Properties

Label 93.2.f.b.16.3
Level $93$
Weight $2$
Character 93.16
Analytic conductor $0.743$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [93,2,Mod(4,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.f (of order \(5\), degree \(4\), 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: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} - 2812 x^{7} + 5846 x^{6} - 4987 x^{5} + 4006 x^{4} - 1014 x^{3} + 2493 x^{2} + \cdots + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.3
Root \(-0.133750 + 0.0971754i\) of defining polynomial
Character \(\chi\) \(=\) 93.16
Dual form 93.2.f.b.64.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.133750 - 0.0971754i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.609588 + 1.87612i) q^{4} +3.79477 q^{5} -0.165325 q^{6} +(0.672649 - 2.07020i) q^{7} +(0.202956 + 0.624635i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.133750 - 0.0971754i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.609588 + 1.87612i) q^{4} +3.79477 q^{5} -0.165325 q^{6} +(0.672649 - 2.07020i) q^{7} +(0.202956 + 0.624635i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.507553 - 0.368759i) q^{10} +(-0.567729 + 1.74729i) q^{11} +(1.59592 - 1.15951i) q^{12} +(-4.39127 - 3.19045i) q^{13} +(-0.111205 - 0.342255i) q^{14} +(-3.07004 - 2.23051i) q^{15} +(-3.10400 - 2.25519i) q^{16} +(1.38416 + 4.26000i) q^{17} +(0.133750 + 0.0971754i) q^{18} +(-4.00286 + 2.90825i) q^{19} +(-2.31325 + 7.11944i) q^{20} +(-1.76102 + 1.27945i) q^{21} +(0.0938596 + 0.288870i) q^{22} +(-2.46512 - 7.58684i) q^{23} +(0.202956 - 0.624635i) q^{24} +9.40030 q^{25} -0.897368 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.47390 + 2.52394i) q^{28} +(3.33754 - 2.42486i) q^{29} -0.627369 q^{30} +(-5.56493 + 0.177633i) q^{31} -1.94787 q^{32} +(1.48633 - 1.07988i) q^{33} +(0.599099 + 0.435271i) q^{34} +(2.55255 - 7.85594i) q^{35} -1.97267 q^{36} -0.574944 q^{37} +(-0.252774 + 0.777959i) q^{38} +(1.67732 + 5.16225i) q^{39} +(0.770172 + 2.37035i) q^{40} +(-0.507553 + 0.368759i) q^{41} +(-0.111205 + 0.342255i) q^{42} +(1.01128 - 0.734741i) q^{43} +(-2.93204 - 2.13025i) q^{44} +(1.17265 + 3.60904i) q^{45} +(-1.06696 - 0.775195i) q^{46} +(1.43433 + 1.04210i) q^{47} +(1.18562 + 3.64897i) q^{48} +(1.82984 + 1.32946i) q^{49} +(1.25729 - 0.913478i) q^{50} +(1.38416 - 4.26000i) q^{51} +(8.66252 - 6.29369i) q^{52} +(1.76892 + 5.44418i) q^{53} +(-0.0510881 - 0.157233i) q^{54} +(-2.15440 + 6.63057i) q^{55} +1.42964 q^{56} +4.94781 q^{57} +(0.210760 - 0.648653i) q^{58} +(6.12685 + 4.45142i) q^{59} +(6.05616 - 4.40006i) q^{60} -6.32685 q^{61} +(-0.727050 + 0.564533i) q^{62} +2.17674 q^{63} +(5.94747 - 4.32109i) q^{64} +(-16.6639 - 12.1070i) q^{65} +(0.0938596 - 0.288870i) q^{66} +6.33093 q^{67} -8.83603 q^{68} +(-2.46512 + 7.58684i) q^{69} +(-0.422000 - 1.29878i) q^{70} +(0.761928 + 2.34497i) q^{71} +(-0.531346 + 0.386046i) q^{72} +(-2.86808 + 8.82704i) q^{73} +(-0.0768990 + 0.0558704i) q^{74} +(-7.60500 - 5.52536i) q^{75} +(-3.01612 - 9.28267i) q^{76} +(3.23536 + 2.35063i) q^{77} +(0.725986 + 0.527459i) q^{78} +(-0.169494 - 0.521649i) q^{79} +(-11.7790 - 8.55792i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.0320511 + 0.0986432i) q^{82} +(-0.206650 + 0.150140i) q^{83} +(-1.32691 - 4.08382i) q^{84} +(5.25256 + 16.1657i) q^{85} +(0.0638610 - 0.196544i) q^{86} -4.12542 q^{87} -1.20664 q^{88} +(1.79170 - 5.51429i) q^{89} +(0.507553 + 0.368759i) q^{90} +(-9.55865 + 6.94477i) q^{91} +15.7365 q^{92} +(4.60653 + 3.12728i) q^{93} +0.293109 q^{94} +(-15.1899 + 11.0361i) q^{95} +(1.57586 + 1.14493i) q^{96} +(3.28602 - 10.1133i) q^{97} +0.373933 q^{98} -1.83721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.133750 0.0971754i 0.0945759 0.0687134i −0.539492 0.841990i \(-0.681384\pi\)
0.634068 + 0.773277i \(0.281384\pi\)
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) −0.609588 + 1.87612i −0.304794 + 0.938059i
\(5\) 3.79477 1.69707 0.848537 0.529136i \(-0.177484\pi\)
0.848537 + 0.529136i \(0.177484\pi\)
\(6\) −0.165325 −0.0674935
\(7\) 0.672649 2.07020i 0.254237 0.782463i −0.739741 0.672891i \(-0.765052\pi\)
0.993979 0.109571i \(-0.0349478\pi\)
\(8\) 0.202956 + 0.624635i 0.0717558 + 0.220842i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0.507553 0.368759i 0.160502 0.116612i
\(11\) −0.567729 + 1.74729i −0.171177 + 0.526828i −0.999438 0.0335139i \(-0.989330\pi\)
0.828262 + 0.560342i \(0.189330\pi\)
\(12\) 1.59592 1.15951i 0.460703 0.334720i
\(13\) −4.39127 3.19045i −1.21792 0.884871i −0.221994 0.975048i \(-0.571257\pi\)
−0.995926 + 0.0901774i \(0.971257\pi\)
\(14\) −0.111205 0.342255i −0.0297209 0.0914716i
\(15\) −3.07004 2.23051i −0.792680 0.575916i
\(16\) −3.10400 2.25519i −0.776000 0.563797i
\(17\) 1.38416 + 4.26000i 0.335708 + 1.03320i 0.966372 + 0.257146i \(0.0827822\pi\)
−0.630665 + 0.776055i \(0.717218\pi\)
\(18\) 0.133750 + 0.0971754i 0.0315253 + 0.0229045i
\(19\) −4.00286 + 2.90825i −0.918319 + 0.667198i −0.943105 0.332495i \(-0.892110\pi\)
0.0247858 + 0.999693i \(0.492110\pi\)
\(20\) −2.31325 + 7.11944i −0.517258 + 1.59196i
\(21\) −1.76102 + 1.27945i −0.384286 + 0.279200i
\(22\) 0.0938596 + 0.288870i 0.0200109 + 0.0615873i
\(23\) −2.46512 7.58684i −0.514012 1.58197i −0.785072 0.619404i \(-0.787374\pi\)
0.271060 0.962562i \(-0.412626\pi\)
\(24\) 0.202956 0.624635i 0.0414283 0.127503i
\(25\) 9.40030 1.88006
\(26\) −0.897368 −0.175988
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 3.47390 + 2.52394i 0.656506 + 0.476980i
\(29\) 3.33754 2.42486i 0.619765 0.450286i −0.233074 0.972459i \(-0.574879\pi\)
0.852839 + 0.522173i \(0.174879\pi\)
\(30\) −0.627369 −0.114541
\(31\) −5.56493 + 0.177633i −0.999491 + 0.0319039i
\(32\) −1.94787 −0.344338
\(33\) 1.48633 1.07988i 0.258738 0.187984i
\(34\) 0.599099 + 0.435271i 0.102745 + 0.0746483i
\(35\) 2.55255 7.85594i 0.431460 1.32790i
\(36\) −1.97267 −0.328778
\(37\) −0.574944 −0.0945201 −0.0472601 0.998883i \(-0.515049\pi\)
−0.0472601 + 0.998883i \(0.515049\pi\)
\(38\) −0.252774 + 0.777959i −0.0410054 + 0.126202i
\(39\) 1.67732 + 5.16225i 0.268586 + 0.826622i
\(40\) 0.770172 + 2.37035i 0.121775 + 0.374785i
\(41\) −0.507553 + 0.368759i −0.0792664 + 0.0575904i −0.626713 0.779250i \(-0.715600\pi\)
0.547446 + 0.836841i \(0.315600\pi\)
\(42\) −0.111205 + 0.342255i −0.0171594 + 0.0528111i
\(43\) 1.01128 0.734741i 0.154219 0.112047i −0.508000 0.861357i \(-0.669615\pi\)
0.662219 + 0.749310i \(0.269615\pi\)
\(44\) −2.93204 2.13025i −0.442022 0.321148i
\(45\) 1.17265 + 3.60904i 0.174808 + 0.538004i
\(46\) −1.06696 0.775195i −0.157315 0.114296i
\(47\) 1.43433 + 1.04210i 0.209218 + 0.152006i 0.687460 0.726222i \(-0.258726\pi\)
−0.478242 + 0.878228i \(0.658726\pi\)
\(48\) 1.18562 + 3.64897i 0.171130 + 0.526683i
\(49\) 1.82984 + 1.32946i 0.261406 + 0.189923i
\(50\) 1.25729 0.913478i 0.177808 0.129185i
\(51\) 1.38416 4.26000i 0.193821 0.596519i
\(52\) 8.66252 6.29369i 1.20128 0.872778i
\(53\) 1.76892 + 5.44418i 0.242980 + 0.747816i 0.995962 + 0.0897746i \(0.0286147\pi\)
−0.752982 + 0.658041i \(0.771385\pi\)
\(54\) −0.0510881 0.157233i −0.00695221 0.0213967i
\(55\) −2.15440 + 6.63057i −0.290500 + 0.894066i
\(56\) 1.42964 0.191043
\(57\) 4.94781 0.655353
\(58\) 0.210760 0.648653i 0.0276742 0.0851723i
\(59\) 6.12685 + 4.45142i 0.797648 + 0.579525i 0.910223 0.414118i \(-0.135910\pi\)
−0.112575 + 0.993643i \(0.535910\pi\)
\(60\) 6.05616 4.40006i 0.781847 0.568045i
\(61\) −6.32685 −0.810070 −0.405035 0.914301i \(-0.632741\pi\)
−0.405035 + 0.914301i \(0.632741\pi\)
\(62\) −0.727050 + 0.564533i −0.0923355 + 0.0716957i
\(63\) 2.17674 0.274243
\(64\) 5.94747 4.32109i 0.743434 0.540136i
\(65\) −16.6639 12.1070i −2.06690 1.50169i
\(66\) 0.0938596 0.288870i 0.0115533 0.0355575i
\(67\) 6.33093 0.773446 0.386723 0.922196i \(-0.373607\pi\)
0.386723 + 0.922196i \(0.373607\pi\)
\(68\) −8.83603 −1.07153
\(69\) −2.46512 + 7.58684i −0.296765 + 0.913349i
\(70\) −0.422000 1.29878i −0.0504386 0.155234i
\(71\) 0.761928 + 2.34497i 0.0904242 + 0.278297i 0.986034 0.166543i \(-0.0532605\pi\)
−0.895610 + 0.444840i \(0.853260\pi\)
\(72\) −0.531346 + 0.386046i −0.0626197 + 0.0454959i
\(73\) −2.86808 + 8.82704i −0.335683 + 1.03313i 0.630701 + 0.776026i \(0.282767\pi\)
−0.966385 + 0.257101i \(0.917233\pi\)
\(74\) −0.0768990 + 0.0558704i −0.00893932 + 0.00649480i
\(75\) −7.60500 5.52536i −0.878150 0.638013i
\(76\) −3.01612 9.28267i −0.345973 1.06480i
\(77\) 3.23536 + 2.35063i 0.368703 + 0.267879i
\(78\) 0.725986 + 0.527459i 0.0822017 + 0.0597230i
\(79\) −0.169494 0.521649i −0.0190696 0.0586901i 0.941069 0.338215i \(-0.109823\pi\)
−0.960138 + 0.279525i \(0.909823\pi\)
\(80\) −11.7790 8.55792i −1.31693 0.956805i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −0.0320511 + 0.0986432i −0.00353946 + 0.0108933i
\(83\) −0.206650 + 0.150140i −0.0226827 + 0.0164800i −0.599069 0.800698i \(-0.704462\pi\)
0.576386 + 0.817177i \(0.304462\pi\)
\(84\) −1.32691 4.08382i −0.144778 0.445581i
\(85\) 5.25256 + 16.1657i 0.569720 + 1.75342i
\(86\) 0.0638610 0.196544i 0.00688631 0.0211939i
\(87\) −4.12542 −0.442292
\(88\) −1.20664 −0.128629
\(89\) 1.79170 5.51429i 0.189920 0.584514i −0.810078 0.586322i \(-0.800575\pi\)
0.999998 + 0.00180792i \(0.000575478\pi\)
\(90\) 0.507553 + 0.368759i 0.0535007 + 0.0388706i
\(91\) −9.55865 + 6.94477i −1.00202 + 0.728009i
\(92\) 15.7365 1.64065
\(93\) 4.60653 + 3.12728i 0.477675 + 0.324283i
\(94\) 0.293109 0.0302319
\(95\) −15.1899 + 11.0361i −1.55846 + 1.13228i
\(96\) 1.57586 + 1.14493i 0.160836 + 0.116854i
\(97\) 3.28602 10.1133i 0.333645 1.02685i −0.633741 0.773546i \(-0.718481\pi\)
0.967386 0.253308i \(-0.0815187\pi\)
\(98\) 0.373933 0.0377729
\(99\) −1.83721 −0.184647
\(100\) −5.73031 + 17.6361i −0.573031 + 1.76361i
\(101\) −3.47541 10.6962i −0.345816 1.06431i −0.961145 0.276043i \(-0.910977\pi\)
0.615329 0.788270i \(-0.289023\pi\)
\(102\) −0.228835 0.704283i −0.0226581 0.0697344i
\(103\) 9.73489 7.07281i 0.959207 0.696905i 0.00624039 0.999981i \(-0.498014\pi\)
0.952966 + 0.303076i \(0.0980136\pi\)
\(104\) 1.10163 3.39046i 0.108024 0.332462i
\(105\) −6.68266 + 4.85524i −0.652161 + 0.473823i
\(106\) 0.765634 + 0.556266i 0.0743650 + 0.0540293i
\(107\) 1.54830 + 4.76518i 0.149680 + 0.460668i 0.997583 0.0694835i \(-0.0221351\pi\)
−0.847903 + 0.530151i \(0.822135\pi\)
\(108\) 1.59592 + 1.15951i 0.153568 + 0.111573i
\(109\) −11.7112 8.50871i −1.12173 0.814987i −0.137262 0.990535i \(-0.543830\pi\)
−0.984471 + 0.175548i \(0.943830\pi\)
\(110\) 0.356176 + 1.09620i 0.0339600 + 0.104518i
\(111\) 0.465139 + 0.337943i 0.0441491 + 0.0320762i
\(112\) −6.75659 + 4.90895i −0.638438 + 0.463852i
\(113\) 1.03361 3.18113i 0.0972341 0.299256i −0.890595 0.454797i \(-0.849712\pi\)
0.987829 + 0.155541i \(0.0497120\pi\)
\(114\) 0.661772 0.480805i 0.0619806 0.0450315i
\(115\) −9.35455 28.7903i −0.872316 2.68471i
\(116\) 2.51481 + 7.73978i 0.233494 + 0.718621i
\(117\) 1.67732 5.16225i 0.155068 0.477250i
\(118\) 1.25204 0.115259
\(119\) 9.75011 0.893791
\(120\) 0.770172 2.37035i 0.0703068 0.216382i
\(121\) 6.16848 + 4.48166i 0.560771 + 0.407424i
\(122\) −0.846218 + 0.614814i −0.0766130 + 0.0556626i
\(123\) 0.627369 0.0565680
\(124\) 3.05905 10.5488i 0.274711 0.947306i
\(125\) 16.6981 1.49353
\(126\) 0.291140 0.211525i 0.0259368 0.0188442i
\(127\) 0.301959 + 0.219386i 0.0267946 + 0.0194674i 0.601102 0.799172i \(-0.294729\pi\)
−0.574307 + 0.818640i \(0.694729\pi\)
\(128\) 1.57942 4.86096i 0.139603 0.429653i
\(129\) −1.25002 −0.110058
\(130\) −3.40531 −0.298665
\(131\) −6.67754 + 20.5514i −0.583419 + 1.79558i 0.0221075 + 0.999756i \(0.492962\pi\)
−0.605527 + 0.795825i \(0.707038\pi\)
\(132\) 1.11994 + 3.44682i 0.0974783 + 0.300007i
\(133\) 3.32814 + 10.2430i 0.288586 + 0.888177i
\(134\) 0.846765 0.615211i 0.0731494 0.0531461i
\(135\) 1.17265 3.60904i 0.100926 0.310617i
\(136\) −2.38002 + 1.72919i −0.204085 + 0.148276i
\(137\) 17.8926 + 12.9997i 1.52867 + 1.11064i 0.956975 + 0.290171i \(0.0937123\pi\)
0.571691 + 0.820469i \(0.306288\pi\)
\(138\) 0.407544 + 1.25429i 0.0346925 + 0.106772i
\(139\) 8.05487 + 5.85221i 0.683205 + 0.496378i 0.874420 0.485171i \(-0.161242\pi\)
−0.191214 + 0.981548i \(0.561242\pi\)
\(140\) 13.1827 + 9.57777i 1.11414 + 0.809470i
\(141\) −0.547865 1.68615i −0.0461385 0.142000i
\(142\) 0.329782 + 0.239601i 0.0276747 + 0.0201068i
\(143\) 8.06769 5.86152i 0.674654 0.490165i
\(144\) 1.18562 3.64897i 0.0988018 0.304081i
\(145\) 12.6652 9.20180i 1.05179 0.764168i
\(146\) 0.474164 + 1.45933i 0.0392421 + 0.120775i
\(147\) −0.698938 2.15111i −0.0576474 0.177420i
\(148\) 0.350479 1.07866i 0.0288092 0.0886655i
\(149\) 8.30109 0.680052 0.340026 0.940416i \(-0.389564\pi\)
0.340026 + 0.940416i \(0.389564\pi\)
\(150\) −1.55410 −0.126892
\(151\) 2.28135 7.02129i 0.185654 0.571384i −0.814305 0.580437i \(-0.802882\pi\)
0.999959 + 0.00905290i \(0.00288167\pi\)
\(152\) −2.62900 1.91008i −0.213240 0.154928i
\(153\) −3.62377 + 2.63282i −0.292965 + 0.212851i
\(154\) 0.661154 0.0532773
\(155\) −21.1176 + 0.674078i −1.69621 + 0.0541433i
\(156\) −10.7075 −0.857283
\(157\) −13.4937 + 9.80377i −1.07692 + 0.782426i −0.977143 0.212584i \(-0.931812\pi\)
−0.0997745 + 0.995010i \(0.531812\pi\)
\(158\) −0.0733613 0.0533001i −0.00583631 0.00424033i
\(159\) 1.76892 5.44418i 0.140285 0.431752i
\(160\) −7.39172 −0.584367
\(161\) −17.3645 −1.36851
\(162\) −0.0510881 + 0.157233i −0.00401386 + 0.0123534i
\(163\) 1.29023 + 3.97093i 0.101059 + 0.311027i 0.988785 0.149344i \(-0.0477163\pi\)
−0.887726 + 0.460371i \(0.847716\pi\)
\(164\) −0.382437 1.17702i −0.0298633 0.0919098i
\(165\) 5.64030 4.09792i 0.439097 0.319022i
\(166\) −0.0130496 + 0.0401625i −0.00101284 + 0.00311722i
\(167\) 7.23255 5.25476i 0.559672 0.406625i −0.271667 0.962391i \(-0.587575\pi\)
0.831339 + 0.555766i \(0.187575\pi\)
\(168\) −1.15660 0.840320i −0.0892337 0.0648321i
\(169\) 5.08711 + 15.6565i 0.391316 + 1.20435i
\(170\) 2.27344 + 1.65175i 0.174365 + 0.126684i
\(171\) −4.00286 2.90825i −0.306106 0.222399i
\(172\) 0.761995 + 2.34518i 0.0581015 + 0.178818i
\(173\) −10.5483 7.66380i −0.801974 0.582668i 0.109519 0.993985i \(-0.465069\pi\)
−0.911492 + 0.411317i \(0.865069\pi\)
\(174\) −0.551777 + 0.400889i −0.0418301 + 0.0303914i
\(175\) 6.32310 19.4605i 0.477982 1.47108i
\(176\) 5.70270 4.14325i 0.429857 0.312309i
\(177\) −2.34025 7.20254i −0.175904 0.541376i
\(178\) −0.296213 0.911648i −0.0222021 0.0683309i
\(179\) −1.47134 + 4.52830i −0.109973 + 0.338461i −0.990865 0.134855i \(-0.956943\pi\)
0.880893 + 0.473316i \(0.156943\pi\)
\(180\) −7.48583 −0.557960
\(181\) 0.605695 0.0450209 0.0225105 0.999747i \(-0.492834\pi\)
0.0225105 + 0.999747i \(0.492834\pi\)
\(182\) −0.603614 + 1.85773i −0.0447428 + 0.137704i
\(183\) 5.11853 + 3.71883i 0.378372 + 0.274904i
\(184\) 4.23870 3.07959i 0.312481 0.227031i
\(185\) −2.18178 −0.160408
\(186\) 0.920020 0.0293672i 0.0674592 0.00215331i
\(187\) −8.22928 −0.601785
\(188\) −2.82945 + 2.05572i −0.206359 + 0.149929i
\(189\) −1.76102 1.27945i −0.128095 0.0930666i
\(190\) −0.959221 + 2.95218i −0.0695892 + 0.214174i
\(191\) 17.3175 1.25305 0.626524 0.779402i \(-0.284477\pi\)
0.626524 + 0.779402i \(0.284477\pi\)
\(192\) −7.35148 −0.530547
\(193\) 3.56122 10.9603i 0.256342 0.788939i −0.737220 0.675652i \(-0.763862\pi\)
0.993562 0.113287i \(-0.0361379\pi\)
\(194\) −0.543261 1.67198i −0.0390038 0.120041i
\(195\) 6.36504 + 19.5896i 0.455810 + 1.40284i
\(196\) −3.60967 + 2.62258i −0.257834 + 0.187327i
\(197\) −3.75741 + 11.5641i −0.267705 + 0.823910i 0.723353 + 0.690478i \(0.242600\pi\)
−0.991058 + 0.133432i \(0.957400\pi\)
\(198\) −0.245728 + 0.178532i −0.0174631 + 0.0126877i
\(199\) −10.2693 7.46109i −0.727972 0.528903i 0.160949 0.986963i \(-0.448545\pi\)
−0.888921 + 0.458060i \(0.848545\pi\)
\(200\) 1.90785 + 5.87175i 0.134905 + 0.415196i
\(201\) −5.12183 3.72123i −0.361266 0.262475i
\(202\) −1.50425 1.09290i −0.105838 0.0768961i
\(203\) −2.77496 8.54045i −0.194764 0.599422i
\(204\) 7.14850 + 5.19369i 0.500495 + 0.363631i
\(205\) −1.92605 + 1.39935i −0.134521 + 0.0977352i
\(206\) 0.614742 1.89198i 0.0428311 0.131821i
\(207\) 6.45376 4.68893i 0.448567 0.325903i
\(208\) 6.43545 + 19.8063i 0.446218 + 1.37332i
\(209\) −2.80901 8.64526i −0.194304 0.598005i
\(210\) −0.422000 + 1.29878i −0.0291207 + 0.0896244i
\(211\) −20.1319 −1.38593 −0.692967 0.720969i \(-0.743697\pi\)
−0.692967 + 0.720969i \(0.743697\pi\)
\(212\) −11.2922 −0.775554
\(213\) 0.761928 2.34497i 0.0522065 0.160675i
\(214\) 0.670145 + 0.486889i 0.0458102 + 0.0332830i
\(215\) 3.83759 2.78817i 0.261722 0.190152i
\(216\) 0.656780 0.0446882
\(217\) −3.37551 + 11.6400i −0.229144 + 0.790175i
\(218\) −2.39322 −0.162089
\(219\) 7.50873 5.45541i 0.507393 0.368642i
\(220\) −11.1264 8.08383i −0.750144 0.545012i
\(221\) 7.51308 23.1229i 0.505385 1.55541i
\(222\) 0.0950523 0.00637950
\(223\) −3.16186 −0.211734 −0.105867 0.994380i \(-0.533762\pi\)
−0.105867 + 0.994380i \(0.533762\pi\)
\(224\) −1.31023 + 4.03248i −0.0875436 + 0.269432i
\(225\) 2.90485 + 8.94021i 0.193657 + 0.596014i
\(226\) −0.170882 0.525920i −0.0113669 0.0349837i
\(227\) −16.6570 + 12.1020i −1.10556 + 0.803238i −0.981959 0.189094i \(-0.939445\pi\)
−0.123603 + 0.992332i \(0.539445\pi\)
\(228\) −3.01612 + 9.28267i −0.199748 + 0.614760i
\(229\) −11.5935 + 8.42314i −0.766117 + 0.556617i −0.900780 0.434275i \(-0.857005\pi\)
0.134663 + 0.990891i \(0.457005\pi\)
\(230\) −4.04889 2.94169i −0.266976 0.193969i
\(231\) −1.23580 3.80339i −0.0813095 0.250245i
\(232\) 2.19203 + 1.59260i 0.143914 + 0.104559i
\(233\) −20.9378 15.2122i −1.37168 0.996584i −0.997604 0.0691854i \(-0.977960\pi\)
−0.374076 0.927398i \(-0.622040\pi\)
\(234\) −0.277302 0.853447i −0.0181278 0.0557916i
\(235\) 5.44295 + 3.95454i 0.355059 + 0.257965i
\(236\) −12.0862 + 8.78117i −0.786747 + 0.571605i
\(237\) −0.169494 + 0.521649i −0.0110098 + 0.0338847i
\(238\) 1.30408 0.947471i 0.0845310 0.0614154i
\(239\) −0.0657790 0.202447i −0.00425489 0.0130952i 0.948907 0.315557i \(-0.102191\pi\)
−0.953161 + 0.302462i \(0.902191\pi\)
\(240\) 4.49917 + 13.8470i 0.290420 + 0.893821i
\(241\) 6.48089 19.9461i 0.417471 1.28484i −0.492551 0.870284i \(-0.663935\pi\)
0.910022 0.414560i \(-0.136065\pi\)
\(242\) 1.26054 0.0810309
\(243\) 1.00000 0.0641500
\(244\) 3.85677 11.8699i 0.246904 0.759893i
\(245\) 6.94384 + 5.04499i 0.443625 + 0.322313i
\(246\) 0.0839110 0.0609649i 0.00534997 0.00388698i
\(247\) 26.8563 1.70882
\(248\) −1.24039 3.44000i −0.0787650 0.218440i
\(249\) 0.255433 0.0161874
\(250\) 2.23338 1.62265i 0.141251 0.102625i
\(251\) 21.4699 + 15.5988i 1.35517 + 0.984589i 0.998736 + 0.0502684i \(0.0160077\pi\)
0.356434 + 0.934320i \(0.383992\pi\)
\(252\) −1.32691 + 4.08382i −0.0835877 + 0.257256i
\(253\) 14.6559 0.921411
\(254\) 0.0617062 0.00387179
\(255\) 5.25256 16.1657i 0.328928 1.01234i
\(256\) 4.28234 + 13.1797i 0.267647 + 0.823731i
\(257\) −8.06572 24.8237i −0.503126 1.54846i −0.803898 0.594767i \(-0.797244\pi\)
0.300772 0.953696i \(-0.402756\pi\)
\(258\) −0.167190 + 0.121471i −0.0104088 + 0.00756244i
\(259\) −0.386735 + 1.19025i −0.0240306 + 0.0739585i
\(260\) 32.8723 23.8831i 2.03865 1.48117i
\(261\) 3.33754 + 2.42486i 0.206588 + 0.150095i
\(262\) 1.10396 + 3.39765i 0.0682030 + 0.209907i
\(263\) 0.0470381 + 0.0341752i 0.00290049 + 0.00210733i 0.589235 0.807962i \(-0.299429\pi\)
−0.586334 + 0.810069i \(0.699429\pi\)
\(264\) 0.976194 + 0.709247i 0.0600806 + 0.0436511i
\(265\) 6.71265 + 20.6594i 0.412355 + 1.26910i
\(266\) 1.44050 + 1.04659i 0.0883229 + 0.0641704i
\(267\) −4.69074 + 3.40802i −0.287068 + 0.208567i
\(268\) −3.85926 + 11.8776i −0.235742 + 0.725539i
\(269\) −20.6190 + 14.9806i −1.25716 + 0.913384i −0.998615 0.0526142i \(-0.983245\pi\)
−0.258550 + 0.965998i \(0.583245\pi\)
\(270\) −0.193868 0.596664i −0.0117984 0.0363118i
\(271\) −0.222463 0.684670i −0.0135136 0.0415907i 0.944072 0.329738i \(-0.106961\pi\)
−0.957586 + 0.288148i \(0.906961\pi\)
\(272\) 5.31067 16.3446i 0.322007 0.991035i
\(273\) 11.8151 0.715085
\(274\) 3.65639 0.220891
\(275\) −5.33682 + 16.4250i −0.321822 + 0.990468i
\(276\) −12.7311 9.24970i −0.766323 0.556766i
\(277\) 26.4925 19.2479i 1.59178 1.15650i 0.690439 0.723391i \(-0.257417\pi\)
0.901343 0.433106i \(-0.142583\pi\)
\(278\) 1.64603 0.0987225
\(279\) −1.88860 5.23767i −0.113067 0.313571i
\(280\) 5.42515 0.324215
\(281\) −9.92831 + 7.21334i −0.592273 + 0.430312i −0.843128 0.537713i \(-0.819288\pi\)
0.250855 + 0.968025i \(0.419288\pi\)
\(282\) −0.237130 0.172285i −0.0141209 0.0102594i
\(283\) −1.66324 + 5.11892i −0.0988693 + 0.304288i −0.988243 0.152893i \(-0.951141\pi\)
0.889373 + 0.457181i \(0.151141\pi\)
\(284\) −4.86391 −0.288620
\(285\) 18.7758 1.11218
\(286\) 0.509462 1.56796i 0.0301251 0.0927155i
\(287\) 0.422000 + 1.29878i 0.0249098 + 0.0766646i
\(288\) −0.601925 1.85253i −0.0354688 0.109162i
\(289\) −2.47841 + 1.80067i −0.145789 + 0.105922i
\(290\) 0.799787 2.46149i 0.0469651 0.144544i
\(291\) −8.60292 + 6.25039i −0.504312 + 0.366404i
\(292\) −14.8122 10.7617i −0.866820 0.629782i
\(293\) −4.77290 14.6895i −0.278836 0.858168i −0.988179 0.153305i \(-0.951008\pi\)
0.709343 0.704863i \(-0.248992\pi\)
\(294\) −0.302518 0.219792i −0.0176432 0.0128185i
\(295\) 23.2500 + 16.8921i 1.35367 + 0.983497i
\(296\) −0.116688 0.359130i −0.00678237 0.0208740i
\(297\) 1.48633 + 1.07988i 0.0862458 + 0.0626613i
\(298\) 1.11027 0.806662i 0.0643165 0.0467287i
\(299\) −13.3804 + 41.1807i −0.773810 + 2.38154i
\(300\) 15.0021 10.8997i 0.866149 0.629294i
\(301\) −0.840822 2.58778i −0.0484642 0.149157i
\(302\) −0.377164 1.16079i −0.0217034 0.0667961i
\(303\) −3.47541 + 10.6962i −0.199657 + 0.614482i
\(304\) 18.9835 1.08878
\(305\) −24.0089 −1.37475
\(306\) −0.228835 + 0.704283i −0.0130816 + 0.0402612i
\(307\) −6.34180 4.60759i −0.361946 0.262969i 0.391917 0.920000i \(-0.371812\pi\)
−0.753863 + 0.657031i \(0.771812\pi\)
\(308\) −6.38229 + 4.63701i −0.363665 + 0.264218i
\(309\) −12.0330 −0.684532
\(310\) −2.75899 + 2.14227i −0.156700 + 0.121673i
\(311\) 18.3548 1.04080 0.520401 0.853922i \(-0.325782\pi\)
0.520401 + 0.853922i \(0.325782\pi\)
\(312\) −2.88410 + 2.09542i −0.163280 + 0.118630i
\(313\) −7.25680 5.27238i −0.410179 0.298012i 0.363495 0.931596i \(-0.381583\pi\)
−0.773674 + 0.633584i \(0.781583\pi\)
\(314\) −0.852108 + 2.62252i −0.0480872 + 0.147997i
\(315\) 8.26023 0.465411
\(316\) 1.08200 0.0608670
\(317\) 6.31352 19.4310i 0.354603 1.09136i −0.601637 0.798770i \(-0.705484\pi\)
0.956239 0.292585i \(-0.0945156\pi\)
\(318\) −0.292446 0.900057i −0.0163996 0.0504727i
\(319\) 2.34212 + 7.20831i 0.131134 + 0.403588i
\(320\) 22.5693 16.3976i 1.26166 0.916651i
\(321\) 1.54830 4.76518i 0.0864178 0.265967i
\(322\) −2.32250 + 1.68740i −0.129428 + 0.0940350i
\(323\) −17.9297 13.0267i −0.997637 0.724825i
\(324\) −0.609588 1.87612i −0.0338660 0.104229i
\(325\) −41.2793 29.9911i −2.28976 1.66361i
\(326\) 0.558445 + 0.405734i 0.0309294 + 0.0224715i
\(327\) 4.47329 + 13.7674i 0.247374 + 0.761338i
\(328\) −0.333350 0.242193i −0.0184062 0.0133729i
\(329\) 3.12216 2.26838i 0.172130 0.125060i
\(330\) 0.356176 1.09620i 0.0196068 0.0603436i
\(331\) −14.3433 + 10.4210i −0.788378 + 0.572790i −0.907482 0.420092i \(-0.861998\pi\)
0.119104 + 0.992882i \(0.461998\pi\)
\(332\) −0.155709 0.479222i −0.00854563 0.0263007i
\(333\) −0.177667 0.546804i −0.00973611 0.0299647i
\(334\) 0.456724 1.40565i 0.0249908 0.0769139i
\(335\) 24.0244 1.31260
\(336\) 8.35161 0.455618
\(337\) −3.16716 + 9.74750i −0.172526 + 0.530980i −0.999512 0.0312424i \(-0.990054\pi\)
0.826986 + 0.562223i \(0.190054\pi\)
\(338\) 2.20183 + 1.59972i 0.119764 + 0.0870135i
\(339\) −2.70603 + 1.96605i −0.146972 + 0.106781i
\(340\) −33.5307 −1.81846
\(341\) 2.84900 9.82440i 0.154282 0.532021i
\(342\) −0.817995 −0.0442321
\(343\) 16.3102 11.8501i 0.880669 0.639843i
\(344\) 0.664191 + 0.482563i 0.0358108 + 0.0260181i
\(345\) −9.35455 + 28.7903i −0.503632 + 1.55002i
\(346\) −2.15557 −0.115884
\(347\) 5.75932 0.309177 0.154588 0.987979i \(-0.450595\pi\)
0.154588 + 0.987979i \(0.450595\pi\)
\(348\) 2.51481 7.73978i 0.134808 0.414896i
\(349\) 5.77449 + 17.7720i 0.309101 + 0.951316i 0.978115 + 0.208066i \(0.0667168\pi\)
−0.669014 + 0.743250i \(0.733283\pi\)
\(350\) −1.04536 3.21730i −0.0558771 0.171972i
\(351\) −4.39127 + 3.19045i −0.234389 + 0.170293i
\(352\) 1.10586 3.40349i 0.0589427 0.181407i
\(353\) 2.51495 1.82722i 0.133857 0.0972528i −0.518842 0.854870i \(-0.673637\pi\)
0.652699 + 0.757617i \(0.273637\pi\)
\(354\) −1.01292 0.735929i −0.0538361 0.0391142i
\(355\) 2.89134 + 8.89864i 0.153457 + 0.472291i
\(356\) 9.25326 + 6.72289i 0.490422 + 0.356312i
\(357\) −7.88800 5.73097i −0.417477 0.303315i
\(358\) 0.243248 + 0.748640i 0.0128561 + 0.0395669i
\(359\) −0.0260459 0.0189235i −0.00137465 0.000998742i 0.587098 0.809516i \(-0.300270\pi\)
−0.588472 + 0.808517i \(0.700270\pi\)
\(360\) −2.01634 + 1.46496i −0.106270 + 0.0772099i
\(361\) 1.69366 5.21256i 0.0891401 0.274345i
\(362\) 0.0810119 0.0588586i 0.00425789 0.00309354i
\(363\) −2.35615 7.25148i −0.123666 0.380604i
\(364\) −7.20237 22.1666i −0.377507 1.16185i
\(365\) −10.8837 + 33.4966i −0.569679 + 1.75329i
\(366\) 1.04598 0.0546744
\(367\) −17.4915 −0.913049 −0.456525 0.889711i \(-0.650906\pi\)
−0.456525 + 0.889711i \(0.650906\pi\)
\(368\) −9.45804 + 29.1089i −0.493034 + 1.51740i
\(369\) −0.507553 0.368759i −0.0264221 0.0191968i
\(370\) −0.291814 + 0.212015i −0.0151707 + 0.0110222i
\(371\) 12.4604 0.646912
\(372\) −8.67523 + 6.73605i −0.449790 + 0.349248i
\(373\) −28.5776 −1.47969 −0.739845 0.672778i \(-0.765101\pi\)
−0.739845 + 0.672778i \(0.765101\pi\)
\(374\) −1.10067 + 0.799684i −0.0569143 + 0.0413507i
\(375\) −13.5091 9.81491i −0.697605 0.506840i
\(376\) −0.359827 + 1.10743i −0.0185566 + 0.0571115i
\(377\) −22.3924 −1.15327
\(378\) −0.359869 −0.0185096
\(379\) 1.73044 5.32576i 0.0888869 0.273566i −0.896725 0.442587i \(-0.854061\pi\)
0.985612 + 0.169021i \(0.0540607\pi\)
\(380\) −11.4455 35.2256i −0.587142 1.80704i
\(381\) −0.115338 0.354975i −0.00590896 0.0181859i
\(382\) 2.31622 1.68283i 0.118508 0.0861012i
\(383\) −2.67494 + 8.23260i −0.136683 + 0.420666i −0.995848 0.0910320i \(-0.970983\pi\)
0.859165 + 0.511698i \(0.170983\pi\)
\(384\) −4.13498 + 3.00424i −0.211012 + 0.153310i
\(385\) 12.2775 + 8.92009i 0.625717 + 0.454610i
\(386\) −0.588757 1.81201i −0.0299669 0.0922287i
\(387\) 1.01128 + 0.734741i 0.0514065 + 0.0373490i
\(388\) 16.9707 + 12.3299i 0.861557 + 0.625958i
\(389\) 0.395952 + 1.21861i 0.0200755 + 0.0617862i 0.960592 0.277961i \(-0.0896585\pi\)
−0.940517 + 0.339747i \(0.889659\pi\)
\(390\) 2.75495 + 2.00159i 0.139502 + 0.101354i
\(391\) 28.9078 21.0028i 1.46193 1.06216i
\(392\) −0.459048 + 1.41281i −0.0231854 + 0.0713574i
\(393\) 17.4820 12.7014i 0.881852 0.640703i
\(394\) 0.621193 + 1.91184i 0.0312953 + 0.0963169i
\(395\) −0.643191 1.97954i −0.0323624 0.0996014i
\(396\) 1.11994 3.44682i 0.0562791 0.173209i
\(397\) −27.3148 −1.37089 −0.685446 0.728123i \(-0.740393\pi\)
−0.685446 + 0.728123i \(0.740393\pi\)
\(398\) −2.09856 −0.105191
\(399\) 3.32814 10.2430i 0.166615 0.512789i
\(400\) −29.1785 21.1994i −1.45893 1.05997i
\(401\) −0.198881 + 0.144495i −0.00993162 + 0.00721574i −0.592740 0.805394i \(-0.701954\pi\)
0.582808 + 0.812610i \(0.301954\pi\)
\(402\) −1.04666 −0.0522026
\(403\) 25.0039 + 16.9746i 1.24553 + 0.845564i
\(404\) 22.1859 1.10379
\(405\) −3.07004 + 2.23051i −0.152551 + 0.110835i
\(406\) −1.20107 0.872632i −0.0596083 0.0433080i
\(407\) 0.326412 1.00459i 0.0161796 0.0497958i
\(408\) 2.94187 0.145644
\(409\) 13.3898 0.662082 0.331041 0.943616i \(-0.392600\pi\)
0.331041 + 0.943616i \(0.392600\pi\)
\(410\) −0.121627 + 0.374329i −0.00600672 + 0.0184868i
\(411\) −6.83435 21.0340i −0.337114 1.03753i
\(412\) 7.33516 + 22.5753i 0.361377 + 1.11221i
\(413\) 13.3365 9.68957i 0.656249 0.476793i
\(414\) 0.407544 1.25429i 0.0200297 0.0616451i
\(415\) −0.784188 + 0.569746i −0.0384943 + 0.0279677i
\(416\) 8.55363 + 6.21457i 0.419376 + 0.304695i
\(417\) −3.07669 9.46907i −0.150666 0.463702i
\(418\) −1.21581 0.883340i −0.0594674 0.0432056i
\(419\) −15.1726 11.0236i −0.741232 0.538537i 0.151865 0.988401i \(-0.451472\pi\)
−0.893097 + 0.449865i \(0.851472\pi\)
\(420\) −5.03533 15.4972i −0.245699 0.756184i
\(421\) 1.45013 + 1.05358i 0.0706750 + 0.0513484i 0.622562 0.782571i \(-0.286092\pi\)
−0.551887 + 0.833919i \(0.686092\pi\)
\(422\) −2.69265 + 1.95632i −0.131076 + 0.0952323i
\(423\) −0.547865 + 1.68615i −0.0266381 + 0.0819836i
\(424\) −3.04161 + 2.20986i −0.147714 + 0.107320i
\(425\) 13.0115 + 40.0453i 0.631150 + 1.94248i
\(426\) −0.125966 0.387682i −0.00610305 0.0187833i
\(427\) −4.25575 + 13.0978i −0.205950 + 0.633849i
\(428\) −9.88388 −0.477755
\(429\) −9.97221 −0.481463
\(430\) 0.242338 0.745839i 0.0116866 0.0359676i
\(431\) 31.4794 + 22.8711i 1.51631 + 1.10166i 0.963280 + 0.268500i \(0.0865279\pi\)
0.553028 + 0.833162i \(0.313472\pi\)
\(432\) −3.10400 + 2.25519i −0.149341 + 0.108503i
\(433\) 4.39518 0.211219 0.105609 0.994408i \(-0.466321\pi\)
0.105609 + 0.994408i \(0.466321\pi\)
\(434\) 0.679647 + 1.88487i 0.0326241 + 0.0904768i
\(435\) −15.6550 −0.750602
\(436\) 23.1024 16.7849i 1.10640 0.803849i
\(437\) 31.9319 + 23.1999i 1.52751 + 1.10980i
\(438\) 0.474164 1.45933i 0.0226564 0.0697294i
\(439\) −21.3648 −1.01968 −0.509842 0.860268i \(-0.670296\pi\)
−0.509842 + 0.860268i \(0.670296\pi\)
\(440\) −4.57893 −0.218292
\(441\) −0.698938 + 2.15111i −0.0332827 + 0.102434i
\(442\) −1.24210 3.82279i −0.0590806 0.181831i
\(443\) −8.60621 26.4872i −0.408893 1.25844i −0.917600 0.397504i \(-0.869876\pi\)
0.508707 0.860940i \(-0.330124\pi\)
\(444\) −0.917565 + 0.666650i −0.0435457 + 0.0316378i
\(445\) 6.79910 20.9255i 0.322308 0.991963i
\(446\) −0.422901 + 0.307255i −0.0200249 + 0.0145490i
\(447\) −6.71572 4.87926i −0.317643 0.230781i
\(448\) −4.94496 15.2190i −0.233628 0.719032i
\(449\) 20.2252 + 14.6945i 0.954485 + 0.693474i 0.951863 0.306522i \(-0.0991655\pi\)
0.00262175 + 0.999997i \(0.499165\pi\)
\(450\) 1.25729 + 0.913478i 0.0592694 + 0.0430617i
\(451\) −0.356176 1.09620i −0.0167717 0.0516179i
\(452\) 5.33811 + 3.87836i 0.251083 + 0.182423i
\(453\) −5.97266 + 4.33939i −0.280620 + 0.203883i
\(454\) −1.05186 + 3.23729i −0.0493663 + 0.151934i
\(455\) −36.2729 + 26.3538i −1.70050 + 1.23549i
\(456\) 1.00419 + 3.09057i 0.0470254 + 0.144729i
\(457\) −2.18390 6.72134i −0.102158 0.314411i 0.886895 0.461972i \(-0.152858\pi\)
−0.989053 + 0.147561i \(0.952858\pi\)
\(458\) −0.732108 + 2.25320i −0.0342092 + 0.105285i
\(459\) 4.47923 0.209072
\(460\) 59.7165 2.78430
\(461\) 2.57562 7.92694i 0.119958 0.369194i −0.872990 0.487737i \(-0.837822\pi\)
0.992949 + 0.118543i \(0.0378224\pi\)
\(462\) −0.534885 0.388617i −0.0248851 0.0180801i
\(463\) −13.8115 + 10.0346i −0.641874 + 0.466349i −0.860494 0.509461i \(-0.829845\pi\)
0.218619 + 0.975810i \(0.429845\pi\)
\(464\) −15.8282 −0.734807
\(465\) 17.4807 + 11.8673i 0.810650 + 0.550333i
\(466\) −4.27869 −0.198206
\(467\) 32.1520 23.3598i 1.48782 1.08096i 0.512887 0.858456i \(-0.328576\pi\)
0.974931 0.222507i \(-0.0714240\pi\)
\(468\) 8.66252 + 6.29369i 0.400425 + 0.290926i
\(469\) 4.25850 13.1063i 0.196639 0.605193i
\(470\) 1.11228 0.0513057
\(471\) 16.6792 0.768536
\(472\) −1.53703 + 4.73049i −0.0707475 + 0.217738i
\(473\) 0.709670 + 2.18414i 0.0326307 + 0.100427i
\(474\) 0.0280215 + 0.0862414i 0.00128707 + 0.00396120i
\(475\) −37.6281 + 27.3384i −1.72649 + 1.25437i
\(476\) −5.94355 + 18.2924i −0.272422 + 0.838429i
\(477\) −4.63110 + 3.36469i −0.212043 + 0.154058i
\(478\) −0.0284708 0.0206853i −0.00130223 0.000946122i
\(479\) −8.98173 27.6429i −0.410386 1.26304i −0.916313 0.400462i \(-0.868850\pi\)
0.505928 0.862576i \(-0.331150\pi\)
\(480\) 5.98003 + 4.34475i 0.272950 + 0.198310i
\(481\) 2.52473 + 1.83433i 0.115118 + 0.0836381i
\(482\) −1.07145 3.29759i −0.0488033 0.150201i
\(483\) 14.0481 + 10.2066i 0.639212 + 0.464415i
\(484\) −12.1684 + 8.84083i −0.553107 + 0.401856i
\(485\) 12.4697 38.3778i 0.566220 1.74265i
\(486\) 0.133750 0.0971754i 0.00606704 0.00440797i
\(487\) −3.03234 9.33260i −0.137409 0.422900i 0.858548 0.512733i \(-0.171367\pi\)
−0.995957 + 0.0898325i \(0.971367\pi\)
\(488\) −1.28407 3.95197i −0.0581272 0.178897i
\(489\) 1.29023 3.97093i 0.0583463 0.179571i
\(490\) 1.41899 0.0641035
\(491\) 20.2163 0.912347 0.456173 0.889891i \(-0.349220\pi\)
0.456173 + 0.889891i \(0.349220\pi\)
\(492\) −0.382437 + 1.17702i −0.0172416 + 0.0530641i
\(493\) 14.9496 + 10.8615i 0.673296 + 0.489178i
\(494\) 3.59204 2.60977i 0.161613 0.117419i
\(495\) −6.97179 −0.313359
\(496\) 17.6741 + 11.9986i 0.793592 + 0.538752i
\(497\) 5.36708 0.240746
\(498\) 0.0341643 0.0248218i 0.00153094 0.00111229i
\(499\) −12.1411 8.82104i −0.543511 0.394884i 0.281876 0.959451i \(-0.409043\pi\)
−0.825387 + 0.564567i \(0.809043\pi\)
\(500\) −10.1790 + 31.3277i −0.455218 + 1.40102i
\(501\) −8.93993 −0.399406
\(502\) 4.38743 0.195821
\(503\) −0.901713 + 2.77519i −0.0402054 + 0.123739i −0.969145 0.246493i \(-0.920722\pi\)
0.928939 + 0.370232i \(0.120722\pi\)
\(504\) 0.441782 + 1.35967i 0.0196786 + 0.0605644i
\(505\) −13.1884 40.5897i −0.586876 1.80622i
\(506\) 1.96024 1.42420i 0.0871432 0.0633133i
\(507\) 5.08711 15.6565i 0.225926 0.695330i
\(508\) −0.595665 + 0.432776i −0.0264284 + 0.0192013i
\(509\) 30.4174 + 22.0996i 1.34823 + 0.979546i 0.999098 + 0.0424725i \(0.0135235\pi\)
0.349132 + 0.937074i \(0.386477\pi\)
\(510\) −0.868378 2.67259i −0.0384524 0.118344i
\(511\) 16.3445 + 11.8750i 0.723040 + 0.525319i
\(512\) 10.1235 + 7.35513i 0.447399 + 0.325054i
\(513\) 1.52896 + 4.70565i 0.0675051 + 0.207759i
\(514\) −3.49105 2.53640i −0.153984 0.111876i
\(515\) 36.9417 26.8397i 1.62784 1.18270i
\(516\) 0.761995 2.34518i 0.0335449 0.103241i
\(517\) −2.63516 + 1.91456i −0.115894 + 0.0842022i
\(518\) 0.0639369 + 0.196777i 0.00280923 + 0.00864591i
\(519\) 4.02910 + 12.4003i 0.176858 + 0.544312i
\(520\) 4.18043 12.8660i 0.183324 0.564213i
\(521\) −3.89717 −0.170738 −0.0853690 0.996349i \(-0.527207\pi\)
−0.0853690 + 0.996349i \(0.527207\pi\)
\(522\) 0.682034 0.0298518
\(523\) 7.43511 22.8829i 0.325115 1.00060i −0.646274 0.763105i \(-0.723674\pi\)
0.971389 0.237494i \(-0.0763262\pi\)
\(524\) −34.4862 25.0557i −1.50654 1.09456i
\(525\) −16.5541 + 12.0273i −0.722480 + 0.524912i
\(526\) 0.00961235 0.000419118
\(527\) −8.45946 23.4607i −0.368500 1.02197i
\(528\) −7.04892 −0.306765
\(529\) −32.8760 + 23.8858i −1.42939 + 1.03851i
\(530\) 2.90541 + 2.11090i 0.126203 + 0.0916918i
\(531\) −2.34025 + 7.20254i −0.101558 + 0.312564i
\(532\) −21.2458 −0.921122
\(533\) 3.40531 0.147500
\(534\) −0.296213 + 0.911648i −0.0128184 + 0.0394509i
\(535\) 5.87546 + 18.0828i 0.254018 + 0.781787i
\(536\) 1.28490 + 3.95452i 0.0554993 + 0.170809i
\(537\) 3.85201 2.79865i 0.166226 0.120770i
\(538\) −1.30206 + 4.00733i −0.0561358 + 0.172768i
\(539\) −3.36180 + 2.44249i −0.144803 + 0.105206i
\(540\) 6.05616 + 4.40006i 0.260616 + 0.189348i
\(541\) 0.940937 + 2.89591i 0.0404540 + 0.124505i 0.969244 0.246102i \(-0.0791498\pi\)
−0.928790 + 0.370607i \(0.879150\pi\)
\(542\) −0.0962876 0.0699570i −0.00413590 0.00300491i
\(543\) −0.490017 0.356018i −0.0210287 0.0152782i
\(544\) −2.69616 8.29792i −0.115597 0.355771i
\(545\) −44.4415 32.2886i −1.90366 1.38309i
\(546\) 1.58028 1.14814i 0.0676298 0.0491359i
\(547\) 2.50709 7.71604i 0.107196 0.329914i −0.883044 0.469290i \(-0.844510\pi\)
0.990239 + 0.139376i \(0.0445098\pi\)
\(548\) −35.2961 + 25.6441i −1.50777 + 1.09546i
\(549\) −1.95510 6.01719i −0.0834418 0.256807i
\(550\) 0.882308 + 2.71547i 0.0376217 + 0.115788i
\(551\) −6.30759 + 19.4128i −0.268712 + 0.827012i
\(552\) −5.23932 −0.223000
\(553\) −1.19393 −0.0507710
\(554\) 1.67296 5.14884i 0.0710773 0.218753i
\(555\) 1.76510 + 1.28242i 0.0749242 + 0.0544356i
\(556\) −15.8896 + 11.5445i −0.673869 + 0.489594i
\(557\) −38.3245 −1.62386 −0.811930 0.583755i \(-0.801583\pi\)
−0.811930 + 0.583755i \(0.801583\pi\)
\(558\) −0.761574 0.517016i −0.0322400 0.0218870i
\(559\) −6.78498 −0.286974
\(560\) −25.6397 + 18.6284i −1.08348 + 0.787192i
\(561\) 6.65763 + 4.83705i 0.281085 + 0.204220i
\(562\) −0.626957 + 1.92957i −0.0264466 + 0.0813942i
\(563\) −9.87177 −0.416045 −0.208023 0.978124i \(-0.566703\pi\)
−0.208023 + 0.978124i \(0.566703\pi\)
\(564\) 3.49740 0.147267
\(565\) 3.92233 12.0717i 0.165014 0.507859i
\(566\) 0.274974 + 0.846284i 0.0115580 + 0.0355720i
\(567\) 0.672649 + 2.07020i 0.0282486 + 0.0869403i
\(568\) −1.31011 + 0.951854i −0.0549712 + 0.0399389i
\(569\) 7.68052 23.6382i 0.321984 0.990965i −0.650800 0.759250i \(-0.725566\pi\)
0.972784 0.231715i \(-0.0744338\pi\)
\(570\) 2.51127 1.82455i 0.105186 0.0764218i
\(571\) 31.3778 + 22.7973i 1.31312 + 0.954037i 0.999991 + 0.00432648i \(0.00137716\pi\)
0.313129 + 0.949711i \(0.398623\pi\)
\(572\) 6.07894 + 18.7091i 0.254173 + 0.782265i
\(573\) −14.0101 10.1790i −0.585281 0.425232i
\(574\) 0.182652 + 0.132705i 0.00762376 + 0.00553898i
\(575\) −23.1728 71.3186i −0.966373 2.97419i
\(576\) 5.94747 + 4.32109i 0.247811 + 0.180045i
\(577\) −7.66964 + 5.57232i −0.319291 + 0.231979i −0.735873 0.677120i \(-0.763228\pi\)
0.416582 + 0.909098i \(0.363228\pi\)
\(578\) −0.156508 + 0.481681i −0.00650986 + 0.0200353i
\(579\) −9.32338 + 6.77383i −0.387467 + 0.281511i
\(580\) 9.54312 + 29.3707i 0.396256 + 1.21955i
\(581\) 0.171817 + 0.528798i 0.00712816 + 0.0219382i
\(582\) −0.543261 + 1.67198i −0.0225189 + 0.0693060i
\(583\) −10.5168 −0.435563
\(584\) −6.09577 −0.252245
\(585\) 6.36504 19.5896i 0.263162 0.809929i
\(586\) −2.06583 1.50091i −0.0853387 0.0620022i
\(587\) −15.4920 + 11.2556i −0.639425 + 0.464569i −0.859653 0.510879i \(-0.829320\pi\)
0.220228 + 0.975448i \(0.429320\pi\)
\(588\) 4.46180 0.184002
\(589\) 21.7590 16.8952i 0.896566 0.696156i
\(590\) 4.75120 0.195604
\(591\) 9.83703 7.14702i 0.404642 0.293989i
\(592\) 1.78462 + 1.29661i 0.0733476 + 0.0532902i
\(593\) −4.72997 + 14.5574i −0.194237 + 0.597799i 0.805748 + 0.592259i \(0.201764\pi\)
−0.999985 + 0.00554061i \(0.998236\pi\)
\(594\) 0.303736 0.0124624
\(595\) 36.9994 1.51683
\(596\) −5.06024 + 15.5738i −0.207276 + 0.637929i
\(597\) 3.92253 + 12.0723i 0.160538 + 0.494086i
\(598\) 2.21211 + 6.80819i 0.0904601 + 0.278408i
\(599\) −18.0799 + 13.1358i −0.738726 + 0.536716i −0.892312 0.451419i \(-0.850918\pi\)
0.153586 + 0.988135i \(0.450918\pi\)
\(600\) 1.90785 5.87175i 0.0778876 0.239713i
\(601\) −30.1238 + 21.8862i −1.22877 + 0.892757i −0.996798 0.0799642i \(-0.974519\pi\)
−0.231977 + 0.972721i \(0.574519\pi\)
\(602\) −0.363929 0.264410i −0.0148327 0.0107766i
\(603\) 1.95637 + 6.02107i 0.0796694 + 0.245197i
\(604\) 11.7821 + 8.56018i 0.479406 + 0.348309i
\(605\) 23.4080 + 17.0069i 0.951670 + 0.691428i
\(606\) 0.574571 + 1.76835i 0.0233404 + 0.0718342i
\(607\) 4.47996 + 3.25488i 0.181836 + 0.132112i 0.674980 0.737836i \(-0.264152\pi\)
−0.493144 + 0.869948i \(0.664152\pi\)
\(608\) 7.79705 5.66489i 0.316212 0.229742i
\(609\) −2.77496 + 8.54045i −0.112447 + 0.346077i
\(610\) −3.21121 + 2.33308i −0.130018 + 0.0944636i
\(611\) −2.97376 9.15230i −0.120306 0.370262i
\(612\) −2.73048 8.40356i −0.110373 0.339694i
\(613\) 2.08442 6.41518i 0.0841889 0.259107i −0.900097 0.435690i \(-0.856504\pi\)
0.984286 + 0.176583i \(0.0565044\pi\)
\(614\) −1.29596 −0.0523008
\(615\) 2.38072 0.0960001
\(616\) −0.811647 + 2.49799i −0.0327022 + 0.100647i
\(617\) −1.94324 1.41185i −0.0782318 0.0568388i 0.547982 0.836490i \(-0.315396\pi\)
−0.626214 + 0.779651i \(0.715396\pi\)
\(618\) −1.60942 + 1.16931i −0.0647402 + 0.0470365i
\(619\) 19.7390 0.793377 0.396689 0.917953i \(-0.370159\pi\)
0.396689 + 0.917953i \(0.370159\pi\)
\(620\) 11.6084 40.0301i 0.466205 1.60765i
\(621\) −7.97728 −0.320117
\(622\) 2.45496 1.78363i 0.0984348 0.0715171i
\(623\) −10.2105 7.41837i −0.409075 0.297211i
\(624\) 6.43545 19.8063i 0.257624 0.792886i
\(625\) 16.3641 0.654564
\(626\) −1.48295 −0.0592704
\(627\) −2.80901 + 8.64526i −0.112181 + 0.345258i
\(628\) −10.1674 31.2921i −0.405724 1.24869i
\(629\) −0.795813 2.44926i −0.0317311 0.0976584i
\(630\) 1.10481 0.802691i 0.0440166 0.0319800i
\(631\) 11.7348 36.1161i 0.467156 1.43776i −0.389094 0.921198i \(-0.627212\pi\)
0.856250 0.516562i \(-0.172788\pi\)
\(632\) 0.291440 0.211744i 0.0115929 0.00842271i
\(633\) 16.2870 + 11.8332i 0.647351 + 0.470328i
\(634\) −1.04378 3.21243i −0.0414539 0.127582i
\(635\) 1.14587 + 0.832521i 0.0454723 + 0.0330376i
\(636\) 9.13561 + 6.63741i 0.362251 + 0.263191i
\(637\) −3.79377 11.6760i −0.150315 0.462621i
\(638\) 1.01373 + 0.736518i 0.0401340 + 0.0291590i
\(639\) −1.99475 + 1.44927i −0.0789112 + 0.0573324i
\(640\) 5.99355 18.4463i 0.236916 0.729152i
\(641\) 21.0275 15.2774i 0.830536 0.603420i −0.0891747 0.996016i \(-0.528423\pi\)
0.919711 + 0.392596i \(0.128423\pi\)
\(642\) −0.255973 0.787803i −0.0101024 0.0310921i
\(643\) −1.25958 3.87659i −0.0496730 0.152878i 0.923143 0.384456i \(-0.125611\pi\)
−0.972816 + 0.231578i \(0.925611\pi\)
\(644\) 10.5852 32.5778i 0.417114 1.28374i
\(645\) −4.74353 −0.186776
\(646\) −3.66398 −0.144158
\(647\) −13.9697 + 42.9944i −0.549207 + 1.69029i 0.161564 + 0.986862i \(0.448346\pi\)
−0.710771 + 0.703423i \(0.751654\pi\)
\(648\) −0.531346 0.386046i −0.0208732 0.0151653i
\(649\) −11.2563 + 8.17819i −0.441849 + 0.321022i
\(650\) −8.43552 −0.330868
\(651\) 9.57267 7.43289i 0.375183 0.291318i
\(652\) −8.23644 −0.322564
\(653\) 25.5028 18.5289i 0.998002 0.725091i 0.0363434 0.999339i \(-0.488429\pi\)
0.961659 + 0.274248i \(0.0884290\pi\)
\(654\) 1.93616 + 1.40670i 0.0757097 + 0.0550063i
\(655\) −25.3397 + 77.9877i −0.990106 + 3.04723i
\(656\) 2.40706 0.0939800
\(657\) −9.28130 −0.362098
\(658\) 0.197159 0.606794i 0.00768607 0.0236553i
\(659\) −1.98299 6.10303i −0.0772464 0.237740i 0.904975 0.425464i \(-0.139889\pi\)
−0.982222 + 0.187724i \(0.939889\pi\)
\(660\) 4.24992 + 13.0799i 0.165428 + 0.509135i
\(661\) 20.8008 15.1127i 0.809057 0.587814i −0.104500 0.994525i \(-0.533324\pi\)
0.913557 + 0.406711i \(0.133324\pi\)
\(662\) −0.905755 + 2.78763i −0.0352032 + 0.108344i
\(663\) −19.6695 + 14.2907i −0.763901 + 0.555006i
\(664\) −0.135723 0.0986087i −0.00526709 0.00382676i
\(665\) 12.6295 + 38.8697i 0.489752 + 1.50730i
\(666\) −0.0768990 0.0558704i −0.00297977 0.00216493i
\(667\) −26.6245 19.3438i −1.03090 0.748995i
\(668\) 5.44967 + 16.7724i 0.210854 + 0.648942i
\(669\) 2.55800 + 1.85850i 0.0988981 + 0.0718537i
\(670\) 3.21328 2.33458i 0.124140 0.0901929i
\(671\) 3.59193 11.0548i 0.138665 0.426767i
\(672\) 3.43023 2.49221i 0.132324 0.0961391i
\(673\) −1.26027 3.87872i −0.0485799 0.149514i 0.923824 0.382818i \(-0.125046\pi\)
−0.972404 + 0.233304i \(0.925046\pi\)
\(674\) 0.523609 + 1.61150i 0.0201687 + 0.0620728i
\(675\) 2.90485 8.94021i 0.111808 0.344109i
\(676\) −32.4745 −1.24902
\(677\) −50.1051 −1.92569 −0.962847 0.270048i \(-0.912961\pi\)
−0.962847 + 0.270048i \(0.912961\pi\)
\(678\) −0.170882 + 0.525920i −0.00656267 + 0.0201978i
\(679\) −18.7263 13.6055i −0.718650 0.522129i
\(680\) −9.03164 + 6.56187i −0.346347 + 0.251636i
\(681\) 20.5891 0.788978
\(682\) −0.573635 1.59087i −0.0219656 0.0609175i
\(683\) −1.95717 −0.0748889 −0.0374444 0.999299i \(-0.511922\pi\)
−0.0374444 + 0.999299i \(0.511922\pi\)
\(684\) 7.89631 5.73701i 0.301923 0.219360i
\(685\) 67.8982 + 49.3310i 2.59426 + 1.88484i
\(686\) 1.02996 3.16990i 0.0393242 0.121027i
\(687\) 14.3303 0.546735
\(688\) −4.79600 −0.182846
\(689\) 9.60155 29.5505i 0.365790 1.12579i
\(690\) 1.54654 + 4.75975i 0.0588757 + 0.181201i
\(691\) −3.53994 10.8948i −0.134666 0.414458i 0.860872 0.508821i \(-0.169919\pi\)
−0.995538 + 0.0943631i \(0.969919\pi\)
\(692\) 20.8083 15.1181i 0.791014 0.574705i
\(693\) −1.23580 + 3.80339i −0.0469441 + 0.144479i
\(694\) 0.770312 0.559664i 0.0292406 0.0212446i
\(695\) 30.5664 + 22.2078i 1.15945 + 0.842390i
\(696\) −0.837280 2.57688i −0.0317370 0.0976765i
\(697\) −2.27344 1.65175i −0.0861128 0.0625646i
\(698\) 2.49935 + 1.81588i 0.0946016 + 0.0687321i
\(699\) 7.99752 + 24.6138i 0.302494 + 0.930981i
\(700\) 32.6557 + 23.7258i 1.23427 + 0.896750i
\(701\) 3.26310 2.37078i 0.123246 0.0895433i −0.524455 0.851438i \(-0.675731\pi\)
0.647701 + 0.761895i \(0.275731\pi\)
\(702\) −0.277302 + 0.853447i −0.0104661 + 0.0322113i
\(703\) 2.30142 1.67208i 0.0867997 0.0630636i
\(704\) 4.17365 + 12.8452i 0.157300 + 0.484120i
\(705\) −2.07902 6.39857i −0.0783005 0.240984i
\(706\) 0.158815 0.488782i 0.00597707 0.0183955i
\(707\) −24.4811 −0.920705
\(708\) 14.9394 0.561457
\(709\) −3.19443 + 9.83145i −0.119969 + 0.369228i −0.992951 0.118525i \(-0.962183\pi\)
0.872982 + 0.487753i \(0.162183\pi\)
\(710\) 1.25145 + 0.909230i 0.0469660 + 0.0341228i
\(711\) 0.443741 0.322397i 0.0166416 0.0120908i
\(712\) 3.80806 0.142713
\(713\) 15.0659 + 41.7824i 0.564221 + 1.56476i
\(714\) −1.61193 −0.0603251
\(715\) 30.6150 22.2431i 1.14494 0.831846i
\(716\) −7.59873 5.52080i −0.283978 0.206322i
\(717\) −0.0657790 + 0.202447i −0.00245656 + 0.00756052i
\(718\) −0.00532255 −0.000198636
\(719\) 12.7817 0.476677 0.238338 0.971182i \(-0.423397\pi\)
0.238338 + 0.971182i \(0.423397\pi\)
\(720\) 4.49917 13.8470i 0.167674 0.516048i
\(721\) −8.09397 24.9107i −0.301435 0.927723i
\(722\) −0.280004 0.861764i −0.0104207 0.0320715i
\(723\) −16.9672 + 12.3274i −0.631017 + 0.458461i
\(724\) −0.369224 + 1.13635i −0.0137221 + 0.0422323i
\(725\) 31.3738 22.7944i 1.16519 0.846564i
\(726\) −1.01980 0.740929i −0.0378484 0.0274985i
\(727\) −6.60823 20.3380i −0.245086 0.754296i −0.995622 0.0934673i \(-0.970205\pi\)
0.750537 0.660829i \(-0.229795\pi\)
\(728\) −6.27793 4.56118i −0.232676 0.169049i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 1.79935 + 5.53781i 0.0665968 + 0.204964i
\(731\) 4.52977 + 3.29107i 0.167540 + 0.121725i
\(732\) −10.0972 + 7.33601i −0.373201 + 0.271147i
\(733\) −6.50250 + 20.0127i −0.240175 + 0.739184i 0.756217 + 0.654321i \(0.227045\pi\)
−0.996393 + 0.0848633i \(0.972955\pi\)
\(734\) −2.33950 + 1.69974i −0.0863524 + 0.0627387i
\(735\) −2.65231 8.16297i −0.0978319 0.301096i
\(736\) 4.80172 + 14.7782i 0.176994 + 0.544731i
\(737\) −3.59425 + 11.0620i −0.132396 + 0.407473i
\(738\) −0.103720 −0.00381797
\(739\) −27.7811 −1.02195 −0.510973 0.859597i \(-0.670715\pi\)
−0.510973 + 0.859597i \(0.670715\pi\)
\(740\) 1.32999 4.09328i 0.0488913 0.150472i
\(741\) −21.7272 15.7857i −0.798168 0.579903i
\(742\) 1.66659 1.21085i 0.0611823 0.0444515i
\(743\) 29.6418 1.08745 0.543727 0.839262i \(-0.317013\pi\)
0.543727 + 0.839262i \(0.317013\pi\)
\(744\) −1.01848 + 3.51210i −0.0373393 + 0.128760i
\(745\) 31.5007 1.15410
\(746\) −3.82226 + 2.77703i −0.139943 + 0.101674i
\(747\) −0.206650 0.150140i −0.00756091 0.00549332i
\(748\) 5.01647 15.4391i 0.183420 0.564510i
\(749\) 10.9064 0.398510
\(750\) −2.76061 −0.100803
\(751\) 1.45667 4.48317i 0.0531547 0.163593i −0.920955 0.389669i \(-0.872590\pi\)
0.974110 + 0.226075i \(0.0725895\pi\)
\(752\) −2.10202 6.46936i −0.0766529 0.235913i
\(753\) −8.20078 25.2394i −0.298853 0.919776i
\(754\) −2.99500 + 2.17599i −0.109071 + 0.0792450i
\(755\) 8.65722 26.6442i 0.315069 0.969681i
\(756\) 3.47390 2.52394i 0.126345 0.0917948i
\(757\) −3.46488 2.51739i −0.125933 0.0914959i 0.523036 0.852311i \(-0.324799\pi\)
−0.648969 + 0.760815i \(0.724799\pi\)
\(758\) −0.286085 0.880479i −0.0103911 0.0319804i
\(759\) −11.8569 8.61454i −0.430378 0.312688i
\(760\) −9.97645 7.24832i −0.361884 0.262924i
\(761\) −6.70566 20.6379i −0.243080 0.748123i −0.995946 0.0899499i \(-0.971329\pi\)
0.752866 0.658174i \(-0.228671\pi\)
\(762\) −0.0499213 0.0362700i −0.00180846 0.00131392i
\(763\) −25.4923 + 18.5212i −0.922883 + 0.670514i
\(764\) −10.5565 + 32.4896i −0.381921 + 1.17543i
\(765\) −13.7514 + 9.99097i −0.497183 + 0.361224i
\(766\) 0.442233 + 1.36105i 0.0159785 + 0.0491768i
\(767\) −12.7027 39.0948i −0.458666 1.41163i
\(768\) 4.28234 13.1797i 0.154526 0.475582i
\(769\) 20.4596 0.737793 0.368897 0.929470i \(-0.379736\pi\)
0.368897 + 0.929470i \(0.379736\pi\)
\(770\) 2.50893 0.0904155
\(771\) −8.06572 + 24.8237i −0.290480 + 0.894005i
\(772\) 18.3919 + 13.3625i 0.661940 + 0.480928i
\(773\) 23.3893 16.9933i 0.841253 0.611206i −0.0814672 0.996676i \(-0.525961\pi\)
0.922720 + 0.385470i \(0.125961\pi\)
\(774\) 0.206658 0.00742819
\(775\) −52.3120 + 1.66981i −1.87910 + 0.0599812i
\(776\) 6.98406 0.250713
\(777\) 1.01249 0.735614i 0.0363227 0.0263900i
\(778\) 0.171378 + 0.124513i 0.00614420 + 0.00446402i
\(779\) 0.959221 2.95218i 0.0343677 0.105773i
\(780\) −40.6324 −1.45487
\(781\) −4.52992 −0.162093
\(782\) 1.82548 5.61826i 0.0652792 0.200909i
\(783\) −1.27483 3.92351i −0.0455585 0.140215i
\(784\) −2.68165 8.25328i −0.0957733 0.294760i
\(785\) −51.2057 + 37.2031i −1.82761 + 1.32784i
\(786\) 1.10396 3.39765i 0.0393770 0.121190i
\(787\) 1.15909 0.842131i 0.0413172 0.0300187i −0.566935 0.823763i \(-0.691871\pi\)
0.608252 + 0.793744i \(0.291871\pi\)
\(788\) −19.4052 14.0987i −0.691282 0.502246i
\(789\) −0.0179669 0.0552966i −0.000639640 0.00196861i
\(790\) −0.278389 0.202262i −0.00990465 0.00719615i
\(791\) −5.89033 4.27957i −0.209436 0.152164i
\(792\) −0.372873 1.14759i −0.0132495 0.0407777i
\(793\) 27.7829 + 20.1855i 0.986600 + 0.716807i
\(794\) −3.65337 + 2.65433i −0.129653 + 0.0941987i
\(795\) 6.71265 20.6594i 0.238073 0.732714i
\(796\) 20.2579 14.7183i 0.718024 0.521675i
\(797\) 11.6792 + 35.9450i 0.413700 + 1.27324i 0.913409 + 0.407044i \(0.133440\pi\)
−0.499709 + 0.866193i \(0.666560\pi\)
\(798\) −0.550223 1.69341i −0.0194777 0.0599462i
\(799\) −2.45401 + 7.55267i −0.0868167 + 0.267194i
\(800\) −18.3106 −0.647376
\(801\) 5.79807 0.204865
\(802\) −0.0125590 + 0.0386526i −0.000443473 + 0.00136487i
\(803\) −13.7951 10.0227i −0.486819 0.353695i
\(804\) 10.1037 7.34075i 0.356329 0.258888i
\(805\) −65.8941 −2.32246
\(806\) 4.99379 0.159402i 0.175899 0.00561471i
\(807\) 25.4865 0.897168
\(808\) 5.97587 4.34173i 0.210231 0.152741i
\(809\) 16.1165 + 11.7093i 0.566624 + 0.411677i 0.833877 0.551950i \(-0.186116\pi\)
−0.267253 + 0.963626i \(0.586116\pi\)
\(810\) −0.193868 + 0.596664i −0.00681182 + 0.0209646i
\(811\) −16.2353 −0.570097 −0.285049 0.958513i \(-0.592010\pi\)
−0.285049 + 0.958513i \(0.592010\pi\)
\(812\) 17.7145 0.621657
\(813\) −0.222463 + 0.684670i −0.00780211 + 0.0240124i
\(814\) −0.0539640 0.166084i −0.00189144 0.00582124i
\(815\) 4.89614 + 15.0688i 0.171504 + 0.527836i
\(816\) −13.9035 + 10.1015i −0.486721 + 0.353623i
\(817\) −1.91122 + 5.88213i −0.0668651 + 0.205790i
\(818\) 1.79089 1.30116i 0.0626170 0.0454939i
\(819\) −9.55865 6.94477i −0.334006 0.242670i
\(820\) −1.45126 4.46652i −0.0506802 0.155978i
\(821\) 15.6089 + 11.3405i 0.544755 + 0.395788i 0.825848 0.563893i \(-0.190697\pi\)
−0.281093 + 0.959681i \(0.590697\pi\)
\(822\) −2.95808 2.14917i −0.103175 0.0749610i
\(823\) −7.82297 24.0766i −0.272692 0.839259i −0.989821 0.142319i \(-0.954544\pi\)
0.717129 0.696940i \(-0.245456\pi\)
\(824\) 6.39368 + 4.64528i 0.222734 + 0.161826i
\(825\) 13.9720 10.1512i 0.486442 0.353421i
\(826\) 0.842182 2.59197i 0.0293032 0.0901861i
\(827\) −18.6574 + 13.5554i −0.648781 + 0.471367i −0.862856 0.505450i \(-0.831326\pi\)
0.214074 + 0.976817i \(0.431326\pi\)
\(828\) 4.86285 + 14.9663i 0.168996 + 0.520116i
\(829\) 13.5217 + 41.6156i 0.469629 + 1.44537i 0.853066 + 0.521803i \(0.174740\pi\)
−0.383437 + 0.923567i \(0.625260\pi\)
\(830\) −0.0495202 + 0.152408i −0.00171887 + 0.00529014i
\(831\) −32.7466 −1.13597
\(832\) −39.9032 −1.38339
\(833\) −3.13070 + 9.63531i −0.108472 + 0.333844i
\(834\) −1.33167 0.967514i −0.0461119 0.0335023i
\(835\) 27.4459 19.9406i 0.949804 0.690073i
\(836\) 17.9319 0.620187
\(837\) −1.55072 + 5.34745i −0.0536007 + 0.184835i
\(838\) −3.10057 −0.107107
\(839\) −45.8543 + 33.3151i −1.58307 + 1.15017i −0.669995 + 0.742365i \(0.733704\pi\)
−0.913071 + 0.407800i \(0.866296\pi\)
\(840\) −4.38904 3.18882i −0.151436 0.110025i
\(841\) −3.70230 + 11.3945i −0.127666 + 0.392914i
\(842\) 0.296338 0.0102125
\(843\) 12.2721 0.422672
\(844\) 12.2721 37.7698i 0.422424 1.30009i
\(845\) 19.3044 + 59.4129i 0.664092 + 2.04386i
\(846\) 0.0905756 + 0.278763i 0.00311405 + 0.00958407i
\(847\) 13.4272 9.75541i 0.461363 0.335200i
\(848\) 6.78692 20.8880i 0.233064 0.717296i
\(849\) 4.35442 3.16367i 0.149443 0.108577i
\(850\) 5.63171 + 4.09167i 0.193166 + 0.140343i
\(851\) 1.41730 + 4.36201i 0.0485845 + 0.149528i
\(852\) 3.93499 + 2.85893i 0.134810 + 0.0979455i
\(853\) −8.91433 6.47664i −0.305221 0.221756i 0.424622 0.905371i \(-0.360407\pi\)
−0.729843 + 0.683615i \(0.760407\pi\)
\(854\) 0.703580 + 2.16540i 0.0240760 + 0.0740983i
\(855\) −15.1899 11.0361i −0.519485 0.377428i
\(856\) −2.66226 + 1.93425i −0.0909943 + 0.0661112i
\(857\) −8.20636 + 25.2566i −0.280324 + 0.862749i 0.707437 + 0.706776i \(0.249851\pi\)
−0.987761 + 0.155973i \(0.950149\pi\)
\(858\) −1.33379 + 0.969054i −0.0455348 + 0.0330829i
\(859\) −9.81939 30.2210i −0.335033 1.03113i −0.966706 0.255891i \(-0.917631\pi\)
0.631672 0.775235i \(-0.282369\pi\)
\(860\) 2.89160 + 8.89942i 0.0986026 + 0.303468i
\(861\) 0.422000 1.29878i 0.0143817 0.0442623i
\(862\) 6.43289 0.219105
\(863\) 33.7840 1.15002 0.575011 0.818146i \(-0.304998\pi\)
0.575011 + 0.818146i \(0.304998\pi\)
\(864\) −0.601925 + 1.85253i −0.0204779 + 0.0630245i
\(865\) −40.0285 29.0824i −1.36101 0.988830i
\(866\) 0.587857 0.427103i 0.0199762 0.0145136i
\(867\) 3.06348 0.104041
\(868\) −19.7804 13.4285i −0.671389 0.455792i
\(869\) 1.00770 0.0341838
\(870\) −2.09387 + 1.52128i −0.0709888 + 0.0515764i
\(871\) −27.8008 20.1985i −0.941996 0.684400i
\(872\) 2.93797 9.04214i 0.0994922 0.306205i
\(873\) 10.6338 0.359899
\(874\) 6.52537 0.220724
\(875\) 11.2320 34.5685i 0.379710 1.16863i
\(876\) 5.65777 + 17.4128i 0.191158 + 0.588325i
\(877\) 14.5494 + 44.7783i 0.491297 + 1.51206i 0.822649 + 0.568549i \(0.192495\pi\)
−0.331352 + 0.943507i \(0.607505\pi\)
\(878\) −2.85755 + 2.07613i −0.0964375 + 0.0700659i
\(879\) −4.77290 + 14.6895i −0.160986 + 0.495463i
\(880\) 21.6404 15.7227i 0.729499 0.530012i
\(881\) −19.1363 13.9034i −0.644720 0.468416i 0.216749 0.976227i \(-0.430455\pi\)
−0.861468 + 0.507811i \(0.830455\pi\)
\(882\) 0.115552 + 0.355631i 0.00389083 + 0.0119747i
\(883\) −22.1615 16.1012i −0.745792 0.541850i 0.148727 0.988878i \(-0.452482\pi\)
−0.894520 + 0.447028i \(0.852482\pi\)
\(884\) 38.8014 + 28.1909i 1.30503 + 0.948162i
\(885\) −8.88071 27.3320i −0.298522 0.918756i
\(886\) −3.72499 2.70636i −0.125143 0.0909220i
\(887\) −3.85119 + 2.79805i −0.129310 + 0.0939494i −0.650560 0.759455i \(-0.725466\pi\)
0.521250 + 0.853404i \(0.325466\pi\)
\(888\) −0.116688 + 0.359130i −0.00391580 + 0.0120516i
\(889\) 0.657287 0.477547i 0.0220447 0.0160164i
\(890\) −1.12406 3.45950i −0.0376785 0.115963i
\(891\) −0.567729 1.74729i −0.0190196 0.0585364i
\(892\) 1.92743 5.93203i 0.0645353 0.198619i
\(893\) −8.77211 −0.293547
\(894\) −1.37237 −0.0458991
\(895\) −5.58338 + 17.1839i −0.186632 + 0.574394i
\(896\) −9.00078 6.53945i −0.300695 0.218468i
\(897\) 35.0304 25.4511i 1.16963 0.849787i
\(898\) 4.13307 0.137922
\(899\) −18.1424 + 14.0870i −0.605084 + 0.469829i
\(900\) −18.5437 −0.618122
\(901\) −20.7437 + 15.0712i −0.691074 + 0.502095i
\(902\) −0.154162 0.112005i −0.00513303 0.00372937i
\(903\) −0.840822 + 2.58778i −0.0279808 + 0.0861161i
\(904\) 2.19683 0.0730653
\(905\) 2.29847 0.0764038
\(906\) −0.377164 + 1.16079i −0.0125304 + 0.0385647i
\(907\) −1.22381 3.76650i −0.0406359 0.125064i 0.928681 0.370881i \(-0.120944\pi\)
−0.969316 + 0.245816i \(0.920944\pi\)
\(908\) −12.5509 38.6277i −0.416516 1.28190i
\(909\) 9.09875 6.61063i 0.301786 0.219261i
\(910\) −2.29058 + 7.04967i −0.0759319 + 0.233694i
\(911\) −15.9452 + 11.5848i −0.528287 + 0.383823i −0.819716 0.572770i \(-0.805869\pi\)
0.291430 + 0.956592i \(0.405869\pi\)
\(912\) −15.3580 11.1582i −0.508554 0.369486i
\(913\) −0.145017 0.446315i −0.00479935 0.0147709i
\(914\) −0.945246 0.686762i −0.0312660 0.0227161i
\(915\) 19.4236 + 14.1121i 0.642126 + 0.466532i
\(916\) −8.73558 26.8853i −0.288632 0.888317i
\(917\) 38.0538 + 27.6477i 1.25665 + 0.913008i
\(918\) 0.599099 0.435271i 0.0197732 0.0143661i
\(919\) −15.7080 + 48.3442i −0.518158 + 1.59473i 0.259302 + 0.965796i \(0.416507\pi\)
−0.777461 + 0.628931i \(0.783493\pi\)
\(920\) 16.0849 11.6864i 0.530303 0.385288i
\(921\) 2.42235 + 7.45524i 0.0798192 + 0.245658i
\(922\) −0.425813 1.31052i −0.0140234 0.0431596i
\(923\) 4.13568 12.7283i 0.136128 0.418957i
\(924\) 7.88894 0.259527
\(925\) −5.40464 −0.177703
\(926\) −0.872173 + 2.68427i −0.0286614 + 0.0882107i
\(927\) 9.73489 + 7.07281i 0.319736 + 0.232302i
\(928\) −6.50109 + 4.72332i −0.213409 + 0.155050i
\(929\) 39.5892 1.29888 0.649440 0.760413i \(-0.275004\pi\)
0.649440 + 0.760413i \(0.275004\pi\)
\(930\) 3.49127 0.111442i 0.114483 0.00365432i
\(931\) −11.1910 −0.366770
\(932\) 41.3033 30.0086i 1.35293 0.982964i
\(933\) −14.8493 10.7887i −0.486145 0.353205i
\(934\) 2.03035 6.24877i 0.0664350 0.204466i
\(935\) −31.2282 −1.02127
\(936\) 3.56494 0.116524
\(937\) 10.8973 33.5384i 0.355999 1.09565i −0.599430 0.800428i \(-0.704606\pi\)
0.955428 0.295224i \(-0.0953941\pi\)
\(938\) −0.704034 2.16679i −0.0229875 0.0707484i
\(939\) 2.77185 + 8.53088i 0.0904560 + 0.278395i
\(940\) −10.7371 + 7.80098i −0.350207 + 0.254440i
\(941\) −16.4461 + 50.6160i −0.536129 + 1.65003i 0.205069 + 0.978748i \(0.434258\pi\)
−0.741198 + 0.671287i \(0.765742\pi\)
\(942\) 2.23085 1.62081i 0.0726849 0.0528087i
\(943\) 4.04889 + 2.94169i 0.131850 + 0.0957946i
\(944\) −8.97896 27.6344i −0.292240 0.899423i
\(945\) −6.68266 4.85524i −0.217387 0.157941i
\(946\) 0.307164 + 0.223167i 0.00998675 + 0.00725580i
\(947\) 9.03900 + 27.8192i 0.293728 + 0.904002i 0.983646 + 0.180114i \(0.0576467\pi\)
−0.689918 + 0.723888i \(0.742353\pi\)
\(948\) −0.875353 0.635981i −0.0284302 0.0206557i
\(949\) 40.7567 29.6115i 1.32302 0.961229i
\(950\) −2.37615 + 7.31305i −0.0770926 + 0.237267i
\(951\) −16.5290 + 12.0090i −0.535990 + 0.389420i
\(952\) 1.97884 + 6.09026i 0.0641347 + 0.197386i
\(953\) −4.17645 12.8538i −0.135288 0.416375i 0.860346 0.509710i \(-0.170247\pi\)
−0.995635 + 0.0933349i \(0.970247\pi\)
\(954\) −0.292446 + 0.900057i −0.00946830 + 0.0291404i
\(955\) 65.7158 2.12651
\(956\) 0.419912 0.0135809
\(957\) 2.34212 7.20831i 0.0757100 0.233012i
\(958\) −3.88752 2.82445i −0.125600 0.0912539i
\(959\) 38.9474 28.2970i 1.25768 0.913757i
\(960\) −27.8972 −0.900378
\(961\) 30.9369 1.97703i 0.997964 0.0637753i
\(962\) 0.515936 0.0166344
\(963\) −4.05351 + 2.94505i −0.130622 + 0.0949028i
\(964\) 33.4706 + 24.3178i 1.07802 + 0.783225i
\(965\) 13.5140 41.5918i 0.435031 1.33889i
\(966\) 2.87077 0.0923656
\(967\) 40.8022 1.31211 0.656055 0.754713i \(-0.272224\pi\)
0.656055 + 0.754713i \(0.272224\pi\)
\(968\) −1.54747 + 4.76263i −0.0497376 + 0.153077i
\(969\) 6.84855 + 21.0777i 0.220007 + 0.677112i
\(970\) −2.06155 6.34480i −0.0661924 0.203719i
\(971\) 30.6447 22.2647i 0.983436 0.714508i 0.0249621 0.999688i \(-0.492054\pi\)
0.958474 + 0.285180i \(0.0920535\pi\)
\(972\) −0.609588 + 1.87612i −0.0195525 + 0.0601765i
\(973\) 17.5334 12.7387i 0.562093 0.408385i
\(974\) −1.31248 0.953570i −0.0420544 0.0305543i
\(975\) 15.7673 + 48.5267i 0.504957 + 1.55410i
\(976\) 19.6385 + 14.2682i 0.628614 + 0.456715i
\(977\) −9.12710 6.63123i −0.292002 0.212152i 0.432134 0.901810i \(-0.357761\pi\)
−0.724135 + 0.689658i \(0.757761\pi\)
\(978\) −0.213307 0.656492i −0.00682081 0.0209923i
\(979\) 8.61787 + 6.26125i 0.275428 + 0.200110i
\(980\) −13.6979 + 9.95209i −0.437563 + 0.317908i
\(981\) 4.47329 13.7674i 0.142821 0.439559i
\(982\) 2.70393 1.96452i 0.0862860 0.0626904i
\(983\) 2.45209 + 7.54675i 0.0782094 + 0.240704i 0.982515 0.186181i \(-0.0596110\pi\)
−0.904306 + 0.426885i \(0.859611\pi\)
\(984\) 0.127328 + 0.391877i 0.00405908 + 0.0124926i
\(985\) −14.2585 + 43.8832i −0.454314 + 1.39824i
\(986\) 3.05499 0.0972906
\(987\) −3.85920 −0.122840
\(988\) −16.3713 + 50.3855i −0.520839 + 1.60298i
\(989\) −8.06730 5.86124i −0.256525 0.186376i
\(990\) −0.932480 + 0.677487i −0.0296362 + 0.0215319i
\(991\) 16.3050 0.517944 0.258972 0.965885i \(-0.416616\pi\)
0.258972 + 0.965885i \(0.416616\pi\)
\(992\) 10.8398 0.346007i 0.344163 0.0109857i
\(993\) 17.7293 0.562621
\(994\) 0.717849 0.521548i 0.0227688 0.0165425i
\(995\) −38.9697 28.3131i −1.23542 0.897587i
\(996\) −0.155709 + 0.479222i −0.00493382 + 0.0151847i
\(997\) 34.7532 1.10064 0.550322 0.834953i \(-0.314505\pi\)
0.550322 + 0.834953i \(0.314505\pi\)
\(998\) −2.48107 −0.0785369
\(999\) −0.177667 + 0.546804i −0.00562115 + 0.0173001i
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 93.2.f.b.16.3 16
3.2 odd 2 279.2.i.c.109.2 16
31.2 even 5 inner 93.2.f.b.64.3 yes 16
31.8 even 5 2883.2.a.p.1.4 8
31.23 odd 10 2883.2.a.o.1.4 8
93.2 odd 10 279.2.i.c.64.2 16
93.8 odd 10 8649.2.a.bh.1.5 8
93.23 even 10 8649.2.a.bg.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.f.b.16.3 16 1.1 even 1 trivial
93.2.f.b.64.3 yes 16 31.2 even 5 inner
279.2.i.c.64.2 16 93.2 odd 10
279.2.i.c.109.2 16 3.2 odd 2
2883.2.a.o.1.4 8 31.23 odd 10
2883.2.a.p.1.4 8 31.8 even 5
8649.2.a.bg.1.5 8 93.23 even 10
8649.2.a.bh.1.5 8 93.8 odd 10