Properties

Label 546.2.z.a.131.5
Level $546$
Weight $2$
Character 546.131
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(131,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.z (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.5
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.a.521.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.115738 + 1.72818i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85995 + 3.22152i) q^{5} +(0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} -1.00000i q^{8} +(-2.97321 + 0.400031i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.115738 + 1.72818i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85995 + 3.22152i) q^{5} +(0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} -1.00000i q^{8} +(-2.97321 + 0.400031i) q^{9} +(3.22152 - 1.85995i) q^{10} +(0.553597 - 0.319619i) q^{11} +(-1.43878 + 0.964322i) q^{12} +1.00000i q^{13} +(0.209090 + 2.63748i) q^{14} +(-5.78264 - 2.84147i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.63964 + 6.30404i) q^{17} +(2.77489 + 1.14017i) q^{18} +(-4.62720 - 2.67151i) q^{19} -3.71990 q^{20} +(3.59312 - 2.84421i) q^{21} -0.639239 q^{22} +(-4.07685 - 2.35377i) q^{23} +(1.72818 - 0.115738i) q^{24} +(-4.41881 - 7.65361i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-1.03544 - 5.09194i) q^{27} +(1.13766 - 2.38867i) q^{28} -2.98058i q^{29} +(3.58718 + 5.35211i) q^{30} +(0.608107 - 0.351091i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.616432 + 0.919723i) q^{33} -7.27927i q^{34} +(9.81114 - 0.777791i) q^{35} +(-1.83304 - 2.37486i) q^{36} +(5.21987 - 9.04107i) q^{37} +(2.67151 + 4.62720i) q^{38} +(-1.72818 + 0.115738i) q^{39} +(3.22152 + 1.85995i) q^{40} -11.6843 q^{41} +(-4.53383 + 0.666599i) q^{42} -3.57757 q^{43} +(0.553597 + 0.319619i) q^{44} +(4.24131 - 10.3223i) q^{45} +(2.35377 + 4.07685i) q^{46} +(3.53495 - 6.12272i) q^{47} +(-1.55452 - 0.763858i) q^{48} +(-2.50111 + 6.53792i) q^{49} +8.83762i q^{50} +(-10.4733 + 7.01956i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-6.65923 + 3.84471i) q^{53} +(-1.64926 + 4.92747i) q^{54} +2.37790i q^{55} +(-2.17958 + 1.49982i) q^{56} +(4.08131 - 8.30582i) q^{57} +(-1.49029 + 2.58126i) q^{58} +(1.35119 + 2.34033i) q^{59} +(-0.430532 - 6.42865i) q^{60} +(10.0041 + 5.77587i) q^{61} -0.702181 q^{62} +(5.33116 + 5.88037i) q^{63} -1.00000 q^{64} +(-3.22152 - 1.85995i) q^{65} +(-0.0739840 - 1.10472i) q^{66} +(-1.15384 - 1.99852i) q^{67} +(-3.63964 + 6.30404i) q^{68} +(3.59590 - 7.31796i) q^{69} +(-8.88559 - 4.23198i) q^{70} +10.9092i q^{71} +(0.400031 + 2.97321i) q^{72} +(-8.28825 + 4.78522i) q^{73} +(-9.04107 + 5.21987i) q^{74} +(12.7154 - 8.52231i) q^{75} -5.34303i q^{76} +(-1.52693 - 0.727237i) q^{77} +(1.55452 + 0.763858i) q^{78} +(-5.00806 + 8.67422i) q^{79} +(-1.85995 - 3.22152i) q^{80} +(8.67995 - 2.37875i) q^{81} +(10.1189 + 5.84214i) q^{82} -6.70374 q^{83} +(4.25971 + 1.68962i) q^{84} -27.0781 q^{85} +(3.09826 + 1.78878i) q^{86} +(5.15097 - 0.344965i) q^{87} +(-0.319619 - 0.553597i) q^{88} +(-1.95052 + 3.37839i) q^{89} +(-8.83423 + 6.81872i) q^{90} +(2.17958 - 1.49982i) q^{91} -4.70754i q^{92} +(0.677129 + 1.01028i) q^{93} +(-6.12272 + 3.53495i) q^{94} +(17.2127 - 9.93775i) q^{95} +(0.964322 + 1.43878i) q^{96} +3.50071i q^{97} +(5.43499 - 4.41145i) q^{98} +(-1.51810 + 1.17175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.115738 + 1.72818i 0.0668211 + 0.997765i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.85995 + 3.22152i −0.831794 + 1.44071i 0.0648203 + 0.997897i \(0.479353\pi\)
−0.896614 + 0.442812i \(0.853981\pi\)
\(6\) 0.763858 1.55452i 0.311844 0.634629i
\(7\) −1.49982 2.17958i −0.566877 0.823803i
\(8\) 1.00000i 0.353553i
\(9\) −2.97321 + 0.400031i −0.991070 + 0.133344i
\(10\) 3.22152 1.85995i 1.01874 0.588167i
\(11\) 0.553597 0.319619i 0.166916 0.0963689i −0.414215 0.910179i \(-0.635944\pi\)
0.581131 + 0.813810i \(0.302610\pi\)
\(12\) −1.43878 + 0.964322i −0.415340 + 0.278376i
\(13\) 1.00000i 0.277350i
\(14\) 0.209090 + 2.63748i 0.0558815 + 0.704895i
\(15\) −5.78264 2.84147i −1.49307 0.733665i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.63964 + 6.30404i 0.882742 + 1.52895i 0.848280 + 0.529548i \(0.177638\pi\)
0.0344615 + 0.999406i \(0.489028\pi\)
\(18\) 2.77489 + 1.14017i 0.654048 + 0.268740i
\(19\) −4.62720 2.67151i −1.06155 0.612887i −0.135691 0.990751i \(-0.543325\pi\)
−0.925861 + 0.377864i \(0.876659\pi\)
\(20\) −3.71990 −0.831794
\(21\) 3.59312 2.84421i 0.784082 0.620657i
\(22\) −0.639239 −0.136286
\(23\) −4.07685 2.35377i −0.850083 0.490795i 0.0105961 0.999944i \(-0.496627\pi\)
−0.860679 + 0.509148i \(0.829960\pi\)
\(24\) 1.72818 0.115738i 0.352763 0.0236248i
\(25\) −4.41881 7.65361i −0.883762 1.53072i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −1.03544 5.09194i −0.199270 0.979945i
\(28\) 1.13766 2.38867i 0.214998 0.451415i
\(29\) 2.98058i 0.553479i −0.960945 0.276740i \(-0.910746\pi\)
0.960945 0.276740i \(-0.0892540\pi\)
\(30\) 3.58718 + 5.35211i 0.654926 + 0.977156i
\(31\) 0.608107 0.351091i 0.109219 0.0630577i −0.444395 0.895831i \(-0.646581\pi\)
0.553615 + 0.832773i \(0.313248\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.616432 + 0.919723i 0.107307 + 0.160103i
\(34\) 7.27927i 1.24839i
\(35\) 9.81114 0.777791i 1.65838 0.131471i
\(36\) −1.83304 2.37486i −0.305507 0.395810i
\(37\) 5.21987 9.04107i 0.858141 1.48634i −0.0155596 0.999879i \(-0.504953\pi\)
0.873700 0.486465i \(-0.161714\pi\)
\(38\) 2.67151 + 4.62720i 0.433377 + 0.750630i
\(39\) −1.72818 + 0.115738i −0.276730 + 0.0185328i
\(40\) 3.22152 + 1.85995i 0.509368 + 0.294084i
\(41\) −11.6843 −1.82478 −0.912389 0.409325i \(-0.865764\pi\)
−0.912389 + 0.409325i \(0.865764\pi\)
\(42\) −4.53383 + 0.666599i −0.699586 + 0.102859i
\(43\) −3.57757 −0.545574 −0.272787 0.962075i \(-0.587945\pi\)
−0.272787 + 0.962075i \(0.587945\pi\)
\(44\) 0.553597 + 0.319619i 0.0834579 + 0.0481844i
\(45\) 4.24131 10.3223i 0.632257 1.53876i
\(46\) 2.35377 + 4.07685i 0.347045 + 0.601099i
\(47\) 3.53495 6.12272i 0.515626 0.893090i −0.484210 0.874952i \(-0.660893\pi\)
0.999835 0.0181379i \(-0.00577380\pi\)
\(48\) −1.55452 0.763858i −0.224375 0.110253i
\(49\) −2.50111 + 6.53792i −0.357301 + 0.933989i
\(50\) 8.83762i 1.24983i
\(51\) −10.4733 + 7.01956i −1.46655 + 0.982935i
\(52\) −0.866025 + 0.500000i −0.120096 + 0.0693375i
\(53\) −6.65923 + 3.84471i −0.914715 + 0.528111i −0.881945 0.471352i \(-0.843766\pi\)
−0.0327700 + 0.999463i \(0.510433\pi\)
\(54\) −1.64926 + 4.92747i −0.224435 + 0.670544i
\(55\) 2.37790i 0.320636i
\(56\) −2.17958 + 1.49982i −0.291258 + 0.200421i
\(57\) 4.08131 8.30582i 0.540583 1.10013i
\(58\) −1.49029 + 2.58126i −0.195684 + 0.338935i
\(59\) 1.35119 + 2.34033i 0.175910 + 0.304685i 0.940476 0.339861i \(-0.110380\pi\)
−0.764566 + 0.644546i \(0.777047\pi\)
\(60\) −0.430532 6.42865i −0.0555814 0.829935i
\(61\) 10.0041 + 5.77587i 1.28089 + 0.739524i 0.977012 0.213186i \(-0.0683841\pi\)
0.303881 + 0.952710i \(0.401717\pi\)
\(62\) −0.702181 −0.0891771
\(63\) 5.33116 + 5.88037i 0.671663 + 0.740857i
\(64\) −1.00000 −0.125000
\(65\) −3.22152 1.85995i −0.399581 0.230698i
\(66\) −0.0739840 1.10472i −0.00910680 0.135982i
\(67\) −1.15384 1.99852i −0.140965 0.244158i 0.786896 0.617086i \(-0.211687\pi\)
−0.927860 + 0.372928i \(0.878354\pi\)
\(68\) −3.63964 + 6.30404i −0.441371 + 0.764477i
\(69\) 3.59590 7.31796i 0.432895 0.880978i
\(70\) −8.88559 4.23198i −1.06203 0.505819i
\(71\) 10.9092i 1.29468i 0.762201 + 0.647340i \(0.224119\pi\)
−0.762201 + 0.647340i \(0.775881\pi\)
\(72\) 0.400031 + 2.97321i 0.0471441 + 0.350396i
\(73\) −8.28825 + 4.78522i −0.970066 + 0.560068i −0.899256 0.437422i \(-0.855892\pi\)
−0.0708097 + 0.997490i \(0.522558\pi\)
\(74\) −9.04107 + 5.21987i −1.05100 + 0.606797i
\(75\) 12.7154 8.52231i 1.46825 0.984072i
\(76\) 5.34303i 0.612887i
\(77\) −1.52693 0.727237i −0.174010 0.0828764i
\(78\) 1.55452 + 0.763858i 0.176014 + 0.0864899i
\(79\) −5.00806 + 8.67422i −0.563451 + 0.975926i 0.433741 + 0.901038i \(0.357193\pi\)
−0.997192 + 0.0748885i \(0.976140\pi\)
\(80\) −1.85995 3.22152i −0.207948 0.360177i
\(81\) 8.67995 2.37875i 0.964439 0.264306i
\(82\) 10.1189 + 5.84214i 1.11744 + 0.645156i
\(83\) −6.70374 −0.735831 −0.367916 0.929859i \(-0.619928\pi\)
−0.367916 + 0.929859i \(0.619928\pi\)
\(84\) 4.25971 + 1.68962i 0.464773 + 0.184353i
\(85\) −27.0781 −2.93704
\(86\) 3.09826 + 1.78878i 0.334094 + 0.192889i
\(87\) 5.15097 0.344965i 0.552242 0.0369841i
\(88\) −0.319619 0.553597i −0.0340716 0.0590137i
\(89\) −1.95052 + 3.37839i −0.206754 + 0.358109i −0.950690 0.310142i \(-0.899623\pi\)
0.743936 + 0.668251i \(0.232957\pi\)
\(90\) −8.83423 + 6.81872i −0.931210 + 0.718757i
\(91\) 2.17958 1.49982i 0.228482 0.157223i
\(92\) 4.70754i 0.490795i
\(93\) 0.677129 + 1.01028i 0.0702150 + 0.104762i
\(94\) −6.12272 + 3.53495i −0.631510 + 0.364602i
\(95\) 17.2127 9.93775i 1.76598 1.01959i
\(96\) 0.964322 + 1.43878i 0.0984207 + 0.146845i
\(97\) 3.50071i 0.355443i 0.984081 + 0.177721i \(0.0568726\pi\)
−0.984081 + 0.177721i \(0.943127\pi\)
\(98\) 5.43499 4.41145i 0.549017 0.445624i
\(99\) −1.51810 + 1.17175i −0.152575 + 0.117765i
\(100\) 4.41881 7.65361i 0.441881 0.765361i
\(101\) −0.886720 1.53584i −0.0882319 0.152822i 0.818532 0.574461i \(-0.194788\pi\)
−0.906764 + 0.421639i \(0.861455\pi\)
\(102\) 12.5799 0.842486i 1.24560 0.0834185i
\(103\) 7.16629 + 4.13746i 0.706115 + 0.407676i 0.809621 0.586953i \(-0.199673\pi\)
−0.103506 + 0.994629i \(0.533006\pi\)
\(104\) 1.00000 0.0980581
\(105\) 2.47968 + 16.8654i 0.241992 + 1.64589i
\(106\) 7.68941 0.746862
\(107\) −14.4332 8.33299i −1.39531 0.805580i −0.401410 0.915898i \(-0.631480\pi\)
−0.993896 + 0.110318i \(0.964813\pi\)
\(108\) 3.89203 3.44269i 0.374511 0.331273i
\(109\) 5.02724 + 8.70744i 0.481523 + 0.834022i 0.999775 0.0212061i \(-0.00675061\pi\)
−0.518253 + 0.855228i \(0.673417\pi\)
\(110\) 1.18895 2.05932i 0.113362 0.196349i
\(111\) 16.2287 + 7.97447i 1.54036 + 0.756904i
\(112\) 2.63748 0.209090i 0.249218 0.0197571i
\(113\) 9.55689i 0.899036i 0.893271 + 0.449518i \(0.148404\pi\)
−0.893271 + 0.449518i \(0.851596\pi\)
\(114\) −7.68743 + 5.15240i −0.719994 + 0.482566i
\(115\) 15.1655 8.75579i 1.41419 0.816481i
\(116\) 2.58126 1.49029i 0.239664 0.138370i
\(117\) −0.400031 2.97321i −0.0369829 0.274873i
\(118\) 2.70238i 0.248774i
\(119\) 8.28135 17.3878i 0.759150 1.59393i
\(120\) −2.84147 + 5.78264i −0.259390 + 0.527880i
\(121\) −5.29569 + 9.17240i −0.481426 + 0.833854i
\(122\) −5.77587 10.0041i −0.522922 0.905728i
\(123\) −1.35231 20.1925i −0.121934 1.82070i
\(124\) 0.608107 + 0.351091i 0.0546096 + 0.0315289i
\(125\) 14.2756 1.27684
\(126\) −1.67674 7.75813i −0.149376 0.691149i
\(127\) 2.68673 0.238409 0.119204 0.992870i \(-0.461966\pi\)
0.119204 + 0.992870i \(0.461966\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −0.414059 6.18268i −0.0364558 0.544354i
\(130\) 1.85995 + 3.22152i 0.163128 + 0.282546i
\(131\) −3.14262 + 5.44318i −0.274572 + 0.475573i −0.970027 0.242997i \(-0.921870\pi\)
0.695455 + 0.718570i \(0.255203\pi\)
\(132\) −0.488288 + 0.993707i −0.0425000 + 0.0864911i
\(133\) 1.11717 + 14.0921i 0.0968710 + 1.22194i
\(134\) 2.30769i 0.199354i
\(135\) 18.3297 + 6.13506i 1.57757 + 0.528022i
\(136\) 6.30404 3.63964i 0.540567 0.312096i
\(137\) −12.5020 + 7.21801i −1.06811 + 0.616676i −0.927666 0.373411i \(-0.878188\pi\)
−0.140449 + 0.990088i \(0.544855\pi\)
\(138\) −6.77312 + 4.53959i −0.576566 + 0.386435i
\(139\) 8.02304i 0.680505i 0.940334 + 0.340253i \(0.110513\pi\)
−0.940334 + 0.340253i \(0.889487\pi\)
\(140\) 5.57916 + 8.10780i 0.471525 + 0.685234i
\(141\) 10.9903 + 5.40040i 0.925548 + 0.454796i
\(142\) 5.45459 9.44762i 0.457739 0.792827i
\(143\) 0.319619 + 0.553597i 0.0267279 + 0.0462941i
\(144\) 1.14017 2.77489i 0.0950140 0.231241i
\(145\) 9.60200 + 5.54372i 0.797403 + 0.460381i
\(146\) 9.57044 0.792056
\(147\) −11.5882 3.56568i −0.955777 0.294093i
\(148\) 10.4397 0.858141
\(149\) −12.9471 7.47499i −1.06066 0.612375i −0.135048 0.990839i \(-0.543119\pi\)
−0.925616 + 0.378464i \(0.876452\pi\)
\(150\) −15.2730 + 1.02285i −1.24704 + 0.0835150i
\(151\) 2.84087 + 4.92054i 0.231187 + 0.400428i 0.958158 0.286241i \(-0.0924058\pi\)
−0.726971 + 0.686668i \(0.759072\pi\)
\(152\) −2.67151 + 4.62720i −0.216688 + 0.375315i
\(153\) −13.3432 17.2873i −1.07873 1.39759i
\(154\) 0.958740 + 1.39327i 0.0772575 + 0.112273i
\(155\) 2.61204i 0.209804i
\(156\) −0.964322 1.43878i −0.0772075 0.115194i
\(157\) −3.76719 + 2.17499i −0.300654 + 0.173583i −0.642737 0.766087i \(-0.722201\pi\)
0.342083 + 0.939670i \(0.388868\pi\)
\(158\) 8.67422 5.00806i 0.690084 0.398420i
\(159\) −7.41507 11.0634i −0.588053 0.877382i
\(160\) 3.71990i 0.294084i
\(161\) 0.984298 + 12.4160i 0.0775736 + 0.978521i
\(162\) −8.70643 2.27992i −0.684042 0.179127i
\(163\) 11.6978 20.2611i 0.916240 1.58697i 0.111163 0.993802i \(-0.464542\pi\)
0.805076 0.593171i \(-0.202124\pi\)
\(164\) −5.84214 10.1189i −0.456194 0.790152i
\(165\) −4.10944 + 0.275213i −0.319920 + 0.0214253i
\(166\) 5.80561 + 3.35187i 0.450603 + 0.260156i
\(167\) −2.43964 −0.188785 −0.0943923 0.995535i \(-0.530091\pi\)
−0.0943923 + 0.995535i \(0.530091\pi\)
\(168\) −2.84421 3.59312i −0.219435 0.277215i
\(169\) −1.00000 −0.0769231
\(170\) 23.4504 + 13.5391i 1.79856 + 1.03840i
\(171\) 14.8263 + 6.09195i 1.13380 + 0.465863i
\(172\) −1.78878 3.09826i −0.136393 0.236240i
\(173\) 1.18592 2.05407i 0.0901638 0.156168i −0.817416 0.576048i \(-0.804594\pi\)
0.907580 + 0.419879i \(0.137928\pi\)
\(174\) −4.63336 2.27674i −0.351254 0.172599i
\(175\) −10.0542 + 21.1101i −0.760028 + 1.59578i
\(176\) 0.639239i 0.0481844i
\(177\) −3.88813 + 2.60596i −0.292250 + 0.195876i
\(178\) 3.37839 1.95052i 0.253221 0.146197i
\(179\) 8.34373 4.81725i 0.623639 0.360058i −0.154645 0.987970i \(-0.549423\pi\)
0.778285 + 0.627912i \(0.216090\pi\)
\(180\) 11.0600 1.48807i 0.824366 0.110914i
\(181\) 10.6638i 0.792636i −0.918113 0.396318i \(-0.870288\pi\)
0.918113 0.396318i \(-0.129712\pi\)
\(182\) −2.63748 + 0.209090i −0.195503 + 0.0154987i
\(183\) −8.82388 + 17.9574i −0.652280 + 1.32745i
\(184\) −2.35377 + 4.07685i −0.173522 + 0.300550i
\(185\) 19.4174 + 33.6319i 1.42759 + 2.47266i
\(186\) −0.0812688 1.21350i −0.00595892 0.0889778i
\(187\) 4.02979 + 2.32660i 0.294687 + 0.170138i
\(188\) 7.06990 0.515626
\(189\) −9.54531 + 9.89379i −0.694319 + 0.719667i
\(190\) −19.8755 −1.44192
\(191\) 8.44258 + 4.87433i 0.610884 + 0.352694i 0.773311 0.634027i \(-0.218599\pi\)
−0.162428 + 0.986720i \(0.551932\pi\)
\(192\) −0.115738 1.72818i −0.00835264 0.124721i
\(193\) −1.46371 2.53522i −0.105360 0.182489i 0.808525 0.588462i \(-0.200266\pi\)
−0.913885 + 0.405972i \(0.866933\pi\)
\(194\) 1.75035 3.03170i 0.125668 0.217663i
\(195\) 2.84147 5.78264i 0.203482 0.414103i
\(196\) −6.91256 + 1.10294i −0.493755 + 0.0787812i
\(197\) 2.60658i 0.185711i −0.995680 0.0928556i \(-0.970400\pi\)
0.995680 0.0928556i \(-0.0295995\pi\)
\(198\) 1.90059 0.255715i 0.135069 0.0181729i
\(199\) −9.74629 + 5.62702i −0.690896 + 0.398889i −0.803948 0.594700i \(-0.797271\pi\)
0.113052 + 0.993589i \(0.463937\pi\)
\(200\) −7.65361 + 4.41881i −0.541192 + 0.312457i
\(201\) 3.32025 2.22535i 0.234193 0.156964i
\(202\) 1.77344i 0.124779i
\(203\) −6.49640 + 4.47031i −0.455958 + 0.313755i
\(204\) −11.3158 5.56033i −0.792261 0.389301i
\(205\) 21.7321 37.6412i 1.51784 2.62897i
\(206\) −4.13746 7.16629i −0.288270 0.499299i
\(207\) 13.0629 + 5.36739i 0.907936 + 0.373060i
\(208\) −0.866025 0.500000i −0.0600481 0.0346688i
\(209\) −3.41547 −0.236253
\(210\) 6.28523 15.8457i 0.433722 1.09346i
\(211\) 0.972576 0.0669549 0.0334775 0.999439i \(-0.489342\pi\)
0.0334775 + 0.999439i \(0.489342\pi\)
\(212\) −6.65923 3.84471i −0.457358 0.264056i
\(213\) −18.8530 + 1.26260i −1.29179 + 0.0865120i
\(214\) 8.33299 + 14.4332i 0.569631 + 0.986631i
\(215\) 6.65408 11.5252i 0.453805 0.786013i
\(216\) −5.09194 + 1.03544i −0.346463 + 0.0704526i
\(217\) −1.67728 0.798845i −0.113861 0.0542291i
\(218\) 10.0545i 0.680976i
\(219\) −9.22899 13.7698i −0.623637 0.930474i
\(220\) −2.05932 + 1.18895i −0.138840 + 0.0801591i
\(221\) −6.30404 + 3.63964i −0.424055 + 0.244829i
\(222\) −10.0673 15.0205i −0.675670 1.00811i
\(223\) 11.7623i 0.787661i −0.919183 0.393830i \(-0.871150\pi\)
0.919183 0.393830i \(-0.128850\pi\)
\(224\) −2.38867 1.13766i −0.159599 0.0760132i
\(225\) 16.1997 + 20.9881i 1.07998 + 1.39921i
\(226\) 4.77844 8.27651i 0.317857 0.550545i
\(227\) −3.46041 5.99360i −0.229675 0.397809i 0.728037 0.685538i \(-0.240433\pi\)
−0.957712 + 0.287729i \(0.907100\pi\)
\(228\) 9.23371 0.618389i 0.611517 0.0409538i
\(229\) −8.65357 4.99614i −0.571844 0.330154i 0.186042 0.982542i \(-0.440434\pi\)
−0.757885 + 0.652388i \(0.773767\pi\)
\(230\) −17.5116 −1.15468
\(231\) 1.08007 2.72298i 0.0710636 0.179159i
\(232\) −2.98058 −0.195684
\(233\) 1.71349 + 0.989282i 0.112254 + 0.0648100i 0.555076 0.831800i \(-0.312689\pi\)
−0.442822 + 0.896610i \(0.646023\pi\)
\(234\) −1.14017 + 2.77489i −0.0745351 + 0.181400i
\(235\) 13.1496 + 22.7759i 0.857789 + 1.48573i
\(236\) −1.35119 + 2.34033i −0.0879550 + 0.152343i
\(237\) −15.5702 7.65090i −1.01140 0.496979i
\(238\) −15.8657 + 10.9176i −1.02842 + 0.707681i
\(239\) 10.7072i 0.692588i 0.938126 + 0.346294i \(0.112560\pi\)
−0.938126 + 0.346294i \(0.887440\pi\)
\(240\) 5.35211 3.58718i 0.345477 0.231551i
\(241\) −17.1442 + 9.89818i −1.10435 + 0.637598i −0.937361 0.348360i \(-0.886739\pi\)
−0.166991 + 0.985958i \(0.553405\pi\)
\(242\) 9.17240 5.29569i 0.589624 0.340420i
\(243\) 5.11550 + 14.7252i 0.328160 + 0.944622i
\(244\) 11.5517i 0.739524i
\(245\) −16.4101 20.2176i −1.04841 1.29165i
\(246\) −8.92513 + 18.1634i −0.569046 + 1.15806i
\(247\) 2.67151 4.62720i 0.169984 0.294421i
\(248\) −0.351091 0.608107i −0.0222943 0.0386148i
\(249\) −0.775875 11.5853i −0.0491691 0.734187i
\(250\) −12.3630 7.13778i −0.781905 0.451433i
\(251\) −27.2102 −1.71749 −0.858747 0.512400i \(-0.828756\pi\)
−0.858747 + 0.512400i \(0.828756\pi\)
\(252\) −2.42697 + 7.55711i −0.152884 + 0.476053i
\(253\) −3.00925 −0.189190
\(254\) −2.32678 1.34337i −0.145995 0.0842903i
\(255\) −3.13396 46.7959i −0.196256 2.93047i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 11.3753 19.7025i 0.709569 1.22901i −0.255447 0.966823i \(-0.582223\pi\)
0.965017 0.262187i \(-0.0844439\pi\)
\(258\) −2.73275 + 5.56138i −0.170134 + 0.346237i
\(259\) −27.5345 + 2.18284i −1.71091 + 0.135635i
\(260\) 3.71990i 0.230698i
\(261\) 1.19232 + 8.86188i 0.0738029 + 0.548537i
\(262\) 5.44318 3.14262i 0.336281 0.194152i
\(263\) −1.66747 + 0.962712i −0.102820 + 0.0593634i −0.550528 0.834816i \(-0.685574\pi\)
0.447708 + 0.894180i \(0.352240\pi\)
\(264\) 0.919723 0.616432i 0.0566051 0.0379388i
\(265\) 28.6038i 1.75712i
\(266\) 6.07855 12.7627i 0.372700 0.782532i
\(267\) −6.06422 2.97983i −0.371124 0.182363i
\(268\) 1.15384 1.99852i 0.0704823 0.122079i
\(269\) 9.29729 + 16.1034i 0.566866 + 0.981840i 0.996873 + 0.0790149i \(0.0251775\pi\)
−0.430008 + 0.902825i \(0.641489\pi\)
\(270\) −12.8064 14.4780i −0.779375 0.881100i
\(271\) −5.08642 2.93665i −0.308978 0.178389i 0.337491 0.941329i \(-0.390422\pi\)
−0.646469 + 0.762940i \(0.723755\pi\)
\(272\) −7.27927 −0.441371
\(273\) 2.84421 + 3.59312i 0.172139 + 0.217465i
\(274\) 14.4360 0.872112
\(275\) −4.89248 2.82468i −0.295028 0.170334i
\(276\) 8.13548 0.544840i 0.489699 0.0327955i
\(277\) −3.58404 6.20773i −0.215344 0.372987i 0.738035 0.674762i \(-0.235754\pi\)
−0.953379 + 0.301776i \(0.902421\pi\)
\(278\) 4.01152 6.94815i 0.240595 0.416723i
\(279\) −1.66758 + 1.28713i −0.0998355 + 0.0770583i
\(280\) −0.777791 9.81114i −0.0464819 0.586328i
\(281\) 1.56977i 0.0936448i −0.998903 0.0468224i \(-0.985091\pi\)
0.998903 0.0468224i \(-0.0149095\pi\)
\(282\) −6.81766 10.1720i −0.405986 0.605735i
\(283\) 17.3559 10.0204i 1.03170 0.595653i 0.114230 0.993454i \(-0.463560\pi\)
0.917472 + 0.397801i \(0.130227\pi\)
\(284\) −9.44762 + 5.45459i −0.560613 + 0.323670i
\(285\) 19.1664 + 28.5964i 1.13532 + 1.69391i
\(286\) 0.639239i 0.0377990i
\(287\) 17.5243 + 25.4668i 1.03442 + 1.50326i
\(288\) −2.37486 + 1.83304i −0.139940 + 0.108013i
\(289\) −17.9939 + 31.1664i −1.05847 + 1.83332i
\(290\) −5.54372 9.60200i −0.325538 0.563849i
\(291\) −6.04985 + 0.405163i −0.354649 + 0.0237511i
\(292\) −8.28825 4.78522i −0.485033 0.280034i
\(293\) 17.0764 0.997617 0.498808 0.866712i \(-0.333771\pi\)
0.498808 + 0.866712i \(0.333771\pi\)
\(294\) 8.25282 + 8.88206i 0.481314 + 0.518012i
\(295\) −10.0526 −0.585284
\(296\) −9.04107 5.21987i −0.525502 0.303399i
\(297\) −2.20070 2.48794i −0.127697 0.144365i
\(298\) 7.47499 + 12.9471i 0.433014 + 0.750003i
\(299\) 2.35377 4.07685i 0.136122 0.235771i
\(300\) 13.7382 + 6.75069i 0.793177 + 0.389751i
\(301\) 5.36569 + 7.79758i 0.309273 + 0.449445i
\(302\) 5.68175i 0.326948i
\(303\) 2.55159 1.71017i 0.146585 0.0982465i
\(304\) 4.62720 2.67151i 0.265388 0.153222i
\(305\) −37.2142 + 21.4856i −2.13088 + 1.23026i
\(306\) 2.91193 + 21.6428i 0.166464 + 1.23724i
\(307\) 2.27545i 0.129867i 0.997890 + 0.0649335i \(0.0206835\pi\)
−0.997890 + 0.0649335i \(0.979316\pi\)
\(308\) −0.133658 1.68598i −0.00761588 0.0960675i
\(309\) −6.32086 + 12.8635i −0.359581 + 0.731778i
\(310\) 1.30602 2.26209i 0.0741770 0.128478i
\(311\) 10.8605 + 18.8110i 0.615844 + 1.06667i 0.990236 + 0.139402i \(0.0445181\pi\)
−0.374392 + 0.927270i \(0.622149\pi\)
\(312\) 0.115738 + 1.72818i 0.00655235 + 0.0978389i
\(313\) −14.3547 8.28769i −0.811376 0.468448i 0.0360575 0.999350i \(-0.488520\pi\)
−0.847434 + 0.530902i \(0.821853\pi\)
\(314\) 4.34997 0.245483
\(315\) −28.8594 + 6.23729i −1.62604 + 0.351432i
\(316\) −10.0161 −0.563451
\(317\) −7.12729 4.11494i −0.400308 0.231118i 0.286309 0.958137i \(-0.407572\pi\)
−0.686617 + 0.727019i \(0.740905\pi\)
\(318\) 0.889954 + 13.2887i 0.0499062 + 0.745193i
\(319\) −0.952651 1.65004i −0.0533382 0.0923845i
\(320\) 1.85995 3.22152i 0.103974 0.180089i
\(321\) 12.7304 25.9075i 0.710544 1.44602i
\(322\) 5.35559 11.2448i 0.298455 0.626646i
\(323\) 38.8934i 2.16408i
\(324\) 6.40003 + 6.32768i 0.355557 + 0.351538i
\(325\) 7.65361 4.41881i 0.424546 0.245112i
\(326\) −20.2611 + 11.6978i −1.12216 + 0.647879i
\(327\) −14.4662 + 9.69576i −0.799982 + 0.536177i
\(328\) 11.6843i 0.645156i
\(329\) −18.6467 + 1.47824i −1.02803 + 0.0814982i
\(330\) 3.69649 + 1.81638i 0.203485 + 0.0999884i
\(331\) −11.3043 + 19.5795i −0.621338 + 1.07619i 0.367899 + 0.929866i \(0.380077\pi\)
−0.989237 + 0.146323i \(0.953256\pi\)
\(332\) −3.35187 5.80561i −0.183958 0.318624i
\(333\) −11.9031 + 28.9691i −0.652283 + 1.58750i
\(334\) 2.11279 + 1.21982i 0.115607 + 0.0667455i
\(335\) 8.58436 0.469014
\(336\) 0.666599 + 4.53383i 0.0363660 + 0.247341i
\(337\) 1.33284 0.0726044 0.0363022 0.999341i \(-0.488442\pi\)
0.0363022 + 0.999341i \(0.488442\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) −16.5160 + 1.10609i −0.897027 + 0.0600746i
\(340\) −13.5391 23.4504i −0.734259 1.27177i
\(341\) 0.224431 0.388726i 0.0121536 0.0210507i
\(342\) −9.79399 12.6889i −0.529598 0.686139i
\(343\) 18.0011 4.35432i 0.971969 0.235111i
\(344\) 3.57757i 0.192889i
\(345\) 16.8868 + 25.1953i 0.909154 + 1.35647i
\(346\) −2.05407 + 1.18592i −0.110428 + 0.0637554i
\(347\) 19.2344 11.1050i 1.03255 0.596146i 0.114839 0.993384i \(-0.463365\pi\)
0.917716 + 0.397238i \(0.130031\pi\)
\(348\) 2.87423 + 4.28839i 0.154075 + 0.229882i
\(349\) 17.4181i 0.932371i 0.884687 + 0.466185i \(0.154372\pi\)
−0.884687 + 0.466185i \(0.845628\pi\)
\(350\) 19.2623 13.2548i 1.02961 0.708499i
\(351\) 5.09194 1.03544i 0.271788 0.0552675i
\(352\) 0.319619 0.553597i 0.0170358 0.0295068i
\(353\) 14.4605 + 25.0463i 0.769653 + 1.33308i 0.937751 + 0.347307i \(0.112904\pi\)
−0.168099 + 0.985770i \(0.553763\pi\)
\(354\) 4.67020 0.312767i 0.248218 0.0166234i
\(355\) −35.1442 20.2905i −1.86526 1.07691i
\(356\) −3.90103 −0.206754
\(357\) 31.0076 + 12.2992i 1.64110 + 0.650945i
\(358\) −9.63450 −0.509199
\(359\) 3.51757 + 2.03087i 0.185650 + 0.107185i 0.589945 0.807444i \(-0.299150\pi\)
−0.404294 + 0.914629i \(0.632483\pi\)
\(360\) −10.3223 4.24131i −0.544033 0.223536i
\(361\) 4.77397 + 8.26875i 0.251261 + 0.435198i
\(362\) −5.33192 + 9.23515i −0.280239 + 0.485389i
\(363\) −16.4645 8.09031i −0.864160 0.424631i
\(364\) 2.38867 + 1.13766i 0.125200 + 0.0596297i
\(365\) 35.6011i 1.86344i
\(366\) 16.6204 11.1396i 0.868761 0.582275i
\(367\) 8.01993 4.63031i 0.418637 0.241700i −0.275857 0.961199i \(-0.588962\pi\)
0.694494 + 0.719499i \(0.255628\pi\)
\(368\) 4.07685 2.35377i 0.212521 0.122699i
\(369\) 34.7398 4.67407i 1.80848 0.243322i
\(370\) 38.8347i 2.01892i
\(371\) 18.3674 + 8.74795i 0.953590 + 0.454171i
\(372\) −0.536367 + 1.09155i −0.0278093 + 0.0565943i
\(373\) −3.06884 + 5.31539i −0.158899 + 0.275220i −0.934472 0.356037i \(-0.884128\pi\)
0.775573 + 0.631258i \(0.217461\pi\)
\(374\) −2.32660 4.02979i −0.120306 0.208375i
\(375\) 1.65222 + 24.6707i 0.0853202 + 1.27399i
\(376\) −6.12272 3.53495i −0.315755 0.182301i
\(377\) 2.98058 0.153508
\(378\) 13.2134 3.79561i 0.679623 0.195225i
\(379\) 15.9194 0.817725 0.408863 0.912596i \(-0.365926\pi\)
0.408863 + 0.912596i \(0.365926\pi\)
\(380\) 17.2127 + 9.93775i 0.882992 + 0.509796i
\(381\) 0.310956 + 4.64315i 0.0159307 + 0.237876i
\(382\) −4.87433 8.44258i −0.249392 0.431960i
\(383\) 13.7676 23.8462i 0.703491 1.21848i −0.263742 0.964593i \(-0.584957\pi\)
0.967233 0.253889i \(-0.0817099\pi\)
\(384\) −0.763858 + 1.55452i −0.0389805 + 0.0793286i
\(385\) 5.18282 3.56641i 0.264141 0.181761i
\(386\) 2.92742i 0.149002i
\(387\) 10.6369 1.43114i 0.540702 0.0727487i
\(388\) −3.03170 + 1.75035i −0.153911 + 0.0888607i
\(389\) 16.1727 9.33731i 0.819988 0.473420i −0.0304242 0.999537i \(-0.509686\pi\)
0.850412 + 0.526117i \(0.176352\pi\)
\(390\) −5.35211 + 3.58718i −0.271014 + 0.181644i
\(391\) 34.2675i 1.73298i
\(392\) 6.53792 + 2.50111i 0.330215 + 0.126325i
\(393\) −9.77051 4.80103i −0.492857 0.242180i
\(394\) −1.30329 + 2.25737i −0.0656589 + 0.113724i
\(395\) −18.6295 32.2672i −0.937351 1.62354i
\(396\) −1.77382 0.728840i −0.0891377 0.0366256i
\(397\) −2.58988 1.49527i −0.129982 0.0750452i 0.433599 0.901106i \(-0.357243\pi\)
−0.563581 + 0.826061i \(0.690577\pi\)
\(398\) 11.2540 0.564114
\(399\) −24.2244 + 3.56166i −1.21274 + 0.178306i
\(400\) 8.83762 0.441881
\(401\) 8.68481 + 5.01418i 0.433699 + 0.250396i 0.700921 0.713239i \(-0.252772\pi\)
−0.267222 + 0.963635i \(0.586106\pi\)
\(402\) −3.98810 + 0.267086i −0.198908 + 0.0133211i
\(403\) 0.351091 + 0.608107i 0.0174891 + 0.0302920i
\(404\) 0.886720 1.53584i 0.0441160 0.0764111i
\(405\) −8.48105 + 32.3870i −0.421427 + 1.60932i
\(406\) 7.86120 0.623208i 0.390145 0.0309293i
\(407\) 6.67348i 0.330792i
\(408\) 7.01956 + 10.4733i 0.347520 + 0.518504i
\(409\) 28.0742 16.2086i 1.38818 0.801466i 0.395069 0.918651i \(-0.370721\pi\)
0.993110 + 0.117186i \(0.0373873\pi\)
\(410\) −37.6412 + 21.7321i −1.85897 + 1.07327i
\(411\) −13.9210 20.7702i −0.686671 1.02452i
\(412\) 8.27492i 0.407676i
\(413\) 3.07440 6.45509i 0.151281 0.317634i
\(414\) −8.62913 11.1798i −0.424098 0.549455i
\(415\) 12.4686 21.5963i 0.612060 1.06012i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) −13.8652 + 0.928567i −0.678984 + 0.0454721i
\(418\) 2.95788 + 1.70774i 0.144675 + 0.0835281i
\(419\) 35.0674 1.71315 0.856577 0.516019i \(-0.172587\pi\)
0.856577 + 0.516019i \(0.172587\pi\)
\(420\) −13.3660 + 10.5802i −0.652195 + 0.516259i
\(421\) 12.0494 0.587249 0.293625 0.955921i \(-0.405138\pi\)
0.293625 + 0.955921i \(0.405138\pi\)
\(422\) −0.842276 0.486288i −0.0410013 0.0236721i
\(423\) −8.06088 + 19.6182i −0.391933 + 0.953870i
\(424\) 3.84471 + 6.65923i 0.186715 + 0.323401i
\(425\) 32.1657 55.7127i 1.56027 2.70246i
\(426\) 16.9585 + 8.33306i 0.821641 + 0.403738i
\(427\) −2.41535 30.4674i −0.116887 1.47442i
\(428\) 16.6660i 0.805580i
\(429\) −0.919723 + 0.616432i −0.0444047 + 0.0297616i
\(430\) −11.5252 + 6.65408i −0.555795 + 0.320888i
\(431\) −12.1267 + 7.00133i −0.584121 + 0.337242i −0.762769 0.646671i \(-0.776161\pi\)
0.178649 + 0.983913i \(0.442827\pi\)
\(432\) 4.92747 + 1.64926i 0.237073 + 0.0793499i
\(433\) 23.7265i 1.14022i 0.821568 + 0.570110i \(0.193100\pi\)
−0.821568 + 0.570110i \(0.806900\pi\)
\(434\) 1.05314 + 1.53046i 0.0505524 + 0.0734643i
\(435\) −8.46923 + 17.2356i −0.406068 + 0.826384i
\(436\) −5.02724 + 8.70744i −0.240761 + 0.417011i
\(437\) 12.5763 + 21.7827i 0.601605 + 1.04201i
\(438\) 1.10766 + 16.5394i 0.0529261 + 0.790285i
\(439\) −23.8048 13.7437i −1.13614 0.655950i −0.190668 0.981655i \(-0.561065\pi\)
−0.945472 + 0.325704i \(0.894399\pi\)
\(440\) 2.37790 0.113362
\(441\) 4.82095 20.4391i 0.229569 0.973292i
\(442\) 7.27927 0.346240
\(443\) −19.7056 11.3770i −0.936242 0.540540i −0.0474616 0.998873i \(-0.515113\pi\)
−0.888780 + 0.458334i \(0.848447\pi\)
\(444\) 1.20827 + 18.0417i 0.0573419 + 0.856223i
\(445\) −7.25571 12.5673i −0.343954 0.595746i
\(446\) −5.88114 + 10.1864i −0.278480 + 0.482342i
\(447\) 11.4197 23.2400i 0.540131 1.09921i
\(448\) 1.49982 + 2.17958i 0.0708596 + 0.102975i
\(449\) 12.2342i 0.577368i 0.957425 + 0.288684i \(0.0932176\pi\)
−0.957425 + 0.288684i \(0.906782\pi\)
\(450\) −3.53532 26.2761i −0.166657 1.23867i
\(451\) −6.46838 + 3.73452i −0.304584 + 0.175852i
\(452\) −8.27651 + 4.77844i −0.389294 + 0.224759i
\(453\) −8.17477 + 5.47903i −0.384084 + 0.257427i
\(454\) 6.92081i 0.324810i
\(455\) 0.777791 + 9.81114i 0.0364634 + 0.459953i
\(456\) −8.30582 4.08131i −0.388956 0.191125i
\(457\) −9.42161 + 16.3187i −0.440724 + 0.763357i −0.997743 0.0671429i \(-0.978612\pi\)
0.557019 + 0.830500i \(0.311945\pi\)
\(458\) 4.99614 + 8.65357i 0.233454 + 0.404355i
\(459\) 28.3312 25.0603i 1.32239 1.16971i
\(460\) 15.1655 + 8.75579i 0.707094 + 0.408241i
\(461\) −18.7725 −0.874324 −0.437162 0.899383i \(-0.644016\pi\)
−0.437162 + 0.899383i \(0.644016\pi\)
\(462\) −2.29686 + 1.81813i −0.106860 + 0.0845870i
\(463\) 21.8455 1.01525 0.507624 0.861579i \(-0.330524\pi\)
0.507624 + 0.861579i \(0.330524\pi\)
\(464\) 2.58126 + 1.49029i 0.119832 + 0.0691849i
\(465\) −4.51408 + 0.302311i −0.209335 + 0.0140194i
\(466\) −0.989282 1.71349i −0.0458276 0.0793758i
\(467\) −13.6271 + 23.6028i −0.630586 + 1.09221i 0.356846 + 0.934163i \(0.383852\pi\)
−0.987432 + 0.158043i \(0.949481\pi\)
\(468\) 2.37486 1.83304i 0.109778 0.0847324i
\(469\) −2.62537 + 5.51230i −0.121228 + 0.254534i
\(470\) 26.2993i 1.21310i
\(471\) −4.19477 6.25864i −0.193285 0.288383i
\(472\) 2.34033 1.35119i 0.107722 0.0621936i
\(473\) −1.98053 + 1.14346i −0.0910649 + 0.0525763i
\(474\) 9.65877 + 14.4110i 0.443642 + 0.661919i
\(475\) 47.2197i 2.16659i
\(476\) 19.1989 1.52202i 0.879981 0.0697617i
\(477\) 18.2613 14.0950i 0.836127 0.645366i
\(478\) 5.35358 9.27267i 0.244867 0.424122i
\(479\) −4.07896 7.06496i −0.186372 0.322806i 0.757666 0.652643i \(-0.226340\pi\)
−0.944038 + 0.329836i \(0.893006\pi\)
\(480\) −6.42865 + 0.430532i −0.293426 + 0.0196510i
\(481\) 9.04107 + 5.21987i 0.412237 + 0.238005i
\(482\) 19.7964 0.901700
\(483\) −21.3432 + 3.13805i −0.971150 + 0.142786i
\(484\) −10.5914 −0.481426
\(485\) −11.2776 6.51113i −0.512090 0.295655i
\(486\) 2.93245 15.3102i 0.133018 0.694483i
\(487\) 15.7854 + 27.3411i 0.715304 + 1.23894i 0.962842 + 0.270065i \(0.0870453\pi\)
−0.247538 + 0.968878i \(0.579621\pi\)
\(488\) 5.77587 10.0041i 0.261461 0.452864i
\(489\) 36.3687 + 17.8709i 1.64465 + 0.808148i
\(490\) 4.10281 + 25.7140i 0.185346 + 1.16164i
\(491\) 10.4465i 0.471445i 0.971820 + 0.235722i \(0.0757456\pi\)
−0.971820 + 0.235722i \(0.924254\pi\)
\(492\) 16.8111 11.2674i 0.757902 0.507974i
\(493\) 18.7897 10.8482i 0.846244 0.488579i
\(494\) −4.62720 + 2.67151i −0.208187 + 0.120197i
\(495\) −0.951234 7.07000i −0.0427548 0.317773i
\(496\) 0.702181i 0.0315289i
\(497\) 23.7774 16.3617i 1.06656 0.733924i
\(498\) −5.12071 + 10.4211i −0.229464 + 0.466979i
\(499\) −9.01724 + 15.6183i −0.403667 + 0.699172i −0.994165 0.107867i \(-0.965598\pi\)
0.590498 + 0.807039i \(0.298931\pi\)
\(500\) 7.13778 + 12.3630i 0.319211 + 0.552890i
\(501\) −0.282358 4.21613i −0.0126148 0.188363i
\(502\) 23.5647 + 13.6051i 1.05175 + 0.607226i
\(503\) −1.94837 −0.0868734 −0.0434367 0.999056i \(-0.513831\pi\)
−0.0434367 + 0.999056i \(0.513831\pi\)
\(504\) 5.88037 5.33116i 0.261932 0.237469i
\(505\) 6.59701 0.293563
\(506\) 2.60608 + 1.50462i 0.115855 + 0.0668887i
\(507\) −0.115738 1.72818i −0.00514009 0.0767512i
\(508\) 1.34337 + 2.32678i 0.0596022 + 0.103234i
\(509\) 9.25943 16.0378i 0.410417 0.710863i −0.584518 0.811381i \(-0.698716\pi\)
0.994935 + 0.100517i \(0.0320498\pi\)
\(510\) −20.6839 + 42.0934i −0.915897 + 1.86393i
\(511\) 22.8606 + 10.8879i 1.01129 + 0.481653i
\(512\) 1.00000i 0.0441942i
\(513\) −8.81202 + 26.3276i −0.389060 + 1.16239i
\(514\) −19.7025 + 11.3753i −0.869042 + 0.501741i
\(515\) −26.6578 + 15.3909i −1.17468 + 0.678205i
\(516\) 5.14732 3.44992i 0.226598 0.151874i
\(517\) 4.51936i 0.198761i
\(518\) 24.9370 + 11.8769i 1.09567 + 0.521840i
\(519\) 3.68706 + 1.81175i 0.161844 + 0.0795269i
\(520\) −1.85995 + 3.22152i −0.0815641 + 0.141273i
\(521\) −11.1032 19.2313i −0.486441 0.842541i 0.513437 0.858127i \(-0.328372\pi\)
−0.999879 + 0.0155863i \(0.995039\pi\)
\(522\) 3.39836 8.27078i 0.148742 0.362002i
\(523\) 12.1280 + 7.00210i 0.530320 + 0.306181i 0.741147 0.671343i \(-0.234282\pi\)
−0.210827 + 0.977523i \(0.567616\pi\)
\(524\) −6.28524 −0.274572
\(525\) −37.6458 14.9323i −1.64300 0.651698i
\(526\) 1.92542 0.0839525
\(527\) 4.42658 + 2.55569i 0.192825 + 0.111327i
\(528\) −1.10472 + 0.0739840i −0.0480768 + 0.00321974i
\(529\) −0.419511 0.726614i −0.0182396 0.0315919i
\(530\) −14.3019 + 24.7716i −0.621235 + 1.07601i
\(531\) −4.95358 6.41778i −0.214967 0.278508i
\(532\) −11.6455 + 8.01355i −0.504898 + 0.347432i
\(533\) 11.6843i 0.506102i
\(534\) 3.76185 + 5.61272i 0.162791 + 0.242886i
\(535\) 53.6899 30.9978i 2.32121 1.34015i
\(536\) −1.99852 + 1.15384i −0.0863228 + 0.0498385i
\(537\) 9.29076 + 13.8619i 0.400926 + 0.598186i
\(538\) 18.5946i 0.801669i
\(539\) 0.705041 + 4.41878i 0.0303682 + 0.190330i
\(540\) 3.85172 + 18.9415i 0.165752 + 0.815112i
\(541\) 4.23557 7.33622i 0.182101 0.315409i −0.760495 0.649344i \(-0.775043\pi\)
0.942596 + 0.333935i \(0.108377\pi\)
\(542\) 2.93665 + 5.08642i 0.126140 + 0.218481i
\(543\) 18.4290 1.23421i 0.790865 0.0529649i
\(544\) 6.30404 + 3.63964i 0.270283 + 0.156048i
\(545\) −37.4016 −1.60211
\(546\) −0.666599 4.53383i −0.0285278 0.194030i
\(547\) −15.3032 −0.654318 −0.327159 0.944969i \(-0.606091\pi\)
−0.327159 + 0.944969i \(0.606091\pi\)
\(548\) −12.5020 7.21801i −0.534057 0.308338i
\(549\) −32.0548 13.1709i −1.36806 0.562121i
\(550\) 2.82468 + 4.89248i 0.120445 + 0.208616i
\(551\) −7.96265 + 13.7917i −0.339220 + 0.587547i
\(552\) −7.31796 3.59590i −0.311473 0.153052i
\(553\) 26.4173 2.09427i 1.12338 0.0890573i
\(554\) 7.16807i 0.304542i
\(555\) −55.8746 + 37.4492i −2.37174 + 1.58963i
\(556\) −6.94815 + 4.01152i −0.294667 + 0.170126i
\(557\) 5.44584 3.14416i 0.230748 0.133222i −0.380169 0.924917i \(-0.624134\pi\)
0.610917 + 0.791695i \(0.290801\pi\)
\(558\) 2.08773 0.280894i 0.0883808 0.0118912i
\(559\) 3.57757i 0.151315i
\(560\) −4.23198 + 8.88559i −0.178834 + 0.375485i
\(561\) −3.55438 + 7.23347i −0.150066 + 0.305397i
\(562\) −0.784886 + 1.35946i −0.0331084 + 0.0573455i
\(563\) 9.26195 + 16.0422i 0.390344 + 0.676096i 0.992495 0.122286i \(-0.0390226\pi\)
−0.602150 + 0.798383i \(0.705689\pi\)
\(564\) 0.818254 + 12.2181i 0.0344547 + 0.514473i
\(565\) −30.7877 17.7753i −1.29525 0.747813i
\(566\) −20.0409 −0.842381
\(567\) −18.2030 15.3509i −0.764454 0.644679i
\(568\) 10.9092 0.457739
\(569\) −13.7196 7.92099i −0.575154 0.332065i 0.184051 0.982917i \(-0.441079\pi\)
−0.759205 + 0.650852i \(0.774412\pi\)
\(570\) −2.30034 34.3484i −0.0963508 1.43870i
\(571\) 11.5912 + 20.0765i 0.485075 + 0.840174i 0.999853 0.0171491i \(-0.00545899\pi\)
−0.514778 + 0.857324i \(0.672126\pi\)
\(572\) −0.319619 + 0.553597i −0.0133640 + 0.0231471i
\(573\) −7.44659 + 15.1544i −0.311086 + 0.633086i
\(574\) −2.44306 30.8170i −0.101971 1.28628i
\(575\) 41.6035i 1.73499i
\(576\) 2.97321 0.400031i 0.123884 0.0166679i
\(577\) −18.4472 + 10.6505i −0.767968 + 0.443386i −0.832149 0.554552i \(-0.812890\pi\)
0.0641814 + 0.997938i \(0.479556\pi\)
\(578\) 31.1664 17.9939i 1.29635 0.748448i
\(579\) 4.21191 2.82297i 0.175041 0.117319i
\(580\) 11.0874i 0.460381i
\(581\) 10.0544 + 14.6113i 0.417126 + 0.606180i
\(582\) 5.44191 + 2.67404i 0.225574 + 0.110843i
\(583\) −2.45769 + 4.25684i −0.101787 + 0.176300i
\(584\) 4.78522 + 8.28825i 0.198014 + 0.342970i
\(585\) 10.3223 + 4.24131i 0.426775 + 0.175356i
\(586\) −14.7886 8.53822i −0.610913 0.352711i
\(587\) −33.7288 −1.39214 −0.696068 0.717976i \(-0.745069\pi\)
−0.696068 + 0.717976i \(0.745069\pi\)
\(588\) −2.70612 11.8185i −0.111598 0.487387i
\(589\) −3.75177 −0.154589
\(590\) 8.70579 + 5.02629i 0.358412 + 0.206929i
\(591\) 4.50464 0.301680i 0.185296 0.0124094i
\(592\) 5.21987 + 9.04107i 0.214535 + 0.371586i
\(593\) −17.5003 + 30.3114i −0.718651 + 1.24474i 0.242884 + 0.970055i \(0.421907\pi\)
−0.961534 + 0.274684i \(0.911427\pi\)
\(594\) 0.661892 + 3.25497i 0.0271577 + 0.133553i
\(595\) 40.6122 + 59.0189i 1.66494 + 2.41954i
\(596\) 14.9500i 0.612375i
\(597\) −10.8525 16.1921i −0.444164 0.662698i
\(598\) −4.07685 + 2.35377i −0.166715 + 0.0962529i
\(599\) 2.10938 1.21785i 0.0861871 0.0497601i −0.456287 0.889833i \(-0.650821\pi\)
0.542474 + 0.840072i \(0.317488\pi\)
\(600\) −8.52231 12.7154i −0.347922 0.519103i
\(601\) 3.59313i 0.146567i −0.997311 0.0732833i \(-0.976652\pi\)
0.997311 0.0732833i \(-0.0233477\pi\)
\(602\) −0.748031 9.43574i −0.0304875 0.384572i
\(603\) 4.23009 + 5.48044i 0.172263 + 0.223181i
\(604\) −2.84087 + 4.92054i −0.115593 + 0.200214i
\(605\) −19.6994 34.1204i −0.800895 1.38719i
\(606\) −3.06482 + 0.205254i −0.124500 + 0.00833786i
\(607\) −37.0768 21.4063i −1.50490 0.868856i −0.999984 0.00568830i \(-0.998189\pi\)
−0.504918 0.863167i \(-0.668477\pi\)
\(608\) −5.34303 −0.216688
\(609\) −8.47738 10.7096i −0.343521 0.433973i
\(610\) 42.9712 1.73985
\(611\) 6.12272 + 3.53495i 0.247699 + 0.143009i
\(612\) 8.29960 20.1992i 0.335491 0.816504i
\(613\) −6.21541 10.7654i −0.251038 0.434811i 0.712774 0.701394i \(-0.247439\pi\)
−0.963812 + 0.266583i \(0.914105\pi\)
\(614\) 1.13773 1.97060i 0.0459149 0.0795270i
\(615\) 67.5660 + 33.2006i 2.72452 + 1.33878i
\(616\) −0.727237 + 1.52693i −0.0293012 + 0.0615217i
\(617\) 38.6142i 1.55455i −0.629161 0.777275i \(-0.716601\pi\)
0.629161 0.777275i \(-0.283399\pi\)
\(618\) 11.9058 7.97968i 0.478920 0.320990i
\(619\) −6.51713 + 3.76267i −0.261946 + 0.151234i −0.625222 0.780447i \(-0.714991\pi\)
0.363276 + 0.931681i \(0.381658\pi\)
\(620\) −2.26209 + 1.30602i −0.0908479 + 0.0524510i
\(621\) −7.76395 + 23.1963i −0.311556 + 0.930835i
\(622\) 21.7210i 0.870935i
\(623\) 10.2889 0.815665i 0.412215 0.0326789i
\(624\) 0.763858 1.55452i 0.0305788 0.0622305i
\(625\) −4.45773 + 7.72102i −0.178309 + 0.308841i
\(626\) 8.28769 + 14.3547i 0.331243 + 0.573729i
\(627\) −0.395298 5.90255i −0.0157867 0.235725i
\(628\) −3.76719 2.17499i −0.150327 0.0867914i
\(629\) 75.9937 3.03007
\(630\) 28.1116 + 9.02806i 1.11999 + 0.359686i
\(631\) −28.1181 −1.11936 −0.559682 0.828707i \(-0.689077\pi\)
−0.559682 + 0.828707i \(0.689077\pi\)
\(632\) 8.67422 + 5.00806i 0.345042 + 0.199210i
\(633\) 0.112564 + 1.68079i 0.00447400 + 0.0668053i
\(634\) 4.11494 + 7.12729i 0.163425 + 0.283061i
\(635\) −4.99718 + 8.65537i −0.198307 + 0.343478i
\(636\) 5.87362 11.9533i 0.232904 0.473980i
\(637\) −6.53792 2.50111i −0.259042 0.0990976i
\(638\) 1.90530i 0.0754316i
\(639\) −4.36400 32.4353i −0.172637 1.28312i
\(640\) −3.22152 + 1.85995i −0.127342 + 0.0735209i
\(641\) 35.4835 20.4864i 1.40151 0.809164i 0.406965 0.913444i \(-0.366587\pi\)
0.994548 + 0.104279i \(0.0332536\pi\)
\(642\) −23.9787 + 16.0714i −0.946362 + 0.634286i
\(643\) 13.7897i 0.543812i 0.962324 + 0.271906i \(0.0876539\pi\)
−0.962324 + 0.271906i \(0.912346\pi\)
\(644\) −10.2605 + 7.06045i −0.404319 + 0.278221i
\(645\) 20.6878 + 10.1656i 0.814580 + 0.400268i
\(646\) −19.4467 + 33.6826i −0.765119 + 1.32523i
\(647\) −12.9910 22.5010i −0.510728 0.884607i −0.999923 0.0124324i \(-0.996043\pi\)
0.489195 0.872175i \(-0.337291\pi\)
\(648\) −2.37875 8.67995i −0.0934461 0.340981i
\(649\) 1.49603 + 0.863734i 0.0587243 + 0.0339045i
\(650\) −8.83762 −0.346640
\(651\) 1.18642 2.99109i 0.0464996 0.117230i
\(652\) 23.3955 0.916240
\(653\) 7.09560 + 4.09665i 0.277672 + 0.160314i 0.632369 0.774667i \(-0.282083\pi\)
−0.354697 + 0.934981i \(0.615416\pi\)
\(654\) 17.3760 1.16368i 0.679454 0.0455036i
\(655\) −11.6902 20.2481i −0.456775 0.791157i
\(656\) 5.84214 10.1189i 0.228097 0.395076i
\(657\) 22.7285 17.5430i 0.886722 0.684419i
\(658\) 16.8876 + 8.04315i 0.658349 + 0.313555i
\(659\) 12.0959i 0.471188i −0.971852 0.235594i \(-0.924296\pi\)
0.971852 0.235594i \(-0.0757035\pi\)
\(660\) −2.29306 3.42127i −0.0892573 0.133173i
\(661\) −41.8718 + 24.1747i −1.62862 + 0.940287i −0.644121 + 0.764924i \(0.722777\pi\)
−0.984504 + 0.175363i \(0.943890\pi\)
\(662\) 19.5795 11.3043i 0.760981 0.439352i
\(663\) −7.01956 10.4733i −0.272617 0.406748i
\(664\) 6.70374i 0.260156i
\(665\) −47.4759 22.6116i −1.84104 0.876840i
\(666\) 24.7929 19.1365i 0.960705 0.741523i
\(667\) −7.01560 + 12.1514i −0.271645 + 0.470503i
\(668\) −1.21982 2.11279i −0.0471962 0.0817462i
\(669\) 20.3273 1.36134i 0.785900 0.0526324i
\(670\) −7.43427 4.29218i −0.287211 0.165821i
\(671\) 7.38432 0.285068
\(672\) 1.68962 4.25971i 0.0651787 0.164322i
\(673\) −37.0135 −1.42677 −0.713383 0.700774i \(-0.752838\pi\)
−0.713383 + 0.700774i \(0.752838\pi\)
\(674\) −1.15427 0.666420i −0.0444609 0.0256695i
\(675\) −34.3963 + 30.4252i −1.32391 + 1.17106i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 3.06663 5.31156i 0.117860 0.204140i −0.801059 0.598585i \(-0.795730\pi\)
0.918919 + 0.394445i \(0.129063\pi\)
\(678\) 14.8563 + 7.30011i 0.570554 + 0.280359i
\(679\) 7.63006 5.25041i 0.292815 0.201492i
\(680\) 27.0781i 1.03840i
\(681\) 9.95752 6.67389i 0.381573 0.255744i
\(682\) −0.388726 + 0.224431i −0.0148851 + 0.00859390i
\(683\) 3.42887 1.97966i 0.131202 0.0757496i −0.432962 0.901412i \(-0.642532\pi\)
0.564164 + 0.825662i \(0.309198\pi\)
\(684\) 2.13737 + 15.8859i 0.0817246 + 0.607414i
\(685\) 53.7005i 2.05179i
\(686\) −17.7666 5.22961i −0.678331 0.199667i
\(687\) 7.63268 15.5332i 0.291205 0.592627i
\(688\) 1.78878 3.09826i 0.0681967 0.118120i
\(689\) −3.84471 6.65923i −0.146472 0.253696i
\(690\) −2.02675 30.2631i −0.0771570 1.15210i
\(691\) 33.1863 + 19.1601i 1.26247 + 0.728885i 0.973551 0.228470i \(-0.0733723\pi\)
0.288915 + 0.957355i \(0.406706\pi\)
\(692\) 2.37184 0.0901638
\(693\) 4.83080 + 1.55141i 0.183507 + 0.0589332i
\(694\) −22.2099 −0.843078
\(695\) −25.8464 14.9224i −0.980410 0.566040i
\(696\) −0.344965 5.15097i −0.0130759 0.195247i
\(697\) −42.5265 73.6581i −1.61081 2.79000i
\(698\) 8.70906 15.0845i 0.329643 0.570958i
\(699\) −1.51134 + 3.07571i −0.0571642 + 0.116334i
\(700\) −23.3090 + 1.84785i −0.880998 + 0.0698423i
\(701\) 13.5430i 0.511511i −0.966741 0.255756i \(-0.917676\pi\)
0.966741 0.255756i \(-0.0823243\pi\)
\(702\) −4.92747 1.64926i −0.185975 0.0622472i
\(703\) −48.3067 + 27.8899i −1.82192 + 1.05189i
\(704\) −0.553597 + 0.319619i −0.0208645 + 0.0120461i
\(705\) −37.8389 + 25.3610i −1.42509 + 0.955150i
\(706\) 28.9209i 1.08845i
\(707\) −2.01757 + 4.23616i −0.0758787 + 0.159317i
\(708\) −4.20090 2.06424i −0.157879 0.0775787i
\(709\) 1.67931 2.90864i 0.0630677 0.109236i −0.832768 0.553623i \(-0.813245\pi\)
0.895835 + 0.444386i \(0.146578\pi\)
\(710\) 20.2905 + 35.1442i 0.761488 + 1.31894i
\(711\) 11.4201 27.7937i 0.428286 1.04234i
\(712\) 3.37839 + 1.95052i 0.126611 + 0.0730987i
\(713\) −3.30555 −0.123794
\(714\) −20.7038 26.1553i −0.774819 0.978836i
\(715\) −2.37790 −0.0889285
\(716\) 8.34373 + 4.81725i 0.311820 + 0.180029i
\(717\) −18.5039 + 1.23922i −0.691041 + 0.0462795i
\(718\) −2.03087 3.51757i −0.0757914 0.131275i
\(719\) −5.76707 + 9.98887i −0.215076 + 0.372522i −0.953296 0.302038i \(-0.902333\pi\)
0.738220 + 0.674560i \(0.235666\pi\)
\(720\) 6.81872 + 8.83423i 0.254119 + 0.329232i
\(721\) −1.73020 21.8249i −0.0644360 0.812802i
\(722\) 9.54793i 0.355337i
\(723\) −19.0901 28.4826i −0.709967 1.05928i
\(724\) 9.23515 5.33192i 0.343222 0.198159i
\(725\) −22.8122 + 13.1706i −0.847223 + 0.489144i
\(726\) 10.2135 + 15.2386i 0.379058 + 0.565559i
\(727\) 22.1982i 0.823284i 0.911346 + 0.411642i \(0.135045\pi\)
−0.911346 + 0.411642i \(0.864955\pi\)
\(728\) −1.49982 2.17958i −0.0555868 0.0807805i
\(729\) −24.8557 + 10.5448i −0.920583 + 0.390547i
\(730\) −17.8005 + 30.8314i −0.658827 + 1.14112i
\(731\) −13.0210 22.5531i −0.481601 0.834157i
\(732\) −19.9635 + 1.33697i −0.737871 + 0.0494158i
\(733\) 17.0396 + 9.83784i 0.629373 + 0.363369i 0.780509 0.625144i \(-0.214960\pi\)
−0.151136 + 0.988513i \(0.548293\pi\)
\(734\) −9.26062 −0.341816
\(735\) 33.0403 30.6996i 1.21871 1.13237i
\(736\) −4.70754 −0.173522
\(737\) −1.27753 0.737582i −0.0470584 0.0271692i
\(738\) −32.4226 13.3220i −1.19349 0.490391i
\(739\) −4.31359 7.47135i −0.158678 0.274838i 0.775714 0.631084i \(-0.217390\pi\)
−0.934392 + 0.356246i \(0.884056\pi\)
\(740\) −19.4174 + 33.6319i −0.713796 + 1.23633i
\(741\) 8.30582 + 4.08131i 0.305122 + 0.149931i
\(742\) −11.5327 16.7597i −0.423379 0.615267i
\(743\) 11.8689i 0.435428i 0.976013 + 0.217714i \(0.0698601\pi\)
−0.976013 + 0.217714i \(0.930140\pi\)
\(744\) 1.01028 0.677129i 0.0370388 0.0248247i
\(745\) 48.1617 27.8062i 1.76451 1.01874i
\(746\) 5.31539 3.06884i 0.194610 0.112358i
\(747\) 19.9316 2.68170i 0.729260 0.0981183i
\(748\) 4.65320i 0.170138i
\(749\) 3.48468 + 43.9561i 0.127327 + 1.60612i
\(750\) 10.9045 22.1916i 0.398176 0.810322i
\(751\) 22.4815 38.9390i 0.820360 1.42091i −0.0850545 0.996376i \(-0.527106\pi\)
0.905414 0.424529i \(-0.139560\pi\)
\(752\) 3.53495 + 6.12272i 0.128906 + 0.223272i
\(753\) −3.14924 47.0241i −0.114765 1.71365i
\(754\) −2.58126 1.49029i −0.0940038 0.0542731i
\(755\) −21.1355 −0.769200
\(756\) −13.3409 3.31959i −0.485205 0.120732i
\(757\) 23.3891 0.850093 0.425046 0.905172i \(-0.360258\pi\)
0.425046 + 0.905172i \(0.360258\pi\)
\(758\) −13.7866 7.95971i −0.500752 0.289110i
\(759\) −0.348283 5.20052i −0.0126419 0.188767i
\(760\) −9.93775 17.2127i −0.360480 0.624370i
\(761\) −23.3116 + 40.3768i −0.845044 + 1.46366i 0.0405392 + 0.999178i \(0.487092\pi\)
−0.885583 + 0.464481i \(0.846241\pi\)
\(762\) 2.05228 4.17657i 0.0743463 0.151301i
\(763\) 11.4386 24.0168i 0.414105 0.869467i
\(764\) 9.74865i 0.352694i
\(765\) 80.5090 10.8321i 2.91081 0.391635i
\(766\) −23.8462 + 13.7676i −0.861597 + 0.497443i
\(767\) −2.34033 + 1.35119i −0.0845045 + 0.0487887i
\(768\) 1.43878 0.964322i 0.0519175 0.0347970i
\(769\) 29.3721i 1.05918i 0.848252 + 0.529592i \(0.177655\pi\)
−0.848252 + 0.529592i \(0.822345\pi\)
\(770\) −6.27166 + 0.497194i −0.226015 + 0.0179176i
\(771\) 35.3661 + 17.3782i 1.27368 + 0.625860i
\(772\) 1.46371 2.53522i 0.0526801 0.0912446i
\(773\) 27.2086 + 47.1267i 0.978626 + 1.69503i 0.667411 + 0.744690i \(0.267403\pi\)
0.311215 + 0.950340i \(0.399264\pi\)
\(774\) −9.92735 4.07903i −0.356831 0.146618i
\(775\) −5.37422 3.10281i −0.193048 0.111456i
\(776\) 3.50071 0.125668
\(777\) −6.95912 47.3320i −0.249657 1.69803i
\(778\) −18.6746 −0.669518
\(779\) 54.0655 + 31.2147i 1.93710 + 1.11838i
\(780\) 6.42865 0.430532i 0.230183 0.0154155i
\(781\) 3.48678 + 6.03929i 0.124767 + 0.216103i
\(782\) −17.1338 + 29.6765i −0.612702 + 1.06123i
\(783\) −15.1769 + 3.08620i −0.542379 + 0.110292i
\(784\) −4.41145 5.43499i −0.157552 0.194107i
\(785\) 16.1814i 0.577540i
\(786\) 6.06100 + 9.04307i 0.216189 + 0.322556i
\(787\) −1.22692 + 0.708362i −0.0437349 + 0.0252504i −0.521708 0.853124i \(-0.674705\pi\)
0.477973 + 0.878374i \(0.341372\pi\)
\(788\) 2.25737 1.30329i 0.0804153 0.0464278i
\(789\) −1.85673 2.77026i −0.0661013 0.0986238i
\(790\) 37.2590i 1.32561i
\(791\) 20.8300 14.3336i 0.740628 0.509643i
\(792\) 1.17175 + 1.51810i 0.0416364 + 0.0539434i
\(793\) −5.77587 + 10.0041i −0.205107 + 0.355256i
\(794\) 1.49527 + 2.58988i 0.0530650 + 0.0919113i
\(795\) 49.4325 3.31054i 1.75319 0.117413i
\(796\) −9.74629 5.62702i −0.345448 0.199445i
\(797\) 22.8484 0.809331 0.404665 0.914465i \(-0.367388\pi\)
0.404665 + 0.914465i \(0.367388\pi\)
\(798\) 22.7598 + 9.02771i 0.805687 + 0.319577i
\(799\) 51.4638 1.82066
\(800\) −7.65361 4.41881i −0.270596 0.156229i
\(801\) 4.44783 10.8249i 0.157156 0.382480i
\(802\) −5.01418 8.68481i −0.177057 0.306671i
\(803\) −3.05890 + 5.29817i −0.107946 + 0.186968i
\(804\) 3.58734 + 1.76275i 0.126516 + 0.0621673i
\(805\) −41.8293 19.9222i −1.47429 0.702167i
\(806\) 0.702181i 0.0247333i
\(807\) −26.7535 + 17.9311i −0.941767 + 0.631206i
\(808\) −1.53584 + 0.886720i −0.0540308 + 0.0311947i
\(809\) 16.9162 9.76655i 0.594740 0.343374i −0.172229 0.985057i \(-0.555097\pi\)
0.766970 + 0.641683i \(0.221764\pi\)
\(810\) 23.5383 23.8075i 0.827052 0.836509i
\(811\) 44.6035i 1.56624i 0.621870 + 0.783120i \(0.286373\pi\)
−0.621870 + 0.783120i \(0.713627\pi\)
\(812\) −7.11960 3.39089i −0.249849 0.118997i
\(813\) 4.48637 9.13014i 0.157344 0.320208i
\(814\) −3.33674 + 5.77941i −0.116953 + 0.202568i
\(815\) 43.5145 + 75.3693i 1.52425 + 2.64007i
\(816\) −0.842486 12.5799i −0.0294929 0.440384i
\(817\) 16.5541 + 9.55751i 0.579155 + 0.334375i
\(818\) −32.4173 −1.13344
\(819\) −5.88037 + 5.33116i −0.205477 + 0.186286i
\(820\) 43.4643 1.51784
\(821\) −30.6156 17.6759i −1.06849 0.616894i −0.140723 0.990049i \(-0.544943\pi\)
−0.927769 + 0.373155i \(0.878276\pi\)
\(822\) 1.67079 + 24.9480i 0.0582755 + 0.870163i
\(823\) −28.0658 48.6113i −0.978311 1.69448i −0.668544 0.743672i \(-0.733082\pi\)
−0.309767 0.950813i \(-0.600251\pi\)
\(824\) 4.13746 7.16629i 0.144135 0.249649i
\(825\) 4.31530 8.78201i 0.150240 0.305750i
\(826\) −5.89005 + 4.05307i −0.204941 + 0.141024i
\(827\) 5.37342i 0.186852i 0.995626 + 0.0934261i \(0.0297819\pi\)
−0.995626 + 0.0934261i \(0.970218\pi\)
\(828\) 1.88316 + 13.9965i 0.0654444 + 0.486413i
\(829\) 22.5316 13.0086i 0.782554 0.451808i −0.0547805 0.998498i \(-0.517446\pi\)
0.837335 + 0.546691i \(0.184113\pi\)
\(830\) −21.5963 + 12.4686i −0.749617 + 0.432792i
\(831\) 10.3133 6.91233i 0.357763 0.239786i
\(832\) 1.00000i 0.0346688i
\(833\) −50.3184 + 8.02858i −1.74343 + 0.278174i
\(834\) 12.4719 + 6.12846i 0.431868 + 0.212211i
\(835\) 4.53760 7.85935i 0.157030 0.271984i
\(836\) −1.70774 2.95788i −0.0590633 0.102301i
\(837\) −2.41739 2.73291i −0.0835572 0.0944633i
\(838\) −30.3692 17.5337i −1.04909 0.605691i
\(839\) −33.1916 −1.14590 −0.572950 0.819590i \(-0.694201\pi\)
−0.572950 + 0.819590i \(0.694201\pi\)
\(840\) 16.8654 2.47968i 0.581911 0.0855571i
\(841\) 20.1162 0.693661
\(842\) −10.4350 6.02468i −0.359615 0.207624i
\(843\) 2.71285 0.181682i 0.0934355 0.00625745i
\(844\) 0.486288 + 0.842276i 0.0167387 + 0.0289923i
\(845\) 1.85995 3.22152i 0.0639841 0.110824i
\(846\) 16.7900 12.9594i 0.577253 0.445554i
\(847\) 27.9345 2.21455i 0.959841 0.0760927i
\(848\) 7.68941i 0.264056i
\(849\) 19.3258 + 28.8344i 0.663261 + 0.989594i
\(850\) −55.7127 + 32.1657i −1.91093 + 1.10328i
\(851\) −42.5613 + 24.5728i −1.45898 + 0.842343i
\(852\) −10.5199 15.6959i −0.360407 0.537732i
\(853\) 45.1819i 1.54700i 0.633797 + 0.773499i \(0.281495\pi\)
−0.633797 + 0.773499i \(0.718505\pi\)
\(854\) −13.1420 + 27.5932i −0.449709 + 0.944221i
\(855\) −47.2015 + 36.4326i −1.61426 + 1.24597i
\(856\) −8.33299 + 14.4332i −0.284816 + 0.493315i
\(857\) −16.9269 29.3183i −0.578212 1.00149i −0.995684 0.0928029i \(-0.970417\pi\)
0.417473 0.908690i \(-0.362916\pi\)
\(858\) 1.10472 0.0739840i 0.0377145 0.00252577i
\(859\) 48.6477 + 28.0868i 1.65984 + 0.958309i 0.972787 + 0.231700i \(0.0744288\pi\)
0.687052 + 0.726608i \(0.258905\pi\)
\(860\) 13.3082 0.453805
\(861\) −41.9830 + 33.2325i −1.43078 + 1.13256i
\(862\) 14.0027 0.476933
\(863\) 13.2859 + 7.67064i 0.452258 + 0.261111i 0.708784 0.705426i \(-0.249244\pi\)
−0.256525 + 0.966538i \(0.582578\pi\)
\(864\) −3.44269 3.89203i −0.117123 0.132410i
\(865\) 4.41150 + 7.64093i 0.149995 + 0.259800i
\(866\) 11.8632 20.5477i 0.403129 0.698240i
\(867\) −55.9437 27.4896i −1.89995 0.933596i
\(868\) −0.146819 1.85199i −0.00498335 0.0628605i
\(869\) 6.40270i 0.217197i
\(870\) 15.9524 10.6919i 0.540836 0.362488i
\(871\) 1.99852 1.15384i 0.0677172 0.0390965i
\(872\) 8.70744 5.02724i 0.294871 0.170244i
\(873\) −1.40039 10.4083i −0.0473960 0.352269i
\(874\) 25.1525i 0.850797i
\(875\) −21.4107 31.1147i −0.723814 1.05187i
\(876\) 7.31046 14.8774i 0.246998 0.502661i
\(877\) 27.0824 46.9081i 0.914508 1.58397i 0.106888 0.994271i \(-0.465912\pi\)
0.807620 0.589703i \(-0.200755\pi\)
\(878\) 13.7437 + 23.8048i 0.463827 + 0.803372i
\(879\) 1.97639 + 29.5112i 0.0666619 + 0.995387i
\(880\) −2.05932 1.18895i −0.0694198 0.0400795i
\(881\) 33.5277 1.12958 0.564788 0.825236i \(-0.308958\pi\)
0.564788 + 0.825236i \(0.308958\pi\)
\(882\) −14.3946 + 15.2903i −0.484693 + 0.514852i
\(883\) 18.1979 0.612407 0.306203 0.951966i \(-0.400941\pi\)
0.306203 + 0.951966i \(0.400941\pi\)
\(884\) −6.30404 3.63964i −0.212028 0.122414i
\(885\) −1.16346 17.3727i −0.0391093 0.583976i
\(886\) 11.3770 + 19.7056i 0.382219 + 0.662023i
\(887\) −3.80995 + 6.59903i −0.127926 + 0.221574i −0.922873 0.385105i \(-0.874165\pi\)
0.794947 + 0.606679i \(0.207499\pi\)
\(888\) 7.97447 16.2287i 0.267606 0.544601i
\(889\) −4.02960 5.85594i −0.135148 0.196402i
\(890\) 14.5114i 0.486424i
\(891\) 4.04490 4.09115i 0.135509 0.137059i
\(892\) 10.1864 5.88114i 0.341067 0.196915i
\(893\) −32.7138 + 18.8873i −1.09473 + 0.632041i
\(894\) −21.5097 + 14.4166i −0.719392 + 0.482163i
\(895\) 35.8394i 1.19798i
\(896\) −0.209090 2.63748i −0.00698519 0.0881119i
\(897\) 7.31796 + 3.59590i 0.244339 + 0.120063i
\(898\) 6.11710 10.5951i 0.204130 0.353564i
\(899\) −1.04645 1.81251i −0.0349012 0.0604506i
\(900\) −10.0764 + 24.5234i −0.335879 + 0.817448i
\(901\) −48.4743 27.9867i −1.61491 0.932371i
\(902\) 7.46905 0.248692
\(903\) −12.8546 + 10.1753i −0.427774 + 0.338614i
\(904\) 9.55689 0.317857
\(905\) 34.3538 + 19.8342i 1.14196 + 0.659310i
\(906\) 9.81908 0.657592i 0.326217 0.0218470i
\(907\) −14.0093 24.2648i −0.465171 0.805700i 0.534038 0.845460i \(-0.320674\pi\)
−0.999209 + 0.0397603i \(0.987341\pi\)
\(908\) 3.46041 5.99360i 0.114838 0.198905i
\(909\) 3.25079 + 4.21167i 0.107822 + 0.139692i
\(910\) 4.23198 8.88559i 0.140289 0.294554i
\(911\) 10.0668i 0.333529i 0.985997 + 0.166765i \(0.0533320\pi\)
−0.985997 + 0.166765i \(0.946668\pi\)
\(912\) 5.15240 + 7.68743i 0.170613 + 0.254556i
\(913\) −3.71117 + 2.14265i −0.122822 + 0.0709112i
\(914\) 16.3187 9.42161i 0.539775 0.311639i
\(915\) −41.4381 61.8261i −1.36990 2.04391i
\(916\) 9.99228i 0.330154i
\(917\) 16.5772 1.31418i 0.547427 0.0433980i
\(918\) −37.0656 + 7.53723i −1.22335 + 0.248766i
\(919\) 2.87061 4.97204i 0.0946926 0.164012i −0.814788 0.579759i \(-0.803147\pi\)
0.909480 + 0.415747i \(0.136480\pi\)
\(920\) −8.75579 15.1655i −0.288670 0.499991i
\(921\) −3.93239 + 0.263356i −0.129577 + 0.00867786i
\(922\) 16.2575 + 9.38627i 0.535412 + 0.309120i
\(923\) −10.9092 −0.359080
\(924\) 2.89820 0.426116i 0.0953439 0.0140182i
\(925\) −92.2624 −3.03357
\(926\) −18.9188 10.9228i −0.621710 0.358944i
\(927\) −22.9620 9.43479i −0.754171 0.309879i
\(928\) −1.49029 2.58126i −0.0489211 0.0847339i
\(929\) −19.1734 + 33.2093i −0.629058 + 1.08956i 0.358683 + 0.933460i \(0.383226\pi\)
−0.987741 + 0.156101i \(0.950107\pi\)
\(930\) 4.06046 + 1.99523i 0.133148 + 0.0654261i
\(931\) 29.0393 23.5705i 0.951724 0.772492i
\(932\) 1.97856i 0.0648100i
\(933\) −31.2518 + 20.9461i −1.02314 + 0.685744i
\(934\) 23.6028 13.6271i 0.772307 0.445891i
\(935\) −14.9904 + 8.65470i −0.490238 + 0.283039i
\(936\) −2.97321 + 0.400031i −0.0971824 + 0.0130754i
\(937\) 5.20813i 0.170142i −0.996375 0.0850711i \(-0.972888\pi\)
0.996375 0.0850711i \(-0.0271117\pi\)
\(938\) 5.02978 3.46111i 0.164228 0.113009i
\(939\) 12.6612 25.7667i 0.413184 0.840865i
\(940\) −13.1496 + 22.7759i −0.428894 + 0.742867i
\(941\) −16.0739 27.8409i −0.523995 0.907586i −0.999610 0.0279326i \(-0.991108\pi\)
0.475615 0.879654i \(-0.342226\pi\)
\(942\) 0.503455 + 7.51753i 0.0164035 + 0.244934i
\(943\) 47.6351 + 27.5021i 1.55121 + 0.895593i
\(944\) −2.70238 −0.0879550
\(945\) −14.1193 49.1524i −0.459300 1.59893i
\(946\) 2.28692 0.0743542
\(947\) −23.4484 13.5380i −0.761971 0.439924i 0.0680317 0.997683i \(-0.478328\pi\)
−0.830003 + 0.557759i \(0.811661\pi\)
\(948\) −1.15924 17.3097i −0.0376505 0.562192i
\(949\) −4.78522 8.28825i −0.155335 0.269048i
\(950\) 23.6098 40.8934i 0.766004 1.32676i
\(951\) 6.28646 12.7935i 0.203852 0.414857i
\(952\) −17.3878 8.28135i −0.563540 0.268400i
\(953\) 8.80705i 0.285288i −0.989774 0.142644i \(-0.954440\pi\)
0.989774 0.142644i \(-0.0455604\pi\)
\(954\) −22.8622 + 3.07600i −0.740192 + 0.0995892i
\(955\) −31.4055 + 18.1320i −1.01626 + 0.586737i
\(956\) −9.27267 + 5.35358i −0.299900 + 0.173147i
\(957\) 2.74131 1.83732i 0.0886139 0.0593922i
\(958\) 8.15791i 0.263570i
\(959\) 34.4828 + 16.4233i 1.11351 + 0.530336i
\(960\) 5.78264 + 2.84147i 0.186634 + 0.0917081i
\(961\) −15.2535 + 26.4198i −0.492047 + 0.852251i
\(962\) −5.21987 9.04107i −0.168295 0.291496i
\(963\) 46.2463 + 19.0020i 1.49027 + 0.612331i
\(964\) −17.1442 9.89818i −0.552176 0.318799i
\(965\) 10.8897 0.350552
\(966\) 20.0528 + 7.95398i 0.645188 + 0.255915i
\(967\) 48.3827 1.55588 0.777942 0.628336i \(-0.216264\pi\)
0.777942 + 0.628336i \(0.216264\pi\)
\(968\) 9.17240 + 5.29569i 0.294812 + 0.170210i
\(969\) 67.2147 4.50142i 2.15925 0.144607i
\(970\) 6.51113 + 11.2776i 0.209060 + 0.362102i
\(971\) −0.914961 + 1.58476i −0.0293625 + 0.0508574i −0.880333 0.474356i \(-0.842681\pi\)
0.850971 + 0.525213i \(0.176014\pi\)
\(972\) −10.1946 + 11.7928i −0.326993 + 0.378253i
\(973\) 17.4868 12.0331i 0.560602 0.385763i
\(974\) 31.5708i 1.01159i
\(975\) 8.52231 + 12.7154i 0.272932 + 0.407218i
\(976\) −10.0041 + 5.77587i −0.320223 + 0.184881i
\(977\) −27.4543 + 15.8507i −0.878341 + 0.507110i −0.870111 0.492856i \(-0.835953\pi\)
−0.00822977 + 0.999966i \(0.502620\pi\)
\(978\) −22.5608 33.6610i −0.721415 1.07636i
\(979\) 2.49369i 0.0796987i
\(980\) 9.30387 24.3204i 0.297201 0.776887i
\(981\) −18.4303 23.8780i −0.588434 0.762366i
\(982\) 5.22326 9.04695i 0.166681 0.288700i
\(983\) 1.09220 + 1.89174i 0.0348357 + 0.0603372i 0.882918 0.469528i \(-0.155576\pi\)
−0.848082 + 0.529865i \(0.822243\pi\)
\(984\) −20.1925 + 1.35231i −0.643714 + 0.0431101i
\(985\) 8.39717 + 4.84811i 0.267556 + 0.154474i
\(986\) −21.6964 −0.690955
\(987\) −4.71279 32.0538i −0.150010 1.02028i
\(988\) 5.34303 0.169984
\(989\) 14.5852 + 8.42077i 0.463783 + 0.267765i
\(990\) −2.71121 + 6.59842i −0.0861679 + 0.209711i
\(991\) 3.92400 + 6.79656i 0.124650 + 0.215900i 0.921596 0.388150i \(-0.126886\pi\)
−0.796946 + 0.604050i \(0.793553\pi\)
\(992\) 0.351091 0.608107i 0.0111471 0.0193074i
\(993\) −35.1453 17.2697i −1.11530 0.548037i
\(994\) −28.7727 + 2.28099i −0.912614 + 0.0723487i
\(995\) 41.8639i 1.32717i
\(996\) 9.64520 6.46456i 0.305620 0.204837i
\(997\) 42.0066 24.2525i 1.33036 0.768085i 0.345008 0.938600i \(-0.387876\pi\)
0.985355 + 0.170514i \(0.0545429\pi\)
\(998\) 15.6183 9.01724i 0.494389 0.285436i
\(999\) −51.4415 17.2178i −1.62754 0.544747i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.z.a.131.5 32
3.2 odd 2 546.2.z.b.131.9 yes 32
7.3 odd 6 546.2.z.b.521.9 yes 32
21.17 even 6 inner 546.2.z.a.521.5 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.5 32 1.1 even 1 trivial
546.2.z.a.521.5 yes 32 21.17 even 6 inner
546.2.z.b.131.9 yes 32 3.2 odd 2
546.2.z.b.521.9 yes 32 7.3 odd 6