Properties

Label 363.2.f.e.239.2
Level $363$
Weight $2$
Character 363.239
Analytic conductor $2.899$
Analytic rank $0$
Dimension $8$
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] = [363,2,Mod(161,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), degree \(4\), 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 239.2
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 363.239
Dual form 363.2.f.e.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.53884 - 1.11803i) q^{2} +(1.08779 + 1.34786i) q^{3} +(0.500000 - 1.53884i) q^{4} +(1.53884 - 2.11803i) q^{5} +(3.18088 + 0.857960i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(0.224514 + 0.690983i) q^{8} +(-0.633446 + 2.93236i) q^{9} +O(q^{10})\) \(q+(1.53884 - 1.11803i) q^{2} +(1.08779 + 1.34786i) q^{3} +(0.500000 - 1.53884i) q^{4} +(1.53884 - 2.11803i) q^{5} +(3.18088 + 0.857960i) q^{6} +(-0.690983 - 0.224514i) q^{7} +(0.224514 + 0.690983i) q^{8} +(-0.633446 + 2.93236i) q^{9} -4.97980i q^{10} +(2.61803 - 1.00000i) q^{12} +(-1.80902 - 2.48990i) q^{13} +(-1.31433 + 0.427051i) q^{14} +(4.52874 - 0.229825i) q^{15} +(3.73607 + 2.71441i) q^{16} +(-2.12663 - 1.54508i) q^{17} +(2.30371 + 5.22066i) q^{18} +(-4.04508 + 1.31433i) q^{19} +(-2.48990 - 3.42705i) q^{20} +(-0.449028 - 1.17557i) q^{21} +1.76393i q^{23} +(-0.687124 + 1.05425i) q^{24} +(-0.572949 - 1.76336i) q^{25} +(-5.56758 - 1.80902i) q^{26} +(-4.64146 + 2.33598i) q^{27} +(-0.690983 + 0.951057i) q^{28} +(1.17557 - 3.61803i) q^{29} +(6.71206 - 5.41695i) q^{30} +(0.690983 - 0.502029i) q^{31} +7.33094 q^{32} -5.00000 q^{34} +(-1.53884 + 1.11803i) q^{35} +(4.19572 + 2.44095i) q^{36} +(0.927051 - 2.85317i) q^{37} +(-4.75528 + 6.54508i) q^{38} +(1.38821 - 5.14677i) q^{39} +(1.80902 + 0.587785i) q^{40} +(0.951057 + 2.92705i) q^{41} +(-2.00531 - 1.30699i) q^{42} +1.62460i q^{43} +(5.23607 + 5.85410i) q^{45} +(1.97214 + 2.71441i) q^{46} +(-6.96767 + 2.26393i) q^{47} +(0.405395 + 7.98839i) q^{48} +(-5.23607 - 3.80423i) q^{49} +(-2.85317 - 2.07295i) q^{50} +(-0.230757 - 4.54711i) q^{51} +(-4.73607 + 1.53884i) q^{52} +(2.85317 + 3.92705i) q^{53} +(-4.53077 + 8.78402i) q^{54} -0.527864i q^{56} +(-6.17171 - 4.02250i) q^{57} +(-2.23607 - 6.88191i) q^{58} +(2.48990 + 0.809017i) q^{59} +(1.91071 - 7.08393i) q^{60} +(-2.50000 + 3.44095i) q^{61} +(0.502029 - 1.54508i) q^{62} +(1.09606 - 1.88399i) q^{63} +(3.80902 - 2.76741i) q^{64} -8.05748 q^{65} -8.32624 q^{67} +(-3.44095 + 2.50000i) q^{68} +(-2.37753 + 1.91878i) q^{69} +(-1.11803 + 3.44095i) q^{70} +(6.06961 - 8.35410i) q^{71} +(-2.16843 + 0.220655i) q^{72} +(-14.4721 - 4.70228i) q^{73} +(-1.76336 - 5.42705i) q^{74} +(1.75351 - 2.69041i) q^{75} +6.88191i q^{76} +(-3.61803 - 9.47214i) q^{78} +(6.28115 + 8.64527i) q^{79} +(11.4984 - 3.73607i) q^{80} +(-8.19749 - 3.71499i) q^{81} +(4.73607 + 3.44095i) q^{82} +(11.7229 + 8.51722i) q^{83} +(-2.03353 + 0.103198i) q^{84} +(-6.54508 + 2.12663i) q^{85} +(1.81636 + 2.50000i) q^{86} +(6.15537 - 2.35114i) q^{87} -9.47214i q^{89} +(14.6026 + 3.15443i) q^{90} +(0.690983 + 2.12663i) q^{91} +(2.71441 + 0.881966i) q^{92} +(1.42830 + 0.385248i) q^{93} +(-8.19098 + 11.2739i) q^{94} +(-3.44095 + 10.5902i) q^{95} +(7.97449 + 9.88107i) q^{96} +(5.35410 - 3.88998i) q^{97} -12.3107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 4 q^{4} + 10 q^{6} - 10 q^{7} - 10 q^{9} + 12 q^{12} - 10 q^{13} + 4 q^{15} + 12 q^{16} + 20 q^{18} - 10 q^{19} + 20 q^{24} - 18 q^{25} - 2 q^{27} - 10 q^{28} + 30 q^{30} + 10 q^{31} - 40 q^{34} - 6 q^{37} + 10 q^{39} + 10 q^{40} - 10 q^{42} + 24 q^{45} - 20 q^{46} - 14 q^{48} - 24 q^{49} + 10 q^{51} - 20 q^{52} - 10 q^{57} - 8 q^{60} - 20 q^{61} - 10 q^{63} + 26 q^{64} - 4 q^{67} + 34 q^{69} + 20 q^{72} - 80 q^{73} + 6 q^{75} - 20 q^{78} + 10 q^{79} - 2 q^{81} + 20 q^{82} - 10 q^{84} - 30 q^{85} + 30 q^{90} + 10 q^{91} - 70 q^{94} + 30 q^{96} + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53884 1.11803i 1.08813 0.790569i 0.109044 0.994037i \(-0.465221\pi\)
0.979082 + 0.203468i \(0.0652211\pi\)
\(3\) 1.08779 + 1.34786i 0.628033 + 0.778187i
\(4\) 0.500000 1.53884i 0.250000 0.769421i
\(5\) 1.53884 2.11803i 0.688191 0.947214i −0.311805 0.950146i \(-0.600933\pi\)
0.999996 + 0.00293261i \(0.000933479\pi\)
\(6\) 3.18088 + 0.857960i 1.29859 + 0.350261i
\(7\) −0.690983 0.224514i −0.261167 0.0848583i 0.175507 0.984478i \(-0.443844\pi\)
−0.436674 + 0.899620i \(0.643844\pi\)
\(8\) 0.224514 + 0.690983i 0.0793777 + 0.244299i
\(9\) −0.633446 + 2.93236i −0.211149 + 0.977454i
\(10\) 4.97980i 1.57475i
\(11\) 0 0
\(12\) 2.61803 1.00000i 0.755761 0.288675i
\(13\) −1.80902 2.48990i −0.501731 0.690574i 0.480767 0.876849i \(-0.340358\pi\)
−0.982498 + 0.186275i \(0.940358\pi\)
\(14\) −1.31433 + 0.427051i −0.351269 + 0.114134i
\(15\) 4.52874 0.229825i 1.16932 0.0593405i
\(16\) 3.73607 + 2.71441i 0.934017 + 0.678603i
\(17\) −2.12663 1.54508i −0.515783 0.374738i 0.299230 0.954181i \(-0.403270\pi\)
−0.815013 + 0.579443i \(0.803270\pi\)
\(18\) 2.30371 + 5.22066i 0.542989 + 1.23052i
\(19\) −4.04508 + 1.31433i −0.928006 + 0.301527i −0.733747 0.679423i \(-0.762230\pi\)
−0.194259 + 0.980950i \(0.562230\pi\)
\(20\) −2.48990 3.42705i −0.556758 0.766312i
\(21\) −0.449028 1.17557i −0.0979859 0.256531i
\(22\) 0 0
\(23\) 1.76393i 0.367805i 0.982944 + 0.183903i \(0.0588731\pi\)
−0.982944 + 0.183903i \(0.941127\pi\)
\(24\) −0.687124 + 1.05425i −0.140259 + 0.215199i
\(25\) −0.572949 1.76336i −0.114590 0.352671i
\(26\) −5.56758 1.80902i −1.09189 0.354777i
\(27\) −4.64146 + 2.33598i −0.893250 + 0.449560i
\(28\) −0.690983 + 0.951057i −0.130584 + 0.179733i
\(29\) 1.17557 3.61803i 0.218298 0.671852i −0.780605 0.625025i \(-0.785089\pi\)
0.998903 0.0468274i \(-0.0149111\pi\)
\(30\) 6.71206 5.41695i 1.22545 0.988995i
\(31\) 0.690983 0.502029i 0.124104 0.0901670i −0.524002 0.851717i \(-0.675561\pi\)
0.648106 + 0.761550i \(0.275561\pi\)
\(32\) 7.33094 1.29594
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) −1.53884 + 1.11803i −0.260112 + 0.188982i
\(36\) 4.19572 + 2.44095i 0.699286 + 0.406826i
\(37\) 0.927051 2.85317i 0.152406 0.469058i −0.845483 0.534003i \(-0.820687\pi\)
0.997889 + 0.0649448i \(0.0206871\pi\)
\(38\) −4.75528 + 6.54508i −0.771409 + 1.06175i
\(39\) 1.38821 5.14677i 0.222291 0.824143i
\(40\) 1.80902 + 0.587785i 0.286031 + 0.0929370i
\(41\) 0.951057 + 2.92705i 0.148530 + 0.457129i 0.997448 0.0713961i \(-0.0227454\pi\)
−0.848918 + 0.528525i \(0.822745\pi\)
\(42\) −2.00531 1.30699i −0.309426 0.201673i
\(43\) 1.62460i 0.247749i 0.992298 + 0.123874i \(0.0395320\pi\)
−0.992298 + 0.123874i \(0.960468\pi\)
\(44\) 0 0
\(45\) 5.23607 + 5.85410i 0.780547 + 0.872678i
\(46\) 1.97214 + 2.71441i 0.290776 + 0.400218i
\(47\) −6.96767 + 2.26393i −1.01634 + 0.330228i −0.769376 0.638797i \(-0.779433\pi\)
−0.246963 + 0.969025i \(0.579433\pi\)
\(48\) 0.405395 + 7.98839i 0.0585138 + 1.15302i
\(49\) −5.23607 3.80423i −0.748010 0.543461i
\(50\) −2.85317 2.07295i −0.403499 0.293159i
\(51\) −0.230757 4.54711i −0.0323125 0.636723i
\(52\) −4.73607 + 1.53884i −0.656774 + 0.213399i
\(53\) 2.85317 + 3.92705i 0.391913 + 0.539422i 0.958691 0.284448i \(-0.0918104\pi\)
−0.566778 + 0.823870i \(0.691810\pi\)
\(54\) −4.53077 + 8.78402i −0.616560 + 1.19535i
\(55\) 0 0
\(56\) 0.527864i 0.0705388i
\(57\) −6.17171 4.02250i −0.817463 0.532793i
\(58\) −2.23607 6.88191i −0.293610 0.903639i
\(59\) 2.48990 + 0.809017i 0.324157 + 0.105325i 0.466575 0.884482i \(-0.345488\pi\)
−0.142418 + 0.989807i \(0.545488\pi\)
\(60\) 1.91071 7.08393i 0.246671 0.914531i
\(61\) −2.50000 + 3.44095i −0.320092 + 0.440569i −0.938495 0.345292i \(-0.887780\pi\)
0.618403 + 0.785861i \(0.287780\pi\)
\(62\) 0.502029 1.54508i 0.0637577 0.196226i
\(63\) 1.09606 1.88399i 0.138090 0.237361i
\(64\) 3.80902 2.76741i 0.476127 0.345927i
\(65\) −8.05748 −0.999407
\(66\) 0 0
\(67\) −8.32624 −1.01721 −0.508606 0.860999i \(-0.669839\pi\)
−0.508606 + 0.860999i \(0.669839\pi\)
\(68\) −3.44095 + 2.50000i −0.417277 + 0.303170i
\(69\) −2.37753 + 1.91878i −0.286221 + 0.230994i
\(70\) −1.11803 + 3.44095i −0.133631 + 0.411273i
\(71\) 6.06961 8.35410i 0.720330 0.991449i −0.279183 0.960238i \(-0.590063\pi\)
0.999513 0.0312115i \(-0.00993653\pi\)
\(72\) −2.16843 + 0.220655i −0.255552 + 0.0260045i
\(73\) −14.4721 4.70228i −1.69384 0.550360i −0.706321 0.707891i \(-0.749647\pi\)
−0.987514 + 0.157531i \(0.949647\pi\)
\(74\) −1.76336 5.42705i −0.204986 0.630882i
\(75\) 1.75351 2.69041i 0.202478 0.310661i
\(76\) 6.88191i 0.789409i
\(77\) 0 0
\(78\) −3.61803 9.47214i −0.409662 1.07251i
\(79\) 6.28115 + 8.64527i 0.706685 + 0.972668i 0.999862 + 0.0166102i \(0.00528743\pi\)
−0.293177 + 0.956058i \(0.594713\pi\)
\(80\) 11.4984 3.73607i 1.28556 0.417705i
\(81\) −8.19749 3.71499i −0.910832 0.412777i
\(82\) 4.73607 + 3.44095i 0.523011 + 0.379990i
\(83\) 11.7229 + 8.51722i 1.28676 + 0.934886i 0.999735 0.0230363i \(-0.00733333\pi\)
0.287026 + 0.957923i \(0.407333\pi\)
\(84\) −2.03353 + 0.103198i −0.221876 + 0.0112598i
\(85\) −6.54508 + 2.12663i −0.709914 + 0.230665i
\(86\) 1.81636 + 2.50000i 0.195863 + 0.269582i
\(87\) 6.15537 2.35114i 0.659925 0.252069i
\(88\) 0 0
\(89\) 9.47214i 1.00404i −0.864855 0.502022i \(-0.832590\pi\)
0.864855 0.502022i \(-0.167410\pi\)
\(90\) 14.6026 + 3.15443i 1.53925 + 0.332507i
\(91\) 0.690983 + 2.12663i 0.0724347 + 0.222931i
\(92\) 2.71441 + 0.881966i 0.282997 + 0.0919513i
\(93\) 1.42830 + 0.385248i 0.148108 + 0.0399484i
\(94\) −8.19098 + 11.2739i −0.844835 + 1.16282i
\(95\) −3.44095 + 10.5902i −0.353035 + 1.08653i
\(96\) 7.97449 + 9.88107i 0.813893 + 1.00848i
\(97\) 5.35410 3.88998i 0.543627 0.394968i −0.281803 0.959472i \(-0.590933\pi\)
0.825430 + 0.564504i \(0.190933\pi\)
\(98\) −12.3107 −1.24357
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) 10.0984 7.33688i 1.00482 0.730047i 0.0417064 0.999130i \(-0.486721\pi\)
0.963117 + 0.269083i \(0.0867206\pi\)
\(102\) −5.43893 6.73929i −0.538534 0.667290i
\(103\) −2.09017 + 6.43288i −0.205951 + 0.633851i 0.793722 + 0.608280i \(0.208140\pi\)
−0.999673 + 0.0255706i \(0.991860\pi\)
\(104\) 1.31433 1.80902i 0.128880 0.177389i
\(105\) −3.18088 0.857960i −0.310422 0.0837284i
\(106\) 8.78115 + 2.85317i 0.852901 + 0.277124i
\(107\) 0.0530006 + 0.163119i 0.00512376 + 0.0157693i 0.953586 0.301122i \(-0.0973610\pi\)
−0.948462 + 0.316891i \(0.897361\pi\)
\(108\) 1.27398 + 8.31047i 0.122589 + 0.799675i
\(109\) 7.60845i 0.728758i 0.931251 + 0.364379i \(0.118719\pi\)
−0.931251 + 0.364379i \(0.881281\pi\)
\(110\) 0 0
\(111\) 4.85410 1.85410i 0.460731 0.175984i
\(112\) −1.97214 2.71441i −0.186349 0.256488i
\(113\) 18.9681 6.16312i 1.78437 0.579777i 0.785153 0.619302i \(-0.212584\pi\)
0.999219 + 0.0395244i \(0.0125843\pi\)
\(114\) −13.9946 + 0.710198i −1.31071 + 0.0665161i
\(115\) 3.73607 + 2.71441i 0.348390 + 0.253120i
\(116\) −4.97980 3.61803i −0.462363 0.335926i
\(117\) 8.44720 3.72747i 0.780944 0.344605i
\(118\) 4.73607 1.53884i 0.435990 0.141662i
\(119\) 1.12257 + 1.54508i 0.102906 + 0.141638i
\(120\) 1.17557 + 3.07768i 0.107314 + 0.280953i
\(121\) 0 0
\(122\) 8.09017i 0.732450i
\(123\) −2.91071 + 4.46589i −0.262450 + 0.402676i
\(124\) −0.427051 1.31433i −0.0383503 0.118030i
\(125\) 7.83297 + 2.54508i 0.700602 + 0.227639i
\(126\) −0.419712 4.12460i −0.0373909 0.367448i
\(127\) 7.76393 10.6861i 0.688938 0.948241i −0.311060 0.950390i \(-0.600684\pi\)
0.999998 + 0.00214903i \(0.000684058\pi\)
\(128\) −1.76336 + 5.42705i −0.155860 + 0.479688i
\(129\) −2.18973 + 1.76721i −0.192795 + 0.155595i
\(130\) −12.3992 + 9.00854i −1.08748 + 0.790101i
\(131\) 4.08174 0.356623 0.178312 0.983974i \(-0.442936\pi\)
0.178312 + 0.983974i \(0.442936\pi\)
\(132\) 0 0
\(133\) 3.09017 0.267952
\(134\) −12.8128 + 9.30902i −1.10685 + 0.804177i
\(135\) −2.19479 + 13.4255i −0.188897 + 1.15548i
\(136\) 0.590170 1.81636i 0.0506067 0.155751i
\(137\) −5.11855 + 7.04508i −0.437308 + 0.601902i −0.969611 0.244651i \(-0.921327\pi\)
0.532304 + 0.846554i \(0.321327\pi\)
\(138\) −1.51338 + 5.61086i −0.128828 + 0.477628i
\(139\) 1.64590 + 0.534785i 0.139603 + 0.0453598i 0.377985 0.925812i \(-0.376617\pi\)
−0.238382 + 0.971171i \(0.576617\pi\)
\(140\) 0.951057 + 2.92705i 0.0803789 + 0.247381i
\(141\) −10.6308 6.92876i −0.895274 0.583507i
\(142\) 19.6417i 1.64829i
\(143\) 0 0
\(144\) −10.3262 + 9.23607i −0.860520 + 0.769672i
\(145\) −5.85410 8.05748i −0.486157 0.669137i
\(146\) −27.5276 + 8.94427i −2.27820 + 0.740233i
\(147\) −0.568158 11.1957i −0.0468609 0.923403i
\(148\) −3.92705 2.85317i −0.322802 0.234529i
\(149\) 0.138757 + 0.100813i 0.0113674 + 0.00825893i 0.593454 0.804868i \(-0.297764\pi\)
−0.582087 + 0.813126i \(0.697764\pi\)
\(150\) −0.309593 6.10059i −0.0252782 0.498111i
\(151\) 16.7082 5.42882i 1.35969 0.441791i 0.463753 0.885964i \(-0.346502\pi\)
0.895941 + 0.444173i \(0.146502\pi\)
\(152\) −1.81636 2.50000i −0.147326 0.202777i
\(153\) 5.87785 5.25731i 0.475196 0.425028i
\(154\) 0 0
\(155\) 2.23607i 0.179605i
\(156\) −7.22597 4.70962i −0.578540 0.377071i
\(157\) −1.14590 3.52671i −0.0914526 0.281462i 0.894860 0.446346i \(-0.147275\pi\)
−0.986313 + 0.164884i \(0.947275\pi\)
\(158\) 19.3314 + 6.28115i 1.53792 + 0.499702i
\(159\) −2.18947 + 8.11746i −0.173637 + 0.643756i
\(160\) 11.2812 15.5272i 0.891853 1.22753i
\(161\) 0.396027 1.21885i 0.0312113 0.0960586i
\(162\) −16.7681 + 3.44829i −1.31743 + 0.270924i
\(163\) 10.0172 7.27794i 0.784609 0.570052i −0.121750 0.992561i \(-0.538850\pi\)
0.906359 + 0.422509i \(0.138850\pi\)
\(164\) 4.97980 0.388857
\(165\) 0 0
\(166\) 27.5623 2.13925
\(167\) 0.0857567 0.0623059i 0.00663605 0.00482138i −0.584462 0.811421i \(-0.698695\pi\)
0.591098 + 0.806600i \(0.298695\pi\)
\(168\) 0.711486 0.574203i 0.0548924 0.0443007i
\(169\) 1.09017 3.35520i 0.0838592 0.258092i
\(170\) −7.69421 + 10.5902i −0.590119 + 0.812229i
\(171\) −1.29174 12.6942i −0.0987818 0.970750i
\(172\) 2.50000 + 0.812299i 0.190623 + 0.0619372i
\(173\) −6.84915 21.0795i −0.520731 1.60265i −0.772605 0.634887i \(-0.781047\pi\)
0.251874 0.967760i \(-0.418953\pi\)
\(174\) 6.84348 10.4999i 0.518803 0.795999i
\(175\) 1.34708i 0.101830i
\(176\) 0 0
\(177\) 1.61803 + 4.23607i 0.121619 + 0.318402i
\(178\) −10.5902 14.5761i −0.793767 1.09253i
\(179\) 3.75123 1.21885i 0.280380 0.0911009i −0.165452 0.986218i \(-0.552908\pi\)
0.445831 + 0.895117i \(0.352908\pi\)
\(180\) 11.6266 5.13043i 0.866593 0.382400i
\(181\) −9.89919 7.19218i −0.735801 0.534591i 0.155592 0.987821i \(-0.450271\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(182\) 3.44095 + 2.50000i 0.255061 + 0.185312i
\(183\) −7.35738 + 0.373373i −0.543873 + 0.0276005i
\(184\) −1.21885 + 0.396027i −0.0898546 + 0.0291955i
\(185\) −4.61653 6.35410i −0.339414 0.467163i
\(186\) 2.62866 1.00406i 0.192742 0.0736210i
\(187\) 0 0
\(188\) 11.8541i 0.864549i
\(189\) 3.73163 0.572051i 0.271436 0.0416106i
\(190\) 6.54508 + 20.1437i 0.474830 + 1.46138i
\(191\) −18.7966 6.10739i −1.36008 0.441915i −0.464007 0.885831i \(-0.653589\pi\)
−0.896068 + 0.443916i \(0.853589\pi\)
\(192\) 7.87347 + 2.12367i 0.568219 + 0.153262i
\(193\) −11.8713 + 16.3395i −0.854517 + 1.17614i 0.128333 + 0.991731i \(0.459037\pi\)
−0.982849 + 0.184410i \(0.940963\pi\)
\(194\) 3.88998 11.9721i 0.279284 0.859549i
\(195\) −8.76481 10.8603i −0.627661 0.777725i
\(196\) −8.47214 + 6.15537i −0.605153 + 0.439669i
\(197\) 15.8374 1.12837 0.564186 0.825648i \(-0.309190\pi\)
0.564186 + 0.825648i \(0.309190\pi\)
\(198\) 0 0
\(199\) −2.23607 −0.158511 −0.0792553 0.996854i \(-0.525254\pi\)
−0.0792553 + 0.996854i \(0.525254\pi\)
\(200\) 1.08981 0.791796i 0.0770615 0.0559884i
\(201\) −9.05716 11.2226i −0.638843 0.791581i
\(202\) 7.33688 22.5806i 0.516221 1.58877i
\(203\) −1.62460 + 2.23607i −0.114024 + 0.156941i
\(204\) −7.11267 1.91846i −0.497986 0.134319i
\(205\) 7.66312 + 2.48990i 0.535215 + 0.173902i
\(206\) 3.97574 + 12.2361i 0.277003 + 0.852527i
\(207\) −5.17249 1.11736i −0.359513 0.0776616i
\(208\) 14.2128i 0.985484i
\(209\) 0 0
\(210\) −5.85410 + 2.23607i −0.403971 + 0.154303i
\(211\) 3.98278 + 5.48183i 0.274186 + 0.377384i 0.923797 0.382882i \(-0.125068\pi\)
−0.649611 + 0.760266i \(0.725068\pi\)
\(212\) 7.46969 2.42705i 0.513021 0.166691i
\(213\) 17.8626 0.906491i 1.22392 0.0621118i
\(214\) 0.263932 + 0.191758i 0.0180420 + 0.0131083i
\(215\) 3.44095 + 2.50000i 0.234671 + 0.170499i
\(216\) −2.65620 2.68271i −0.180731 0.182535i
\(217\) −0.590170 + 0.191758i −0.0400633 + 0.0130174i
\(218\) 8.50651 + 11.7082i 0.576133 + 0.792980i
\(219\) −9.40456 24.6215i −0.635502 1.66376i
\(220\) 0 0
\(221\) 8.09017i 0.544204i
\(222\) 5.39675 8.28022i 0.362206 0.555732i
\(223\) 1.92705 + 5.93085i 0.129045 + 0.397159i 0.994616 0.103626i \(-0.0330446\pi\)
−0.865571 + 0.500785i \(0.833045\pi\)
\(224\) −5.06555 1.64590i −0.338457 0.109971i
\(225\) 5.53373 0.563102i 0.368915 0.0375402i
\(226\) 22.2984 30.6911i 1.48327 2.04154i
\(227\) 1.95511 6.01722i 0.129765 0.399377i −0.864974 0.501817i \(-0.832665\pi\)
0.994739 + 0.102440i \(0.0326650\pi\)
\(228\) −9.27584 + 7.48604i −0.614308 + 0.495775i
\(229\) −20.3262 + 14.7679i −1.34320 + 0.975889i −0.343876 + 0.939015i \(0.611740\pi\)
−0.999320 + 0.0368735i \(0.988260\pi\)
\(230\) 8.78402 0.579201
\(231\) 0 0
\(232\) 2.76393 0.181461
\(233\) 5.79210 4.20820i 0.379453 0.275689i −0.381667 0.924300i \(-0.624650\pi\)
0.761120 + 0.648611i \(0.224650\pi\)
\(234\) 8.83146 15.1802i 0.577330 0.992364i
\(235\) −5.92705 + 18.2416i −0.386638 + 1.18995i
\(236\) 2.48990 3.42705i 0.162079 0.223082i
\(237\) −4.82005 + 17.8703i −0.313096 + 1.16080i
\(238\) 3.45492 + 1.12257i 0.223949 + 0.0727654i
\(239\) 7.97172 + 24.5344i 0.515648 + 1.58700i 0.782100 + 0.623153i \(0.214149\pi\)
−0.266452 + 0.963848i \(0.585851\pi\)
\(240\) 17.5435 + 11.4342i 1.13243 + 0.738076i
\(241\) 19.5762i 1.26101i 0.776185 + 0.630506i \(0.217152\pi\)
−0.776185 + 0.630506i \(0.782848\pi\)
\(242\) 0 0
\(243\) −3.90983 15.0902i −0.250816 0.968035i
\(244\) 4.04508 + 5.56758i 0.258960 + 0.356428i
\(245\) −16.1150 + 5.23607i −1.02955 + 0.334520i
\(246\) 0.513904 + 10.1266i 0.0327653 + 0.645647i
\(247\) 10.5902 + 7.69421i 0.673836 + 0.489571i
\(248\) 0.502029 + 0.364745i 0.0318788 + 0.0231613i
\(249\) 1.27204 + 25.0658i 0.0806123 + 1.58848i
\(250\) 14.8992 4.84104i 0.942307 0.306174i
\(251\) −2.74717 3.78115i −0.173400 0.238664i 0.713468 0.700688i \(-0.247123\pi\)
−0.886868 + 0.462024i \(0.847123\pi\)
\(252\) −2.35114 2.62866i −0.148108 0.165590i
\(253\) 0 0
\(254\) 25.1246i 1.57646i
\(255\) −9.98604 6.50854i −0.625350 0.407580i
\(256\) 6.26393 + 19.2784i 0.391496 + 1.20490i
\(257\) −10.7189 3.48278i −0.668626 0.217250i −0.0450171 0.998986i \(-0.514334\pi\)
−0.623609 + 0.781736i \(0.714334\pi\)
\(258\) −1.39384 + 5.16765i −0.0867768 + 0.321724i
\(259\) −1.28115 + 1.76336i −0.0796070 + 0.109570i
\(260\) −4.02874 + 12.3992i −0.249852 + 0.768965i
\(261\) 9.86472 + 5.73903i 0.610611 + 0.355237i
\(262\) 6.28115 4.56352i 0.388051 0.281936i
\(263\) −23.2744 −1.43516 −0.717580 0.696476i \(-0.754750\pi\)
−0.717580 + 0.696476i \(0.754750\pi\)
\(264\) 0 0
\(265\) 12.7082 0.780659
\(266\) 4.75528 3.45492i 0.291565 0.211834i
\(267\) 12.7671 10.3036i 0.781334 0.630573i
\(268\) −4.16312 + 12.8128i −0.254303 + 0.782664i
\(269\) 13.6578 18.7984i 0.832732 1.14616i −0.154677 0.987965i \(-0.549434\pi\)
0.987408 0.158192i \(-0.0505665\pi\)
\(270\) 11.6327 + 23.1135i 0.707945 + 1.40665i
\(271\) 22.4615 + 7.29818i 1.36444 + 0.443333i 0.897522 0.440969i \(-0.145365\pi\)
0.466916 + 0.884302i \(0.345365\pi\)
\(272\) −3.75123 11.5451i −0.227451 0.700024i
\(273\) −2.11475 + 3.24466i −0.127991 + 0.196376i
\(274\) 16.5640i 1.00067i
\(275\) 0 0
\(276\) 1.76393 + 4.61803i 0.106176 + 0.277973i
\(277\) 12.0729 + 16.6170i 0.725393 + 0.998418i 0.999327 + 0.0366697i \(0.0116749\pi\)
−0.273934 + 0.961748i \(0.588325\pi\)
\(278\) 3.13068 1.01722i 0.187766 0.0610089i
\(279\) 1.03443 + 2.34422i 0.0619296 + 0.140345i
\(280\) −1.11803 0.812299i −0.0668153 0.0485442i
\(281\) −13.3148 9.67376i −0.794294 0.577088i 0.114941 0.993372i \(-0.463332\pi\)
−0.909235 + 0.416284i \(0.863332\pi\)
\(282\) −24.1057 + 1.22332i −1.43547 + 0.0728474i
\(283\) 7.56231 2.45714i 0.449532 0.146062i −0.0754970 0.997146i \(-0.524054\pi\)
0.525029 + 0.851084i \(0.324054\pi\)
\(284\) −9.82084 13.5172i −0.582759 0.802099i
\(285\) −18.0171 + 6.88191i −1.06724 + 0.407649i
\(286\) 0 0
\(287\) 2.23607i 0.131991i
\(288\) −4.64376 + 21.4970i −0.273636 + 1.26672i
\(289\) −3.11803 9.59632i −0.183414 0.564490i
\(290\) −18.0171 5.85410i −1.05800 0.343765i
\(291\) 11.0673 + 2.98511i 0.648774 + 0.174990i
\(292\) −14.4721 + 19.9192i −0.846918 + 1.16568i
\(293\) −3.02468 + 9.30902i −0.176704 + 0.543839i −0.999707 0.0241980i \(-0.992297\pi\)
0.823003 + 0.568037i \(0.192297\pi\)
\(294\) −13.3914 16.5931i −0.781004 0.967731i
\(295\) 5.54508 4.02874i 0.322847 0.234562i
\(296\) 2.17963 0.126688
\(297\) 0 0
\(298\) 0.326238 0.0188985
\(299\) 4.39201 3.19098i 0.253997 0.184539i
\(300\) −3.26336 4.04358i −0.188410 0.233456i
\(301\) 0.364745 1.12257i 0.0210236 0.0647039i
\(302\) 19.6417 27.0344i 1.13025 1.55566i
\(303\) 20.8739 + 5.63020i 1.19918 + 0.323446i
\(304\) −18.6803 6.06961i −1.07139 0.348116i
\(305\) 3.44095 + 10.5902i 0.197028 + 0.606391i
\(306\) 3.16723 14.6618i 0.181059 0.838160i
\(307\) 5.87785i 0.335467i −0.985832 0.167733i \(-0.946355\pi\)
0.985832 0.167733i \(-0.0536448\pi\)
\(308\) 0 0
\(309\) −10.9443 + 4.18034i −0.622598 + 0.237811i
\(310\) −2.50000 3.44095i −0.141990 0.195433i
\(311\) 4.75528 1.54508i 0.269647 0.0876137i −0.171072 0.985258i \(-0.554723\pi\)
0.440720 + 0.897645i \(0.354723\pi\)
\(312\) 3.86801 0.196294i 0.218983 0.0111129i
\(313\) −8.89919 6.46564i −0.503012 0.365459i 0.307154 0.951660i \(-0.400623\pi\)
−0.810166 + 0.586200i \(0.800623\pi\)
\(314\) −5.70634 4.14590i −0.322027 0.233967i
\(315\) −2.30371 5.22066i −0.129799 0.294151i
\(316\) 16.4443 5.34307i 0.925063 0.300571i
\(317\) −0.138757 0.190983i −0.00779339 0.0107267i 0.805103 0.593136i \(-0.202110\pi\)
−0.812896 + 0.582409i \(0.802110\pi\)
\(318\) 5.70634 + 14.9394i 0.319996 + 0.837759i
\(319\) 0 0
\(320\) 12.3262i 0.689058i
\(321\) −0.162208 + 0.248876i −0.00905357 + 0.0138909i
\(322\) −0.753289 2.31838i −0.0419791 0.129199i
\(323\) 10.6331 + 3.45492i 0.591643 + 0.192237i
\(324\) −9.81553 + 10.7571i −0.545307 + 0.597619i
\(325\) −3.35410 + 4.61653i −0.186052 + 0.256079i
\(326\) 7.27794 22.3992i 0.403088 1.24058i
\(327\) −10.2551 + 8.27636i −0.567109 + 0.457684i
\(328\) −1.80902 + 1.31433i −0.0998863 + 0.0725716i
\(329\) 5.32282 0.293457
\(330\) 0 0
\(331\) −22.8885 −1.25807 −0.629034 0.777378i \(-0.716549\pi\)
−0.629034 + 0.777378i \(0.716549\pi\)
\(332\) 18.9681 13.7812i 1.04101 0.756339i
\(333\) 7.77929 + 4.52578i 0.426302 + 0.248011i
\(334\) 0.0623059 0.191758i 0.00340923 0.0104925i
\(335\) −12.8128 + 17.6353i −0.700036 + 0.963517i
\(336\) 1.51338 5.61086i 0.0825619 0.306097i
\(337\) −9.79837 3.18368i −0.533751 0.173426i 0.0297256 0.999558i \(-0.490537\pi\)
−0.563477 + 0.826132i \(0.690537\pi\)
\(338\) −2.07363 6.38197i −0.112790 0.347133i
\(339\) 28.9403 + 18.8622i 1.57182 + 1.02445i
\(340\) 11.1352i 0.603889i
\(341\) 0 0
\(342\) −16.1803 18.0902i −0.874933 0.978204i
\(343\) 5.75329 + 7.91872i 0.310648 + 0.427571i
\(344\) −1.12257 + 0.364745i −0.0605249 + 0.0196657i
\(345\) 0.405395 + 7.98839i 0.0218257 + 0.430080i
\(346\) −34.1074 24.7805i −1.83362 1.33221i
\(347\) −24.8990 18.0902i −1.33665 0.971131i −0.999560 0.0296578i \(-0.990558\pi\)
−0.337087 0.941473i \(-0.609442\pi\)
\(348\) −0.540350 10.6477i −0.0289658 0.570777i
\(349\) −15.4894 + 5.03280i −0.829126 + 0.269399i −0.692677 0.721248i \(-0.743569\pi\)
−0.136449 + 0.990647i \(0.543569\pi\)
\(350\) 1.50609 + 2.07295i 0.0805037 + 0.110804i
\(351\) 14.2128 + 7.33094i 0.758626 + 0.391297i
\(352\) 0 0
\(353\) 15.5967i 0.830131i 0.909792 + 0.415066i \(0.136241\pi\)
−0.909792 + 0.415066i \(0.863759\pi\)
\(354\) 7.22597 + 4.70962i 0.384056 + 0.250314i
\(355\) −8.35410 25.7113i −0.443390 1.36461i
\(356\) −14.5761 4.73607i −0.772533 0.251011i
\(357\) −0.861441 + 3.19379i −0.0455923 + 0.169033i
\(358\) 4.40983 6.06961i 0.233067 0.320789i
\(359\) 7.71445 23.7426i 0.407153 1.25309i −0.511931 0.859027i \(-0.671069\pi\)
0.919084 0.394062i \(-0.128931\pi\)
\(360\) −2.86951 + 4.93236i −0.151237 + 0.259958i
\(361\) −0.736068 + 0.534785i −0.0387404 + 0.0281466i
\(362\) −23.2744 −1.22327
\(363\) 0 0
\(364\) 3.61803 0.189637
\(365\) −32.2299 + 23.4164i −1.68699 + 1.22567i
\(366\) −10.9044 + 8.80037i −0.569982 + 0.460003i
\(367\) −7.10081 + 21.8541i −0.370659 + 1.14077i 0.575701 + 0.817660i \(0.304729\pi\)
−0.946361 + 0.323112i \(0.895271\pi\)
\(368\) −4.78804 + 6.59017i −0.249594 + 0.343536i
\(369\) −9.18562 + 0.934712i −0.478184 + 0.0486591i
\(370\) −14.2082 4.61653i −0.738649 0.240002i
\(371\) −1.08981 3.35410i −0.0565803 0.174136i
\(372\) 1.30699 2.00531i 0.0677642 0.103971i
\(373\) 19.5357i 1.01152i 0.862675 + 0.505759i \(0.168788\pi\)
−0.862675 + 0.505759i \(0.831212\pi\)
\(374\) 0 0
\(375\) 5.09017 + 13.3262i 0.262855 + 0.688164i
\(376\) −3.12868 4.30625i −0.161349 0.222078i
\(377\) −11.1352 + 3.61803i −0.573490 + 0.186338i
\(378\) 5.10282 5.05239i 0.262461 0.259867i
\(379\) 26.6074 + 19.3314i 1.36673 + 0.992987i 0.997985 + 0.0634569i \(0.0202125\pi\)
0.368745 + 0.929530i \(0.379787\pi\)
\(380\) 14.5761 + 10.5902i 0.747739 + 0.543264i
\(381\) 22.8489 1.15954i 1.17058 0.0594049i
\(382\) −35.7533 + 11.6169i −1.82930 + 0.594375i
\(383\) 8.47375 + 11.6631i 0.432988 + 0.595958i 0.968636 0.248484i \(-0.0799324\pi\)
−0.535647 + 0.844442i \(0.679932\pi\)
\(384\) −9.23305 + 3.52671i −0.471172 + 0.179972i
\(385\) 0 0
\(386\) 38.4164i 1.95534i
\(387\) −4.76391 1.02910i −0.242163 0.0523119i
\(388\) −3.30902 10.1841i −0.167990 0.517020i
\(389\) 9.14729 + 2.97214i 0.463786 + 0.150693i 0.531584 0.847006i \(-0.321597\pi\)
−0.0677974 + 0.997699i \(0.521597\pi\)
\(390\) −25.6299 6.91300i −1.29782 0.350053i
\(391\) 2.72542 3.75123i 0.137831 0.189708i
\(392\) 1.45309 4.47214i 0.0733919 0.225877i
\(393\) 4.44006 + 5.50161i 0.223971 + 0.277520i
\(394\) 24.3713 17.7068i 1.22781 0.892056i
\(395\) 27.9767 1.40766
\(396\) 0 0
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) −3.44095 + 2.50000i −0.172479 + 0.125314i
\(399\) 3.36144 + 4.16511i 0.168283 + 0.208516i
\(400\) 2.64590 8.14324i 0.132295 0.407162i
\(401\) −12.4292 + 17.1074i −0.620687 + 0.854302i −0.997403 0.0720266i \(-0.977053\pi\)
0.376716 + 0.926329i \(0.377053\pi\)
\(402\) −26.4848 7.14358i −1.32094 0.356290i
\(403\) −2.50000 0.812299i −0.124534 0.0404635i
\(404\) −6.24112 19.2082i −0.310508 0.955644i
\(405\) −20.4831 + 11.6458i −1.01781 + 0.578684i
\(406\) 5.25731i 0.260916i
\(407\) 0 0
\(408\) 3.09017 1.18034i 0.152986 0.0584355i
\(409\) −20.1246 27.6992i −0.995098 1.36963i −0.928285 0.371869i \(-0.878717\pi\)
−0.0668129 0.997766i \(-0.521283\pi\)
\(410\) 14.5761 4.73607i 0.719863 0.233898i
\(411\) −15.0637 + 0.764452i −0.743036 + 0.0377076i
\(412\) 8.85410 + 6.43288i 0.436210 + 0.316925i
\(413\) −1.53884 1.11803i −0.0757215 0.0550149i
\(414\) −9.20888 + 4.06358i −0.452592 + 0.199714i
\(415\) 36.0795 11.7229i 1.77107 0.575457i
\(416\) −13.2618 18.2533i −0.650213 0.894941i
\(417\) 1.06957 + 2.80017i 0.0523770 + 0.137125i
\(418\) 0 0
\(419\) 5.85410i 0.285992i −0.989723 0.142996i \(-0.954326\pi\)
0.989723 0.142996i \(-0.0456735\pi\)
\(420\) −2.91071 + 4.46589i −0.142028 + 0.217913i
\(421\) 7.98936 + 24.5887i 0.389377 + 1.19838i 0.933255 + 0.359216i \(0.116956\pi\)
−0.543877 + 0.839165i \(0.683044\pi\)
\(422\) 12.2577 + 3.98278i 0.596697 + 0.193879i
\(423\) −2.22502 21.8658i −0.108184 1.06315i
\(424\) −2.07295 + 2.85317i −0.100671 + 0.138562i
\(425\) −1.50609 + 4.63525i −0.0730559 + 0.224843i
\(426\) 26.4742 21.3659i 1.28268 1.03518i
\(427\) 2.50000 1.81636i 0.120983 0.0878996i
\(428\) 0.277515 0.0134142
\(429\) 0 0
\(430\) 8.09017 0.390143
\(431\) −18.2416 + 13.2533i −0.878666 + 0.638388i −0.932898 0.360140i \(-0.882729\pi\)
0.0542320 + 0.998528i \(0.482729\pi\)
\(432\) −23.6816 3.87145i −1.13938 0.186265i
\(433\) −1.85410 + 5.70634i −0.0891025 + 0.274229i −0.985672 0.168674i \(-0.946051\pi\)
0.896569 + 0.442903i \(0.146051\pi\)
\(434\) −0.693786 + 0.954915i −0.0333028 + 0.0458374i
\(435\) 4.49234 16.6553i 0.215391 0.798561i
\(436\) 11.7082 + 3.80423i 0.560721 + 0.182189i
\(437\) −2.31838 7.13525i −0.110903 0.341326i
\(438\) −41.9998 27.3739i −2.00683 1.30798i
\(439\) 25.3480i 1.20979i −0.796304 0.604897i \(-0.793214\pi\)
0.796304 0.604897i \(-0.206786\pi\)
\(440\) 0 0
\(441\) 14.4721 12.9443i 0.689149 0.616394i
\(442\) 9.04508 + 12.4495i 0.430231 + 0.592162i
\(443\) −9.95959 + 3.23607i −0.473195 + 0.153750i −0.535899 0.844282i \(-0.680027\pi\)
0.0627048 + 0.998032i \(0.480027\pi\)
\(444\) −0.426119 8.39675i −0.0202227 0.398492i
\(445\) −20.0623 14.5761i −0.951045 0.690974i
\(446\) 9.59632 + 6.97214i 0.454399 + 0.330140i
\(447\) 0.0150563 + 0.296688i 0.000712141 + 0.0140329i
\(448\) −3.25329 + 1.05706i −0.153703 + 0.0499413i
\(449\) −4.63677 6.38197i −0.218823 0.301184i 0.685466 0.728104i \(-0.259598\pi\)
−0.904289 + 0.426921i \(0.859598\pi\)
\(450\) 7.88597 7.05342i 0.371748 0.332502i
\(451\) 0 0
\(452\) 32.2705i 1.51788i
\(453\) 25.4922 + 16.6149i 1.19773 + 0.780636i
\(454\) −3.71885 11.4454i −0.174534 0.537161i
\(455\) 5.56758 + 1.80902i 0.261012 + 0.0848080i
\(456\) 1.39384 5.16765i 0.0652726 0.241998i
\(457\) 6.34346 8.73102i 0.296734 0.408420i −0.634453 0.772962i \(-0.718774\pi\)
0.931187 + 0.364542i \(0.118774\pi\)
\(458\) −14.7679 + 45.4508i −0.690058 + 2.12378i
\(459\) 13.4800 + 2.20369i 0.629190 + 0.102859i
\(460\) 6.04508 4.39201i 0.281854 0.204779i
\(461\) −26.8666 −1.25130 −0.625651 0.780103i \(-0.715167\pi\)
−0.625651 + 0.780103i \(0.715167\pi\)
\(462\) 0 0
\(463\) −0.270510 −0.0125717 −0.00628583 0.999980i \(-0.502001\pi\)
−0.00628583 + 0.999980i \(0.502001\pi\)
\(464\) 14.2128 10.3262i 0.659815 0.479384i
\(465\) 3.01390 2.43236i 0.139766 0.112798i
\(466\) 4.20820 12.9515i 0.194941 0.599968i
\(467\) −13.9026 + 19.1353i −0.643335 + 0.885474i −0.998788 0.0492200i \(-0.984326\pi\)
0.355453 + 0.934694i \(0.384326\pi\)
\(468\) −1.51240 14.8626i −0.0699105 0.687026i
\(469\) 5.75329 + 1.86936i 0.265662 + 0.0863189i
\(470\) 11.2739 + 34.6976i 0.520027 + 1.60048i
\(471\) 3.50702 5.38081i 0.161595 0.247935i
\(472\) 1.90211i 0.0875518i
\(473\) 0 0
\(474\) 12.5623 + 32.8885i 0.577006 + 1.51062i
\(475\) 4.63525 + 6.37988i 0.212680 + 0.292729i
\(476\) 2.93893 0.954915i 0.134705 0.0437685i
\(477\) −13.3229 + 5.87895i −0.610012 + 0.269179i
\(478\) 39.6976 + 28.8420i 1.81572 + 1.31920i
\(479\) 18.5191 + 13.4549i 0.846159 + 0.614771i 0.924084 0.382188i \(-0.124829\pi\)
−0.0779250 + 0.996959i \(0.524829\pi\)
\(480\) 33.1999 1.68483i 1.51536 0.0769017i
\(481\) −8.78115 + 2.85317i −0.400386 + 0.130093i
\(482\) 21.8868 + 30.1246i 0.996917 + 1.37214i
\(483\) 2.07363 0.792055i 0.0943533 0.0360397i
\(484\) 0 0
\(485\) 17.3262i 0.786744i
\(486\) −22.8879 18.8501i −1.03822 0.855056i
\(487\) −2.30902 7.10642i −0.104632 0.322023i 0.885012 0.465568i \(-0.154150\pi\)
−0.989644 + 0.143545i \(0.954150\pi\)
\(488\) −2.93893 0.954915i −0.133039 0.0432270i
\(489\) 20.7062 + 5.58497i 0.936367 + 0.252561i
\(490\) −18.9443 + 26.0746i −0.855815 + 1.17793i
\(491\) −8.24924 + 25.3885i −0.372283 + 1.14577i 0.573011 + 0.819548i \(0.305775\pi\)
−0.945294 + 0.326221i \(0.894225\pi\)
\(492\) 5.41695 + 6.71206i 0.244215 + 0.302603i
\(493\) −8.09017 + 5.87785i −0.364363 + 0.264725i
\(494\) 24.8990 1.12026
\(495\) 0 0
\(496\) 3.94427 0.177103
\(497\) −6.06961 + 4.40983i −0.272259 + 0.197808i
\(498\) 29.9819 + 37.1501i 1.34352 + 1.66474i
\(499\) 3.39261 10.4414i 0.151874 0.467420i −0.845957 0.533252i \(-0.820970\pi\)
0.997831 + 0.0658313i \(0.0209699\pi\)
\(500\) 7.83297 10.7812i 0.350301 0.482148i
\(501\) 0.177264 + 0.0478125i 0.00791959 + 0.00213610i
\(502\) −8.45492 2.74717i −0.377361 0.122612i
\(503\) −1.62460 5.00000i −0.0724373 0.222939i 0.908283 0.418357i \(-0.137394\pi\)
−0.980720 + 0.195418i \(0.937394\pi\)
\(504\) 1.54789 + 0.334374i 0.0689484 + 0.0148942i
\(505\) 32.6789i 1.45419i
\(506\) 0 0
\(507\) 5.70820 2.18034i 0.253510 0.0968323i
\(508\) −12.5623 17.2905i −0.557362 0.767143i
\(509\) 0.257270 0.0835921i 0.0114033 0.00370516i −0.303310 0.952892i \(-0.598092\pi\)
0.314713 + 0.949187i \(0.398092\pi\)
\(510\) −22.6437 + 1.14912i −1.00268 + 0.0508841i
\(511\) 8.94427 + 6.49839i 0.395671 + 0.287472i
\(512\) 21.9601 + 15.9549i 0.970507 + 0.705114i
\(513\) 15.7049 15.5497i 0.693387 0.686534i
\(514\) −20.3885 + 6.62464i −0.899300 + 0.292200i
\(515\) 10.4086 + 14.3262i 0.458659 + 0.631289i
\(516\) 1.62460 + 4.25325i 0.0715190 + 0.187239i
\(517\) 0 0
\(518\) 4.14590i 0.182160i
\(519\) 20.9618 32.1617i 0.920122 1.41174i
\(520\) −1.80902 5.56758i −0.0793306 0.244155i
\(521\) 19.2986 + 6.27051i 0.845489 + 0.274716i 0.699555 0.714578i \(-0.253381\pi\)
0.145934 + 0.989294i \(0.453381\pi\)
\(522\) 21.5967 2.19764i 0.945261 0.0961880i
\(523\) −1.87132 + 2.57565i −0.0818272 + 0.112626i −0.847968 0.530047i \(-0.822174\pi\)
0.766141 + 0.642672i \(0.222174\pi\)
\(524\) 2.04087 6.28115i 0.0891558 0.274393i
\(525\) −1.81568 + 1.46534i −0.0792427 + 0.0639526i
\(526\) −35.8156 + 26.0216i −1.56163 + 1.13459i
\(527\) −2.24514 −0.0977998
\(528\) 0 0
\(529\) 19.8885 0.864719
\(530\) 19.5559 14.2082i 0.849455 0.617165i
\(531\) −3.94955 + 6.78881i −0.171396 + 0.294609i
\(532\) 1.54508 4.75528i 0.0669879 0.206168i
\(533\) 5.56758 7.66312i 0.241159 0.331927i
\(534\) 8.12672 30.1297i 0.351677 1.30384i
\(535\) 0.427051 + 0.138757i 0.0184630 + 0.00599900i
\(536\) −1.86936 5.75329i −0.0807439 0.248504i
\(537\) 5.72336 + 3.73028i 0.246981 + 0.160973i
\(538\) 44.1976i 1.90550i
\(539\) 0 0
\(540\) 19.5623 + 10.0902i 0.841828 + 0.434212i
\(541\) 14.5344 + 20.0049i 0.624884 + 0.860080i 0.997697 0.0678270i \(-0.0216066\pi\)
−0.372813 + 0.927907i \(0.621607\pi\)
\(542\) 42.7243 13.8820i 1.83517 0.596281i
\(543\) −1.07415 21.1663i −0.0460960 0.908331i
\(544\) −15.5902 11.3269i −0.668423 0.485638i
\(545\) 16.1150 + 11.7082i 0.690289 + 0.501524i
\(546\) 0.373373 + 7.35738i 0.0159789 + 0.314867i
\(547\) −29.2082 + 9.49032i −1.24885 + 0.405777i −0.857510 0.514468i \(-0.827989\pi\)
−0.391343 + 0.920245i \(0.627989\pi\)
\(548\) 8.28199 + 11.3992i 0.353789 + 0.486949i
\(549\) −8.50651 9.51057i −0.363049 0.405901i
\(550\) 0 0
\(551\) 16.1803i 0.689306i
\(552\) −1.85963 1.21204i −0.0791512 0.0515879i
\(553\) −2.39919 7.38394i −0.102024 0.313997i
\(554\) 37.1567 + 12.0729i 1.57864 + 0.512930i
\(555\) 3.54264 13.1343i 0.150377 0.557521i
\(556\) 1.64590 2.26538i 0.0698016 0.0960737i
\(557\) 2.48990 7.66312i 0.105500 0.324697i −0.884347 0.466830i \(-0.845396\pi\)
0.989848 + 0.142133i \(0.0453961\pi\)
\(558\) 4.21274 + 2.45086i 0.178340 + 0.103753i
\(559\) 4.04508 2.93893i 0.171089 0.124303i
\(560\) −8.78402 −0.371193
\(561\) 0 0
\(562\) −31.3050 −1.32052
\(563\) 18.6049 13.5172i 0.784101 0.569683i −0.122106 0.992517i \(-0.538965\pi\)
0.906207 + 0.422834i \(0.138965\pi\)
\(564\) −15.9777 + 12.8947i −0.672781 + 0.542966i
\(565\) 16.1353 49.6592i 0.678815 2.08918i
\(566\) 8.89002 12.2361i 0.373676 0.514320i
\(567\) 4.83026 + 4.40745i 0.202852 + 0.185095i
\(568\) 7.13525 + 2.31838i 0.299389 + 0.0972773i
\(569\) −2.52265 7.76393i −0.105755 0.325481i 0.884152 0.467200i \(-0.154737\pi\)
−0.989907 + 0.141719i \(0.954737\pi\)
\(570\) −20.0312 + 30.7339i −0.839015 + 1.28730i
\(571\) 6.04937i 0.253158i 0.991957 + 0.126579i \(0.0403997\pi\)
−0.991957 + 0.126579i \(0.959600\pi\)
\(572\) 0 0
\(573\) −12.2148 31.9787i −0.510280 1.33593i
\(574\) −2.50000 3.44095i −0.104348 0.143623i
\(575\) 3.11044 1.01064i 0.129714 0.0421467i
\(576\) 5.70225 + 12.9224i 0.237594 + 0.538434i
\(577\) 6.47214 + 4.70228i 0.269439 + 0.195759i 0.714298 0.699842i \(-0.246746\pi\)
−0.444859 + 0.895601i \(0.646746\pi\)
\(578\) −15.5272 11.2812i −0.645845 0.469234i
\(579\) −34.9368 + 1.77297i −1.45192 + 0.0736822i
\(580\) −15.3262 + 4.97980i −0.636387 + 0.206775i
\(581\) −6.18812 8.51722i −0.256727 0.353354i
\(582\) 20.3682 7.77997i 0.844290 0.322490i
\(583\) 0 0
\(584\) 11.0557i 0.457489i
\(585\) 5.10398 23.6274i 0.211024 0.976875i
\(586\) 5.75329 + 17.7068i 0.237666 + 0.731461i
\(587\) 5.65334 + 1.83688i 0.233338 + 0.0758162i 0.423352 0.905965i \(-0.360853\pi\)
−0.190014 + 0.981781i \(0.560853\pi\)
\(588\) −17.5124 4.72353i −0.722200 0.194795i
\(589\) −2.13525 + 2.93893i −0.0879816 + 0.121096i
\(590\) 4.02874 12.3992i 0.165861 0.510466i
\(591\) 17.2277 + 21.3466i 0.708655 + 0.878083i
\(592\) 11.2082 8.14324i 0.460654 0.334685i
\(593\) −3.35520 −0.137781 −0.0688907 0.997624i \(-0.521946\pi\)
−0.0688907 + 0.997624i \(0.521946\pi\)
\(594\) 0 0
\(595\) 5.00000 0.204980
\(596\) 0.224514 0.163119i 0.00919645 0.00668161i
\(597\) −2.43236 3.01390i −0.0995499 0.123351i
\(598\) 3.19098 9.82084i 0.130489 0.401604i
\(599\) 4.87380 6.70820i 0.199138 0.274090i −0.697756 0.716335i \(-0.745818\pi\)
0.896894 + 0.442246i \(0.145818\pi\)
\(600\) 2.25271 + 0.607611i 0.0919666 + 0.0248056i
\(601\) −16.5451 5.37582i −0.674888 0.219284i −0.0485321 0.998822i \(-0.515454\pi\)
−0.626356 + 0.779537i \(0.715454\pi\)
\(602\) −0.693786 2.13525i −0.0282766 0.0870265i
\(603\) 5.27423 24.4155i 0.214783 0.994278i
\(604\) 28.4257i 1.15663i
\(605\) 0 0
\(606\) 38.4164 14.6738i 1.56056 0.596081i
\(607\) −7.27458 10.0126i −0.295266 0.406399i 0.635450 0.772142i \(-0.280815\pi\)
−0.930716 + 0.365744i \(0.880815\pi\)
\(608\) −29.6543 + 9.63525i −1.20264 + 0.390761i
\(609\) −4.78112 + 0.242632i −0.193741 + 0.00983196i
\(610\) 17.1353 + 12.4495i 0.693786 + 0.504065i
\(611\) 18.2416 + 13.2533i 0.737976 + 0.536171i
\(612\) −5.15124 11.6737i −0.208227 0.471883i
\(613\) −22.3607 + 7.26543i −0.903139 + 0.293448i −0.723532 0.690291i \(-0.757483\pi\)
−0.179607 + 0.983738i \(0.557483\pi\)
\(614\) −6.57164 9.04508i −0.265210 0.365030i
\(615\) 4.97980 + 13.0373i 0.200805 + 0.525714i
\(616\) 0 0
\(617\) 20.2361i 0.814673i 0.913278 + 0.407337i \(0.133542\pi\)
−0.913278 + 0.407337i \(0.866458\pi\)
\(618\) −12.1677 + 18.6689i −0.489458 + 0.750975i
\(619\) 3.83688 + 11.8087i 0.154217 + 0.474632i 0.998081 0.0619260i \(-0.0197243\pi\)
−0.843863 + 0.536558i \(0.819724\pi\)
\(620\) −3.44095 1.11803i −0.138192 0.0449013i
\(621\) −4.12052 8.18723i −0.165351 0.328542i
\(622\) 5.59017 7.69421i 0.224145 0.308510i
\(623\) −2.12663 + 6.54508i −0.0852015 + 0.262223i
\(624\) 19.1569 15.4605i 0.766890 0.618916i
\(625\) 24.9443 18.1231i 0.997771 0.724923i
\(626\) −20.9232 −0.836261
\(627\) 0 0
\(628\) −6.00000 −0.239426
\(629\) −6.37988 + 4.63525i −0.254383 + 0.184820i
\(630\) −9.38191 5.45814i −0.373784 0.217458i
\(631\) −3.84752 + 11.8415i −0.153168 + 0.471401i −0.997971 0.0636762i \(-0.979718\pi\)
0.844803 + 0.535077i \(0.179718\pi\)
\(632\) −4.56352 + 6.28115i −0.181527 + 0.249851i
\(633\) −3.05632 + 11.3313i −0.121478 + 0.450378i
\(634\) −0.427051 0.138757i −0.0169604 0.00551076i
\(635\) −10.6861 32.8885i −0.424066 1.30514i
\(636\) 11.3967 + 7.42798i 0.451910 + 0.294539i
\(637\) 19.9192i 0.789227i
\(638\) 0 0
\(639\) 20.6525 + 23.0902i 0.816999 + 0.913433i
\(640\) 8.78115 + 12.0862i 0.347106 + 0.477750i
\(641\) 16.9803 5.51722i 0.670680 0.217917i 0.0461695 0.998934i \(-0.485299\pi\)
0.624510 + 0.781016i \(0.285299\pi\)
\(642\) 0.0286389 + 0.564334i 0.00113029 + 0.0222725i
\(643\) −6.39919 4.64928i −0.252359 0.183350i 0.454412 0.890791i \(-0.349849\pi\)
−0.706772 + 0.707442i \(0.749849\pi\)
\(644\) −1.67760 1.21885i −0.0661067 0.0480293i
\(645\) 0.373373 + 7.35738i 0.0147015 + 0.289697i
\(646\) 20.2254 6.57164i 0.795759 0.258558i
\(647\) −25.9560 35.7254i −1.02044 1.40451i −0.911897 0.410419i \(-0.865382\pi\)
−0.108540 0.994092i \(-0.534618\pi\)
\(648\) 0.726543 6.49839i 0.0285413 0.255281i
\(649\) 0 0
\(650\) 10.8541i 0.425733i
\(651\) −0.900441 0.586874i −0.0352911 0.0230014i
\(652\) −6.19098 19.0539i −0.242458 0.746208i
\(653\) −33.4257 10.8607i −1.30805 0.425011i −0.429675 0.902984i \(-0.641372\pi\)
−0.878375 + 0.477972i \(0.841372\pi\)
\(654\) −6.52775 + 24.2016i −0.255255 + 0.946357i
\(655\) 6.28115 8.64527i 0.245425 0.337798i
\(656\) −4.39201 + 13.5172i −0.171479 + 0.527759i
\(657\) 22.9561 39.4589i 0.895603 1.53944i
\(658\) 8.19098 5.95110i 0.319318 0.231998i
\(659\) 39.8384 1.55188 0.775941 0.630805i \(-0.217275\pi\)
0.775941 + 0.630805i \(0.217275\pi\)
\(660\) 0 0
\(661\) 32.4508 1.26219 0.631096 0.775705i \(-0.282605\pi\)
0.631096 + 0.775705i \(0.282605\pi\)
\(662\) −35.2218 + 25.5902i −1.36894 + 0.994590i
\(663\) −10.9044 + 8.80037i −0.423492 + 0.341778i
\(664\) −3.25329 + 10.0126i −0.126252 + 0.388564i
\(665\) 4.75528 6.54508i 0.184402 0.253808i
\(666\) 17.0311 1.73305i 0.659940 0.0671543i
\(667\) 6.38197 + 2.07363i 0.247111 + 0.0802911i
\(668\) −0.0530006 0.163119i −0.00205065 0.00631126i
\(669\) −5.89773 + 9.04889i −0.228020 + 0.349850i
\(670\) 41.4630i 1.60185i
\(671\) 0 0
\(672\) −3.29180 8.61803i −0.126984 0.332448i
\(673\) −17.6631 24.3112i −0.680863 0.937128i 0.319081 0.947728i \(-0.396626\pi\)
−0.999944 + 0.0105998i \(0.996626\pi\)
\(674\) −18.6376 + 6.05573i −0.717894 + 0.233258i
\(675\) 6.77849 + 6.84615i 0.260904 + 0.263508i
\(676\) −4.61803 3.35520i −0.177617 0.129046i
\(677\) −31.9524 23.2148i −1.22803 0.892217i −0.231290 0.972885i \(-0.574295\pi\)
−0.996741 + 0.0806684i \(0.974295\pi\)
\(678\) 65.6231 3.33024i 2.52024 0.127897i
\(679\) −4.57295 + 1.48584i −0.175494 + 0.0570214i
\(680\) −2.93893 4.04508i −0.112703 0.155122i
\(681\) 10.2371 3.91023i 0.392287 0.149840i
\(682\) 0 0
\(683\) 9.00000i 0.344375i 0.985064 + 0.172188i \(0.0550836\pi\)
−0.985064 + 0.172188i \(0.944916\pi\)
\(684\) −20.1802 4.35932i −0.771611 0.166683i
\(685\) 7.04508 + 21.6825i 0.269179 + 0.828447i
\(686\) 17.7068 + 5.75329i 0.676049 + 0.219662i
\(687\) −42.0156 11.3326i −1.60299 0.432366i
\(688\) −4.40983 + 6.06961i −0.168123 + 0.231402i
\(689\) 4.61653 14.2082i 0.175876 0.541289i
\(690\) 9.55513 + 11.8396i 0.363758 + 0.450727i
\(691\) −27.7984 + 20.1967i −1.05750 + 0.768319i −0.973624 0.228158i \(-0.926730\pi\)
−0.0838757 + 0.996476i \(0.526730\pi\)
\(692\) −35.8626 −1.36329
\(693\) 0 0
\(694\) −58.5410 −2.22219
\(695\) 3.66547 2.66312i 0.139039 0.101018i
\(696\) 3.00656 + 3.72539i 0.113964 + 0.141211i
\(697\) 2.50000 7.69421i 0.0946943 0.291439i
\(698\) −18.2088 + 25.0623i −0.689214 + 0.948622i
\(699\) 11.9726 + 3.22930i 0.452846 + 0.122144i
\(700\) 2.07295 + 0.673542i 0.0783501 + 0.0254575i
\(701\) 5.39607 + 16.6074i 0.203807 + 0.627252i 0.999760 + 0.0218948i \(0.00696990\pi\)
−0.795954 + 0.605358i \(0.793030\pi\)
\(702\) 30.0676 4.60929i 1.13483 0.173967i
\(703\) 12.7598i 0.481244i
\(704\) 0 0
\(705\) −31.0344 + 11.8541i −1.16882 + 0.446451i
\(706\) 17.4377 + 24.0009i 0.656276 + 0.903287i
\(707\) −8.62502 + 2.80244i −0.324377 + 0.105397i
\(708\) 7.32766 0.371864i 0.275390 0.0139755i
\(709\) −14.1631 10.2901i −0.531907 0.386453i 0.289164 0.957280i \(-0.406623\pi\)
−0.821071 + 0.570827i \(0.806623\pi\)
\(710\) −41.6017 30.2254i −1.56129 1.13434i
\(711\) −29.3298 + 12.9423i −1.09995 + 0.485374i
\(712\) 6.54508 2.12663i 0.245287 0.0796987i
\(713\) 0.885544 + 1.21885i 0.0331639 + 0.0456462i
\(714\) 2.24514 + 5.87785i 0.0840222 + 0.219973i
\(715\) 0 0
\(716\) 6.38197i 0.238505i
\(717\) −24.3974 + 37.4330i −0.911139 + 1.39796i
\(718\) −14.6738 45.1612i −0.547620 1.68540i
\(719\) −9.62908 3.12868i −0.359104 0.116680i 0.123908 0.992294i \(-0.460457\pi\)
−0.483012 + 0.875614i \(0.660457\pi\)
\(720\) 3.67186 + 36.0842i 0.136842 + 1.34478i
\(721\) 2.88854 3.97574i 0.107575 0.148064i
\(722\) −0.534785 + 1.64590i −0.0199026 + 0.0612540i
\(723\) −26.3859 + 21.2947i −0.981302 + 0.791957i
\(724\) −16.0172 + 11.6372i −0.595275 + 0.432493i
\(725\) −7.05342 −0.261958
\(726\) 0 0
\(727\) −21.1459 −0.784258 −0.392129 0.919910i \(-0.628261\pi\)
−0.392129 + 0.919910i \(0.628261\pi\)
\(728\) −1.31433 + 0.954915i −0.0487122 + 0.0353915i
\(729\) 16.0864 21.6848i 0.595791 0.803139i
\(730\) −23.4164 + 72.0683i −0.866680 + 2.66737i
\(731\) 2.51014 3.45492i 0.0928410 0.127785i
\(732\) −3.10413 + 11.5085i −0.114732 + 0.425368i
\(733\) −32.6869 10.6206i −1.20732 0.392282i −0.364870 0.931058i \(-0.618887\pi\)
−0.842449 + 0.538777i \(0.818887\pi\)
\(734\) 13.5065 + 41.5689i 0.498536 + 1.53434i
\(735\) −24.5871 16.0250i −0.906909 0.591090i
\(736\) 12.9313i 0.476653i
\(737\) 0 0
\(738\) −13.0902 + 11.7082i −0.481856 + 0.430985i
\(739\) −9.57295 13.1760i −0.352147 0.484688i 0.595793 0.803138i \(-0.296838\pi\)
−0.947940 + 0.318450i \(0.896838\pi\)
\(740\) −12.0862 + 3.92705i −0.444298 + 0.144361i
\(741\) 1.14912 + 22.6437i 0.0422141 + 0.831837i
\(742\) −5.42705 3.94298i −0.199233 0.144751i
\(743\) −33.8218 24.5729i −1.24080 0.901494i −0.243149 0.969989i \(-0.578180\pi\)
−0.997651 + 0.0684950i \(0.978180\pi\)
\(744\) 0.0544744 + 1.07343i 0.00199713 + 0.0393538i
\(745\) 0.427051 0.138757i 0.0156459 0.00508367i
\(746\) 21.8415 + 30.0623i 0.799676 + 1.10066i
\(747\) −32.4014 + 28.9807i −1.18551 + 1.06035i
\(748\) 0 0
\(749\) 0.124612i 0.00455322i
\(750\) 22.7322 + 14.8160i 0.830061 + 0.541003i
\(751\) 1.71885 + 5.29007i 0.0627216 + 0.193037i 0.977507 0.210903i \(-0.0676404\pi\)
−0.914785 + 0.403940i \(0.867640\pi\)
\(752\) −32.1769 10.4549i −1.17337 0.381252i
\(753\) 2.10813 7.81588i 0.0768246 0.284826i
\(754\) −13.0902 + 18.0171i −0.476716 + 0.656143i
\(755\) 14.2128 43.7426i 0.517258 1.59196i
\(756\) 0.985520 6.02842i 0.0358430 0.219251i
\(757\) 20.1353 14.6291i 0.731828 0.531704i −0.158313 0.987389i \(-0.550606\pi\)
0.890141 + 0.455685i \(0.150606\pi\)
\(758\) 62.5577 2.27220
\(759\) 0 0
\(760\) −8.09017 −0.293461
\(761\) 35.7239 25.9549i 1.29499 0.940865i 0.295096 0.955468i \(-0.404648\pi\)
0.999893 + 0.0146026i \(0.00464833\pi\)
\(762\) 33.8644 27.3302i 1.22678 0.990068i
\(763\) 1.70820 5.25731i 0.0618411 0.190327i
\(764\) −18.7966 + 25.8713i −0.680038 + 0.935992i
\(765\) −2.09008 20.5397i −0.0755670 0.742613i
\(766\) 26.0795 + 8.47375i 0.942292 + 0.306169i
\(767\) −2.48990 7.66312i −0.0899050 0.276699i
\(768\) −19.1707 + 29.4137i −0.691765 + 1.06137i
\(769\) 26.8666i 0.968835i −0.874837 0.484417i \(-0.839032\pi\)
0.874837 0.484417i \(-0.160968\pi\)
\(770\) 0 0
\(771\) −6.96556 18.2361i −0.250858 0.656756i
\(772\) 19.2082 + 26.4378i 0.691318 + 0.951518i
\(773\) −7.44945 + 2.42047i −0.267938 + 0.0870584i −0.439905 0.898044i \(-0.644988\pi\)
0.171967 + 0.985103i \(0.444988\pi\)
\(774\) −8.48147 + 3.74260i −0.304860 + 0.134525i
\(775\) −1.28115 0.930812i −0.0460204 0.0334358i
\(776\) 3.88998 + 2.82624i 0.139642 + 0.101456i
\(777\) −3.77037 + 0.191339i −0.135261 + 0.00686425i
\(778\) 17.3992 5.65334i 0.623791 0.202682i
\(779\) −7.69421 10.5902i −0.275674 0.379432i
\(780\) −21.0948 + 8.05748i −0.755313 + 0.288504i
\(781\) 0 0
\(782\) 8.81966i 0.315390i
\(783\) 2.99530 + 19.5391i 0.107043 + 0.698270i
\(784\) −9.23607 28.4257i −0.329860 1.01520i
\(785\) −9.23305 3.00000i −0.329542 0.107075i
\(786\) 12.9835 + 3.50197i 0.463107 + 0.124911i
\(787\) −32.0344 + 44.0916i −1.14190 + 1.57170i −0.378726 + 0.925509i \(0.623638\pi\)
−0.763178 + 0.646188i \(0.776362\pi\)
\(788\) 7.91872 24.3713i 0.282093 0.868192i
\(789\) −25.3175 31.3706i −0.901328 1.11682i
\(790\) 43.0517 31.2789i 1.53171 1.11285i
\(791\) −14.4904 −0.515218
\(792\) 0 0
\(793\) 13.0902 0.464846
\(794\) −35.3934 + 25.7148i −1.25606 + 0.912583i
\(795\) 13.8238 + 17.1289i 0.490280 + 0.607498i
\(796\) −1.11803 + 3.44095i −0.0396277 + 0.121961i
\(797\) −12.9718 + 17.8541i −0.459483 + 0.632425i −0.974402 0.224815i \(-0.927822\pi\)
0.514918 + 0.857239i \(0.327822\pi\)
\(798\) 9.82946 + 2.65124i 0.347959 + 0.0938530i
\(799\) 18.3156 + 5.95110i 0.647959 + 0.210535i
\(800\) −4.20025 12.9271i −0.148501 0.457040i
\(801\) 27.7757 + 6.00009i 0.981407 + 0.212003i
\(802\) 40.2219i 1.42028i
\(803\) 0 0
\(804\) −21.7984 + 8.32624i −0.768769 + 0.293644i
\(805\) −1.97214 2.71441i −0.0695087 0.0956705i
\(806\) −4.75528 + 1.54508i −0.167498 + 0.0544233i
\(807\) 40.1943 2.03978i 1.41491 0.0718038i
\(808\) 7.33688 + 5.33056i 0.258111 + 0.187528i
\(809\) 21.1805 + 15.3885i 0.744667 + 0.541032i 0.894169 0.447729i \(-0.147767\pi\)
−0.149502 + 0.988761i \(0.547767\pi\)
\(810\) −18.4999 + 40.8218i −0.650020 + 1.43433i
\(811\) 12.2984 3.99598i 0.431854 0.140318i −0.0850200 0.996379i \(-0.527095\pi\)
0.516874 + 0.856061i \(0.327095\pi\)
\(812\) 2.62866 + 3.61803i 0.0922477 + 0.126968i
\(813\) 14.5964 + 38.2138i 0.511917 + 1.34022i
\(814\) 0 0
\(815\) 32.4164i 1.13550i
\(816\) 11.4806 17.6147i 0.401902 0.616638i
\(817\) −2.13525 6.57164i −0.0747031 0.229913i
\(818\) −61.9372 20.1246i −2.16558 0.703641i
\(819\) −6.67374 + 0.679108i −0.233199 + 0.0237299i
\(820\) 7.66312 10.5474i 0.267608 0.368330i
\(821\) −11.4252 + 35.1631i −0.398742 + 1.22720i 0.527267 + 0.849700i \(0.323217\pi\)
−0.926009 + 0.377502i \(0.876783\pi\)
\(822\) −22.3259 + 18.0181i −0.778706 + 0.628452i
\(823\) 11.4271 8.30224i 0.398322 0.289398i −0.370535 0.928818i \(-0.620826\pi\)
0.768857 + 0.639421i \(0.220826\pi\)
\(824\) −4.91428 −0.171197
\(825\) 0 0
\(826\) −3.61803 −0.125888
\(827\) 0.277515 0.201626i 0.00965013 0.00701123i −0.582950 0.812508i \(-0.698102\pi\)
0.592600 + 0.805497i \(0.298102\pi\)
\(828\) −4.30568 + 7.40096i −0.149633 + 0.257201i
\(829\) 8.73607 26.8869i 0.303416 0.933819i −0.676847 0.736123i \(-0.736654\pi\)
0.980263 0.197696i \(-0.0633457\pi\)
\(830\) 42.4140 58.3779i 1.47221 2.02633i
\(831\) −9.26458 + 34.3483i −0.321385 + 1.19153i
\(832\) −13.7812 4.47777i −0.477776 0.155239i
\(833\) 5.25731 + 16.1803i 0.182155 + 0.560616i
\(834\) 4.77658 + 3.11320i 0.165400 + 0.107801i
\(835\) 0.277515i 0.00960379i
\(836\) 0 0
\(837\) −2.03444 + 3.94427i −0.0703206 + 0.136334i
\(838\) −6.54508 9.00854i −0.226096 0.311195i
\(839\) 28.2012 9.16312i 0.973613 0.316346i 0.221339 0.975197i \(-0.428957\pi\)
0.752274 + 0.658851i \(0.228957\pi\)
\(840\) −0.121316 2.39056i −0.00418581 0.0824821i
\(841\) 11.7533 + 8.53926i 0.405286 + 0.294457i
\(842\) 39.7854 + 28.9058i 1.37109 + 0.996158i
\(843\) −1.44477 28.4694i −0.0497605 0.980539i
\(844\) 10.4271 3.38795i 0.358914 0.116618i
\(845\) −5.42882 7.47214i −0.186757 0.257049i
\(846\) −27.8707 31.1604i −0.958213 1.07131i
\(847\) 0 0
\(848\) 22.4164i 0.769783i
\(849\) 11.5380 + 7.52008i 0.395985 + 0.258088i
\(850\) 2.86475 + 8.81678i 0.0982599 + 0.302413i
\(851\) 5.03280 + 1.63525i 0.172522 + 0.0560558i
\(852\) 7.53634 27.9409i 0.258191 0.957241i
\(853\) 26.6074 36.6219i 0.911020 1.25391i −0.0557975 0.998442i \(-0.517770\pi\)
0.966817 0.255469i \(-0.0822299\pi\)
\(854\) 1.81636 5.59017i 0.0621544 0.191292i
\(855\) −28.8745 16.7984i −0.987489 0.574494i
\(856\) −0.100813 + 0.0732450i −0.00344572 + 0.00250346i
\(857\) 24.2380 0.827953 0.413976 0.910288i \(-0.364140\pi\)
0.413976 + 0.910288i \(0.364140\pi\)
\(858\) 0 0
\(859\) 34.5279 1.17808 0.589038 0.808106i \(-0.299507\pi\)
0.589038 + 0.808106i \(0.299507\pi\)
\(860\) 5.56758 4.04508i 0.189853 0.137936i
\(861\) 3.01390 2.43236i 0.102714 0.0828947i
\(862\) −13.2533 + 40.7894i −0.451409 + 1.38929i
\(863\) 22.9969 31.6525i 0.782823 1.07746i −0.212142 0.977239i \(-0.568044\pi\)
0.994965 0.100224i \(-0.0319560\pi\)
\(864\) −34.0263 + 17.1249i −1.15760 + 0.582603i
\(865\) −55.1869 17.9313i −1.87641 0.609683i
\(866\) 3.52671 + 10.8541i 0.119843 + 0.368837i
\(867\) 9.54274 14.6414i 0.324088 0.497248i
\(868\) 1.00406i 0.0340799i
\(869\) 0 0
\(870\) −11.7082 30.6525i −0.396945 1.03922i
\(871\) 15.0623 + 20.7315i 0.510367 + 0.702460i
\(872\) −5.25731 + 1.70820i −0.178035 + 0.0578471i
\(873\) 8.01530 + 18.1643i 0.271277 + 0.614767i
\(874\) −11.5451 8.38800i −0.390518 0.283728i
\(875\) −4.84104 3.51722i −0.163657 0.118904i
\(876\) −42.5908 + 2.16140i −1.43901 + 0.0730270i
\(877\) 7.72542 2.51014i 0.260869 0.0847615i −0.175662 0.984450i \(-0.556207\pi\)
0.436532 + 0.899689i \(0.356207\pi\)
\(878\) −28.3399 39.0066i −0.956427 1.31641i
\(879\) −15.8374 + 6.04937i −0.534184 + 0.204040i
\(880\) 0 0
\(881\) 34.9230i 1.17659i −0.808648 0.588293i \(-0.799800\pi\)
0.808648 0.588293i \(-0.200200\pi\)
\(882\) 7.79819 36.0995i 0.262579 1.21553i
\(883\) −5.50658 16.9475i −0.185311 0.570329i 0.814642 0.579963i \(-0.196933\pi\)
−0.999954 + 0.00963455i \(0.996933\pi\)
\(884\) 12.4495 + 4.04508i 0.418722 + 0.136051i
\(885\) 11.4620 + 3.09159i 0.385292 + 0.103923i
\(886\) −11.7082 + 16.1150i −0.393345 + 0.541393i
\(887\) 3.02468 9.30902i 0.101559 0.312566i −0.887349 0.461099i \(-0.847455\pi\)
0.988907 + 0.148533i \(0.0474552\pi\)
\(888\) 2.37097 + 2.93783i 0.0795644 + 0.0985871i
\(889\) −7.76393 + 5.64083i −0.260394 + 0.189187i
\(890\) −47.1693 −1.58112
\(891\) 0 0
\(892\) 10.0902 0.337844
\(893\) 25.2093 18.3156i 0.843596 0.612908i
\(894\) 0.354877 + 0.439723i 0.0118689 + 0.0147065i
\(895\) 3.19098 9.82084i 0.106663 0.328274i
\(896\) 2.43690 3.35410i 0.0814110 0.112053i
\(897\) 9.07856 + 2.44871i 0.303124 + 0.0817599i
\(898\) −14.2705 4.63677i −0.476213 0.154731i
\(899\) −1.00406 3.09017i −0.0334872 0.103063i
\(900\) 1.90034 8.79709i 0.0633446 0.293236i
\(901\) 12.7598i 0.425089i
\(902\) 0 0
\(903\) 1.90983 0.729490i 0.0635552 0.0242759i
\(904\) 8.51722 + 11.7229i 0.283279 + 0.389899i
\(905\) −30.4666 + 9.89919i −1.01274 + 0.329060i
\(906\) 57.8045 2.93347i 1.92043 0.0974579i
\(907\) −34.2984 24.9192i −1.13886 0.827429i −0.151899 0.988396i \(-0.548539\pi\)
−0.986960 + 0.160967i \(0.948539\pi\)
\(908\) −8.28199 6.01722i −0.274848 0.199688i
\(909\) 15.1176 + 34.2595i 0.501420 + 1.13632i
\(910\) 10.5902 3.44095i 0.351061 0.114067i
\(911\) 33.9278 + 46.6976i 1.12408 + 1.54716i 0.798857 + 0.601521i \(0.205438\pi\)
0.325220 + 0.945638i \(0.394562\pi\)
\(912\) −12.1392 31.7809i −0.401970 1.05237i
\(913\) 0 0
\(914\) 20.5279i 0.679001i
\(915\) −10.5310 + 16.1578i −0.348145 + 0.534159i
\(916\) 12.5623 + 38.6628i 0.415070 + 1.27745i
\(917\) −2.82041 0.916408i −0.0931383 0.0302625i
\(918\) 23.2073 11.6799i 0.765956 0.385495i
\(919\) 18.3926 25.3153i 0.606716 0.835073i −0.389586 0.920990i \(-0.627382\pi\)
0.996302 + 0.0859168i \(0.0273819\pi\)
\(920\) −1.03681 + 3.19098i −0.0341827 + 0.105204i
\(921\) 7.92252 6.39384i 0.261056 0.210684i
\(922\) −41.3435 + 30.0378i −1.36157 + 0.989242i
\(923\) −31.7809 −1.04608
\(924\) 0 0
\(925\) −5.56231 −0.182887
\(926\) −0.416272 + 0.302439i −0.0136795 + 0.00993877i
\(927\) −17.5395 10.2040i −0.576074 0.335144i
\(928\) 8.61803 26.5236i 0.282901 0.870679i
\(929\) 17.8128 24.5172i 0.584419 0.804384i −0.409752 0.912197i \(-0.634385\pi\)
0.994171 + 0.107813i \(0.0343848\pi\)
\(930\) 1.91846 7.11267i 0.0629087 0.233234i
\(931\) 26.1803 + 8.50651i 0.858026 + 0.278790i
\(932\) −3.57971 11.0172i −0.117257 0.360881i
\(933\) 7.25528 + 4.72873i 0.237527 + 0.154812i
\(934\) 44.9897i 1.47211i
\(935\) 0 0
\(936\) 4.47214 + 5.00000i 0.146176 + 0.163430i
\(937\) −22.2599 30.6381i −0.727198 1.00090i −0.999254 0.0386209i \(-0.987704\pi\)
0.272056 0.962281i \(-0.412296\pi\)
\(938\) 10.9434 3.55573i 0.357315 0.116099i
\(939\) −0.965638 19.0281i −0.0315124 0.620958i
\(940\) 25.1074 + 18.2416i 0.818913 + 0.594975i
\(941\) 39.1648 + 28.4549i 1.27674 + 0.927604i 0.999449 0.0331832i \(-0.0105645\pi\)
0.277288 + 0.960787i \(0.410564\pi\)
\(942\) −0.619187 12.2012i −0.0201742 0.397536i
\(943\) −5.16312 + 1.67760i −0.168134 + 0.0546301i
\(944\) 7.10642 + 9.78115i 0.231294 + 0.318349i
\(945\) 4.53077 8.78402i 0.147386 0.285744i
\(946\) 0 0
\(947\) 23.8541i 0.775154i 0.921837 + 0.387577i \(0.126688\pi\)
−0.921837 + 0.387577i \(0.873312\pi\)
\(948\) 25.0895 + 16.3524i 0.814870 + 0.531103i
\(949\) 14.4721 + 44.5407i 0.469785 + 1.44585i
\(950\) 14.2658 + 4.63525i 0.462845 + 0.150388i
\(951\) 0.106480 0.394774i 0.00345285 0.0128014i
\(952\) −0.815595 + 1.12257i −0.0264336 + 0.0363827i
\(953\) 13.7638 42.3607i 0.445854 1.37220i −0.435691 0.900096i \(-0.643496\pi\)
0.881545 0.472101i \(-0.156504\pi\)
\(954\) −13.9289 + 23.9422i −0.450965 + 0.775157i
\(955\) −41.8607 + 30.4136i −1.35458 + 0.984160i
\(956\) 41.7405 1.34998
\(957\) 0 0
\(958\) 43.5410 1.40675
\(959\) 5.11855 3.71885i 0.165287 0.120088i
\(960\) 16.6140 13.4083i 0.536215 0.432751i
\(961\) −9.35410 + 28.7890i −0.301745 + 0.928676i
\(962\) −10.3229 + 14.2082i −0.332823 + 0.458091i
\(963\) −0.511897 + 0.0520897i −0.0164956 + 0.00167857i
\(964\) 30.1246 + 9.78808i 0.970248 + 0.315253i
\(965\) 16.3395 + 50.2877i 0.525986 + 1.61882i
\(966\) 2.30544 3.53723i 0.0741763 0.113809i
\(967\) 20.9232i 0.672846i −0.941711 0.336423i \(-0.890783\pi\)
0.941711 0.336423i \(-0.109217\pi\)
\(968\) 0 0
\(969\) 6.90983 + 18.0902i 0.221976 + 0.581140i
\(970\) −19.3713 26.6623i −0.621976 0.856076i
\(971\) 13.4863 4.38197i 0.432796 0.140624i −0.0845134 0.996422i \(-0.526934\pi\)
0.517310 + 0.855798i \(0.326934\pi\)
\(972\) −25.1763 1.52848i −0.807530 0.0490259i
\(973\) −1.01722 0.739054i −0.0326106 0.0236930i
\(974\) −11.4984 8.35410i −0.368434 0.267683i
\(975\) −9.87097 + 0.500932i −0.316124 + 0.0160427i
\(976\) −18.6803 + 6.06961i −0.597943 + 0.194283i
\(977\) 30.5321 + 42.0238i 0.976808 + 1.34446i 0.938532 + 0.345193i \(0.112187\pi\)
0.0382760 + 0.999267i \(0.487813\pi\)
\(978\) 38.1078 14.5559i 1.21855 0.465446i
\(979\) 0 0
\(980\) 27.4164i 0.875785i
\(981\) −22.3107 4.81955i −0.712327 0.153876i
\(982\) 15.6910 + 48.2919i 0.500719 + 1.54106i
\(983\) −5.04531 1.63932i −0.160920 0.0522862i 0.227449 0.973790i \(-0.426962\pi\)
−0.388369 + 0.921504i \(0.626962\pi\)
\(984\) −3.73935 1.00859i −0.119206 0.0321528i
\(985\) 24.3713 33.5442i 0.776535 1.06881i
\(986\) −5.87785 + 18.0902i −0.187189 + 0.576108i
\(987\) 5.79009 + 7.17441i 0.184301 + 0.228364i
\(988\) 17.1353 12.4495i 0.545145 0.396071i
\(989\) −2.86568 −0.0911234
\(990\) 0 0
\(991\) 7.56231 0.240225 0.120112 0.992760i \(-0.461675\pi\)
0.120112 + 0.992760i \(0.461675\pi\)
\(992\) 5.06555 3.68034i 0.160831 0.116851i
\(993\) −24.8978 30.8505i −0.790108 0.979012i
\(994\) −4.40983 + 13.5721i −0.139871 + 0.430480i
\(995\) −3.44095 + 4.73607i −0.109086 + 0.150143i
\(996\) 39.2083 + 10.5754i 1.24236 + 0.335095i
\(997\) 38.8435 + 12.6210i 1.23018 + 0.399711i 0.850781 0.525520i \(-0.176129\pi\)
0.379403 + 0.925231i \(0.376129\pi\)
\(998\) −6.45313 19.8607i −0.204270 0.628679i
\(999\) 2.36208 + 15.4085i 0.0747330 + 0.487502i
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 363.2.f.e.239.2 8
3.2 odd 2 inner 363.2.f.e.239.1 8
11.2 odd 10 363.2.d.f.362.7 8
11.3 even 5 33.2.f.a.17.1 yes 8
11.4 even 5 363.2.f.d.161.2 8
11.5 even 5 363.2.f.b.233.1 8
11.6 odd 10 33.2.f.a.2.2 yes 8
11.7 odd 10 inner 363.2.f.e.161.1 8
11.8 odd 10 363.2.f.b.215.2 8
11.9 even 5 363.2.d.f.362.1 8
11.10 odd 2 363.2.f.d.239.1 8
33.2 even 10 363.2.d.f.362.2 8
33.5 odd 10 363.2.f.b.233.2 8
33.8 even 10 363.2.f.b.215.1 8
33.14 odd 10 33.2.f.a.17.2 yes 8
33.17 even 10 33.2.f.a.2.1 8
33.20 odd 10 363.2.d.f.362.8 8
33.26 odd 10 363.2.f.d.161.1 8
33.29 even 10 inner 363.2.f.e.161.2 8
33.32 even 2 363.2.f.d.239.2 8
44.3 odd 10 528.2.bn.c.17.2 8
44.39 even 10 528.2.bn.c.497.1 8
55.3 odd 20 825.2.bs.a.149.2 8
55.14 even 10 825.2.bi.b.776.2 8
55.17 even 20 825.2.bs.d.299.2 8
55.28 even 20 825.2.bs.a.299.1 8
55.39 odd 10 825.2.bi.b.101.1 8
55.47 odd 20 825.2.bs.d.149.1 8
99.14 odd 30 891.2.u.a.512.1 16
99.25 even 15 891.2.u.a.215.1 16
99.47 odd 30 891.2.u.a.215.2 16
99.50 even 30 891.2.u.a.431.1 16
99.58 even 15 891.2.u.a.512.2 16
99.61 odd 30 891.2.u.a.134.1 16
99.83 even 30 891.2.u.a.134.2 16
99.94 odd 30 891.2.u.a.431.2 16
132.47 even 10 528.2.bn.c.17.1 8
132.83 odd 10 528.2.bn.c.497.2 8
165.14 odd 10 825.2.bi.b.776.1 8
165.17 odd 20 825.2.bs.a.299.2 8
165.47 even 20 825.2.bs.a.149.1 8
165.83 odd 20 825.2.bs.d.299.1 8
165.113 even 20 825.2.bs.d.149.2 8
165.149 even 10 825.2.bi.b.101.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.f.a.2.1 8 33.17 even 10
33.2.f.a.2.2 yes 8 11.6 odd 10
33.2.f.a.17.1 yes 8 11.3 even 5
33.2.f.a.17.2 yes 8 33.14 odd 10
363.2.d.f.362.1 8 11.9 even 5
363.2.d.f.362.2 8 33.2 even 10
363.2.d.f.362.7 8 11.2 odd 10
363.2.d.f.362.8 8 33.20 odd 10
363.2.f.b.215.1 8 33.8 even 10
363.2.f.b.215.2 8 11.8 odd 10
363.2.f.b.233.1 8 11.5 even 5
363.2.f.b.233.2 8 33.5 odd 10
363.2.f.d.161.1 8 33.26 odd 10
363.2.f.d.161.2 8 11.4 even 5
363.2.f.d.239.1 8 11.10 odd 2
363.2.f.d.239.2 8 33.32 even 2
363.2.f.e.161.1 8 11.7 odd 10 inner
363.2.f.e.161.2 8 33.29 even 10 inner
363.2.f.e.239.1 8 3.2 odd 2 inner
363.2.f.e.239.2 8 1.1 even 1 trivial
528.2.bn.c.17.1 8 132.47 even 10
528.2.bn.c.17.2 8 44.3 odd 10
528.2.bn.c.497.1 8 44.39 even 10
528.2.bn.c.497.2 8 132.83 odd 10
825.2.bi.b.101.1 8 55.39 odd 10
825.2.bi.b.101.2 8 165.149 even 10
825.2.bi.b.776.1 8 165.14 odd 10
825.2.bi.b.776.2 8 55.14 even 10
825.2.bs.a.149.1 8 165.47 even 20
825.2.bs.a.149.2 8 55.3 odd 20
825.2.bs.a.299.1 8 55.28 even 20
825.2.bs.a.299.2 8 165.17 odd 20
825.2.bs.d.149.1 8 55.47 odd 20
825.2.bs.d.149.2 8 165.113 even 20
825.2.bs.d.299.1 8 165.83 odd 20
825.2.bs.d.299.2 8 55.17 even 20
891.2.u.a.134.1 16 99.61 odd 30
891.2.u.a.134.2 16 99.83 even 30
891.2.u.a.215.1 16 99.25 even 15
891.2.u.a.215.2 16 99.47 odd 30
891.2.u.a.431.1 16 99.50 even 30
891.2.u.a.431.2 16 99.94 odd 30
891.2.u.a.512.1 16 99.14 odd 30
891.2.u.a.512.2 16 99.58 even 15