Properties

Label 315.2.u.a.59.15
Level $315$
Weight $2$
Character 315.59
Analytic conductor $2.515$
Analytic rank $0$
Dimension $88$
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(59,315)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.u (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: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.15
Character \(\chi\) \(=\) 315.59
Dual form 315.2.u.a.299.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.601450 + 1.04174i) q^{2} +(0.375988 - 1.69075i) q^{3} +(0.276517 + 0.478941i) q^{4} +(1.70560 + 1.44600i) q^{5} +(1.53519 + 1.40858i) q^{6} +(-0.552728 + 2.58737i) q^{7} -3.07104 q^{8} +(-2.71727 - 1.27140i) q^{9} +O(q^{10})\) \(q+(-0.601450 + 1.04174i) q^{2} +(0.375988 - 1.69075i) q^{3} +(0.276517 + 0.478941i) q^{4} +(1.70560 + 1.44600i) q^{5} +(1.53519 + 1.40858i) q^{6} +(-0.552728 + 2.58737i) q^{7} -3.07104 q^{8} +(-2.71727 - 1.27140i) q^{9} +(-2.53219 + 0.907096i) q^{10} +4.84953i q^{11} +(0.913736 - 0.287444i) q^{12} +(0.669156 - 1.15901i) q^{13} +(-2.36293 - 2.13197i) q^{14} +(3.08612 - 2.34006i) q^{15} +(1.29404 - 2.24135i) q^{16} +(0.153866 + 0.0888348i) q^{17} +(2.95877 - 2.06600i) q^{18} +(4.78531 - 2.76280i) q^{19} +(-0.220924 + 1.21673i) q^{20} +(4.16678 + 1.90734i) q^{21} +(-5.05196 - 2.91675i) q^{22} +0.826816 q^{23} +(-1.15467 + 5.19236i) q^{24} +(0.818145 + 4.93261i) q^{25} +(0.804927 + 1.39417i) q^{26} +(-3.17128 + 4.11618i) q^{27} +(-1.39204 + 0.450727i) q^{28} +(-6.88138 + 3.97297i) q^{29} +(0.581597 + 4.62236i) q^{30} +(3.73111 - 2.15416i) q^{31} +(-1.51444 - 2.62308i) q^{32} +(8.19934 + 1.82336i) q^{33} +(-0.185086 + 0.106859i) q^{34} +(-4.68408 + 3.61378i) q^{35} +(-0.142443 - 1.65297i) q^{36} +(7.14549 - 4.12545i) q^{37} +6.64675i q^{38} +(-1.70800 - 1.56715i) q^{39} +(-5.23797 - 4.44074i) q^{40} +(0.278013 - 0.481532i) q^{41} +(-4.49307 + 3.19353i) q^{42} +(4.31274 - 2.48996i) q^{43} +(-2.32264 + 1.34098i) q^{44} +(-2.79612 - 6.09768i) q^{45} +(-0.497288 + 0.861329i) q^{46} +(6.86068 + 3.96102i) q^{47} +(-3.30302 - 3.03062i) q^{48} +(-6.38898 - 2.86022i) q^{49} +(-5.63058 - 2.11442i) q^{50} +(0.208049 - 0.226749i) q^{51} +0.740130 q^{52} +(2.12855 - 3.68675i) q^{53} +(-2.38063 - 5.77933i) q^{54} +(-7.01244 + 8.27136i) q^{55} +(1.69745 - 7.94593i) q^{56} +(-2.87199 - 9.12955i) q^{57} -9.55816i q^{58} +(-1.12039 - 1.94058i) q^{59} +(1.97411 + 0.831000i) q^{60} +(-9.91668 - 5.72540i) q^{61} +5.18247i q^{62} +(4.79150 - 6.32784i) q^{63} +8.81961 q^{64} +(2.81725 - 1.00921i) q^{65} +(-6.83096 + 7.44493i) q^{66} +(0.134618 - 0.0777216i) q^{67} +0.0982572i q^{68} +(0.310873 - 1.39794i) q^{69} +(-0.947380 - 7.05311i) q^{70} -10.3336i q^{71} +(8.34484 + 3.90453i) q^{72} +(-5.28792 + 9.15894i) q^{73} +9.92500i q^{74} +(8.64742 + 0.471323i) q^{75} +(2.64644 + 1.52792i) q^{76} +(-12.5475 - 2.68047i) q^{77} +(2.65984 - 0.836737i) q^{78} +(6.15184 - 10.6553i) q^{79} +(5.44812 - 1.95165i) q^{80} +(5.76707 + 6.90948i) q^{81} +(0.334421 + 0.579234i) q^{82} +(14.4831 - 8.36182i) q^{83} +(0.238679 + 2.52305i) q^{84} +(0.133979 + 0.374008i) q^{85} +5.99034i q^{86} +(4.12998 + 13.1285i) q^{87} -14.8931i q^{88} +(2.49855 + 4.32762i) q^{89} +(8.03393 + 0.754617i) q^{90} +(2.62893 + 2.37197i) q^{91} +(0.228628 + 0.395996i) q^{92} +(-2.23929 - 7.11832i) q^{93} +(-8.25271 + 4.76471i) q^{94} +(12.1569 + 2.20735i) q^{95} +(-5.00438 + 1.57429i) q^{96} +(-1.52201 - 2.63620i) q^{97} +(6.82227 - 4.93539i) q^{98} +(6.16570 - 13.1775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9} - 6 q^{10} - 12 q^{14} - 6 q^{15} - 26 q^{16} - 12 q^{19} + 6 q^{20} - 12 q^{21} - 42 q^{24} - 2 q^{25} + 12 q^{26} + 6 q^{29} - 18 q^{30} - 6 q^{31} + 12 q^{34} - 36 q^{36} - 6 q^{41} + 84 q^{44} - 12 q^{45} - 18 q^{46} + 10 q^{49} + 30 q^{50} - 6 q^{51} - 48 q^{54} - 90 q^{56} - 6 q^{59} + 54 q^{60} + 12 q^{61} - 8 q^{64} + 54 q^{65} + 78 q^{66} - 60 q^{69} - 30 q^{70} + 12 q^{75} + 48 q^{76} + 8 q^{79} + 69 q^{80} + 42 q^{81} + 120 q^{84} - 7 q^{85} - 72 q^{89} - 33 q^{90} + 20 q^{91} - 6 q^{94} - 93 q^{95} - 12 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.601450 + 1.04174i −0.425289 + 0.736622i −0.996447 0.0842176i \(-0.973161\pi\)
0.571158 + 0.820840i \(0.306494\pi\)
\(3\) 0.375988 1.69075i 0.217077 0.976155i
\(4\) 0.276517 + 0.478941i 0.138258 + 0.239470i
\(5\) 1.70560 + 1.44600i 0.762768 + 0.646673i
\(6\) 1.53519 + 1.40858i 0.626737 + 0.575051i
\(7\) −0.552728 + 2.58737i −0.208911 + 0.977935i
\(8\) −3.07104 −1.08578
\(9\) −2.71727 1.27140i −0.905755 0.423801i
\(10\) −2.53219 + 0.907096i −0.800750 + 0.286849i
\(11\) 4.84953i 1.46219i 0.682277 + 0.731094i \(0.260990\pi\)
−0.682277 + 0.731094i \(0.739010\pi\)
\(12\) 0.913736 0.287444i 0.263773 0.0829780i
\(13\) 0.669156 1.15901i 0.185590 0.321452i −0.758185 0.652040i \(-0.773914\pi\)
0.943775 + 0.330588i \(0.107247\pi\)
\(14\) −2.36293 2.13197i −0.631521 0.569794i
\(15\) 3.08612 2.34006i 0.796831 0.604202i
\(16\) 1.29404 2.24135i 0.323511 0.560337i
\(17\) 0.153866 + 0.0888348i 0.0373181 + 0.0215456i 0.518543 0.855052i \(-0.326475\pi\)
−0.481225 + 0.876597i \(0.659808\pi\)
\(18\) 2.95877 2.06600i 0.697389 0.486962i
\(19\) 4.78531 2.76280i 1.09783 0.633830i 0.162177 0.986762i \(-0.448148\pi\)
0.935649 + 0.352931i \(0.114815\pi\)
\(20\) −0.220924 + 1.21673i −0.0494000 + 0.272068i
\(21\) 4.16678 + 1.90734i 0.909266 + 0.416217i
\(22\) −5.05196 2.91675i −1.07708 0.621853i
\(23\) 0.826816 0.172403 0.0862016 0.996278i \(-0.472527\pi\)
0.0862016 + 0.996278i \(0.472527\pi\)
\(24\) −1.15467 + 5.19236i −0.235697 + 1.05989i
\(25\) 0.818145 + 4.93261i 0.163629 + 0.986522i
\(26\) 0.804927 + 1.39417i 0.157859 + 0.273420i
\(27\) −3.17128 + 4.11618i −0.610313 + 0.792160i
\(28\) −1.39204 + 0.450727i −0.263070 + 0.0851795i
\(29\) −6.88138 + 3.97297i −1.27784 + 0.737762i −0.976451 0.215739i \(-0.930784\pi\)
−0.301390 + 0.953501i \(0.597451\pi\)
\(30\) 0.581597 + 4.62236i 0.106185 + 0.843924i
\(31\) 3.73111 2.15416i 0.670128 0.386899i −0.125997 0.992031i \(-0.540213\pi\)
0.796125 + 0.605132i \(0.206880\pi\)
\(32\) −1.51444 2.62308i −0.267717 0.463700i
\(33\) 8.19934 + 1.82336i 1.42732 + 0.317407i
\(34\) −0.185086 + 0.106859i −0.0317419 + 0.0183262i
\(35\) −4.68408 + 3.61378i −0.791754 + 0.610840i
\(36\) −0.142443 1.65297i −0.0237405 0.275496i
\(37\) 7.14549 4.12545i 1.17471 0.678220i 0.219926 0.975517i \(-0.429418\pi\)
0.954785 + 0.297297i \(0.0960851\pi\)
\(38\) 6.64675i 1.07824i
\(39\) −1.70800 1.56715i −0.273499 0.250945i
\(40\) −5.23797 4.44074i −0.828196 0.702142i
\(41\) 0.278013 0.481532i 0.0434183 0.0752027i −0.843500 0.537130i \(-0.819509\pi\)
0.886918 + 0.461927i \(0.152842\pi\)
\(42\) −4.49307 + 3.19353i −0.693295 + 0.492773i
\(43\) 4.31274 2.48996i 0.657686 0.379715i −0.133709 0.991021i \(-0.542689\pi\)
0.791395 + 0.611305i \(0.209355\pi\)
\(44\) −2.32264 + 1.34098i −0.350151 + 0.202160i
\(45\) −2.79612 6.09768i −0.416821 0.908989i
\(46\) −0.497288 + 0.861329i −0.0733212 + 0.126996i
\(47\) 6.86068 + 3.96102i 1.00073 + 0.577774i 0.908465 0.417960i \(-0.137255\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(48\) −3.30302 3.03062i −0.476749 0.437433i
\(49\) −6.38898 2.86022i −0.912712 0.408603i
\(50\) −5.63058 2.11442i −0.796284 0.299024i
\(51\) 0.208049 0.226749i 0.0291327 0.0317512i
\(52\) 0.740130 0.102638
\(53\) 2.12855 3.68675i 0.292378 0.506414i −0.681993 0.731359i \(-0.738887\pi\)
0.974372 + 0.224944i \(0.0722200\pi\)
\(54\) −2.38063 5.77933i −0.323963 0.786468i
\(55\) −7.01244 + 8.27136i −0.945557 + 1.11531i
\(56\) 1.69745 7.94593i 0.226831 1.06182i
\(57\) −2.87199 9.12955i −0.380404 1.20924i
\(58\) 9.55816i 1.25505i
\(59\) −1.12039 1.94058i −0.145863 0.252641i 0.783832 0.620973i \(-0.213262\pi\)
−0.929694 + 0.368332i \(0.879929\pi\)
\(60\) 1.97411 + 0.831000i 0.254857 + 0.107282i
\(61\) −9.91668 5.72540i −1.26970 0.733062i −0.294770 0.955568i \(-0.595243\pi\)
−0.974931 + 0.222506i \(0.928576\pi\)
\(62\) 5.18247i 0.658175i
\(63\) 4.79150 6.32784i 0.603672 0.797233i
\(64\) 8.81961 1.10245
\(65\) 2.81725 1.00921i 0.349437 0.125177i
\(66\) −6.83096 + 7.44493i −0.840834 + 0.916408i
\(67\) 0.134618 0.0777216i 0.0164462 0.00949521i −0.491754 0.870734i \(-0.663644\pi\)
0.508201 + 0.861239i \(0.330311\pi\)
\(68\) 0.0982572i 0.0119154i
\(69\) 0.310873 1.39794i 0.0374247 0.168292i
\(70\) −0.947380 7.05311i −0.113234 0.843007i
\(71\) 10.3336i 1.22638i −0.789936 0.613189i \(-0.789886\pi\)
0.789936 0.613189i \(-0.210114\pi\)
\(72\) 8.34484 + 3.90453i 0.983449 + 0.460153i
\(73\) −5.28792 + 9.15894i −0.618904 + 1.07197i 0.370782 + 0.928720i \(0.379090\pi\)
−0.989686 + 0.143253i \(0.954244\pi\)
\(74\) 9.92500i 1.15376i
\(75\) 8.64742 + 0.471323i 0.998518 + 0.0544237i
\(76\) 2.64644 + 1.52792i 0.303567 + 0.175265i
\(77\) −12.5475 2.68047i −1.42992 0.305468i
\(78\) 2.65984 0.836737i 0.301168 0.0947418i
\(79\) 6.15184 10.6553i 0.692136 1.19881i −0.279001 0.960291i \(-0.590003\pi\)
0.971137 0.238524i \(-0.0766634\pi\)
\(80\) 5.44812 1.95165i 0.609119 0.218202i
\(81\) 5.76707 + 6.90948i 0.640786 + 0.767720i
\(82\) 0.334421 + 0.579234i 0.0369306 + 0.0639657i
\(83\) 14.4831 8.36182i 1.58973 0.917829i 0.596376 0.802705i \(-0.296607\pi\)
0.993351 0.115124i \(-0.0367267\pi\)
\(84\) 0.238679 + 2.52305i 0.0260420 + 0.275288i
\(85\) 0.133979 + 0.374008i 0.0145321 + 0.0405669i
\(86\) 5.99034i 0.645955i
\(87\) 4.12998 + 13.1285i 0.442780 + 1.40752i
\(88\) 14.8931i 1.58761i
\(89\) 2.49855 + 4.32762i 0.264846 + 0.458726i 0.967523 0.252782i \(-0.0813456\pi\)
−0.702677 + 0.711509i \(0.748012\pi\)
\(90\) 8.03393 + 0.754617i 0.846851 + 0.0795436i
\(91\) 2.62893 + 2.37197i 0.275587 + 0.248650i
\(92\) 0.228628 + 0.395996i 0.0238362 + 0.0412854i
\(93\) −2.23929 7.11832i −0.232204 0.738135i
\(94\) −8.25271 + 4.76471i −0.851202 + 0.491442i
\(95\) 12.1569 + 2.20735i 1.24727 + 0.226469i
\(96\) −5.00438 + 1.57429i −0.510758 + 0.160675i
\(97\) −1.52201 2.63620i −0.154537 0.267665i 0.778354 0.627826i \(-0.216055\pi\)
−0.932890 + 0.360161i \(0.882722\pi\)
\(98\) 6.82227 4.93539i 0.689153 0.498550i
\(99\) 6.16570 13.1775i 0.619676 1.32439i
\(100\) −2.13620 + 1.75579i −0.213620 + 0.175579i
\(101\) −12.1132 −1.20530 −0.602652 0.798004i \(-0.705889\pi\)
−0.602652 + 0.798004i \(0.705889\pi\)
\(102\) 0.111082 + 0.353111i 0.0109988 + 0.0349632i
\(103\) −7.57454 −0.746341 −0.373171 0.927763i \(-0.621729\pi\)
−0.373171 + 0.927763i \(0.621729\pi\)
\(104\) −2.05500 + 3.55937i −0.201510 + 0.349025i
\(105\) 4.34883 + 9.27834i 0.424402 + 0.905474i
\(106\) 2.56043 + 4.43479i 0.248691 + 0.430745i
\(107\) −10.1290 17.5440i −0.979210 1.69604i −0.665277 0.746597i \(-0.731686\pi\)
−0.313934 0.949445i \(-0.601647\pi\)
\(108\) −2.84832 0.380662i −0.274080 0.0366293i
\(109\) −2.79600 + 4.84281i −0.267808 + 0.463857i −0.968295 0.249808i \(-0.919633\pi\)
0.700488 + 0.713665i \(0.252966\pi\)
\(110\) −4.39899 12.2800i −0.419427 1.17085i
\(111\) −4.28849 13.6323i −0.407045 1.29393i
\(112\) 5.08395 + 4.58703i 0.480388 + 0.433433i
\(113\) 0.735088 1.27321i 0.0691513 0.119774i −0.829377 0.558690i \(-0.811304\pi\)
0.898528 + 0.438916i \(0.144638\pi\)
\(114\) 11.2380 + 2.49910i 1.05253 + 0.234062i
\(115\) 1.41022 + 1.19558i 0.131504 + 0.111488i
\(116\) −3.80563 2.19718i −0.353344 0.204003i
\(117\) −3.29184 + 2.29858i −0.304331 + 0.212504i
\(118\) 2.69544 0.248135
\(119\) −0.314895 + 0.349008i −0.0288664 + 0.0319935i
\(120\) −9.47759 + 7.18643i −0.865182 + 0.656028i
\(121\) −12.5179 −1.13799
\(122\) 11.9288 6.88708i 1.07998 0.623527i
\(123\) −0.709621 0.651100i −0.0639843 0.0587077i
\(124\) 2.06343 + 1.19132i 0.185301 + 0.106984i
\(125\) −5.73715 + 9.59610i −0.513146 + 0.858301i
\(126\) 3.71013 + 8.79738i 0.330524 + 0.783733i
\(127\) 8.14098i 0.722395i 0.932489 + 0.361197i \(0.117632\pi\)
−0.932489 + 0.361197i \(0.882368\pi\)
\(128\) −2.27568 + 3.94159i −0.201143 + 0.348390i
\(129\) −2.58836 8.22795i −0.227893 0.724431i
\(130\) −0.643098 + 3.54183i −0.0564034 + 0.310639i
\(131\) 10.2924 0.899252 0.449626 0.893217i \(-0.351557\pi\)
0.449626 + 0.893217i \(0.351557\pi\)
\(132\) 1.39397 + 4.43119i 0.121330 + 0.385685i
\(133\) 4.50342 + 13.9085i 0.390496 + 1.20602i
\(134\) 0.186983i 0.0161528i
\(135\) −11.3610 + 2.43488i −0.977796 + 0.209561i
\(136\) −0.472530 0.272815i −0.0405191 0.0233937i
\(137\) −2.80002 −0.239222 −0.119611 0.992821i \(-0.538165\pi\)
−0.119611 + 0.992821i \(0.538165\pi\)
\(138\) 1.26932 + 1.16464i 0.108051 + 0.0991407i
\(139\) 12.5228 + 7.23003i 1.06217 + 0.613243i 0.926031 0.377447i \(-0.123198\pi\)
0.136137 + 0.990690i \(0.456531\pi\)
\(140\) −3.02601 1.24413i −0.255745 0.105148i
\(141\) 9.27662 10.1104i 0.781233 0.851450i
\(142\) 10.7650 + 6.21517i 0.903377 + 0.521565i
\(143\) 5.62066 + 3.24509i 0.470023 + 0.271368i
\(144\) −6.36592 + 4.44509i −0.530493 + 0.370425i
\(145\) −17.4818 3.17421i −1.45179 0.263604i
\(146\) −6.36083 11.0173i −0.526426 0.911797i
\(147\) −7.23810 + 9.72676i −0.596988 + 0.802250i
\(148\) 3.95169 + 2.28151i 0.324827 + 0.187539i
\(149\) 6.05577i 0.496108i 0.968746 + 0.248054i \(0.0797911\pi\)
−0.968746 + 0.248054i \(0.920209\pi\)
\(150\) −5.69198 + 8.72490i −0.464749 + 0.712385i
\(151\) −14.3134 −1.16480 −0.582402 0.812901i \(-0.697887\pi\)
−0.582402 + 0.812901i \(0.697887\pi\)
\(152\) −14.6959 + 8.48468i −1.19199 + 0.688199i
\(153\) −0.305151 0.437014i −0.0246700 0.0353305i
\(154\) 10.3391 11.4591i 0.833146 0.923402i
\(155\) 9.47871 + 1.72107i 0.761349 + 0.138240i
\(156\) 0.278280 1.25138i 0.0222802 0.100190i
\(157\) −1.89351 3.27966i −0.151119 0.261746i 0.780520 0.625131i \(-0.214954\pi\)
−0.931639 + 0.363385i \(0.881621\pi\)
\(158\) 7.40004 + 12.8172i 0.588716 + 1.01969i
\(159\) −5.43307 4.98501i −0.430870 0.395337i
\(160\) 1.20996 6.66381i 0.0956560 0.526821i
\(161\) −0.457004 + 2.13928i −0.0360170 + 0.168599i
\(162\) −10.6665 + 1.85210i −0.838039 + 0.145515i
\(163\) −1.42373 + 0.821991i −0.111515 + 0.0643833i −0.554720 0.832037i \(-0.687175\pi\)
0.443205 + 0.896420i \(0.353841\pi\)
\(164\) 0.307500 0.0240117
\(165\) 11.3482 + 14.9662i 0.883457 + 1.16512i
\(166\) 20.1169i 1.56137i
\(167\) −3.15992 1.82438i −0.244522 0.141175i 0.372731 0.927939i \(-0.378421\pi\)
−0.617253 + 0.786764i \(0.711755\pi\)
\(168\) −12.7964 5.85753i −0.987260 0.451918i
\(169\) 5.60446 + 9.70721i 0.431112 + 0.746709i
\(170\) −0.470201 0.0853755i −0.0360628 0.00654800i
\(171\) −16.5156 + 1.42321i −1.26298 + 0.108836i
\(172\) 2.38509 + 1.37703i 0.181861 + 0.104998i
\(173\) −8.70486 5.02575i −0.661818 0.382101i 0.131151 0.991362i \(-0.458133\pi\)
−0.792969 + 0.609261i \(0.791466\pi\)
\(174\) −16.1605 3.59375i −1.22512 0.272442i
\(175\) −13.2147 0.609545i −0.998938 0.0460773i
\(176\) 10.8695 + 6.27551i 0.819319 + 0.473034i
\(177\) −3.70228 + 1.16467i −0.278281 + 0.0875419i
\(178\) −6.01101 −0.450544
\(179\) 12.1422 + 7.01032i 0.907552 + 0.523976i 0.879643 0.475635i \(-0.157782\pi\)
0.0279095 + 0.999610i \(0.491115\pi\)
\(180\) 2.14726 3.02529i 0.160047 0.225491i
\(181\) 16.3088i 1.21223i −0.795379 0.606113i \(-0.792728\pi\)
0.795379 0.606113i \(-0.207272\pi\)
\(182\) −4.05215 + 1.31205i −0.300365 + 0.0972554i
\(183\) −13.4088 + 14.6139i −0.991204 + 1.08029i
\(184\) −2.53919 −0.187191
\(185\) 18.1528 + 3.29604i 1.33462 + 0.242329i
\(186\) 8.76227 + 1.94855i 0.642480 + 0.142874i
\(187\) −0.430807 + 0.746180i −0.0315037 + 0.0545661i
\(188\) 4.38115i 0.319528i
\(189\) −8.89725 10.4804i −0.647179 0.762338i
\(190\) −9.61122 + 11.3367i −0.697271 + 0.822450i
\(191\) 13.0759 + 7.54940i 0.946142 + 0.546255i 0.891880 0.452272i \(-0.149386\pi\)
0.0542615 + 0.998527i \(0.482720\pi\)
\(192\) 3.31606 14.9117i 0.239316 1.07616i
\(193\) 1.47631 0.852345i 0.106267 0.0613532i −0.445925 0.895070i \(-0.647125\pi\)
0.552191 + 0.833717i \(0.313792\pi\)
\(194\) 3.66164 0.262891
\(195\) −0.647068 5.14271i −0.0463375 0.368277i
\(196\) −0.396783 3.85084i −0.0283416 0.275060i
\(197\) −1.72122 −0.122632 −0.0613158 0.998118i \(-0.519530\pi\)
−0.0613158 + 0.998118i \(0.519530\pi\)
\(198\) 10.0192 + 14.3486i 0.712030 + 1.01971i
\(199\) 22.0950 + 12.7566i 1.56627 + 0.904288i 0.996598 + 0.0824185i \(0.0262644\pi\)
0.569675 + 0.821870i \(0.307069\pi\)
\(200\) −2.51256 15.1483i −0.177665 1.07114i
\(201\) −0.0807932 0.256827i −0.00569871 0.0181152i
\(202\) 7.28545 12.6188i 0.512603 0.887854i
\(203\) −6.47602 20.0007i −0.454527 1.40377i
\(204\) 0.166128 + 0.0369435i 0.0116313 + 0.00258656i
\(205\) 1.17048 0.419294i 0.0817496 0.0292847i
\(206\) 4.55570 7.89071i 0.317411 0.549772i
\(207\) −2.24668 1.05122i −0.156155 0.0730646i
\(208\) −1.73183 2.99962i −0.120081 0.207986i
\(209\) 13.3983 + 23.2065i 0.926779 + 1.60523i
\(210\) −12.2812 1.05010i −0.847486 0.0724638i
\(211\) 0.0469655 0.0813465i 0.00323324 0.00560013i −0.864404 0.502797i \(-0.832304\pi\)
0.867637 + 0.497197i \(0.165637\pi\)
\(212\) 2.35431 0.161695
\(213\) −17.4716 3.88532i −1.19713 0.266218i
\(214\) 24.3684 1.66579
\(215\) 10.9563 + 1.98936i 0.747213 + 0.135673i
\(216\) 9.73914 12.6410i 0.662664 0.860109i
\(217\) 3.51132 + 10.8444i 0.238364 + 0.736169i
\(218\) −3.36330 5.82541i −0.227792 0.394547i
\(219\) 13.4973 + 12.3842i 0.912062 + 0.836846i
\(220\) −5.90055 1.07138i −0.397815 0.0722321i
\(221\) 0.205921 0.118889i 0.0138518 0.00799731i
\(222\) 16.7807 + 3.73168i 1.12625 + 0.250454i
\(223\) 5.21542 + 9.03337i 0.349250 + 0.604919i 0.986116 0.166055i \(-0.0531030\pi\)
−0.636866 + 0.770974i \(0.719770\pi\)
\(224\) 7.62396 2.46856i 0.509397 0.164938i
\(225\) 4.04821 14.4434i 0.269881 0.962894i
\(226\) 0.884237 + 1.53154i 0.0588186 + 0.101877i
\(227\) 0.608344i 0.0403772i 0.999796 + 0.0201886i \(0.00642667\pi\)
−0.999796 + 0.0201886i \(0.993573\pi\)
\(228\) 3.57836 3.89998i 0.236983 0.258283i
\(229\) 4.97008i 0.328432i 0.986424 + 0.164216i \(0.0525095\pi\)
−0.986424 + 0.164216i \(0.947491\pi\)
\(230\) −2.09366 + 0.750002i −0.138052 + 0.0494536i
\(231\) −9.24972 + 20.2069i −0.608587 + 1.32952i
\(232\) 21.1330 12.2012i 1.38745 0.801045i
\(233\) 1.46329 + 2.53449i 0.0958633 + 0.166040i 0.909969 0.414677i \(-0.136105\pi\)
−0.814105 + 0.580717i \(0.802772\pi\)
\(234\) −0.414645 4.81173i −0.0271062 0.314553i
\(235\) 5.97394 + 16.6765i 0.389697 + 1.08785i
\(236\) 0.619614 1.07320i 0.0403334 0.0698596i
\(237\) −15.7024 14.4075i −1.01998 0.935866i
\(238\) −0.174183 0.537950i −0.0112906 0.0348701i
\(239\) −17.9962 10.3901i −1.16408 0.672080i −0.211800 0.977313i \(-0.567932\pi\)
−0.952278 + 0.305233i \(0.901266\pi\)
\(240\) −1.25133 9.94521i −0.0807730 0.641960i
\(241\) 2.37450i 0.152955i −0.997071 0.0764774i \(-0.975633\pi\)
0.997071 0.0764774i \(-0.0243673\pi\)
\(242\) 7.52891 13.0405i 0.483977 0.838272i
\(243\) 13.8505 7.15280i 0.888513 0.458852i
\(244\) 6.33267i 0.405408i
\(245\) −6.76116 14.1169i −0.431955 0.901895i
\(246\) 1.10508 0.347637i 0.0704572 0.0221645i
\(247\) 7.39498i 0.470531i
\(248\) −11.4584 + 6.61551i −0.727610 + 0.420086i
\(249\) −8.69228 27.6312i −0.550851 1.75106i
\(250\) −6.54605 11.7482i −0.414009 0.743021i
\(251\) 10.4701 0.660869 0.330435 0.943829i \(-0.392805\pi\)
0.330435 + 0.943829i \(0.392805\pi\)
\(252\) 4.35559 + 0.545091i 0.274376 + 0.0343375i
\(253\) 4.00967i 0.252086i
\(254\) −8.48079 4.89639i −0.532132 0.307227i
\(255\) 0.682728 0.0859026i 0.0427541 0.00537943i
\(256\) 6.08220 + 10.5347i 0.380137 + 0.658417i
\(257\) 9.94322i 0.620241i −0.950697 0.310120i \(-0.899631\pi\)
0.950697 0.310120i \(-0.100369\pi\)
\(258\) 10.1282 + 2.25230i 0.630552 + 0.140222i
\(259\) 6.72456 + 20.7683i 0.417844 + 1.29048i
\(260\) 1.26237 + 1.07023i 0.0782887 + 0.0663730i
\(261\) 23.7498 2.04661i 1.47008 0.126682i
\(262\) −6.19037 + 10.7220i −0.382442 + 0.662409i
\(263\) −25.0978 −1.54760 −0.773798 0.633433i \(-0.781645\pi\)
−0.773798 + 0.633433i \(0.781645\pi\)
\(264\) −25.1805 5.59963i −1.54975 0.344633i
\(265\) 8.96151 3.21024i 0.550501 0.197203i
\(266\) −17.1976 3.67384i −1.05445 0.225258i
\(267\) 8.25634 2.59729i 0.505280 0.158952i
\(268\) 0.0744481 + 0.0429826i 0.00454764 + 0.00262558i
\(269\) −3.90321 + 6.76057i −0.237983 + 0.412199i −0.960135 0.279535i \(-0.909820\pi\)
0.722152 + 0.691734i \(0.243153\pi\)
\(270\) 4.29653 13.2996i 0.261478 0.809390i
\(271\) −16.2132 + 9.36071i −0.984884 + 0.568623i −0.903741 0.428080i \(-0.859190\pi\)
−0.0811425 + 0.996703i \(0.525857\pi\)
\(272\) 0.398220 0.229912i 0.0241456 0.0139405i
\(273\) 4.99886 3.55303i 0.302545 0.215039i
\(274\) 1.68407 2.91689i 0.101738 0.176216i
\(275\) −23.9208 + 3.96762i −1.44248 + 0.239256i
\(276\) 0.755492 0.237664i 0.0454752 0.0143057i
\(277\) 12.1099i 0.727613i 0.931475 + 0.363807i \(0.118523\pi\)
−0.931475 + 0.363807i \(0.881477\pi\)
\(278\) −15.0636 + 8.69700i −0.903457 + 0.521611i
\(279\) −12.8772 + 1.10968i −0.770940 + 0.0664348i
\(280\) 14.3850 11.0981i 0.859669 0.663236i
\(281\) 28.1997 16.2811i 1.68225 0.971248i 0.722091 0.691799i \(-0.243181\pi\)
0.960160 0.279450i \(-0.0901520\pi\)
\(282\) 4.95300 + 15.7447i 0.294947 + 0.937586i
\(283\) 15.1847 + 26.3006i 0.902634 + 1.56341i 0.824062 + 0.566500i \(0.191703\pi\)
0.0785728 + 0.996908i \(0.474964\pi\)
\(284\) 4.94920 2.85742i 0.293681 0.169557i
\(285\) 8.30290 19.7243i 0.491821 1.16836i
\(286\) −6.76109 + 3.90352i −0.399792 + 0.230820i
\(287\) 1.09224 + 0.985478i 0.0644727 + 0.0581709i
\(288\) 0.780137 + 9.05307i 0.0459700 + 0.533457i
\(289\) −8.48422 14.6951i −0.499072 0.864417i
\(290\) 13.8211 16.3024i 0.811605 0.957310i
\(291\) −5.02940 + 1.58216i −0.294829 + 0.0927477i
\(292\) −5.84879 −0.342274
\(293\) 24.5241 + 14.1590i 1.43271 + 0.827177i 0.997327 0.0730662i \(-0.0232785\pi\)
0.435386 + 0.900244i \(0.356612\pi\)
\(294\) −5.77942 13.3904i −0.337062 0.780943i
\(295\) 0.895140 4.92994i 0.0521170 0.287032i
\(296\) −21.9441 + 12.6694i −1.27547 + 0.736396i
\(297\) −19.9616 15.3792i −1.15829 0.892393i
\(298\) −6.30855 3.64224i −0.365444 0.210989i
\(299\) 0.553269 0.958290i 0.0319964 0.0554193i
\(300\) 2.16542 + 4.27193i 0.125021 + 0.246640i
\(301\) 4.05868 + 12.5349i 0.233939 + 0.722501i
\(302\) 8.60876 14.9108i 0.495379 0.858021i
\(303\) −4.55440 + 20.4803i −0.261643 + 1.17656i
\(304\) 14.3008i 0.820204i
\(305\) −8.63495 24.1048i −0.494436 1.38024i
\(306\) 0.638788 0.0550468i 0.0365171 0.00314682i
\(307\) −17.2849 −0.986503 −0.493251 0.869887i \(-0.664192\pi\)
−0.493251 + 0.869887i \(0.664192\pi\)
\(308\) −2.18582 6.75072i −0.124548 0.384658i
\(309\) −2.84793 + 12.8066i −0.162013 + 0.728544i
\(310\) −7.49388 + 8.83923i −0.425624 + 0.502035i
\(311\) −7.49347 12.9791i −0.424915 0.735975i 0.571497 0.820604i \(-0.306363\pi\)
−0.996413 + 0.0846290i \(0.973030\pi\)
\(312\) 5.24535 + 4.81278i 0.296960 + 0.272470i
\(313\) 6.73830 11.6711i 0.380871 0.659688i −0.610316 0.792158i \(-0.708957\pi\)
0.991187 + 0.132470i \(0.0422908\pi\)
\(314\) 4.55541 0.257077
\(315\) 17.3225 3.86424i 0.976010 0.217725i
\(316\) 6.80434 0.382774
\(317\) −0.392277 + 0.679444i −0.0220325 + 0.0381614i −0.876831 0.480798i \(-0.840347\pi\)
0.854799 + 0.518959i \(0.173680\pi\)
\(318\) 8.46081 2.66161i 0.474459 0.149256i
\(319\) −19.2670 33.3715i −1.07875 1.86844i
\(320\) 15.0427 + 12.7532i 0.840914 + 0.712925i
\(321\) −33.4709 + 10.5293i −1.86816 + 0.587690i
\(322\) −1.95371 1.76275i −0.108876 0.0982342i
\(323\) 0.981732 0.0546250
\(324\) −1.71454 + 4.67267i −0.0952521 + 0.259593i
\(325\) 6.26442 + 2.35244i 0.347487 + 0.130490i
\(326\) 1.97755i 0.109526i
\(327\) 7.13671 + 6.54816i 0.394661 + 0.362114i
\(328\) −0.853788 + 1.47880i −0.0471426 + 0.0816533i
\(329\) −14.0407 + 15.5618i −0.774090 + 0.857949i
\(330\) −22.4163 + 2.82047i −1.23398 + 0.155262i
\(331\) −0.497985 + 0.862535i −0.0273717 + 0.0474092i −0.879387 0.476108i \(-0.842047\pi\)
0.852015 + 0.523517i \(0.175380\pi\)
\(332\) 8.00964 + 4.62437i 0.439586 + 0.253795i
\(333\) −24.6613 + 2.12516i −1.35143 + 0.116458i
\(334\) 3.80107 2.19455i 0.207985 0.120080i
\(335\) 0.341990 + 0.0620959i 0.0186849 + 0.00339266i
\(336\) 9.66702 6.87102i 0.527379 0.374845i
\(337\) −1.68117 0.970624i −0.0915792 0.0528733i 0.453511 0.891251i \(-0.350171\pi\)
−0.545090 + 0.838377i \(0.683505\pi\)
\(338\) −13.4832 −0.733390
\(339\) −1.87630 1.72156i −0.101906 0.0935024i
\(340\) −0.142080 + 0.167587i −0.00770538 + 0.00908871i
\(341\) 10.4467 + 18.0941i 0.565718 + 0.979853i
\(342\) 8.45069 18.0610i 0.456961 0.976626i
\(343\) 10.9318 14.9498i 0.590263 0.807211i
\(344\) −13.2446 + 7.64677i −0.714101 + 0.412286i
\(345\) 2.55165 1.93480i 0.137376 0.104166i
\(346\) 10.4711 6.04548i 0.562928 0.325007i
\(347\) 0.765596 + 1.32605i 0.0410993 + 0.0711861i 0.885843 0.463984i \(-0.153581\pi\)
−0.844744 + 0.535171i \(0.820247\pi\)
\(348\) −5.14576 + 5.60826i −0.275842 + 0.300634i
\(349\) −7.58071 + 4.37673i −0.405786 + 0.234281i −0.688978 0.724783i \(-0.741940\pi\)
0.283191 + 0.959063i \(0.408607\pi\)
\(350\) 8.58297 13.3997i 0.458779 0.716244i
\(351\) 2.64863 + 6.42992i 0.141373 + 0.343204i
\(352\) 12.7207 7.34431i 0.678016 0.391453i
\(353\) 3.01173i 0.160298i −0.996783 0.0801491i \(-0.974460\pi\)
0.996783 0.0801491i \(-0.0255396\pi\)
\(354\) 1.01345 4.55731i 0.0538643 0.242218i
\(355\) 14.9425 17.6251i 0.793065 0.935441i
\(356\) −1.38178 + 2.39332i −0.0732343 + 0.126845i
\(357\) 0.471689 + 0.663631i 0.0249644 + 0.0351231i
\(358\) −14.6059 + 8.43270i −0.771944 + 0.445682i
\(359\) −17.7753 + 10.2626i −0.938143 + 0.541637i −0.889378 0.457173i \(-0.848862\pi\)
−0.0487650 + 0.998810i \(0.515529\pi\)
\(360\) 8.58700 + 18.7262i 0.452574 + 0.986959i
\(361\) 5.76616 9.98728i 0.303482 0.525646i
\(362\) 16.9896 + 9.80894i 0.892952 + 0.515546i
\(363\) −4.70659 + 21.1647i −0.247032 + 1.11086i
\(364\) −0.409091 + 1.91499i −0.0214422 + 0.100373i
\(365\) −22.2629 + 7.97514i −1.16530 + 0.417438i
\(366\) −7.15925 22.7580i −0.374220 1.18958i
\(367\) −8.48758 −0.443048 −0.221524 0.975155i \(-0.571103\pi\)
−0.221524 + 0.975155i \(0.571103\pi\)
\(368\) 1.06994 1.85318i 0.0557743 0.0966039i
\(369\) −1.36766 + 0.954985i −0.0711973 + 0.0497145i
\(370\) −14.3516 + 16.9281i −0.746104 + 0.880049i
\(371\) 8.36249 + 7.54511i 0.434159 + 0.391723i
\(372\) 2.79005 3.04082i 0.144657 0.157659i
\(373\) 5.80495i 0.300569i −0.988643 0.150284i \(-0.951981\pi\)
0.988643 0.150284i \(-0.0480189\pi\)
\(374\) −0.518217 0.897579i −0.0267964 0.0464127i
\(375\) 14.0675 + 13.3081i 0.726443 + 0.687227i
\(376\) −21.0695 12.1645i −1.08657 0.627334i
\(377\) 10.6341i 0.547686i
\(378\) 16.2691 2.96519i 0.836793 0.152513i
\(379\) −33.3868 −1.71496 −0.857482 0.514513i \(-0.827973\pi\)
−0.857482 + 0.514513i \(0.827973\pi\)
\(380\) 2.30438 + 6.43278i 0.118212 + 0.329995i
\(381\) 13.7644 + 3.06091i 0.705169 + 0.156815i
\(382\) −15.7290 + 9.08116i −0.804768 + 0.464633i
\(383\) 13.7010i 0.700090i 0.936733 + 0.350045i \(0.113834\pi\)
−0.936733 + 0.350045i \(0.886166\pi\)
\(384\) 5.80861 + 5.32958i 0.296419 + 0.271974i
\(385\) −17.5251 22.7156i −0.893162 1.15769i
\(386\) 2.05057i 0.104371i
\(387\) −14.8846 + 1.28266i −0.756627 + 0.0652014i
\(388\) 0.841721 1.45790i 0.0427319 0.0740138i
\(389\) 1.11589i 0.0565781i −0.999600 0.0282891i \(-0.990994\pi\)
0.999600 0.0282891i \(-0.00900589\pi\)
\(390\) 5.74655 + 2.41900i 0.290988 + 0.122491i
\(391\) 0.127219 + 0.0734501i 0.00643375 + 0.00371453i
\(392\) 19.6208 + 8.78387i 0.991002 + 0.443652i
\(393\) 3.86982 17.4019i 0.195207 0.877809i
\(394\) 1.03522 1.79306i 0.0521539 0.0903332i
\(395\) 25.9002 9.27809i 1.30318 0.466832i
\(396\) 8.01614 0.690781i 0.402826 0.0347131i
\(397\) −13.9181 24.1068i −0.698529 1.20989i −0.968976 0.247153i \(-0.920505\pi\)
0.270447 0.962735i \(-0.412828\pi\)
\(398\) −26.5781 + 15.3449i −1.33224 + 0.769168i
\(399\) 25.2090 2.38475i 1.26203 0.119387i
\(400\) 12.1144 + 4.54927i 0.605721 + 0.227463i
\(401\) 24.5684i 1.22689i −0.789739 0.613443i \(-0.789784\pi\)
0.789739 0.613443i \(-0.210216\pi\)
\(402\) 0.316141 + 0.0703032i 0.0157677 + 0.00350640i
\(403\) 5.76587i 0.287219i
\(404\) −3.34949 5.80148i −0.166643 0.288635i
\(405\) −0.154808 + 20.1240i −0.00769245 + 0.999970i
\(406\) 24.7305 + 5.28306i 1.22736 + 0.262194i
\(407\) 20.0065 + 34.6523i 0.991685 + 1.71765i
\(408\) −0.638928 + 0.696355i −0.0316316 + 0.0344747i
\(409\) 7.17694 4.14361i 0.354877 0.204888i −0.311954 0.950097i \(-0.600984\pi\)
0.666831 + 0.745209i \(0.267650\pi\)
\(410\) −0.267187 + 1.47152i −0.0131954 + 0.0726730i
\(411\) −1.05277 + 4.73413i −0.0519294 + 0.233517i
\(412\) −2.09448 3.62775i −0.103188 0.178727i
\(413\) 5.64026 1.82626i 0.277539 0.0898644i
\(414\) 2.44636 1.70821i 0.120232 0.0839538i
\(415\) 36.7936 + 6.68070i 1.80613 + 0.327943i
\(416\) −4.05358 −0.198743
\(417\) 16.9326 18.4545i 0.829192 0.903720i
\(418\) −32.2336 −1.57660
\(419\) 8.68558 15.0439i 0.424319 0.734941i −0.572038 0.820227i \(-0.693847\pi\)
0.996357 + 0.0852859i \(0.0271804\pi\)
\(420\) −3.24125 + 4.64845i −0.158157 + 0.226821i
\(421\) 9.54538 + 16.5331i 0.465213 + 0.805773i 0.999211 0.0397127i \(-0.0126443\pi\)
−0.533998 + 0.845486i \(0.679311\pi\)
\(422\) 0.0564947 + 0.0978517i 0.00275012 + 0.00476335i
\(423\) −13.6063 19.4858i −0.661559 0.947433i
\(424\) −6.53686 + 11.3222i −0.317458 + 0.549853i
\(425\) −0.312302 + 0.831642i −0.0151489 + 0.0403406i
\(426\) 14.5558 15.8641i 0.705230 0.768616i
\(427\) 20.2950 22.4936i 0.982142 1.08854i
\(428\) 5.60169 9.70241i 0.270768 0.468984i
\(429\) 7.59993 8.28301i 0.366928 0.399908i
\(430\) −8.66206 + 10.2171i −0.417722 + 0.492714i
\(431\) −6.23832 3.60170i −0.300489 0.173488i 0.342173 0.939637i \(-0.388837\pi\)
−0.642663 + 0.766149i \(0.722170\pi\)
\(432\) 5.12203 + 12.4345i 0.246434 + 0.598254i
\(433\) −14.5747 −0.700416 −0.350208 0.936672i \(-0.613889\pi\)
−0.350208 + 0.936672i \(0.613889\pi\)
\(434\) −13.4090 2.86450i −0.643652 0.137500i
\(435\) −11.9397 + 28.3639i −0.572467 + 1.35995i
\(436\) −3.09256 −0.148107
\(437\) 3.95658 2.28433i 0.189269 0.109274i
\(438\) −21.0191 + 6.61221i −1.00433 + 0.315944i
\(439\) 35.6686 + 20.5933i 1.70237 + 0.982864i 0.943351 + 0.331796i \(0.107655\pi\)
0.759020 + 0.651068i \(0.225679\pi\)
\(440\) 21.5355 25.4017i 1.02666 1.21098i
\(441\) 13.7241 + 15.8950i 0.653528 + 0.756903i
\(442\) 0.286022i 0.0136047i
\(443\) 9.35967 16.2114i 0.444691 0.770228i −0.553339 0.832956i \(-0.686647\pi\)
0.998031 + 0.0627279i \(0.0199800\pi\)
\(444\) 5.34325 5.82350i 0.253579 0.276371i
\(445\) −1.99622 + 10.9941i −0.0946300 + 0.521170i
\(446\) −12.5472 −0.594129
\(447\) 10.2388 + 2.27690i 0.484278 + 0.107694i
\(448\) −4.87484 + 22.8196i −0.230315 + 1.07812i
\(449\) 29.3492i 1.38507i 0.721383 + 0.692536i \(0.243507\pi\)
−0.721383 + 0.692536i \(0.756493\pi\)
\(450\) 12.6115 + 12.9042i 0.594512 + 0.608309i
\(451\) 2.33520 + 1.34823i 0.109960 + 0.0634857i
\(452\) 0.813056 0.0382430
\(453\) −5.38164 + 24.2003i −0.252852 + 1.13703i
\(454\) −0.633737 0.365888i −0.0297428 0.0171720i
\(455\) 1.05403 + 7.84708i 0.0494136 + 0.367877i
\(456\) 8.81999 + 28.0372i 0.413034 + 1.31296i
\(457\) −31.6536 18.2752i −1.48069 0.854878i −0.480931 0.876758i \(-0.659701\pi\)
−0.999761 + 0.0218806i \(0.993035\pi\)
\(458\) −5.17754 2.98925i −0.241931 0.139679i
\(459\) −0.853614 + 0.351622i −0.0398433 + 0.0164123i
\(460\) −0.182663 + 1.00601i −0.00851671 + 0.0469054i
\(461\) −9.65949 16.7307i −0.449887 0.779228i 0.548491 0.836156i \(-0.315202\pi\)
−0.998378 + 0.0569289i \(0.981869\pi\)
\(462\) −15.4871 21.7893i −0.720527 1.01373i
\(463\) −27.7204 16.0044i −1.28828 0.743787i −0.309931 0.950759i \(-0.600306\pi\)
−0.978347 + 0.206972i \(0.933639\pi\)
\(464\) 20.5648i 0.954696i
\(465\) 6.47378 15.3790i 0.300214 0.713185i
\(466\) −3.52038 −0.163079
\(467\) −17.3160 + 9.99738i −0.801288 + 0.462624i −0.843921 0.536467i \(-0.819759\pi\)
0.0426334 + 0.999091i \(0.486425\pi\)
\(468\) −2.01113 0.941003i −0.0929646 0.0434979i
\(469\) 0.126688 + 0.391265i 0.00584990 + 0.0180670i
\(470\) −20.9656 3.80677i −0.967072 0.175593i
\(471\) −6.25702 + 1.96834i −0.288308 + 0.0906965i
\(472\) 3.44077 + 5.95959i 0.158374 + 0.274312i
\(473\) 12.0751 + 20.9147i 0.555215 + 0.961661i
\(474\) 24.4531 7.69249i 1.12317 0.353328i
\(475\) 17.5429 + 21.3437i 0.804924 + 0.979317i
\(476\) −0.254228 0.0543094i −0.0116525 0.00248927i
\(477\) −10.4712 + 7.31165i −0.479442 + 0.334777i
\(478\) 21.6476 12.4983i 0.990139 0.571657i
\(479\) −11.7517 −0.536948 −0.268474 0.963287i \(-0.586519\pi\)
−0.268474 + 0.963287i \(0.586519\pi\)
\(480\) −10.8119 4.55126i −0.493494 0.207735i
\(481\) 11.0423i 0.503484i
\(482\) 2.47361 + 1.42814i 0.112670 + 0.0650500i
\(483\) 3.44516 + 1.57702i 0.156760 + 0.0717570i
\(484\) −3.46142 5.99535i −0.157337 0.272516i
\(485\) 1.21601 6.69713i 0.0552162 0.304101i
\(486\) −0.879038 + 18.7307i −0.0398740 + 0.849643i
\(487\) −21.2046 12.2425i −0.960873 0.554760i −0.0644315 0.997922i \(-0.520523\pi\)
−0.896442 + 0.443162i \(0.853857\pi\)
\(488\) 30.4545 + 17.5829i 1.37861 + 0.795942i
\(489\) 0.854476 + 2.71623i 0.0386407 + 0.122832i
\(490\) 18.7727 + 1.44722i 0.848062 + 0.0653788i
\(491\) −1.14468 0.660881i −0.0516587 0.0298252i 0.473948 0.880553i \(-0.342828\pi\)
−0.525607 + 0.850728i \(0.676162\pi\)
\(492\) 0.115616 0.519906i 0.00521239 0.0234392i
\(493\) −1.41175 −0.0635821
\(494\) 7.70366 + 4.44771i 0.346604 + 0.200112i
\(495\) 29.5709 13.5599i 1.32911 0.609470i
\(496\) 11.1503i 0.500664i
\(497\) 26.7370 + 5.71169i 1.19932 + 0.256204i
\(498\) 34.0126 + 7.56370i 1.52414 + 0.338937i
\(499\) 17.5038 0.783579 0.391789 0.920055i \(-0.371856\pi\)
0.391789 + 0.920055i \(0.371856\pi\)
\(500\) −6.18238 0.0942719i −0.276484 0.00421597i
\(501\) −4.27266 + 4.65669i −0.190889 + 0.208046i
\(502\) −6.29726 + 10.9072i −0.281060 + 0.486811i
\(503\) 4.31586i 0.192435i −0.995360 0.0962174i \(-0.969326\pi\)
0.995360 0.0962174i \(-0.0306744\pi\)
\(504\) −14.7149 + 19.4331i −0.655453 + 0.865617i
\(505\) −20.6602 17.5157i −0.919367 0.779437i
\(506\) −4.17704 2.41162i −0.185692 0.107209i
\(507\) 18.5197 5.82595i 0.822487 0.258739i
\(508\) −3.89905 + 2.25112i −0.172992 + 0.0998771i
\(509\) 6.83736 0.303061 0.151530 0.988453i \(-0.451580\pi\)
0.151530 + 0.988453i \(0.451580\pi\)
\(510\) −0.321138 + 0.762892i −0.0142202 + 0.0337814i
\(511\) −20.7748 18.7442i −0.919023 0.829195i
\(512\) −23.7352 −1.04896
\(513\) −3.80337 + 28.4589i −0.167923 + 1.25649i
\(514\) 10.3583 + 5.98035i 0.456883 + 0.263782i
\(515\) −12.9191 10.9528i −0.569285 0.482638i
\(516\) 3.22498 3.51484i 0.141972 0.154732i
\(517\) −19.2091 + 33.2711i −0.844814 + 1.46326i
\(518\) −25.6797 5.48582i −1.12830 0.241033i
\(519\) −11.7702 + 12.8281i −0.516655 + 0.563092i
\(520\) −8.65188 + 3.09932i −0.379410 + 0.135914i
\(521\) 10.7730 18.6594i 0.471975 0.817484i −0.527511 0.849548i \(-0.676875\pi\)
0.999486 + 0.0320639i \(0.0102080\pi\)
\(522\) −12.1523 + 25.9721i −0.531890 + 1.13677i
\(523\) 6.82813 + 11.8267i 0.298573 + 0.517144i 0.975810 0.218621i \(-0.0701560\pi\)
−0.677237 + 0.735765i \(0.736823\pi\)
\(524\) 2.84602 + 4.92945i 0.124329 + 0.215344i
\(525\) −5.99916 + 22.1136i −0.261825 + 0.965115i
\(526\) 15.0951 26.1454i 0.658176 1.13999i
\(527\) 0.765457 0.0333438
\(528\) 14.6971 16.0181i 0.639609 0.697097i
\(529\) −22.3164 −0.970277
\(530\) −2.04566 + 11.2664i −0.0888578 + 0.489380i
\(531\) 0.577152 + 6.69753i 0.0250462 + 0.290648i
\(532\) −5.41606 + 6.00279i −0.234816 + 0.260254i
\(533\) −0.372067 0.644440i −0.0161160 0.0279138i
\(534\) −2.26007 + 10.1631i −0.0978026 + 0.439801i
\(535\) 8.09261 44.5697i 0.349874 1.92691i
\(536\) −0.413417 + 0.238686i −0.0178569 + 0.0103097i
\(537\) 16.4180 17.8937i 0.708490 0.772168i
\(538\) −4.69517 8.13228i −0.202423 0.350607i
\(539\) 13.8707 30.9836i 0.597455 1.33456i
\(540\) −4.30766 4.76794i −0.185372 0.205180i
\(541\) −20.3541 35.2543i −0.875091 1.51570i −0.856666 0.515871i \(-0.827468\pi\)
−0.0184247 0.999830i \(-0.505865\pi\)
\(542\) 22.5200i 0.967316i
\(543\) −27.5741 6.13192i −1.18332 0.263146i
\(544\) 0.538139i 0.0230725i
\(545\) −11.7716 + 4.21687i −0.504239 + 0.180631i
\(546\) 0.694782 + 7.34449i 0.0297339 + 0.314315i
\(547\) −7.04001 + 4.06455i −0.301009 + 0.173788i −0.642896 0.765953i \(-0.722267\pi\)
0.341887 + 0.939741i \(0.388934\pi\)
\(548\) −0.774251 1.34104i −0.0330744 0.0572865i
\(549\) 19.6670 + 28.1655i 0.839366 + 1.20208i
\(550\) 10.2539 27.3057i 0.437230 1.16432i
\(551\) −21.9531 + 38.0238i −0.935232 + 1.61987i
\(552\) −0.954703 + 4.29313i −0.0406349 + 0.182728i
\(553\) 24.1689 + 21.8066i 1.02777 + 0.927310i
\(554\) −12.6154 7.28349i −0.535976 0.309446i
\(555\) 12.3980 29.4525i 0.526265 1.25019i
\(556\) 7.99689i 0.339144i
\(557\) −21.2535 + 36.8121i −0.900538 + 1.55978i −0.0737411 + 0.997277i \(0.523494\pi\)
−0.826797 + 0.562500i \(0.809839\pi\)
\(558\) 6.58901 14.0822i 0.278935 0.596146i
\(559\) 6.66468i 0.281886i
\(560\) 2.03833 + 15.1751i 0.0861351 + 0.641263i
\(561\) 1.09962 + 1.00894i 0.0464262 + 0.0425975i
\(562\) 39.1690i 1.65224i
\(563\) −26.9569 + 15.5636i −1.13610 + 0.655926i −0.945461 0.325734i \(-0.894389\pi\)
−0.190636 + 0.981661i \(0.561055\pi\)
\(564\) 7.40742 + 1.64726i 0.311909 + 0.0693621i
\(565\) 3.09483 1.10865i 0.130201 0.0466411i
\(566\) −36.5312 −1.53552
\(567\) −21.0650 + 11.1025i −0.884647 + 0.466261i
\(568\) 31.7350i 1.33157i
\(569\) −24.9082 14.3808i −1.04421 0.602874i −0.123186 0.992384i \(-0.539311\pi\)
−0.921022 + 0.389510i \(0.872644\pi\)
\(570\) 15.5538 + 20.5126i 0.651477 + 0.859179i
\(571\) −3.11881 5.40194i −0.130518 0.226064i 0.793358 0.608755i \(-0.208331\pi\)
−0.923876 + 0.382691i \(0.874997\pi\)
\(572\) 3.58929i 0.150076i
\(573\) 17.6805 19.2697i 0.738615 0.805001i
\(574\) −1.68354 + 0.545113i −0.0702695 + 0.0227526i
\(575\) 0.676455 + 4.07836i 0.0282101 + 0.170079i
\(576\) −23.9652 11.2133i −0.998551 0.467219i
\(577\) 10.5494 18.2721i 0.439178 0.760679i −0.558448 0.829540i \(-0.688603\pi\)
0.997626 + 0.0688603i \(0.0219363\pi\)
\(578\) 20.4113 0.848999
\(579\) −0.886030 2.81653i −0.0368221 0.117051i
\(580\) −3.31375 9.25048i −0.137596 0.384105i
\(581\) 13.6299 + 42.0950i 0.565465 + 1.74639i
\(582\) 1.37673 6.19092i 0.0570674 0.256622i
\(583\) 17.8790 + 10.3225i 0.740473 + 0.427512i
\(584\) 16.2394 28.1275i 0.671992 1.16392i
\(585\) −8.93832 0.839565i −0.369554 0.0347117i
\(586\) −29.5000 + 17.0318i −1.21863 + 0.703579i
\(587\) −4.05248 + 2.33970i −0.167264 + 0.0965697i −0.581295 0.813693i \(-0.697454\pi\)
0.414031 + 0.910263i \(0.364120\pi\)
\(588\) −6.66000 0.777010i −0.274654 0.0320434i
\(589\) 11.9030 20.6167i 0.490456 0.849495i
\(590\) 4.59734 + 3.89761i 0.189269 + 0.160462i
\(591\) −0.647156 + 2.91014i −0.0266204 + 0.119707i
\(592\) 21.3541i 0.877646i
\(593\) 20.4747 11.8211i 0.840795 0.485433i −0.0167392 0.999860i \(-0.505328\pi\)
0.857534 + 0.514426i \(0.171995\pi\)
\(594\) 28.0270 11.5450i 1.14996 0.473695i
\(595\) −1.04175 + 0.139929i −0.0427077 + 0.00573653i
\(596\) −2.90036 + 1.67452i −0.118803 + 0.0685911i
\(597\) 29.8756 32.5608i 1.22273 1.33262i
\(598\) 0.665527 + 1.15273i 0.0272154 + 0.0471385i
\(599\) −3.72589 + 2.15114i −0.152236 + 0.0878932i −0.574183 0.818727i \(-0.694680\pi\)
0.421947 + 0.906620i \(0.361347\pi\)
\(600\) −26.5566 1.44745i −1.08417 0.0590920i
\(601\) −15.0355 + 8.68073i −0.613309 + 0.354094i −0.774260 0.632868i \(-0.781877\pi\)
0.160950 + 0.986963i \(0.448544\pi\)
\(602\) −15.4992 3.31103i −0.631702 0.134947i
\(603\) −0.464608 + 0.0400370i −0.0189203 + 0.00163043i
\(604\) −3.95788 6.85525i −0.161044 0.278936i
\(605\) −21.3506 18.1010i −0.868026 0.735910i
\(606\) −18.5959 17.0624i −0.755408 0.693112i
\(607\) 24.5149 0.995027 0.497514 0.867456i \(-0.334246\pi\)
0.497514 + 0.867456i \(0.334246\pi\)
\(608\) −14.4941 8.36818i −0.587814 0.339375i
\(609\) −36.2510 + 3.42931i −1.46897 + 0.138963i
\(610\) 30.3045 + 5.50245i 1.22699 + 0.222788i
\(611\) 9.18173 5.30107i 0.371453 0.214459i
\(612\) 0.124924 0.266991i 0.00504977 0.0107925i
\(613\) 5.95742 + 3.43952i 0.240618 + 0.138921i 0.615461 0.788168i \(-0.288970\pi\)
−0.374843 + 0.927088i \(0.622303\pi\)
\(614\) 10.3960 18.0064i 0.419549 0.726680i
\(615\) −0.268836 2.13663i −0.0108405 0.0861572i
\(616\) 38.5340 + 8.23183i 1.55258 + 0.331670i
\(617\) 13.5669 23.4986i 0.546184 0.946018i −0.452348 0.891842i \(-0.649413\pi\)
0.998531 0.0541761i \(-0.0172532\pi\)
\(618\) −11.6283 10.6694i −0.467760 0.429185i
\(619\) 7.46176i 0.299913i 0.988693 + 0.149957i \(0.0479134\pi\)
−0.988693 + 0.149957i \(0.952087\pi\)
\(620\) 1.79673 + 5.01565i 0.0721584 + 0.201433i
\(621\) −2.62207 + 3.40333i −0.105220 + 0.136571i
\(622\) 18.0278 0.722848
\(623\) −12.5782 + 4.07269i −0.503934 + 0.163169i
\(624\) −5.72276 + 1.80027i −0.229094 + 0.0720687i
\(625\) −23.6613 + 8.07118i −0.946451 + 0.322847i
\(626\) 8.10550 + 14.0391i 0.323961 + 0.561117i
\(627\) 44.2740 13.9278i 1.76813 0.556222i
\(628\) 1.04718 1.81376i 0.0417869 0.0723770i
\(629\) 1.46593 0.0584506
\(630\) −6.39305 + 20.3697i −0.254705 + 0.811547i
\(631\) 24.0063 0.955675 0.477838 0.878448i \(-0.341421\pi\)
0.477838 + 0.878448i \(0.341421\pi\)
\(632\) −18.8926 + 32.7229i −0.751505 + 1.30165i
\(633\) −0.119878 0.109992i −0.00476473 0.00437179i
\(634\) −0.471870 0.817302i −0.0187403 0.0324592i
\(635\) −11.7719 + 13.8853i −0.467153 + 0.551019i
\(636\) 0.885193 3.98056i 0.0351002 0.157839i
\(637\) −7.59026 + 5.49097i −0.300737 + 0.217560i
\(638\) 46.3526 1.83512
\(639\) −13.1382 + 28.0793i −0.519740 + 1.11080i
\(640\) −9.58094 + 3.43213i −0.378720 + 0.135667i
\(641\) 1.01519i 0.0400977i −0.999799 0.0200489i \(-0.993618\pi\)
0.999799 0.0200489i \(-0.00638218\pi\)
\(642\) 9.16222 41.2009i 0.361604 1.62607i
\(643\) 11.6653 20.2050i 0.460036 0.796806i −0.538926 0.842353i \(-0.681170\pi\)
0.998962 + 0.0455470i \(0.0145031\pi\)
\(644\) −1.15096 + 0.372669i −0.0453541 + 0.0146852i
\(645\) 7.48294 17.7764i 0.294640 0.699944i
\(646\) −0.590462 + 1.02271i −0.0232314 + 0.0402380i
\(647\) −7.50341 4.33210i −0.294990 0.170312i 0.345200 0.938529i \(-0.387811\pi\)
−0.640190 + 0.768217i \(0.721144\pi\)
\(648\) −17.7109 21.2193i −0.695751 0.833572i
\(649\) 9.41088 5.43338i 0.369409 0.213279i
\(650\) −6.21837 + 5.11103i −0.243905 + 0.200471i
\(651\) 19.6554 1.85939i 0.770358 0.0728752i
\(652\) −0.787370 0.454589i −0.0308358 0.0178031i
\(653\) 8.61151 0.336995 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(654\) −11.1139 + 3.49622i −0.434587 + 0.136713i
\(655\) 17.5547 + 14.8829i 0.685920 + 0.581522i
\(656\) −0.719521 1.24625i −0.0280926 0.0486578i
\(657\) 26.0134 18.1642i 1.01488 0.708654i
\(658\) −7.76656 23.9864i −0.302772 0.935088i
\(659\) 9.77598 5.64416i 0.380818 0.219865i −0.297356 0.954767i \(-0.596105\pi\)
0.678174 + 0.734901i \(0.262772\pi\)
\(660\) −4.02996 + 9.57352i −0.156866 + 0.372649i
\(661\) −25.6911 + 14.8328i −0.999268 + 0.576928i −0.908032 0.418901i \(-0.862415\pi\)
−0.0912365 + 0.995829i \(0.529082\pi\)
\(662\) −0.599026 1.03754i −0.0232818 0.0403253i
\(663\) −0.123587 0.392862i −0.00479972 0.0152575i
\(664\) −44.4782 + 25.6795i −1.72609 + 0.996558i
\(665\) −12.4307 + 30.2342i −0.482040 + 1.17243i
\(666\) 12.6187 26.9689i 0.488963 1.04502i
\(667\) −5.68964 + 3.28492i −0.220304 + 0.127192i
\(668\) 2.01789i 0.0780744i
\(669\) 17.2341 5.42153i 0.666308 0.209608i
\(670\) −0.270378 + 0.318918i −0.0104456 + 0.0123209i
\(671\) 27.7655 48.0912i 1.07187 1.85654i
\(672\) −1.30720 13.8184i −0.0504265 0.533055i
\(673\) −32.0418 + 18.4993i −1.23512 + 0.713097i −0.968093 0.250592i \(-0.919375\pi\)
−0.267027 + 0.963689i \(0.586041\pi\)
\(674\) 2.02228 1.16756i 0.0778953 0.0449729i
\(675\) −22.8981 12.2751i −0.881348 0.472467i
\(676\) −3.09945 + 5.36841i −0.119210 + 0.206477i
\(677\) −4.82344 2.78481i −0.185380 0.107029i 0.404438 0.914565i \(-0.367467\pi\)
−0.589818 + 0.807536i \(0.700800\pi\)
\(678\) 2.92192 0.919182i 0.112216 0.0353010i
\(679\) 7.66207 2.48090i 0.294043 0.0952083i
\(680\) −0.411455 1.14859i −0.0157786 0.0440466i
\(681\) 1.02856 + 0.228730i 0.0394144 + 0.00876495i
\(682\) −25.1326 −0.962376
\(683\) −4.18195 + 7.24335i −0.160018 + 0.277159i −0.934875 0.354977i \(-0.884489\pi\)
0.774857 + 0.632137i \(0.217822\pi\)
\(684\) −5.24847 7.51646i −0.200680 0.287399i
\(685\) −4.77571 4.04884i −0.182471 0.154698i
\(686\) 8.99883 + 20.3797i 0.343577 + 0.778099i
\(687\) 8.40316 + 1.86869i 0.320601 + 0.0712950i
\(688\) 12.8885i 0.491368i
\(689\) −2.84866 4.93402i −0.108525 0.187971i
\(690\) 0.480874 + 3.82185i 0.0183066 + 0.145495i
\(691\) 36.2384 + 20.9222i 1.37857 + 0.795920i 0.991988 0.126334i \(-0.0403210\pi\)
0.386586 + 0.922253i \(0.373654\pi\)
\(692\) 5.55882i 0.211315i
\(693\) 30.6870 + 23.2365i 1.16570 + 0.882682i
\(694\) −1.84187 −0.0699164
\(695\) 10.9042 + 30.4395i 0.413620 + 1.15464i
\(696\) −12.6833 40.3181i −0.480761 1.52825i
\(697\) 0.0855536 0.0493944i 0.00324057 0.00187095i
\(698\) 10.5295i 0.398548i
\(699\) 4.83537 1.52112i 0.182891 0.0575340i
\(700\) −3.36215 6.49761i −0.127077 0.245587i
\(701\) 15.3454i 0.579588i 0.957089 + 0.289794i \(0.0935868\pi\)
−0.957089 + 0.289794i \(0.906413\pi\)
\(702\) −8.29133 1.10809i −0.312936 0.0418222i
\(703\) 22.7956 39.4831i 0.859753 1.48914i
\(704\) 42.7710i 1.61199i
\(705\) 30.4419 3.83027i 1.14651 0.144256i
\(706\) 3.13744 + 1.81140i 0.118079 + 0.0681730i
\(707\) 6.69527 31.3412i 0.251802 1.17871i
\(708\) −1.58155 1.45112i −0.0594383 0.0545365i
\(709\) 21.9874 38.0833i 0.825753 1.43025i −0.0755890 0.997139i \(-0.524084\pi\)
0.901342 0.433107i \(-0.142583\pi\)
\(710\) 9.37360 + 26.1668i 0.351785 + 0.982022i
\(711\) −30.2633 + 21.1318i −1.13496 + 0.792505i
\(712\) −7.67315 13.2903i −0.287564 0.498075i
\(713\) 3.08495 1.78109i 0.115532 0.0667025i
\(714\) −0.975029 + 0.0922369i −0.0364895 + 0.00345188i
\(715\) 4.89419 + 13.6623i 0.183032 + 0.510942i
\(716\) 7.75387i 0.289776i
\(717\) −24.3334 + 26.5205i −0.908748 + 0.990427i
\(718\) 24.6896i 0.921409i
\(719\) −17.9724 31.1291i −0.670257 1.16092i −0.977831 0.209395i \(-0.932850\pi\)
0.307574 0.951524i \(-0.400483\pi\)
\(720\) −17.2853 1.62359i −0.644187 0.0605076i
\(721\) 4.18665 19.5981i 0.155919 0.729873i
\(722\) 6.93611 + 12.0137i 0.258135 + 0.447103i
\(723\) −4.01468 0.892782i −0.149308 0.0332029i
\(724\) 7.81096 4.50966i 0.290292 0.167600i
\(725\) −25.2271 30.6927i −0.936910 1.13990i
\(726\) −19.2174 17.6326i −0.713223 0.654406i
\(727\) 8.52472 + 14.7652i 0.316164 + 0.547612i 0.979684 0.200546i \(-0.0642716\pi\)
−0.663520 + 0.748158i \(0.730938\pi\)
\(728\) −8.07356 7.28442i −0.299226 0.269979i
\(729\) −6.88595 26.1072i −0.255035 0.966932i
\(730\) 5.08200 27.9889i 0.188093 1.03591i
\(731\) 0.884780 0.0327248
\(732\) −10.7070 2.38101i −0.395741 0.0880045i
\(733\) 28.3240 1.04617 0.523086 0.852280i \(-0.324781\pi\)
0.523086 + 0.852280i \(0.324781\pi\)
\(734\) 5.10485 8.84186i 0.188423 0.326359i
\(735\) −26.4102 + 6.12365i −0.974157 + 0.225874i
\(736\) −1.25216 2.16881i −0.0461553 0.0799433i
\(737\) 0.376913 + 0.652833i 0.0138838 + 0.0240474i
\(738\) −0.172272 1.99912i −0.00634140 0.0735886i
\(739\) −19.2000 + 33.2554i −0.706283 + 1.22332i 0.259943 + 0.965624i \(0.416296\pi\)
−0.966226 + 0.257695i \(0.917037\pi\)
\(740\) 3.44093 + 9.60551i 0.126491 + 0.353105i
\(741\) −12.5031 2.78042i −0.459311 0.102141i
\(742\) −12.8897 + 4.17355i −0.473195 + 0.153216i
\(743\) 16.8404 29.1685i 0.617815 1.07009i −0.372068 0.928205i \(-0.621351\pi\)
0.989884 0.141882i \(-0.0453154\pi\)
\(744\) 6.87696 + 21.8606i 0.252121 + 0.801450i
\(745\) −8.75667 + 10.3287i −0.320820 + 0.378415i
\(746\) 6.04725 + 3.49138i 0.221406 + 0.127829i
\(747\) −49.9857 + 4.30746i −1.82888 + 0.157602i
\(748\) −0.476501 −0.0174226
\(749\) 50.9914 16.5105i 1.86319 0.603281i
\(750\) −22.3245 + 6.65055i −0.815175 + 0.242844i
\(751\) −0.226011 −0.00824726 −0.00412363 0.999991i \(-0.501313\pi\)
−0.00412363 + 0.999991i \(0.501313\pi\)
\(752\) 17.7561 10.2515i 0.647497 0.373832i
\(753\) 3.93664 17.7024i 0.143459 0.645110i
\(754\) −11.0780 6.39590i −0.403438 0.232925i
\(755\) −24.4129 20.6972i −0.888475 0.753247i
\(756\) 2.55926 7.15926i 0.0930794 0.260380i
\(757\) 34.2892i 1.24626i 0.782117 + 0.623132i \(0.214140\pi\)
−0.782117 + 0.623132i \(0.785860\pi\)
\(758\) 20.0805 34.7804i 0.729356 1.26328i
\(759\) 6.77935 + 1.50759i 0.246075 + 0.0547219i
\(760\) −37.3342 6.77886i −1.35425 0.245895i
\(761\) −32.3061 −1.17110 −0.585548 0.810637i \(-0.699121\pi\)
−0.585548 + 0.810637i \(0.699121\pi\)
\(762\) −11.4672 + 12.4979i −0.415414 + 0.452752i
\(763\) −10.9847 9.91103i −0.397673 0.358804i
\(764\) 8.35013i 0.302097i
\(765\) 0.111458 1.18662i 0.00402976 0.0429024i
\(766\) −14.2729 8.24048i −0.515702 0.297741i
\(767\) −2.99887 −0.108283
\(768\) 20.0983 6.32256i 0.725236 0.228146i
\(769\) 27.8876 + 16.1009i 1.00565 + 0.580614i 0.909916 0.414793i \(-0.136146\pi\)
0.0957371 + 0.995407i \(0.469479\pi\)
\(770\) 34.2043 4.59435i 1.23264 0.165569i
\(771\) −16.8115 3.73853i −0.605451 0.134640i
\(772\) 0.816446 + 0.471375i 0.0293845 + 0.0169652i
\(773\) 2.36050 + 1.36284i 0.0849014 + 0.0490178i 0.541850 0.840475i \(-0.317724\pi\)
−0.456948 + 0.889493i \(0.651058\pi\)
\(774\) 7.61613 16.2774i 0.273756 0.585077i
\(775\) 13.6782 + 16.6417i 0.491336 + 0.597788i
\(776\) 4.67415 + 8.09587i 0.167792 + 0.290625i
\(777\) 37.6423 3.56093i 1.35041 0.127748i
\(778\) 1.16247 + 0.671154i 0.0416767 + 0.0240621i
\(779\) 3.07238i 0.110079i
\(780\) 2.28413 1.73195i 0.0817849 0.0620138i
\(781\) 50.1133 1.79320
\(782\) −0.153032 + 0.0883530i −0.00547241 + 0.00315950i
\(783\) 5.46933 40.9244i 0.195458 1.46252i
\(784\) −14.6784 + 10.6187i −0.524228 + 0.379239i
\(785\) 1.51283 8.33182i 0.0539951 0.297375i
\(786\) 15.8008 + 14.4977i 0.563594 + 0.517116i
\(787\) 10.9287 + 18.9291i 0.389566 + 0.674749i 0.992391 0.123125i \(-0.0392916\pi\)
−0.602825 + 0.797874i \(0.705958\pi\)
\(788\) −0.475945 0.824361i −0.0169548 0.0293666i
\(789\) −9.43646 + 42.4341i −0.335947 + 1.51069i
\(790\) −5.91228 + 32.5616i −0.210349 + 1.15849i
\(791\) 2.88796 + 2.60568i 0.102684 + 0.0926475i
\(792\) −18.9351 + 40.4685i −0.672831 + 1.43799i
\(793\) −13.2716 + 7.66237i −0.471289 + 0.272099i
\(794\) 33.4841 1.18831
\(795\) −2.05829 16.3587i −0.0730000 0.580182i
\(796\) 14.1096i 0.500101i
\(797\) 25.7774 + 14.8826i 0.913081 + 0.527167i 0.881421 0.472331i \(-0.156587\pi\)
0.0316595 + 0.999499i \(0.489921\pi\)
\(798\) −12.6776 + 27.6955i −0.448783 + 0.980411i
\(799\) 0.703752 + 1.21893i 0.0248970 + 0.0431228i
\(800\) 11.6996 9.61619i 0.413644 0.339984i
\(801\) −1.28709 14.9359i −0.0454770 0.527736i
\(802\) 25.5939 + 14.7766i 0.903751 + 0.521781i
\(803\) −44.4166 25.6439i −1.56743 0.904954i
\(804\) 0.100664 0.109712i 0.00355016 0.00386925i
\(805\) −3.87288 + 2.98793i −0.136501 + 0.105311i
\(806\) 6.00655 + 3.46788i 0.211572 + 0.122151i
\(807\) 9.96286 + 9.14125i 0.350709 + 0.321787i
\(808\) 37.2000 1.30869
\(809\) −47.4017 27.3674i −1.66655 0.962185i −0.969475 0.245190i \(-0.921150\pi\)
−0.697079 0.716995i \(-0.745517\pi\)
\(810\) −20.8709 12.2649i −0.733329 0.430943i
\(811\) 27.7732i 0.975250i −0.873053 0.487625i \(-0.837863\pi\)
0.873053 0.487625i \(-0.162137\pi\)
\(812\) 7.78841 8.63214i 0.273320 0.302929i
\(813\) 9.73064 + 30.9320i 0.341269 + 1.08483i
\(814\) −48.1316 −1.68701
\(815\) −3.61692 0.656732i −0.126695 0.0230043i
\(816\) −0.238998 0.759734i −0.00836661 0.0265960i
\(817\) 13.7585 23.8305i 0.481350 0.833723i
\(818\) 9.96869i 0.348547i
\(819\) −4.12778 9.78771i −0.144236 0.342010i
\(820\) 0.524473 + 0.444647i 0.0183154 + 0.0155277i
\(821\) 7.37054 + 4.25538i 0.257234 + 0.148514i 0.623072 0.782165i \(-0.285884\pi\)
−0.365838 + 0.930678i \(0.619218\pi\)
\(822\) −4.29855 3.94406i −0.149929 0.137565i
\(823\) 40.6898 23.4923i 1.41836 0.818889i 0.422202 0.906502i \(-0.361257\pi\)
0.996155 + 0.0876130i \(0.0279239\pi\)
\(824\) 23.2617 0.810360
\(825\) −2.28570 + 41.9359i −0.0795777 + 1.46002i
\(826\) −1.48984 + 6.97410i −0.0518383 + 0.242660i
\(827\) −41.3483 −1.43782 −0.718910 0.695103i \(-0.755359\pi\)
−0.718910 + 0.695103i \(0.755359\pi\)
\(828\) −0.117774 1.36671i −0.00409294 0.0474963i
\(829\) −25.5639 14.7593i −0.887871 0.512613i −0.0146257 0.999893i \(-0.504656\pi\)
−0.873246 + 0.487280i \(0.837989\pi\)
\(830\) −29.0891 + 34.3113i −1.00970 + 1.19096i
\(831\) 20.4748 + 4.55317i 0.710263 + 0.157948i
\(832\) 5.90169 10.2220i 0.204604 0.354385i
\(833\) −0.728962 1.00766i −0.0252571 0.0349132i
\(834\) 9.04070 + 28.7388i 0.313054 + 0.995144i
\(835\) −2.75150 7.68092i −0.0952196 0.265809i
\(836\) −7.40970 + 12.8340i −0.256270 + 0.443872i
\(837\) −2.96549 + 22.1894i −0.102502 + 0.766978i
\(838\) 10.4479 + 18.0963i 0.360916 + 0.625125i
\(839\) −17.1084 29.6327i −0.590649 1.02303i −0.994145 0.108053i \(-0.965539\pi\)
0.403496 0.914981i \(-0.367795\pi\)
\(840\) −13.3554 28.4942i −0.460807 0.983143i
\(841\) 17.0690 29.5643i 0.588585 1.01946i
\(842\) −22.9643 −0.791401
\(843\) −16.9245 53.8001i −0.582911 1.85297i
\(844\) 0.0519469 0.00178809
\(845\) −4.47770 + 24.6607i −0.154037 + 0.848354i
\(846\) 28.4827 2.45446i 0.979255 0.0843861i
\(847\) 6.91901 32.3886i 0.237740 1.11288i
\(848\) −5.50887 9.54164i −0.189175 0.327661i
\(849\) 50.1770 15.7847i 1.72207 0.541731i
\(850\) −0.678522 0.825529i −0.0232731 0.0283154i
\(851\) 5.90801 3.41099i 0.202524 0.116927i
\(852\) −2.97035 9.44222i −0.101762 0.323485i
\(853\) −8.99562 15.5809i −0.308004 0.533479i 0.669921 0.742432i \(-0.266328\pi\)
−0.977926 + 0.208953i \(0.932994\pi\)
\(854\) 11.2261 + 34.6708i 0.384148 + 1.18641i
\(855\) −30.2270 21.4542i −1.03374 0.733718i
\(856\) 31.1067 + 53.8783i 1.06320 + 1.84152i
\(857\) 38.1025i 1.30156i 0.759267 + 0.650779i \(0.225557\pi\)
−0.759267 + 0.650779i \(0.774443\pi\)
\(858\) 4.05778 + 12.8990i 0.138530 + 0.440364i
\(859\) 36.9289i 1.26000i 0.776596 + 0.629998i \(0.216944\pi\)
−0.776596 + 0.629998i \(0.783056\pi\)
\(860\) 2.07681 + 5.79751i 0.0708187 + 0.197693i
\(861\) 2.07686 1.47617i 0.0707793 0.0503078i
\(862\) 7.50408 4.33248i 0.255590 0.147565i
\(863\) −8.62089 14.9318i −0.293458 0.508285i 0.681167 0.732128i \(-0.261473\pi\)
−0.974625 + 0.223844i \(0.928140\pi\)
\(864\) 15.5998 + 2.08483i 0.530716 + 0.0709273i
\(865\) −7.57975 21.1592i −0.257719 0.719434i
\(866\) 8.76596 15.1831i 0.297879 0.515942i
\(867\) −28.0357 + 8.81951i −0.952142 + 0.299526i
\(868\) −4.22291 + 4.68038i −0.143335 + 0.158863i
\(869\) 51.6732 + 29.8335i 1.75289 + 1.01203i
\(870\) −22.3667 29.4976i −0.758302 1.00006i
\(871\) 0.208032i 0.00704888i
\(872\) 8.58662 14.8725i 0.290780 0.503645i
\(873\) 0.784037 + 9.09833i 0.0265356 + 0.307932i
\(874\) 5.49564i 0.185893i
\(875\) −21.6576 20.1482i −0.732161 0.681132i
\(876\) −2.19907 + 9.88883i −0.0742998 + 0.334113i
\(877\) 37.4385i 1.26421i 0.774883 + 0.632104i \(0.217809\pi\)
−0.774883 + 0.632104i \(0.782191\pi\)
\(878\) −42.9058 + 24.7717i −1.44800 + 0.836003i
\(879\) 33.1601 36.1405i 1.11846 1.21899i
\(880\) 9.46461 + 26.4208i 0.319052 + 0.890646i
\(881\) 13.5005 0.454845 0.227422 0.973796i \(-0.426970\pi\)
0.227422 + 0.973796i \(0.426970\pi\)
\(882\) −24.8128 + 4.73693i −0.835490 + 0.159501i
\(883\) 42.0832i 1.41621i −0.706106 0.708107i \(-0.749550\pi\)
0.706106 0.708107i \(-0.250450\pi\)
\(884\) 0.113881 + 0.0657493i 0.00383024 + 0.00221139i
\(885\) −7.99873 3.36705i −0.268874 0.113182i
\(886\) 11.2587 + 19.5007i 0.378245 + 0.655139i
\(887\) 0.117873i 0.00395779i 0.999998 + 0.00197889i \(0.000629902\pi\)
−0.999998 + 0.00197889i \(0.999370\pi\)
\(888\) 13.1701 + 41.8655i 0.441960 + 1.40491i
\(889\) −21.0637 4.49974i −0.706455 0.150917i
\(890\) −10.2524 8.69194i −0.343660 0.291355i
\(891\) −33.5077 + 27.9676i −1.12255 + 0.936950i
\(892\) −2.88430 + 4.99575i −0.0965735 + 0.167270i
\(893\) 43.7740 1.46484
\(894\) −8.53006 + 9.29674i −0.285288 + 0.310929i
\(895\) 10.5728 + 29.5145i 0.353411 + 0.986561i
\(896\) −8.94052 8.06664i −0.298682 0.269488i
\(897\) −1.41221 1.29574i −0.0471522 0.0432636i
\(898\) −30.5742 17.6520i −1.02028 0.589056i
\(899\) −17.1168 + 29.6472i −0.570878 + 0.988789i
\(900\) 8.03693 2.05499i 0.267898 0.0684996i
\(901\) 0.655024 0.378178i 0.0218220 0.0125989i
\(902\) −2.80902 + 1.62179i −0.0935300 + 0.0539996i
\(903\) 22.7194 2.14924i 0.756055 0.0715222i
\(904\) −2.25749 + 3.91008i −0.0750829 + 0.130047i
\(905\) 23.5826 27.8163i 0.783913 0.924646i
\(906\) −21.9737 20.1615i −0.730026 0.669822i
\(907\) 30.9106i 1.02637i 0.858278 + 0.513185i \(0.171534\pi\)
−0.858278 + 0.513185i \(0.828466\pi\)
\(908\) −0.291361 + 0.168217i −0.00966914 + 0.00558248i
\(909\) 32.9147 + 15.4007i 1.09171 + 0.510808i
\(910\) −8.80858 3.62160i −0.292001 0.120055i
\(911\) 1.06893 0.617149i 0.0354153 0.0204471i −0.482188 0.876068i \(-0.660158\pi\)
0.517603 + 0.855621i \(0.326824\pi\)
\(912\) −24.1790 5.37691i −0.800646 0.178047i
\(913\) 40.5509 + 70.2363i 1.34204 + 2.32448i
\(914\) 38.0761 21.9832i 1.25944 0.727140i
\(915\) −44.0018 + 5.53642i −1.45466 + 0.183028i
\(916\) −2.38038 + 1.37431i −0.0786498 + 0.0454085i
\(917\) −5.68890 + 26.6303i −0.187864 + 0.879410i
\(918\) 0.147106 1.10073i 0.00485523 0.0363294i
\(919\) 13.9885 + 24.2289i 0.461439 + 0.799236i 0.999033 0.0439676i \(-0.0139998\pi\)
−0.537594 + 0.843204i \(0.680667\pi\)
\(920\) −4.33084 3.67168i −0.142784 0.121052i
\(921\) −6.49892 + 29.2245i −0.214147 + 0.962979i
\(922\) 23.2388 0.765329
\(923\) −11.9768 6.91481i −0.394221 0.227604i
\(924\) −12.2356 + 1.15748i −0.402522 + 0.0380783i
\(925\) 26.1953 + 31.8707i 0.861295 + 1.04790i
\(926\) 33.3449 19.2517i 1.09578 0.632649i
\(927\) 20.5820 + 9.63028i 0.676003 + 0.316300i
\(928\) 20.8428 + 12.0336i 0.684200 + 0.395023i
\(929\) 16.1569 27.9846i 0.530091 0.918145i −0.469293 0.883043i \(-0.655491\pi\)
0.999384 0.0351021i \(-0.0111756\pi\)
\(930\) 12.1273 + 15.9937i 0.397670 + 0.524455i
\(931\) −38.4755 + 3.96444i −1.26098 + 0.129929i
\(932\) −0.809248 + 1.40166i −0.0265078 + 0.0459129i
\(933\) −24.7618 + 7.78960i −0.810665 + 0.255020i
\(934\) 24.0517i 0.786995i
\(935\) −1.81376 + 0.649735i −0.0593164 + 0.0212486i
\(936\) 10.1094 7.05903i 0.330436 0.230732i
\(937\) 10.8762 0.355309 0.177655 0.984093i \(-0.443149\pi\)
0.177655 + 0.984093i \(0.443149\pi\)
\(938\) −0.483794 0.103350i −0.0157964 0.00337451i
\(939\) −17.1994 15.7810i −0.561280 0.514992i
\(940\) −6.33516 + 7.47249i −0.206630 + 0.243726i
\(941\) 14.4640 + 25.0523i 0.471512 + 0.816682i 0.999469 0.0325890i \(-0.0103752\pi\)
−0.527957 + 0.849271i \(0.677042\pi\)
\(942\) 1.71278 7.70206i 0.0558054 0.250947i
\(943\) 0.229865 0.398139i 0.00748545 0.0129652i
\(944\) −5.79935 −0.188753
\(945\) −0.0204276 30.7408i −0.000664510 1.00000i
\(946\) −29.0503 −0.944508
\(947\) 7.48891 12.9712i 0.243357 0.421507i −0.718311 0.695722i \(-0.755085\pi\)
0.961668 + 0.274215i \(0.0884180\pi\)
\(948\) 2.55835 11.5044i 0.0830913 0.373647i
\(949\) 7.07688 + 12.2575i 0.229725 + 0.397896i
\(950\) −32.7858 + 5.43800i −1.06371 + 0.176432i
\(951\) 1.00128 + 0.918705i 0.0324687 + 0.0297910i
\(952\) 0.967055 1.07182i 0.0313424 0.0347378i
\(953\) −2.69591 −0.0873291 −0.0436645 0.999046i \(-0.513903\pi\)
−0.0436645 + 0.999046i \(0.513903\pi\)
\(954\) −1.31896 15.3058i −0.0427030 0.495545i
\(955\) 11.3859 + 31.7841i 0.368438 + 1.02851i
\(956\) 11.4922i 0.371683i
\(957\) −63.6670 + 20.0285i −2.05806 + 0.647428i
\(958\) 7.06805 12.2422i 0.228358 0.395528i
\(959\) 1.54765 7.24469i 0.0499761 0.233943i
\(960\) 27.2183 20.6384i 0.878468 0.666103i
\(961\) −6.21919 + 10.7720i −0.200619 + 0.347482i
\(962\) 11.5032 + 6.64137i 0.370878 + 0.214126i
\(963\) 5.21780 + 60.5498i 0.168141 + 1.95119i
\(964\) 1.13724 0.656588i 0.0366282 0.0211473i
\(965\) 3.75048 + 0.680983i 0.120732 + 0.0219216i
\(966\) −3.71494 + 2.64047i −0.119526 + 0.0849556i
\(967\) −40.4969 23.3809i −1.30229 0.751879i −0.321496 0.946911i \(-0.604186\pi\)
−0.980797 + 0.195031i \(0.937519\pi\)
\(968\) 38.4431 1.23561
\(969\) 0.369119 1.65986i 0.0118578 0.0533225i
\(970\) 6.24530 + 5.29475i 0.200525 + 0.170004i
\(971\) 2.32650 + 4.02961i 0.0746609 + 0.129316i 0.900939 0.433946i \(-0.142879\pi\)
−0.826278 + 0.563263i \(0.809546\pi\)
\(972\) 7.25567 + 4.65572i 0.232726 + 0.149332i
\(973\) −25.6285 + 28.4049i −0.821611 + 0.910618i
\(974\) 25.5070 14.7265i 0.817298 0.471867i
\(975\) 6.33274 9.70707i 0.202810 0.310875i
\(976\) −25.6652 + 14.8178i −0.821524 + 0.474307i
\(977\) −24.3981 42.2587i −0.780563 1.35197i −0.931614 0.363449i \(-0.881599\pi\)
0.151051 0.988526i \(-0.451734\pi\)
\(978\) −3.34353 0.743533i −0.106914 0.0237756i
\(979\) −20.9869 + 12.1168i −0.670744 + 0.387254i
\(980\) 4.89158 7.14175i 0.156256 0.228135i
\(981\) 13.7546 9.60436i 0.439151 0.306644i
\(982\) 1.37693 0.794974i 0.0439398 0.0253686i
\(983\) 14.5174i 0.463034i −0.972831 0.231517i \(-0.925631\pi\)
0.972831 0.231517i \(-0.0743688\pi\)
\(984\) 2.17927 + 1.99955i 0.0694727 + 0.0637435i
\(985\) −2.93571 2.48889i −0.0935394 0.0793025i
\(986\) 0.849097 1.47068i 0.0270408 0.0468360i
\(987\) 21.0319 + 29.5904i 0.669454 + 0.941872i
\(988\) 3.54176 2.04483i 0.112678 0.0650549i
\(989\) 3.56584 2.05874i 0.113387 0.0654641i
\(990\) −3.65954 + 38.9608i −0.116308 + 1.23826i
\(991\) −11.6281 + 20.1405i −0.369380 + 0.639785i −0.989469 0.144747i \(-0.953763\pi\)
0.620089 + 0.784532i \(0.287097\pi\)
\(992\) −11.3011 6.52468i −0.358810 0.207159i
\(993\) 1.27109 + 1.16627i 0.0403370 + 0.0370105i
\(994\) −22.0310 + 24.4177i −0.698782 + 0.774483i
\(995\) 19.2392 + 53.7070i 0.609924 + 1.70263i
\(996\) 10.8302 11.8036i 0.343167 0.374011i
\(997\) −22.5621 −0.714548 −0.357274 0.934000i \(-0.616294\pi\)
−0.357274 + 0.934000i \(0.616294\pi\)
\(998\) −10.5277 + 18.2345i −0.333248 + 0.577202i
\(999\) −5.67924 + 42.4951i −0.179683 + 1.34449i
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.u.a.59.15 88
3.2 odd 2 945.2.u.a.584.30 88
5.4 even 2 inner 315.2.u.a.59.30 yes 88
7.5 odd 6 315.2.bq.a.194.30 yes 88
9.2 odd 6 315.2.bq.a.164.15 yes 88
9.7 even 3 945.2.bq.a.899.30 88
15.14 odd 2 945.2.u.a.584.15 88
21.5 even 6 945.2.bq.a.719.15 88
35.19 odd 6 315.2.bq.a.194.15 yes 88
45.29 odd 6 315.2.bq.a.164.30 yes 88
45.34 even 6 945.2.bq.a.899.15 88
63.47 even 6 inner 315.2.u.a.299.30 yes 88
63.61 odd 6 945.2.u.a.89.15 88
105.89 even 6 945.2.bq.a.719.30 88
315.124 odd 6 945.2.u.a.89.30 88
315.299 even 6 inner 315.2.u.a.299.15 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.u.a.59.15 88 1.1 even 1 trivial
315.2.u.a.59.30 yes 88 5.4 even 2 inner
315.2.u.a.299.15 yes 88 315.299 even 6 inner
315.2.u.a.299.30 yes 88 63.47 even 6 inner
315.2.bq.a.164.15 yes 88 9.2 odd 6
315.2.bq.a.164.30 yes 88 45.29 odd 6
315.2.bq.a.194.15 yes 88 35.19 odd 6
315.2.bq.a.194.30 yes 88 7.5 odd 6
945.2.u.a.89.15 88 63.61 odd 6
945.2.u.a.89.30 88 315.124 odd 6
945.2.u.a.584.15 88 15.14 odd 2
945.2.u.a.584.30 88 3.2 odd 2
945.2.bq.a.719.15 88 21.5 even 6
945.2.bq.a.719.30 88 105.89 even 6
945.2.bq.a.899.15 88 45.34 even 6
945.2.bq.a.899.30 88 9.7 even 3