Properties

Label 336.2.bq.b.37.12
Level $336$
Weight $2$
Character 336.37
Analytic conductor $2.683$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(37,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bq (of order \(12\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.12
Character \(\chi\) \(=\) 336.37
Dual form 336.2.bq.b.109.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.485523 - 1.32826i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.52854 + 1.28980i) q^{4} +(-0.879995 + 0.235794i) q^{5} +(0.125201 + 1.40866i) q^{6} +(-1.69105 - 2.03479i) q^{7} +(2.45532 + 1.40406i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.485523 - 1.32826i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.52854 + 1.28980i) q^{4} +(-0.879995 + 0.235794i) q^{5} +(0.125201 + 1.40866i) q^{6} +(-1.69105 - 2.03479i) q^{7} +(2.45532 + 1.40406i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.740453 + 1.05438i) q^{10} +(0.0635968 - 0.237347i) q^{11} +(1.81028 - 0.850236i) q^{12} +(-4.10057 + 4.10057i) q^{13} +(-1.88168 + 3.23408i) q^{14} +0.911038 q^{15} +(0.672839 - 3.94300i) q^{16} +(3.38683 + 5.86615i) q^{17} +(0.243654 - 1.39307i) q^{18} +(1.39522 + 5.20705i) q^{19} +(1.04098 - 1.49544i) q^{20} +(1.10679 + 2.40313i) q^{21} +(-0.346135 + 0.0307643i) q^{22} +(4.95390 + 2.86014i) q^{23} +(-2.00826 - 1.99170i) q^{24} +(-3.61133 + 2.08500i) q^{25} +(7.43753 + 3.45569i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(5.20929 + 0.929130i) q^{28} +(0.0308357 - 0.0308357i) q^{29} +(-0.442330 - 1.21009i) q^{30} +(-4.53789 - 7.85985i) q^{31} +(-5.56400 + 1.02072i) q^{32} +(-0.122860 + 0.212799i) q^{33} +(6.14738 - 7.34673i) q^{34} +(1.96791 + 1.39186i) q^{35} +(-1.96865 + 0.352731i) q^{36} +(-4.30646 + 1.15391i) q^{37} +(6.23889 - 4.38136i) q^{38} +(5.02215 - 2.89954i) q^{39} +(-2.49174 - 0.656617i) q^{40} -4.70384i q^{41} +(2.65460 - 2.63687i) q^{42} +(-1.74674 - 1.74674i) q^{43} +(0.208919 + 0.444820i) q^{44} +(-0.879995 - 0.235794i) q^{45} +(1.39376 - 7.96872i) q^{46} +(-3.98947 + 6.90997i) q^{47} +(-1.67044 + 3.63451i) q^{48} +(-1.28071 + 6.88184i) q^{49} +(4.52281 + 3.78446i) q^{50} +(-1.75315 - 6.54284i) q^{51} +(0.978955 - 11.5568i) q^{52} +(-1.03734 + 3.87140i) q^{53} +(-0.595903 + 1.28254i) q^{54} +0.223860i q^{55} +(-1.29511 - 7.37039i) q^{56} -5.39073i q^{57} +(-0.0559292 - 0.0259863i) q^{58} +(-1.17710 + 4.39298i) q^{59} +(-1.39255 + 1.17506i) q^{60} +(2.52924 + 9.43924i) q^{61} +(-8.23665 + 9.84361i) q^{62} +(-0.447098 - 2.60770i) q^{63} +(4.05722 + 6.89485i) q^{64} +(2.64159 - 4.57537i) q^{65} +(0.342303 + 0.0598704i) q^{66} +(-4.40639 - 1.18069i) q^{67} +(-12.7430 - 4.59830i) q^{68} +(-4.04484 - 4.04484i) q^{69} +(0.893290 - 3.28967i) q^{70} -15.2208i q^{71} +(1.42434 + 2.44361i) q^{72} +(-4.56397 + 2.63501i) q^{73} +(3.62357 + 5.15983i) q^{74} +(4.02792 - 1.07928i) q^{75} +(-8.84870 - 6.15960i) q^{76} +(-0.590495 + 0.271959i) q^{77} +(-6.28970 - 5.26292i) q^{78} +(4.25415 - 7.36841i) q^{79} +(0.337642 + 3.62848i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-6.24790 + 2.28382i) q^{82} +(-11.0999 + 11.0999i) q^{83} +(-4.79131 - 2.24573i) q^{84} +(-4.36359 - 4.36359i) q^{85} +(-1.47204 + 3.16821i) q^{86} +(-0.0377659 + 0.0218041i) q^{87} +(0.489400 - 0.493469i) q^{88} +(-3.86247 - 2.23000i) q^{89} +(0.114063 + 1.28334i) q^{90} +(15.2780 + 1.40952i) q^{91} +(-11.2612 + 2.01772i) q^{92} +(2.34898 + 8.76652i) q^{93} +(11.1152 + 1.94410i) q^{94} +(-2.45558 - 4.25319i) q^{95} +(5.63860 + 0.454134i) q^{96} +7.40529 q^{97} +(9.76267 - 1.64018i) q^{98} +(0.173750 - 0.173750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.485523 1.32826i −0.343317 0.939220i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) −1.52854 + 1.28980i −0.764268 + 0.644899i
\(5\) −0.879995 + 0.235794i −0.393546 + 0.105450i −0.450165 0.892946i \(-0.648635\pi\)
0.0566187 + 0.998396i \(0.481968\pi\)
\(6\) 0.125201 + 1.40866i 0.0511130 + 0.575083i
\(7\) −1.69105 2.03479i −0.639156 0.769077i
\(8\) 2.45532 + 1.40406i 0.868088 + 0.496411i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0.740453 + 1.05438i 0.234152 + 0.333423i
\(11\) 0.0635968 0.237347i 0.0191752 0.0715627i −0.955675 0.294423i \(-0.904873\pi\)
0.974850 + 0.222860i \(0.0715393\pi\)
\(12\) 1.81028 0.850236i 0.522582 0.245442i
\(13\) −4.10057 + 4.10057i −1.13729 + 1.13729i −0.148360 + 0.988933i \(0.547399\pi\)
−0.988933 + 0.148360i \(0.952601\pi\)
\(14\) −1.88168 + 3.23408i −0.502899 + 0.864345i
\(15\) 0.911038 0.235229
\(16\) 0.672839 3.94300i 0.168210 0.985751i
\(17\) 3.38683 + 5.86615i 0.821426 + 1.42275i 0.904621 + 0.426218i \(0.140154\pi\)
−0.0831948 + 0.996533i \(0.526512\pi\)
\(18\) 0.243654 1.39307i 0.0574297 0.328349i
\(19\) 1.39522 + 5.20705i 0.320087 + 1.19458i 0.919160 + 0.393885i \(0.128869\pi\)
−0.599073 + 0.800694i \(0.704464\pi\)
\(20\) 1.04098 1.49544i 0.232770 0.334390i
\(21\) 1.10679 + 2.40313i 0.241520 + 0.524406i
\(22\) −0.346135 + 0.0307643i −0.0737963 + 0.00655896i
\(23\) 4.95390 + 2.86014i 1.03296 + 0.596380i 0.917831 0.396971i \(-0.129939\pi\)
0.115129 + 0.993351i \(0.463272\pi\)
\(24\) −2.00826 1.99170i −0.409935 0.406555i
\(25\) −3.61133 + 2.08500i −0.722267 + 0.417001i
\(26\) 7.43753 + 3.45569i 1.45862 + 0.677717i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 5.20929 + 0.929130i 0.984464 + 0.175589i
\(29\) 0.0308357 0.0308357i 0.00572605 0.00572605i −0.704238 0.709964i \(-0.748711\pi\)
0.709964 + 0.704238i \(0.248711\pi\)
\(30\) −0.442330 1.21009i −0.0807580 0.220932i
\(31\) −4.53789 7.85985i −0.815028 1.41167i −0.909308 0.416124i \(-0.863388\pi\)
0.0942794 0.995546i \(-0.469945\pi\)
\(32\) −5.56400 + 1.02072i −0.983586 + 0.180439i
\(33\) −0.122860 + 0.212799i −0.0213871 + 0.0370436i
\(34\) 6.14738 7.34673i 1.05427 1.25995i
\(35\) 1.96791 + 1.39186i 0.332637 + 0.235268i
\(36\) −1.96865 + 0.352731i −0.328108 + 0.0587885i
\(37\) −4.30646 + 1.15391i −0.707977 + 0.189702i −0.594801 0.803873i \(-0.702769\pi\)
−0.113176 + 0.993575i \(0.536102\pi\)
\(38\) 6.23889 4.38136i 1.01208 0.710750i
\(39\) 5.02215 2.89954i 0.804188 0.464298i
\(40\) −2.49174 0.656617i −0.393979 0.103820i
\(41\) 4.70384i 0.734616i −0.930099 0.367308i \(-0.880280\pi\)
0.930099 0.367308i \(-0.119720\pi\)
\(42\) 2.65460 2.63687i 0.409614 0.406878i
\(43\) −1.74674 1.74674i −0.266376 0.266376i 0.561262 0.827638i \(-0.310316\pi\)
−0.827638 + 0.561262i \(0.810316\pi\)
\(44\) 0.208919 + 0.444820i 0.0314958 + 0.0670591i
\(45\) −0.879995 0.235794i −0.131182 0.0351501i
\(46\) 1.39376 7.96872i 0.205499 1.17492i
\(47\) −3.98947 + 6.90997i −0.581924 + 1.00792i 0.413327 + 0.910583i \(0.364367\pi\)
−0.995251 + 0.0973395i \(0.968967\pi\)
\(48\) −1.67044 + 3.63451i −0.241107 + 0.524596i
\(49\) −1.28071 + 6.88184i −0.182959 + 0.983121i
\(50\) 4.52281 + 3.78446i 0.639622 + 0.535204i
\(51\) −1.75315 6.54284i −0.245490 0.916181i
\(52\) 0.978955 11.5568i 0.135757 1.60264i
\(53\) −1.03734 + 3.87140i −0.142489 + 0.531778i 0.857365 + 0.514709i \(0.172100\pi\)
−0.999854 + 0.0170687i \(0.994567\pi\)
\(54\) −0.595903 + 1.28254i −0.0810922 + 0.174531i
\(55\) 0.223860i 0.0301852i
\(56\) −1.29511 7.37039i −0.173066 0.984910i
\(57\) 5.39073i 0.714020i
\(58\) −0.0559292 0.0259863i −0.00734387 0.00341217i
\(59\) −1.17710 + 4.39298i −0.153245 + 0.571917i 0.846005 + 0.533176i \(0.179002\pi\)
−0.999249 + 0.0387414i \(0.987665\pi\)
\(60\) −1.39255 + 1.17506i −0.179778 + 0.151699i
\(61\) 2.52924 + 9.43924i 0.323836 + 1.20857i 0.915477 + 0.402370i \(0.131813\pi\)
−0.591642 + 0.806201i \(0.701520\pi\)
\(62\) −8.23665 + 9.84361i −1.04606 + 1.25014i
\(63\) −0.447098 2.60770i −0.0563290 0.328539i
\(64\) 4.05722 + 6.89485i 0.507153 + 0.861856i
\(65\) 2.64159 4.57537i 0.327649 0.567505i
\(66\) 0.342303 + 0.0598704i 0.0421346 + 0.00736953i
\(67\) −4.40639 1.18069i −0.538326 0.144244i −0.0205957 0.999788i \(-0.506556\pi\)
−0.517730 + 0.855544i \(0.673223\pi\)
\(68\) −12.7430 4.59830i −1.54532 0.557626i
\(69\) −4.04484 4.04484i −0.486942 0.486942i
\(70\) 0.893290 3.28967i 0.106769 0.393190i
\(71\) 15.2208i 1.80638i −0.429240 0.903190i \(-0.641219\pi\)
0.429240 0.903190i \(-0.358781\pi\)
\(72\) 1.42434 + 2.44361i 0.167860 + 0.287983i
\(73\) −4.56397 + 2.63501i −0.534172 + 0.308405i −0.742714 0.669609i \(-0.766462\pi\)
0.208541 + 0.978014i \(0.433128\pi\)
\(74\) 3.62357 + 5.15983i 0.421232 + 0.599818i
\(75\) 4.02792 1.07928i 0.465104 0.124624i
\(76\) −8.84870 6.15960i −1.01501 0.706554i
\(77\) −0.590495 + 0.271959i −0.0672932 + 0.0309926i
\(78\) −6.28970 5.26292i −0.712169 0.595908i
\(79\) 4.25415 7.36841i 0.478629 0.829010i −0.521070 0.853514i \(-0.674467\pi\)
0.999700 + 0.0245033i \(0.00780043\pi\)
\(80\) 0.337642 + 3.62848i 0.0377495 + 0.405676i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −6.24790 + 2.28382i −0.689966 + 0.252206i
\(83\) −11.0999 + 11.0999i −1.21837 + 1.21837i −0.250168 + 0.968202i \(0.580486\pi\)
−0.968202 + 0.250168i \(0.919514\pi\)
\(84\) −4.79131 2.24573i −0.522775 0.245030i
\(85\) −4.36359 4.36359i −0.473298 0.473298i
\(86\) −1.47204 + 3.16821i −0.158734 + 0.341637i
\(87\) −0.0377659 + 0.0218041i −0.00404893 + 0.00233765i
\(88\) 0.489400 0.493469i 0.0521702 0.0526040i
\(89\) −3.86247 2.23000i −0.409421 0.236379i 0.281120 0.959673i \(-0.409294\pi\)
−0.690541 + 0.723293i \(0.742627\pi\)
\(90\) 0.114063 + 1.28334i 0.0120233 + 0.135276i
\(91\) 15.2780 + 1.40952i 1.60157 + 0.147758i
\(92\) −11.2612 + 2.01772i −1.17406 + 0.210362i
\(93\) 2.34898 + 8.76652i 0.243578 + 0.909046i
\(94\) 11.1152 + 1.94410i 1.14644 + 0.200518i
\(95\) −2.45558 4.25319i −0.251937 0.436369i
\(96\) 5.63860 + 0.454134i 0.575487 + 0.0463499i
\(97\) 7.40529 0.751893 0.375947 0.926641i \(-0.377318\pi\)
0.375947 + 0.926641i \(0.377318\pi\)
\(98\) 9.76267 1.64018i 0.986179 0.165683i
\(99\) 0.173750 0.173750i 0.0174625 0.0174625i
\(100\) 2.83081 7.84490i 0.283081 0.784490i
\(101\) −0.540960 + 2.01889i −0.0538276 + 0.200887i −0.987603 0.156972i \(-0.949827\pi\)
0.933775 + 0.357859i \(0.116493\pi\)
\(102\) −7.83939 + 5.50533i −0.776215 + 0.545109i
\(103\) 0.873143 + 0.504109i 0.0860333 + 0.0496714i 0.542399 0.840121i \(-0.317516\pi\)
−0.456366 + 0.889792i \(0.650849\pi\)
\(104\) −15.8257 + 4.31077i −1.55183 + 0.422706i
\(105\) −1.54061 1.85377i −0.150348 0.180909i
\(106\) 5.64587 0.501801i 0.548375 0.0487392i
\(107\) 0.959271 0.257036i 0.0927362 0.0248486i −0.212153 0.977237i \(-0.568047\pi\)
0.304889 + 0.952388i \(0.401381\pi\)
\(108\) 1.99286 + 0.168812i 0.191763 + 0.0162440i
\(109\) −18.5384 4.96734i −1.77565 0.475785i −0.785874 0.618387i \(-0.787786\pi\)
−0.989780 + 0.142602i \(0.954453\pi\)
\(110\) 0.297343 0.108689i 0.0283506 0.0103631i
\(111\) 4.45837 0.423170
\(112\) −9.16098 + 5.29873i −0.865631 + 0.500683i
\(113\) 15.8290 1.48907 0.744536 0.667583i \(-0.232671\pi\)
0.744536 + 0.667583i \(0.232671\pi\)
\(114\) −7.16028 + 2.61732i −0.670622 + 0.245135i
\(115\) −5.03381 1.34881i −0.469406 0.125777i
\(116\) −0.00736161 + 0.0869053i −0.000683508 + 0.00806896i
\(117\) −5.60148 + 1.50091i −0.517857 + 0.138759i
\(118\) 6.40651 0.569406i 0.589767 0.0524181i
\(119\) 6.20908 16.8114i 0.569186 1.54110i
\(120\) 2.23689 + 1.27915i 0.204200 + 0.116770i
\(121\) 9.47399 + 5.46981i 0.861272 + 0.497256i
\(122\) 11.3097 7.94244i 1.02394 0.719075i
\(123\) −1.21744 + 4.54356i −0.109773 + 0.409679i
\(124\) 17.0739 + 6.16109i 1.53328 + 0.553283i
\(125\) 5.90733 5.90733i 0.528368 0.528368i
\(126\) −3.24662 + 1.85996i −0.289232 + 0.165698i
\(127\) −9.29912 −0.825163 −0.412582 0.910921i \(-0.635373\pi\)
−0.412582 + 0.910921i \(0.635373\pi\)
\(128\) 7.18826 8.73664i 0.635358 0.772218i
\(129\) 1.23513 + 2.13931i 0.108747 + 0.188356i
\(130\) −7.35982 1.28727i −0.645499 0.112901i
\(131\) −2.64808 9.88277i −0.231364 0.863462i −0.979754 0.200203i \(-0.935840\pi\)
0.748390 0.663258i \(-0.230827\pi\)
\(132\) −0.0866728 0.483735i −0.00754390 0.0421038i
\(133\) 8.23584 11.6444i 0.714138 1.00969i
\(134\) 0.571145 + 6.42607i 0.0493394 + 0.555128i
\(135\) 0.788982 + 0.455519i 0.0679048 + 0.0392048i
\(136\) 0.0793128 + 19.1586i 0.00680102 + 1.64284i
\(137\) −0.203435 + 0.117453i −0.0173806 + 0.0100347i −0.508665 0.860964i \(-0.669861\pi\)
0.491285 + 0.870999i \(0.336528\pi\)
\(138\) −3.40873 + 7.33646i −0.290170 + 0.624521i
\(139\) 5.35760 + 5.35760i 0.454426 + 0.454426i 0.896821 0.442395i \(-0.145871\pi\)
−0.442395 + 0.896821i \(0.645871\pi\)
\(140\) −4.80324 + 0.410690i −0.405948 + 0.0347096i
\(141\) 5.64196 5.64196i 0.475139 0.475139i
\(142\) −20.2172 + 7.39006i −1.69659 + 0.620160i
\(143\) 0.712473 + 1.23404i 0.0595800 + 0.103196i
\(144\) 2.55420 3.07832i 0.212850 0.256527i
\(145\) −0.0198644 + 0.0344062i −0.00164965 + 0.00285728i
\(146\) 5.71588 + 4.78277i 0.473050 + 0.395825i
\(147\) 3.01822 6.31588i 0.248939 0.520925i
\(148\) 5.09426 7.31825i 0.418745 0.601557i
\(149\) 10.9324 2.92933i 0.895616 0.239980i 0.218484 0.975841i \(-0.429889\pi\)
0.677133 + 0.735861i \(0.263222\pi\)
\(150\) −3.38921 4.82610i −0.276727 0.394049i
\(151\) −5.48259 + 3.16538i −0.446167 + 0.257595i −0.706210 0.708002i \(-0.749597\pi\)
0.260043 + 0.965597i \(0.416263\pi\)
\(152\) −3.88529 + 14.7440i −0.315138 + 1.19589i
\(153\) 6.77365i 0.547617i
\(154\) 0.647930 + 0.652287i 0.0522117 + 0.0525628i
\(155\) 5.84662 + 5.84662i 0.469612 + 0.469612i
\(156\) −3.93671 + 10.9096i −0.315189 + 0.873468i
\(157\) −3.23789 0.867590i −0.258412 0.0692412i 0.127287 0.991866i \(-0.459373\pi\)
−0.385699 + 0.922625i \(0.626040\pi\)
\(158\) −11.8526 2.07308i −0.942944 0.164925i
\(159\) 2.00398 3.47100i 0.158926 0.275268i
\(160\) 4.65562 2.21018i 0.368059 0.174730i
\(161\) −2.55752 14.9168i −0.201561 1.17561i
\(162\) 0.907543 1.08460i 0.0713033 0.0852145i
\(163\) 2.06655 + 7.71248i 0.161865 + 0.604088i 0.998419 + 0.0562044i \(0.0178998\pi\)
−0.836554 + 0.547884i \(0.815433\pi\)
\(164\) 6.06700 + 7.18998i 0.473753 + 0.561443i
\(165\) 0.0579392 0.216232i 0.00451056 0.0168336i
\(166\) 20.1328 + 9.35426i 1.56260 + 0.726031i
\(167\) 15.7174i 1.21625i 0.793842 + 0.608124i \(0.208078\pi\)
−0.793842 + 0.608124i \(0.791922\pi\)
\(168\) −0.656622 + 7.45445i −0.0506595 + 0.575123i
\(169\) 20.6293i 1.58687i
\(170\) −3.67735 + 7.91460i −0.282040 + 0.607022i
\(171\) −1.39522 + 5.20705i −0.106696 + 0.398193i
\(172\) 4.92291 + 0.417011i 0.375368 + 0.0317968i
\(173\) −2.45178 9.15015i −0.186405 0.695673i −0.994325 0.106381i \(-0.966074\pi\)
0.807920 0.589292i \(-0.200593\pi\)
\(174\) 0.0472977 + 0.0395764i 0.00358563 + 0.00300028i
\(175\) 10.3495 + 3.82245i 0.782347 + 0.288950i
\(176\) −0.893069 0.410459i −0.0673176 0.0309395i
\(177\) 2.27397 3.93864i 0.170922 0.296046i
\(178\) −1.08669 + 6.21306i −0.0814511 + 0.465689i
\(179\) 16.6018 + 4.44844i 1.24088 + 0.332492i 0.818805 0.574071i \(-0.194637\pi\)
0.422071 + 0.906563i \(0.361303\pi\)
\(180\) 1.64923 0.774597i 0.122926 0.0577351i
\(181\) 3.95699 + 3.95699i 0.294121 + 0.294121i 0.838706 0.544585i \(-0.183313\pi\)
−0.544585 + 0.838706i \(0.683313\pi\)
\(182\) −5.54563 20.9775i −0.411070 1.55496i
\(183\) 9.77222i 0.722383i
\(184\) 8.14762 + 13.9781i 0.600651 + 1.03048i
\(185\) 3.51758 2.03087i 0.258617 0.149313i
\(186\) 10.5037 7.37640i 0.770169 0.540864i
\(187\) 1.60770 0.430783i 0.117567 0.0315020i
\(188\) −2.81442 15.7077i −0.205263 1.14560i
\(189\) −0.243059 + 2.63456i −0.0176800 + 0.191636i
\(190\) −4.45709 + 5.32667i −0.323352 + 0.386437i
\(191\) −6.27087 + 10.8615i −0.453744 + 0.785907i −0.998615 0.0526123i \(-0.983245\pi\)
0.544871 + 0.838520i \(0.316579\pi\)
\(192\) −2.13446 7.71000i −0.154041 0.556421i
\(193\) 11.8642 + 20.5495i 0.854006 + 1.47918i 0.877564 + 0.479460i \(0.159167\pi\)
−0.0235575 + 0.999722i \(0.507499\pi\)
\(194\) −3.59544 9.83613i −0.258137 0.706193i
\(195\) −3.73578 + 3.73578i −0.267524 + 0.267524i
\(196\) −6.91858 12.1710i −0.494184 0.869357i
\(197\) −0.164168 0.164168i −0.0116965 0.0116965i 0.701234 0.712931i \(-0.252633\pi\)
−0.712931 + 0.701234i \(0.752633\pi\)
\(198\) −0.315144 0.146425i −0.0223963 0.0104060i
\(199\) −5.86216 + 3.38452i −0.415557 + 0.239922i −0.693175 0.720770i \(-0.743789\pi\)
0.277617 + 0.960692i \(0.410455\pi\)
\(200\) −11.7945 + 0.0488267i −0.833995 + 0.00345257i
\(201\) 3.95066 + 2.28091i 0.278658 + 0.160883i
\(202\) 2.94426 0.261683i 0.207157 0.0184120i
\(203\) −0.114889 0.0105994i −0.00806361 0.000743932i
\(204\) 11.1187 + 7.73976i 0.778465 + 0.541891i
\(205\) 1.10914 + 4.13935i 0.0774655 + 0.289105i
\(206\) 0.245656 1.40452i 0.0171157 0.0978572i
\(207\) 2.86014 + 4.95390i 0.198793 + 0.344320i
\(208\) 13.4095 + 18.9276i 0.929784 + 1.31239i
\(209\) 1.32461 0.0916250
\(210\) −1.71428 + 2.94637i −0.118297 + 0.203319i
\(211\) 9.02662 9.02662i 0.621418 0.621418i −0.324476 0.945894i \(-0.605188\pi\)
0.945894 + 0.324476i \(0.105188\pi\)
\(212\) −3.40772 7.25553i −0.234043 0.498312i
\(213\) −3.93944 + 14.7022i −0.269926 + 1.00738i
\(214\) −0.807158 1.14936i −0.0551762 0.0785688i
\(215\) 1.94900 + 1.12525i 0.132921 + 0.0767417i
\(216\) −0.743355 2.72900i −0.0505789 0.185685i
\(217\) −8.31933 + 22.5250i −0.564753 + 1.52910i
\(218\) 2.40290 + 27.0355i 0.162745 + 1.83107i
\(219\) 5.09045 1.36398i 0.343981 0.0921693i
\(220\) −0.288734 0.342177i −0.0194664 0.0230696i
\(221\) −37.9425 10.1667i −2.55229 0.683883i
\(222\) −2.16464 5.92186i −0.145281 0.397449i
\(223\) −2.43216 −0.162869 −0.0814347 0.996679i \(-0.525950\pi\)
−0.0814347 + 0.996679i \(0.525950\pi\)
\(224\) 11.4859 + 9.59548i 0.767437 + 0.641125i
\(225\) −4.17001 −0.278001
\(226\) −7.68536 21.0250i −0.511223 1.39857i
\(227\) −14.4014 3.85884i −0.955854 0.256120i −0.253009 0.967464i \(-0.581420\pi\)
−0.702844 + 0.711344i \(0.748087\pi\)
\(228\) 6.95296 + 8.23993i 0.460471 + 0.545702i
\(229\) −4.20550 + 1.12686i −0.277908 + 0.0744651i −0.395081 0.918646i \(-0.629283\pi\)
0.117173 + 0.993111i \(0.462617\pi\)
\(230\) 0.652470 + 7.34108i 0.0430226 + 0.484056i
\(231\) 0.640763 0.109861i 0.0421591 0.00722829i
\(232\) 0.119007 0.0324164i 0.00781318 0.00212824i
\(233\) 10.4959 + 6.05983i 0.687611 + 0.396992i 0.802716 0.596361i \(-0.203387\pi\)
−0.115105 + 0.993353i \(0.536721\pi\)
\(234\) 4.71325 + 6.71148i 0.308114 + 0.438743i
\(235\) 1.88139 7.02143i 0.122728 0.458028i
\(236\) −3.86683 8.23304i −0.251709 0.535925i
\(237\) −6.01628 + 6.01628i −0.390799 + 0.390799i
\(238\) −25.3445 0.0849337i −1.64284 0.00550544i
\(239\) −3.46391 −0.224062 −0.112031 0.993705i \(-0.535736\pi\)
−0.112031 + 0.993705i \(0.535736\pi\)
\(240\) 0.612982 3.59223i 0.0395678 0.231877i
\(241\) 2.80174 + 4.85276i 0.180476 + 0.312594i 0.942043 0.335493i \(-0.108903\pi\)
−0.761567 + 0.648086i \(0.775570\pi\)
\(242\) 2.66548 15.2396i 0.171343 0.979640i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) −16.0407 11.1660i −1.02690 0.714830i
\(245\) −0.495678 6.35798i −0.0316677 0.406196i
\(246\) 6.62611 0.588924i 0.422465 0.0375484i
\(247\) −27.0731 15.6307i −1.72262 0.994555i
\(248\) −0.106268 25.6699i −0.00674805 1.63004i
\(249\) 13.5945 7.84880i 0.861518 0.497398i
\(250\) −10.7146 4.97831i −0.677651 0.314856i
\(251\) 2.18974 + 2.18974i 0.138215 + 0.138215i 0.772829 0.634614i \(-0.218841\pi\)
−0.634614 + 0.772829i \(0.718841\pi\)
\(252\) 4.04681 + 3.40930i 0.254925 + 0.214765i
\(253\) 0.993896 0.993896i 0.0624857 0.0624857i
\(254\) 4.51493 + 12.3516i 0.283292 + 0.775010i
\(255\) 3.08553 + 5.34429i 0.193223 + 0.334672i
\(256\) −15.0946 5.30601i −0.943411 0.331626i
\(257\) 13.7503 23.8163i 0.857723 1.48562i −0.0163724 0.999866i \(-0.505212\pi\)
0.874096 0.485754i \(-0.161455\pi\)
\(258\) 2.24187 2.67926i 0.139573 0.166804i
\(259\) 9.63039 + 6.81140i 0.598403 + 0.423240i
\(260\) 1.86354 + 10.4007i 0.115572 + 0.645026i
\(261\) 0.0421224 0.0112867i 0.00260731 0.000698626i
\(262\) −11.8412 + 8.31565i −0.731549 + 0.513742i
\(263\) −5.30472 + 3.06268i −0.327103 + 0.188853i −0.654554 0.756015i \(-0.727144\pi\)
0.327451 + 0.944868i \(0.393810\pi\)
\(264\) −0.600443 + 0.349988i −0.0369547 + 0.0215403i
\(265\) 3.65141i 0.224305i
\(266\) −19.4654 5.28571i −1.19350 0.324088i
\(267\) 3.15369 + 3.15369i 0.193003 + 0.193003i
\(268\) 8.25817 3.87863i 0.504448 0.236925i
\(269\) 20.5707 + 5.51190i 1.25422 + 0.336066i 0.823964 0.566642i \(-0.191758\pi\)
0.430253 + 0.902708i \(0.358424\pi\)
\(270\) 0.221978 1.26914i 0.0135091 0.0772372i
\(271\) −3.06988 + 5.31719i −0.186482 + 0.322996i −0.944075 0.329731i \(-0.893042\pi\)
0.757593 + 0.652727i \(0.226375\pi\)
\(272\) 25.4091 9.40729i 1.54065 0.570401i
\(273\) −14.3926 5.31574i −0.871082 0.321723i
\(274\) 0.254781 + 0.213188i 0.0153919 + 0.0128792i
\(275\) 0.265199 + 0.989738i 0.0159921 + 0.0596834i
\(276\) 11.3997 + 0.965651i 0.686182 + 0.0581254i
\(277\) 7.53920 28.1367i 0.452986 1.69057i −0.240955 0.970536i \(-0.577460\pi\)
0.693941 0.720032i \(-0.255873\pi\)
\(278\) 4.51504 9.71752i 0.270794 0.582818i
\(279\) 9.07577i 0.543352i
\(280\) 2.87758 + 6.18053i 0.171968 + 0.369358i
\(281\) 2.53476i 0.151211i −0.997138 0.0756055i \(-0.975911\pi\)
0.997138 0.0756055i \(-0.0240890\pi\)
\(282\) −10.2333 4.75468i −0.609383 0.283137i
\(283\) −4.87418 + 18.1907i −0.289740 + 1.08132i 0.655566 + 0.755138i \(0.272430\pi\)
−0.945306 + 0.326186i \(0.894236\pi\)
\(284\) 19.6318 + 23.2656i 1.16493 + 1.38056i
\(285\) 1.27110 + 4.74382i 0.0752937 + 0.281000i
\(286\) 1.29320 1.54550i 0.0764685 0.0913875i
\(287\) −9.57130 + 7.95441i −0.564976 + 0.469534i
\(288\) −5.32893 1.89804i −0.314010 0.111843i
\(289\) −14.4412 + 25.0128i −0.849480 + 1.47134i
\(290\) 0.0553449 + 0.00968007i 0.00324996 + 0.000568433i
\(291\) −7.15296 1.91663i −0.419314 0.112355i
\(292\) 3.57756 9.91431i 0.209361 0.580191i
\(293\) −9.46667 9.46667i −0.553049 0.553049i 0.374271 0.927319i \(-0.377893\pi\)
−0.927319 + 0.374271i \(0.877893\pi\)
\(294\) −9.85453 0.942474i −0.574728 0.0549662i
\(295\) 4.14335i 0.241235i
\(296\) −12.1939 3.21330i −0.708756 0.186769i
\(297\) −0.212799 + 0.122860i −0.0123479 + 0.00712904i
\(298\) −9.19882 13.0988i −0.532874 0.758792i
\(299\) −32.0420 + 8.58563i −1.85304 + 0.496520i
\(300\) −4.76477 + 6.84492i −0.275094 + 0.395192i
\(301\) −0.600422 + 6.50808i −0.0346077 + 0.375119i
\(302\) 6.86636 + 5.74543i 0.395115 + 0.330612i
\(303\) 1.04506 1.81009i 0.0600368 0.103987i
\(304\) 21.4702 1.99787i 1.23140 0.114586i
\(305\) −4.45143 7.71011i −0.254888 0.441480i
\(306\) 8.99715 3.28876i 0.514333 0.188006i
\(307\) 11.8266 11.8266i 0.674980 0.674980i −0.283880 0.958860i \(-0.591622\pi\)
0.958860 + 0.283880i \(0.0916217\pi\)
\(308\) 0.551820 1.17732i 0.0314429 0.0670839i
\(309\) −0.712918 0.712918i −0.0405565 0.0405565i
\(310\) 4.92715 10.6045i 0.279843 0.602295i
\(311\) 5.84539 3.37484i 0.331462 0.191370i −0.325028 0.945704i \(-0.605374\pi\)
0.656490 + 0.754335i \(0.272040\pi\)
\(312\) 16.4021 0.0679015i 0.928588 0.00384417i
\(313\) −14.8332 8.56397i −0.838424 0.484064i 0.0183042 0.999832i \(-0.494173\pi\)
−0.856728 + 0.515768i \(0.827507\pi\)
\(314\) 0.419687 + 4.72199i 0.0236843 + 0.266477i
\(315\) 1.00832 + 2.18934i 0.0568126 + 0.123355i
\(316\) 3.00114 + 16.7499i 0.168827 + 0.942254i
\(317\) 4.80055 + 17.9159i 0.269626 + 1.00626i 0.959358 + 0.282192i \(0.0910615\pi\)
−0.689732 + 0.724064i \(0.742272\pi\)
\(318\) −5.58337 0.976556i −0.313100 0.0547625i
\(319\) −0.00535770 0.00927981i −0.000299974 0.000519570i
\(320\) −5.19610 5.11077i −0.290471 0.285700i
\(321\) −0.993110 −0.0554300
\(322\) −18.5716 + 10.6395i −1.03495 + 0.592915i
\(323\) −25.8200 + 25.8200i −1.43666 + 1.43666i
\(324\) −1.88127 0.678851i −0.104515 0.0377139i
\(325\) 6.25882 23.3582i 0.347177 1.29568i
\(326\) 9.24080 6.48950i 0.511801 0.359420i
\(327\) 16.6210 + 9.59617i 0.919146 + 0.530669i
\(328\) 6.60447 11.5494i 0.364671 0.637711i
\(329\) 20.8067 3.56737i 1.14711 0.196675i
\(330\) −0.315342 + 0.0280274i −0.0173590 + 0.00154286i
\(331\) −24.8780 + 6.66605i −1.36742 + 0.366399i −0.866536 0.499115i \(-0.833659\pi\)
−0.500885 + 0.865514i \(0.666992\pi\)
\(332\) 2.64995 31.2832i 0.145435 1.71689i
\(333\) −4.30646 1.15391i −0.235992 0.0632339i
\(334\) 20.8767 7.63115i 1.14232 0.417558i
\(335\) 4.15600 0.227067
\(336\) 10.2202 2.74714i 0.557560 0.149869i
\(337\) −27.7235 −1.51020 −0.755099 0.655611i \(-0.772411\pi\)
−0.755099 + 0.655611i \(0.772411\pi\)
\(338\) −27.4011 + 10.0160i −1.49042 + 0.544799i
\(339\) −15.2897 4.09686i −0.830422 0.222511i
\(340\) 12.2981 + 1.04175i 0.666956 + 0.0564968i
\(341\) −2.15410 + 0.577190i −0.116651 + 0.0312566i
\(342\) 7.59372 0.674924i 0.410621 0.0364957i
\(343\) 16.1688 9.03156i 0.873035 0.487658i
\(344\) −1.83629 6.74135i −0.0990059 0.363469i
\(345\) 4.51319 + 2.60569i 0.242982 + 0.140286i
\(346\) −10.9634 + 7.69920i −0.589394 + 0.413911i
\(347\) 2.08349 7.77567i 0.111847 0.417420i −0.887184 0.461415i \(-0.847342\pi\)
0.999032 + 0.0439950i \(0.0140086\pi\)
\(348\) 0.0296035 0.0820388i 0.00158692 0.00439774i
\(349\) 16.0269 16.0269i 0.857903 0.857903i −0.133188 0.991091i \(-0.542521\pi\)
0.991091 + 0.133188i \(0.0425214\pi\)
\(350\) 0.0522871 15.6027i 0.00279486 0.833997i
\(351\) 5.79908 0.309532
\(352\) −0.111590 + 1.38551i −0.00594774 + 0.0738480i
\(353\) −12.4021 21.4810i −0.660095 1.14332i −0.980590 0.196067i \(-0.937183\pi\)
0.320496 0.947250i \(-0.396150\pi\)
\(354\) −6.33559 1.10812i −0.336733 0.0588961i
\(355\) 3.58898 + 13.3943i 0.190483 + 0.710894i
\(356\) 8.78016 1.57318i 0.465348 0.0833782i
\(357\) −10.3486 + 14.6316i −0.547707 + 0.774384i
\(358\) −2.15188 24.2113i −0.113730 1.27961i
\(359\) 14.3866 + 8.30614i 0.759298 + 0.438381i 0.829044 0.559184i \(-0.188885\pi\)
−0.0697454 + 0.997565i \(0.522219\pi\)
\(360\) −1.82960 1.81452i −0.0964286 0.0956335i
\(361\) −8.71223 + 5.03001i −0.458538 + 0.264737i
\(362\) 3.33469 7.17711i 0.175268 0.377221i
\(363\) −7.73548 7.73548i −0.406007 0.406007i
\(364\) −25.1710 + 17.5511i −1.31932 + 0.919927i
\(365\) 3.39495 3.39495i 0.177700 0.177700i
\(366\) −12.9800 + 4.74464i −0.678477 + 0.248006i
\(367\) −5.62737 9.74689i −0.293746 0.508784i 0.680946 0.732334i \(-0.261569\pi\)
−0.974692 + 0.223550i \(0.928235\pi\)
\(368\) 14.6107 17.6088i 0.761636 0.917925i
\(369\) 2.35192 4.07364i 0.122436 0.212065i
\(370\) −4.40539 3.68621i −0.229025 0.191637i
\(371\) 9.63166 4.43596i 0.500051 0.230304i
\(372\) −14.8975 10.3702i −0.772402 0.537671i
\(373\) 20.9534 5.61445i 1.08493 0.290705i 0.328314 0.944569i \(-0.393519\pi\)
0.756613 + 0.653863i \(0.226853\pi\)
\(374\) −1.35277 1.92629i −0.0699499 0.0996060i
\(375\) −7.23498 + 4.17711i −0.373613 + 0.215705i
\(376\) −19.4975 + 11.3647i −1.00550 + 0.586092i
\(377\) 0.252888i 0.0130244i
\(378\) 3.61739 0.956295i 0.186058 0.0491865i
\(379\) −2.33732 2.33732i −0.120060 0.120060i 0.644524 0.764584i \(-0.277056\pi\)
−0.764584 + 0.644524i \(0.777056\pi\)
\(380\) 9.23921 + 3.33395i 0.473961 + 0.171028i
\(381\) 8.98226 + 2.40679i 0.460175 + 0.123304i
\(382\) 17.4715 + 3.05584i 0.893918 + 0.156350i
\(383\) −4.25703 + 7.37340i −0.217524 + 0.376763i −0.954050 0.299646i \(-0.903131\pi\)
0.736526 + 0.676409i \(0.236465\pi\)
\(384\) −9.20453 + 6.57849i −0.469717 + 0.335707i
\(385\) 0.455507 0.378558i 0.0232148 0.0192931i
\(386\) 21.5346 25.7360i 1.09608 1.30993i
\(387\) −0.639352 2.38610i −0.0325001 0.121292i
\(388\) −11.3192 + 9.55133i −0.574647 + 0.484895i
\(389\) −3.88898 + 14.5139i −0.197179 + 0.735883i 0.794513 + 0.607248i \(0.207726\pi\)
−0.991692 + 0.128635i \(0.958940\pi\)
\(390\) 6.77588 + 3.14827i 0.343110 + 0.159419i
\(391\) 38.7471i 1.95953i
\(392\) −12.8071 + 15.0990i −0.646856 + 0.762612i
\(393\) 10.2314i 0.516106i
\(394\) −0.138350 + 0.297764i −0.00696996 + 0.0150011i
\(395\) −2.00621 + 7.48727i −0.100943 + 0.376725i
\(396\) −0.0414804 + 0.489685i −0.00208447 + 0.0246076i
\(397\) −2.59273 9.67621i −0.130126 0.485635i 0.869845 0.493325i \(-0.164219\pi\)
−0.999970 + 0.00769021i \(0.997552\pi\)
\(398\) 7.34172 + 6.14319i 0.368007 + 0.307930i
\(399\) −10.9690 + 9.11599i −0.549136 + 0.456370i
\(400\) 5.79134 + 15.6424i 0.289567 + 0.782119i
\(401\) −3.06081 + 5.30148i −0.152849 + 0.264743i −0.932274 0.361753i \(-0.882178\pi\)
0.779424 + 0.626496i \(0.215512\pi\)
\(402\) 1.11151 6.35493i 0.0554369 0.316955i
\(403\) 50.8378 + 13.6219i 2.53241 + 0.678557i
\(404\) −1.77709 3.78368i −0.0884134 0.188245i
\(405\) −0.644201 0.644201i −0.0320106 0.0320106i
\(406\) 0.0417024 + 0.157748i 0.00206966 + 0.00782891i
\(407\) 1.09551i 0.0543023i
\(408\) 4.88200 18.5263i 0.241695 0.917190i
\(409\) 18.0632 10.4288i 0.893168 0.515671i 0.0181904 0.999835i \(-0.494209\pi\)
0.874977 + 0.484164i \(0.160876\pi\)
\(410\) 4.95962 3.48297i 0.244938 0.172012i
\(411\) 0.226902 0.0607983i 0.0111923 0.00299896i
\(412\) −1.98483 + 0.355630i −0.0977855 + 0.0175206i
\(413\) 10.9293 5.03360i 0.537796 0.247687i
\(414\) 5.19139 6.20423i 0.255143 0.304921i
\(415\) 7.15056 12.3851i 0.351007 0.607962i
\(416\) 18.6301 27.0011i 0.913414 1.32384i
\(417\) −3.78840 6.56170i −0.185519 0.321328i
\(418\) −0.643127 1.75942i −0.0314564 0.0860560i
\(419\) −4.46804 + 4.46804i −0.218278 + 0.218278i −0.807772 0.589494i \(-0.799327\pi\)
0.589494 + 0.807772i \(0.299327\pi\)
\(420\) 4.74586 + 0.846473i 0.231574 + 0.0413037i
\(421\) −0.515100 0.515100i −0.0251044 0.0251044i 0.694443 0.719548i \(-0.255651\pi\)
−0.719548 + 0.694443i \(0.755651\pi\)
\(422\) −16.3723 7.60705i −0.796992 0.370305i
\(423\) −6.90997 + 3.98947i −0.335974 + 0.193975i
\(424\) −7.98269 + 8.04905i −0.387673 + 0.390897i
\(425\) −24.4619 14.1231i −1.18658 0.685071i
\(426\) 21.4410 1.90566i 1.03882 0.0923295i
\(427\) 14.9298 21.1087i 0.722502 1.02152i
\(428\) −1.13475 + 1.63015i −0.0548504 + 0.0787965i
\(429\) −0.368803 1.37639i −0.0178060 0.0664529i
\(430\) 0.548344 3.13511i 0.0264435 0.151188i
\(431\) 17.8742 + 30.9591i 0.860971 + 1.49125i 0.870992 + 0.491296i \(0.163477\pi\)
−0.0100211 + 0.999950i \(0.503190\pi\)
\(432\) −3.26389 + 2.31236i −0.157034 + 0.111253i
\(433\) 22.1382 1.06389 0.531946 0.846778i \(-0.321461\pi\)
0.531946 + 0.846778i \(0.321461\pi\)
\(434\) 33.9582 + 0.113800i 1.63005 + 0.00546256i
\(435\) 0.0280925 0.0280925i 0.00134693 0.00134693i
\(436\) 34.7434 16.3180i 1.66391 0.781491i
\(437\) −7.98107 + 29.7857i −0.381786 + 1.42485i
\(438\) −4.28325 6.09918i −0.204661 0.291430i
\(439\) −10.6653 6.15762i −0.509027 0.293887i 0.223406 0.974725i \(-0.428282\pi\)
−0.732434 + 0.680838i \(0.761616\pi\)
\(440\) −0.314313 + 0.549648i −0.0149843 + 0.0262034i
\(441\) −4.55005 + 5.31950i −0.216669 + 0.253309i
\(442\) 4.91801 + 55.3335i 0.233926 + 2.63195i
\(443\) −5.09678 + 1.36568i −0.242155 + 0.0648853i −0.377855 0.925865i \(-0.623338\pi\)
0.135700 + 0.990750i \(0.456672\pi\)
\(444\) −6.81478 + 5.75040i −0.323415 + 0.272902i
\(445\) 3.92477 + 1.05164i 0.186052 + 0.0498525i
\(446\) 1.18087 + 3.23053i 0.0559158 + 0.152970i
\(447\) −11.3180 −0.535325
\(448\) 7.16858 19.9151i 0.338684 0.940900i
\(449\) −25.7102 −1.21334 −0.606670 0.794954i \(-0.707495\pi\)
−0.606670 + 0.794954i \(0.707495\pi\)
\(450\) 2.02463 + 5.53885i 0.0954422 + 0.261104i
\(451\) −1.11644 0.299149i −0.0525711 0.0140864i
\(452\) −24.1953 + 20.4163i −1.13805 + 0.960301i
\(453\) 6.11504 1.63852i 0.287310 0.0769844i
\(454\) 1.86667 + 21.0023i 0.0876072 + 0.985687i
\(455\) −13.7770 + 2.36210i −0.645874 + 0.110737i
\(456\) 7.56892 13.2360i 0.354447 0.619832i
\(457\) 3.46724 + 2.00181i 0.162191 + 0.0936407i 0.578898 0.815400i \(-0.303483\pi\)
−0.416708 + 0.909041i \(0.636816\pi\)
\(458\) 3.53863 + 5.03888i 0.165349 + 0.235451i
\(459\) 1.75315 6.54284i 0.0818300 0.305394i
\(460\) 9.43405 4.43091i 0.439865 0.206592i
\(461\) 5.80743 5.80743i 0.270479 0.270479i −0.558814 0.829293i \(-0.688743\pi\)
0.829293 + 0.558814i \(0.188743\pi\)
\(462\) −0.457028 0.797758i −0.0212629 0.0371150i
\(463\) 6.56637 0.305165 0.152583 0.988291i \(-0.451241\pi\)
0.152583 + 0.988291i \(0.451241\pi\)
\(464\) −0.100838 0.142333i −0.00468128 0.00660764i
\(465\) −4.13419 7.16062i −0.191718 0.332066i
\(466\) 2.95300 16.8835i 0.136795 0.782112i
\(467\) −5.62557 20.9949i −0.260320 0.971529i −0.965053 0.262056i \(-0.915600\pi\)
0.704732 0.709473i \(-0.251067\pi\)
\(468\) 6.62619 9.51898i 0.306296 0.440015i
\(469\) 5.04897 + 10.9627i 0.233140 + 0.506209i
\(470\) −10.2397 + 0.910100i −0.472323 + 0.0419798i
\(471\) 2.90301 + 1.67606i 0.133764 + 0.0772286i
\(472\) −9.05816 + 9.13347i −0.416936 + 0.420402i
\(473\) −0.525671 + 0.303496i −0.0241704 + 0.0139548i
\(474\) 10.9122 + 5.07012i 0.501214 + 0.232879i
\(475\) −15.8953 15.8953i −0.729328 0.729328i
\(476\) 12.1925 + 33.7053i 0.558844 + 1.54488i
\(477\) −2.83406 + 2.83406i −0.129763 + 0.129763i
\(478\) 1.68181 + 4.60096i 0.0769241 + 0.210443i
\(479\) 2.85264 + 4.94092i 0.130341 + 0.225757i 0.923808 0.382856i \(-0.125060\pi\)
−0.793467 + 0.608613i \(0.791726\pi\)
\(480\) −5.06902 + 0.929911i −0.231368 + 0.0424445i
\(481\) 12.9272 22.3906i 0.589431 1.02092i
\(482\) 5.08540 6.07756i 0.231634 0.276825i
\(483\) −1.39037 + 15.0704i −0.0632638 + 0.685728i
\(484\) −21.5363 + 3.85874i −0.978922 + 0.175397i
\(485\) −6.51662 + 1.74612i −0.295904 + 0.0792874i
\(486\) −1.15734 + 0.812757i −0.0524978 + 0.0368674i
\(487\) −32.9747 + 19.0379i −1.49423 + 0.862692i −0.999978 0.00662909i \(-0.997890\pi\)
−0.494248 + 0.869321i \(0.664557\pi\)
\(488\) −7.04318 + 26.7276i −0.318830 + 1.20990i
\(489\) 7.98455i 0.361074i
\(490\) −8.20436 + 3.74533i −0.370635 + 0.169197i
\(491\) 4.83139 + 4.83139i 0.218038 + 0.218038i 0.807671 0.589633i \(-0.200728\pi\)
−0.589633 + 0.807671i \(0.700728\pi\)
\(492\) −3.99937 8.51524i −0.180305 0.383897i
\(493\) 0.285322 + 0.0764519i 0.0128503 + 0.00344322i
\(494\) −7.61693 + 43.5491i −0.342702 + 1.95936i
\(495\) −0.111930 + 0.193868i −0.00503087 + 0.00871373i
\(496\) −34.0447 + 12.6045i −1.52865 + 0.565958i
\(497\) −30.9711 + 25.7392i −1.38925 + 1.15456i
\(498\) −17.0257 14.2463i −0.762939 0.638390i
\(499\) −6.55657 24.4694i −0.293512 1.09540i −0.942392 0.334511i \(-0.891429\pi\)
0.648879 0.760891i \(-0.275238\pi\)
\(500\) −1.41030 + 16.6488i −0.0630703 + 0.744559i
\(501\) 4.06796 15.1818i 0.181743 0.678274i
\(502\) 1.84537 3.97170i 0.0823628 0.177266i
\(503\) 39.5772i 1.76466i 0.470632 + 0.882330i \(0.344026\pi\)
−0.470632 + 0.882330i \(0.655974\pi\)
\(504\) 2.56360 7.03050i 0.114192 0.313163i
\(505\) 1.90417i 0.0847345i
\(506\) −1.80271 0.837591i −0.0801402 0.0372354i
\(507\) −5.33926 + 19.9264i −0.237125 + 0.884963i
\(508\) 14.2140 11.9940i 0.630645 0.532147i
\(509\) 7.06761 + 26.3767i 0.313266 + 1.16913i 0.925593 + 0.378521i \(0.123567\pi\)
−0.612327 + 0.790605i \(0.709766\pi\)
\(510\) 5.60050 6.69315i 0.247994 0.296378i
\(511\) 13.0796 + 4.83078i 0.578606 + 0.213701i
\(512\) 0.281010 + 22.6257i 0.0124190 + 0.999923i
\(513\) 2.69537 4.66851i 0.119003 0.206120i
\(514\) −38.3103 6.70064i −1.68979 0.295553i
\(515\) −0.887228 0.237732i −0.0390959 0.0104757i
\(516\) −4.64723 1.67694i −0.204583 0.0738233i
\(517\) 1.38634 + 1.38634i 0.0609711 + 0.0609711i
\(518\) 4.37151 16.0987i 0.192073 0.707337i
\(519\) 9.47293i 0.415816i
\(520\) 12.9101 7.52506i 0.566144 0.329996i
\(521\) −21.8879 + 12.6370i −0.958925 + 0.553635i −0.895842 0.444373i \(-0.853427\pi\)
−0.0630828 + 0.998008i \(0.520093\pi\)
\(522\) −0.0354430 0.0504694i −0.00155130 0.00220899i
\(523\) 14.1981 3.80436i 0.620838 0.166353i 0.0653292 0.997864i \(-0.479190\pi\)
0.555509 + 0.831511i \(0.312524\pi\)
\(524\) 16.7945 + 11.6907i 0.733670 + 0.510709i
\(525\) −9.00751 6.37084i −0.393120 0.278046i
\(526\) 6.64360 + 5.55903i 0.289675 + 0.242385i
\(527\) 30.7380 53.2399i 1.33897 2.31916i
\(528\) 0.756404 + 0.627616i 0.0329182 + 0.0273135i
\(529\) 4.86076 + 8.41908i 0.211337 + 0.366047i
\(530\) −4.85002 + 1.77284i −0.210671 + 0.0770075i
\(531\) −3.21588 + 3.21588i −0.139557 + 0.139557i
\(532\) 2.43010 + 28.4214i 0.105358 + 1.23222i
\(533\) 19.2884 + 19.2884i 0.835473 + 0.835473i
\(534\) 2.65772 5.72010i 0.115011 0.247533i
\(535\) −0.783547 + 0.452381i −0.0338757 + 0.0195581i
\(536\) −9.16135 9.08581i −0.395710 0.392447i
\(537\) −14.8848 8.59372i −0.642325 0.370846i
\(538\) −2.66632 29.9993i −0.114953 1.29336i
\(539\) 1.55193 + 0.741636i 0.0668465 + 0.0319445i
\(540\) −1.79352 + 0.321351i −0.0771806 + 0.0138288i
\(541\) 5.46362 + 20.3905i 0.234899 + 0.876656i 0.978194 + 0.207692i \(0.0665953\pi\)
−0.743295 + 0.668964i \(0.766738\pi\)
\(542\) 8.55310 + 1.49598i 0.367387 + 0.0642576i
\(543\) −2.79802 4.84630i −0.120074 0.207975i
\(544\) −24.8320 29.1823i −1.06466 1.25118i
\(545\) 17.4850 0.748973
\(546\) −0.0727138 + 21.6980i −0.00311186 + 0.928591i
\(547\) 3.95525 3.95525i 0.169114 0.169114i −0.617476 0.786590i \(-0.711845\pi\)
0.786590 + 0.617476i \(0.211845\pi\)
\(548\) 0.159467 0.441922i 0.00681208 0.0188780i
\(549\) −2.52924 + 9.43924i −0.107945 + 0.402857i
\(550\) 1.18587 0.832793i 0.0505655 0.0355104i
\(551\) 0.203586 + 0.117540i 0.00867305 + 0.00500739i
\(552\) −4.25219 15.6106i −0.180985 0.664431i
\(553\) −22.1871 + 3.80404i −0.943492 + 0.161764i
\(554\) −41.0332 + 3.64700i −1.74333 + 0.154946i
\(555\) −3.92335 + 1.05126i −0.166537 + 0.0446234i
\(556\) −15.0995 1.27906i −0.640362 0.0542440i
\(557\) 14.0332 + 3.76019i 0.594607 + 0.159325i 0.543558 0.839372i \(-0.317077\pi\)
0.0510493 + 0.998696i \(0.483743\pi\)
\(558\) −12.0550 + 4.40649i −0.510327 + 0.186542i
\(559\) 14.3253 0.605895
\(560\) 6.81221 6.82296i 0.287868 0.288323i
\(561\) −1.66442 −0.0702717
\(562\) −3.36681 + 1.23068i −0.142020 + 0.0519132i
\(563\) 22.4852 + 6.02490i 0.947639 + 0.253919i 0.699360 0.714770i \(-0.253468\pi\)
0.248279 + 0.968689i \(0.420135\pi\)
\(564\) −1.34694 + 15.9009i −0.0567165 + 0.669550i
\(565\) −13.9295 + 3.73240i −0.586018 + 0.157023i
\(566\) 26.5284 2.35783i 1.11507 0.0991070i
\(567\) 0.916652 2.48188i 0.0384958 0.104229i
\(568\) 21.3710 37.3721i 0.896706 1.56810i
\(569\) 16.9620 + 9.79303i 0.711085 + 0.410545i 0.811463 0.584404i \(-0.198672\pi\)
−0.100378 + 0.994949i \(0.532005\pi\)
\(570\) 5.68387 3.99159i 0.238071 0.167189i
\(571\) 5.19060 19.3716i 0.217220 0.810676i −0.768153 0.640266i \(-0.778824\pi\)
0.985373 0.170410i \(-0.0545091\pi\)
\(572\) −2.68070 0.967326i −0.112086 0.0404459i
\(573\) 8.86834 8.86834i 0.370480 0.370480i
\(574\) 15.2126 + 8.85110i 0.634961 + 0.369438i
\(575\) −23.8536 −0.994763
\(576\) 0.0662356 + 7.99973i 0.00275982 + 0.333322i
\(577\) 3.79129 + 6.56670i 0.157833 + 0.273375i 0.934087 0.357045i \(-0.116216\pi\)
−0.776254 + 0.630421i \(0.782882\pi\)
\(578\) 40.2350 + 7.03728i 1.67356 + 0.292712i
\(579\) −6.14138 22.9199i −0.255227 0.952520i
\(580\) −0.0140136 0.0782121i −0.000581882 0.00324758i
\(581\) 41.3563 + 3.81545i 1.71575 + 0.158292i
\(582\) 0.927148 + 10.4315i 0.0384315 + 0.432401i
\(583\) 0.852893 + 0.492418i 0.0353232 + 0.0203939i
\(584\) −14.9057 + 0.0617068i −0.616804 + 0.00255344i
\(585\) 4.57537 2.64159i 0.189168 0.109216i
\(586\) −7.97789 + 17.1705i −0.329563 + 0.709305i
\(587\) −26.6533 26.6533i −1.10010 1.10010i −0.994398 0.105704i \(-0.966290\pi\)
−0.105704 0.994398i \(-0.533710\pi\)
\(588\) 3.53275 + 13.5469i 0.145688 + 0.558667i
\(589\) 34.5952 34.5952i 1.42547 1.42547i
\(590\) −5.50344 + 2.01169i −0.226573 + 0.0828201i
\(591\) 0.116084 + 0.201064i 0.00477506 + 0.00827065i
\(592\) 1.65233 + 17.7568i 0.0679102 + 0.729799i
\(593\) −4.10035 + 7.10201i −0.168381 + 0.291645i −0.937851 0.347039i \(-0.887187\pi\)
0.769470 + 0.638683i \(0.220521\pi\)
\(594\) 0.266508 + 0.223001i 0.0109350 + 0.00914984i
\(595\) −1.49993 + 16.2580i −0.0614913 + 0.666514i
\(596\) −12.9323 + 18.5782i −0.529728 + 0.760991i
\(597\) 6.53839 1.75196i 0.267598 0.0717028i
\(598\) 26.9610 + 38.3915i 1.10252 + 1.56995i
\(599\) 35.9742 20.7697i 1.46987 0.848629i 0.470439 0.882432i \(-0.344095\pi\)
0.999428 + 0.0338038i \(0.0107621\pi\)
\(600\) 11.4052 + 3.00547i 0.465616 + 0.122698i
\(601\) 14.4179i 0.588117i 0.955787 + 0.294058i \(0.0950060\pi\)
−0.955787 + 0.294058i \(0.904994\pi\)
\(602\) 8.93592 2.36231i 0.364201 0.0962804i
\(603\) −3.22570 3.22570i −0.131361 0.131361i
\(604\) 4.29764 11.9098i 0.174868 0.484604i
\(605\) −9.62682 2.57950i −0.391386 0.104872i
\(606\) −2.91166 0.509263i −0.118278 0.0206874i
\(607\) 14.1963 24.5886i 0.576208 0.998022i −0.419701 0.907663i \(-0.637865\pi\)
0.995909 0.0903598i \(-0.0288017\pi\)
\(608\) −13.0780 27.5479i −0.530381 1.11722i
\(609\) 0.108231 + 0.0399736i 0.00438573 + 0.00161981i
\(610\) −8.07974 + 9.65608i −0.327139 + 0.390963i
\(611\) −11.9757 44.6939i −0.484485 1.80812i
\(612\) −8.73664 10.3538i −0.353158 0.418526i
\(613\) −9.82021 + 36.6495i −0.396634 + 1.48026i 0.422344 + 0.906436i \(0.361207\pi\)
−0.818978 + 0.573824i \(0.805459\pi\)
\(614\) −21.4509 9.96669i −0.865686 0.402223i
\(615\) 4.28537i 0.172803i
\(616\) −1.83170 0.161345i −0.0738014 0.00650076i
\(617\) 37.1945i 1.49739i 0.662913 + 0.748696i \(0.269320\pi\)
−0.662913 + 0.748696i \(0.730680\pi\)
\(618\) −0.600801 + 1.29308i −0.0241678 + 0.0520152i
\(619\) 11.5565 43.1295i 0.464495 1.73352i −0.194062 0.980989i \(-0.562166\pi\)
0.658557 0.752531i \(-0.271167\pi\)
\(620\) −16.4777 1.39580i −0.661762 0.0560568i
\(621\) −1.48052 5.52536i −0.0594110 0.221725i
\(622\) −7.32073 6.12562i −0.293534 0.245615i
\(623\) 1.99405 + 11.6303i 0.0798900 + 0.465959i
\(624\) −8.05380 21.7533i −0.322410 0.870829i
\(625\) 6.61951 11.4653i 0.264780 0.458613i
\(626\) −4.17328 + 23.8604i −0.166798 + 0.953652i
\(627\) −1.27947 0.342834i −0.0510972 0.0136915i
\(628\) 6.06825 2.85009i 0.242149 0.113731i
\(629\) −21.3542 21.3542i −0.851449 0.851449i
\(630\) 2.41844 2.40229i 0.0963532 0.0957095i
\(631\) 0.677252i 0.0269610i −0.999909 0.0134805i \(-0.995709\pi\)
0.999909 0.0134805i \(-0.00429110\pi\)
\(632\) 20.7910 12.1187i 0.827022 0.482057i
\(633\) −11.0553 + 6.38279i −0.439409 + 0.253693i
\(634\) 21.4661 15.0749i 0.852529 0.598702i
\(635\) 8.18318 2.19268i 0.324740 0.0870137i
\(636\) 1.41373 + 7.89029i 0.0560582 + 0.312870i
\(637\) −22.9678 33.4711i −0.910019 1.32617i
\(638\) −0.00972469 + 0.0116220i −0.000385004 + 0.000460118i
\(639\) 7.61042 13.1816i 0.301063 0.521457i
\(640\) −4.26558 + 9.38316i −0.168612 + 0.370902i
\(641\) 20.5629 + 35.6160i 0.812185 + 1.40675i 0.911332 + 0.411673i \(0.135055\pi\)
−0.0991466 + 0.995073i \(0.531611\pi\)
\(642\) 0.482178 + 1.31911i 0.0190300 + 0.0520610i
\(643\) −12.1195 + 12.1195i −0.477945 + 0.477945i −0.904474 0.426529i \(-0.859736\pi\)
0.426529 + 0.904474i \(0.359736\pi\)
\(644\) 23.1489 + 19.5021i 0.912193 + 0.768490i
\(645\) −1.59135 1.59135i −0.0626594 0.0626594i
\(646\) 46.8317 + 21.7594i 1.84257 + 0.856111i
\(647\) −8.94599 + 5.16497i −0.351703 + 0.203056i −0.665435 0.746456i \(-0.731754\pi\)
0.313732 + 0.949512i \(0.398421\pi\)
\(648\) 0.0117090 + 2.82840i 0.000459974 + 0.111110i
\(649\) 0.967799 + 0.558759i 0.0379894 + 0.0219332i
\(650\) −34.0645 + 3.02763i −1.33612 + 0.118754i
\(651\) 13.8658 19.6043i 0.543442 0.768353i
\(652\) −13.1064 9.12336i −0.513284 0.357299i
\(653\) −0.436099 1.62754i −0.0170659 0.0636907i 0.956868 0.290524i \(-0.0938295\pi\)
−0.973934 + 0.226833i \(0.927163\pi\)
\(654\) 4.67628 26.7362i 0.182857 1.04547i
\(655\) 4.66060 + 8.07239i 0.182105 + 0.315415i
\(656\) −18.5472 3.16492i −0.724148 0.123569i
\(657\) −5.27002 −0.205603
\(658\) −14.8405 25.9046i −0.578543 1.00987i
\(659\) 17.3312 17.3312i 0.675130 0.675130i −0.283764 0.958894i \(-0.591583\pi\)
0.958894 + 0.283764i \(0.0915834\pi\)
\(660\) 0.190334 + 0.405248i 0.00740872 + 0.0157743i
\(661\) 8.84438 33.0077i 0.344007 1.28385i −0.549762 0.835321i \(-0.685282\pi\)
0.893768 0.448529i \(-0.148052\pi\)
\(662\) 20.9331 + 29.8079i 0.813588 + 1.15852i
\(663\) 34.0183 + 19.6405i 1.32116 + 0.762773i
\(664\) −42.8387 + 11.6689i −1.66246 + 0.452841i
\(665\) −4.50183 + 12.1889i −0.174574 + 0.472667i
\(666\) 0.558192 + 6.28033i 0.0216295 + 0.243358i
\(667\) 0.240951 0.0645627i 0.00932968 0.00249988i
\(668\) −20.2723 24.0246i −0.784358 0.929539i
\(669\) 2.34929 + 0.629489i 0.0908286 + 0.0243375i
\(670\) −2.01783 5.52024i −0.0779557 0.213265i
\(671\) 2.40122 0.0926982
\(672\) −8.61107 12.2413i −0.332179 0.472218i
\(673\) −28.5513 −1.10057 −0.550285 0.834977i \(-0.685481\pi\)
−0.550285 + 0.834977i \(0.685481\pi\)
\(674\) 13.4604 + 36.8240i 0.518476 + 1.41841i
\(675\) 4.02792 + 1.07928i 0.155035 + 0.0415414i
\(676\) 26.6077 + 31.5327i 1.02337 + 1.21279i
\(677\) −12.7667 + 3.42083i −0.490664 + 0.131473i −0.495664 0.868514i \(-0.665075\pi\)
0.00499978 + 0.999988i \(0.498409\pi\)
\(678\) 1.98181 + 22.2978i 0.0761109 + 0.856340i
\(679\) −12.5227 15.0682i −0.480577 0.578264i
\(680\) −4.58728 16.8408i −0.175914 0.645815i
\(681\) 12.9119 + 7.45471i 0.494786 + 0.285665i
\(682\) 1.81252 + 2.58097i 0.0694051 + 0.0988303i
\(683\) 12.2955 45.8875i 0.470475 1.75584i −0.167593 0.985856i \(-0.553599\pi\)
0.638068 0.769980i \(-0.279734\pi\)
\(684\) −4.58340 9.75872i −0.175251 0.373134i
\(685\) 0.151327 0.151327i 0.00578192 0.00578192i
\(686\) −19.8466 17.0913i −0.757746 0.652550i
\(687\) 4.35386 0.166110
\(688\) −8.06269 + 5.71214i −0.307387 + 0.217773i
\(689\) −11.6213 20.1286i −0.442735 0.766840i
\(690\) 1.26977 7.25981i 0.0483394 0.276376i
\(691\) 0.834633 + 3.11489i 0.0317509 + 0.118496i 0.979982 0.199084i \(-0.0637965\pi\)
−0.948232 + 0.317580i \(0.897130\pi\)
\(692\) 15.5495 + 10.8240i 0.591102 + 0.411468i
\(693\) −0.647363 0.0597244i −0.0245913 0.00226874i
\(694\) −11.3397 + 1.00786i −0.430448 + 0.0382579i
\(695\) −5.97796 3.45138i −0.226757 0.130918i
\(696\) −0.123342 0.000510610i −0.00467526 1.93546e-5i
\(697\) 27.5934 15.9311i 1.04518 0.603432i
\(698\) −29.0694 13.5065i −1.10029 0.511227i
\(699\) −8.56989 8.56989i −0.324143 0.324143i
\(700\) −20.7497 + 7.50600i −0.784266 + 0.283700i
\(701\) 10.4427 10.4427i 0.394415 0.394415i −0.481843 0.876258i \(-0.660032\pi\)
0.876258 + 0.481843i \(0.160032\pi\)
\(702\) −2.81559 7.70267i −0.106267 0.290719i
\(703\) −12.0169 20.8140i −0.453228 0.785013i
\(704\) 1.89450 0.524478i 0.0714015 0.0197670i
\(705\) −3.63456 + 6.29524i −0.136885 + 0.237093i
\(706\) −22.5108 + 26.9026i −0.847205 + 1.01249i
\(707\) 5.02280 2.31330i 0.188902 0.0870008i
\(708\) 1.60420 + 8.95331i 0.0602896 + 0.336486i
\(709\) −24.5700 + 6.58352i −0.922747 + 0.247249i −0.688759 0.724990i \(-0.741844\pi\)
−0.233988 + 0.972240i \(0.575178\pi\)
\(710\) 16.0485 11.2703i 0.602289 0.422967i
\(711\) 7.36841 4.25415i 0.276337 0.159543i
\(712\) −6.35255 10.8985i −0.238072 0.408439i
\(713\) 51.9159i 1.94426i
\(714\) 24.4590 + 6.64169i 0.915354 + 0.248559i
\(715\) −0.917952 0.917952i −0.0343295 0.0343295i
\(716\) −31.1140 + 14.6134i −1.16279 + 0.546128i
\(717\) 3.34588 + 0.896526i 0.124954 + 0.0334814i
\(718\) 4.04764 23.1420i 0.151057 0.863651i
\(719\) 15.8217 27.4039i 0.590048 1.02199i −0.404177 0.914681i \(-0.632442\pi\)
0.994225 0.107313i \(-0.0342246\pi\)
\(720\) −1.52183 + 3.31118i −0.0567153 + 0.123400i
\(721\) −0.450772 2.62913i −0.0167876 0.0979140i
\(722\) 10.9111 + 9.12990i 0.406070 + 0.339780i
\(723\) −1.45029 5.41255i −0.0539368 0.201295i
\(724\) −11.1521 0.944678i −0.414465 0.0351087i
\(725\) −0.0470655 + 0.175651i −0.00174797 + 0.00652350i
\(726\) −6.51896 + 14.0305i −0.241941 + 0.520719i
\(727\) 9.24889i 0.343022i −0.985182 0.171511i \(-0.945135\pi\)
0.985182 0.171511i \(-0.0548650\pi\)
\(728\) 35.5335 + 24.9121i 1.31696 + 0.923305i
\(729\) 1.00000i 0.0370370i
\(730\) −6.15770 2.86104i −0.227907 0.105892i
\(731\) 4.33075 16.1626i 0.160179 0.597795i
\(732\) 12.6042 + 14.9372i 0.465865 + 0.552094i
\(733\) 2.93011 + 10.9353i 0.108226 + 0.403906i 0.998691 0.0511461i \(-0.0162874\pi\)
−0.890465 + 0.455052i \(0.849621\pi\)
\(734\) −10.2142 + 12.2069i −0.377012 + 0.450566i
\(735\) −1.16678 + 6.26962i −0.0430372 + 0.231259i
\(736\) −30.4829 10.8573i −1.12362 0.400205i
\(737\) −0.560465 + 0.970754i −0.0206450 + 0.0357582i
\(738\) −6.55275 1.14611i −0.241210 0.0421887i
\(739\) 30.2212 + 8.09773i 1.11170 + 0.297880i 0.767522 0.641023i \(-0.221490\pi\)
0.344182 + 0.938903i \(0.388156\pi\)
\(740\) −2.75732 + 7.64123i −0.101361 + 0.280897i
\(741\) 22.1051 + 22.1051i 0.812050 + 0.812050i
\(742\) −10.5685 10.6396i −0.387982 0.390591i
\(743\) 14.5158i 0.532532i 0.963900 + 0.266266i \(0.0857900\pi\)
−0.963900 + 0.266266i \(0.914210\pi\)
\(744\) −6.54122 + 24.8228i −0.239813 + 0.910046i
\(745\) −8.92974 + 5.15559i −0.327160 + 0.188886i
\(746\) −17.6308 25.1056i −0.645510 0.919181i
\(747\) −15.1627 + 4.06284i −0.554775 + 0.148652i
\(748\) −1.90181 + 2.73208i −0.0695370 + 0.0998947i
\(749\) −2.14519 1.51725i −0.0783834 0.0554392i
\(750\) 9.06103 + 7.58182i 0.330862 + 0.276849i
\(751\) −25.0676 + 43.4183i −0.914729 + 1.58436i −0.107431 + 0.994213i \(0.534262\pi\)
−0.807298 + 0.590144i \(0.799071\pi\)
\(752\) 24.5618 + 20.3798i 0.895675 + 0.743175i
\(753\) −1.54838 2.68187i −0.0564260 0.0977327i
\(754\) 0.335900 0.122783i 0.0122328 0.00447149i
\(755\) 4.07828 4.07828i 0.148424 0.148424i
\(756\) −3.02653 4.34052i −0.110074 0.157863i
\(757\) 18.2019 + 18.2019i 0.661559 + 0.661559i 0.955747 0.294188i \(-0.0950493\pi\)
−0.294188 + 0.955747i \(0.595049\pi\)
\(758\) −1.96974 + 4.23939i −0.0715443 + 0.153982i
\(759\) −1.21727 + 0.702791i −0.0441841 + 0.0255097i
\(760\) −0.0575049 13.8908i −0.00208592 0.503871i
\(761\) 28.0441 + 16.1913i 1.01660 + 0.586933i 0.913117 0.407698i \(-0.133669\pi\)
0.103481 + 0.994631i \(0.467002\pi\)
\(762\) −1.16426 13.0993i −0.0421766 0.474538i
\(763\) 21.2418 + 46.1216i 0.769005 + 1.66972i
\(764\) −4.42386 24.6903i −0.160049 0.893263i
\(765\) −1.59719 5.96078i −0.0577464 0.215513i
\(766\) 11.8607 + 2.07448i 0.428543 + 0.0749541i
\(767\) −13.1870 22.8405i −0.476153 0.824722i
\(768\) 13.2069 + 9.03198i 0.476565 + 0.325913i
\(769\) −3.57122 −0.128782 −0.0643908 0.997925i \(-0.520510\pi\)
−0.0643908 + 0.997925i \(0.520510\pi\)
\(770\) −0.723981 0.421232i −0.0260905 0.0151801i
\(771\) −19.4459 + 19.4459i −0.700328 + 0.700328i
\(772\) −44.6396 16.1081i −1.60661 0.579743i
\(773\) −2.16206 + 8.06890i −0.0777638 + 0.290218i −0.993846 0.110773i \(-0.964667\pi\)
0.916082 + 0.400991i \(0.131334\pi\)
\(774\) −2.85893 + 2.00773i −0.102762 + 0.0721663i
\(775\) 32.7756 + 18.9230i 1.17734 + 0.679735i
\(776\) 18.1824 + 10.3975i 0.652709 + 0.373248i
\(777\) −7.53932 9.07183i −0.270472 0.325450i
\(778\) 21.1664 1.88125i 0.758851 0.0674461i
\(779\) 24.4931 6.56291i 0.877556 0.235141i
\(780\) 0.891866 10.5287i 0.0319339 0.376987i
\(781\) −3.61261 0.967997i −0.129269 0.0346377i
\(782\) 51.4662 18.8126i 1.84043 0.672738i
\(783\) −0.0436083 −0.00155843
\(784\) 26.2734 + 9.68022i 0.938337 + 0.345722i
\(785\) 3.05390 0.108998
\(786\) 13.5899 4.96758i 0.484737 0.177188i
\(787\) −5.41380 1.45062i −0.192981 0.0517091i 0.161034 0.986949i \(-0.448517\pi\)
−0.354015 + 0.935240i \(0.615184\pi\)
\(788\) 0.462679 + 0.0391928i 0.0164823 + 0.00139619i
\(789\) 5.91665 1.58536i 0.210638 0.0564404i
\(790\) 10.9191 0.970480i 0.388483 0.0345281i
\(791\) −26.7677 32.2087i −0.951749 1.14521i
\(792\) 0.670567 0.182657i 0.0238276 0.00649042i
\(793\) −49.0776 28.3349i −1.74280 1.00620i
\(794\) −11.5937 + 8.14184i −0.411444 + 0.288943i
\(795\) −0.945055 + 3.52699i −0.0335177 + 0.125090i
\(796\) 4.59517 12.7344i 0.162871 0.451357i
\(797\) 15.2112 15.2112i 0.538810 0.538810i −0.384370 0.923179i \(-0.625581\pi\)
0.923179 + 0.384370i \(0.125581\pi\)
\(798\) 17.4341 + 10.1436i 0.617160 + 0.359080i
\(799\) −54.0466 −1.91203
\(800\) 17.9653 15.2871i 0.635168 0.540481i
\(801\) −2.23000 3.86247i −0.0787931 0.136474i
\(802\) 8.52782 + 1.49155i 0.301128 + 0.0526686i
\(803\) 0.335157 + 1.25082i 0.0118274 + 0.0441405i
\(804\) −8.98064 + 1.60910i −0.316723 + 0.0567485i
\(805\) 5.76789 + 12.5236i 0.203291 + 0.441400i
\(806\) −6.58946 74.1394i −0.232104 2.61145i
\(807\) −18.4432 10.6482i −0.649231 0.374833i
\(808\) −4.16288 + 4.19749i −0.146450 + 0.147667i
\(809\) −46.2165 + 26.6831i −1.62489 + 0.938128i −0.639299 + 0.768958i \(0.720776\pi\)
−0.985587 + 0.169170i \(0.945891\pi\)
\(810\) −0.542891 + 1.16844i −0.0190752 + 0.0410548i
\(811\) −25.1259 25.1259i −0.882291 0.882291i 0.111477 0.993767i \(-0.464442\pi\)
−0.993767 + 0.111477i \(0.964442\pi\)
\(812\) 0.189283 0.131982i 0.00664252 0.00463165i
\(813\) 4.34147 4.34147i 0.152262 0.152262i
\(814\) 1.45512 0.531894i 0.0510018 0.0186429i
\(815\) −3.63712 6.29967i −0.127403 0.220668i
\(816\) −26.9781 + 2.51040i −0.944421 + 0.0878815i
\(817\) 6.65828 11.5325i 0.232944 0.403470i
\(818\) −22.6222 18.9292i −0.790967 0.661843i
\(819\) 12.5264 + 8.85970i 0.437708 + 0.309583i
\(820\) −7.03429 4.89658i −0.245648 0.170996i
\(821\) −46.6659 + 12.5041i −1.62865 + 0.436395i −0.953526 0.301309i \(-0.902576\pi\)
−0.675124 + 0.737705i \(0.735910\pi\)
\(822\) −0.190922 0.271866i −0.00665917 0.00948241i
\(823\) −28.6183 + 16.5228i −0.997571 + 0.575948i −0.907529 0.419990i \(-0.862033\pi\)
−0.0900421 + 0.995938i \(0.528700\pi\)
\(824\) 1.43605 + 2.46370i 0.0500271 + 0.0858270i
\(825\) 1.02465i 0.0356738i
\(826\) −11.9923 12.0730i −0.417267 0.420073i
\(827\) 26.8280 + 26.8280i 0.932899 + 0.932899i 0.997886 0.0649868i \(-0.0207005\pi\)
−0.0649868 + 0.997886i \(0.520701\pi\)
\(828\) −10.7614 3.88321i −0.373983 0.134951i
\(829\) 6.21128 + 1.66431i 0.215727 + 0.0578038i 0.365064 0.930983i \(-0.381047\pi\)
−0.149337 + 0.988786i \(0.547714\pi\)
\(830\) −19.9224 3.48452i −0.691517 0.120949i
\(831\) −14.5646 + 25.2266i −0.505241 + 0.875103i
\(832\) −44.9097 11.6359i −1.55696 0.403401i
\(833\) −44.7075 + 15.7948i −1.54902 + 0.547256i
\(834\) −6.87627 + 8.21782i −0.238106 + 0.284560i
\(835\) −3.70607 13.8312i −0.128254 0.478650i
\(836\) −2.02471 + 1.70848i −0.0700260 + 0.0590889i
\(837\) −2.34898 + 8.76652i −0.0811927 + 0.303015i
\(838\) 8.10404 + 3.76537i 0.279949 + 0.130073i
\(839\) 10.3142i 0.356085i 0.984023 + 0.178043i \(0.0569765\pi\)
−0.984023 + 0.178043i \(0.943024\pi\)
\(840\) −1.17989 6.71471i −0.0407101 0.231680i
\(841\) 28.9981i 0.999934i
\(842\) −0.434092 + 0.934278i −0.0149598 + 0.0321973i
\(843\) −0.656044 + 2.44839i −0.0225953 + 0.0843270i
\(844\) −2.15498 + 25.4400i −0.0741776 + 0.875682i
\(845\) 4.86427 + 18.1537i 0.167336 + 0.624507i
\(846\) 8.65399 + 7.24123i 0.297530 + 0.248959i
\(847\) −4.89108 28.5273i −0.168059 0.980208i
\(848\) 14.5670 + 6.69506i 0.500233 + 0.229909i
\(849\) 9.41619 16.3093i 0.323163 0.559735i
\(850\) −6.88228 + 39.3488i −0.236060 + 1.34965i
\(851\) −24.6341 6.60069i −0.844446 0.226269i
\(852\) −12.9413 27.5539i −0.443362 0.943981i
\(853\) 22.3537 + 22.3537i 0.765378 + 0.765378i 0.977289 0.211911i \(-0.0679688\pi\)
−0.211911 + 0.977289i \(0.567969\pi\)
\(854\) −35.2865 9.58184i −1.20748 0.327884i
\(855\) 4.91117i 0.167958i
\(856\) 2.71621 + 0.715769i 0.0928383 + 0.0244645i
\(857\) 43.4484 25.0850i 1.48417 0.856886i 0.484332 0.874884i \(-0.339063\pi\)
0.999838 + 0.0179986i \(0.00572943\pi\)
\(858\) −1.64914 + 1.15814i −0.0563007 + 0.0395381i
\(859\) −55.3438 + 14.8293i −1.88831 + 0.505970i −0.889511 + 0.456913i \(0.848955\pi\)
−0.998796 + 0.0490574i \(0.984378\pi\)
\(860\) −4.43046 + 0.793824i −0.151078 + 0.0270692i
\(861\) 11.3039 5.20614i 0.385237 0.177425i
\(862\) 32.4433 38.7729i 1.10502 1.32061i
\(863\) −0.534925 + 0.926517i −0.0182091 + 0.0315390i −0.874986 0.484148i \(-0.839130\pi\)
0.856777 + 0.515687i \(0.172463\pi\)
\(864\) 4.65610 + 3.21259i 0.158404 + 0.109295i
\(865\) 4.31510 + 7.47398i 0.146718 + 0.254123i
\(866\) −10.7486 29.4052i −0.365252 0.999229i
\(867\) 20.4229 20.4229i 0.693598 0.693598i
\(868\) −16.3363 45.1605i −0.554492 1.53285i
\(869\) −1.47832 1.47832i −0.0501484 0.0501484i
\(870\) −0.0509537 0.0236745i −0.00172749 0.000802642i
\(871\) 22.9102 13.2272i 0.776282 0.448187i
\(872\) −38.5432 38.2254i −1.30524 1.29448i
\(873\) 6.41317 + 3.70264i 0.217053 + 0.125316i
\(874\) 43.4381 3.86075i 1.46932 0.130592i
\(875\) −22.0097 2.03057i −0.744065 0.0686459i
\(876\) −6.02167 + 8.65055i −0.203453 + 0.292275i
\(877\) 3.74714 + 13.9845i 0.126532 + 0.472223i 0.999890 0.0148561i \(-0.00472900\pi\)
−0.873358 + 0.487079i \(0.838062\pi\)
\(878\) −3.00065 + 17.1559i −0.101267 + 0.578985i
\(879\) 6.69395 + 11.5943i 0.225781 + 0.391064i
\(880\) 0.882680 + 0.150622i 0.0297551 + 0.00507745i
\(881\) −48.5795 −1.63669 −0.818343 0.574730i \(-0.805107\pi\)
−0.818343 + 0.574730i \(0.805107\pi\)
\(882\) 9.27481 + 3.46090i 0.312299 + 0.116535i
\(883\) −7.27449 + 7.27449i −0.244806 + 0.244806i −0.818835 0.574029i \(-0.805380\pi\)
0.574029 + 0.818835i \(0.305380\pi\)
\(884\) 71.1093 33.3981i 2.39167 1.12330i
\(885\) −1.07238 + 4.00217i −0.0360476 + 0.134532i
\(886\) 4.28857 + 6.10677i 0.144077 + 0.205161i
\(887\) 25.4229 + 14.6779i 0.853616 + 0.492836i 0.861869 0.507130i \(-0.169294\pi\)
−0.00825303 + 0.999966i \(0.502627\pi\)
\(888\) 10.9467 + 6.25983i 0.367349 + 0.210066i
\(889\) 15.7253 + 18.9217i 0.527408 + 0.634614i
\(890\) −0.508719 5.72370i −0.0170523 0.191859i
\(891\) 0.237347 0.0635968i 0.00795141 0.00213057i
\(892\) 3.71764 3.13700i 0.124476 0.105034i
\(893\) −41.5467 11.1324i −1.39031 0.372532i
\(894\) 5.49517 + 15.0333i 0.183786 + 0.502788i
\(895\) −15.6584 −0.523403
\(896\) −29.9329 + 0.147522i −0.999988 + 0.00492838i
\(897\) 33.1723 1.10759
\(898\) 12.4829 + 34.1498i 0.416560 + 1.13959i
\(899\) −0.382293 0.102435i −0.0127502 0.00341640i
\(900\) 6.37401 5.37847i 0.212467 0.179282i
\(901\) −26.2235 + 7.02657i −0.873632 + 0.234089i
\(902\) 0.144710 + 1.62816i 0.00481832 + 0.0542119i
\(903\) 2.26438 6.13092i 0.0753538 0.204024i
\(904\) 38.8654 + 22.2250i 1.29264 + 0.739191i
\(905\) −4.41517 2.54910i −0.146765 0.0847349i
\(906\) −5.14537 7.32681i −0.170943 0.243417i
\(907\) 0.692542 2.58460i 0.0229955 0.0858203i −0.953475 0.301474i \(-0.902521\pi\)
0.976470 + 0.215653i \(0.0691881\pi\)
\(908\) 26.9902 12.6765i 0.895700 0.420685i
\(909\) −1.47793 + 1.47793i −0.0490199 + 0.0490199i
\(910\) 9.82651 + 17.1525i 0.325746 + 0.568600i
\(911\) 56.2699 1.86430 0.932152 0.362067i \(-0.117929\pi\)
0.932152 + 0.362067i \(0.117929\pi\)
\(912\) −21.2557 3.62710i −0.703846 0.120105i
\(913\) 1.92860 + 3.34044i 0.0638274 + 0.110552i
\(914\) 0.975496 5.57731i 0.0322666 0.184481i
\(915\) 2.30423 + 8.59951i 0.0761756 + 0.284291i
\(916\) 4.97484 7.14670i 0.164373 0.236134i
\(917\) −15.6313 + 22.1005i −0.516191 + 0.729824i
\(918\) −9.54177 + 0.848066i −0.314925 + 0.0279904i
\(919\) 20.0969 + 11.6029i 0.662934 + 0.382745i 0.793394 0.608708i \(-0.208312\pi\)
−0.130460 + 0.991454i \(0.541645\pi\)
\(920\) −10.4658 10.3795i −0.345048 0.342203i
\(921\) −14.4846 + 8.36267i −0.477283 + 0.275559i
\(922\) −10.5334 4.89413i −0.346899 0.161179i
\(923\) 62.4141 + 62.4141i 2.05438 + 2.05438i
\(924\) −0.837730 + 0.994380i −0.0275593 + 0.0327127i
\(925\) 13.1461 13.1461i 0.432242 0.432242i
\(926\) −3.18812 8.72183i −0.104768 0.286617i
\(927\) 0.504109 + 0.873143i 0.0165571 + 0.0286778i
\(928\) −0.140096 + 0.203045i −0.00459886 + 0.00666526i
\(929\) 8.13123 14.0837i 0.266777 0.462071i −0.701251 0.712915i \(-0.747375\pi\)
0.968028 + 0.250843i \(0.0807079\pi\)
\(930\) −7.50391 + 8.96791i −0.246063 + 0.294069i
\(931\) −37.6210 + 2.93300i −1.23298 + 0.0961250i
\(932\) −23.8593 + 4.27498i −0.781539 + 0.140031i
\(933\) −6.51969 + 1.74695i −0.213445 + 0.0571924i
\(934\) −25.1553 + 17.6657i −0.823107 + 0.578040i
\(935\) −1.31320 + 0.758174i −0.0429461 + 0.0247949i
\(936\) −15.8608 4.17960i −0.518427 0.136614i
\(937\) 27.3129i 0.892272i 0.894965 + 0.446136i \(0.147200\pi\)
−0.894965 + 0.446136i \(0.852800\pi\)
\(938\) 12.1098 12.0290i 0.395400 0.392759i
\(939\) 12.1113 + 12.1113i 0.395237 + 0.395237i
\(940\) 6.18047 + 13.1591i 0.201585 + 0.429203i
\(941\) 48.1992 + 12.9149i 1.57125 + 0.421015i 0.936203 0.351459i \(-0.114314\pi\)
0.635046 + 0.772474i \(0.280981\pi\)
\(942\) 0.816754 4.66971i 0.0266113 0.152147i
\(943\) 13.4536 23.3023i 0.438110 0.758828i
\(944\) 16.5295 + 7.59706i 0.537991 + 0.247263i
\(945\) −0.407323 2.37572i −0.0132502 0.0772820i
\(946\) 0.658347 + 0.550872i 0.0214047 + 0.0179104i
\(947\) 2.92152 + 10.9033i 0.0949366 + 0.354308i 0.997010 0.0772748i \(-0.0246219\pi\)
−0.902073 + 0.431583i \(0.857955\pi\)
\(948\) 1.43630 16.9559i 0.0466490 0.550701i
\(949\) 7.90984 29.5199i 0.256764 0.958257i
\(950\) −13.3956 + 28.8307i −0.434609 + 0.935390i
\(951\) 18.5479i 0.601456i
\(952\) 38.8496 32.5595i 1.25912 1.05526i
\(953\) 9.33432i 0.302368i 0.988506 + 0.151184i \(0.0483086\pi\)
−0.988506 + 0.151184i \(0.951691\pi\)
\(954\) 5.14037 + 2.38836i 0.166425 + 0.0773261i
\(955\) 2.95727 11.0367i 0.0956949 0.357138i
\(956\) 5.29471 4.46775i 0.171243 0.144497i
\(957\) 0.00277335 + 0.0103503i 8.96497e−5 + 0.000334577i
\(958\) 5.17779 6.18798i 0.167287 0.199924i
\(959\) 0.583011 + 0.215328i 0.0188264 + 0.00695330i
\(960\) 3.69629 + 6.28147i 0.119297 + 0.202734i
\(961\) −25.6848 + 44.4874i −0.828542 + 1.43508i
\(962\) −36.0170 6.29953i −1.16123 0.203105i
\(963\) 0.959271 + 0.257036i 0.0309121 + 0.00828287i
\(964\) −10.5416 3.80393i −0.339523 0.122516i
\(965\) −15.2859 15.2859i −0.492071 0.492071i
\(966\) 20.6924 5.47027i 0.665769 0.176003i
\(967\) 27.1548i 0.873240i 0.899646 + 0.436620i \(0.143825\pi\)
−0.899646 + 0.436620i \(0.856175\pi\)
\(968\) 15.5818 + 26.7322i 0.500817 + 0.859206i
\(969\) 31.6229 18.2575i 1.01587 0.586515i
\(970\) 5.48327 + 7.80796i 0.176057 + 0.250699i
\(971\) −16.5921 + 4.44585i −0.532467 + 0.142674i −0.515027 0.857174i \(-0.672218\pi\)
−0.0174399 + 0.999848i \(0.505552\pi\)
\(972\) 1.64146 + 1.14263i 0.0526500 + 0.0366498i
\(973\) 1.84161 19.9615i 0.0590394 0.639938i
\(974\) 41.2973 + 34.5555i 1.32325 + 1.10723i
\(975\) −12.0911 + 20.9424i −0.387225 + 0.670694i
\(976\) 38.9207 3.62171i 1.24582 0.115928i
\(977\) 18.4730 + 31.9961i 0.591003 + 1.02365i 0.994098 + 0.108489i \(0.0346012\pi\)
−0.403095 + 0.915158i \(0.632065\pi\)
\(978\) −10.6055 + 3.87668i −0.339128 + 0.123963i
\(979\) −0.774923 + 0.774923i −0.0247666 + 0.0247666i
\(980\) 8.95817 + 9.07906i 0.286158 + 0.290020i
\(981\) −13.5710 13.5710i −0.433290 0.433290i
\(982\) 4.07158 8.76309i 0.129929 0.279641i
\(983\) −10.2069 + 5.89298i −0.325551 + 0.187957i −0.653864 0.756612i \(-0.726853\pi\)
0.328313 + 0.944569i \(0.393520\pi\)
\(984\) −9.36864 + 9.44654i −0.298661 + 0.301145i
\(985\) 0.183177 + 0.105757i 0.00583649 + 0.00336970i
\(986\) −0.0369827 0.416100i −0.00117777 0.0132513i
\(987\) −21.0210 1.93936i −0.669107 0.0617304i
\(988\) 61.5425 11.0268i 1.95793 0.350810i
\(989\) −3.65727 13.6491i −0.116294 0.434017i
\(990\) 0.311851 + 0.0545442i 0.00991129 + 0.00173353i
\(991\) 8.72751 + 15.1165i 0.277238 + 0.480191i 0.970697 0.240305i \(-0.0772475\pi\)
−0.693459 + 0.720496i \(0.743914\pi\)
\(992\) 33.2715 + 39.1003i 1.05637 + 1.24144i
\(993\) 25.7556 0.817331
\(994\) 49.2254 + 28.6407i 1.56134 + 0.908428i
\(995\) 4.36062 4.36062i 0.138241 0.138241i
\(996\) −10.6563 + 29.5314i −0.337659 + 0.935737i
\(997\) 12.7338 47.5230i 0.403282 1.50507i −0.403920 0.914794i \(-0.632353\pi\)
0.807202 0.590275i \(-0.200981\pi\)
\(998\) −29.3184 + 20.5893i −0.928056 + 0.651742i
\(999\) 3.86106 + 2.22919i 0.122159 + 0.0705283i
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 336.2.bq.b.37.12 120
7.4 even 3 inner 336.2.bq.b.277.30 yes 120
16.13 even 4 inner 336.2.bq.b.205.30 yes 120
112.109 even 12 inner 336.2.bq.b.109.12 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bq.b.37.12 120 1.1 even 1 trivial
336.2.bq.b.109.12 yes 120 112.109 even 12 inner
336.2.bq.b.205.30 yes 120 16.13 even 4 inner
336.2.bq.b.277.30 yes 120 7.4 even 3 inner