Properties

Label 315.2.z.b.104.19
Level $315$
Weight $2$
Character 315.104
Analytic conductor $2.515$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(104,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.104");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.z (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 104.19
Character \(\chi\) \(=\) 315.104
Dual form 315.2.z.b.209.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.139034 - 0.240814i) q^{2} +(-1.62845 - 0.590047i) q^{3} +(0.961339 - 1.66509i) q^{4} +(0.326583 - 2.21209i) q^{5} +(0.0843182 + 0.474190i) q^{6} +(1.72305 - 2.00776i) q^{7} -1.09077 q^{8} +(2.30369 + 1.92172i) q^{9} +O(q^{10})\) \(q+(-0.139034 - 0.240814i) q^{2} +(-1.62845 - 0.590047i) q^{3} +(0.961339 - 1.66509i) q^{4} +(0.326583 - 2.21209i) q^{5} +(0.0843182 + 0.474190i) q^{6} +(1.72305 - 2.00776i) q^{7} -1.09077 q^{8} +(2.30369 + 1.92172i) q^{9} +(-0.578109 + 0.228910i) q^{10} +(-3.37792 + 1.95024i) q^{11} +(-2.54797 + 2.14427i) q^{12} +(-0.562755 + 0.974721i) q^{13} +(-0.723060 - 0.135788i) q^{14} +(-1.83706 + 3.40958i) q^{15} +(-1.77102 - 3.06750i) q^{16} +2.20034i q^{17} +(0.142487 - 0.821946i) q^{18} -3.75853i q^{19} +(-3.36937 - 2.67036i) q^{20} +(-3.99057 + 2.25285i) q^{21} +(0.939292 + 0.542300i) q^{22} +(3.74981 - 6.49487i) q^{23} +(1.77627 + 0.643607i) q^{24} +(-4.78669 - 1.44486i) q^{25} +0.312969 q^{26} +(-2.61753 - 4.48871i) q^{27} +(-1.68666 - 4.79917i) q^{28} +(-3.65123 + 2.10804i) q^{29} +(1.07649 - 0.0316571i) q^{30} +(5.45664 + 3.15039i) q^{31} +(-1.58324 + 2.74225i) q^{32} +(6.65150 - 1.18274i) q^{33} +(0.529874 - 0.305923i) q^{34} +(-3.87862 - 4.46725i) q^{35} +(5.41446 - 1.98842i) q^{36} +4.76824i q^{37} +(-0.905108 + 0.522564i) q^{38} +(1.49155 - 1.25523i) q^{39} +(-0.356228 + 2.41289i) q^{40} +(-4.00455 + 6.93608i) q^{41} +(1.09734 + 0.647764i) q^{42} +(5.00066 - 2.88713i) q^{43} +7.49937i q^{44} +(5.00337 - 4.46837i) q^{45} -2.08541 q^{46} +(3.16020 - 1.82454i) q^{47} +(1.07405 + 6.04026i) q^{48} +(-1.06219 - 6.91894i) q^{49} +(0.317570 + 1.35359i) q^{50} +(1.29831 - 3.58314i) q^{51} +(1.08200 + 1.87407i) q^{52} -1.53097 q^{53} +(-0.717020 + 1.25442i) q^{54} +(3.21094 + 8.10917i) q^{55} +(-1.87946 + 2.19001i) q^{56} +(-2.21771 + 6.12057i) q^{57} +(1.01529 + 0.586178i) q^{58} +(1.96328 - 3.40050i) q^{59} +(3.91121 + 6.33663i) q^{60} +(7.66449 - 4.42510i) q^{61} -1.75205i q^{62} +(7.82773 - 1.31402i) q^{63} -6.20360 q^{64} +(1.97238 + 1.56319i) q^{65} +(-1.20961 - 1.43734i) q^{66} +(-2.87948 - 1.66247i) q^{67} +(3.66376 + 2.11527i) q^{68} +(-9.93866 + 8.36399i) q^{69} +(-0.536515 + 1.55513i) q^{70} -3.21485i q^{71} +(-2.51280 - 2.09616i) q^{72} +15.4204 q^{73} +(1.14826 - 0.662948i) q^{74} +(6.94234 + 5.17725i) q^{75} +(-6.25829 - 3.61322i) q^{76} +(-1.90471 + 10.1424i) q^{77} +(-0.509654 - 0.184666i) q^{78} +(-0.582671 - 1.00922i) q^{79} +(-7.36398 + 2.91587i) q^{80} +(1.61396 + 8.85410i) q^{81} +2.22708 q^{82} +(4.46093 - 2.57552i) q^{83} +(-0.0851023 + 8.81041i) q^{84} +(4.86736 + 0.718594i) q^{85} +(-1.39052 - 0.802820i) q^{86} +(7.18968 - 1.27843i) q^{87} +(3.68454 - 2.12727i) q^{88} +16.1207 q^{89} +(-1.77169 - 0.583627i) q^{90} +(0.987347 + 2.80937i) q^{91} +(-7.20969 - 12.4875i) q^{92} +(-7.02698 - 8.34993i) q^{93} +(-0.878751 - 0.507347i) q^{94} +(-8.31421 - 1.22747i) q^{95} +(4.19628 - 3.53143i) q^{96} +(-4.30467 - 7.45591i) q^{97} +(-1.51850 + 1.21776i) q^{98} +(-11.5295 - 1.99867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 52 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 52 q^{4} - 4 q^{9} - 24 q^{11} - 12 q^{14} - 34 q^{15} - 28 q^{16} + 20 q^{21} - 22 q^{25} - 48 q^{29} + 36 q^{30} - 40 q^{36} + 16 q^{39} - 24 q^{46} + 20 q^{49} - 42 q^{50} - 8 q^{51} + 24 q^{56} + 116 q^{60} + 128 q^{64} + 90 q^{65} - 6 q^{70} + 12 q^{74} - 32 q^{79} + 68 q^{81} - 4 q^{84} - 2 q^{85} + 156 q^{86} - 8 q^{91} - 24 q^{95} - 116 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.139034 0.240814i −0.0983120 0.170281i 0.812674 0.582719i \(-0.198011\pi\)
−0.910986 + 0.412437i \(0.864678\pi\)
\(3\) −1.62845 0.590047i −0.940185 0.340664i
\(4\) 0.961339 1.66509i 0.480669 0.832544i
\(5\) 0.326583 2.21209i 0.146052 0.989277i
\(6\) 0.0843182 + 0.474190i 0.0344228 + 0.193587i
\(7\) 1.72305 2.00776i 0.651252 0.758861i
\(8\) −1.09077 −0.385646
\(9\) 2.30369 + 1.92172i 0.767896 + 0.640574i
\(10\) −0.578109 + 0.228910i −0.182814 + 0.0723878i
\(11\) −3.37792 + 1.95024i −1.01848 + 0.588020i −0.913663 0.406472i \(-0.866759\pi\)
−0.104817 + 0.994492i \(0.533426\pi\)
\(12\) −2.54797 + 2.14427i −0.735536 + 0.618999i
\(13\) −0.562755 + 0.974721i −0.156080 + 0.270339i −0.933452 0.358703i \(-0.883219\pi\)
0.777372 + 0.629042i \(0.216553\pi\)
\(14\) −0.723060 0.135788i −0.193246 0.0362910i
\(15\) −1.83706 + 3.40958i −0.474327 + 0.880349i
\(16\) −1.77102 3.06750i −0.442756 0.766876i
\(17\) 2.20034i 0.533661i 0.963743 + 0.266831i \(0.0859764\pi\)
−0.963743 + 0.266831i \(0.914024\pi\)
\(18\) 0.142487 0.821946i 0.0335845 0.193735i
\(19\) 3.75853i 0.862266i −0.902288 0.431133i \(-0.858114\pi\)
0.902288 0.431133i \(-0.141886\pi\)
\(20\) −3.36937 2.67036i −0.753414 0.597110i
\(21\) −3.99057 + 2.25285i −0.870814 + 0.491612i
\(22\) 0.939292 + 0.542300i 0.200258 + 0.115619i
\(23\) 3.74981 6.49487i 0.781890 1.35427i −0.148949 0.988845i \(-0.547589\pi\)
0.930839 0.365429i \(-0.119078\pi\)
\(24\) 1.77627 + 0.643607i 0.362579 + 0.131376i
\(25\) −4.78669 1.44486i −0.957337 0.288972i
\(26\) 0.312969 0.0613782
\(27\) −2.61753 4.48871i −0.503744 0.863853i
\(28\) −1.68666 4.79917i −0.318748 0.906958i
\(29\) −3.65123 + 2.10804i −0.678016 + 0.391453i −0.799107 0.601189i \(-0.794694\pi\)
0.121091 + 0.992641i \(0.461361\pi\)
\(30\) 1.07649 0.0316571i 0.196539 0.00577977i
\(31\) 5.45664 + 3.15039i 0.980042 + 0.565827i 0.902283 0.431145i \(-0.141890\pi\)
0.0777590 + 0.996972i \(0.475224\pi\)
\(32\) −1.58324 + 2.74225i −0.279880 + 0.484766i
\(33\) 6.65150 1.18274i 1.15788 0.205888i
\(34\) 0.529874 0.305923i 0.0908726 0.0524653i
\(35\) −3.87862 4.46725i −0.655607 0.755102i
\(36\) 5.41446 1.98842i 0.902411 0.331403i
\(37\) 4.76824i 0.783894i 0.919988 + 0.391947i \(0.128198\pi\)
−0.919988 + 0.391947i \(0.871802\pi\)
\(38\) −0.905108 + 0.522564i −0.146828 + 0.0847711i
\(39\) 1.49155 1.25523i 0.238839 0.200998i
\(40\) −0.356228 + 2.41289i −0.0563245 + 0.381511i
\(41\) −4.00455 + 6.93608i −0.625405 + 1.08323i 0.363057 + 0.931767i \(0.381733\pi\)
−0.988462 + 0.151467i \(0.951600\pi\)
\(42\) 1.09734 + 0.647764i 0.169324 + 0.0999521i
\(43\) 5.00066 2.88713i 0.762593 0.440283i −0.0676328 0.997710i \(-0.521545\pi\)
0.830226 + 0.557427i \(0.188211\pi\)
\(44\) 7.49937i 1.13057i
\(45\) 5.00337 4.46837i 0.745858 0.666105i
\(46\) −2.08541 −0.307477
\(47\) 3.16020 1.82454i 0.460962 0.266137i −0.251487 0.967861i \(-0.580919\pi\)
0.712449 + 0.701724i \(0.247586\pi\)
\(48\) 1.07405 + 6.04026i 0.155026 + 0.871836i
\(49\) −1.06219 6.91894i −0.151741 0.988420i
\(50\) 0.317570 + 1.35359i 0.0449112 + 0.191426i
\(51\) 1.29831 3.58314i 0.181799 0.501740i
\(52\) 1.08200 + 1.87407i 0.150046 + 0.259887i
\(53\) −1.53097 −0.210295 −0.105147 0.994457i \(-0.533531\pi\)
−0.105147 + 0.994457i \(0.533531\pi\)
\(54\) −0.717020 + 1.25442i −0.0975740 + 0.170705i
\(55\) 3.21094 + 8.10917i 0.432963 + 1.09344i
\(56\) −1.87946 + 2.19001i −0.251153 + 0.292652i
\(57\) −2.21771 + 6.12057i −0.293743 + 0.810690i
\(58\) 1.01529 + 0.586178i 0.133314 + 0.0769690i
\(59\) 1.96328 3.40050i 0.255597 0.442707i −0.709461 0.704745i \(-0.751061\pi\)
0.965057 + 0.262038i \(0.0843947\pi\)
\(60\) 3.91121 + 6.33663i 0.504934 + 0.818055i
\(61\) 7.66449 4.42510i 0.981338 0.566576i 0.0786641 0.996901i \(-0.474935\pi\)
0.902674 + 0.430326i \(0.141601\pi\)
\(62\) 1.75205i 0.222510i
\(63\) 7.82773 1.31402i 0.986201 0.165551i
\(64\) −6.20360 −0.775450
\(65\) 1.97238 + 1.56319i 0.244644 + 0.193890i
\(66\) −1.20961 1.43734i −0.148892 0.176924i
\(67\) −2.87948 1.66247i −0.351784 0.203103i 0.313686 0.949527i \(-0.398436\pi\)
−0.665471 + 0.746424i \(0.731769\pi\)
\(68\) 3.66376 + 2.11527i 0.444297 + 0.256515i
\(69\) −9.93866 + 8.36399i −1.19647 + 1.00691i
\(70\) −0.536515 + 1.55513i −0.0641258 + 0.185873i
\(71\) 3.21485i 0.381532i −0.981636 0.190766i \(-0.938903\pi\)
0.981636 0.190766i \(-0.0610972\pi\)
\(72\) −2.51280 2.09616i −0.296136 0.247035i
\(73\) 15.4204 1.80482 0.902410 0.430878i \(-0.141796\pi\)
0.902410 + 0.430878i \(0.141796\pi\)
\(74\) 1.14826 0.662948i 0.133482 0.0770662i
\(75\) 6.94234 + 5.17725i 0.801632 + 0.597818i
\(76\) −6.25829 3.61322i −0.717875 0.414465i
\(77\) −1.90471 + 10.1424i −0.217062 + 1.15583i
\(78\) −0.509654 0.184666i −0.0577069 0.0209094i
\(79\) −0.582671 1.00922i −0.0655556 0.113546i 0.831385 0.555697i \(-0.187549\pi\)
−0.896940 + 0.442152i \(0.854215\pi\)
\(80\) −7.36398 + 2.91587i −0.823318 + 0.326004i
\(81\) 1.61396 + 8.85410i 0.179329 + 0.983789i
\(82\) 2.22708 0.245939
\(83\) 4.46093 2.57552i 0.489651 0.282700i −0.234779 0.972049i \(-0.575437\pi\)
0.724429 + 0.689349i \(0.242103\pi\)
\(84\) −0.0851023 + 8.81041i −0.00928542 + 0.961294i
\(85\) 4.86736 + 0.718594i 0.527939 + 0.0779424i
\(86\) −1.39052 0.802820i −0.149944 0.0865703i
\(87\) 7.18968 1.27843i 0.770814 0.137062i
\(88\) 3.68454 2.12727i 0.392773 0.226768i
\(89\) 16.1207 1.70879 0.854394 0.519626i \(-0.173929\pi\)
0.854394 + 0.519626i \(0.173929\pi\)
\(90\) −1.77169 0.583627i −0.186752 0.0615197i
\(91\) 0.987347 + 2.80937i 0.103502 + 0.294502i
\(92\) −7.20969 12.4875i −0.751662 1.30192i
\(93\) −7.02698 8.34993i −0.728664 0.865847i
\(94\) −0.878751 0.507347i −0.0906362 0.0523289i
\(95\) −8.31421 1.22747i −0.853020 0.125936i
\(96\) 4.19628 3.53143i 0.428281 0.360425i
\(97\) −4.30467 7.45591i −0.437073 0.757033i 0.560389 0.828229i \(-0.310652\pi\)
−0.997462 + 0.0711966i \(0.977318\pi\)
\(98\) −1.51850 + 1.21776i −0.153392 + 0.123012i
\(99\) −11.5295 1.99867i −1.15876 0.200874i
\(100\) −7.00745 + 6.58125i −0.700745 + 0.658125i
\(101\) −3.34652 5.79635i −0.332992 0.576758i 0.650105 0.759844i \(-0.274725\pi\)
−0.983097 + 0.183086i \(0.941391\pi\)
\(102\) −1.04338 + 0.185529i −0.103310 + 0.0183701i
\(103\) −4.64528 + 8.04587i −0.457713 + 0.792783i −0.998840 0.0481584i \(-0.984665\pi\)
0.541126 + 0.840941i \(0.317998\pi\)
\(104\) 0.613838 1.06320i 0.0601918 0.104255i
\(105\) 3.68025 + 9.56325i 0.359156 + 0.933278i
\(106\) 0.212857 + 0.368679i 0.0206745 + 0.0358093i
\(107\) 6.54742 0.632963 0.316482 0.948599i \(-0.397498\pi\)
0.316482 + 0.948599i \(0.397498\pi\)
\(108\) −9.99043 + 0.0432452i −0.961330 + 0.00416127i
\(109\) 10.4793 1.00374 0.501869 0.864944i \(-0.332646\pi\)
0.501869 + 0.864944i \(0.332646\pi\)
\(110\) 1.50637 1.90069i 0.143627 0.181224i
\(111\) 2.81349 7.76483i 0.267044 0.737005i
\(112\) −9.21037 1.72968i −0.870298 0.163439i
\(113\) 7.45902 12.9194i 0.701686 1.21536i −0.266189 0.963921i \(-0.585764\pi\)
0.967874 0.251434i \(-0.0809022\pi\)
\(114\) 1.78226 0.316913i 0.166924 0.0296816i
\(115\) −13.1426 10.4160i −1.22555 0.971301i
\(116\) 8.10615i 0.752637i
\(117\) −3.16956 + 1.16399i −0.293026 + 0.107611i
\(118\) −1.09185 −0.100513
\(119\) 4.41775 + 3.79130i 0.404975 + 0.347548i
\(120\) 2.00382 3.71907i 0.182923 0.339503i
\(121\) 2.10689 3.64923i 0.191535 0.331748i
\(122\) −2.13125 1.23048i −0.192955 0.111402i
\(123\) 10.6138 8.93217i 0.957015 0.805387i
\(124\) 10.4914 6.05719i 0.942152 0.543952i
\(125\) −4.75941 + 10.1167i −0.425695 + 0.904867i
\(126\) −1.40476 1.70233i −0.125146 0.151656i
\(127\) 10.3433i 0.917817i 0.888484 + 0.458909i \(0.151759\pi\)
−0.888484 + 0.458909i \(0.848241\pi\)
\(128\) 4.02899 + 6.97841i 0.356116 + 0.616810i
\(129\) −9.84686 + 1.75092i −0.866968 + 0.154160i
\(130\) 0.102210 0.692315i 0.00896443 0.0607201i
\(131\) 3.19648 5.53646i 0.279277 0.483723i −0.691928 0.721967i \(-0.743238\pi\)
0.971205 + 0.238244i \(0.0765718\pi\)
\(132\) 4.42498 12.2123i 0.385145 1.06295i
\(133\) −7.54622 6.47614i −0.654340 0.561553i
\(134\) 0.924560i 0.0798698i
\(135\) −10.7843 + 4.32428i −0.928163 + 0.372175i
\(136\) 2.40007i 0.205805i
\(137\) 3.00732 + 5.20883i 0.256932 + 0.445020i 0.965419 0.260705i \(-0.0839549\pi\)
−0.708486 + 0.705725i \(0.750622\pi\)
\(138\) 3.39598 + 1.23049i 0.289085 + 0.104746i
\(139\) −8.76489 5.06041i −0.743428 0.429219i 0.0798861 0.996804i \(-0.474544\pi\)
−0.823315 + 0.567585i \(0.807878\pi\)
\(140\) −11.1670 + 2.16371i −0.943786 + 0.182867i
\(141\) −6.22278 + 1.10651i −0.524053 + 0.0931845i
\(142\) −0.774181 + 0.446973i −0.0649678 + 0.0375092i
\(143\) 4.39004i 0.367113i
\(144\) 1.81500 10.4700i 0.151250 0.872499i
\(145\) 3.47074 + 8.76529i 0.288229 + 0.727918i
\(146\) −2.14396 3.71345i −0.177435 0.307327i
\(147\) −2.35279 + 11.8939i −0.194055 + 0.980991i
\(148\) 7.93954 + 4.58389i 0.652626 + 0.376794i
\(149\) −3.20395 1.84980i −0.262478 0.151542i 0.362987 0.931794i \(-0.381757\pi\)
−0.625464 + 0.780253i \(0.715090\pi\)
\(150\) 0.281534 2.39163i 0.0229872 0.195276i
\(151\) 7.28902 + 12.6249i 0.593172 + 1.02740i 0.993802 + 0.111164i \(0.0354578\pi\)
−0.400630 + 0.916240i \(0.631209\pi\)
\(152\) 4.09970i 0.332530i
\(153\) −4.22845 + 5.06890i −0.341850 + 0.409796i
\(154\) 2.70726 0.951459i 0.218157 0.0766708i
\(155\) 8.75100 11.0417i 0.702897 0.886892i
\(156\) −0.656184 3.69026i −0.0525368 0.295457i
\(157\) −12.2454 + 21.2096i −0.977288 + 1.69271i −0.305118 + 0.952314i \(0.598696\pi\)
−0.672169 + 0.740397i \(0.734637\pi\)
\(158\) −0.162022 + 0.280631i −0.0128898 + 0.0223258i
\(159\) 2.49311 + 0.903345i 0.197716 + 0.0716399i
\(160\) 5.54904 + 4.39784i 0.438690 + 0.347680i
\(161\) −6.57900 18.7197i −0.518498 1.47532i
\(162\) 1.90780 1.61969i 0.149891 0.127255i
\(163\) 0.669436i 0.0524343i −0.999656 0.0262172i \(-0.991654\pi\)
0.999656 0.0262172i \(-0.00834613\pi\)
\(164\) 7.69945 + 13.3358i 0.601226 + 1.04135i
\(165\) −0.444056 15.1000i −0.0345697 1.17553i
\(166\) −1.24044 0.716170i −0.0962771 0.0555856i
\(167\) −16.1059 9.29874i −1.24631 0.719558i −0.275940 0.961175i \(-0.588989\pi\)
−0.970372 + 0.241616i \(0.922322\pi\)
\(168\) 4.35281 2.45735i 0.335826 0.189588i
\(169\) 5.86661 + 10.1613i 0.451278 + 0.781636i
\(170\) −0.503681 1.27204i −0.0386306 0.0975608i
\(171\) 7.22286 8.65849i 0.552346 0.662131i
\(172\) 11.1020i 0.846523i
\(173\) −16.4993 + 9.52589i −1.25442 + 0.724240i −0.971984 0.235046i \(-0.924476\pi\)
−0.282437 + 0.959286i \(0.591143\pi\)
\(174\) −1.30748 1.55363i −0.0991195 0.117780i
\(175\) −11.1486 + 7.12094i −0.842758 + 0.538292i
\(176\) 11.9647 + 6.90785i 0.901876 + 0.520699i
\(177\) −5.20355 + 4.37911i −0.391123 + 0.329154i
\(178\) −2.24132 3.88209i −0.167994 0.290975i
\(179\) 8.36128i 0.624951i −0.949926 0.312476i \(-0.898842\pi\)
0.949926 0.312476i \(-0.101158\pi\)
\(180\) −2.63029 12.6267i −0.196050 0.941136i
\(181\) 18.3422i 1.36336i 0.731649 + 0.681682i \(0.238751\pi\)
−0.731649 + 0.681682i \(0.761249\pi\)
\(182\) 0.539262 0.628366i 0.0399727 0.0465776i
\(183\) −15.0922 + 2.68363i −1.11565 + 0.198380i
\(184\) −4.09020 + 7.08443i −0.301533 + 0.522271i
\(185\) 10.5478 + 1.55722i 0.775488 + 0.114489i
\(186\) −1.03379 + 2.85312i −0.0758013 + 0.209201i
\(187\) −4.29120 7.43257i −0.313804 0.543524i
\(188\) 7.01601i 0.511695i
\(189\) −13.5224 2.47891i −0.983609 0.180314i
\(190\) 0.860367 + 2.17284i 0.0624176 + 0.157634i
\(191\) 17.3610 10.0234i 1.25620 0.725267i 0.283865 0.958864i \(-0.408383\pi\)
0.972333 + 0.233597i \(0.0750498\pi\)
\(192\) 10.1022 + 3.66041i 0.729066 + 0.264168i
\(193\) −21.5370 12.4344i −1.55027 0.895047i −0.998119 0.0613015i \(-0.980475\pi\)
−0.552148 0.833746i \(-0.686192\pi\)
\(194\) −1.19699 + 2.07325i −0.0859391 + 0.148851i
\(195\) −2.28957 3.70938i −0.163959 0.265634i
\(196\) −12.5418 4.88282i −0.895841 0.348773i
\(197\) 18.9873 1.35279 0.676396 0.736538i \(-0.263541\pi\)
0.676396 + 0.736538i \(0.263541\pi\)
\(198\) 1.12168 + 3.05435i 0.0797147 + 0.217063i
\(199\) 24.4502i 1.73323i −0.498980 0.866613i \(-0.666292\pi\)
0.498980 0.866613i \(-0.333708\pi\)
\(200\) 5.22119 + 1.57601i 0.369194 + 0.111441i
\(201\) 3.70815 + 4.40627i 0.261553 + 0.310795i
\(202\) −0.930563 + 1.61178i −0.0654742 + 0.113405i
\(203\) −2.05882 + 10.9630i −0.144501 + 0.769454i
\(204\) −4.71814 5.60641i −0.330336 0.392527i
\(205\) 14.0354 + 11.1236i 0.980276 + 0.776907i
\(206\) 2.58341 0.179995
\(207\) 21.1197 7.75605i 1.46792 0.539083i
\(208\) 3.98661 0.276422
\(209\) 7.33004 + 12.6960i 0.507030 + 0.878201i
\(210\) 1.79129 2.21588i 0.123610 0.152910i
\(211\) −10.4862 + 18.1627i −0.721903 + 1.25037i 0.238333 + 0.971183i \(0.423399\pi\)
−0.960236 + 0.279189i \(0.909934\pi\)
\(212\) −1.47178 + 2.54920i −0.101082 + 0.175080i
\(213\) −1.89691 + 5.23521i −0.129974 + 0.358711i
\(214\) −0.910315 1.57671i −0.0622279 0.107782i
\(215\) −4.75347 12.0048i −0.324184 0.818720i
\(216\) 2.85513 + 4.89616i 0.194267 + 0.333142i
\(217\) 15.7273 5.52732i 1.06764 0.375219i
\(218\) −1.45698 2.52357i −0.0986795 0.170918i
\(219\) −25.1113 9.09876i −1.69686 0.614837i
\(220\) 16.5893 + 2.44917i 1.11845 + 0.165123i
\(221\) −2.14472 1.23825i −0.144269 0.0832940i
\(222\) −2.26105 + 0.402049i −0.151752 + 0.0269838i
\(223\) −4.33310 7.50516i −0.290166 0.502582i 0.683683 0.729779i \(-0.260377\pi\)
−0.973849 + 0.227197i \(0.927044\pi\)
\(224\) 2.77777 + 7.90380i 0.185598 + 0.528095i
\(225\) −8.25041 12.5272i −0.550028 0.835146i
\(226\) −4.14823 −0.275936
\(227\) −0.0478623 + 0.0276333i −0.00317673 + 0.00183409i −0.501588 0.865107i \(-0.667250\pi\)
0.498411 + 0.866941i \(0.333917\pi\)
\(228\) 8.05932 + 9.57663i 0.533742 + 0.634228i
\(229\) −18.0499 10.4211i −1.19277 0.688645i −0.233835 0.972276i \(-0.575127\pi\)
−0.958933 + 0.283632i \(0.908461\pi\)
\(230\) −0.681059 + 4.61311i −0.0449077 + 0.304180i
\(231\) 9.08623 15.3925i 0.597830 1.01275i
\(232\) 3.98266 2.29939i 0.261474 0.150962i
\(233\) −18.7251 −1.22672 −0.613360 0.789804i \(-0.710182\pi\)
−0.613360 + 0.789804i \(0.710182\pi\)
\(234\) 0.720983 + 0.601439i 0.0471321 + 0.0393173i
\(235\) −3.00398 7.58651i −0.195958 0.494889i
\(236\) −3.77475 6.53806i −0.245715 0.425591i
\(237\) 0.353365 + 1.98726i 0.0229535 + 0.129086i
\(238\) 0.298781 1.59098i 0.0193671 0.103128i
\(239\) 13.4849 + 7.78551i 0.872266 + 0.503603i 0.868101 0.496388i \(-0.165341\pi\)
0.00416535 + 0.999991i \(0.498674\pi\)
\(240\) 13.7124 0.403249i 0.885129 0.0260296i
\(241\) −12.1131 + 6.99348i −0.780270 + 0.450489i −0.836526 0.547927i \(-0.815417\pi\)
0.0562556 + 0.998416i \(0.482084\pi\)
\(242\) −1.17172 −0.0753208
\(243\) 2.59609 15.3708i 0.166539 0.986035i
\(244\) 17.0161i 1.08934i
\(245\) −15.6522 + 0.0900426i −0.999983 + 0.00575261i
\(246\) −3.62668 1.31408i −0.231228 0.0837827i
\(247\) 3.66352 + 2.11513i 0.233104 + 0.134583i
\(248\) −5.95195 3.43636i −0.377950 0.218209i
\(249\) −8.78407 + 1.56194i −0.556668 + 0.0989839i
\(250\) 3.09797 0.260435i 0.195933 0.0164714i
\(251\) −0.652928 −0.0412125 −0.0206062 0.999788i \(-0.506560\pi\)
−0.0206062 + 0.999788i \(0.506560\pi\)
\(252\) 5.33714 14.2971i 0.336208 0.900631i
\(253\) 29.2522i 1.83907i
\(254\) 2.49081 1.43807i 0.156287 0.0902324i
\(255\) −7.50223 4.04216i −0.469808 0.253130i
\(256\) −5.08326 + 8.80447i −0.317704 + 0.550279i
\(257\) 16.1212 + 9.30761i 1.00562 + 0.580592i 0.909905 0.414817i \(-0.136154\pi\)
0.0957107 + 0.995409i \(0.469488\pi\)
\(258\) 1.79070 + 2.12783i 0.111484 + 0.132473i
\(259\) 9.57347 + 8.21592i 0.594866 + 0.510513i
\(260\) 4.49898 1.78144i 0.279015 0.110480i
\(261\) −12.4624 2.16039i −0.771400 0.133725i
\(262\) −1.77768 −0.109825
\(263\) 10.3418 + 17.9126i 0.637704 + 1.10454i 0.985935 + 0.167127i \(0.0534489\pi\)
−0.348232 + 0.937408i \(0.613218\pi\)
\(264\) −7.25527 + 1.29010i −0.446531 + 0.0794000i
\(265\) −0.499988 + 3.38664i −0.0307140 + 0.208040i
\(266\) −0.510365 + 2.71764i −0.0312925 + 0.166629i
\(267\) −26.2517 9.51196i −1.60658 0.582122i
\(268\) −5.53631 + 3.19639i −0.338184 + 0.195251i
\(269\) 22.4594 1.36937 0.684686 0.728838i \(-0.259939\pi\)
0.684686 + 0.728838i \(0.259939\pi\)
\(270\) 2.54073 + 1.99578i 0.154624 + 0.121460i
\(271\) 22.6415i 1.37538i 0.726007 + 0.687688i \(0.241374\pi\)
−0.726007 + 0.687688i \(0.758626\pi\)
\(272\) 6.74955 3.89686i 0.409252 0.236282i
\(273\) 0.0498178 5.15750i 0.00301511 0.312146i
\(274\) 0.836240 1.44841i 0.0505191 0.0875016i
\(275\) 18.9869 4.45458i 1.14495 0.268621i
\(276\) 4.37236 + 24.5894i 0.263185 + 1.48011i
\(277\) −10.0059 + 5.77690i −0.601195 + 0.347100i −0.769512 0.638633i \(-0.779500\pi\)
0.168317 + 0.985733i \(0.446167\pi\)
\(278\) 2.81428i 0.168789i
\(279\) 6.51622 + 17.7437i 0.390116 + 1.06229i
\(280\) 4.23070 + 4.87275i 0.252832 + 0.291202i
\(281\) −1.53335 + 0.885280i −0.0914720 + 0.0528114i −0.545038 0.838411i \(-0.683485\pi\)
0.453566 + 0.891223i \(0.350152\pi\)
\(282\) 1.13164 + 1.34469i 0.0673883 + 0.0800753i
\(283\) −1.20095 + 2.08011i −0.0713892 + 0.123650i −0.899510 0.436899i \(-0.856077\pi\)
0.828121 + 0.560549i \(0.189410\pi\)
\(284\) −5.35300 3.09056i −0.317642 0.183391i
\(285\) 12.8150 + 6.90465i 0.759095 + 0.408996i
\(286\) −1.05718 + 0.610365i −0.0625125 + 0.0360916i
\(287\) 7.02593 + 19.9914i 0.414727 + 1.18005i
\(288\) −8.91713 + 3.27474i −0.525447 + 0.192966i
\(289\) 12.1585 0.715206
\(290\) 1.62826 2.05448i 0.0956145 0.120643i
\(291\) 2.61060 + 14.6815i 0.153036 + 0.860646i
\(292\) 14.8242 25.6763i 0.867522 1.50259i
\(293\) 19.1317 + 11.0457i 1.11769 + 0.645296i 0.940809 0.338937i \(-0.110067\pi\)
0.176876 + 0.984233i \(0.443401\pi\)
\(294\) 3.19133 1.08707i 0.186122 0.0633993i
\(295\) −6.88103 5.45349i −0.400629 0.317514i
\(296\) 5.20106i 0.302306i
\(297\) 17.5959 + 10.0577i 1.02102 + 0.583606i
\(298\) 1.02874i 0.0595934i
\(299\) 4.22046 + 7.31004i 0.244075 + 0.422751i
\(300\) 15.2945 6.58251i 0.883030 0.380041i
\(301\) 2.81973 15.0148i 0.162527 0.865438i
\(302\) 2.02684 3.51060i 0.116632 0.202012i
\(303\) 2.02952 + 11.4137i 0.116593 + 0.655698i
\(304\) −11.5293 + 6.65645i −0.661251 + 0.381773i
\(305\) −7.28562 18.3997i −0.417174 1.05356i
\(306\) 1.80856 + 0.313520i 0.103389 + 0.0179227i
\(307\) 2.21602 0.126475 0.0632375 0.997999i \(-0.479857\pi\)
0.0632375 + 0.997999i \(0.479857\pi\)
\(308\) 15.0569 + 12.9218i 0.857948 + 0.736288i
\(309\) 12.3120 10.3613i 0.700408 0.589436i
\(310\) −3.87569 0.572189i −0.220124 0.0324982i
\(311\) −6.27958 + 10.8766i −0.356082 + 0.616753i −0.987303 0.158851i \(-0.949221\pi\)
0.631220 + 0.775604i \(0.282554\pi\)
\(312\) −1.62694 + 1.36917i −0.0921074 + 0.0775140i
\(313\) 11.1371 + 19.2900i 0.629505 + 1.09033i 0.987651 + 0.156669i \(0.0500756\pi\)
−0.358146 + 0.933666i \(0.616591\pi\)
\(314\) 6.81010 0.384316
\(315\) −0.350332 17.7448i −0.0197390 0.999805i
\(316\) −2.24058 −0.126042
\(317\) −9.33715 16.1724i −0.524427 0.908334i −0.999596 0.0284391i \(-0.990946\pi\)
0.475169 0.879895i \(-0.342387\pi\)
\(318\) −0.129089 0.725971i −0.00723893 0.0407104i
\(319\) 8.22236 14.2415i 0.460364 0.797374i
\(320\) −2.02599 + 13.7229i −0.113256 + 0.767134i
\(321\) −10.6621 3.86329i −0.595103 0.215628i
\(322\) −3.59327 + 4.18700i −0.200245 + 0.233332i
\(323\) 8.27005 0.460158
\(324\) 16.2944 + 5.82441i 0.905246 + 0.323578i
\(325\) 4.10207 3.85258i 0.227542 0.213703i
\(326\) −0.161210 + 0.0930745i −0.00892859 + 0.00515492i
\(327\) −17.0650 6.18330i −0.943699 0.341937i
\(328\) 4.36805 7.56568i 0.241185 0.417745i
\(329\) 1.78195 9.48869i 0.0982419 0.523128i
\(330\) −3.57455 + 2.20635i −0.196773 + 0.121455i
\(331\) −4.37772 7.58243i −0.240621 0.416768i 0.720270 0.693694i \(-0.244018\pi\)
−0.960891 + 0.276925i \(0.910685\pi\)
\(332\) 9.90379i 0.543541i
\(333\) −9.16323 + 10.9845i −0.502142 + 0.601949i
\(334\) 5.17137i 0.282965i
\(335\) −4.61792 + 5.82674i −0.252304 + 0.318349i
\(336\) 13.9780 + 8.25124i 0.762563 + 0.450142i
\(337\) 26.0333 + 15.0303i 1.41812 + 0.818755i 0.996134 0.0878455i \(-0.0279982\pi\)
0.421991 + 0.906600i \(0.361332\pi\)
\(338\) 1.63132 2.82553i 0.0887321 0.153688i
\(339\) −19.7697 + 16.6374i −1.07374 + 0.903620i
\(340\) 5.87570 7.41376i 0.318655 0.402068i
\(341\) −24.5761 −1.33087
\(342\) −3.08931 0.535541i −0.167051 0.0289588i
\(343\) −15.7218 9.78908i −0.848895 0.528561i
\(344\) −5.45458 + 3.14920i −0.294091 + 0.169794i
\(345\) 15.2561 + 24.7167i 0.821361 + 1.33070i
\(346\) 4.58794 + 2.64885i 0.246649 + 0.142403i
\(347\) −15.0673 + 26.0973i −0.808855 + 1.40098i 0.104803 + 0.994493i \(0.466579\pi\)
−0.913658 + 0.406484i \(0.866755\pi\)
\(348\) 4.78301 13.2005i 0.256396 0.707618i
\(349\) 17.8865 10.3268i 0.957442 0.552779i 0.0620572 0.998073i \(-0.480234\pi\)
0.895385 + 0.445293i \(0.146901\pi\)
\(350\) 3.26487 + 1.69470i 0.174514 + 0.0905854i
\(351\) 5.84827 0.0253152i 0.312158 0.00135122i
\(352\) 12.3508i 0.658299i
\(353\) 5.39424 3.11437i 0.287107 0.165761i −0.349530 0.936925i \(-0.613659\pi\)
0.636636 + 0.771164i \(0.280325\pi\)
\(354\) 1.77802 + 0.644243i 0.0945008 + 0.0342411i
\(355\) −7.11153 1.04991i −0.377441 0.0557236i
\(356\) 15.4974 26.8423i 0.821362 1.42264i
\(357\) −4.95704 8.78063i −0.262354 0.464720i
\(358\) −2.01352 + 1.16250i −0.106418 + 0.0614402i
\(359\) 2.77267i 0.146336i 0.997320 + 0.0731681i \(0.0233110\pi\)
−0.997320 + 0.0731681i \(0.976689\pi\)
\(360\) −5.45754 + 4.87397i −0.287638 + 0.256881i
\(361\) 4.87344 0.256497
\(362\) 4.41706 2.55019i 0.232156 0.134035i
\(363\) −5.58417 + 4.69942i −0.293093 + 0.246656i
\(364\) 5.62702 + 1.05674i 0.294936 + 0.0553881i
\(365\) 5.03603 34.1113i 0.263598 1.78547i
\(366\) 2.74459 + 3.26131i 0.143462 + 0.170472i
\(367\) 1.76576 + 3.05839i 0.0921720 + 0.159647i 0.908425 0.418048i \(-0.137286\pi\)
−0.816253 + 0.577695i \(0.803952\pi\)
\(368\) −26.5640 −1.38475
\(369\) −22.5544 + 8.28293i −1.17414 + 0.431192i
\(370\) −1.09150 2.75656i −0.0567443 0.143307i
\(371\) −2.63794 + 3.07382i −0.136955 + 0.159585i
\(372\) −20.6587 + 3.67342i −1.07110 + 0.190458i
\(373\) 9.51368 + 5.49272i 0.492600 + 0.284402i 0.725652 0.688062i \(-0.241538\pi\)
−0.233053 + 0.972464i \(0.574871\pi\)
\(374\) −1.19325 + 2.06676i −0.0617013 + 0.106870i
\(375\) 13.7198 13.6663i 0.708487 0.705723i
\(376\) −3.44706 + 1.99016i −0.177768 + 0.102635i
\(377\) 4.74524i 0.244392i
\(378\) 1.28312 + 3.60104i 0.0659964 + 0.185217i
\(379\) −9.39813 −0.482749 −0.241375 0.970432i \(-0.577598\pi\)
−0.241375 + 0.970432i \(0.577598\pi\)
\(380\) −10.0366 + 12.6639i −0.514868 + 0.649643i
\(381\) 6.10302 16.8435i 0.312667 0.862918i
\(382\) −4.82755 2.78719i −0.246999 0.142605i
\(383\) −32.0566 18.5079i −1.63801 0.945708i −0.981516 0.191380i \(-0.938704\pi\)
−0.656498 0.754328i \(-0.727963\pi\)
\(384\) −2.44341 13.7413i −0.124690 0.701232i
\(385\) 21.8139 + 7.52573i 1.11174 + 0.383547i
\(386\) 6.91522i 0.351976i
\(387\) 17.0682 + 2.95883i 0.867627 + 0.150406i
\(388\) −16.5530 −0.840351
\(389\) −16.7084 + 9.64661i −0.847151 + 0.489103i −0.859688 0.510819i \(-0.829342\pi\)
0.0125378 + 0.999921i \(0.496009\pi\)
\(390\) −0.574943 + 1.06709i −0.0291134 + 0.0540343i
\(391\) 14.2909 + 8.25087i 0.722724 + 0.417265i
\(392\) 1.15860 + 7.54699i 0.0585183 + 0.381181i
\(393\) −8.47207 + 7.12976i −0.427359 + 0.359649i
\(394\) −2.63989 4.57242i −0.132996 0.230355i
\(395\) −2.42277 + 0.959328i −0.121903 + 0.0482690i
\(396\) −14.4117 + 17.2762i −0.724216 + 0.868163i
\(397\) −17.9506 −0.900914 −0.450457 0.892798i \(-0.648739\pi\)
−0.450457 + 0.892798i \(0.648739\pi\)
\(398\) −5.88795 + 3.39941i −0.295136 + 0.170397i
\(399\) 8.46740 + 14.9987i 0.423900 + 0.750874i
\(400\) 4.04522 + 17.2421i 0.202261 + 0.862103i
\(401\) −26.7496 15.4439i −1.33581 0.771232i −0.349630 0.936888i \(-0.613693\pi\)
−0.986184 + 0.165655i \(0.947026\pi\)
\(402\) 0.545534 1.50560i 0.0272088 0.0750924i
\(403\) −6.14151 + 3.54580i −0.305930 + 0.176629i
\(404\) −12.8686 −0.640236
\(405\) 20.1132 0.678632i 0.999431 0.0337215i
\(406\) 2.92630 1.02844i 0.145230 0.0510407i
\(407\) −9.29922 16.1067i −0.460945 0.798380i
\(408\) −1.41616 + 3.90839i −0.0701102 + 0.193494i
\(409\) 16.1406 + 9.31875i 0.798099 + 0.460783i 0.842806 0.538218i \(-0.180902\pi\)
−0.0447071 + 0.999000i \(0.514235\pi\)
\(410\) 0.727324 4.92649i 0.0359200 0.243302i
\(411\) −1.82381 10.2568i −0.0899618 0.505929i
\(412\) 8.93138 + 15.4696i 0.440018 + 0.762133i
\(413\) −3.44454 9.80102i −0.169495 0.482276i
\(414\) −4.80413 4.00758i −0.236110 0.196962i
\(415\) −4.24042 10.7091i −0.208154 0.525689i
\(416\) −1.78195 3.08643i −0.0873673 0.151325i
\(417\) 11.2873 + 13.4123i 0.552741 + 0.656804i
\(418\) 2.03825 3.53036i 0.0996942 0.172675i
\(419\) 0.339246 0.587591i 0.0165732 0.0287057i −0.857620 0.514284i \(-0.828058\pi\)
0.874193 + 0.485578i \(0.161391\pi\)
\(420\) 19.4616 + 3.06558i 0.949630 + 0.149585i
\(421\) −4.37357 7.57525i −0.213155 0.369195i 0.739545 0.673107i \(-0.235041\pi\)
−0.952700 + 0.303912i \(0.901707\pi\)
\(422\) 5.83178 0.283887
\(423\) 10.7864 + 1.86985i 0.524451 + 0.0909152i
\(424\) 1.66994 0.0810995
\(425\) 3.17919 10.5323i 0.154213 0.510894i
\(426\) 1.52445 0.271070i 0.0738598 0.0131334i
\(427\) 4.32179 23.0131i 0.209146 1.11368i
\(428\) 6.29429 10.9020i 0.304246 0.526970i
\(429\) −2.59033 + 7.14895i −0.125062 + 0.345154i
\(430\) −2.23003 + 2.81378i −0.107542 + 0.135693i
\(431\) 32.6691i 1.57362i 0.617197 + 0.786808i \(0.288268\pi\)
−0.617197 + 0.786808i \(0.711732\pi\)
\(432\) −9.13343 + 15.9789i −0.439432 + 0.768785i
\(433\) −12.4518 −0.598395 −0.299197 0.954191i \(-0.596719\pi\)
−0.299197 + 0.954191i \(0.596719\pi\)
\(434\) −3.51769 3.01887i −0.168855 0.144910i
\(435\) −0.479985 16.3217i −0.0230135 0.782567i
\(436\) 10.0742 17.4490i 0.482466 0.835656i
\(437\) −24.4112 14.0938i −1.16774 0.674198i
\(438\) 1.30022 + 7.31220i 0.0621269 + 0.349390i
\(439\) −1.69366 + 0.977836i −0.0808341 + 0.0466696i −0.539872 0.841747i \(-0.681527\pi\)
0.459038 + 0.888417i \(0.348194\pi\)
\(440\) −3.50241 8.84527i −0.166971 0.421681i
\(441\) 10.8493 17.9803i 0.516636 0.856205i
\(442\) 0.688639i 0.0327552i
\(443\) −5.48741 9.50448i −0.260715 0.451571i 0.705717 0.708494i \(-0.250625\pi\)
−0.966432 + 0.256922i \(0.917292\pi\)
\(444\) −10.2244 12.1493i −0.485229 0.576582i
\(445\) 5.26473 35.6604i 0.249572 1.69046i
\(446\) −1.20490 + 2.08695i −0.0570536 + 0.0988198i
\(447\) 4.12599 + 4.90278i 0.195153 + 0.231894i
\(448\) −10.6891 + 12.4553i −0.505013 + 0.588459i
\(449\) 2.63460i 0.124334i −0.998066 0.0621672i \(-0.980199\pi\)
0.998066 0.0621672i \(-0.0198012\pi\)
\(450\) −1.86964 + 3.72853i −0.0881356 + 0.175764i
\(451\) 31.2393i 1.47100i
\(452\) −14.3413 24.8398i −0.674558 1.16837i
\(453\) −4.42047 24.8599i −0.207692 1.16802i
\(454\) 0.0133090 + 0.00768395i 0.000624622 + 0.000360626i
\(455\) 6.53703 1.26661i 0.306461 0.0593795i
\(456\) 2.41902 6.67615i 0.113281 0.312640i
\(457\) 20.8336 12.0283i 0.974556 0.562660i 0.0739338 0.997263i \(-0.476445\pi\)
0.900622 + 0.434603i \(0.143111\pi\)
\(458\) 5.79555i 0.270808i
\(459\) 9.87670 5.75946i 0.461005 0.268829i
\(460\) −29.9781 + 11.8703i −1.39774 + 0.553454i
\(461\) 4.20670 + 7.28621i 0.195925 + 0.339353i 0.947203 0.320633i \(-0.103896\pi\)
−0.751278 + 0.659986i \(0.770562\pi\)
\(462\) −4.97003 0.0480070i −0.231227 0.00223349i
\(463\) 4.96696 + 2.86767i 0.230834 + 0.133272i 0.610957 0.791664i \(-0.290785\pi\)
−0.380123 + 0.924936i \(0.624118\pi\)
\(464\) 12.9328 + 7.46676i 0.600391 + 0.346636i
\(465\) −20.7657 + 12.8174i −0.962986 + 0.594391i
\(466\) 2.60342 + 4.50926i 0.120601 + 0.208887i
\(467\) 11.3573i 0.525555i 0.964856 + 0.262778i \(0.0846386\pi\)
−0.964856 + 0.262778i \(0.915361\pi\)
\(468\) −1.10887 + 6.39658i −0.0512574 + 0.295682i
\(469\) −8.29933 + 2.91678i −0.383227 + 0.134684i
\(470\) −1.40928 + 1.77819i −0.0650054 + 0.0820216i
\(471\) 32.4556 27.3134i 1.49548 1.25854i
\(472\) −2.14149 + 3.70917i −0.0985700 + 0.170728i
\(473\) −11.2612 + 19.5050i −0.517791 + 0.896840i
\(474\) 0.429431 0.361392i 0.0197244 0.0165993i
\(475\) −5.43056 + 17.9909i −0.249171 + 0.825480i
\(476\) 10.5598 3.71122i 0.484008 0.170104i
\(477\) −3.52688 2.94210i −0.161485 0.134710i
\(478\) 4.32981i 0.198041i
\(479\) −10.0564 17.4183i −0.459490 0.795860i 0.539444 0.842022i \(-0.318635\pi\)
−0.998934 + 0.0461613i \(0.985301\pi\)
\(480\) −6.44140 10.4358i −0.294008 0.476329i
\(481\) −4.64770 2.68335i −0.211917 0.122350i
\(482\) 3.36826 + 1.94466i 0.153420 + 0.0885770i
\(483\) −0.331951 + 34.3660i −0.0151043 + 1.56371i
\(484\) −4.05086 7.01630i −0.184130 0.318923i
\(485\) −17.8990 + 7.08735i −0.812751 + 0.321820i
\(486\) −4.06244 + 1.51189i −0.184276 + 0.0685806i
\(487\) 3.87738i 0.175701i −0.996134 0.0878505i \(-0.972000\pi\)
0.996134 0.0878505i \(-0.0279998\pi\)
\(488\) −8.36022 + 4.82678i −0.378449 + 0.218498i
\(489\) −0.394999 + 1.09014i −0.0178625 + 0.0492980i
\(490\) 2.19788 + 3.75676i 0.0992899 + 0.169713i
\(491\) 3.76295 + 2.17254i 0.169820 + 0.0980454i 0.582501 0.812830i \(-0.302074\pi\)
−0.412681 + 0.910876i \(0.635408\pi\)
\(492\) −4.66938 26.2598i −0.210512 1.18388i
\(493\) −4.63840 8.03395i −0.208903 0.361831i
\(494\) 1.17630i 0.0529244i
\(495\) −8.18658 + 24.8516i −0.367959 + 1.11699i
\(496\) 22.3177i 1.00209i
\(497\) −6.45463 5.53935i −0.289530 0.248474i
\(498\) 1.59742 + 1.89817i 0.0715823 + 0.0850589i
\(499\) −11.0873 + 19.2038i −0.496336 + 0.859679i −0.999991 0.00422558i \(-0.998655\pi\)
0.503655 + 0.863905i \(0.331988\pi\)
\(500\) 12.2698 + 17.6504i 0.548723 + 0.789352i
\(501\) 20.7409 + 24.6458i 0.926636 + 1.10109i
\(502\) 0.0907793 + 0.157234i 0.00405168 + 0.00701772i
\(503\) 12.4192i 0.553745i 0.960907 + 0.276873i \(0.0892980\pi\)
−0.960907 + 0.276873i \(0.910702\pi\)
\(504\) −8.53827 + 1.43330i −0.380325 + 0.0638442i
\(505\) −13.9150 + 5.50983i −0.619208 + 0.245184i
\(506\) 7.04434 4.06705i 0.313159 0.180803i
\(507\) −3.55785 20.0087i −0.158010 0.888617i
\(508\) 17.2225 + 9.94339i 0.764123 + 0.441167i
\(509\) −2.86404 + 4.96067i −0.126947 + 0.219878i −0.922492 0.386016i \(-0.873851\pi\)
0.795546 + 0.605894i \(0.207184\pi\)
\(510\) 0.0696564 + 2.36864i 0.00308444 + 0.104885i
\(511\) 26.5701 30.9604i 1.17539 1.36961i
\(512\) 18.9429 0.837168
\(513\) −16.8710 + 9.83807i −0.744871 + 0.434361i
\(514\) 5.17630i 0.228317i
\(515\) 16.2811 + 12.9034i 0.717432 + 0.568593i
\(516\) −6.55073 + 18.0791i −0.288380 + 0.795889i
\(517\) −7.11659 + 12.3263i −0.312987 + 0.542110i
\(518\) 0.647472 3.44772i 0.0284483 0.151484i
\(519\) 32.4890 5.77704i 1.42611 0.253584i
\(520\) −2.15142 1.70509i −0.0943461 0.0747730i
\(521\) −15.1109 −0.662019 −0.331009 0.943627i \(-0.607389\pi\)
−0.331009 + 0.943627i \(0.607389\pi\)
\(522\) 1.21244 + 3.30148i 0.0530671 + 0.144502i
\(523\) 16.8190 0.735443 0.367721 0.929936i \(-0.380138\pi\)
0.367721 + 0.929936i \(0.380138\pi\)
\(524\) −6.14579 10.6448i −0.268480 0.465021i
\(525\) 22.3567 5.01786i 0.975725 0.218997i
\(526\) 2.87573 4.98091i 0.125388 0.217178i
\(527\) −6.93194 + 12.0065i −0.301960 + 0.523010i
\(528\) −15.4080 18.3088i −0.670548 0.796790i
\(529\) −16.6222 28.7905i −0.722705 1.25176i
\(530\) 0.885068 0.350455i 0.0384449 0.0152228i
\(531\) 11.0576 4.06081i 0.479859 0.176224i
\(532\) −18.0378 + 6.33935i −0.782039 + 0.274846i
\(533\) −4.50716 7.80663i −0.195227 0.338143i
\(534\) 1.35927 + 7.64427i 0.0588212 + 0.330800i
\(535\) 2.13827 14.4835i 0.0924457 0.626176i
\(536\) 3.14086 + 1.81338i 0.135664 + 0.0783259i
\(537\) −4.93355 + 13.6159i −0.212898 + 0.587570i
\(538\) −3.12262 5.40853i −0.134626 0.233178i
\(539\) 17.0816 + 21.3001i 0.735756 + 0.917460i
\(540\) −3.16704 + 22.1139i −0.136288 + 0.951629i
\(541\) −4.64414 −0.199667 −0.0998336 0.995004i \(-0.531831\pi\)
−0.0998336 + 0.995004i \(0.531831\pi\)
\(542\) 5.45241 3.14795i 0.234201 0.135216i
\(543\) 10.8228 29.8693i 0.464449 1.28181i
\(544\) −6.03389 3.48367i −0.258701 0.149361i
\(545\) 3.42237 23.1812i 0.146598 0.992974i
\(546\) −1.24893 + 0.705071i −0.0534491 + 0.0301743i
\(547\) −10.9243 + 6.30715i −0.467090 + 0.269674i −0.715021 0.699103i \(-0.753583\pi\)
0.247931 + 0.968778i \(0.420249\pi\)
\(548\) 11.5642 0.493998
\(549\) 26.1604 + 4.53499i 1.11650 + 0.193549i
\(550\) −3.71255 3.95297i −0.158304 0.168555i
\(551\) 7.92312 + 13.7233i 0.337536 + 0.584630i
\(552\) 10.8408 9.12321i 0.461416 0.388310i
\(553\) −3.03023 0.569069i −0.128859 0.0241993i
\(554\) 2.78232 + 1.60637i 0.118209 + 0.0682482i
\(555\) −16.2577 8.75954i −0.690100 0.371822i
\(556\) −16.8521 + 9.72954i −0.714687 + 0.412625i
\(557\) 33.8955 1.43620 0.718099 0.695941i \(-0.245013\pi\)
0.718099 + 0.695941i \(0.245013\pi\)
\(558\) 3.36695 4.03618i 0.142535 0.170865i
\(559\) 6.49899i 0.274878i
\(560\) −6.83415 + 19.8093i −0.288796 + 0.837095i
\(561\) 2.60243 + 14.6356i 0.109875 + 0.617914i
\(562\) 0.426376 + 0.246168i 0.0179856 + 0.0103840i
\(563\) 21.3728 + 12.3396i 0.900754 + 0.520051i 0.877445 0.479677i \(-0.159246\pi\)
0.0233095 + 0.999728i \(0.492580\pi\)
\(564\) −4.13978 + 11.4252i −0.174316 + 0.481088i
\(565\) −26.1429 20.7193i −1.09984 0.871667i
\(566\) 0.667893 0.0280737
\(567\) 20.5578 + 12.0156i 0.863348 + 0.504609i
\(568\) 3.50667i 0.147136i
\(569\) −17.4111 + 10.0523i −0.729910 + 0.421414i −0.818389 0.574664i \(-0.805133\pi\)
0.0884793 + 0.996078i \(0.471799\pi\)
\(570\) −0.118984 4.04602i −0.00498370 0.169469i
\(571\) −14.8326 + 25.6908i −0.620723 + 1.07512i 0.368628 + 0.929577i \(0.379828\pi\)
−0.989351 + 0.145547i \(0.953506\pi\)
\(572\) −7.30979 4.22031i −0.305638 0.176460i
\(573\) −34.1858 + 6.07875i −1.42813 + 0.253943i
\(574\) 3.83737 4.47143i 0.160169 0.186634i
\(575\) −27.3334 + 25.6709i −1.13988 + 1.07055i
\(576\) −14.2912 11.9216i −0.595465 0.496733i
\(577\) 8.61964 0.358840 0.179420 0.983773i \(-0.442578\pi\)
0.179420 + 0.983773i \(0.442578\pi\)
\(578\) −1.69045 2.92794i −0.0703133 0.121786i
\(579\) 27.7350 + 32.9566i 1.15263 + 1.36963i
\(580\) 17.9315 + 2.64733i 0.744567 + 0.109924i
\(581\) 2.51539 13.3942i 0.104356 0.555686i
\(582\) 3.17256 2.66990i 0.131507 0.110671i
\(583\) 5.17149 2.98576i 0.214181 0.123658i
\(584\) −16.8201 −0.696022
\(585\) 1.53974 + 7.39148i 0.0636602 + 0.305600i
\(586\) 6.14291i 0.253761i
\(587\) −13.9832 + 8.07323i −0.577150 + 0.333218i −0.760000 0.649923i \(-0.774801\pi\)
0.182850 + 0.983141i \(0.441468\pi\)
\(588\) 17.5425 + 15.3517i 0.723442 + 0.633091i
\(589\) 11.8409 20.5090i 0.487894 0.845057i
\(590\) −0.356580 + 2.41527i −0.0146801 + 0.0994352i
\(591\) −30.9199 11.2034i −1.27188 0.460847i
\(592\) 14.6266 8.44466i 0.601149 0.347073i
\(593\) 24.8119i 1.01890i −0.860500 0.509451i \(-0.829849\pi\)
0.860500 0.509451i \(-0.170151\pi\)
\(594\) −0.0243950 5.63570i −0.00100094 0.231236i
\(595\) 9.82947 8.53430i 0.402969 0.349872i
\(596\) −6.16016 + 3.55657i −0.252330 + 0.145683i
\(597\) −14.4268 + 39.8158i −0.590448 + 1.62955i
\(598\) 1.17358 2.03269i 0.0479911 0.0831230i
\(599\) −8.83663 5.10183i −0.361055 0.208455i 0.308488 0.951228i \(-0.400177\pi\)
−0.669543 + 0.742773i \(0.733510\pi\)
\(600\) −7.57251 5.64721i −0.309146 0.230546i
\(601\) 7.38829 4.26563i 0.301375 0.173999i −0.341686 0.939814i \(-0.610998\pi\)
0.643060 + 0.765816i \(0.277664\pi\)
\(602\) −4.00781 + 1.40854i −0.163346 + 0.0574077i
\(603\) −3.43862 9.36337i −0.140031 0.381306i
\(604\) 28.0289 1.14048
\(605\) −7.38436 5.85240i −0.300217 0.237934i
\(606\) 2.46640 2.07563i 0.100191 0.0843166i
\(607\) 5.82829 10.0949i 0.236563 0.409739i −0.723163 0.690678i \(-0.757312\pi\)
0.959726 + 0.280939i \(0.0906457\pi\)
\(608\) 10.3068 + 5.95065i 0.417997 + 0.241331i
\(609\) 9.82140 16.6379i 0.397983 0.674203i
\(610\) −3.41796 + 4.31267i −0.138389 + 0.174615i
\(611\) 4.10708i 0.166155i
\(612\) 4.37520 + 11.9137i 0.176857 + 0.481582i
\(613\) 27.5449i 1.11253i −0.831006 0.556264i \(-0.812234\pi\)
0.831006 0.556264i \(-0.187766\pi\)
\(614\) −0.308103 0.533649i −0.0124340 0.0215363i
\(615\) −16.2925 26.3958i −0.656976 1.06438i
\(616\) 2.07761 11.0631i 0.0837093 0.445743i
\(617\) 1.41400 2.44912i 0.0569255 0.0985979i −0.836158 0.548488i \(-0.815204\pi\)
0.893084 + 0.449890i \(0.148537\pi\)
\(618\) −4.20695 1.52434i −0.169229 0.0613178i
\(619\) −34.7815 + 20.0811i −1.39799 + 0.807127i −0.994181 0.107718i \(-0.965646\pi\)
−0.403804 + 0.914845i \(0.632312\pi\)
\(620\) −9.97276 25.1860i −0.400516 1.01149i
\(621\) −38.9689 + 0.168683i −1.56377 + 0.00676901i
\(622\) 3.49231 0.140029
\(623\) 27.7768 32.3664i 1.11285 1.29673i
\(624\) −6.49199 2.35229i −0.259888 0.0941669i
\(625\) 20.8248 + 13.8322i 0.832990 + 0.553288i
\(626\) 3.09687 5.36393i 0.123776 0.214386i
\(627\) −4.44535 24.9999i −0.177530 0.998399i
\(628\) 23.5439 + 40.7793i 0.939505 + 1.62727i
\(629\) −10.4918 −0.418334
\(630\) −4.22449 + 2.55150i −0.168308 + 0.101654i
\(631\) −3.49540 −0.139150 −0.0695748 0.997577i \(-0.522164\pi\)
−0.0695748 + 0.997577i \(0.522164\pi\)
\(632\) 0.635561 + 1.10082i 0.0252813 + 0.0437885i
\(633\) 27.7932 23.3897i 1.10468 0.929655i
\(634\) −2.59637 + 4.49704i −0.103115 + 0.178600i
\(635\) 22.8803 + 3.37793i 0.907975 + 0.134049i
\(636\) 3.90087 3.28282i 0.154679 0.130172i
\(637\) 7.34179 + 2.85834i 0.290892 + 0.113251i
\(638\) −4.57276 −0.181037
\(639\) 6.17804 7.40600i 0.244400 0.292977i
\(640\) 16.7527 6.63346i 0.662208 0.262210i
\(641\) −21.1062 + 12.1856i −0.833643 + 0.481304i −0.855098 0.518466i \(-0.826503\pi\)
0.0214552 + 0.999770i \(0.493170\pi\)
\(642\) 0.552067 + 3.10472i 0.0217883 + 0.122534i
\(643\) 10.0485 17.4044i 0.396272 0.686364i −0.596990 0.802248i \(-0.703637\pi\)
0.993263 + 0.115885i \(0.0369703\pi\)
\(644\) −37.4946 7.04138i −1.47750 0.277469i
\(645\) 0.657379 + 22.3540i 0.0258843 + 0.880186i
\(646\) −1.14982 1.99155i −0.0452391 0.0783564i
\(647\) 24.4186i 0.959995i −0.877270 0.479997i \(-0.840638\pi\)
0.877270 0.479997i \(-0.159362\pi\)
\(648\) −1.76047 9.65781i −0.0691576 0.379395i
\(649\) 15.3155i 0.601184i
\(650\) −1.49808 0.452197i −0.0587597 0.0177366i
\(651\) −28.8725 0.278888i −1.13160 0.0109305i
\(652\) −1.11467 0.643555i −0.0436539 0.0252036i
\(653\) −1.14878 + 1.98974i −0.0449552 + 0.0778646i −0.887627 0.460562i \(-0.847648\pi\)
0.842672 + 0.538427i \(0.180981\pi\)
\(654\) 0.883598 + 4.96920i 0.0345514 + 0.194311i
\(655\) −11.2032 8.87900i −0.437746 0.346931i
\(656\) 28.3686 1.10761
\(657\) 35.5238 + 29.6337i 1.38591 + 1.15612i
\(658\) −2.53276 + 0.890134i −0.0987374 + 0.0347010i
\(659\) 19.0737 11.0122i 0.743006 0.428975i −0.0801553 0.996782i \(-0.525542\pi\)
0.823161 + 0.567808i \(0.192208\pi\)
\(660\) −25.5697 13.7768i −0.995299 0.536261i
\(661\) 37.5209 + 21.6627i 1.45939 + 0.842581i 0.998981 0.0451250i \(-0.0143686\pi\)
0.460411 + 0.887706i \(0.347702\pi\)
\(662\) −1.21731 + 2.10843i −0.0473119 + 0.0819467i
\(663\) 2.76194 + 3.28192i 0.107265 + 0.127459i
\(664\) −4.86586 + 2.80931i −0.188832 + 0.109022i
\(665\) −16.7903 + 14.5779i −0.651099 + 0.565308i
\(666\) 3.91924 + 0.679411i 0.151867 + 0.0263267i
\(667\) 31.6190i 1.22429i
\(668\) −30.9665 + 17.8785i −1.19813 + 0.691740i
\(669\) 2.62784 + 14.7785i 0.101598 + 0.571370i
\(670\) 2.04521 + 0.301945i 0.0790133 + 0.0116652i
\(671\) −17.2600 + 29.8952i −0.666316 + 1.15409i
\(672\) 0.140156 14.5099i 0.00540663 0.559733i
\(673\) 10.2322 5.90757i 0.394423 0.227720i −0.289652 0.957132i \(-0.593539\pi\)
0.684075 + 0.729412i \(0.260206\pi\)
\(674\) 8.35892i 0.321974i
\(675\) 6.04374 + 25.2680i 0.232624 + 0.972567i
\(676\) 22.5592 0.867662
\(677\) 28.8446 16.6535i 1.10859 0.640044i 0.170125 0.985422i \(-0.445583\pi\)
0.938464 + 0.345378i \(0.112249\pi\)
\(678\) 6.75519 + 2.44765i 0.259431 + 0.0940016i
\(679\) −22.3868 4.20418i −0.859128 0.161342i
\(680\) −5.30918 0.783822i −0.203598 0.0300582i
\(681\) 0.0942462 0.0167584i 0.00361152 0.000642183i
\(682\) 3.41692 + 5.91828i 0.130841 + 0.226623i
\(683\) 27.9312 1.06876 0.534379 0.845245i \(-0.320545\pi\)
0.534379 + 0.845245i \(0.320545\pi\)
\(684\) −7.47353 20.3504i −0.285757 0.778118i
\(685\) 12.5045 4.95135i 0.477774 0.189181i
\(686\) −0.171489 + 5.14704i −0.00654747 + 0.196515i
\(687\) 23.2443 + 27.6205i 0.886826 + 1.05379i
\(688\) −17.7126 10.2264i −0.675285 0.389876i
\(689\) 0.861561 1.49227i 0.0328229 0.0568509i
\(690\) 3.83102 7.11036i 0.145845 0.270687i
\(691\) 10.8297 6.25254i 0.411982 0.237858i −0.279659 0.960099i \(-0.590221\pi\)
0.691641 + 0.722241i \(0.256888\pi\)
\(692\) 36.6305i 1.39248i
\(693\) −23.8788 + 19.7046i −0.907079 + 0.748517i
\(694\) 8.37947 0.318080
\(695\) −14.0566 + 17.7361i −0.533195 + 0.672768i
\(696\) −7.84230 + 1.39448i −0.297262 + 0.0528576i
\(697\) −15.2617 8.81137i −0.578080 0.333754i
\(698\) −4.97367 2.87155i −0.188256 0.108690i
\(699\) 30.4928 + 11.0487i 1.15334 + 0.417899i
\(700\) 1.13937 + 25.4091i 0.0430640 + 0.960374i
\(701\) 11.0234i 0.416348i 0.978092 + 0.208174i \(0.0667521\pi\)
−0.978092 + 0.208174i \(0.933248\pi\)
\(702\) −0.819206 1.40483i −0.0309189 0.0530218i
\(703\) 17.9216 0.675925
\(704\) 20.9552 12.0985i 0.789780 0.455980i
\(705\) 0.415435 + 14.1267i 0.0156462 + 0.532043i
\(706\) −1.49997 0.866007i −0.0564520 0.0325926i
\(707\) −17.4039 3.26840i −0.654541 0.122921i
\(708\) 2.28922 + 12.8742i 0.0860342 + 0.483841i
\(709\) −3.18737 5.52069i −0.119704 0.207334i 0.799946 0.600072i \(-0.204861\pi\)
−0.919650 + 0.392738i \(0.871528\pi\)
\(710\) 0.735912 + 1.85853i 0.0276183 + 0.0697494i
\(711\) 0.597141 3.44465i 0.0223945 0.129184i
\(712\) −17.5840 −0.658988
\(713\) 40.9228 23.6268i 1.53257 0.884830i
\(714\) −1.42530 + 2.41453i −0.0533406 + 0.0903616i
\(715\) −9.71115 1.43371i −0.363177 0.0536177i
\(716\) −13.9223 8.03803i −0.520300 0.300395i
\(717\) −17.3657 20.6350i −0.648532 0.770630i
\(718\) 0.667700 0.385497i 0.0249183 0.0143866i
\(719\) −24.8171 −0.925523 −0.462762 0.886483i \(-0.653141\pi\)
−0.462762 + 0.886483i \(0.653141\pi\)
\(720\) −22.5678 7.43427i −0.841052 0.277059i
\(721\) 8.15009 + 23.1901i 0.303525 + 0.863643i
\(722\) −0.677575 1.17359i −0.0252167 0.0436767i
\(723\) 23.8520 4.24124i 0.887064 0.157733i
\(724\) 30.5414 + 17.6331i 1.13506 + 0.655327i
\(725\) 20.5231 4.81500i 0.762209 0.178825i
\(726\) 1.90808 + 0.691368i 0.0708155 + 0.0256591i
\(727\) 16.7759 + 29.0568i 0.622185 + 1.07766i 0.989078 + 0.147393i \(0.0470881\pi\)
−0.366893 + 0.930263i \(0.619579\pi\)
\(728\) −1.07697 3.06438i −0.0399152 0.113574i
\(729\) −13.2971 + 23.4987i −0.492484 + 0.870322i
\(730\) −8.91467 + 3.52989i −0.329947 + 0.130647i
\(731\) 6.35268 + 11.0032i 0.234962 + 0.406967i
\(732\) −10.0403 + 27.7098i −0.371100 + 1.02418i
\(733\) −3.06647 + 5.31129i −0.113263 + 0.196177i −0.917084 0.398694i \(-0.869464\pi\)
0.803821 + 0.594871i \(0.202797\pi\)
\(734\) 0.491003 0.850441i 0.0181232 0.0313904i
\(735\) 25.5420 + 9.08892i 0.942129 + 0.335250i
\(736\) 11.8737 + 20.5658i 0.437670 + 0.758067i
\(737\) 12.9689 0.477714
\(738\) 5.13049 + 4.27982i 0.188856 + 0.157542i
\(739\) −26.4425 −0.972703 −0.486351 0.873763i \(-0.661673\pi\)
−0.486351 + 0.873763i \(0.661673\pi\)
\(740\) 12.7329 16.0660i 0.468071 0.590596i
\(741\) −4.71782 5.60603i −0.173314 0.205943i
\(742\) 1.10698 + 0.207888i 0.0406386 + 0.00763181i
\(743\) −3.39717 + 5.88407i −0.124630 + 0.215865i −0.921588 0.388169i \(-0.873108\pi\)
0.796958 + 0.604034i \(0.206441\pi\)
\(744\) 7.66484 + 9.10787i 0.281006 + 0.333911i
\(745\) −5.13828 + 6.48331i −0.188252 + 0.237530i
\(746\) 3.05471i 0.111841i
\(747\) 15.2260 + 2.63948i 0.557091 + 0.0965734i
\(748\) −16.5012 −0.603343
\(749\) 11.2815 13.1456i 0.412219 0.480331i
\(750\) −5.19856 1.40384i −0.189824 0.0512611i
\(751\) 1.44669 2.50574i 0.0527904 0.0914356i −0.838423 0.545021i \(-0.816522\pi\)
0.891213 + 0.453585i \(0.149855\pi\)
\(752\) −11.1936 6.46261i −0.408187 0.235667i
\(753\) 1.06326 + 0.385258i 0.0387473 + 0.0140396i
\(754\) −1.14272 + 0.659750i −0.0416154 + 0.0240267i
\(755\) 30.3080 12.0009i 1.10302 0.436756i
\(756\) −17.1272 + 20.1329i −0.622911 + 0.732226i
\(757\) 14.1367i 0.513807i −0.966437 0.256904i \(-0.917298\pi\)
0.966437 0.256904i \(-0.0827023\pi\)
\(758\) 1.30666 + 2.26320i 0.0474601 + 0.0822033i
\(759\) 17.2602 47.6357i 0.626504 1.72907i
\(760\) 9.06891 + 1.33889i 0.328964 + 0.0485667i
\(761\) −17.1796 + 29.7559i −0.622759 + 1.07865i 0.366211 + 0.930532i \(0.380655\pi\)
−0.988970 + 0.148118i \(0.952678\pi\)
\(762\) −4.90468 + 0.872126i −0.177678 + 0.0315938i
\(763\) 18.0564 21.0400i 0.653686 0.761698i
\(764\) 38.5435i 1.39445i
\(765\) 9.83193 + 11.0091i 0.355474 + 0.398036i
\(766\) 10.2929i 0.371898i
\(767\) 2.20969 + 3.82729i 0.0797872 + 0.138196i
\(768\) 13.4729 11.3383i 0.486161 0.409134i
\(769\) 19.0787 + 11.0151i 0.687995 + 0.397214i 0.802860 0.596167i \(-0.203310\pi\)
−0.114866 + 0.993381i \(0.536644\pi\)
\(770\) −1.22057 6.29943i −0.0439863 0.227016i
\(771\) −20.7607 24.6693i −0.747678 0.888441i
\(772\) −41.4087 + 23.9073i −1.49033 + 0.860444i
\(773\) 43.6119i 1.56861i 0.620374 + 0.784306i \(0.286981\pi\)
−0.620374 + 0.784306i \(0.713019\pi\)
\(774\) −1.66054 4.52165i −0.0596868 0.162527i
\(775\) −21.5674 22.9640i −0.774722 0.824893i
\(776\) 4.69542 + 8.13270i 0.168556 + 0.291947i
\(777\) −10.7421 19.0280i −0.385371 0.682626i
\(778\) 4.64608 + 2.68242i 0.166570 + 0.0961693i
\(779\) 26.0695 + 15.0512i 0.934035 + 0.539266i
\(780\) −8.37749 + 0.246363i −0.299962 + 0.00882121i
\(781\) 6.26973 + 10.8595i 0.224348 + 0.388583i
\(782\) 4.58861i 0.164089i
\(783\) 19.0196 + 10.8715i 0.679704 + 0.388514i
\(784\) −19.3427 + 15.5119i −0.690811 + 0.553995i
\(785\) 42.9185 + 34.0146i 1.53183 + 1.21403i
\(786\) 2.89486 + 1.04891i 0.103256 + 0.0374135i
\(787\) 7.53521 13.0514i 0.268601 0.465231i −0.699900 0.714241i \(-0.746772\pi\)
0.968501 + 0.249010i \(0.0801053\pi\)
\(788\) 18.2533 31.6156i 0.650246 1.12626i
\(789\) −6.27186 35.2718i −0.223284 1.25571i
\(790\) 0.567867 + 0.450057i 0.0202038 + 0.0160123i
\(791\) −13.0868 37.2367i −0.465311 1.32398i
\(792\) 12.5761 + 2.18010i 0.446871 + 0.0774664i
\(793\) 9.96099i 0.353725i
\(794\) 2.49575 + 4.32276i 0.0885707 + 0.153409i
\(795\) 2.81249 5.21996i 0.0997486 0.185133i
\(796\) −40.7117 23.5049i −1.44299 0.833109i
\(797\) −14.5248 8.38591i −0.514496 0.297044i 0.220184 0.975458i \(-0.429334\pi\)
−0.734680 + 0.678414i \(0.762668\pi\)
\(798\) 2.43464 4.12440i 0.0861854 0.146002i
\(799\) 4.01461 + 6.95352i 0.142027 + 0.245998i
\(800\) 11.5406 10.8387i 0.408023 0.383207i
\(801\) 37.1370 + 30.9795i 1.31217 + 1.09461i
\(802\) 8.58893i 0.303286i
\(803\) −52.0888 + 30.0735i −1.83817 + 1.06127i
\(804\) 10.9016 1.93847i 0.384471 0.0683647i
\(805\) −43.5583 + 8.43981i −1.53523 + 0.297464i
\(806\) 1.70776 + 0.985975i 0.0601532 + 0.0347295i
\(807\) −36.5739 13.2521i −1.28746 0.466495i
\(808\) 3.65030 + 6.32250i 0.128417 + 0.222425i
\(809\) 3.56551i 0.125357i 0.998034 + 0.0626783i \(0.0199642\pi\)
−0.998034 + 0.0626783i \(0.980036\pi\)
\(810\) −2.95984 4.74918i −0.103998 0.166869i
\(811\) 22.3247i 0.783927i −0.919981 0.391963i \(-0.871796\pi\)
0.919981 0.391963i \(-0.128204\pi\)
\(812\) 16.2752 + 13.9673i 0.571147 + 0.490157i
\(813\) 13.3596 36.8706i 0.468541 1.29311i
\(814\) −2.58582 + 4.47877i −0.0906329 + 0.156981i
\(815\) −1.48085 0.218626i −0.0518720 0.00765815i
\(816\) −13.2906 + 2.36327i −0.465265 + 0.0827312i
\(817\) −10.8514 18.7951i −0.379642 0.657558i
\(818\) 5.18250i 0.181202i
\(819\) −3.12429 + 8.36932i −0.109172 + 0.292448i
\(820\) 32.0146 12.6766i 1.11800 0.442687i
\(821\) 17.9005 10.3349i 0.624732 0.360689i −0.153977 0.988074i \(-0.549208\pi\)
0.778709 + 0.627385i \(0.215875\pi\)
\(822\) −2.21640 + 1.86524i −0.0773060 + 0.0650577i
\(823\) 16.5005 + 9.52657i 0.575172 + 0.332075i 0.759212 0.650843i \(-0.225584\pi\)
−0.184041 + 0.982919i \(0.558918\pi\)
\(824\) 5.06695 8.77621i 0.176516 0.305734i
\(825\) −33.5475 3.94910i −1.16798 0.137490i
\(826\) −1.88131 + 2.19217i −0.0654593 + 0.0762754i
\(827\) −33.1487 −1.15269 −0.576346 0.817205i \(-0.695522\pi\)
−0.576346 + 0.817205i \(0.695522\pi\)
\(828\) 7.38873 42.6224i 0.256776 1.48123i
\(829\) 10.7440i 0.373153i 0.982440 + 0.186577i \(0.0597393\pi\)
−0.982440 + 0.186577i \(0.940261\pi\)
\(830\) −1.98934 + 2.51008i −0.0690510 + 0.0871263i
\(831\) 19.7027 3.50344i 0.683479 0.121533i
\(832\) 3.49111 6.04677i 0.121032 0.209634i
\(833\) 15.2240 2.33717i 0.527482 0.0809782i
\(834\) 1.66056 4.58291i 0.0575005 0.158693i
\(835\) −25.8296 + 32.5909i −0.893869 + 1.12785i
\(836\) 28.1866 0.974855
\(837\) −0.141718 32.7395i −0.00489850 1.13164i
\(838\) −0.188667 −0.00651739
\(839\) −15.5637 26.9571i −0.537319 0.930663i −0.999047 0.0436420i \(-0.986104\pi\)
0.461729 0.887021i \(-0.347229\pi\)
\(840\) −4.01432 10.4313i −0.138507 0.359915i
\(841\) −5.61236 + 9.72090i −0.193530 + 0.335203i
\(842\) −1.21615 + 2.10644i −0.0419114 + 0.0725927i
\(843\) 3.01934 0.536884i 0.103992 0.0184913i
\(844\) 20.1617 + 34.9210i 0.693993 + 1.20203i
\(845\) 24.3936 9.65898i 0.839165 0.332279i
\(846\) −1.04939 2.85749i −0.0360787 0.0982424i
\(847\) −3.69650 10.5179i −0.127013 0.361400i
\(848\) 2.71138 + 4.69625i 0.0931093 + 0.161270i
\(849\) 3.18305 2.67873i 0.109242 0.0919339i
\(850\) −2.97836 + 0.698763i −0.102157 + 0.0239674i
\(851\) 30.9691 + 17.8800i 1.06161 + 0.612919i
\(852\) 6.89351 + 8.19134i 0.236168 + 0.280631i
\(853\) −24.0094 41.5855i −0.822067 1.42386i −0.904141 0.427235i \(-0.859488\pi\)
0.0820742 0.996626i \(-0.473846\pi\)
\(854\) −6.14276 + 2.15886i −0.210201 + 0.0738747i
\(855\) −16.7945 18.8053i −0.574359 0.643128i
\(856\) −7.14175 −0.244100
\(857\) −8.16059 + 4.71152i −0.278760 + 0.160942i −0.632862 0.774265i \(-0.718120\pi\)
0.354102 + 0.935207i \(0.384787\pi\)
\(858\) 2.08171 0.370160i 0.0710685 0.0126370i
\(859\) 18.0598 + 10.4268i 0.616193 + 0.355759i 0.775385 0.631489i \(-0.217556\pi\)
−0.159192 + 0.987248i \(0.550889\pi\)
\(860\) −24.5587 3.62574i −0.837446 0.123637i
\(861\) 0.354501 36.7006i 0.0120814 1.25075i
\(862\) 7.86719 4.54213i 0.267958 0.154705i
\(863\) 34.2268 1.16509 0.582546 0.812797i \(-0.302056\pi\)
0.582546 + 0.812797i \(0.302056\pi\)
\(864\) 16.4533 0.0712209i 0.559754 0.00242298i
\(865\) 15.6837 + 39.6090i 0.533263 + 1.34675i
\(866\) 1.73122 + 2.99857i 0.0588294 + 0.101896i
\(867\) −19.7995 7.17409i −0.672426 0.243645i
\(868\) 5.91579 31.5010i 0.200795 1.06921i
\(869\) 3.93643 + 2.27270i 0.133534 + 0.0770960i
\(870\) −3.86377 + 2.38487i −0.130994 + 0.0808545i
\(871\) 3.24088 1.87113i 0.109813 0.0634007i
\(872\) −11.4306 −0.387088
\(873\) 4.41157 25.4485i 0.149309 0.861300i
\(874\) 7.83808i 0.265127i
\(875\) 12.1112 + 26.9874i 0.409434 + 0.912340i
\(876\) −39.2907 + 33.0655i −1.32751 + 1.11718i
\(877\) −9.80216 5.65928i −0.330995 0.191100i 0.325288 0.945615i \(-0.394539\pi\)
−0.656283 + 0.754515i \(0.727872\pi\)
\(878\) 0.470954 + 0.271905i 0.0158939 + 0.00917636i
\(879\) −24.6375 29.2759i −0.831002 0.987453i
\(880\) 19.1883 24.2111i 0.646836 0.816156i
\(881\) 5.55530 0.187163 0.0935814 0.995612i \(-0.470168\pi\)
0.0935814 + 0.995612i \(0.470168\pi\)
\(882\) −5.83835 0.112799i −0.196587 0.00379814i
\(883\) 53.8781i 1.81314i −0.422054 0.906571i \(-0.638691\pi\)
0.422054 0.906571i \(-0.361309\pi\)
\(884\) −4.12360 + 2.38076i −0.138692 + 0.0800738i
\(885\) 7.98759 + 12.9409i 0.268500 + 0.435002i
\(886\) −1.52588 + 2.64289i −0.0512628 + 0.0887898i
\(887\) 32.6535 + 18.8525i 1.09640 + 0.633004i 0.935272 0.353930i \(-0.115155\pi\)
0.161124 + 0.986934i \(0.448488\pi\)
\(888\) −3.06887 + 8.46966i −0.102985 + 0.284223i
\(889\) 20.7668 + 17.8220i 0.696496 + 0.597731i
\(890\) −9.31951 + 3.69019i −0.312391 + 0.123695i
\(891\) −22.7195 26.7608i −0.761131 0.896521i
\(892\) −16.6623 −0.557896
\(893\) −6.85759 11.8777i −0.229481 0.397472i
\(894\) 0.607006 1.67525i 0.0203013 0.0560288i
\(895\) −18.4959 2.73065i −0.618250 0.0912756i
\(896\) 20.9531 + 3.93493i 0.699995 + 0.131457i
\(897\) −2.55952 14.3943i −0.0854600 0.480612i
\(898\) −0.634449 + 0.366299i −0.0211718 + 0.0122236i
\(899\) −26.5646 −0.885978
\(900\) −28.7903 + 1.69478i −0.959678 + 0.0564928i
\(901\) 3.36866i 0.112226i
\(902\) −7.52288 + 4.34333i −0.250484 + 0.144617i
\(903\) −13.4512 + 22.7870i −0.447629 + 0.758305i
\(904\) −8.13609 + 14.0921i −0.270602 + 0.468697i
\(905\) 40.5746 + 5.99024i 1.34874 + 0.199122i
\(906\) −5.37203 + 4.52089i −0.178474 + 0.150197i
\(907\) −9.23572 + 5.33225i −0.306667 + 0.177054i −0.645434 0.763816i \(-0.723324\pi\)
0.338767 + 0.940870i \(0.389990\pi\)
\(908\) 0.106260i 0.00352636i
\(909\) 3.42963 19.7841i 0.113754 0.656197i
\(910\) −1.21389 1.39811i −0.0402400 0.0463469i
\(911\) −4.89096 + 2.82380i −0.162045 + 0.0935566i −0.578829 0.815449i \(-0.696490\pi\)
0.416785 + 0.909005i \(0.363157\pi\)
\(912\) 22.7025 4.03685i 0.751755 0.133673i
\(913\) −10.0458 + 17.3998i −0.332466 + 0.575849i
\(914\) −5.79317 3.34469i −0.191621 0.110632i
\(915\) 1.00756 + 34.2618i 0.0333090 + 1.13266i
\(916\) −34.7041 + 20.0364i −1.14665 + 0.662021i
\(917\) −5.60818 15.9574i −0.185198 0.526958i
\(918\) −2.76016 1.57769i −0.0910988 0.0520715i
\(919\) −47.2303 −1.55798 −0.778991 0.627035i \(-0.784268\pi\)
−0.778991 + 0.627035i \(0.784268\pi\)
\(920\) 14.3356 + 11.3615i 0.472631 + 0.374579i
\(921\) −3.60868 1.30756i −0.118910 0.0430855i
\(922\) 1.16975 2.02606i 0.0385236 0.0667249i
\(923\) 3.13358 + 1.80917i 0.103143 + 0.0595496i
\(924\) −16.8950 29.9268i −0.555803 0.984519i
\(925\) 6.88944 22.8241i 0.226523 0.750451i
\(926\) 1.59482i 0.0524090i
\(927\) −26.1632 + 9.60822i −0.859313 + 0.315575i
\(928\) 13.3501i 0.438238i
\(929\) −17.3900 30.1203i −0.570546 0.988215i −0.996510 0.0834744i \(-0.973398\pi\)
0.425964 0.904740i \(-0.359935\pi\)
\(930\) 5.97374 + 3.21862i 0.195887 + 0.105543i
\(931\) −26.0051 + 3.99226i −0.852281 + 0.130841i
\(932\) −18.0011 + 31.1789i −0.589646 + 1.02130i
\(933\) 16.6437 14.0067i 0.544889 0.458557i
\(934\) 2.73501 1.57906i 0.0894923 0.0516684i
\(935\) −17.8430 + 7.06517i −0.583527 + 0.231056i
\(936\) 3.45726 1.26965i 0.113004 0.0414999i
\(937\) 10.0549 0.328478 0.164239 0.986421i \(-0.447483\pi\)
0.164239 + 0.986421i \(0.447483\pi\)
\(938\) 1.85629 + 1.59306i 0.0606101 + 0.0520154i
\(939\) −6.75416 37.9842i −0.220414 1.23957i
\(940\) −15.5200 2.29131i −0.506208 0.0747342i
\(941\) 7.14794 12.3806i 0.233016 0.403596i −0.725678 0.688034i \(-0.758474\pi\)
0.958694 + 0.284438i \(0.0918071\pi\)
\(942\) −11.0899 4.01828i −0.361329 0.130923i
\(943\) 30.0326 + 52.0180i 0.977996 + 1.69394i
\(944\) −13.9080 −0.452668
\(945\) −9.89976 + 29.1032i −0.322039 + 0.946726i
\(946\) 6.26277 0.203620
\(947\) −10.2445 17.7440i −0.332902 0.576604i 0.650177 0.759783i \(-0.274695\pi\)
−0.983080 + 0.183179i \(0.941361\pi\)
\(948\) 3.64866 + 1.32205i 0.118503 + 0.0429381i
\(949\) −8.67791 + 15.0306i −0.281697 + 0.487913i
\(950\) 5.08750 1.19360i 0.165060 0.0387254i
\(951\) 5.66258 + 31.8453i 0.183622 + 1.03266i
\(952\) −4.81877 4.13545i −0.156177 0.134031i
\(953\) −7.96676 −0.258069 −0.129034 0.991640i \(-0.541188\pi\)
−0.129034 + 0.991640i \(0.541188\pi\)
\(954\) −0.218143 + 1.25838i −0.00706264 + 0.0407414i
\(955\) −16.5028 41.6776i −0.534019 1.34866i
\(956\) 25.9271 14.9690i 0.838543 0.484133i
\(957\) −21.7929 + 18.3400i −0.704464 + 0.592850i
\(958\) −2.79638 + 4.84346i −0.0903468 + 0.156485i
\(959\) 15.6398 + 2.93711i 0.505036 + 0.0948443i
\(960\) 11.3964 21.1516i 0.367817 0.682666i
\(961\) 4.34996 + 7.53434i 0.140321 + 0.243043i
\(962\) 1.49231i 0.0481140i
\(963\) 15.0832 + 12.5823i 0.486050 + 0.405460i
\(964\) 26.8924i 0.866146i
\(965\) −34.5396 + 43.5809i −1.11187 + 1.40292i
\(966\) 8.32198 4.69811i 0.267755 0.151159i
\(967\) −37.3555 21.5672i −1.20127 0.693555i −0.240435 0.970665i \(-0.577290\pi\)
−0.960838 + 0.277110i \(0.910623\pi\)
\(968\) −2.29813 + 3.98048i −0.0738648 + 0.127938i
\(969\) −13.4674 4.87972i −0.432634 0.156759i
\(970\) 4.19530 + 3.32494i 0.134703 + 0.106758i
\(971\) 36.3745 1.16731 0.583657 0.812000i \(-0.301621\pi\)
0.583657 + 0.812000i \(0.301621\pi\)
\(972\) −23.0980 19.0992i −0.740867 0.612608i
\(973\) −25.2624 + 8.87843i −0.809877 + 0.284629i
\(974\) −0.933729 + 0.539089i −0.0299186 + 0.0172735i
\(975\) −8.95321 + 3.85331i −0.286732 + 0.123405i
\(976\) −27.1480 15.6739i −0.868986 0.501709i
\(977\) −4.35270 + 7.53909i −0.139255 + 0.241197i −0.927215 0.374530i \(-0.877804\pi\)
0.787960 + 0.615727i \(0.211137\pi\)
\(978\) 0.317440 0.0564457i 0.0101506 0.00180493i
\(979\) −54.4543 + 31.4392i −1.74037 + 1.00480i
\(980\) −14.8972 + 26.1489i −0.475872 + 0.835295i
\(981\) 24.1411 + 20.1384i 0.770766 + 0.642968i
\(982\) 1.20823i 0.0385562i
\(983\) 3.85927 2.22815i 0.123092 0.0710670i −0.437190 0.899369i \(-0.644026\pi\)
0.560282 + 0.828302i \(0.310693\pi\)
\(984\) −11.5773 + 9.74297i −0.369069 + 0.310595i
\(985\) 6.20094 42.0017i 0.197578 1.33829i
\(986\) −1.28979 + 2.23399i −0.0410754 + 0.0711446i
\(987\) −8.50059 + 14.4004i −0.270577 + 0.458370i
\(988\) 7.04377 4.06672i 0.224092 0.129380i
\(989\) 43.3048i 1.37701i
\(990\) 7.12282 1.48377i 0.226378 0.0471573i
\(991\) −35.7538 −1.13576 −0.567878 0.823113i \(-0.692235\pi\)
−0.567878 + 0.823113i \(0.692235\pi\)
\(992\) −17.2783 + 9.97565i −0.548587 + 0.316727i
\(993\) 2.65490 + 14.9307i 0.0842506 + 0.473810i
\(994\) −0.436539 + 2.32453i −0.0138462 + 0.0737295i
\(995\) −54.0860 7.98501i −1.71464 0.253142i
\(996\) −5.84370 + 16.1278i −0.185165 + 0.511029i
\(997\) −18.9102 32.7534i −0.598891 1.03731i −0.992985 0.118240i \(-0.962275\pi\)
0.394094 0.919070i \(-0.371058\pi\)
\(998\) 6.16606 0.195183
\(999\) 21.4032 12.4810i 0.677169 0.394882i
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 315.2.z.b.104.19 80
3.2 odd 2 945.2.z.b.314.21 80
5.4 even 2 inner 315.2.z.b.104.22 yes 80
7.6 odd 2 inner 315.2.z.b.104.20 yes 80
9.2 odd 6 inner 315.2.z.b.209.21 yes 80
9.7 even 3 945.2.z.b.629.20 80
15.14 odd 2 945.2.z.b.314.19 80
21.20 even 2 945.2.z.b.314.22 80
35.34 odd 2 inner 315.2.z.b.104.21 yes 80
45.29 odd 6 inner 315.2.z.b.209.20 yes 80
45.34 even 6 945.2.z.b.629.22 80
63.20 even 6 inner 315.2.z.b.209.22 yes 80
63.34 odd 6 945.2.z.b.629.19 80
105.104 even 2 945.2.z.b.314.20 80
315.34 odd 6 945.2.z.b.629.21 80
315.209 even 6 inner 315.2.z.b.209.19 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.z.b.104.19 80 1.1 even 1 trivial
315.2.z.b.104.20 yes 80 7.6 odd 2 inner
315.2.z.b.104.21 yes 80 35.34 odd 2 inner
315.2.z.b.104.22 yes 80 5.4 even 2 inner
315.2.z.b.209.19 yes 80 315.209 even 6 inner
315.2.z.b.209.20 yes 80 45.29 odd 6 inner
315.2.z.b.209.21 yes 80 9.2 odd 6 inner
315.2.z.b.209.22 yes 80 63.20 even 6 inner
945.2.z.b.314.19 80 15.14 odd 2
945.2.z.b.314.20 80 105.104 even 2
945.2.z.b.314.21 80 3.2 odd 2
945.2.z.b.314.22 80 21.20 even 2
945.2.z.b.629.19 80 63.34 odd 6
945.2.z.b.629.20 80 9.7 even 3
945.2.z.b.629.21 80 315.34 odd 6
945.2.z.b.629.22 80 45.34 even 6