Properties

Label 128.2.k.a.13.4
Level $128$
Weight $2$
Character 128.13
Analytic conductor $1.022$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.k (of order \(32\), degree \(16\), 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: \(1.02208514587\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(15\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 13.4
Character \(\chi\) \(=\) 128.13
Dual form 128.2.k.a.69.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10268 - 0.885498i) q^{2} +(-0.152748 - 0.503541i) q^{3} +(0.431788 + 1.95283i) q^{4} +(0.326146 + 3.31141i) q^{5} +(-0.277453 + 0.690500i) q^{6} +(-2.79715 + 4.18623i) q^{7} +(1.25311 - 2.53569i) q^{8} +(2.26419 - 1.51288i) q^{9} +O(q^{10})\) \(q+(-1.10268 - 0.885498i) q^{2} +(-0.152748 - 0.503541i) q^{3} +(0.431788 + 1.95283i) q^{4} +(0.326146 + 3.31141i) q^{5} +(-0.277453 + 0.690500i) q^{6} +(-2.79715 + 4.18623i) q^{7} +(1.25311 - 2.53569i) q^{8} +(2.26419 - 1.51288i) q^{9} +(2.57262 - 3.94022i) q^{10} +(0.621979 - 0.332455i) q^{11} +(0.917377 - 0.515713i) q^{12} +(-1.36543 - 0.134483i) q^{13} +(6.79124 - 2.13918i) q^{14} +(1.61762 - 0.670038i) q^{15} +(-3.62712 + 1.68642i) q^{16} +(4.49202 + 1.86065i) q^{17} +(-3.83632 - 0.336715i) q^{18} +(-1.40216 + 1.15072i) q^{19} +(-6.32582 + 2.06674i) q^{20} +(2.53520 + 0.769043i) q^{21} +(-0.980230 - 0.184171i) q^{22} +(0.653713 - 3.28644i) q^{23} +(-1.46823 - 0.243671i) q^{24} +(-5.95517 + 1.18456i) q^{25} +(1.38654 + 1.35737i) q^{26} +(-2.32792 - 1.91047i) q^{27} +(-9.38278 - 3.65480i) q^{28} +(-0.313783 + 0.587047i) q^{29} +(-2.37702 - 0.693560i) q^{30} +(4.78518 - 4.78518i) q^{31} +(5.49286 + 1.35223i) q^{32} +(-0.262411 - 0.262411i) q^{33} +(-3.30563 - 6.02937i) q^{34} +(-14.7746 - 7.89720i) q^{35} +(3.93205 + 3.76834i) q^{36} +(-3.81898 + 4.65344i) q^{37} +(2.56508 - 0.0272648i) q^{38} +(0.140848 + 0.708090i) q^{39} +(8.80542 + 3.32256i) q^{40} +(8.11985 + 1.61514i) q^{41} +(-2.11451 - 3.09292i) q^{42} +(-2.43760 + 8.03569i) q^{43} +(0.917792 + 1.07107i) q^{44} +(5.74823 + 7.00424i) q^{45} +(-3.63096 + 3.04501i) q^{46} +(2.23827 - 5.40366i) q^{47} +(1.40321 + 1.56881i) q^{48} +(-7.02169 - 16.9519i) q^{49} +(7.61555 + 3.96711i) q^{50} +(0.250771 - 2.54612i) q^{51} +(-0.326952 - 2.72452i) q^{52} +(-5.12053 - 9.57984i) q^{53} +(0.875220 + 4.16800i) q^{54} +(1.30375 + 1.95120i) q^{55} +(7.10985 + 12.3385i) q^{56} +(0.793610 + 0.530273i) q^{57} +(0.865831 - 0.369469i) q^{58} +(7.56634 - 0.745220i) q^{59} +(2.00694 + 2.86962i) q^{60} +(8.30945 - 2.52065i) q^{61} +(-9.51377 + 1.03924i) q^{62} +13.7102i q^{63} +(-4.85944 - 6.35499i) q^{64} -4.56535i q^{65} +(0.0569898 + 0.521718i) q^{66} +(2.23525 - 0.678056i) q^{67} +(-1.69395 + 9.57557i) q^{68} +(-1.75471 + 0.172824i) q^{69} +(9.29866 + 21.7909i) q^{70} +(4.06751 + 2.71782i) q^{71} +(-0.998926 - 7.63708i) q^{72} +(0.905790 + 1.35561i) q^{73} +(8.33171 - 1.74954i) q^{74} +(1.50611 + 2.81773i) q^{75} +(-2.85260 - 2.24131i) q^{76} +(-0.348037 + 3.53367i) q^{77} +(0.471703 - 0.905514i) q^{78} +(-0.578602 - 1.39687i) q^{79} +(-6.76740 - 11.4609i) q^{80} +(2.51985 - 6.08347i) q^{81} +(-7.52336 - 8.97108i) q^{82} +(-1.34512 - 1.63903i) q^{83} +(-0.407147 + 5.28288i) q^{84} +(-4.69634 + 15.4818i) q^{85} +(9.80347 - 6.70227i) q^{86} +(0.343532 + 0.0683328i) q^{87} +(-0.0635950 - 1.99375i) q^{88} +(0.138358 + 0.695573i) q^{89} +(-0.136197 - 12.8135i) q^{90} +(4.38228 - 5.33982i) q^{91} +(6.70013 - 0.142450i) q^{92} +(-3.14046 - 1.67861i) q^{93} +(-7.25301 + 3.97650i) q^{94} +(-4.26782 - 4.26782i) q^{95} +(-0.158116 - 2.97243i) q^{96} +(-1.85489 + 1.85489i) q^{97} +(-7.26818 + 24.9101i) q^{98} +(0.905313 - 1.69372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{15}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10268 0.885498i −0.779710 0.626141i
\(3\) −0.152748 0.503541i −0.0881888 0.290720i 0.901741 0.432276i \(-0.142289\pi\)
−0.989930 + 0.141556i \(0.954789\pi\)
\(4\) 0.431788 + 1.95283i 0.215894 + 0.976417i
\(5\) 0.326146 + 3.31141i 0.145857 + 1.48091i 0.737849 + 0.674966i \(0.235842\pi\)
−0.591992 + 0.805944i \(0.701658\pi\)
\(6\) −0.277453 + 0.690500i −0.113270 + 0.281895i
\(7\) −2.79715 + 4.18623i −1.05722 + 1.58225i −0.272748 + 0.962086i \(0.587932\pi\)
−0.784475 + 0.620160i \(0.787068\pi\)
\(8\) 1.25311 2.53569i 0.443041 0.896502i
\(9\) 2.26419 1.51288i 0.754729 0.504294i
\(10\) 2.57262 3.94022i 0.813533 1.24601i
\(11\) 0.621979 0.332455i 0.187534 0.100239i −0.374958 0.927042i \(-0.622343\pi\)
0.562492 + 0.826803i \(0.309843\pi\)
\(12\) 0.917377 0.515713i 0.264824 0.148874i
\(13\) −1.36543 0.134483i −0.378701 0.0372988i −0.0931240 0.995655i \(-0.529685\pi\)
−0.285577 + 0.958356i \(0.592185\pi\)
\(14\) 6.79124 2.13918i 1.81504 0.571721i
\(15\) 1.61762 0.670038i 0.417666 0.173003i
\(16\) −3.62712 + 1.68642i −0.906780 + 0.421605i
\(17\) 4.49202 + 1.86065i 1.08947 + 0.451275i 0.853823 0.520563i \(-0.174278\pi\)
0.235651 + 0.971838i \(0.424278\pi\)
\(18\) −3.83632 0.336715i −0.904229 0.0793644i
\(19\) −1.40216 + 1.15072i −0.321677 + 0.263993i −0.781348 0.624096i \(-0.785467\pi\)
0.459671 + 0.888089i \(0.347967\pi\)
\(20\) −6.32582 + 2.06674i −1.41450 + 0.462136i
\(21\) 2.53520 + 0.769043i 0.553225 + 0.167819i
\(22\) −0.980230 0.184171i −0.208986 0.0392655i
\(23\) 0.653713 3.28644i 0.136309 0.685269i −0.850835 0.525433i \(-0.823903\pi\)
0.987144 0.159836i \(-0.0510966\pi\)
\(24\) −1.46823 0.243671i −0.299702 0.0497392i
\(25\) −5.95517 + 1.18456i −1.19103 + 0.236911i
\(26\) 1.38654 + 1.35737i 0.271923 + 0.266203i
\(27\) −2.32792 1.91047i −0.448008 0.367671i
\(28\) −9.38278 3.65480i −1.77318 0.690693i
\(29\) −0.313783 + 0.587047i −0.0582681 + 0.109012i −0.909369 0.415990i \(-0.863435\pi\)
0.851101 + 0.525002i \(0.175935\pi\)
\(30\) −2.37702 0.693560i −0.433983 0.126626i
\(31\) 4.78518 4.78518i 0.859443 0.859443i −0.131829 0.991272i \(-0.542085\pi\)
0.991272 + 0.131829i \(0.0420850\pi\)
\(32\) 5.49286 + 1.35223i 0.971009 + 0.239043i
\(33\) −0.262411 0.262411i −0.0456798 0.0456798i
\(34\) −3.30563 6.02937i −0.566911 1.03403i
\(35\) −14.7746 7.89720i −2.49737 1.33487i
\(36\) 3.93205 + 3.76834i 0.655342 + 0.628056i
\(37\) −3.81898 + 4.65344i −0.627837 + 0.765021i −0.985656 0.168770i \(-0.946021\pi\)
0.357819 + 0.933791i \(0.383521\pi\)
\(38\) 2.56508 0.0272648i 0.416111 0.00442293i
\(39\) 0.140848 + 0.708090i 0.0225537 + 0.113385i
\(40\) 8.80542 + 3.32256i 1.39226 + 0.525342i
\(41\) 8.11985 + 1.61514i 1.26811 + 0.252242i 0.782895 0.622154i \(-0.213742\pi\)
0.485212 + 0.874396i \(0.338742\pi\)
\(42\) −2.11451 3.09292i −0.326276 0.477247i
\(43\) −2.43760 + 8.03569i −0.371731 + 1.22543i 0.549195 + 0.835694i \(0.314934\pi\)
−0.920926 + 0.389738i \(0.872566\pi\)
\(44\) 0.917792 + 1.07107i 0.138362 + 0.161470i
\(45\) 5.74823 + 7.00424i 0.856896 + 1.04413i
\(46\) −3.63096 + 3.04501i −0.535357 + 0.448963i
\(47\) 2.23827 5.40366i 0.326485 0.788204i −0.672363 0.740221i \(-0.734721\pi\)
0.998848 0.0479830i \(-0.0152793\pi\)
\(48\) 1.40321 + 1.56881i 0.202537 + 0.226438i
\(49\) −7.02169 16.9519i −1.00310 2.42169i
\(50\) 7.61555 + 3.96711i 1.07700 + 0.561034i
\(51\) 0.250771 2.54612i 0.0351150 0.356529i
\(52\) −0.326952 2.72452i −0.0453401 0.377823i
\(53\) −5.12053 9.57984i −0.703359 1.31589i −0.938955 0.344041i \(-0.888204\pi\)
0.235595 0.971851i \(-0.424296\pi\)
\(54\) 0.875220 + 4.16800i 0.119102 + 0.567193i
\(55\) 1.30375 + 1.95120i 0.175798 + 0.263100i
\(56\) 7.10985 + 12.3385i 0.950093 + 1.64880i
\(57\) 0.793610 + 0.530273i 0.105116 + 0.0702364i
\(58\) 0.865831 0.369469i 0.113689 0.0485136i
\(59\) 7.56634 0.745220i 0.985054 0.0970193i 0.407355 0.913270i \(-0.366451\pi\)
0.577698 + 0.816250i \(0.303951\pi\)
\(60\) 2.00694 + 2.86962i 0.259095 + 0.370466i
\(61\) 8.30945 2.52065i 1.06392 0.322736i 0.290658 0.956827i \(-0.406126\pi\)
0.773258 + 0.634091i \(0.218626\pi\)
\(62\) −9.51377 + 1.03924i −1.20825 + 0.131983i
\(63\) 13.7102i 1.72732i
\(64\) −4.85944 6.35499i −0.607430 0.794373i
\(65\) 4.56535i 0.566263i
\(66\) 0.0569898 + 0.521718i 0.00701496 + 0.0642190i
\(67\) 2.23525 0.678056i 0.273079 0.0828377i −0.150775 0.988568i \(-0.548177\pi\)
0.423854 + 0.905730i \(0.360677\pi\)
\(68\) −1.69395 + 9.57557i −0.205422 + 1.16121i
\(69\) −1.75471 + 0.172824i −0.211242 + 0.0208055i
\(70\) 9.29866 + 21.7909i 1.11140 + 2.60452i
\(71\) 4.06751 + 2.71782i 0.482724 + 0.322546i 0.773010 0.634394i \(-0.218750\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(72\) −0.998926 7.63708i −0.117725 0.900038i
\(73\) 0.905790 + 1.35561i 0.106015 + 0.158662i 0.880684 0.473705i \(-0.157084\pi\)
−0.774669 + 0.632367i \(0.782084\pi\)
\(74\) 8.33171 1.74954i 0.968542 0.203380i
\(75\) 1.50611 + 2.81773i 0.173911 + 0.325364i
\(76\) −2.85260 2.24131i −0.327215 0.257096i
\(77\) −0.348037 + 3.53367i −0.0396624 + 0.402700i
\(78\) 0.471703 0.905514i 0.0534098 0.102529i
\(79\) −0.578602 1.39687i −0.0650978 0.157160i 0.887983 0.459877i \(-0.152106\pi\)
−0.953081 + 0.302717i \(0.902106\pi\)
\(80\) −6.76740 11.4609i −0.756619 1.28136i
\(81\) 2.51985 6.08347i 0.279984 0.675941i
\(82\) −7.52336 8.97108i −0.830816 0.990690i
\(83\) −1.34512 1.63903i −0.147646 0.179907i 0.693936 0.720037i \(-0.255875\pi\)
−0.841582 + 0.540130i \(0.818375\pi\)
\(84\) −0.407147 + 5.28288i −0.0444234 + 0.576409i
\(85\) −4.69634 + 15.4818i −0.509390 + 1.67923i
\(86\) 9.80347 6.70227i 1.05714 0.722725i
\(87\) 0.343532 + 0.0683328i 0.0368305 + 0.00732604i
\(88\) −0.0635950 1.99375i −0.00677925 0.212534i
\(89\) 0.138358 + 0.695573i 0.0146659 + 0.0737306i 0.987425 0.158087i \(-0.0505327\pi\)
−0.972759 + 0.231818i \(0.925533\pi\)
\(90\) −0.136197 12.8135i −0.0143564 1.35066i
\(91\) 4.38228 5.33982i 0.459387 0.559765i
\(92\) 6.70013 0.142450i 0.698537 0.0148514i
\(93\) −3.14046 1.67861i −0.325650 0.174064i
\(94\) −7.25301 + 3.97650i −0.748091 + 0.410145i
\(95\) −4.26782 4.26782i −0.437869 0.437869i
\(96\) −0.158116 2.97243i −0.0161376 0.303372i
\(97\) −1.85489 + 1.85489i −0.188335 + 0.188335i −0.794976 0.606641i \(-0.792517\pi\)
0.606641 + 0.794976i \(0.292517\pi\)
\(98\) −7.26818 + 24.9101i −0.734197 + 2.51630i
\(99\) 0.905313 1.69372i 0.0909874 0.170225i
\(100\) −4.88461 11.1180i −0.488461 1.11180i
\(101\) −14.7200 12.0804i −1.46469 1.20204i −0.935396 0.353602i \(-0.884957\pi\)
−0.529294 0.848438i \(-0.677543\pi\)
\(102\) −2.53111 + 2.58549i −0.250617 + 0.256002i
\(103\) 10.8994 2.16803i 1.07395 0.213623i 0.373724 0.927540i \(-0.378081\pi\)
0.700230 + 0.713918i \(0.253081\pi\)
\(104\) −2.05203 + 3.29378i −0.201218 + 0.322981i
\(105\) −1.71978 + 8.64590i −0.167833 + 0.843754i
\(106\) −2.83664 + 15.0977i −0.275519 + 1.46642i
\(107\) −4.98951 1.51355i −0.482354 0.146320i 0.0397374 0.999210i \(-0.487348\pi\)
−0.522091 + 0.852890i \(0.674848\pi\)
\(108\) 2.72567 5.37096i 0.262278 0.516821i
\(109\) 3.80691 3.12425i 0.364636 0.299249i −0.434178 0.900827i \(-0.642961\pi\)
0.798814 + 0.601578i \(0.205461\pi\)
\(110\) 0.290170 3.30601i 0.0276666 0.315216i
\(111\) 2.92654 + 1.21221i 0.277775 + 0.115058i
\(112\) 3.08586 19.9011i 0.291586 1.88048i
\(113\) −8.66929 + 3.59094i −0.815538 + 0.337807i −0.751161 0.660119i \(-0.770506\pi\)
−0.0643769 + 0.997926i \(0.520506\pi\)
\(114\) −0.405539 1.28746i −0.0379822 0.120582i
\(115\) 11.0960 + 1.09286i 1.03470 + 0.101909i
\(116\) −1.28189 0.359287i −0.119021 0.0333590i
\(117\) −3.29504 + 1.76123i −0.304626 + 0.162826i
\(118\) −9.00311 5.87824i −0.828804 0.541136i
\(119\) −20.3540 + 13.6001i −1.86584 + 1.24672i
\(120\) 0.328038 4.94140i 0.0299456 0.451086i
\(121\) −5.83494 + 8.73261i −0.530449 + 0.793873i
\(122\) −11.3947 4.57855i −1.03162 0.414522i
\(123\) −0.426998 4.33539i −0.0385011 0.390909i
\(124\) 11.4108 + 7.27848i 1.02472 + 0.653627i
\(125\) −1.03529 3.41291i −0.0925995 0.305260i
\(126\) 12.1403 15.1179i 1.08155 1.34681i
\(127\) 11.1962 0.993502 0.496751 0.867893i \(-0.334526\pi\)
0.496751 + 0.867893i \(0.334526\pi\)
\(128\) −0.268937 + 11.3105i −0.0237709 + 0.999717i
\(129\) 4.41864 0.389039
\(130\) −4.04261 + 5.03411i −0.354560 + 0.441520i
\(131\) 3.96227 + 13.0619i 0.346185 + 1.14122i 0.941298 + 0.337578i \(0.109608\pi\)
−0.595112 + 0.803643i \(0.702892\pi\)
\(132\) 0.399139 0.625750i 0.0347405 0.0544645i
\(133\) −0.895137 9.08848i −0.0776182 0.788071i
\(134\) −3.06517 1.23163i −0.264791 0.106397i
\(135\) 5.56713 8.33180i 0.479142 0.717087i
\(136\) 10.3470 9.05876i 0.887250 0.776782i
\(137\) −1.18215 + 0.789890i −0.100998 + 0.0674848i −0.605044 0.796192i \(-0.706844\pi\)
0.504046 + 0.863677i \(0.331844\pi\)
\(138\) 2.08791 + 1.36322i 0.177735 + 0.116045i
\(139\) −5.48088 + 2.92959i −0.464882 + 0.248485i −0.687170 0.726496i \(-0.741147\pi\)
0.222288 + 0.974981i \(0.428647\pi\)
\(140\) 9.04242 32.2623i 0.764224 2.72666i
\(141\) −3.06285 0.301665i −0.257939 0.0254047i
\(142\) −2.07852 6.59865i −0.174425 0.553746i
\(143\) −0.893977 + 0.370297i −0.0747581 + 0.0309658i
\(144\) −5.66112 + 9.30577i −0.471760 + 0.775481i
\(145\) −2.04630 0.847604i −0.169936 0.0703897i
\(146\) 0.201597 2.29687i 0.0166843 0.190091i
\(147\) −7.46341 + 6.12506i −0.615572 + 0.505187i
\(148\) −10.7364 5.44854i −0.882526 0.447867i
\(149\) 4.11444 + 1.24810i 0.337068 + 0.102249i 0.454281 0.890858i \(-0.349896\pi\)
−0.117213 + 0.993107i \(0.537396\pi\)
\(150\) 0.834346 4.44071i 0.0681241 0.362582i
\(151\) −2.42212 + 12.1768i −0.197109 + 0.990935i 0.747880 + 0.663834i \(0.231072\pi\)
−0.944989 + 0.327101i \(0.893928\pi\)
\(152\) 1.16081 + 4.99741i 0.0941545 + 0.405343i
\(153\) 12.9857 2.58302i 1.04983 0.208825i
\(154\) 3.51283 3.58831i 0.283072 0.289154i
\(155\) 17.4064 + 14.2850i 1.39811 + 1.14740i
\(156\) −1.32197 + 0.580797i −0.105842 + 0.0465010i
\(157\) 7.47869 13.9916i 0.596864 1.11665i −0.384250 0.923229i \(-0.625540\pi\)
0.981115 0.193426i \(-0.0619599\pi\)
\(158\) −0.598914 + 2.05264i −0.0476470 + 0.163300i
\(159\) −4.04169 + 4.04169i −0.320527 + 0.320527i
\(160\) −2.68633 + 18.6302i −0.212373 + 1.47284i
\(161\) 11.9292 + 11.9292i 0.940156 + 0.940156i
\(162\) −8.16548 + 4.47677i −0.641541 + 0.351728i
\(163\) −2.10541 1.12537i −0.164909 0.0881455i 0.386878 0.922131i \(-0.373554\pi\)
−0.551786 + 0.833986i \(0.686054\pi\)
\(164\) 0.351954 + 16.5541i 0.0274830 + 1.29266i
\(165\) 0.783366 0.954534i 0.0609850 0.0743104i
\(166\) 0.0318708 + 2.99842i 0.00247365 + 0.232722i
\(167\) 3.07768 + 15.4726i 0.238158 + 1.19730i 0.895968 + 0.444118i \(0.146483\pi\)
−0.657810 + 0.753184i \(0.728517\pi\)
\(168\) 5.12693 5.46477i 0.395551 0.421616i
\(169\) −10.9039 2.16892i −0.838762 0.166840i
\(170\) 18.8876 12.9128i 1.44861 0.990364i
\(171\) −1.43384 + 4.72674i −0.109649 + 0.361463i
\(172\) −16.7449 1.29052i −1.27679 0.0984009i
\(173\) −3.82406 4.65963i −0.290738 0.354265i 0.607073 0.794646i \(-0.292343\pi\)
−0.897811 + 0.440381i \(0.854843\pi\)
\(174\) −0.318296 0.379546i −0.0241300 0.0287733i
\(175\) 11.6987 28.2431i 0.884336 2.13498i
\(176\) −1.69534 + 2.25477i −0.127791 + 0.169960i
\(177\) −1.53099 3.69613i −0.115076 0.277818i
\(178\) 0.463365 0.889508i 0.0347306 0.0666714i
\(179\) 0.907550 9.21451i 0.0678335 0.688725i −0.899789 0.436324i \(-0.856280\pi\)
0.967623 0.252400i \(-0.0812200\pi\)
\(180\) −11.1961 + 14.2497i −0.834508 + 1.06211i
\(181\) 11.1067 + 20.7792i 0.825555 + 1.54450i 0.838702 + 0.544590i \(0.183315\pi\)
−0.0131475 + 0.999914i \(0.504185\pi\)
\(182\) −9.56063 + 2.00759i −0.708681 + 0.148813i
\(183\) −2.53850 3.79913i −0.187651 0.280840i
\(184\) −7.51421 5.77587i −0.553955 0.425803i
\(185\) −16.6550 11.1285i −1.22450 0.818186i
\(186\) 1.97650 + 4.63183i 0.144924 + 0.339622i
\(187\) 3.41253 0.336104i 0.249549 0.0245784i
\(188\) 11.5189 + 2.03773i 0.840102 + 0.148617i
\(189\) 14.5092 4.40132i 1.05539 0.320149i
\(190\) 0.926876 + 8.48516i 0.0672426 + 0.615578i
\(191\) 2.09966i 0.151926i −0.997111 0.0759629i \(-0.975797\pi\)
0.997111 0.0759629i \(-0.0242030\pi\)
\(192\) −2.45773 + 3.41764i −0.177371 + 0.246647i
\(193\) 3.65943i 0.263412i −0.991289 0.131706i \(-0.957955\pi\)
0.991289 0.131706i \(-0.0420454\pi\)
\(194\) 3.68784 0.402841i 0.264772 0.0289223i
\(195\) −2.29884 + 0.697346i −0.164624 + 0.0499380i
\(196\) 30.0723 21.0318i 2.14802 1.50227i
\(197\) −3.21234 + 0.316388i −0.228870 + 0.0225417i −0.211802 0.977313i \(-0.567933\pi\)
−0.0170680 + 0.999854i \(0.505433\pi\)
\(198\) −2.49805 + 1.06597i −0.177529 + 0.0757554i
\(199\) −18.4517 12.3291i −1.30801 0.873984i −0.310936 0.950431i \(-0.600642\pi\)
−0.997074 + 0.0764472i \(0.975642\pi\)
\(200\) −4.45880 + 16.5848i −0.315285 + 1.17273i
\(201\) −0.682858 1.02197i −0.0481651 0.0720842i
\(202\) 5.53421 + 26.3552i 0.389386 + 1.85435i
\(203\) −1.57982 2.95563i −0.110881 0.207444i
\(204\) 5.08044 0.609670i 0.355702 0.0426855i
\(205\) −2.70014 + 27.4150i −0.188586 + 1.91474i
\(206\) −13.9383 7.26079i −0.971130 0.505883i
\(207\) −3.49186 8.43010i −0.242701 0.585932i
\(208\) 5.17936 1.81490i 0.359124 0.125840i
\(209\) −0.489550 + 1.18188i −0.0338629 + 0.0817522i
\(210\) 9.55229 8.01077i 0.659170 0.552796i
\(211\) 11.8024 + 14.3812i 0.812508 + 0.990044i 0.999970 + 0.00777218i \(0.00247399\pi\)
−0.187462 + 0.982272i \(0.560026\pi\)
\(212\) 16.4969 14.1360i 1.13301 0.970865i
\(213\) 0.747233 2.46330i 0.0511996 0.168782i
\(214\) 4.16156 + 6.08715i 0.284478 + 0.416109i
\(215\) −27.4045 5.45110i −1.86897 0.371762i
\(216\) −7.76150 + 3.50885i −0.528103 + 0.238747i
\(217\) 6.64700 + 33.4167i 0.451228 + 2.26847i
\(218\) −6.96431 + 0.0740250i −0.471682 + 0.00501360i
\(219\) 0.544248 0.663168i 0.0367769 0.0448128i
\(220\) −3.24743 + 3.38852i −0.218942 + 0.228454i
\(221\) −5.88329 3.14468i −0.395753 0.211534i
\(222\) −2.15361 3.92812i −0.144541 0.263638i
\(223\) −1.61455 1.61455i −0.108119 0.108119i 0.650978 0.759097i \(-0.274359\pi\)
−0.759097 + 0.650978i \(0.774359\pi\)
\(224\) −21.0251 + 19.2120i −1.40480 + 1.28365i
\(225\) −11.6915 + 11.6915i −0.779435 + 0.779435i
\(226\) 12.7392 + 3.71700i 0.847398 + 0.247251i
\(227\) 9.75042 18.2417i 0.647158 1.21075i −0.317754 0.948173i \(-0.602929\pi\)
0.964912 0.262574i \(-0.0845714\pi\)
\(228\) −0.692865 + 1.77875i −0.0458861 + 0.117801i
\(229\) −9.03968 7.41867i −0.597359 0.490240i 0.286445 0.958097i \(-0.407526\pi\)
−0.883804 + 0.467857i \(0.845026\pi\)
\(230\) −11.2675 11.0305i −0.742958 0.727330i
\(231\) 1.83251 0.364509i 0.120570 0.0239829i
\(232\) 1.09537 + 1.53129i 0.0719143 + 0.100534i
\(233\) 3.47551 17.4726i 0.227688 1.14467i −0.682633 0.730762i \(-0.739165\pi\)
0.910321 0.413904i \(-0.135835\pi\)
\(234\) 5.19293 + 0.975678i 0.339472 + 0.0637821i
\(235\) 18.6238 + 5.64945i 1.21488 + 0.368530i
\(236\) 4.72234 + 14.4540i 0.307398 + 0.940877i
\(237\) −0.615001 + 0.504718i −0.0399486 + 0.0327850i
\(238\) 34.4867 + 3.02690i 2.23544 + 0.196205i
\(239\) −16.9567 7.02371i −1.09684 0.454326i −0.240453 0.970661i \(-0.577296\pi\)
−0.856387 + 0.516335i \(0.827296\pi\)
\(240\) −4.73732 + 5.15829i −0.305793 + 0.332966i
\(241\) −9.27974 + 3.84379i −0.597760 + 0.247600i −0.660985 0.750399i \(-0.729861\pi\)
0.0632250 + 0.997999i \(0.479861\pi\)
\(242\) 14.1667 4.46241i 0.910673 0.286854i
\(243\) −12.4392 1.22515i −0.797973 0.0785935i
\(244\) 8.51032 + 15.1386i 0.544817 + 0.969149i
\(245\) 53.8445 28.7805i 3.44000 1.83872i
\(246\) −3.36813 + 5.15863i −0.214744 + 0.328902i
\(247\) 2.06929 1.38266i 0.131666 0.0879763i
\(248\) −6.13738 18.1301i −0.389724 1.15126i
\(249\) −0.619855 + 0.927679i −0.0392817 + 0.0587893i
\(250\) −1.88053 + 4.68008i −0.118935 + 0.295994i
\(251\) −0.0939938 0.954335i −0.00593284 0.0602371i 0.991762 0.128091i \(-0.0408849\pi\)
−0.997695 + 0.0678537i \(0.978385\pi\)
\(252\) −26.7737 + 5.91988i −1.68658 + 0.372917i
\(253\) −0.685996 2.26143i −0.0431282 0.142175i
\(254\) −12.3458 9.91421i −0.774643 0.622073i
\(255\) 8.51306 0.533109
\(256\) 10.3120 12.2337i 0.644499 0.764605i
\(257\) 5.88176 0.366894 0.183447 0.983030i \(-0.441274\pi\)
0.183447 + 0.983030i \(0.441274\pi\)
\(258\) −4.87233 3.91269i −0.303338 0.243594i
\(259\) −8.79812 29.0035i −0.546688 1.80219i
\(260\) 8.91538 1.97126i 0.552908 0.122253i
\(261\) 0.177669 + 1.80390i 0.0109974 + 0.111659i
\(262\) 7.19715 17.9116i 0.444641 1.10658i
\(263\) 12.0560 18.0431i 0.743405 1.11258i −0.246262 0.969203i \(-0.579202\pi\)
0.989668 0.143381i \(-0.0457975\pi\)
\(264\) −0.994220 + 0.336563i −0.0611900 + 0.0207140i
\(265\) 30.0528 20.0806i 1.84613 1.23354i
\(266\) −7.06078 + 10.8143i −0.432924 + 0.663066i
\(267\) 0.329116 0.175916i 0.0201416 0.0107659i
\(268\) 2.28928 + 4.07230i 0.139840 + 0.248755i
\(269\) 7.32312 + 0.721264i 0.446498 + 0.0439763i 0.318768 0.947833i \(-0.396731\pi\)
0.127730 + 0.991809i \(0.459231\pi\)
\(270\) −13.5165 + 4.25759i −0.822590 + 0.259109i
\(271\) −18.0769 + 7.48772i −1.09810 + 0.454846i −0.856823 0.515611i \(-0.827565\pi\)
−0.241273 + 0.970457i \(0.577565\pi\)
\(272\) −19.4309 + 0.826607i −1.17817 + 0.0501204i
\(273\) −3.35820 1.39101i −0.203248 0.0841879i
\(274\) 2.00298 + 0.175802i 0.121004 + 0.0106206i
\(275\) −3.31018 + 2.71660i −0.199611 + 0.163817i
\(276\) −1.09516 3.35203i −0.0659207 0.201769i
\(277\) −21.8104 6.61610i −1.31046 0.397523i −0.443666 0.896192i \(-0.646322\pi\)
−0.866792 + 0.498669i \(0.833822\pi\)
\(278\) 8.63778 + 1.62292i 0.518059 + 0.0973361i
\(279\) 3.59513 18.0739i 0.215235 1.08206i
\(280\) −38.5390 + 27.5678i −2.30315 + 1.64749i
\(281\) −11.3542 + 2.25849i −0.677335 + 0.134730i −0.521758 0.853093i \(-0.674724\pi\)
−0.155577 + 0.987824i \(0.549724\pi\)
\(282\) 3.11021 + 3.04479i 0.185210 + 0.181314i
\(283\) 4.70800 + 3.86376i 0.279862 + 0.229677i 0.763844 0.645401i \(-0.223310\pi\)
−0.483982 + 0.875078i \(0.660810\pi\)
\(284\) −3.55116 + 9.11669i −0.210722 + 0.540976i
\(285\) −1.49712 + 2.80092i −0.0886819 + 0.165912i
\(286\) 1.31366 + 0.383296i 0.0776786 + 0.0226648i
\(287\) −29.4738 + 29.4738i −1.73978 + 1.73978i
\(288\) 14.4826 5.24833i 0.853397 0.309261i
\(289\) 4.69536 + 4.69536i 0.276197 + 0.276197i
\(290\) 1.50585 + 2.74662i 0.0884266 + 0.161287i
\(291\) 1.21734 + 0.650683i 0.0713619 + 0.0381437i
\(292\) −2.25617 + 2.35419i −0.132032 + 0.137769i
\(293\) 2.46615 3.00501i 0.144074 0.175555i −0.695974 0.718067i \(-0.745027\pi\)
0.840048 + 0.542513i \(0.182527\pi\)
\(294\) 13.6534 0.145125i 0.796285 0.00846387i
\(295\) 4.93546 + 24.8122i 0.287354 + 1.44462i
\(296\) 7.01409 + 15.5150i 0.407686 + 0.901792i
\(297\) −2.08306 0.414347i −0.120872 0.0240429i
\(298\) −3.43170 5.01958i −0.198793 0.290776i
\(299\) −1.33457 + 4.39947i −0.0771799 + 0.254428i
\(300\) −4.85225 + 4.15785i −0.280145 + 0.240053i
\(301\) −26.8209 32.6814i −1.54593 1.88372i
\(302\) 13.4534 11.2823i 0.774154 0.649223i
\(303\) −3.83452 + 9.25735i −0.220287 + 0.531821i
\(304\) 3.14519 6.53842i 0.180389 0.375004i
\(305\) 11.0570 + 26.6940i 0.633122 + 1.52849i
\(306\) −16.6063 8.65059i −0.949318 0.494521i
\(307\) −1.36837 + 13.8933i −0.0780971 + 0.792933i 0.873753 + 0.486370i \(0.161679\pi\)
−0.951850 + 0.306564i \(0.900821\pi\)
\(308\) −7.05096 + 0.846139i −0.401766 + 0.0482133i
\(309\) −2.75656 5.15715i −0.156815 0.293380i
\(310\) −6.54422 31.1651i −0.371687 1.77006i
\(311\) −13.9422 20.8659i −0.790588 1.18320i −0.979547 0.201214i \(-0.935511\pi\)
0.188959 0.981985i \(-0.439489\pi\)
\(312\) 1.97199 + 0.530167i 0.111642 + 0.0300148i
\(313\) −3.96869 2.65179i −0.224323 0.149888i 0.438330 0.898814i \(-0.355570\pi\)
−0.662654 + 0.748926i \(0.730570\pi\)
\(314\) −20.6361 + 8.80589i −1.16456 + 0.496945i
\(315\) −45.4000 + 4.47151i −2.55800 + 0.251941i
\(316\) 2.47802 1.73306i 0.139400 0.0974925i
\(317\) 4.88695 1.48244i 0.274478 0.0832621i −0.150045 0.988679i \(-0.547942\pi\)
0.424523 + 0.905417i \(0.360442\pi\)
\(318\) 8.03559 0.877767i 0.450614 0.0492227i
\(319\) 0.469450i 0.0262842i
\(320\) 19.4591 18.1643i 1.08780 1.01541i
\(321\) 2.74361i 0.153133i
\(322\) −2.59077 23.7174i −0.144378 1.32172i
\(323\) −8.43959 + 2.56012i −0.469592 + 0.142449i
\(324\) 12.9680 + 2.29409i 0.720447 + 0.127450i
\(325\) 8.29065 0.816558i 0.459883 0.0452945i
\(326\) 1.32508 + 3.10525i 0.0733893 + 0.171984i
\(327\) −2.15468 1.43971i −0.119154 0.0796164i
\(328\) 14.2705 18.5655i 0.787959 1.02511i
\(329\) 16.3602 + 24.4847i 0.901966 + 1.34989i
\(330\) −1.70904 + 0.358873i −0.0940794 + 0.0197553i
\(331\) −12.7344 23.8244i −0.699947 1.30951i −0.940805 0.338949i \(-0.889929\pi\)
0.240858 0.970560i \(-0.422571\pi\)
\(332\) 2.61995 3.33450i 0.143788 0.183005i
\(333\) −1.60678 + 16.3139i −0.0880511 + 0.893998i
\(334\) 10.3072 19.7865i 0.563986 1.08267i
\(335\) 2.97434 + 7.18070i 0.162506 + 0.392323i
\(336\) −10.4924 + 1.48599i −0.572407 + 0.0810674i
\(337\) 2.48720 6.00462i 0.135486 0.327093i −0.841546 0.540186i \(-0.818354\pi\)
0.977032 + 0.213093i \(0.0683539\pi\)
\(338\) 10.1029 + 12.0470i 0.549525 + 0.655270i
\(339\) 3.13240 + 3.81684i 0.170128 + 0.207302i
\(340\) −32.2611 2.48634i −1.74961 0.134841i
\(341\) 1.38543 4.56714i 0.0750251 0.247324i
\(342\) 5.76658 3.94240i 0.311821 0.213180i
\(343\) 56.0391 + 11.1469i 3.02583 + 0.601874i
\(344\) 17.3214 + 16.2506i 0.933910 + 0.876173i
\(345\) −1.14458 5.75420i −0.0616222 0.309796i
\(346\) 0.0906060 + 8.52425i 0.00487101 + 0.458267i
\(347\) 17.6051 21.4519i 0.945092 1.15160i −0.0432070 0.999066i \(-0.513758\pi\)
0.988299 0.152531i \(-0.0487425\pi\)
\(348\) 0.0148903 + 0.700366i 0.000798207 + 0.0375436i
\(349\) 3.02469 + 1.61673i 0.161908 + 0.0865417i 0.550361 0.834927i \(-0.314490\pi\)
−0.388452 + 0.921469i \(0.626990\pi\)
\(350\) −37.9090 + 20.7838i −2.02632 + 1.11094i
\(351\) 2.92168 + 2.92168i 0.155948 + 0.155948i
\(352\) 3.86600 0.985066i 0.206058 0.0525042i
\(353\) −11.2283 + 11.2283i −0.597624 + 0.597624i −0.939680 0.342056i \(-0.888877\pi\)
0.342056 + 0.939680i \(0.388877\pi\)
\(354\) −1.58473 + 5.43132i −0.0842276 + 0.288672i
\(355\) −7.67324 + 14.3556i −0.407253 + 0.761917i
\(356\) −1.29860 + 0.570531i −0.0688256 + 0.0302381i
\(357\) 9.95722 + 8.17168i 0.526992 + 0.432491i
\(358\) −9.16016 + 9.35698i −0.484130 + 0.494532i
\(359\) −4.02630 + 0.800881i −0.212500 + 0.0422689i −0.300192 0.953879i \(-0.597051\pi\)
0.0876922 + 0.996148i \(0.472051\pi\)
\(360\) 24.9637 5.79866i 1.31570 0.305616i
\(361\) −3.06483 + 15.4079i −0.161307 + 0.810945i
\(362\) 6.15282 32.7477i 0.323385 1.72118i
\(363\) 5.28850 + 1.60425i 0.277574 + 0.0842012i
\(364\) 12.3200 + 6.25219i 0.645743 + 0.327704i
\(365\) −4.19357 + 3.44157i −0.219501 + 0.180140i
\(366\) −0.564981 + 6.43704i −0.0295320 + 0.336469i
\(367\) 10.5999 + 4.39063i 0.553311 + 0.229189i 0.641778 0.766890i \(-0.278197\pi\)
−0.0884674 + 0.996079i \(0.528197\pi\)
\(368\) 3.17121 + 13.0227i 0.165311 + 0.678857i
\(369\) 20.8284 8.62739i 1.08428 0.449124i
\(370\) 8.51080 + 27.0192i 0.442456 + 1.40466i
\(371\) 54.4263 + 5.36052i 2.82567 + 0.278304i
\(372\) 1.92203 6.85760i 0.0996529 0.355550i
\(373\) −23.9484 + 12.8007i −1.24000 + 0.662795i −0.955248 0.295806i \(-0.904412\pi\)
−0.284754 + 0.958601i \(0.591912\pi\)
\(374\) −4.06053 2.65117i −0.209965 0.137089i
\(375\) −1.56040 + 1.04263i −0.0805787 + 0.0538410i
\(376\) −10.8972 12.4469i −0.561980 0.641901i
\(377\) 0.507396 0.759372i 0.0261322 0.0391096i
\(378\) −19.8963 7.99465i −1.02336 0.411200i
\(379\) −2.77466 28.1716i −0.142525 1.44708i −0.754552 0.656241i \(-0.772146\pi\)
0.612027 0.790837i \(-0.290354\pi\)
\(380\) 6.49154 10.1771i 0.333009 0.522076i
\(381\) −1.71019 5.63775i −0.0876158 0.288831i
\(382\) −1.85924 + 2.31524i −0.0951270 + 0.118458i
\(383\) 4.29522 0.219475 0.109738 0.993961i \(-0.464999\pi\)
0.109738 + 0.993961i \(0.464999\pi\)
\(384\) 5.73639 1.59223i 0.292734 0.0812532i
\(385\) −11.8150 −0.602147
\(386\) −3.24042 + 4.03517i −0.164933 + 0.205385i
\(387\) 6.63787 + 21.8821i 0.337422 + 1.11233i
\(388\) −4.42321 2.82137i −0.224554 0.143233i
\(389\) 2.75229 + 27.9445i 0.139547 + 1.41684i 0.768725 + 0.639580i \(0.220892\pi\)
−0.629178 + 0.777261i \(0.716608\pi\)
\(390\) 3.15238 + 1.26667i 0.159627 + 0.0641405i
\(391\) 9.05141 13.5464i 0.457749 0.685070i
\(392\) −51.7836 3.43769i −2.61547 0.173629i
\(393\) 5.97196 3.99033i 0.301245 0.201286i
\(394\) 3.82233 + 2.49565i 0.192566 + 0.125729i
\(395\) 4.43690 2.37158i 0.223245 0.119327i
\(396\) 3.69846 + 1.03660i 0.185855 + 0.0520910i
\(397\) 20.1791 + 1.98747i 1.01276 + 0.0997482i 0.590760 0.806848i \(-0.298828\pi\)
0.422000 + 0.906596i \(0.361328\pi\)
\(398\) 9.42893 + 29.9339i 0.472630 + 1.50045i
\(399\) −4.43969 + 1.83898i −0.222263 + 0.0920642i
\(400\) 19.6025 14.3394i 0.980123 0.716972i
\(401\) 14.2384 + 5.89776i 0.711034 + 0.294520i 0.708732 0.705477i \(-0.249267\pi\)
0.00230158 + 0.999997i \(0.499267\pi\)
\(402\) −0.151980 + 1.73157i −0.00758010 + 0.0863629i
\(403\) −7.17733 + 5.89029i −0.357528 + 0.293416i
\(404\) 17.2350 33.9618i 0.857475 1.68966i
\(405\) 20.9667 + 6.36019i 1.04184 + 0.316040i
\(406\) −0.875177 + 4.65802i −0.0434343 + 0.231174i
\(407\) −0.828268 + 4.16399i −0.0410557 + 0.206401i
\(408\) −6.14194 3.82645i −0.304071 0.189437i
\(409\) −0.996038 + 0.198124i −0.0492509 + 0.00979662i −0.219654 0.975578i \(-0.570493\pi\)
0.170403 + 0.985374i \(0.445493\pi\)
\(410\) 27.2533 27.8388i 1.34594 1.37486i
\(411\) 0.578313 + 0.474609i 0.0285261 + 0.0234107i
\(412\) 8.94005 + 20.3487i 0.440445 + 1.00251i
\(413\) −18.0445 + 33.7589i −0.887913 + 1.66117i
\(414\) −3.61444 + 12.3877i −0.177640 + 0.608822i
\(415\) 4.98880 4.98880i 0.244891 0.244891i
\(416\) −7.31824 2.58507i −0.358806 0.126743i
\(417\) 2.31236 + 2.31236i 0.113237 + 0.113237i
\(418\) 1.58636 0.869732i 0.0775916 0.0425400i
\(419\) 3.58820 + 1.91793i 0.175295 + 0.0936971i 0.556711 0.830707i \(-0.312063\pi\)
−0.381415 + 0.924404i \(0.624563\pi\)
\(420\) −17.6266 + 0.374755i −0.860090 + 0.0182862i
\(421\) −6.76913 + 8.24821i −0.329907 + 0.401993i −0.911375 0.411576i \(-0.864979\pi\)
0.581468 + 0.813569i \(0.302479\pi\)
\(422\) −0.279641 26.3088i −0.0136127 1.28069i
\(423\) −3.10723 15.6211i −0.151079 0.759525i
\(424\) −30.7081 + 0.979502i −1.49132 + 0.0475688i
\(425\) −28.9548 5.75946i −1.40451 0.279375i
\(426\) −3.00520 + 2.05455i −0.145602 + 0.0995431i
\(427\) −12.6908 + 41.8359i −0.614150 + 2.02458i
\(428\) 0.801305 10.3972i 0.0387325 0.502568i
\(429\) 0.323013 + 0.393592i 0.0155952 + 0.0190028i
\(430\) 25.3914 + 30.2774i 1.22448 + 1.46011i
\(431\) −3.38606 + 8.17468i −0.163101 + 0.393760i −0.984209 0.177013i \(-0.943357\pi\)
0.821108 + 0.570773i \(0.193357\pi\)
\(432\) 11.6655 + 3.00367i 0.561256 + 0.144514i
\(433\) −12.4740 30.1149i −0.599462 1.44723i −0.874131 0.485691i \(-0.838568\pi\)
0.274668 0.961539i \(-0.411432\pi\)
\(434\) 22.2609 42.7337i 1.06856 2.05128i
\(435\) −0.114237 + 1.15986i −0.00547723 + 0.0556112i
\(436\) 7.74492 + 6.08525i 0.370914 + 0.291431i
\(437\) 2.86516 + 5.36033i 0.137059 + 0.256420i
\(438\) −1.18736 + 0.249329i −0.0567344 + 0.0119134i
\(439\) −3.41397 5.10936i −0.162940 0.243857i 0.741011 0.671493i \(-0.234346\pi\)
−0.903951 + 0.427636i \(0.859346\pi\)
\(440\) 6.58139 0.860842i 0.313755 0.0410391i
\(441\) −41.5446 27.7592i −1.97831 1.32187i
\(442\) 3.70275 + 8.67721i 0.176122 + 0.412733i
\(443\) −18.6769 + 1.83951i −0.887365 + 0.0873978i −0.531419 0.847109i \(-0.678341\pi\)
−0.355945 + 0.934507i \(0.615841\pi\)
\(444\) −1.10361 + 6.23846i −0.0523748 + 0.296064i
\(445\) −2.25821 + 0.685020i −0.107049 + 0.0324730i
\(446\) 0.350646 + 3.21001i 0.0166036 + 0.151999i
\(447\) 2.26243i 0.107009i
\(448\) 40.1960 2.56689i 1.89908 0.121274i
\(449\) 8.40638i 0.396721i −0.980129 0.198361i \(-0.936438\pi\)
0.980129 0.198361i \(-0.0635617\pi\)
\(450\) 23.2448 2.53914i 1.09577 0.119696i
\(451\) 5.58734 1.69490i 0.263098 0.0798098i
\(452\) −10.7558 15.3792i −0.505910 0.723375i
\(453\) 6.50150 0.640342i 0.305467 0.0300859i
\(454\) −26.9046 + 11.4808i −1.26269 + 0.538819i
\(455\) 19.1116 + 12.7700i 0.895966 + 0.598666i
\(456\) 2.33909 1.34786i 0.109538 0.0631193i
\(457\) −17.9435 26.8544i −0.839363 1.25620i −0.964507 0.264057i \(-0.914939\pi\)
0.125144 0.992139i \(-0.460061\pi\)
\(458\) 3.39862 + 16.1850i 0.158807 + 0.756276i
\(459\) −6.90232 12.9133i −0.322173 0.602743i
\(460\) 2.65693 + 22.1404i 0.123880 + 1.03230i
\(461\) 2.07673 21.0854i 0.0967231 0.982046i −0.817253 0.576279i \(-0.804504\pi\)
0.913976 0.405767i \(-0.132996\pi\)
\(462\) −2.34344 1.22075i −0.109027 0.0567944i
\(463\) 15.0941 + 36.4405i 0.701484 + 1.69353i 0.720256 + 0.693708i \(0.244024\pi\)
−0.0187726 + 0.999824i \(0.505976\pi\)
\(464\) 0.148122 2.65846i 0.00687638 0.123416i
\(465\) 4.53433 10.9468i 0.210274 0.507647i
\(466\) −19.3043 + 16.1890i −0.894253 + 0.749942i
\(467\) 16.0077 + 19.5054i 0.740747 + 0.902602i 0.997966 0.0637506i \(-0.0203062\pi\)
−0.257219 + 0.966353i \(0.582806\pi\)
\(468\) −4.86215 5.67418i −0.224753 0.262289i
\(469\) −3.41383 + 11.2539i −0.157636 + 0.519657i
\(470\) −15.5334 22.7208i −0.716501 1.04803i
\(471\) −8.18772 1.62864i −0.377270 0.0750437i
\(472\) 7.59180 20.1197i 0.349441 0.926086i
\(473\) 1.15537 + 5.80843i 0.0531239 + 0.267072i
\(474\) 1.12507 0.0119586i 0.0516763 0.000549278i
\(475\) 6.98698 8.51366i 0.320585 0.390634i
\(476\) −35.3473 33.8755i −1.62014 1.55268i
\(477\) −26.0870 13.9438i −1.19444 0.638442i
\(478\) 12.4783 + 22.7600i 0.570744 + 1.04102i
\(479\) −9.89404 9.89404i −0.452070 0.452070i 0.443971 0.896041i \(-0.353569\pi\)
−0.896041 + 0.443971i \(0.853569\pi\)
\(480\) 9.79138 1.49303i 0.446913 0.0681473i
\(481\) 5.84035 5.84035i 0.266297 0.266297i
\(482\) 13.6362 + 3.97873i 0.621112 + 0.181226i
\(483\) 4.18470 7.82902i 0.190410 0.356233i
\(484\) −19.5728 7.62404i −0.889672 0.346547i
\(485\) −6.74727 5.53734i −0.306378 0.251438i
\(486\) 12.6315 + 12.3658i 0.572976 + 0.560924i
\(487\) −3.77353 + 0.750601i −0.170995 + 0.0340130i −0.279845 0.960045i \(-0.590283\pi\)
0.108850 + 0.994058i \(0.465283\pi\)
\(488\) 4.02107 24.2288i 0.182025 1.09679i
\(489\) −0.245072 + 1.23206i −0.0110825 + 0.0557156i
\(490\) −84.8581 15.9436i −3.83350 0.720260i
\(491\) −36.8156 11.1679i −1.66146 0.503999i −0.686643 0.726995i \(-0.740916\pi\)
−0.974819 + 0.222996i \(0.928416\pi\)
\(492\) 8.28191 2.70582i 0.373378 0.121988i
\(493\) −2.50181 + 2.05318i −0.112676 + 0.0924708i
\(494\) −3.50610 0.307731i −0.157747 0.0138455i
\(495\) 5.90388 + 2.44547i 0.265360 + 0.109916i
\(496\) −9.28660 + 25.4262i −0.416981 + 1.14167i
\(497\) −22.7549 + 9.42537i −1.02069 + 0.422786i
\(498\) 1.50496 0.474049i 0.0674387 0.0212426i
\(499\) −17.3609 1.70990i −0.777179 0.0765455i −0.298354 0.954455i \(-0.596437\pi\)
−0.478826 + 0.877910i \(0.658937\pi\)
\(500\) 6.21781 3.49541i 0.278069 0.156319i
\(501\) 7.32096 3.91313i 0.327076 0.174826i
\(502\) −0.741417 + 1.13555i −0.0330911 + 0.0506822i
\(503\) 5.53508 3.69842i 0.246797 0.164904i −0.426019 0.904714i \(-0.640084\pi\)
0.672816 + 0.739810i \(0.265084\pi\)
\(504\) 34.7647 + 17.1803i 1.54854 + 0.765272i
\(505\) 35.2022 52.6838i 1.56648 2.34440i
\(506\) −1.24606 + 3.10107i −0.0553939 + 0.137859i
\(507\) 0.573403 + 5.82186i 0.0254657 + 0.258558i
\(508\) 4.83438 + 21.8643i 0.214491 + 0.970072i
\(509\) −3.85818 12.7187i −0.171011 0.563747i −0.999990 0.00446778i \(-0.998578\pi\)
0.828979 0.559280i \(-0.188922\pi\)
\(510\) −9.38715 7.53830i −0.415670 0.333801i
\(511\) −8.20852 −0.363124
\(512\) −22.2037 + 4.35855i −0.981273 + 0.192622i
\(513\) 5.46252 0.241176
\(514\) −6.48568 5.20829i −0.286071 0.229728i
\(515\) 10.7341 + 35.3855i 0.472999 + 1.55927i
\(516\) 1.90791 + 8.62887i 0.0839912 + 0.379865i
\(517\) −0.404316 4.10509i −0.0177818 0.180542i
\(518\) −15.9811 + 39.7722i −0.702168 + 1.74749i
\(519\) −1.76220 + 2.63732i −0.0773519 + 0.115765i
\(520\) −11.5763 5.72088i −0.507655 0.250877i
\(521\) 12.9212 8.63367i 0.566088 0.378248i −0.239345 0.970935i \(-0.576933\pi\)
0.805433 + 0.592687i \(0.201933\pi\)
\(522\) 1.40144 2.14644i 0.0613394 0.0939473i
\(523\) 11.6761 6.24101i 0.510560 0.272900i −0.195936 0.980617i \(-0.562775\pi\)
0.706497 + 0.707716i \(0.250275\pi\)
\(524\) −23.7968 + 13.3776i −1.03957 + 0.584404i
\(525\) −16.0085 1.57670i −0.698668 0.0688128i
\(526\) −29.2710 + 9.22011i −1.27628 + 0.402016i
\(527\) 30.3987 12.5915i 1.32419 0.548496i
\(528\) 1.39433 + 0.509260i 0.0606803 + 0.0221627i
\(529\) 10.8759 + 4.50495i 0.472866 + 0.195867i
\(530\) −50.9198 4.46925i −2.21182 0.194132i
\(531\) 16.0042 13.1343i 0.694522 0.569980i
\(532\) 17.3618 5.67235i 0.752728 0.245927i
\(533\) −10.8698 3.29733i −0.470825 0.142823i
\(534\) −0.518681 0.0974530i −0.0224455 0.00421720i
\(535\) 3.38468 17.0160i 0.146333 0.735664i
\(536\) 1.08167 6.51758i 0.0467211 0.281517i
\(537\) −4.77851 + 0.950505i −0.206208 + 0.0410173i
\(538\) −7.43635 7.27993i −0.320604 0.313860i
\(539\) −10.0031 8.20931i −0.430863 0.353600i
\(540\) 18.6744 + 7.27411i 0.803620 + 0.313028i
\(541\) −14.5357 + 27.1944i −0.624938 + 1.16918i 0.347865 + 0.937545i \(0.386907\pi\)
−0.972803 + 0.231633i \(0.925593\pi\)
\(542\) 26.5634 + 7.75057i 1.14099 + 0.332916i
\(543\) 8.76665 8.76665i 0.376213 0.376213i
\(544\) 22.1580 + 16.2946i 0.950015 + 0.698623i
\(545\) 11.5873 + 11.5873i 0.496345 + 0.496345i
\(546\) 2.47127 + 4.50751i 0.105760 + 0.192904i
\(547\) −32.0670 17.1401i −1.37108 0.732860i −0.388988 0.921243i \(-0.627175\pi\)
−0.982096 + 0.188383i \(0.939675\pi\)
\(548\) −2.05296 1.96748i −0.0876982 0.0840468i
\(549\) 15.0007 18.2784i 0.640215 0.780104i
\(550\) 6.05560 0.0643662i 0.258212 0.00274458i
\(551\) −0.235554 1.18421i −0.0100349 0.0504490i
\(552\) −1.76061 + 4.66596i −0.0749366 + 0.198597i
\(553\) 7.46605 + 1.48509i 0.317489 + 0.0631524i
\(554\) 18.1912 + 26.6084i 0.772871 + 1.13048i
\(555\) −3.05966 + 10.0863i −0.129875 + 0.428142i
\(556\) −8.08758 9.43828i −0.342990 0.400272i
\(557\) 10.5461 + 12.8504i 0.446851 + 0.544490i 0.946909 0.321502i \(-0.104188\pi\)
−0.500057 + 0.865992i \(0.666688\pi\)
\(558\) −19.9687 + 16.7462i −0.845343 + 0.708924i
\(559\) 4.40903 10.6443i 0.186482 0.450207i
\(560\) 66.9073 + 3.72788i 2.82735 + 0.157532i
\(561\) −0.690497 1.66701i −0.0291528 0.0703811i
\(562\) 14.5199 + 7.56374i 0.612485 + 0.319057i
\(563\) 2.99062 30.3642i 0.126039 1.27970i −0.699204 0.714922i \(-0.746462\pi\)
0.825243 0.564777i \(-0.191038\pi\)
\(564\) −0.733401 6.11150i −0.0308818 0.257340i
\(565\) −14.7185 27.5364i −0.619214 1.15847i
\(566\) −1.77005 8.42940i −0.0744008 0.354314i
\(567\) 18.4184 + 27.5650i 0.773499 + 1.15762i
\(568\) 11.9886 6.90821i 0.503030 0.289862i
\(569\) 27.1855 + 18.1648i 1.13968 + 0.761507i 0.974418 0.224744i \(-0.0721544\pi\)
0.165258 + 0.986250i \(0.447154\pi\)
\(570\) 4.13105 1.76281i 0.173031 0.0738359i
\(571\) 17.8071 1.75385i 0.745205 0.0733963i 0.281715 0.959498i \(-0.409097\pi\)
0.463490 + 0.886102i \(0.346597\pi\)
\(572\) −1.10914 1.58590i −0.0463753 0.0663097i
\(573\) −1.05726 + 0.320717i −0.0441678 + 0.0133981i
\(574\) 58.5990 6.40105i 2.44587 0.267175i
\(575\) 20.3456i 0.848472i
\(576\) −20.6170 7.03712i −0.859043 0.293213i
\(577\) 19.6083i 0.816306i 0.912914 + 0.408153i \(0.133827\pi\)
−0.912914 + 0.408153i \(0.866173\pi\)
\(578\) −1.01973 9.33518i −0.0424151 0.388292i
\(579\) −1.84267 + 0.558969i −0.0765789 + 0.0232300i
\(580\) 0.771664 4.36206i 0.0320416 0.181125i
\(581\) 10.6238 1.04636i 0.440751 0.0434102i
\(582\) −0.766156 1.79545i −0.0317582 0.0744237i
\(583\) −6.36973 4.25612i −0.263807 0.176270i
\(584\) 4.57246 0.598075i 0.189210 0.0247485i
\(585\) −6.90684 10.3368i −0.285563 0.427375i
\(586\) −5.38030 + 1.12979i −0.222258 + 0.0466710i
\(587\) −1.72772 3.23234i −0.0713107 0.133413i 0.843740 0.536753i \(-0.180349\pi\)
−0.915050 + 0.403340i \(0.867849\pi\)
\(588\) −15.1838 11.9301i −0.626171 0.491988i
\(589\) −1.20317 + 12.2160i −0.0495756 + 0.503350i
\(590\) 16.5290 31.7302i 0.680487 1.30631i
\(591\) 0.649992 + 1.56922i 0.0267371 + 0.0645491i
\(592\) 6.00425 23.3190i 0.246773 0.958405i
\(593\) −2.08184 + 5.02600i −0.0854909 + 0.206393i −0.960843 0.277092i \(-0.910629\pi\)
0.875353 + 0.483485i \(0.160629\pi\)
\(594\) 1.93004 + 2.30144i 0.0791905 + 0.0944292i
\(595\) −51.6739 62.9648i −2.11842 2.58130i
\(596\) −0.660771 + 8.57373i −0.0270662 + 0.351194i
\(597\) −3.38973 + 11.1744i −0.138732 + 0.457339i
\(598\) 5.36732 3.66944i 0.219486 0.150054i
\(599\) 47.5331 + 9.45491i 1.94215 + 0.386317i 0.998460 + 0.0554825i \(0.0176697\pi\)
0.943689 + 0.330835i \(0.107330\pi\)
\(600\) 9.03222 0.288103i 0.368739 0.0117617i
\(601\) −3.73405 18.7723i −0.152315 0.765739i −0.979125 0.203258i \(-0.934847\pi\)
0.826810 0.562481i \(-0.190153\pi\)
\(602\) 0.635486 + 59.7868i 0.0259005 + 2.43673i
\(603\) 4.03521 4.91692i 0.164326 0.200232i
\(604\) −24.8251 + 0.527802i −1.01012 + 0.0214760i
\(605\) −30.8203 16.4738i −1.25302 0.669755i
\(606\) 12.4256 6.81239i 0.504755 0.276735i
\(607\) −5.47353 5.47353i −0.222164 0.222164i 0.587245 0.809409i \(-0.300212\pi\)
−0.809409 + 0.587245i \(0.800212\pi\)
\(608\) −9.25788 + 4.42470i −0.375457 + 0.179445i
\(609\) −1.24697 + 1.24697i −0.0505297 + 0.0505297i
\(610\) 11.4451 39.2257i 0.463401 1.58820i
\(611\) −3.78289 + 7.07729i −0.153039 + 0.286316i
\(612\) 10.6513 + 24.2436i 0.430552 + 0.979990i
\(613\) −10.2489 8.41105i −0.413949 0.339719i 0.404256 0.914646i \(-0.367531\pi\)
−0.818205 + 0.574927i \(0.805031\pi\)
\(614\) 13.8114 14.1081i 0.557382 0.569358i
\(615\) 14.2170 2.82794i 0.573285 0.114033i
\(616\) 8.52417 + 5.31059i 0.343449 + 0.213970i
\(617\) −3.42804 + 17.2339i −0.138008 + 0.693811i 0.848382 + 0.529385i \(0.177577\pi\)
−0.986389 + 0.164426i \(0.947423\pi\)
\(618\) −1.52706 + 8.12759i −0.0614273 + 0.326940i
\(619\) 3.47145 + 1.05305i 0.139529 + 0.0423258i 0.359277 0.933231i \(-0.383023\pi\)
−0.219748 + 0.975557i \(0.570523\pi\)
\(620\) −20.3805 + 40.1599i −0.818499 + 1.61286i
\(621\) −7.80044 + 6.40165i −0.313021 + 0.256890i
\(622\) −3.10304 + 35.3541i −0.124421 + 1.41757i
\(623\) −3.29884 1.36642i −0.132165 0.0547446i
\(624\) −1.70501 2.33080i −0.0682550 0.0933066i
\(625\) −17.0843 + 7.07657i −0.683374 + 0.283063i
\(626\) 2.02802 + 6.43833i 0.0810560 + 0.257327i
\(627\) 0.669901 + 0.0659795i 0.0267533 + 0.00263497i
\(628\) 30.5526 + 8.56322i 1.21918 + 0.341710i
\(629\) −25.8134 + 13.7975i −1.02925 + 0.550144i
\(630\) 54.0210 + 35.2710i 2.15225 + 1.40523i
\(631\) −24.3971 + 16.3016i −0.971233 + 0.648957i −0.936584 0.350442i \(-0.886031\pi\)
−0.0346487 + 0.999400i \(0.511031\pi\)
\(632\) −4.26708 0.283273i −0.169735 0.0112680i
\(633\) 5.43875 8.13967i 0.216171 0.323523i
\(634\) −6.70142 2.69273i −0.266147 0.106942i
\(635\) 3.65160 + 37.0753i 0.144909 + 1.47129i
\(636\) −9.63791 6.14760i −0.382168 0.243768i
\(637\) 7.30787 + 24.0908i 0.289548 + 0.954512i
\(638\) 0.415697 0.517651i 0.0164576 0.0204940i
\(639\) 13.3213 0.526984
\(640\) −37.5415 + 2.79831i −1.48396 + 0.110613i
\(641\) 13.6451 0.538950 0.269475 0.963007i \(-0.413150\pi\)
0.269475 + 0.963007i \(0.413150\pi\)
\(642\) 2.42946 3.02531i 0.0958832 0.119400i
\(643\) 1.36401 + 4.49655i 0.0537915 + 0.177327i 0.979720 0.200373i \(-0.0642153\pi\)
−0.925928 + 0.377699i \(0.876715\pi\)
\(644\) −18.1449 + 28.4467i −0.715010 + 1.12096i
\(645\) 1.44112 + 14.6319i 0.0567441 + 0.576132i
\(646\) 11.5731 + 4.65026i 0.455338 + 0.182962i
\(647\) −2.61226 + 3.90952i −0.102698 + 0.153699i −0.879260 0.476343i \(-0.841962\pi\)
0.776561 + 0.630042i \(0.216962\pi\)
\(648\) −12.2681 14.0128i −0.481938 0.550475i
\(649\) 4.45836 2.97898i 0.175006 0.116935i
\(650\) −9.86496 6.44095i −0.386936 0.252635i
\(651\) 15.8114 8.45136i 0.619697 0.331235i
\(652\) 1.28856 4.59744i 0.0504640 0.180050i
\(653\) −5.92552 0.583613i −0.231883 0.0228385i −0.0185921 0.999827i \(-0.505918\pi\)
−0.213291 + 0.976989i \(0.568418\pi\)
\(654\) 1.10105 + 3.49551i 0.0430547 + 0.136685i
\(655\) −41.9610 + 17.3808i −1.63955 + 0.679124i
\(656\) −32.1755 + 7.83517i −1.25624 + 0.305912i
\(657\) 4.10175 + 1.69900i 0.160025 + 0.0662844i
\(658\) 3.64121 41.4856i 0.141949 1.61728i
\(659\) −28.8837 + 23.7042i −1.12515 + 0.923385i −0.997654 0.0684546i \(-0.978193\pi\)
−0.127493 + 0.991839i \(0.540693\pi\)
\(660\) 2.20229 + 1.11763i 0.0857242 + 0.0435036i
\(661\) 29.6848 + 9.00480i 1.15461 + 0.350246i 0.808814 0.588065i \(-0.200110\pi\)
0.345793 + 0.938311i \(0.387610\pi\)
\(662\) −7.05454 + 37.5469i −0.274182 + 1.45930i
\(663\) −0.684820 + 3.44282i −0.0265962 + 0.133708i
\(664\) −5.84164 + 1.35692i −0.226700 + 0.0526586i
\(665\) 29.8038 5.92834i 1.15574 0.229891i
\(666\) 16.2177 16.5662i 0.628424 0.641926i
\(667\) 1.72417 + 1.41499i 0.0667601 + 0.0547886i
\(668\) −28.8864 + 12.6911i −1.11765 + 0.491032i
\(669\) −0.566375 + 1.05961i −0.0218973 + 0.0409670i
\(670\) 3.07876 10.5518i 0.118943 0.407650i
\(671\) 4.33031 4.33031i 0.167170 0.167170i
\(672\) 12.8855 + 7.65242i 0.497070 + 0.295198i
\(673\) −29.1649 29.1649i −1.12423 1.12423i −0.991099 0.133126i \(-0.957498\pi\)
−0.133126 0.991099i \(-0.542502\pi\)
\(674\) −8.05965 + 4.41875i −0.310446 + 0.170204i
\(675\) 16.1262 + 8.61964i 0.620698 + 0.331770i
\(676\) −0.472628 22.2300i −0.0181780 0.855001i
\(677\) 23.6997 28.8781i 0.910852 1.10988i −0.0827082 0.996574i \(-0.526357\pi\)
0.993560 0.113303i \(-0.0361431\pi\)
\(678\) −0.0742180 6.98246i −0.00285033 0.268160i
\(679\) −2.57659 12.9534i −0.0988805 0.497106i
\(680\) 33.3719 + 31.3088i 1.27976 + 1.20064i
\(681\) −10.6748 2.12335i −0.409060 0.0813671i
\(682\) −5.57187 + 3.80928i −0.213358 + 0.145865i
\(683\) 12.3113 40.5849i 0.471078 1.55294i −0.323775 0.946134i \(-0.604952\pi\)
0.794853 0.606802i \(-0.207548\pi\)
\(684\) −9.84965 0.759105i −0.376611 0.0290251i
\(685\) −3.00121 3.65698i −0.114670 0.139726i
\(686\) −51.9224 61.9139i −1.98241 2.36388i
\(687\) −2.35482 + 5.68503i −0.0898419 + 0.216898i
\(688\) −4.71008 33.2572i −0.179570 1.26792i
\(689\) 5.70339 + 13.7692i 0.217282 + 0.524564i
\(690\) −3.83323 + 7.35854i −0.145929 + 0.280135i
\(691\) −0.924158 + 9.38313i −0.0351566 + 0.356951i 0.961472 + 0.274904i \(0.0886459\pi\)
−0.996628 + 0.0820475i \(0.973854\pi\)
\(692\) 7.44830 9.47972i 0.283142 0.360365i
\(693\) 4.55801 + 8.52744i 0.173145 + 0.323931i
\(694\) −38.4083 + 8.06519i −1.45796 + 0.306150i
\(695\) −11.4887 17.1940i −0.435789 0.652205i
\(696\) 0.603754 0.785462i 0.0228852 0.0297729i
\(697\) 33.4693 + 22.3635i 1.26774 + 0.847076i
\(698\) −1.90364 4.46109i −0.0720540 0.168855i
\(699\) −9.32903 + 0.918829i −0.352856 + 0.0347533i
\(700\) 60.2054 + 10.6505i 2.27555 + 0.402553i
\(701\) −8.24589 + 2.50136i −0.311443 + 0.0944752i −0.442137 0.896948i \(-0.645779\pi\)
0.130694 + 0.991423i \(0.458279\pi\)
\(702\) −0.634524 5.80880i −0.0239486 0.219239i
\(703\) 10.9194i 0.411834i
\(704\) −5.13522 2.33713i −0.193541 0.0880837i
\(705\) 10.2408i 0.385689i
\(706\) 22.3239 2.43855i 0.840170 0.0917759i
\(707\) 91.7450 27.8306i 3.45043 1.04668i
\(708\) 6.55687 4.58571i 0.246422 0.172342i
\(709\) 44.9459 4.42679i 1.68798 0.166251i 0.792052 0.610453i \(-0.209013\pi\)
0.895927 + 0.444202i \(0.146513\pi\)
\(710\) 21.1730 9.03496i 0.794607 0.339076i
\(711\) −3.42336 2.28742i −0.128386 0.0857848i
\(712\) 1.93714 + 0.520795i 0.0725972 + 0.0195176i
\(713\) −12.5981 18.8543i −0.471801 0.706100i
\(714\) −3.74358 17.8278i −0.140100 0.667189i
\(715\) −1.51777 2.83956i −0.0567616 0.106193i
\(716\) 18.3863 2.20642i 0.687127 0.0824577i
\(717\) −0.946627 + 9.61127i −0.0353524 + 0.358939i
\(718\) 5.14888 + 2.68217i 0.192155 + 0.100098i
\(719\) 9.66284 + 23.3282i 0.360363 + 0.869994i 0.995247 + 0.0973857i \(0.0310481\pi\)
−0.634884 + 0.772608i \(0.718952\pi\)
\(720\) −32.6616 15.7113i −1.21723 0.585525i
\(721\) −21.4115 + 51.6918i −0.797405 + 1.92510i
\(722\) 17.0232 14.2761i 0.633538 0.531300i
\(723\) 3.35296 + 4.08560i 0.124698 + 0.151945i
\(724\) −35.7825 + 30.6617i −1.32985 + 1.13953i
\(725\) 1.17324 3.86766i 0.0435731 0.143641i
\(726\) −4.41094 6.45192i −0.163705 0.239453i
\(727\) −11.9804 2.38305i −0.444329 0.0883825i −0.0321449 0.999483i \(-0.510234\pi\)
−0.412184 + 0.911101i \(0.635234\pi\)
\(728\) −8.04866 17.8035i −0.298303 0.659840i
\(729\) −2.57069 12.9238i −0.0952109 0.478658i
\(730\) 7.67165 0.0815435i 0.283941 0.00301806i
\(731\) −25.9014 + 31.5609i −0.957997 + 1.16732i
\(732\) 6.32298 6.59768i 0.233704 0.243857i
\(733\) 24.3012 + 12.9893i 0.897585 + 0.479769i 0.854588 0.519306i \(-0.173809\pi\)
0.0429968 + 0.999075i \(0.486309\pi\)
\(734\) −7.80038 14.2276i −0.287917 0.525152i
\(735\) −22.7168 22.7168i −0.837921 0.837921i
\(736\) 8.03477 17.1679i 0.296166 0.632819i
\(737\) 1.16486 1.16486i 0.0429081 0.0429081i
\(738\) −30.6065 8.93026i −1.12664 0.328727i
\(739\) −12.7995 + 23.9461i −0.470836 + 0.880872i 0.528651 + 0.848839i \(0.322698\pi\)
−0.999487 + 0.0320329i \(0.989802\pi\)
\(740\) 14.5407 37.3297i 0.534528 1.37227i
\(741\) −1.01230 0.830776i −0.0371879 0.0305193i
\(742\) −55.2678 54.1053i −2.02895 1.98627i
\(743\) −22.2732 + 4.43041i −0.817124 + 0.162536i −0.585920 0.810369i \(-0.699267\pi\)
−0.231205 + 0.972905i \(0.574267\pi\)
\(744\) −8.19177 + 5.85975i −0.300325 + 0.214829i
\(745\) −2.79108 + 14.0317i −0.102257 + 0.514081i
\(746\) 37.7423 + 7.09125i 1.38184 + 0.259629i
\(747\) −5.52525 1.67607i −0.202158 0.0613241i
\(748\) 2.12984 + 6.51897i 0.0778747 + 0.238357i
\(749\) 20.2925 16.6536i 0.741470 0.608509i
\(750\) 2.64386 + 0.232052i 0.0965401 + 0.00847335i
\(751\) −6.48123 2.68461i −0.236503 0.0979629i 0.261284 0.965262i \(-0.415854\pi\)
−0.497787 + 0.867299i \(0.665854\pi\)
\(752\) 0.994365 + 23.3744i 0.0362608 + 0.852375i
\(753\) −0.466190 + 0.193102i −0.0169889 + 0.00703703i
\(754\) −1.23192 + 0.388043i −0.0448637 + 0.0141317i
\(755\) −41.1125 4.04922i −1.49624 0.147366i
\(756\) 14.8599 + 26.4336i 0.540451 + 0.961382i
\(757\) 9.59534 5.12881i 0.348748 0.186410i −0.287716 0.957716i \(-0.592896\pi\)
0.636465 + 0.771306i \(0.280396\pi\)
\(758\) −21.8863 + 33.5211i −0.794947 + 1.21754i
\(759\) −1.03394 + 0.690854i −0.0375295 + 0.0250764i
\(760\) −16.1699 + 5.47382i −0.586544 + 0.198556i
\(761\) −9.24873 + 13.8417i −0.335266 + 0.501761i −0.960350 0.278796i \(-0.910065\pi\)
0.625084 + 0.780557i \(0.285065\pi\)
\(762\) −3.10642 + 7.73098i −0.112534 + 0.280064i
\(763\) 2.43033 + 24.6756i 0.0879840 + 0.893317i
\(764\) 4.10028 0.906605i 0.148343 0.0327998i
\(765\) 12.7887 + 42.1586i 0.462376 + 1.52425i
\(766\) −4.73623 3.80340i −0.171127 0.137423i
\(767\) −10.4315 −0.376660
\(768\) −7.73529 3.32384i −0.279123 0.119939i
\(769\) 0.795075 0.0286711 0.0143356 0.999897i \(-0.495437\pi\)
0.0143356 + 0.999897i \(0.495437\pi\)
\(770\) 13.0281 + 10.4621i 0.469500 + 0.377029i
\(771\) −0.898425 2.96171i −0.0323560 0.106663i
\(772\) 7.14626 1.58010i 0.257200 0.0568690i
\(773\) 4.30443 + 43.7036i 0.154820 + 1.57191i 0.687875 + 0.725829i \(0.258544\pi\)
−0.533056 + 0.846080i \(0.678956\pi\)
\(774\) 12.0571 30.0067i 0.433385 1.07857i
\(775\) −22.8282 + 34.1649i −0.820015 + 1.22724i
\(776\) 2.37905 + 7.02780i 0.0854028 + 0.252283i
\(777\) −13.2606 + 8.86043i −0.475720 + 0.317866i
\(778\) 21.7099 33.2508i 0.778337 1.19210i
\(779\) −13.2439 + 7.07899i −0.474511 + 0.253631i
\(780\) −2.35441 4.18815i −0.0843015 0.149960i
\(781\) 3.43346 + 0.338166i 0.122859 + 0.0121005i
\(782\) −21.9761 + 6.92227i −0.785862 + 0.247540i
\(783\) 1.85200 0.767124i 0.0661851 0.0274148i
\(784\) 54.0564 + 49.6449i 1.93059 + 1.77303i
\(785\) 48.7713 + 20.2017i 1.74072 + 0.721031i
\(786\) −10.1186 0.888109i −0.360917 0.0316778i
\(787\) −12.7849 + 10.4923i −0.455732 + 0.374010i −0.834071 0.551658i \(-0.813996\pi\)
0.378339 + 0.925667i \(0.376496\pi\)
\(788\) −2.00490 6.13656i −0.0714218 0.218606i
\(789\) −10.9270 3.31466i −0.389010 0.118005i
\(790\) −6.99249 1.31379i −0.248782 0.0467426i
\(791\) 9.21681 46.3360i 0.327712 1.64752i
\(792\) −3.16030 4.41801i −0.112296 0.156987i
\(793\) −11.6849 + 2.32428i −0.414944 + 0.0825375i
\(794\) −20.4911 20.0601i −0.727202 0.711906i
\(795\) −14.7019 12.0655i −0.521423 0.427921i
\(796\) 16.1094 41.3567i 0.570981 1.46585i
\(797\) 22.5800 42.2442i 0.799824 1.49637i −0.0670003 0.997753i \(-0.521343\pi\)
0.866825 0.498613i \(-0.166157\pi\)
\(798\) 6.52395 + 1.90354i 0.230945 + 0.0673845i
\(799\) 20.1087 20.1087i 0.711394 0.711394i
\(800\) −34.3127 1.54617i −1.21314 0.0546655i
\(801\) 1.36559 + 1.36559i 0.0482507 + 0.0482507i
\(802\) −10.4779 19.1114i −0.369989 0.674848i
\(803\) 1.01406 + 0.542027i 0.0357855 + 0.0191277i
\(804\) 1.70089 1.77478i 0.0599856 0.0625917i
\(805\) −35.6120 + 43.3933i −1.25516 + 1.52941i
\(806\) 13.1301 0.139563i 0.462488 0.00491588i
\(807\) −0.755402 3.79766i −0.0265914 0.133684i
\(808\) −49.0777 + 22.1872i −1.72655 + 0.780545i
\(809\) −6.25043 1.24329i −0.219754 0.0437117i 0.0839854 0.996467i \(-0.473235\pi\)
−0.303739 + 0.952755i \(0.598235\pi\)
\(810\) −17.4876 25.5792i −0.614450 0.898762i
\(811\) 12.8477 42.3531i 0.451142 1.48722i −0.376742 0.926318i \(-0.622956\pi\)
0.827884 0.560899i \(-0.189544\pi\)
\(812\) 5.08971 4.36132i 0.178614 0.153052i
\(813\) 6.53158 + 7.95875i 0.229073 + 0.279126i
\(814\) 4.60051 3.85810i 0.161248 0.135226i
\(815\) 3.03988 7.33893i 0.106482 0.257071i
\(816\) 3.38425 + 9.65800i 0.118473 + 0.338098i
\(817\) −5.82893 14.0723i −0.203929 0.492327i
\(818\) 1.27375 + 0.663523i 0.0445355 + 0.0231995i
\(819\) 1.84378 18.7202i 0.0644269 0.654137i
\(820\) −54.7027 + 6.56452i −1.91030 + 0.229243i
\(821\) −16.4302 30.7387i −0.573417 1.07279i −0.986756 0.162211i \(-0.948138\pi\)
0.413339 0.910577i \(-0.364362\pi\)
\(822\) −0.217426 1.03543i −0.00758361 0.0361149i
\(823\) 21.7036 + 32.4818i 0.756541 + 1.13224i 0.987243 + 0.159220i \(0.0508978\pi\)
−0.230702 + 0.973024i \(0.574102\pi\)
\(824\) 8.16071 30.3544i 0.284292 1.05744i
\(825\) 1.87354 + 1.25186i 0.0652283 + 0.0435841i
\(826\) 49.7907 21.2468i 1.73244 0.739270i
\(827\) 10.0406 0.988908i 0.349144 0.0343877i 0.0780748 0.996948i \(-0.475123\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(828\) 14.9548 10.4590i 0.519716 0.363476i
\(829\) 46.3064 14.0469i 1.60829 0.487868i 0.646786 0.762672i \(-0.276113\pi\)
0.961500 + 0.274804i \(0.0886128\pi\)
\(830\) −9.91860 + 1.08346i −0.344280 + 0.0376074i
\(831\) 11.9930i 0.416033i
\(832\) 5.78057 + 9.33078i 0.200405 + 0.323486i
\(833\) 89.2129i 3.09104i
\(834\) −0.502194 4.59737i −0.0173895 0.159194i
\(835\) −50.2323 + 15.2378i −1.73836 + 0.527326i
\(836\) −2.51939 0.445689i −0.0871350 0.0154145i
\(837\) −20.2815 + 1.99755i −0.701030 + 0.0690454i
\(838\) −2.25830 5.29220i −0.0780115 0.182816i
\(839\) −20.1994 13.4968i −0.697361 0.465962i 0.155679 0.987808i \(-0.450244\pi\)
−0.853040 + 0.521846i \(0.825244\pi\)
\(840\) 19.7683 + 15.1951i 0.682070 + 0.524280i
\(841\) 15.8654 + 23.7442i 0.547082 + 0.818766i
\(842\) 14.7679 3.10105i 0.508937 0.106869i
\(843\) 2.87157 + 5.37233i 0.0989022 + 0.185033i
\(844\) −22.9880 + 29.2577i −0.791280 + 1.00709i
\(845\) 3.62594 36.8147i 0.124736 1.26647i
\(846\) −10.4062 + 19.9765i −0.357772 + 0.686806i
\(847\) −20.2355 48.8528i −0.695300 1.67860i
\(848\) 34.7284 + 26.1119i 1.19258 + 0.896685i
\(849\) 1.22643 2.96085i 0.0420908 0.101616i
\(850\) 26.8277 + 31.9902i 0.920184 + 1.09725i
\(851\) 12.7967 + 15.5929i 0.438666 + 0.534516i
\(852\) 5.13306 + 0.395601i 0.175856 + 0.0135531i
\(853\) −6.42788 + 21.1899i −0.220086 + 0.725528i 0.775472 + 0.631382i \(0.217512\pi\)
−0.995558 + 0.0941457i \(0.969988\pi\)
\(854\) 51.0394 34.8938i 1.74653 1.19404i
\(855\) −16.1198 3.20643i −0.551287 0.109658i
\(856\) −10.0903 + 10.7552i −0.344879 + 0.367605i
\(857\) 6.17540 + 31.0458i 0.210947 + 1.06050i 0.930563 + 0.366132i \(0.119318\pi\)
−0.719616 + 0.694373i \(0.755682\pi\)
\(858\) −0.00765335 0.720031i −0.000261281 0.0245815i
\(859\) −35.2256 + 42.9225i −1.20188 + 1.46450i −0.353239 + 0.935533i \(0.614920\pi\)
−0.848643 + 0.528965i \(0.822580\pi\)
\(860\) −1.18785 55.8702i −0.0405052 1.90516i
\(861\) 19.3433 + 10.3392i 0.659218 + 0.352359i
\(862\) 10.9724 6.01567i 0.373721 0.204894i
\(863\) 27.6535 + 27.6535i 0.941336 + 0.941336i 0.998372 0.0570361i \(-0.0181650\pi\)
−0.0570361 + 0.998372i \(0.518165\pi\)
\(864\) −10.2035 13.6418i −0.347131 0.464105i
\(865\) 14.1828 14.1828i 0.482228 0.482228i
\(866\) −12.9119 + 44.2527i −0.438764 + 1.50377i
\(867\) 1.64710 3.08151i 0.0559385 0.104654i
\(868\) −62.3872 + 27.4094i −2.11756 + 0.930336i
\(869\) −0.824275 0.676465i −0.0279616 0.0229475i
\(870\) 1.15302 1.17780i 0.0390911 0.0399311i
\(871\) −3.14326 + 0.625233i −0.106505 + 0.0211852i
\(872\) −3.15166 13.5682i −0.106729 0.459476i
\(873\) −1.39359 + 7.00604i −0.0471658 + 0.237119i
\(874\) 1.58722 8.44780i 0.0536886 0.285751i
\(875\) 17.1831 + 5.21243i 0.580894 + 0.176212i
\(876\) 1.53006 + 0.776478i 0.0516958 + 0.0262348i
\(877\) 30.7221 25.2130i 1.03741 0.851383i 0.0483432 0.998831i \(-0.484606\pi\)
0.989070 + 0.147448i \(0.0471059\pi\)
\(878\) −0.759830 + 8.65703i −0.0256430 + 0.292161i
\(879\) −1.88985 0.782800i −0.0637430 0.0264032i
\(880\) −8.01941 4.87857i −0.270334 0.164457i
\(881\) −26.4880 + 10.9717i −0.892402 + 0.369645i −0.781294 0.624163i \(-0.785440\pi\)
−0.111108 + 0.993808i \(0.535440\pi\)
\(882\) 21.2295 + 67.3970i 0.714834 + 2.26937i
\(883\) 23.3517 + 2.29995i 0.785849 + 0.0773993i 0.482978 0.875632i \(-0.339555\pi\)
0.302870 + 0.953032i \(0.402055\pi\)
\(884\) 3.60071 12.8469i 0.121105 0.432089i
\(885\) 11.7401 6.27522i 0.394639 0.210939i
\(886\) 22.2234 + 14.5099i 0.746610 + 0.487471i
\(887\) 12.8641 8.59554i 0.431935 0.288610i −0.320534 0.947237i \(-0.603862\pi\)
0.752470 + 0.658627i \(0.228862\pi\)
\(888\) 6.74106 5.90176i 0.226215 0.198050i
\(889\) −31.3174 + 46.8699i −1.05035 + 1.57196i
\(890\) 3.09665 + 1.24428i 0.103800 + 0.0417085i
\(891\) −0.455181 4.62153i −0.0152491 0.154827i
\(892\) 2.45581 3.85010i 0.0822267 0.128911i
\(893\) 3.07969 + 10.1524i 0.103058 + 0.339737i
\(894\) −2.00338 + 2.49473i −0.0670031 + 0.0834363i
\(895\) 30.8091 1.02983
\(896\) −46.5961 32.7630i −1.55667 1.09454i
\(897\) 2.41917 0.0807736
\(898\) −7.44383 + 9.26951i −0.248404 + 0.309327i
\(899\) 1.30762 + 4.31064i 0.0436115 + 0.143768i
\(900\) −27.8799 17.7834i −0.929329 0.592778i
\(901\) −5.17674 52.5603i −0.172462 1.75104i
\(902\) −7.66185 3.07865i −0.255112 0.102508i
\(903\) −12.3596 + 18.4974i −0.411301 + 0.615556i
\(904\) −1.75806 + 26.4825i −0.0584720 + 0.880794i
\(905\) −65.1861 + 43.5559i −2.16686 + 1.44785i
\(906\) −7.73607 5.05097i −0.257014 0.167807i
\(907\) 34.2148 18.2882i 1.13608 0.607249i 0.207448 0.978246i \(-0.433484\pi\)
0.928634 + 0.370997i \(0.120984\pi\)
\(908\) 39.8332 + 11.1644i 1.32191 + 0.370503i
\(909\) −51.6049 5.08264i −1.71163 0.168580i
\(910\) −9.76613 31.0044i −0.323744 1.02779i
\(911\) −29.6525 + 12.2825i −0.982431 + 0.406936i −0.815325 0.579003i \(-0.803442\pi\)
−0.167105 + 0.985939i \(0.553442\pi\)
\(912\) −3.77278 0.585005i −0.124929 0.0193715i
\(913\) −1.38154 0.572252i −0.0457222 0.0189388i
\(914\) −3.99361 + 45.5006i −0.132097 + 1.50503i
\(915\) 11.7526 9.64509i 0.388528 0.318857i
\(916\) 10.5842 20.8563i 0.349712 0.689111i
\(917\) −65.7630 19.9490i −2.17169 0.658774i
\(918\) −3.82370 + 20.3512i −0.126201 + 0.671690i
\(919\) −6.00870 + 30.2078i −0.198209 + 0.996462i 0.745707 + 0.666274i \(0.232112\pi\)
−0.943915 + 0.330188i \(0.892888\pi\)
\(920\) 16.6756 26.7664i 0.549778 0.882463i
\(921\) 7.20487 1.43314i 0.237409 0.0472235i
\(922\) −20.9611 + 21.4114i −0.690316 + 0.705148i
\(923\) −5.18838 4.25800i −0.170778 0.140154i
\(924\) 1.50308 + 3.42120i 0.0494478 + 0.112549i
\(925\) 17.2304 32.2359i 0.566533 1.05991i
\(926\) 15.6240 53.5478i 0.513437 1.75969i
\(927\) 21.3984 21.3984i 0.702815 0.702815i
\(928\) −2.51739 + 2.80026i −0.0826374 + 0.0919230i
\(929\) 9.26916 + 9.26916i 0.304111 + 0.304111i 0.842620 0.538509i \(-0.181012\pi\)
−0.538509 + 0.842620i \(0.681012\pi\)
\(930\) −14.6933 + 8.05567i −0.481812 + 0.264156i
\(931\) 29.3523 + 15.6891i 0.961983 + 0.514191i
\(932\) 35.6217 0.757346i 1.16683 0.0248077i
\(933\) −8.37722 + 10.2077i −0.274258 + 0.334184i
\(934\) −0.379281 35.6829i −0.0124104 1.16758i
\(935\) 2.22596 + 11.1907i 0.0727967 + 0.365974i
\(936\) 0.336905 + 10.5622i 0.0110121 + 0.345237i
\(937\) 42.7257 + 8.49867i 1.39579 + 0.277640i 0.834968 0.550298i \(-0.185486\pi\)
0.560820 + 0.827938i \(0.310486\pi\)
\(938\) 13.7296 9.38646i 0.448289 0.306479i
\(939\) −0.729079 + 2.40345i −0.0237926 + 0.0784337i
\(940\) −2.99094 + 38.8085i −0.0975536 + 1.26579i
\(941\) −1.27388 1.55223i −0.0415274 0.0506013i 0.751833 0.659354i \(-0.229170\pi\)
−0.793360 + 0.608753i \(0.791670\pi\)
\(942\) 7.58624 + 9.04607i 0.247173 + 0.294737i
\(943\) 10.6161 25.6295i 0.345708 0.834612i
\(944\) −26.1873 + 15.4630i −0.852323 + 0.503278i
\(945\) 19.3067 + 46.6106i 0.628048 + 1.51624i
\(946\) 3.86935 7.42789i 0.125804 0.241502i
\(947\) −1.12702 + 11.4428i −0.0366232 + 0.371841i 0.959352 + 0.282212i \(0.0910682\pi\)
−0.995975 + 0.0896293i \(0.971432\pi\)
\(948\) −1.25118 0.983063i −0.0406365 0.0319284i
\(949\) −1.05448 1.97280i −0.0342300 0.0640398i
\(950\) −15.2432 + 3.20085i −0.494555 + 0.103849i
\(951\) −1.49294 2.23434i −0.0484119 0.0724535i
\(952\) 8.97987 + 68.6537i 0.291039 + 2.22508i
\(953\) 10.8458 + 7.24692i 0.351329 + 0.234751i 0.718694 0.695326i \(-0.244740\pi\)
−0.367365 + 0.930077i \(0.619740\pi\)
\(954\) 16.4183 + 38.4755i 0.531562 + 1.24569i
\(955\) 6.95283 0.684794i 0.224988 0.0221594i
\(956\) 6.39443 36.1464i 0.206811 1.16906i
\(957\) 0.236388 0.0717074i 0.00764132 0.00231797i
\(958\) 2.14877 + 19.6711i 0.0694236 + 0.635544i
\(959\) 7.15820i 0.231150i
\(960\) −12.1188 7.02391i −0.391132 0.226696i
\(961\) 14.7959i 0.477286i
\(962\) −11.6116 + 1.26840i −0.374374 + 0.0408947i
\(963\) −13.5870 + 4.12157i −0.437835 + 0.132816i
\(964\) −11.5132 16.4621i −0.370814 0.530208i
\(965\) 12.1179 1.19351i 0.390089 0.0384204i
\(966\) −11.5470 + 4.92733i −0.371517 + 0.158534i
\(967\) −45.2137 30.2108i −1.45397 0.971514i −0.996613 0.0822320i \(-0.973795\pi\)
−0.457360 0.889282i \(-0.651205\pi\)
\(968\) 14.8314 + 25.7385i 0.476698 + 0.827267i
\(969\) 2.57825 + 3.85863i 0.0828254 + 0.123957i
\(970\) 2.53675 + 12.0806i 0.0814501 + 0.387884i
\(971\) 13.7540 + 25.7319i 0.441387 + 0.825777i 0.999993 0.00365591i \(-0.00116372\pi\)
−0.558606 + 0.829433i \(0.688664\pi\)
\(972\) −2.97856 24.8206i −0.0955374 0.796122i
\(973\) 3.06690 31.1387i 0.0983201 0.998261i
\(974\) 4.82563 + 2.51378i 0.154623 + 0.0805467i
\(975\) −1.67755 4.04996i −0.0537245 0.129702i
\(976\) −25.8885 + 23.1559i −0.828671 + 0.741202i
\(977\) 9.09060 21.9466i 0.290834 0.702135i −0.709162 0.705046i \(-0.750926\pi\)
0.999996 + 0.00291043i \(0.000926420\pi\)
\(978\) 1.36122 1.14155i 0.0435270 0.0365028i
\(979\) 0.317303 + 0.386635i 0.0101410 + 0.0123569i
\(980\) 79.4529 + 92.7223i 2.53803 + 2.96191i
\(981\) 3.89294 12.8333i 0.124292 0.409736i
\(982\) 30.7065 + 44.9146i 0.979883 + 1.43328i
\(983\) −18.3364 3.64734i −0.584840 0.116332i −0.106203 0.994345i \(-0.533869\pi\)
−0.478638 + 0.878013i \(0.658869\pi\)
\(984\) −11.5283 4.34997i −0.367508 0.138672i
\(985\) −2.09539 10.5342i −0.0667645 0.335648i
\(986\) 4.57678 0.0486475i 0.145754 0.00154925i
\(987\) 9.83009 11.9780i 0.312895 0.381264i
\(988\) 3.59359 + 3.44397i 0.114327 + 0.109567i
\(989\) 24.8153 + 13.2641i 0.789081 + 0.421772i
\(990\) −4.34461 7.92443i −0.138081 0.251855i
\(991\) −32.4448 32.4448i −1.03064 1.03064i −0.999515 0.0311265i \(-0.990091\pi\)
−0.0311265 0.999515i \(-0.509909\pi\)
\(992\) 32.7550 19.8136i 1.03997 0.629083i
\(993\) −10.0514 + 10.0514i −0.318972 + 0.318972i
\(994\) 33.4374 + 9.75624i 1.06057 + 0.309449i
\(995\) 34.8087 65.1224i 1.10351 2.06452i
\(996\) −2.07925 0.809914i −0.0658835 0.0256631i
\(997\) 27.5601 + 22.6180i 0.872837 + 0.716319i 0.960037 0.279872i \(-0.0902920\pi\)
−0.0872003 + 0.996191i \(0.527792\pi\)
\(998\) 17.6293 + 17.2585i 0.558046 + 0.546307i
\(999\) 17.7806 3.53677i 0.562552 0.111899i
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 128.2.k.a.13.4 240
4.3 odd 2 512.2.k.a.401.8 240
128.59 odd 32 512.2.k.a.369.8 240
128.69 even 32 inner 128.2.k.a.69.4 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.2.k.a.13.4 240 1.1 even 1 trivial
128.2.k.a.69.4 yes 240 128.69 even 32 inner
512.2.k.a.369.8 240 128.59 odd 32
512.2.k.a.401.8 240 4.3 odd 2