Properties

Label 361.2.e.i.28.2
Level $361$
Weight $2$
Character 361.28
Analytic conductor $2.883$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [361,2,Mod(28,361)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(361, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("361.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.e (of order \(9\), degree \(6\), not 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: \(2.88259951297\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.6053445140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 28.2
Root \(0.473442 - 0.397265i\) of defining polynomial
Character \(\chi\) \(=\) 361.28
Dual form 361.2.e.i.245.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.107320 + 0.608645i) q^{2} +(-2.00553 + 1.68284i) q^{3} +(1.52045 - 0.553400i) q^{4} +(1.16152 + 0.422760i) q^{5} +(-1.23949 - 1.04005i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(0.669258 - 3.79555i) q^{9} +O(q^{10})\) \(q+(0.107320 + 0.608645i) q^{2} +(-2.00553 + 1.68284i) q^{3} +(1.52045 - 0.553400i) q^{4} +(1.16152 + 0.422760i) q^{5} +(-1.23949 - 1.04005i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(0.669258 - 3.79555i) q^{9} +(-0.132655 + 0.752326i) q^{10} +(-0.309017 - 0.535233i) q^{11} +(-2.11803 + 3.66854i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-1.74229 - 0.634140i) q^{14} +(-3.04091 + 1.10680i) q^{15} +(1.42032 - 1.19179i) q^{16} +(0.909234 + 5.15652i) q^{17} +2.38197 q^{18} +2.00000 q^{20} +(-1.36385 - 7.73478i) q^{21} +(0.292603 - 0.245523i) q^{22} +(-7.15861 + 2.60552i) q^{23} +(-5.50106 - 2.00222i) q^{24} +(-2.65981 - 2.23185i) q^{25} +(-0.309017 + 0.535233i) q^{26} +(1.11803 + 1.93649i) q^{27} +(-0.842906 + 4.78036i) q^{28} +(0.239976 - 1.36097i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(-1.07295 + 1.85840i) q^{31} +(4.30366 + 3.61120i) q^{32} +(1.52045 + 0.553400i) q^{33} +(-3.04091 + 1.10680i) q^{34} +(-2.84065 + 2.38359i) q^{35} +(-1.08288 - 6.14133i) q^{36} -2.14590 q^{37} -2.61803 q^{39} +(0.479952 + 2.72194i) q^{40} +(2.29813 - 1.92836i) q^{41} +(4.56136 - 1.66020i) q^{42} +(6.44075 + 2.34424i) q^{43} +(-0.766044 - 0.642788i) q^{44} +(2.38197 - 4.12569i) q^{45} +(-2.35410 - 4.07742i) q^{46} +(0.520945 - 2.95442i) q^{47} +(-0.842906 + 4.78036i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(1.07295 - 1.85840i) q^{50} +(-10.5011 - 8.81146i) q^{51} +(1.52045 + 0.553400i) q^{52} +(8.76380 - 3.18976i) q^{53} +(-1.05865 + 0.888311i) q^{54} +(-0.132655 - 0.752326i) q^{55} -6.70820 q^{56} +0.854102 q^{58} +(2.66137 + 15.0934i) q^{59} +(-4.01106 + 3.36568i) q^{60} +(5.41632 - 1.97138i) q^{61} +(-1.24626 - 0.453600i) q^{62} +(8.85724 + 7.43211i) q^{63} +(0.118034 - 0.204441i) q^{64} +(0.618034 + 1.07047i) q^{65} +(-0.173648 + 0.984808i) q^{66} +(1.21554 - 6.89365i) q^{67} +(4.23607 + 7.33708i) q^{68} +(9.97214 - 17.2722i) q^{69} +(-1.75562 - 1.47314i) q^{70} +(1.38336 + 0.503500i) q^{71} +(8.09830 - 2.94754i) q^{72} +(8.20296 - 6.88310i) q^{73} +(-0.230299 - 1.30609i) q^{74} +9.09017 q^{75} +1.85410 q^{77} +(-0.280969 - 1.59345i) q^{78} +(10.2776 - 8.62390i) q^{79} +(2.15358 - 0.783840i) q^{80} +(5.36396 + 1.95232i) q^{81} +(1.42032 + 1.19179i) q^{82} +(0.236068 - 0.408882i) q^{83} +(-6.35410 - 11.0056i) q^{84} +(-1.12387 + 6.37381i) q^{85} +(-0.735585 + 4.17171i) q^{86} +(1.80902 + 3.13331i) q^{87} +(0.690983 - 1.19682i) q^{88} +(9.37337 + 7.86519i) q^{89} +(2.76671 + 1.00700i) q^{90} +(-2.81908 + 1.02606i) q^{91} +(-9.44245 + 7.92315i) q^{92} +(-0.975561 - 5.53268i) q^{93} +1.85410 q^{94} -14.7082 q^{96} +(-1.24087 - 7.03734i) q^{97} +(0.946883 - 0.794529i) q^{98} +(-2.23832 + 0.814680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65} + 24 q^{68} + 66 q^{69} + 42 q^{75} - 18 q^{77} - 24 q^{83} - 36 q^{84} + 15 q^{87} + 15 q^{88} - 18 q^{94} - 96 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.107320 + 0.608645i 0.0758870 + 0.430377i 0.998954 + 0.0457364i \(0.0145634\pi\)
−0.923067 + 0.384640i \(0.874325\pi\)
\(3\) −2.00553 + 1.68284i −1.15789 + 0.971588i −0.999874 0.0158480i \(-0.994955\pi\)
−0.158019 + 0.987436i \(0.550511\pi\)
\(4\) 1.52045 0.553400i 0.760227 0.276700i
\(5\) 1.16152 + 0.422760i 0.519449 + 0.189064i 0.588421 0.808555i \(-0.299750\pi\)
−0.0689720 + 0.997619i \(0.521972\pi\)
\(6\) −1.23949 1.04005i −0.506018 0.424600i
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) 1.11803 + 1.93649i 0.395285 + 0.684653i
\(9\) 0.669258 3.79555i 0.223086 1.26518i
\(10\) −0.132655 + 0.752326i −0.0419493 + 0.237906i
\(11\) −0.309017 0.535233i −0.0931721 0.161379i 0.815672 0.578514i \(-0.196367\pi\)
−0.908844 + 0.417136i \(0.863034\pi\)
\(12\) −2.11803 + 3.66854i −0.611424 + 1.05902i
\(13\) 0.766044 + 0.642788i 0.212463 + 0.178277i 0.742808 0.669504i \(-0.233493\pi\)
−0.530346 + 0.847781i \(0.677938\pi\)
\(14\) −1.74229 0.634140i −0.465646 0.169481i
\(15\) −3.04091 + 1.10680i −0.785159 + 0.285775i
\(16\) 1.42032 1.19179i 0.355081 0.297948i
\(17\) 0.909234 + 5.15652i 0.220522 + 1.25064i 0.871064 + 0.491170i \(0.163431\pi\)
−0.650542 + 0.759470i \(0.725458\pi\)
\(18\) 2.38197 0.561435
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) −1.36385 7.73478i −0.297617 1.68787i
\(22\) 0.292603 0.245523i 0.0623832 0.0523457i
\(23\) −7.15861 + 2.60552i −1.49267 + 0.543289i −0.954152 0.299323i \(-0.903239\pi\)
−0.538522 + 0.842612i \(0.681017\pi\)
\(24\) −5.50106 2.00222i −1.12290 0.408702i
\(25\) −2.65981 2.23185i −0.531962 0.446369i
\(26\) −0.309017 + 0.535233i −0.0606032 + 0.104968i
\(27\) 1.11803 + 1.93649i 0.215166 + 0.372678i
\(28\) −0.842906 + 4.78036i −0.159294 + 0.903403i
\(29\) 0.239976 1.36097i 0.0445624 0.252726i −0.954386 0.298576i \(-0.903488\pi\)
0.998948 + 0.0458498i \(0.0145996\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) −1.07295 + 1.85840i −0.192707 + 0.333779i −0.946147 0.323739i \(-0.895060\pi\)
0.753439 + 0.657518i \(0.228393\pi\)
\(32\) 4.30366 + 3.61120i 0.760787 + 0.638376i
\(33\) 1.52045 + 0.553400i 0.264677 + 0.0963346i
\(34\) −3.04091 + 1.10680i −0.521512 + 0.189815i
\(35\) −2.84065 + 2.38359i −0.480157 + 0.402900i
\(36\) −1.08288 6.14133i −0.180480 1.02355i
\(37\) −2.14590 −0.352783 −0.176392 0.984320i \(-0.556443\pi\)
−0.176392 + 0.984320i \(0.556443\pi\)
\(38\) 0 0
\(39\) −2.61803 −0.419221
\(40\) 0.479952 + 2.72194i 0.0758870 + 0.430377i
\(41\) 2.29813 1.92836i 0.358908 0.301160i −0.445447 0.895308i \(-0.646955\pi\)
0.804355 + 0.594149i \(0.202511\pi\)
\(42\) 4.56136 1.66020i 0.703834 0.256175i
\(43\) 6.44075 + 2.34424i 0.982205 + 0.357493i 0.782697 0.622403i \(-0.213843\pi\)
0.199508 + 0.979896i \(0.436066\pi\)
\(44\) −0.766044 0.642788i −0.115486 0.0969039i
\(45\) 2.38197 4.12569i 0.355083 0.615021i
\(46\) −2.35410 4.07742i −0.347093 0.601183i
\(47\) 0.520945 2.95442i 0.0759876 0.430947i −0.922952 0.384914i \(-0.874231\pi\)
0.998940 0.0460327i \(-0.0146579\pi\)
\(48\) −0.842906 + 4.78036i −0.121663 + 0.689985i
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 1.07295 1.85840i 0.151738 0.262818i
\(51\) −10.5011 8.81146i −1.47045 1.23385i
\(52\) 1.52045 + 0.553400i 0.210849 + 0.0767428i
\(53\) 8.76380 3.18976i 1.20380 0.438147i 0.339251 0.940696i \(-0.389826\pi\)
0.864549 + 0.502548i \(0.167604\pi\)
\(54\) −1.05865 + 0.888311i −0.144064 + 0.120884i
\(55\) −0.132655 0.752326i −0.0178873 0.101444i
\(56\) −6.70820 −0.896421
\(57\) 0 0
\(58\) 0.854102 0.112149
\(59\) 2.66137 + 15.0934i 0.346481 + 1.96499i 0.240671 + 0.970607i \(0.422632\pi\)
0.105810 + 0.994386i \(0.466256\pi\)
\(60\) −4.01106 + 3.36568i −0.517826 + 0.434507i
\(61\) 5.41632 1.97138i 0.693489 0.252409i 0.0288608 0.999583i \(-0.490812\pi\)
0.664628 + 0.747174i \(0.268590\pi\)
\(62\) −1.24626 0.453600i −0.158275 0.0576073i
\(63\) 8.85724 + 7.43211i 1.11591 + 0.936357i
\(64\) 0.118034 0.204441i 0.0147542 0.0255551i
\(65\) 0.618034 + 1.07047i 0.0766577 + 0.132775i
\(66\) −0.173648 + 0.984808i −0.0213746 + 0.121221i
\(67\) 1.21554 6.89365i 0.148502 0.842194i −0.815987 0.578070i \(-0.803806\pi\)
0.964489 0.264124i \(-0.0850828\pi\)
\(68\) 4.23607 + 7.33708i 0.513699 + 0.889752i
\(69\) 9.97214 17.2722i 1.20050 2.07933i
\(70\) −1.75562 1.47314i −0.209836 0.176074i
\(71\) 1.38336 + 0.503500i 0.164174 + 0.0597545i 0.422800 0.906223i \(-0.361047\pi\)
−0.258626 + 0.965978i \(0.583270\pi\)
\(72\) 8.09830 2.94754i 0.954394 0.347371i
\(73\) 8.20296 6.88310i 0.960084 0.805606i −0.0208829 0.999782i \(-0.506648\pi\)
0.980967 + 0.194176i \(0.0622033\pi\)
\(74\) −0.230299 1.30609i −0.0267717 0.151830i
\(75\) 9.09017 1.04964
\(76\) 0 0
\(77\) 1.85410 0.211295
\(78\) −0.280969 1.59345i −0.0318134 0.180423i
\(79\) 10.2776 8.62390i 1.15632 0.970265i 0.156468 0.987683i \(-0.449989\pi\)
0.999848 + 0.0174184i \(0.00554472\pi\)
\(80\) 2.15358 0.783840i 0.240778 0.0876360i
\(81\) 5.36396 + 1.95232i 0.595995 + 0.216925i
\(82\) 1.42032 + 1.19179i 0.156849 + 0.131612i
\(83\) 0.236068 0.408882i 0.0259118 0.0448806i −0.852779 0.522272i \(-0.825084\pi\)
0.878691 + 0.477392i \(0.158418\pi\)
\(84\) −6.35410 11.0056i −0.693289 1.20081i
\(85\) −1.12387 + 6.37381i −0.121901 + 0.691337i
\(86\) −0.735585 + 4.17171i −0.0793202 + 0.449847i
\(87\) 1.80902 + 3.13331i 0.193947 + 0.335926i
\(88\) 0.690983 1.19682i 0.0736590 0.127581i
\(89\) 9.37337 + 7.86519i 0.993575 + 0.833709i 0.986081 0.166263i \(-0.0531701\pi\)
0.00749401 + 0.999972i \(0.497615\pi\)
\(90\) 2.76671 + 1.00700i 0.291637 + 0.106147i
\(91\) −2.81908 + 1.02606i −0.295520 + 0.107560i
\(92\) −9.44245 + 7.92315i −0.984443 + 0.826046i
\(93\) −0.975561 5.53268i −0.101161 0.573713i
\(94\) 1.85410 0.191236
\(95\) 0 0
\(96\) −14.7082 −1.50115
\(97\) −1.24087 7.03734i −0.125991 0.714533i −0.980714 0.195448i \(-0.937384\pi\)
0.854723 0.519085i \(-0.173727\pi\)
\(98\) 0.946883 0.794529i 0.0956496 0.0802596i
\(99\) −2.23832 + 0.814680i −0.224959 + 0.0818785i
\(100\) −5.27923 1.92148i −0.527923 0.192148i
\(101\) 10.0967 + 8.47216i 1.00466 + 0.843011i 0.987623 0.156843i \(-0.0501318\pi\)
0.0170383 + 0.999855i \(0.494576\pi\)
\(102\) 4.23607 7.33708i 0.419433 0.726480i
\(103\) −0.663119 1.14856i −0.0653391 0.113171i 0.831505 0.555517i \(-0.187480\pi\)
−0.896844 + 0.442346i \(0.854146\pi\)
\(104\) −0.388289 + 2.20210i −0.0380749 + 0.215933i
\(105\) 1.68581 9.56071i 0.164518 0.933030i
\(106\) 2.88197 + 4.99171i 0.279921 + 0.484838i
\(107\) −5.20820 + 9.02087i −0.503496 + 0.872081i 0.496496 + 0.868039i \(0.334620\pi\)
−0.999992 + 0.00404164i \(0.998714\pi\)
\(108\) 2.77157 + 2.32563i 0.266695 + 0.223784i
\(109\) −15.7006 5.71454i −1.50384 0.547354i −0.546790 0.837270i \(-0.684150\pi\)
−0.957052 + 0.289916i \(0.906373\pi\)
\(110\) 0.443663 0.161480i 0.0423016 0.0153965i
\(111\) 4.30366 3.61120i 0.408486 0.342760i
\(112\) 0.965884 + 5.47780i 0.0912675 + 0.517604i
\(113\) −11.2361 −1.05700 −0.528500 0.848933i \(-0.677245\pi\)
−0.528500 + 0.848933i \(0.677245\pi\)
\(114\) 0 0
\(115\) −9.41641 −0.878085
\(116\) −0.388289 2.20210i −0.0360517 0.204460i
\(117\) 2.95241 2.47737i 0.272951 0.229033i
\(118\) −8.90090 + 3.23966i −0.819394 + 0.298235i
\(119\) −14.7609 5.37252i −1.35313 0.492498i
\(120\) −5.54315 4.65125i −0.506018 0.424600i
\(121\) 5.30902 9.19549i 0.482638 0.835953i
\(122\) 1.78115 + 3.08505i 0.161258 + 0.279307i
\(123\) −1.36385 + 7.73478i −0.122974 + 0.697422i
\(124\) −0.602930 + 3.41939i −0.0541447 + 0.307070i
\(125\) −5.23607 9.06914i −0.468328 0.811168i
\(126\) −3.57295 + 6.18853i −0.318304 + 0.551318i
\(127\) −7.84128 6.57962i −0.695801 0.583847i 0.224774 0.974411i \(-0.427836\pi\)
−0.920576 + 0.390564i \(0.872280\pi\)
\(128\) 10.6955 + 3.89286i 0.945362 + 0.344084i
\(129\) −16.8621 + 6.13730i −1.48463 + 0.540359i
\(130\) −0.585206 + 0.491046i −0.0513260 + 0.0430676i
\(131\) 0.678935 + 3.85043i 0.0593188 + 0.336414i 0.999996 0.00288963i \(-0.000919800\pi\)
−0.940677 + 0.339303i \(0.889809\pi\)
\(132\) 2.61803 0.227871
\(133\) 0 0
\(134\) 4.32624 0.373730
\(135\) 0.479952 + 2.72194i 0.0413077 + 0.234267i
\(136\) −8.96900 + 7.52589i −0.769086 + 0.645340i
\(137\) 1.38336 0.503500i 0.118188 0.0430169i −0.282249 0.959341i \(-0.591080\pi\)
0.400437 + 0.916324i \(0.368858\pi\)
\(138\) 11.5829 + 4.21582i 0.986000 + 0.358875i
\(139\) −7.50599 6.29827i −0.636650 0.534213i 0.266338 0.963880i \(-0.414186\pi\)
−0.902987 + 0.429667i \(0.858631\pi\)
\(140\) −3.00000 + 5.19615i −0.253546 + 0.439155i
\(141\) 3.92705 + 6.80185i 0.330717 + 0.572819i
\(142\) −0.157990 + 0.896008i −0.0132583 + 0.0751913i
\(143\) 0.107320 0.608645i 0.00897459 0.0508974i
\(144\) −3.57295 6.18853i −0.297746 0.515711i
\(145\) 0.854102 1.47935i 0.0709293 0.122853i
\(146\) 5.06971 + 4.25399i 0.419572 + 0.352063i
\(147\) 4.92029 + 1.79084i 0.405819 + 0.147706i
\(148\) −3.26274 + 1.18754i −0.268196 + 0.0976152i
\(149\) −10.0277 + 8.41420i −0.821497 + 0.689318i −0.953322 0.301955i \(-0.902361\pi\)
0.131825 + 0.991273i \(0.457916\pi\)
\(150\) 0.975561 + 5.53268i 0.0796543 + 0.451742i
\(151\) 9.90983 0.806451 0.403225 0.915101i \(-0.367889\pi\)
0.403225 + 0.915101i \(0.367889\pi\)
\(152\) 0 0
\(153\) 20.1803 1.63148
\(154\) 0.198983 + 1.12849i 0.0160345 + 0.0909363i
\(155\) −2.03191 + 1.70498i −0.163207 + 0.136947i
\(156\) −3.98060 + 1.44882i −0.318703 + 0.115998i
\(157\) 10.4737 + 3.81212i 0.835894 + 0.304240i 0.724275 0.689511i \(-0.242174\pi\)
0.111618 + 0.993751i \(0.464397\pi\)
\(158\) 6.35188 + 5.32986i 0.505329 + 0.424021i
\(159\) −12.2082 + 21.1452i −0.968174 + 1.67693i
\(160\) 3.47214 + 6.01392i 0.274496 + 0.475442i
\(161\) 3.96857 22.5069i 0.312767 1.77379i
\(162\) −0.612607 + 3.47427i −0.0481310 + 0.272964i
\(163\) −3.11803 5.40059i −0.244223 0.423007i 0.717690 0.696363i \(-0.245200\pi\)
−0.961913 + 0.273356i \(0.911866\pi\)
\(164\) 2.42705 4.20378i 0.189521 0.328260i
\(165\) 1.53209 + 1.28558i 0.119273 + 0.100082i
\(166\) 0.274199 + 0.0998001i 0.0212819 + 0.00774599i
\(167\) 14.8133 5.39158i 1.14628 0.417213i 0.302105 0.953275i \(-0.402311\pi\)
0.844179 + 0.536062i \(0.180089\pi\)
\(168\) 13.4535 11.2888i 1.03796 0.870952i
\(169\) −2.08378 11.8177i −0.160291 0.909053i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) 11.0902 0.845618
\(173\) −1.47117 8.34343i −0.111851 0.634339i −0.988261 0.152773i \(-0.951180\pi\)
0.876410 0.481565i \(-0.159932\pi\)
\(174\) −1.71293 + 1.43732i −0.129857 + 0.108963i
\(175\) 9.78822 3.56262i 0.739920 0.269309i
\(176\) −1.07679 0.391920i −0.0811662 0.0295421i
\(177\) −30.7372 25.7916i −2.31035 1.93862i
\(178\) −3.78115 + 6.54915i −0.283409 + 0.490879i
\(179\) 3.88197 + 6.72376i 0.290152 + 0.502558i 0.973845 0.227212i \(-0.0729609\pi\)
−0.683694 + 0.729769i \(0.739628\pi\)
\(180\) 1.33852 7.59110i 0.0997671 0.565807i
\(181\) −2.08378 + 11.8177i −0.154886 + 0.878402i 0.804004 + 0.594624i \(0.202699\pi\)
−0.958890 + 0.283778i \(0.908412\pi\)
\(182\) −0.927051 1.60570i −0.0687176 0.119022i
\(183\) −7.54508 + 13.0685i −0.557749 + 0.966049i
\(184\) −13.0491 10.9495i −0.961995 0.807210i
\(185\) −2.49251 0.907200i −0.183253 0.0666987i
\(186\) 3.26274 1.18754i 0.239236 0.0870747i
\(187\) 2.47897 2.08010i 0.181280 0.152112i
\(188\) −0.842906 4.78036i −0.0614752 0.348643i
\(189\) −6.70820 −0.487950
\(190\) 0 0
\(191\) 9.76393 0.706493 0.353247 0.935530i \(-0.385078\pi\)
0.353247 + 0.935530i \(0.385078\pi\)
\(192\) 0.107320 + 0.608645i 0.00774519 + 0.0439251i
\(193\) −17.5763 + 14.7483i −1.26517 + 1.06161i −0.270061 + 0.962843i \(0.587044\pi\)
−0.995111 + 0.0987622i \(0.968512\pi\)
\(194\) 4.15007 1.51050i 0.297957 0.108448i
\(195\) −3.04091 1.10680i −0.217764 0.0792596i
\(196\) −2.47897 2.08010i −0.177069 0.148579i
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) −0.736068 1.27491i −0.0523101 0.0906037i
\(199\) 2.32973 13.2126i 0.165151 0.936615i −0.783759 0.621066i \(-0.786700\pi\)
0.948909 0.315550i \(-0.102189\pi\)
\(200\) 1.34819 7.64598i 0.0953316 0.540652i
\(201\) 9.16312 + 15.8710i 0.646317 + 1.11945i
\(202\) −4.07295 + 7.05455i −0.286572 + 0.496357i
\(203\) 3.17594 + 2.66493i 0.222907 + 0.187042i
\(204\) −20.8427 7.58612i −1.45928 0.531135i
\(205\) 3.48457 1.26828i 0.243373 0.0885805i
\(206\) 0.627896 0.526867i 0.0437476 0.0367086i
\(207\) 5.09843 + 28.9146i 0.354365 + 2.00971i
\(208\) 1.85410 0.128559
\(209\) 0 0
\(210\) 6.00000 0.414039
\(211\) −0.495610 2.81074i −0.0341192 0.193499i 0.962984 0.269558i \(-0.0868776\pi\)
−0.997103 + 0.0760584i \(0.975766\pi\)
\(212\) 11.5597 9.69977i 0.793926 0.666183i
\(213\) −3.62167 + 1.31818i −0.248153 + 0.0903202i
\(214\) −6.04945 2.20182i −0.413532 0.150513i
\(215\) 6.49003 + 5.44578i 0.442617 + 0.371399i
\(216\) −2.50000 + 4.33013i −0.170103 + 0.294628i
\(217\) −3.21885 5.57521i −0.218510 0.378470i
\(218\) 1.79313 10.1694i 0.121446 0.688756i
\(219\) −4.86813 + 27.6085i −0.328958 + 1.86561i
\(220\) −0.618034 1.07047i −0.0416678 0.0721708i
\(221\) −2.61803 + 4.53457i −0.176108 + 0.305028i
\(222\) 2.65981 + 2.23185i 0.178515 + 0.149792i
\(223\) 18.4673 + 6.72154i 1.23666 + 0.450108i 0.875874 0.482540i \(-0.160286\pi\)
0.360787 + 0.932648i \(0.382508\pi\)
\(224\) −15.8377 + 5.76444i −1.05820 + 0.385153i
\(225\) −10.2512 + 8.60176i −0.683412 + 0.573451i
\(226\) −1.20586 6.83877i −0.0802126 0.454908i
\(227\) 10.4164 0.691361 0.345681 0.938352i \(-0.387648\pi\)
0.345681 + 0.938352i \(0.387648\pi\)
\(228\) 0 0
\(229\) −11.3820 −0.752141 −0.376071 0.926591i \(-0.622725\pi\)
−0.376071 + 0.926591i \(0.622725\pi\)
\(230\) −1.01057 5.73125i −0.0666352 0.377907i
\(231\) −3.71846 + 3.12016i −0.244657 + 0.205291i
\(232\) 2.90381 1.05690i 0.190644 0.0693889i
\(233\) −12.6597 4.60774i −0.829362 0.301863i −0.107765 0.994176i \(-0.534369\pi\)
−0.721597 + 0.692313i \(0.756592\pi\)
\(234\) 1.82469 + 1.53110i 0.119284 + 0.100091i
\(235\) 1.85410 3.21140i 0.120948 0.209489i
\(236\) 12.3992 + 21.4760i 0.807118 + 1.39797i
\(237\) −6.09932 + 34.5910i −0.396194 + 2.24693i
\(238\) 1.68581 9.56071i 0.109275 0.619729i
\(239\) −7.66312 13.2729i −0.495686 0.858553i 0.504302 0.863528i \(-0.331750\pi\)
−0.999988 + 0.00497428i \(0.998417\pi\)
\(240\) −3.00000 + 5.19615i −0.193649 + 0.335410i
\(241\) 14.6930 + 12.3289i 0.946459 + 0.794173i 0.978698 0.205307i \(-0.0658193\pi\)
−0.0322388 + 0.999480i \(0.510264\pi\)
\(242\) 6.16655 + 2.24444i 0.396401 + 0.144278i
\(243\) −20.3467 + 7.40558i −1.30524 + 0.475068i
\(244\) 7.14431 5.99479i 0.457368 0.383777i
\(245\) −0.429282 2.43458i −0.0274258 0.155540i
\(246\) −4.85410 −0.309486
\(247\) 0 0
\(248\) −4.79837 −0.304697
\(249\) 0.214641 + 1.21729i 0.0136023 + 0.0771426i
\(250\) 4.95794 4.16021i 0.313568 0.263115i
\(251\) −18.1931 + 6.62174i −1.14834 + 0.417961i −0.844918 0.534896i \(-0.820351\pi\)
−0.303420 + 0.952857i \(0.598128\pi\)
\(252\) 17.5800 + 6.39858i 1.10743 + 0.403073i
\(253\) 3.60669 + 3.02638i 0.226751 + 0.190267i
\(254\) 3.16312 5.47868i 0.198472 0.343763i
\(255\) −8.47214 14.6742i −0.530546 0.918932i
\(256\) −1.13953 + 6.46261i −0.0712208 + 0.403913i
\(257\) 4.23019 23.9906i 0.263872 1.49649i −0.508357 0.861147i \(-0.669747\pi\)
0.772228 0.635345i \(-0.219142\pi\)
\(258\) −5.54508 9.60437i −0.345222 0.597942i
\(259\) 3.21885 5.57521i 0.200009 0.346426i
\(260\) 1.53209 + 1.28558i 0.0950161 + 0.0797280i
\(261\) −5.00503 1.82168i −0.309803 0.112759i
\(262\) −2.27068 + 0.826460i −0.140283 + 0.0510589i
\(263\) 2.25544 1.89254i 0.139077 0.116699i −0.570595 0.821231i \(-0.693288\pi\)
0.709672 + 0.704532i \(0.248843\pi\)
\(264\) 0.628265 + 3.56307i 0.0386670 + 0.219292i
\(265\) 11.5279 0.708151
\(266\) 0 0
\(267\) −32.0344 −1.96048
\(268\) −1.96678 11.1542i −0.120140 0.681349i
\(269\) −11.2408 + 9.43211i −0.685361 + 0.575086i −0.917567 0.397580i \(-0.869850\pi\)
0.232206 + 0.972667i \(0.425406\pi\)
\(270\) −1.60519 + 0.584240i −0.0976885 + 0.0355557i
\(271\) −7.38044 2.68626i −0.448330 0.163179i 0.107981 0.994153i \(-0.465561\pi\)
−0.556311 + 0.830974i \(0.687784\pi\)
\(272\) 7.43692 + 6.24031i 0.450929 + 0.378375i
\(273\) 3.92705 6.80185i 0.237676 0.411667i
\(274\) 0.454915 + 0.787936i 0.0274824 + 0.0476010i
\(275\) −0.372631 + 2.11330i −0.0224705 + 0.127437i
\(276\) 5.60372 31.7802i 0.337304 1.91295i
\(277\) 7.70820 + 13.3510i 0.463141 + 0.802184i 0.999115 0.0420503i \(-0.0133890\pi\)
−0.535974 + 0.844234i \(0.680056\pi\)
\(278\) 3.02786 5.24441i 0.181599 0.314539i
\(279\) 6.33558 + 5.31618i 0.379301 + 0.318271i
\(280\) −7.79174 2.83596i −0.465646 0.169481i
\(281\) 7.99357 2.90942i 0.476856 0.173562i −0.0923994 0.995722i \(-0.529454\pi\)
0.569256 + 0.822161i \(0.307231\pi\)
\(282\) −3.71846 + 3.12016i −0.221431 + 0.185803i
\(283\) −0.526925 2.98834i −0.0313225 0.177638i 0.965133 0.261760i \(-0.0843028\pi\)
−0.996456 + 0.0841213i \(0.973192\pi\)
\(284\) 2.38197 0.141344
\(285\) 0 0
\(286\) 0.381966 0.0225861
\(287\) 1.56283 + 8.86327i 0.0922512 + 0.523182i
\(288\) 16.5868 13.9179i 0.977384 0.820123i
\(289\) −9.78822 + 3.56262i −0.575778 + 0.209566i
\(290\) 0.992060 + 0.361080i 0.0582558 + 0.0212034i
\(291\) 14.3313 + 12.0254i 0.840117 + 0.704942i
\(292\) 8.66312 15.0050i 0.506971 0.878099i
\(293\) −8.42705 14.5961i −0.492314 0.852712i 0.507647 0.861565i \(-0.330515\pi\)
−0.999961 + 0.00885289i \(0.997182\pi\)
\(294\) −0.561937 + 3.18690i −0.0327728 + 0.185864i
\(295\) −3.28964 + 18.6565i −0.191530 + 1.08622i
\(296\) −2.39919 4.15551i −0.139450 0.241534i
\(297\) 0.690983 1.19682i 0.0400949 0.0694464i
\(298\) −6.19743 5.20026i −0.359007 0.301243i
\(299\) −7.15861 2.60552i −0.413993 0.150681i
\(300\) 13.8212 5.03050i 0.797967 0.290436i
\(301\) −15.7516 + 13.2172i −0.907909 + 0.761826i
\(302\) 1.06353 + 6.03157i 0.0611991 + 0.347078i
\(303\) −34.5066 −1.98235
\(304\) 0 0
\(305\) 7.12461 0.407954
\(306\) 2.16576 + 12.2827i 0.123808 + 0.702153i
\(307\) 1.28218 1.07587i 0.0731777 0.0614033i −0.605465 0.795872i \(-0.707013\pi\)
0.678643 + 0.734468i \(0.262568\pi\)
\(308\) 2.81908 1.02606i 0.160632 0.0584652i
\(309\) 3.26274 + 1.18754i 0.185611 + 0.0675568i
\(310\) −1.25579 1.05373i −0.0713242 0.0598481i
\(311\) 9.32624 16.1535i 0.528842 0.915982i −0.470592 0.882351i \(-0.655960\pi\)
0.999434 0.0336310i \(-0.0107071\pi\)
\(312\) −2.92705 5.06980i −0.165712 0.287021i
\(313\) 0.751243 4.26051i 0.0424628 0.240818i −0.956188 0.292755i \(-0.905428\pi\)
0.998650 + 0.0519361i \(0.0165392\pi\)
\(314\) −1.19618 + 6.78389i −0.0675045 + 0.382837i
\(315\) 7.14590 + 12.3771i 0.402626 + 0.697368i
\(316\) 10.8541 18.7999i 0.610591 1.05757i
\(317\) −13.7888 11.5702i −0.774456 0.649846i 0.167390 0.985891i \(-0.446466\pi\)
−0.941846 + 0.336045i \(0.890911\pi\)
\(318\) −14.1801 5.16114i −0.795182 0.289422i
\(319\) −0.802593 + 0.292120i −0.0449366 + 0.0163556i
\(320\) 0.223529 0.187563i 0.0124956 0.0104851i
\(321\) −4.73547 26.8562i −0.264308 1.49897i
\(322\) 14.1246 0.787134
\(323\) 0 0
\(324\) 9.23607 0.513115
\(325\) −0.602930 3.41939i −0.0334445 0.189673i
\(326\) 2.95241 2.47737i 0.163519 0.137209i
\(327\) 41.1046 14.9609i 2.27309 0.827338i
\(328\) 6.30365 + 2.29434i 0.348061 + 0.126684i
\(329\) 6.89440 + 5.78509i 0.380101 + 0.318942i
\(330\) −0.618034 + 1.07047i −0.0340217 + 0.0589272i
\(331\) −3.47214 6.01392i −0.190846 0.330555i 0.754685 0.656087i \(-0.227790\pi\)
−0.945531 + 0.325533i \(0.894456\pi\)
\(332\) 0.132655 0.752326i 0.00728041 0.0412893i
\(333\) −1.43616 + 8.14486i −0.0787010 + 0.446336i
\(334\) 4.87132 + 8.43738i 0.266547 + 0.461673i
\(335\) 4.32624 7.49326i 0.236368 0.409401i
\(336\) −11.1554 9.36047i −0.608576 0.510655i
\(337\) 21.7300 + 7.90908i 1.18371 + 0.430835i 0.857511 0.514466i \(-0.172010\pi\)
0.326199 + 0.945301i \(0.394232\pi\)
\(338\) 6.96914 2.53656i 0.379071 0.137971i
\(339\) 22.5343 18.9085i 1.22389 1.02697i
\(340\) 1.81847 + 10.3130i 0.0986202 + 0.559303i
\(341\) 1.32624 0.0718198
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 2.66137 + 15.0934i 0.143492 + 0.813781i
\(345\) 18.8849 15.8463i 1.01673 0.853136i
\(346\) 4.92029 1.79084i 0.264517 0.0962762i
\(347\) −1.33099 0.484440i −0.0714512 0.0260061i 0.306047 0.952016i \(-0.400993\pi\)
−0.377498 + 0.926010i \(0.623216\pi\)
\(348\) 4.48450 + 3.76294i 0.240395 + 0.201715i
\(349\) −12.9894 + 22.4982i −0.695304 + 1.20430i 0.274774 + 0.961509i \(0.411397\pi\)
−0.970078 + 0.242793i \(0.921936\pi\)
\(350\) 3.21885 + 5.57521i 0.172055 + 0.298007i
\(351\) −0.388289 + 2.20210i −0.0207253 + 0.117539i
\(352\) 0.602930 3.41939i 0.0321363 0.182254i
\(353\) 15.7254 + 27.2372i 0.836980 + 1.44969i 0.892408 + 0.451229i \(0.149014\pi\)
−0.0554283 + 0.998463i \(0.517652\pi\)
\(354\) 12.3992 21.4760i 0.659009 1.14144i
\(355\) 1.39394 + 1.16965i 0.0739827 + 0.0620788i
\(356\) 18.6044 + 6.77144i 0.986030 + 0.358886i
\(357\) 38.6445 14.0654i 2.04528 0.744422i
\(358\) −3.67577 + 3.08434i −0.194270 + 0.163012i
\(359\) −3.82624 21.6997i −0.201941 1.14527i −0.902181 0.431358i \(-0.858035\pi\)
0.700240 0.713908i \(-0.253076\pi\)
\(360\) 10.6525 0.561435
\(361\) 0 0
\(362\) −7.41641 −0.389798
\(363\) 4.82714 + 27.3761i 0.253359 + 1.43687i
\(364\) −3.71846 + 3.12016i −0.194900 + 0.163541i
\(365\) 12.4378 4.52700i 0.651026 0.236954i
\(366\) −8.76380 3.18976i −0.458091 0.166731i
\(367\) 1.48940 + 1.24975i 0.0777460 + 0.0652366i 0.680832 0.732439i \(-0.261618\pi\)
−0.603086 + 0.797676i \(0.706063\pi\)
\(368\) −7.06231 + 12.2323i −0.368148 + 0.637651i
\(369\) −5.78115 10.0133i −0.300955 0.521269i
\(370\) 0.284665 1.61442i 0.0147990 0.0839295i
\(371\) −4.85845 + 27.5537i −0.252238 + 1.43051i
\(372\) −4.54508 7.87232i −0.235652 0.408161i
\(373\) 1.73607 3.00696i 0.0898902 0.155694i −0.817574 0.575823i \(-0.804682\pi\)
0.907465 + 0.420129i \(0.138015\pi\)
\(374\) 1.53209 + 1.28558i 0.0792224 + 0.0664755i
\(375\) 25.7630 + 9.37696i 1.33040 + 0.484224i
\(376\) 6.30365 2.29434i 0.325086 0.118322i
\(377\) 1.05865 0.888311i 0.0545231 0.0457503i
\(378\) −0.719928 4.08291i −0.0370291 0.210002i
\(379\) −25.1246 −1.29056 −0.645282 0.763944i \(-0.723260\pi\)
−0.645282 + 0.763944i \(0.723260\pi\)
\(380\) 0 0
\(381\) 26.7984 1.37292
\(382\) 1.04787 + 5.94277i 0.0536137 + 0.304058i
\(383\) −2.00553 + 1.68284i −0.102478 + 0.0859891i −0.692587 0.721334i \(-0.743529\pi\)
0.590109 + 0.807323i \(0.299085\pi\)
\(384\) −28.0013 + 10.1916i −1.42894 + 0.520090i
\(385\) 2.15358 + 0.783840i 0.109757 + 0.0399482i
\(386\) −10.8628 9.11495i −0.552900 0.463939i
\(387\) 13.2082 22.8773i 0.671411 1.16292i
\(388\) −5.78115 10.0133i −0.293494 0.508346i
\(389\) −4.21453 + 23.9018i −0.213685 + 1.21187i 0.669488 + 0.742822i \(0.266513\pi\)
−0.883174 + 0.469046i \(0.844598\pi\)
\(390\) 0.347296 1.96962i 0.0175860 0.0997354i
\(391\) −19.9443 34.5445i −1.00863 1.74699i
\(392\) 2.23607 3.87298i 0.112938 0.195615i
\(393\) −7.84128 6.57962i −0.395540 0.331898i
\(394\) −1.74229 0.634140i −0.0877751 0.0319475i
\(395\) 15.5835 5.67192i 0.784090 0.285385i
\(396\) −2.95241 + 2.47737i −0.148364 + 0.124492i
\(397\) −0.438959 2.48946i −0.0220307 0.124942i 0.971809 0.235770i \(-0.0757611\pi\)
−0.993840 + 0.110827i \(0.964650\pi\)
\(398\) 8.29180 0.415630
\(399\) 0 0
\(400\) −6.43769 −0.321885
\(401\) 0.0193542 + 0.109763i 0.000966501 + 0.00548130i 0.985287 0.170907i \(-0.0546697\pi\)
−0.984321 + 0.176388i \(0.943559\pi\)
\(402\) −8.67640 + 7.28037i −0.432740 + 0.363112i
\(403\) −2.01648 + 0.733940i −0.100448 + 0.0365602i
\(404\) 20.0401 + 7.29400i 0.997033 + 0.362890i
\(405\) 5.40500 + 4.53533i 0.268577 + 0.225363i
\(406\) −1.28115 + 2.21902i −0.0635826 + 0.110128i
\(407\) 0.663119 + 1.14856i 0.0328696 + 0.0569318i
\(408\) 5.32275 30.1868i 0.263515 1.49447i
\(409\) 3.76959 21.3784i 0.186394 1.05709i −0.737757 0.675067i \(-0.764115\pi\)
0.924151 0.382028i \(-0.124774\pi\)
\(410\) 1.14590 + 1.98475i 0.0565919 + 0.0980200i
\(411\) −1.92705 + 3.33775i −0.0950544 + 0.164639i
\(412\) −1.64385 1.37936i −0.0809868 0.0679560i
\(413\) −43.2059 15.7256i −2.12602 0.773808i
\(414\) −17.0516 + 6.20626i −0.838039 + 0.305021i
\(415\) 0.447058 0.375126i 0.0219452 0.0184142i
\(416\) 0.975561 + 5.53268i 0.0478308 + 0.271262i
\(417\) 25.6525 1.25621
\(418\) 0 0
\(419\) 8.94427 0.436956 0.218478 0.975842i \(-0.429891\pi\)
0.218478 + 0.975842i \(0.429891\pi\)
\(420\) −2.72770 15.4696i −0.133098 0.754837i
\(421\) 14.1932 11.9095i 0.691733 0.580433i −0.227676 0.973737i \(-0.573113\pi\)
0.919408 + 0.393304i \(0.128668\pi\)
\(422\) 1.65755 0.603300i 0.0806885 0.0293682i
\(423\) −10.8650 3.95454i −0.528275 0.192276i
\(424\) 15.9752 + 13.4048i 0.775823 + 0.650993i
\(425\) 9.09017 15.7446i 0.440938 0.763727i
\(426\) −1.19098 2.06284i −0.0577033 0.0999451i
\(427\) −3.00269 + 17.0291i −0.145310 + 0.824096i
\(428\) −2.92668 + 16.5981i −0.141467 + 0.802297i
\(429\) 0.809017 + 1.40126i 0.0390597 + 0.0676534i
\(430\) −2.61803 + 4.53457i −0.126253 + 0.218676i
\(431\) 2.79796 + 2.34777i 0.134773 + 0.113088i 0.707682 0.706531i \(-0.249741\pi\)
−0.572909 + 0.819619i \(0.694185\pi\)
\(432\) 3.89587 + 1.41798i 0.187440 + 0.0682226i
\(433\) −22.1413 + 8.05878i −1.06404 + 0.387280i −0.813946 0.580940i \(-0.802685\pi\)
−0.250098 + 0.968221i \(0.580463\pi\)
\(434\) 3.04787 2.55747i 0.146303 0.122762i
\(435\) 0.776578 + 4.40419i 0.0372341 + 0.211165i
\(436\) −27.0344 −1.29471
\(437\) 0 0
\(438\) −17.3262 −0.827880
\(439\) −2.53470 14.3750i −0.120975 0.686081i −0.983618 0.180268i \(-0.942304\pi\)
0.862643 0.505813i \(-0.168807\pi\)
\(440\) 1.30856 1.09801i 0.0623832 0.0523457i
\(441\) −7.24334 + 2.63636i −0.344921 + 0.125541i
\(442\) −3.04091 1.10680i −0.144641 0.0526451i
\(443\) −26.3645 22.1224i −1.25262 1.05107i −0.996428 0.0844415i \(-0.973089\pi\)
−0.256187 0.966627i \(-0.582466\pi\)
\(444\) 4.54508 7.87232i 0.215700 0.373604i
\(445\) 7.56231 + 13.0983i 0.358488 + 0.620919i
\(446\) −2.10911 + 11.9614i −0.0998694 + 0.566388i
\(447\) 5.95101 33.7499i 0.281473 1.59631i
\(448\) 0.354102 + 0.613323i 0.0167297 + 0.0289768i
\(449\) −16.4443 + 28.4823i −0.776053 + 1.34416i 0.158147 + 0.987416i \(0.449448\pi\)
−0.934201 + 0.356748i \(0.883885\pi\)
\(450\) −6.33558 5.31618i −0.298662 0.250607i
\(451\) −1.74229 0.634140i −0.0820410 0.0298605i
\(452\) −17.0839 + 6.21804i −0.803561 + 0.292472i
\(453\) −19.8745 + 16.6767i −0.933784 + 0.783538i
\(454\) 1.11789 + 6.33989i 0.0524654 + 0.297546i
\(455\) −3.70820 −0.173843
\(456\) 0 0
\(457\) 6.29180 0.294318 0.147159 0.989113i \(-0.452987\pi\)
0.147159 + 0.989113i \(0.452987\pi\)
\(458\) −1.22152 6.92757i −0.0570778 0.323704i
\(459\) −8.96900 + 7.52589i −0.418637 + 0.351278i
\(460\) −14.3172 + 5.21104i −0.667544 + 0.242966i
\(461\) −2.87145 1.04512i −0.133737 0.0486761i 0.274285 0.961648i \(-0.411559\pi\)
−0.408021 + 0.912972i \(0.633781\pi\)
\(462\) −2.29813 1.92836i −0.106919 0.0897156i
\(463\) 2.63525 4.56440i 0.122471 0.212125i −0.798271 0.602299i \(-0.794252\pi\)
0.920741 + 0.390173i \(0.127585\pi\)
\(464\) −1.28115 2.21902i −0.0594760 0.103016i
\(465\) 1.20586 6.83877i 0.0559204 0.317140i
\(466\) 1.44584 8.19974i 0.0669771 0.379846i
\(467\) −0.972136 1.68379i −0.0449851 0.0779165i 0.842656 0.538452i \(-0.180991\pi\)
−0.887641 + 0.460536i \(0.847657\pi\)
\(468\) 3.11803 5.40059i 0.144131 0.249643i
\(469\) 16.0869 + 13.4985i 0.742826 + 0.623305i
\(470\) 2.15358 + 0.783840i 0.0993374 + 0.0361559i
\(471\) −27.4206 + 9.98026i −1.26347 + 0.459866i
\(472\) −26.2527 + 22.0287i −1.20838 + 1.01395i
\(473\) −0.735585 4.17171i −0.0338223 0.191816i
\(474\) −21.7082 −0.997091
\(475\) 0 0
\(476\) −25.4164 −1.16496
\(477\) −6.24166 35.3982i −0.285786 1.62077i
\(478\) 7.25608 6.08857i 0.331885 0.278485i
\(479\) −11.1916 + 4.07340i −0.511356 + 0.186118i −0.584795 0.811181i \(-0.698825\pi\)
0.0734385 + 0.997300i \(0.476603\pi\)
\(480\) −17.0839 6.21804i −0.779771 0.283814i
\(481\) −1.64385 1.37936i −0.0749533 0.0628933i
\(482\) −5.92705 + 10.2660i −0.269970 + 0.467601i
\(483\) 29.9164 + 51.8167i 1.36124 + 2.35774i
\(484\) 2.98333 16.9193i 0.135606 0.769061i
\(485\) 1.53380 8.69863i 0.0696464 0.394984i
\(486\) −6.69098 11.5891i −0.303509 0.525693i
\(487\) −9.09017 + 15.7446i −0.411915 + 0.713458i −0.995099 0.0988824i \(-0.968473\pi\)
0.583184 + 0.812340i \(0.301807\pi\)
\(488\) 9.87320 + 8.28460i 0.446939 + 0.375026i
\(489\) 15.3416 + 5.58390i 0.693773 + 0.252513i
\(490\) 1.43572 0.522560i 0.0648593 0.0236069i
\(491\) 23.1459 19.4217i 1.04456 0.876488i 0.0520474 0.998645i \(-0.483425\pi\)
0.992511 + 0.122156i \(0.0389809\pi\)
\(492\) 2.20676 + 12.5151i 0.0994883 + 0.564226i
\(493\) 7.23607 0.325896
\(494\) 0 0
\(495\) −2.94427 −0.132335
\(496\) 0.690896 + 3.91827i 0.0310222 + 0.175935i
\(497\) −3.38316 + 2.83881i −0.151756 + 0.127338i
\(498\) −0.717861 + 0.261280i −0.0321681 + 0.0117082i
\(499\) 14.2125 + 5.17292i 0.636238 + 0.231572i 0.639944 0.768421i \(-0.278957\pi\)
−0.00370599 + 0.999993i \(0.501180\pi\)
\(500\) −12.9801 10.8916i −0.580486 0.487086i
\(501\) −20.6353 + 35.7413i −0.921915 + 1.59680i
\(502\) −5.98278 10.3625i −0.267024 0.462500i
\(503\) −3.09664 + 17.5619i −0.138072 + 0.783046i 0.834599 + 0.550858i \(0.185700\pi\)
−0.972671 + 0.232188i \(0.925412\pi\)
\(504\) −4.48952 + 25.4613i −0.199979 + 1.13414i
\(505\) 8.14590 + 14.1091i 0.362488 + 0.627847i
\(506\) −1.45492 + 2.51999i −0.0646789 + 0.112027i
\(507\) 24.0664 + 20.1941i 1.06882 + 0.896850i
\(508\) −15.5635 5.66464i −0.690518 0.251328i
\(509\) −25.4041 + 9.24632i −1.12602 + 0.409836i −0.836844 0.547441i \(-0.815602\pi\)
−0.289171 + 0.957277i \(0.593380\pi\)
\(510\) 8.02212 6.73136i 0.355226 0.298070i
\(511\) 5.57838 + 31.6366i 0.246773 + 1.39952i
\(512\) 18.7082 0.826794
\(513\) 0 0
\(514\) 15.0557 0.664080
\(515\) −0.284665 1.61442i −0.0125438 0.0711396i
\(516\) −22.2417 + 18.6630i −0.979135 + 0.821592i
\(517\) −1.74229 + 0.634140i −0.0766256 + 0.0278895i
\(518\) 3.73877 + 1.36080i 0.164272 + 0.0597901i
\(519\) 16.9911 + 14.2572i 0.745828 + 0.625824i
\(520\) −1.38197 + 2.39364i −0.0606032 + 0.104968i
\(521\) −13.6353 23.6170i −0.597371 1.03468i −0.993208 0.116356i \(-0.962879\pi\)
0.395836 0.918321i \(-0.370455\pi\)
\(522\) 0.571614 3.24179i 0.0250189 0.141889i
\(523\) −3.89257 + 22.0759i −0.170210 + 0.965310i 0.773318 + 0.634018i \(0.218595\pi\)
−0.943528 + 0.331292i \(0.892516\pi\)
\(524\) 3.16312 + 5.47868i 0.138181 + 0.239337i
\(525\) −13.6353 + 23.6170i −0.595091 + 1.03073i
\(526\) 1.39394 + 1.16965i 0.0607787 + 0.0509994i
\(527\) −10.5585 3.84296i −0.459933 0.167402i
\(528\) 2.81908 1.02606i 0.122685 0.0446535i
\(529\) 26.8379 22.5197i 1.16687 0.979118i
\(530\) 1.23718 + 7.01637i 0.0537395 + 0.304772i
\(531\) 59.0689 2.56337
\(532\) 0 0
\(533\) 3.00000 0.129944
\(534\) −3.43795 19.4976i −0.148775 0.843743i
\(535\) −9.86312 + 8.27614i −0.426420 + 0.357809i
\(536\) 14.7085 5.35346i 0.635311 0.231234i
\(537\) −19.1004 6.95198i −0.824244 0.300000i
\(538\) −6.94717 5.82937i −0.299514 0.251322i
\(539\) −0.618034 + 1.07047i −0.0266206 + 0.0461082i
\(540\) 2.23607 + 3.87298i 0.0962250 + 0.166667i
\(541\) 4.13853 23.4707i 0.177929 1.00909i −0.756779 0.653670i \(-0.773228\pi\)
0.934708 0.355416i \(-0.115661\pi\)
\(542\) 0.842906 4.78036i 0.0362059 0.205334i
\(543\) −15.7082 27.2074i −0.674104 1.16758i
\(544\) −14.7082 + 25.4754i −0.630609 + 1.09225i
\(545\) −15.8207 13.2752i −0.677685 0.568645i
\(546\) 4.56136 + 1.66020i 0.195208 + 0.0710500i
\(547\) 35.6359 12.9704i 1.52368 0.554575i 0.561618 0.827396i \(-0.310179\pi\)
0.962065 + 0.272821i \(0.0879567\pi\)
\(548\) 1.82469 1.53110i 0.0779470 0.0654053i
\(549\) −3.85756 21.8773i −0.164636 0.933700i
\(550\) −1.32624 −0.0565510
\(551\) 0 0
\(552\) 44.5967 1.89816
\(553\) 6.98920 + 39.6377i 0.297211 + 1.68557i
\(554\) −7.29877 + 6.12439i −0.310095 + 0.260201i
\(555\) 6.52548 2.37508i 0.276991 0.100817i
\(556\) −14.8980 5.42242i −0.631815 0.229962i
\(557\) −17.7572 14.9000i −0.752395 0.631335i 0.183740 0.982975i \(-0.441180\pi\)
−0.936135 + 0.351640i \(0.885624\pi\)
\(558\) −2.55573 + 4.42665i −0.108193 + 0.187395i
\(559\) 3.42705 + 5.93583i 0.144949 + 0.251059i
\(560\) −1.19390 + 6.77094i −0.0504514 + 0.286124i
\(561\) −1.47117 + 8.34343i −0.0621129 + 0.352260i
\(562\) 2.62868 + 4.55300i 0.110884 + 0.192057i
\(563\) 10.4164 18.0417i 0.438999 0.760369i −0.558613 0.829428i \(-0.688666\pi\)
0.997613 + 0.0690592i \(0.0219997\pi\)
\(564\) 9.73505 + 8.16868i 0.409920 + 0.343963i
\(565\) −13.0510 4.75016i −0.549058 0.199841i
\(566\) 1.76229 0.641421i 0.0740745 0.0269609i
\(567\) −13.1182 + 11.0075i −0.550913 + 0.462271i
\(568\) 0.571614 + 3.24179i 0.0239844 + 0.136022i
\(569\) −28.0902 −1.17760 −0.588801 0.808278i \(-0.700400\pi\)
−0.588801 + 0.808278i \(0.700400\pi\)
\(570\) 0 0
\(571\) 22.3262 0.934324 0.467162 0.884172i \(-0.345276\pi\)
0.467162 + 0.884172i \(0.345276\pi\)
\(572\) −0.173648 0.984808i −0.00726060 0.0411769i
\(573\) −19.5819 + 16.4311i −0.818044 + 0.686420i
\(574\) −5.22686 + 1.90242i −0.218165 + 0.0794055i
\(575\) 24.8557 + 9.04672i 1.03655 + 0.377274i
\(576\) −0.696970 0.584827i −0.0290404 0.0243678i
\(577\) −14.0623 + 24.3566i −0.585421 + 1.01398i 0.409401 + 0.912354i \(0.365738\pi\)
−0.994823 + 0.101625i \(0.967596\pi\)
\(578\) −3.21885 5.57521i −0.133886 0.231898i
\(579\) 10.4309 59.1563i 0.433491 2.45845i
\(580\) 0.479952 2.72194i 0.0199289 0.113022i
\(581\) 0.708204 + 1.22665i 0.0293812 + 0.0508898i
\(582\) −5.78115 + 10.0133i −0.239636 + 0.415063i
\(583\) −4.41543 3.70498i −0.182868 0.153445i
\(584\) 22.5003 + 8.18942i 0.931067 + 0.338881i
\(585\) 4.47663 1.62936i 0.185086 0.0673658i
\(586\) 7.97943 6.69554i 0.329627 0.276590i
\(587\) 6.62027 + 37.5454i 0.273248 + 1.54967i 0.744473 + 0.667652i \(0.232701\pi\)
−0.471225 + 0.882013i \(0.656188\pi\)
\(588\) 8.47214 0.349385
\(589\) 0 0
\(590\) −11.7082 −0.482019
\(591\) −1.36385 7.73478i −0.0561013 0.318166i
\(592\) −3.04787 + 2.55747i −0.125267 + 0.105111i
\(593\) 11.9418 4.34646i 0.490391 0.178488i −0.0849760 0.996383i \(-0.527081\pi\)
0.575367 + 0.817895i \(0.304859\pi\)
\(594\) 0.802593 + 0.292120i 0.0329308 + 0.0119858i
\(595\) −14.8738 12.4806i −0.609768 0.511656i
\(596\) −10.5902 + 18.3427i −0.433790 + 0.751347i
\(597\) 17.5623 + 30.4188i 0.718777 + 1.24496i
\(598\) 0.817571 4.63668i 0.0334330 0.189608i
\(599\) −0.274988 + 1.55953i −0.0112357 + 0.0637208i −0.989910 0.141697i \(-0.954744\pi\)
0.978674 + 0.205418i \(0.0658553\pi\)
\(600\) 10.1631 + 17.6030i 0.414908 + 0.718641i
\(601\) 16.8541 29.1922i 0.687493 1.19077i −0.285153 0.958482i \(-0.592044\pi\)
0.972646 0.232291i \(-0.0746222\pi\)
\(602\) −9.73505 8.16868i −0.396771 0.332930i
\(603\) −25.3517 9.22726i −1.03240 0.375763i
\(604\) 15.0674 5.48410i 0.613086 0.223145i
\(605\) 10.0540 8.43634i 0.408755 0.342986i
\(606\) −3.70326 21.0022i −0.150435 0.853158i
\(607\) −27.2705 −1.10688 −0.553438 0.832890i \(-0.686684\pi\)
−0.553438 + 0.832890i \(0.686684\pi\)
\(608\) 0 0
\(609\) −10.8541 −0.439830
\(610\) 0.764617 + 4.33636i 0.0309584 + 0.175574i
\(611\) 2.29813 1.92836i 0.0929725 0.0780132i
\(612\) 30.6833 11.1678i 1.24030 0.451432i
\(613\) 1.93175 + 0.703100i 0.0780227 + 0.0283980i 0.380737 0.924684i \(-0.375670\pi\)
−0.302714 + 0.953081i \(0.597893\pi\)
\(614\) 0.792428 + 0.664926i 0.0319798 + 0.0268342i
\(615\) −4.85410 + 8.40755i −0.195736 + 0.339025i
\(616\) 2.07295 + 3.59045i 0.0835215 + 0.144663i
\(617\) 4.05056 22.9719i 0.163069 0.924812i −0.787963 0.615722i \(-0.788864\pi\)
0.951033 0.309090i \(-0.100024\pi\)
\(618\) −0.372631 + 2.11330i −0.0149894 + 0.0850093i
\(619\) 15.0623 + 26.0887i 0.605405 + 1.04859i 0.991987 + 0.126338i \(0.0403222\pi\)
−0.386582 + 0.922255i \(0.626344\pi\)
\(620\) −2.14590 + 3.71680i −0.0861813 + 0.149270i
\(621\) −13.0491 10.9495i −0.523644 0.439389i
\(622\) 10.8326 + 3.94276i 0.434350 + 0.158090i
\(623\) −34.4944 + 12.5549i −1.38199 + 0.503003i
\(624\) −3.71846 + 3.12016i −0.148857 + 0.124906i
\(625\) 0.766901 + 4.34931i 0.0306760 + 0.173973i
\(626\) 2.67376 0.106865
\(627\) 0 0
\(628\) 18.0344 0.719653
\(629\) −1.95112 11.0654i −0.0777964 0.441205i
\(630\) −6.76633 + 5.67762i −0.269577 + 0.226202i
\(631\) 14.4343 5.25366i 0.574621 0.209145i −0.0383309 0.999265i \(-0.512204\pi\)
0.612952 + 0.790120i \(0.289982\pi\)
\(632\) 28.1908 + 10.2606i 1.12137 + 0.408145i
\(633\) 5.72399 + 4.80300i 0.227508 + 0.190902i
\(634\) 5.56231 9.63420i 0.220907 0.382623i
\(635\) −6.32624 10.9574i −0.251049 0.434830i
\(636\) −6.86025 + 38.9064i −0.272026 + 1.54274i
\(637\) 0.347296 1.96962i 0.0137604 0.0780390i
\(638\) −0.263932 0.457144i −0.0104492 0.0180985i
\(639\) 2.83688 4.91362i 0.112225 0.194380i
\(640\) 10.7774 + 9.04330i 0.426014 + 0.357468i
\(641\) −1.40336 0.510780i −0.0554293 0.0201746i 0.314157 0.949371i \(-0.398278\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(642\) 15.8377 5.76444i 0.625063 0.227504i
\(643\) −28.8862 + 24.2384i −1.13916 + 0.955868i −0.999411 0.0343192i \(-0.989074\pi\)
−0.139748 + 0.990187i \(0.544629\pi\)
\(644\) −6.42129 36.4169i −0.253034 1.43503i
\(645\) −22.1803 −0.873350
\(646\) 0 0
\(647\) −1.47214 −0.0578756 −0.0289378 0.999581i \(-0.509212\pi\)
−0.0289378 + 0.999581i \(0.509212\pi\)
\(648\) 2.21643 + 12.5700i 0.0870697 + 0.493797i
\(649\) 7.25608 6.08857i 0.284826 0.238997i
\(650\) 2.01648 0.733940i 0.0790930 0.0287875i
\(651\) 15.8377 + 5.76444i 0.620727 + 0.225926i
\(652\) −7.72952 6.48584i −0.302711 0.254005i
\(653\) 1.71885 2.97713i 0.0672637 0.116504i −0.830432 0.557120i \(-0.811906\pi\)
0.897696 + 0.440616i \(0.145240\pi\)
\(654\) 13.5172 + 23.4125i 0.528565 + 0.915502i
\(655\) −0.839210 + 4.75939i −0.0327906 + 0.185965i
\(656\) 0.965884 5.47780i 0.0377114 0.213872i
\(657\) −20.6353 35.7413i −0.805058 1.39440i
\(658\) −2.78115 + 4.81710i −0.108421 + 0.187790i
\(659\) −35.0673 29.4249i −1.36603 1.14623i −0.974069 0.226250i \(-0.927353\pi\)
−0.391958 0.919983i \(-0.628202\pi\)
\(660\) 3.04091 + 1.10680i 0.118367 + 0.0430821i
\(661\) −20.1248 + 7.32484i −0.782766 + 0.284903i −0.702325 0.711856i \(-0.747855\pi\)
−0.0804402 + 0.996759i \(0.525633\pi\)
\(662\) 3.28771 2.75871i 0.127780 0.107220i
\(663\) −2.38040 13.4999i −0.0924473 0.524294i
\(664\) 1.05573 0.0409702
\(665\) 0 0
\(666\) −5.11146 −0.198065
\(667\) 1.82814 + 10.3679i 0.0707860 + 0.401448i
\(668\) 19.5392 16.3953i 0.755993 0.634354i
\(669\) −48.3480 + 17.5972i −1.86924 + 0.680348i
\(670\) 5.02503 + 1.82896i 0.194134 + 0.0706589i
\(671\) −2.72888 2.28981i −0.105347 0.0883970i
\(672\) 22.0623 38.2130i 0.851072 1.47410i
\(673\) −3.06231 5.30407i −0.118043 0.204457i 0.800949 0.598733i \(-0.204329\pi\)
−0.918992 + 0.394276i \(0.870995\pi\)
\(674\) −2.48174 + 14.0747i −0.0955932 + 0.542136i
\(675\) 1.34819 7.64598i 0.0518920 0.294294i
\(676\) −9.70820 16.8151i −0.373392 0.646735i
\(677\) 5.87132 10.1694i 0.225653 0.390843i −0.730862 0.682525i \(-0.760882\pi\)
0.956515 + 0.291682i \(0.0942150\pi\)
\(678\) 13.9269 + 11.6861i 0.534861 + 0.448802i
\(679\) 20.1448 + 7.33212i 0.773088 + 0.281381i
\(680\) −13.5994 + 4.94976i −0.521512 + 0.189815i
\(681\) −20.8904 + 17.5291i −0.800523 + 0.671718i
\(682\) 0.142332 + 0.807208i 0.00545019 + 0.0309096i
\(683\) 21.6525 0.828509 0.414254 0.910161i \(-0.364042\pi\)
0.414254 + 0.910161i \(0.364042\pi\)
\(684\) 0 0
\(685\) 1.81966 0.0695256
\(686\) −1.60981 9.12967i −0.0614627 0.348572i
\(687\) 22.8269 19.1540i 0.870900 0.730772i
\(688\) 11.9418 4.34646i 0.455277 0.165707i
\(689\) 8.76380 + 3.18976i 0.333874 + 0.121520i
\(690\) 11.6715 + 9.79356i 0.444327 + 0.372834i
\(691\) 8.40983 14.5663i 0.319925 0.554126i −0.660547 0.750785i \(-0.729676\pi\)
0.980472 + 0.196658i \(0.0630089\pi\)
\(692\) −6.85410 11.8717i −0.260554 0.451293i
\(693\) 1.24087 7.03734i 0.0471368 0.267326i
\(694\) 0.152010 0.862089i 0.00577020 0.0327245i
\(695\) −6.05573 10.4888i −0.229707 0.397864i
\(696\) −4.04508 + 7.00629i −0.153329 + 0.265573i
\(697\) 12.0332 + 10.0970i 0.455789 + 0.382453i
\(698\) −15.0874 5.49138i −0.571068 0.207852i
\(699\) 33.1434 12.0632i 1.25360 0.456273i
\(700\) 12.9110 10.8336i 0.487990 0.409472i
\(701\) 6.70824 + 38.0443i 0.253367 + 1.43691i 0.800231 + 0.599692i \(0.204710\pi\)
−0.546864 + 0.837221i \(0.684179\pi\)
\(702\) −1.38197 −0.0521589
\(703\) 0 0
\(704\) −0.145898 −0.00549874
\(705\) 1.68581 + 9.56071i 0.0634914 + 0.360077i
\(706\) −14.8901 + 12.4943i −0.560398 + 0.470230i
\(707\) −37.1564 + 13.5238i −1.39741 + 0.508616i
\(708\) −61.0077 22.2050i −2.29281 0.834514i
\(709\) 33.2589 + 27.9075i 1.24906 + 1.04809i 0.996759 + 0.0804414i \(0.0256330\pi\)
0.252305 + 0.967648i \(0.418811\pi\)
\(710\) −0.562306 + 0.973942i −0.0211030 + 0.0365514i
\(711\) −25.8541 44.7806i −0.969605 1.67940i
\(712\) −4.75113 + 26.9450i −0.178056 + 1.00981i
\(713\) 2.83872 16.0992i 0.106311 0.602919i
\(714\) 12.7082 + 22.0113i 0.475593 + 0.823751i
\(715\) 0.381966 0.661585i 0.0142847 0.0247419i
\(716\) 9.62328 + 8.07489i 0.359639 + 0.301773i
\(717\) 37.7048 + 13.7234i 1.40811 + 0.512511i
\(718\) 12.7968 4.65764i 0.477571 0.173822i
\(719\) 13.7624 11.5480i 0.513252 0.430669i −0.349020 0.937115i \(-0.613486\pi\)
0.862272 + 0.506446i \(0.169041\pi\)
\(720\) −1.53380 8.69863i −0.0571614 0.324179i
\(721\) 3.97871 0.148175
\(722\) 0 0
\(723\) −50.2148 −1.86751
\(724\) 3.37162 + 19.1214i 0.125305 + 0.710642i
\(725\) −3.67577 + 3.08434i −0.136515 + 0.114549i
\(726\) −16.1442 + 5.87602i −0.599169 + 0.218080i
\(727\) −39.5318 14.3884i −1.46615 0.533636i −0.519101 0.854713i \(-0.673733\pi\)
−0.947053 + 0.321077i \(0.895955\pi\)
\(728\) −5.13878 4.31195i −0.190456 0.159812i
\(729\) 19.7812 34.2620i 0.732635 1.26896i
\(730\) 4.09017 + 7.08438i 0.151384 + 0.262205i
\(731\) −6.23198 + 35.3433i −0.230498 + 1.30722i
\(732\) −4.23986 + 24.0455i −0.156710 + 0.888746i
\(733\) −20.4787 35.4702i −0.756399 1.31012i −0.944676 0.328005i \(-0.893624\pi\)
0.188277 0.982116i \(-0.439710\pi\)
\(734\) −0.600813 + 1.04064i −0.0221764 + 0.0384107i
\(735\) 4.95794 + 4.16021i 0.182877 + 0.153452i
\(736\) −40.2173 14.6379i −1.48243 0.539560i
\(737\) −4.06533 + 1.47966i −0.149748 + 0.0545040i
\(738\) 5.47408 4.59329i 0.201504 0.169082i
\(739\) −4.34120 24.6202i −0.159694 0.905668i −0.954368 0.298633i \(-0.903470\pi\)
0.794674 0.607036i \(-0.207642\pi\)
\(740\) −4.29180 −0.157770
\(741\) 0 0
\(742\) −17.2918 −0.634802
\(743\) −7.18221 40.7323i −0.263490 1.49432i −0.773302 0.634038i \(-0.781396\pi\)
0.509812 0.860286i \(-0.329715\pi\)
\(744\) 9.62328 8.07489i 0.352807 0.296040i
\(745\) −15.2045 + 5.53400i −0.557051 + 0.202750i
\(746\) 2.01648 + 0.733940i 0.0738287 + 0.0268715i
\(747\) −1.39394 1.16965i −0.0510016 0.0427954i
\(748\) 2.61803 4.53457i 0.0957248 0.165800i
\(749\) −15.6246 27.0626i −0.570911 0.988847i
\(750\) −2.94234 + 16.6869i −0.107439 + 0.609318i
\(751\) 4.14222 23.4917i 0.151152 0.857224i −0.811068 0.584952i \(-0.801114\pi\)
0.962220 0.272273i \(-0.0877754\pi\)
\(752\) −2.78115 4.81710i −0.101418 0.175661i
\(753\) 25.3435 43.8962i 0.923567 1.59966i
\(754\) 0.654280 + 0.549006i 0.0238275 + 0.0199936i
\(755\) 11.5105 + 4.18948i 0.418910 + 0.152471i
\(756\) −10.1995 + 3.71232i −0.370953 + 0.135016i
\(757\) −12.0596 + 10.1192i −0.438312 + 0.367788i −0.835077 0.550132i \(-0.814577\pi\)
0.396765 + 0.917920i \(0.370133\pi\)
\(758\) −2.69639 15.2920i −0.0979371 0.555429i
\(759\) −12.3262 −0.447414
\(760\) 0 0
\(761\) −30.8885 −1.11971 −0.559854 0.828591i \(-0.689143\pi\)
−0.559854 + 0.828591i \(0.689143\pi\)
\(762\) 2.87601 + 16.3107i 0.104187 + 0.590874i
\(763\) 38.3977 32.2195i 1.39009 1.16642i
\(764\) 14.8456 5.40336i 0.537096 0.195487i
\(765\) 23.4399 + 8.53144i 0.847473 + 0.308455i
\(766\) −1.23949 1.04005i −0.0447844 0.0375786i
\(767\) −7.66312 + 13.2729i −0.276699 + 0.479257i
\(768\) −8.59017 14.8786i −0.309971 0.536886i
\(769\) −7.22918 + 40.9987i −0.260691 + 1.47845i 0.520340 + 0.853959i \(0.325805\pi\)
−0.781031 + 0.624492i \(0.785306\pi\)
\(770\) −0.245957 + 1.39489i −0.00886366 + 0.0502683i
\(771\) 31.8885 + 55.2326i 1.14844 + 1.98915i
\(772\) −18.5623 + 32.1509i −0.668072 + 1.15713i
\(773\) −22.1563 18.5913i −0.796906 0.668684i 0.150538 0.988604i \(-0.451899\pi\)
−0.947444 + 0.319920i \(0.896344\pi\)
\(774\) 15.3416 + 5.58390i 0.551444 + 0.200709i
\(775\) 7.00151 2.54834i 0.251502 0.0915391i
\(776\) 12.2404 10.2709i 0.439405 0.368705i
\(777\) 2.92668 + 16.5981i 0.104994 + 0.595452i
\(778\) −15.0000 −0.537776
\(779\) 0 0
\(780\) −5.23607 −0.187481
\(781\) −0.157990 0.896008i −0.00565334 0.0320617i
\(782\) 18.8849 15.8463i 0.675322 0.566663i
\(783\) 2.90381 1.05690i 0.103774 0.0377705i
\(784\) −3.48457 1.26828i −0.124449 0.0452957i
\(785\) 10.5539 + 8.85574i 0.376683 + 0.316075i
\(786\) 3.16312 5.47868i 0.112825 0.195418i
\(787\) 19.0000 + 32.9090i 0.677277 + 1.17308i 0.975798 + 0.218675i \(0.0701734\pi\)
−0.298521 + 0.954403i \(0.596493\pi\)
\(788\) −0.842906 + 4.78036i −0.0300273 + 0.170293i
\(789\) −1.33852 + 7.59110i −0.0476524 + 0.270250i
\(790\) 5.12461 + 8.87609i 0.182326 + 0.315797i
\(791\) 16.8541 29.1922i 0.599263 1.03795i
\(792\) −4.08013 3.42364i −0.144981 0.121654i
\(793\) 5.41632 + 1.97138i 0.192339 + 0.0700058i
\(794\) 1.46809 0.534340i 0.0521005 0.0189630i
\(795\) −23.1195 + 19.3995i −0.819964 + 0.688031i
\(796\) −3.76959 21.3784i −0.133610 0.757738i
\(797\) 33.7082 1.19401 0.597003 0.802239i \(-0.296358\pi\)
0.597003 + 0.802239i \(0.296358\pi\)
\(798\) 0 0
\(799\) 15.7082 0.555716
\(800\) −3.38728 19.2102i −0.119758 0.679184i
\(801\) 36.1259 30.3133i 1.27645 1.07107i
\(802\) −0.0647295 + 0.0235596i −0.00228568 + 0.000831919i
\(803\) −6.21892 2.26350i −0.219461 0.0798772i
\(804\) 22.7151 + 19.0602i 0.801100 + 0.672203i
\(805\) 14.1246 24.4645i 0.497827 0.862262i
\(806\) −0.663119 1.14856i −0.0233574 0.0404562i
\(807\) 6.67094 37.8328i 0.234828 1.33178i
\(808\) −5.11778 + 29.0244i −0.180043 + 1.02107i
\(809\) 0.100813 + 0.174613i 0.00354440 + 0.00613908i 0.867792 0.496927i \(-0.165538\pi\)
−0.864248 + 0.503066i \(0.832205\pi\)
\(810\) −2.18034 + 3.77646i −0.0766093 + 0.132691i
\(811\) 18.3688 + 15.4132i 0.645014 + 0.541231i 0.905554 0.424232i \(-0.139456\pi\)
−0.260539 + 0.965463i \(0.583900\pi\)
\(812\) 6.30365 + 2.29434i 0.221215 + 0.0805156i
\(813\) 19.3222 7.03272i 0.677661 0.246648i
\(814\) −0.627896 + 0.526867i −0.0220077 + 0.0184667i
\(815\) −1.33852 7.59110i −0.0468862 0.265905i
\(816\) −25.4164 −0.889752
\(817\) 0 0
\(818\) 13.4164 0.469094
\(819\) 2.00777 + 11.3866i 0.0701573 + 0.397882i
\(820\) 4.59627 3.85673i 0.160509 0.134683i
\(821\) 49.8484 18.1433i 1.73972 0.633207i 0.740478 0.672080i \(-0.234599\pi\)
0.999244 + 0.0388731i \(0.0123768\pi\)
\(822\) −2.23832 0.814680i −0.0780702 0.0284152i
\(823\) 18.0762 + 15.1677i 0.630095 + 0.528713i 0.900959 0.433905i \(-0.142865\pi\)
−0.270863 + 0.962618i \(0.587309\pi\)
\(824\) 1.48278 2.56825i 0.0516551 0.0894692i
\(825\) −2.80902 4.86536i −0.0977974 0.169390i
\(826\) 4.93446 27.9847i 0.171692 0.973712i
\(827\) 2.88200 16.3446i 0.100217 0.568358i −0.892807 0.450440i \(-0.851267\pi\)
0.993023 0.117917i \(-0.0376218\pi\)
\(828\) 23.7533 + 41.1419i 0.825484 + 1.42978i
\(829\) 10.1631 17.6030i 0.352980 0.611379i −0.633790 0.773505i \(-0.718502\pi\)
0.986770 + 0.162126i \(0.0518351\pi\)
\(830\) 0.276297 + 0.231840i 0.00959040 + 0.00804730i
\(831\) −37.9266 13.8042i −1.31566 0.478861i
\(832\) 0.221831 0.0807400i 0.00769062 0.00279916i
\(833\) 8.02212 6.73136i 0.277950 0.233228i
\(834\) 2.75304 + 15.6132i 0.0953298 + 0.540642i
\(835\) 19.4853 0.674316
\(836\) 0 0
\(837\) −4.79837 −0.165856
\(838\) 0.959904 + 5.44388i 0.0331593 + 0.188056i
\(839\) −30.4873 + 25.5819i −1.05254 + 0.883185i −0.993358 0.115062i \(-0.963293\pi\)
−0.0591810 + 0.998247i \(0.518849\pi\)
\(840\) 20.3990 7.42464i 0.703834 0.256175i
\(841\) 25.4564 + 9.26538i 0.877808 + 0.319496i
\(842\) 8.77186 + 7.36046i 0.302298 + 0.253658i
\(843\) −11.1353 + 19.2868i −0.383519 + 0.664274i
\(844\) −2.30902 3.99933i −0.0794796 0.137663i
\(845\) 2.57569 14.6075i 0.0886065 0.502512i
\(846\) 1.24087 7.03734i 0.0426621 0.241949i
\(847\) 15.9271 + 27.5865i 0.547260 + 0.947882i
\(848\) 8.64590 14.9751i 0.296901 0.514248i
\(849\) 6.08567 + 5.10648i 0.208859 + 0.175254i
\(850\) 10.5585 + 3.84296i 0.362152 + 0.131812i
\(851\) 15.3616 5.59118i 0.526591 0.191663i
\(852\) −4.77711 + 4.00847i −0.163661 + 0.137328i
\(853\) 3.00269 + 17.0291i 0.102810 + 0.583065i 0.992072 + 0.125668i \(0.0401073\pi\)
−0.889262 + 0.457398i \(0.848782\pi\)
\(854\) −10.6869 −0.365699
\(855\) 0 0
\(856\) −23.2918 −0.796097
\(857\) 1.45551 + 8.25463i 0.0497194 + 0.281973i 0.999523 0.0308732i \(-0.00982880\pi\)
−0.949804 + 0.312846i \(0.898718\pi\)
\(858\) −0.766044 + 0.642788i −0.0261523 + 0.0219444i
\(859\) −17.4229 + 6.34140i −0.594460 + 0.216366i −0.621690 0.783263i \(-0.713554\pi\)
0.0272298 + 0.999629i \(0.491331\pi\)
\(860\) 12.8815 + 4.68848i 0.439255 + 0.159876i
\(861\) −18.0498 15.1456i −0.615135 0.516159i
\(862\) −1.12868 + 1.95493i −0.0384429 + 0.0665850i
\(863\) −22.4721 38.9229i −0.764960 1.32495i −0.940268 0.340436i \(-0.889425\pi\)
0.175307 0.984514i \(-0.443908\pi\)
\(864\) −2.18142 + 12.3715i −0.0742135 + 0.420885i
\(865\) 1.81847 10.3130i 0.0618297 0.350654i
\(866\) −7.28115 12.6113i −0.247424 0.428550i
\(867\) 13.6353 23.6170i 0.463078 0.802074i
\(868\) −7.97943 6.69554i −0.270840 0.227261i
\(869\) −7.79174 2.83596i −0.264317 0.0962034i
\(870\) −2.59725 + 0.945320i −0.0880549 + 0.0320494i
\(871\) 5.36231 4.49951i 0.181695 0.152460i
\(872\) −6.48761 36.7931i −0.219698 1.24597i
\(873\) −27.5410 −0.932122
\(874\) 0 0
\(875\) 31.4164 1.06207
\(876\) 7.87680 + 44.6715i 0.266132 + 1.50931i
\(877\) −26.1837 + 21.9707i −0.884159 + 0.741898i −0.967030 0.254663i \(-0.918036\pi\)
0.0828706 + 0.996560i \(0.473591\pi\)
\(878\) 8.47724 3.08546i 0.286093 0.104129i
\(879\) 41.4636 + 15.0915i 1.39853 + 0.509024i
\(880\) −1.08503 0.910449i −0.0365764 0.0306912i
\(881\) 11.7254 20.3090i 0.395040 0.684229i −0.598067 0.801446i \(-0.704064\pi\)
0.993106 + 0.117218i \(0.0373975\pi\)
\(882\) −2.38197 4.12569i −0.0802050 0.138919i
\(883\) 2.41770 13.7115i 0.0813621 0.461428i −0.916720 0.399529i \(-0.869174\pi\)
0.998082 0.0618981i \(-0.0197154\pi\)
\(884\) −1.47117 + 8.34343i −0.0494808 + 0.280620i
\(885\) −24.7984 42.9520i −0.833588 1.44382i
\(886\) 10.6353 18.4208i 0.357298 0.618859i
\(887\) −44.9304 37.7011i −1.50862 1.26588i −0.866396 0.499358i \(-0.833569\pi\)
−0.642219 0.766521i \(-0.721986\pi\)
\(888\) 11.8047 + 4.29656i 0.396140 + 0.144183i
\(889\) 28.8563 10.5028i 0.967808 0.352253i
\(890\) −7.16062 + 6.00847i −0.240024 + 0.201404i
\(891\) −0.612607 3.47427i −0.0205231 0.116392i
\(892\) 31.7984 1.06469
\(893\) 0 0
\(894\) 21.1803 0.708377
\(895\) 1.66646 + 9.45095i 0.0557035 + 0.315910i
\(896\) −26.1573 + 21.9486i −0.873853 + 0.733250i
\(897\) 18.7415 6.82134i 0.625760 0.227758i
\(898\) −19.1004 6.95198i −0.637389 0.231991i
\(899\) 2.27175 + 1.90622i 0.0757671 + 0.0635761i
\(900\) −10.8262 + 18.7516i −0.360875 + 0.625053i
\(901\) 24.4164 + 42.2905i 0.813428 + 1.40890i
\(902\) 0.198983 1.12849i 0.00662541 0.0375746i
\(903\) 9.34797 53.0150i 0.311081 1.76423i
\(904\) −12.5623 21.7586i −0.417816 0.723679i
\(905\) −7.41641 + 12.8456i −0.246530 + 0.427002i
\(906\) −12.2831 10.3067i −0.408079 0.342419i
\(907\) −16.4708 5.99488i −0.546904 0.199057i 0.0537663 0.998554i \(-0.482877\pi\)
−0.600670 + 0.799497i \(0.705100\pi\)
\(908\) 15.8377 5.76444i 0.525592 0.191300i
\(909\) 38.9138 32.6526i 1.29069 1.08302i
\(910\) −0.397966 2.25698i −0.0131925 0.0748181i
\(911\) −5.61803 −0.186134 −0.0930669 0.995660i \(-0.529667\pi\)
−0.0930669 + 0.995660i \(0.529667\pi\)
\(912\) 0 0
\(913\) −0.291796 −0.00965704
\(914\) 0.675239 + 3.82947i 0.0223349 + 0.126668i
\(915\) −14.2886 + 11.9896i −0.472367 + 0.396363i
\(916\) −17.3058 + 6.29878i −0.571798 + 0.208118i
\(917\) −11.0221 4.01172i −0.363982 0.132479i
\(918\) −5.54315 4.65125i −0.182951 0.153514i
\(919\) −18.3541 + 31.7902i −0.605446 + 1.04866i 0.386535 + 0.922275i \(0.373672\pi\)
−0.991981 + 0.126388i \(0.959661\pi\)
\(920\) −10.5279 18.2348i −0.347093 0.601183i
\(921\) −0.760920 + 4.31539i −0.0250732 + 0.142197i
\(922\) 0.327942 1.85985i 0.0108002 0.0612510i
\(923\) 0.736068 + 1.27491i 0.0242280 + 0.0419641i
\(924\) −3.92705 + 6.80185i −0.129190 + 0.223764i
\(925\) 5.70768 + 4.78931i 0.187667 + 0.157472i
\(926\) 3.06091 + 1.11408i 0.100588 + 0.0366110i
\(927\) −4.80320 + 1.74822i −0.157758 + 0.0574191i
\(928\) 5.94752 4.99056i 0.195237 0.163823i
\(929\) 3.23299 + 18.3352i 0.106071 + 0.601558i 0.990787 + 0.135428i \(0.0432409\pi\)
−0.884716 + 0.466130i \(0.845648\pi\)
\(930\) 4.29180 0.140734
\(931\) 0 0
\(932\) −21.7984 −0.714029
\(933\) 8.47973 + 48.0909i 0.277614 + 1.57443i
\(934\) 0.920499 0.772390i 0.0301196 0.0252734i
\(935\) 3.75877 1.36808i 0.122925 0.0447410i
\(936\) 8.09830 + 2.94754i 0.264701 + 0.0963434i
\(937\) 15.6562 + 13.1371i 0.511465 + 0.429170i 0.861644 0.507512i \(-0.169435\pi\)
−0.350179 + 0.936683i \(0.613879\pi\)
\(938\) −6.48936 + 11.2399i −0.211885 + 0.366996i
\(939\) 5.66312 + 9.80881i 0.184809 + 0.320098i
\(940\) 1.04189 5.90885i 0.0339827 0.192725i
\(941\) −8.62804 + 48.9321i −0.281266 + 1.59514i 0.437059 + 0.899433i \(0.356020\pi\)
−0.718326 + 0.695707i \(0.755091\pi\)
\(942\) −9.01722 15.6183i −0.293797 0.508871i
\(943\) −11.4271 + 19.7922i −0.372116 + 0.644524i
\(944\) 21.7682 + 18.2657i 0.708496 + 0.594498i
\(945\) −7.79174 2.83596i −0.253465 0.0922538i
\(946\) 2.46015 0.895420i 0.0799863 0.0291126i
\(947\) −1.03226 + 0.866172i −0.0335441 + 0.0281468i −0.659406 0.751787i \(-0.729192\pi\)
0.625862 + 0.779934i \(0.284748\pi\)
\(948\) 9.86891 + 55.9694i 0.320527 + 1.81780i
\(949\) 10.7082 0.347603
\(950\) 0 0
\(951\) 47.1246 1.52812
\(952\) −6.09932 34.5910i −0.197680 1.12110i
\(953\) −23.5238 + 19.7389i −0.762012 + 0.639404i −0.938650 0.344872i \(-0.887922\pi\)
0.176638 + 0.984276i \(0.443478\pi\)
\(954\) 20.8751 7.59790i 0.675855 0.245991i
\(955\) 11.3410 + 4.12780i 0.366987 + 0.133573i
\(956\) −18.9967 15.9401i −0.614396 0.515539i
\(957\) 1.11803 1.93649i 0.0361409 0.0625979i
\(958\) −3.68034 6.37454i −0.118906 0.205952i
\(959\) −0.766901 + 4.34931i −0.0247645 + 0.140447i
\(960\) −0.132655 + 0.752326i −0.00428143 + 0.0242812i
\(961\) 13.1976 + 22.8588i 0.425728 + 0.737382i
\(962\) 0.663119 1.14856i 0.0213798 0.0370309i
\(963\) 30.7535 + 25.8053i 0.991019 + 0.831564i
\(964\) 29.1628 + 10.6144i 0.939272 + 0.341867i
\(965\) −26.6503 + 9.69992i −0.857904 + 0.312252i
\(966\) −28.3273 + 23.7695i −0.911417 + 0.764770i
\(967\) −10.5128 59.6213i −0.338070 1.91729i −0.394524 0.918885i \(-0.629091\pi\)
0.0564543 0.998405i \(-0.482020\pi\)
\(968\) 23.7426 0.763118
\(969\) 0 0
\(970\) 5.45898 0.175277
\(971\) 2.51904 + 14.2862i 0.0808399 + 0.458466i 0.998177 + 0.0603544i \(0.0192231\pi\)
−0.917337 + 0.398111i \(0.869666\pi\)
\(972\) −26.8379 + 22.5197i −0.860827 + 0.722320i
\(973\) 27.6224 10.0537i 0.885533 0.322308i
\(974\) −10.5585 3.84296i −0.338315 0.123136i
\(975\) 6.96347 + 5.84305i 0.223010 + 0.187127i
\(976\) 5.34346 9.25514i 0.171040 0.296250i
\(977\) 27.6803 + 47.9438i 0.885573 + 1.53386i 0.845056 + 0.534678i \(0.179567\pi\)
0.0405165 + 0.999179i \(0.487100\pi\)
\(978\) −1.75214 + 9.93688i −0.0560272 + 0.317746i
\(979\) 1.31318 7.44742i 0.0419694 0.238020i
\(980\) −2.00000 3.46410i −0.0638877 0.110657i
\(981\) −32.1976 + 55.7678i −1.02799 + 1.78053i
\(982\) 14.3049 + 12.0033i 0.456489 + 0.383040i
\(983\) 28.5497 + 10.3912i 0.910594 + 0.331429i 0.754490 0.656311i \(-0.227884\pi\)
0.156104 + 0.987741i \(0.450106\pi\)
\(984\) −16.5032 + 6.00666i −0.526102 + 0.191485i
\(985\) −2.84065 + 2.38359i −0.0905106 + 0.0759474i
\(986\) 0.776578 + 4.40419i 0.0247313 + 0.140258i
\(987\) −23.5623 −0.749996
\(988\) 0 0
\(989\) −52.2148 −1.66033
\(990\) −0.315981 1.79202i −0.0100425 0.0569540i
\(991\) 37.1155 31.1436i 1.17901 0.989309i 0.179028 0.983844i \(-0.442705\pi\)
0.999985 0.00546523i \(-0.00173964\pi\)
\(992\) −11.3287 + 4.12330i −0.359686 + 0.130915i
\(993\) 17.0839 + 6.21804i 0.542142 + 0.197324i
\(994\) −2.09091 1.75448i −0.0663197 0.0556488i
\(995\) 8.29180 14.3618i 0.262868 0.455300i
\(996\) 1.00000 + 1.73205i 0.0316862 + 0.0548821i
\(997\) 4.56552 25.8924i 0.144592 0.820019i −0.823103 0.567893i \(-0.807759\pi\)
0.967694 0.252127i \(-0.0811300\pi\)
\(998\) −1.62318 + 9.20551i −0.0513809 + 0.291395i
\(999\) −2.39919 4.15551i −0.0759069 0.131475i
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 361.2.e.i.28.2 12
19.2 odd 18 361.2.e.j.245.1 12
19.3 odd 18 361.2.e.j.62.2 12
19.4 even 9 361.2.c.g.68.1 4
19.5 even 9 inner 361.2.e.i.54.2 12
19.6 even 9 361.2.a.c.1.2 2
19.7 even 3 inner 361.2.e.i.99.1 12
19.8 odd 6 361.2.e.j.234.1 12
19.9 even 9 361.2.c.g.292.1 4
19.10 odd 18 361.2.c.d.292.2 4
19.11 even 3 inner 361.2.e.i.234.2 12
19.12 odd 6 361.2.e.j.99.2 12
19.13 odd 18 361.2.a.f.1.1 yes 2
19.14 odd 18 361.2.e.j.54.1 12
19.15 odd 18 361.2.c.d.68.2 4
19.16 even 9 inner 361.2.e.i.62.1 12
19.17 even 9 inner 361.2.e.i.245.2 12
19.18 odd 2 361.2.e.j.28.1 12
57.32 even 18 3249.2.a.i.1.2 2
57.44 odd 18 3249.2.a.o.1.1 2
76.51 even 18 5776.2.a.s.1.1 2
76.63 odd 18 5776.2.a.bg.1.2 2
95.44 even 18 9025.2.a.s.1.1 2
95.89 odd 18 9025.2.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
361.2.a.c.1.2 2 19.6 even 9
361.2.a.f.1.1 yes 2 19.13 odd 18
361.2.c.d.68.2 4 19.15 odd 18
361.2.c.d.292.2 4 19.10 odd 18
361.2.c.g.68.1 4 19.4 even 9
361.2.c.g.292.1 4 19.9 even 9
361.2.e.i.28.2 12 1.1 even 1 trivial
361.2.e.i.54.2 12 19.5 even 9 inner
361.2.e.i.62.1 12 19.16 even 9 inner
361.2.e.i.99.1 12 19.7 even 3 inner
361.2.e.i.234.2 12 19.11 even 3 inner
361.2.e.i.245.2 12 19.17 even 9 inner
361.2.e.j.28.1 12 19.18 odd 2
361.2.e.j.54.1 12 19.14 odd 18
361.2.e.j.62.2 12 19.3 odd 18
361.2.e.j.99.2 12 19.12 odd 6
361.2.e.j.234.1 12 19.8 odd 6
361.2.e.j.245.1 12 19.2 odd 18
3249.2.a.i.1.2 2 57.32 even 18
3249.2.a.o.1.1 2 57.44 odd 18
5776.2.a.s.1.1 2 76.51 even 18
5776.2.a.bg.1.2 2 76.63 odd 18
9025.2.a.n.1.2 2 95.89 odd 18
9025.2.a.s.1.1 2 95.44 even 18