) q^{5} +(2.07550 - 1.30088i) q^{6} +(0.387383 - 2.19696i) q^{7} +(2.61855 - 1.06920i) q^{8} +(-2.94832 - 0.554439i) q^{9} +(-3.21359 - 1.67976i) q^{10} +(3.07018 + 1.43165i) q^{11} +(-3.24435 - 1.21416i) q^{12} +(0.323330 - 3.69567i) q^{13} +(-2.80088 + 1.45206i) q^{14} +(1.49523 + 4.18180i) q^{15} +(-3.45057 - 2.02325i) q^{16} +(-4.87637 + 2.81537i) q^{17} +(1.90983 + 3.78847i) q^{18} +(4.54940 - 1.21901i) q^{19} +(0.873501 + 5.05317i) q^{20} +(3.72655 + 1.02123i) q^{21} +(-1.02904 - 4.67892i) q^{22} +(5.25881 - 0.927270i) q^{23} +(1.42299 + 4.68776i) q^{24} +(1.01199 - 1.20604i) q^{25} +(-4.42953 + 2.81147i) q^{26} +(1.43010 - 4.99548i) q^{27} +(4.03731 + 1.89918i) q^{28} +(0.224692 + 2.56825i) q^{29} +(3.41345 - 5.27206i) q^{30} +(8.28625 - 1.46109i) q^{31} +(0.691197 + 5.61447i) q^{32} +(-2.96250 + 5.06462i) q^{33} +(7.35179 + 3.05970i) q^{34} +(-1.48045 - 5.52512i) q^{35} +(2.61543 - 5.39996i) q^{36} +(1.66736 - 6.22267i) q^{37} +(-5.27753 - 4.06371i) q^{38} +(6.32150 + 1.15167i) q^{39} +(4.92645 - 5.32213i) q^{40} +(4.49818 - 3.77442i) q^{41} +(-2.05396 - 5.06374i) q^{42} +(-4.33870 + 9.30438i) q^{43} +(-4.37239 + 5.17538i) q^{44} +(-7.45218 + 1.90643i) q^{45} +(-5.55919 - 5.11128i) q^{46} +(-0.437552 + 2.48148i) q^{47} +(4.04391 - 5.62554i) q^{48} +(1.90128 + 0.692009i) q^{49} +(-2.22422 - 0.100858i) q^{50} +(-4.07146 - 8.86223i) q^{51} +(6.96355 + 2.56108i) q^{52} +(-3.02276 + 3.02276i) q^{53} +(-6.84051 + 2.68467i) q^{54} +8.68590 q^{55} +(-1.33460 - 6.16705i) q^{56} +(1.37097 + 8.04174i) q^{57} +(2.69219 - 2.45863i) q^{58} +(3.37861 + 7.24546i) q^{59} +(-8.85498 + 0.694140i) q^{60} +(-7.89795 - 11.2794i) q^{61} +(-8.75956 - 8.05379i) q^{62} +(-2.36021 + 6.26256i) q^{63} +(5.71363 - 5.59951i) q^{64} +(-3.25333 - 8.93846i) q^{65} +(8.23456 - 1.02254i) q^{66} +(-6.97578 - 0.610301i) q^{67} +(-2.87810 - 10.8875i) q^{68} +(0.753812 + 9.21827i) q^{69} +(-4.93526 + 6.40942i) q^{70} +(-7.24759 + 4.18440i) q^{71} +(-8.31314 + 1.70051i) q^{72} +(-7.40104 - 4.27299i) q^{73} +(-8.42297 + 3.47233i) q^{74} +(1.91724 + 1.93912i) q^{75} +(-0.0316729 + 9.41972i) q^{76} +(4.33461 - 6.19046i) q^{77} +(-4.13655 - 8.09100i) q^{78} +(-2.05260 + 2.44620i) q^{79} +(-10.2109 - 0.962576i) q^{80} +(8.38519 + 3.26933i) q^{81} +(-8.10432 - 1.81098i) q^{82} +(4.52695 - 0.396056i) q^{83} +(-3.92427 + 6.65737i) q^{84} +(-8.28104 + 11.8265i) q^{85} +(14.1798 - 3.11858i) q^{86} +(-4.46525 - 0.0253375i) q^{87} +(9.57013 + 0.466212i) q^{88} +(-4.33345 + 7.50575i) q^{89} +(8.54337 + 6.73422i) q^{90} +(-7.99400 - 2.14199i) q^{91} +(-0.966580 + 10.6360i) q^{92} +(1.18777 + 14.5251i) q^{93} +(3.16361 - 1.64012i) q^{94} +(9.25107 - 7.76257i) q^{95} +(-9.79368 + 0.289516i) q^{96} +(13.0880 - 4.76365i) q^{97} +(-0.855843 - 2.73039i) q^{98} +(-8.25810 - 5.92318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 12 q^{16} - 36 q^{17} - 12 q^{18} - 6 q^{19} + 30 q^{20} - 12 q^{21} - 12 q^{22} - 24 q^{23} - 42 q^{24} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{32} - 24 q^{33} - 24 q^{34} - 18 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 24 q^{39} - 12 q^{40} + 48 q^{42} - 12 q^{43} - 18 q^{44} - 12 q^{45} - 6 q^{46} - 12 q^{48} - 24 q^{49} + 144 q^{50} - 30 q^{51} - 12 q^{52} - 180 q^{54} - 48 q^{55} - 54 q^{56} - 66 q^{58} + 24 q^{59} - 72 q^{60} - 12 q^{61} - 216 q^{62} - 6 q^{64} - 24 q^{65} - 6 q^{66} - 12 q^{67} - 114 q^{68} - 12 q^{69} + 30 q^{70} - 36 q^{71} - 48 q^{72} - 96 q^{74} + 72 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{81} - 24 q^{82} - 72 q^{83} - 192 q^{84} - 42 q^{85} - 72 q^{86} - 24 q^{87} - 12 q^{88} - 66 q^{90} - 6 q^{91} - 126 q^{92} - 12 q^{93} - 12 q^{94} + 96 q^{96} - 24 q^{97} - 18 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.859031 1.12342i −0.607427 0.794376i
\(3\) −0.160747 + 1.72458i −0.0928070 + 0.995684i
\(4\) −0.524131 + 1.93010i −0.262065 + 0.965050i
\(5\) 2.32382 1.08362i 1.03925 0.484608i 0.173364 0.984858i \(-0.444536\pi\)
0.865881 + 0.500250i \(0.166758\pi\)
\(6\) 2.07550 1.30088i 0.847321 0.531082i
\(7\) 0.387383 2.19696i 0.146417 0.830373i −0.819801 0.572648i \(-0.805916\pi\)
0.966218 0.257725i \(-0.0829728\pi\)
\(8\) 2.61855 1.06920i 0.925798 0.378019i
\(9\) −2.94832 0.554439i −0.982774 0.184813i
\(10\) −3.21359 1.67976i −1.01623 0.531187i
\(11\) 3.07018 + 1.43165i 0.925693 + 0.431658i 0.826198 0.563380i \(-0.190499\pi\)
0.0994951 + 0.995038i \(0.468277\pi\)
\(12\) −3.24435 1.21416i −0.936564 0.350498i
\(13\) 0.323330 3.69567i 0.0896755 1.02500i −0.809416 0.587235i \(-0.800216\pi\)
0.899092 0.437760i \(-0.144228\pi\)
\(14\) −2.80088 + 1.45206i −0.748566 + 0.388081i
\(15\) 1.49523 + 4.18180i 0.386067 + 1.07973i
\(16\) −3.45057 2.02325i −0.862643 0.505812i
\(17\) −4.87637 + 2.81537i −1.18269 + 0.682828i −0.956636 0.291286i \(-0.905917\pi\)
−0.226057 + 0.974114i \(0.572584\pi\)
\(18\) 1.90983 + 3.78847i 0.450152 + 0.892952i
\(19\) 4.54940 1.21901i 1.04370 0.279660i 0.304057 0.952654i \(-0.401659\pi\)
0.739648 + 0.672994i \(0.234992\pi\)
\(20\) 0.873501 + 5.05317i 0.195321 + 1.12992i
\(21\) 3.72655 + 1.02123i 0.813201 + 0.222850i
\(22\) −1.02904 4.67892i −0.219392 0.997548i
\(23\) 5.25881 0.927270i 1.09654 0.193349i 0.404020 0.914750i \(-0.367613\pi\)
0.692518 + 0.721401i \(0.256502\pi\)
\(24\) 1.42299 + 4.68776i 0.290467 + 0.956885i
\(25\) 1.01199 1.20604i 0.202398 0.241209i
\(26\) −4.42953 + 2.81147i −0.868703 + 0.551374i
\(27\) 1.43010 4.99548i 0.275224 0.961380i
\(28\) 4.03731 + 1.89918i 0.762981 + 0.358912i
\(29\) 0.224692 + 2.56825i 0.0417243 + 0.476911i 0.988097 + 0.153834i \(0.0491620\pi\)
−0.946372 + 0.323078i \(0.895282\pi\)
\(30\) 3.41345 5.27206i 0.623208 0.962542i
\(31\) 8.28625 1.46109i 1.48825 0.262419i 0.630383 0.776284i \(-0.282898\pi\)
0.857871 + 0.513865i \(0.171787\pi\)
\(32\) 0.691197 + 5.61447i 0.122188 + 0.992507i
\(33\) −2.96250 + 5.06462i −0.515705 + 0.881637i
\(34\) 7.35179 + 3.05970i 1.26082 + 0.524735i
\(35\) −1.48045 5.52512i −0.250242 0.933916i
\(36\) 2.61543 5.39996i 0.435905 0.899993i
\(37\) 1.66736 6.22267i 0.274112 1.02300i −0.682322 0.731052i \(-0.739030\pi\)
0.956434 0.291949i \(-0.0943037\pi\)
\(38\) −5.27753 4.06371i −0.856129 0.659220i
\(39\) 6.32150 + 1.15167i 1.01225 + 0.184415i
\(40\) 4.92645 5.32213i 0.778940 0.841503i
\(41\) 4.49818 3.77442i 0.702497 0.589465i −0.219986 0.975503i \(-0.570601\pi\)
0.922483 + 0.386038i \(0.126157\pi\)
\(42\) −2.05396 5.06374i −0.316934 0.781352i
\(43\) −4.33870 + 9.30438i −0.661646 + 1.41890i 0.233155 + 0.972440i \(0.425095\pi\)
−0.894801 + 0.446465i \(0.852683\pi\)
\(44\) −4.37239 + 5.17538i −0.659163 + 0.780217i
\(45\) −7.45218 + 1.90643i −1.11090 + 0.284194i
\(46\) −5.55919 5.11128i −0.819658 0.753617i
\(47\) −0.437552 + 2.48148i −0.0638236 + 0.361962i 0.936123 + 0.351672i \(0.114387\pi\)
−0.999947 + 0.0102900i \(0.996725\pi\)
\(48\) 4.04391 5.62554i 0.583689 0.811977i
\(49\) 1.90128 + 0.692009i 0.271611 + 0.0988584i
\(50\) −2.22422 0.100858i −0.314552 0.0142635i
\(51\) −4.07146 8.86223i −0.570119 1.24096i
\(52\) 6.96355 + 2.56108i 0.965671 + 0.355157i
\(53\) −3.02276 + 3.02276i −0.415208 + 0.415208i −0.883548 0.468340i \(-0.844852\pi\)
0.468340 + 0.883548i \(0.344852\pi\)
\(54\) −6.84051 + 2.68467i −0.930875 + 0.365337i
\(55\) 8.68590 1.17121
\(56\) −1.33460 6.16705i −0.178344 0.824106i
\(57\) 1.37097 + 8.04174i 0.181590 + 1.06515i
\(58\) 2.69219 2.45863i 0.353502 0.322833i
\(59\) 3.37861 + 7.24546i 0.439858 + 0.943278i 0.993848 + 0.110755i \(0.0353268\pi\)
−0.553990 + 0.832523i \(0.686895\pi\)
\(60\) −8.85498 + 0.694140i −1.14317 + 0.0896130i
\(61\) −7.89795 11.2794i −1.01123 1.44419i −0.892386 0.451272i \(-0.850970\pi\)
−0.118843 0.992913i \(-0.537918\pi\)
\(62\) −8.75956 8.05379i −1.11246 1.02283i
\(63\) −2.36021 + 6.26256i −0.297359 + 0.789009i
\(64\) 5.71363 5.59951i 0.714203 0.699938i
\(65\) −3.25333 8.93846i −0.403526 1.10868i
\(66\) 8.23456 1.02254i 1.01360 0.125866i
\(67\) −6.97578 0.610301i −0.852227 0.0745602i −0.347333 0.937742i \(-0.612913\pi\)
−0.504894 + 0.863182i \(0.668468\pi\)
\(68\) −2.87810 10.8875i −0.349021 1.32030i
\(69\) 0.753812 + 9.21827i 0.0907483 + 1.10975i
\(70\) −4.93526 + 6.40942i −0.589877 + 0.766072i
\(71\) −7.24759 + 4.18440i −0.860131 + 0.496597i −0.864056 0.503395i \(-0.832084\pi\)
0.00392502 + 0.999992i \(0.498751\pi\)
\(72\) −8.31314 + 1.70051i −0.979713 + 0.200408i
\(73\) −7.40104 4.27299i −0.866226 0.500116i −0.000133575 1.00000i \(-0.500043\pi\)
−0.866092 + 0.499884i \(0.833376\pi\)
\(74\) −8.42297 + 3.47233i −0.979150 + 0.403650i
\(75\) 1.91724 + 1.93912i 0.221384 + 0.223910i
\(76\) −0.0316729 + 9.41972i −0.00363313 + 1.08052i
\(77\) 4.33461 6.19046i 0.493974 0.705468i
\(78\) −4.13655 8.09100i −0.468372 0.916125i
\(79\) −2.05260 + 2.44620i −0.230936 + 0.275219i −0.869051 0.494722i \(-0.835270\pi\)
0.638115 + 0.769941i \(0.279714\pi\)
\(80\) −10.2109 0.962576i −1.14162 0.107619i
\(81\) 8.38519 + 3.26933i 0.931688 + 0.363259i
\(82\) −8.10432 1.81098i −0.894972 0.199990i
\(83\) 4.52695 0.396056i 0.496897 0.0434728i 0.164047 0.986453i \(-0.447545\pi\)
0.332850 + 0.942980i \(0.391990\pi\)
\(84\) −3.92427 + 6.65737i −0.428173 + 0.726378i
\(85\) −8.28104 + 11.8265i −0.898204 + 1.28277i
\(86\) 14.1798 3.11858i 1.52904 0.336285i
\(87\) −4.46525 0.0253375i −0.478725 0.00271647i
\(88\) 9.57013 + 0.466212i 1.02018 + 0.0496983i
\(89\) −4.33345 + 7.50575i −0.459344 + 0.795608i −0.998926 0.0463252i \(-0.985249\pi\)
0.539582 + 0.841933i \(0.318582\pi\)
\(90\) 8.54337 + 6.73422i 0.900550 + 0.709849i
\(91\) −7.99400 2.14199i −0.837999 0.224541i
\(92\) −0.966580 + 10.6360i −0.100773 + 1.10888i
\(93\) 1.18777 + 14.5251i 0.123166 + 1.50619i
\(94\) 3.16361 1.64012i 0.326302 0.169165i
\(95\) 9.25107 7.76257i 0.949139 0.796422i
\(96\) −9.79368 + 0.289516i −0.999563 + 0.0295486i
\(97\) 13.0880 4.76365i 1.32889 0.483675i 0.422591 0.906320i \(-0.361121\pi\)
0.906295 + 0.422645i \(0.138898\pi\)
\(98\) −0.855843 2.73039i −0.0864532 0.275811i
\(99\) −8.25810 5.92318i −0.829970 0.595302i
\(100\) 1.79737 + 2.58537i 0.179737 + 0.258537i
\(101\) 4.46175 + 6.37203i 0.443960 + 0.634041i 0.977300 0.211860i \(-0.0679521\pi\)
−0.533340 + 0.845901i \(0.679063\pi\)
\(102\) −6.45846 + 12.1869i −0.639483 + 1.20668i
\(103\) 3.64159 + 1.32543i 0.358816 + 0.130598i 0.515137 0.857108i \(-0.327741\pi\)
−0.156321 + 0.987706i \(0.549963\pi\)
\(104\) −3.10476 10.0230i −0.304446 0.982838i
\(105\) 9.76647 1.66501i 0.953110 0.162488i
\(106\) 5.99246 + 0.799174i 0.582039 + 0.0776226i
\(107\) −1.18062 1.18062i −0.114135 0.114135i 0.647733 0.761868i \(-0.275717\pi\)
−0.761868 + 0.647733i \(0.775717\pi\)
\(108\) 8.89221 + 5.37853i 0.855653 + 0.517549i
\(109\) −4.83143 + 4.83143i −0.462767 + 0.462767i −0.899561 0.436795i \(-0.856114\pi\)
0.436795 + 0.899561i \(0.356114\pi\)
\(110\) −7.46146 9.75789i −0.711422 0.930378i
\(111\) 10.4634 + 3.87576i 0.993146 + 0.367871i
\(112\) −5.78170 + 6.79700i −0.546319 + 0.642256i
\(113\) −1.43875 + 3.95292i −0.135346 + 0.371860i −0.988788 0.149329i \(-0.952289\pi\)
0.853442 + 0.521188i \(0.174511\pi\)
\(114\) 7.85652 8.44828i 0.735830 0.791253i
\(115\) 11.2157 7.85334i 1.04587 0.732328i
\(116\) −5.07474 0.912418i −0.471178 0.0847159i
\(117\) −3.00231 + 10.7168i −0.277563 + 0.990766i
\(118\) 5.23734 10.0197i 0.482136 0.922385i
\(119\) 4.29624 + 11.8038i 0.393836 + 1.08205i
\(120\) 8.38651 + 9.35155i 0.765580 + 0.853676i
\(121\) 0.305701 + 0.364321i 0.0277910 + 0.0331201i
\(122\) −5.88693 + 18.5621i −0.532978 + 1.68053i
\(123\) 5.78620 + 8.36417i 0.521724 + 0.754172i
\(124\) −1.52303 + 16.7591i −0.136772 + 1.50501i
\(125\) −2.27333 + 8.48419i −0.203333 + 0.758849i
\(126\) 9.06297 2.72824i 0.807393 0.243051i
\(127\) −9.91223 5.72283i −0.879568 0.507819i −0.00905216 0.999959i \(-0.502881\pi\)
−0.870516 + 0.492140i \(0.836215\pi\)
\(128\) −11.1988 1.60863i −0.989840 0.142185i
\(129\) −15.3487 8.97807i −1.35138 0.790475i
\(130\) −7.24690 + 11.3333i −0.635595 + 0.993993i
\(131\) −9.77845 6.84695i −0.854347 0.598221i 0.0622371 0.998061i \(-0.480176\pi\)
−0.916585 + 0.399841i \(0.869065\pi\)
\(132\) −8.22248 8.37245i −0.715675 0.728728i
\(133\) −0.915751 10.4671i −0.0794057 0.907611i
\(134\) 5.30679 + 8.36097i 0.458437 + 0.722278i
\(135\) −2.08987 13.1583i −0.179868 1.13249i
\(136\) −9.75883 + 12.5860i −0.836813 + 1.07924i
\(137\) −11.9065 9.99076i −1.01724 0.853568i −0.0279641 0.999609i \(-0.508902\pi\)
−0.989279 + 0.146041i \(0.953347\pi\)
\(138\) 9.70841 8.76562i 0.826435 0.746180i
\(139\) −17.0866 11.9642i −1.44927 1.01479i −0.992105 0.125407i \(-0.959976\pi\)
−0.457164 0.889382i \(-0.651135\pi\)
\(140\) 11.4400 + 0.0384659i 0.966856 + 0.00325096i
\(141\) −4.20917 1.15348i −0.354476 0.0971407i
\(142\) 10.9267 + 4.54754i 0.916951 + 0.381621i
\(143\) 6.28358 10.8835i 0.525459 0.910122i
\(144\) 9.05163 + 7.87832i 0.754303 + 0.656527i
\(145\) 3.30514 + 5.72467i 0.274477 + 0.475408i
\(146\) 1.55737 + 11.9851i 0.128889 + 0.991892i
\(147\) −1.49905 + 3.16766i −0.123639 + 0.261264i
\(148\) 11.1365 + 6.47966i 0.915412 + 0.532625i
\(149\) −0.768388 + 8.78271i −0.0629488 + 0.719508i 0.897493 + 0.441028i \(0.145386\pi\)
−0.960442 + 0.278480i \(0.910169\pi\)
\(150\) 0.531473 3.81962i 0.0433946 0.311871i
\(151\) −10.0779 + 3.66805i −0.820126 + 0.298501i −0.717800 0.696250i \(-0.754851\pi\)
−0.102326 + 0.994751i \(0.532628\pi\)
\(152\) 10.6095 8.05625i 0.860542 0.653448i
\(153\) 15.9381 5.59698i 1.28852 0.452489i
\(154\) −10.6780 + 0.448228i −0.860460 + 0.0361192i
\(155\) 17.6725 12.3744i 1.41949 0.993938i
\(156\) −5.53613 + 11.5975i −0.443246 + 0.928543i
\(157\) −2.46663 + 1.15021i −0.196859 + 0.0917967i −0.518548 0.855049i \(-0.673527\pi\)
0.321689 + 0.946845i \(0.395749\pi\)
\(158\) 4.51135 + 0.204569i 0.358904 + 0.0162747i
\(159\) −4.72708 5.69887i −0.374881 0.451950i
\(160\) 7.69015 + 12.2980i 0.607960 + 0.972245i
\(161\) 11.9126i 0.938845i
\(162\) −3.53033 12.2285i −0.277369 0.960764i
\(163\) −11.5411 11.5411i −0.903969 0.903969i 0.0918077 0.995777i \(-0.470735\pi\)
−0.995777 + 0.0918077i \(0.970735\pi\)
\(164\) 4.92737 + 10.6602i 0.384763 + 0.832423i
\(165\) −1.39623 + 14.9795i −0.108696 + 1.16615i
\(166\) −4.33372 4.74542i −0.336362 0.368316i
\(167\) −0.948023 + 2.60467i −0.0733602 + 0.201556i −0.970953 0.239270i \(-0.923092\pi\)
0.897593 + 0.440825i \(0.145314\pi\)
\(168\) 10.8501 1.31030i 0.837101 0.101091i
\(169\) −0.750966 0.132416i −0.0577666 0.0101858i
\(170\) 20.3998 0.856316i 1.56459 0.0656764i
\(171\) −14.0890 + 1.07166i −1.07741 + 0.0819521i
\(172\) −15.6843 13.2508i −1.19592 1.01037i
\(173\) −23.0700 10.7577i −1.75398 0.817895i −0.983612 0.180298i \(-0.942294\pi\)
−0.770370 0.637597i \(-0.779928\pi\)
\(174\) 3.80733 + 5.03811i 0.288633 + 0.381938i
\(175\) −2.25760 2.69050i −0.170659 0.203383i
\(176\) −7.69729 11.1517i −0.580205 0.840593i
\(177\) −13.0384 + 4.66199i −0.980029 + 0.350417i
\(178\) 12.1547 1.57941i 0.911030 0.118382i
\(179\) 11.0063 + 2.94912i 0.822647 + 0.220428i 0.645503 0.763757i \(-0.276648\pi\)
0.177144 + 0.984185i \(0.443314\pi\)
\(180\) 0.226311 15.3827i 0.0168682 1.14656i
\(181\) −3.48455 + 0.933683i −0.259005 + 0.0694001i −0.385985 0.922505i \(-0.626138\pi\)
0.126980 + 0.991905i \(0.459472\pi\)
\(182\) 4.46075 + 10.8206i 0.330653 + 0.802078i
\(183\) 20.7218 11.8075i 1.53180 0.872834i
\(184\) 12.7790 8.05082i 0.942082 0.593514i
\(185\) −2.86834 16.2672i −0.210885 1.19599i
\(186\) 15.2974 13.8119i 1.12166 1.01274i
\(187\) −19.0019 + 1.66245i −1.38956 + 0.121571i
\(188\) −4.56018 2.14514i −0.332585 0.156451i
\(189\) −10.4209 5.07705i −0.758007 0.369301i
\(190\) −16.6676 3.72452i −1.20919 0.270205i
\(191\) 13.1151 + 11.0049i 0.948974 + 0.796283i 0.979124 0.203262i \(-0.0651543\pi\)
−0.0301507 + 0.999545i \(0.509599\pi\)
\(192\) 8.73832 + 10.7537i 0.630634 + 0.776080i
\(193\) 1.19205 + 6.76044i 0.0858055 + 0.486627i 0.997180 + 0.0750489i \(0.0239113\pi\)
−0.911374 + 0.411578i \(0.864978\pi\)
\(194\) −16.5946 10.6112i −1.19142 0.761838i
\(195\) 15.9380 4.17379i 1.14134 0.298891i
\(196\) −2.33216 + 3.30695i −0.166583 + 0.236211i
\(197\) −1.83323 6.84172i −0.130612 0.487452i 0.869365 0.494171i \(-0.164528\pi\)
−0.999977 + 0.00671816i \(0.997862\pi\)
\(198\) 0.439770 + 14.3655i 0.0312531 + 1.02091i
\(199\) 10.3737 + 17.9678i 0.735372 + 1.27370i 0.954560 + 0.298019i \(0.0963259\pi\)
−0.219188 + 0.975683i \(0.570341\pi\)
\(200\) 1.36045 4.24011i 0.0961983 0.299821i
\(201\) 2.17384 11.9322i 0.153331 0.841629i
\(202\) 3.32567 10.4862i 0.233993 0.737805i
\(203\) 5.72938 + 0.501256i 0.402123 + 0.0351812i
\(204\) 19.2390 3.21337i 1.34700 0.224981i
\(205\) 6.36294 13.6454i 0.444407 0.953034i
\(206\) −1.63923 5.22961i −0.114210 0.364364i
\(207\) −16.0188 0.181799i −1.11338 0.0126359i
\(208\) −8.59295 + 12.0980i −0.595814 + 0.838847i
\(209\) 15.7126 + 2.77056i 1.08687 + 0.191644i
\(210\) −10.2602 9.54152i −0.708021 0.658428i
\(211\) 4.10132 + 8.79532i 0.282347 + 0.605495i 0.995420 0.0955946i \(-0.0304752\pi\)
−0.713074 + 0.701089i \(0.752697\pi\)
\(212\) −4.24990 7.41854i −0.291885 0.509508i
\(213\) −6.05129 13.1717i −0.414628 0.902507i
\(214\) −0.312139 + 2.34052i −0.0213374 + 0.159995i
\(215\) 26.3232i 1.79523i
\(216\) −1.59636 14.6100i −0.108618 0.994084i
\(217\) 18.7706i 1.27423i
\(218\) 9.57805 + 1.27736i 0.648708 + 0.0865137i
\(219\) 8.55878 12.0768i 0.578349 0.816073i
\(220\) −4.55255 + 16.7647i −0.306933 + 1.13027i
\(221\) 8.82803 + 18.9318i 0.593838 + 1.27349i
\(222\) −4.63433 15.0842i −0.311036 1.01239i
\(223\) −9.52429 1.67939i −0.637794 0.112460i −0.154605 0.987976i \(-0.549410\pi\)
−0.483189 + 0.875516i \(0.660522\pi\)
\(224\) 12.6025 + 0.656418i 0.842041 + 0.0438588i
\(225\) −3.65235 + 2.99472i −0.243490 + 0.199648i
\(226\) 5.67671 1.77937i 0.377609 0.118362i
\(227\) 8.15382 17.4859i 0.541188 1.16058i −0.425578 0.904922i \(-0.639929\pi\)
0.966767 0.255660i \(-0.0822929\pi\)
\(228\) −16.2399 1.56881i −1.07552 0.103897i
\(229\) −13.2309 1.15755i −0.874322 0.0764933i −0.358845 0.933397i \(-0.616829\pi\)
−0.515476 + 0.856904i \(0.672385\pi\)
\(230\) −18.4572 5.85368i −1.21703 0.385980i
\(231\) 9.97914 + 8.47045i 0.656579 + 0.557315i
\(232\) 3.33433 + 6.48484i 0.218910 + 0.425751i
\(233\) −9.76034 16.9054i −0.639421 1.10751i −0.985560 0.169327i \(-0.945841\pi\)
0.346139 0.938183i \(-0.387493\pi\)
\(234\) 14.6185 5.83320i 0.955639 0.381328i
\(235\) 1.67218 + 6.24067i 0.109081 + 0.407096i
\(236\) −15.7553 + 2.72349i −1.02558 + 0.177284i
\(237\) −3.88870 3.93309i −0.252598 0.255481i
\(238\) 9.57001 14.9663i 0.620331 0.970122i
\(239\) 2.95020 + 16.7314i 0.190832 + 1.08226i 0.918230 + 0.396048i \(0.129619\pi\)
−0.727397 + 0.686217i \(0.759270\pi\)
\(240\) 3.30141 17.4548i 0.213105 1.12670i
\(241\) 19.3717 + 16.2548i 1.24784 + 1.04706i 0.996869 + 0.0790684i \(0.0251945\pi\)
0.250972 + 0.967994i \(0.419250\pi\)
\(242\) 0.146677 0.656393i 0.00942876 0.0421945i
\(243\) −6.98609 + 13.9354i −0.448158 + 0.893954i
\(244\) 25.9100 9.33194i 1.65872 0.597416i
\(245\) 5.16811 0.452151i 0.330178 0.0288869i
\(246\) 4.42592 13.6854i 0.282186 0.872549i
\(247\) −3.03410 17.2072i −0.193055 1.09487i
\(248\) 20.1358 12.6856i 1.27862 0.805535i
\(249\) −0.0446615 + 7.87072i −0.00283031 + 0.498787i
\(250\) 11.4842 4.73429i 0.726321 0.299423i
\(251\) −4.05465 + 1.08644i −0.255927 + 0.0685755i −0.384501 0.923124i \(-0.625627\pi\)
0.128574 + 0.991700i \(0.458960\pi\)
\(252\) −10.8503 7.83785i −0.683506 0.493738i
\(253\) 17.4730 + 4.68187i 1.09852 + 0.294347i
\(254\) 2.08579 + 16.0517i 0.130874 + 1.00717i
\(255\) −19.0646 16.1823i −1.19387 1.01338i
\(256\) 7.81292 + 13.9627i 0.488307 + 0.872672i
\(257\) 16.1871 + 19.2910i 1.00972 + 1.20334i 0.979010 + 0.203812i \(0.0653332\pi\)
0.0307126 + 0.999528i \(0.490222\pi\)
\(258\) 3.09888 + 24.9554i 0.192928 + 1.55366i
\(259\) −13.0251 6.07368i −0.809337 0.377400i
\(260\) 18.9573 1.59434i 1.17568 0.0988766i
\(261\) 0.761470 7.69659i 0.0471338 0.476407i
\(262\) 0.708021 + 16.8670i 0.0437417 + 1.04205i
\(263\) 12.7193 + 2.24276i 0.784309 + 0.138295i 0.551441 0.834214i \(-0.314078\pi\)
0.232867 + 0.972508i \(0.425189\pi\)
\(264\) −2.34238 + 16.4295i −0.144164 + 1.01116i
\(265\) −3.74884 + 10.2999i −0.230290 + 0.632715i
\(266\) −10.9722 + 10.0203i −0.672751 + 0.614385i
\(267\) −12.2476 8.67988i −0.749544 0.531200i
\(268\) 4.83416 13.1441i 0.295294 0.802902i
\(269\) −13.0484 13.0484i −0.795577 0.795577i 0.186818 0.982395i \(-0.440183\pi\)
−0.982395 + 0.186818i \(0.940183\pi\)
\(270\) −12.9870 + 13.6512i −0.790362 + 0.830784i
\(271\) 7.20125i 0.437445i −0.975787 0.218722i \(-0.929811\pi\)
0.975787 0.218722i \(-0.0701889\pi\)
\(272\) 22.5225 + 0.151461i 1.36563 + 0.00918368i
\(273\) 4.97902 13.4419i 0.301344 0.813543i
\(274\) −0.995712 + 21.9584i −0.0601532 + 1.32655i
\(275\) 4.83362 2.25395i 0.291478 0.135918i
\(276\) −18.1873 3.37665i −1.09475 0.203250i
\(277\) 26.9359 18.8607i 1.61842 1.13323i 0.720119 0.693850i \(-0.244087\pi\)
0.898301 0.439380i \(-0.144802\pi\)
\(278\) 1.23718 + 29.4730i 0.0742011 + 1.76767i
\(279\) −25.2406 0.286459i −1.51112 0.0171498i
\(280\) −9.78410 12.8849i −0.584712 0.770021i
\(281\) 1.94955 0.709578i 0.116300 0.0423299i −0.283214 0.959057i \(-0.591401\pi\)
0.399515 + 0.916727i \(0.369179\pi\)
\(282\) 2.31997 + 5.71953i 0.138152 + 0.340593i
\(283\) −2.60836 + 29.8137i −0.155051 + 1.77224i 0.377660 + 0.925944i \(0.376729\pi\)
−0.532711 + 0.846297i \(0.678827\pi\)
\(284\) −4.27763 16.1818i −0.253830 0.960211i
\(285\) 11.9001 + 17.2020i 0.704898 + 1.01896i
\(286\) −17.6245 + 2.29017i −1.04216 + 0.135420i
\(287\) −6.54973 11.3445i −0.386618 0.669642i
\(288\) 1.07501 16.9365i 0.0633454 0.997992i
\(289\) 7.35266 12.7352i 0.432509 0.749128i
\(290\) 3.59197 8.63072i 0.210928 0.506813i
\(291\) 6.11142 + 23.3370i 0.358258 + 1.36804i
\(292\) 12.1264 12.0451i 0.709644 0.704888i
\(293\) 9.42876 + 6.60209i 0.550834 + 0.385698i 0.815601 0.578614i \(-0.196406\pi\)
−0.264768 + 0.964312i \(0.585295\pi\)
\(294\) 4.84633 1.03707i 0.282644 0.0604829i
\(295\) 15.7026 + 13.1760i 0.914240 + 0.767139i
\(296\) −2.28721 18.0771i −0.132941 1.05071i
\(297\) 11.5424 13.2896i 0.669760 0.771140i
\(298\) 10.5267 6.68140i 0.609796 0.387043i
\(299\) −1.72656 19.7347i −0.0998495 1.14128i
\(300\) −4.74758 + 2.68411i −0.274102 + 0.154967i
\(301\) 18.7606 + 13.1363i 1.08134 + 0.757165i
\(302\) 12.7780 + 8.17069i 0.735288 + 0.470170i
\(303\) −11.7063 + 6.67034i −0.672507 + 0.383201i
\(304\) −18.1644 4.99830i −1.04180 0.286672i
\(305\) −30.5760 17.6531i −1.75078 1.01081i
\(306\) −19.9790 13.0971i −1.14212 0.748712i
\(307\) −6.80927 + 25.4126i −0.388626 + 1.45037i 0.443746 + 0.896153i \(0.353649\pi\)
−0.832371 + 0.554218i \(0.813017\pi\)
\(308\) 9.67630 + 11.6108i 0.551359 + 0.661589i
\(309\) −2.87118 + 6.06713i −0.163335 + 0.345147i
\(310\) −29.0829 9.22358i −1.65180 0.523864i
\(311\) −8.13703 9.69733i −0.461408 0.549885i 0.484300 0.874902i \(-0.339074\pi\)
−0.945708 + 0.325017i \(0.894630\pi\)
\(312\) 17.7845 3.74322i 1.00685 0.211918i
\(313\) 4.62575 + 12.7091i 0.261463 + 0.718363i 0.999069 + 0.0431326i \(0.0137338\pi\)
−0.737606 + 0.675231i \(0.764044\pi\)
\(314\) 3.41108 + 1.78299i 0.192498 + 0.100620i
\(315\) 1.30151 + 17.1107i 0.0733315 + 0.964076i
\(316\) −3.64557 5.24386i −0.205079 0.294990i
\(317\) −12.3972 + 8.68060i −0.696295 + 0.487551i −0.867342 0.497712i \(-0.834174\pi\)
0.171048 + 0.985263i \(0.445285\pi\)
\(318\) −2.34150 + 10.2060i −0.131305 + 0.572323i
\(319\) −2.98697 + 8.20665i −0.167238 + 0.459484i
\(320\) 7.20974 19.2036i 0.403037 1.07352i
\(321\) 2.22585 1.84629i 0.124235 0.103050i
\(322\) −13.3828 + 10.2333i −0.745795 + 0.570279i
\(323\) −18.7526 + 18.7526i −1.04342 + 1.04342i
\(324\) −10.7051 + 14.4707i −0.594726 + 0.803928i
\(325\) −4.12994 4.12994i −0.229088 0.229088i
\(326\) −3.05130 + 22.8796i −0.168996 + 1.26719i
\(327\) −7.55552 9.10879i −0.417821 0.503717i
\(328\) 7.74310 14.6930i 0.427541 0.811283i
\(329\) 5.28222 + 1.92257i 0.291218 + 0.105995i
\(330\) 18.0276 11.2993i 0.992387 0.622006i
\(331\) 7.73707 + 11.0497i 0.425268 + 0.607345i 0.973418 0.229035i \(-0.0735569\pi\)
−0.548151 + 0.836380i \(0.684668\pi\)
\(332\) −1.60828 + 8.94504i −0.0882660 + 0.490923i
\(333\) −8.36600 + 17.4220i −0.458454 + 0.954719i
\(334\) 3.74051 1.17247i 0.204672 0.0641547i
\(335\) −16.8718 + 6.14083i −0.921805 + 0.335510i
\(336\) −10.7926 11.0636i −0.588782 0.603567i
\(337\) 2.05835 1.72716i 0.112125 0.0940843i −0.585001 0.811032i \(-0.698906\pi\)
0.697127 + 0.716948i \(0.254462\pi\)
\(338\) 0.496345 + 0.957397i 0.0269976 + 0.0520755i
\(339\) −6.58584 3.11664i −0.357694 0.169273i
\(340\) −18.4861 22.1819i −1.00255 1.20298i
\(341\) 27.5320 + 7.37718i 1.49094 + 0.399496i
\(342\) 13.3068 + 14.9072i 0.719548 + 0.806088i
\(343\) 10.0648 17.4328i 0.543449 0.941282i
\(344\) −1.41289 + 29.0029i −0.0761778 + 1.56373i
\(345\) 11.7408 + 20.6048i 0.632103 + 1.10932i
\(346\) 7.73246 + 35.1585i 0.415700 + 1.89013i
\(347\) 7.50660 10.7205i 0.402975 0.575508i −0.565459 0.824776i \(-0.691301\pi\)
0.968435 + 0.249268i \(0.0801900\pi\)
\(348\) 2.38928 8.60510i 0.128079 0.461282i
\(349\) −3.59334 + 0.314376i −0.192347 + 0.0168282i −0.182922 0.983127i \(-0.558556\pi\)
−0.00942487 + 0.999956i \(0.503000\pi\)
\(350\) −1.08321 + 4.84745i −0.0578999 + 0.259107i
\(351\) −17.9993 6.90039i −0.960730 0.368315i
\(352\) −5.91583 + 18.2269i −0.315315 + 0.971500i
\(353\) −5.82864 + 6.94631i −0.310227 + 0.369715i −0.898519 0.438934i \(-0.855356\pi\)
0.588292 + 0.808649i \(0.299801\pi\)
\(354\) 16.4378 + 10.6428i 0.873658 + 0.565659i
\(355\) −12.3078 + 17.5774i −0.653232 + 0.932913i
\(356\) −12.2156 12.2980i −0.647423 0.651792i
\(357\) −21.0472 + 5.51177i −1.11394 + 0.291714i
\(358\) −6.14164 14.8980i −0.324596 0.787384i
\(359\) 5.72146 + 3.30329i 0.301967 + 0.174341i 0.643326 0.765592i \(-0.277554\pi\)
−0.341359 + 0.939933i \(0.610887\pi\)
\(360\) −17.4756 + 12.9599i −0.921043 + 0.683049i
\(361\) 2.75659 1.59152i 0.145083 0.0837640i
\(362\) 4.04226 + 3.11254i 0.212456 + 0.163592i
\(363\) −0.677439 + 0.468642i −0.0355563 + 0.0245973i
\(364\) 8.32415 14.3065i 0.436304 0.749866i
\(365\) −21.8290 1.90979i −1.14258 0.0999629i
\(366\) −31.0654 13.1362i −1.62382 0.686643i
\(367\) 4.93236 + 13.5515i 0.257467 + 0.707384i 0.999322 + 0.0368240i \(0.0117241\pi\)
−0.741855 + 0.670560i \(0.766054\pi\)
\(368\) −20.0220 7.44027i −1.04372 0.387851i
\(369\) −15.3548 + 8.63423i −0.799336 + 0.449480i
\(370\) −15.8108 + 17.1963i −0.821965 + 0.893995i
\(371\) 5.46991 + 7.81184i 0.283984 + 0.405571i
\(372\) −28.6575 5.32054i −1.48582 0.275857i
\(373\) −4.90694 10.5230i −0.254072 0.544858i 0.737358 0.675502i \(-0.236073\pi\)
−0.991429 + 0.130644i \(0.958295\pi\)
\(374\) 18.1909 + 19.9190i 0.940628 + 1.02999i
\(375\) −14.2662 5.28434i −0.736704 0.272882i
\(376\) 1.50745 + 6.96572i 0.0777406 + 0.359230i
\(377\) 9.56405 0.492574
\(378\) 3.24821 + 16.0683i 0.167070 + 0.826465i
\(379\) 4.22810 4.22810i 0.217183 0.217183i −0.590127 0.807310i \(-0.700922\pi\)
0.807310 + 0.590127i \(0.200922\pi\)
\(380\) 10.1338 + 21.9241i 0.519851 + 1.12468i
\(381\) 11.4628 16.1745i 0.587257 0.828643i
\(382\) 1.09678 24.1872i 0.0561162 1.23753i
\(383\) 24.1043 + 8.77325i 1.23167 + 0.448292i 0.874170 0.485620i \(-0.161406\pi\)
0.357502 + 0.933912i \(0.383628\pi\)
\(384\) 4.57437 19.0545i 0.233435 0.972372i
\(385\) 3.36477 19.0826i 0.171485 0.972538i
\(386\) 6.57079 7.14660i 0.334444 0.363752i
\(387\) 17.9506 25.0268i 0.912480 1.27218i
\(388\) 2.33449 + 27.7580i 0.118516 + 1.40920i
\(389\) 5.75460 12.3408i 0.291770 0.625702i −0.704714 0.709492i \(-0.748925\pi\)
0.996483 + 0.0837897i \(0.0267024\pi\)
\(390\) −18.3802 14.3196i −0.930715 0.725102i
\(391\) −23.0333 + 19.3272i −1.16484 + 0.977420i
\(392\) 5.71849 0.220784i 0.288827 0.0111513i
\(393\) 13.3799 15.7631i 0.674928 0.795141i
\(394\) −6.11130 + 7.93674i −0.307883 + 0.399847i
\(395\) −2.11915 + 7.90876i −0.106626 + 0.397933i
\(396\) 15.7607 12.8344i 0.792003 0.644955i
\(397\) 2.32880 + 8.69122i 0.116879 + 0.436200i 0.999421 0.0340352i \(-0.0108358\pi\)
−0.882541 + 0.470235i \(0.844169\pi\)
\(398\) 11.2740 27.0889i 0.565113 1.35784i
\(399\) 18.1985 + 0.103265i 0.911063 + 0.00516972i
\(400\) −5.93207 + 2.11403i −0.296604 + 0.105702i
\(401\) 10.1222 1.78482i 0.505479 0.0891296i 0.0849074 0.996389i \(-0.472941\pi\)
0.420572 + 0.907259i \(0.361829\pi\)
\(402\) −15.2722 + 7.80796i −0.761707 + 0.389426i
\(403\) −2.72052 31.0957i −0.135519 1.54899i
\(404\) −14.6372 + 5.27184i −0.728228 + 0.262284i
\(405\) 23.0284 1.48900i 1.14429 0.0739888i
\(406\) −4.35859 6.86707i −0.216313 0.340807i
\(407\) 14.0277 16.7176i 0.695330 0.828662i
\(408\) −20.1368 18.8530i −0.996922 0.933363i
\(409\) 4.05357 0.714753i 0.200436 0.0353423i −0.0725287 0.997366i \(-0.523107\pi\)
0.272965 + 0.962024i \(0.411996\pi\)
\(410\) −20.7954 + 4.57357i −1.02701 + 0.225872i
\(411\) 19.1437 18.9277i 0.944291 0.933635i
\(412\) −4.46688 + 6.33393i −0.220067 + 0.312050i
\(413\) 17.2268 4.61591i 0.847676 0.227134i
\(414\) 13.5564 + 18.1519i 0.666260 + 0.892119i
\(415\) 10.0906 5.82584i 0.495330 0.285979i
\(416\) 20.9727 0.739117i 1.02827 0.0362382i
\(417\) 23.3798 27.5440i 1.14491 1.34884i
\(418\) −10.3852 20.0319i −0.507955 0.979790i
\(419\) −0.902111 + 10.3112i −0.0440710 + 0.503734i 0.941794 + 0.336191i \(0.109139\pi\)
−0.985865 + 0.167543i \(0.946417\pi\)
\(420\) −1.90528 + 19.7229i −0.0929679 + 0.962381i
\(421\) −22.1225 10.3159i −1.07819 0.502767i −0.199369 0.979924i \(-0.563889\pi\)
−0.878818 + 0.477158i \(0.841667\pi\)
\(422\) 6.35764 12.1629i 0.309485 0.592083i
\(423\) 2.66588 7.07361i 0.129619 0.343931i
\(424\) −4.68332 + 11.1472i −0.227442 + 0.541355i
\(425\) −1.53938 + 8.73024i −0.0746708 + 0.423479i
\(426\) −9.59901 + 18.1130i −0.465073 + 0.877577i
\(427\) −27.8400 + 12.9820i −1.34727 + 0.628244i
\(428\) 2.89752 1.65992i 0.140057 0.0802352i
\(429\) 17.7593 + 12.5860i 0.857428 + 0.607657i
\(430\) 29.5719 22.6125i 1.42609 1.09047i
\(431\) 12.6586 0.609742 0.304871 0.952394i \(-0.401387\pi\)
0.304871 + 0.952394i \(0.401387\pi\)
\(432\) −15.0418 + 14.3438i −0.723698 + 0.690117i
\(433\) −24.2581 −1.16577 −0.582886 0.812554i \(-0.698076\pi\)
−0.582886 + 0.812554i \(0.698076\pi\)
\(434\) −21.0872 + 16.1245i −1.01222 + 0.774001i
\(435\) −10.4039 + 4.77974i −0.498829 + 0.229171i
\(436\) −6.79284 11.8574i −0.325318 0.567868i
\(437\) 22.7941 10.6291i 1.09039 0.508457i
\(438\) −20.9195 + 0.759245i −0.999573 + 0.0362781i
\(439\) 2.24627 12.7392i 0.107208 0.608009i −0.883107 0.469172i \(-0.844552\pi\)
0.990315 0.138837i \(-0.0443364\pi\)
\(440\) 22.7445 9.28695i 1.08430 0.442738i
\(441\) −5.22190 3.09441i −0.248662 0.147353i
\(442\) 13.6847 26.1805i 0.650916 1.24528i
\(443\) −37.0701 17.2861i −1.76125 0.821285i −0.980520 0.196419i \(-0.937069\pi\)
−0.780732 0.624866i \(-0.785154\pi\)
\(444\) −12.9648 + 18.1641i −0.615283 + 0.862029i
\(445\) −1.93681 + 22.1378i −0.0918136 + 1.04943i
\(446\) 6.29501 + 12.1424i 0.298077 + 0.574959i
\(447\) −15.0229 2.73693i −0.710560 0.129452i
\(448\) −10.0885 14.7218i −0.476638 0.695538i
\(449\) −28.3756 + 16.3826i −1.33913 + 0.773145i −0.986678 0.162687i \(-0.947984\pi\)
−0.352448 + 0.935831i \(0.614651\pi\)
\(450\) 6.50180 + 1.53056i 0.306498 + 0.0721512i
\(451\) 19.2138 5.14833i 0.904743 0.242425i
\(452\) −6.87544 4.84877i −0.323394 0.228067i
\(453\) −4.70584 17.9697i −0.221100 0.844289i
\(454\) −26.6484 + 5.86082i −1.25067 + 0.275062i
\(455\) −20.8977 + 3.68483i −0.979701 + 0.172748i
\(456\) 12.1882 + 19.5919i 0.570764 + 0.917473i
\(457\) 0.0996178 0.118720i 0.00465992 0.00555348i −0.763709 0.645560i \(-0.776624\pi\)
0.768369 + 0.640007i \(0.221068\pi\)
\(458\) 10.0653 + 15.8582i 0.470322 + 0.741004i
\(459\) 7.09042 + 28.3861i 0.330952 + 1.32495i
\(460\) 9.27923 + 25.7637i 0.432646 + 1.20124i
\(461\) 2.15635 + 24.6472i 0.100431 + 1.14794i 0.864442 + 0.502732i \(0.167672\pi\)
−0.764011 + 0.645203i \(0.776773\pi\)
\(462\) 0.943452 18.4871i 0.0438934 0.860098i
\(463\) 18.2129 3.21143i 0.846427 0.149248i 0.266417 0.963858i \(-0.414160\pi\)
0.580009 + 0.814610i \(0.303049\pi\)
\(464\) 4.42089 9.31653i 0.205234 0.432509i
\(465\) 18.4998 + 32.4667i 0.857909 + 1.50561i
\(466\) −10.6074 + 25.4872i −0.491378 + 1.18067i
\(467\) 1.09906 + 4.10174i 0.0508584 + 0.189806i 0.986682 0.162664i \(-0.0520086\pi\)
−0.935823 + 0.352470i \(0.885342\pi\)
\(468\) −19.1108 11.4117i −0.883399 0.527508i
\(469\) −4.04311 + 15.0891i −0.186693 + 0.696749i
\(470\) 5.57441 7.23948i 0.257129 0.333933i
\(471\) −1.58712 4.43879i −0.0731307 0.204528i
\(472\) 16.5939 + 15.3602i 0.763797 + 0.707010i
\(473\) −26.6412 + 22.3546i −1.22496 + 1.02786i
\(474\) −1.07798 + 7.74728i −0.0495132 + 0.355844i
\(475\) 3.13377 6.72040i 0.143787 0.308353i
\(476\) −25.0344 + 2.10543i −1.14745 + 0.0965021i
\(477\) 10.5880 7.23612i 0.484791 0.331319i
\(478\) 16.2620 17.6871i 0.743808 0.808989i
\(479\) −0.360381 + 2.04382i −0.0164662 + 0.0933846i −0.991933 0.126761i \(-0.959542\pi\)
0.975467 + 0.220145i \(0.0706531\pi\)
\(480\) −22.4451 + 11.2854i −1.02447 + 0.515105i
\(481\) −22.4579 8.17399i −1.02399 0.372702i
\(482\) 1.62001 35.7259i 0.0737893 1.62727i
\(483\) 20.5442 + 1.91491i 0.934793 + 0.0871314i
\(484\) −0.863403 + 0.399083i −0.0392456 + 0.0181401i
\(485\) 25.2523 25.2523i 1.14665 1.14665i
\(486\) 21.6565 4.12262i 0.982359 0.187006i
\(487\) 11.7360 0.531808 0.265904 0.964000i \(-0.414330\pi\)
0.265904 + 0.964000i \(0.414330\pi\)
\(488\) −32.7412 21.0913i −1.48212 0.954760i
\(489\) 21.7587 18.0483i 0.983962 0.816173i
\(490\) −4.94752 5.41753i −0.223506 0.244739i
\(491\) 0.295570 + 0.633853i 0.0133389 + 0.0286054i 0.912864 0.408263i \(-0.133865\pi\)
−0.899525 + 0.436868i \(0.856088\pi\)
\(492\) −19.1764 + 6.78403i −0.864539 + 0.305848i
\(493\) −8.32626 11.8911i −0.374996 0.535549i
\(494\) −16.7245 + 18.1901i −0.752472 + 0.818412i
\(495\) −25.6088 4.81580i −1.15103 0.216454i
\(496\) −31.5485 11.7236i −1.41657 0.526403i
\(497\) 6.38537 + 17.5436i 0.286423 + 0.786940i
\(498\) 8.88047 6.71102i 0.397943 0.300728i
\(499\) 12.1209 + 1.06044i 0.542607 + 0.0474720i 0.355165 0.934804i \(-0.384425\pi\)
0.187442 + 0.982276i \(0.439980\pi\)
\(500\) −15.1838 8.83459i −0.679041 0.395095i
\(501\) −4.33956 2.05363i −0.193877 0.0917494i
\(502\) 4.70359 + 3.62177i 0.209932 + 0.161648i
\(503\) −30.7440 + 17.7501i −1.37081 + 0.791437i −0.991030 0.133640i \(-0.957333\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(504\) 0.515592 + 18.9224i 0.0229663 + 0.842870i
\(505\) 17.2732 + 9.97266i 0.768645 + 0.443777i
\(506\) −9.75015 23.6513i −0.433447 1.05143i
\(507\) 0.349076 1.27381i 0.0155030 0.0565720i
\(508\) 16.2409 16.1321i 0.720575 0.715746i
\(509\) 11.0728 15.8136i 0.490793 0.700926i −0.494999 0.868894i \(-0.664832\pi\)
0.985792 + 0.167968i \(0.0537205\pi\)
\(510\) −1.80242 + 35.3187i −0.0798123 + 1.56394i
\(511\) −12.2546 + 14.6045i −0.542113 + 0.646065i
\(512\) 8.97444 20.7716i 0.396618 0.917984i
\(513\) 0.416588 24.4697i 0.0183928 1.08037i
\(514\) 7.76664 34.7564i 0.342572 1.53304i
\(515\) 9.89866 0.866021i 0.436187 0.0381614i
\(516\) 25.3733 24.9188i 1.11700 1.09699i
\(517\) −4.89597 + 6.99217i −0.215324 + 0.307515i
\(518\) 4.36565 + 19.8500i 0.191816 + 0.872161i
\(519\) 22.2609 38.0567i 0.977147 1.67051i
\(520\) −18.0760 19.9274i −0.792685 0.873872i
\(521\) −13.3464 + 23.1167i −0.584718 + 1.01276i 0.410192 + 0.911999i \(0.365462\pi\)
−0.994910 + 0.100763i \(0.967872\pi\)
\(522\) −9.30061 + 5.75616i −0.407077 + 0.251940i
\(523\) 6.45100 + 1.72854i 0.282083 + 0.0755838i 0.397086 0.917781i \(-0.370021\pi\)
−0.115004 + 0.993365i \(0.536688\pi\)
\(524\) 18.3405 15.2847i 0.801208 0.667715i
\(525\) 5.00288 3.46091i 0.218344 0.151047i
\(526\) −8.40676 16.2157i −0.366552 0.707040i
\(527\) −36.2933 + 30.4537i −1.58096 + 1.32658i
\(528\) 20.4693 11.4820i 0.890813 0.499688i
\(529\) 5.18231 1.88621i 0.225318 0.0820090i
\(530\) 14.7914 4.63639i 0.642498 0.201392i
\(531\) −5.94407 23.2352i −0.257951 1.00832i
\(532\) 20.6825 + 3.71863i 0.896699 + 0.161223i
\(533\) −12.4946 17.8442i −0.541202 0.772917i
\(534\) 0.769988 + 21.2155i 0.0333206 + 0.918084i
\(535\) −4.02290 1.46421i −0.173925 0.0633035i
\(536\) −18.9190 + 5.86039i −0.817175 + 0.253130i
\(537\) −6.85520 + 18.5071i −0.295824 + 0.798639i
\(538\) −3.44982 + 25.8678i −0.148732 + 1.11524i
\(539\) 4.84655 + 4.84655i 0.208756 + 0.208756i
\(540\) 26.4922 + 2.86300i 1.14004 + 0.123204i
\(541\) 27.1044 27.1044i 1.16531 1.16531i 0.182012 0.983296i \(-0.441739\pi\)
0.983296 0.182012i \(-0.0582609\pi\)
\(542\) −8.09000 + 6.18610i −0.347495 + 0.265716i
\(543\) −1.05008 6.15946i −0.0450631 0.264328i
\(544\) −19.1774 25.4322i −0.822222 1.09040i
\(545\) −5.99197 + 16.4628i −0.256668 + 0.705189i
\(546\) −19.3780 + 5.95353i −0.829303 + 0.254787i
\(547\) −6.09483 + 4.26765i −0.260596 + 0.182472i −0.696572 0.717487i \(-0.745292\pi\)
0.435976 + 0.899958i \(0.356403\pi\)
\(548\) 25.5237 17.7443i 1.09032 0.758000i
\(549\) 17.0319 + 37.6344i 0.726905 + 1.60620i
\(550\) −6.68435 3.49395i −0.285022 0.148983i
\(551\) 4.15293 + 11.4101i 0.176921 + 0.486086i
\(552\) 11.8301 + 23.3325i 0.503521 + 0.993099i
\(553\) 4.57905 + 5.45710i 0.194721 + 0.232060i
\(554\) −44.3272 14.0583i −1.88328 0.597279i
\(555\) 28.5150 2.33178i 1.21040 0.0989785i
\(556\) 32.0477 26.7081i 1.35913 1.13268i
\(557\) 8.91279 33.2630i 0.377647 1.40940i −0.471792 0.881710i \(-0.656393\pi\)
0.849439 0.527687i \(-0.176941\pi\)
\(558\) 21.3607 + 28.6018i 0.904269 + 1.21081i
\(559\) 32.9831 + 19.0428i 1.39504 + 0.805425i
\(560\) −6.07029 + 22.0602i −0.256517 + 0.932212i
\(561\) 0.187467 33.0375i 0.00791488 1.39484i
\(562\) −2.47188 1.58061i −0.104270 0.0666739i
\(563\) −16.1367 11.2991i −0.680083 0.476199i 0.181781 0.983339i \(-0.441814\pi\)
−0.861864 + 0.507140i \(0.830703\pi\)
\(564\) 4.43249 7.51954i 0.186642 0.316630i
\(565\) 0.940060 + 10.7449i 0.0395486 + 0.452043i
\(566\) 35.7339 22.6806i 1.50201 0.953338i
\(567\) 10.4309 17.1555i 0.438055 0.720462i
\(568\) −14.5042 + 18.7062i −0.608585 + 0.784894i
\(569\) −8.04250 6.74846i −0.337159 0.282910i 0.458450 0.888720i \(-0.348405\pi\)
−0.795609 + 0.605810i \(0.792849\pi\)
\(570\) 9.10246 28.1457i 0.381260 1.17890i
\(571\) −9.44733 6.61509i −0.395358 0.276833i 0.358945 0.933359i \(-0.383136\pi\)
−0.754304 + 0.656526i \(0.772025\pi\)
\(572\) 17.7128 + 17.8323i 0.740609 + 0.745606i
\(573\) −21.0869 + 20.8489i −0.880918 + 0.870977i
\(574\) −7.11814 + 17.1033i −0.297105 + 0.713879i
\(575\) 4.20354 7.28074i 0.175300 0.303628i
\(576\) −19.9502 + 13.3413i −0.831258 + 0.555887i
\(577\) 16.5843 + 28.7249i 0.690415 + 1.19583i 0.971702 + 0.236211i \(0.0759055\pi\)
−0.281287 + 0.959624i \(0.590761\pi\)
\(578\) −20.6231 + 2.67981i −0.857807 + 0.111466i
\(579\) −11.8505 + 0.969060i −0.492490 + 0.0402728i
\(580\) −12.7815 + 3.37877i −0.530723 + 0.140296i
\(581\) 0.883543 10.0989i 0.0366556 0.418975i
\(582\) 20.9673 26.9129i 0.869122 1.11558i
\(583\) −13.6079 + 4.95288i −0.563582 + 0.205127i
\(584\) −23.9487 3.27587i −0.991003 0.135556i
\(585\) 4.63604 + 28.1572i 0.191677 + 1.16416i
\(586\) −0.682701 16.2638i −0.0282021 0.671852i
\(587\) 27.3084 19.1215i 1.12714 0.789229i 0.147312 0.989090i \(-0.452938\pi\)
0.979824 + 0.199861i \(0.0640489\pi\)
\(588\) −5.32821 4.55358i −0.219732 0.187786i
\(589\) 35.9164 16.7481i 1.47991 0.690093i
\(590\) 1.31317 28.9592i 0.0540623 1.19223i
\(591\) 12.0938 2.06177i 0.497470 0.0848098i
\(592\) −18.3434 + 18.0983i −0.753908 + 0.743835i
\(593\) 15.0796i 0.619246i −0.950859 0.309623i \(-0.899797\pi\)
0.950859 0.309623i \(-0.100203\pi\)
\(594\) −24.8451 1.55079i −1.01940 0.0636295i
\(595\) 22.7745 + 22.7745i 0.933664 + 0.933664i
\(596\) −16.5488 6.08635i −0.677864 0.249307i
\(597\) −32.6543 + 15.0020i −1.33645 + 0.613990i
\(598\) −20.6871 + 18.8923i −0.845958 + 0.772565i
\(599\) −8.54899 + 23.4881i −0.349302 + 0.959700i 0.633289 + 0.773916i \(0.281705\pi\)
−0.982591 + 0.185784i \(0.940518\pi\)
\(600\) 7.09369 + 3.02778i 0.289599 + 0.123609i
\(601\) −8.34345 1.47117i −0.340336 0.0600105i 0.000868013 1.00000i \(-0.499724\pi\)
−0.341204 + 0.939989i \(0.610835\pi\)
\(602\) −1.35839 32.3605i −0.0553637 1.31892i
\(603\) 20.2285 + 5.66701i 0.823767 + 0.230778i
\(604\) −1.79757 21.3738i −0.0731422 0.869689i
\(605\) 1.10518 + 0.515354i 0.0449320 + 0.0209521i
\(606\) 17.5496 + 7.42099i 0.712904 + 0.301457i
\(607\) 11.1484 + 13.2861i 0.452499 + 0.539268i 0.943272 0.332020i \(-0.107730\pi\)
−0.490773 + 0.871287i \(0.663286\pi\)
\(608\) 9.98862 + 24.6999i 0.405092 + 1.00171i
\(609\) −1.78543 + 9.80017i −0.0723493 + 0.397123i
\(610\) 6.43400 + 49.5142i 0.260505 + 2.00477i
\(611\) 9.02928 + 2.41939i 0.365286 + 0.0978780i
\(612\) 2.44910 + 33.6956i 0.0989989 + 1.36206i
\(613\) 24.8573 6.66050i 1.00398 0.269015i 0.280867 0.959747i \(-0.409378\pi\)
0.723111 + 0.690732i \(0.242711\pi\)
\(614\) 34.3983 14.1805i 1.38820 0.572279i
\(615\) 22.5097 + 13.1668i 0.907677 + 0.530937i
\(616\) 4.73156 20.8446i 0.190640 0.839852i
\(617\) 0.0475097 + 0.269441i 0.00191267 + 0.0108473i 0.985749 0.168222i \(-0.0538025\pi\)
−0.983836 + 0.179069i \(0.942691\pi\)
\(618\) 9.28235 1.98633i 0.373391 0.0799019i
\(619\) 5.86512 0.513132i 0.235739 0.0206245i 0.0313260 0.999509i \(-0.490027\pi\)
0.204413 + 0.978885i \(0.434471\pi\)
\(620\) 14.6212 + 40.5955i 0.587201 + 1.63036i
\(621\) 2.88849 27.5964i 0.115911 1.10740i
\(622\) −3.90419 + 17.4716i −0.156544 + 0.700547i
\(623\) 14.8111 + 12.4280i 0.593395 + 0.497918i
\(624\) −19.4827 16.7639i −0.779931 0.671093i
\(625\) 5.27773 + 29.9315i 0.211109 + 1.19726i
\(626\) 10.3040 16.1142i 0.411831 0.644053i
\(627\) −7.30380 + 26.6523i −0.291686 + 1.06439i
\(628\) −0.927182 5.36371i −0.0369986 0.214035i
\(629\) 9.38848 + 35.0383i 0.374343 + 1.39707i
\(630\) 18.1044 16.1607i 0.721295 0.643858i
\(631\) 20.1923 + 34.9740i 0.803842 + 1.39229i 0.917070 + 0.398726i \(0.130547\pi\)
−0.113228 + 0.993569i \(0.536119\pi\)
\(632\) −2.75938 + 8.60013i −0.109762 + 0.342095i
\(633\) −15.8275 + 5.65923i −0.629085 + 0.224934i
\(634\) 20.4015 + 6.47029i 0.810247 + 0.256968i
\(635\) −29.2356 2.55779i −1.16018 0.101503i
\(636\) 13.4770 6.13678i 0.534398 0.243339i
\(637\) 3.17218 6.80276i 0.125686 0.269535i
\(638\) 11.7854 3.69415i 0.466588 0.146253i
\(639\) 23.6882 8.31861i 0.937092 0.329079i
\(640\) −27.7671 + 8.39698i −1.09759 + 0.331920i
\(641\) −20.3611 3.59021i −0.804214 0.141805i −0.243593 0.969877i \(-0.578326\pi\)
−0.560621 + 0.828073i \(0.689437\pi\)
\(642\) −3.98623 0.914538i −0.157324 0.0360940i
\(643\) −20.6120 44.2027i −0.812860 1.74318i −0.654869 0.755742i \(-0.727276\pi\)
−0.157991 0.987441i \(-0.550502\pi\)
\(644\) 22.9925 + 6.24376i 0.906032 + 0.246039i
\(645\) −45.3964 4.23137i −1.78748 0.166610i
\(646\) 37.1761 + 4.95792i 1.46267 + 0.195067i
\(647\) 31.6381i 1.24382i −0.783088 0.621911i \(-0.786356\pi\)
0.783088 0.621911i \(-0.213644\pi\)
\(648\) 25.4526 0.404536i 0.999874 0.0158917i
\(649\) 27.0818i 1.06305i
\(650\) −1.09190 + 8.18738i −0.0428277 + 0.321136i
\(651\) 32.3713 + 3.01730i 1.26873 + 0.118257i
\(652\) 28.3245 16.2264i 1.10927 0.635476i
\(653\) 3.09991 + 6.64778i 0.121309 + 0.260148i 0.957580 0.288169i \(-0.0930465\pi\)
−0.836271 + 0.548317i \(0.815269\pi\)
\(654\) −3.74254 + 16.3127i −0.146345 + 0.637879i
\(655\) −30.1429 5.31500i −1.17778 0.207674i
\(656\) −23.1579 + 3.92297i −0.904163 + 0.153166i
\(657\) 19.4515 + 16.7016i 0.758876 + 0.651590i
\(658\) −2.37774 7.58568i −0.0926941 0.295721i
\(659\) −17.8315 + 38.2397i −0.694616 + 1.48961i 0.169084 + 0.985602i \(0.445919\pi\)
−0.863700 + 0.504006i \(0.831859\pi\)
\(660\) −28.1801 10.5461i −1.09691 0.410505i
\(661\) 2.57621 + 0.225389i 0.100203 + 0.00876663i 0.137147 0.990551i \(-0.456207\pi\)
−0.0369439 + 0.999317i \(0.511762\pi\)
\(662\) 5.76701 18.1840i 0.224141 0.706740i
\(663\) −34.0683 + 12.1814i −1.32310 + 0.473086i
\(664\) 11.4306 5.87730i 0.443592 0.228083i
\(665\) −13.4703 23.3313i −0.522357 0.904750i
\(666\) 26.7588 5.56752i 1.03688 0.215737i
\(667\) 3.56307 + 13.2976i 0.137963 + 0.514884i
\(668\) −4.53039 3.19497i −0.175286 0.123617i
\(669\) 4.42723 16.1554i 0.171167 0.624604i
\(670\) 21.3921 + 13.6789i 0.826450 + 0.528462i
\(671\) −8.09992 45.9370i −0.312694 1.77338i
\(672\) −3.15785 + 21.6285i −0.121817 + 0.834337i
\(673\) −20.3151 17.0464i −0.783091 0.657091i 0.160934 0.986965i \(-0.448549\pi\)
−0.944025 + 0.329874i \(0.892994\pi\)
\(674\) −3.70850 0.828699i −0.142846 0.0319203i
\(675\) −4.57751 6.78014i −0.176188 0.260968i
\(676\) 0.649180 1.38004i 0.0249685 0.0530783i
\(677\) −40.0832 + 3.50682i −1.54052 + 0.134778i −0.825531 0.564357i \(-0.809124\pi\)
−0.714990 + 0.699135i \(0.753569\pi\)
\(678\) 2.15615 + 10.0759i 0.0828064 + 0.386964i
\(679\) −5.39547 30.5992i −0.207059 1.17429i
\(680\) −9.03939 + 39.8225i −0.346645 + 1.52712i
\(681\) 28.8451 + 16.8727i 1.10535 + 0.646563i
\(682\) −15.3632 37.2671i −0.588287 1.42703i
\(683\) −41.2359 + 11.0491i −1.57785 + 0.422783i −0.938259 0.345935i \(-0.887562\pi\)
−0.639588 + 0.768717i \(0.720895\pi\)
\(684\) 5.31604 27.7548i 0.203264 1.06123i
\(685\) −38.4948 10.3146i −1.47081 0.394102i
\(686\) −28.2303 + 3.66831i −1.07784 + 0.140057i
\(687\) 4.12311 22.6316i 0.157306 0.863449i
\(688\) 33.7961 23.3272i 1.28846 0.889340i
\(689\) 10.1938 + 12.1485i 0.388352 + 0.462820i
\(690\) 13.0621 30.8900i 0.497264 1.17596i
\(691\) 11.9905 + 5.59124i 0.456138 + 0.212701i 0.637087 0.770792i \(-0.280139\pi\)
−0.180949 + 0.983493i \(0.557917\pi\)
\(692\) 32.8552 38.8890i 1.24897 1.47834i
\(693\) −16.2120 + 15.8482i −0.615844 + 0.602023i
\(694\) −18.4920 + 0.776234i −0.701948 + 0.0294654i
\(695\) −52.6709 9.28730i −1.99792 0.352287i
\(696\) −11.7196 + 4.70790i −0.444230 + 0.178452i
\(697\) −11.3084 + 31.0695i −0.428335 + 1.17684i
\(698\) 3.43997 + 3.76676i 0.130205 + 0.142574i
\(699\) 30.7236 14.1150i 1.16207 0.533877i
\(700\) 6.37622 2.94722i 0.240998 0.111394i
\(701\) −15.7474 15.7474i −0.594770 0.594770i 0.344146 0.938916i \(-0.388168\pi\)
−0.938916 + 0.344146i \(0.888168\pi\)
\(702\) 7.70992 + 26.1483i 0.290992 + 0.986905i
\(703\) 30.3419i 1.14437i
\(704\) 25.5583 9.01157i 0.963266 0.339636i
\(705\) −11.0313 + 1.88064i −0.415463 + 0.0708289i
\(706\) 12.8106 + 0.580902i 0.482133 + 0.0218625i
\(707\) 15.7275 7.33386i 0.591494 0.275818i
\(708\) −2.16426 27.6090i −0.0813379 1.03761i
\(709\) 23.9938 16.8006i 0.901107 0.630962i −0.0284685 0.999595i \(-0.509063\pi\)
0.929575 + 0.368633i \(0.120174\pi\)
\(710\) 30.3196 1.27272i 1.13787 0.0477641i
\(711\) 7.40800 6.07413i 0.277822 0.227798i
\(712\) −3.32221 + 24.2875i −0.124505 + 0.910213i
\(713\) 42.2210 15.3672i 1.58119 0.575505i
\(714\) 24.2722 + 18.9100i 0.908364 + 0.707688i
\(715\) 2.80841 32.1003i 0.105029 1.20048i
\(716\) −11.4608 + 19.6975i −0.428311 + 0.736129i
\(717\) −29.3288 + 2.39832i −1.09530 + 0.0895671i
\(718\) −1.20395 9.26521i −0.0449308 0.345775i
\(719\) 14.8093 + 25.6504i 0.552293 + 0.956599i 0.998109 + 0.0614745i \(0.0195803\pi\)
−0.445816 + 0.895125i \(0.647086\pi\)
\(720\) 29.5715 + 8.49933i 1.10206 + 0.316751i
\(721\) 4.32261 7.48697i 0.160982 0.278829i
\(722\) −4.15593 1.72963i −0.154668 0.0643703i
\(723\) −31.1465 + 30.7951i −1.15835 + 1.14528i
\(724\) 0.0242595 7.21491i 0.000901596 0.268140i
\(725\) 3.32480 + 2.32805i 0.123480 + 0.0864617i
\(726\) 1.10842 + 0.358468i 0.0411374 + 0.0133040i
\(727\) −1.77350 1.48814i −0.0657754 0.0551921i 0.609307 0.792934i \(-0.291448\pi\)
−0.675083 + 0.737742i \(0.735892\pi\)
\(728\) −23.2229 + 2.93827i −0.860698 + 0.108900i
\(729\) −22.9096 14.2881i −0.848504 0.529189i
\(730\) 16.6063 + 26.1636i 0.614626 + 0.968359i
\(731\) −5.03818 57.5867i −0.186344 2.12992i
\(732\) 11.9287 + 46.1839i 0.440897 + 1.70700i
\(733\) 29.3583 + 20.5569i 1.08437 + 0.759287i 0.972142 0.234394i \(-0.0753107\pi\)
0.112233 + 0.993682i \(0.464200\pi\)
\(734\) 10.9870 17.1823i 0.405537 0.634210i
\(735\) −0.0509870 + 8.98547i −0.00188068 + 0.331434i
\(736\) 8.84100 + 28.8845i 0.325884 + 1.06470i
\(737\) −20.5431 11.8606i −0.756716 0.436890i
\(738\) 22.8901 + 9.83271i 0.842594 + 0.361947i
\(739\) −4.80324 + 17.9259i −0.176690 + 0.659417i 0.819567 + 0.572983i \(0.194214\pi\)
−0.996258 + 0.0864339i \(0.972453\pi\)
\(740\) 32.9006 + 2.98994i 1.20945 + 0.109912i
\(741\) 30.1629 2.46653i 1.10806 0.0906104i
\(742\) 4.07713 12.8556i 0.149676 0.471944i
\(743\) −9.99252 11.9086i −0.366590 0.436885i 0.550944 0.834542i \(-0.314268\pi\)
−0.917534 + 0.397657i \(0.869823\pi\)
\(744\) 18.6405 + 36.7648i 0.683394 + 1.34786i
\(745\) 7.73149 + 21.2421i 0.283260 + 0.778250i
\(746\) −7.60646 + 14.5521i −0.278492 + 0.532790i
\(747\) −13.5665 1.34221i −0.496372 0.0491090i
\(748\) 6.75079 37.5470i 0.246834 1.37285i
\(749\) −3.05113 + 2.13643i −0.111486 + 0.0780633i
\(750\) 6.31860 + 20.5663i 0.230723 + 0.750975i
\(751\) 6.33011 17.3918i 0.230989 0.634637i −0.769000 0.639248i \(-0.779246\pi\)
0.999989 + 0.00461145i \(0.00146787\pi\)
\(752\) 6.53047 7.67726i 0.238142 0.279961i
\(753\) −1.22188 7.16719i −0.0445277 0.261187i
\(754\) −8.21582 10.7444i −0.299202 0.391289i
\(755\) −19.4444 + 19.4444i −0.707655 + 0.707655i
\(756\) 15.2611 17.4523i 0.555041 0.634734i
\(757\) −23.4001 23.4001i −0.850492 0.850492i 0.139702 0.990194i \(-0.455386\pi\)
−0.990194 + 0.139702i \(0.955386\pi\)
\(758\) −8.38200 1.11785i −0.304448 0.0406021i
\(759\) −10.8830 + 29.3809i −0.395027 + 1.06646i
\(760\) 15.9247 30.2179i 0.577648 1.09612i
\(761\) −45.8398 16.6843i −1.66169 0.604807i −0.671066 0.741398i \(-0.734163\pi\)
−0.990627 + 0.136591i \(0.956385\pi\)
\(762\) −28.0176 + 1.01686i −1.01497 + 0.0368369i
\(763\) 8.74284 + 12.4861i 0.316512 + 0.452026i
\(764\) −28.1145 + 19.5454i −1.01715 + 0.707129i
\(765\) 30.9722 30.2771i 1.11980 1.09467i
\(766\) −10.8503 34.6157i −0.392038 1.25071i
\(767\) 27.8693 10.1436i 1.00630 0.366263i
\(768\) −25.3357 + 11.2295i −0.914224 + 0.405210i
\(769\) 41.5423 34.8581i 1.49805 1.25701i 0.614288 0.789082i \(-0.289443\pi\)
0.883764 0.467933i \(-0.155001\pi\)
\(770\) −24.3281 + 12.6125i −0.876725 + 0.454522i
\(771\) −35.8708 + 24.8149i −1.29186 + 0.893686i
\(772\) −13.6731 1.24258i −0.492106 0.0447216i
\(773\) 0.921911 + 0.247025i 0.0331588 + 0.00888489i 0.275360 0.961341i \(-0.411203\pi\)
−0.242201 + 0.970226i \(0.577870\pi\)
\(774\) −43.5356 + 1.33275i −1.56485 + 0.0479048i
\(775\) 6.62347 11.4722i 0.237922 0.412093i
\(776\) 29.1784 26.4676i 1.04744 0.950130i
\(777\) 12.5683 21.4864i 0.450884 0.770819i
\(778\) −18.8072 + 4.13630i −0.674271 + 0.148293i
\(779\) 15.8630 22.6547i 0.568349 0.811687i
\(780\) −0.297764 + 32.9496i −0.0106617 + 1.17978i
\(781\) −28.2420 + 2.47085i −1.01058 + 0.0884140i
\(782\) 41.4988 + 9.27330i 1.48400 + 0.331612i
\(783\) 13.1510 + 2.55041i 0.469977 + 0.0911443i
\(784\) −5.16040 6.23459i −0.184300 0.222664i
\(785\) −4.48563 + 5.34577i −0.160099 + 0.190799i
\(786\) −29.2023 1.49028i −1.04161 0.0531565i
\(787\) 17.4613 24.9373i 0.622427 0.888917i −0.376876 0.926264i \(-0.623002\pi\)
0.999302 + 0.0373465i \(0.0118905\pi\)
\(788\) 14.1661 + 0.0476321i 0.504645 + 0.00169682i
\(789\) −5.91241 + 21.5750i −0.210487 + 0.768089i
\(790\) 10.7053 4.41319i 0.380876 0.157014i
\(791\) 8.12707 + 4.69216i 0.288965 + 0.166834i
\(792\) −27.9573 6.68059i −0.993420 0.237385i
\(793\) −44.2388 + 25.5413i −1.57097 + 0.906998i
\(794\) 7.76334 10.0822i 0.275511 0.357806i
\(795\) −17.1603 8.12083i −0.608612 0.288016i
\(796\) −40.1168 + 10.6048i −1.42190 + 0.375878i
\(797\) 44.5395 + 3.89670i 1.57767 + 0.138028i 0.842063 0.539380i \(-0.181341\pi\)
0.735608 + 0.677408i \(0.236897\pi\)
\(798\) −15.5170 20.5332i −0.549297 0.726867i
\(799\) −4.85263 13.3325i −0.171674 0.471670i
\(800\) 7.47078 + 4.84817i 0.264132 + 0.171409i
\(801\) 16.9379 19.7267i 0.598470 0.697010i
\(802\) −10.7004 9.83825i −0.377844 0.347401i
\(803\) −16.6051 23.7145i −0.585980 0.836866i
\(804\) 21.8909 + 10.4497i 0.772031 + 0.368534i
\(805\) −12.9087 27.6828i −0.454972 0.975690i
\(806\) −32.5964 + 29.7684i −1.14816 + 1.04855i
\(807\) 24.6005 20.4055i 0.865978 0.718308i
\(808\) 18.4963 + 11.9150i 0.650697 + 0.419169i
\(809\) −2.58392 −0.0908458 −0.0454229 0.998968i \(-0.514464\pi\)
−0.0454229 + 0.998968i \(0.514464\pi\)
\(810\) −21.4549 24.5914i −0.753848 0.864054i
\(811\) −29.1090 + 29.1090i −1.02216 + 1.02216i −0.0224071 + 0.999749i \(0.507133\pi\)
−0.999749 + 0.0224071i \(0.992867\pi\)
\(812\) −3.97042 + 10.7955i −0.139334 + 0.378849i
\(813\) 12.4191 + 1.15758i 0.435557 + 0.0405979i
\(814\) −30.8311 1.39805i −1.08063 0.0490017i
\(815\) −39.3256 14.3134i −1.37752 0.501375i
\(816\) −3.88162 + 38.8174i −0.135884 + 1.35888i
\(817\) −8.39639 + 47.6183i −0.293752 + 1.66595i
\(818\) −4.28511 3.93985i −0.149825 0.137754i
\(819\) 22.3813 + 10.7474i 0.782065 + 0.375546i
\(820\) 23.0019 + 19.4331i 0.803262 + 0.678633i
\(821\) 3.04624 6.53268i 0.106314 0.227992i −0.845953 0.533258i \(-0.820968\pi\)
0.952267 + 0.305266i \(0.0987453\pi\)
\(822\) −37.7088 5.24691i −1.31524 0.183007i
\(823\) 15.3288 12.8624i 0.534329 0.448356i −0.335264 0.942124i \(-0.608825\pi\)
0.869593 + 0.493769i \(0.164381\pi\)
\(824\) 10.9528 0.422876i 0.381560 0.0147316i
\(825\) 3.11012 + 8.69825i 0.108281 + 0.302834i
\(826\) −19.9840 15.3877i −0.695331 0.535406i
\(827\) 3.17280 11.8410i 0.110329 0.411753i −0.888566 0.458749i \(-0.848298\pi\)
0.998895 + 0.0469952i \(0.0149645\pi\)
\(828\) 8.74682 30.8225i 0.303973 1.07116i
\(829\) −5.19578 19.3909i −0.180457 0.673475i −0.995558 0.0941551i \(-0.969985\pi\)
0.815101 0.579319i \(-0.196682\pi\)
\(830\) −15.2130 6.33143i −0.528052 0.219767i
\(831\) 28.1969 + 49.4848i 0.978139 + 1.71661i
\(832\) −18.8466 22.9262i −0.653387 0.794823i
\(833\) −11.2196 + 1.97832i −0.388736 + 0.0685447i
\(834\) −51.0273 2.60408i −1.76693 0.0901718i
\(835\) 0.619427 + 7.08009i 0.0214362 + 0.245017i
\(836\) −13.5829 + 28.8748i −0.469776 + 0.998657i
\(837\) 4.55136 43.4833i 0.157318 1.50300i
\(838\) 12.3587 7.84417i 0.426924 0.270973i
\(839\) 14.7825 17.6171i 0.510349 0.608211i −0.447921 0.894073i \(-0.647836\pi\)
0.958271 + 0.285862i \(0.0922800\pi\)
\(840\) 23.7938 14.8022i 0.820963 0.510725i
\(841\) 22.0140 3.88167i 0.759104 0.133851i
\(842\) 7.41489 + 33.7145i 0.255534 + 1.16188i
\(843\) 0.910338 + 3.47621i 0.0313537 + 0.119727i
\(844\) −19.1255 + 3.30607i −0.658326 + 0.113800i
\(845\) −1.88860 + 0.506049i −0.0649698 + 0.0174086i
\(846\) −10.2367 + 3.08156i −0.351945 + 0.105946i
\(847\) 0.918822 0.530482i 0.0315711 0.0182276i
\(848\) 16.5460 4.31445i 0.568193 0.148159i
\(849\) −50.9967 9.29077i −1.75020 0.318858i
\(850\) 11.1301 5.77019i 0.381758 0.197916i
\(851\) 2.99823 34.2699i 0.102778 1.17476i
\(852\) 28.5943 4.77593i 0.979624 0.163621i
\(853\) −17.6836 8.24602i −0.605476 0.282338i 0.0956052 0.995419i \(-0.469521\pi\)
−0.701082 + 0.713081i \(0.747299\pi\)
\(854\) 38.4997 + 20.1240i 1.31743 + 0.688629i
\(855\) −31.5790 + 17.7574i −1.07998 + 0.607290i
\(856\) −4.35384 1.82920i −0.148811 0.0625207i
\(857\) −3.10522 + 17.6106i −0.106072 + 0.601567i 0.884714 + 0.466134i \(0.154354\pi\)
−0.990787 + 0.135433i \(0.956758\pi\)
\(858\) −1.11650 30.7629i −0.0381165 1.05023i
\(859\) 19.4454 9.06753i 0.663468 0.309380i −0.0615563 0.998104i \(-0.519606\pi\)
0.725024 + 0.688724i \(0.241829\pi\)
\(860\) −50.8065 13.7968i −1.73249 0.470467i
\(861\) 20.6172 9.47192i 0.702633 0.322802i
\(862\) −10.8741 14.2209i −0.370374 0.484364i
\(863\) 37.9394 1.29147 0.645737 0.763560i \(-0.276550\pi\)
0.645737 + 0.763560i \(0.276550\pi\)
\(864\) 29.0354 + 4.57641i 0.987806 + 0.155693i
\(865\) −65.2679 −2.21918
\(866\) 20.8385 + 27.2520i 0.708121 + 0.926060i
\(867\) 20.7809 + 14.7273i 0.705755 + 0.500167i
\(868\) 36.2291 + 9.83823i 1.22969 + 0.333931i
\(869\) −9.80394 + 4.57165i −0.332576 + 0.155083i
\(870\) 14.3069 + 7.58198i 0.485050 + 0.257053i
\(871\) −4.51095 + 25.5829i −0.152848 + 0.866843i
\(872\) −7.48558 + 17.8171i −0.253494 + 0.603363i
\(873\) −41.2288 + 6.78826i −1.39538 + 0.229748i
\(874\) −31.5217 16.4766i −1.06624 0.557328i
\(875\) 17.7588 + 8.28106i 0.600357 + 0.279951i
\(876\) 18.8235 + 22.8491i 0.635986 + 0.772000i
\(877\) −3.18787 + 36.4376i −0.107647 + 1.23041i 0.729712 + 0.683755i \(0.239654\pi\)
−0.837358 + 0.546654i \(0.815901\pi\)
\(878\) −16.2410 + 8.41988i −0.548109 + 0.284157i
\(879\) −12.9014 + 15.1993i −0.435155 + 0.512661i
\(880\) −29.9713 17.5737i −1.01033 0.592411i
\(881\) 38.7225 22.3565i 1.30460 0.753208i 0.323407 0.946260i \(-0.395172\pi\)
0.981189 + 0.193052i \(0.0618385\pi\)
\(882\) 1.00947 + 8.52457i 0.0339906 + 0.287037i
\(883\) 9.70507 2.60047i 0.326602 0.0875126i −0.0917927 0.995778i \(-0.529260\pi\)
0.418394 + 0.908266i \(0.362593\pi\)
\(884\) −41.1673 + 7.11626i −1.38460 + 0.239346i
\(885\) −25.2472 + 24.9623i −0.848676 + 0.839099i
\(886\) 12.4249 + 56.4944i 0.417423 + 1.89797i
\(887\) −12.1363 + 2.13995i −0.407496 + 0.0718526i −0.373639 0.927574i \(-0.621890\pi\)
−0.0338569 + 0.999427i \(0.510779\pi\)
\(888\) 31.5430 1.03862i 1.05851 0.0348539i
\(889\) −16.4127 + 19.5598i −0.550463 + 0.656016i
\(890\) 26.5338 16.8412i 0.889415 0.564520i
\(891\) 21.0635 + 22.0420i 0.705654 + 0.738436i
\(892\) 8.23337 17.5026i 0.275673 0.586031i
\(893\) 1.03435 + 11.8226i 0.0346131 + 0.395630i
\(894\) 9.83045 + 19.2281i 0.328779 + 0.643085i
\(895\) 28.7723 5.07334i 0.961753 0.169583i
\(896\) −7.87232 + 23.9801i −0.262996 + 0.801118i
\(897\) 34.3114 + 0.194696i 1.14563 + 0.00650072i
\(898\) 42.7800 + 17.8044i 1.42759 + 0.594140i
\(899\) 5.61429 + 20.9528i 0.187247 + 0.698816i
\(900\) −3.86579 8.61902i −0.128860 0.287301i
\(901\) 6.22989 23.2503i 0.207548 0.774579i
\(902\) −22.2890 17.1626i −0.742142 0.571451i
\(903\) −25.6703 + 30.2425i −0.854254 + 1.00641i
\(904\) 0.459029 + 11.8892i 0.0152671 + 0.395430i
\(905\) −7.08573 + 5.94563i −0.235538 + 0.197640i
\(906\) −16.1450 + 20.7231i −0.536381 + 0.688480i
\(907\) 3.80958 8.16967i 0.126495 0.271269i −0.832854 0.553493i \(-0.813294\pi\)
0.959349 + 0.282224i \(0.0910722\pi\)
\(908\) 29.4759 + 24.9026i 0.978193 + 0.826422i
\(909\) −9.62176 21.2606i −0.319134 0.705169i
\(910\) 22.0914 + 20.3115i 0.732323 + 0.673319i
\(911\) −1.38700 + 7.86607i −0.0459534 + 0.260615i −0.999125 0.0418141i \(-0.986686\pi\)
0.953172 + 0.302429i \(0.0977974\pi\)
\(912\) 11.5398 30.5224i 0.382121 1.01070i
\(913\) 14.4655 + 5.26502i 0.478739 + 0.174247i
\(914\) −0.218947 0.00992824i −0.00724211 0.000328397i
\(915\) 35.3591 49.8930i 1.16893 1.64941i
\(916\) 9.16891 24.9302i 0.302949 0.823718i
\(917\) −18.8305 + 18.8305i −0.621837 + 0.621837i
\(918\) 25.7985 32.3500i 0.851478 1.06771i
\(919\) −2.03955 −0.0672785 −0.0336393 0.999434i \(-0.510710\pi\)
−0.0336393 + 0.999434i \(0.510710\pi\)
\(920\) 20.9722 32.5562i 0.691433 1.07335i
\(921\) −42.7313 15.8281i −1.40804 0.521553i
\(922\) 25.8367 23.5952i 0.850887 0.777067i
\(923\) 13.1208 + 28.1377i 0.431877 + 0.926163i
\(924\) −21.5792 + 14.8211i −0.709903 + 0.487579i
\(925\) −5.81746 8.30819i −0.191277 0.273172i
\(926\) −19.2533 17.7020i −0.632701 0.581724i
\(927\) −10.0017 5.92683i −0.328499 0.194663i
\(928\) −14.2640 + 3.03669i −0.468240 + 0.0996843i
\(929\) −16.5309 45.4182i −0.542360 1.49012i −0.843811 0.536640i \(-0.819693\pi\)
0.301451 0.953482i \(-0.402529\pi\)
\(930\) 20.5817 48.6730i 0.674902 1.59605i
\(931\) 9.49324 + 0.830551i 0.311128 + 0.0272202i
\(932\) 37.7448 9.97779i 1.23637 0.326834i
\(933\) 18.0318 12.4741i 0.590334 0.408384i
\(934\) 3.66384 4.75823i 0.119885 0.155694i
\(935\) −42.3557 + 24.4541i −1.38518 + 0.799733i
\(936\) 3.59667 + 31.2725i 0.117561 + 1.02217i
\(937\) 19.8964 + 11.4872i 0.649988 + 0.375271i 0.788452 0.615097i \(-0.210883\pi\)
−0.138463 + 0.990368i \(0.544216\pi\)
\(938\) 20.4245 8.41990i 0.666883 0.274920i
\(939\) −22.6615 + 5.93451i −0.739529 + 0.193665i
\(940\) −12.9216 0.0434475i −0.421455 0.00141710i
\(941\) −4.46412 + 6.37543i −0.145526 + 0.207833i −0.885297 0.465026i \(-0.846045\pi\)
0.739771 + 0.672859i \(0.234934\pi\)
\(942\) −3.62322 + 5.59605i −0.118051 + 0.182329i
\(943\) 20.1551 24.0200i 0.656342 0.782198i
\(944\) 3.00122 31.8368i 0.0976814 1.03620i
\(945\) −29.7178 0.505934i −0.966721 0.0164580i
\(946\) 47.9991 + 10.7258i 1.56059 + 0.348727i
\(947\) 22.5758 1.97513i 0.733616 0.0641831i 0.285776 0.958297i \(-0.407749\pi\)
0.447840 + 0.894113i \(0.352193\pi\)
\(948\) 9.62944 5.44413i 0.312750 0.176817i
\(949\) −18.1846 + 25.9702i −0.590296 + 0.843030i
\(950\) −10.2418 + 2.25250i −0.332288 + 0.0730807i
\(951\) −12.9775 22.7752i −0.420826 0.738538i
\(952\) 23.8706 + 26.3154i 0.773649 + 0.852887i
\(953\) 0.983838 1.70406i 0.0318696 0.0551998i −0.849651 0.527346i \(-0.823187\pi\)
0.881520 + 0.472146i \(0.156521\pi\)
\(954\) −17.2246 5.67867i −0.557667 0.183854i
\(955\) 42.4022 + 11.3616i 1.37210 + 0.367654i
\(956\) −33.8396 3.07527i −1.09445 0.0994612i
\(957\) −13.6728 6.47045i −0.441980 0.209160i
\(958\) 2.60564 1.35085i 0.0841845 0.0436439i
\(959\) −26.5617 + 22.2879i −0.857722 + 0.719714i
\(960\) 31.9592 + 15.5207i 1.03148 + 0.500927i
\(961\) 37.3967 13.6113i 1.20634 0.439073i
\(962\) 10.1092 + 32.2512i 0.325934 + 1.03982i
\(963\) 2.82627 + 4.13543i 0.0910752 + 0.133262i
\(964\) −41.5267 + 28.8697i −1.33748 + 0.929830i
\(965\) 10.0958 + 14.4183i 0.324996 + 0.464143i
\(966\) −15.4969 24.7247i −0.498603 0.795503i
\(967\) 12.4988 + 4.54919i 0.401934 + 0.146292i 0.535074 0.844805i \(-0.320284\pi\)
−0.133140 + 0.991097i \(0.542506\pi\)
\(968\) 1.19003 + 0.627137i 0.0382489 + 0.0201570i
\(969\) −29.3259 35.3547i −0.942082 1.13576i
\(970\) −50.0613 6.67634i −1.60737 0.214364i
\(971\) 37.2480 + 37.2480i 1.19535 + 1.19535i 0.975545 + 0.219802i \(0.0705411\pi\)
0.219802 + 0.975545i \(0.429459\pi\)
\(972\) −23.2350 20.7878i −0.745264 0.666770i
\(973\) −32.9039 + 32.9039i −1.05485 + 1.05485i
\(974\) −10.0816 13.1844i −0.323034 0.422455i
\(975\) 7.78626 6.45851i 0.249360 0.206838i
\(976\) 4.43133 + 54.9001i 0.141843 + 1.75731i
\(977\) −18.0611 + 49.6224i −0.577825 + 1.58756i 0.214012 + 0.976831i \(0.431347\pi\)
−0.791838 + 0.610731i \(0.790875\pi\)
\(978\) −38.9672 8.94002i −1.24603 0.285870i
\(979\) −24.0500 + 16.8400i −0.768642 + 0.538209i
\(980\) −1.83607 + 10.2119i −0.0586510 + 0.326209i
\(981\) 16.9233 11.5659i 0.540320 0.369270i
\(982\) 0.458177 0.876548i 0.0146210 0.0279718i
\(983\) −8.51629 23.3983i −0.271627 0.746290i −0.998243 0.0592462i \(-0.981130\pi\)
0.726616 0.687044i \(-0.241092\pi\)
\(984\) 24.0944 + 15.7154i 0.768102 + 0.500989i
\(985\) −11.6739 13.9124i −0.371962 0.443287i
\(986\) −6.20618 + 19.5687i −0.197645 + 0.623194i
\(987\) −4.16472 + 8.80054i −0.132564 + 0.280124i
\(988\) 34.8020 + 3.16273i 1.10720 + 0.100620i
\(989\) −14.1887 + 52.9531i −0.451176 + 1.68381i
\(990\) 16.5886 + 32.9063i 0.527221 + 1.04583i
\(991\) −52.6117 30.3754i −1.67127 0.964905i −0.966931 0.255037i \(-0.917912\pi\)
−0.704334 0.709869i \(-0.748754\pi\)
\(992\) 13.9307 + 45.5130i 0.442299 + 1.44504i
\(993\) −20.2997 + 11.5670i −0.644192 + 0.367066i
\(994\) 14.2236 22.2440i 0.451145 0.705536i
\(995\) 43.5768 + 30.5128i 1.38148 + 0.967321i
\(996\) −15.1679 4.21149i −0.480613 0.133446i
\(997\) −3.02286 34.5514i −0.0957349 1.09425i −0.880367 0.474293i \(-0.842704\pi\)
0.784632 0.619961i \(-0.212852\pi\)
\(998\) −9.22094 14.5278i −0.291884 0.459870i
\(999\) −28.7007 17.2283i −0.908050 0.545080i
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 432.2.bj.a.11.21 840
16.3 odd 4 inner 432.2.bj.a.227.60 yes 840
27.5 odd 18 inner 432.2.bj.a.59.60 yes 840
432.275 even 36 inner 432.2.bj.a.275.21 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.bj.a.11.21 840 1.1 even 1 trivial
432.2.bj.a.59.60 yes 840 27.5 odd 18 inner
432.2.bj.a.227.60 yes 840 16.3 odd 4 inner
432.2.bj.a.275.21 yes 840 432.275 even 36 inner