Properties

Label 585.2.bt.b.571.15
Level $585$
Weight $2$
Character 585.571
Analytic conductor $4.671$
Analytic rank $0$
Dimension $108$
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] = [585,2,Mod(376,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.376");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bt (of order \(6\), degree \(2\), 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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 571.15
Character \(\chi\) \(=\) 585.571
Dual form 585.2.bt.b.376.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22618 + 0.707937i) q^{2} +(1.65800 + 0.501035i) q^{3} +(0.00235097 - 0.00407201i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.38771 + 0.559399i) q^{6} +(-0.00992873 + 0.00573236i) q^{7} -2.82509i q^{8} +(2.49793 + 1.66143i) q^{9} +O(q^{10})\) \(q+(-1.22618 + 0.707937i) q^{2} +(1.65800 + 0.501035i) q^{3} +(0.00235097 - 0.00407201i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.38771 + 0.559399i) q^{6} +(-0.00992873 + 0.00573236i) q^{7} -2.82509i q^{8} +(2.49793 + 1.66143i) q^{9} -1.41587 q^{10} +(-3.20924 + 1.85286i) q^{11} +(0.00593813 - 0.00557347i) q^{12} +(-3.01269 + 1.98083i) q^{13} +(0.00811630 - 0.0140578i) q^{14} +(1.18535 + 1.26291i) q^{15} +(2.00469 + 3.47223i) q^{16} +4.64895 q^{17} +(-4.23911 - 0.268844i) q^{18} +6.04019i q^{19} +(0.00407201 - 0.00235097i) q^{20} +(-0.0193339 + 0.00452960i) q^{21} +(2.62341 - 4.54388i) q^{22} +(-2.42067 + 4.19273i) q^{23} +(1.41547 - 4.68400i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.29181 - 4.56166i) q^{26} +(3.30913 + 4.00620i) q^{27} +5.39065e-5i q^{28} +(-4.46472 - 7.73312i) q^{29} +(-2.34752 - 0.709403i) q^{30} +(5.72460 + 3.30510i) q^{31} +(-0.0230347 - 0.0132991i) q^{32} +(-6.24926 + 1.46409i) q^{33} +(-5.70047 + 3.29117i) q^{34} -0.0114647 q^{35} +(0.0126379 - 0.00626559i) q^{36} +4.52388i q^{37} +(-4.27608 - 7.40639i) q^{38} +(-5.98751 + 1.77475i) q^{39} +(1.41255 - 2.44660i) q^{40} +(-3.46246 - 1.99905i) q^{41} +(0.0205003 - 0.0192414i) q^{42} +(-0.571044 - 0.989078i) q^{43} +0.0174241i q^{44} +(1.33255 + 2.68781i) q^{45} -6.85474i q^{46} +(8.97044 - 5.17908i) q^{47} +(1.58407 + 6.76137i) q^{48} +(-3.49993 + 6.06206i) q^{49} +(-1.22618 - 0.707937i) q^{50} +(7.70796 + 2.32929i) q^{51} +(0.000983196 + 0.0169246i) q^{52} +2.37762 q^{53} +(-6.89374 - 2.56968i) q^{54} -3.70571 q^{55} +(0.0161944 + 0.0280496i) q^{56} +(-3.02635 + 10.0146i) q^{57} +(10.9491 + 6.32148i) q^{58} +(-1.19273 - 0.688625i) q^{59} +(0.00792930 - 0.00185770i) q^{60} +(-4.33838 - 7.51430i) q^{61} -9.35922 q^{62} +(-0.0343252 - 0.00217690i) q^{63} -7.98110 q^{64} +(-3.59948 + 0.209104i) q^{65} +(6.62626 - 6.21933i) q^{66} +(8.37253 + 4.83388i) q^{67} +(0.0109296 - 0.0189305i) q^{68} +(-6.11418 + 5.73870i) q^{69} +(0.0140578 - 0.00811630i) q^{70} -5.79546i q^{71} +(4.69370 - 7.05688i) q^{72} +1.97265i q^{73} +(-3.20262 - 5.54710i) q^{74} +(0.395091 + 1.68639i) q^{75} +(0.0245957 + 0.0142003i) q^{76} +(0.0212424 - 0.0367930i) q^{77} +(6.08537 - 6.41496i) q^{78} +(-0.376913 - 0.652832i) q^{79} +4.00938i q^{80} +(3.47929 + 8.30027i) q^{81} +5.66082 q^{82} +(-7.33925 + 4.23732i) q^{83} +(-2.70090e-5 + 8.93769e-5i) q^{84} +(4.02611 + 2.32447i) q^{85} +(1.40041 + 0.808527i) q^{86} +(-3.52794 - 15.0585i) q^{87} +(5.23449 + 9.06640i) q^{88} -3.56933i q^{89} +(-3.53675 - 2.35238i) q^{90} +(0.0185574 - 0.0369370i) q^{91} +(0.0113819 + 0.0197140i) q^{92} +(7.83542 + 8.34808i) q^{93} +(-7.33293 + 12.7010i) q^{94} +(-3.02010 + 5.23096i) q^{95} +(-0.0315282 - 0.0335911i) q^{96} +(-0.00405446 + 0.00234084i) q^{97} -9.91094i q^{98} +(-11.0948 - 0.703634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22618 + 0.707937i −0.867043 + 0.500587i −0.866364 0.499412i \(-0.833549\pi\)
−0.000678402 1.00000i \(0.500216\pi\)
\(3\) 1.65800 + 0.501035i 0.957247 + 0.289273i
\(4\) 0.00235097 0.00407201i 0.00117549 0.00203600i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) −2.38771 + 0.559399i −0.974780 + 0.228374i
\(7\) −0.00992873 + 0.00573236i −0.00375271 + 0.00216663i −0.501875 0.864940i \(-0.667356\pi\)
0.498122 + 0.867107i \(0.334023\pi\)
\(8\) 2.82509i 0.998821i
\(9\) 2.49793 + 1.66143i 0.832643 + 0.553811i
\(10\) −1.41587 −0.447739
\(11\) −3.20924 + 1.85286i −0.967622 + 0.558657i −0.898510 0.438952i \(-0.855350\pi\)
−0.0691115 + 0.997609i \(0.522016\pi\)
\(12\) 0.00593813 0.00557347i 0.00171419 0.00160892i
\(13\) −3.01269 + 1.98083i −0.835570 + 0.549384i
\(14\) 0.00811630 0.0140578i 0.00216917 0.00375712i
\(15\) 1.18535 + 1.26291i 0.306057 + 0.326082i
\(16\) 2.00469 + 3.47223i 0.501173 + 0.868057i
\(17\) 4.64895 1.12754 0.563768 0.825933i \(-0.309351\pi\)
0.563768 + 0.825933i \(0.309351\pi\)
\(18\) −4.23911 0.268844i −0.999167 0.0633671i
\(19\) 6.04019i 1.38572i 0.721074 + 0.692858i \(0.243649\pi\)
−0.721074 + 0.692858i \(0.756351\pi\)
\(20\) 0.00407201 0.00235097i 0.000910528 0.000525694i
\(21\) −0.0193339 + 0.00452960i −0.00421901 + 0.000988441i
\(22\) 2.62341 4.54388i 0.559313 0.968759i
\(23\) −2.42067 + 4.19273i −0.504745 + 0.874245i 0.495240 + 0.868756i \(0.335080\pi\)
−0.999985 + 0.00548811i \(0.998253\pi\)
\(24\) 1.41547 4.68400i 0.288932 0.956118i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 2.29181 4.56166i 0.449461 0.894615i
\(27\) 3.30913 + 4.00620i 0.636842 + 0.770994i
\(28\) 0 5.39065e-5i 0 1.01874e-5i
\(29\) −4.46472 7.73312i −0.829077 1.43600i −0.898763 0.438435i \(-0.855533\pi\)
0.0696859 0.997569i \(-0.477800\pi\)
\(30\) −2.34752 0.709403i −0.428597 0.129519i
\(31\) 5.72460 + 3.30510i 1.02817 + 0.593614i 0.916460 0.400127i \(-0.131034\pi\)
0.111709 + 0.993741i \(0.464367\pi\)
\(32\) −0.0230347 0.0132991i −0.00407200 0.00235097i
\(33\) −6.24926 + 1.46409i −1.08786 + 0.254866i
\(34\) −5.70047 + 3.29117i −0.977622 + 0.564430i
\(35\) −0.0114647 −0.00193789
\(36\) 0.0126379 0.00626559i 0.00210632 0.00104427i
\(37\) 4.52388i 0.743721i 0.928289 + 0.371860i \(0.121280\pi\)
−0.928289 + 0.371860i \(0.878720\pi\)
\(38\) −4.27608 7.40639i −0.693672 1.20147i
\(39\) −5.98751 + 1.77475i −0.958769 + 0.284188i
\(40\) 1.41255 2.44660i 0.223343 0.386842i
\(41\) −3.46246 1.99905i −0.540746 0.312200i 0.204635 0.978838i \(-0.434399\pi\)
−0.745381 + 0.666639i \(0.767732\pi\)
\(42\) 0.0205003 0.0192414i 0.00316326 0.00296901i
\(43\) −0.571044 0.989078i −0.0870834 0.150833i 0.819194 0.573517i \(-0.194421\pi\)
−0.906277 + 0.422684i \(0.861088\pi\)
\(44\) 0.0174241i 0.00262677i
\(45\) 1.33255 + 2.68781i 0.198645 + 0.400674i
\(46\) 6.85474i 1.01068i
\(47\) 8.97044 5.17908i 1.30847 0.755447i 0.326631 0.945152i \(-0.394086\pi\)
0.981841 + 0.189705i \(0.0607531\pi\)
\(48\) 1.58407 + 6.76137i 0.228641 + 0.975920i
\(49\) −3.49993 + 6.06206i −0.499991 + 0.866009i
\(50\) −1.22618 0.707937i −0.173409 0.100117i
\(51\) 7.70796 + 2.32929i 1.07933 + 0.326165i
\(52\) 0.000983196 0.0169246i 0.000136345 0.00234702i
\(53\) 2.37762 0.326591 0.163295 0.986577i \(-0.447788\pi\)
0.163295 + 0.986577i \(0.447788\pi\)
\(54\) −6.89374 2.56968i −0.938119 0.349690i
\(55\) −3.70571 −0.499678
\(56\) 0.0161944 + 0.0280496i 0.00216407 + 0.00374828i
\(57\) −3.02635 + 10.0146i −0.400850 + 1.32647i
\(58\) 10.9491 + 6.32148i 1.43769 + 0.830051i
\(59\) −1.19273 0.688625i −0.155281 0.0896513i 0.420346 0.907364i \(-0.361909\pi\)
−0.575627 + 0.817712i \(0.695242\pi\)
\(60\) 0.00792930 0.00185770i 0.00102367 0.000239828i
\(61\) −4.33838 7.51430i −0.555473 0.962108i −0.997867 0.0652867i \(-0.979204\pi\)
0.442393 0.896821i \(-0.354130\pi\)
\(62\) −9.35922 −1.18862
\(63\) −0.0343252 0.00217690i −0.00432457 0.000274264i
\(64\) −7.98110 −0.997638
\(65\) −3.59948 + 0.209104i −0.446461 + 0.0259362i
\(66\) 6.62626 6.21933i 0.815636 0.765547i
\(67\) 8.37253 + 4.83388i 1.02287 + 0.590553i 0.914933 0.403605i \(-0.132243\pi\)
0.107934 + 0.994158i \(0.465576\pi\)
\(68\) 0.0109296 0.0189305i 0.00132540 0.00229567i
\(69\) −6.11418 + 5.73870i −0.736061 + 0.690859i
\(70\) 0.0140578 0.00811630i 0.00168023 0.000970083i
\(71\) 5.79546i 0.687794i −0.939007 0.343897i \(-0.888253\pi\)
0.939007 0.343897i \(-0.111747\pi\)
\(72\) 4.69370 7.05688i 0.553158 0.831661i
\(73\) 1.97265i 0.230882i 0.993314 + 0.115441i \(0.0368280\pi\)
−0.993314 + 0.115441i \(0.963172\pi\)
\(74\) −3.20262 5.54710i −0.372297 0.644838i
\(75\) 0.395091 + 1.68639i 0.0456212 + 0.194727i
\(76\) 0.0245957 + 0.0142003i 0.00282132 + 0.00162889i
\(77\) 0.0212424 0.0367930i 0.00242080 0.00419295i
\(78\) 6.08537 6.41496i 0.689032 0.726351i
\(79\) −0.376913 0.652832i −0.0424060 0.0734494i 0.844043 0.536275i \(-0.180169\pi\)
−0.886449 + 0.462826i \(0.846836\pi\)
\(80\) 4.00938i 0.448263i
\(81\) 3.47929 + 8.30027i 0.386588 + 0.922253i
\(82\) 5.66082 0.625133
\(83\) −7.33925 + 4.23732i −0.805587 + 0.465106i −0.845421 0.534100i \(-0.820650\pi\)
0.0398338 + 0.999206i \(0.487317\pi\)
\(84\) −2.70090e−5 0 8.93769e-5i −2.94693e−6 0 9.75182e-6i
\(85\) 4.02611 + 2.32447i 0.436693 + 0.252125i
\(86\) 1.40041 + 0.808527i 0.151010 + 0.0871858i
\(87\) −3.52794 15.0585i −0.378235 1.61444i
\(88\) 5.23449 + 9.06640i 0.557998 + 0.966481i
\(89\) 3.56933i 0.378348i −0.981944 0.189174i \(-0.939419\pi\)
0.981944 0.189174i \(-0.0605811\pi\)
\(90\) −3.53675 2.35238i −0.372807 0.247963i
\(91\) 0.0185574 0.0369370i 0.00194534 0.00387205i
\(92\) 0.0113819 + 0.0197140i 0.00118664 + 0.00205533i
\(93\) 7.83542 + 8.34808i 0.812495 + 0.865656i
\(94\) −7.33293 + 12.7010i −0.756334 + 1.31001i
\(95\) −3.02010 + 5.23096i −0.309855 + 0.536685i
\(96\) −0.0315282 0.0335911i −0.00321783 0.00342837i
\(97\) −0.00405446 + 0.00234084i −0.000411668 + 0.000237676i −0.500206 0.865907i \(-0.666742\pi\)
0.499794 + 0.866144i \(0.333409\pi\)
\(98\) 9.91094i 1.00116i
\(99\) −11.0948 0.703634i −1.11507 0.0707179i
\(100\) 0.00470195 0.000470195
\(101\) −1.00162 1.73486i −0.0996649 0.172625i 0.811881 0.583823i \(-0.198444\pi\)
−0.911546 + 0.411198i \(0.865110\pi\)
\(102\) −11.1004 + 2.60062i −1.09910 + 0.257500i
\(103\) 8.12311 14.0696i 0.800394 1.38632i −0.118963 0.992899i \(-0.537957\pi\)
0.919357 0.393424i \(-0.128710\pi\)
\(104\) 5.59603 + 8.51113i 0.548736 + 0.834585i
\(105\) −0.0190085 0.00574422i −0.00185504 0.000560579i
\(106\) −2.91540 + 1.68320i −0.283168 + 0.163487i
\(107\) −2.25946 −0.218430 −0.109215 0.994018i \(-0.534834\pi\)
−0.109215 + 0.994018i \(0.534834\pi\)
\(108\) 0.0240930 0.00405631i 0.00231835 0.000390319i
\(109\) 8.34833i 0.799625i 0.916597 + 0.399812i \(0.130925\pi\)
−0.916597 + 0.399812i \(0.869075\pi\)
\(110\) 4.54388 2.62341i 0.433242 0.250132i
\(111\) −2.26662 + 7.50059i −0.215138 + 0.711924i
\(112\) −0.0398081 0.0229832i −0.00376151 0.00217171i
\(113\) 4.45996 7.72487i 0.419558 0.726695i −0.576337 0.817212i \(-0.695519\pi\)
0.995895 + 0.0905169i \(0.0288519\pi\)
\(114\) −3.37888 14.4223i −0.316461 1.35077i
\(115\) −4.19273 + 2.42067i −0.390974 + 0.225729i
\(116\) −0.0419857 −0.00389828
\(117\) −10.8165 0.0574092i −0.999986 0.00530749i
\(118\) 1.95001 0.179513
\(119\) −0.0461582 + 0.0266494i −0.00423131 + 0.00244295i
\(120\) 3.56783 3.34873i 0.325697 0.305696i
\(121\) 1.36614 2.36623i 0.124195 0.215112i
\(122\) 10.6393 + 6.14261i 0.963238 + 0.556126i
\(123\) −4.73917 5.04924i −0.427316 0.455275i
\(124\) 0.0269168 0.0155404i 0.00241720 0.00139557i
\(125\) 1.00000i 0.0894427i
\(126\) 0.0436301 0.0216308i 0.00388688 0.00192702i
\(127\) 18.7915 1.66748 0.833739 0.552159i \(-0.186196\pi\)
0.833739 + 0.552159i \(0.186196\pi\)
\(128\) 9.83237 5.67672i 0.869067 0.501756i
\(129\) −0.451229 1.92600i −0.0397285 0.169575i
\(130\) 4.26559 2.80461i 0.374117 0.245980i
\(131\) −1.48159 + 2.56619i −0.129447 + 0.224209i −0.923463 0.383688i \(-0.874654\pi\)
0.794015 + 0.607898i \(0.207987\pi\)
\(132\) −0.00873006 + 0.0288891i −0.000759854 + 0.00251447i
\(133\) −0.0346245 0.0599715i −0.00300233 0.00520019i
\(134\) −13.6884 −1.18249
\(135\) 0.862688 + 5.12404i 0.0742484 + 0.441007i
\(136\) 13.1337i 1.12621i
\(137\) 17.0849 9.86395i 1.45966 0.842734i 0.460664 0.887574i \(-0.347611\pi\)
0.998994 + 0.0448403i \(0.0142779\pi\)
\(138\) 3.43447 11.3652i 0.292361 0.967467i
\(139\) 9.05260 15.6796i 0.767831 1.32992i −0.170906 0.985287i \(-0.554669\pi\)
0.938737 0.344635i \(-0.111997\pi\)
\(140\) −2.69532e−5 0 4.66844e-5i −2.27796e−6 0 3.94555e-6i
\(141\) 17.4679 4.09242i 1.47106 0.344644i
\(142\) 4.10282 + 7.10630i 0.344301 + 0.596347i
\(143\) 5.99825 11.9390i 0.501599 0.998393i
\(144\) −0.761294 + 12.0040i −0.0634412 + 1.00034i
\(145\) 8.92943i 0.741549i
\(146\) −1.39651 2.41883i −0.115576 0.200184i
\(147\) −8.84020 + 8.29731i −0.729127 + 0.684351i
\(148\) 0.0184213 + 0.0106355i 0.00151422 + 0.000874234i
\(149\) −10.4375 6.02608i −0.855071 0.493676i 0.00728749 0.999973i \(-0.497680\pi\)
−0.862359 + 0.506298i \(0.831014\pi\)
\(150\) −1.67831 1.78812i −0.137034 0.145999i
\(151\) 16.7981 9.69837i 1.36701 0.789242i 0.376463 0.926432i \(-0.377140\pi\)
0.990545 + 0.137190i \(0.0438069\pi\)
\(152\) 17.0641 1.38408
\(153\) 11.6127 + 7.72391i 0.938834 + 0.624441i
\(154\) 0.0601533i 0.00484729i
\(155\) 3.30510 + 5.72460i 0.265472 + 0.459811i
\(156\) −0.00684967 + 0.0285536i −0.000548412 + 0.00228611i
\(157\) 8.35313 14.4680i 0.666652 1.15468i −0.312182 0.950022i \(-0.601060\pi\)
0.978834 0.204653i \(-0.0656068\pi\)
\(158\) 0.924329 + 0.533661i 0.0735356 + 0.0424558i
\(159\) 3.94209 + 1.19127i 0.312628 + 0.0944738i
\(160\) −0.0132991 0.0230347i −0.00105139 0.00182105i
\(161\) 0.0555046i 0.00437438i
\(162\) −10.1423 7.71454i −0.796856 0.606112i
\(163\) 7.00872i 0.548965i −0.961592 0.274483i \(-0.911493\pi\)
0.961592 0.274483i \(-0.0885065\pi\)
\(164\) −0.0162803 + 0.00939944i −0.00127128 + 0.000733973i
\(165\) −6.14407 1.85669i −0.478315 0.144543i
\(166\) 5.99951 10.3915i 0.465652 0.806534i
\(167\) 15.4948 + 8.94595i 1.19903 + 0.692259i 0.960338 0.278838i \(-0.0899491\pi\)
0.238689 + 0.971096i \(0.423282\pi\)
\(168\) 0.0127966 + 0.0546202i 0.000987275 + 0.00421404i
\(169\) 5.15262 11.9353i 0.396355 0.918097i
\(170\) −6.58233 −0.504842
\(171\) −10.0354 + 15.0880i −0.767424 + 1.15381i
\(172\) −0.00537004 −0.000409462
\(173\) 12.9562 + 22.4409i 0.985045 + 1.70615i 0.641737 + 0.766925i \(0.278214\pi\)
0.343308 + 0.939223i \(0.388452\pi\)
\(174\) 14.9864 + 15.9669i 1.13611 + 1.21045i
\(175\) −0.00992873 0.00573236i −0.000750542 0.000433325i
\(176\) −12.8671 7.42880i −0.969892 0.559967i
\(177\) −1.63253 1.73934i −0.122708 0.130737i
\(178\) 2.52686 + 4.37665i 0.189396 + 0.328044i
\(179\) 3.63380 0.271603 0.135801 0.990736i \(-0.456639\pi\)
0.135801 + 0.990736i \(0.456639\pi\)
\(180\) 0.0140776 0.000892797i 0.00104928 6.65452e-5i
\(181\) −9.03354 −0.671458 −0.335729 0.941959i \(-0.608983\pi\)
−0.335729 + 0.941959i \(0.608983\pi\)
\(182\) 0.00339430 + 0.0584290i 0.000251602 + 0.00433104i
\(183\) −3.42811 14.6324i −0.253413 1.08166i
\(184\) 11.8448 + 6.83863i 0.873214 + 0.504150i
\(185\) −2.26194 + 3.91779i −0.166301 + 0.288042i
\(186\) −15.5176 4.68930i −1.13780 0.343836i
\(187\) −14.9196 + 8.61383i −1.09103 + 0.629905i
\(188\) 0.0487035i 0.00355207i
\(189\) −0.0558204 0.0208074i −0.00406034 0.00151352i
\(190\) 8.55216i 0.620439i
\(191\) 10.5689 + 18.3058i 0.764737 + 1.32456i 0.940385 + 0.340111i \(0.110465\pi\)
−0.175648 + 0.984453i \(0.556202\pi\)
\(192\) −13.2327 3.99881i −0.954986 0.288589i
\(193\) −0.210790 0.121700i −0.0151730 0.00876015i 0.492394 0.870372i \(-0.336122\pi\)
−0.507567 + 0.861612i \(0.669455\pi\)
\(194\) 0.00331434 0.00574060i 0.000237956 0.000412151i
\(195\) −6.07271 1.45677i −0.434876 0.104322i
\(196\) 0.0164565 + 0.0285035i 0.00117546 + 0.00203596i
\(197\) 18.3729i 1.30901i −0.756057 0.654506i \(-0.772877\pi\)
0.756057 0.654506i \(-0.227123\pi\)
\(198\) 14.1024 6.99167i 1.00222 0.496876i
\(199\) −13.3674 −0.947587 −0.473793 0.880636i \(-0.657116\pi\)
−0.473793 + 0.880636i \(0.657116\pi\)
\(200\) 2.44660 1.41255i 0.173001 0.0998821i
\(201\) 11.4597 + 12.2095i 0.808306 + 0.861192i
\(202\) 2.45634 + 1.41817i 0.172828 + 0.0997820i
\(203\) 0.0886580 + 0.0511867i 0.00622257 + 0.00359260i
\(204\) 0.0276061 0.0259108i 0.00193281 0.00181412i
\(205\) −1.99905 3.46246i −0.139620 0.241829i
\(206\) 23.0026i 1.60267i
\(207\) −13.0126 + 6.45135i −0.904438 + 0.448400i
\(208\) −12.9174 6.48979i −0.895661 0.449986i
\(209\) −11.1916 19.3844i −0.774139 1.34085i
\(210\) 0.0273745 0.00641335i 0.00188902 0.000442563i
\(211\) −8.07314 + 13.9831i −0.555778 + 0.962635i 0.442065 + 0.896983i \(0.354246\pi\)
−0.997843 + 0.0656523i \(0.979087\pi\)
\(212\) 0.00558972 0.00968167i 0.000383903 0.000664940i
\(213\) 2.90373 9.60887i 0.198960 0.658389i
\(214\) 2.77051 1.59956i 0.189388 0.109343i
\(215\) 1.14209i 0.0778898i
\(216\) 11.3179 9.34860i 0.770085 0.636091i
\(217\) −0.0757841 −0.00514456
\(218\) −5.91010 10.2366i −0.400282 0.693309i
\(219\) −0.988368 + 3.27066i −0.0667877 + 0.221011i
\(220\) −0.00871203 + 0.0150897i −0.000587365 + 0.00101735i
\(221\) −14.0058 + 9.20878i −0.942135 + 0.619450i
\(222\) −2.53065 10.8017i −0.169846 0.724964i
\(223\) −19.0098 + 10.9753i −1.27299 + 0.734959i −0.975549 0.219782i \(-0.929465\pi\)
−0.297438 + 0.954741i \(0.596132\pi\)
\(224\) 0.000304940 0 2.03747e−5 0
\(225\) −0.189878 + 2.99399i −0.0126586 + 0.199599i
\(226\) 12.6295i 0.840101i
\(227\) 0.780807 0.450799i 0.0518240 0.0299206i −0.473864 0.880598i \(-0.657141\pi\)
0.525688 + 0.850677i \(0.323808\pi\)
\(228\) 0.0336648 + 0.0358675i 0.00222951 + 0.00237538i
\(229\) −1.49691 0.864240i −0.0989184 0.0571106i 0.449725 0.893167i \(-0.351522\pi\)
−0.548643 + 0.836057i \(0.684855\pi\)
\(230\) 3.42737 5.93638i 0.225994 0.391433i
\(231\) 0.0536546 0.0503596i 0.00353021 0.00331342i
\(232\) −21.8468 + 12.6132i −1.43431 + 0.828100i
\(233\) 18.1858 1.19139 0.595696 0.803210i \(-0.296876\pi\)
0.595696 + 0.803210i \(0.296876\pi\)
\(234\) 13.3037 7.58701i 0.869687 0.495979i
\(235\) 10.3582 0.675692
\(236\) −0.00560817 + 0.00323788i −0.000365061 + 0.000210768i
\(237\) −0.297830 1.27124i −0.0193461 0.0825761i
\(238\) 0.0377323 0.0653542i 0.00244582 0.00423628i
\(239\) 12.8933 + 7.44396i 0.833999 + 0.481510i 0.855220 0.518265i \(-0.173422\pi\)
−0.0212209 + 0.999775i \(0.506755\pi\)
\(240\) −2.00884 + 6.64755i −0.129670 + 0.429098i
\(241\) −8.04501 + 4.64479i −0.518225 + 0.299197i −0.736208 0.676755i \(-0.763385\pi\)
0.217983 + 0.975952i \(0.430052\pi\)
\(242\) 3.86858i 0.248682i
\(243\) 1.60993 + 15.5051i 0.103277 + 0.994653i
\(244\) −0.0407977 −0.00261181
\(245\) −6.06206 + 3.49993i −0.387291 + 0.223603i
\(246\) 9.38564 + 2.83627i 0.598406 + 0.180834i
\(247\) −11.9646 18.1972i −0.761289 1.15786i
\(248\) 9.33722 16.1725i 0.592914 1.02696i
\(249\) −14.2915 + 3.34825i −0.905688 + 0.212187i
\(250\) −0.707937 1.22618i −0.0447739 0.0775507i
\(251\) −3.40713 −0.215056 −0.107528 0.994202i \(-0.534294\pi\)
−0.107528 + 0.994202i \(0.534294\pi\)
\(252\) −8.95619e−5 0 0.000134654i −5.64187e−6 0 8.48243e-6i
\(253\) 17.9406i 1.12792i
\(254\) −23.0419 + 13.3032i −1.44577 + 0.834718i
\(255\) 5.51064 + 5.87120i 0.345090 + 0.367669i
\(256\) −0.0564231 + 0.0977276i −0.00352644 + 0.00610797i
\(257\) −15.0941 + 26.1437i −0.941543 + 1.63080i −0.179013 + 0.983847i \(0.557290\pi\)
−0.762530 + 0.646953i \(0.776043\pi\)
\(258\) 1.91678 + 2.04219i 0.119334 + 0.127141i
\(259\) −0.0259325 0.0449164i −0.00161137 0.00279097i
\(260\) −0.00761082 + 0.0151487i −0.000472003 + 0.000939483i
\(261\) 1.69551 26.7346i 0.104949 1.65483i
\(262\) 4.19550i 0.259199i
\(263\) −9.48439 16.4275i −0.584833 1.01296i −0.994896 0.100903i \(-0.967827\pi\)
0.410064 0.912057i \(-0.365507\pi\)
\(264\) 4.13620 + 17.6547i 0.254565 + 1.08657i
\(265\) 2.05908 + 1.18881i 0.126488 + 0.0730279i
\(266\) 0.0849121 + 0.0490240i 0.00520630 + 0.00300586i
\(267\) 1.78836 5.91795i 0.109446 0.362173i
\(268\) 0.0393672 0.0227287i 0.00240473 0.00138837i
\(269\) 3.45377 0.210580 0.105290 0.994442i \(-0.466423\pi\)
0.105290 + 0.994442i \(0.466423\pi\)
\(270\) −4.68531 5.67228i −0.285139 0.345204i
\(271\) 13.5998i 0.826131i −0.910701 0.413065i \(-0.864458\pi\)
0.910701 0.413065i \(-0.135542\pi\)
\(272\) 9.31971 + 16.1422i 0.565090 + 0.978765i
\(273\) 0.0492748 0.0519436i 0.00298225 0.00314377i
\(274\) −13.9661 + 24.1900i −0.843724 + 1.46137i
\(275\) −3.20924 1.85286i −0.193524 0.111731i
\(276\) 0.00899376 + 0.0383885i 0.000541360 + 0.00231072i
\(277\) −3.82426 6.62382i −0.229778 0.397987i 0.727964 0.685615i \(-0.240467\pi\)
−0.957742 + 0.287628i \(0.907133\pi\)
\(278\) 25.6347i 1.53747i
\(279\) 8.80845 + 17.7669i 0.527348 + 1.06368i
\(280\) 0.0323889i 0.00193561i
\(281\) −19.5232 + 11.2717i −1.16466 + 0.672414i −0.952415 0.304803i \(-0.901409\pi\)
−0.212240 + 0.977218i \(0.568076\pi\)
\(282\) −18.5217 + 17.3842i −1.10295 + 1.03522i
\(283\) 0.221480 0.383614i 0.0131656 0.0228035i −0.859368 0.511358i \(-0.829142\pi\)
0.872533 + 0.488555i \(0.162476\pi\)
\(284\) −0.0235991 0.0136250i −0.00140035 0.000808493i
\(285\) −7.62822 + 7.15976i −0.451857 + 0.424108i
\(286\) 1.09713 + 18.8858i 0.0648747 + 1.11674i
\(287\) 0.0458371 0.00270568
\(288\) −0.0354435 0.0714907i −0.00208853 0.00421263i
\(289\) 4.61272 0.271337
\(290\) 6.32148 + 10.9491i 0.371210 + 0.642955i
\(291\) −0.00789513 + 0.00184969i −0.000462821 + 0.000108431i
\(292\) 0.00803265 + 0.00463765i 0.000470075 + 0.000271398i
\(293\) −0.131806 0.0760981i −0.00770018 0.00444570i 0.496145 0.868240i \(-0.334748\pi\)
−0.503845 + 0.863794i \(0.668082\pi\)
\(294\) 4.96573 16.4323i 0.289607 0.958353i
\(295\) −0.688625 1.19273i −0.0400933 0.0694436i
\(296\) 12.7804 0.742844
\(297\) −18.0427 6.72553i −1.04694 0.390255i
\(298\) 17.0643 0.988511
\(299\) −1.01235 17.4263i −0.0585454 1.00779i
\(300\) 0.00779583 + 0.00235584i 0.000450092 + 0.000136014i
\(301\) 0.0113395 + 0.00654686i 0.000653597 + 0.000377355i
\(302\) −13.7317 + 23.7840i −0.790169 + 1.36861i
\(303\) −0.791462 3.37824i −0.0454683 0.194075i
\(304\) −20.9729 + 12.1087i −1.20288 + 0.694483i
\(305\) 8.67677i 0.496830i
\(306\) −19.7074 1.24984i −1.12660 0.0714487i
\(307\) 12.2212i 0.697503i −0.937215 0.348751i \(-0.886606\pi\)
0.937215 0.348751i \(-0.113394\pi\)
\(308\) −9.98809e−5 0 0.000172999i −5.69124e−6 0 9.85752e-6i
\(309\) 20.5175 19.2575i 1.16720 1.09552i
\(310\) −8.10532 4.67961i −0.460351 0.265784i
\(311\) 14.5035 25.1209i 0.822421 1.42447i −0.0814542 0.996677i \(-0.525956\pi\)
0.903875 0.427797i \(-0.140710\pi\)
\(312\) 5.01384 + 16.9153i 0.283853 + 0.957638i
\(313\) 13.4272 + 23.2565i 0.758949 + 1.31454i 0.943387 + 0.331693i \(0.107620\pi\)
−0.184439 + 0.982844i \(0.559047\pi\)
\(314\) 23.6540i 1.33487i
\(315\) −0.0286380 0.0190478i −0.00161357 0.00107322i
\(316\) −0.00354445 −0.000199391
\(317\) −26.8476 + 15.5005i −1.50791 + 0.870595i −0.507956 + 0.861383i \(0.669599\pi\)
−0.999958 + 0.00921179i \(0.997068\pi\)
\(318\) −5.67707 + 1.33004i −0.318354 + 0.0745848i
\(319\) 28.6567 + 16.5449i 1.60447 + 0.926339i
\(320\) −6.91184 3.99055i −0.386384 0.223079i
\(321\) −3.74619 1.13207i −0.209092 0.0631859i
\(322\) 0.0392938 + 0.0680589i 0.00218976 + 0.00379277i
\(323\) 28.0806i 1.56244i
\(324\) 0.0419785 + 0.00534604i 0.00233214 + 0.000297002i
\(325\) −3.22180 1.61865i −0.178713 0.0897867i
\(326\) 4.96173 + 8.59397i 0.274805 + 0.475976i
\(327\) −4.18280 + 13.8415i −0.231310 + 0.765438i
\(328\) −5.64751 + 9.78177i −0.311832 + 0.540108i
\(329\) −0.0593767 + 0.102843i −0.00327354 + 0.00566994i
\(330\) 8.84818 2.07297i 0.487076 0.114113i
\(331\) 25.1339 14.5110i 1.38148 0.797599i 0.389147 0.921175i \(-0.372770\pi\)
0.992335 + 0.123576i \(0.0394363\pi\)
\(332\) 0.0398473i 0.00218690i
\(333\) −7.51611 + 11.3003i −0.411880 + 0.619254i
\(334\) −25.3327 −1.38614
\(335\) 4.83388 + 8.37253i 0.264103 + 0.457440i
\(336\) −0.0544864 0.0580514i −0.00297248 0.00316696i
\(337\) 8.04981 13.9427i 0.438501 0.759506i −0.559073 0.829119i \(-0.688843\pi\)
0.997574 + 0.0696121i \(0.0221761\pi\)
\(338\) 2.13136 + 18.2826i 0.115931 + 0.994440i
\(339\) 11.2650 10.5732i 0.611833 0.574260i
\(340\) 0.0189305 0.0109296i 0.00102665 0.000592738i
\(341\) −24.4955 −1.32651
\(342\) 1.62387 25.6050i 0.0878088 1.38456i
\(343\) 0.160504i 0.00866643i
\(344\) −2.79424 + 1.61325i −0.150655 + 0.0869808i
\(345\) −8.16439 + 1.91277i −0.439556 + 0.102980i
\(346\) −31.7735 18.3444i −1.70815 0.986202i
\(347\) −6.18075 + 10.7054i −0.331800 + 0.574694i −0.982865 0.184328i \(-0.940989\pi\)
0.651065 + 0.759022i \(0.274323\pi\)
\(348\) −0.0696123 0.0210363i −0.00373161 0.00112766i
\(349\) 0.966423 0.557965i 0.0517314 0.0298672i −0.473911 0.880573i \(-0.657158\pi\)
0.525643 + 0.850705i \(0.323825\pi\)
\(350\) 0.0162326 0.000867669
\(351\) −17.9050 5.51463i −0.955698 0.294349i
\(352\) 0.0985651 0.00525354
\(353\) −13.4303 + 7.75398i −0.714822 + 0.412703i −0.812844 0.582481i \(-0.802082\pi\)
0.0980218 + 0.995184i \(0.468749\pi\)
\(354\) 3.23312 + 0.977025i 0.171839 + 0.0519283i
\(355\) 2.89773 5.01901i 0.153796 0.266382i
\(356\) −0.0145343 0.00839140i −0.000770318 0.000444743i
\(357\) −0.0898825 + 0.0210579i −0.00475709 + 0.00111450i
\(358\) −4.45570 + 2.57250i −0.235491 + 0.135961i
\(359\) 25.6452i 1.35350i −0.736213 0.676750i \(-0.763388\pi\)
0.736213 0.676750i \(-0.236612\pi\)
\(360\) 7.59330 3.76459i 0.400202 0.198411i
\(361\) −17.4839 −0.920208
\(362\) 11.0768 6.39518i 0.582183 0.336123i
\(363\) 3.45063 3.23872i 0.181111 0.169989i
\(364\) −0.000106780 0 0.000162404i −5.59677e−6 0 8.51226e-6i
\(365\) −0.986326 + 1.70837i −0.0516267 + 0.0894200i
\(366\) 14.5623 + 15.5151i 0.761185 + 0.810988i
\(367\) 9.19797 + 15.9314i 0.480130 + 0.831610i 0.999740 0.0227937i \(-0.00725608\pi\)
−0.519610 + 0.854404i \(0.673923\pi\)
\(368\) −19.4108 −1.01186
\(369\) −5.32769 10.7461i −0.277348 0.559421i
\(370\) 6.40524i 0.332993i
\(371\) −0.0236067 + 0.0136293i −0.00122560 + 0.000707601i
\(372\) 0.0524143 0.0122798i 0.00271756 0.000636675i
\(373\) −7.49714 + 12.9854i −0.388187 + 0.672360i −0.992206 0.124610i \(-0.960232\pi\)
0.604018 + 0.796970i \(0.293565\pi\)
\(374\) 12.1961 21.1243i 0.630646 1.09231i
\(375\) −0.501035 + 1.65800i −0.0258733 + 0.0856188i
\(376\) −14.6314 25.3423i −0.754556 1.30693i
\(377\) 28.7688 + 14.4536i 1.48167 + 0.744401i
\(378\) 0.0831765 0.0140037i 0.00427814 0.000720271i
\(379\) 31.4375i 1.61483i 0.589981 + 0.807417i \(0.299135\pi\)
−0.589981 + 0.807417i \(0.700865\pi\)
\(380\) 0.0142003 + 0.0245957i 0.000728462 + 0.00126173i
\(381\) 31.1563 + 9.41521i 1.59619 + 0.482356i
\(382\) −25.9188 14.9642i −1.32612 0.765636i
\(383\) −23.3236 13.4659i −1.19178 0.688074i −0.233069 0.972460i \(-0.574877\pi\)
−0.958710 + 0.284386i \(0.908210\pi\)
\(384\) 19.1463 4.48564i 0.977056 0.228907i
\(385\) 0.0367930 0.0212424i 0.00187515 0.00108262i
\(386\) 0.344624 0.0175409
\(387\) 0.216858 3.41940i 0.0110235 0.173818i
\(388\) 0 2.20130e-5i 0 1.11754e-6i
\(389\) 9.70578 + 16.8109i 0.492103 + 0.852347i 0.999959 0.00909505i \(-0.00289508\pi\)
−0.507856 + 0.861442i \(0.669562\pi\)
\(390\) 8.47756 2.51283i 0.429278 0.127242i
\(391\) −11.2536 + 19.4918i −0.569118 + 0.985742i
\(392\) 17.1259 + 9.88764i 0.864988 + 0.499401i
\(393\) −3.74223 + 3.51242i −0.188771 + 0.177178i
\(394\) 13.0068 + 22.5285i 0.655275 + 1.13497i
\(395\) 0.753826i 0.0379291i
\(396\) −0.0289489 + 0.0435240i −0.00145474 + 0.00218716i
\(397\) 16.7410i 0.840208i −0.907476 0.420104i \(-0.861994\pi\)
0.907476 0.420104i \(-0.138006\pi\)
\(398\) 16.3908 9.46325i 0.821598 0.474350i
\(399\) −0.0273597 0.116781i −0.00136970 0.00584635i
\(400\) −2.00469 + 3.47223i −0.100235 + 0.173611i
\(401\) −5.03467 2.90677i −0.251420 0.145157i 0.368995 0.929432i \(-0.379702\pi\)
−0.620414 + 0.784274i \(0.713035\pi\)
\(402\) −22.6953 6.85834i −1.13194 0.342063i
\(403\) −23.7933 + 1.38222i −1.18523 + 0.0688533i
\(404\) −0.00941913 −0.000468619
\(405\) −1.13699 + 8.92789i −0.0564973 + 0.443631i
\(406\) −0.144948 −0.00719364
\(407\) −8.38209 14.5182i −0.415485 0.719641i
\(408\) 6.58045 21.7757i 0.325781 1.07806i
\(409\) −14.1966 8.19644i −0.701979 0.405288i 0.106105 0.994355i \(-0.466162\pi\)
−0.808084 + 0.589067i \(0.799495\pi\)
\(410\) 4.90241 + 2.83041i 0.242113 + 0.139784i
\(411\) 33.2689 7.79432i 1.64103 0.384465i
\(412\) −0.0381944 0.0661547i −0.00188171 0.00325921i
\(413\) 0.0157898 0.000776964
\(414\) 11.3887 17.1227i 0.559723 0.841532i
\(415\) −8.47464 −0.416004
\(416\) 0.0957397 0.00556178i 0.00469402 0.000272689i
\(417\) 22.8652 21.4610i 1.11971 1.05095i
\(418\) 27.4459 + 15.8459i 1.34242 + 0.775049i
\(419\) 12.1069 20.9698i 0.591462 1.02444i −0.402574 0.915388i \(-0.631884\pi\)
0.994036 0.109055i \(-0.0347823\pi\)
\(420\) −6.80790e−5 0 6.38982e-5i −3.32191e−6 0 3.11791e-6i
\(421\) 27.4941 15.8737i 1.33998 0.773638i 0.353176 0.935557i \(-0.385102\pi\)
0.986804 + 0.161919i \(0.0517684\pi\)
\(422\) 22.8611i 1.11286i
\(423\) 31.0122 + 1.96679i 1.50786 + 0.0956286i
\(424\) 6.71699i 0.326206i
\(425\) 2.32447 + 4.02611i 0.112754 + 0.195295i
\(426\) 3.24198 + 13.8379i 0.157074 + 0.670448i
\(427\) 0.0861493 + 0.0497383i 0.00416906 + 0.00240701i
\(428\) −0.00531193 + 0.00920054i −0.000256762 + 0.000444725i
\(429\) 15.9270 16.7896i 0.768962 0.810609i
\(430\) 0.808527 + 1.40041i 0.0389907 + 0.0675338i
\(431\) 17.8910i 0.861777i 0.902405 + 0.430888i \(0.141800\pi\)
−0.902405 + 0.430888i \(0.858200\pi\)
\(432\) −7.27666 + 19.5212i −0.350099 + 0.939216i
\(433\) −25.4679 −1.22391 −0.611955 0.790892i \(-0.709617\pi\)
−0.611955 + 0.790892i \(0.709617\pi\)
\(434\) 0.0929252 0.0536504i 0.00446055 0.00257530i
\(435\) 4.47396 14.8050i 0.214510 0.709846i
\(436\) 0.0339944 + 0.0196267i 0.00162804 + 0.000939949i
\(437\) −25.3249 14.6213i −1.21145 0.699433i
\(438\) −1.10350 4.71013i −0.0527273 0.225059i
\(439\) 3.31068 + 5.73426i 0.158010 + 0.273681i 0.934151 0.356878i \(-0.116159\pi\)
−0.776141 + 0.630559i \(0.782825\pi\)
\(440\) 10.4690i 0.499089i
\(441\) −18.8143 + 9.32770i −0.895919 + 0.444176i
\(442\) 10.6545 21.2069i 0.506783 1.00871i
\(443\) −8.33283 14.4329i −0.395905 0.685727i 0.597312 0.802009i \(-0.296236\pi\)
−0.993216 + 0.116282i \(0.962902\pi\)
\(444\) 0.0252137 + 0.0268634i 0.00119659 + 0.00127488i
\(445\) 1.78466 3.09113i 0.0846012 0.146534i
\(446\) 15.5396 26.9154i 0.735823 1.27448i
\(447\) −14.2861 15.2208i −0.675707 0.719918i
\(448\) 0.0792422 0.0457505i 0.00374384 0.00216151i
\(449\) 5.30273i 0.250251i 0.992141 + 0.125126i \(0.0399334\pi\)
−0.992141 + 0.125126i \(0.960067\pi\)
\(450\) −1.88673 3.80560i −0.0889412 0.179398i
\(451\) 14.8158 0.697650
\(452\) −0.0209705 0.0363219i −0.000986369 0.00170844i
\(453\) 32.7104 7.66348i 1.53687 0.360062i
\(454\) −0.638275 + 1.10553i −0.0299557 + 0.0518849i
\(455\) 0.0345396 0.0227097i 0.00161924 0.00106464i
\(456\) 28.2923 + 8.54971i 1.32491 + 0.400377i
\(457\) 29.4541 17.0053i 1.37780 0.795476i 0.385909 0.922537i \(-0.373888\pi\)
0.991895 + 0.127061i \(0.0405544\pi\)
\(458\) 2.44731 0.114355
\(459\) 15.3840 + 18.6246i 0.718062 + 0.869323i
\(460\) 0.0227638i 0.00106137i
\(461\) −2.59939 + 1.50076i −0.121066 + 0.0698972i −0.559310 0.828959i \(-0.688934\pi\)
0.438244 + 0.898856i \(0.355600\pi\)
\(462\) −0.0301389 + 0.0997342i −0.00140219 + 0.00464005i
\(463\) 25.6151 + 14.7889i 1.19044 + 0.687298i 0.958405 0.285411i \(-0.0921300\pi\)
0.232030 + 0.972709i \(0.425463\pi\)
\(464\) 17.9008 31.0050i 0.831022 1.43937i
\(465\) 2.61163 + 11.1474i 0.121112 + 0.516947i
\(466\) −22.2991 + 12.8744i −1.03299 + 0.596396i
\(467\) 9.39049 0.434540 0.217270 0.976112i \(-0.430285\pi\)
0.217270 + 0.976112i \(0.430285\pi\)
\(468\) −0.0256631 + 0.0439099i −0.00118628 + 0.00202974i
\(469\) −0.110838 −0.00511803
\(470\) −12.7010 + 7.33293i −0.585854 + 0.338243i
\(471\) 21.0985 19.8028i 0.972167 0.912465i
\(472\) −1.94543 + 3.36958i −0.0895456 + 0.155098i
\(473\) 3.66524 + 2.11612i 0.168528 + 0.0972995i
\(474\) 1.26515 + 1.34793i 0.0581104 + 0.0619125i
\(475\) −5.23096 + 3.02010i −0.240013 + 0.138572i
\(476\) 0 0.000250608i 0 1.14866e-5i
\(477\) 5.93912 + 3.95025i 0.271933 + 0.180869i
\(478\) −21.0794 −0.964151
\(479\) −4.16324 + 2.40365i −0.190223 + 0.109825i −0.592087 0.805874i \(-0.701696\pi\)
0.401864 + 0.915699i \(0.368363\pi\)
\(480\) −0.0105087 0.0448548i −0.000479654 0.00204733i
\(481\) −8.96103 13.6290i −0.408588 0.621431i
\(482\) 6.57644 11.3907i 0.299549 0.518833i
\(483\) 0.0278098 0.0920267i 0.00126539 0.00418736i
\(484\) −0.00642354 0.0111259i −0.000291979 0.000505722i
\(485\) −0.00468168 −0.000212584
\(486\) −12.9507 17.8724i −0.587456 0.810707i
\(487\) 3.65883i 0.165797i −0.996558 0.0828987i \(-0.973582\pi\)
0.996558 0.0828987i \(-0.0264178\pi\)
\(488\) −21.2286 + 12.2563i −0.960974 + 0.554818i
\(489\) 3.51161 11.6205i 0.158801 0.525495i
\(490\) 4.95547 8.58312i 0.223865 0.387746i
\(491\) −1.64741 + 2.85340i −0.0743467 + 0.128772i −0.900802 0.434230i \(-0.857020\pi\)
0.826455 + 0.563002i \(0.190354\pi\)
\(492\) −0.0317022 + 0.00742727i −0.00142925 + 0.000334847i
\(493\) −20.7562 35.9509i −0.934814 1.61915i
\(494\) 27.5533 + 13.8430i 1.23968 + 0.622825i
\(495\) −9.25660 6.15679i −0.416053 0.276727i
\(496\) 26.5028i 1.19001i
\(497\) 0.0332216 + 0.0575416i 0.00149019 + 0.00258109i
\(498\) 15.1537 14.2231i 0.679053 0.637351i
\(499\) −12.0212 6.94041i −0.538141 0.310696i 0.206184 0.978513i \(-0.433895\pi\)
−0.744325 + 0.667818i \(0.767229\pi\)
\(500\) 0.00407201 + 0.00235097i 0.000182106 + 0.000105139i
\(501\) 21.2082 + 22.5958i 0.947513 + 1.00951i
\(502\) 4.17776 2.41203i 0.186463 0.107654i
\(503\) −14.3269 −0.638806 −0.319403 0.947619i \(-0.603482\pi\)
−0.319403 + 0.947619i \(0.603482\pi\)
\(504\) −0.00614994 + 0.0969718i −0.000273940 + 0.00431947i
\(505\) 2.00324i 0.0891430i
\(506\) 12.7008 + 21.9985i 0.564621 + 0.977953i
\(507\) 14.5230 17.2070i 0.644990 0.764191i
\(508\) 0.0441784 0.0765192i 0.00196010 0.00339499i
\(509\) −20.2696 11.7027i −0.898434 0.518711i −0.0217423 0.999764i \(-0.506921\pi\)
−0.876692 + 0.481052i \(0.840255\pi\)
\(510\) −10.9135 3.29798i −0.483258 0.146037i
\(511\) −0.0113079 0.0195859i −0.000500234 0.000866431i
\(512\) 22.5471i 0.996451i
\(513\) −24.1982 + 19.9878i −1.06838 + 0.882482i
\(514\) 42.7426i 1.88530i
\(515\) 14.0696 8.12311i 0.619983 0.357947i
\(516\) −0.00890353 0.00269058i −0.000391956 0.000118446i
\(517\) −19.1922 + 33.2418i −0.844071 + 1.46197i
\(518\) 0.0635960 + 0.0367171i 0.00279425 + 0.00161326i
\(519\) 10.2378 + 43.6985i 0.449389 + 1.91815i
\(520\) 0.590738 + 10.1689i 0.0259056 + 0.445935i
\(521\) −40.3139 −1.76619 −0.883093 0.469198i \(-0.844543\pi\)
−0.883093 + 0.469198i \(0.844543\pi\)
\(522\) 16.8474 + 33.9818i 0.737391 + 1.48734i
\(523\) −20.3832 −0.891297 −0.445648 0.895208i \(-0.647027\pi\)
−0.445648 + 0.895208i \(0.647027\pi\)
\(524\) 0.00696637 + 0.0120661i 0.000304327 + 0.000527110i
\(525\) −0.0135897 0.0144789i −0.000593104 0.000631910i
\(526\) 23.2592 + 13.4287i 1.01415 + 0.585520i
\(527\) 26.6134 + 15.3652i 1.15930 + 0.669321i
\(528\) −17.6115 18.7638i −0.766442 0.816590i
\(529\) −0.219320 0.379874i −0.00953567 0.0165163i
\(530\) −3.36641 −0.146227
\(531\) −1.83526 3.70178i −0.0796434 0.160644i
\(532\) −0.000325606 0 −1.41168e−5 0
\(533\) 14.3911 0.836020i 0.623348 0.0362120i
\(534\) 1.99668 + 8.52254i 0.0864048 + 0.368806i
\(535\) −1.95675 1.12973i −0.0845977 0.0488425i
\(536\) 13.6562 23.6532i 0.589857 1.02166i
\(537\) 6.02483 + 1.82066i 0.259991 + 0.0785672i
\(538\) −4.23496 + 2.44505i −0.182582 + 0.105414i
\(539\) 25.9395i 1.11729i
\(540\) 0.0228933 + 0.00853361i 0.000985169 + 0.000367228i
\(541\) 12.9137i 0.555204i −0.960696 0.277602i \(-0.910460\pi\)
0.960696 0.277602i \(-0.0895396\pi\)
\(542\) 9.62783 + 16.6759i 0.413551 + 0.716291i
\(543\) −14.9776 4.52612i −0.642751 0.194234i
\(544\) −0.107087 0.0618268i −0.00459132 0.00265080i
\(545\) −4.17416 + 7.22987i −0.178802 + 0.309693i
\(546\) −0.0236472 + 0.0985759i −0.00101201 + 0.00421866i
\(547\) −3.77468 6.53794i −0.161394 0.279542i 0.773975 0.633216i \(-0.218266\pi\)
−0.935369 + 0.353674i \(0.884932\pi\)
\(548\) 0.0927595i 0.00396249i
\(549\) 1.64753 25.9781i 0.0703149 1.10872i
\(550\) 5.24682 0.223725
\(551\) 46.7095 26.9678i 1.98989 1.14887i
\(552\) 16.2124 + 17.2731i 0.690044 + 0.735193i
\(553\) 0.00748453 + 0.00432120i 0.000318275 + 0.000183756i
\(554\) 9.37850 + 5.41468i 0.398454 + 0.230048i
\(555\) −5.71325 + 5.36239i −0.242514 + 0.227621i
\(556\) −0.0425648 0.0737244i −0.00180515 0.00312661i
\(557\) 19.3602i 0.820318i −0.912014 0.410159i \(-0.865473\pi\)
0.912014 0.410159i \(-0.134527\pi\)
\(558\) −23.3787 15.5497i −0.989697 0.658272i
\(559\) 3.67958 + 1.84864i 0.155629 + 0.0781893i
\(560\) −0.0229832 0.0398081i −0.000971218 0.00168220i
\(561\) −29.0525 + 6.80649i −1.22660 + 0.287370i
\(562\) 15.9593 27.6424i 0.673204 1.16602i
\(563\) 15.2746 26.4563i 0.643746 1.11500i −0.340844 0.940120i \(-0.610713\pi\)
0.984590 0.174880i \(-0.0559539\pi\)
\(564\) 0.0244022 0.0807505i 0.00102752 0.00340021i
\(565\) 7.72487 4.45996i 0.324988 0.187632i
\(566\) 0.627175i 0.0263621i
\(567\) −0.0821250 0.0624667i −0.00344893 0.00262335i
\(568\) −16.3727 −0.686984
\(569\) −23.1980 40.1802i −0.972512 1.68444i −0.687911 0.725795i \(-0.741472\pi\)
−0.284601 0.958646i \(-0.591861\pi\)
\(570\) 4.28493 14.1795i 0.179476 0.593913i
\(571\) −3.72019 + 6.44356i −0.155685 + 0.269655i −0.933308 0.359076i \(-0.883092\pi\)
0.777623 + 0.628731i \(0.216425\pi\)
\(572\) −0.0345141 0.0524933i −0.00144311 0.00219485i
\(573\) 8.35134 + 35.6465i 0.348882 + 1.48915i
\(574\) −0.0562047 + 0.0324498i −0.00234594 + 0.00135443i
\(575\) −4.84135 −0.201898
\(576\) −19.9362 13.2601i −0.830676 0.552503i
\(577\) 18.5451i 0.772042i 0.922490 + 0.386021i \(0.126151\pi\)
−0.922490 + 0.386021i \(0.873849\pi\)
\(578\) −5.65605 + 3.26552i −0.235261 + 0.135828i
\(579\) −0.288515 0.307392i −0.0119903 0.0127748i
\(580\) −0.0363607 0.0209929i −0.00150980 0.000871681i
\(581\) 0.0485796 0.0841424i 0.00201542 0.00349081i
\(582\) 0.00837141 0.00785732i 0.000347006 0.000325696i
\(583\) −7.63034 + 4.40538i −0.316017 + 0.182452i
\(584\) 5.57293 0.230609
\(585\) −9.33866 5.45797i −0.386106 0.225659i
\(586\) 0.215491 0.00890185
\(587\) −13.2268 + 7.63650i −0.545929 + 0.315192i −0.747478 0.664286i \(-0.768736\pi\)
0.201550 + 0.979478i \(0.435402\pi\)
\(588\) 0.0130036 + 0.0555041i 0.000536261 + 0.00228895i
\(589\) −19.9635 + 34.5777i −0.822580 + 1.42475i
\(590\) 1.68876 + 0.975007i 0.0695252 + 0.0401404i
\(591\) 9.20545 30.4622i 0.378661 1.25305i
\(592\) −15.7079 + 9.06898i −0.645592 + 0.372733i
\(593\) 15.5028i 0.636624i −0.947986 0.318312i \(-0.896884\pi\)
0.947986 0.318312i \(-0.103116\pi\)
\(594\) 26.8849 4.52637i 1.10310 0.185719i
\(595\) −0.0532989 −0.00218504
\(596\) −0.0490764 + 0.0283343i −0.00201025 + 0.00116062i
\(597\) −22.1631 6.69751i −0.907074 0.274111i
\(598\) 13.5781 + 20.6512i 0.555249 + 0.844491i
\(599\) −23.4811 + 40.6704i −0.959410 + 1.66175i −0.235474 + 0.971881i \(0.575664\pi\)
−0.723936 + 0.689867i \(0.757669\pi\)
\(600\) 4.76420 1.11617i 0.194498 0.0455674i
\(601\) 9.90852 + 17.1621i 0.404177 + 0.700055i 0.994225 0.107313i \(-0.0342247\pi\)
−0.590048 + 0.807368i \(0.700891\pi\)
\(602\) −0.0185391 −0.000755596
\(603\) 12.8828 + 25.9851i 0.524629 + 1.05819i
\(604\) 0.0912024i 0.00371097i
\(605\) 2.36623 1.36614i 0.0962009 0.0555416i
\(606\) 3.36206 + 3.58204i 0.136574 + 0.145510i
\(607\) 9.73052 16.8538i 0.394950 0.684073i −0.598145 0.801388i \(-0.704095\pi\)
0.993095 + 0.117315i \(0.0374287\pi\)
\(608\) 0.0803291 0.139134i 0.00325777 0.00564263i
\(609\) 0.121349 + 0.129288i 0.00491729 + 0.00523903i
\(610\) 6.14261 + 10.6393i 0.248707 + 0.430773i
\(611\) −16.7663 + 33.3719i −0.678291 + 1.35008i
\(612\) 0.0587530 0.0291284i 0.00237495 0.00117745i
\(613\) 35.8156i 1.44658i −0.690546 0.723288i \(-0.742630\pi\)
0.690546 0.723288i \(-0.257370\pi\)
\(614\) 8.65187 + 14.9855i 0.349161 + 0.604765i
\(615\) −1.57962 6.74236i −0.0636963 0.271878i
\(616\) −0.103944 0.0600119i −0.00418801 0.00241795i
\(617\) −7.87734 4.54798i −0.317130 0.183095i 0.332983 0.942933i \(-0.391945\pi\)
−0.650112 + 0.759838i \(0.725278\pi\)
\(618\) −11.5251 + 38.1383i −0.463608 + 1.53415i
\(619\) −4.43877 + 2.56273i −0.178409 + 0.103005i −0.586545 0.809917i \(-0.699512\pi\)
0.408136 + 0.912921i \(0.366179\pi\)
\(620\) 0.0310808 0.00124824
\(621\) −24.8072 + 4.17657i −0.995481 + 0.167600i
\(622\) 41.0704i 1.64677i
\(623\) 0.0204607 + 0.0354389i 0.000819739 + 0.00141983i
\(624\) −18.1654 17.2322i −0.727200 0.689838i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −32.9284 19.0112i −1.31608 0.759840i
\(627\) −8.84340 37.7468i −0.353172 1.50746i
\(628\) −0.0392760 0.0680280i −0.00156728 0.00271461i
\(629\) 21.0313i 0.838572i
\(630\) 0.0486002 + 0.00308222i 0.00193628 + 0.000122798i
\(631\) 44.9471i 1.78931i 0.446753 + 0.894657i \(0.352580\pi\)
−0.446753 + 0.894657i \(0.647420\pi\)
\(632\) −1.84431 + 1.06481i −0.0733628 + 0.0423560i
\(633\) −20.3913 + 19.1390i −0.810481 + 0.760708i
\(634\) 21.9468 38.0129i 0.871617 1.50969i
\(635\) 16.2739 + 9.39576i 0.645811 + 0.372859i
\(636\) 0.0141186 0.0132516i 0.000559839 0.000525459i
\(637\) −1.46370 25.1959i −0.0579939 0.998298i
\(638\) −46.8512 −1.85485
\(639\) 9.62876 14.4766i 0.380908 0.572687i
\(640\) 11.3534 0.448784
\(641\) 8.58775 + 14.8744i 0.339196 + 0.587504i 0.984282 0.176606i \(-0.0565118\pi\)
−0.645086 + 0.764110i \(0.723178\pi\)
\(642\) 5.39495 1.26394i 0.212922 0.0498838i
\(643\) 22.8056 + 13.1668i 0.899366 + 0.519249i 0.876994 0.480500i \(-0.159545\pi\)
0.0223716 + 0.999750i \(0.492878\pi\)
\(644\) −0.000226015 0 0.000130490i −8.90625e−6 0 5.14202e-6i
\(645\) 0.572226 1.89358i 0.0225314 0.0745598i
\(646\) −19.8793 34.4319i −0.782140 1.35471i
\(647\) 8.35488 0.328464 0.164232 0.986422i \(-0.447485\pi\)
0.164232 + 0.986422i \(0.447485\pi\)
\(648\) 23.4490 9.82931i 0.921165 0.386132i
\(649\) 5.10369 0.200337
\(650\) 5.09642 0.296065i 0.199898 0.0116126i
\(651\) −0.125650 0.0379705i −0.00492461 0.00148818i
\(652\) −0.0285395 0.0164773i −0.00111769 0.000645301i
\(653\) −9.65746 + 16.7272i −0.377926 + 0.654587i −0.990760 0.135625i \(-0.956696\pi\)
0.612835 + 0.790211i \(0.290029\pi\)
\(654\) −4.67005 19.9334i −0.182613 0.779459i
\(655\) −2.56619 + 1.48159i −0.100269 + 0.0578906i
\(656\) 16.0299i 0.625864i
\(657\) −3.27743 + 4.92754i −0.127865 + 0.192242i
\(658\) 0.168140i 0.00655478i
\(659\) 4.11302 + 7.12397i 0.160221 + 0.277510i 0.934948 0.354785i \(-0.115446\pi\)
−0.774727 + 0.632296i \(0.782113\pi\)
\(660\) −0.0220050 + 0.0206536i −0.000856543 + 0.000803942i
\(661\) −15.8360 9.14292i −0.615949 0.355618i 0.159341 0.987224i \(-0.449063\pi\)
−0.775290 + 0.631605i \(0.782396\pi\)
\(662\) −20.5458 + 35.5864i −0.798536 + 1.38311i
\(663\) −27.8356 + 8.25074i −1.08105 + 0.320432i
\(664\) 11.9708 + 20.7341i 0.464558 + 0.804638i
\(665\) 0.0692491i 0.00268536i
\(666\) 1.21622 19.1772i 0.0471274 0.743102i
\(667\) 43.2305 1.67389
\(668\) 0.0728559 0.0420634i 0.00281888 0.00162748i
\(669\) −37.0172 + 8.67247i −1.43117 + 0.335297i
\(670\) −11.8545 6.84418i −0.457978 0.264414i
\(671\) 27.8458 + 16.0768i 1.07498 + 0.620638i
\(672\) 0.000505591 0 0.000152786i 1.95036e−5 0 5.89384e-6i
\(673\) 6.31801 + 10.9431i 0.243542 + 0.421826i 0.961721 0.274032i \(-0.0883574\pi\)
−0.718179 + 0.695858i \(0.755024\pi\)
\(674\) 22.7951i 0.878033i
\(675\) −1.81491 + 4.86889i −0.0698559 + 0.187404i
\(676\) −0.0364868 0.0490410i −0.00140334 0.00188619i
\(677\) 1.00014 + 1.73230i 0.0384386 + 0.0665775i 0.884605 0.466342i \(-0.154428\pi\)
−0.846166 + 0.532919i \(0.821095\pi\)
\(678\) −6.32781 + 20.9397i −0.243018 + 0.804184i
\(679\) 2.68371e−5 0 4.64832e-5i 1.02991e−6 0 1.78386e-6i
\(680\) 6.56686 11.3741i 0.251827 0.436178i
\(681\) 1.52044 0.356213i 0.0582636 0.0136501i
\(682\) 30.0360 17.3413i 1.15014 0.664032i
\(683\) 11.3285i 0.433475i −0.976230 0.216737i \(-0.930458\pi\)
0.976230 0.216737i \(-0.0695415\pi\)
\(684\) 0.0378454 + 0.0763355i 0.00144706 + 0.00291876i
\(685\) 19.7279 0.753764
\(686\) 0.113627 + 0.196808i 0.00433830 + 0.00751416i
\(687\) −2.04886 2.18291i −0.0781688 0.0832833i
\(688\) 2.28953 3.96559i 0.0872877 0.151187i
\(689\) −7.16303 + 4.70966i −0.272890 + 0.179424i
\(690\) 8.65692 8.12529i 0.329563 0.309324i
\(691\) 15.1112 8.72447i 0.574858 0.331895i −0.184229 0.982883i \(-0.558979\pi\)
0.759087 + 0.650989i \(0.225646\pi\)
\(692\) 0.121839 0.00463163
\(693\) 0.114191 0.0566134i 0.00433776 0.00215056i
\(694\) 17.5023i 0.664379i
\(695\) 15.6796 9.05260i 0.594759 0.343385i
\(696\) −42.5416 + 9.96675i −1.61254 + 0.377789i
\(697\) −16.0968 9.29349i −0.609710 0.352016i
\(698\) −0.790008 + 1.36833i −0.0299022 + 0.0517922i
\(699\) 30.1521 + 9.11172i 1.14046 + 0.344637i
\(700\) −4.66844e−5 0 2.69532e-5i −1.76450e−6 0 1.01874e-6i
\(701\) −14.9281 −0.563828 −0.281914 0.959440i \(-0.590969\pi\)
−0.281914 + 0.959440i \(0.590969\pi\)
\(702\) 25.8588 5.91367i 0.975979 0.223197i
\(703\) −27.3251 −1.03059
\(704\) 25.6133 14.7878i 0.965336 0.557337i
\(705\) 17.1738 + 5.18980i 0.646804 + 0.195459i
\(706\) 10.9787 19.0156i 0.413188 0.715662i
\(707\) 0.0198896 + 0.0114833i 0.000748027 + 0.000431873i
\(708\) −0.0109206 + 0.00255851i −0.000410423 + 9.61548e-5i
\(709\) 28.4274 16.4125i 1.06761 0.616386i 0.140084 0.990140i \(-0.455263\pi\)
0.927528 + 0.373753i \(0.121929\pi\)
\(710\) 8.20565i 0.307952i
\(711\) 0.143135 2.25694i 0.00536799 0.0846420i
\(712\) −10.0837 −0.377902
\(713\) −27.7148 + 16.0011i −1.03793 + 0.599247i
\(714\) 0.0953048 0.0894521i 0.00356669 0.00334766i
\(715\) 11.1642 7.34038i 0.417516 0.274515i
\(716\) 0.00854296 0.0147968i 0.000319265 0.000552984i
\(717\) 17.6474 + 18.8021i 0.659055 + 0.702177i
\(718\) 18.1552 + 31.4457i 0.677545 + 1.17354i
\(719\) 26.2659 0.979554 0.489777 0.871848i \(-0.337078\pi\)
0.489777 + 0.871848i \(0.337078\pi\)
\(720\) −6.66131 + 10.0151i −0.248253 + 0.373242i
\(721\) 0.186258i 0.00693662i
\(722\) 21.4385 12.3775i 0.797860 0.460644i
\(723\) −15.6658 + 3.67023i −0.582618 + 0.136497i
\(724\) −0.0212376 + 0.0367846i −0.000789290 + 0.00136709i
\(725\) 4.46472 7.73312i 0.165815 0.287201i
\(726\) −1.93829 + 6.41410i −0.0719368 + 0.238050i
\(727\) −14.8130 25.6568i −0.549382 0.951558i −0.998317 0.0579934i \(-0.981530\pi\)
0.448935 0.893565i \(-0.351804\pi\)
\(728\) −0.104350 0.0524263i −0.00386748 0.00194305i
\(729\) −5.09933 + 26.5141i −0.188864 + 0.982003i
\(730\) 2.79303i 0.103375i
\(731\) −2.65476 4.59817i −0.0981897 0.170070i
\(732\) −0.0676426 0.0204411i −0.00250014 0.000755524i
\(733\) −40.5515 23.4124i −1.49780 0.864758i −0.497807 0.867288i \(-0.665861\pi\)
−0.999997 + 0.00253007i \(0.999195\pi\)
\(734\) −22.5568 13.0232i −0.832587 0.480694i
\(735\) −11.8045 + 2.76559i −0.435415 + 0.102010i
\(736\) 0.111519 0.0643855i 0.00411064 0.00237328i
\(737\) −35.8259 −1.31967
\(738\) 14.1403 + 9.40506i 0.520512 + 0.346205i
\(739\) 9.80336i 0.360622i −0.983610 0.180311i \(-0.942290\pi\)
0.983610 0.180311i \(-0.0577105\pi\)
\(740\) 0.0106355 + 0.0184213i 0.000390969 + 0.000677179i
\(741\) −10.7199 36.1657i −0.393804 1.32858i
\(742\) 0.0192975 0.0334242i 0.000708432 0.00122704i
\(743\) 3.08670 + 1.78211i 0.113240 + 0.0653792i 0.555550 0.831483i \(-0.312508\pi\)
−0.442310 + 0.896862i \(0.645841\pi\)
\(744\) 23.5841 22.1358i 0.864635 0.811537i
\(745\) −6.02608 10.4375i −0.220778 0.382399i
\(746\) 21.2300i 0.777287i
\(747\) −25.3729 1.60915i −0.928347 0.0588757i
\(748\) 0.0810035i 0.00296178i
\(749\) 0.0224336 0.0129520i 0.000819705 0.000473257i
\(750\) −0.559399 2.38771i −0.0204264 0.0871870i
\(751\) −7.98664 + 13.8333i −0.291437 + 0.504783i −0.974150 0.225904i \(-0.927467\pi\)
0.682713 + 0.730687i \(0.260800\pi\)
\(752\) 35.9659 + 20.7649i 1.31154 + 0.757219i
\(753\) −5.64901 1.70709i −0.205862 0.0622098i
\(754\) −45.5081 + 2.64369i −1.65731 + 0.0962777i
\(755\) 19.3967 0.705920
\(756\) −0.000215960 0 0.000178383i −7.85440e−6 0 6.48774e-6i
\(757\) −5.47878 −0.199130 −0.0995648 0.995031i \(-0.531745\pi\)
−0.0995648 + 0.995031i \(0.531745\pi\)
\(758\) −22.2558 38.5481i −0.808366 1.40013i
\(759\) 8.98888 29.7456i 0.326276 1.07970i
\(760\) 14.7780 + 8.53205i 0.536053 + 0.309490i
\(761\) −24.3314 14.0478i −0.882013 0.509231i −0.0106917 0.999943i \(-0.503403\pi\)
−0.871322 + 0.490712i \(0.836737\pi\)
\(762\) −44.8688 + 10.5120i −1.62542 + 0.380808i
\(763\) −0.0478556 0.0828883i −0.00173249 0.00300076i
\(764\) 0.0993886 0.00359575
\(765\) 6.19497 + 12.4955i 0.223980 + 0.451775i
\(766\) 38.1320 1.37776
\(767\) 4.95739 0.287988i 0.179001 0.0103987i
\(768\) −0.142514 + 0.133762i −0.00514254 + 0.00482674i
\(769\) 6.60502 + 3.81341i 0.238183 + 0.137515i 0.614341 0.789040i \(-0.289422\pi\)
−0.376158 + 0.926555i \(0.622755\pi\)
\(770\) −0.0300767 + 0.0520943i −0.00108389 + 0.00187735i
\(771\) −38.1249 + 35.7836i −1.37303 + 1.28872i
\(772\) −0.000991126 0 0.000572227i −3.56714e−5 0 2.05949e-5i
\(773\) 40.5127i 1.45714i −0.684971 0.728570i \(-0.740185\pi\)
0.684971 0.728570i \(-0.259815\pi\)
\(774\) 2.15481 + 4.34633i 0.0774531 + 0.156226i
\(775\) 6.61020i 0.237445i
\(776\) 0.00661309 + 0.0114542i 0.000237396 + 0.000411182i
\(777\) −0.0204914 0.0874644i −0.000735124 0.00313777i
\(778\) −23.8021 13.7422i −0.853348 0.492681i
\(779\) 12.0747 20.9139i 0.432620 0.749320i
\(780\) −0.0202088 + 0.0213033i −0.000723590 + 0.000762780i
\(781\) 10.7381 + 18.5990i 0.384241 + 0.665525i
\(782\) 31.8673i 1.13957i
\(783\) 16.2061 43.4764i 0.579159 1.55372i
\(784\) −28.0651 −1.00233
\(785\) 14.4680 8.35313i 0.516387 0.298136i
\(786\) 2.10209 6.95614i 0.0749791 0.248117i
\(787\) 35.7232 + 20.6248i 1.27340 + 0.735196i 0.975626 0.219442i \(-0.0704236\pi\)
0.297771 + 0.954637i \(0.403757\pi\)
\(788\) −0.0748144 0.0431941i −0.00266515 0.00153873i
\(789\) −7.49440 31.9887i −0.266808 1.13883i
\(790\) 0.533661 + 0.924329i 0.0189868 + 0.0328861i
\(791\) 0.102264i 0.00363610i
\(792\) −1.98783 + 31.3440i −0.0706345 + 1.11376i
\(793\) 27.9548 + 14.0447i 0.992703 + 0.498741i
\(794\) 11.8516 + 20.5276i 0.420597 + 0.728496i
\(795\) 2.81832 + 3.00271i 0.0999553 + 0.106495i
\(796\) −0.0314263 + 0.0544319i −0.00111388 + 0.00192929i
\(797\) 8.17615 14.1615i 0.289614 0.501626i −0.684104 0.729385i \(-0.739806\pi\)
0.973718 + 0.227759i \(0.0731397\pi\)
\(798\) 0.116222 + 0.123826i 0.00411420 + 0.00438338i
\(799\) 41.7031 24.0773i 1.47535 0.851793i
\(800\) 0.0265982i 0.000940387i
\(801\) 5.93020 8.91593i 0.209533 0.315029i
\(802\) 8.23124 0.290655
\(803\) −3.65504 6.33071i −0.128984 0.223406i
\(804\) 0.0766587 0.0179598i 0.00270354 0.000633393i
\(805\) 0.0277523 0.0480684i 0.000978141 0.00169419i
\(806\) 28.1964 18.5390i 0.993177 0.653009i
\(807\) 5.72635 + 1.73046i 0.201577 + 0.0609150i
\(808\) −4.90113 + 2.82967i −0.172421 + 0.0995474i
\(809\) −27.3316 −0.960927 −0.480463 0.877015i \(-0.659532\pi\)
−0.480463 + 0.877015i \(0.659532\pi\)
\(810\) −4.92624 11.7522i −0.173090 0.412928i
\(811\) 55.6820i 1.95526i 0.210336 + 0.977629i \(0.432544\pi\)
−0.210336 + 0.977629i \(0.567456\pi\)
\(812\) 0.000416865 0 0.000240677i 1.46291e−5 0 8.44611e-6i
\(813\) 6.81399 22.5485i 0.238977 0.790811i
\(814\) 20.5560 + 11.8680i 0.720486 + 0.415973i
\(815\) 3.50436 6.06973i 0.122752 0.212613i
\(816\) 7.36426 + 31.4333i 0.257801 + 1.10038i
\(817\) 5.97422 3.44922i 0.209012 0.120673i
\(818\) 23.2103 0.811528
\(819\) 0.107723 0.0614340i 0.00376415 0.00214668i
\(820\) −0.0187989 −0.000656485
\(821\) 1.33908 0.773119i 0.0467343 0.0269820i −0.476451 0.879201i \(-0.658077\pi\)
0.523185 + 0.852219i \(0.324744\pi\)
\(822\) −35.2759 + 33.1096i −1.23039 + 1.15483i
\(823\) 15.9113 27.5591i 0.554631 0.960650i −0.443301 0.896373i \(-0.646193\pi\)
0.997932 0.0642768i \(-0.0204741\pi\)
\(824\) −39.7480 22.9485i −1.38469 0.799450i
\(825\) −4.39257 4.67997i −0.152930 0.162936i
\(826\) −0.0193612 + 0.0111782i −0.000673661 + 0.000388938i
\(827\) 22.7332i 0.790510i 0.918571 + 0.395255i \(0.129344\pi\)
−0.918571 + 0.395255i \(0.870656\pi\)
\(828\) −0.00432234 + 0.0681543i −0.000150212 + 0.00236853i
\(829\) 36.3527 1.26258 0.631291 0.775546i \(-0.282526\pi\)
0.631291 + 0.775546i \(0.282526\pi\)
\(830\) 10.3915 5.99951i 0.360693 0.208246i
\(831\) −3.02186 12.8984i −0.104827 0.447440i
\(832\) 24.0446 15.8092i 0.833597 0.548086i
\(833\) −16.2710 + 28.1822i −0.563757 + 0.976456i
\(834\) −12.8439 + 42.5023i −0.444747 + 1.47173i
\(835\) 8.94595 + 15.4948i 0.309587 + 0.536221i
\(836\) −0.105245 −0.00363996
\(837\) 5.70254 + 33.8709i 0.197109 + 1.17075i
\(838\) 34.2838i 1.18431i
\(839\) 8.60189 4.96630i 0.296970 0.171456i −0.344111 0.938929i \(-0.611820\pi\)
0.641081 + 0.767473i \(0.278486\pi\)
\(840\) −0.0162280 + 0.0537008i −0.000559918 + 0.00185285i
\(841\) −25.3674 + 43.9376i −0.874738 + 1.51509i
\(842\) −22.4752 + 38.9282i −0.774547 + 1.34155i
\(843\) −38.0170 + 8.90671i −1.30937 + 0.306763i
\(844\) 0.0379595 + 0.0657477i 0.00130662 + 0.00226313i
\(845\) 10.4299 7.75993i 0.358801 0.266950i
\(846\) −39.4190 + 19.5430i −1.35525 + 0.671904i
\(847\) 0.0313249i 0.00107634i
\(848\) 4.76639 + 8.25563i 0.163678 + 0.283499i
\(849\) 0.559418 0.525063i 0.0191992 0.0180201i
\(850\) −5.70047 3.29117i −0.195524 0.112886i
\(851\) −18.9674 10.9508i −0.650194 0.375390i
\(852\) −0.0323008 0.0344142i −0.00110661 0.00117901i
\(853\) −8.72420 + 5.03692i −0.298711 + 0.172461i −0.641864 0.766819i \(-0.721839\pi\)
0.343153 + 0.939280i \(0.388505\pi\)
\(854\) −0.140847 −0.00481967
\(855\) −16.2349 + 8.04888i −0.555221 + 0.275266i
\(856\) 6.38319i 0.218173i
\(857\) 9.28122 + 16.0755i 0.317040 + 0.549130i 0.979869 0.199641i \(-0.0639776\pi\)
−0.662829 + 0.748771i \(0.730644\pi\)
\(858\) −7.64342 + 31.8624i −0.260942 + 1.08777i
\(859\) −20.4160 + 35.3616i −0.696586 + 1.20652i 0.273058 + 0.961998i \(0.411965\pi\)
−0.969643 + 0.244524i \(0.921368\pi\)
\(860\) −0.00465059 0.00268502i −0.000158584 9.15584e-5i
\(861\) 0.0759980 + 0.0229660i 0.00259000 + 0.000782679i
\(862\) −12.6657 21.9376i −0.431395 0.747197i
\(863\) 24.6388i 0.838714i 0.907821 + 0.419357i \(0.137744\pi\)
−0.907821 + 0.419357i \(0.862256\pi\)
\(864\) −0.0229459 0.136290i −0.000780636 0.00463668i
\(865\) 25.9125i 0.881051i
\(866\) 31.2284 18.0297i 1.06118 0.612674i
\(867\) 7.64790 + 2.31114i 0.259736 + 0.0784903i
\(868\) −0.000178166 0 0.000308593i −6.04736e−6 0 1.04743e-5i
\(869\) 2.41921 + 1.39673i 0.0820660 + 0.0473808i
\(870\) 4.99512 + 21.3209i 0.169350 + 0.722847i
\(871\) −34.7990 + 2.02157i −1.17912 + 0.0684982i
\(872\) 23.5848 0.798682
\(873\) −0.0140169 0.000888949i −0.000474400 3.00864e-5i
\(874\) 41.4040 1.40051
\(875\) −0.00573236 0.00992873i −0.000193789 0.000335652i
\(876\) 0.0109945 + 0.0117139i 0.000371470 + 0.000395775i
\(877\) −41.5931 24.0138i −1.40450 0.810889i −0.409650 0.912243i \(-0.634349\pi\)
−0.994850 + 0.101354i \(0.967683\pi\)
\(878\) −8.11900 4.68751i −0.274003 0.158196i
\(879\) −0.180406 0.192210i −0.00608495 0.00648308i
\(880\) −7.42880 12.8671i −0.250425 0.433749i
\(881\) 16.2470 0.547374 0.273687 0.961819i \(-0.411757\pi\)
0.273687 + 0.961819i \(0.411757\pi\)
\(882\) 16.4663 24.7568i 0.554451 0.833605i
\(883\) −13.1468 −0.442426 −0.221213 0.975225i \(-0.571002\pi\)
−0.221213 + 0.975225i \(0.571002\pi\)
\(884\) 0.00457083 + 0.0786815i 0.000153734 + 0.00264634i
\(885\) −0.544139 2.32258i −0.0182910 0.0780726i
\(886\) 20.4352 + 11.7982i 0.686533 + 0.396370i
\(887\) 7.81958 13.5439i 0.262556 0.454760i −0.704365 0.709838i \(-0.748768\pi\)
0.966920 + 0.255078i \(0.0821013\pi\)
\(888\) 21.1899 + 6.40341i 0.711085 + 0.214884i
\(889\) −0.186576 + 0.107720i −0.00625756 + 0.00361280i
\(890\) 5.05372i 0.169401i
\(891\) −26.5451 20.1909i −0.889293 0.676422i
\(892\) 0.103210i 0.00345574i
\(893\) 31.2827 + 54.1832i 1.04683 + 1.81317i
\(894\) 28.2927 + 8.54983i 0.946249 + 0.285949i
\(895\) 3.14696 + 1.81690i 0.105191 + 0.0607322i
\(896\) −0.0650820 + 0.112725i −0.00217424 + 0.00376589i
\(897\) 7.05274 29.4001i 0.235484 0.981641i
\(898\) −3.75400 6.50213i −0.125273 0.216979i
\(899\) 59.0254i 1.96861i
\(900\) 0.0117451 + 0.00781196i 0.000391504 + 0.000260399i
\(901\) 11.0534 0.368243
\(902\) −18.1669 + 10.4887i −0.604892 + 0.349235i
\(903\) 0.0155207 + 0.0165362i 0.000516496 + 0.000550289i
\(904\) −21.8235 12.5998i −0.725838 0.419063i
\(905\) −7.82328 4.51677i −0.260055 0.150143i
\(906\) −34.6837 + 32.5538i −1.15229 + 1.08153i
\(907\) 12.4039 + 21.4842i 0.411864 + 0.713370i 0.995094 0.0989378i \(-0.0315445\pi\)
−0.583229 + 0.812307i \(0.698211\pi\)
\(908\) 0.00423927i 0.000140685i
\(909\) 0.380372 5.99767i 0.0126161 0.198930i
\(910\) −0.0262749 + 0.0522981i −0.000871005 + 0.00173367i
\(911\) −9.44811 16.3646i −0.313030 0.542183i 0.665987 0.745963i \(-0.268011\pi\)
−0.979017 + 0.203780i \(0.934677\pi\)
\(912\) −40.8400 + 9.56809i −1.35235 + 0.316831i
\(913\) 15.7023 27.1971i 0.519669 0.900094i
\(914\) −24.0774 + 41.7033i −0.796410 + 1.37942i
\(915\) 4.34736 14.3861i 0.143719 0.475589i
\(916\) −0.00703838 + 0.00406361i −0.000232555 + 0.000134265i
\(917\) 0.0339721i 0.00112186i
\(918\) −32.0487 11.9463i −1.05776 0.394288i
\(919\) 16.2588 0.536328 0.268164 0.963373i \(-0.413583\pi\)
0.268164 + 0.963373i \(0.413583\pi\)
\(920\) 6.83863 + 11.8448i 0.225463 + 0.390513i
\(921\) 6.12327 20.2628i 0.201768 0.667682i
\(922\) 2.12488 3.68041i 0.0699793 0.121208i
\(923\) 11.4798 + 17.4599i 0.377863 + 0.574701i
\(924\) −7.89241e−5 0 0.000336876i −2.59641e−6 0 1.10824e-5i
\(925\) −3.91779 + 2.26194i −0.128816 + 0.0743721i
\(926\) −41.8784 −1.37621
\(927\) 43.6667 21.6490i 1.43420 0.711045i
\(928\) 0.237507i 0.00779654i
\(929\) −50.0587 + 28.9014i −1.64237 + 0.948224i −0.662386 + 0.749163i \(0.730456\pi\)
−0.979987 + 0.199062i \(0.936211\pi\)
\(930\) −11.0940 11.8198i −0.363786 0.387588i
\(931\) −36.6160 21.1403i −1.20004 0.692845i
\(932\) 0.0427543 0.0740527i 0.00140046 0.00242568i
\(933\) 36.6333 34.3836i 1.19932 1.12567i
\(934\) −11.5145 + 6.64788i −0.376765 + 0.217525i
\(935\) −17.2277 −0.563405
\(936\) −0.162186 + 30.5576i −0.00530123 + 0.998807i
\(937\) 25.0975 0.819898 0.409949 0.912108i \(-0.365546\pi\)
0.409949 + 0.912108i \(0.365546\pi\)
\(938\) 0.135908 0.0784665i 0.00443755 0.00256202i
\(939\) 10.6099 + 45.2868i 0.346241 + 1.47788i
\(940\) 0.0243518 0.0421785i 0.000794267 0.00137571i
\(941\) 46.5349 + 26.8670i 1.51700 + 0.875838i 0.999801 + 0.0199705i \(0.00635724\pi\)
0.517195 + 0.855867i \(0.326976\pi\)
\(942\) −11.8515 + 39.2183i −0.386142 + 1.27780i
\(943\) 16.7630 9.67811i 0.545878 0.315163i
\(944\) 5.52192i 0.179723i
\(945\) −0.0379382 0.0459300i −0.00123413 0.00149410i
\(946\) −5.99234 −0.194828
\(947\) 0.109296 0.0631019i 0.00355163 0.00205054i −0.498223 0.867049i \(-0.666014\pi\)
0.501775 + 0.864998i \(0.332681\pi\)
\(948\) −0.00587669 0.00177589i −0.000190866 5.76783e-5i
\(949\) −3.90749 5.94299i −0.126843 0.192918i
\(950\) 4.27608 7.40639i 0.138734 0.240295i
\(951\) −52.2797 + 12.2482i −1.69528 + 0.397176i
\(952\) 0.0752871 + 0.130401i 0.00244007 + 0.00422632i
\(953\) 9.74893 0.315799 0.157899 0.987455i \(-0.449528\pi\)
0.157899 + 0.987455i \(0.449528\pi\)
\(954\) −10.0790 0.639208i −0.326319 0.0206951i
\(955\) 21.1378i 0.684002i
\(956\) 0.0606237 0.0350011i 0.00196071 0.00113202i
\(957\) 39.2232 + 41.7895i 1.26791 + 1.35086i
\(958\) 3.40326 5.89462i 0.109954 0.190447i
\(959\) −0.113087 + 0.195873i −0.00365178 + 0.00632507i
\(960\) −9.46042 10.0794i −0.305334 0.325311i
\(961\) 6.34739 + 10.9940i 0.204754 + 0.354645i
\(962\) 20.6364 + 10.3679i 0.665344 + 0.334273i
\(963\) −5.64397 3.75394i −0.181874 0.120969i
\(964\) 0.0436791i 0.00140681i
\(965\) −0.121700 0.210790i −0.00391766 0.00678559i
\(966\) 0.0310493 + 0.132529i 0.000998994 + 0.00426406i
\(967\) −16.8821 9.74690i −0.542893 0.313439i 0.203358 0.979104i \(-0.434815\pi\)
−0.746250 + 0.665665i \(0.768148\pi\)
\(968\) −6.68482 3.85948i −0.214858 0.124048i
\(969\) −14.0693 + 46.5576i −0.451972 + 1.49564i
\(970\) 0.00574060 0.00331434i 0.000184320 0.000106417i
\(971\) −9.64346 −0.309473 −0.154737 0.987956i \(-0.549453\pi\)
−0.154737 + 0.987956i \(0.549453\pi\)
\(972\) 0.0669218 + 0.0298964i 0.00214652 + 0.000958928i
\(973\) 0.207571i 0.00665441i
\(974\) 2.59022 + 4.48640i 0.0829960 + 0.143753i
\(975\) −4.53074 4.29796i −0.145100 0.137645i
\(976\) 17.3942 30.1277i 0.556776 0.964364i
\(977\) −31.9311 18.4354i −1.02157 0.589801i −0.107009 0.994258i \(-0.534127\pi\)
−0.914557 + 0.404457i \(0.867461\pi\)
\(978\) 3.92067 + 16.7348i 0.125369 + 0.535120i
\(979\) 6.61345 + 11.4548i 0.211367 + 0.366098i
\(980\) 0.0329130i 0.00105137i
\(981\) −13.8702 + 20.8535i −0.442841 + 0.665802i
\(982\) 4.66506i 0.148868i
\(983\) −4.06226 + 2.34535i −0.129566 + 0.0748050i −0.563382 0.826196i \(-0.690500\pi\)
0.433816 + 0.901001i \(0.357167\pi\)
\(984\) −14.2646 + 13.3886i −0.454738 + 0.426812i
\(985\) 9.18643 15.9114i 0.292704 0.506978i
\(986\) 50.9019 + 29.3882i 1.62105 + 0.935912i
\(987\) −0.149975 + 0.140765i −0.00477375 + 0.00448059i
\(988\) −0.102228 + 0.00593869i −0.00325230 + 0.000188935i
\(989\) 5.52925 0.175820
\(990\) 15.7089 + 0.996257i 0.499262 + 0.0316631i
\(991\) 31.0206 0.985402 0.492701 0.870199i \(-0.336010\pi\)
0.492701 + 0.870199i \(0.336010\pi\)
\(992\) −0.0879097 0.152264i −0.00279113 0.00483439i
\(993\) 48.9425 11.4664i 1.55314 0.363874i
\(994\) −0.0814717 0.0470377i −0.00258412 0.00149194i
\(995\) −11.5765 6.68368i −0.366999 0.211887i
\(996\) −0.0199649 + 0.0660668i −0.000632612 + 0.00209341i
\(997\) 0.519357 + 0.899552i 0.0164482 + 0.0284891i 0.874132 0.485688i \(-0.161431\pi\)
−0.857684 + 0.514177i \(0.828097\pi\)
\(998\) 19.6535 0.622121
\(999\) −18.1236 + 14.9701i −0.573404 + 0.473633i
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 585.2.bt.b.571.15 yes 108
9.7 even 3 inner 585.2.bt.b.376.40 yes 108
13.12 even 2 inner 585.2.bt.b.571.40 yes 108
117.25 even 6 inner 585.2.bt.b.376.15 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.bt.b.376.15 108 117.25 even 6 inner
585.2.bt.b.376.40 yes 108 9.7 even 3 inner
585.2.bt.b.571.15 yes 108 1.1 even 1 trivial
585.2.bt.b.571.40 yes 108 13.12 even 2 inner