Properties

Label 315.2.bo.b.4.2
Level $315$
Weight $2$
Character 315.4
Analytic conductor $2.515$
Analytic rank $0$
Dimension $84$
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] = [315,2,Mod(4,315)]
 
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([2, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bo (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: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Character \(\chi\) \(=\) 315.4
Dual form 315.2.bo.b.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.26777 - 1.30930i) q^{2} +(1.21970 - 1.22977i) q^{3} +(2.42851 + 4.20630i) q^{4} +(2.23375 - 0.101685i) q^{5} +(-4.37613 + 1.19187i) q^{6} +(-0.957411 + 2.46645i) q^{7} -7.48135i q^{8} +(-0.0246457 - 2.99990i) q^{9} +O(q^{10})\) \(q+(-2.26777 - 1.30930i) q^{2} +(1.21970 - 1.22977i) q^{3} +(2.42851 + 4.20630i) q^{4} +(2.23375 - 0.101685i) q^{5} +(-4.37613 + 1.19187i) q^{6} +(-0.957411 + 2.46645i) q^{7} -7.48135i q^{8} +(-0.0246457 - 2.99990i) q^{9} +(-5.19877 - 2.69405i) q^{10} -0.314780 q^{11} +(8.13482 + 2.14394i) q^{12} +(3.79969 + 2.19375i) q^{13} +(5.40049 - 4.33979i) q^{14} +(2.59947 - 2.87102i) q^{15} +(-4.93828 + 8.55335i) q^{16} +(5.91468 + 3.41484i) q^{17} +(-3.87186 + 6.83534i) q^{18} +(-0.895825 - 1.55161i) q^{19} +(5.85241 + 9.14889i) q^{20} +(1.86539 + 4.18573i) q^{21} +(0.713848 + 0.412140i) q^{22} -4.99453i q^{23} +(-9.20030 - 9.12503i) q^{24} +(4.97932 - 0.454279i) q^{25} +(-5.74454 - 9.94983i) q^{26} +(-3.71923 - 3.62868i) q^{27} +(-12.6997 + 1.96263i) q^{28} +(-1.08098 - 1.87231i) q^{29} +(-9.65400 + 3.10733i) q^{30} +(0.600903 + 1.04080i) q^{31} +(9.43964 - 5.44998i) q^{32} +(-0.383939 + 0.387106i) q^{33} +(-8.94207 - 15.4881i) q^{34} +(-1.88782 + 5.60679i) q^{35} +(12.5586 - 7.38894i) q^{36} +(-3.66688 + 2.11708i) q^{37} +4.69160i q^{38} +(7.33230 - 1.99700i) q^{39} +(-0.760741 - 16.7115i) q^{40} +(-0.938078 + 1.62480i) q^{41} +(1.25007 - 11.9346i) q^{42} +(6.02612 - 3.47918i) q^{43} +(-0.764446 - 1.32406i) q^{44} +(-0.360097 - 6.69853i) q^{45} +(-6.53932 + 11.3264i) q^{46} +(-8.58385 - 4.95589i) q^{47} +(4.49538 + 16.5055i) q^{48} +(-5.16673 - 4.72281i) q^{49} +(-11.8867 - 5.48920i) q^{50} +(11.4136 - 3.10857i) q^{51} +21.3102i q^{52} +(-7.37483 - 4.25786i) q^{53} +(3.68333 + 13.0986i) q^{54} +(-0.703142 + 0.0320084i) q^{55} +(18.4524 + 7.16273i) q^{56} +(-3.00076 - 0.790855i) q^{57} +5.66127i q^{58} +(2.68662 + 4.65335i) q^{59} +(18.3892 + 3.96185i) q^{60} +(-3.01308 + 5.21881i) q^{61} -3.14704i q^{62} +(7.42269 + 2.81135i) q^{63} -8.78941 q^{64} +(8.71065 + 4.51393i) q^{65} +(1.37752 - 0.375176i) q^{66} +(2.73520 - 1.57917i) q^{67} +33.1719i q^{68} +(-6.14211 - 6.09185i) q^{69} +(11.6221 - 10.2432i) q^{70} -5.30674 q^{71} +(-22.4433 + 0.184383i) q^{72} +(9.64105 + 5.56626i) q^{73} +11.0875 q^{74} +(5.51464 - 6.67748i) q^{75} +(4.35103 - 7.53621i) q^{76} +(0.301374 - 0.776389i) q^{77} +(-19.2426 - 5.07141i) q^{78} +(-0.754973 + 1.30765i) q^{79} +(-10.1612 + 19.6082i) q^{80} +(-8.99879 + 0.147869i) q^{81} +(4.25468 - 2.45644i) q^{82} +(-13.0279 + 7.52166i) q^{83} +(-13.0763 + 18.0115i) q^{84} +(13.5592 + 7.02649i) q^{85} -18.2211 q^{86} +(-3.62097 - 0.954312i) q^{87} +2.35498i q^{88} +(2.27311 + 3.93714i) q^{89} +(-7.95374 + 15.6622i) q^{90} +(-9.04864 + 7.27142i) q^{91} +(21.0085 - 12.1293i) q^{92} +(2.01286 + 0.530492i) q^{93} +(12.9774 + 22.4776i) q^{94} +(-2.15883 - 3.37483i) q^{95} +(4.81137 - 18.2559i) q^{96} +(5.77551 - 3.33449i) q^{97} +(5.53338 + 17.4750i) q^{98} +(0.00775799 + 0.944309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26777 1.30930i −1.60355 0.925811i −0.990769 0.135560i \(-0.956717\pi\)
−0.612783 0.790251i \(-0.709950\pi\)
\(3\) 1.21970 1.22977i 0.704196 0.710005i
\(4\) 2.42851 + 4.20630i 1.21425 + 2.10315i
\(5\) 2.23375 0.101685i 0.998965 0.0454749i
\(6\) −4.37613 + 1.19187i −1.78655 + 0.486578i
\(7\) −0.957411 + 2.46645i −0.361867 + 0.932230i
\(8\) 7.48135i 2.64506i
\(9\) −0.0246457 2.99990i −0.00821524 0.999966i
\(10\) −5.19877 2.69405i −1.64399 0.851932i
\(11\) −0.314780 −0.0949098 −0.0474549 0.998873i \(-0.515111\pi\)
−0.0474549 + 0.998873i \(0.515111\pi\)
\(12\) 8.13482 + 2.14394i 2.34832 + 0.618903i
\(13\) 3.79969 + 2.19375i 1.05384 + 0.608438i 0.923723 0.383061i \(-0.125130\pi\)
0.130121 + 0.991498i \(0.458463\pi\)
\(14\) 5.40049 4.33979i 1.44334 1.15986i
\(15\) 2.59947 2.87102i 0.671180 0.741294i
\(16\) −4.93828 + 8.55335i −1.23457 + 2.13834i
\(17\) 5.91468 + 3.41484i 1.43452 + 0.828221i 0.997461 0.0712115i \(-0.0226865\pi\)
0.437060 + 0.899433i \(0.356020\pi\)
\(18\) −3.87186 + 6.83534i −0.912607 + 1.61110i
\(19\) −0.895825 1.55161i −0.205516 0.355965i 0.744781 0.667309i \(-0.232554\pi\)
−0.950297 + 0.311345i \(0.899221\pi\)
\(20\) 5.85241 + 9.14889i 1.30864 + 2.04576i
\(21\) 1.86539 + 4.18573i 0.407062 + 0.913400i
\(22\) 0.713848 + 0.412140i 0.152193 + 0.0878686i
\(23\) 4.99453i 1.04143i −0.853730 0.520716i \(-0.825665\pi\)
0.853730 0.520716i \(-0.174335\pi\)
\(24\) −9.20030 9.12503i −1.87800 1.86264i
\(25\) 4.97932 0.454279i 0.995864 0.0908558i
\(26\) −5.74454 9.94983i −1.12660 1.95132i
\(27\) −3.71923 3.62868i −0.715767 0.698340i
\(28\) −12.6997 + 1.96263i −2.40002 + 0.370902i
\(29\) −1.08098 1.87231i −0.200732 0.347679i 0.748032 0.663662i \(-0.230999\pi\)
−0.948765 + 0.315984i \(0.897666\pi\)
\(30\) −9.65400 + 3.10733i −1.76257 + 0.567318i
\(31\) 0.600903 + 1.04080i 0.107925 + 0.186932i 0.914930 0.403613i \(-0.132246\pi\)
−0.807004 + 0.590546i \(0.798913\pi\)
\(32\) 9.43964 5.44998i 1.66871 0.963430i
\(33\) −0.383939 + 0.387106i −0.0668351 + 0.0673865i
\(34\) −8.94207 15.4881i −1.53355 2.65619i
\(35\) −1.88782 + 5.60679i −0.319100 + 0.947721i
\(36\) 12.5586 7.38894i 2.09310 1.23149i
\(37\) −3.66688 + 2.11708i −0.602832 + 0.348045i −0.770155 0.637857i \(-0.779821\pi\)
0.167323 + 0.985902i \(0.446488\pi\)
\(38\) 4.69160i 0.761077i
\(39\) 7.33230 1.99700i 1.17411 0.319776i
\(40\) −0.760741 16.7115i −0.120284 2.64232i
\(41\) −0.938078 + 1.62480i −0.146503 + 0.253751i −0.929933 0.367730i \(-0.880135\pi\)
0.783430 + 0.621481i \(0.213469\pi\)
\(42\) 1.25007 11.9346i 0.192891 1.84155i
\(43\) 6.02612 3.47918i 0.918975 0.530571i 0.0356673 0.999364i \(-0.488644\pi\)
0.883308 + 0.468793i \(0.155311\pi\)
\(44\) −0.764446 1.32406i −0.115245 0.199609i
\(45\) −0.360097 6.69853i −0.0536801 0.998558i
\(46\) −6.53932 + 11.3264i −0.964170 + 1.66999i
\(47\) −8.58385 4.95589i −1.25208 0.722891i −0.280560 0.959836i \(-0.590520\pi\)
−0.971523 + 0.236946i \(0.923854\pi\)
\(48\) 4.49538 + 16.5055i 0.648852 + 2.38236i
\(49\) −5.16673 4.72281i −0.738104 0.674687i
\(50\) −11.8867 5.48920i −1.68104 0.776290i
\(51\) 11.4136 3.10857i 1.59823 0.435287i
\(52\) 21.3102i 2.95519i
\(53\) −7.37483 4.25786i −1.01301 0.584862i −0.100939 0.994893i \(-0.532185\pi\)
−0.912072 + 0.410031i \(0.865518\pi\)
\(54\) 3.68333 + 13.0986i 0.501238 + 1.78249i
\(55\) −0.703142 + 0.0320084i −0.0948116 + 0.00431602i
\(56\) 18.4524 + 7.16273i 2.46580 + 0.957160i
\(57\) −3.00076 0.790855i −0.397461 0.104751i
\(58\) 5.66127i 0.743362i
\(59\) 2.68662 + 4.65335i 0.349767 + 0.605815i 0.986208 0.165511i \(-0.0529273\pi\)
−0.636441 + 0.771326i \(0.719594\pi\)
\(60\) 18.3892 + 3.96185i 2.37404 + 0.511473i
\(61\) −3.01308 + 5.21881i −0.385785 + 0.668200i −0.991878 0.127194i \(-0.959403\pi\)
0.606093 + 0.795394i \(0.292736\pi\)
\(62\) 3.14704i 0.399674i
\(63\) 7.42269 + 2.81135i 0.935171 + 0.354197i
\(64\) −8.78941 −1.09868
\(65\) 8.71065 + 4.51393i 1.08042 + 0.559885i
\(66\) 1.37752 0.375176i 0.169561 0.0461810i
\(67\) 2.73520 1.57917i 0.334158 0.192926i −0.323528 0.946219i \(-0.604869\pi\)
0.657686 + 0.753292i \(0.271536\pi\)
\(68\) 33.1719i 4.02268i
\(69\) −6.14211 6.09185i −0.739423 0.733373i
\(70\) 11.6221 10.2432i 1.38910 1.22429i
\(71\) −5.30674 −0.629795 −0.314897 0.949126i \(-0.601970\pi\)
−0.314897 + 0.949126i \(0.601970\pi\)
\(72\) −22.4433 + 0.184383i −2.64497 + 0.0217298i
\(73\) 9.64105 + 5.56626i 1.12840 + 0.651482i 0.943532 0.331282i \(-0.107481\pi\)
0.184867 + 0.982763i \(0.440814\pi\)
\(74\) 11.0875 1.28890
\(75\) 5.51464 6.67748i 0.636776 0.771049i
\(76\) 4.35103 7.53621i 0.499098 0.864463i
\(77\) 0.301374 0.776389i 0.0343448 0.0884777i
\(78\) −19.2426 5.07141i −2.17879 0.574225i
\(79\) −0.754973 + 1.30765i −0.0849410 + 0.147122i −0.905366 0.424632i \(-0.860404\pi\)
0.820425 + 0.571754i \(0.193737\pi\)
\(80\) −10.1612 + 19.6082i −1.13605 + 2.19227i
\(81\) −8.99879 + 0.147869i −0.999865 + 0.0164299i
\(82\) 4.25468 2.45644i 0.469851 0.271269i
\(83\) −13.0279 + 7.52166i −1.43000 + 0.825610i −0.997120 0.0758428i \(-0.975835\pi\)
−0.432878 + 0.901452i \(0.642502\pi\)
\(84\) −13.0763 + 18.0115i −1.42674 + 1.96521i
\(85\) 13.5592 + 7.02649i 1.47070 + 0.762129i
\(86\) −18.2211 −1.96483
\(87\) −3.62097 0.954312i −0.388209 0.102313i
\(88\) 2.35498i 0.251042i
\(89\) 2.27311 + 3.93714i 0.240949 + 0.417336i 0.960985 0.276601i \(-0.0892080\pi\)
−0.720036 + 0.693937i \(0.755875\pi\)
\(90\) −7.95374 + 15.6622i −0.838398 + 1.65094i
\(91\) −9.04864 + 7.27142i −0.948555 + 0.762251i
\(92\) 21.0085 12.1293i 2.19029 1.26456i
\(93\) 2.01286 + 0.530492i 0.208724 + 0.0550094i
\(94\) 12.9774 + 22.4776i 1.33852 + 2.31839i
\(95\) −2.15883 3.37483i −0.221491 0.346251i
\(96\) 4.81137 18.2559i 0.491058 1.86324i
\(97\) 5.77551 3.33449i 0.586414 0.338566i −0.177264 0.984163i \(-0.556725\pi\)
0.763678 + 0.645597i \(0.223391\pi\)
\(98\) 5.53338 + 17.4750i 0.558955 + 1.76524i
\(99\) 0.00775799 + 0.944309i 0.000779707 + 0.0949066i
\(100\) 14.0031 + 19.8413i 1.40031 + 1.98413i
\(101\) −5.51932 −0.549193 −0.274597 0.961560i \(-0.588544\pi\)
−0.274597 + 0.961560i \(0.588544\pi\)
\(102\) −29.9534 7.89427i −2.96583 0.781649i
\(103\) 13.2647i 1.30701i −0.756920 0.653507i \(-0.773297\pi\)
0.756920 0.653507i \(-0.226703\pi\)
\(104\) 16.4122 28.4268i 1.60935 2.78748i
\(105\) 4.59246 + 9.16020i 0.448178 + 0.893944i
\(106\) 11.1496 + 19.3116i 1.08294 + 1.87571i
\(107\) −2.87199 + 1.65815i −0.277646 + 0.160299i −0.632357 0.774677i \(-0.717912\pi\)
0.354711 + 0.934976i \(0.384579\pi\)
\(108\) 6.23112 24.4565i 0.599590 2.35333i
\(109\) 6.26516 10.8516i 0.600094 1.03939i −0.392712 0.919661i \(-0.628463\pi\)
0.992806 0.119732i \(-0.0382035\pi\)
\(110\) 1.63647 + 0.848032i 0.156031 + 0.0808567i
\(111\) −1.86900 + 7.09161i −0.177398 + 0.673106i
\(112\) −16.3684 20.3691i −1.54667 1.92470i
\(113\) 3.70610 + 2.13972i 0.348640 + 0.201287i 0.664086 0.747656i \(-0.268821\pi\)
−0.315446 + 0.948944i \(0.602154\pi\)
\(114\) 5.76956 + 5.72236i 0.540369 + 0.535948i
\(115\) −0.507869 11.1566i −0.0473591 1.04035i
\(116\) 5.25032 9.09383i 0.487480 0.844341i
\(117\) 6.48739 11.4528i 0.599759 1.05881i
\(118\) 14.0703i 1.29527i
\(119\) −14.0853 + 11.3188i −1.29120 + 1.03760i
\(120\) −21.4791 19.4475i −1.96076 1.77531i
\(121\) −10.9009 −0.990992
\(122\) 13.6659 7.89002i 1.23725 0.714329i
\(123\) 0.853944 + 3.13539i 0.0769976 + 0.282709i
\(124\) −2.91860 + 5.05516i −0.262098 + 0.453967i
\(125\) 11.0764 1.52107i 0.990702 0.136049i
\(126\) −13.1520 16.0940i −1.17168 1.43376i
\(127\) 11.8000i 1.04708i 0.852000 + 0.523542i \(0.175390\pi\)
−0.852000 + 0.523542i \(0.824610\pi\)
\(128\) 1.05304 + 0.607974i 0.0930767 + 0.0537378i
\(129\) 3.07151 11.6543i 0.270431 1.02610i
\(130\) −13.8436 21.6414i −1.21417 1.89807i
\(131\) 16.0159 1.39931 0.699656 0.714480i \(-0.253337\pi\)
0.699656 + 0.714480i \(0.253337\pi\)
\(132\) −2.56068 0.674871i −0.222879 0.0587400i
\(133\) 4.68465 0.723972i 0.406210 0.0627764i
\(134\) −8.27039 −0.714453
\(135\) −8.67683 7.72739i −0.746783 0.665068i
\(136\) 25.5476 44.2498i 2.19069 3.79439i
\(137\) 15.1496i 1.29432i 0.762356 + 0.647158i \(0.224043\pi\)
−0.762356 + 0.647158i \(0.775957\pi\)
\(138\) 5.95282 + 21.8567i 0.506738 + 1.86057i
\(139\) −4.74095 + 8.21157i −0.402122 + 0.696496i −0.993982 0.109545i \(-0.965061\pi\)
0.591860 + 0.806041i \(0.298394\pi\)
\(140\) −28.1684 + 5.67540i −2.38067 + 0.479659i
\(141\) −16.5643 + 4.51141i −1.39497 + 0.379929i
\(142\) 12.0345 + 6.94809i 1.00991 + 0.583071i
\(143\) −1.19607 0.690550i −0.100020 0.0577467i
\(144\) 25.7809 + 14.6035i 2.14841 + 1.21696i
\(145\) −2.60502 4.07236i −0.216335 0.338191i
\(146\) −14.5758 25.2460i −1.20630 2.08937i
\(147\) −12.1098 + 0.593435i −0.998801 + 0.0489457i
\(148\) −17.8101 10.2827i −1.46398 0.845230i
\(149\) 3.22380 0.264104 0.132052 0.991243i \(-0.457843\pi\)
0.132052 + 0.991243i \(0.457843\pi\)
\(150\) −21.2487 + 7.92267i −1.73495 + 0.646884i
\(151\) −18.2702 −1.48681 −0.743403 0.668844i \(-0.766789\pi\)
−0.743403 + 0.668844i \(0.766789\pi\)
\(152\) −11.6082 + 6.70198i −0.941547 + 0.543602i
\(153\) 10.0984 17.8276i 0.816408 1.44128i
\(154\) −1.69997 + 1.36608i −0.136987 + 0.110082i
\(155\) 1.44810 + 2.26378i 0.116315 + 0.181831i
\(156\) 26.2065 + 25.9921i 2.09820 + 2.08103i
\(157\) −9.62453 + 5.55672i −0.768121 + 0.443475i −0.832204 0.554470i \(-0.812921\pi\)
0.0640829 + 0.997945i \(0.479588\pi\)
\(158\) 3.42420 1.97696i 0.272415 0.157279i
\(159\) −14.2313 + 3.87598i −1.12861 + 0.307385i
\(160\) 20.5317 13.1338i 1.62317 1.03832i
\(161\) 12.3188 + 4.78182i 0.970854 + 0.376860i
\(162\) 20.6007 + 11.4467i 1.61855 + 0.899340i
\(163\) 4.13275 2.38605i 0.323702 0.186890i −0.329339 0.944212i \(-0.606826\pi\)
0.653042 + 0.757322i \(0.273493\pi\)
\(164\) −9.11252 −0.711568
\(165\) −0.818262 + 0.903740i −0.0637016 + 0.0703561i
\(166\) 39.3923 3.05744
\(167\) 2.02760 + 1.17064i 0.156900 + 0.0905865i 0.576395 0.817172i \(-0.304459\pi\)
−0.419494 + 0.907758i \(0.637793\pi\)
\(168\) 31.3149 13.9557i 2.41600 1.07670i
\(169\) 3.12510 + 5.41283i 0.240392 + 0.416372i
\(170\) −21.5493 33.6874i −1.65276 2.58371i
\(171\) −4.63261 + 2.72562i −0.354264 + 0.208434i
\(172\) 29.2690 + 16.8984i 2.23174 + 1.28849i
\(173\) −5.20904 3.00744i −0.396036 0.228652i 0.288736 0.957409i \(-0.406765\pi\)
−0.684772 + 0.728757i \(0.740098\pi\)
\(174\) 6.96204 + 6.90508i 0.527791 + 0.523473i
\(175\) −3.64680 + 12.7162i −0.275672 + 0.961252i
\(176\) 1.55447 2.69243i 0.117173 0.202949i
\(177\) 8.99941 + 2.37181i 0.676437 + 0.178276i
\(178\) 11.9047i 0.892293i
\(179\) 6.06882 10.5115i 0.453605 0.785666i −0.545002 0.838435i \(-0.683471\pi\)
0.998607 + 0.0527683i \(0.0168045\pi\)
\(180\) 27.3015 17.7821i 2.03494 1.32540i
\(181\) 3.69759 0.274840 0.137420 0.990513i \(-0.456119\pi\)
0.137420 + 0.990513i \(0.456119\pi\)
\(182\) 30.0406 4.64252i 2.22676 0.344127i
\(183\) 2.74284 + 10.0708i 0.202757 + 0.744453i
\(184\) −37.3659 −2.75465
\(185\) −7.97564 + 5.10190i −0.586381 + 0.375099i
\(186\) −3.87012 3.83846i −0.283771 0.281449i
\(187\) −1.86182 1.07492i −0.136150 0.0786063i
\(188\) 48.1416i 3.51109i
\(189\) 12.5108 5.69915i 0.910025 0.414552i
\(190\) 0.477065 + 10.4799i 0.0346099 + 0.760290i
\(191\) −9.37952 + 16.2458i −0.678678 + 1.17550i 0.296701 + 0.954970i \(0.404113\pi\)
−0.975379 + 0.220534i \(0.929220\pi\)
\(192\) −10.7205 + 10.8089i −0.773684 + 0.780066i
\(193\) −18.2070 + 10.5118i −1.31057 + 0.756659i −0.982191 0.187887i \(-0.939836\pi\)
−0.328381 + 0.944545i \(0.606503\pi\)
\(194\) −17.4633 −1.25379
\(195\) 16.1755 5.20639i 1.15835 0.372838i
\(196\) 7.31811 33.2022i 0.522722 2.37158i
\(197\) 4.59975i 0.327719i 0.986484 + 0.163859i \(0.0523943\pi\)
−0.986484 + 0.163859i \(0.947606\pi\)
\(198\) 1.21879 2.15163i 0.0866153 0.152910i
\(199\) −2.46619 + 4.27156i −0.174823 + 0.302803i −0.940100 0.340898i \(-0.889269\pi\)
0.765277 + 0.643701i \(0.222602\pi\)
\(200\) −3.39862 37.2520i −0.240319 2.63412i
\(201\) 1.39413 5.28977i 0.0983342 0.373112i
\(202\) 12.5165 + 7.22642i 0.880660 + 0.508449i
\(203\) 5.65289 0.873606i 0.396755 0.0613151i
\(204\) 40.7936 + 40.4599i 2.85613 + 2.83276i
\(205\) −1.93022 + 3.72479i −0.134812 + 0.260151i
\(206\) −17.3675 + 30.0813i −1.21005 + 2.09587i
\(207\) −14.9831 + 0.123094i −1.04140 + 0.00855562i
\(208\) −37.5279 + 21.6667i −2.60209 + 1.50232i
\(209\) 0.281988 + 0.488417i 0.0195055 + 0.0337845i
\(210\) 1.57879 26.7861i 0.108947 1.84841i
\(211\) 7.62342 13.2041i 0.524818 0.909011i −0.474765 0.880113i \(-0.657467\pi\)
0.999582 0.0288981i \(-0.00919982\pi\)
\(212\) 41.3609i 2.84068i
\(213\) −6.47266 + 6.52605i −0.443499 + 0.447158i
\(214\) 8.68401 0.593626
\(215\) 13.1071 8.38441i 0.893897 0.571812i
\(216\) −27.1474 + 27.8249i −1.84715 + 1.89324i
\(217\) −3.14238 + 0.485628i −0.213319 + 0.0329666i
\(218\) −28.4158 + 16.4059i −1.92456 + 1.11115i
\(219\) 18.6044 5.06704i 1.25717 0.342399i
\(220\) −1.84222 2.87989i −0.124203 0.194162i
\(221\) 14.9826 + 25.9507i 1.00784 + 1.74563i
\(222\) 13.5235 13.6350i 0.907636 0.915124i
\(223\) −9.21120 + 5.31809i −0.616827 + 0.356125i −0.775633 0.631184i \(-0.782569\pi\)
0.158805 + 0.987310i \(0.449236\pi\)
\(224\) 4.40447 + 28.5003i 0.294286 + 1.90425i
\(225\) −1.48551 14.9263i −0.0990340 0.995084i
\(226\) −5.60304 9.70474i −0.372708 0.645550i
\(227\) 7.44981i 0.494461i −0.968957 0.247230i \(-0.920480\pi\)
0.968957 0.247230i \(-0.0795205\pi\)
\(228\) −3.96080 14.5427i −0.262310 0.963113i
\(229\) −9.63956 −0.637000 −0.318500 0.947923i \(-0.603179\pi\)
−0.318500 + 0.947923i \(0.603179\pi\)
\(230\) −13.4555 + 25.9654i −0.887230 + 1.71211i
\(231\) −0.587189 1.31758i −0.0386342 0.0866906i
\(232\) −14.0074 + 8.08717i −0.919630 + 0.530949i
\(233\) −6.53325 + 3.77197i −0.428007 + 0.247110i −0.698497 0.715613i \(-0.746148\pi\)
0.270490 + 0.962723i \(0.412814\pi\)
\(234\) −29.7069 + 17.4783i −1.94200 + 1.14259i
\(235\) −19.6782 10.1974i −1.28366 0.665204i
\(236\) −13.0489 + 22.6014i −0.849413 + 1.47123i
\(237\) 0.687261 + 2.52339i 0.0446424 + 0.163912i
\(238\) 46.7619 7.22665i 3.03112 0.468434i
\(239\) −12.3847 + 21.4509i −0.801098 + 1.38754i 0.117796 + 0.993038i \(0.462417\pi\)
−0.918894 + 0.394505i \(0.870916\pi\)
\(240\) 11.7199 + 36.4121i 0.756518 + 2.35039i
\(241\) −0.246396 −0.0158717 −0.00793587 0.999969i \(-0.502526\pi\)
−0.00793587 + 0.999969i \(0.502526\pi\)
\(242\) 24.7207 + 14.2725i 1.58911 + 0.917472i
\(243\) −10.7940 + 11.2468i −0.692436 + 0.721479i
\(244\) −29.2691 −1.87376
\(245\) −12.0214 10.0242i −0.768022 0.640424i
\(246\) 2.16860 8.22839i 0.138265 0.524623i
\(247\) 7.86087i 0.500175i
\(248\) 7.78655 4.49557i 0.494447 0.285469i
\(249\) −6.64030 + 25.1955i −0.420812 + 1.59670i
\(250\) −27.1102 11.0528i −1.71460 0.699042i
\(251\) 2.91065 0.183718 0.0918592 0.995772i \(-0.470719\pi\)
0.0918592 + 0.995772i \(0.470719\pi\)
\(252\) 6.20068 + 38.0494i 0.390606 + 2.39689i
\(253\) 1.57218i 0.0988421i
\(254\) 15.4497 26.7597i 0.969403 1.67905i
\(255\) 25.1791 8.10439i 1.57678 0.507516i
\(256\) 7.19738 + 12.4662i 0.449836 + 0.779139i
\(257\) 10.8826i 0.678840i −0.940635 0.339420i \(-0.889769\pi\)
0.940635 0.339420i \(-0.110231\pi\)
\(258\) −22.2244 + 22.4077i −1.38363 + 1.39504i
\(259\) −1.71094 11.0711i −0.106313 0.687924i
\(260\) 2.16693 + 47.6017i 0.134387 + 2.95213i
\(261\) −5.59009 + 3.28897i −0.346018 + 0.203582i
\(262\) −36.3202 20.9695i −2.24387 1.29550i
\(263\) 15.8980i 0.980313i −0.871634 0.490156i \(-0.836940\pi\)
0.871634 0.490156i \(-0.163060\pi\)
\(264\) 2.89607 + 2.87238i 0.178241 + 0.176783i
\(265\) −16.9065 8.76110i −1.03856 0.538190i
\(266\) −11.5716 4.49179i −0.709499 0.275409i
\(267\) 7.61427 + 2.00675i 0.465986 + 0.122811i
\(268\) 13.2849 + 7.67005i 0.811505 + 0.468523i
\(269\) 12.0935 20.9465i 0.737353 1.27713i −0.216330 0.976320i \(-0.569409\pi\)
0.953683 0.300813i \(-0.0972580\pi\)
\(270\) 9.55959 + 28.8844i 0.581778 + 1.75785i
\(271\) −15.8668 27.4821i −0.963841 1.66942i −0.712698 0.701471i \(-0.752527\pi\)
−0.251143 0.967950i \(-0.580806\pi\)
\(272\) −58.4167 + 33.7269i −3.54203 + 2.04499i
\(273\) −2.09453 + 19.9967i −0.126767 + 1.21025i
\(274\) 19.8353 34.3557i 1.19829 2.07550i
\(275\) −1.56739 + 0.142998i −0.0945173 + 0.00862310i
\(276\) 10.7080 40.6296i 0.644546 2.44562i
\(277\) 2.11326i 0.126973i 0.997983 + 0.0634866i \(0.0202220\pi\)
−0.997983 + 0.0634866i \(0.979778\pi\)
\(278\) 21.5027 12.4146i 1.28965 0.744579i
\(279\) 3.10747 1.82830i 0.186039 0.109457i
\(280\) 41.9464 + 14.1234i 2.50678 + 0.844037i
\(281\) −6.35502 11.0072i −0.379109 0.656636i 0.611824 0.790994i \(-0.290436\pi\)
−0.990933 + 0.134358i \(0.957103\pi\)
\(282\) 43.4708 + 11.4568i 2.58865 + 0.682242i
\(283\) 11.6151 6.70597i 0.690445 0.398629i −0.113334 0.993557i \(-0.536153\pi\)
0.803779 + 0.594928i \(0.202820\pi\)
\(284\) −12.8875 22.3217i −0.764730 1.32455i
\(285\) −6.78338 1.46144i −0.401813 0.0865684i
\(286\) 1.80827 + 3.13201i 0.106925 + 0.185200i
\(287\) −3.10936 3.86932i −0.183539 0.228399i
\(288\) −16.5820 28.1837i −0.977106 1.66074i
\(289\) 14.8223 + 25.6730i 0.871900 + 1.51018i
\(290\) 0.575667 + 12.6459i 0.0338043 + 0.742593i
\(291\) 2.94377 11.1696i 0.172567 0.654774i
\(292\) 54.0708i 3.16426i
\(293\) −4.43660 2.56147i −0.259189 0.149643i 0.364776 0.931095i \(-0.381146\pi\)
−0.623965 + 0.781453i \(0.714479\pi\)
\(294\) 28.2392 + 14.5096i 1.64694 + 0.846215i
\(295\) 6.47442 + 10.1213i 0.376955 + 0.589283i
\(296\) 15.8386 + 27.4332i 0.920599 + 1.59452i
\(297\) 1.17074 + 1.14224i 0.0679333 + 0.0662793i
\(298\) −7.31083 4.22091i −0.423505 0.244511i
\(299\) 10.9568 18.9777i 0.633647 1.09751i
\(300\) 41.4798 + 6.97990i 2.39484 + 0.402985i
\(301\) 2.81175 + 18.1941i 0.162066 + 1.04869i
\(302\) 41.4325 + 23.9210i 2.38417 + 1.37650i
\(303\) −6.73194 + 6.78747i −0.386740 + 0.389930i
\(304\) 17.6953 1.01490
\(305\) −6.19981 + 11.9639i −0.355000 + 0.685052i
\(306\) −46.2424 + 27.2070i −2.64350 + 1.55532i
\(307\) 6.74809i 0.385134i 0.981284 + 0.192567i \(0.0616812\pi\)
−0.981284 + 0.192567i \(0.938319\pi\)
\(308\) 3.99761 0.617797i 0.227785 0.0352022i
\(309\) −16.3125 16.1791i −0.927987 0.920394i
\(310\) −0.320007 7.02971i −0.0181752 0.399261i
\(311\) −5.45910 9.45544i −0.309557 0.536169i 0.668708 0.743525i \(-0.266847\pi\)
−0.978266 + 0.207356i \(0.933514\pi\)
\(312\) −14.9403 54.8555i −0.845825 3.10558i
\(313\) 16.8868 + 9.74960i 0.954498 + 0.551080i 0.894475 0.447117i \(-0.147549\pi\)
0.0600227 + 0.998197i \(0.480883\pi\)
\(314\) 29.1016 1.64230
\(315\) 16.8663 + 5.52509i 0.950311 + 0.311303i
\(316\) −7.33382 −0.412560
\(317\) 21.5858 + 12.4626i 1.21238 + 0.699967i 0.963277 0.268511i \(-0.0865314\pi\)
0.249101 + 0.968477i \(0.419865\pi\)
\(318\) 37.3480 + 9.84311i 2.09437 + 0.551974i
\(319\) 0.340270 + 0.589365i 0.0190515 + 0.0329981i
\(320\) −19.6334 + 0.893752i −1.09754 + 0.0499622i
\(321\) −1.46385 + 5.55432i −0.0817041 + 0.310012i
\(322\) −21.6752 26.9729i −1.20791 1.50314i
\(323\) 12.2364i 0.680852i
\(324\) −22.4756 37.4925i −1.24864 2.08291i
\(325\) 19.9165 + 9.19728i 1.10477 + 0.510173i
\(326\) −12.4962 −0.692098
\(327\) −5.70326 20.9404i −0.315391 1.15801i
\(328\) 12.1557 + 7.01809i 0.671186 + 0.387509i
\(329\) 20.4417 16.4268i 1.12699 0.905639i
\(330\) 3.03889 0.978125i 0.167285 0.0538440i
\(331\) 3.33016 5.76801i 0.183042 0.317039i −0.759873 0.650072i \(-0.774739\pi\)
0.942915 + 0.333033i \(0.108072\pi\)
\(332\) −63.2767 36.5328i −3.47276 2.00500i
\(333\) 6.44139 + 10.9481i 0.352986 + 0.599952i
\(334\) −3.06541 5.30945i −0.167732 0.290520i
\(335\) 5.94919 3.80561i 0.325039 0.207922i
\(336\) −45.0138 4.71492i −2.45571 0.257220i
\(337\) −20.4661 11.8161i −1.11486 0.643665i −0.174777 0.984608i \(-0.555920\pi\)
−0.940084 + 0.340943i \(0.889254\pi\)
\(338\) 16.3667i 0.890232i
\(339\) 7.15169 1.94781i 0.388426 0.105790i
\(340\) 3.37308 + 74.0978i 0.182931 + 4.01852i
\(341\) −0.189152 0.327622i −0.0102432 0.0177417i
\(342\) 14.0743 0.115628i 0.761052 0.00625243i
\(343\) 16.5952 8.22179i 0.896059 0.443935i
\(344\) −26.0290 45.0835i −1.40339 2.43074i
\(345\) −14.3394 12.9831i −0.772008 0.698989i
\(346\) 7.87526 + 13.6403i 0.423376 + 0.733310i
\(347\) −27.2627 + 15.7402i −1.46354 + 0.844976i −0.999173 0.0406668i \(-0.987052\pi\)
−0.464368 + 0.885642i \(0.653718\pi\)
\(348\) −4.77943 17.5484i −0.256205 0.940695i
\(349\) 2.83168 + 4.90462i 0.151576 + 0.262538i 0.931807 0.362954i \(-0.118232\pi\)
−0.780231 + 0.625492i \(0.784898\pi\)
\(350\) 24.9193 24.0625i 1.33199 1.28620i
\(351\) −6.17151 21.9469i −0.329411 1.17144i
\(352\) −2.97141 + 1.71555i −0.158377 + 0.0914389i
\(353\) 28.2756i 1.50496i −0.658616 0.752479i \(-0.728858\pi\)
0.658616 0.752479i \(-0.271142\pi\)
\(354\) −17.3032 17.1616i −0.919652 0.912128i
\(355\) −11.8540 + 0.539616i −0.629143 + 0.0286399i
\(356\) −11.0405 + 19.1227i −0.585146 + 1.01350i
\(357\) −3.26039 + 31.1273i −0.172558 + 1.64743i
\(358\) −27.5253 + 15.8917i −1.45476 + 0.839905i
\(359\) 9.01174 + 15.6088i 0.475622 + 0.823801i 0.999610 0.0279246i \(-0.00888983\pi\)
−0.523988 + 0.851725i \(0.675556\pi\)
\(360\) −50.1141 + 2.69401i −2.64124 + 0.141987i
\(361\) 7.89500 13.6745i 0.415526 0.719712i
\(362\) −8.38527 4.84124i −0.440720 0.254450i
\(363\) −13.2959 + 13.4056i −0.697853 + 0.703610i
\(364\) −52.5604 20.4026i −2.75492 1.06939i
\(365\) 22.1017 + 11.4533i 1.15686 + 0.599494i
\(366\) 6.96549 26.4294i 0.364092 1.38148i
\(367\) 5.37797i 0.280728i 0.990100 + 0.140364i \(0.0448272\pi\)
−0.990100 + 0.140364i \(0.955173\pi\)
\(368\) 42.7200 + 24.6644i 2.22693 + 1.28572i
\(369\) 4.89735 + 2.77410i 0.254946 + 0.144414i
\(370\) 24.7668 1.12743i 1.28756 0.0586125i
\(371\) 17.5625 14.1131i 0.911801 0.732716i
\(372\) 2.65683 + 9.75498i 0.137750 + 0.505772i
\(373\) 22.3803i 1.15881i −0.815041 0.579403i \(-0.803286\pi\)
0.815041 0.579403i \(-0.196714\pi\)
\(374\) 2.81479 + 4.87535i 0.145549 + 0.252099i
\(375\) 11.6394 15.4766i 0.601053 0.799209i
\(376\) −37.0767 + 64.2188i −1.91209 + 3.31183i
\(377\) 9.48559i 0.488533i
\(378\) −35.8334 3.45596i −1.84307 0.177755i
\(379\) −5.57377 −0.286306 −0.143153 0.989701i \(-0.545724\pi\)
−0.143153 + 0.989701i \(0.545724\pi\)
\(380\) 8.95282 17.2765i 0.459270 0.886265i
\(381\) 14.5113 + 14.3926i 0.743436 + 0.737353i
\(382\) 42.5411 24.5611i 2.17659 1.25666i
\(383\) 2.13584i 0.109136i −0.998510 0.0545682i \(-0.982622\pi\)
0.998510 0.0545682i \(-0.0173782\pi\)
\(384\) 2.03207 0.553446i 0.103698 0.0282429i
\(385\) 0.594249 1.76491i 0.0302857 0.0899480i
\(386\) 55.0524 2.80209
\(387\) −10.5857 17.9920i −0.538102 0.914586i
\(388\) 28.0517 + 16.1957i 1.42411 + 0.822211i
\(389\) −20.6792 −1.04847 −0.524237 0.851572i \(-0.675650\pi\)
−0.524237 + 0.851572i \(0.675650\pi\)
\(390\) −43.4989 9.37161i −2.20265 0.474550i
\(391\) 17.0555 29.5411i 0.862536 1.49396i
\(392\) −35.3330 + 38.6541i −1.78459 + 1.95233i
\(393\) 19.5346 19.6957i 0.985390 0.993519i
\(394\) 6.02243 10.4312i 0.303406 0.525514i
\(395\) −1.55345 + 2.99774i −0.0781628 + 0.150833i
\(396\) −3.95320 + 2.32589i −0.198656 + 0.116881i
\(397\) −16.7451 + 9.66778i −0.840412 + 0.485212i −0.857404 0.514644i \(-0.827924\pi\)
0.0169924 + 0.999856i \(0.494591\pi\)
\(398\) 11.1855 6.45793i 0.560677 0.323707i
\(399\) 4.82357 6.64405i 0.241480 0.332618i
\(400\) −20.7037 + 44.8332i −1.03518 + 2.24166i
\(401\) −2.11017 −0.105377 −0.0526885 0.998611i \(-0.516779\pi\)
−0.0526885 + 0.998611i \(0.516779\pi\)
\(402\) −10.0874 + 10.1706i −0.503115 + 0.507266i
\(403\) 5.27293i 0.262664i
\(404\) −13.4037 23.2159i −0.666860 1.15503i
\(405\) −20.0860 + 1.24535i −0.998083 + 0.0618817i
\(406\) −13.9632 5.42017i −0.692984 0.268998i
\(407\) 1.15426 0.666414i 0.0572147 0.0330329i
\(408\) −23.2563 85.3892i −1.15136 4.22740i
\(409\) 8.72420 + 15.1108i 0.431384 + 0.747179i 0.996993 0.0774949i \(-0.0246921\pi\)
−0.565609 + 0.824674i \(0.691359\pi\)
\(410\) 9.25414 5.91973i 0.457029 0.292355i
\(411\) 18.6304 + 18.4780i 0.918971 + 0.911453i
\(412\) 55.7955 32.2135i 2.74884 1.58705i
\(413\) −14.0494 + 2.17122i −0.691328 + 0.106839i
\(414\) 34.1393 + 19.3381i 1.67786 + 0.950418i
\(415\) −28.3363 + 18.1263i −1.39097 + 0.889785i
\(416\) 47.8236 2.34475
\(417\) 4.31575 + 15.8459i 0.211343 + 0.775979i
\(418\) 1.47682i 0.0722337i
\(419\) −7.25445 + 12.5651i −0.354403 + 0.613844i −0.987016 0.160624i \(-0.948649\pi\)
0.632612 + 0.774469i \(0.281983\pi\)
\(420\) −27.3777 + 41.5629i −1.33590 + 2.02806i
\(421\) 6.83590 + 11.8401i 0.333161 + 0.577053i 0.983130 0.182909i \(-0.0585512\pi\)
−0.649968 + 0.759961i \(0.725218\pi\)
\(422\) −34.5762 + 19.9626i −1.68315 + 0.971764i
\(423\) −14.6556 + 25.8728i −0.712580 + 1.25798i
\(424\) −31.8545 + 55.1736i −1.54699 + 2.67947i
\(425\) 31.0024 + 14.3167i 1.50384 + 0.694461i
\(426\) 23.2230 6.32494i 1.12516 0.306444i
\(427\) −9.98716 12.4281i −0.483312 0.601440i
\(428\) −13.9493 8.05364i −0.674265 0.389287i
\(429\) −2.30806 + 0.628616i −0.111434 + 0.0303499i
\(430\) −40.7015 + 1.85281i −1.96280 + 0.0893507i
\(431\) 5.94074 10.2897i 0.286155 0.495635i −0.686733 0.726909i \(-0.740956\pi\)
0.972889 + 0.231274i \(0.0742894\pi\)
\(432\) 49.4040 13.8925i 2.37695 0.668402i
\(433\) 33.4088i 1.60552i −0.596299 0.802762i \(-0.703363\pi\)
0.596299 0.802762i \(-0.296637\pi\)
\(434\) 7.76201 + 3.01301i 0.372588 + 0.144629i
\(435\) −8.18540 1.76350i −0.392460 0.0845534i
\(436\) 60.8600 2.91466
\(437\) −7.74959 + 4.47423i −0.370713 + 0.214031i
\(438\) −48.8247 12.8678i −2.33293 0.614848i
\(439\) 19.2440 33.3316i 0.918466 1.59083i 0.116720 0.993165i \(-0.462762\pi\)
0.801746 0.597665i \(-0.203905\pi\)
\(440\) 0.239466 + 5.26045i 0.0114161 + 0.250782i
\(441\) −14.0406 + 15.6161i −0.668601 + 0.743622i
\(442\) 78.4668i 3.73228i
\(443\) 13.1041 + 7.56565i 0.622594 + 0.359455i 0.777878 0.628415i \(-0.216296\pi\)
−0.155284 + 0.987870i \(0.549629\pi\)
\(444\) −34.3683 + 9.36044i −1.63105 + 0.444227i
\(445\) 5.47791 + 8.56346i 0.259678 + 0.405947i
\(446\) 27.8518 1.31882
\(447\) 3.93208 3.96452i 0.185981 0.187515i
\(448\) 8.41508 21.6786i 0.397575 1.02422i
\(449\) −24.0844 −1.13661 −0.568307 0.822816i \(-0.692401\pi\)
−0.568307 + 0.822816i \(0.692401\pi\)
\(450\) −16.1741 + 35.7942i −0.762454 + 1.68736i
\(451\) 0.295288 0.511455i 0.0139046 0.0240835i
\(452\) 20.7853i 0.977656i
\(453\) −22.2842 + 22.4680i −1.04700 + 1.05564i
\(454\) −9.75399 + 16.8944i −0.457778 + 0.792894i
\(455\) −19.4731 + 17.1627i −0.912911 + 0.804598i
\(456\) −5.91666 + 22.4497i −0.277073 + 1.05131i
\(457\) −3.64559 2.10478i −0.170533 0.0984575i 0.412304 0.911046i \(-0.364724\pi\)
−0.582837 + 0.812589i \(0.698058\pi\)
\(458\) 21.8603 + 12.6210i 1.02146 + 0.589742i
\(459\) −9.60670 34.1631i −0.448403 1.59460i
\(460\) 45.6945 29.2300i 2.13052 1.36286i
\(461\) 9.31892 + 16.1408i 0.434025 + 0.751754i 0.997216 0.0745733i \(-0.0237595\pi\)
−0.563190 + 0.826327i \(0.690426\pi\)
\(462\) −0.393499 + 3.75677i −0.0183072 + 0.174781i
\(463\) −11.3163 6.53346i −0.525912 0.303636i 0.213438 0.976957i \(-0.431534\pi\)
−0.739350 + 0.673321i \(0.764867\pi\)
\(464\) 21.3527 0.991273
\(465\) 4.55017 + 0.980311i 0.211009 + 0.0454608i
\(466\) 19.7545 0.915109
\(467\) 9.18440 5.30261i 0.425003 0.245376i −0.272212 0.962237i \(-0.587755\pi\)
0.697216 + 0.716861i \(0.254422\pi\)
\(468\) 63.9284 0.525205i 2.95509 0.0242776i
\(469\) 1.27623 + 8.25815i 0.0589306 + 0.381326i
\(470\) 31.2741 + 48.8898i 1.44256 + 2.25512i
\(471\) −4.90561 + 18.6135i −0.226038 + 0.857663i
\(472\) 34.8134 20.0995i 1.60242 0.925155i
\(473\) −1.89690 + 1.09518i −0.0872198 + 0.0503564i
\(474\) 1.74531 6.62227i 0.0801647 0.304171i
\(475\) −5.16546 7.31903i −0.237008 0.335820i
\(476\) −81.8167 31.7591i −3.75006 1.45568i
\(477\) −12.5914 + 22.2287i −0.576520 + 1.01778i
\(478\) 56.1711 32.4304i 2.56921 1.48333i
\(479\) −25.2819 −1.15516 −0.577581 0.816334i \(-0.696003\pi\)
−0.577581 + 0.816334i \(0.696003\pi\)
\(480\) 8.89107 41.2685i 0.405820 1.88364i
\(481\) −18.5774 −0.847055
\(482\) 0.558767 + 0.322604i 0.0254512 + 0.0146942i
\(483\) 20.9058 9.31677i 0.951245 0.423928i
\(484\) −26.4729 45.8525i −1.20332 2.08420i
\(485\) 12.5620 8.03572i 0.570411 0.364883i
\(486\) 39.2036 11.3725i 1.77831 0.515865i
\(487\) −12.9851 7.49694i −0.588410 0.339719i 0.176059 0.984380i \(-0.443665\pi\)
−0.764468 + 0.644661i \(0.776998\pi\)
\(488\) 39.0437 + 22.5419i 1.76743 + 1.02042i
\(489\) 2.10646 7.99259i 0.0952573 0.361437i
\(490\) 14.1372 + 38.4722i 0.638651 + 1.73800i
\(491\) −18.2753 + 31.6537i −0.824751 + 1.42851i 0.0773588 + 0.997003i \(0.475351\pi\)
−0.902110 + 0.431507i \(0.857982\pi\)
\(492\) −11.1146 + 11.2063i −0.501084 + 0.505217i
\(493\) 14.7655i 0.665003i
\(494\) −10.2922 + 17.8266i −0.463068 + 0.802057i
\(495\) 0.113352 + 2.10857i 0.00509477 + 0.0947729i
\(496\) −11.8697 −0.532966
\(497\) 5.08074 13.0888i 0.227902 0.587113i
\(498\) 48.0469 48.4433i 2.15303 2.17080i
\(499\) −4.42640 −0.198153 −0.0990765 0.995080i \(-0.531589\pi\)
−0.0990765 + 0.995080i \(0.531589\pi\)
\(500\) 33.2972 + 42.8967i 1.48909 + 1.91840i
\(501\) 3.91268 1.06564i 0.174806 0.0476095i
\(502\) −6.60067 3.81090i −0.294602 0.170089i
\(503\) 29.2058i 1.30222i 0.758982 + 0.651112i \(0.225697\pi\)
−0.758982 + 0.651112i \(0.774303\pi\)
\(504\) 21.0327 55.5317i 0.936870 2.47358i
\(505\) −12.3288 + 0.561233i −0.548625 + 0.0249745i
\(506\) 2.05845 3.56534i 0.0915092 0.158499i
\(507\) 10.4682 + 2.75891i 0.464910 + 0.122528i
\(508\) −49.6345 + 28.6565i −2.20217 + 1.27143i
\(509\) 16.5856 0.735144 0.367572 0.929995i \(-0.380189\pi\)
0.367572 + 0.929995i \(0.380189\pi\)
\(510\) −67.7114 14.5881i −2.99831 0.645970i
\(511\) −22.9593 + 18.4499i −1.01566 + 0.816177i
\(512\) 40.1259i 1.77333i
\(513\) −2.29853 + 9.02147i −0.101483 + 0.398308i
\(514\) −14.2486 + 24.6792i −0.628477 + 1.08855i
\(515\) −1.34883 29.6302i −0.0594364 1.30566i
\(516\) 56.4806 15.3829i 2.48642 0.677193i
\(517\) 2.70203 + 1.56002i 0.118835 + 0.0686094i
\(518\) −10.6153 + 27.3468i −0.466410 + 1.20155i
\(519\) −10.0519 + 2.73771i −0.441231 + 0.120172i
\(520\) 33.7703 65.1674i 1.48093 2.85778i
\(521\) 13.0489 22.6013i 0.571681 0.990180i −0.424713 0.905328i \(-0.639625\pi\)
0.996394 0.0848522i \(-0.0270418\pi\)
\(522\) 16.9832 0.139526i 0.743337 0.00610690i
\(523\) 3.47559 2.00663i 0.151977 0.0877439i −0.422083 0.906557i \(-0.638701\pi\)
0.574060 + 0.818813i \(0.305368\pi\)
\(524\) 38.8946 + 67.3675i 1.69912 + 2.94296i
\(525\) 11.1899 + 19.9947i 0.488366 + 0.872639i
\(526\) −20.8152 + 36.0529i −0.907585 + 1.57198i
\(527\) 8.20796i 0.357544i
\(528\) −1.41506 5.19560i −0.0615824 0.226109i
\(529\) −1.94537 −0.0845813
\(530\) 26.8691 + 42.0037i 1.16712 + 1.82453i
\(531\) 13.8934 8.17426i 0.602921 0.354733i
\(532\) 14.4219 + 17.9468i 0.625270 + 0.778095i
\(533\) −7.12882 + 4.11582i −0.308783 + 0.178276i
\(534\) −14.6400 14.5202i −0.633533 0.628349i
\(535\) −6.24672 + 3.99593i −0.270069 + 0.172759i
\(536\) −11.8143 20.4630i −0.510301 0.883867i
\(537\) −5.52452 20.2841i −0.238401 0.875325i
\(538\) −54.8504 + 31.6679i −2.36477 + 1.36530i
\(539\) 1.62638 + 1.48665i 0.0700533 + 0.0640344i
\(540\) 11.4319 55.2634i 0.491953 2.37816i
\(541\) 6.84667 + 11.8588i 0.294361 + 0.509848i 0.974836 0.222923i \(-0.0715598\pi\)
−0.680475 + 0.732771i \(0.738226\pi\)
\(542\) 83.0974i 3.56934i
\(543\) 4.50996 4.54717i 0.193541 0.195138i
\(544\) 74.4433 3.19173
\(545\) 12.8914 24.8768i 0.552207 1.06561i
\(546\) 30.9315 42.6054i 1.32374 1.82334i
\(547\) −22.5081 + 12.9951i −0.962378 + 0.555629i −0.896904 0.442225i \(-0.854189\pi\)
−0.0654737 + 0.997854i \(0.520856\pi\)
\(548\) −63.7237 + 36.7909i −2.72214 + 1.57163i
\(549\) 15.7302 + 8.91031i 0.671346 + 0.380283i
\(550\) 3.74170 + 1.72789i 0.159547 + 0.0736776i
\(551\) −1.93673 + 3.35452i −0.0825076 + 0.142907i
\(552\) −45.5753 + 45.9512i −1.93981 + 1.95581i
\(553\) −2.50243 3.11406i −0.106414 0.132423i
\(554\) 2.76688 4.79237i 0.117553 0.203608i
\(555\) −3.45379 + 16.0310i −0.146605 + 0.680477i
\(556\) −46.0537 −1.95311
\(557\) 19.8471 + 11.4588i 0.840951 + 0.485523i 0.857587 0.514339i \(-0.171963\pi\)
−0.0166366 + 0.999862i \(0.505296\pi\)
\(558\) −9.44080 + 0.0775611i −0.399661 + 0.00328342i
\(559\) 30.5299 1.29128
\(560\) −38.6343 43.8351i −1.63260 1.85237i
\(561\) −3.59278 + 0.978517i −0.151687 + 0.0413130i
\(562\) 33.2824i 1.40393i
\(563\) 23.0180 13.2895i 0.970095 0.560085i 0.0708297 0.997488i \(-0.477435\pi\)
0.899265 + 0.437404i \(0.144102\pi\)
\(564\) −59.2029 58.7185i −2.49289 2.47250i
\(565\) 8.49608 + 4.40274i 0.357433 + 0.185225i
\(566\) −35.1204 −1.47622
\(567\) 8.25083 22.3366i 0.346502 0.938049i
\(568\) 39.7016i 1.66584i
\(569\) −10.1201 + 17.5286i −0.424259 + 0.734837i −0.996351 0.0853519i \(-0.972799\pi\)
0.572092 + 0.820189i \(0.306132\pi\)
\(570\) 13.4697 + 12.1957i 0.564182 + 0.510820i
\(571\) −15.8154 27.3931i −0.661856 1.14637i −0.980128 0.198368i \(-0.936436\pi\)
0.318272 0.947999i \(-0.396898\pi\)
\(572\) 6.70802i 0.280476i
\(573\) 8.53829 + 31.3497i 0.356692 + 1.30965i
\(574\) 1.98521 + 12.8458i 0.0828609 + 0.536172i
\(575\) −2.26891 24.8694i −0.0946201 1.03713i
\(576\) 0.216621 + 26.3674i 0.00902589 + 1.09864i
\(577\) 17.8855 + 10.3262i 0.744582 + 0.429885i 0.823733 0.566978i \(-0.191888\pi\)
−0.0791509 + 0.996863i \(0.525221\pi\)
\(578\) 77.6271i 3.22886i
\(579\) −9.28010 + 35.2117i −0.385668 + 1.46335i
\(580\) 10.8032 20.8473i 0.448580 0.865635i
\(581\) −6.07873 39.3340i −0.252188 1.63185i
\(582\) −21.3001 + 21.4758i −0.882917 + 0.890201i
\(583\) 2.32145 + 1.34029i 0.0961446 + 0.0555091i
\(584\) 41.6431 72.1280i 1.72321 2.98468i
\(585\) 13.3267 26.2423i 0.550990 1.08499i
\(586\) 6.70745 + 11.6176i 0.277082 + 0.479920i
\(587\) −3.54451 + 2.04642i −0.146298 + 0.0844650i −0.571362 0.820698i \(-0.693585\pi\)
0.425064 + 0.905163i \(0.360251\pi\)
\(588\) −31.9050 49.4964i −1.31574 2.04120i
\(589\) 1.07661 1.86474i 0.0443609 0.0768353i
\(590\) −1.43074 31.4296i −0.0589025 1.29393i
\(591\) 5.65661 + 5.61033i 0.232682 + 0.230778i
\(592\) 41.8189i 1.71874i
\(593\) −18.8078 + 10.8587i −0.772345 + 0.445913i −0.833710 0.552202i \(-0.813788\pi\)
0.0613658 + 0.998115i \(0.480454\pi\)
\(594\) −1.15944 4.12317i −0.0475724 0.169176i
\(595\) −30.3122 + 26.7158i −1.24268 + 1.09524i
\(596\) 7.82902 + 13.5603i 0.320689 + 0.555450i
\(597\) 2.24500 + 8.24287i 0.0918817 + 0.337358i
\(598\) −49.6948 + 28.6913i −2.03217 + 1.17327i
\(599\) 9.80021 + 16.9745i 0.400426 + 0.693558i 0.993777 0.111386i \(-0.0355289\pi\)
−0.593351 + 0.804944i \(0.702196\pi\)
\(600\) −49.9566 41.2569i −2.03947 1.68431i
\(601\) 9.05705 + 15.6873i 0.369445 + 0.639897i 0.989479 0.144678i \(-0.0462145\pi\)
−0.620034 + 0.784575i \(0.712881\pi\)
\(602\) 17.4451 44.9414i 0.711009 1.83168i
\(603\) −4.80476 8.16641i −0.195665 0.332562i
\(604\) −44.3692 76.8498i −1.80536 3.12697i
\(605\) −24.3500 + 1.10846i −0.989967 + 0.0450653i
\(606\) 24.1533 6.57830i 0.981159 0.267225i
\(607\) 1.74756i 0.0709313i −0.999371 0.0354657i \(-0.988709\pi\)
0.999371 0.0354657i \(-0.0112914\pi\)
\(608\) −16.9125 9.76445i −0.685894 0.396001i
\(609\) 5.82052 8.01727i 0.235859 0.324876i
\(610\) 29.7240 19.0140i 1.20349 0.769854i
\(611\) −21.7440 37.6617i −0.879668 1.52363i
\(612\) 99.5123 0.817545i 4.02255 0.0330473i
\(613\) 34.8373 + 20.1133i 1.40707 + 0.812369i 0.995104 0.0988320i \(-0.0315106\pi\)
0.411961 + 0.911201i \(0.364844\pi\)
\(614\) 8.83524 15.3031i 0.356561 0.617582i
\(615\) 2.22632 + 6.91686i 0.0897741 + 0.278915i
\(616\) −5.80844 2.25468i −0.234029 0.0908438i
\(617\) −1.14184 0.659241i −0.0459687 0.0265400i 0.476840 0.878990i \(-0.341782\pi\)
−0.522808 + 0.852450i \(0.675116\pi\)
\(618\) 15.8098 + 58.0482i 0.635964 + 2.33504i
\(619\) −12.3032 −0.494509 −0.247255 0.968951i \(-0.579528\pi\)
−0.247255 + 0.968951i \(0.579528\pi\)
\(620\) −6.00539 + 11.5888i −0.241182 + 0.465416i
\(621\) −18.1236 + 18.5758i −0.727273 + 0.745422i
\(622\) 28.5903i 1.14637i
\(623\) −11.8870 + 1.83704i −0.476244 + 0.0735995i
\(624\) −19.1279 + 72.5775i −0.765729 + 2.90542i
\(625\) 24.5873 4.52400i 0.983490 0.180960i
\(626\) −25.5302 44.2196i −1.02039 1.76737i
\(627\) 0.944580 + 0.248945i 0.0377229 + 0.00994192i
\(628\) −46.7465 26.9891i −1.86539 1.07698i
\(629\) −28.9179 −1.15303
\(630\) −31.0149 34.6126i −1.23566 1.37900i
\(631\) 9.39194 0.373887 0.186944 0.982371i \(-0.440142\pi\)
0.186944 + 0.982371i \(0.440142\pi\)
\(632\) 9.78299 + 5.64821i 0.389147 + 0.224674i
\(633\) −6.93969 25.4802i −0.275828 1.01275i
\(634\) −32.6343 56.5243i −1.29607 2.24487i
\(635\) 1.19989 + 26.3584i 0.0476161 + 1.04600i
\(636\) −50.8643 50.4481i −2.01690 2.00040i
\(637\) −9.27129 29.2797i −0.367342 1.16011i
\(638\) 1.78206i 0.0705523i
\(639\) 0.130789 + 15.9197i 0.00517392 + 0.629773i
\(640\) 2.41406 + 1.25099i 0.0954241 + 0.0494496i
\(641\) 28.0494 1.10788 0.553942 0.832555i \(-0.313123\pi\)
0.553942 + 0.832555i \(0.313123\pi\)
\(642\) 10.5919 10.6793i 0.418030 0.421478i
\(643\) −5.03941 2.90950i −0.198735 0.114740i 0.397330 0.917676i \(-0.369937\pi\)
−0.596065 + 0.802936i \(0.703270\pi\)
\(644\) 9.80242 + 63.4290i 0.386269 + 2.49945i
\(645\) 5.67592 26.3452i 0.223489 1.03734i
\(646\) −16.0211 + 27.7493i −0.630340 + 1.09178i
\(647\) 10.4692 + 6.04442i 0.411589 + 0.237631i 0.691472 0.722403i \(-0.256963\pi\)
−0.279884 + 0.960034i \(0.590296\pi\)
\(648\) 1.10626 + 67.3231i 0.0434581 + 2.64470i
\(649\) −0.845693 1.46478i −0.0331964 0.0574978i
\(650\) −33.1239 46.9338i −1.29923 1.84089i
\(651\) −3.23556 + 4.45671i −0.126812 + 0.174672i
\(652\) 20.0728 + 11.5891i 0.786113 + 0.453863i
\(653\) 27.4007i 1.07227i −0.844132 0.536136i \(-0.819883\pi\)
0.844132 0.536136i \(-0.180117\pi\)
\(654\) −14.4835 + 54.9552i −0.566350 + 2.14892i
\(655\) 35.7755 1.62857i 1.39786 0.0636336i
\(656\) −9.26499 16.0474i −0.361737 0.626547i
\(657\) 16.4606 29.0594i 0.642190 1.13371i
\(658\) −67.8645 + 10.4879i −2.64564 + 0.408860i
\(659\) 14.9720 + 25.9323i 0.583227 + 1.01018i 0.995094 + 0.0989344i \(0.0315434\pi\)
−0.411867 + 0.911244i \(0.635123\pi\)
\(660\) −5.78855 1.24711i −0.225319 0.0485438i
\(661\) −9.78865 16.9544i −0.380735 0.659452i 0.610433 0.792068i \(-0.290995\pi\)
−0.991167 + 0.132616i \(0.957662\pi\)
\(662\) −15.1041 + 8.72033i −0.587036 + 0.338925i
\(663\) 50.1876 + 13.2270i 1.94913 + 0.513695i
\(664\) 56.2722 + 97.4663i 2.18378 + 3.78243i
\(665\) 10.3907 2.09353i 0.402935 0.0811838i
\(666\) −0.273260 33.2614i −0.0105886 1.28885i
\(667\) −9.35131 + 5.39898i −0.362084 + 0.209049i
\(668\) 11.3716i 0.439980i
\(669\) −4.69493 + 17.8141i −0.181517 + 0.688733i
\(670\) −18.4740 + 0.840975i −0.713714 + 0.0324897i
\(671\) 0.948458 1.64278i 0.0366148 0.0634187i
\(672\) 40.4208 + 29.3454i 1.55927 + 1.13202i
\(673\) 43.2830 24.9895i 1.66844 0.963273i 0.699957 0.714185i \(-0.253203\pi\)
0.968481 0.249087i \(-0.0801307\pi\)
\(674\) 30.9416 + 53.5924i 1.19182 + 2.06430i
\(675\) −20.1677 16.3788i −0.776254 0.630420i
\(676\) −15.1787 + 26.2902i −0.583795 + 1.01116i
\(677\) −23.2857 13.4440i −0.894943 0.516695i −0.0193866 0.999812i \(-0.506171\pi\)
−0.875556 + 0.483117i \(0.839505\pi\)
\(678\) −18.7686 4.94649i −0.720804 0.189969i
\(679\) 2.69481 + 17.4375i 0.103417 + 0.669189i
\(680\) 52.5676 101.441i 2.01588 3.89009i
\(681\) −9.16151 9.08656i −0.351070 0.348198i
\(682\) 0.990626i 0.0379330i
\(683\) 30.0810 + 17.3673i 1.15102 + 0.664540i 0.949135 0.314869i \(-0.101961\pi\)
0.201883 + 0.979410i \(0.435294\pi\)
\(684\) −22.7151 12.8669i −0.868534 0.491979i
\(685\) 1.54049 + 33.8405i 0.0588589 + 1.29298i
\(686\) −48.3989 3.08297i −1.84788 0.117708i
\(687\) −11.7574 + 11.8544i −0.448573 + 0.452273i
\(688\) 68.7247i 2.62011i
\(689\) −18.6814 32.3571i −0.711704 1.23271i
\(690\) 15.5196 + 48.2172i 0.590823 + 1.83560i
\(691\) 11.1032 19.2313i 0.422386 0.731594i −0.573787 0.819005i \(-0.694526\pi\)
0.996172 + 0.0874113i \(0.0278594\pi\)
\(692\) 29.2144i 1.11056i
\(693\) −2.33652 0.884957i −0.0887569 0.0336167i
\(694\) 82.4340 3.12915
\(695\) −9.75513 + 18.8247i −0.370033 + 0.714062i
\(696\) −7.13954 + 27.0898i −0.270624 + 1.02683i
\(697\) −11.0969 + 6.40678i −0.420324 + 0.242674i
\(698\) 14.8300i 0.561325i
\(699\) −3.32998 + 12.6350i −0.125952 + 0.477901i
\(700\) −62.3443 + 15.5418i −2.35639 + 0.587423i
\(701\) 42.8411 1.61809 0.809043 0.587750i \(-0.199986\pi\)
0.809043 + 0.587750i \(0.199986\pi\)
\(702\) −14.7395 + 57.8508i −0.556306 + 2.18344i
\(703\) 6.56977 + 3.79306i 0.247784 + 0.143058i
\(704\) 2.76673 0.104275
\(705\) −36.5419 + 11.7617i −1.37625 + 0.442972i
\(706\) −37.0211 + 64.1225i −1.39331 + 2.41328i
\(707\) 5.28426 13.6131i 0.198735 0.511974i
\(708\) 11.8786 + 43.6141i 0.446425 + 1.63912i
\(709\) −7.74650 + 13.4173i −0.290926 + 0.503898i −0.974029 0.226424i \(-0.927297\pi\)
0.683103 + 0.730322i \(0.260630\pi\)
\(710\) 27.5885 + 14.2966i 1.03538 + 0.536542i
\(711\) 3.94143 + 2.23261i 0.147815 + 0.0837295i
\(712\) 29.4551 17.0059i 1.10388 0.637323i
\(713\) 5.19829 3.00123i 0.194677 0.112397i
\(714\) 48.1486 66.3205i 1.80191 2.48198i
\(715\) −2.74194 1.42090i −0.102543 0.0531385i
\(716\) 58.9527 2.20316
\(717\) 11.2739 + 41.3940i 0.421032 + 1.54589i
\(718\) 47.1961i 1.76134i
\(719\) 18.8811 + 32.7031i 0.704148 + 1.21962i 0.966998 + 0.254783i \(0.0820041\pi\)
−0.262850 + 0.964837i \(0.584663\pi\)
\(720\) 59.0732 + 29.9992i 2.20153 + 1.11800i
\(721\) 32.7168 + 12.6998i 1.21844 + 0.472966i
\(722\) −35.8080 + 20.6738i −1.33264 + 0.769398i
\(723\) −0.300530 + 0.303009i −0.0111768 + 0.0112690i
\(724\) 8.97962 + 15.5532i 0.333725 + 0.578029i
\(725\) −6.23308 8.83176i −0.231491 0.328003i
\(726\) 47.7038 12.9924i 1.77045 0.482195i
\(727\) 38.7333 22.3627i 1.43654 0.829386i 0.438932 0.898520i \(-0.355357\pi\)
0.997607 + 0.0691342i \(0.0220237\pi\)
\(728\) 54.4000 + 67.6961i 2.01620 + 2.50898i
\(729\) 0.665375 + 26.9918i 0.0246435 + 0.999696i
\(730\) −35.1258 54.9111i −1.30006 2.03235i
\(731\) 47.5235 1.75772
\(732\) −35.6997 + 35.9942i −1.31950 + 1.33038i
\(733\) 0.858905i 0.0317244i 0.999874 + 0.0158622i \(0.00504930\pi\)
−0.999874 + 0.0158622i \(0.994951\pi\)
\(734\) 7.04135 12.1960i 0.259901 0.450162i
\(735\) −26.9900 + 2.55698i −0.995542 + 0.0943155i
\(736\) −27.2201 47.1466i −1.00335 1.73785i
\(737\) −0.860987 + 0.497091i −0.0317149 + 0.0183106i
\(738\) −7.47394 12.7031i −0.275119 0.467607i
\(739\) 2.67345 4.63056i 0.0983446 0.170338i −0.812655 0.582745i \(-0.801979\pi\)
0.911000 + 0.412407i \(0.135312\pi\)
\(740\) −40.8290 21.1579i −1.50090 0.777781i
\(741\) −9.66703 9.58793i −0.355127 0.352222i
\(742\) −58.3059 + 9.01068i −2.14048 + 0.330792i
\(743\) 0.343056 + 0.198063i 0.0125855 + 0.00726624i 0.506280 0.862369i \(-0.331020\pi\)
−0.493694 + 0.869636i \(0.664354\pi\)
\(744\) 3.96879 15.0589i 0.145503 0.552086i
\(745\) 7.20118 0.327812i 0.263831 0.0120101i
\(746\) −29.3024 + 50.7532i −1.07284 + 1.85821i
\(747\) 22.8853 + 38.8970i 0.837330 + 1.42317i
\(748\) 10.4419i 0.381792i
\(749\) −1.34005 8.67114i −0.0489644 0.316837i
\(750\) −46.6588 + 19.8580i −1.70374 + 0.725111i
\(751\) 28.9822 1.05758 0.528788 0.848754i \(-0.322647\pi\)
0.528788 + 0.848754i \(0.322647\pi\)
\(752\) 84.7789 48.9471i 3.09157 1.78492i
\(753\) 3.55013 3.57941i 0.129374 0.130441i
\(754\) −12.4194 + 21.5111i −0.452289 + 0.783388i
\(755\) −40.8111 + 1.85780i −1.48527 + 0.0676124i
\(756\) 54.3549 + 38.7836i 1.97687 + 1.41055i
\(757\) 22.9163i 0.832905i 0.909157 + 0.416453i \(0.136727\pi\)
−0.909157 + 0.416453i \(0.863273\pi\)
\(758\) 12.6400 + 7.29772i 0.459106 + 0.265065i
\(759\) 1.93341 + 1.91759i 0.0701784 + 0.0696043i
\(760\) −25.2483 + 16.1510i −0.915852 + 0.585857i
\(761\) −9.86452 −0.357589 −0.178794 0.983886i \(-0.557220\pi\)
−0.178794 + 0.983886i \(0.557220\pi\)
\(762\) −14.0641 51.6385i −0.509488 1.87067i
\(763\) 20.7665 + 25.8421i 0.751799 + 0.935548i
\(764\) −91.1129 −3.29635
\(765\) 20.7446 40.8494i 0.750022 1.47691i
\(766\) −2.79644 + 4.84358i −0.101040 + 0.175006i
\(767\) 23.5751i 0.851247i
\(768\) 24.1092 + 6.35401i 0.869966 + 0.229281i
\(769\) −24.1144 + 41.7673i −0.869586 + 1.50617i −0.00716652 + 0.999974i \(0.502281\pi\)
−0.862420 + 0.506194i \(0.831052\pi\)
\(770\) −3.65840 + 3.22435i −0.131840 + 0.116197i
\(771\) −13.3831 13.2736i −0.481980 0.478036i
\(772\) −88.4319 51.0562i −3.18273 1.83755i
\(773\) −26.3628 15.2206i −0.948204 0.547446i −0.0556817 0.998449i \(-0.517733\pi\)
−0.892523 + 0.451002i \(0.851067\pi\)
\(774\) 0.449073 + 54.6615i 0.0161416 + 1.96477i
\(775\) 3.46490 + 4.90947i 0.124463 + 0.176354i
\(776\) −24.9465 43.2086i −0.895527 1.55110i
\(777\) −15.7017 11.3994i −0.563295 0.408951i
\(778\) 46.8955 + 27.0751i 1.68128 + 0.970690i
\(779\) 3.36141 0.120435
\(780\) 61.1819 + 55.3952i 2.19066 + 1.98347i
\(781\) 1.67046 0.0597737
\(782\) −77.3560 + 44.6615i −2.76624 + 1.59709i
\(783\) −2.77360 + 10.8861i −0.0991203 + 0.389036i
\(784\) 65.9106 20.8703i 2.35395 0.745367i
\(785\) −20.9338 + 13.3910i −0.747159 + 0.477946i
\(786\) −70.0874 + 19.0888i −2.49994 + 0.680874i
\(787\) 4.29455 2.47946i 0.153084 0.0883831i −0.421501 0.906828i \(-0.638497\pi\)
0.574585 + 0.818445i \(0.305163\pi\)
\(788\) −19.3479 + 11.1705i −0.689241 + 0.397933i
\(789\) −19.5508 19.3909i −0.696027 0.690333i
\(790\) 7.44780 4.76424i 0.264981 0.169504i
\(791\) −8.82575 + 7.09230i −0.313808 + 0.252173i
\(792\) 7.06470 0.0580402i 0.251033 0.00206237i
\(793\) −22.8975 + 13.2199i −0.813116 + 0.469452i
\(794\) 50.6319 1.79686
\(795\) −31.3950 + 10.1051i −1.11347 + 0.358391i
\(796\) −23.9566 −0.849119
\(797\) 12.1057 + 6.98923i 0.428806 + 0.247571i 0.698838 0.715280i \(-0.253701\pi\)
−0.270032 + 0.962851i \(0.587034\pi\)
\(798\) −19.6377 + 8.75167i −0.695168 + 0.309806i
\(799\) −33.8472 58.6250i −1.19743 2.07400i
\(800\) 44.5272 31.4254i 1.57427 1.11106i
\(801\) 11.7550 6.91613i 0.415342 0.244369i
\(802\) 4.78538 + 2.76284i 0.168978 + 0.0975592i
\(803\) −3.03481 1.75215i −0.107096 0.0618320i
\(804\) 25.6360 6.98214i 0.904113 0.246241i
\(805\) 28.0033 + 9.42879i 0.986987 + 0.332321i
\(806\) 6.90383 11.9578i 0.243177 0.421195i
\(807\) −11.0089 40.4207i −0.387530 1.42288i
\(808\) 41.2920i 1.45265i
\(809\) 8.69783 15.0651i 0.305799 0.529660i −0.671640 0.740878i \(-0.734410\pi\)
0.977439 + 0.211218i \(0.0677430\pi\)
\(810\) 47.1810 + 23.4744i 1.65777 + 0.824806i
\(811\) −39.6852 −1.39354 −0.696768 0.717297i \(-0.745379\pi\)
−0.696768 + 0.717297i \(0.745379\pi\)
\(812\) 17.4027 + 21.6562i 0.610716 + 0.759983i
\(813\) −53.1494 14.0076i −1.86403 0.491268i
\(814\) −3.49013 −0.122329
\(815\) 8.98893 5.75008i 0.314869 0.201417i
\(816\) −29.7749 + 112.976i −1.04233 + 3.95494i
\(817\) −10.7967 6.23348i −0.377729 0.218082i
\(818\) 45.6902i 1.59752i
\(819\) 22.0365 + 26.9658i 0.770018 + 0.942261i
\(820\) −20.3551 + 0.926607i −0.710832 + 0.0323585i
\(821\) 26.3336 45.6112i 0.919050 1.59184i 0.118188 0.992991i \(-0.462291\pi\)
0.800862 0.598850i \(-0.204375\pi\)
\(822\) −18.0563 66.2965i −0.629786 2.31236i
\(823\) 43.3780 25.0443i 1.51206 0.872989i 0.512160 0.858890i \(-0.328845\pi\)
0.999901 0.0140986i \(-0.00448788\pi\)
\(824\) −99.2382 −3.45713
\(825\) −1.73590 + 2.10194i −0.0604362 + 0.0731801i
\(826\) 34.7036 + 13.4711i 1.20749 + 0.468718i
\(827\) 48.4604i 1.68513i −0.538593 0.842566i \(-0.681044\pi\)
0.538593 0.842566i \(-0.318956\pi\)
\(828\) −36.9043 62.7244i −1.28251 2.17982i
\(829\) −1.64766 + 2.85383i −0.0572256 + 0.0991176i −0.893219 0.449622i \(-0.851559\pi\)
0.835993 + 0.548739i \(0.184892\pi\)
\(830\) 87.9927 4.00561i 3.05427 0.139037i
\(831\) 2.59881 + 2.57755i 0.0901517 + 0.0894141i
\(832\) −33.3971 19.2818i −1.15783 0.668476i
\(833\) −14.4319 45.5775i −0.500036 1.57917i
\(834\) 10.9599 41.5855i 0.379511 1.43999i
\(835\) 4.64820 + 2.40874i 0.160858 + 0.0833578i
\(836\) −1.36962 + 2.37225i −0.0473693 + 0.0820460i
\(837\) 1.54181 6.05144i 0.0532928 0.209169i
\(838\) 32.9028 18.9964i 1.13661 0.656221i
\(839\) −9.72094 16.8372i −0.335604 0.581283i 0.647997 0.761643i \(-0.275607\pi\)
−0.983601 + 0.180360i \(0.942274\pi\)
\(840\) 68.5307 34.3578i 2.36453 1.18546i
\(841\) 12.1630 21.0669i 0.419413 0.726445i
\(842\) 35.8008i 1.23378i
\(843\) −21.2876 5.61036i −0.733182 0.193231i
\(844\) 74.0541 2.54905
\(845\) 7.53111 + 11.7732i 0.259078 + 0.405009i
\(846\) 67.1106 39.4850i 2.30731 1.35752i
\(847\) 10.4367 26.8865i 0.358608 0.923832i
\(848\) 72.8379 42.0530i 2.50126 1.44411i
\(849\) 5.92019 22.4631i 0.203180 0.770933i
\(850\) −51.5614 73.0581i −1.76854 2.50587i
\(851\) 10.5738 + 18.3144i 0.362466 + 0.627809i
\(852\) −43.1694 11.3774i −1.47896 0.389782i
\(853\) −17.7747 + 10.2622i −0.608593 + 0.351372i −0.772415 0.635118i \(-0.780951\pi\)
0.163821 + 0.986490i \(0.447618\pi\)
\(854\) 6.37642 + 41.2603i 0.218197 + 1.41190i
\(855\) −10.0710 + 6.55944i −0.344419 + 0.224328i
\(856\) 12.4052 + 21.4864i 0.424000 + 0.734389i
\(857\) 46.5756i 1.59099i −0.605959 0.795496i \(-0.707211\pi\)
0.605959 0.795496i \(-0.292789\pi\)
\(858\) 6.05719 + 1.59638i 0.206789 + 0.0544995i
\(859\) 32.7246 1.11655 0.558274 0.829657i \(-0.311464\pi\)
0.558274 + 0.829657i \(0.311464\pi\)
\(860\) 67.0980 + 34.7708i 2.28802 + 1.18567i
\(861\) −8.55085 0.895648i −0.291412 0.0305236i
\(862\) −26.9444 + 15.5564i −0.917730 + 0.529852i
\(863\) −25.3916 + 14.6598i −0.864338 + 0.499026i −0.865463 0.500973i \(-0.832975\pi\)
0.00112425 + 0.999999i \(0.499642\pi\)
\(864\) −54.8845 13.9837i −1.86721 0.475735i
\(865\) −11.9415 6.18821i −0.406024 0.210405i
\(866\) −43.7420 + 75.7633i −1.48641 + 2.57454i
\(867\) 49.6506 + 13.0855i 1.68622 + 0.444406i
\(868\) −9.67398 12.0384i −0.328356 0.408611i
\(869\) 0.237650 0.411623i 0.00806174 0.0139633i
\(870\) 16.2536 + 14.7163i 0.551050 + 0.498930i
\(871\) 13.8572 0.469534
\(872\) −81.1845 46.8719i −2.74925 1.58728i
\(873\) −10.1455 17.2438i −0.343372 0.583613i
\(874\) 23.4323 0.792610
\(875\) −6.85302 + 28.7756i −0.231674 + 0.972793i
\(876\) 66.4944 + 65.9504i 2.24664 + 2.22826i
\(877\) 52.7579i 1.78151i 0.454485 + 0.890754i \(0.349823\pi\)
−0.454485 + 0.890754i \(0.650177\pi\)
\(878\) −87.2818 + 50.3922i −2.94562 + 1.70065i
\(879\) −8.56135 + 2.33174i −0.288767 + 0.0786477i
\(880\) 3.19853 6.17228i 0.107822 0.208068i
\(881\) −13.8753 −0.467470 −0.233735 0.972300i \(-0.575095\pi\)
−0.233735 + 0.972300i \(0.575095\pi\)
\(882\) 52.2868 17.0303i 1.76059 0.573438i
\(883\) 27.0155i 0.909144i 0.890710 + 0.454572i \(0.150208\pi\)
−0.890710 + 0.454572i \(0.849792\pi\)
\(884\) −72.7709 + 126.043i −2.44755 + 4.23928i
\(885\) 20.3436 + 4.38293i 0.683844 + 0.147331i
\(886\) −19.8113 34.3143i −0.665575 1.15281i
\(887\) 43.1653i 1.44935i 0.689091 + 0.724675i \(0.258010\pi\)
−0.689091 + 0.724675i \(0.741990\pi\)
\(888\) 53.0548 + 13.9827i 1.78040 + 0.469228i
\(889\) −29.1042 11.2975i −0.976123 0.378906i
\(890\) −1.21053 26.5921i −0.0405770 0.891370i
\(891\) 2.83264 0.0465463i 0.0948970 0.00155936i
\(892\) −44.7389 25.8300i −1.49797 0.864853i
\(893\) 17.7584i 0.594263i
\(894\) −14.1078 + 3.84234i −0.471834 + 0.128507i
\(895\) 12.4874 24.0972i 0.417407 0.805481i
\(896\) −2.50773 + 2.01519i −0.0837774 + 0.0673228i
\(897\) −9.97409 36.6214i −0.333025 1.22275i
\(898\) 54.6178 + 31.5336i 1.82262 + 1.05229i
\(899\) 1.29913 2.25015i 0.0433283 0.0750468i
\(900\) 59.1767 42.4970i 1.97256 1.41657i
\(901\) −29.0798 50.3677i −0.968790 1.67799i
\(902\) −1.33929 + 0.773239i −0.0445935 + 0.0257461i
\(903\) 25.8040 + 18.7337i 0.858704 + 0.623417i
\(904\) 16.0080 27.7266i 0.532417 0.922173i
\(905\) 8.25951 0.375990i 0.274555 0.0124983i
\(906\) 79.9526 21.7756i 2.65625 0.723447i
\(907\) 4.21072i 0.139815i −0.997553 0.0699074i \(-0.977730\pi\)
0.997553 0.0699074i \(-0.0222704\pi\)
\(908\) 31.3361 18.0919i 1.03992 0.600401i
\(909\) 0.136028 + 16.5574i 0.00451175 + 0.549175i
\(910\) 66.6313 13.4249i 2.20881 0.445032i
\(911\) 1.90041 + 3.29160i 0.0629634 + 0.109056i 0.895789 0.444480i \(-0.146612\pi\)
−0.832825 + 0.553536i \(0.813278\pi\)
\(912\) 21.5831 21.7611i 0.714687 0.720582i
\(913\) 4.10092 2.36767i 0.135721 0.0783584i
\(914\) 5.51156 + 9.54630i 0.182306 + 0.315763i
\(915\) 7.15089 + 22.2167i 0.236401 + 0.734463i
\(916\) −23.4097 40.5469i −0.773479 1.33971i
\(917\) −15.3338 + 39.5023i −0.506365 + 1.30448i
\(918\) −22.9438 + 90.0519i −0.757258 + 2.97215i
\(919\) −10.4908 18.1705i −0.346059 0.599391i 0.639487 0.768802i \(-0.279147\pi\)
−0.985545 + 0.169411i \(0.945813\pi\)
\(920\) −83.4662 + 3.79955i −2.75180 + 0.125267i
\(921\) 8.29856 + 8.23067i 0.273447 + 0.271210i
\(922\) 48.8049i 1.60730i
\(923\) −20.1640 11.6417i −0.663706 0.383191i
\(924\) 4.11616 5.66965i 0.135412 0.186518i
\(925\) −17.2968 + 12.2074i −0.568717 + 0.401376i
\(926\) 17.1084 + 29.6327i 0.562218 + 0.973791i
\(927\) −39.7929 + 0.326919i −1.30697 + 0.0107374i
\(928\) −20.4081 11.7826i −0.669928 0.386783i
\(929\) 20.0867 34.7913i 0.659025 1.14146i −0.321844 0.946793i \(-0.604303\pi\)
0.980869 0.194671i \(-0.0623641\pi\)
\(930\) −9.03521 8.18063i −0.296276 0.268254i
\(931\) −2.69949 + 12.2476i −0.0884723 + 0.401398i
\(932\) −31.7321 18.3205i −1.03942 0.600109i
\(933\) −18.2865 4.81942i −0.598672 0.157781i
\(934\) −27.7707 −0.908687
\(935\) −4.26816 2.21180i −0.139584 0.0723336i
\(936\) −85.6821 48.5344i −2.80061 1.58640i
\(937\) 20.8278i 0.680414i −0.940351 0.340207i \(-0.889503\pi\)
0.940351 0.340207i \(-0.110497\pi\)
\(938\) 7.91817 20.3985i 0.258537 0.666034i
\(939\) 32.5866 8.87518i 1.06342 0.289630i
\(940\) −4.89529 107.537i −0.159667 3.50746i
\(941\) −13.5288 23.4326i −0.441027 0.763881i 0.556739 0.830688i \(-0.312052\pi\)
−0.997766 + 0.0668061i \(0.978719\pi\)
\(942\) 35.4953 35.7881i 1.15650 1.16604i
\(943\) 8.11511 + 4.68526i 0.264265 + 0.152573i
\(944\) −53.0690 −1.72725
\(945\) 27.3665 14.0027i 0.890232 0.455507i
\(946\) 5.73565 0.186482
\(947\) 18.7970 + 10.8525i 0.610822 + 0.352658i 0.773287 0.634056i \(-0.218611\pi\)
−0.162465 + 0.986714i \(0.551945\pi\)
\(948\) −8.94509 + 9.01888i −0.290523 + 0.292920i
\(949\) 24.4220 + 42.3001i 0.792772 + 1.37312i
\(950\) 2.13129 + 23.3610i 0.0691483 + 0.757930i
\(951\) 41.6543 11.3448i 1.35073 0.367881i
\(952\) 84.6802 + 105.377i 2.74450 + 3.41529i
\(953\) 7.59489i 0.246023i 0.992405 + 0.123011i \(0.0392551\pi\)
−0.992405 + 0.123011i \(0.960745\pi\)
\(954\) 57.6582 33.9236i 1.86675 1.09832i
\(955\) −19.2996 + 37.2429i −0.624520 + 1.20515i
\(956\) −120.305 −3.89094
\(957\) 1.13981 + 0.300399i 0.0368448 + 0.00971051i
\(958\) 57.3335 + 33.1015i 1.85236 + 1.06946i
\(959\) −37.3657 14.5044i −1.20660 0.468371i
\(960\) −22.8478 + 25.2346i −0.737410 + 0.814443i
\(961\) 14.7778 25.5960i 0.476704 0.825676i
\(962\) 42.1291 + 24.3233i 1.35830 + 0.784213i
\(963\) 5.04505 + 8.57482i 0.162574 + 0.276320i
\(964\) −0.598373 1.03641i −0.0192723 0.0333806i
\(965\) −39.6012 + 25.3323i −1.27481 + 0.815474i
\(966\) −59.6078 6.24354i −1.91785 0.200883i
\(967\) 50.2736 + 29.0255i 1.61669 + 0.933397i 0.987768 + 0.155930i \(0.0498374\pi\)
0.628923 + 0.777467i \(0.283496\pi\)
\(968\) 81.5535i 2.62123i
\(969\) −15.0479 14.9248i −0.483408 0.479453i
\(970\) −39.0088 + 1.77576i −1.25250 + 0.0570162i
\(971\) −15.6909 27.1775i −0.503545 0.872166i −0.999992 0.00409858i \(-0.998695\pi\)
0.496446 0.868067i \(-0.334638\pi\)
\(972\) −73.5205 18.0900i −2.35817 0.580237i
\(973\) −15.7144 19.5552i −0.503779 0.626910i
\(974\) 19.6314 + 34.0026i 0.629031 + 1.08951i
\(975\) 35.6027 13.2746i 1.14020 0.425128i
\(976\) −29.7589 51.5439i −0.952558 1.64988i
\(977\) 29.0100 16.7489i 0.928111 0.535845i 0.0418974 0.999122i \(-0.486660\pi\)
0.886214 + 0.463277i \(0.153326\pi\)
\(978\) −15.2416 + 15.3673i −0.487373 + 0.491393i
\(979\) −0.715529 1.23933i −0.0228684 0.0396092i
\(980\) 12.9707 74.9096i 0.414333 2.39290i
\(981\) −32.7081 18.5274i −1.04429 0.591535i
\(982\) 82.8880 47.8554i 2.64506 1.52713i
\(983\) 16.3973i 0.522993i 0.965204 + 0.261497i \(0.0842161\pi\)
−0.965204 + 0.261497i \(0.915784\pi\)
\(984\) 23.4569 6.38866i 0.747780 0.203663i
\(985\) 0.467726 + 10.2747i 0.0149030 + 0.327380i
\(986\) −19.3324 + 33.4846i −0.615668 + 1.06637i
\(987\) 4.73173 45.1743i 0.150613 1.43791i
\(988\) 33.0652 19.0902i 1.05194 0.607340i
\(989\) −17.3769 30.0977i −0.552553 0.957051i
\(990\) 2.50368 4.93014i 0.0795721 0.156690i
\(991\) 15.8703 27.4882i 0.504138 0.873193i −0.495851 0.868408i \(-0.665144\pi\)
0.999989 0.00478473i \(-0.00152303\pi\)
\(992\) 11.3446 + 6.54982i 0.360192 + 0.207957i
\(993\) −3.03149 11.1306i −0.0962014 0.353218i
\(994\) −28.6590 + 23.0302i −0.909009 + 0.730472i
\(995\) −5.07450 + 9.79239i −0.160873 + 0.310440i
\(996\) −122.106 + 33.2563i −3.86906 + 1.05377i
\(997\) 12.6928i 0.401987i 0.979593 + 0.200993i \(0.0644169\pi\)
−0.979593 + 0.200993i \(0.935583\pi\)
\(998\) 10.0380 + 5.79547i 0.317749 + 0.183452i
\(999\) 21.3202 + 5.43205i 0.674541 + 0.171862i
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.bo.b.4.2 yes 84
3.2 odd 2 945.2.bo.b.739.41 84
5.4 even 2 inner 315.2.bo.b.4.41 yes 84
7.2 even 3 315.2.r.b.184.41 yes 84
9.2 odd 6 945.2.r.b.424.2 84
9.7 even 3 315.2.r.b.214.41 yes 84
15.14 odd 2 945.2.bo.b.739.2 84
21.2 odd 6 945.2.r.b.604.2 84
35.9 even 6 315.2.r.b.184.2 84
45.29 odd 6 945.2.r.b.424.41 84
45.34 even 6 315.2.r.b.214.2 yes 84
63.2 odd 6 945.2.bo.b.289.2 84
63.16 even 3 inner 315.2.bo.b.79.41 yes 84
105.44 odd 6 945.2.r.b.604.41 84
315.79 even 6 inner 315.2.bo.b.79.2 yes 84
315.254 odd 6 945.2.bo.b.289.41 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.r.b.184.2 84 35.9 even 6
315.2.r.b.184.41 yes 84 7.2 even 3
315.2.r.b.214.2 yes 84 45.34 even 6
315.2.r.b.214.41 yes 84 9.7 even 3
315.2.bo.b.4.2 yes 84 1.1 even 1 trivial
315.2.bo.b.4.41 yes 84 5.4 even 2 inner
315.2.bo.b.79.2 yes 84 315.79 even 6 inner
315.2.bo.b.79.41 yes 84 63.16 even 3 inner
945.2.r.b.424.2 84 9.2 odd 6
945.2.r.b.424.41 84 45.29 odd 6
945.2.r.b.604.2 84 21.2 odd 6
945.2.r.b.604.41 84 105.44 odd 6
945.2.bo.b.289.2 84 63.2 odd 6
945.2.bo.b.289.41 84 315.254 odd 6
945.2.bo.b.739.2 84 15.14 odd 2
945.2.bo.b.739.41 84 3.2 odd 2