Properties

Label 552.2.bb.a.85.21
Level $552$
Weight $2$
Character 552.85
Analytic conductor $4.408$
Analytic rank $0$
Dimension $480$
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] = [552,2,Mod(13,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.bb (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(48\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 85.21
Character \(\chi\) \(=\) 552.85
Dual form 552.2.bb.a.13.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.343727 - 1.37181i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.76370 + 0.943055i) q^{4} +(2.78039 - 1.26976i) q^{5} +(0.968204 - 1.03082i) q^{6} +(-4.12553 + 1.21136i) q^{7} +(1.89992 + 2.09530i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.343727 - 1.37181i) q^{2} +(0.540641 + 0.841254i) q^{3} +(-1.76370 + 0.943055i) q^{4} +(2.78039 - 1.26976i) q^{5} +(0.968204 - 1.03082i) q^{6} +(-4.12553 + 1.21136i) q^{7} +(1.89992 + 2.09530i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-2.69756 - 3.37770i) q^{10} +(3.36238 - 2.91352i) q^{11} +(-1.74688 - 0.973868i) q^{12} +(0.440349 - 1.49969i) q^{13} +(3.07982 + 5.24305i) q^{14} +(2.57138 + 1.65253i) q^{15} +(2.22130 - 3.32654i) q^{16} +(0.964453 - 6.70792i) q^{17} +(1.39063 + 0.257203i) q^{18} +(4.18142 - 0.601198i) q^{19} +(-3.70633 + 4.86154i) q^{20} +(-3.24949 - 2.81570i) q^{21} +(-5.15252 - 3.61108i) q^{22} +(2.72085 + 3.94930i) q^{23} +(-0.735508 + 2.73112i) q^{24} +(2.84396 - 3.28211i) q^{25} +(-2.20864 - 0.0885885i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(6.13383 - 6.02709i) q^{28} +(7.62242 + 1.09594i) q^{29} +(1.38309 - 4.09546i) q^{30} +(8.16515 + 5.24742i) q^{31} +(-5.32688 - 1.90377i) q^{32} +(4.26885 + 1.25345i) q^{33} +(-9.53347 + 0.982653i) q^{34} +(-9.93243 + 8.60650i) q^{35} +(-0.125164 - 1.99608i) q^{36} +(-4.59502 - 2.09847i) q^{37} +(-2.26200 - 5.52945i) q^{38} +(1.49969 - 0.440349i) q^{39} +(7.94305 + 3.41332i) q^{40} +(-2.05092 - 4.49090i) q^{41} +(-2.74566 + 5.42551i) q^{42} +(-1.34645 - 2.09512i) q^{43} +(-3.18263 + 8.30949i) q^{44} +3.05661i q^{45} +(4.48245 - 5.08996i) q^{46} -8.03618 q^{47} +(3.99938 + 0.0702120i) q^{48} +(9.66382 - 6.21056i) q^{49} +(-5.47997 - 2.77322i) q^{50} +(6.16448 - 2.81523i) q^{51} +(0.637645 + 3.06028i) q^{52} +(-0.448944 - 1.52896i) q^{53} +(0.535457 + 1.30893i) q^{54} +(5.64925 - 12.3701i) q^{55} +(-10.3764 - 6.34274i) q^{56} +(2.76641 + 3.19261i) q^{57} +(-1.11662 - 10.8332i) q^{58} +(-0.0120042 + 0.0408824i) q^{59} +(-6.09358 - 0.489613i) q^{60} +(-2.01125 + 3.12957i) q^{61} +(4.39186 - 13.0047i) q^{62} +(0.611911 - 4.25593i) q^{63} +(-0.780601 + 7.96183i) q^{64} +(-0.679908 - 4.72886i) q^{65} +(0.252166 - 6.28687i) q^{66} +(-1.84394 - 1.59778i) q^{67} +(4.62492 + 12.7403i) q^{68} +(-1.85136 + 4.42408i) q^{69} +(15.2205 + 10.6671i) q^{70} +(-8.16377 + 9.42149i) q^{71} +(-2.69521 + 0.857808i) q^{72} +(0.866274 + 6.02507i) q^{73} +(-1.29927 + 7.02478i) q^{74} +(4.29865 + 0.618053i) q^{75} +(-6.80783 + 5.00365i) q^{76} +(-10.3423 + 16.0929i) q^{77} +(-1.11956 - 1.90592i) q^{78} +(-14.4682 - 4.24824i) q^{79} +(1.95216 - 12.0696i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-5.45568 + 4.35711i) q^{82} +(-3.46060 - 1.58040i) q^{83} +(8.38651 + 1.90161i) q^{84} +(-5.83590 - 19.8752i) q^{85} +(-2.41128 + 2.56722i) q^{86} +(3.19903 + 7.00490i) q^{87} +(12.4930 + 1.50975i) q^{88} +(0.289229 - 0.185876i) q^{89} +(4.19307 - 1.05064i) q^{90} +6.72044i q^{91} +(-8.52317 - 4.39949i) q^{92} +9.70593i q^{93} +(2.76226 + 11.0241i) q^{94} +(10.8626 - 6.98097i) q^{95} +(-1.27838 - 5.51051i) q^{96} +(2.48781 + 5.44754i) q^{97} +(-11.8414 - 11.1221i) q^{98} +(1.25345 + 4.26885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{4}{11}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.343727 1.37181i −0.243052 0.970013i
\(3\) 0.540641 + 0.841254i 0.312139 + 0.485698i
\(4\) −1.76370 + 0.943055i −0.881851 + 0.471527i
\(5\) 2.78039 1.26976i 1.24343 0.567854i 0.318473 0.947932i \(-0.396830\pi\)
0.924955 + 0.380078i \(0.124103\pi\)
\(6\) 0.968204 1.03082i 0.395267 0.420829i
\(7\) −4.12553 + 1.21136i −1.55930 + 0.457853i −0.943865 0.330332i \(-0.892839\pi\)
−0.615439 + 0.788185i \(0.711021\pi\)
\(8\) 1.89992 + 2.09530i 0.671723 + 0.740802i
\(9\) −0.415415 + 0.909632i −0.138472 + 0.303211i
\(10\) −2.69756 3.37770i −0.853044 1.06812i
\(11\) 3.36238 2.91352i 1.01380 0.878459i 0.0211817 0.999776i \(-0.493257\pi\)
0.992614 + 0.121317i \(0.0387117\pi\)
\(12\) −1.74688 0.973868i −0.504280 0.281131i
\(13\) 0.440349 1.49969i 0.122131 0.415939i −0.875618 0.483005i \(-0.839545\pi\)
0.997749 + 0.0670653i \(0.0213636\pi\)
\(14\) 3.07982 + 5.24305i 0.823115 + 1.40126i
\(15\) 2.57138 + 1.65253i 0.663928 + 0.426681i
\(16\) 2.22130 3.32654i 0.555324 0.831634i
\(17\) 0.964453 6.70792i 0.233914 1.62691i −0.446992 0.894538i \(-0.647505\pi\)
0.680906 0.732371i \(-0.261586\pi\)
\(18\) 1.39063 + 0.257203i 0.327774 + 0.0606234i
\(19\) 4.18142 0.601198i 0.959285 0.137924i 0.355152 0.934808i \(-0.384429\pi\)
0.604132 + 0.796884i \(0.293520\pi\)
\(20\) −3.70633 + 4.86154i −0.828760 + 1.08707i
\(21\) −3.24949 2.81570i −0.709098 0.614437i
\(22\) −5.15252 3.61108i −1.09852 0.769884i
\(23\) 2.72085 + 3.94930i 0.567336 + 0.823487i
\(24\) −0.735508 + 2.73112i −0.150135 + 0.557488i
\(25\) 2.84396 3.28211i 0.568793 0.656422i
\(26\) −2.20864 0.0885885i −0.433151 0.0173736i
\(27\) −0.989821 + 0.142315i −0.190491 + 0.0273885i
\(28\) 6.13383 6.02709i 1.15918 1.13901i
\(29\) 7.62242 + 1.09594i 1.41545 + 0.203511i 0.807220 0.590251i \(-0.200971\pi\)
0.608228 + 0.793762i \(0.291880\pi\)
\(30\) 1.38309 4.09546i 0.252517 0.747725i
\(31\) 8.16515 + 5.24742i 1.46650 + 0.942465i 0.998266 + 0.0588620i \(0.0187472\pi\)
0.468237 + 0.883603i \(0.344889\pi\)
\(32\) −5.32688 1.90377i −0.941669 0.336541i
\(33\) 4.26885 + 1.25345i 0.743111 + 0.218197i
\(34\) −9.53347 + 0.982653i −1.63498 + 0.168524i
\(35\) −9.93243 + 8.60650i −1.67889 + 1.45476i
\(36\) −0.125164 1.99608i −0.0208607 0.332680i
\(37\) −4.59502 2.09847i −0.755416 0.344987i 0.000201366 1.00000i \(-0.499936\pi\)
−0.755618 + 0.655013i \(0.772663\pi\)
\(38\) −2.26200 5.52945i −0.366944 0.896996i
\(39\) 1.49969 0.440349i 0.240143 0.0705123i
\(40\) 7.94305 + 3.41332i 1.25591 + 0.539693i
\(41\) −2.05092 4.49090i −0.320300 0.701360i 0.679167 0.733984i \(-0.262341\pi\)
−0.999468 + 0.0326234i \(0.989614\pi\)
\(42\) −2.74566 + 5.42551i −0.423664 + 0.837174i
\(43\) −1.34645 2.09512i −0.205332 0.319502i 0.723280 0.690555i \(-0.242633\pi\)
−0.928612 + 0.371052i \(0.878997\pi\)
\(44\) −3.18263 + 8.30949i −0.479800 + 1.25270i
\(45\) 3.05661i 0.455652i
\(46\) 4.48245 5.08996i 0.660901 0.750473i
\(47\) −8.03618 −1.17220 −0.586099 0.810239i \(-0.699337\pi\)
−0.586099 + 0.810239i \(0.699337\pi\)
\(48\) 3.99938 + 0.0702120i 0.577261 + 0.0101342i
\(49\) 9.66382 6.21056i 1.38055 0.887223i
\(50\) −5.47997 2.77322i −0.774984 0.392192i
\(51\) 6.16448 2.81523i 0.863200 0.394210i
\(52\) 0.637645 + 3.06028i 0.0884255 + 0.424385i
\(53\) −0.448944 1.52896i −0.0616672 0.210019i 0.922896 0.385050i \(-0.125816\pi\)
−0.984563 + 0.175031i \(0.943998\pi\)
\(54\) 0.535457 + 1.30893i 0.0728665 + 0.178122i
\(55\) 5.64925 12.3701i 0.761745 1.66799i
\(56\) −10.3764 6.34274i −1.38660 0.847585i
\(57\) 2.76641 + 3.19261i 0.366420 + 0.422871i
\(58\) −1.11662 10.8332i −0.146619 1.42247i
\(59\) −0.0120042 + 0.0408824i −0.00156281 + 0.00532243i −0.960271 0.279070i \(-0.909974\pi\)
0.958708 + 0.284393i \(0.0917919\pi\)
\(60\) −6.09358 0.489613i −0.786678 0.0632088i
\(61\) −2.01125 + 3.12957i −0.257514 + 0.400700i −0.945805 0.324735i \(-0.894725\pi\)
0.688291 + 0.725435i \(0.258361\pi\)
\(62\) 4.39186 13.0047i 0.557767 1.65160i
\(63\) 0.611911 4.25593i 0.0770935 0.536197i
\(64\) −0.780601 + 7.96183i −0.0975752 + 0.995228i
\(65\) −0.679908 4.72886i −0.0843322 0.586543i
\(66\) 0.252166 6.28687i 0.0310395 0.773861i
\(67\) −1.84394 1.59778i −0.225273 0.195200i 0.534910 0.844909i \(-0.320345\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(68\) 4.62492 + 12.7403i 0.560854 + 1.54499i
\(69\) −1.85136 + 4.42408i −0.222878 + 0.532596i
\(70\) 15.2205 + 10.6671i 1.81920 + 1.27496i
\(71\) −8.16377 + 9.42149i −0.968861 + 1.11813i 0.0241030 + 0.999709i \(0.492327\pi\)
−0.992964 + 0.118416i \(0.962218\pi\)
\(72\) −2.69521 + 0.857808i −0.317634 + 0.101094i
\(73\) 0.866274 + 6.02507i 0.101390 + 0.705181i 0.975588 + 0.219611i \(0.0704788\pi\)
−0.874198 + 0.485570i \(0.838612\pi\)
\(74\) −1.29927 + 7.02478i −0.151037 + 0.816614i
\(75\) 4.29865 + 0.618053i 0.496365 + 0.0713666i
\(76\) −6.80783 + 5.00365i −0.780911 + 0.573958i
\(77\) −10.3423 + 16.0929i −1.17861 + 1.83395i
\(78\) −1.11956 1.90592i −0.126765 0.215803i
\(79\) −14.4682 4.24824i −1.62780 0.477964i −0.664697 0.747113i \(-0.731439\pi\)
−0.963098 + 0.269149i \(0.913258\pi\)
\(80\) 1.95216 12.0696i 0.218258 1.34942i
\(81\) −0.654861 0.755750i −0.0727623 0.0839722i
\(82\) −5.45568 + 4.35711i −0.602479 + 0.481163i
\(83\) −3.46060 1.58040i −0.379850 0.173472i 0.216334 0.976319i \(-0.430590\pi\)
−0.596184 + 0.802848i \(0.703317\pi\)
\(84\) 8.38651 + 1.90161i 0.915043 + 0.207483i
\(85\) −5.83590 19.8752i −0.632992 2.15577i
\(86\) −2.41128 + 2.56722i −0.260015 + 0.276830i
\(87\) 3.19903 + 7.00490i 0.342972 + 0.751004i
\(88\) 12.4930 + 1.50975i 1.33175 + 0.160940i
\(89\) 0.289229 0.185876i 0.0306583 0.0197029i −0.525222 0.850965i \(-0.676018\pi\)
0.555880 + 0.831262i \(0.312381\pi\)
\(90\) 4.19307 1.05064i 0.441989 0.110747i
\(91\) 6.72044i 0.704494i
\(92\) −8.52317 4.39949i −0.888602 0.458678i
\(93\) 9.70593i 1.00646i
\(94\) 2.76226 + 11.0241i 0.284905 + 1.13705i
\(95\) 10.8626 6.98097i 1.11448 0.716233i
\(96\) −1.27838 5.51051i −0.130474 0.562414i
\(97\) 2.48781 + 5.44754i 0.252599 + 0.553114i 0.992871 0.119193i \(-0.0380307\pi\)
−0.740272 + 0.672307i \(0.765303\pi\)
\(98\) −11.8414 11.1221i −1.19616 1.12351i
\(99\) 1.25345 + 4.26885i 0.125976 + 0.429035i
\(100\) −1.92070 + 8.47068i −0.192070 + 0.847068i
\(101\) 4.95871 + 2.26457i 0.493410 + 0.225333i 0.646550 0.762872i \(-0.276211\pi\)
−0.153140 + 0.988205i \(0.548938\pi\)
\(102\) −5.98084 7.48880i −0.592192 0.741502i
\(103\) 0.882524 + 1.01849i 0.0869577 + 0.100355i 0.797561 0.603238i \(-0.206123\pi\)
−0.710603 + 0.703593i \(0.751578\pi\)
\(104\) 3.97894 1.92663i 0.390167 0.188921i
\(105\) −12.6101 3.70267i −1.23062 0.361343i
\(106\) −1.94312 + 1.14141i −0.188733 + 0.110864i
\(107\) 5.33870 8.30717i 0.516111 0.803085i −0.481181 0.876621i \(-0.659792\pi\)
0.997293 + 0.0735364i \(0.0234285\pi\)
\(108\) 1.61154 1.18446i 0.155071 0.113974i
\(109\) −5.21608 0.749959i −0.499610 0.0718330i −0.112097 0.993697i \(-0.535757\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(110\) −18.9112 3.49772i −1.80311 0.333495i
\(111\) −0.718905 5.00010i −0.0682355 0.474588i
\(112\) −5.13437 + 16.4145i −0.485153 + 1.55103i
\(113\) −5.77675 + 6.66673i −0.543431 + 0.627153i −0.959340 0.282253i \(-0.908918\pi\)
0.415909 + 0.909406i \(0.363464\pi\)
\(114\) 3.42875 4.89236i 0.321131 0.458212i
\(115\) 12.5797 + 7.52577i 1.17306 + 0.701782i
\(116\) −14.4772 + 5.25545i −1.34418 + 0.487956i
\(117\) 1.18124 + 1.02355i 0.109206 + 0.0946272i
\(118\) 0.0602088 + 0.00241497i 0.00554267 + 0.000222316i
\(119\) 4.14686 + 28.8420i 0.380142 + 2.64394i
\(120\) 1.42288 + 8.52750i 0.129890 + 0.778451i
\(121\) 1.25154 8.70467i 0.113777 0.791334i
\(122\) 4.98448 + 1.68333i 0.451274 + 0.152401i
\(123\) 2.66917 4.15331i 0.240671 0.374491i
\(124\) −19.3495 1.55471i −1.73764 0.139617i
\(125\) −0.565899 + 1.92727i −0.0506155 + 0.172381i
\(126\) −6.04864 + 0.623458i −0.538856 + 0.0555421i
\(127\) −2.93568 3.38796i −0.260500 0.300633i 0.610400 0.792093i \(-0.291009\pi\)
−0.870900 + 0.491460i \(0.836463\pi\)
\(128\) 11.1904 1.66586i 0.989100 0.147243i
\(129\) 1.03458 2.26541i 0.0910896 0.199458i
\(130\) −6.25338 + 2.55814i −0.548457 + 0.224364i
\(131\) 5.12627 + 17.4585i 0.447884 + 1.52535i 0.806137 + 0.591730i \(0.201555\pi\)
−0.358252 + 0.933625i \(0.616627\pi\)
\(132\) −8.71105 + 1.81505i −0.758199 + 0.157980i
\(133\) −16.5223 + 7.54549i −1.43267 + 0.654277i
\(134\) −1.55803 + 3.07873i −0.134594 + 0.265962i
\(135\) −2.57138 + 1.65253i −0.221309 + 0.142227i
\(136\) 15.8875 10.7237i 1.36234 0.919549i
\(137\) 17.2542 1.47413 0.737063 0.675825i \(-0.236212\pi\)
0.737063 + 0.675825i \(0.236212\pi\)
\(138\) 6.70534 + 1.01904i 0.570796 + 0.0867461i
\(139\) 3.27624i 0.277887i 0.990300 + 0.138943i \(0.0443706\pi\)
−0.990300 + 0.138943i \(0.955629\pi\)
\(140\) 9.40146 24.5461i 0.794568 2.07453i
\(141\) −4.34469 6.76047i −0.365889 0.569334i
\(142\) 15.7306 + 7.96068i 1.32008 + 0.668046i
\(143\) −2.88876 6.32549i −0.241570 0.528964i
\(144\) 2.10316 + 3.40246i 0.175264 + 0.283538i
\(145\) 22.5849 6.63152i 1.87557 0.550718i
\(146\) 7.96746 3.25934i 0.659392 0.269745i
\(147\) 10.4493 + 4.77204i 0.861844 + 0.393591i
\(148\) 10.0832 0.632267i 0.828836 0.0519720i
\(149\) −5.15486 + 4.46671i −0.422302 + 0.365927i −0.839933 0.542690i \(-0.817406\pi\)
0.417631 + 0.908617i \(0.362861\pi\)
\(150\) −0.629716 6.10936i −0.0514161 0.498827i
\(151\) 7.39297 + 2.17077i 0.601631 + 0.176655i 0.568344 0.822791i \(-0.307584\pi\)
0.0332872 + 0.999446i \(0.489402\pi\)
\(152\) 9.20407 + 7.61913i 0.746549 + 0.617993i
\(153\) 5.70109 + 3.66387i 0.460906 + 0.296206i
\(154\) 25.6312 + 8.65602i 2.06542 + 0.697522i
\(155\) 29.3653 + 4.22209i 2.35867 + 0.339126i
\(156\) −2.22974 + 2.19093i −0.178522 + 0.175415i
\(157\) 1.00715 0.144806i 0.0803790 0.0115568i −0.102008 0.994784i \(-0.532527\pi\)
0.182387 + 0.983227i \(0.441618\pi\)
\(158\) −0.854651 + 21.3077i −0.0679924 + 1.69515i
\(159\) 1.04353 1.20429i 0.0827571 0.0955068i
\(160\) −17.2281 + 1.47066i −1.36200 + 0.116266i
\(161\) −16.0090 12.9970i −1.26168 1.02431i
\(162\) −0.811648 + 1.15811i −0.0637691 + 0.0909900i
\(163\) −12.0504 10.4417i −0.943861 0.817860i 0.0395563 0.999217i \(-0.487406\pi\)
−0.983417 + 0.181357i \(0.941951\pi\)
\(164\) 7.85238 + 5.98647i 0.613168 + 0.467465i
\(165\) 13.4606 1.93535i 1.04791 0.150667i
\(166\) −0.978502 + 5.29049i −0.0759465 + 0.410622i
\(167\) −1.34190 + 9.33313i −0.103839 + 0.722219i 0.869680 + 0.493616i \(0.164325\pi\)
−0.973520 + 0.228604i \(0.926584\pi\)
\(168\) −0.274027 12.1583i −0.0211417 0.938033i
\(169\) 8.88113 + 5.70756i 0.683164 + 0.439043i
\(170\) −25.2590 + 14.8374i −1.93728 + 1.13798i
\(171\) −1.19016 + 4.05330i −0.0910136 + 0.309964i
\(172\) 4.35055 + 2.42539i 0.331726 + 0.184934i
\(173\) 15.8705 13.7519i 1.20661 1.04554i 0.208900 0.977937i \(-0.433012\pi\)
0.997713 0.0675990i \(-0.0215338\pi\)
\(174\) 8.50977 6.79622i 0.645124 0.515220i
\(175\) −7.75703 + 16.9855i −0.586376 + 1.28398i
\(176\) −2.22308 17.6569i −0.167571 1.33094i
\(177\) −0.0408824 + 0.0120042i −0.00307291 + 0.000902287i
\(178\) −0.354403 0.332876i −0.0265636 0.0249501i
\(179\) −10.4028 + 4.75080i −0.777542 + 0.355091i −0.764333 0.644821i \(-0.776932\pi\)
−0.0132085 + 0.999913i \(0.504205\pi\)
\(180\) −2.88255 5.39095i −0.214852 0.401818i
\(181\) −8.18237 12.7320i −0.608190 0.946363i −0.999657 0.0261707i \(-0.991669\pi\)
0.391467 0.920192i \(-0.371968\pi\)
\(182\) 9.21914 2.31000i 0.683368 0.171229i
\(183\) −3.72013 −0.275000
\(184\) −3.10560 + 13.2044i −0.228948 + 0.973439i
\(185\) −15.4405 −1.13521
\(186\) 13.3146 3.33619i 0.976277 0.244622i
\(187\) −16.3008 25.3645i −1.19203 1.85484i
\(188\) 14.1734 7.57856i 1.03370 0.552723i
\(189\) 3.91114 1.78616i 0.284494 0.129924i
\(190\) −13.3103 12.5018i −0.965632 0.906979i
\(191\) −13.2279 + 3.88407i −0.957139 + 0.281041i −0.722756 0.691103i \(-0.757125\pi\)
−0.234383 + 0.972144i \(0.575307\pi\)
\(192\) −7.11994 + 3.64780i −0.513837 + 0.263258i
\(193\) −6.24722 + 13.6795i −0.449685 + 0.984672i 0.540034 + 0.841643i \(0.318411\pi\)
−0.989719 + 0.143029i \(0.954316\pi\)
\(194\) 6.61784 5.28526i 0.475133 0.379460i
\(195\) 3.61059 3.12859i 0.258559 0.224043i
\(196\) −11.1872 + 20.0671i −0.799086 + 1.43336i
\(197\) 4.55156 15.5012i 0.324285 1.10441i −0.622520 0.782604i \(-0.713891\pi\)
0.946805 0.321809i \(-0.104291\pi\)
\(198\) 5.42519 3.18681i 0.385551 0.226476i
\(199\) 14.5454 + 9.34777i 1.03110 + 0.662646i 0.942769 0.333445i \(-0.108211\pi\)
0.0883279 + 0.996091i \(0.471848\pi\)
\(200\) 12.2803 0.276778i 0.868350 0.0195711i
\(201\) 0.347231 2.41505i 0.0244918 0.170344i
\(202\) 1.40210 7.58079i 0.0986516 0.533382i
\(203\) −32.7741 + 4.71221i −2.30029 + 0.330732i
\(204\) −8.21741 + 10.7787i −0.575334 + 0.754657i
\(205\) −11.4047 9.88225i −0.796541 0.690207i
\(206\) 1.09382 1.56073i 0.0762100 0.108742i
\(207\) −4.72269 + 0.834370i −0.328250 + 0.0579927i
\(208\) −4.01063 4.79609i −0.278087 0.332549i
\(209\) 12.3079 14.2041i 0.851358 0.982519i
\(210\) −0.744895 + 18.5714i −0.0514026 + 1.28155i
\(211\) 6.62498 0.952528i 0.456082 0.0655747i 0.0895546 0.995982i \(-0.471456\pi\)
0.366528 + 0.930407i \(0.380547\pi\)
\(212\) 2.23370 + 2.27326i 0.153411 + 0.156128i
\(213\) −12.3395 1.77416i −0.845491 0.121563i
\(214\) −13.2309 4.46825i −0.904445 0.305443i
\(215\) −6.40395 4.11557i −0.436746 0.280680i
\(216\) −2.17878 1.80359i −0.148247 0.122719i
\(217\) −40.0421 11.7574i −2.71823 0.798146i
\(218\) 0.764111 + 7.41323i 0.0517521 + 0.502087i
\(219\) −4.60027 + 3.98615i −0.310857 + 0.269359i
\(220\) 1.70211 + 27.1448i 0.114756 + 1.83010i
\(221\) −9.63511 4.40021i −0.648127 0.295990i
\(222\) −6.61205 + 2.70487i −0.443772 + 0.181539i
\(223\) −13.0418 + 3.82942i −0.873343 + 0.256437i −0.687537 0.726150i \(-0.741308\pi\)
−0.185807 + 0.982586i \(0.559490\pi\)
\(224\) 24.2824 + 1.40124i 1.62243 + 0.0936245i
\(225\) 1.80409 + 3.95040i 0.120272 + 0.263360i
\(226\) 11.1311 + 5.63304i 0.740429 + 0.374705i
\(227\) 13.4607 + 20.9452i 0.893417 + 1.39018i 0.920580 + 0.390554i \(0.127716\pi\)
−0.0271628 + 0.999631i \(0.508647\pi\)
\(228\) −7.88993 3.02193i −0.522523 0.200132i
\(229\) 3.70190i 0.244628i 0.992491 + 0.122314i \(0.0390316\pi\)
−0.992491 + 0.122314i \(0.960968\pi\)
\(230\) 5.99992 19.8437i 0.395623 1.30845i
\(231\) −19.1296 −1.25864
\(232\) 12.1857 + 18.0535i 0.800029 + 1.18527i
\(233\) −17.8866 + 11.4950i −1.17179 + 0.753062i −0.973859 0.227155i \(-0.927058\pi\)
−0.197928 + 0.980216i \(0.563421\pi\)
\(234\) 0.998087 1.97225i 0.0652470 0.128930i
\(235\) −22.3437 + 10.2040i −1.45754 + 0.665638i
\(236\) −0.0173826 0.0834249i −0.00113151 0.00543050i
\(237\) −4.24824 14.4682i −0.275953 0.939808i
\(238\) 38.1403 15.6025i 2.47227 1.01136i
\(239\) 7.44315 16.2982i 0.481457 1.05424i −0.500603 0.865677i \(-0.666888\pi\)
0.982060 0.188568i \(-0.0603845\pi\)
\(240\) 11.2090 4.88304i 0.723537 0.315199i
\(241\) −5.32194 6.14184i −0.342816 0.395631i 0.557993 0.829845i \(-0.311571\pi\)
−0.900809 + 0.434215i \(0.857026\pi\)
\(242\) −12.3713 + 1.27516i −0.795258 + 0.0819704i
\(243\) 0.281733 0.959493i 0.0180732 0.0615515i
\(244\) 0.595897 7.41635i 0.0381484 0.474783i
\(245\) 18.9832 29.5385i 1.21280 1.88715i
\(246\) −6.61500 2.23398i −0.421757 0.142433i
\(247\) 0.939675 6.53558i 0.0597901 0.415849i
\(248\) 4.51819 + 27.0782i 0.286905 + 1.71946i
\(249\) −0.541421 3.76567i −0.0343112 0.238640i
\(250\) 2.83836 + 0.113846i 0.179514 + 0.00720027i
\(251\) −19.0145 16.4762i −1.20018 1.03997i −0.998163 0.0605852i \(-0.980703\pi\)
−0.202022 0.979381i \(-0.564751\pi\)
\(252\) 2.93435 + 8.08327i 0.184847 + 0.509198i
\(253\) 20.6549 + 5.35182i 1.29856 + 0.336466i
\(254\) −3.63855 + 5.19172i −0.228303 + 0.325758i
\(255\) 13.5650 15.6548i 0.849473 0.980344i
\(256\) −6.13169 14.7784i −0.383230 0.923653i
\(257\) 0.499775 + 3.47601i 0.0311751 + 0.216827i 0.999454 0.0330449i \(-0.0105204\pi\)
−0.968279 + 0.249872i \(0.919611\pi\)
\(258\) −3.46332 0.640558i −0.215617 0.0398794i
\(259\) 21.4989 + 3.09108i 1.33588 + 0.192070i
\(260\) 5.65873 + 7.69912i 0.350939 + 0.477479i
\(261\) −4.16337 + 6.47833i −0.257706 + 0.400998i
\(262\) 22.1876 13.0332i 1.37075 0.805194i
\(263\) 0.0134845 + 0.00395940i 0.000831488 + 0.000244147i 0.282148 0.959371i \(-0.408953\pi\)
−0.281317 + 0.959615i \(0.590771\pi\)
\(264\) 5.48412 + 11.3260i 0.337524 + 0.697066i
\(265\) −3.18965 3.68106i −0.195939 0.226126i
\(266\) 16.0301 + 20.0718i 0.982870 + 1.23068i
\(267\) 0.312739 + 0.142823i 0.0191393 + 0.00874062i
\(268\) 4.75896 + 1.07908i 0.290699 + 0.0659152i
\(269\) 2.91995 + 9.94444i 0.178033 + 0.606323i 0.999357 + 0.0358616i \(0.0114176\pi\)
−0.821324 + 0.570462i \(0.806764\pi\)
\(270\) 3.15080 + 2.95942i 0.191752 + 0.180104i
\(271\) −6.33488 13.8715i −0.384817 0.842631i −0.998587 0.0531460i \(-0.983075\pi\)
0.613770 0.789485i \(-0.289652\pi\)
\(272\) −20.1718 18.1086i −1.22309 1.09799i
\(273\) −5.65360 + 3.63335i −0.342171 + 0.219900i
\(274\) −5.93074 23.6694i −0.358289 1.42992i
\(275\) 19.3216i 1.16514i
\(276\) −0.906889 9.54869i −0.0545883 0.574764i
\(277\) 31.1942i 1.87428i 0.348956 + 0.937139i \(0.386536\pi\)
−0.348956 + 0.937139i \(0.613464\pi\)
\(278\) 4.49436 1.12613i 0.269554 0.0675410i
\(279\) −8.16515 + 5.24742i −0.488835 + 0.314155i
\(280\) −36.9041 4.45980i −2.20544 0.266524i
\(281\) 4.35006 + 9.52530i 0.259503 + 0.568232i 0.993874 0.110516i \(-0.0352503\pi\)
−0.734372 + 0.678748i \(0.762523\pi\)
\(282\) −7.78066 + 8.28383i −0.463332 + 0.493295i
\(283\) −3.13391 10.6731i −0.186292 0.634451i −0.998681 0.0513364i \(-0.983652\pi\)
0.812390 0.583115i \(-0.198166\pi\)
\(284\) 5.51348 24.3156i 0.327165 1.44286i
\(285\) 11.7455 + 5.36401i 0.695746 + 0.317736i
\(286\) −7.68441 + 6.13706i −0.454388 + 0.362892i
\(287\) 13.9013 + 16.0429i 0.820565 + 0.946983i
\(288\) 3.94459 4.05465i 0.232437 0.238923i
\(289\) −27.7546 8.14949i −1.63262 0.479382i
\(290\) −16.8602 28.7026i −0.990065 1.68548i
\(291\) −3.23775 + 5.03804i −0.189800 + 0.295335i
\(292\) −7.20982 9.80948i −0.421923 0.574057i
\(293\) 7.58748 + 1.09091i 0.443265 + 0.0637319i 0.360334 0.932823i \(-0.382663\pi\)
0.0829312 + 0.996555i \(0.473572\pi\)
\(294\) 2.95460 15.9747i 0.172316 0.931664i
\(295\) 0.0185346 + 0.128911i 0.00107913 + 0.00750551i
\(296\) −4.33323 13.6149i −0.251864 0.791350i
\(297\) −2.91352 + 3.36238i −0.169059 + 0.195105i
\(298\) 7.89932 + 5.53613i 0.457596 + 0.320700i
\(299\) 7.12085 2.34136i 0.411810 0.135404i
\(300\) −8.16440 + 2.96380i −0.471372 + 0.171115i
\(301\) 8.09277 + 7.01243i 0.466460 + 0.404190i
\(302\) 0.436711 10.8879i 0.0251299 0.626527i
\(303\) 0.775806 + 5.39585i 0.0445689 + 0.309984i
\(304\) 7.28828 15.2451i 0.418011 0.874366i
\(305\) −1.61826 + 11.2552i −0.0926612 + 0.644472i
\(306\) 3.06649 9.08016i 0.175300 0.519078i
\(307\) 15.6100 24.2897i 0.890911 1.38628i −0.0312637 0.999511i \(-0.509953\pi\)
0.922175 0.386773i \(-0.126410\pi\)
\(308\) 3.06422 38.1364i 0.174600 2.17302i
\(309\) −0.379677 + 1.29306i −0.0215991 + 0.0735598i
\(310\) −4.30176 41.7347i −0.244324 2.37037i
\(311\) −11.5864 13.3714i −0.657002 0.758221i 0.325282 0.945617i \(-0.394541\pi\)
−0.982284 + 0.187396i \(0.939995\pi\)
\(312\) 3.77196 + 2.30568i 0.213545 + 0.130533i
\(313\) −5.60739 + 12.2785i −0.316948 + 0.694020i −0.999316 0.0369894i \(-0.988223\pi\)
0.682367 + 0.731009i \(0.260950\pi\)
\(314\) −0.544829 1.33183i −0.0307465 0.0751598i
\(315\) −3.70267 12.6101i −0.208622 0.710500i
\(316\) 29.5239 6.15164i 1.66085 0.346057i
\(317\) −20.5738 + 9.39574i −1.15554 + 0.527718i −0.898626 0.438716i \(-0.855433\pi\)
−0.256915 + 0.966434i \(0.582706\pi\)
\(318\) −2.01075 1.01757i −0.112757 0.0570624i
\(319\) 28.8225 18.5231i 1.61375 1.03709i
\(320\) 7.93924 + 23.1281i 0.443817 + 1.29290i
\(321\) 9.87476 0.551155
\(322\) −12.3267 + 26.4287i −0.686939 + 1.47281i
\(323\) 28.6285i 1.59293i
\(324\) 1.86769 + 0.715348i 0.103761 + 0.0397416i
\(325\) −3.66981 5.71034i −0.203565 0.316753i
\(326\) −10.1820 + 20.1199i −0.563928 + 1.11434i
\(327\) −2.18912 4.79350i −0.121059 0.265081i
\(328\) 5.51320 12.8297i 0.304416 0.708399i
\(329\) 33.1535 9.73475i 1.82781 0.536694i
\(330\) −7.28171 17.8001i −0.400845 0.979866i
\(331\) 11.9404 + 5.45301i 0.656305 + 0.299725i 0.715594 0.698516i \(-0.246156\pi\)
−0.0592890 + 0.998241i \(0.518883\pi\)
\(332\) 7.59387 0.476173i 0.416768 0.0261334i
\(333\) 3.81768 3.30804i 0.209208 0.181279i
\(334\) 13.2645 1.36722i 0.725801 0.0748112i
\(335\) −7.15567 2.10109i −0.390956 0.114795i
\(336\) −16.5846 + 4.55505i −0.904766 + 0.248498i
\(337\) 2.49928 + 1.60619i 0.136144 + 0.0874947i 0.606940 0.794748i \(-0.292397\pi\)
−0.470796 + 0.882242i \(0.656033\pi\)
\(338\) 4.77697 14.1450i 0.259833 0.769388i
\(339\) −8.73155 1.25541i −0.474233 0.0681844i
\(340\) 29.0362 + 29.5505i 1.57471 + 1.60260i
\(341\) 42.7428 6.14548i 2.31465 0.332797i
\(342\) 5.96944 + 0.239433i 0.322790 + 0.0129471i
\(343\) −12.6352 + 14.5818i −0.682236 + 0.787343i
\(344\) 1.83176 6.80178i 0.0987619 0.366727i
\(345\) 0.470008 + 14.6514i 0.0253044 + 0.788807i
\(346\) −24.3200 17.0444i −1.30745 0.916311i
\(347\) 2.45455 + 2.12688i 0.131767 + 0.114177i 0.718251 0.695784i \(-0.244943\pi\)
−0.586484 + 0.809961i \(0.699488\pi\)
\(348\) −12.2481 9.33770i −0.656569 0.500553i
\(349\) −0.607645 + 0.0873661i −0.0325265 + 0.00467660i −0.158559 0.987350i \(-0.550685\pi\)
0.126032 + 0.992026i \(0.459776\pi\)
\(350\) 25.9671 + 4.80275i 1.38800 + 0.256718i
\(351\) −0.222439 + 1.54709i −0.0118729 + 0.0825778i
\(352\) −23.4577 + 9.11879i −1.25030 + 0.486033i
\(353\) 0.0410946 + 0.0264099i 0.00218725 + 0.00140566i 0.541734 0.840550i \(-0.317768\pi\)
−0.539547 + 0.841956i \(0.681404\pi\)
\(354\) 0.0305198 + 0.0519565i 0.00162211 + 0.00276146i
\(355\) −10.7354 + 36.5614i −0.569776 + 1.94048i
\(356\) −0.334823 + 0.600590i −0.0177456 + 0.0318312i
\(357\) −22.0215 + 19.0817i −1.16550 + 1.00991i
\(358\) 10.0929 + 12.6376i 0.533427 + 0.667920i
\(359\) 11.8616 25.9734i 0.626034 1.37082i −0.285015 0.958523i \(-0.591998\pi\)
0.911048 0.412300i \(-0.135274\pi\)
\(360\) −6.40452 + 5.80731i −0.337548 + 0.306072i
\(361\) −1.10749 + 0.325189i −0.0582891 + 0.0171152i
\(362\) −14.6533 + 15.6010i −0.770163 + 0.819968i
\(363\) 7.99947 3.65324i 0.419863 0.191745i
\(364\) −6.33774 11.8529i −0.332188 0.621259i
\(365\) 10.0590 + 15.6521i 0.526511 + 0.819267i
\(366\) 1.27871 + 5.10329i 0.0668392 + 0.266753i
\(367\) 5.55114 0.289767 0.144884 0.989449i \(-0.453719\pi\)
0.144884 + 0.989449i \(0.453719\pi\)
\(368\) 19.1813 0.278425i 0.999895 0.0145139i
\(369\) 4.93705 0.257012
\(370\) 5.30732 + 21.1814i 0.275915 + 1.10117i
\(371\) 3.70426 + 5.76394i 0.192316 + 0.299249i
\(372\) −9.15322 17.1184i −0.474572 0.887546i
\(373\) 4.64756 2.12247i 0.240642 0.109897i −0.291444 0.956588i \(-0.594136\pi\)
0.532086 + 0.846691i \(0.321408\pi\)
\(374\) −29.1922 + 31.0800i −1.50949 + 1.60711i
\(375\) −1.92727 + 0.565899i −0.0995240 + 0.0292229i
\(376\) −15.2681 16.8383i −0.787393 0.868367i
\(377\) 5.00009 10.9487i 0.257518 0.563886i
\(378\) −3.79463 4.75138i −0.195175 0.244384i
\(379\) 25.5280 22.1201i 1.31128 1.13623i 0.329933 0.944004i \(-0.392974\pi\)
0.981350 0.192229i \(-0.0615715\pi\)
\(380\) −12.5750 + 22.5564i −0.645083 + 1.15712i
\(381\) 1.26298 4.30132i 0.0647045 0.220363i
\(382\) 9.87499 + 16.8111i 0.505249 + 0.860130i
\(383\) 7.30520 + 4.69477i 0.373278 + 0.239891i 0.713807 0.700343i \(-0.246970\pi\)
−0.340528 + 0.940234i \(0.610606\pi\)
\(384\) 7.45140 + 8.51332i 0.380253 + 0.434444i
\(385\) −8.32141 + 57.8767i −0.424098 + 2.94967i
\(386\) 20.9130 + 3.86795i 1.06444 + 0.196874i
\(387\) 2.46512 0.354431i 0.125309 0.0180167i
\(388\) −9.52508 7.26171i −0.483563 0.368657i
\(389\) 1.10921 + 0.961134i 0.0562391 + 0.0487314i 0.682527 0.730861i \(-0.260881\pi\)
−0.626288 + 0.779592i \(0.715426\pi\)
\(390\) −5.53288 3.87764i −0.280168 0.196352i
\(391\) 29.1157 14.4423i 1.47245 0.730379i
\(392\) 31.3735 + 8.44907i 1.58460 + 0.426743i
\(393\) −11.9155 + 13.7513i −0.601059 + 0.693659i
\(394\) −22.8291 0.915673i −1.15011 0.0461309i
\(395\) −45.6214 + 6.55936i −2.29546 + 0.330037i
\(396\) −6.23646 6.34691i −0.313394 0.318944i
\(397\) −29.5279 4.24548i −1.48196 0.213074i −0.646625 0.762808i \(-0.723820\pi\)
−0.835340 + 0.549734i \(0.814729\pi\)
\(398\) 7.82367 23.1666i 0.392165 1.16124i
\(399\) −15.2803 9.82006i −0.764973 0.491618i
\(400\) −4.60077 16.7511i −0.230039 0.837555i
\(401\) 17.5265 + 5.14624i 0.875231 + 0.256991i 0.688339 0.725389i \(-0.258340\pi\)
0.186892 + 0.982380i \(0.440159\pi\)
\(402\) −3.43233 + 0.353784i −0.171189 + 0.0176451i
\(403\) 11.4650 9.93450i 0.571113 0.494873i
\(404\) −10.8813 + 0.682311i −0.541365 + 0.0339462i
\(405\) −2.78039 1.26976i −0.138159 0.0630949i
\(406\) 17.7296 + 43.3400i 0.879905 + 2.15093i
\(407\) −21.5641 + 6.33180i −1.06889 + 0.313856i
\(408\) 17.6108 + 7.56776i 0.871864 + 0.374660i
\(409\) −9.03824 19.7910i −0.446912 0.978601i −0.990278 0.139105i \(-0.955577\pi\)
0.543365 0.839496i \(-0.317150\pi\)
\(410\) −9.63642 + 19.0419i −0.475909 + 0.940411i
\(411\) 9.32832 + 14.5151i 0.460132 + 0.715980i
\(412\) −2.51700 0.964041i −0.124004 0.0474949i
\(413\) 0.183203i 0.00901483i
\(414\) 2.76791 + 6.19182i 0.136035 + 0.304311i
\(415\) −11.6285 −0.570822
\(416\) −5.20075 + 7.15036i −0.254988 + 0.350575i
\(417\) −2.75615 + 1.77127i −0.134969 + 0.0867394i
\(418\) −23.7159 12.0018i −1.15998 0.587025i
\(419\) −32.0087 + 14.6179i −1.56373 + 0.714130i −0.994170 0.107823i \(-0.965612\pi\)
−0.569556 + 0.821953i \(0.692885\pi\)
\(420\) 25.7323 5.36163i 1.25561 0.261621i
\(421\) 5.32657 + 18.1406i 0.259601 + 0.884120i 0.981393 + 0.192010i \(0.0615005\pi\)
−0.721792 + 0.692110i \(0.756681\pi\)
\(422\) −3.58387 8.76077i −0.174460 0.426468i
\(423\) 3.33835 7.30997i 0.162316 0.355423i
\(424\) 2.35068 3.84558i 0.114159 0.186758i
\(425\) −19.2733 22.2425i −0.934890 1.07892i
\(426\) 1.80764 + 17.5373i 0.0875802 + 0.849683i
\(427\) 4.50643 15.3475i 0.218081 0.742717i
\(428\) −1.58176 + 19.6861i −0.0764571 + 0.951562i
\(429\) 3.75956 5.85000i 0.181513 0.282441i
\(430\) −3.44455 + 10.1996i −0.166111 + 0.491869i
\(431\) −2.11758 + 14.7281i −0.102000 + 0.709426i 0.873081 + 0.487576i \(0.162119\pi\)
−0.975081 + 0.221850i \(0.928790\pi\)
\(432\) −1.72527 + 3.60880i −0.0830071 + 0.173628i
\(433\) 0.707694 + 4.92212i 0.0340096 + 0.236542i 0.999735 0.0230243i \(-0.00732951\pi\)
−0.965725 + 0.259566i \(0.916420\pi\)
\(434\) −2.36533 + 58.9713i −0.113540 + 2.83071i
\(435\) 17.7891 + 15.4143i 0.852922 + 0.739061i
\(436\) 9.90686 3.59634i 0.474453 0.172233i
\(437\) 13.7513 + 14.8779i 0.657815 + 0.711709i
\(438\) 7.04947 + 4.94052i 0.336836 + 0.236067i
\(439\) −9.06927 + 10.4665i −0.432852 + 0.499538i −0.929709 0.368294i \(-0.879942\pi\)
0.496857 + 0.867832i \(0.334487\pi\)
\(440\) 36.6523 11.6654i 1.74733 0.556125i
\(441\) 1.63483 + 11.3705i 0.0778489 + 0.541451i
\(442\) −2.72438 + 14.7300i −0.129585 + 0.700633i
\(443\) −25.6909 3.69380i −1.22061 0.175498i −0.498264 0.867026i \(-0.666029\pi\)
−0.722350 + 0.691528i \(0.756938\pi\)
\(444\) 5.98330 + 8.14072i 0.283955 + 0.386341i
\(445\) 0.568152 0.884061i 0.0269330 0.0419085i
\(446\) 9.73604 + 16.5745i 0.461015 + 0.784827i
\(447\) −6.54456 1.92166i −0.309547 0.0908912i
\(448\) −6.42428 33.7923i −0.303519 1.59654i
\(449\) 19.5677 + 22.5823i 0.923457 + 1.06573i 0.997652 + 0.0684829i \(0.0218159\pi\)
−0.0741949 + 0.997244i \(0.523639\pi\)
\(450\) 4.79907 3.83272i 0.226230 0.180676i
\(451\) −19.9803 9.12469i −0.940835 0.429665i
\(452\) 3.90139 17.2059i 0.183506 0.809298i
\(453\) 2.17077 + 7.39297i 0.101992 + 0.347352i
\(454\) 24.1060 25.6649i 1.13135 1.20451i
\(455\) 8.53336 + 18.6854i 0.400050 + 0.875987i
\(456\) −1.43352 + 11.8622i −0.0671309 + 0.555497i
\(457\) 19.8959 12.7863i 0.930693 0.598120i 0.0149516 0.999888i \(-0.495241\pi\)
0.915741 + 0.401768i \(0.131604\pi\)
\(458\) 5.07829 1.27244i 0.237293 0.0594574i
\(459\) 6.77690i 0.316318i
\(460\) −29.2840 1.40990i −1.36538 0.0657368i
\(461\) 3.56338i 0.165963i −0.996551 0.0829815i \(-0.973556\pi\)
0.996551 0.0829815i \(-0.0264442\pi\)
\(462\) 6.57538 + 26.2422i 0.305914 + 1.22090i
\(463\) −13.3951 + 8.60848i −0.622521 + 0.400070i −0.813534 0.581517i \(-0.802459\pi\)
0.191013 + 0.981588i \(0.438823\pi\)
\(464\) 20.5773 22.9219i 0.955279 1.06412i
\(465\) 12.3242 + 26.9863i 0.571522 + 1.25146i
\(466\) 21.9170 + 20.5857i 1.01529 + 0.953616i
\(467\) 6.22163 + 21.1889i 0.287903 + 0.980507i 0.968741 + 0.248073i \(0.0797974\pi\)
−0.680838 + 0.732434i \(0.738384\pi\)
\(468\) −3.04862 0.691264i −0.140922 0.0319537i
\(469\) 9.54272 + 4.35801i 0.440642 + 0.201234i
\(470\) 21.6781 + 27.1438i 0.999936 + 1.25205i
\(471\) 0.666322 + 0.768977i 0.0307025 + 0.0354326i
\(472\) −0.108468 + 0.0525209i −0.00499264 + 0.00241747i
\(473\) −10.6314 3.12167i −0.488834 0.143535i
\(474\) −18.3873 + 10.8009i −0.844556 + 0.496100i
\(475\) 9.91863 15.4337i 0.455098 0.708146i
\(476\) −34.5134 46.9581i −1.58192 2.15232i
\(477\) 1.57729 + 0.226780i 0.0722192 + 0.0103835i
\(478\) −24.9164 4.60841i −1.13965 0.210784i
\(479\) 5.04055 + 35.0578i 0.230309 + 1.60183i 0.696773 + 0.717292i \(0.254619\pi\)
−0.466464 + 0.884540i \(0.654472\pi\)
\(480\) −10.5514 13.6981i −0.481605 0.625231i
\(481\) −5.17047 + 5.96705i −0.235753 + 0.272074i
\(482\) −6.59612 + 9.41178i −0.300445 + 0.428695i
\(483\) 2.27869 20.4943i 0.103684 0.932525i
\(484\) 6.00163 + 16.5327i 0.272801 + 0.751488i
\(485\) 13.8342 + 11.9874i 0.628176 + 0.544318i
\(486\) −1.41308 0.0566784i −0.0640985 0.00257098i
\(487\) −5.90140 41.0451i −0.267418 1.85993i −0.472693 0.881227i \(-0.656718\pi\)
0.205276 0.978704i \(-0.434191\pi\)
\(488\) −10.3786 + 1.73175i −0.469818 + 0.0783926i
\(489\) 2.26921 15.7827i 0.102617 0.713718i
\(490\) −47.0462 15.8881i −2.12533 0.717753i
\(491\) 4.03900 6.28481i 0.182278 0.283630i −0.738075 0.674718i \(-0.764265\pi\)
0.920353 + 0.391089i \(0.127901\pi\)
\(492\) −0.790825 + 9.84237i −0.0356532 + 0.443728i
\(493\) 14.7029 50.0736i 0.662187 2.25520i
\(494\) −9.28854 + 0.957407i −0.417911 + 0.0430758i
\(495\) 8.90548 + 10.2775i 0.400272 + 0.461938i
\(496\) 35.5929 15.5056i 1.59817 0.696221i
\(497\) 22.2670 48.7579i 0.998812 2.18709i
\(498\) −4.97966 + 2.03709i −0.223144 + 0.0912841i
\(499\) 5.28300 + 17.9923i 0.236500 + 0.805444i 0.989135 + 0.147007i \(0.0469639\pi\)
−0.752636 + 0.658437i \(0.771218\pi\)
\(500\) −0.819447 3.93281i −0.0366468 0.175881i
\(501\) −8.57701 + 3.91699i −0.383193 + 0.174998i
\(502\) −16.0663 + 31.7475i −0.717074 + 1.41696i
\(503\) 5.35608 3.44214i 0.238816 0.153478i −0.415759 0.909475i \(-0.636484\pi\)
0.654575 + 0.755997i \(0.272848\pi\)
\(504\) 10.0801 6.80380i 0.449001 0.303065i
\(505\) 16.6626 0.741476
\(506\) 0.242003 30.1741i 0.0107584 1.34140i
\(507\) 10.5570i 0.468854i
\(508\) 8.37270 + 3.20684i 0.371479 + 0.142281i
\(509\) 2.69351 + 4.19118i 0.119388 + 0.185771i 0.895804 0.444450i \(-0.146601\pi\)
−0.776416 + 0.630221i \(0.782964\pi\)
\(510\) −26.1381 13.2275i −1.15741 0.585726i
\(511\) −10.8724 23.8072i −0.480966 1.05317i
\(512\) −18.1655 + 13.4912i −0.802811 + 0.596234i
\(513\) −4.05330 + 1.19016i −0.178958 + 0.0525467i
\(514\) 4.59662 1.88039i 0.202748 0.0829406i
\(515\) 3.74700 + 1.71120i 0.165112 + 0.0754043i
\(516\) 0.311717 + 4.97118i 0.0137226 + 0.218844i
\(517\) −27.0207 + 23.4136i −1.18837 + 1.02973i
\(518\) −3.14941 30.5548i −0.138377 1.34250i
\(519\) 20.1491 + 5.91630i 0.884446 + 0.259697i
\(520\) 8.61663 10.4091i 0.377864 0.456468i
\(521\) −25.5726 16.4345i −1.12036 0.720009i −0.156831 0.987626i \(-0.550128\pi\)
−0.963526 + 0.267616i \(0.913764\pi\)
\(522\) 10.3181 + 3.48456i 0.451610 + 0.152515i
\(523\) −22.5741 3.24567i −0.987098 0.141923i −0.370188 0.928957i \(-0.620707\pi\)
−0.616910 + 0.787034i \(0.711616\pi\)
\(524\) −25.5055 25.9572i −1.11421 1.13395i
\(525\) −18.4829 + 2.65744i −0.806660 + 0.115980i
\(526\) 0.000796543 0.0198590i 3.47309e−5 0.000865895i
\(527\) 43.0742 49.7102i 1.87634 2.16541i
\(528\) 13.6520 11.4162i 0.594127 0.496826i
\(529\) −8.19398 + 21.4909i −0.356260 + 0.934387i
\(530\) −3.95332 + 5.64087i −0.171721 + 0.245024i
\(531\) −0.0322012 0.0279025i −0.00139741 0.00121087i
\(532\) 22.0247 28.8895i 0.954890 1.25252i
\(533\) −7.63808 + 1.09819i −0.330842 + 0.0475679i
\(534\) 0.0884285 0.478109i 0.00382668 0.0206898i
\(535\) 4.29553 29.8760i 0.185712 1.29165i
\(536\) −0.155498 6.89927i −0.00671649 0.298003i
\(537\) −9.62081 6.18292i −0.415168 0.266813i
\(538\) 12.6382 7.42379i 0.544871 0.320062i
\(539\) 14.3988 49.0380i 0.620202 2.11221i
\(540\) 2.97673 5.33952i 0.128098 0.229776i
\(541\) −13.9199 + 12.0616i −0.598462 + 0.518570i −0.900574 0.434702i \(-0.856854\pi\)
0.302112 + 0.953272i \(0.402308\pi\)
\(542\) −16.8515 + 13.4582i −0.723833 + 0.578080i
\(543\) 6.28713 13.7669i 0.269806 0.590794i
\(544\) −17.9078 + 33.8962i −0.767792 + 1.45329i
\(545\) −15.4550 + 4.53799i −0.662019 + 0.194386i
\(546\) 6.92754 + 6.50676i 0.296471 + 0.278463i
\(547\) −37.4425 + 17.0994i −1.60093 + 0.731119i −0.997785 0.0665144i \(-0.978812\pi\)
−0.603142 + 0.797634i \(0.706085\pi\)
\(548\) −30.4313 + 16.2716i −1.29996 + 0.695090i
\(549\) −2.01125 3.12957i −0.0858381 0.133567i
\(550\) −26.5055 + 6.64138i −1.13020 + 0.283189i
\(551\) 32.5315 1.38589
\(552\) −12.7872 + 4.52622i −0.544261 + 0.192649i
\(553\) 64.8350 2.75706
\(554\) 42.7924 10.7223i 1.81807 0.455547i
\(555\) −8.34776 12.9894i −0.354343 0.551368i
\(556\) −3.08967 5.77831i −0.131031 0.245055i
\(557\) −8.65993 + 3.95486i −0.366933 + 0.167573i −0.590344 0.807152i \(-0.701008\pi\)
0.223411 + 0.974724i \(0.428281\pi\)
\(558\) 10.0050 + 9.39731i 0.423547 + 0.397820i
\(559\) −3.73494 + 1.09668i −0.157971 + 0.0463845i
\(560\) 6.56697 + 52.1582i 0.277505 + 2.20409i
\(561\) 12.5251 27.4262i 0.528811 1.15793i
\(562\) 11.5716 9.24154i 0.488120 0.389831i
\(563\) −13.8163 + 11.9719i −0.582287 + 0.504555i −0.895460 0.445141i \(-0.853153\pi\)
0.313173 + 0.949696i \(0.398608\pi\)
\(564\) 14.0382 + 7.82618i 0.591116 + 0.329542i
\(565\) −7.59646 + 25.8712i −0.319586 + 1.08841i
\(566\) −13.5642 + 7.96776i −0.570148 + 0.334910i
\(567\) 3.61714 + 2.32459i 0.151905 + 0.0976237i
\(568\) −35.2514 + 0.794507i −1.47912 + 0.0333368i
\(569\) −3.82495 + 26.6031i −0.160350 + 1.11526i 0.737623 + 0.675212i \(0.235948\pi\)
−0.897974 + 0.440049i \(0.854961\pi\)
\(570\) 3.32111 17.9564i 0.139106 0.752109i
\(571\) −14.3037 + 2.05656i −0.598591 + 0.0860644i −0.434949 0.900455i \(-0.643233\pi\)
−0.163643 + 0.986520i \(0.552324\pi\)
\(572\) 11.0602 + 8.43204i 0.462450 + 0.352561i
\(573\) −10.4190 9.02815i −0.435262 0.377157i
\(574\) 17.2295 24.5842i 0.719146 1.02613i
\(575\) 20.7000 + 2.30156i 0.863251 + 0.0959816i
\(576\) −6.91806 4.01752i −0.288252 0.167397i
\(577\) −5.35962 + 6.18533i −0.223124 + 0.257499i −0.856264 0.516539i \(-0.827220\pi\)
0.633140 + 0.774037i \(0.281766\pi\)
\(578\) −1.63950 + 40.8752i −0.0681941 + 1.70018i
\(579\) −14.8854 + 2.14020i −0.618617 + 0.0889437i
\(580\) −33.5791 + 32.9948i −1.39430 + 1.37003i
\(581\) 16.1912 + 2.32795i 0.671726 + 0.0965796i
\(582\) 8.02412 + 2.70986i 0.332610 + 0.112327i
\(583\) −5.96418 3.83294i −0.247011 0.158744i
\(584\) −10.9785 + 13.2623i −0.454293 + 0.548796i
\(585\) 4.58397 + 1.34597i 0.189524 + 0.0556492i
\(586\) −1.11150 10.7835i −0.0459157 0.445463i
\(587\) −1.83263 + 1.58798i −0.0756407 + 0.0655431i −0.691861 0.722031i \(-0.743209\pi\)
0.616220 + 0.787574i \(0.288663\pi\)
\(588\) −22.9298 + 1.43781i −0.945608 + 0.0592942i
\(589\) 37.2967 + 17.0328i 1.53678 + 0.701825i
\(590\) 0.170470 0.0697363i 0.00701816 0.00287100i
\(591\) 15.5012 4.55156i 0.637633 0.187226i
\(592\) −17.1875 + 10.6242i −0.706404 + 0.436650i
\(593\) 15.2780 + 33.4542i 0.627393 + 1.37380i 0.910018 + 0.414569i \(0.136068\pi\)
−0.282624 + 0.959231i \(0.591205\pi\)
\(594\) 5.61399 + 2.84104i 0.230345 + 0.116569i
\(595\) 48.1524 + 74.9265i 1.97405 + 3.07169i
\(596\) 4.87929 12.7393i 0.199863 0.521820i
\(597\) 17.2902i 0.707640i
\(598\) −5.65952 8.96364i −0.231435 0.366551i
\(599\) 5.49196 0.224395 0.112198 0.993686i \(-0.464211\pi\)
0.112198 + 0.993686i \(0.464211\pi\)
\(600\) 6.87209 + 10.1812i 0.280552 + 0.415647i
\(601\) 8.25357 5.30425i 0.336670 0.216365i −0.361371 0.932422i \(-0.617691\pi\)
0.698042 + 0.716057i \(0.254055\pi\)
\(602\) 6.83798 13.5121i 0.278695 0.550711i
\(603\) 2.21939 1.01356i 0.0903807 0.0412755i
\(604\) −15.0862 + 3.14338i −0.613847 + 0.127902i
\(605\) −7.57308 25.7915i −0.307889 1.04857i
\(606\) 7.13540 2.91896i 0.289856 0.118575i
\(607\) −5.76615 + 12.6261i −0.234041 + 0.512478i −0.989816 0.142353i \(-0.954533\pi\)
0.755775 + 0.654831i \(0.227260\pi\)
\(608\) −23.4185 4.75794i −0.949746 0.192960i
\(609\) −21.6832 25.0237i −0.878647 1.01401i
\(610\) 15.9962 1.64880i 0.647668 0.0667578i
\(611\) −3.53873 + 12.0518i −0.143161 + 0.487563i
\(612\) −13.5103 1.08554i −0.546120 0.0438802i
\(613\) 5.58325 8.68770i 0.225505 0.350893i −0.710003 0.704199i \(-0.751306\pi\)
0.935508 + 0.353306i \(0.114943\pi\)
\(614\) −38.6863 13.0649i −1.56125 0.527256i
\(615\) 2.14762 14.9370i 0.0866004 0.602319i
\(616\) −53.3690 + 8.90500i −2.15030 + 0.358793i
\(617\) −2.50992 17.4569i −0.101046 0.702788i −0.975871 0.218349i \(-0.929933\pi\)
0.874825 0.484439i \(-0.160976\pi\)
\(618\) 1.90434 + 0.0763827i 0.0766037 + 0.00307256i
\(619\) 5.30923 + 4.60047i 0.213396 + 0.184909i 0.754999 0.655725i \(-0.227637\pi\)
−0.541603 + 0.840634i \(0.682183\pi\)
\(620\) −55.7732 + 20.2465i −2.23991 + 0.813120i
\(621\) −3.25520 3.52189i −0.130627 0.141328i
\(622\) −14.3604 + 20.4904i −0.575799 + 0.821588i
\(623\) −0.968061 + 1.11720i −0.0387845 + 0.0447597i
\(624\) 1.86642 5.96692i 0.0747166 0.238868i
\(625\) 3.96402 + 27.5704i 0.158561 + 1.10282i
\(626\) 18.7711 + 3.47180i 0.750244 + 0.138761i
\(627\) 18.6034 + 2.67477i 0.742950 + 0.106820i
\(628\) −1.63975 + 1.20519i −0.0654330 + 0.0480922i
\(629\) −18.5081 + 28.7991i −0.737965 + 1.14830i
\(630\) −16.0259 + 9.41379i −0.638489 + 0.375054i
\(631\) 5.65511 + 1.66049i 0.225126 + 0.0661030i 0.392350 0.919816i \(-0.371662\pi\)
−0.167224 + 0.985919i \(0.553480\pi\)
\(632\) −18.5870 38.3865i −0.739352 1.52693i
\(633\) 4.38305 + 5.05831i 0.174211 + 0.201050i
\(634\) 19.9609 + 24.9937i 0.792749 + 0.992627i
\(635\) −12.4642 5.69223i −0.494628 0.225889i
\(636\) −0.704757 + 3.10812i −0.0279454 + 0.123245i
\(637\) −5.05847 17.2276i −0.200424 0.682580i
\(638\) −35.3172 33.1720i −1.39822 1.31329i
\(639\) −5.17874 11.3399i −0.204868 0.448598i
\(640\) 28.9984 18.8409i 1.14626 0.744751i
\(641\) 28.3663 18.2299i 1.12040 0.720039i 0.156867 0.987620i \(-0.449861\pi\)
0.963535 + 0.267581i \(0.0862243\pi\)
\(642\) −3.39422 13.5462i −0.133959 0.534628i
\(643\) 3.77024i 0.148684i −0.997233 0.0743418i \(-0.976314\pi\)
0.997233 0.0743418i \(-0.0236856\pi\)
\(644\) 40.4920 + 7.82555i 1.59561 + 0.308370i
\(645\) 7.61239i 0.299738i
\(646\) −39.2727 + 9.84039i −1.54516 + 0.387165i
\(647\) −2.43144 + 1.56259i −0.0955898 + 0.0614319i −0.587562 0.809179i \(-0.699912\pi\)
0.491973 + 0.870611i \(0.336276\pi\)
\(648\) 0.339342 2.80800i 0.0133306 0.110309i
\(649\) 0.0787491 + 0.172436i 0.00309117 + 0.00676872i
\(650\) −6.57206 + 6.99707i −0.257778 + 0.274448i
\(651\) −11.7574 40.0421i −0.460810 1.56937i
\(652\) 31.1005 + 7.05193i 1.21799 + 0.276175i
\(653\) −4.52421 2.06614i −0.177046 0.0808542i 0.324920 0.945741i \(-0.394663\pi\)
−0.501966 + 0.864887i \(0.667390\pi\)
\(654\) −5.82329 + 4.65070i −0.227709 + 0.181857i
\(655\) 36.4211 + 42.0322i 1.42309 + 1.64233i
\(656\) −19.4948 3.15314i −0.761145 0.123109i
\(657\) −5.84046 1.71491i −0.227858 0.0669051i
\(658\) −24.7500 42.1341i −0.964854 1.64256i
\(659\) 6.45190 10.0393i 0.251330 0.391077i −0.692548 0.721372i \(-0.743512\pi\)
0.943878 + 0.330295i \(0.107148\pi\)
\(660\) −21.9154 + 16.1075i −0.853057 + 0.626983i
\(661\) 40.1955 + 5.77923i 1.56342 + 0.224786i 0.869011 0.494792i \(-0.164756\pi\)
0.694411 + 0.719579i \(0.255665\pi\)
\(662\) 3.37622 18.2543i 0.131220 0.709473i
\(663\) −1.50744 10.4845i −0.0585443 0.407184i
\(664\) −3.26344 10.2536i −0.126646 0.397918i
\(665\) −36.3575 + 41.9588i −1.40988 + 1.62709i
\(666\) −5.85023 4.10005i −0.226692 0.158874i
\(667\) 16.4112 + 33.0851i 0.635446 + 1.28106i
\(668\) −6.43493 17.7264i −0.248975 0.685853i
\(669\) −10.2724 8.90112i −0.397155 0.344137i
\(670\) −0.422694 + 10.5384i −0.0163301 + 0.407134i
\(671\) 2.35546 + 16.3826i 0.0909317 + 0.632444i
\(672\) 11.9492 + 21.1852i 0.460952 + 0.817237i
\(673\) 3.31937 23.0867i 0.127952 0.889927i −0.820193 0.572088i \(-0.806134\pi\)
0.948145 0.317839i \(-0.102957\pi\)
\(674\) 1.34431 3.98062i 0.0517809 0.153328i
\(675\) −2.34792 + 3.65344i −0.0903716 + 0.140621i
\(676\) −21.0462 1.69104i −0.809470 0.0650401i
\(677\) 5.39066 18.3589i 0.207180 0.705589i −0.788690 0.614792i \(-0.789240\pi\)
0.995869 0.0907978i \(-0.0289417\pi\)
\(678\) 1.27910 + 12.4095i 0.0491235 + 0.476585i
\(679\) −16.8625 19.4604i −0.647123 0.746820i
\(680\) 30.5569 49.9894i 1.17181 1.91701i
\(681\) −10.3429 + 22.6477i −0.396339 + 0.867862i
\(682\) −23.1223 56.5224i −0.885398 2.16436i
\(683\) 5.87295 + 20.0014i 0.224722 + 0.765333i 0.992243 + 0.124310i \(0.0396717\pi\)
−0.767521 + 0.641023i \(0.778510\pi\)
\(684\) −1.72340 8.27121i −0.0658960 0.316258i
\(685\) 47.9734 21.9087i 1.83297 0.837088i
\(686\) 24.3465 + 12.3209i 0.929552 + 0.470413i
\(687\) −3.11424 + 2.00140i −0.118816 + 0.0763581i
\(688\) −9.96035 0.174861i −0.379735 0.00666651i
\(689\) −2.49066 −0.0948867
\(690\) 19.9374 5.68086i 0.759003 0.216267i
\(691\) 17.6219i 0.670368i 0.942153 + 0.335184i \(0.108799\pi\)
−0.942153 + 0.335184i \(0.891201\pi\)
\(692\) −15.0221 + 39.2210i −0.571055 + 1.49096i
\(693\) −10.3423 16.0929i −0.392870 0.611318i
\(694\) 2.07397 4.09824i 0.0787270 0.155567i
\(695\) 4.16004 + 9.10922i 0.157799 + 0.345532i
\(696\) −8.59949 + 20.0117i −0.325963 + 0.758541i
\(697\) −32.1026 + 9.42617i −1.21597 + 0.357042i
\(698\) 0.328714 + 0.803541i 0.0124420 + 0.0304145i
\(699\) −19.3404 8.83247i −0.731521 0.334075i
\(700\) −2.33718 37.2727i −0.0883371 1.40878i
\(701\) −2.67368 + 2.31675i −0.100983 + 0.0875025i −0.703889 0.710310i \(-0.748555\pi\)
0.602906 + 0.797812i \(0.294009\pi\)
\(702\) 2.19877 0.226636i 0.0829873 0.00855383i
\(703\) −20.4753 6.01210i −0.772241 0.226751i
\(704\) 20.5722 + 29.0450i 0.775346 + 1.09467i
\(705\) −20.6641 13.2800i −0.778255 0.500154i
\(706\) 0.0221039 0.0654516i 0.000831892 0.00246330i
\(707\) −23.2005 3.33573i −0.872546 0.125453i
\(708\) 0.0607838 0.0597261i 0.00228440 0.00224464i
\(709\) 36.6166 5.26468i 1.37517 0.197719i 0.585210 0.810882i \(-0.301012\pi\)
0.789957 + 0.613163i \(0.210103\pi\)
\(710\) 53.8453 + 2.15973i 2.02078 + 0.0810531i
\(711\) 9.87462 11.3959i 0.370327 0.427380i
\(712\) 0.938981 + 0.252873i 0.0351898 + 0.00947682i
\(713\) 1.49246 + 46.5241i 0.0558931 + 1.74234i
\(714\) 33.7458 + 23.6503i 1.26291 + 0.885090i
\(715\) −16.0637 13.9193i −0.600749 0.520552i
\(716\) 13.8672 18.1894i 0.518241 0.679770i
\(717\) 17.7350 2.54991i 0.662326 0.0952281i
\(718\) −39.7076 7.34411i −1.48188 0.274080i
\(719\) −0.0402410 + 0.279882i −0.00150074 + 0.0104379i −0.990558 0.137094i \(-0.956224\pi\)
0.989057 + 0.147532i \(0.0471329\pi\)
\(720\) 10.1679 + 6.78963i 0.378936 + 0.253035i
\(721\) −4.87464 3.13274i −0.181541 0.116669i
\(722\) 0.826772 + 1.40749i 0.0307693 + 0.0523813i
\(723\) 2.28959 7.79763i 0.0851508 0.289997i
\(724\) 26.4382 + 14.7391i 0.982570 + 0.547773i
\(725\) 25.2749 21.9008i 0.938686 0.813376i
\(726\) −7.76117 9.71800i −0.288044 0.360669i
\(727\) 12.5098 27.3926i 0.463962 1.01594i −0.522604 0.852575i \(-0.675039\pi\)
0.986566 0.163360i \(-0.0522333\pi\)
\(728\) −14.0814 + 12.7683i −0.521890 + 0.473225i
\(729\) 0.959493 0.281733i 0.0355368 0.0104345i
\(730\) 18.0141 19.1790i 0.666730 0.709847i
\(731\) −15.3525 + 7.01124i −0.567832 + 0.259320i
\(732\) 6.56120 3.50828i 0.242509 0.129670i
\(733\) 5.71613 + 8.89447i 0.211130 + 0.328525i 0.930626 0.365972i \(-0.119263\pi\)
−0.719496 + 0.694497i \(0.755627\pi\)
\(734\) −1.90808 7.61509i −0.0704285 0.281078i
\(735\) 35.1125 1.29514
\(736\) −6.97509 26.2173i −0.257105 0.966383i
\(737\) −10.8552 −0.399856
\(738\) −1.69700 6.77267i −0.0624674 0.249305i
\(739\) 1.00644 + 1.56606i 0.0370226 + 0.0576083i 0.859272 0.511520i \(-0.170917\pi\)
−0.822249 + 0.569128i \(0.807281\pi\)
\(740\) 27.2325 14.5612i 1.00108 0.535282i
\(741\) 6.00611 2.74290i 0.220640 0.100763i
\(742\) 6.63376 7.06275i 0.243533 0.259282i
\(743\) −19.2811 + 5.66144i −0.707355 + 0.207698i −0.615572 0.788081i \(-0.711075\pi\)
−0.0917832 + 0.995779i \(0.529257\pi\)
\(744\) −20.3369 + 18.4405i −0.745586 + 0.676061i
\(745\) −8.66085 + 18.9646i −0.317309 + 0.694810i
\(746\) −4.50911 5.64600i −0.165090 0.206715i
\(747\) 2.87517 2.49135i 0.105197 0.0911536i
\(748\) 52.6699 + 29.3629i 1.92580 + 1.07362i
\(749\) −11.9619 + 40.7386i −0.437080 + 1.48856i
\(750\) 1.43876 + 2.44933i 0.0525361 + 0.0894369i
\(751\) −12.7873 8.21787i −0.466614 0.299874i 0.286127 0.958192i \(-0.407632\pi\)
−0.752741 + 0.658317i \(0.771269\pi\)
\(752\) −17.8507 + 26.7327i −0.650950 + 0.974840i
\(753\) 3.58061 24.9037i 0.130485 0.907541i
\(754\) −16.7381 3.09580i −0.609567 0.112742i
\(755\) 23.3117 3.35172i 0.848399 0.121981i
\(756\) −5.21365 + 6.83868i −0.189619 + 0.248720i
\(757\) 5.50446 + 4.76964i 0.200063 + 0.173356i 0.749131 0.662422i \(-0.230472\pi\)
−0.549068 + 0.835778i \(0.685017\pi\)
\(758\) −39.1191 27.4161i −1.42087 0.995798i
\(759\) 6.66464 + 20.2694i 0.241911 + 0.735733i
\(760\) 35.2654 + 9.49717i 1.27921 + 0.344499i
\(761\) −6.34480 + 7.32229i −0.229999 + 0.265433i −0.859005 0.511968i \(-0.828917\pi\)
0.629006 + 0.777401i \(0.283462\pi\)
\(762\) −6.33470 0.254084i −0.229482 0.00920450i
\(763\) 22.4276 3.22460i 0.811932 0.116738i
\(764\) 19.6672 19.3250i 0.711536 0.699154i
\(765\) 20.5035 + 2.94796i 0.741305 + 0.106584i
\(766\) 3.92931 11.6350i 0.141972 0.420391i
\(767\) 0.0560249 + 0.0360050i 0.00202294 + 0.00130007i
\(768\) 9.11738 13.1481i 0.328995 0.474442i
\(769\) −28.2951 8.30819i −1.02035 0.299601i −0.271567 0.962419i \(-0.587542\pi\)
−0.748780 + 0.662818i \(0.769360\pi\)
\(770\) 82.2558 8.47844i 2.96429 0.305542i
\(771\) −2.65401 + 2.29971i −0.0955817 + 0.0828220i
\(772\) −1.88228 30.0180i −0.0677446 1.08037i
\(773\) −24.8174 11.3337i −0.892619 0.407645i −0.0843345 0.996437i \(-0.526876\pi\)
−0.808285 + 0.588792i \(0.799604\pi\)
\(774\) −1.33354 3.25984i −0.0479331 0.117173i
\(775\) 40.4440 11.8754i 1.45279 0.426578i
\(776\) −6.68762 + 15.5626i −0.240071 + 0.558665i
\(777\) 9.02281 + 19.7572i 0.323691 + 0.708785i
\(778\) 0.937224 1.85199i 0.0336011 0.0663969i
\(779\) −11.2757 17.5453i −0.403994 0.628627i
\(780\) −3.41757 + 8.92288i −0.122369 + 0.319490i
\(781\) 55.4639i 1.98465i
\(782\) −29.8199 34.9769i −1.06636 1.25077i
\(783\) −7.70080 −0.275204
\(784\) 0.806554 45.9425i 0.0288055 1.64080i
\(785\) 2.61639 1.68145i 0.0933829 0.0600135i
\(786\) 22.9598 + 11.6191i 0.818947 + 0.414440i
\(787\) 15.9160 7.26860i 0.567345 0.259098i −0.111026 0.993818i \(-0.535414\pi\)
0.678371 + 0.734720i \(0.262686\pi\)
\(788\) 6.59086 + 31.6318i 0.234790 + 1.12684i
\(789\) 0.00395940 + 0.0134845i 0.000140958 + 0.000480060i
\(790\) 24.6795 + 60.3290i 0.878057 + 2.14641i
\(791\) 15.7563 34.5015i 0.560230 1.22673i
\(792\) −6.56309 + 10.7368i −0.233209 + 0.381516i
\(793\) 3.80773 + 4.39436i 0.135217 + 0.156048i
\(794\) 4.32559 + 41.9659i 0.153510 + 1.48931i
\(795\) 1.37224 4.67344i 0.0486685 0.165750i
\(796\) −34.4693 2.76957i −1.22173 0.0981648i
\(797\) 22.7736 35.4364i 0.806682 1.25522i −0.156848 0.987623i \(-0.550133\pi\)
0.963530 0.267599i \(-0.0862303\pi\)
\(798\) −8.21896 + 24.3370i −0.290948 + 0.861522i
\(799\) −7.75052 + 53.9061i −0.274194 + 1.90706i
\(800\) −21.3978 + 12.0692i −0.756528 + 0.426710i
\(801\) 0.0489289 + 0.340308i 0.00172882 + 0.0120242i
\(802\) 1.03531 25.8118i 0.0365581 0.911448i
\(803\) 20.4669 + 17.7347i 0.722261 + 0.625842i
\(804\) 1.66511 + 4.58688i 0.0587238 + 0.161767i
\(805\) −61.0143 15.8092i −2.15047 0.557201i
\(806\) −17.5690 12.3130i −0.618843 0.433708i
\(807\) −6.78715 + 7.83279i −0.238919 + 0.275727i
\(808\) 4.67620 + 14.6925i 0.164508 + 0.516881i
\(809\) −1.17526 8.17415i −0.0413201 0.287388i −0.999996 0.00288662i \(-0.999081\pi\)
0.958676 0.284501i \(-0.0918279\pi\)
\(810\) −0.786170 + 4.25061i −0.0276232 + 0.149351i
\(811\) −7.82595 1.12520i −0.274806 0.0395112i 0.00353380 0.999994i \(-0.498875\pi\)
−0.278340 + 0.960483i \(0.589784\pi\)
\(812\) 53.3599 39.2187i 1.87257 1.37631i
\(813\) 8.24451 12.8287i 0.289148 0.449923i
\(814\) 16.0982 + 27.4054i 0.564241 + 0.960559i
\(815\) −46.7633 13.7310i −1.63805 0.480974i
\(816\) 4.32819 26.7598i 0.151517 0.936781i
\(817\) −6.88966 7.95109i −0.241039 0.278174i
\(818\) −24.0427 + 19.2014i −0.840633 + 0.671362i
\(819\) −6.11313 2.79177i −0.213610 0.0975524i
\(820\) 29.4341 + 6.67408i 1.02788 + 0.233069i
\(821\) −8.77825 29.8960i −0.306363 1.04338i −0.958457 0.285238i \(-0.907927\pi\)
0.652094 0.758138i \(-0.273891\pi\)
\(822\) 16.7056 17.7859i 0.582674 0.620354i
\(823\) 12.2804 + 26.8903i 0.428067 + 0.937336i 0.993636 + 0.112635i \(0.0359292\pi\)
−0.565569 + 0.824701i \(0.691343\pi\)
\(824\) −0.457315 + 3.78420i −0.0159313 + 0.131829i
\(825\) 16.2544 10.4461i 0.565906 0.363685i
\(826\) −0.251319 + 0.0629719i −0.00874450 + 0.00219107i
\(827\) 40.3877i 1.40442i −0.711971 0.702208i \(-0.752197\pi\)
0.711971 0.702208i \(-0.247803\pi\)
\(828\) 7.54257 5.92534i 0.262122 0.205920i
\(829\) 8.00476i 0.278017i −0.990291 0.139008i \(-0.955608\pi\)
0.990291 0.139008i \(-0.0443915\pi\)
\(830\) 3.99705 + 15.9521i 0.138739 + 0.553705i
\(831\) −26.2422 + 16.8649i −0.910333 + 0.585036i
\(832\) 11.5965 + 4.67664i 0.402038 + 0.162133i
\(833\) −32.3396 70.8139i −1.12050 2.45356i
\(834\) 3.37720 + 3.17207i 0.116943 + 0.109840i
\(835\) 8.11984 + 27.6536i 0.280998 + 0.956993i
\(836\) −8.31229 + 36.6589i −0.287486 + 1.26787i
\(837\) −8.82882 4.03199i −0.305169 0.139366i
\(838\) 31.0551 + 38.8851i 1.07278 + 1.34326i
\(839\) −33.5044 38.6661i −1.15670 1.33490i −0.932844 0.360282i \(-0.882681\pi\)
−0.223857 0.974622i \(-0.571865\pi\)
\(840\) −16.2000 33.4568i −0.558954 1.15437i
\(841\) 29.0749 + 8.53717i 1.00258 + 0.294385i
\(842\) 23.0545 13.5424i 0.794511 0.466703i
\(843\) −5.66137 + 8.80927i −0.194988 + 0.303407i
\(844\) −10.7862 + 7.92769i −0.371276 + 0.272882i
\(845\) 31.9402 + 4.59231i 1.09878 + 0.157980i
\(846\) −11.1753 2.06693i −0.384216 0.0710626i
\(847\) 5.38126 + 37.4275i 0.184902 + 1.28602i
\(848\) −6.08338 1.90285i −0.208904 0.0653441i
\(849\) 7.28448 8.40674i 0.250003 0.288519i
\(850\) −23.8877 + 34.0845i −0.819341 + 1.16909i
\(851\) −4.21483 23.8567i −0.144483 0.817799i
\(852\) 23.4364 8.50776i 0.802917 0.291471i
\(853\) 15.0777 + 13.0649i 0.516250 + 0.447333i 0.873605 0.486635i \(-0.161776\pi\)
−0.357355 + 0.933969i \(0.616321\pi\)
\(854\) −22.6028 0.906594i −0.773451 0.0310230i
\(855\) 1.83763 + 12.7810i 0.0628455 + 0.437100i
\(856\) 27.5492 4.59678i 0.941611 0.157115i
\(857\) 3.69701 25.7132i 0.126287 0.878347i −0.823915 0.566713i \(-0.808215\pi\)
0.950202 0.311634i \(-0.100876\pi\)
\(858\) −9.31733 3.14659i −0.318088 0.107423i
\(859\) −5.68827 + 8.85113i −0.194081 + 0.301997i −0.924632 0.380862i \(-0.875627\pi\)
0.730550 + 0.682859i \(0.239264\pi\)
\(860\) 15.1759 + 1.21937i 0.517493 + 0.0415801i
\(861\) −5.98057 + 20.3679i −0.203817 + 0.694137i
\(862\) 20.9319 2.15754i 0.712944 0.0734860i
\(863\) 7.31051 + 8.43677i 0.248853 + 0.287191i 0.866409 0.499336i \(-0.166423\pi\)
−0.617556 + 0.786527i \(0.711877\pi\)
\(864\) 5.54360 + 1.12629i 0.188597 + 0.0383173i
\(865\) 26.6646 58.3873i 0.906624 1.98523i
\(866\) 6.50894 2.66269i 0.221183 0.0904817i
\(867\) −8.14949 27.7546i −0.276771 0.942596i
\(868\) 81.7103 17.0253i 2.77343 0.577876i
\(869\) −61.0248 + 27.8691i −2.07012 + 0.945394i
\(870\) 15.0309 29.7015i 0.509595 1.00698i
\(871\) −3.20816 + 2.06176i −0.108704 + 0.0698599i
\(872\) −8.33874 12.3541i −0.282385 0.418364i
\(873\) −5.98873 −0.202688
\(874\) 15.6829 23.9781i 0.530483 0.811072i
\(875\) 8.63653i 0.291968i
\(876\) 4.35434 11.3687i 0.147120 0.384112i
\(877\) −21.2655 33.0898i −0.718085 1.11736i −0.987996 0.154477i \(-0.950631\pi\)
0.269911 0.962885i \(-0.413006\pi\)
\(878\) 17.4753 + 8.84365i 0.589764 + 0.298459i
\(879\) 3.18436 + 6.97279i 0.107406 + 0.235186i
\(880\) −28.6010 46.2702i −0.964141 1.55977i
\(881\) −7.34472 + 2.15660i −0.247450 + 0.0726578i −0.403105 0.915154i \(-0.632069\pi\)
0.155656 + 0.987811i \(0.450251\pi\)
\(882\) 15.0362 6.15101i 0.506294 0.207115i
\(883\) −4.51069 2.05997i −0.151797 0.0693233i 0.338068 0.941122i \(-0.390227\pi\)
−0.489865 + 0.871798i \(0.662954\pi\)
\(884\) 21.1431 1.32578i 0.711119 0.0445907i
\(885\) −0.0984265 + 0.0852871i −0.00330857 + 0.00286689i
\(886\) 3.76350 + 36.5126i 0.126437 + 1.22667i
\(887\) 17.1493 + 5.03547i 0.575815 + 0.169075i 0.556658 0.830742i \(-0.312083\pi\)
0.0191575 + 0.999816i \(0.493902\pi\)
\(888\) 9.11086 11.0061i 0.305740 0.369341i
\(889\) 16.2153 + 10.4209i 0.543844 + 0.349507i
\(890\) −1.40805 0.475518i −0.0471979 0.0159394i
\(891\) −4.40378 0.633168i −0.147532 0.0212119i
\(892\) 19.3905 19.0531i 0.649242 0.637944i
\(893\) −33.6027 + 4.83134i −1.12447 + 0.161675i
\(894\) −0.386595 + 9.63839i −0.0129297 + 0.322356i
\(895\) −22.8914 + 26.4181i −0.765177 + 0.883061i
\(896\) −44.1483 + 20.4282i −1.47489 + 0.682459i
\(897\) 5.81950 + 4.72461i 0.194307 + 0.157750i
\(898\) 24.2526 34.6053i 0.809321 1.15479i
\(899\) 56.4873 + 48.9466i 1.88396 + 1.63246i
\(900\) −6.90732 5.26598i −0.230244 0.175533i
\(901\) −10.6891 + 1.53687i −0.356107 + 0.0512004i
\(902\) −5.64953 + 30.5455i −0.188109 + 1.01705i
\(903\) −1.52395 + 10.5993i −0.0507138 + 0.352722i
\(904\) −24.9442 + 0.562200i −0.829631 + 0.0186985i
\(905\) −38.9168 25.0103i −1.29364 0.831370i
\(906\) 9.39557 5.51904i 0.312147 0.183358i
\(907\) 14.7649 50.2847i 0.490261 1.66968i −0.227810 0.973706i \(-0.573157\pi\)
0.718071 0.695970i \(-0.245025\pi\)
\(908\) −43.4932 24.2470i −1.44337 0.804666i
\(909\) −4.11985 + 3.56987i −0.136647 + 0.118405i
\(910\) 22.6997 18.1288i 0.752486 0.600964i
\(911\) −1.92923 + 4.22441i −0.0639181 + 0.139961i −0.938895 0.344203i \(-0.888149\pi\)
0.874977 + 0.484164i \(0.160876\pi\)
\(912\) 16.7653 2.11084i 0.555156 0.0698968i
\(913\) −16.2404 + 4.76860i −0.537478 + 0.157818i
\(914\) −24.3792 22.8984i −0.806391 0.757410i
\(915\) −10.3434 + 4.72367i −0.341942 + 0.156160i
\(916\) −3.49109 6.52905i −0.115349 0.215726i
\(917\) −42.2972 65.8157i −1.39678 2.17343i
\(918\) 9.29659 2.32941i 0.306833 0.0768818i
\(919\) 11.6568 0.384523 0.192262 0.981344i \(-0.438418\pi\)
0.192262 + 0.981344i \(0.438418\pi\)
\(920\) 8.13162 + 40.6566i 0.268092 + 1.34041i
\(921\) 28.8732 0.951404
\(922\) −4.88826 + 1.22483i −0.160986 + 0.0403376i
\(923\) 10.5344 + 16.3919i 0.346745 + 0.539545i
\(924\) 33.7390 18.0403i 1.10993 0.593482i
\(925\) −19.9555 + 9.11337i −0.656133 + 0.299646i
\(926\) 16.4134 + 15.4165i 0.539378 + 0.506616i
\(927\) −1.29306 + 0.379677i −0.0424698 + 0.0124702i
\(928\) −38.5173 20.3492i −1.26439 0.667997i
\(929\) −5.17355 + 11.3285i −0.169739 + 0.371676i −0.975316 0.220815i \(-0.929128\pi\)
0.805577 + 0.592491i \(0.201855\pi\)
\(930\) 32.7837 26.1823i 1.07502 0.858553i
\(931\) 36.6748 31.7789i 1.20197 1.04151i
\(932\) 20.7062 37.1417i 0.678253 1.21662i
\(933\) 4.98466 16.9762i 0.163190 0.555775i
\(934\) 26.9286 15.8181i 0.881129 0.517584i
\(935\) −77.5294 49.8251i −2.53548 1.62946i
\(936\) 0.0996130 + 4.41972i 0.00325595 + 0.144463i
\(937\) −2.55289 + 17.7557i −0.0833993 + 0.580055i 0.904678 + 0.426096i \(0.140111\pi\)
−0.988077 + 0.153959i \(0.950798\pi\)
\(938\) 2.69826 14.5887i 0.0881012 0.476339i
\(939\) −13.3609 + 1.92101i −0.436016 + 0.0626897i
\(940\) 29.7847 39.0682i 0.971470 1.27427i
\(941\) −28.6857 24.8563i −0.935127 0.810292i 0.0469256 0.998898i \(-0.485058\pi\)
−0.982053 + 0.188606i \(0.939603\pi\)
\(942\) 0.825854 1.17838i 0.0269078 0.0383938i
\(943\) 12.1557 20.3188i 0.395843 0.661670i
\(944\) 0.109332 + 0.130744i 0.00355845 + 0.00425536i
\(945\) 8.60650 9.93243i 0.279970 0.323102i
\(946\) −0.628012 + 15.6573i −0.0204184 + 0.509062i
\(947\) 10.1925 1.46546i 0.331211 0.0476210i 0.0252967 0.999680i \(-0.491947\pi\)
0.305914 + 0.952059i \(0.401038\pi\)
\(948\) 21.1369 + 21.5112i 0.686494 + 0.698652i
\(949\) 9.41720 + 1.35399i 0.305695 + 0.0439523i
\(950\) −24.5813 8.30145i −0.797523 0.269335i
\(951\) −19.0272 12.2281i −0.617001 0.396522i
\(952\) −52.5541 + 63.4865i −1.70329 + 2.05761i
\(953\) 29.5635 + 8.68063i 0.957656 + 0.281193i 0.722971 0.690878i \(-0.242776\pi\)
0.234685 + 0.972072i \(0.424594\pi\)
\(954\) −0.231060 2.24169i −0.00748083 0.0725773i
\(955\) −31.8469 + 27.5955i −1.03054 + 0.892970i
\(956\) 2.24261 + 35.7645i 0.0725312 + 1.15671i
\(957\) 31.1652 + 14.2327i 1.00743 + 0.460078i
\(958\) 46.3599 18.9650i 1.49782 0.612731i
\(959\) −71.1827 + 20.9011i −2.29861 + 0.674932i
\(960\) −15.1644 + 19.1829i −0.489428 + 0.619126i
\(961\) 26.2563 + 57.4933i 0.846978 + 1.85462i
\(962\) 9.96286 + 5.04185i 0.321216 + 0.162556i
\(963\) 5.33870 + 8.30717i 0.172037 + 0.267695i
\(964\) 15.1784 + 5.81351i 0.488864 + 0.187241i
\(965\) 45.9668i 1.47972i
\(966\) −28.8975 + 3.91855i −0.929762 + 0.126077i
\(967\) −46.3133 −1.48933 −0.744667 0.667436i \(-0.767392\pi\)
−0.744667 + 0.667436i \(0.767392\pi\)
\(968\) 20.6168 13.9158i 0.662648 0.447272i
\(969\) 24.0838 15.4777i 0.773684 0.497216i
\(970\) 11.6892 23.0982i 0.375316 0.741637i
\(971\) 36.0346 16.4564i 1.15640 0.528112i 0.257509 0.966276i \(-0.417098\pi\)
0.898895 + 0.438164i \(0.144371\pi\)
\(972\) 0.407962 + 1.95795i 0.0130854 + 0.0628013i
\(973\) −3.96872 13.5162i −0.127231 0.433310i
\(974\) −54.2774 + 22.2039i −1.73916 + 0.711459i
\(975\) 2.81979 6.17449i 0.0903057 0.197742i
\(976\) 5.94304 + 13.6422i 0.190232 + 0.436676i
\(977\) 33.7798 + 38.9839i 1.08071 + 1.24721i 0.967294 + 0.253659i \(0.0816341\pi\)
0.113417 + 0.993547i \(0.463820\pi\)
\(978\) −22.4308 + 2.31203i −0.717257 + 0.0739305i
\(979\) 0.430945 1.46766i 0.0137731 0.0469067i
\(980\) −5.62438 + 69.9994i −0.179664 + 2.23605i
\(981\) 2.84902 4.43317i 0.0909623 0.141540i
\(982\) −10.0099 3.38047i −0.319427 0.107875i
\(983\) 0.0272197 0.189317i 0.000868175 0.00603829i −0.989383 0.145333i \(-0.953575\pi\)
0.990251 + 0.139295i \(0.0444836\pi\)
\(984\) 13.7737 2.29823i 0.439088 0.0732651i
\(985\) −7.02769 48.8787i −0.223921 1.55740i
\(986\) −73.7451 2.95791i −2.34852 0.0941989i
\(987\) 26.1135 + 22.6275i 0.831203 + 0.720242i
\(988\) 4.50610 + 12.4130i 0.143358 + 0.394910i
\(989\) 4.61077 11.0180i 0.146614 0.350353i
\(990\) 11.0376 15.7492i 0.350799 0.500544i
\(991\) 16.8842 19.4854i 0.536345 0.618975i −0.421302 0.906920i \(-0.638427\pi\)
0.957647 + 0.287945i \(0.0929722\pi\)
\(992\) −33.5049 43.4969i −1.06378 1.38103i
\(993\) 1.86812 + 12.9930i 0.0592829 + 0.412322i
\(994\) −74.5402 13.7866i −2.36427 0.437283i
\(995\) 52.3114 + 7.52124i 1.65838 + 0.238439i
\(996\) 4.50614 + 6.13093i 0.142782 + 0.194266i
\(997\) −0.470747 + 0.732497i −0.0149087 + 0.0231984i −0.848628 0.528990i \(-0.822571\pi\)
0.833719 + 0.552189i \(0.186207\pi\)
\(998\) 22.8660 13.4317i 0.723809 0.425172i
\(999\) 4.84689 + 1.42318i 0.153349 + 0.0450273i
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 552.2.bb.a.85.21 yes 480
8.5 even 2 inner 552.2.bb.a.85.47 yes 480
23.13 even 11 inner 552.2.bb.a.13.47 yes 480
184.13 even 22 inner 552.2.bb.a.13.21 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.bb.a.13.21 480 184.13 even 22 inner
552.2.bb.a.13.47 yes 480 23.13 even 11 inner
552.2.bb.a.85.21 yes 480 1.1 even 1 trivial
552.2.bb.a.85.47 yes 480 8.5 even 2 inner