Properties

Label 160.2.z.a.29.10
Level $160$
Weight $2$
Character 160.29
Analytic conductor $1.278$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [160,2,Mod(29,160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(160, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("160.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.z (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.27760643234\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 29.10
Character \(\chi\) \(=\) 160.29
Dual form 160.2.z.a.149.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.381706 - 1.36173i) q^{2} +(1.23949 - 2.99239i) q^{3} +(-1.70860 + 1.03956i) q^{4} +(-1.80901 + 1.31434i) q^{5} +(-4.54794 - 0.545632i) q^{6} +(-1.10874 - 1.10874i) q^{7} +(2.06778 + 1.92984i) q^{8} +(-5.29676 - 5.29676i) q^{9} +O(q^{10})\) \(q+(-0.381706 - 1.36173i) q^{2} +(1.23949 - 2.99239i) q^{3} +(-1.70860 + 1.03956i) q^{4} +(-1.80901 + 1.31434i) q^{5} +(-4.54794 - 0.545632i) q^{6} +(-1.10874 - 1.10874i) q^{7} +(2.06778 + 1.92984i) q^{8} +(-5.29676 - 5.29676i) q^{9} +(2.48028 + 1.96169i) q^{10} +(4.18025 - 1.73152i) q^{11} +(0.992974 + 6.40133i) q^{12} +(0.229363 + 0.0950054i) q^{13} +(-1.08659 + 1.93301i) q^{14} +(1.69077 + 7.04237i) q^{15} +(1.83864 - 3.55238i) q^{16} +1.91879 q^{17} +(-5.19093 + 9.23454i) q^{18} +(-0.745803 + 1.80053i) q^{19} +(1.72454 - 4.12625i) q^{20} +(-4.69206 + 1.94351i) q^{21} +(-3.95348 - 5.03143i) q^{22} +(3.63165 - 3.63165i) q^{23} +(8.33784 - 3.79558i) q^{24} +(1.54503 - 4.75530i) q^{25} +(0.0418221 - 0.348594i) q^{26} +(-13.4381 + 5.56623i) q^{27} +(3.04700 + 0.741795i) q^{28} +(4.73967 + 1.96323i) q^{29} +(8.94441 - 4.99048i) q^{30} -3.53104 q^{31} +(-5.53919 - 1.14776i) q^{32} -14.6551i q^{33} +(-0.732415 - 2.61287i) q^{34} +(3.46298 + 0.548462i) q^{35} +(14.5563 + 3.54376i) q^{36} +(-4.79534 + 1.98629i) q^{37} +(2.73650 + 0.328308i) q^{38} +(0.568587 - 0.568587i) q^{39} +(-6.27710 - 0.773343i) q^{40} +(2.54424 + 2.54424i) q^{41} +(4.43752 + 5.64745i) q^{42} +(3.16869 + 7.64990i) q^{43} +(-5.34237 + 7.30409i) q^{44} +(16.5436 + 2.62015i) q^{45} +(-6.33154 - 3.55909i) q^{46} +7.33627 q^{47} +(-8.35115 - 9.90506i) q^{48} -4.54139i q^{49} +(-7.06517 - 0.288781i) q^{50} +(2.37832 - 5.74178i) q^{51} +(-0.490654 + 0.0761102i) q^{52} +(0.792117 + 1.91234i) q^{53} +(12.7091 + 16.1743i) q^{54} +(-5.28631 + 8.62659i) q^{55} +(-0.152935 - 4.43232i) q^{56} +(4.46347 + 4.46347i) q^{57} +(0.864231 - 7.20351i) q^{58} +(3.09584 + 7.47402i) q^{59} +(-10.2098 - 10.2750i) q^{60} +(-3.83166 - 1.58713i) q^{61} +(1.34782 + 4.80831i) q^{62} +11.7455i q^{63} +(0.551413 + 7.98097i) q^{64} +(-0.539789 + 0.129595i) q^{65} +(-19.9563 + 5.59396i) q^{66} +(-0.518193 + 1.25103i) q^{67} +(-3.27845 + 1.99470i) q^{68} +(-6.36593 - 15.3687i) q^{69} +(-0.574986 - 4.92499i) q^{70} +(5.24488 - 5.24488i) q^{71} +(-0.730610 - 21.1744i) q^{72} +(-3.78304 + 3.78304i) q^{73} +(4.53520 + 5.77176i) q^{74} +(-12.3147 - 10.5175i) q^{75} +(-0.597474 - 3.85169i) q^{76} +(-6.55462 - 2.71501i) q^{77} +(-0.991293 - 0.557227i) q^{78} -5.57057i q^{79} +(1.34292 + 8.84288i) q^{80} +24.6390i q^{81} +(2.49341 - 4.43571i) q^{82} +(-3.79865 - 1.57345i) q^{83} +(5.99646 - 8.19836i) q^{84} +(-3.47112 + 2.52194i) q^{85} +(9.20757 - 7.23491i) q^{86} +(11.7495 - 11.7495i) q^{87} +(11.9854 + 4.48683i) q^{88} +(-5.22531 + 5.22531i) q^{89} +(-2.74686 - 23.5280i) q^{90} +(-0.148968 - 0.359641i) q^{91} +(-2.42973 + 9.98035i) q^{92} +(-4.37669 + 10.5663i) q^{93} +(-2.80030 - 9.99000i) q^{94} +(-1.01734 - 4.23741i) q^{95} +(-10.3003 + 15.1528i) q^{96} +8.97673i q^{97} +(-6.18413 + 1.73347i) q^{98} +(-31.3132 - 12.9703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.381706 1.36173i −0.269907 0.962886i
\(3\) 1.23949 2.99239i 0.715620 1.72766i 0.0301628 0.999545i \(-0.490397\pi\)
0.685457 0.728113i \(-0.259603\pi\)
\(4\) −1.70860 + 1.03956i −0.854301 + 0.519779i
\(5\) −1.80901 + 1.31434i −0.809014 + 0.587790i
\(6\) −4.54794 0.545632i −1.85669 0.222754i
\(7\) −1.10874 1.10874i −0.419065 0.419065i 0.465817 0.884881i \(-0.345761\pi\)
−0.884881 + 0.465817i \(0.845761\pi\)
\(8\) 2.06778 + 1.92984i 0.731070 + 0.682302i
\(9\) −5.29676 5.29676i −1.76559 1.76559i
\(10\) 2.48028 + 1.96169i 0.784333 + 0.620340i
\(11\) 4.18025 1.73152i 1.26039 0.522072i 0.350363 0.936614i \(-0.386058\pi\)
0.910030 + 0.414542i \(0.136058\pi\)
\(12\) 0.992974 + 6.40133i 0.286647 + 1.84790i
\(13\) 0.229363 + 0.0950054i 0.0636139 + 0.0263498i 0.414264 0.910157i \(-0.364039\pi\)
−0.350650 + 0.936507i \(0.614039\pi\)
\(14\) −1.08659 + 1.93301i −0.290403 + 0.516620i
\(15\) 1.69077 + 7.04237i 0.436554 + 1.81833i
\(16\) 1.83864 3.55238i 0.459659 0.888095i
\(17\) 1.91879 0.465376 0.232688 0.972551i \(-0.425248\pi\)
0.232688 + 0.972551i \(0.425248\pi\)
\(18\) −5.19093 + 9.23454i −1.22351 + 2.17660i
\(19\) −0.745803 + 1.80053i −0.171099 + 0.413069i −0.986048 0.166464i \(-0.946765\pi\)
0.814949 + 0.579533i \(0.196765\pi\)
\(20\) 1.72454 4.12625i 0.385620 0.922658i
\(21\) −4.69206 + 1.94351i −1.02389 + 0.424110i
\(22\) −3.95348 5.03143i −0.842885 1.07270i
\(23\) 3.63165 3.63165i 0.757251 0.757251i −0.218570 0.975821i \(-0.570139\pi\)
0.975821 + 0.218570i \(0.0701393\pi\)
\(24\) 8.33784 3.79558i 1.70195 0.774770i
\(25\) 1.54503 4.75530i 0.309006 0.951060i
\(26\) 0.0418221 0.348594i 0.00820198 0.0683650i
\(27\) −13.4381 + 5.56623i −2.58616 + 1.07122i
\(28\) 3.04700 + 0.741795i 0.575828 + 0.140186i
\(29\) 4.73967 + 1.96323i 0.880134 + 0.364564i 0.776549 0.630057i \(-0.216968\pi\)
0.103585 + 0.994621i \(0.466968\pi\)
\(30\) 8.94441 4.99048i 1.63302 0.911133i
\(31\) −3.53104 −0.634194 −0.317097 0.948393i \(-0.602708\pi\)
−0.317097 + 0.948393i \(0.602708\pi\)
\(32\) −5.53919 1.14776i −0.979200 0.202896i
\(33\) 14.6551i 2.55113i
\(34\) −0.732415 2.61287i −0.125608 0.448104i
\(35\) 3.46298 + 0.548462i 0.585351 + 0.0927069i
\(36\) 14.5563 + 3.54376i 2.42606 + 0.590626i
\(37\) −4.79534 + 1.98629i −0.788349 + 0.326545i −0.740279 0.672299i \(-0.765307\pi\)
−0.0480692 + 0.998844i \(0.515307\pi\)
\(38\) 2.73650 + 0.328308i 0.443919 + 0.0532586i
\(39\) 0.568587 0.568587i 0.0910467 0.0910467i
\(40\) −6.27710 0.773343i −0.992496 0.122276i
\(41\) 2.54424 + 2.54424i 0.397343 + 0.397343i 0.877295 0.479952i \(-0.159346\pi\)
−0.479952 + 0.877295i \(0.659346\pi\)
\(42\) 4.43752 + 5.64745i 0.684725 + 0.871421i
\(43\) 3.16869 + 7.64990i 0.483221 + 1.16660i 0.958071 + 0.286532i \(0.0925025\pi\)
−0.474849 + 0.880067i \(0.657497\pi\)
\(44\) −5.34237 + 7.30409i −0.805392 + 1.10113i
\(45\) 16.5436 + 2.62015i 2.46618 + 0.390589i
\(46\) −6.33154 3.55909i −0.933534 0.524760i
\(47\) 7.33627 1.07010 0.535052 0.844819i \(-0.320292\pi\)
0.535052 + 0.844819i \(0.320292\pi\)
\(48\) −8.35115 9.90506i −1.20538 1.42967i
\(49\) 4.54139i 0.648770i
\(50\) −7.06517 0.288781i −0.999166 0.0408399i
\(51\) 2.37832 5.74178i 0.333032 0.804010i
\(52\) −0.490654 + 0.0761102i −0.0680415 + 0.0105546i
\(53\) 0.792117 + 1.91234i 0.108806 + 0.262680i 0.968899 0.247457i \(-0.0795948\pi\)
−0.860093 + 0.510137i \(0.829595\pi\)
\(54\) 12.7091 + 16.1743i 1.72949 + 2.20105i
\(55\) −5.28631 + 8.62659i −0.712806 + 1.16321i
\(56\) −0.152935 4.43232i −0.0204367 0.592294i
\(57\) 4.46347 + 4.46347i 0.591201 + 0.591201i
\(58\) 0.864231 7.20351i 0.113479 0.945868i
\(59\) 3.09584 + 7.47402i 0.403044 + 0.973035i 0.986923 + 0.161194i \(0.0515344\pi\)
−0.583878 + 0.811841i \(0.698466\pi\)
\(60\) −10.2098 10.2750i −1.31808 1.32649i
\(61\) −3.83166 1.58713i −0.490594 0.203211i 0.123652 0.992326i \(-0.460540\pi\)
−0.614245 + 0.789115i \(0.710540\pi\)
\(62\) 1.34782 + 4.80831i 0.171173 + 0.610657i
\(63\) 11.7455i 1.47979i
\(64\) 0.551413 + 7.98097i 0.0689267 + 0.997622i
\(65\) −0.539789 + 0.129595i −0.0669526 + 0.0160743i
\(66\) −19.9563 + 5.59396i −2.45645 + 0.688568i
\(67\) −0.518193 + 1.25103i −0.0633073 + 0.152837i −0.952367 0.304953i \(-0.901359\pi\)
0.889060 + 0.457791i \(0.151359\pi\)
\(68\) −3.27845 + 1.99470i −0.397571 + 0.241893i
\(69\) −6.36593 15.3687i −0.766367 1.85017i
\(70\) −0.574986 4.92499i −0.0687239 0.588649i
\(71\) 5.24488 5.24488i 0.622452 0.622452i −0.323705 0.946158i \(-0.604929\pi\)
0.946158 + 0.323705i \(0.104929\pi\)
\(72\) −0.730610 21.1744i −0.0861032 2.49543i
\(73\) −3.78304 + 3.78304i −0.442771 + 0.442771i −0.892942 0.450171i \(-0.851363\pi\)
0.450171 + 0.892942i \(0.351363\pi\)
\(74\) 4.53520 + 5.77176i 0.527206 + 0.670954i
\(75\) −12.3147 10.5175i −1.42198 1.21445i
\(76\) −0.597474 3.85169i −0.0685350 0.441819i
\(77\) −6.55462 2.71501i −0.746968 0.309404i
\(78\) −0.991293 0.557227i −0.112242 0.0630935i
\(79\) 5.57057i 0.626739i −0.949631 0.313369i \(-0.898542\pi\)
0.949631 0.313369i \(-0.101458\pi\)
\(80\) 1.34292 + 8.84288i 0.150143 + 0.988664i
\(81\) 24.6390i 2.73767i
\(82\) 2.49341 4.43571i 0.275351 0.489842i
\(83\) −3.79865 1.57345i −0.416956 0.172709i 0.164335 0.986405i \(-0.447452\pi\)
−0.581291 + 0.813696i \(0.697452\pi\)
\(84\) 5.99646 8.19836i 0.654267 0.894514i
\(85\) −3.47112 + 2.52194i −0.376495 + 0.273543i
\(86\) 9.20757 7.23491i 0.992878 0.780160i
\(87\) 11.7495 11.7495i 1.25968 1.25968i
\(88\) 11.9854 + 4.48683i 1.27765 + 0.478298i
\(89\) −5.22531 + 5.22531i −0.553882 + 0.553882i −0.927559 0.373677i \(-0.878097\pi\)
0.373677 + 0.927559i \(0.378097\pi\)
\(90\) −2.74686 23.5280i −0.289545 2.48007i
\(91\) −0.148968 0.359641i −0.0156161 0.0377006i
\(92\) −2.42973 + 9.98035i −0.253317 + 1.04052i
\(93\) −4.37669 + 10.5663i −0.453841 + 1.09567i
\(94\) −2.80030 9.99000i −0.288829 1.03039i
\(95\) −1.01734 4.23741i −0.104377 0.434749i
\(96\) −10.3003 + 15.1528i −1.05127 + 1.54653i
\(97\) 8.97673i 0.911449i 0.890121 + 0.455724i \(0.150620\pi\)
−0.890121 + 0.455724i \(0.849380\pi\)
\(98\) −6.18413 + 1.73347i −0.624692 + 0.175107i
\(99\) −31.3132 12.9703i −3.14709 1.30357i
\(100\) 2.30358 + 9.73106i 0.230358 + 0.973106i
\(101\) 2.96848 + 7.16655i 0.295375 + 0.713098i 0.999994 + 0.00351218i \(0.00111796\pi\)
−0.704619 + 0.709586i \(0.748882\pi\)
\(102\) −8.72656 1.04696i −0.864058 0.103664i
\(103\) 8.17515 + 8.17515i 0.805522 + 0.805522i 0.983952 0.178431i \(-0.0571021\pi\)
−0.178431 + 0.983952i \(0.557102\pi\)
\(104\) 0.290927 + 0.639085i 0.0285277 + 0.0626674i
\(105\) 5.93354 9.68279i 0.579054 0.944943i
\(106\) 2.30173 1.80860i 0.223564 0.175667i
\(107\) 2.00192 + 4.83305i 0.193532 + 0.467229i 0.990622 0.136633i \(-0.0436280\pi\)
−0.797089 + 0.603861i \(0.793628\pi\)
\(108\) 17.1739 23.4801i 1.65256 2.25938i
\(109\) −2.32832 + 5.62105i −0.223012 + 0.538399i −0.995296 0.0968782i \(-0.969114\pi\)
0.772284 + 0.635277i \(0.219114\pi\)
\(110\) 13.7649 + 3.90569i 1.31243 + 0.372393i
\(111\) 16.8115i 1.59568i
\(112\) −5.97724 + 1.90010i −0.564796 + 0.179543i
\(113\) −16.5391 −1.55587 −0.777934 0.628346i \(-0.783732\pi\)
−0.777934 + 0.628346i \(0.783732\pi\)
\(114\) 4.37429 7.78176i 0.409690 0.728828i
\(115\) −1.79647 + 11.3429i −0.167522 + 1.05773i
\(116\) −10.1391 + 1.57278i −0.941392 + 0.146029i
\(117\) −0.711661 1.71810i −0.0657931 0.158839i
\(118\) 8.99588 7.06857i 0.828138 0.650715i
\(119\) −2.12744 2.12744i −0.195023 0.195023i
\(120\) −10.0945 + 17.8250i −0.921501 + 1.62719i
\(121\) 6.69817 6.69817i 0.608925 0.608925i
\(122\) −0.698665 + 5.82349i −0.0632541 + 0.527234i
\(123\) 10.7669 4.45980i 0.970820 0.402127i
\(124\) 6.03314 3.67072i 0.541792 0.329641i
\(125\) 3.45510 + 10.6331i 0.309034 + 0.951051i
\(126\) 15.9941 4.48331i 1.42487 0.399405i
\(127\) 14.9371i 1.32545i −0.748862 0.662726i \(-0.769399\pi\)
0.748862 0.662726i \(-0.230601\pi\)
\(128\) 10.6574 3.79726i 0.941993 0.335633i
\(129\) 26.8191 2.36129
\(130\) 0.382514 + 0.685579i 0.0335487 + 0.0601292i
\(131\) 0.144904 + 0.0600212i 0.0126603 + 0.00524408i 0.389005 0.921236i \(-0.372819\pi\)
−0.376344 + 0.926480i \(0.622819\pi\)
\(132\) 15.2349 + 25.0398i 1.32603 + 2.17943i
\(133\) 2.82322 1.16942i 0.244804 0.101401i
\(134\) 1.90136 + 0.228112i 0.164252 + 0.0197059i
\(135\) 16.9937 27.7315i 1.46258 2.38675i
\(136\) 3.96764 + 3.70297i 0.340222 + 0.317527i
\(137\) 5.31592 5.31592i 0.454169 0.454169i −0.442566 0.896736i \(-0.645932\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(138\) −18.4981 + 14.5350i −1.57466 + 1.23730i
\(139\) 16.1550 6.69164i 1.37025 0.567577i 0.428396 0.903591i \(-0.359079\pi\)
0.941857 + 0.336014i \(0.109079\pi\)
\(140\) −6.48701 + 2.66287i −0.548253 + 0.225054i
\(141\) 9.09323 21.9530i 0.765788 1.84878i
\(142\) −9.14409 5.14009i −0.767355 0.431347i
\(143\) 1.12330 0.0939350
\(144\) −28.5549 + 9.07729i −2.37958 + 0.756441i
\(145\) −11.1545 + 2.67802i −0.926327 + 0.222397i
\(146\) 6.59548 + 3.70746i 0.545846 + 0.306832i
\(147\) −13.5896 5.62900i −1.12085 0.464272i
\(148\) 6.12845 8.37882i 0.503756 0.688735i
\(149\) −18.6169 + 7.71137i −1.52516 + 0.631740i −0.978616 0.205694i \(-0.934055\pi\)
−0.546539 + 0.837434i \(0.684055\pi\)
\(150\) −9.62135 + 20.7838i −0.785580 + 1.69699i
\(151\) −7.87634 7.87634i −0.640967 0.640967i 0.309826 0.950793i \(-0.399729\pi\)
−0.950793 + 0.309826i \(0.899729\pi\)
\(152\) −5.01689 + 2.28381i −0.406923 + 0.185241i
\(153\) −10.1634 10.1634i −0.821661 0.821661i
\(154\) −1.19517 + 9.96193i −0.0963094 + 0.802756i
\(155\) 6.38769 4.64098i 0.513071 0.372773i
\(156\) −0.380409 + 1.56257i −0.0304571 + 0.125105i
\(157\) 3.37959 8.15905i 0.269721 0.651163i −0.729749 0.683715i \(-0.760363\pi\)
0.999470 + 0.0325515i \(0.0103633\pi\)
\(158\) −7.58560 + 2.12632i −0.603478 + 0.169161i
\(159\) 6.70429 0.531685
\(160\) 11.5290 5.20407i 0.911447 0.411418i
\(161\) −8.05311 −0.634674
\(162\) 33.5516 9.40486i 2.63606 0.738915i
\(163\) −3.43659 + 8.29666i −0.269175 + 0.649845i −0.999445 0.0333134i \(-0.989394\pi\)
0.730270 + 0.683158i \(0.239394\pi\)
\(164\) −6.99198 1.70220i −0.545982 0.132920i
\(165\) 19.2618 + 26.5113i 1.49953 + 2.06390i
\(166\) −0.692646 + 5.77333i −0.0537598 + 0.448097i
\(167\) 10.1529 + 10.1529i 0.785659 + 0.785659i 0.980779 0.195121i \(-0.0625098\pi\)
−0.195121 + 0.980779i \(0.562510\pi\)
\(168\) −13.4528 5.03618i −1.03791 0.388550i
\(169\) −9.14881 9.14881i −0.703754 0.703754i
\(170\) 4.75915 + 3.76407i 0.365010 + 0.288691i
\(171\) 13.4873 5.58662i 1.03140 0.427219i
\(172\) −13.3666 9.77659i −1.01919 0.745458i
\(173\) −14.1393 5.85667i −1.07499 0.445275i −0.226240 0.974072i \(-0.572643\pi\)
−0.848748 + 0.528797i \(0.822643\pi\)
\(174\) −20.4845 11.5148i −1.55293 0.872934i
\(175\) −6.98543 + 3.55936i −0.528049 + 0.269062i
\(176\) 1.53495 18.0335i 0.115701 1.35932i
\(177\) 26.2025 1.96950
\(178\) 9.10998 + 5.12092i 0.682822 + 0.383829i
\(179\) 7.22558 17.4441i 0.540065 1.30383i −0.384611 0.923079i \(-0.625665\pi\)
0.924676 0.380754i \(-0.124335\pi\)
\(180\) −30.9902 + 12.7213i −2.30988 + 0.948187i
\(181\) 2.29370 0.950080i 0.170489 0.0706189i −0.295806 0.955248i \(-0.595588\pi\)
0.466296 + 0.884629i \(0.345588\pi\)
\(182\) −0.432870 + 0.340131i −0.0320865 + 0.0252122i
\(183\) −9.49861 + 9.49861i −0.702157 + 0.702157i
\(184\) 14.5180 0.500933i 1.07028 0.0369293i
\(185\) 6.06415 9.89592i 0.445845 0.727563i
\(186\) 16.0590 + 1.92665i 1.17750 + 0.141269i
\(187\) 8.02104 3.32242i 0.586556 0.242960i
\(188\) −12.5348 + 7.62648i −0.914191 + 0.556218i
\(189\) 21.0708 + 8.72782i 1.53268 + 0.634856i
\(190\) −5.38187 + 3.00278i −0.390442 + 0.217845i
\(191\) −23.1537 −1.67534 −0.837670 0.546176i \(-0.816083\pi\)
−0.837670 + 0.546176i \(0.816083\pi\)
\(192\) 24.5657 + 8.24229i 1.77287 + 0.594836i
\(193\) 26.3284i 1.89516i 0.319524 + 0.947578i \(0.396477\pi\)
−0.319524 + 0.947578i \(0.603523\pi\)
\(194\) 12.2239 3.42647i 0.877621 0.246006i
\(195\) −0.281263 + 1.77589i −0.0201417 + 0.127174i
\(196\) 4.72104 + 7.75942i 0.337217 + 0.554244i
\(197\) 18.7771 7.77771i 1.33781 0.554139i 0.404937 0.914345i \(-0.367294\pi\)
0.932873 + 0.360206i \(0.117294\pi\)
\(198\) −5.70964 + 47.5909i −0.405767 + 3.38214i
\(199\) −16.0879 + 16.0879i −1.14044 + 1.14044i −0.152069 + 0.988370i \(0.548593\pi\)
−0.988370 + 0.152069i \(0.951407\pi\)
\(200\) 12.3718 6.85124i 0.874816 0.484456i
\(201\) 3.10127 + 3.10127i 0.218747 + 0.218747i
\(202\) 8.62579 6.77777i 0.606909 0.476883i
\(203\) −3.07834 7.43178i −0.216057 0.521609i
\(204\) 1.90531 + 12.2828i 0.133399 + 0.859970i
\(205\) −7.94654 1.25856i −0.555011 0.0879017i
\(206\) 8.01182 14.2528i 0.558210 0.993042i
\(207\) −38.4719 −2.67398
\(208\) 0.759211 0.640106i 0.0526418 0.0443833i
\(209\) 8.81802i 0.609955i
\(210\) −15.4502 4.38389i −1.06616 0.302517i
\(211\) −1.08515 + 2.61979i −0.0747050 + 0.180354i −0.956821 0.290679i \(-0.906119\pi\)
0.882116 + 0.471033i \(0.156119\pi\)
\(212\) −3.34140 2.44397i −0.229488 0.167853i
\(213\) −9.19376 22.1957i −0.629946 1.52082i
\(214\) 5.81715 4.57087i 0.397652 0.312458i
\(215\) −15.7868 9.67401i −1.07665 0.659762i
\(216\) −38.5289 14.4236i −2.62156 0.981404i
\(217\) 3.91501 + 3.91501i 0.265768 + 0.265768i
\(218\) 8.54307 + 1.02494i 0.578610 + 0.0694178i
\(219\) 6.63130 + 16.0094i 0.448102 + 1.08181i
\(220\) 0.0643524 20.2348i 0.00433863 1.36423i
\(221\) 0.440101 + 0.182296i 0.0296044 + 0.0122625i
\(222\) 22.8927 6.41706i 1.53646 0.430685i
\(223\) 18.8546i 1.26260i −0.775540 0.631298i \(-0.782522\pi\)
0.775540 0.631298i \(-0.217478\pi\)
\(224\) 4.86897 + 7.41409i 0.325321 + 0.495375i
\(225\) −33.3713 + 17.0040i −2.22475 + 1.13360i
\(226\) 6.31307 + 22.5217i 0.419939 + 1.49812i
\(227\) 1.91430 4.62152i 0.127056 0.306741i −0.847532 0.530744i \(-0.821913\pi\)
0.974588 + 0.224003i \(0.0719125\pi\)
\(228\) −12.2663 2.98625i −0.812357 0.197769i
\(229\) 2.03950 + 4.92379i 0.134774 + 0.325373i 0.976830 0.214017i \(-0.0686547\pi\)
−0.842056 + 0.539390i \(0.818655\pi\)
\(230\) 16.1317 1.88335i 1.06369 0.124184i
\(231\) −16.2488 + 16.2488i −1.06909 + 1.06909i
\(232\) 6.01185 + 13.2063i 0.394697 + 0.867039i
\(233\) 18.5844 18.5844i 1.21751 1.21751i 0.249004 0.968502i \(-0.419897\pi\)
0.968502 0.249004i \(-0.0801033\pi\)
\(234\) −2.06794 + 1.62490i −0.135185 + 0.106223i
\(235\) −13.2714 + 9.64234i −0.865729 + 0.628997i
\(236\) −13.0592 9.55182i −0.850084 0.621770i
\(237\) −16.6693 6.90467i −1.08279 0.448506i
\(238\) −2.08494 + 3.70906i −0.135147 + 0.240422i
\(239\) 18.9001i 1.22255i −0.791420 0.611273i \(-0.790658\pi\)
0.791420 0.611273i \(-0.209342\pi\)
\(240\) 28.1259 + 6.94211i 1.81552 + 0.448111i
\(241\) 21.2156i 1.36662i −0.730129 0.683309i \(-0.760540\pi\)
0.730129 0.683309i \(-0.239460\pi\)
\(242\) −11.6778 6.56435i −0.750678 0.421972i
\(243\) 33.4154 + 13.8411i 2.14360 + 0.887907i
\(244\) 8.19669 1.27147i 0.524739 0.0813976i
\(245\) 5.96892 + 8.21541i 0.381340 + 0.524864i
\(246\) −10.1828 12.9593i −0.649234 0.826253i
\(247\) −0.342119 + 0.342119i −0.0217685 + 0.0217685i
\(248\) −7.30141 6.81435i −0.463640 0.432712i
\(249\) −9.41678 + 9.41678i −0.596764 + 0.596764i
\(250\) 13.1605 8.76361i 0.832344 0.554260i
\(251\) 3.91571 + 9.45336i 0.247157 + 0.596691i 0.997960 0.0638355i \(-0.0203333\pi\)
−0.750803 + 0.660526i \(0.770333\pi\)
\(252\) −12.2101 20.0683i −0.769163 1.26418i
\(253\) 8.89294 21.4695i 0.559094 1.34977i
\(254\) −20.3402 + 5.70158i −1.27626 + 0.357749i
\(255\) 3.24424 + 13.5129i 0.203162 + 0.846208i
\(256\) −9.23884 13.0631i −0.577427 0.816442i
\(257\) 15.2871i 0.953583i −0.879017 0.476791i \(-0.841800\pi\)
0.879017 0.476791i \(-0.158200\pi\)
\(258\) −10.2370 36.5202i −0.637328 2.27365i
\(259\) 7.51907 + 3.11450i 0.467212 + 0.193526i
\(260\) 0.787563 0.782570i 0.0488426 0.0485329i
\(261\) −14.7061 35.5036i −0.910284 2.19762i
\(262\) 0.0264218 0.220230i 0.00163234 0.0136059i
\(263\) −0.224977 0.224977i −0.0138727 0.0138727i 0.700136 0.714009i \(-0.253123\pi\)
−0.714009 + 0.700136i \(0.753123\pi\)
\(264\) 28.2821 30.3036i 1.74064 1.86506i
\(265\) −3.94641 2.41833i −0.242426 0.148557i
\(266\) −2.67006 3.39808i −0.163712 0.208350i
\(267\) 9.15947 + 22.1129i 0.560550 + 1.35329i
\(268\) −0.415132 2.67620i −0.0253582 0.163475i
\(269\) −10.6586 + 25.7320i −0.649863 + 1.56891i 0.163110 + 0.986608i \(0.447847\pi\)
−0.812973 + 0.582301i \(0.802153\pi\)
\(270\) −44.2494 12.5555i −2.69293 0.764101i
\(271\) 5.96969i 0.362633i 0.983425 + 0.181317i \(0.0580359\pi\)
−0.983425 + 0.181317i \(0.941964\pi\)
\(272\) 3.52796 6.81629i 0.213914 0.413298i
\(273\) −1.26083 −0.0763089
\(274\) −9.26794 5.20971i −0.559897 0.314730i
\(275\) −1.77527 22.5536i −0.107053 1.36003i
\(276\) 26.8535 + 19.6412i 1.61639 + 1.18226i
\(277\) 10.1647 + 24.5396i 0.610735 + 1.47444i 0.862195 + 0.506577i \(0.169089\pi\)
−0.251460 + 0.967868i \(0.580911\pi\)
\(278\) −15.2787 19.4445i −0.916353 1.16620i
\(279\) 18.7031 + 18.7031i 1.11972 + 1.11972i
\(280\) 6.10223 + 7.81711i 0.364678 + 0.467162i
\(281\) 4.36054 4.36054i 0.260128 0.260128i −0.564978 0.825106i \(-0.691115\pi\)
0.825106 + 0.564978i \(0.191115\pi\)
\(282\) −33.3649 4.00291i −1.98685 0.238370i
\(283\) 0.228332 0.0945784i 0.0135730 0.00562210i −0.375887 0.926666i \(-0.622662\pi\)
0.389460 + 0.921044i \(0.372662\pi\)
\(284\) −3.50905 + 14.4138i −0.208224 + 0.855299i
\(285\) −13.9410 2.20795i −0.825791 0.130788i
\(286\) −0.428770 1.52963i −0.0253537 0.0904487i
\(287\) 5.64180i 0.333025i
\(288\) 23.2604 + 35.4191i 1.37063 + 2.08709i
\(289\) −13.3182 −0.783425
\(290\) 7.90445 + 14.1671i 0.464165 + 0.831922i
\(291\) 26.8619 + 11.1266i 1.57467 + 0.652250i
\(292\) 2.53102 10.3964i 0.148116 0.608403i
\(293\) −12.1130 + 5.01736i −0.707648 + 0.293117i −0.707331 0.706883i \(-0.750101\pi\)
−0.000317126 1.00000i \(0.500101\pi\)
\(294\) −2.47793 + 20.6540i −0.144516 + 1.20456i
\(295\) −15.4238 9.45159i −0.898008 0.550293i
\(296\) −13.7489 5.14703i −0.799140 0.299165i
\(297\) −46.5365 + 46.5365i −2.70032 + 2.70032i
\(298\) 17.6070 + 22.4077i 1.01994 + 1.29804i
\(299\) 1.17799 0.487941i 0.0681251 0.0282183i
\(300\) 31.9744 + 5.16835i 1.84604 + 0.298395i
\(301\) 4.96850 11.9950i 0.286379 0.691381i
\(302\) −7.71898 + 13.7319i −0.444177 + 0.790180i
\(303\) 25.1245 1.44337
\(304\) 5.02490 + 5.95989i 0.288198 + 0.341823i
\(305\) 9.01753 2.16497i 0.516342 0.123966i
\(306\) −9.96033 + 17.7192i −0.569394 + 1.01294i
\(307\) 7.65695 + 3.17161i 0.437005 + 0.181013i 0.590329 0.807163i \(-0.298998\pi\)
−0.153324 + 0.988176i \(0.548998\pi\)
\(308\) 14.0216 2.17504i 0.798957 0.123934i
\(309\) 34.5963 14.3302i 1.96811 0.815219i
\(310\) −8.75797 6.92679i −0.497419 0.393415i
\(311\) 5.55499 + 5.55499i 0.314995 + 0.314995i 0.846841 0.531846i \(-0.178502\pi\)
−0.531846 + 0.846841i \(0.678502\pi\)
\(312\) 2.27299 0.0784282i 0.128683 0.00444012i
\(313\) −2.81614 2.81614i −0.159178 0.159178i 0.623025 0.782202i \(-0.285904\pi\)
−0.782202 + 0.623025i \(0.785904\pi\)
\(314\) −12.4004 1.48772i −0.699796 0.0839569i
\(315\) −15.4375 21.2476i −0.869805 1.19717i
\(316\) 5.79094 + 9.51789i 0.325766 + 0.535423i
\(317\) −0.353554 + 0.853555i −0.0198576 + 0.0479404i −0.933497 0.358584i \(-0.883260\pi\)
0.913640 + 0.406525i \(0.133260\pi\)
\(318\) −2.55907 9.12941i −0.143505 0.511952i
\(319\) 23.2124 1.29964
\(320\) −11.4872 13.7129i −0.642155 0.766575i
\(321\) 16.9437 0.945707
\(322\) 3.07392 + 10.9661i 0.171303 + 0.611119i
\(323\) −1.43104 + 3.45484i −0.0796253 + 0.192232i
\(324\) −25.6137 42.0982i −1.42298 2.33879i
\(325\) 0.806152 0.943905i 0.0447173 0.0523584i
\(326\) 12.6096 + 1.51281i 0.698379 + 0.0837869i
\(327\) 13.9345 + 13.9345i 0.770578 + 0.770578i
\(328\) 0.350941 + 10.1709i 0.0193775 + 0.561594i
\(329\) −8.13402 8.13402i −0.448443 0.448443i
\(330\) 28.7488 36.3489i 1.58257 2.00094i
\(331\) −13.5438 + 5.61003i −0.744435 + 0.308355i −0.722469 0.691404i \(-0.756993\pi\)
−0.0219663 + 0.999759i \(0.506993\pi\)
\(332\) 8.12608 1.26052i 0.445977 0.0691799i
\(333\) 35.9206 + 14.8788i 1.96844 + 0.815354i
\(334\) 9.95010 17.7010i 0.544445 0.968555i
\(335\) −0.706859 2.94420i −0.0386198 0.160859i
\(336\) −1.72288 + 20.2414i −0.0939910 + 1.10426i
\(337\) −9.32051 −0.507721 −0.253860 0.967241i \(-0.581700\pi\)
−0.253860 + 0.967241i \(0.581700\pi\)
\(338\) −8.96602 + 15.9503i −0.487687 + 0.867584i
\(339\) −20.5000 + 49.4915i −1.11341 + 2.68801i
\(340\) 3.30904 7.91743i 0.179458 0.429383i
\(341\) −14.7606 + 6.11406i −0.799333 + 0.331095i
\(342\) −12.7556 16.2336i −0.689745 0.877810i
\(343\) −12.7964 + 12.7964i −0.690941 + 0.690941i
\(344\) −8.21095 + 21.9334i −0.442705 + 1.18257i
\(345\) 31.7157 + 19.4351i 1.70752 + 1.04635i
\(346\) −2.57815 + 21.4893i −0.138602 + 1.15527i
\(347\) 14.2421 5.89927i 0.764556 0.316690i 0.0338910 0.999426i \(-0.489210\pi\)
0.730665 + 0.682736i \(0.239210\pi\)
\(348\) −7.86094 + 32.2896i −0.421391 + 1.73090i
\(349\) 8.50240 + 3.52181i 0.455123 + 0.188518i 0.598455 0.801156i \(-0.295782\pi\)
−0.143332 + 0.989675i \(0.545782\pi\)
\(350\) 7.51326 + 8.15362i 0.401600 + 0.435829i
\(351\) −3.61102 −0.192742
\(352\) −25.1426 + 4.79330i −1.34010 + 0.255484i
\(353\) 23.7299i 1.26302i 0.775369 + 0.631508i \(0.217564\pi\)
−0.775369 + 0.631508i \(0.782436\pi\)
\(354\) −10.0016 35.6806i −0.531581 1.89640i
\(355\) −2.59449 + 16.3816i −0.137701 + 0.869444i
\(356\) 3.49596 14.3600i 0.185285 0.761078i
\(357\) −9.00309 + 3.72920i −0.476494 + 0.197370i
\(358\) −26.5121 3.18075i −1.40121 0.168108i
\(359\) 21.8338 21.8338i 1.15234 1.15234i 0.166262 0.986082i \(-0.446830\pi\)
0.986082 0.166262i \(-0.0531698\pi\)
\(360\) 29.1520 + 37.3445i 1.53645 + 1.96823i
\(361\) 10.7494 + 10.7494i 0.565755 + 0.565755i
\(362\) −2.16927 2.76074i −0.114014 0.145101i
\(363\) −11.7412 28.3459i −0.616255 1.48777i
\(364\) 0.628395 + 0.459621i 0.0329368 + 0.0240907i
\(365\) 1.87136 11.8158i 0.0979515 0.618465i
\(366\) 16.5602 + 9.30883i 0.865615 + 0.486581i
\(367\) −22.3410 −1.16619 −0.583096 0.812403i \(-0.698159\pi\)
−0.583096 + 0.812403i \(0.698159\pi\)
\(368\) −6.22372 19.5783i −0.324434 1.02059i
\(369\) 26.9524i 1.40309i
\(370\) −15.7903 4.48038i −0.820897 0.232924i
\(371\) 1.24204 2.99854i 0.0644833 0.155676i
\(372\) −3.50623 22.6033i −0.181790 1.17193i
\(373\) −4.46689 10.7840i −0.231287 0.558376i 0.765042 0.643980i \(-0.222718\pi\)
−0.996329 + 0.0856038i \(0.972718\pi\)
\(374\) −7.58591 9.65428i −0.392258 0.499211i
\(375\) 36.1009 + 2.84056i 1.86424 + 0.146686i
\(376\) 15.1698 + 14.1578i 0.782322 + 0.730135i
\(377\) 0.900588 + 0.900588i 0.0463826 + 0.0463826i
\(378\) 3.84205 32.0242i 0.197614 1.64715i
\(379\) 5.89190 + 14.2243i 0.302647 + 0.730654i 0.999904 + 0.0138332i \(0.00440340\pi\)
−0.697258 + 0.716821i \(0.745597\pi\)
\(380\) 6.14326 + 6.18246i 0.315142 + 0.317153i
\(381\) −44.6976 18.5144i −2.28993 0.948520i
\(382\) 8.83789 + 31.5290i 0.452186 + 1.61316i
\(383\) 11.4609i 0.585623i 0.956170 + 0.292811i \(0.0945908\pi\)
−0.956170 + 0.292811i \(0.905409\pi\)
\(384\) 1.84688 36.5979i 0.0942483 1.86763i
\(385\) 15.4258 3.70350i 0.786172 0.188748i
\(386\) 35.8520 10.0497i 1.82482 0.511516i
\(387\) 23.7359 57.3035i 1.20656 2.91290i
\(388\) −9.33183 15.3376i −0.473752 0.778651i
\(389\) −2.69641 6.50970i −0.136713 0.330055i 0.840664 0.541556i \(-0.182165\pi\)
−0.977378 + 0.211501i \(0.932165\pi\)
\(390\) 2.52564 0.294865i 0.127891 0.0149311i
\(391\) 6.96838 6.96838i 0.352406 0.352406i
\(392\) 8.76417 9.39058i 0.442657 0.474296i
\(393\) 0.359214 0.359214i 0.0181199 0.0181199i
\(394\) −17.7584 22.6004i −0.894657 1.13859i
\(395\) 7.32162 + 10.0772i 0.368391 + 0.507040i
\(396\) 66.9852 10.3907i 3.36613 0.522154i
\(397\) 4.71519 + 1.95310i 0.236649 + 0.0980231i 0.497856 0.867260i \(-0.334121\pi\)
−0.261208 + 0.965283i \(0.584121\pi\)
\(398\) 28.0481 + 15.7664i 1.40593 + 0.790301i
\(399\) 9.89766i 0.495503i
\(400\) −14.0519 14.2318i −0.702595 0.711590i
\(401\) 36.3732i 1.81639i 0.418548 + 0.908195i \(0.362539\pi\)
−0.418548 + 0.908195i \(0.637461\pi\)
\(402\) 3.03931 5.40686i 0.151587 0.269670i
\(403\) −0.809891 0.335468i −0.0403436 0.0167108i
\(404\) −12.5220 9.15886i −0.622993 0.455670i
\(405\) −32.3840 44.5722i −1.60917 2.21481i
\(406\) −8.94503 + 7.02862i −0.443935 + 0.348825i
\(407\) −16.6064 + 16.6064i −0.823149 + 0.823149i
\(408\) 15.9986 7.28294i 0.792048 0.360559i
\(409\) −11.7007 + 11.7007i −0.578561 + 0.578561i −0.934507 0.355946i \(-0.884159\pi\)
0.355946 + 0.934507i \(0.384159\pi\)
\(410\) 1.31943 + 11.3014i 0.0651618 + 0.558138i
\(411\) −9.31828 22.4963i −0.459637 1.10966i
\(412\) −22.4666 5.46953i −1.10685 0.269464i
\(413\) 4.85427 11.7192i 0.238863 0.576666i
\(414\) 14.6850 + 52.3882i 0.721726 + 2.57474i
\(415\) 8.93985 2.14632i 0.438840 0.105359i
\(416\) −1.16144 0.789506i −0.0569445 0.0387087i
\(417\) 56.6364i 2.77350i
\(418\) 12.0077 3.36589i 0.587318 0.164631i
\(419\) −21.2609 8.80654i −1.03866 0.430227i −0.202830 0.979214i \(-0.565014\pi\)
−0.835831 + 0.548987i \(0.815014\pi\)
\(420\) −0.0722313 + 22.7123i −0.00352453 + 1.10825i
\(421\) 3.01400 + 7.27645i 0.146894 + 0.354632i 0.980151 0.198253i \(-0.0635267\pi\)
−0.833257 + 0.552885i \(0.813527\pi\)
\(422\) 3.98165 + 0.477693i 0.193824 + 0.0232537i
\(423\) −38.8584 38.8584i −1.88936 1.88936i
\(424\) −2.05259 + 5.48295i −0.0996827 + 0.266276i
\(425\) 2.96459 9.12444i 0.143804 0.442600i
\(426\) −26.7152 + 20.9916i −1.29435 + 1.01705i
\(427\) 2.48861 + 6.00803i 0.120432 + 0.290749i
\(428\) −8.44471 6.17665i −0.408191 0.298560i
\(429\) 1.39232 3.36135i 0.0672217 0.162288i
\(430\) −7.14746 + 25.1899i −0.344681 + 1.21476i
\(431\) 19.0379i 0.917022i 0.888689 + 0.458511i \(0.151617\pi\)
−0.888689 + 0.458511i \(0.848383\pi\)
\(432\) −4.93434 + 57.9714i −0.237404 + 2.78915i
\(433\) 15.6165 0.750480 0.375240 0.926928i \(-0.377560\pi\)
0.375240 + 0.926928i \(0.377560\pi\)
\(434\) 3.83679 6.82556i 0.184172 0.327637i
\(435\) −5.81215 + 36.6979i −0.278671 + 1.75953i
\(436\) −1.86525 12.0246i −0.0893293 0.575872i
\(437\) 3.83039 + 9.24737i 0.183232 + 0.442362i
\(438\) 19.2692 15.1409i 0.920718 0.723460i
\(439\) −12.2988 12.2988i −0.586988 0.586988i 0.349827 0.936814i \(-0.386240\pi\)
−0.936814 + 0.349827i \(0.886240\pi\)
\(440\) −27.5789 + 7.63613i −1.31477 + 0.364038i
\(441\) −24.0546 + 24.0546i −1.14546 + 1.14546i
\(442\) 0.0802479 0.668881i 0.00381701 0.0318154i
\(443\) −22.4589 + 9.30278i −1.06705 + 0.441989i −0.845950 0.533262i \(-0.820966\pi\)
−0.221104 + 0.975250i \(0.570966\pi\)
\(444\) −17.4766 28.7242i −0.829401 1.36319i
\(445\) 2.58481 16.3205i 0.122532 0.773664i
\(446\) −25.6748 + 7.19691i −1.21574 + 0.340783i
\(447\) 65.2672i 3.08703i
\(448\) 8.23746 9.46020i 0.389183 0.446953i
\(449\) 12.3908 0.584760 0.292380 0.956302i \(-0.405553\pi\)
0.292380 + 0.956302i \(0.405553\pi\)
\(450\) 35.8929 + 38.9521i 1.69201 + 1.83622i
\(451\) 15.0410 + 6.23017i 0.708251 + 0.293367i
\(452\) 28.2587 17.1934i 1.32918 0.808708i
\(453\) −33.3317 + 13.8065i −1.56606 + 0.648684i
\(454\) −7.02395 0.842688i −0.329650 0.0395493i
\(455\) 0.742174 + 0.454799i 0.0347937 + 0.0213213i
\(456\) 0.615670 + 17.8433i 0.0288314 + 0.835587i
\(457\) 3.47830 3.47830i 0.162708 0.162708i −0.621057 0.783765i \(-0.713297\pi\)
0.783765 + 0.621057i \(0.213297\pi\)
\(458\) 5.92637 4.65669i 0.276921 0.217593i
\(459\) −25.7849 + 10.6804i −1.20354 + 0.498521i
\(460\) −8.72216 21.2480i −0.406673 0.990694i
\(461\) −3.21021 + 7.75012i −0.149514 + 0.360959i −0.980837 0.194831i \(-0.937584\pi\)
0.831323 + 0.555790i \(0.187584\pi\)
\(462\) 28.3286 + 15.9241i 1.31797 + 0.740857i
\(463\) 7.17604 0.333499 0.166749 0.985999i \(-0.446673\pi\)
0.166749 + 0.985999i \(0.446673\pi\)
\(464\) 15.6887 13.2274i 0.728329 0.614068i
\(465\) −5.97017 24.8669i −0.276860 1.15318i
\(466\) −32.4007 18.2131i −1.50093 0.843707i
\(467\) −13.0655 5.41189i −0.604598 0.250432i 0.0593191 0.998239i \(-0.481107\pi\)
−0.663917 + 0.747807i \(0.731107\pi\)
\(468\) 3.00201 + 2.19574i 0.138768 + 0.101498i
\(469\) 1.96161 0.812524i 0.0905786 0.0375189i
\(470\) 18.1960 + 14.3915i 0.839319 + 0.663828i
\(471\) −20.2261 20.2261i −0.931970 0.931970i
\(472\) −8.02218 + 21.4291i −0.369251 + 0.986355i
\(473\) 26.4919 + 26.4919i 1.21810 + 1.21810i
\(474\) −3.03949 + 25.3346i −0.139608 + 1.16366i
\(475\) 7.40976 + 6.32838i 0.339983 + 0.290366i
\(476\) 5.84656 + 1.42335i 0.267977 + 0.0652392i
\(477\) 5.93354 14.3248i 0.271678 0.655889i
\(478\) −25.7368 + 7.21428i −1.17717 + 0.329973i
\(479\) 14.4463 0.660068 0.330034 0.943969i \(-0.392940\pi\)
0.330034 + 0.943969i \(0.392940\pi\)
\(480\) −1.28257 40.9497i −0.0585410 1.86909i
\(481\) −1.28858 −0.0587543
\(482\) −28.8899 + 8.09813i −1.31590 + 0.368860i
\(483\) −9.98175 + 24.0981i −0.454185 + 1.09650i
\(484\) −4.48136 + 18.4076i −0.203698 + 0.836711i
\(485\) −11.7985 16.2390i −0.535740 0.737374i
\(486\) 6.09296 50.7859i 0.276382 2.30369i
\(487\) −22.6108 22.6108i −1.02459 1.02459i −0.999690 0.0249022i \(-0.992073\pi\)
−0.0249022 0.999690i \(-0.507927\pi\)
\(488\) −4.86012 10.6763i −0.220007 0.483295i
\(489\) 20.5672 + 20.5672i 0.930083 + 0.930083i
\(490\) 8.90878 11.2639i 0.402458 0.508852i
\(491\) 5.48701 2.27280i 0.247625 0.102570i −0.255419 0.966831i \(-0.582213\pi\)
0.503044 + 0.864261i \(0.332213\pi\)
\(492\) −13.7601 + 18.8129i −0.620355 + 0.848150i
\(493\) 9.09445 + 3.76704i 0.409593 + 0.169659i
\(494\) 0.596462 + 0.335284i 0.0268361 + 0.0150852i
\(495\) 73.6933 17.6926i 3.31227 0.795225i
\(496\) −6.49230 + 12.5436i −0.291513 + 0.563225i
\(497\) −11.6304 −0.521696
\(498\) 16.4175 + 9.22864i 0.735687 + 0.413545i
\(499\) 8.04441 19.4209i 0.360117 0.869400i −0.635165 0.772377i \(-0.719068\pi\)
0.995282 0.0970234i \(-0.0309322\pi\)
\(500\) −16.9571 14.5759i −0.758344 0.651854i
\(501\) 42.9661 17.7971i 1.91958 0.795117i
\(502\) 11.3782 8.94053i 0.507836 0.399035i
\(503\) 11.3902 11.3902i 0.507862 0.507862i −0.406007 0.913870i \(-0.633079\pi\)
0.913870 + 0.406007i \(0.133079\pi\)
\(504\) −22.6669 + 24.2870i −1.00966 + 1.08183i
\(505\) −14.7893 9.06276i −0.658114 0.403288i
\(506\) −32.6300 3.91474i −1.45058 0.174031i
\(507\) −38.7167 + 16.0370i −1.71947 + 0.712227i
\(508\) 15.5280 + 25.5215i 0.688943 + 1.13234i
\(509\) −5.87100 2.43185i −0.260227 0.107790i 0.248756 0.968566i \(-0.419978\pi\)
−0.508983 + 0.860777i \(0.669978\pi\)
\(510\) 17.1625 9.57570i 0.759968 0.424019i
\(511\) 8.38882 0.371100
\(512\) −14.2618 + 17.5670i −0.630290 + 0.776360i
\(513\) 28.3469i 1.25155i
\(514\) −20.8168 + 5.83517i −0.918192 + 0.257378i
\(515\) −25.5338 4.04401i −1.12516 0.178200i
\(516\) −45.8231 + 27.8800i −2.01725 + 1.22735i
\(517\) 30.6674 12.7029i 1.34875 0.558672i
\(518\) 1.37103 11.4277i 0.0602394 0.502106i
\(519\) −35.0509 + 35.0509i −1.53856 + 1.53856i
\(520\) −1.36626 0.773734i −0.0599146 0.0339305i
\(521\) 22.5895 + 22.5895i 0.989663 + 0.989663i 0.999947 0.0102837i \(-0.00327345\pi\)
−0.0102837 + 0.999947i \(0.503273\pi\)
\(522\) −42.7329 + 33.5776i −1.87037 + 1.46965i
\(523\) 9.50265 + 22.9414i 0.415522 + 1.00316i 0.983629 + 0.180204i \(0.0576758\pi\)
−0.568108 + 0.822954i \(0.692324\pi\)
\(524\) −0.309979 + 0.0480839i −0.0135415 + 0.00210055i
\(525\) 1.99263 + 25.3149i 0.0869654 + 1.10483i
\(526\) −0.220482 + 0.392233i −0.00961349 + 0.0171022i
\(527\) −6.77534 −0.295138
\(528\) −52.0607 26.9455i −2.26565 1.17265i
\(529\) 3.37774i 0.146858i
\(530\) −1.78674 + 6.29702i −0.0776109 + 0.273525i
\(531\) 23.1902 55.9860i 1.00637 2.42959i
\(532\) −3.60808 + 4.93297i −0.156430 + 0.213871i
\(533\) 0.341839 + 0.825272i 0.0148067 + 0.0357465i
\(534\) 26.6155 20.9133i 1.15177 0.905008i
\(535\) −9.97375 6.11184i −0.431203 0.264238i
\(536\) −3.48579 + 1.58682i −0.150563 + 0.0685401i
\(537\) −43.2435 43.2435i −1.86610 1.86610i
\(538\) 39.1084 + 4.69197i 1.68608 + 0.202285i
\(539\) −7.86349 18.9841i −0.338704 0.817705i
\(540\) −0.206871 + 65.0480i −0.00890230 + 2.79922i
\(541\) 16.8094 + 6.96270i 0.722695 + 0.299350i 0.713546 0.700608i \(-0.247088\pi\)
0.00914852 + 0.999958i \(0.497088\pi\)
\(542\) 8.12909 2.27867i 0.349175 0.0978772i
\(543\) 8.04125i 0.345083i
\(544\) −10.6286 2.20231i −0.455696 0.0944231i
\(545\) −3.17602 13.2287i −0.136046 0.566657i
\(546\) 0.481266 + 1.71691i 0.0205963 + 0.0734768i
\(547\) 3.38844 8.18042i 0.144879 0.349769i −0.834737 0.550649i \(-0.814380\pi\)
0.979616 + 0.200880i \(0.0643801\pi\)
\(548\) −3.55657 + 14.6090i −0.151929 + 0.624065i
\(549\) 11.8888 + 28.7020i 0.507400 + 1.22497i
\(550\) −30.0342 + 11.0263i −1.28066 + 0.470162i
\(551\) −7.06971 + 7.06971i −0.301180 + 0.301180i
\(552\) 16.4959 44.0643i 0.702110 1.87550i
\(553\) −6.17632 + 6.17632i −0.262644 + 0.262644i
\(554\) 29.5364 23.2084i 1.25488 0.986031i
\(555\) −22.0960 30.4122i −0.937924 1.29093i
\(556\) −20.6462 + 28.2274i −0.875593 + 1.19711i
\(557\) 7.38272 + 3.05802i 0.312816 + 0.129573i 0.533568 0.845757i \(-0.320851\pi\)
−0.220752 + 0.975330i \(0.570851\pi\)
\(558\) 18.3294 32.6075i 0.775945 1.38039i
\(559\) 2.05565i 0.0869447i
\(560\) 8.31551 11.2934i 0.351394 0.477234i
\(561\) 28.1202i 1.18724i
\(562\) −7.60231 4.27342i −0.320684 0.180263i
\(563\) −24.6682 10.2179i −1.03964 0.430634i −0.203458 0.979084i \(-0.565218\pi\)
−0.836183 + 0.548450i \(0.815218\pi\)
\(564\) 7.28472 + 46.9619i 0.306742 + 1.97745i
\(565\) 29.9194 21.7380i 1.25872 0.914523i
\(566\) −0.215946 0.274825i −0.00907688 0.0115518i
\(567\) 27.3183 27.3183i 1.14726 1.14726i
\(568\) 20.9670 0.723454i 0.879757 0.0303555i
\(569\) 23.2386 23.2386i 0.974212 0.974212i −0.0254642 0.999676i \(-0.508106\pi\)
0.999676 + 0.0254642i \(0.00810639\pi\)
\(570\) 2.31473 + 19.8266i 0.0969532 + 0.830444i
\(571\) −16.0535 38.7567i −0.671820 1.62192i −0.778516 0.627625i \(-0.784027\pi\)
0.106696 0.994292i \(-0.465973\pi\)
\(572\) −1.91927 + 1.16774i −0.0802487 + 0.0488255i
\(573\) −28.6987 + 69.2849i −1.19891 + 2.89442i
\(574\) −7.68260 + 2.15351i −0.320665 + 0.0898858i
\(575\) −11.6586 22.8806i −0.486196 0.954186i
\(576\) 39.3526 45.1940i 1.63969 1.88308i
\(577\) 11.8847i 0.494766i 0.968918 + 0.247383i \(0.0795705\pi\)
−0.968918 + 0.247383i \(0.920429\pi\)
\(578\) 5.08365 + 18.1358i 0.211452 + 0.754350i
\(579\) 78.7848 + 32.6337i 3.27418 + 1.35621i
\(580\) 16.2746 16.1714i 0.675765 0.671480i
\(581\) 2.46717 + 5.95627i 0.102355 + 0.247108i
\(582\) 4.89799 40.8256i 0.203028 1.69228i
\(583\) 6.62249 + 6.62249i 0.274276 + 0.274276i
\(584\) −15.1232 + 0.521815i −0.625801 + 0.0215929i
\(585\) 3.54557 + 2.17270i 0.146591 + 0.0898300i
\(586\) 11.4559 + 14.5794i 0.473238 + 0.602270i
\(587\) −1.65474 3.99490i −0.0682986 0.164887i 0.886044 0.463600i \(-0.153443\pi\)
−0.954343 + 0.298713i \(0.903443\pi\)
\(588\) 29.0709 4.50948i 1.19886 0.185968i
\(589\) 2.63346 6.35773i 0.108510 0.261966i
\(590\) −6.98313 + 24.6107i −0.287491 + 1.01321i
\(591\) 65.8287i 2.70783i
\(592\) −1.76081 + 20.6869i −0.0723687 + 0.850228i
\(593\) −5.41135 −0.222218 −0.111109 0.993808i \(-0.535440\pi\)
−0.111109 + 0.993808i \(0.535440\pi\)
\(594\) 81.1332 + 45.6067i 3.32894 + 1.87127i
\(595\) 6.64475 + 1.05238i 0.272408 + 0.0431436i
\(596\) 23.7924 32.5290i 0.974576 1.33244i
\(597\) 28.2005 + 68.0819i 1.15417 + 2.78641i
\(598\) −1.11409 1.41785i −0.0455585 0.0579804i
\(599\) 29.2738 + 29.2738i 1.19610 + 1.19610i 0.975326 + 0.220770i \(0.0708571\pi\)
0.220770 + 0.975326i \(0.429143\pi\)
\(600\) −5.16694 45.5132i −0.210940 1.85807i
\(601\) −17.4678 + 17.4678i −0.712528 + 0.712528i −0.967064 0.254535i \(-0.918078\pi\)
0.254535 + 0.967064i \(0.418078\pi\)
\(602\) −18.2304 2.18717i −0.743017 0.0891424i
\(603\) 9.37113 3.88165i 0.381622 0.158073i
\(604\) 21.6454 + 5.26961i 0.880740 + 0.214417i
\(605\) −3.31339 + 20.9207i −0.134708 + 0.850548i
\(606\) −9.59018 34.2127i −0.389574 1.38980i
\(607\) 21.2575i 0.862815i −0.902157 0.431408i \(-0.858017\pi\)
0.902157 0.431408i \(-0.141983\pi\)
\(608\) 6.19771 9.11747i 0.251350 0.369762i
\(609\) −26.0544 −1.05578
\(610\) −6.39015 11.4530i −0.258730 0.463720i
\(611\) 1.68267 + 0.696985i 0.0680736 + 0.0281970i
\(612\) 27.9306 + 6.79974i 1.12903 + 0.274863i
\(613\) 37.6123 15.5795i 1.51914 0.629250i 0.541725 0.840556i \(-0.317771\pi\)
0.977420 + 0.211305i \(0.0677715\pi\)
\(614\) 1.39617 11.6373i 0.0563447 0.469643i
\(615\) −13.6158 + 22.2192i −0.549041 + 0.895965i
\(616\) −8.31395 18.2634i −0.334979 0.735854i
\(617\) −1.34494 + 1.34494i −0.0541452 + 0.0541452i −0.733661 0.679516i \(-0.762190\pi\)
0.679516 + 0.733661i \(0.262190\pi\)
\(618\) −32.7195 41.6407i −1.31617 1.67504i
\(619\) −11.4734 + 4.75245i −0.461156 + 0.191017i −0.601151 0.799135i \(-0.705291\pi\)
0.139996 + 0.990152i \(0.455291\pi\)
\(620\) −6.08943 + 14.5700i −0.244558 + 0.585144i
\(621\) −28.5877 + 69.0169i −1.14719 + 2.76955i
\(622\) 5.44401 9.68475i 0.218285 0.388323i
\(623\) 11.5870 0.464225
\(624\) −0.974413 3.06526i −0.0390077 0.122709i
\(625\) −20.2258 14.6942i −0.809031 0.587766i
\(626\) −2.75988 + 4.90975i −0.110307 + 0.196233i
\(627\) 26.3870 + 10.9298i 1.05379 + 0.436496i
\(628\) 2.70744 + 17.4538i 0.108039 + 0.696484i
\(629\) −9.20126 + 3.81129i −0.366878 + 0.151966i
\(630\) −23.0409 + 29.1320i −0.917971 + 1.16065i
\(631\) 13.2287 + 13.2287i 0.526626 + 0.526626i 0.919565 0.392939i \(-0.128542\pi\)
−0.392939 + 0.919565i \(0.628542\pi\)
\(632\) 10.7503 11.5187i 0.427625 0.458190i
\(633\) 6.49441 + 6.49441i 0.258130 + 0.258130i
\(634\) 1.29726 + 0.155637i 0.0515209 + 0.00618114i
\(635\) 19.6324 + 27.0213i 0.779088 + 1.07231i
\(636\) −11.4550 + 6.96950i −0.454218 + 0.276359i
\(637\) 0.431456 1.04163i 0.0170949 0.0412708i
\(638\) −8.86030 31.6089i −0.350783 1.25141i
\(639\) −55.5617 −2.19799
\(640\) −14.2885 + 20.8767i −0.564803 + 0.825226i
\(641\) −27.5272 −1.08726 −0.543629 0.839326i \(-0.682950\pi\)
−0.543629 + 0.839326i \(0.682950\pi\)
\(642\) −6.46752 23.0727i −0.255253 0.910608i
\(643\) 5.01605 12.1098i 0.197814 0.477564i −0.793582 0.608463i \(-0.791786\pi\)
0.991396 + 0.130899i \(0.0417863\pi\)
\(644\) 13.7596 8.37168i 0.542202 0.329890i
\(645\) −48.5159 + 35.2493i −1.91031 + 1.38794i
\(646\) 5.25079 + 0.629955i 0.206589 + 0.0247853i
\(647\) 23.8449 + 23.8449i 0.937440 + 0.937440i 0.998155 0.0607154i \(-0.0193382\pi\)
−0.0607154 + 0.998155i \(0.519338\pi\)
\(648\) −47.5494 + 50.9480i −1.86792 + 2.00143i
\(649\) 25.8828 + 25.8828i 1.01599 + 1.01599i
\(650\) −1.59305 0.737465i −0.0624847 0.0289257i
\(651\) 16.5679 6.86263i 0.649345 0.268968i
\(652\) −2.75310 17.7482i −0.107820 0.695074i
\(653\) −25.8492 10.7071i −1.01156 0.419000i −0.185534 0.982638i \(-0.559401\pi\)
−0.826022 + 0.563638i \(0.809401\pi\)
\(654\) 13.6561 24.2938i 0.533995 0.949963i
\(655\) −0.341021 + 0.0818740i −0.0133248 + 0.00319908i
\(656\) 13.7160 4.36018i 0.535521 0.170236i
\(657\) 40.0757 1.56350
\(658\) −7.97151 + 14.1811i −0.310762 + 0.552838i
\(659\) 12.0853 29.1765i 0.470776 1.13655i −0.493045 0.870004i \(-0.664116\pi\)
0.963821 0.266550i \(-0.0858837\pi\)
\(660\) −60.4708 25.2734i −2.35382 0.983767i
\(661\) −9.01626 + 3.73466i −0.350692 + 0.145261i −0.551074 0.834457i \(-0.685782\pi\)
0.200382 + 0.979718i \(0.435782\pi\)
\(662\) 12.8091 + 16.3016i 0.497839 + 0.633579i
\(663\) 1.09100 1.09100i 0.0423710 0.0423710i
\(664\) −4.81825 10.5844i −0.186985 0.410753i
\(665\) −3.57022 + 5.82615i −0.138447 + 0.225928i
\(666\) 6.54977 54.5934i 0.253798 2.11545i
\(667\) 24.3426 10.0830i 0.942549 0.390416i
\(668\) −27.9019 6.79276i −1.07956 0.262820i
\(669\) −56.4203 23.3701i −2.18133 0.903538i
\(670\) −3.73939 + 2.08637i −0.144465 + 0.0806034i
\(671\) −18.7654 −0.724432
\(672\) 28.2209 5.38017i 1.08864 0.207544i
\(673\) 7.29415i 0.281169i −0.990069 0.140584i \(-0.955102\pi\)
0.990069 0.140584i \(-0.0448981\pi\)
\(674\) 3.55770 + 12.6920i 0.137037 + 0.488877i
\(675\) 5.70689 + 72.5020i 0.219658 + 2.79060i
\(676\) 25.1424 + 6.12094i 0.967015 + 0.235421i
\(677\) −37.9662 + 15.7261i −1.45916 + 0.604404i −0.964358 0.264600i \(-0.914760\pi\)
−0.494803 + 0.869005i \(0.664760\pi\)
\(678\) 75.2188 + 9.02427i 2.88876 + 0.346575i
\(679\) 9.95286 9.95286i 0.381956 0.381956i
\(680\) −12.0445 1.48389i −0.461884 0.0569044i
\(681\) −11.4566 11.4566i −0.439020 0.439020i
\(682\) 13.9599 + 17.7662i 0.534552 + 0.680303i
\(683\) −7.25600 17.5175i −0.277643 0.670290i 0.722126 0.691761i \(-0.243165\pi\)
−0.999769 + 0.0214711i \(0.993165\pi\)
\(684\) −17.2368 + 23.5661i −0.659065 + 0.901073i
\(685\) −2.62963 + 16.6035i −0.100473 + 0.634385i
\(686\) 22.3097 + 12.5407i 0.851787 + 0.478808i
\(687\) 17.2619 0.658581
\(688\) 33.0014 + 2.80898i 1.25817 + 0.107091i
\(689\) 0.513876i 0.0195771i
\(690\) 14.3593 50.6066i 0.546649 1.92656i
\(691\) −18.7477 + 45.2609i −0.713196 + 1.72181i −0.0213397 + 0.999772i \(0.506793\pi\)
−0.691856 + 0.722035i \(0.743207\pi\)
\(692\) 30.2467 4.69187i 1.14981 0.178358i
\(693\) 20.3375 + 49.0990i 0.772556 + 1.86511i
\(694\) −13.4695 17.1421i −0.511295 0.650704i
\(695\) −20.4295 + 33.3384i −0.774937 + 1.26460i
\(696\) 46.9702 1.62068i 1.78040 0.0614316i
\(697\) 4.88187 + 4.88187i 0.184914 + 0.184914i
\(698\) 1.55033 12.9222i 0.0586808 0.489114i
\(699\) −32.5767 78.6471i −1.23216 2.97471i
\(700\) 8.23515 13.3433i 0.311260 0.504329i
\(701\) 41.0788 + 17.0154i 1.55152 + 0.642662i 0.983591 0.180413i \(-0.0577433\pi\)
0.567933 + 0.823075i \(0.307743\pi\)
\(702\) 1.37835 + 4.91722i 0.0520224 + 0.185589i
\(703\) 10.1155i 0.381514i
\(704\) 16.1242 + 32.4077i 0.607705 + 1.22141i
\(705\) 12.4039 + 51.6647i 0.467159 + 1.94581i
\(706\) 32.3137 9.05785i 1.21614 0.340897i
\(707\) 4.65457 11.2371i 0.175053 0.422615i
\(708\) −44.7696 + 27.2390i −1.68254 + 1.02370i
\(709\) 5.04952 + 12.1906i 0.189639 + 0.457828i 0.989890 0.141836i \(-0.0453007\pi\)
−0.800252 + 0.599665i \(0.795301\pi\)
\(710\) 23.2976 2.71996i 0.874342 0.102078i
\(711\) −29.5060 + 29.5060i −1.10656 + 1.10656i
\(712\) −20.8888 + 0.720756i −0.782842 + 0.0270115i
\(713\) −12.8235 + 12.8235i −0.480244 + 0.480244i
\(714\) 8.51469 + 10.8363i 0.318654 + 0.405538i
\(715\) −2.03206 + 1.47640i −0.0759947 + 0.0552141i
\(716\) 5.78852 + 37.3164i 0.216327 + 1.39458i
\(717\) −56.5565 23.4265i −2.11214 0.874877i
\(718\) −38.0658 21.3976i −1.42060 0.798551i
\(719\) 34.8987i 1.30150i 0.759292 + 0.650750i \(0.225546\pi\)
−0.759292 + 0.650750i \(0.774454\pi\)
\(720\) 39.7255 53.9517i 1.48048 2.01066i
\(721\) 18.1282i 0.675131i
\(722\) 10.5346 18.7408i 0.392057 0.697459i
\(723\) −63.4855 26.2965i −2.36105 0.977979i
\(724\) −2.93135 + 4.00774i −0.108943 + 0.148947i
\(725\) 16.6587 19.5053i 0.618689 0.724408i
\(726\) −34.1176 + 26.8082i −1.26622 + 0.994944i
\(727\) 11.4015 11.4015i 0.422859 0.422859i −0.463328 0.886187i \(-0.653345\pi\)
0.886187 + 0.463328i \(0.153345\pi\)
\(728\) 0.386017 1.03114i 0.0143067 0.0382167i
\(729\) 30.5688 30.5688i 1.13218 1.13218i
\(730\) −16.8041 + 1.96186i −0.621949 + 0.0726117i
\(731\) 6.08007 + 14.6786i 0.224879 + 0.542907i
\(732\) 6.35497 26.1037i 0.234887 0.964820i
\(733\) 15.0396 36.3087i 0.555498 1.34109i −0.357799 0.933799i \(-0.616473\pi\)
0.913297 0.407293i \(-0.133527\pi\)
\(734\) 8.52771 + 30.4224i 0.314763 + 1.12291i
\(735\) 31.9822 7.67844i 1.17968 0.283223i
\(736\) −24.2846 + 15.9482i −0.895144 + 0.587857i
\(737\) 6.12687i 0.225686i
\(738\) −36.7019 + 10.2879i −1.35101 + 0.378703i
\(739\) −10.3322 4.27973i −0.380076 0.157432i 0.184462 0.982840i \(-0.440946\pi\)
−0.564538 + 0.825407i \(0.690946\pi\)
\(740\) −0.0738212 + 23.2122i −0.00271372 + 0.853298i
\(741\) 0.599702 + 1.44781i 0.0220306 + 0.0531866i
\(742\) −4.55729 0.546753i −0.167303 0.0200719i
\(743\) 25.7144 + 25.7144i 0.943369 + 0.943369i 0.998480 0.0551116i \(-0.0175514\pi\)
−0.0551116 + 0.998480i \(0.517551\pi\)
\(744\) −29.4412 + 13.4024i −1.07937 + 0.491354i
\(745\) 23.5428 38.4188i 0.862541 1.40756i
\(746\) −12.9799 + 10.1990i −0.475227 + 0.373413i
\(747\) 11.7863 + 28.4547i 0.431240 + 1.04110i
\(748\) −10.2509 + 14.0150i −0.374810 + 0.512440i
\(749\) 3.13899 7.57820i 0.114696 0.276902i
\(750\) −9.91186 50.2438i −0.361930 1.83464i
\(751\) 22.1568i 0.808513i −0.914646 0.404256i \(-0.867530\pi\)
0.914646 0.404256i \(-0.132470\pi\)
\(752\) 13.4887 26.0612i 0.491883 0.950355i
\(753\) 33.1416 1.20775
\(754\) 0.882595 1.57011i 0.0321422 0.0571802i
\(755\) 24.6005 + 3.89620i 0.895306 + 0.141797i
\(756\) −45.0747 + 6.99199i −1.63935 + 0.254296i
\(757\) −2.58172 6.23282i −0.0938341 0.226536i 0.869993 0.493064i \(-0.164123\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(758\) 17.1207 13.4527i 0.621850 0.488623i
\(759\) −53.2223 53.2223i −1.93185 1.93185i
\(760\) 6.07390 10.7253i 0.220324 0.389048i
\(761\) 8.45933 8.45933i 0.306650 0.306650i −0.536958 0.843609i \(-0.680427\pi\)
0.843609 + 0.536958i \(0.180427\pi\)
\(762\) −8.15016 + 67.9330i −0.295249 + 2.46095i
\(763\) 8.81379 3.65079i 0.319081 0.132167i
\(764\) 39.5604 24.0696i 1.43124 0.870807i
\(765\) 31.7438 + 5.02753i 1.14770 + 0.181771i
\(766\) 15.6066 4.37468i 0.563888 0.158064i
\(767\) 2.00839i 0.0725187i
\(768\) −50.5413 + 11.4547i −1.82375 + 0.413335i
\(769\) −23.5540 −0.849380 −0.424690 0.905339i \(-0.639617\pi\)
−0.424690 + 0.905339i \(0.639617\pi\)
\(770\) −10.9313 19.5921i −0.393936 0.706050i
\(771\) −45.7450 18.9482i −1.64746 0.682402i
\(772\) −27.3699 44.9847i −0.985063 1.61903i
\(773\) 38.1645 15.8083i 1.37268 0.568584i 0.430168 0.902749i \(-0.358454\pi\)
0.942515 + 0.334165i \(0.108454\pi\)
\(774\) −87.0918 10.4487i −3.13045 0.375571i
\(775\) −5.45556 + 16.7912i −0.195970 + 0.603156i
\(776\) −17.3237 + 18.5619i −0.621884 + 0.666333i
\(777\) 18.6396 18.6396i 0.668692 0.668692i
\(778\) −7.83520 + 6.15656i −0.280906 + 0.220723i
\(779\) −6.47847 + 2.68347i −0.232115 + 0.0961453i
\(780\) −1.36558 3.32668i −0.0488956 0.119114i
\(781\) 12.8433 31.0065i 0.459570 1.10950i
\(782\) −12.1489 6.82916i −0.434444 0.244210i
\(783\) −74.6198 −2.66669
\(784\) −16.1327 8.34996i −0.576170 0.298213i
\(785\) 4.61005 + 19.2017i 0.164540 + 0.685339i
\(786\) −0.626265 0.352037i −0.0223381 0.0125568i
\(787\) −11.7801 4.87949i −0.419916 0.173935i 0.162712 0.986674i \(-0.447976\pi\)
−0.582629 + 0.812739i \(0.697976\pi\)
\(788\) −23.9971 + 32.8089i −0.854862 + 1.16877i
\(789\) −0.952077 + 0.394363i −0.0338948 + 0.0140397i
\(790\) 10.9277 13.8166i 0.388791 0.491572i
\(791\) 18.3376 + 18.3376i 0.652009 + 0.652009i
\(792\) −39.7180 87.2493i −1.41132 3.10027i
\(793\) −0.728057 0.728057i −0.0258541 0.0258541i
\(794\) 0.859767 7.16631i 0.0305120 0.254323i
\(795\) −12.1281 + 8.81170i −0.430140 + 0.312519i
\(796\) 10.7635 44.2120i 0.381501 1.56705i
\(797\) −7.47151 + 18.0378i −0.264654 + 0.638932i −0.999215 0.0396107i \(-0.987388\pi\)
0.734561 + 0.678543i \(0.237388\pi\)
\(798\) −13.4779 + 3.77799i −0.477113 + 0.133740i
\(799\) 14.0768 0.498001
\(800\) −14.0161 + 24.5672i −0.495545 + 0.868582i
\(801\) 55.3544 1.95585
\(802\) 49.5303 13.8839i 1.74898 0.490256i
\(803\) −9.26366 + 22.3645i −0.326908 + 0.789225i
\(804\) −8.52279 2.07488i −0.300576 0.0731755i
\(805\) 14.5682 10.5845i 0.513460 0.373055i
\(806\) −0.147675 + 1.23090i −0.00520165 + 0.0433566i
\(807\) 63.7891 + 63.7891i 2.24548 + 2.24548i
\(808\) −7.69215 + 20.5475i −0.270609 + 0.722860i
\(809\) −17.0500 17.0500i −0.599446 0.599446i 0.340719 0.940165i \(-0.389329\pi\)
−0.940165 + 0.340719i \(0.889329\pi\)
\(810\) −48.3340 + 61.1116i −1.69828 + 2.14724i
\(811\) 10.6070 4.39355i 0.372461 0.154278i −0.188598 0.982054i \(-0.560394\pi\)
0.561059 + 0.827776i \(0.310394\pi\)
\(812\) 12.9854 + 9.49783i 0.455699 + 0.333309i
\(813\) 17.8637 + 7.39937i 0.626506 + 0.259507i
\(814\) 28.9522 + 16.2746i 1.01477 + 0.570426i
\(815\) −4.68780 19.5256i −0.164206 0.683951i
\(816\) −16.0241 19.0058i −0.560957 0.665335i
\(817\) −16.1371 −0.564565
\(818\) 20.3993 + 11.4669i 0.713246 + 0.400931i
\(819\) −1.11588 + 2.69398i −0.0389921 + 0.0941351i
\(820\) 14.8858 6.11052i 0.519836 0.213389i
\(821\) −35.4060 + 14.6657i −1.23568 + 0.511835i −0.902362 0.430980i \(-0.858168\pi\)
−0.333317 + 0.942815i \(0.608168\pi\)
\(822\) −27.0770 + 21.2759i −0.944419 + 0.742083i
\(823\) 29.3918 29.3918i 1.02453 1.02453i 0.0248432 0.999691i \(-0.492091\pi\)
0.999691 0.0248432i \(-0.00790864\pi\)
\(824\) 1.12764 + 32.6812i 0.0392833 + 1.13850i
\(825\) −69.6896 22.6426i −2.42628 0.788315i
\(826\) −17.8113 2.13688i −0.619735 0.0743517i
\(827\) −9.29213 + 3.84893i −0.323119 + 0.133840i −0.538346 0.842724i \(-0.680951\pi\)
0.215227 + 0.976564i \(0.430951\pi\)
\(828\) 65.7331 39.9938i 2.28438 1.38988i
\(829\) −50.9527 21.1053i −1.76966 0.733017i −0.994912 0.100746i \(-0.967877\pi\)
−0.774747 0.632271i \(-0.782123\pi\)
\(830\) −6.33510 11.3544i −0.219895 0.394116i
\(831\) 86.0312 2.98439
\(832\) −0.631761 + 1.88293i −0.0219024 + 0.0652788i
\(833\) 8.71399i 0.301922i
\(834\) −77.1233 + 21.6185i −2.67056 + 0.748586i
\(835\) −31.7112 5.02237i −1.09741 0.173806i
\(836\) −9.16685 15.0665i −0.317042 0.521085i
\(837\) 47.4504 19.6546i 1.64012 0.679362i
\(838\) −3.87670 + 32.3130i −0.133918 + 1.11623i
\(839\) 28.1226 28.1226i 0.970901 0.970901i −0.0286876 0.999588i \(-0.509133\pi\)
0.999588 + 0.0286876i \(0.00913280\pi\)
\(840\) 30.9555 8.57106i 1.06807 0.295730i
\(841\) −1.89593 1.89593i −0.0653769 0.0653769i
\(842\) 8.75807 6.88171i 0.301823 0.237160i
\(843\) −7.64360 18.4533i −0.263260 0.635565i
\(844\) −0.869333 5.60426i −0.0299237 0.192907i
\(845\) 28.5749 + 4.52565i 0.983007 + 0.155687i
\(846\) −38.0821 + 67.7471i −1.30929 + 2.32919i
\(847\) −14.8531 −0.510358
\(848\) 8.24977 + 0.702194i 0.283298 + 0.0241134i
\(849\) 0.800489i 0.0274727i
\(850\) −13.5566 0.554112i −0.464988 0.0190059i
\(851\) −10.2015 + 24.6285i −0.349701 + 0.844254i
\(852\) 38.7822 + 28.3661i 1.32866 + 0.971808i
\(853\) 0.409103 + 0.987663i 0.0140074 + 0.0338169i 0.930729 0.365711i \(-0.119174\pi\)
−0.916721 + 0.399528i \(0.869174\pi\)
\(854\) 7.23138 5.68210i 0.247453 0.194438i
\(855\) −17.0559 + 27.8331i −0.583300 + 0.951872i
\(856\) −5.18751 + 13.8571i −0.177305 + 0.473625i
\(857\) −35.0911 35.0911i −1.19869 1.19869i −0.974559 0.224130i \(-0.928046\pi\)
−0.224130 0.974559i \(-0.571954\pi\)
\(858\) −5.10870 0.612909i −0.174408 0.0209244i
\(859\) 0.950659 + 2.29509i 0.0324361 + 0.0783076i 0.939268 0.343186i \(-0.111506\pi\)
−0.906831 + 0.421493i \(0.861506\pi\)
\(860\) 37.0300 + 0.117765i 1.26271 + 0.00401577i
\(861\) −16.8825 6.99295i −0.575354 0.238319i
\(862\) 25.9244 7.26687i 0.882988 0.247510i
\(863\) 14.4929i 0.493346i −0.969099 0.246673i \(-0.920663\pi\)
0.969099 0.246673i \(-0.0793373\pi\)
\(864\) 80.8247 15.4088i 2.74971 0.524218i
\(865\) 33.2757 7.98900i 1.13141 0.271634i
\(866\) −5.96090 21.2654i −0.202560 0.722627i
\(867\) −16.5078 + 39.8534i −0.560634 + 1.35349i
\(868\) −10.7591 2.61931i −0.365187 0.0889051i
\(869\) −9.64554 23.2864i −0.327203 0.789937i
\(870\) 52.1910 6.09324i 1.76944 0.206580i
\(871\) −0.237709 + 0.237709i −0.00805445 + 0.00805445i
\(872\) −15.6622 + 7.12981i −0.530389 + 0.241446i
\(873\) 47.5475 47.5475i 1.60924 1.60924i
\(874\) 11.1303 8.74572i 0.376489 0.295828i
\(875\) 7.95851 15.6201i 0.269047 0.528057i
\(876\) −27.9729 20.4600i −0.945118 0.691280i
\(877\) −12.1206 5.02050i −0.409282 0.169530i 0.168537 0.985695i \(-0.446096\pi\)
−0.577819 + 0.816165i \(0.696096\pi\)
\(878\) −12.0530 + 21.4421i −0.406770 + 0.723634i
\(879\) 42.4658i 1.43233i
\(880\) 20.9253 + 34.6402i 0.705393 + 1.16772i
\(881\) 25.7354i 0.867049i 0.901142 + 0.433524i \(0.142730\pi\)
−0.901142 + 0.433524i \(0.857270\pi\)
\(882\) 41.9376 + 23.5740i 1.41211 + 0.793779i
\(883\) −14.7846 6.12399i −0.497542 0.206089i 0.119778 0.992801i \(-0.461782\pi\)
−0.617320 + 0.786712i \(0.711782\pi\)
\(884\) −0.941464 + 0.146040i −0.0316649 + 0.00491185i
\(885\) −47.4005 + 34.4389i −1.59335 + 1.15765i
\(886\) 21.2405 + 27.0320i 0.713590 + 0.908157i
\(887\) −11.4787 + 11.4787i −0.385418 + 0.385418i −0.873050 0.487631i \(-0.837861\pi\)
0.487631 + 0.873050i \(0.337861\pi\)
\(888\) −32.4436 + 34.7625i −1.08874 + 1.16655i
\(889\) −16.5614 + 16.5614i −0.555450 + 0.555450i
\(890\) −23.2107 + 2.70981i −0.778023 + 0.0908332i
\(891\) 42.6629 + 102.997i 1.42926 + 3.45054i
\(892\) 19.6004 + 32.2150i 0.656271 + 1.07864i
\(893\) −5.47141 + 13.2092i −0.183094 + 0.442027i
\(894\) 88.8761 24.9129i 2.97246 0.833211i
\(895\) 9.85630 + 41.0534i 0.329460 + 1.37226i
\(896\) −16.0265 7.60615i −0.535408 0.254104i
\(897\) 4.12981i 0.137890i
\(898\) −4.72966 16.8729i −0.157831 0.563058i
\(899\) −16.7360 6.93226i −0.558176 0.231204i
\(900\) 39.3416 63.7445i 1.31139 2.12482i
\(901\) 1.51991 + 3.66938i 0.0506355 + 0.122245i
\(902\) 2.74257 22.8598i 0.0913174 0.761147i
\(903\) −29.7354 29.7354i −0.989532 0.989532i
\(904\) −34.1992 31.9179i −1.13745 1.06157i
\(905\) −2.90059 + 4.73340i −0.0964189 + 0.157343i
\(906\) 31.5235 + 40.1187i 1.04730 + 1.33286i
\(907\) −7.50202 18.1115i −0.249100 0.601382i 0.749028 0.662539i \(-0.230521\pi\)
−0.998128 + 0.0611569i \(0.980521\pi\)
\(908\) 1.53357 + 9.88636i 0.0508934 + 0.328090i
\(909\) 22.2361 53.6828i 0.737526 1.78055i
\(910\) 0.336020 1.18424i 0.0111389 0.0392571i
\(911\) 28.3807i 0.940296i 0.882588 + 0.470148i \(0.155799\pi\)
−0.882588 + 0.470148i \(0.844201\pi\)
\(912\) 24.0626 7.64925i 0.796794 0.253292i
\(913\) −18.6038 −0.615695
\(914\) −6.06419 3.40881i −0.200586 0.112753i
\(915\) 4.69868 29.6674i 0.155334 0.980776i
\(916\) −8.60327 6.29262i −0.284260 0.207914i
\(917\) −0.0941130 0.227209i −0.00310788 0.00750310i
\(918\) 24.3861 + 31.0352i 0.804861 + 1.02431i
\(919\) 6.80537 + 6.80537i 0.224488 + 0.224488i 0.810385 0.585897i \(-0.199258\pi\)
−0.585897 + 0.810385i \(0.699258\pi\)
\(920\) −25.6047 + 19.9877i −0.844163 + 0.658975i
\(921\) 18.9814 18.9814i 0.625459 0.625459i
\(922\) 11.7789 + 1.41316i 0.387918 + 0.0465398i
\(923\) 1.70127 0.704691i 0.0559981 0.0231952i
\(924\) 10.8711 44.6542i 0.357633 1.46901i
\(925\) 2.03649 + 25.8722i 0.0669593 + 0.850671i
\(926\) −2.73914 9.77181i −0.0900137 0.321122i
\(927\) 86.6036i 2.84443i
\(928\) −24.0006 16.3147i −0.787859 0.535557i
\(929\) −29.8361 −0.978890 −0.489445 0.872034i \(-0.662801\pi\)
−0.489445 + 0.872034i \(0.662801\pi\)
\(930\) −31.5831 + 17.6216i −1.03565 + 0.577835i
\(931\) 8.17689 + 3.38698i 0.267987 + 0.111004i
\(932\) −12.4338 + 51.0730i −0.407282 + 1.67295i
\(933\) 23.5081 9.73736i 0.769619 0.318787i
\(934\) −2.38236 + 19.8573i −0.0779530 + 0.649752i
\(935\) −10.1433 + 16.5527i −0.331723 + 0.541330i
\(936\) 1.84411 4.92605i 0.0602766 0.161013i
\(937\) −34.3699 + 34.3699i −1.12281 + 1.12281i −0.131498 + 0.991316i \(0.541979\pi\)
−0.991316 + 0.131498i \(0.958021\pi\)
\(938\) −1.85519 2.36103i −0.0605742 0.0770903i
\(939\) −11.9176 + 4.93642i −0.388915 + 0.161094i
\(940\) 12.6517 30.2713i 0.412653 0.987341i
\(941\) 21.1030 50.9471i 0.687937 1.66083i −0.0609599 0.998140i \(-0.519416\pi\)
0.748897 0.662687i \(-0.230584\pi\)
\(942\) −19.8220 + 35.2629i −0.645836 + 1.14893i
\(943\) 18.4796 0.601777
\(944\) 32.2427 + 2.74440i 1.04941 + 0.0893225i
\(945\) −49.5886 + 11.9055i −1.61312 + 0.387286i
\(946\) 25.9626 46.1868i 0.844116 1.50166i
\(947\) 1.27735 + 0.529095i 0.0415082 + 0.0171933i 0.403341 0.915050i \(-0.367849\pi\)
−0.361833 + 0.932243i \(0.617849\pi\)
\(948\) 35.6591 5.53143i 1.15815 0.179653i
\(949\) −1.22710 + 0.508281i −0.0398333 + 0.0164995i
\(950\) 5.78918 12.5057i 0.187826 0.405737i
\(951\) 2.11594 + 2.11594i 0.0686142 + 0.0686142i
\(952\) −0.293450 8.50472i −0.00951077 0.275639i
\(953\) −2.96077 2.96077i −0.0959089 0.0959089i 0.657524 0.753433i \(-0.271604\pi\)
−0.753433 + 0.657524i \(0.771604\pi\)
\(954\) −21.7714 2.61199i −0.704875 0.0845663i
\(955\) 41.8852 30.4318i 1.35537 0.984749i
\(956\) 19.6478 + 32.2927i 0.635454 + 1.04442i
\(957\) 28.7715 69.4605i 0.930050 2.24534i
\(958\) −5.51424 19.6719i −0.178157 0.635571i
\(959\) −11.7879 −0.380652
\(960\) −55.2727 + 17.3772i −1.78392 + 0.560848i
\(961\) −18.5317 −0.597798
\(962\) 0.491860 + 1.75470i 0.0158582 + 0.0565737i
\(963\) 14.9958 36.2031i 0.483234 1.16663i
\(964\) 22.0549 + 36.2490i 0.710340 + 1.16750i
\(965\) −34.6044 47.6282i −1.11395 1.53321i
\(966\) 36.6251 + 4.39404i 1.17839 + 0.141376i
\(967\) −31.2533 31.2533i −1.00504 1.00504i −0.999987 0.00505130i \(-0.998392\pi\)
−0.00505130 0.999987i \(-0.501608\pi\)
\(968\) 26.7768 0.923915i 0.860637 0.0296957i
\(969\) 8.56447 + 8.56447i 0.275131 + 0.275131i
\(970\) −17.6095 + 22.2648i −0.565408 + 0.714879i
\(971\) −55.8924 + 23.1514i −1.79367 + 0.742963i −0.804923 + 0.593380i \(0.797793\pi\)
−0.988749 + 0.149583i \(0.952207\pi\)
\(972\) −71.4822 + 11.0883i −2.29279 + 0.355658i
\(973\) −25.3310 10.4925i −0.812076 0.336373i
\(974\) −22.1590 + 39.4204i −0.710021 + 1.26311i
\(975\) −1.82532 3.58228i −0.0584570 0.114725i
\(976\) −12.6831 + 10.6934i −0.405976 + 0.342287i
\(977\) 32.6357 1.04411 0.522055 0.852912i \(-0.325166\pi\)
0.522055 + 0.852912i \(0.325166\pi\)
\(978\) 20.1563 35.8576i 0.644529 1.14660i
\(979\) −12.7954 + 30.8908i −0.408943 + 0.987275i
\(980\) −18.7389 7.83182i −0.598593 0.250178i
\(981\) 42.1059 17.4408i 1.34434 0.556843i
\(982\) −5.18935 6.60427i −0.165599 0.210751i
\(983\) 1.16983 1.16983i 0.0373119 0.0373119i −0.688205 0.725517i \(-0.741601\pi\)
0.725517 + 0.688205i \(0.241601\pi\)
\(984\) 30.8703 + 11.5566i 0.984110 + 0.368410i
\(985\) −23.7453 + 38.7494i −0.756589 + 1.23466i
\(986\) 1.65828 13.8221i 0.0528104 0.440184i
\(987\) −34.4222 + 14.2581i −1.09567 + 0.453842i
\(988\) 0.228893 0.940199i 0.00728204 0.0299117i
\(989\) 39.2893 + 16.2742i 1.24933 + 0.517489i
\(990\) −52.2217 93.5967i −1.65972 2.97470i
\(991\) −14.3222 −0.454961 −0.227480 0.973783i \(-0.573049\pi\)
−0.227480 + 0.973783i \(0.573049\pi\)
\(992\) 19.5591 + 4.05277i 0.621003 + 0.128676i
\(993\) 47.4820i 1.50679i
\(994\) 4.43940 + 15.8375i 0.140809 + 0.502334i
\(995\) 7.95820 50.2480i 0.252292 1.59297i
\(996\) 6.30023 25.8788i 0.199630 0.820002i
\(997\) −29.2035 + 12.0965i −0.924884 + 0.383100i −0.793735 0.608263i \(-0.791867\pi\)
−0.131149 + 0.991363i \(0.541867\pi\)
\(998\) −29.5166 3.54121i −0.934332 0.112095i
\(999\) 53.3839 53.3839i 1.68899 1.68899i
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 160.2.z.a.29.10 88
4.3 odd 2 640.2.z.a.209.1 88
5.2 odd 4 800.2.y.f.701.21 88
5.3 odd 4 800.2.y.f.701.2 88
5.4 even 2 inner 160.2.z.a.29.13 yes 88
20.19 odd 2 640.2.z.a.209.22 88
32.11 odd 8 640.2.z.a.49.22 88
32.21 even 8 inner 160.2.z.a.149.13 yes 88
160.53 odd 8 800.2.y.f.501.2 88
160.117 odd 8 800.2.y.f.501.21 88
160.139 odd 8 640.2.z.a.49.1 88
160.149 even 8 inner 160.2.z.a.149.10 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.z.a.29.10 88 1.1 even 1 trivial
160.2.z.a.29.13 yes 88 5.4 even 2 inner
160.2.z.a.149.10 yes 88 160.149 even 8 inner
160.2.z.a.149.13 yes 88 32.21 even 8 inner
640.2.z.a.49.1 88 160.139 odd 8
640.2.z.a.49.22 88 32.11 odd 8
640.2.z.a.209.1 88 4.3 odd 2
640.2.z.a.209.22 88 20.19 odd 2
800.2.y.f.501.2 88 160.53 odd 8
800.2.y.f.501.21 88 160.117 odd 8
800.2.y.f.701.2 88 5.3 odd 4
800.2.y.f.701.21 88 5.2 odd 4