Properties

Label 152.2.p.a.125.17
Level $152$
Weight $2$
Character 152.125
Analytic conductor $1.214$
Analytic rank $0$
Dimension $36$
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] = [152,2,Mod(45,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.p (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: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 125.17
Character \(\chi\) \(=\) 152.125
Dual form 152.2.p.a.45.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35164 + 0.416007i) q^{2} +(1.63085 + 0.941569i) q^{3} +(1.65388 + 1.12459i) q^{4} +(-3.38526 - 1.95448i) q^{5} +(1.81262 + 1.95111i) q^{6} +0.489256 q^{7} +(1.76761 + 2.20806i) q^{8} +(0.273104 + 0.473030i) q^{9} +O(q^{10})\) \(q+(1.35164 + 0.416007i) q^{2} +(1.63085 + 0.941569i) q^{3} +(1.65388 + 1.12459i) q^{4} +(-3.38526 - 1.95448i) q^{5} +(1.81262 + 1.95111i) q^{6} +0.489256 q^{7} +(1.76761 + 2.20806i) q^{8} +(0.273104 + 0.473030i) q^{9} +(-3.76259 - 4.05006i) q^{10} -1.19595i q^{11} +(1.63834 + 3.39126i) q^{12} +(-3.60074 + 2.07889i) q^{13} +(0.661299 + 0.203534i) q^{14} +(-3.68056 - 6.37492i) q^{15} +(1.47061 + 3.71985i) q^{16} +(1.07966 - 1.87003i) q^{17} +(0.172355 + 0.752981i) q^{18} +(-4.24232 + 1.00138i) q^{19} +(-3.40082 - 7.03949i) q^{20} +(0.797900 + 0.460668i) q^{21} +(0.497525 - 1.61650i) q^{22} +(-0.606476 - 1.05045i) q^{23} +(0.803663 + 5.26534i) q^{24} +(5.14001 + 8.90275i) q^{25} +(-5.73175 + 1.31198i) q^{26} -4.62083i q^{27} +(0.809169 + 0.550210i) q^{28} +(8.31695 - 4.80179i) q^{29} +(-2.32279 - 10.1478i) q^{30} +5.98736 q^{31} +(0.440261 + 5.63970i) q^{32} +(1.12607 - 1.95042i) q^{33} +(2.23727 - 2.07847i) q^{34} +(-1.65626 - 0.956242i) q^{35} +(-0.0802825 + 1.08946i) q^{36} +8.92838i q^{37} +(-6.15068 - 0.411330i) q^{38} -7.82967 q^{39} +(-1.66822 - 10.9296i) q^{40} +(-3.32609 + 5.76096i) q^{41} +(0.886835 + 0.954591i) q^{42} +(-2.90264 - 1.67584i) q^{43} +(1.34495 - 1.97796i) q^{44} -2.13511i q^{45} +(-0.382745 - 1.67213i) q^{46} +(-2.95386 - 5.11624i) q^{47} +(-1.10415 + 7.45119i) q^{48} -6.76063 q^{49} +(3.24384 + 14.1716i) q^{50} +(3.52153 - 2.03316i) q^{51} +(-8.29307 - 0.611117i) q^{52} +(-0.375598 + 0.216852i) q^{53} +(1.92230 - 6.24571i) q^{54} +(-2.33747 + 4.04862i) q^{55} +(0.864816 + 1.08031i) q^{56} +(-7.86143 - 2.36134i) q^{57} +(13.2391 - 3.03040i) q^{58} +(8.71384 + 5.03094i) q^{59} +(1.08195 - 14.6824i) q^{60} +(1.58032 - 0.912395i) q^{61} +(8.09277 + 2.49078i) q^{62} +(0.133618 + 0.231433i) q^{63} +(-1.75108 + 7.80601i) q^{64} +16.2526 q^{65} +(2.33344 - 2.16781i) q^{66} +(6.58679 - 3.80289i) q^{67} +(3.88865 - 1.87863i) q^{68} -2.28416i q^{69} +(-1.84087 - 1.98151i) q^{70} +(-6.86266 + 11.8865i) q^{71} +(-0.561737 + 1.43917i) q^{72} +(-3.34971 + 5.80187i) q^{73} +(-3.71427 + 12.0680i) q^{74} +19.3587i q^{75} +(-8.14240 - 3.11469i) q^{76} -0.585127i q^{77} +(-10.5829 - 3.25720i) q^{78} +(4.39456 - 7.61160i) q^{79} +(2.29197 - 15.4670i) q^{80} +(5.17014 - 8.95495i) q^{81} +(-6.89229 + 6.40308i) q^{82} +1.47727i q^{83} +(0.801568 + 1.65920i) q^{84} +(-7.30990 + 4.22037i) q^{85} +(-3.22617 - 3.47265i) q^{86} +18.0849 q^{87} +(2.64074 - 2.11399i) q^{88} +(-3.15315 - 5.46141i) q^{89} +(0.888221 - 2.88591i) q^{90} +(-1.76168 + 1.01711i) q^{91} +(0.178281 - 2.41934i) q^{92} +(9.76446 + 5.63751i) q^{93} +(-1.86418 - 8.14416i) q^{94} +(16.3185 + 4.90161i) q^{95} +(-4.59216 + 9.61201i) q^{96} +(-1.02763 + 1.77991i) q^{97} +(-9.13796 - 2.81247i) q^{98} +(0.565723 - 0.326620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35164 + 0.416007i 0.955756 + 0.294161i
\(3\) 1.63085 + 0.941569i 0.941569 + 0.543615i 0.890452 0.455078i \(-0.150388\pi\)
0.0511172 + 0.998693i \(0.483722\pi\)
\(4\) 1.65388 + 1.12459i 0.826938 + 0.562293i
\(5\) −3.38526 1.95448i −1.51394 0.874071i −0.999867 0.0163224i \(-0.994804\pi\)
−0.514069 0.857749i \(-0.671862\pi\)
\(6\) 1.81262 + 1.95111i 0.739999 + 0.796536i
\(7\) 0.489256 0.184921 0.0924607 0.995716i \(-0.470527\pi\)
0.0924607 + 0.995716i \(0.470527\pi\)
\(8\) 1.76761 + 2.20806i 0.624946 + 0.780668i
\(9\) 0.273104 + 0.473030i 0.0910347 + 0.157677i
\(10\) −3.76259 4.05006i −1.18983 1.28074i
\(11\) 1.19595i 0.360594i −0.983612 0.180297i \(-0.942294\pi\)
0.983612 0.180297i \(-0.0577058\pi\)
\(12\) 1.63834 + 3.39126i 0.472948 + 0.978974i
\(13\) −3.60074 + 2.07889i −0.998666 + 0.576580i −0.907853 0.419288i \(-0.862280\pi\)
−0.0908128 + 0.995868i \(0.528946\pi\)
\(14\) 0.661299 + 0.203534i 0.176740 + 0.0543967i
\(15\) −3.68056 6.37492i −0.950317 1.64600i
\(16\) 1.47061 + 3.71985i 0.367654 + 0.929963i
\(17\) 1.07966 1.87003i 0.261857 0.453550i −0.704878 0.709328i \(-0.748998\pi\)
0.966735 + 0.255778i \(0.0823317\pi\)
\(18\) 0.172355 + 0.752981i 0.0406246 + 0.177479i
\(19\) −4.24232 + 1.00138i −0.973254 + 0.229732i
\(20\) −3.40082 7.03949i −0.760447 1.57408i
\(21\) 0.797900 + 0.460668i 0.174116 + 0.100526i
\(22\) 0.497525 1.61650i 0.106073 0.344639i
\(23\) −0.606476 1.05045i −0.126459 0.219033i 0.795843 0.605503i \(-0.207028\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(24\) 0.803663 + 5.26534i 0.164047 + 1.07478i
\(25\) 5.14001 + 8.90275i 1.02800 + 1.78055i
\(26\) −5.73175 + 1.31198i −1.12409 + 0.257301i
\(27\) 4.62083i 0.889279i
\(28\) 0.809169 + 0.550210i 0.152918 + 0.103980i
\(29\) 8.31695 4.80179i 1.54442 0.891670i 0.545867 0.837872i \(-0.316201\pi\)
0.998552 0.0537984i \(-0.0171328\pi\)
\(30\) −2.32279 10.1478i −0.424082 1.85272i
\(31\) 5.98736 1.07536 0.537681 0.843148i \(-0.319301\pi\)
0.537681 + 0.843148i \(0.319301\pi\)
\(32\) 0.440261 + 5.63970i 0.0778279 + 0.996967i
\(33\) 1.12607 1.95042i 0.196024 0.339524i
\(34\) 2.23727 2.07847i 0.383688 0.356455i
\(35\) −1.65626 0.956242i −0.279959 0.161634i
\(36\) −0.0802825 + 1.08946i −0.0133804 + 0.181577i
\(37\) 8.92838i 1.46782i 0.679249 + 0.733908i \(0.262306\pi\)
−0.679249 + 0.733908i \(0.737694\pi\)
\(38\) −6.15068 0.411330i −0.997771 0.0667265i
\(39\) −7.82967 −1.25375
\(40\) −1.66822 10.9296i −0.263769 1.72813i
\(41\) −3.32609 + 5.76096i −0.519448 + 0.899711i 0.480296 + 0.877106i \(0.340529\pi\)
−0.999744 + 0.0226044i \(0.992804\pi\)
\(42\) 0.886835 + 0.954591i 0.136842 + 0.147297i
\(43\) −2.90264 1.67584i −0.442648 0.255563i 0.262072 0.965048i \(-0.415594\pi\)
−0.704720 + 0.709485i \(0.748927\pi\)
\(44\) 1.34495 1.97796i 0.202759 0.298189i
\(45\) 2.13511i 0.318283i
\(46\) −0.382745 1.67213i −0.0564327 0.246542i
\(47\) −2.95386 5.11624i −0.430865 0.746281i 0.566083 0.824348i \(-0.308458\pi\)
−0.996948 + 0.0780677i \(0.975125\pi\)
\(48\) −1.10415 + 7.45119i −0.159371 + 1.07549i
\(49\) −6.76063 −0.965804
\(50\) 3.24384 + 14.1716i 0.458749 + 2.00417i
\(51\) 3.52153 2.03316i 0.493113 0.284699i
\(52\) −8.29307 0.611117i −1.15004 0.0847466i
\(53\) −0.375598 + 0.216852i −0.0515924 + 0.0297869i −0.525574 0.850748i \(-0.676150\pi\)
0.473982 + 0.880535i \(0.342816\pi\)
\(54\) 1.92230 6.24571i 0.261591 0.849933i
\(55\) −2.33747 + 4.04862i −0.315185 + 0.545916i
\(56\) 0.864816 + 1.08031i 0.115566 + 0.144362i
\(57\) −7.86143 2.36134i −1.04127 0.312768i
\(58\) 13.2391 3.03040i 1.73838 0.397911i
\(59\) 8.71384 + 5.03094i 1.13444 + 0.654972i 0.945049 0.326929i \(-0.106014\pi\)
0.189396 + 0.981901i \(0.439347\pi\)
\(60\) 1.08195 14.6824i 0.139679 1.89549i
\(61\) 1.58032 0.912395i 0.202339 0.116820i −0.395407 0.918506i \(-0.629397\pi\)
0.597746 + 0.801686i \(0.296063\pi\)
\(62\) 8.09277 + 2.49078i 1.02778 + 0.316330i
\(63\) 0.133618 + 0.231433i 0.0168343 + 0.0291578i
\(64\) −1.75108 + 7.80601i −0.218885 + 0.975751i
\(65\) 16.2526 2.01589
\(66\) 2.33344 2.16781i 0.287226 0.266839i
\(67\) 6.58679 3.80289i 0.804705 0.464597i −0.0404088 0.999183i \(-0.512866\pi\)
0.845114 + 0.534587i \(0.179533\pi\)
\(68\) 3.88865 1.87863i 0.471568 0.227817i
\(69\) 2.28416i 0.274980i
\(70\) −1.84087 1.98151i −0.220026 0.236836i
\(71\) −6.86266 + 11.8865i −0.814447 + 1.41066i 0.0952767 + 0.995451i \(0.469626\pi\)
−0.909724 + 0.415213i \(0.863707\pi\)
\(72\) −0.561737 + 1.43917i −0.0662014 + 0.169607i
\(73\) −3.34971 + 5.80187i −0.392054 + 0.679057i −0.992720 0.120443i \(-0.961569\pi\)
0.600667 + 0.799500i \(0.294902\pi\)
\(74\) −3.71427 + 12.0680i −0.431775 + 1.40287i
\(75\) 19.3587i 2.23535i
\(76\) −8.14240 3.11469i −0.933997 0.357280i
\(77\) 0.585127i 0.0666815i
\(78\) −10.5829 3.25720i −1.19828 0.368805i
\(79\) 4.39456 7.61160i 0.494426 0.856371i −0.505553 0.862796i \(-0.668712\pi\)
0.999979 + 0.00642403i \(0.00204485\pi\)
\(80\) 2.29197 15.4670i 0.256250 1.72926i
\(81\) 5.17014 8.95495i 0.574460 0.994994i
\(82\) −6.89229 + 6.40308i −0.761126 + 0.707102i
\(83\) 1.47727i 0.162152i 0.996708 + 0.0810758i \(0.0258356\pi\)
−0.996708 + 0.0810758i \(0.974164\pi\)
\(84\) 0.801568 + 1.65920i 0.0874582 + 0.181033i
\(85\) −7.30990 + 4.22037i −0.792870 + 0.457764i
\(86\) −3.22617 3.47265i −0.347887 0.374466i
\(87\) 18.0849 1.93890
\(88\) 2.64074 2.11399i 0.281504 0.225352i
\(89\) −3.15315 5.46141i −0.334233 0.578909i 0.649104 0.760700i \(-0.275144\pi\)
−0.983337 + 0.181791i \(0.941811\pi\)
\(90\) 0.888221 2.88591i 0.0936267 0.304201i
\(91\) −1.76168 + 1.01711i −0.184675 + 0.106622i
\(92\) 0.178281 2.41934i 0.0185871 0.252234i
\(93\) 9.76446 + 5.63751i 1.01253 + 0.584583i
\(94\) −1.86418 8.14416i −0.192275 0.840006i
\(95\) 16.3185 + 4.90161i 1.67425 + 0.502895i
\(96\) −4.59216 + 9.61201i −0.468686 + 0.981021i
\(97\) −1.02763 + 1.77991i −0.104340 + 0.180722i −0.913468 0.406910i \(-0.866606\pi\)
0.809128 + 0.587632i \(0.199940\pi\)
\(98\) −9.13796 2.81247i −0.923073 0.284102i
\(99\) 0.565723 0.326620i 0.0568573 0.0328266i
\(100\) −1.51097 + 20.5044i −0.151097 + 2.05044i
\(101\) −4.58086 + 2.64476i −0.455812 + 0.263163i −0.710282 0.703917i \(-0.751433\pi\)
0.254469 + 0.967081i \(0.418099\pi\)
\(102\) 5.60566 1.28312i 0.555043 0.127048i
\(103\) −3.31362 −0.326501 −0.163250 0.986585i \(-0.552198\pi\)
−0.163250 + 0.986585i \(0.552198\pi\)
\(104\) −10.9550 4.27599i −1.07423 0.419295i
\(105\) −1.80074 3.11897i −0.175734 0.304380i
\(106\) −0.597886 + 0.136855i −0.0580719 + 0.0132925i
\(107\) 14.4353i 1.39551i −0.716335 0.697757i \(-0.754182\pi\)
0.716335 0.697757i \(-0.245818\pi\)
\(108\) 5.19652 7.64228i 0.500035 0.735379i
\(109\) 7.50604 + 4.33361i 0.718948 + 0.415085i 0.814365 0.580352i \(-0.197085\pi\)
−0.0954172 + 0.995437i \(0.530419\pi\)
\(110\) −4.84368 + 4.49988i −0.461827 + 0.429047i
\(111\) −8.40668 + 14.5608i −0.797927 + 1.38205i
\(112\) 0.719507 + 1.81996i 0.0679870 + 0.171970i
\(113\) −1.55186 −0.145987 −0.0729933 0.997332i \(-0.523255\pi\)
−0.0729933 + 0.997332i \(0.523255\pi\)
\(114\) −9.64350 6.46210i −0.903197 0.605231i
\(115\) 4.74139i 0.442137i
\(116\) 19.1552 + 1.41155i 1.77852 + 0.131059i
\(117\) −1.96676 1.13551i −0.181827 0.104978i
\(118\) 9.68509 + 10.4250i 0.891585 + 0.959703i
\(119\) 0.528232 0.914925i 0.0484230 0.0838711i
\(120\) 7.57040 19.3953i 0.691080 1.77054i
\(121\) 9.56969 0.869972
\(122\) 2.51558 0.575810i 0.227750 0.0521314i
\(123\) −10.8487 + 6.26349i −0.978193 + 0.564760i
\(124\) 9.90235 + 6.73330i 0.889258 + 0.604668i
\(125\) 20.6394i 1.84604i
\(126\) 0.0843259 + 0.368400i 0.00751235 + 0.0328197i
\(127\) −7.34720 12.7257i −0.651959 1.12923i −0.982647 0.185485i \(-0.940614\pi\)
0.330689 0.943740i \(-0.392719\pi\)
\(128\) −5.61418 + 9.82247i −0.496228 + 0.868192i
\(129\) −3.15583 5.46606i −0.277856 0.481260i
\(130\) 21.9677 + 6.76120i 1.92670 + 0.592996i
\(131\) −8.51234 4.91460i −0.743727 0.429391i 0.0796960 0.996819i \(-0.474605\pi\)
−0.823423 + 0.567428i \(0.807938\pi\)
\(132\) 4.05580 1.95938i 0.353012 0.170542i
\(133\) −2.07558 + 0.489929i −0.179975 + 0.0424822i
\(134\) 10.4850 2.39999i 0.905768 0.207328i
\(135\) −9.03133 + 15.6427i −0.777293 + 1.34631i
\(136\) 6.03758 0.921533i 0.517719 0.0790208i
\(137\) −9.12092 15.7979i −0.779253 1.34971i −0.932373 0.361497i \(-0.882266\pi\)
0.153121 0.988208i \(-0.451068\pi\)
\(138\) 0.950225 3.08736i 0.0808885 0.262814i
\(139\) 18.4790 10.6689i 1.56737 0.904922i 0.570897 0.821022i \(-0.306596\pi\)
0.996474 0.0838999i \(-0.0267376\pi\)
\(140\) −1.66387 3.44411i −0.140623 0.291081i
\(141\) 11.1251i 0.936900i
\(142\) −14.2207 + 13.2113i −1.19338 + 1.10867i
\(143\) 2.48626 + 4.30632i 0.207911 + 0.360113i
\(144\) −1.35797 + 1.71155i −0.113164 + 0.142629i
\(145\) −37.5401 −3.11753
\(146\) −6.94123 + 6.44855i −0.574460 + 0.533686i
\(147\) −11.0255 6.36560i −0.909371 0.525026i
\(148\) −10.0407 + 14.7664i −0.825343 + 1.21379i
\(149\) −7.56378 4.36695i −0.619649 0.357755i 0.157083 0.987585i \(-0.449791\pi\)
−0.776732 + 0.629831i \(0.783124\pi\)
\(150\) −8.05334 + 26.1660i −0.657553 + 2.13645i
\(151\) 15.1038 1.22913 0.614563 0.788867i \(-0.289332\pi\)
0.614563 + 0.788867i \(0.289332\pi\)
\(152\) −9.70988 7.59725i −0.787575 0.616218i
\(153\) 1.17944 0.0953524
\(154\) 0.243417 0.790883i 0.0196151 0.0637312i
\(155\) −20.2688 11.7022i −1.62803 0.939943i
\(156\) −12.9493 8.80513i −1.03677 0.704975i
\(157\) −3.04528 1.75819i −0.243040 0.140319i 0.373533 0.927617i \(-0.378146\pi\)
−0.616573 + 0.787298i \(0.711479\pi\)
\(158\) 9.10635 8.45999i 0.724462 0.673041i
\(159\) −0.816723 −0.0647704
\(160\) 9.53229 19.9523i 0.753594 1.57737i
\(161\) −0.296722 0.513937i −0.0233850 0.0405039i
\(162\) 10.7135 9.95307i 0.841732 0.781987i
\(163\) 22.0891i 1.73015i 0.501639 + 0.865077i \(0.332731\pi\)
−0.501639 + 0.865077i \(0.667269\pi\)
\(164\) −11.9796 + 5.78744i −0.935452 + 0.451923i
\(165\) −7.62411 + 4.40178i −0.593536 + 0.342678i
\(166\) −0.614555 + 1.99674i −0.0476987 + 0.154977i
\(167\) −6.39584 11.0779i −0.494925 0.857235i 0.505058 0.863086i \(-0.331471\pi\)
−0.999983 + 0.00585014i \(0.998138\pi\)
\(168\) 0.393197 + 2.57610i 0.0303358 + 0.198750i
\(169\) 2.14356 3.71276i 0.164889 0.285597i
\(170\) −11.6361 + 2.66347i −0.892446 + 0.204279i
\(171\) −1.63228 1.73326i −0.124823 0.132546i
\(172\) −2.91598 6.03589i −0.222341 0.460232i
\(173\) 5.20348 + 3.00423i 0.395613 + 0.228407i 0.684589 0.728929i \(-0.259982\pi\)
−0.288976 + 0.957336i \(0.593315\pi\)
\(174\) 24.4443 + 7.52343i 1.85312 + 0.570350i
\(175\) 2.51478 + 4.35572i 0.190099 + 0.329262i
\(176\) 4.44877 1.75879i 0.335339 0.132574i
\(177\) 9.47395 + 16.4094i 0.712105 + 1.23340i
\(178\) −1.98994 8.69361i −0.149153 0.651614i
\(179\) 4.64276i 0.347016i −0.984832 0.173508i \(-0.944490\pi\)
0.984832 0.173508i \(-0.0555102\pi\)
\(180\) 2.40111 3.53121i 0.178968 0.263201i
\(181\) −6.13908 + 3.54440i −0.456314 + 0.263453i −0.710493 0.703704i \(-0.751528\pi\)
0.254179 + 0.967157i \(0.418195\pi\)
\(182\) −2.80429 + 0.641895i −0.207868 + 0.0475804i
\(183\) 3.43633 0.254021
\(184\) 1.24744 3.19592i 0.0919623 0.235607i
\(185\) 17.4504 30.2249i 1.28298 2.22218i
\(186\) 10.8528 + 11.6820i 0.795767 + 0.856565i
\(187\) −2.23648 1.29123i −0.163547 0.0944241i
\(188\) 0.868327 11.7835i 0.0633292 0.859401i
\(189\) 2.26077i 0.164447i
\(190\) 20.0177 + 13.4138i 1.45224 + 0.973143i
\(191\) 10.9370 0.791377 0.395689 0.918385i \(-0.370506\pi\)
0.395689 + 0.918385i \(0.370506\pi\)
\(192\) −10.2056 + 11.0816i −0.736528 + 0.799748i
\(193\) −2.29535 + 3.97566i −0.165223 + 0.286174i −0.936734 0.350041i \(-0.886168\pi\)
0.771512 + 0.636215i \(0.219501\pi\)
\(194\) −2.12945 + 1.97830i −0.152885 + 0.142034i
\(195\) 26.5055 + 15.3030i 1.89810 + 1.09587i
\(196\) −11.1812 7.60291i −0.798660 0.543065i
\(197\) 14.9951i 1.06836i 0.845371 + 0.534179i \(0.179379\pi\)
−0.845371 + 0.534179i \(0.820621\pi\)
\(198\) 0.900531 0.206129i 0.0639980 0.0146490i
\(199\) −6.16263 10.6740i −0.436857 0.756659i 0.560588 0.828095i \(-0.310575\pi\)
−0.997445 + 0.0714360i \(0.977242\pi\)
\(200\) −10.5723 + 27.0861i −0.747573 + 1.91528i
\(201\) 14.3227 1.01025
\(202\) −7.29192 + 1.66910i −0.513058 + 0.117438i
\(203\) 4.06911 2.34930i 0.285596 0.164889i
\(204\) 8.11064 + 0.597673i 0.567858 + 0.0418455i
\(205\) 22.5194 13.0016i 1.57282 0.908069i
\(206\) −4.47883 1.37849i −0.312055 0.0960439i
\(207\) 0.331262 0.573763i 0.0230243 0.0398793i
\(208\) −13.0285 10.3370i −0.903361 0.716741i
\(209\) 1.19760 + 5.07361i 0.0828397 + 0.350949i
\(210\) −1.13644 4.96485i −0.0784218 0.342607i
\(211\) −20.0234 11.5605i −1.37847 0.795860i −0.386495 0.922291i \(-0.626314\pi\)
−0.991975 + 0.126431i \(0.959648\pi\)
\(212\) −0.865061 0.0637464i −0.0594127 0.00437812i
\(213\) −22.3839 + 12.9233i −1.53372 + 0.885492i
\(214\) 6.00519 19.5114i 0.410506 1.33377i
\(215\) 6.55079 + 11.3463i 0.446760 + 0.773812i
\(216\) 10.2031 8.16784i 0.694231 0.555751i
\(217\) 2.92935 0.198857
\(218\) 8.34267 + 8.98006i 0.565037 + 0.608207i
\(219\) −10.9257 + 6.30796i −0.738291 + 0.426253i
\(220\) −8.41891 + 4.06723i −0.567603 + 0.274213i
\(221\) 8.97802i 0.603927i
\(222\) −17.4202 + 16.1838i −1.16917 + 1.08618i
\(223\) −0.514660 + 0.891417i −0.0344642 + 0.0596937i −0.882743 0.469856i \(-0.844306\pi\)
0.848279 + 0.529550i \(0.177639\pi\)
\(224\) 0.215400 + 2.75925i 0.0143920 + 0.184360i
\(225\) −2.80751 + 4.86276i −0.187168 + 0.324184i
\(226\) −2.09756 0.645584i −0.139528 0.0429436i
\(227\) 10.8311i 0.718885i −0.933167 0.359442i \(-0.882967\pi\)
0.933167 0.359442i \(-0.117033\pi\)
\(228\) −10.3463 12.7462i −0.685200 0.844139i
\(229\) 7.93635i 0.524449i −0.965007 0.262224i \(-0.915544\pi\)
0.965007 0.262224i \(-0.0844560\pi\)
\(230\) −1.97245 + 6.40866i −0.130059 + 0.422575i
\(231\) 0.550938 0.954252i 0.0362490 0.0627852i
\(232\) 25.3038 + 9.87662i 1.66128 + 0.648432i
\(233\) −8.61835 + 14.9274i −0.564607 + 0.977928i 0.432479 + 0.901644i \(0.357639\pi\)
−0.997086 + 0.0762841i \(0.975694\pi\)
\(234\) −2.18597 2.35298i −0.142901 0.153819i
\(235\) 23.0931i 1.50643i
\(236\) 8.75389 + 18.1200i 0.569830 + 1.17951i
\(237\) 14.3337 8.27556i 0.931073 0.537555i
\(238\) 1.09460 1.01690i 0.0709522 0.0659161i
\(239\) −2.50368 −0.161950 −0.0809749 0.996716i \(-0.525803\pi\)
−0.0809749 + 0.996716i \(0.525803\pi\)
\(240\) 18.3011 23.0662i 1.18133 1.48892i
\(241\) 4.56111 + 7.90007i 0.293807 + 0.508888i 0.974707 0.223488i \(-0.0717445\pi\)
−0.680900 + 0.732376i \(0.738411\pi\)
\(242\) 12.9348 + 3.98106i 0.831481 + 0.255912i
\(243\) 4.85814 2.80485i 0.311650 0.179931i
\(244\) 3.63971 + 0.268210i 0.233009 + 0.0171704i
\(245\) 22.8865 + 13.2135i 1.46217 + 0.844182i
\(246\) −17.2692 + 3.95287i −1.10104 + 0.252026i
\(247\) 13.1937 12.4250i 0.839497 0.790584i
\(248\) 10.5833 + 13.2205i 0.672043 + 0.839500i
\(249\) −1.39095 + 2.40920i −0.0881481 + 0.152677i
\(250\) 8.58613 27.8971i 0.543034 1.76437i
\(251\) 9.69555 5.59773i 0.611978 0.353326i −0.161761 0.986830i \(-0.551717\pi\)
0.773739 + 0.633504i \(0.218384\pi\)
\(252\) −0.0392787 + 0.533026i −0.00247433 + 0.0335775i
\(253\) −1.25629 + 0.725317i −0.0789820 + 0.0456003i
\(254\) −4.63680 20.2571i −0.290939 1.27104i
\(255\) −15.8951 −0.995389
\(256\) −11.6746 + 10.9409i −0.729662 + 0.683808i
\(257\) 6.29483 + 10.9030i 0.392660 + 0.680108i 0.992800 0.119788i \(-0.0382214\pi\)
−0.600139 + 0.799896i \(0.704888\pi\)
\(258\) −1.99164 8.70101i −0.123994 0.541702i
\(259\) 4.36826i 0.271431i
\(260\) 26.8798 + 18.2775i 1.66702 + 1.13352i
\(261\) 4.54279 + 2.62278i 0.281191 + 0.162346i
\(262\) −9.46114 10.1840i −0.584511 0.629168i
\(263\) −2.08534 + 3.61192i −0.128588 + 0.222721i −0.923130 0.384489i \(-0.874378\pi\)
0.794542 + 0.607209i \(0.207711\pi\)
\(264\) 6.29710 0.961144i 0.387560 0.0591543i
\(265\) 1.69533 0.104143
\(266\) −3.00925 0.201245i −0.184509 0.0123392i
\(267\) 11.8756i 0.726777i
\(268\) 15.1704 + 1.11791i 0.926681 + 0.0682871i
\(269\) −9.35654 5.40200i −0.570478 0.329366i 0.186862 0.982386i \(-0.440168\pi\)
−0.757340 + 0.653020i \(0.773502\pi\)
\(270\) −18.7146 + 17.3863i −1.13893 + 1.05809i
\(271\) 0.627938 1.08762i 0.0381445 0.0660682i −0.846323 0.532670i \(-0.821189\pi\)
0.884467 + 0.466602i \(0.154522\pi\)
\(272\) 8.54402 + 1.26609i 0.518057 + 0.0767682i
\(273\) −3.83071 −0.231845
\(274\) −5.75619 25.1475i −0.347744 1.51921i
\(275\) 10.6473 6.14721i 0.642055 0.370691i
\(276\) 2.56873 3.77771i 0.154619 0.227391i
\(277\) 9.05640i 0.544146i −0.962277 0.272073i \(-0.912291\pi\)
0.962277 0.272073i \(-0.0877093\pi\)
\(278\) 29.4154 6.73310i 1.76422 0.403824i
\(279\) 1.63517 + 2.83220i 0.0978953 + 0.169560i
\(280\) −0.816187 5.34739i −0.0487765 0.319568i
\(281\) 0.0974157 + 0.168729i 0.00581133 + 0.0100655i 0.868916 0.494959i \(-0.164817\pi\)
−0.863105 + 0.505024i \(0.831484\pi\)
\(282\) 4.62811 15.0371i 0.275600 0.895447i
\(283\) 19.7126 + 11.3811i 1.17179 + 0.676536i 0.954102 0.299482i \(-0.0968138\pi\)
0.217692 + 0.976018i \(0.430147\pi\)
\(284\) −24.7173 + 11.9411i −1.46670 + 0.708574i
\(285\) 21.9978 + 23.3588i 1.30304 + 1.38366i
\(286\) 1.56907 + 6.85491i 0.0927811 + 0.405339i
\(287\) −1.62731 + 2.81858i −0.0960570 + 0.166376i
\(288\) −2.54751 + 1.74848i −0.150113 + 0.103030i
\(289\) 6.16865 + 10.6844i 0.362862 + 0.628495i
\(290\) −50.7408 15.6169i −2.97960 0.917058i
\(291\) −3.35182 + 1.93517i −0.196487 + 0.113442i
\(292\) −12.0647 + 5.82854i −0.706033 + 0.341089i
\(293\) 6.04147i 0.352946i 0.984305 + 0.176473i \(0.0564689\pi\)
−0.984305 + 0.176473i \(0.943531\pi\)
\(294\) −12.2545 13.1907i −0.714694 0.769298i
\(295\) −19.6658 34.0621i −1.14498 1.98317i
\(296\) −19.7144 + 15.7819i −1.14588 + 0.917306i
\(297\) −5.52630 −0.320668
\(298\) −8.40685 9.04915i −0.486996 0.524203i
\(299\) 4.36753 + 2.52159i 0.252581 + 0.145827i
\(300\) −21.7705 + 32.0169i −1.25692 + 1.84849i
\(301\) −1.42013 0.819913i −0.0818550 0.0472590i
\(302\) 20.4149 + 6.28327i 1.17475 + 0.361562i
\(303\) −9.96090 −0.572238
\(304\) −9.96378 14.3081i −0.571462 0.820628i
\(305\) −7.13304 −0.408437
\(306\) 1.59419 + 0.490657i 0.0911336 + 0.0280490i
\(307\) −6.17141 3.56307i −0.352221 0.203355i 0.313442 0.949607i \(-0.398518\pi\)
−0.665663 + 0.746252i \(0.731851\pi\)
\(308\) 0.658026 0.967728i 0.0374945 0.0551414i
\(309\) −5.40400 3.12000i −0.307423 0.177491i
\(310\) −22.5280 24.2491i −1.27950 1.37726i
\(311\) −20.7970 −1.17929 −0.589644 0.807663i \(-0.700732\pi\)
−0.589644 + 0.807663i \(0.700732\pi\)
\(312\) −13.8398 17.2884i −0.783527 0.978763i
\(313\) 6.42109 + 11.1217i 0.362941 + 0.628633i 0.988444 0.151589i \(-0.0484391\pi\)
−0.625502 + 0.780223i \(0.715106\pi\)
\(314\) −3.38471 3.64330i −0.191010 0.205604i
\(315\) 1.04461i 0.0588574i
\(316\) 15.8279 7.64658i 0.890392 0.430154i
\(317\) −22.8516 + 13.1934i −1.28347 + 0.741014i −0.977482 0.211021i \(-0.932321\pi\)
−0.305992 + 0.952034i \(0.598988\pi\)
\(318\) −1.10392 0.339763i −0.0619047 0.0190529i
\(319\) −5.74272 9.94669i −0.321531 0.556908i
\(320\) 21.1846 23.0029i 1.18425 1.28590i
\(321\) 13.5918 23.5418i 0.758623 1.31397i
\(322\) −0.187260 0.818098i −0.0104356 0.0455908i
\(323\) −2.70767 + 9.01443i −0.150659 + 0.501576i
\(324\) 18.6214 8.99611i 1.03452 0.499784i
\(325\) −37.0157 21.3710i −2.05326 1.18545i
\(326\) −9.18923 + 29.8566i −0.508944 + 1.65360i
\(327\) 8.16079 + 14.1349i 0.451293 + 0.781662i
\(328\) −18.5998 + 2.83894i −1.02700 + 0.156754i
\(329\) −1.44520 2.50315i −0.0796762 0.138003i
\(330\) −12.1362 + 2.77795i −0.668078 + 0.152921i
\(331\) 5.22679i 0.287290i 0.989629 + 0.143645i \(0.0458824\pi\)
−0.989629 + 0.143645i \(0.954118\pi\)
\(332\) −1.66132 + 2.44323i −0.0911767 + 0.134089i
\(333\) −4.22339 + 2.43838i −0.231441 + 0.133622i
\(334\) −4.03640 17.6341i −0.220862 0.964895i
\(335\) −29.7307 −1.62436
\(336\) −0.540213 + 3.64554i −0.0294710 + 0.198880i
\(337\) −16.9498 + 29.3579i −0.923313 + 1.59923i −0.129062 + 0.991637i \(0.541196\pi\)
−0.794252 + 0.607589i \(0.792137\pi\)
\(338\) 4.44186 4.12658i 0.241605 0.224457i
\(339\) −2.53084 1.46118i −0.137456 0.0793605i
\(340\) −16.8358 1.24063i −0.913052 0.0672828i
\(341\) 7.16061i 0.387769i
\(342\) −1.48520 3.02179i −0.0803106 0.163400i
\(343\) −6.73247 −0.363519
\(344\) −1.43039 9.37144i −0.0771214 0.505274i
\(345\) −4.46434 + 7.73247i −0.240352 + 0.416302i
\(346\) 5.78346 + 6.22533i 0.310921 + 0.334676i
\(347\) 13.2221 + 7.63379i 0.709800 + 0.409803i 0.810987 0.585064i \(-0.198931\pi\)
−0.101187 + 0.994867i \(0.532264\pi\)
\(348\) 29.9101 + 20.3380i 1.60335 + 1.09023i
\(349\) 27.6642i 1.48083i −0.672148 0.740416i \(-0.734628\pi\)
0.672148 0.740416i \(-0.265372\pi\)
\(350\) 1.58707 + 6.93355i 0.0848325 + 0.370614i
\(351\) 9.60619 + 16.6384i 0.512740 + 0.888093i
\(352\) 6.74482 0.526532i 0.359500 0.0280643i
\(353\) 13.6507 0.726556 0.363278 0.931681i \(-0.381658\pi\)
0.363278 + 0.931681i \(0.381658\pi\)
\(354\) 5.97898 + 26.1208i 0.317779 + 1.38831i
\(355\) 46.4638 26.8259i 2.46604 1.42377i
\(356\) 0.926909 12.5785i 0.0491261 0.666659i
\(357\) 1.72293 0.994734i 0.0911871 0.0526469i
\(358\) 1.93142 6.27535i 0.102079 0.331662i
\(359\) 8.92820 15.4641i 0.471212 0.816163i −0.528246 0.849092i \(-0.677150\pi\)
0.999458 + 0.0329283i \(0.0104833\pi\)
\(360\) 4.71446 3.77405i 0.248474 0.198910i
\(361\) 16.9945 8.49631i 0.894447 0.447174i
\(362\) −9.77233 + 2.23686i −0.513622 + 0.117567i
\(363\) 15.6067 + 9.01053i 0.819139 + 0.472930i
\(364\) −4.05743 0.298992i −0.212667 0.0156715i
\(365\) 22.6793 13.0939i 1.18709 0.685366i
\(366\) 4.64469 + 1.42954i 0.242782 + 0.0747232i
\(367\) 8.72640 + 15.1146i 0.455514 + 0.788974i 0.998718 0.0506272i \(-0.0161220\pi\)
−0.543203 + 0.839601i \(0.682789\pi\)
\(368\) 3.01561 3.80080i 0.157200 0.198131i
\(369\) −3.63348 −0.189151
\(370\) 36.1604 33.5938i 1.87989 1.74646i
\(371\) −0.183764 + 0.106096i −0.00954053 + 0.00550823i
\(372\) 9.80934 + 20.3047i 0.508591 + 1.05275i
\(373\) 25.7573i 1.33366i 0.745208 + 0.666832i \(0.232350\pi\)
−0.745208 + 0.666832i \(0.767650\pi\)
\(374\) −2.48576 2.67567i −0.128535 0.138356i
\(375\) 19.4334 33.6596i 1.00354 1.73818i
\(376\) 6.07569 15.5659i 0.313330 0.802748i
\(377\) −19.9648 + 34.5800i −1.02824 + 1.78096i
\(378\) 0.940495 3.05575i 0.0483738 0.157171i
\(379\) 13.0547i 0.670575i −0.942116 0.335288i \(-0.891167\pi\)
0.942116 0.335288i \(-0.108833\pi\)
\(380\) 21.4766 + 26.4582i 1.10172 + 1.35728i
\(381\) 27.6716i 1.41766i
\(382\) 14.7830 + 4.54989i 0.756363 + 0.232793i
\(383\) −8.34823 + 14.4596i −0.426575 + 0.738849i −0.996566 0.0828016i \(-0.973613\pi\)
0.569991 + 0.821651i \(0.306947\pi\)
\(384\) −18.4044 + 10.7328i −0.939196 + 0.547705i
\(385\) −1.14362 + 1.98081i −0.0582843 + 0.100951i
\(386\) −4.75639 + 4.41879i −0.242094 + 0.224910i
\(387\) 1.83071i 0.0930604i
\(388\) −3.70124 + 1.78809i −0.187902 + 0.0907766i
\(389\) −0.327382 + 0.189014i −0.0165990 + 0.00958341i −0.508277 0.861194i \(-0.669717\pi\)
0.491678 + 0.870777i \(0.336384\pi\)
\(390\) 29.4598 + 31.7106i 1.49176 + 1.60573i
\(391\) −2.61916 −0.132457
\(392\) −11.9502 14.9279i −0.603576 0.753972i
\(393\) −9.25488 16.0299i −0.466847 0.808602i
\(394\) −6.23807 + 20.2680i −0.314270 + 1.02109i
\(395\) −29.7535 + 17.1782i −1.49706 + 0.864328i
\(396\) 1.30295 + 0.0960142i 0.0654756 + 0.00482490i
\(397\) 9.22821 + 5.32791i 0.463151 + 0.267400i 0.713368 0.700790i \(-0.247169\pi\)
−0.250218 + 0.968190i \(0.580502\pi\)
\(398\) −3.88922 16.9911i −0.194949 0.851688i
\(399\) −3.84625 1.15530i −0.192553 0.0578374i
\(400\) −25.5579 + 32.2126i −1.27790 + 1.61063i
\(401\) 11.7585 20.3664i 0.587194 1.01705i −0.407404 0.913248i \(-0.633566\pi\)
0.994598 0.103802i \(-0.0331007\pi\)
\(402\) 19.3592 + 5.95835i 0.965549 + 0.297176i
\(403\) −21.5589 + 12.4471i −1.07393 + 0.620032i
\(404\) −10.5504 0.777462i −0.524904 0.0386802i
\(405\) −35.0046 + 20.2099i −1.73939 + 1.00424i
\(406\) 6.47732 1.48264i 0.321464 0.0735822i
\(407\) 10.6779 0.529285
\(408\) 10.7141 + 4.18192i 0.530425 + 0.207036i
\(409\) 2.74949 + 4.76225i 0.135953 + 0.235478i 0.925961 0.377619i \(-0.123257\pi\)
−0.790008 + 0.613097i \(0.789924\pi\)
\(410\) 35.8469 8.20526i 1.77035 0.405229i
\(411\) 34.3519i 1.69445i
\(412\) −5.48032 3.72645i −0.269996 0.183589i
\(413\) 4.26329 + 2.46141i 0.209783 + 0.121118i
\(414\) 0.686438 0.637715i 0.0337366 0.0313420i
\(415\) 2.88730 5.00095i 0.141732 0.245487i
\(416\) −13.3096 19.3918i −0.652555 0.950763i
\(417\) 40.1819 1.96772
\(418\) −0.491931 + 7.35592i −0.0240612 + 0.359790i
\(419\) 28.8551i 1.40966i 0.709375 + 0.704831i \(0.248977\pi\)
−0.709375 + 0.704831i \(0.751023\pi\)
\(420\) 0.529350 7.18346i 0.0258296 0.350517i
\(421\) 12.5239 + 7.23070i 0.610379 + 0.352403i 0.773114 0.634267i \(-0.218698\pi\)
−0.162735 + 0.986670i \(0.552031\pi\)
\(422\) −22.2553 23.9556i −1.08337 1.16614i
\(423\) 1.61343 2.79454i 0.0784474 0.135875i
\(424\) −1.14273 0.446034i −0.0554961 0.0216613i
\(425\) 22.1979 1.07676
\(426\) −35.6312 + 8.15588i −1.72634 + 0.395154i
\(427\) 0.773178 0.446395i 0.0374167 0.0216026i
\(428\) 16.2337 23.8742i 0.784688 1.15400i
\(429\) 9.36393i 0.452095i
\(430\) 4.13419 + 18.0613i 0.199368 + 0.870994i
\(431\) 6.28107 + 10.8791i 0.302549 + 0.524029i 0.976713 0.214552i \(-0.0688292\pi\)
−0.674164 + 0.738582i \(0.735496\pi\)
\(432\) 17.1888 6.79546i 0.826996 0.326947i
\(433\) −4.15773 7.20140i −0.199808 0.346077i 0.748658 0.662956i \(-0.230698\pi\)
−0.948466 + 0.316879i \(0.897365\pi\)
\(434\) 3.95944 + 1.21863i 0.190059 + 0.0584961i
\(435\) −61.2221 35.3466i −2.93537 1.69474i
\(436\) 7.54054 + 15.6084i 0.361126 + 0.747509i
\(437\) 3.62476 + 3.84902i 0.173396 + 0.184123i
\(438\) −17.3918 + 3.98094i −0.831013 + 0.190217i
\(439\) 9.33720 16.1725i 0.445640 0.771871i −0.552457 0.833542i \(-0.686309\pi\)
0.998097 + 0.0616705i \(0.0196428\pi\)
\(440\) −13.0714 + 1.99512i −0.623152 + 0.0951134i
\(441\) −1.84636 3.19798i −0.0879217 0.152285i
\(442\) −3.73492 + 12.1351i −0.177652 + 0.577206i
\(443\) −13.1120 + 7.57023i −0.622971 + 0.359673i −0.778025 0.628233i \(-0.783778\pi\)
0.155054 + 0.987906i \(0.450445\pi\)
\(444\) −30.2785 + 14.6277i −1.43695 + 0.694202i
\(445\) 24.6511i 1.16857i
\(446\) −1.06647 + 0.990776i −0.0504989 + 0.0469146i
\(447\) −8.22357 14.2436i −0.388962 0.673701i
\(448\) −0.856724 + 3.81913i −0.0404764 + 0.180437i
\(449\) 19.2630 0.909076 0.454538 0.890727i \(-0.349804\pi\)
0.454538 + 0.890727i \(0.349804\pi\)
\(450\) −5.81770 + 5.40477i −0.274249 + 0.254783i
\(451\) 6.88984 + 3.97785i 0.324430 + 0.187310i
\(452\) −2.56658 1.74520i −0.120722 0.0820872i
\(453\) 24.6319 + 14.2212i 1.15731 + 0.668172i
\(454\) 4.50581 14.6398i 0.211468 0.687078i
\(455\) 7.95168 0.372781
\(456\) −8.68198 21.5325i −0.406571 1.00835i
\(457\) −22.0334 −1.03068 −0.515340 0.856986i \(-0.672334\pi\)
−0.515340 + 0.856986i \(0.672334\pi\)
\(458\) 3.30158 10.7271i 0.154273 0.501245i
\(459\) −8.64111 4.98895i −0.403332 0.232864i
\(460\) −5.33210 + 7.84167i −0.248610 + 0.365620i
\(461\) −10.2154 5.89784i −0.475777 0.274690i 0.242878 0.970057i \(-0.421908\pi\)
−0.718655 + 0.695367i \(0.755242\pi\)
\(462\) 1.14165 1.06061i 0.0531142 0.0493442i
\(463\) 25.0641 1.16483 0.582413 0.812893i \(-0.302109\pi\)
0.582413 + 0.812893i \(0.302109\pi\)
\(464\) 30.0930 + 23.8762i 1.39703 + 1.10843i
\(465\) −22.0368 38.1689i −1.02193 1.77004i
\(466\) −17.8588 + 16.5913i −0.827295 + 0.768575i
\(467\) 31.3644i 1.45137i 0.688027 + 0.725685i \(0.258477\pi\)
−0.688027 + 0.725685i \(0.741523\pi\)
\(468\) −1.97580 4.08977i −0.0913312 0.189050i
\(469\) 3.22263 1.86058i 0.148807 0.0859138i
\(470\) −9.60689 + 31.2136i −0.443133 + 1.43978i
\(471\) −3.31092 5.73468i −0.152559 0.264240i
\(472\) 4.29409 + 28.1334i 0.197651 + 1.29495i
\(473\) −2.00422 + 3.47142i −0.0921543 + 0.159616i
\(474\) 22.8167 5.22268i 1.04801 0.239886i
\(475\) −30.7205 32.6212i −1.40955 1.49676i
\(476\) 1.90254 0.919131i 0.0872029 0.0421283i
\(477\) −0.205155 0.118446i −0.00939340 0.00542328i
\(478\) −3.38409 1.04155i −0.154785 0.0476394i
\(479\) 8.62337 + 14.9361i 0.394012 + 0.682448i 0.992975 0.118328i \(-0.0377536\pi\)
−0.598963 + 0.800777i \(0.704420\pi\)
\(480\) 34.3322 23.5639i 1.56704 1.07554i
\(481\) −18.5611 32.1488i −0.846314 1.46586i
\(482\) 2.87850 + 12.5755i 0.131112 + 0.572799i
\(483\) 1.11754i 0.0508497i
\(484\) 15.8271 + 10.7619i 0.719413 + 0.489179i
\(485\) 6.95760 4.01698i 0.315929 0.182401i
\(486\) 7.73330 1.77013i 0.350790 0.0802948i
\(487\) 11.4106 0.517062 0.258531 0.966003i \(-0.416762\pi\)
0.258531 + 0.966003i \(0.416762\pi\)
\(488\) 4.80801 + 1.87667i 0.217649 + 0.0849529i
\(489\) −20.7984 + 36.0240i −0.940538 + 1.62906i
\(490\) 25.4375 + 27.3809i 1.14915 + 1.23694i
\(491\) −11.9691 6.91038i −0.540159 0.311861i 0.204984 0.978765i \(-0.434286\pi\)
−0.745143 + 0.666904i \(0.767619\pi\)
\(492\) −24.9862 1.84123i −1.12647 0.0830092i
\(493\) 20.7373i 0.933961i
\(494\) 23.0021 11.3055i 1.03491 0.508658i
\(495\) −2.55349 −0.114771
\(496\) 8.80510 + 22.2721i 0.395361 + 1.00005i
\(497\) −3.35759 + 5.81552i −0.150609 + 0.260862i
\(498\) −2.88232 + 2.67773i −0.129160 + 0.119992i
\(499\) 6.98310 + 4.03170i 0.312607 + 0.180484i 0.648092 0.761562i \(-0.275567\pi\)
−0.335486 + 0.942045i \(0.608900\pi\)
\(500\) 23.2107 34.1350i 1.03802 1.52656i
\(501\) 24.0885i 1.07619i
\(502\) 15.4336 3.53271i 0.688836 0.157673i
\(503\) −3.74154 6.48053i −0.166827 0.288953i 0.770476 0.637469i \(-0.220019\pi\)
−0.937303 + 0.348517i \(0.886685\pi\)
\(504\) −0.274833 + 0.704121i −0.0122420 + 0.0313640i
\(505\) 20.6766 0.920094
\(506\) −1.99979 + 0.457746i −0.0889014 + 0.0203493i
\(507\) 6.99163 4.03662i 0.310509 0.179273i
\(508\) 2.15980 29.3093i 0.0958258 1.30039i
\(509\) −3.71493 + 2.14482i −0.164661 + 0.0950673i −0.580066 0.814569i \(-0.696973\pi\)
0.415405 + 0.909637i \(0.363640\pi\)
\(510\) −21.4845 6.61247i −0.951349 0.292805i
\(511\) −1.63886 + 2.83860i −0.0724991 + 0.125572i
\(512\) −20.3314 + 9.93152i −0.898528 + 0.438916i
\(513\) 4.62719 + 19.6030i 0.204295 + 0.865494i
\(514\) 3.97265 + 17.3556i 0.175226 + 0.765523i
\(515\) 11.2175 + 6.47641i 0.494301 + 0.285385i
\(516\) 0.927698 12.5892i 0.0408396 0.554209i
\(517\) −6.11879 + 3.53269i −0.269104 + 0.155367i
\(518\) −1.81723 + 5.90433i −0.0798444 + 0.259421i
\(519\) 5.65738 + 9.79887i 0.248331 + 0.430123i
\(520\) 28.7284 + 35.8868i 1.25982 + 1.57374i
\(521\) −39.3980 −1.72606 −0.863028 0.505156i \(-0.831435\pi\)
−0.863028 + 0.505156i \(0.831435\pi\)
\(522\) 5.04913 + 5.43489i 0.220994 + 0.237879i
\(523\) −18.2456 + 10.5341i −0.797825 + 0.460624i −0.842710 0.538368i \(-0.819041\pi\)
0.0448854 + 0.998992i \(0.485708\pi\)
\(524\) −8.55147 17.7010i −0.373573 0.773272i
\(525\) 9.47134i 0.413363i
\(526\) −4.32122 + 4.01451i −0.188414 + 0.175041i
\(527\) 6.46434 11.1966i 0.281591 0.487730i
\(528\) 8.91128 + 1.32051i 0.387814 + 0.0574680i
\(529\) 10.7644 18.6444i 0.468016 0.810628i
\(530\) 2.29148 + 0.705270i 0.0995357 + 0.0306350i
\(531\) 5.49588i 0.238501i
\(532\) −3.98372 1.52388i −0.172716 0.0660687i
\(533\) 27.6583i 1.19801i
\(534\) 4.94034 16.0516i 0.213790 0.694621i
\(535\) −28.2136 + 48.8673i −1.21978 + 2.11272i
\(536\) 20.0399 + 7.82201i 0.865593 + 0.337859i
\(537\) 4.37148 7.57162i 0.188643 0.326739i
\(538\) −10.3994 11.1940i −0.448351 0.482606i
\(539\) 8.08540i 0.348263i
\(540\) −32.5283 + 15.7146i −1.39979 + 0.676250i
\(541\) 19.5856 11.3077i 0.842050 0.486158i −0.0159104 0.999873i \(-0.505065\pi\)
0.857961 + 0.513716i \(0.171731\pi\)
\(542\) 1.30121 1.20885i 0.0558916 0.0519244i
\(543\) −13.3492 −0.572868
\(544\) 11.0218 + 5.26568i 0.472554 + 0.225764i
\(545\) −16.9399 29.3408i −0.725628 1.25682i
\(546\) −5.17775 1.59360i −0.221587 0.0681999i
\(547\) 9.70216 5.60155i 0.414834 0.239505i −0.278030 0.960572i \(-0.589682\pi\)
0.692865 + 0.721067i \(0.256348\pi\)
\(548\) 2.68121 36.3850i 0.114536 1.55429i
\(549\) 0.863181 + 0.498358i 0.0368397 + 0.0212694i
\(550\) 16.9486 3.87949i 0.722691 0.165422i
\(551\) −30.4747 + 28.6991i −1.29827 + 1.22262i
\(552\) 5.04356 4.03751i 0.214668 0.171848i
\(553\) 2.15006 3.72402i 0.0914300 0.158361i
\(554\) 3.76753 12.2410i 0.160067 0.520071i
\(555\) 56.9177 32.8614i 2.41602 1.39489i
\(556\) 42.5601 + 3.13625i 1.80495 + 0.133007i
\(557\) −21.9660 + 12.6821i −0.930730 + 0.537357i −0.887042 0.461688i \(-0.847244\pi\)
−0.0436877 + 0.999045i \(0.513911\pi\)
\(558\) 1.03195 + 4.50837i 0.0436861 + 0.190855i
\(559\) 13.9355 0.589410
\(560\) 1.12136 7.56730i 0.0473860 0.319777i
\(561\) −2.43156 4.21159i −0.102661 0.177814i
\(562\) 0.0614788 + 0.268587i 0.00259333 + 0.0113296i
\(563\) 22.4078i 0.944377i −0.881498 0.472189i \(-0.843464\pi\)
0.881498 0.472189i \(-0.156536\pi\)
\(564\) 12.5111 18.3995i 0.526812 0.774758i
\(565\) 5.25345 + 3.03308i 0.221014 + 0.127603i
\(566\) 21.9098 + 23.5838i 0.920938 + 0.991299i
\(567\) 2.52952 4.38126i 0.106230 0.183996i
\(568\) −38.3766 + 5.85753i −1.61025 + 0.245776i
\(569\) 1.05189 0.0440977 0.0220489 0.999757i \(-0.492981\pi\)
0.0220489 + 0.999757i \(0.492981\pi\)
\(570\) 20.0157 + 40.7240i 0.838367 + 1.70574i
\(571\) 2.94384i 0.123196i −0.998101 0.0615980i \(-0.980380\pi\)
0.998101 0.0615980i \(-0.0196197\pi\)
\(572\) −0.730867 + 9.91813i −0.0305591 + 0.414698i
\(573\) 17.8366 + 10.2980i 0.745136 + 0.430205i
\(574\) −3.37209 + 3.13274i −0.140748 + 0.130758i
\(575\) 6.23458 10.7986i 0.260000 0.450333i
\(576\) −4.17070 + 1.30354i −0.173779 + 0.0543142i
\(577\) −9.49207 −0.395160 −0.197580 0.980287i \(-0.563308\pi\)
−0.197580 + 0.980287i \(0.563308\pi\)
\(578\) 3.89302 + 17.0077i 0.161928 + 0.707427i
\(579\) −7.48671 + 4.32245i −0.311137 + 0.179635i
\(580\) −62.0867 42.2170i −2.57801 1.75297i
\(581\) 0.722764i 0.0299853i
\(582\) −5.33550 + 1.22128i −0.221164 + 0.0506238i
\(583\) 0.259345 + 0.449198i 0.0107410 + 0.0186039i
\(584\) −18.7319 + 2.85910i −0.775131 + 0.118310i
\(585\) 4.43866 + 7.68798i 0.183516 + 0.317859i
\(586\) −2.51329 + 8.16590i −0.103823 + 0.337330i
\(587\) 31.4850 + 18.1779i 1.29952 + 0.750281i 0.980322 0.197406i \(-0.0632516\pi\)
0.319203 + 0.947686i \(0.396585\pi\)
\(588\) −11.0762 22.9271i −0.456776 0.945497i
\(589\) −25.4003 + 5.99560i −1.04660 + 0.247044i
\(590\) −12.4110 54.2209i −0.510953 2.23224i
\(591\) −14.1189 + 24.4547i −0.580776 + 1.00593i
\(592\) −33.2122 + 13.1302i −1.36501 + 0.539648i
\(593\) −10.8381 18.7722i −0.445069 0.770883i 0.552988 0.833189i \(-0.313488\pi\)
−0.998057 + 0.0623068i \(0.980154\pi\)
\(594\) −7.46958 2.29898i −0.306481 0.0943282i
\(595\) −3.57641 + 2.06484i −0.146619 + 0.0846503i
\(596\) −7.59855 15.7285i −0.311249 0.644265i
\(597\) 23.2102i 0.949929i
\(598\) 4.85434 + 5.22521i 0.198509 + 0.213675i
\(599\) 18.4914 + 32.0280i 0.755537 + 1.30863i 0.945107 + 0.326761i \(0.105957\pi\)
−0.189570 + 0.981867i \(0.560709\pi\)
\(600\) −42.7452 + 34.2187i −1.74506 + 1.39697i
\(601\) 7.60104 0.310053 0.155026 0.987910i \(-0.450454\pi\)
0.155026 + 0.987910i \(0.450454\pi\)
\(602\) −1.57842 1.69901i −0.0643316 0.0692467i
\(603\) 3.59776 + 2.07717i 0.146512 + 0.0845889i
\(604\) 24.9798 + 16.9855i 1.01641 + 0.691129i
\(605\) −32.3959 18.7038i −1.31708 0.760418i
\(606\) −13.4636 4.14380i −0.546920 0.168330i
\(607\) 11.7787 0.478082 0.239041 0.971009i \(-0.423167\pi\)
0.239041 + 0.971009i \(0.423167\pi\)
\(608\) −7.51519 23.4845i −0.304781 0.952422i
\(609\) 8.84813 0.358544
\(610\) −9.64133 2.96740i −0.390366 0.120146i
\(611\) 21.2722 + 12.2815i 0.860581 + 0.496857i
\(612\) 1.95065 + 1.32639i 0.0788506 + 0.0536160i
\(613\) −39.9556 23.0684i −1.61379 0.931723i −0.988481 0.151347i \(-0.951639\pi\)
−0.625311 0.780376i \(-0.715028\pi\)
\(614\) −6.85928 7.38334i −0.276818 0.297967i
\(615\) 48.9675 1.97456
\(616\) 1.29200 1.03428i 0.0520561 0.0416723i
\(617\) 6.93405 + 12.0101i 0.279154 + 0.483510i 0.971175 0.238368i \(-0.0766126\pi\)
−0.692020 + 0.721878i \(0.743279\pi\)
\(618\) −6.00634 6.46523i −0.241610 0.260070i
\(619\) 37.5313i 1.50851i 0.656581 + 0.754255i \(0.272002\pi\)
−0.656581 + 0.754255i \(0.727998\pi\)
\(620\) −20.3620 42.1480i −0.817756 1.69270i
\(621\) −4.85394 + 2.80242i −0.194782 + 0.112457i
\(622\) −28.1101 8.65169i −1.12711 0.346901i
\(623\) −1.54270 2.67203i −0.0618068 0.107053i
\(624\) −11.5144 29.1252i −0.460946 1.16594i
\(625\) −14.6393 + 25.3560i −0.585571 + 1.01424i
\(626\) 4.05233 + 17.7037i 0.161964 + 0.707583i
\(627\) −2.82406 + 9.40190i −0.112782 + 0.375476i
\(628\) −3.05928 6.33251i −0.122078 0.252695i
\(629\) 16.6964 + 9.63966i 0.665728 + 0.384358i
\(630\) 0.434567 1.41195i 0.0173136 0.0562533i
\(631\) −10.0514 17.4096i −0.400141 0.693064i 0.593602 0.804759i \(-0.297706\pi\)
−0.993743 + 0.111695i \(0.964372\pi\)
\(632\) 24.5748 3.75091i 0.977532 0.149203i
\(633\) −21.7701 37.7069i −0.865283 1.49871i
\(634\) −36.3757 + 8.32631i −1.44466 + 0.330680i
\(635\) 57.4399i 2.27943i
\(636\) −1.35076 0.918475i −0.0535611 0.0364199i
\(637\) 24.3433 14.0546i 0.964516 0.556863i
\(638\) −3.62422 15.8334i −0.143484 0.626850i
\(639\) −7.49688 −0.296572
\(640\) 38.2033 22.2788i 1.51012 0.880648i
\(641\) 6.69127 11.5896i 0.264289 0.457763i −0.703088 0.711103i \(-0.748196\pi\)
0.967377 + 0.253340i \(0.0815293\pi\)
\(642\) 28.1648 26.1657i 1.11158 1.03268i
\(643\) 17.6624 + 10.1974i 0.696536 + 0.402145i 0.806056 0.591839i \(-0.201598\pi\)
−0.109520 + 0.993985i \(0.534931\pi\)
\(644\) 0.0872252 1.18368i 0.00343716 0.0466434i
\(645\) 24.6721i 0.971463i
\(646\) −7.40987 + 11.0579i −0.291537 + 0.435066i
\(647\) 24.2724 0.954245 0.477122 0.878837i \(-0.341680\pi\)
0.477122 + 0.878837i \(0.341680\pi\)
\(648\) 28.9119 4.41290i 1.13577 0.173355i
\(649\) 6.01677 10.4213i 0.236179 0.409074i
\(650\) −41.1415 44.2847i −1.61370 1.73699i
\(651\) 4.77732 + 2.75819i 0.187238 + 0.108102i
\(652\) −24.8411 + 36.5327i −0.972853 + 1.43073i
\(653\) 1.03991i 0.0406947i −0.999793 0.0203474i \(-0.993523\pi\)
0.999793 0.0203474i \(-0.00647721\pi\)
\(654\) 5.15026 + 22.5003i 0.201391 + 0.879831i
\(655\) 19.2110 + 33.2745i 0.750636 + 1.30014i
\(656\) −26.3213 3.90042i −1.02767 0.152286i
\(657\) −3.65928 −0.142762
\(658\) −0.912059 3.98458i −0.0355558 0.155335i
\(659\) 2.36159 1.36347i 0.0919946 0.0531131i −0.453297 0.891360i \(-0.649752\pi\)
0.545292 + 0.838246i \(0.316419\pi\)
\(660\) −17.5595 1.29396i −0.683503 0.0503674i
\(661\) 31.5724 18.2284i 1.22803 0.709001i 0.261409 0.965228i \(-0.415813\pi\)
0.966617 + 0.256227i \(0.0824795\pi\)
\(662\) −2.17438 + 7.06475i −0.0845096 + 0.274579i
\(663\) −8.45342 + 14.6418i −0.328304 + 0.568639i
\(664\) −3.26191 + 2.61125i −0.126587 + 0.101336i
\(665\) 7.98393 + 2.39814i 0.309604 + 0.0929959i
\(666\) −6.72290 + 1.53885i −0.260507 + 0.0596294i
\(667\) −10.0881 5.82434i −0.390611 0.225519i
\(668\) 1.88014 25.5142i 0.0727448 0.987173i
\(669\) −1.67866 + 0.969176i −0.0649008 + 0.0374705i
\(670\) −40.1853 12.3682i −1.55249 0.477825i
\(671\) −1.09118 1.88998i −0.0421246 0.0729620i
\(672\) −2.24674 + 4.70273i −0.0866700 + 0.181412i
\(673\) −2.67705 −0.103193 −0.0515964 0.998668i \(-0.516431\pi\)
−0.0515964 + 0.998668i \(0.516431\pi\)
\(674\) −35.1231 + 32.6301i −1.35289 + 1.25687i
\(675\) 41.1381 23.7511i 1.58341 0.914180i
\(676\) 7.72050 3.72982i 0.296942 0.143455i
\(677\) 0.404843i 0.0155594i −0.999970 0.00777969i \(-0.997524\pi\)
0.999970 0.00777969i \(-0.00247638\pi\)
\(678\) −2.81293 3.02784i −0.108030 0.116284i
\(679\) −0.502775 + 0.870831i −0.0192947 + 0.0334194i
\(680\) −22.2399 8.68072i −0.852862 0.332890i
\(681\) 10.1982 17.6638i 0.390796 0.676879i
\(682\) 2.97886 9.67858i 0.114067 0.370612i
\(683\) 15.0013i 0.574008i −0.957929 0.287004i \(-0.907341\pi\)
0.957929 0.287004i \(-0.0926593\pi\)
\(684\) −0.750379 4.70224i −0.0286914 0.179795i
\(685\) 71.3067i 2.72449i
\(686\) −9.09989 2.80075i −0.347435 0.106933i
\(687\) 7.47262 12.9430i 0.285098 0.493805i
\(688\) 1.96521 13.2619i 0.0749229 0.505605i
\(689\) 0.901621 1.56165i 0.0343490 0.0594943i
\(690\) −9.25096 + 8.59434i −0.352178 + 0.327181i
\(691\) 31.7559i 1.20805i −0.796965 0.604025i \(-0.793563\pi\)
0.796965 0.604025i \(-0.206437\pi\)
\(692\) 5.22740 + 10.8204i 0.198716 + 0.411329i
\(693\) 0.276783 0.159801i 0.0105141 0.00607033i
\(694\) 14.6959 + 15.8186i 0.557847 + 0.600467i
\(695\) −83.4085 −3.16386
\(696\) 31.9671 + 39.9325i 1.21171 + 1.51364i
\(697\) 7.18213 + 12.4398i 0.272043 + 0.471191i
\(698\) 11.5085 37.3922i 0.435604 1.41531i
\(699\) −28.1104 + 16.2295i −1.06323 + 0.613858i
\(700\) −0.739252 + 10.0319i −0.0279411 + 0.379170i
\(701\) −8.48325 4.89781i −0.320408 0.184988i 0.331166 0.943572i \(-0.392558\pi\)
−0.651574 + 0.758585i \(0.725891\pi\)
\(702\) 6.06244 + 26.4854i 0.228812 + 0.999628i
\(703\) −8.94067 37.8770i −0.337204 1.42856i
\(704\) 9.33562 + 2.09421i 0.351850 + 0.0789284i
\(705\) −21.7438 + 37.6613i −0.818917 + 1.41841i
\(706\) 18.4509 + 5.67880i 0.694410 + 0.213725i
\(707\) −2.24121 + 1.29396i −0.0842894 + 0.0486645i
\(708\) −2.78499 + 37.7933i −0.104666 + 1.42036i
\(709\) 6.34809 3.66507i 0.238407 0.137645i −0.376037 0.926605i \(-0.622713\pi\)
0.614445 + 0.788960i \(0.289380\pi\)
\(710\) 73.9622 16.9297i 2.77575 0.635362i
\(711\) 4.80069 0.180040
\(712\) 6.48559 16.6160i 0.243058 0.622712i
\(713\) −3.63119 6.28940i −0.135989 0.235540i
\(714\) 2.74260 0.627774i 0.102639 0.0234939i
\(715\) 19.4374i 0.726917i
\(716\) 5.22118 7.67854i 0.195125 0.286961i
\(717\) −4.08312 2.35739i −0.152487 0.0880384i
\(718\) 18.5009 17.1877i 0.690447 0.641440i
\(719\) 9.42588 16.3261i 0.351526 0.608861i −0.634991 0.772520i \(-0.718996\pi\)
0.986517 + 0.163659i \(0.0523295\pi\)
\(720\) 7.94229 3.13992i 0.295992 0.117018i
\(721\) −1.62121 −0.0603769
\(722\) 26.5050 4.41415i 0.986414 0.164278i
\(723\) 17.1784i 0.638871i
\(724\) −14.1393 1.04192i −0.525481 0.0387227i
\(725\) 85.4983 + 49.3625i 3.17533 + 1.83328i
\(726\) 17.3462 + 18.6715i 0.643779 + 0.692965i
\(727\) −6.42156 + 11.1225i −0.238162 + 0.412509i −0.960187 0.279358i \(-0.909878\pi\)
0.722025 + 0.691867i \(0.243212\pi\)
\(728\) −5.35982 2.09205i −0.198648 0.0775366i
\(729\) −20.4570 −0.757667
\(730\) 36.1015 8.26353i 1.33617 0.305847i
\(731\) −6.26775 + 3.61869i −0.231821 + 0.133842i
\(732\) 5.68327 + 3.86445i 0.210060 + 0.142834i
\(733\) 11.3621i 0.419668i −0.977737 0.209834i \(-0.932708\pi\)
0.977737 0.209834i \(-0.0672923\pi\)
\(734\) 5.50721 + 24.0597i 0.203275 + 0.888061i
\(735\) 24.8829 + 43.0985i 0.917820 + 1.58971i
\(736\) 5.65719 3.88281i 0.208527 0.143122i
\(737\) −4.54808 7.87750i −0.167531 0.290172i
\(738\) −4.91116 1.51155i −0.180782 0.0556410i
\(739\) −43.2806 24.9881i −1.59210 0.919201i −0.992946 0.118571i \(-0.962169\pi\)
−0.599158 0.800631i \(-0.704498\pi\)
\(740\) 62.8512 30.3638i 2.31046 1.11620i
\(741\) 33.2159 7.84045i 1.22022 0.288026i
\(742\) −0.292519 + 0.0669569i −0.0107387 + 0.00245807i
\(743\) 16.6574 28.8515i 0.611102 1.05846i −0.379953 0.925006i \(-0.624060\pi\)
0.991055 0.133454i \(-0.0426069\pi\)
\(744\) 4.81182 + 31.5255i 0.176410 + 1.15578i
\(745\) 17.0703 + 29.5666i 0.625406 + 1.08324i
\(746\) −10.7152 + 34.8147i −0.392312 + 1.27466i
\(747\) −0.698794 + 0.403449i −0.0255676 + 0.0147614i
\(748\) −2.24676 4.65064i −0.0821495 0.170044i
\(749\) 7.06256i 0.258060i
\(750\) 40.2697 37.4114i 1.47044 1.36607i
\(751\) −3.06260 5.30457i −0.111756 0.193567i 0.804723 0.593651i \(-0.202314\pi\)
−0.916478 + 0.400085i \(0.868981\pi\)
\(752\) 14.6877 18.5120i 0.535604 0.675062i
\(753\) 21.0826 0.768292
\(754\) −41.3708 + 38.4344i −1.50664 + 1.39970i
\(755\) −51.1302 29.5200i −1.86082 1.07434i
\(756\) 2.54243 3.73903i 0.0924671 0.135987i
\(757\) −17.9603 10.3694i −0.652779 0.376882i 0.136741 0.990607i \(-0.456337\pi\)
−0.789520 + 0.613725i \(0.789671\pi\)
\(758\) 5.43085 17.6453i 0.197257 0.640906i
\(759\) −2.73174 −0.0991561
\(760\) 18.0218 + 44.6965i 0.653720 + 1.62131i
\(761\) −10.5548 −0.382612 −0.191306 0.981530i \(-0.561272\pi\)
−0.191306 + 0.981530i \(0.561272\pi\)
\(762\) 11.5116 37.4021i 0.417020 1.35493i
\(763\) 3.67237 + 2.12025i 0.132949 + 0.0767580i
\(764\) 18.0885 + 12.2996i 0.654420 + 0.444986i
\(765\) −3.99273 2.30520i −0.144357 0.0833448i
\(766\) −17.2991 + 16.0712i −0.625042 + 0.580678i
\(767\) −41.8350 −1.51058
\(768\) −29.3411 + 6.85054i −1.05876 + 0.247198i
\(769\) 16.3756 + 28.3633i 0.590519 + 1.02281i 0.994163 + 0.107892i \(0.0344101\pi\)
−0.403644 + 0.914916i \(0.632257\pi\)
\(770\) −2.36980 + 2.20159i −0.0854016 + 0.0793399i
\(771\) 23.7081i 0.853825i
\(772\) −8.26719 + 3.99393i −0.297543 + 0.143745i
\(773\) 4.46602 2.57846i 0.160632 0.0927407i −0.417529 0.908663i \(-0.637104\pi\)
0.578161 + 0.815923i \(0.303771\pi\)
\(774\) 0.761590 2.47447i 0.0273748 0.0889430i
\(775\) 30.7751 + 53.3040i 1.10547 + 1.91474i
\(776\) −5.74661 + 0.877121i −0.206291 + 0.0314868i
\(777\) −4.11302 + 7.12396i −0.147554 + 0.255571i
\(778\) −0.521135 + 0.119287i −0.0186836 + 0.00427663i
\(779\) 8.34144 27.7705i 0.298863 0.994981i
\(780\) 26.6273 + 55.1169i 0.953411 + 1.97350i
\(781\) 14.2157 + 8.20742i 0.508677 + 0.293685i
\(782\) −3.54017 1.08959i −0.126596 0.0389637i
\(783\) −22.1883 38.4312i −0.792944 1.37342i
\(784\) −9.94228 25.1485i −0.355081 0.898162i
\(785\) 6.87271 + 11.9039i 0.245298 + 0.424868i
\(786\) −5.84073 25.5168i −0.208332 0.910154i
\(787\) 26.8237i 0.956160i −0.878316 0.478080i \(-0.841333\pi\)
0.878316 0.478080i \(-0.158667\pi\)
\(788\) −16.8633 + 24.8001i −0.600730 + 0.883466i
\(789\) −6.80175 + 3.92699i −0.242149 + 0.139805i
\(790\) −47.3623 + 10.8411i −1.68507 + 0.385709i
\(791\) −0.759256 −0.0269960
\(792\) 1.72118 + 0.671812i 0.0611594 + 0.0238718i
\(793\) −3.79354 + 6.57060i −0.134712 + 0.233329i
\(794\) 10.2568 + 11.0404i 0.364000 + 0.391810i
\(795\) 2.76482 + 1.59627i 0.0980582 + 0.0566139i
\(796\) 1.81158 24.5839i 0.0642099 0.871352i
\(797\) 9.72241i 0.344385i −0.985063 0.172193i \(-0.944915\pi\)
0.985063 0.172193i \(-0.0550852\pi\)
\(798\) −4.71814 3.16162i −0.167020 0.111920i
\(799\) −12.7567 −0.451301
\(800\) −47.9459 + 32.9076i −1.69514 + 1.16346i
\(801\) 1.72228 2.98307i 0.0608536 0.105402i
\(802\) 24.3659 22.6365i 0.860391 0.799321i
\(803\) 6.93876 + 4.00610i 0.244864 + 0.141372i
\(804\) 23.6880 + 16.1071i 0.835412 + 0.568055i
\(805\) 2.31975i 0.0817605i
\(806\) −34.3180 + 7.85531i −1.20880 + 0.276691i
\(807\) −10.1727 17.6197i −0.358096 0.620241i
\(808\) −13.9370 5.43990i −0.490302 0.191375i
\(809\) −29.8008 −1.04774 −0.523869 0.851799i \(-0.675512\pi\)
−0.523869 + 0.851799i \(0.675512\pi\)
\(810\) −55.7211 + 12.7544i −1.95784 + 0.448145i
\(811\) −5.19792 + 3.00102i −0.182524 + 0.105380i −0.588478 0.808513i \(-0.700273\pi\)
0.405954 + 0.913893i \(0.366939\pi\)
\(812\) 9.37181 + 0.690609i 0.328886 + 0.0242356i
\(813\) 2.04814 1.18249i 0.0718314 0.0414719i
\(814\) 14.4327 + 4.44209i 0.505867 + 0.155695i
\(815\) 43.1728 74.7775i 1.51228 2.61934i
\(816\) 12.7419 + 10.1096i 0.446054 + 0.353906i
\(817\) 13.9920 + 4.20280i 0.489520 + 0.147037i
\(818\) 1.73519 + 7.58067i 0.0606696 + 0.265052i
\(819\) −0.962247 0.555553i −0.0336236 0.0194126i
\(820\) 51.8657 + 3.82198i 1.81123 + 0.133469i
\(821\) −38.6024 + 22.2871i −1.34723 + 0.777826i −0.987857 0.155367i \(-0.950344\pi\)
−0.359377 + 0.933193i \(0.617011\pi\)
\(822\) 14.2906 46.4315i 0.498443 1.61948i
\(823\) 6.40581 + 11.0952i 0.223292 + 0.386754i 0.955806 0.293999i \(-0.0949862\pi\)
−0.732513 + 0.680753i \(0.761653\pi\)
\(824\) −5.85720 7.31668i −0.204045 0.254889i
\(825\) 23.1521 0.806052
\(826\) 4.73849 + 5.10051i 0.164873 + 0.177470i
\(827\) −29.3556 + 16.9485i −1.02079 + 0.589356i −0.914334 0.404961i \(-0.867285\pi\)
−0.106460 + 0.994317i \(0.533952\pi\)
\(828\) 1.19311 0.576400i 0.0414635 0.0200313i
\(829\) 36.0492i 1.25204i 0.779808 + 0.626019i \(0.215317\pi\)
−0.779808 + 0.626019i \(0.784683\pi\)
\(830\) 5.98303 5.55837i 0.207674 0.192934i
\(831\) 8.52723 14.7696i 0.295806 0.512351i
\(832\) −9.92265 31.7477i −0.344006 1.10065i
\(833\) −7.29921 + 12.6426i −0.252903 + 0.438040i
\(834\) 54.3116 + 16.7160i 1.88066 + 0.578826i
\(835\) 50.0022i 1.73040i
\(836\) −3.72503 + 9.73794i −0.128833 + 0.336794i
\(837\) 27.6666i 0.956296i
\(838\) −12.0039 + 39.0017i −0.414668 + 1.34729i
\(839\) 20.1187 34.8467i 0.694576 1.20304i −0.275747 0.961230i \(-0.588925\pi\)
0.970323 0.241811i \(-0.0777413\pi\)
\(840\) 3.70386 9.48926i 0.127795 0.327411i
\(841\) 31.6144 54.7578i 1.09015 1.88820i
\(842\) 13.9199 + 14.9834i 0.479710 + 0.516361i
\(843\) 0.366894i 0.0126365i
\(844\) −20.1155 41.6378i −0.692403 1.43323i
\(845\) −14.5130 + 8.37911i −0.499264 + 0.288250i
\(846\) 3.34332 3.10602i 0.114946 0.106787i
\(847\) 4.68203 0.160876
\(848\) −1.35902 1.07826i −0.0466688 0.0370277i
\(849\) 21.4322 + 37.1216i 0.735550 + 1.27401i
\(850\) 30.0037 + 9.23450i 1.02912 + 0.316741i
\(851\) 9.37879 5.41485i 0.321501 0.185619i
\(852\) −51.5535 3.79898i −1.76619 0.130151i
\(853\) 14.2070 + 8.20240i 0.486437 + 0.280845i 0.723095 0.690748i \(-0.242719\pi\)
−0.236658 + 0.971593i \(0.576052\pi\)
\(854\) 1.23076 0.281719i 0.0421159 0.00964021i
\(855\) 2.13805 + 9.05781i 0.0731197 + 0.309771i
\(856\) 31.8741 25.5161i 1.08943 0.872121i
\(857\) −1.65316 + 2.86335i −0.0564708 + 0.0978103i −0.892879 0.450297i \(-0.851318\pi\)
0.836408 + 0.548107i \(0.184651\pi\)
\(858\) −3.89546 + 12.6567i −0.132989 + 0.432092i
\(859\) 16.7788 9.68722i 0.572484 0.330524i −0.185657 0.982615i \(-0.559441\pi\)
0.758141 + 0.652091i \(0.226108\pi\)
\(860\) −1.92569 + 26.1323i −0.0656655 + 0.891104i
\(861\) −5.30778 + 3.06445i −0.180889 + 0.104436i
\(862\) 3.96397 + 17.3177i 0.135013 + 0.589842i
\(863\) 10.9104 0.371395 0.185697 0.982607i \(-0.440546\pi\)
0.185697 + 0.982607i \(0.440546\pi\)
\(864\) 26.0601 2.03437i 0.886581 0.0692107i
\(865\) −11.7434 20.3402i −0.399289 0.691588i
\(866\) −2.62393 11.4634i −0.0891648 0.389541i
\(867\) 23.2328i 0.789028i
\(868\) 4.84478 + 3.29431i 0.164443 + 0.111816i
\(869\) −9.10312 5.25569i −0.308802 0.178287i
\(870\) −68.0459 73.2447i −2.30697 2.48323i
\(871\) −15.8116 + 27.3864i −0.535754 + 0.927954i
\(872\) 3.69890 + 24.2340i 0.125260 + 0.820666i
\(873\) −1.12260 −0.0379943
\(874\) 3.29816 + 6.71042i 0.111562 + 0.226983i
\(875\) 10.0979i 0.341373i
\(876\) −25.1636 1.85431i −0.850200 0.0626513i
\(877\) −44.7132 25.8152i −1.50986 0.871716i −0.999934 0.0114961i \(-0.996341\pi\)
−0.509923 0.860220i \(-0.670326\pi\)
\(878\) 19.3484 17.9751i 0.652978 0.606630i
\(879\) −5.68846 + 9.85270i −0.191867 + 0.332323i
\(880\) −18.4978 2.74109i −0.623560 0.0924021i
\(881\) 49.1021 1.65429 0.827145 0.561988i \(-0.189963\pi\)
0.827145 + 0.561988i \(0.189963\pi\)
\(882\) −1.16523 5.09063i −0.0392354 0.171410i
\(883\) −4.71395 + 2.72160i −0.158637 + 0.0915892i −0.577217 0.816591i \(-0.695861\pi\)
0.418580 + 0.908180i \(0.362528\pi\)
\(884\) −10.0965 + 14.8485i −0.339584 + 0.499410i
\(885\) 74.0667i 2.48972i
\(886\) −20.8721 + 4.77756i −0.701210 + 0.160505i
\(887\) −21.5809 37.3792i −0.724616 1.25507i −0.959132 0.282959i \(-0.908684\pi\)
0.234516 0.972112i \(-0.424649\pi\)
\(888\) −47.0109 + 7.17541i −1.57758 + 0.240791i
\(889\) −3.59466 6.22613i −0.120561 0.208818i
\(890\) −10.2550 + 33.3195i −0.343749 + 1.11687i
\(891\) −10.7097 6.18325i −0.358789 0.207147i
\(892\) −1.85366 + 0.895515i −0.0620651 + 0.0299841i
\(893\) 17.6545 + 18.7468i 0.590786 + 0.627337i
\(894\) −5.18988 22.6734i −0.173575 0.758312i
\(895\) −9.07419 + 15.7170i −0.303317 + 0.525360i
\(896\) −2.74677 + 4.80570i −0.0917632 + 0.160547i
\(897\) 4.74851 + 8.22465i 0.158548 + 0.274613i
\(898\) 26.0367 + 8.01353i 0.868854 + 0.267415i
\(899\) 49.7966 28.7501i 1.66081 0.958868i
\(900\) −10.1119 + 4.88511i −0.337062 + 0.162837i
\(901\) 0.936509i 0.0311996i
\(902\) 7.65779 + 8.24286i 0.254977 + 0.274457i
\(903\) −1.54401 2.67430i −0.0513814 0.0889952i
\(904\) −2.74309 3.42660i −0.0912338 0.113967i
\(905\) 27.7099 0.921107
\(906\) 27.3774 + 29.4691i 0.909553 + 0.979044i
\(907\) 8.20476 + 4.73702i 0.272435 + 0.157290i 0.629993 0.776600i \(-0.283058\pi\)
−0.357559 + 0.933891i \(0.616391\pi\)
\(908\) 12.1805 17.9133i 0.404224 0.594473i
\(909\) −2.50210 1.44459i −0.0829895 0.0479140i
\(910\) 10.7478 + 3.30796i 0.356287 + 0.109658i
\(911\) −9.10534 −0.301673 −0.150837 0.988559i \(-0.548197\pi\)
−0.150837 + 0.988559i \(0.548197\pi\)
\(912\) −2.77728 32.7160i −0.0919650 1.08333i
\(913\) 1.76675 0.0584709
\(914\) −29.7813 9.16606i −0.985078 0.303186i
\(915\) −11.6329 6.71625i −0.384571 0.222032i
\(916\) 8.92510 13.1257i 0.294894 0.433687i
\(917\) −4.16471 2.40450i −0.137531 0.0794035i
\(918\) −9.60425 10.3380i −0.316988 0.341206i
\(919\) −43.9744 −1.45058 −0.725291 0.688442i \(-0.758295\pi\)
−0.725291 + 0.688442i \(0.758295\pi\)
\(920\) −10.4693 + 8.38094i −0.345162 + 0.276312i
\(921\) −6.70975 11.6216i −0.221094 0.382945i
\(922\) −11.3540 12.2214i −0.373923 0.402491i
\(923\) 57.0668i 1.87838i
\(924\) 1.98432 0.958639i 0.0652794 0.0315369i
\(925\) −79.4871 + 45.8919i −2.61352 + 1.50892i
\(926\) 33.8776 + 10.4268i 1.11329 + 0.342647i
\(927\) −0.904963 1.56744i −0.0297229 0.0514816i
\(928\) 30.7423 + 44.7910i 1.00916 + 1.47034i
\(929\) −25.4485 + 44.0781i −0.834939 + 1.44616i 0.0591415 + 0.998250i \(0.481164\pi\)
−0.894080 + 0.447907i \(0.852170\pi\)
\(930\) −13.9074 60.7582i −0.456041 1.99234i
\(931\) 28.6807 6.76993i 0.939973 0.221876i
\(932\) −31.0409 + 14.9960i −1.01678 + 0.491212i
\(933\) −33.9167 19.5818i −1.11038 0.641079i
\(934\) −13.0478 + 42.3935i −0.426937 + 1.38716i
\(935\) 5.04737 + 8.74230i 0.165067 + 0.285904i
\(936\) −0.969196 6.34986i −0.0316792 0.207552i
\(937\) 10.7225 + 18.5719i 0.350288 + 0.606716i 0.986300 0.164963i \(-0.0527505\pi\)
−0.636012 + 0.771679i \(0.719417\pi\)
\(938\) 5.12986 1.17421i 0.167496 0.0383393i
\(939\) 24.1836i 0.789202i
\(940\) −25.9702 + 38.1931i −0.847054 + 1.24572i
\(941\) −29.0422 + 16.7675i −0.946748 + 0.546605i −0.892069 0.451899i \(-0.850747\pi\)
−0.0546785 + 0.998504i \(0.517413\pi\)
\(942\) −2.08951 9.12860i −0.0680800 0.297426i
\(943\) 8.06878 0.262756
\(944\) −5.89964 + 39.8127i −0.192017 + 1.29579i
\(945\) −4.41863 + 7.65329i −0.143738 + 0.248962i
\(946\) −4.15313 + 3.85835i −0.135030 + 0.125446i
\(947\) −18.0649 10.4298i −0.587030 0.338922i 0.176892 0.984230i \(-0.443396\pi\)
−0.763922 + 0.645308i \(0.776729\pi\)
\(948\) 33.0127 + 2.43271i 1.07220 + 0.0790107i
\(949\) 27.8547i 0.904202i
\(950\) −27.9525 56.8722i −0.906900 1.84518i
\(951\) −49.6899 −1.61130
\(952\) 2.95392 0.450865i 0.0957372 0.0146126i
\(953\) 11.0364 19.1156i 0.357504 0.619215i −0.630039 0.776563i \(-0.716961\pi\)
0.987543 + 0.157348i \(0.0502945\pi\)
\(954\) −0.228022 0.245443i −0.00738247 0.00794651i
\(955\) −37.0248 21.3763i −1.19809 0.691720i
\(956\) −4.14078 2.81561i −0.133923 0.0910632i
\(957\) 21.6287i 0.699156i
\(958\) 5.44219 + 23.7757i 0.175829 + 0.768157i
\(959\) −4.46246 7.72921i −0.144100 0.249589i
\(960\) 56.2076 17.5675i 1.81409 0.566989i
\(961\) 4.84848 0.156402
\(962\) −11.7139 51.1752i −0.377670 1.64996i
\(963\) 6.82834 3.94234i 0.220040 0.127040i
\(964\) −1.34080 + 18.1951i −0.0431841 + 0.586024i
\(965\) 15.5407 8.97243i 0.500273 0.288833i
\(966\) 0.464903 1.51051i 0.0149580 0.0485999i
\(967\) 14.5509 25.2029i 0.467926 0.810471i −0.531403 0.847119i \(-0.678335\pi\)
0.999328 + 0.0366485i \(0.0116682\pi\)
\(968\) 16.9155 + 21.1305i 0.543686 + 0.679159i
\(969\) −12.9035 + 12.1517i −0.414520 + 0.390368i
\(970\) 11.0753 2.53510i 0.355606 0.0813973i
\(971\) 47.1524 + 27.2235i 1.51319 + 0.873643i 0.999881 + 0.0154408i \(0.00491514\pi\)
0.513312 + 0.858202i \(0.328418\pi\)
\(972\) 11.1890 + 0.824521i 0.358889 + 0.0264465i
\(973\) 9.04097 5.21981i 0.289840 0.167339i
\(974\) 15.4230 + 4.74688i 0.494185 + 0.152100i
\(975\) −40.2445 69.7056i −1.28886 2.23237i
\(976\) 5.71801 + 4.53676i 0.183029 + 0.145218i
\(977\) −60.9156 −1.94886 −0.974431 0.224687i \(-0.927864\pi\)
−0.974431 + 0.224687i \(0.927864\pi\)
\(978\) −43.0983 + 40.0392i −1.37813 + 1.28031i
\(979\) −6.53160 + 3.77102i −0.208751 + 0.120522i
\(980\) 22.9917 + 47.5914i 0.734443 + 1.52025i
\(981\) 4.73411i 0.151149i
\(982\) −13.3032 14.3196i −0.424523 0.456957i
\(983\) −23.2627 + 40.2922i −0.741965 + 1.28512i 0.209634 + 0.977780i \(0.432773\pi\)
−0.951599 + 0.307342i \(0.900561\pi\)
\(984\) −33.0065 12.8831i −1.05221 0.410699i
\(985\) 29.3077 50.7624i 0.933821 1.61743i
\(986\) 8.62686 28.0294i 0.274735 0.892639i
\(987\) 5.44300i 0.173253i
\(988\) 35.7938 5.71194i 1.13875 0.181721i
\(989\) 4.06542i 0.129273i
\(990\) −3.45141 1.06227i −0.109693 0.0337612i
\(991\) 20.4460 35.4135i 0.649489 1.12495i −0.333756 0.942659i \(-0.608316\pi\)
0.983245 0.182288i \(-0.0583505\pi\)
\(992\) 2.63600 + 33.7669i 0.0836932 + 1.07210i
\(993\) −4.92138 + 8.52408i −0.156175 + 0.270503i
\(994\) −6.95757 + 6.46373i −0.220681 + 0.205017i
\(995\) 48.1790i 1.52738i
\(996\) −5.00982 + 2.42028i −0.158742 + 0.0766894i
\(997\) 17.3447 10.0140i 0.549313 0.317146i −0.199532 0.979891i \(-0.563942\pi\)
0.748845 + 0.662745i \(0.230609\pi\)
\(998\) 7.76145 + 8.35443i 0.245684 + 0.264455i
\(999\) 41.2565 1.30530
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 152.2.p.a.125.17 yes 36
4.3 odd 2 608.2.t.a.49.5 36
8.3 odd 2 608.2.t.a.49.14 36
8.5 even 2 inner 152.2.p.a.125.5 yes 36
19.7 even 3 inner 152.2.p.a.45.5 36
76.7 odd 6 608.2.t.a.273.14 36
152.45 even 6 inner 152.2.p.a.45.17 yes 36
152.83 odd 6 608.2.t.a.273.5 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.p.a.45.5 36 19.7 even 3 inner
152.2.p.a.45.17 yes 36 152.45 even 6 inner
152.2.p.a.125.5 yes 36 8.5 even 2 inner
152.2.p.a.125.17 yes 36 1.1 even 1 trivial
608.2.t.a.49.5 36 4.3 odd 2
608.2.t.a.49.14 36 8.3 odd 2
608.2.t.a.273.5 36 152.83 odd 6
608.2.t.a.273.14 36 76.7 odd 6