Properties

Label 210.2.t.f.59.2
Level $210$
Weight $2$
Character 210.59
Analytic conductor $1.677$
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] = [210,2,Mod(59,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.2
Root \(-1.72286 + 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 210.59
Dual form 210.2.t.f.89.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.01575 - 1.40294i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 + 2.85008i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.01575 - 1.40294i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.792893 + 2.09077i) q^{5} +(0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 + 2.85008i) q^{9} +(-2.20711 + 0.358719i) q^{10} +(4.05781 + 2.34278i) q^{11} +(1.72286 - 0.178197i) q^{12} +1.04456 q^{13} +(-1.22938 + 2.34278i) q^{14} +(3.73861 - 1.01132i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.73861 - 1.58114i) q^{17} +(-2.93649 + 0.614017i) q^{18} +(-1.23861 + 0.715113i) q^{19} +(-1.41421 - 1.73205i) q^{20} +(1.70058 - 4.25535i) q^{21} +4.68556i q^{22} +(2.23861 + 3.87739i) q^{23} +(1.01575 + 1.40294i) q^{24} +(-3.74264 - 3.31552i) q^{25} +(0.522278 + 0.904612i) q^{26} +(4.94975 - 1.58114i) q^{27} +(-2.64360 + 0.106711i) q^{28} -6.92163i q^{29} +(2.74514 + 2.73207i) q^{30} +(-5.73861 - 3.31319i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.834952 - 8.07256i) q^{33} -3.16228i q^{34} +(-5.79642 + 1.18383i) q^{35} +(-2.00000 - 2.23607i) q^{36} +(2.30615 - 1.33146i) q^{37} +(-1.23861 - 0.715113i) q^{38} +(-1.06101 - 1.46545i) q^{39} +(0.792893 - 2.09077i) q^{40} +1.04456 q^{41} +(4.53553 - 0.654929i) q^{42} +6.92163i q^{43} +(-4.05781 + 2.34278i) q^{44} +(-5.21633 - 4.21780i) q^{45} +(-2.23861 + 3.87739i) q^{46} +(9.71584 - 5.60944i) q^{47} +(-0.707107 + 1.58114i) q^{48} +(-3.00000 + 6.32456i) q^{49} +(1.00000 - 4.89898i) q^{50} +(0.563508 + 5.44816i) q^{51} +(-0.522278 + 0.904612i) q^{52} +(2.50000 - 4.33013i) q^{53} +(3.84418 + 3.49604i) q^{54} +(-8.11562 + 6.62638i) q^{55} +(-1.41421 - 2.23607i) q^{56} +(2.26139 + 1.01132i) q^{57} +(5.99430 - 3.46081i) q^{58} +(5.28720 - 9.15769i) q^{59} +(-0.993475 + 3.74340i) q^{60} +(3.00000 - 1.73205i) q^{61} -6.62638i q^{62} +(-7.69738 + 1.93657i) q^{63} +1.00000 q^{64} +(-0.828222 + 2.18393i) q^{65} +(6.57357 - 4.75937i) q^{66} +(12.3583 + 7.13505i) q^{67} +(2.73861 - 1.58114i) q^{68} +(3.16588 - 7.07912i) q^{69} +(-3.92344 - 4.42793i) q^{70} +6.92163i q^{71} +(0.936492 - 2.85008i) q^{72} +(1.75166 - 3.03397i) q^{73} +(2.30615 + 1.33146i) q^{74} +(-0.849876 + 8.61845i) q^{75} -1.43023i q^{76} +(0.500000 + 12.3867i) q^{77} +(0.738613 - 1.65159i) q^{78} +(-5.73861 - 9.93957i) q^{79} +(2.20711 - 0.358719i) q^{80} +(-7.24597 - 5.33816i) q^{81} +(0.522278 + 0.904612i) q^{82} +4.06775i q^{83} +(2.83495 + 3.60042i) q^{84} +(5.47723 - 4.47214i) q^{85} +(-5.99430 + 3.46081i) q^{86} +(-9.71064 + 7.03066i) q^{87} +(-4.05781 - 2.34278i) q^{88} +(2.45877 + 4.25871i) q^{89} +(1.04456 - 6.62638i) q^{90} +(1.47723 + 2.33570i) q^{91} -4.47723 q^{92} +(1.18080 + 11.4163i) q^{93} +(9.71584 + 5.60944i) q^{94} +(-0.513050 - 3.15666i) q^{95} +(-1.72286 + 0.178197i) q^{96} -11.9886 q^{97} +(-6.97723 + 0.564201i) q^{98} +(-10.4772 + 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9} - 12 q^{10} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 12 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} + 4 q^{32} + 12 q^{33} + 8 q^{35} - 16 q^{36} + 12 q^{38} - 8 q^{39} + 12 q^{40} + 8 q^{42} - 24 q^{45} + 4 q^{46} + 12 q^{47} - 24 q^{49} + 8 q^{50} + 20 q^{51} + 20 q^{53} + 40 q^{57} - 4 q^{60} + 24 q^{61} - 20 q^{63} + 8 q^{64} - 16 q^{65} + 12 q^{66} - 8 q^{70} - 8 q^{72} - 24 q^{75} + 4 q^{77} - 16 q^{78} - 24 q^{79} + 12 q^{80} + 4 q^{81} + 4 q^{84} - 12 q^{87} - 32 q^{91} + 8 q^{92} + 20 q^{93} + 12 q^{94} - 12 q^{95} - 12 q^{98} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.01575 1.40294i −0.586445 0.809989i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.792893 + 2.09077i −0.354593 + 0.935021i
\(6\) 0.707107 1.58114i 0.288675 0.645497i
\(7\) 1.41421 + 2.23607i 0.534522 + 0.845154i
\(8\) −1.00000 −0.353553
\(9\) −0.936492 + 2.85008i −0.312164 + 0.950028i
\(10\) −2.20711 + 0.358719i −0.697948 + 0.113437i
\(11\) 4.05781 + 2.34278i 1.22348 + 0.706374i 0.965657 0.259819i \(-0.0836628\pi\)
0.257819 + 0.966193i \(0.416996\pi\)
\(12\) 1.72286 0.178197i 0.497347 0.0514410i
\(13\) 1.04456 0.289708 0.144854 0.989453i \(-0.453729\pi\)
0.144854 + 0.989453i \(0.453729\pi\)
\(14\) −1.22938 + 2.34278i −0.328567 + 0.626134i
\(15\) 3.73861 1.01132i 0.965306 0.261123i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.73861 1.58114i −0.664211 0.383482i 0.129668 0.991557i \(-0.458609\pi\)
−0.793880 + 0.608075i \(0.791942\pi\)
\(18\) −2.93649 + 0.614017i −0.692138 + 0.144725i
\(19\) −1.23861 + 0.715113i −0.284157 + 0.164058i −0.635304 0.772262i \(-0.719125\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(20\) −1.41421 1.73205i −0.316228 0.387298i
\(21\) 1.70058 4.25535i 0.371097 0.928594i
\(22\) 4.68556i 0.998964i
\(23\) 2.23861 + 3.87739i 0.466783 + 0.808492i 0.999280 0.0379400i \(-0.0120796\pi\)
−0.532497 + 0.846432i \(0.678746\pi\)
\(24\) 1.01575 + 1.40294i 0.207340 + 0.286374i
\(25\) −3.74264 3.31552i −0.748528 0.663103i
\(26\) 0.522278 + 0.904612i 0.102427 + 0.177409i
\(27\) 4.94975 1.58114i 0.952579 0.304290i
\(28\) −2.64360 + 0.106711i −0.499593 + 0.0201665i
\(29\) 6.92163i 1.28531i −0.766154 0.642657i \(-0.777832\pi\)
0.766154 0.642657i \(-0.222168\pi\)
\(30\) 2.74514 + 2.73207i 0.501191 + 0.498806i
\(31\) −5.73861 3.31319i −1.03069 0.595066i −0.113504 0.993537i \(-0.536208\pi\)
−0.917181 + 0.398471i \(0.869541\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.834952 8.07256i −0.145347 1.40525i
\(34\) 3.16228i 0.542326i
\(35\) −5.79642 + 1.18383i −0.979775 + 0.200104i
\(36\) −2.00000 2.23607i −0.333333 0.372678i
\(37\) 2.30615 1.33146i 0.379129 0.218890i −0.298310 0.954469i \(-0.596423\pi\)
0.677439 + 0.735579i \(0.263090\pi\)
\(38\) −1.23861 0.715113i −0.200930 0.116007i
\(39\) −1.06101 1.46545i −0.169898 0.234660i
\(40\) 0.792893 2.09077i 0.125367 0.330580i
\(41\) 1.04456 0.163132 0.0815661 0.996668i \(-0.474008\pi\)
0.0815661 + 0.996668i \(0.474008\pi\)
\(42\) 4.53553 0.654929i 0.699848 0.101058i
\(43\) 6.92163i 1.05554i 0.849388 + 0.527769i \(0.176971\pi\)
−0.849388 + 0.527769i \(0.823029\pi\)
\(44\) −4.05781 + 2.34278i −0.611738 + 0.353187i
\(45\) −5.21633 4.21780i −0.777605 0.628753i
\(46\) −2.23861 + 3.87739i −0.330065 + 0.571690i
\(47\) 9.71584 5.60944i 1.41720 0.818221i 0.421149 0.906992i \(-0.361627\pi\)
0.996052 + 0.0887705i \(0.0282938\pi\)
\(48\) −0.707107 + 1.58114i −0.102062 + 0.228218i
\(49\) −3.00000 + 6.32456i −0.428571 + 0.903508i
\(50\) 1.00000 4.89898i 0.141421 0.692820i
\(51\) 0.563508 + 5.44816i 0.0789069 + 0.762895i
\(52\) −0.522278 + 0.904612i −0.0724269 + 0.125447i
\(53\) 2.50000 4.33013i 0.343401 0.594789i −0.641661 0.766989i \(-0.721754\pi\)
0.985062 + 0.172200i \(0.0550875\pi\)
\(54\) 3.84418 + 3.49604i 0.523127 + 0.475750i
\(55\) −8.11562 + 6.62638i −1.09431 + 0.893501i
\(56\) −1.41421 2.23607i −0.188982 0.298807i
\(57\) 2.26139 + 1.01132i 0.299528 + 0.133953i
\(58\) 5.99430 3.46081i 0.787091 0.454427i
\(59\) 5.28720 9.15769i 0.688334 1.19223i −0.284042 0.958812i \(-0.591676\pi\)
0.972376 0.233418i \(-0.0749911\pi\)
\(60\) −0.993475 + 3.74340i −0.128257 + 0.483270i
\(61\) 3.00000 1.73205i 0.384111 0.221766i −0.295495 0.955344i \(-0.595484\pi\)
0.679605 + 0.733578i \(0.262151\pi\)
\(62\) 6.62638i 0.841551i
\(63\) −7.69738 + 1.93657i −0.969779 + 0.243985i
\(64\) 1.00000 0.125000
\(65\) −0.828222 + 2.18393i −0.102728 + 0.270883i
\(66\) 6.57357 4.75937i 0.809150 0.585838i
\(67\) 12.3583 + 7.13505i 1.50980 + 0.871685i 0.999935 + 0.0114319i \(0.00363898\pi\)
0.509868 + 0.860253i \(0.329694\pi\)
\(68\) 2.73861 1.58114i 0.332106 0.191741i
\(69\) 3.16588 7.07912i 0.381127 0.852225i
\(70\) −3.92344 4.42793i −0.468941 0.529239i
\(71\) 6.92163i 0.821446i 0.911760 + 0.410723i \(0.134724\pi\)
−0.911760 + 0.410723i \(0.865276\pi\)
\(72\) 0.936492 2.85008i 0.110367 0.335886i
\(73\) 1.75166 3.03397i 0.205017 0.355099i −0.745121 0.666929i \(-0.767608\pi\)
0.950138 + 0.311830i \(0.100942\pi\)
\(74\) 2.30615 + 1.33146i 0.268084 + 0.154779i
\(75\) −0.849876 + 8.61845i −0.0981353 + 0.995173i
\(76\) 1.43023i 0.164058i
\(77\) 0.500000 + 12.3867i 0.0569803 + 1.41160i
\(78\) 0.738613 1.65159i 0.0836314 0.187006i
\(79\) −5.73861 9.93957i −0.645644 1.11829i −0.984152 0.177325i \(-0.943256\pi\)
0.338508 0.940964i \(-0.390078\pi\)
\(80\) 2.20711 0.358719i 0.246762 0.0401061i
\(81\) −7.24597 5.33816i −0.805107 0.593129i
\(82\) 0.522278 + 0.904612i 0.0576760 + 0.0998977i
\(83\) 4.06775i 0.446494i 0.974762 + 0.223247i \(0.0716656\pi\)
−0.974762 + 0.223247i \(0.928334\pi\)
\(84\) 2.83495 + 3.60042i 0.309319 + 0.392838i
\(85\) 5.47723 4.47214i 0.594089 0.485071i
\(86\) −5.99430 + 3.46081i −0.646382 + 0.373189i
\(87\) −9.71064 + 7.03066i −1.04109 + 0.753766i
\(88\) −4.05781 2.34278i −0.432564 0.249741i
\(89\) 2.45877 + 4.25871i 0.260629 + 0.451423i 0.966409 0.257008i \(-0.0827367\pi\)
−0.705780 + 0.708431i \(0.749403\pi\)
\(90\) 1.04456 6.62638i 0.110106 0.698482i
\(91\) 1.47723 + 2.33570i 0.154855 + 0.244848i
\(92\) −4.47723 −0.466783
\(93\) 1.18080 + 11.4163i 0.122443 + 1.18382i
\(94\) 9.71584 + 5.60944i 1.00211 + 0.578570i
\(95\) −0.513050 3.15666i −0.0526378 0.323867i
\(96\) −1.72286 + 0.178197i −0.175839 + 0.0181872i
\(97\) −11.9886 −1.21726 −0.608629 0.793455i \(-0.708280\pi\)
−0.608629 + 0.793455i \(0.708280\pi\)
\(98\) −6.97723 + 0.564201i −0.704806 + 0.0569930i
\(99\) −10.4772 + 9.37112i −1.05300 + 0.941833i
\(100\) 4.74264 1.58346i 0.474264 0.158346i
\(101\) −5.65685 + 9.79796i −0.562878 + 0.974933i 0.434366 + 0.900737i \(0.356973\pi\)
−0.997244 + 0.0741967i \(0.976361\pi\)
\(102\) −4.43649 + 3.21209i −0.439278 + 0.318045i
\(103\) −2.45877 4.25871i −0.242270 0.419624i 0.719091 0.694916i \(-0.244559\pi\)
−0.961360 + 0.275293i \(0.911225\pi\)
\(104\) −1.04456 −0.102427
\(105\) 7.54858 + 6.92957i 0.736666 + 0.676256i
\(106\) 5.00000 0.485643
\(107\) −2.73861 4.74342i −0.264752 0.458563i 0.702747 0.711440i \(-0.251957\pi\)
−0.967499 + 0.252877i \(0.918623\pi\)
\(108\) −1.10557 + 5.07718i −0.106383 + 0.488552i
\(109\) 10.2158 17.6944i 0.978500 1.69481i 0.310634 0.950529i \(-0.399459\pi\)
0.667866 0.744282i \(-0.267208\pi\)
\(110\) −9.79642 3.71515i −0.934052 0.354225i
\(111\) −4.21043 1.88296i −0.399637 0.178723i
\(112\) 1.22938 2.34278i 0.116166 0.221372i
\(113\) −17.4772 −1.64412 −0.822060 0.569402i \(-0.807175\pi\)
−0.822060 + 0.569402i \(0.807175\pi\)
\(114\) 0.254862 + 2.46408i 0.0238700 + 0.230782i
\(115\) −9.88171 + 1.60607i −0.921475 + 0.149767i
\(116\) 5.99430 + 3.46081i 0.556557 + 0.321328i
\(117\) −0.978218 + 2.97707i −0.0904363 + 0.275231i
\(118\) 10.5744 0.973452
\(119\) −0.337449 8.35979i −0.0309339 0.766341i
\(120\) −3.73861 + 1.01132i −0.341287 + 0.0923207i
\(121\) 5.47723 + 9.48683i 0.497930 + 0.862439i
\(122\) 3.00000 + 1.73205i 0.271607 + 0.156813i
\(123\) −1.06101 1.46545i −0.0956682 0.132135i
\(124\) 5.73861 3.31319i 0.515343 0.297533i
\(125\) 9.89949 5.19615i 0.885438 0.464758i
\(126\) −5.52581 5.69784i −0.492278 0.507604i
\(127\) 8.73085i 0.774738i −0.921925 0.387369i \(-0.873384\pi\)
0.921925 0.387369i \(-0.126616\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 9.71064 7.03066i 0.854974 0.619015i
\(130\) −2.30545 + 0.374703i −0.202201 + 0.0328636i
\(131\) 6.88624 + 11.9273i 0.601654 + 1.04209i 0.992571 + 0.121669i \(0.0388245\pi\)
−0.390917 + 0.920426i \(0.627842\pi\)
\(132\) 7.40852 + 3.31319i 0.644829 + 0.288376i
\(133\) −3.35071 1.75830i −0.290543 0.152464i
\(134\) 14.2701i 1.23275i
\(135\) −0.618823 + 11.6025i −0.0532598 + 0.998581i
\(136\) 2.73861 + 1.58114i 0.234834 + 0.135582i
\(137\) −1.73861 + 3.01137i −0.148540 + 0.257278i −0.930688 0.365814i \(-0.880791\pi\)
0.782148 + 0.623092i \(0.214124\pi\)
\(138\) 7.71363 0.797828i 0.656628 0.0679156i
\(139\) 20.1810i 1.71173i 0.517202 + 0.855863i \(0.326974\pi\)
−0.517202 + 0.855863i \(0.673026\pi\)
\(140\) 1.87298 5.61177i 0.158296 0.474281i
\(141\) −17.7386 7.93295i −1.49386 0.668075i
\(142\) −5.99430 + 3.46081i −0.503031 + 0.290425i
\(143\) 4.23861 + 2.44716i 0.354451 + 0.204642i
\(144\) 2.93649 0.614017i 0.244708 0.0511681i
\(145\) 14.4715 + 5.48811i 1.20180 + 0.455763i
\(146\) 3.50333 0.289937
\(147\) 11.9202 2.21536i 0.983165 0.182720i
\(148\) 2.66291i 0.218890i
\(149\) 2.12132 1.22474i 0.173785 0.100335i −0.410584 0.911823i \(-0.634675\pi\)
0.584370 + 0.811488i \(0.301342\pi\)
\(150\) −7.88874 + 3.57321i −0.644113 + 0.291751i
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 1.23861 0.715113i 0.100465 0.0580034i
\(153\) 7.07107 6.32456i 0.571662 0.511310i
\(154\) −10.4772 + 6.62638i −0.844279 + 0.533969i
\(155\) 11.4772 9.37112i 0.921873 0.752706i
\(156\) 1.79962 0.186137i 0.144085 0.0149029i
\(157\) 7.22369 12.5118i 0.576513 0.998550i −0.419362 0.907819i \(-0.637746\pi\)
0.995875 0.0907311i \(-0.0289204\pi\)
\(158\) 5.73861 9.93957i 0.456540 0.790750i
\(159\) −8.61430 + 0.890985i −0.683158 + 0.0706597i
\(160\) 1.41421 + 1.73205i 0.111803 + 0.136931i
\(161\) −5.50423 + 10.4891i −0.433794 + 0.826661i
\(162\) 1.00000 8.94427i 0.0785674 0.702728i
\(163\) 12.7279 7.34847i 0.996928 0.575577i 0.0895899 0.995979i \(-0.471444\pi\)
0.907338 + 0.420402i \(0.138111\pi\)
\(164\) −0.522278 + 0.904612i −0.0407831 + 0.0706383i
\(165\) 17.5399 + 4.65498i 1.36548 + 0.362390i
\(166\) −3.52277 + 2.03387i −0.273420 + 0.157859i
\(167\) 4.29068i 0.332023i 0.986124 + 0.166011i \(0.0530889\pi\)
−0.986124 + 0.166011i \(0.946911\pi\)
\(168\) −1.70058 + 4.25535i −0.131203 + 0.328308i
\(169\) −11.9089 −0.916069
\(170\) 6.61160 + 2.50735i 0.507086 + 0.192305i
\(171\) −0.878183 4.19985i −0.0671564 0.321170i
\(172\) −5.99430 3.46081i −0.457061 0.263885i
\(173\) −0.977226 + 0.564201i −0.0742971 + 0.0428954i −0.536688 0.843781i \(-0.680325\pi\)
0.462391 + 0.886676i \(0.346992\pi\)
\(174\) −10.9441 4.89433i −0.829666 0.371038i
\(175\) 2.12082 13.0576i 0.160319 0.987065i
\(176\) 4.68556i 0.353187i
\(177\) −18.2182 + 1.88433i −1.36936 + 0.141635i
\(178\) −2.45877 + 4.25871i −0.184293 + 0.319204i
\(179\) −16.7857 9.69125i −1.25462 0.724358i −0.282600 0.959238i \(-0.591197\pi\)
−0.972024 + 0.234880i \(0.924530\pi\)
\(180\) 6.26089 2.40858i 0.466659 0.179525i
\(181\) 3.16228i 0.235050i 0.993070 + 0.117525i \(0.0374961\pi\)
−0.993070 + 0.117525i \(0.962504\pi\)
\(182\) −1.28416 + 2.44716i −0.0951884 + 0.181396i
\(183\) −5.47723 2.44949i −0.404888 0.181071i
\(184\) −2.23861 3.87739i −0.165033 0.285845i
\(185\) 0.955238 + 5.87733i 0.0702305 + 0.432110i
\(186\) −9.29642 + 6.73076i −0.681647 + 0.493524i
\(187\) −7.40852 12.8319i −0.541764 0.938364i
\(188\) 11.2189i 0.818221i
\(189\) 10.5355 + 8.83190i 0.766347 + 0.642426i
\(190\) 2.47723 2.02265i 0.179717 0.146738i
\(191\) 14.1099 8.14637i 1.02096 0.589451i 0.106577 0.994304i \(-0.466011\pi\)
0.914381 + 0.404854i \(0.132678\pi\)
\(192\) −1.01575 1.40294i −0.0733057 0.101249i
\(193\) 6.36396 + 3.67423i 0.458088 + 0.264477i 0.711240 0.702949i \(-0.248134\pi\)
−0.253152 + 0.967427i \(0.581467\pi\)
\(194\) −5.99430 10.3824i −0.430366 0.745416i
\(195\) 3.90519 1.05638i 0.279657 0.0756492i
\(196\) −3.97723 5.76035i −0.284088 0.411454i
\(197\) −9.00000 −0.641223 −0.320612 0.947211i \(-0.603888\pi\)
−0.320612 + 0.947211i \(0.603888\pi\)
\(198\) −13.3542 4.38799i −0.949044 0.311841i
\(199\) 13.4317 + 7.75478i 0.952146 + 0.549722i 0.893747 0.448571i \(-0.148067\pi\)
0.0583993 + 0.998293i \(0.481400\pi\)
\(200\) 3.74264 + 3.31552i 0.264645 + 0.234442i
\(201\) −2.54289 24.5854i −0.179361 1.73412i
\(202\) −11.3137 −0.796030
\(203\) 15.4772 9.78866i 1.08629 0.687029i
\(204\) −5.00000 2.23607i −0.350070 0.156556i
\(205\) −0.828222 + 2.18393i −0.0578455 + 0.152532i
\(206\) 2.45877 4.25871i 0.171311 0.296719i
\(207\) −13.1473 + 2.74909i −0.913803 + 0.191075i
\(208\) −0.522278 0.904612i −0.0362135 0.0627236i
\(209\) −6.70141 −0.463546
\(210\) −2.22689 + 10.0020i −0.153670 + 0.690207i
\(211\) 24.4772 1.68508 0.842541 0.538632i \(-0.181059\pi\)
0.842541 + 0.538632i \(0.181059\pi\)
\(212\) 2.50000 + 4.33013i 0.171701 + 0.297394i
\(213\) 9.71064 7.03066i 0.665362 0.481733i
\(214\) 2.73861 4.74342i 0.187208 0.324253i
\(215\) −14.4715 5.48811i −0.986950 0.374286i
\(216\) −4.94975 + 1.58114i −0.336788 + 0.107583i
\(217\) −0.707107 17.5175i −0.0480015 1.18916i
\(218\) 20.4317 1.38381
\(219\) −6.03574 + 0.624282i −0.407857 + 0.0421851i
\(220\) −1.68080 10.3415i −0.113320 0.697226i
\(221\) −2.86064 1.65159i −0.192427 0.111098i
\(222\) −0.474523 4.58782i −0.0318479 0.307915i
\(223\) −21.8881 −1.46574 −0.732868 0.680371i \(-0.761819\pi\)
−0.732868 + 0.680371i \(0.761819\pi\)
\(224\) 2.64360 0.106711i 0.176633 0.00712992i
\(225\) 12.9545 7.56189i 0.863630 0.504126i
\(226\) −8.73861 15.1357i −0.581284 1.00681i
\(227\) −9.00000 5.19615i −0.597351 0.344881i 0.170648 0.985332i \(-0.445414\pi\)
−0.767999 + 0.640451i \(0.778747\pi\)
\(228\) −2.00653 + 1.45276i −0.132885 + 0.0962112i
\(229\) −11.7386 + 6.77729i −0.775709 + 0.447856i −0.834908 0.550390i \(-0.814479\pi\)
0.0591982 + 0.998246i \(0.481146\pi\)
\(230\) −6.33175 7.75478i −0.417503 0.511335i
\(231\) 16.8700 13.2833i 1.10996 0.873979i
\(232\) 6.92163i 0.454427i
\(233\) −2.00000 3.46410i −0.131024 0.226941i 0.793047 0.609160i \(-0.208493\pi\)
−0.924072 + 0.382219i \(0.875160\pi\)
\(234\) −3.06733 + 0.641375i −0.200518 + 0.0419280i
\(235\) 4.02443 + 24.7613i 0.262525 + 1.61525i
\(236\) 5.28720 + 9.15769i 0.344167 + 0.596115i
\(237\) −8.11562 + 18.1471i −0.527166 + 1.17878i
\(238\) 7.07107 4.47214i 0.458349 0.289886i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −2.74514 2.73207i −0.177198 0.176354i
\(241\) −18.4545 10.6547i −1.18876 0.686328i −0.230732 0.973017i \(-0.574112\pi\)
−0.958024 + 0.286689i \(0.907445\pi\)
\(242\) −5.47723 + 9.48683i −0.352089 + 0.609837i
\(243\) −0.129018 + 15.5879i −0.00827648 + 0.999966i
\(244\) 3.46410i 0.221766i
\(245\) −10.8445 11.2870i −0.692830 0.721100i
\(246\) 0.738613 1.65159i 0.0470922 0.105301i
\(247\) −1.29380 + 0.746976i −0.0823226 + 0.0475290i
\(248\) 5.73861 + 3.31319i 0.364402 + 0.210388i
\(249\) 5.70682 4.13183i 0.361655 0.261844i
\(250\) 9.44975 + 5.97514i 0.597655 + 0.377901i
\(251\) 8.85494 0.558919 0.279459 0.960158i \(-0.409845\pi\)
0.279459 + 0.960158i \(0.409845\pi\)
\(252\) 2.17157 7.63441i 0.136796 0.480923i
\(253\) 20.9783i 1.31889i
\(254\) 7.56114 4.36543i 0.474428 0.273911i
\(255\) −11.8377 3.14164i −0.741303 0.196737i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.52277 5.49798i 0.594014 0.342954i −0.172669 0.984980i \(-0.555239\pi\)
0.766683 + 0.642026i \(0.221906\pi\)
\(258\) 10.9441 + 4.89433i 0.681347 + 0.304708i
\(259\) 6.23861 + 3.27374i 0.387649 + 0.203421i
\(260\) −1.47723 1.80922i −0.0916136 0.112203i
\(261\) 19.7272 + 6.48204i 1.22108 + 0.401229i
\(262\) −6.88624 + 11.9273i −0.425433 + 0.736872i
\(263\) −1.00000 + 1.73205i −0.0616626 + 0.106803i −0.895209 0.445647i \(-0.852974\pi\)
0.833546 + 0.552450i \(0.186307\pi\)
\(264\) 0.834952 + 8.07256i 0.0513878 + 0.496832i
\(265\) 7.07107 + 8.66025i 0.434372 + 0.531995i
\(266\) −0.152621 3.78095i −0.00935778 0.231825i
\(267\) 3.47723 7.77531i 0.212803 0.475841i
\(268\) −12.3583 + 7.13505i −0.754901 + 0.435842i
\(269\) −8.79052 + 15.2256i −0.535968 + 0.928323i 0.463148 + 0.886281i \(0.346720\pi\)
−0.999116 + 0.0420423i \(0.986614\pi\)
\(270\) −10.3574 + 5.26531i −0.630333 + 0.320437i
\(271\) −5.47723 + 3.16228i −0.332718 + 0.192095i −0.657047 0.753850i \(-0.728195\pi\)
0.324329 + 0.945944i \(0.394861\pi\)
\(272\) 3.16228i 0.191741i
\(273\) 1.77635 4.44495i 0.107510 0.269021i
\(274\) −3.47723 −0.210067
\(275\) −7.41941 22.2219i −0.447407 1.34003i
\(276\) 4.54776 + 6.28129i 0.273743 + 0.378089i
\(277\) −8.48528 4.89898i −0.509831 0.294351i 0.222933 0.974834i \(-0.428437\pi\)
−0.732764 + 0.680483i \(0.761770\pi\)
\(278\) −17.4772 + 10.0905i −1.04821 + 0.605187i
\(279\) 14.8170 13.2528i 0.887073 0.793422i
\(280\) 5.79642 1.18383i 0.346403 0.0707475i
\(281\) 1.80922i 0.107929i 0.998543 + 0.0539646i \(0.0171858\pi\)
−0.998543 + 0.0539646i \(0.982814\pi\)
\(282\) −1.99917 19.3286i −0.119049 1.15100i
\(283\) 4.61230 7.98873i 0.274173 0.474881i −0.695753 0.718281i \(-0.744929\pi\)
0.969926 + 0.243400i \(0.0782627\pi\)
\(284\) −5.99430 3.46081i −0.355696 0.205361i
\(285\) −3.90748 + 3.92617i −0.231459 + 0.232566i
\(286\) 4.89433i 0.289408i
\(287\) 1.47723 + 2.33570i 0.0871979 + 0.137872i
\(288\) 2.00000 + 2.23607i 0.117851 + 0.131762i
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 2.48292 + 15.2768i 0.145802 + 0.897083i
\(291\) 12.1775 + 16.8193i 0.713856 + 0.985966i
\(292\) 1.75166 + 3.03397i 0.102508 + 0.177550i
\(293\) 8.05661i 0.470672i −0.971914 0.235336i \(-0.924381\pi\)
0.971914 0.235336i \(-0.0756190\pi\)
\(294\) 7.87868 + 9.21555i 0.459494 + 0.537462i
\(295\) 14.9545 + 18.3154i 0.870682 + 1.06636i
\(296\) −2.30615 + 1.33146i −0.134042 + 0.0773893i
\(297\) 23.7894 + 5.18020i 1.38040 + 0.300586i
\(298\) 2.12132 + 1.22474i 0.122885 + 0.0709476i
\(299\) 2.33836 + 4.05015i 0.135231 + 0.234226i
\(300\) −7.03886 5.04524i −0.406389 0.291287i
\(301\) −15.4772 + 9.78866i −0.892092 + 0.564209i
\(302\) 2.00000 0.115087
\(303\) 19.4919 2.01607i 1.11978 0.115820i
\(304\) 1.23861 + 0.715113i 0.0710393 + 0.0410146i
\(305\) 1.24264 + 7.64564i 0.0711534 + 0.437788i
\(306\) 9.01276 + 2.96145i 0.515225 + 0.169295i
\(307\) 11.9886 0.684226 0.342113 0.939659i \(-0.388857\pi\)
0.342113 + 0.939659i \(0.388857\pi\)
\(308\) −10.9772 5.76035i −0.625485 0.328227i
\(309\) −3.47723 + 7.77531i −0.197812 + 0.442322i
\(310\) 13.8542 + 5.25401i 0.786868 + 0.298408i
\(311\) −8.79052 + 15.2256i −0.498465 + 0.863366i −0.999998 0.00177176i \(-0.999436\pi\)
0.501534 + 0.865138i \(0.332769\pi\)
\(312\) 1.06101 + 1.46545i 0.0600679 + 0.0829649i
\(313\) 11.6190 + 20.1246i 0.656742 + 1.13751i 0.981454 + 0.191697i \(0.0613992\pi\)
−0.324712 + 0.945813i \(0.605267\pi\)
\(314\) 14.4474 0.815313
\(315\) 2.05428 17.6290i 0.115746 0.993279i
\(316\) 11.4772 0.645644
\(317\) −4.95445 8.58136i −0.278270 0.481977i 0.692685 0.721240i \(-0.256428\pi\)
−0.970955 + 0.239263i \(0.923094\pi\)
\(318\) −5.07877 7.01471i −0.284803 0.393365i
\(319\) 16.2158 28.0867i 0.907913 1.57255i
\(320\) −0.792893 + 2.09077i −0.0443241 + 0.116878i
\(321\) −3.87298 + 8.66025i −0.216169 + 0.483368i
\(322\) −11.8360 + 0.477769i −0.659594 + 0.0266250i
\(323\) 4.52277 0.251654
\(324\) 8.24597 3.60611i 0.458109 0.200339i
\(325\) −3.90940 3.46324i −0.216854 0.192106i
\(326\) 12.7279 + 7.34847i 0.704934 + 0.406994i
\(327\) −35.2009 + 3.64086i −1.94662 + 0.201340i
\(328\) −1.04456 −0.0576760
\(329\) 26.2834 + 13.7923i 1.44905 + 0.760396i
\(330\) 4.73861 + 17.5175i 0.260852 + 0.964306i
\(331\) −10.7158 18.5604i −0.588996 1.02017i −0.994364 0.106017i \(-0.966190\pi\)
0.405369 0.914153i \(-0.367143\pi\)
\(332\) −3.52277 2.03387i −0.193337 0.111623i
\(333\) 1.63507 + 7.81962i 0.0896014 + 0.428512i
\(334\) −3.71584 + 2.14534i −0.203322 + 0.117388i
\(335\) −24.7165 + 20.1810i −1.35041 + 1.10260i
\(336\) −4.53553 + 0.654929i −0.247434 + 0.0357293i
\(337\) 17.1464i 0.934025i 0.884251 + 0.467013i \(0.154670\pi\)
−0.884251 + 0.467013i \(0.845330\pi\)
\(338\) −5.95445 10.3134i −0.323879 0.560976i
\(339\) 17.7525 + 24.5195i 0.964186 + 1.33172i
\(340\) 1.13437 + 6.97948i 0.0615199 + 0.378516i
\(341\) −15.5241 26.8886i −0.840679 1.45610i
\(342\) 3.19808 2.86045i 0.172933 0.154676i
\(343\) −18.3848 + 2.23607i −0.992685 + 0.120736i
\(344\) 6.92163i 0.373189i
\(345\) 12.2906 + 12.2321i 0.661704 + 0.658554i
\(346\) −0.977226 0.564201i −0.0525360 0.0303317i
\(347\) −8.73861 + 15.1357i −0.469113 + 0.812528i −0.999377 0.0353049i \(-0.988760\pi\)
0.530263 + 0.847833i \(0.322093\pi\)
\(348\) −1.23341 11.9250i −0.0661179 0.639247i
\(349\) 11.7436i 0.628623i −0.949320 0.314311i \(-0.898226\pi\)
0.949320 0.314311i \(-0.101774\pi\)
\(350\) 12.3687 4.69214i 0.661133 0.250805i
\(351\) 5.17029 1.65159i 0.275970 0.0881553i
\(352\) 4.05781 2.34278i 0.216282 0.124871i
\(353\) −0.522774 0.301824i −0.0278245 0.0160645i 0.486023 0.873946i \(-0.338447\pi\)
−0.513848 + 0.857881i \(0.671780\pi\)
\(354\) −10.7410 14.8353i −0.570876 0.788485i
\(355\) −14.4715 5.48811i −0.768069 0.291279i
\(356\) −4.91754 −0.260629
\(357\) −11.3855 + 8.96491i −0.602587 + 0.474473i
\(358\) 19.3825i 1.02440i
\(359\) −9.86729 + 5.69688i −0.520775 + 0.300670i −0.737252 0.675618i \(-0.763877\pi\)
0.216476 + 0.976288i \(0.430544\pi\)
\(360\) 5.21633 + 4.21780i 0.274925 + 0.222298i
\(361\) −8.47723 + 14.6830i −0.446170 + 0.772789i
\(362\) −2.73861 + 1.58114i −0.143938 + 0.0831028i
\(363\) 7.74597 17.3205i 0.406558 0.909091i
\(364\) −2.76139 + 0.111466i −0.144736 + 0.00584238i
\(365\) 4.95445 + 6.06794i 0.259328 + 0.317610i
\(366\) −0.617292 5.96816i −0.0322664 0.311961i
\(367\) 0.184829 0.320133i 0.00964798 0.0167108i −0.861161 0.508332i \(-0.830262\pi\)
0.870809 + 0.491621i \(0.163596\pi\)
\(368\) 2.23861 3.87739i 0.116696 0.202123i
\(369\) −0.978218 + 2.97707i −0.0509240 + 0.154980i
\(370\) −4.61230 + 3.76593i −0.239782 + 0.195781i
\(371\) 13.2180 0.533554i 0.686244 0.0277008i
\(372\) −10.4772 4.68556i −0.543219 0.242935i
\(373\) −20.1042 + 11.6072i −1.04096 + 0.600997i −0.920104 0.391673i \(-0.871896\pi\)
−0.120853 + 0.992670i \(0.538563\pi\)
\(374\) 7.40852 12.8319i 0.383085 0.663523i
\(375\) −17.3453 8.61041i −0.895710 0.444640i
\(376\) −9.71584 + 5.60944i −0.501056 + 0.289285i
\(377\) 7.23003i 0.372365i
\(378\) −2.38089 + 13.5400i −0.122460 + 0.696422i
\(379\) −20.4772 −1.05184 −0.525922 0.850533i \(-0.676280\pi\)
−0.525922 + 0.850533i \(0.676280\pi\)
\(380\) 2.99028 + 1.13402i 0.153398 + 0.0581739i
\(381\) −12.2489 + 8.86839i −0.627529 + 0.454341i
\(382\) 14.1099 + 8.14637i 0.721927 + 0.416805i
\(383\) −15.7158 + 9.07354i −0.803042 + 0.463636i −0.844534 0.535502i \(-0.820122\pi\)
0.0414919 + 0.999139i \(0.486789\pi\)
\(384\) 0.707107 1.58114i 0.0360844 0.0806872i
\(385\) −26.2943 8.77597i −1.34008 0.447265i
\(386\) 7.34847i 0.374027i
\(387\) −19.7272 6.48204i −1.00279 0.329501i
\(388\) 5.99430 10.3824i 0.304315 0.527088i
\(389\) −6.36396 3.67423i −0.322666 0.186291i 0.329914 0.944011i \(-0.392980\pi\)
−0.652580 + 0.757720i \(0.726313\pi\)
\(390\) 2.86745 + 2.85380i 0.145199 + 0.144508i
\(391\) 14.1582i 0.716012i
\(392\) 3.00000 6.32456i 0.151523 0.319438i
\(393\) 9.73861 21.7762i 0.491248 1.09846i
\(394\) −4.50000 7.79423i −0.226707 0.392668i
\(395\) 25.3315 4.11710i 1.27456 0.207154i
\(396\) −2.87701 13.7591i −0.144575 0.691421i
\(397\) 7.44073 + 12.8877i 0.373439 + 0.646816i 0.990092 0.140419i \(-0.0448451\pi\)
−0.616653 + 0.787235i \(0.711512\pi\)
\(398\) 15.5096i 0.777424i
\(399\) 0.936697 + 6.48684i 0.0468935 + 0.324748i
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) 0.827520 0.477769i 0.0413244 0.0238586i −0.479195 0.877708i \(-0.659072\pi\)
0.520520 + 0.853850i \(0.325738\pi\)
\(402\) 20.0201 14.4949i 0.998513 0.722939i
\(403\) −5.99430 3.46081i −0.298598 0.172395i
\(404\) −5.65685 9.79796i −0.281439 0.487467i
\(405\) 16.9061 10.9171i 0.840073 0.542473i
\(406\) 16.2158 + 8.50934i 0.804779 + 0.422312i
\(407\) 12.4772 0.618473
\(408\) −0.563508 5.44816i −0.0278978 0.269724i
\(409\) 13.4317 + 7.75478i 0.664154 + 0.383449i 0.793858 0.608103i \(-0.208069\pi\)
−0.129704 + 0.991553i \(0.541403\pi\)
\(410\) −2.30545 + 0.374703i −0.113858 + 0.0185052i
\(411\) 5.99077 0.619631i 0.295503 0.0305641i
\(412\) 4.91754 0.242270
\(413\) 27.9545 1.12840i 1.37555 0.0555251i
\(414\) −8.95445 10.0114i −0.440087 0.492033i
\(415\) −8.50473 3.22529i −0.417481 0.158323i
\(416\) 0.522278 0.904612i 0.0256068 0.0443523i
\(417\) 28.3127 20.4989i 1.38648 1.00383i
\(418\) −3.35071 5.80359i −0.163888 0.283863i
\(419\) −8.85494 −0.432592 −0.216296 0.976328i \(-0.569398\pi\)
−0.216296 + 0.976328i \(0.569398\pi\)
\(420\) −9.77547 + 3.07248i −0.476994 + 0.149922i
\(421\) 18.9545 0.923783 0.461892 0.886936i \(-0.347171\pi\)
0.461892 + 0.886936i \(0.347171\pi\)
\(422\) 12.2386 + 21.1979i 0.595766 + 1.03190i
\(423\) 6.88858 + 32.9442i 0.334934 + 1.60180i
\(424\) −2.50000 + 4.33013i −0.121411 + 0.210290i
\(425\) 5.00735 + 14.9975i 0.242892 + 0.727488i
\(426\) 10.9441 + 4.89433i 0.530241 + 0.237131i
\(427\) 8.11562 + 4.25871i 0.392743 + 0.206094i
\(428\) 5.47723 0.264752
\(429\) −0.872155 8.43224i −0.0421080 0.407112i
\(430\) −2.48292 15.2768i −0.119737 0.736711i
\(431\) −6.63699 3.83187i −0.319693 0.184575i 0.331563 0.943433i \(-0.392424\pi\)
−0.651256 + 0.758858i \(0.725757\pi\)
\(432\) −3.84418 3.49604i −0.184953 0.168203i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 14.8170 9.37112i 0.711240 0.449828i
\(435\) −7.00000 25.8773i −0.335624 1.24072i
\(436\) 10.2158 + 17.6944i 0.489250 + 0.847406i
\(437\) −5.54555 3.20172i −0.265280 0.153159i
\(438\) −3.55851 4.91496i −0.170032 0.234846i
\(439\) −7.69306 + 4.44159i −0.367170 + 0.211986i −0.672221 0.740350i \(-0.734660\pi\)
0.305051 + 0.952336i \(0.401326\pi\)
\(440\) 8.11562 6.62638i 0.386897 0.315900i
\(441\) −15.2160 14.4731i −0.724574 0.689198i
\(442\) 3.30318i 0.157116i
\(443\) −7.52277 13.0298i −0.357418 0.619066i 0.630111 0.776505i \(-0.283009\pi\)
−0.987529 + 0.157439i \(0.949676\pi\)
\(444\) 3.73591 2.70486i 0.177298 0.128367i
\(445\) −10.8535 + 1.76402i −0.514507 + 0.0836224i
\(446\) −10.9441 18.9557i −0.518216 0.897576i
\(447\) −3.87298 1.73205i −0.183186 0.0819232i
\(448\) 1.41421 + 2.23607i 0.0668153 + 0.105644i
\(449\) 25.8773i 1.22122i 0.791930 + 0.610612i \(0.209077\pi\)
−0.791930 + 0.610612i \(0.790923\pi\)
\(450\) 13.0260 + 7.43794i 0.614052 + 0.350628i
\(451\) 4.23861 + 2.44716i 0.199588 + 0.115232i
\(452\) 8.73861 15.1357i 0.411030 0.711924i
\(453\) −3.44572 + 0.356394i −0.161894 + 0.0167448i
\(454\) 10.3923i 0.487735i
\(455\) −6.05469 + 1.23658i −0.283848 + 0.0579717i
\(456\) −2.26139 1.01132i −0.105899 0.0473595i
\(457\) 9.59425 5.53924i 0.448800 0.259115i −0.258523 0.966005i \(-0.583236\pi\)
0.707323 + 0.706890i \(0.249902\pi\)
\(458\) −11.7386 6.77729i −0.548509 0.316682i
\(459\) −16.0554 3.49611i −0.749404 0.163184i
\(460\) 3.54996 9.36085i 0.165518 0.436452i
\(461\) −31.7876 −1.48050 −0.740248 0.672334i \(-0.765292\pi\)
−0.740248 + 0.672334i \(0.765292\pi\)
\(462\) 19.9387 + 7.96817i 0.927632 + 0.370713i
\(463\) 22.5741i 1.04911i −0.851377 0.524554i \(-0.824232\pi\)
0.851377 0.524554i \(-0.175768\pi\)
\(464\) −5.99430 + 3.46081i −0.278279 + 0.160664i
\(465\) −24.8052 6.58314i −1.15031 0.305286i
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 24.2614 14.0073i 1.12268 0.648181i 0.180599 0.983557i \(-0.442197\pi\)
0.942085 + 0.335375i \(0.108863\pi\)
\(468\) −2.08911 2.33570i −0.0965693 0.107968i
\(469\) 1.52277 + 37.7244i 0.0703152 + 1.74195i
\(470\) −19.4317 + 15.8659i −0.896316 + 0.731839i
\(471\) −24.8908 + 2.57448i −1.14691 + 0.118626i
\(472\) −5.28720 + 9.15769i −0.243363 + 0.421517i
\(473\) −16.2158 + 28.0867i −0.745605 + 1.29143i
\(474\) −19.7737 + 2.04521i −0.908234 + 0.0939395i
\(475\) 7.00665 + 1.43023i 0.321487 + 0.0656233i
\(476\) 7.40852 + 3.88766i 0.339569 + 0.178190i
\(477\) 10.0000 + 11.1803i 0.457869 + 0.511913i
\(478\) 0 0
\(479\) 21.1810 36.6866i 0.967784 1.67625i 0.265844 0.964016i \(-0.414349\pi\)
0.701940 0.712236i \(-0.252317\pi\)
\(480\) 0.993475 3.74340i 0.0453457 0.170862i
\(481\) 2.40890 1.39078i 0.109836 0.0634141i
\(482\) 21.3094i 0.970615i
\(483\) 20.3066 2.93227i 0.923983 0.133423i
\(484\) −10.9545 −0.497930
\(485\) 9.50569 25.0654i 0.431631 1.13816i
\(486\) −13.5640 + 7.68223i −0.615278 + 0.348473i
\(487\) −14.7526 8.51743i −0.668505 0.385962i 0.127005 0.991902i \(-0.459464\pi\)
−0.795510 + 0.605941i \(0.792797\pi\)
\(488\) −3.00000 + 1.73205i −0.135804 + 0.0784063i
\(489\) −23.2379 10.3923i −1.05085 0.469956i
\(490\) 4.35258 15.0351i 0.196629 0.679218i
\(491\) 13.8433i 0.624737i −0.949961 0.312369i \(-0.898878\pi\)
0.949961 0.312369i \(-0.101122\pi\)
\(492\) 1.79962 0.186137i 0.0811333 0.00839169i
\(493\) −10.9441 + 18.9557i −0.492895 + 0.853720i
\(494\) −1.29380 0.746976i −0.0582108 0.0336080i
\(495\) −11.2855 29.3358i −0.507247 1.31854i
\(496\) 6.62638i 0.297533i
\(497\) −15.4772 + 9.78866i −0.694248 + 0.439081i
\(498\) 6.43168 + 2.87633i 0.288210 + 0.128892i
\(499\) −0.954451 1.65316i −0.0427271 0.0740055i 0.843871 0.536546i \(-0.180271\pi\)
−0.886598 + 0.462541i \(0.846938\pi\)
\(500\) −0.449747 + 11.1713i −0.0201133 + 0.499595i
\(501\) 6.01958 4.35827i 0.268935 0.194713i
\(502\) 4.42747 + 7.66860i 0.197608 + 0.342266i
\(503\) 15.5096i 0.691537i −0.938320 0.345769i \(-0.887618\pi\)
0.938320 0.345769i \(-0.112382\pi\)
\(504\) 7.69738 1.93657i 0.342869 0.0862617i
\(505\) −16.0000 19.5959i −0.711991 0.872007i
\(506\) −18.1677 + 10.4891i −0.807655 + 0.466300i
\(507\) 12.0965 + 16.7075i 0.537225 + 0.742006i
\(508\) 7.56114 + 4.36543i 0.335471 + 0.193684i
\(509\) 12.3583 + 21.4051i 0.547770 + 0.948766i 0.998427 + 0.0560688i \(0.0178566\pi\)
−0.450656 + 0.892697i \(0.648810\pi\)
\(510\) −3.19808 11.8225i −0.141614 0.523511i
\(511\) 9.26139 0.373843i 0.409700 0.0165378i
\(512\) −1.00000 −0.0441942
\(513\) −5.00013 + 5.49805i −0.220761 + 0.242745i
\(514\) 9.52277 + 5.49798i 0.420032 + 0.242505i
\(515\) 10.8535 1.76402i 0.478264 0.0777319i
\(516\) 1.23341 + 11.9250i 0.0542980 + 0.524968i
\(517\) 52.5667 2.31188
\(518\) 0.284162 + 7.03967i 0.0124853 + 0.309305i
\(519\) 1.78416 + 0.797901i 0.0783160 + 0.0350240i
\(520\) 0.828222 2.18393i 0.0363199 0.0957715i
\(521\) 17.7981 30.8272i 0.779748 1.35056i −0.152339 0.988328i \(-0.548680\pi\)
0.932087 0.362235i \(-0.117986\pi\)
\(522\) 4.24999 + 20.3253i 0.186017 + 0.889614i
\(523\) −8.45307 14.6412i −0.369627 0.640213i 0.619880 0.784697i \(-0.287181\pi\)
−0.989507 + 0.144484i \(0.953848\pi\)
\(524\) −13.7725 −0.601654
\(525\) −20.4734 + 10.2879i −0.893530 + 0.449003i
\(526\) −2.00000 −0.0872041
\(527\) 10.4772 + 18.1471i 0.456395 + 0.790500i
\(528\) −6.57357 + 4.75937i −0.286078 + 0.207125i
\(529\) 1.47723 2.55863i 0.0642272 0.111245i
\(530\) −3.96447 + 10.4539i −0.172205 + 0.454086i
\(531\) 21.1488 + 23.6451i 0.917779 + 1.02611i
\(532\) 3.19808 2.02265i 0.138655 0.0876928i
\(533\) 1.09110 0.0472607
\(534\) 8.47223 0.876291i 0.366629 0.0379208i
\(535\) 12.0888 1.96479i 0.522645 0.0849452i
\(536\) −12.3583 7.13505i −0.533796 0.308187i
\(537\) 3.45390 + 33.3933i 0.149047 + 1.44103i
\(538\) −17.5810 −0.757973
\(539\) −26.9905 + 18.6355i −1.16256 + 0.802689i
\(540\) −9.73861 6.33715i −0.419083 0.272707i
\(541\) −4.26139 7.38094i −0.183211 0.317331i 0.759761 0.650202i \(-0.225316\pi\)
−0.942972 + 0.332871i \(0.891983\pi\)
\(542\) −5.47723 3.16228i −0.235267 0.135831i
\(543\) 4.43649 3.21209i 0.190388 0.137844i
\(544\) −2.73861 + 1.58114i −0.117417 + 0.0677908i
\(545\) 28.8948 + 35.3887i 1.23772 + 1.51589i
\(546\) 4.73762 0.684110i 0.202751 0.0292772i
\(547\) 3.61845i 0.154714i 0.997003 + 0.0773569i \(0.0246481\pi\)
−0.997003 + 0.0773569i \(0.975352\pi\)
\(548\) −1.73861 3.01137i −0.0742699 0.128639i
\(549\) 2.12702 + 10.1723i 0.0907789 + 0.434143i
\(550\) 15.5350 17.5364i 0.662416 0.747753i
\(551\) 4.94975 + 8.57321i 0.210866 + 0.365231i
\(552\) −3.16588 + 7.07912i −0.134749 + 0.301307i
\(553\) 14.1099 26.8886i 0.600015 1.14342i
\(554\) 9.79796i 0.416275i
\(555\) 7.27527 7.31006i 0.308818 0.310295i
\(556\) −17.4772 10.0905i −0.741199 0.427932i
\(557\) 13.9317 24.1304i 0.590304 1.02244i −0.403887 0.914809i \(-0.632341\pi\)
0.994191 0.107628i \(-0.0343255\pi\)
\(558\) 18.8857 + 6.20555i 0.799497 + 0.262702i
\(559\) 7.23003i 0.305798i
\(560\) 3.92344 + 4.42793i 0.165796 + 0.187114i
\(561\) −10.4772 + 23.4278i −0.442349 + 0.989122i
\(562\) −1.56683 + 0.904612i −0.0660929 + 0.0381588i
\(563\) −9.00000 5.19615i −0.379305 0.218992i 0.298211 0.954500i \(-0.403610\pi\)
−0.677516 + 0.735508i \(0.736943\pi\)
\(564\) 15.7394 11.3956i 0.662750 0.479842i
\(565\) 13.8576 36.5409i 0.582993 1.53729i
\(566\) 9.22460 0.387739
\(567\) 1.68915 23.7518i 0.0709375 0.997481i
\(568\) 6.92163i 0.290425i
\(569\) 6.54879 3.78095i 0.274540 0.158505i −0.356409 0.934330i \(-0.615999\pi\)
0.630949 + 0.775824i \(0.282666\pi\)
\(570\) −5.35390 1.42089i −0.224250 0.0595147i
\(571\) −7.47723 + 12.9509i −0.312912 + 0.541980i −0.978991 0.203901i \(-0.934638\pi\)
0.666079 + 0.745881i \(0.267971\pi\)
\(572\) −4.23861 + 2.44716i −0.177225 + 0.102321i
\(573\) −25.7611 11.5207i −1.07618 0.481284i
\(574\) −1.28416 + 2.44716i −0.0535999 + 0.102143i
\(575\) 4.47723 21.9338i 0.186713 0.914704i
\(576\) −0.936492 + 2.85008i −0.0390205 + 0.118754i
\(577\) −0.337449 + 0.584480i −0.0140482 + 0.0243322i −0.872964 0.487785i \(-0.837805\pi\)
0.858916 + 0.512117i \(0.171138\pi\)
\(578\) 3.50000 6.06218i 0.145581 0.252153i
\(579\) −1.30948 12.6604i −0.0544199 0.526148i
\(580\) −11.9886 + 9.78866i −0.497800 + 0.406452i
\(581\) −9.09576 + 5.75267i −0.377356 + 0.238661i
\(582\) −8.47723 + 18.9557i −0.351392 + 0.785737i
\(583\) 20.2891 11.7139i 0.840287 0.485140i
\(584\) −1.75166 + 3.03397i −0.0724843 + 0.125547i
\(585\) −5.44875 4.40573i −0.225278 0.182155i
\(586\) 6.97723 4.02830i 0.288227 0.166408i
\(587\) 21.0864i 0.870330i 0.900351 + 0.435165i \(0.143310\pi\)
−0.900351 + 0.435165i \(0.856690\pi\)
\(588\) −4.04156 + 11.4309i −0.166671 + 0.471403i
\(589\) 9.47723 0.390502
\(590\) −8.38437 + 22.1086i −0.345179 + 0.910198i
\(591\) 9.14178 + 12.6265i 0.376042 + 0.519384i
\(592\) −2.30615 1.33146i −0.0947821 0.0547225i
\(593\) 1.43168 0.826579i 0.0587919 0.0339435i −0.470316 0.882498i \(-0.655860\pi\)
0.529108 + 0.848555i \(0.322527\pi\)
\(594\) 7.40852 + 23.1923i 0.303975 + 0.951593i
\(595\) 17.7460 + 5.92289i 0.727514 + 0.242815i
\(596\) 2.44949i 0.100335i
\(597\) −2.76376 26.7208i −0.113113 1.09361i
\(598\) −2.33836 + 4.05015i −0.0956225 + 0.165623i
\(599\) 20.4739 + 11.8206i 0.836540 + 0.482977i 0.856087 0.516832i \(-0.172889\pi\)
−0.0195464 + 0.999809i \(0.506222\pi\)
\(600\) 0.849876 8.61845i 0.0346961 0.351847i
\(601\) 4.06775i 0.165927i −0.996553 0.0829635i \(-0.973562\pi\)
0.996553 0.0829635i \(-0.0264385\pi\)
\(602\) −16.2158 8.50934i −0.660908 0.346815i
\(603\) −31.9089 + 28.5402i −1.29943 + 1.16225i
\(604\) 1.00000 + 1.73205i 0.0406894 + 0.0704761i
\(605\) −24.1776 + 3.92957i −0.982961 + 0.159760i
\(606\) 11.4919 + 15.8725i 0.466828 + 0.644775i
\(607\) 6.14692 + 10.6468i 0.249496 + 0.432140i 0.963386 0.268118i \(-0.0864017\pi\)
−0.713890 + 0.700258i \(0.753068\pi\)
\(608\) 1.43023i 0.0580034i
\(609\) −29.4540 11.7708i −1.19353 0.476976i
\(610\) −6.00000 + 4.89898i −0.242933 + 0.198354i
\(611\) 10.1487 5.85938i 0.410574 0.237045i
\(612\) 1.94169 + 9.28600i 0.0784882 + 0.375364i
\(613\) 5.07016 + 2.92726i 0.204782 + 0.118231i 0.598884 0.800836i \(-0.295611\pi\)
−0.394102 + 0.919067i \(0.628944\pi\)
\(614\) 5.99430 + 10.3824i 0.241910 + 0.419001i
\(615\) 3.90519 1.05638i 0.157473 0.0425975i
\(616\) −0.500000 12.3867i −0.0201456 0.499076i
\(617\) −14.5228 −0.584665 −0.292332 0.956317i \(-0.594431\pi\)
−0.292332 + 0.956317i \(0.594431\pi\)
\(618\) −8.47223 + 0.876291i −0.340803 + 0.0352496i
\(619\) 26.1475 + 15.0963i 1.05096 + 0.606771i 0.922917 0.384998i \(-0.125798\pi\)
0.128040 + 0.991769i \(0.459131\pi\)
\(620\) 2.37701 + 14.6251i 0.0954631 + 0.587359i
\(621\) 17.2113 + 15.6525i 0.690664 + 0.628115i
\(622\) −17.5810 −0.704936
\(623\) −6.04555 + 11.5207i −0.242210 + 0.461567i
\(624\) −0.738613 + 1.65159i −0.0295682 + 0.0661165i
\(625\) 3.01472 + 24.8176i 0.120589 + 0.992703i
\(626\) −11.6190 + 20.1246i −0.464387 + 0.804341i
\(627\) 6.80698 + 9.40169i 0.271845 + 0.375467i
\(628\) 7.22369 + 12.5118i 0.288257 + 0.499275i
\(629\) −8.42087 −0.335762
\(630\) 16.2943 7.03542i 0.649179 0.280298i
\(631\) 3.47723 0.138426 0.0692131 0.997602i \(-0.477951\pi\)
0.0692131 + 0.997602i \(0.477951\pi\)
\(632\) 5.73861 + 9.93957i 0.228270 + 0.395375i
\(633\) −24.8628 34.3401i −0.988208 1.36490i
\(634\) 4.95445 8.58136i 0.196766 0.340809i
\(635\) 18.2542 + 6.92263i 0.724396 + 0.274716i
\(636\) 3.53553 7.90569i 0.140193 0.313481i
\(637\) −3.13367 + 6.60635i −0.124160 + 0.261753i
\(638\) 32.4317 1.28398
\(639\) −19.7272 6.48204i −0.780397 0.256426i
\(640\) −2.20711 + 0.358719i −0.0872436 + 0.0141796i
\(641\) −13.9251 8.03966i −0.550008 0.317547i 0.199117 0.979976i \(-0.436193\pi\)
−0.749125 + 0.662428i \(0.769526\pi\)
\(642\) −9.43649 + 0.976025i −0.372429 + 0.0385206i
\(643\) −26.0663 −1.02796 −0.513978 0.857803i \(-0.671829\pi\)
−0.513978 + 0.857803i \(0.671829\pi\)
\(644\) −6.33175 10.0114i −0.249506 0.394504i
\(645\) 7.00000 + 25.8773i 0.275625 + 1.01892i
\(646\) 2.26139 + 3.91684i 0.0889731 + 0.154106i
\(647\) −17.6703 10.2019i −0.694691 0.401080i 0.110676 0.993857i \(-0.464698\pi\)
−0.805367 + 0.592777i \(0.798032\pi\)
\(648\) 7.24597 + 5.33816i 0.284648 + 0.209703i
\(649\) 42.9089 24.7735i 1.68432 0.972444i
\(650\) 1.04456 5.11726i 0.0409709 0.200715i
\(651\) −23.8578 + 18.7855i −0.935060 + 0.736261i
\(652\) 14.6969i 0.575577i
\(653\) 19.9317 + 34.5227i 0.779987 + 1.35098i 0.931949 + 0.362590i \(0.118108\pi\)
−0.151962 + 0.988386i \(0.548559\pi\)
\(654\) −20.7535 28.6645i −0.811528 1.12087i
\(655\) −30.3973 + 4.94046i −1.18772 + 0.193040i
\(656\) −0.522278 0.904612i −0.0203915 0.0353192i
\(657\) 7.00665 + 7.83368i 0.273356 + 0.305621i
\(658\) 1.19718 + 29.6582i 0.0466708 + 1.15620i
\(659\) 34.2929i 1.33586i 0.744224 + 0.667930i \(0.232819\pi\)
−0.744224 + 0.667930i \(0.767181\pi\)
\(660\) −12.8013 + 12.8625i −0.498289 + 0.500672i
\(661\) 0.522774 + 0.301824i 0.0203336 + 0.0117396i 0.510132 0.860096i \(-0.329596\pi\)
−0.489799 + 0.871836i \(0.662930\pi\)
\(662\) 10.7158 18.5604i 0.416483 0.721370i
\(663\) 0.588616 + 5.69091i 0.0228600 + 0.221017i
\(664\) 4.06775i 0.157859i
\(665\) 6.33295 5.61141i 0.245581 0.217601i
\(666\) −5.95445 + 5.32582i −0.230730 + 0.206371i
\(667\) 26.8378 15.4948i 1.03917 0.599963i
\(668\) −3.71584 2.14534i −0.143770 0.0830057i
\(669\) 22.2329 + 30.7077i 0.859574 + 1.18723i
\(670\) −29.8355 11.3147i −1.15265 0.437124i
\(671\) 16.2312 0.626600
\(672\) −2.83495 3.60042i −0.109361 0.138889i
\(673\) 14.1585i 0.545771i −0.962047 0.272885i \(-0.912022\pi\)
0.962047 0.272885i \(-0.0879780\pi\)
\(674\) −14.8492 + 8.57321i −0.571971 + 0.330228i
\(675\) −23.7674 10.4933i −0.914808 0.403888i
\(676\) 5.95445 10.3134i 0.229017 0.396670i
\(677\) 28.5000 16.4545i 1.09534 0.632397i 0.160350 0.987060i \(-0.448738\pi\)
0.934994 + 0.354663i \(0.115404\pi\)
\(678\) −12.3583 + 27.6339i −0.474616 + 1.06127i
\(679\) −16.9545 26.8073i −0.650652 1.02877i
\(680\) −5.47723 + 4.47214i −0.210042 + 0.171499i
\(681\) 1.85188 + 17.9045i 0.0709641 + 0.686101i
\(682\) 15.5241 26.8886i 0.594450 1.02962i
\(683\) −9.47723 + 16.4150i −0.362636 + 0.628104i −0.988394 0.151913i \(-0.951456\pi\)
0.625758 + 0.780017i \(0.284790\pi\)
\(684\) 4.07627 + 1.33940i 0.155860 + 0.0512131i
\(685\) −4.91754 6.02273i −0.187890 0.230117i
\(686\) −11.1289 14.8036i −0.424903 0.565206i
\(687\) 21.4317 + 9.58454i 0.817669 + 0.365673i
\(688\) 5.99430 3.46081i 0.228531 0.131942i
\(689\) 2.61139 4.52306i 0.0994861 0.172315i
\(690\) −4.44801 + 16.7600i −0.169333 + 0.638043i
\(691\) 3.00000 1.73205i 0.114125 0.0658903i −0.441851 0.897089i \(-0.645678\pi\)
0.555976 + 0.831198i \(0.312345\pi\)
\(692\) 1.12840i 0.0428954i
\(693\) −35.7715 10.1750i −1.35885 0.386517i
\(694\) −17.4772 −0.663426
\(695\) −42.1938 16.0013i −1.60050 0.606966i
\(696\) 9.71064 7.03066i 0.368081 0.266497i
\(697\) −2.86064 1.65159i −0.108354 0.0625584i
\(698\) 10.1703 5.87182i 0.384951 0.222252i
\(699\) −2.82843 + 6.32456i −0.106981 + 0.239217i
\(700\) 10.2478 + 8.36551i 0.387332 + 0.316187i
\(701\) 51.7546i 1.95474i −0.211531 0.977371i \(-0.567845\pi\)
0.211531 0.977371i \(-0.432155\pi\)
\(702\) 4.01546 + 3.65181i 0.151554 + 0.137829i
\(703\) −1.90428 + 3.29832i −0.0718214 + 0.124398i
\(704\) 4.05781 + 2.34278i 0.152935 + 0.0882968i
\(705\) 30.6508 30.7974i 1.15438 1.15990i
\(706\) 0.603648i 0.0227186i
\(707\) −29.9089 + 1.20730i −1.12484 + 0.0454050i
\(708\) 7.47723 16.7196i 0.281011 0.628360i
\(709\) 11.2158 + 19.4264i 0.421220 + 0.729574i 0.996059 0.0886924i \(-0.0282688\pi\)
−0.574839 + 0.818266i \(0.694935\pi\)
\(710\) −2.48292 15.2768i −0.0931824 0.573327i
\(711\) 33.7028 7.04721i 1.26395 0.264291i
\(712\) −2.45877 4.25871i −0.0921463 0.159602i
\(713\) 29.6678i 1.11107i
\(714\) −13.4566 5.37771i −0.503601 0.201256i
\(715\) −8.47723 + 6.92163i −0.317030 + 0.258854i
\(716\) 16.7857 9.69125i 0.627312 0.362179i
\(717\) 0 0
\(718\) −9.86729 5.69688i −0.368244 0.212606i
\(719\) −0.401865 0.696051i −0.0149870 0.0259583i 0.858435 0.512923i \(-0.171437\pi\)
−0.873422 + 0.486965i \(0.838104\pi\)
\(720\) −1.04456 + 6.62638i −0.0389283 + 0.246951i
\(721\) 6.04555 11.5207i 0.225148 0.429054i
\(722\) −16.9545 −0.630979
\(723\) 3.79726 + 36.7130i 0.141222 + 1.36537i
\(724\) −2.73861 1.58114i −0.101780 0.0587626i
\(725\) −22.9488 + 25.9052i −0.852295 + 0.962093i
\(726\) 18.8730 1.95205i 0.700442 0.0724474i
\(727\) −15.1223 −0.560854 −0.280427 0.959875i \(-0.590476\pi\)
−0.280427 + 0.959875i \(0.590476\pi\)
\(728\) −1.47723 2.33570i −0.0547496 0.0865668i
\(729\) 22.0000 15.6525i 0.814815 0.579721i
\(730\) −2.77776 + 7.32465i −0.102810 + 0.271097i
\(731\) 10.9441 18.9557i 0.404780 0.701100i
\(732\) 4.85993 3.51867i 0.179628 0.130054i
\(733\) 1.19718 + 2.07357i 0.0442187 + 0.0765891i 0.887288 0.461216i \(-0.152587\pi\)
−0.843069 + 0.537805i \(0.819253\pi\)
\(734\) 0.369657 0.0136443
\(735\) −4.81967 + 26.6790i −0.177776 + 0.984071i
\(736\) 4.47723 0.165033
\(737\) 33.4317 + 57.9054i 1.23147 + 2.13297i
\(738\) −3.06733 + 0.641375i −0.112910 + 0.0236093i
\(739\) −3.23861 + 5.60944i −0.119134 + 0.206347i −0.919425 0.393266i \(-0.871345\pi\)
0.800291 + 0.599612i \(0.204679\pi\)
\(740\) −5.56754 2.11140i −0.204667 0.0776168i
\(741\) 2.36215 + 1.05638i 0.0867756 + 0.0388072i
\(742\) 7.07107 + 11.1803i 0.259587 + 0.410443i
\(743\) −13.4317 −0.492760 −0.246380 0.969173i \(-0.579241\pi\)
−0.246380 + 0.969173i \(0.579241\pi\)
\(744\) −1.18080 11.4163i −0.0432903 0.418543i
\(745\) 0.878680 + 5.40629i 0.0321923 + 0.198071i
\(746\) −20.1042 11.6072i −0.736068 0.424969i
\(747\) −11.5934 3.80941i −0.424181 0.139379i
\(748\) 14.8170 0.541764
\(749\) 6.73362 12.8319i 0.246041 0.468868i
\(750\) −1.21584 19.3267i −0.0443961 0.705712i
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −9.71584 5.60944i −0.354300 0.204555i
\(753\) −8.99443 12.4230i −0.327775 0.452718i
\(754\) 6.26139 3.61501i 0.228026 0.131651i
\(755\) 2.82843 + 3.46410i 0.102937 + 0.126072i
\(756\) −12.9164 + 4.70809i −0.469766 + 0.171232i
\(757\) 48.1361i 1.74954i −0.484541 0.874768i \(-0.661014\pi\)
0.484541 0.874768i \(-0.338986\pi\)
\(758\) −10.2386 17.7338i −0.371883 0.644121i
\(759\) 29.4313 21.3088i 1.06829 0.773459i
\(760\) 0.513050 + 3.15666i 0.0186103 + 0.114504i
\(761\) 0.891935 + 1.54488i 0.0323326 + 0.0560018i 0.881739 0.471738i \(-0.156373\pi\)
−0.849406 + 0.527739i \(0.823040\pi\)
\(762\) −13.8047 6.17364i −0.500091 0.223648i
\(763\) 54.0131 2.18028i 1.95541 0.0789315i
\(764\) 16.2927i 0.589451i
\(765\) 7.61659 + 19.7987i 0.275378 + 0.715823i
\(766\) −15.7158 9.07354i −0.567836 0.327840i
\(767\) 5.52277 9.56573i 0.199416 0.345398i
\(768\) 1.72286 0.178197i 0.0621683 0.00643013i
\(769\) 16.1921i 0.583902i −0.956433 0.291951i \(-0.905696\pi\)
0.956433 0.291951i \(-0.0943045\pi\)
\(770\) −5.54692 27.1595i −0.199897 0.978760i
\(771\) −17.3861 7.77531i −0.626146 0.280021i
\(772\) −6.36396 + 3.67423i −0.229044 + 0.132239i
\(773\) 14.0228 + 8.09605i 0.504364 + 0.291195i 0.730514 0.682898i \(-0.239281\pi\)
−0.226150 + 0.974093i \(0.572614\pi\)
\(774\) −4.24999 20.3253i −0.152763 0.730578i
\(775\) 10.4926 + 31.4265i 0.376907 + 1.12887i
\(776\) 11.9886 0.430366
\(777\) −1.74402 12.0777i −0.0625663 0.433286i
\(778\) 7.34847i 0.263455i
\(779\) −1.29380 + 0.746976i −0.0463552 + 0.0267632i
\(780\) −1.03774 + 3.91019i −0.0371571 + 0.140007i
\(781\) −16.2158 + 28.0867i −0.580248 + 1.00502i
\(782\) 12.2614 7.07912i 0.438466 0.253149i
\(783\) −10.9441 34.2603i −0.391108 1.22436i
\(784\) 6.97723 0.564201i 0.249187 0.0201501i
\(785\) 20.4317 + 25.0236i 0.729238 + 0.893130i
\(786\) 23.7280 2.45421i 0.846351 0.0875389i
\(787\) −25.0862 + 43.4506i −0.894226 + 1.54884i −0.0594664 + 0.998230i \(0.518940\pi\)
−0.834760 + 0.550615i \(0.814393\pi\)
\(788\) 4.50000 7.79423i 0.160306 0.277658i
\(789\) 3.44572 0.356394i 0.122671 0.0126880i
\(790\) 16.2312 + 19.8791i 0.577482 + 0.707268i
\(791\) −24.7165 39.0803i −0.878819 1.38953i
\(792\) 10.4772 9.37112i 0.372292 0.332988i
\(793\) 3.13367 1.80922i 0.111280 0.0642474i
\(794\) −7.44073 + 12.8877i −0.264061 + 0.457368i
\(795\) 4.96737 18.7170i 0.176175 0.663823i
\(796\) −13.4317 + 7.75478i −0.476073 + 0.274861i
\(797\) 54.2183i 1.92051i −0.279121 0.960256i \(-0.590043\pi\)
0.279121 0.960256i \(-0.409957\pi\)
\(798\) −5.14942 + 4.05462i −0.182288 + 0.143532i
\(799\) −35.4772 −1.25509
\(800\) −4.74264 + 1.58346i −0.167678 + 0.0559839i
\(801\) −14.4403 + 3.01945i −0.510223 + 0.106687i
\(802\) 0.827520 + 0.477769i 0.0292207 + 0.0168706i
\(803\) 14.2158 8.20752i 0.501666 0.289637i
\(804\) 22.5630 + 10.0905i 0.795736 + 0.355864i
\(805\) −17.5661 19.8249i −0.619125 0.698735i
\(806\) 6.92163i 0.243804i
\(807\) 30.2897 3.13289i 1.06625 0.110283i
\(808\) 5.65685 9.79796i 0.199007 0.344691i
\(809\) −7.65776 4.42121i −0.269233 0.155441i 0.359306 0.933220i \(-0.383013\pi\)
−0.628539 + 0.777778i \(0.716347\pi\)
\(810\) 17.9075 + 9.18262i 0.629206 + 0.322644i
\(811\) 38.3280i 1.34588i −0.739697 0.672940i \(-0.765031\pi\)
0.739697 0.672940i \(-0.234969\pi\)
\(812\) 0.738613 + 18.2980i 0.0259202 + 0.642134i
\(813\) 10.0000 + 4.47214i 0.350715 + 0.156845i
\(814\) 6.23861 + 10.8056i 0.218663 + 0.378736i
\(815\) 5.27208 + 32.4377i 0.184673 + 1.13624i
\(816\) 4.43649 3.21209i 0.155308 0.112446i
\(817\) −4.94975 8.57321i −0.173170 0.299939i
\(818\) 15.5096i 0.542279i
\(819\) −8.04035 + 2.02286i −0.280953 + 0.0706843i
\(820\) −1.47723 1.80922i −0.0515870 0.0631809i
\(821\) −10.1403 + 5.85452i −0.353900 + 0.204324i −0.666401 0.745593i \(-0.732166\pi\)
0.312502 + 0.949917i \(0.398833\pi\)
\(822\) 3.53200 + 4.87835i 0.123193 + 0.170152i
\(823\) −2.76401 1.59580i −0.0963474 0.0556262i 0.451052 0.892498i \(-0.351049\pi\)
−0.547400 + 0.836871i \(0.684382\pi\)
\(824\) 2.45877 + 4.25871i 0.0856553 + 0.148359i
\(825\) −23.6398 + 32.9810i −0.823031 + 1.14825i
\(826\) 14.9545 + 23.6451i 0.520332 + 0.822717i
\(827\) 3.90890 0.135926 0.0679629 0.997688i \(-0.478350\pi\)
0.0679629 + 0.997688i \(0.478350\pi\)
\(828\) 4.19288 12.7605i 0.145713 0.443457i
\(829\) −43.6931 25.2262i −1.51752 0.876142i −0.999788 0.0206012i \(-0.993442\pi\)
−0.517735 0.855541i \(-0.673225\pi\)
\(830\) −1.45918 8.97796i −0.0506489 0.311629i
\(831\) 1.74597 + 16.8805i 0.0605669 + 0.585578i
\(832\) 1.04456 0.0362135
\(833\) 18.2158 12.5771i 0.631141 0.435770i
\(834\) 31.9089 + 14.2701i 1.10491 + 0.494133i
\(835\) −8.97083 3.40205i −0.310448 0.117733i
\(836\) 3.35071 5.80359i 0.115887 0.200721i
\(837\) −33.6433 7.32591i −1.16288 0.253220i
\(838\) −4.42747 7.66860i −0.152944 0.264907i
\(839\) 40.1440 1.38593 0.692963 0.720973i \(-0.256305\pi\)
0.692963 + 0.720973i \(0.256305\pi\)
\(840\) −7.54858 6.92957i −0.260451 0.239093i
\(841\) −18.9089 −0.652031
\(842\) 9.47723 + 16.4150i 0.326607 + 0.565700i
\(843\) 2.53824 1.83773i 0.0874215 0.0632946i
\(844\) −12.2386 + 21.1979i −0.421270 + 0.729662i
\(845\) 9.44249 24.8988i 0.324831 0.856544i
\(846\) −25.0862 + 22.4378i −0.862481 + 0.771426i
\(847\) −13.4672 + 25.6639i −0.462740 + 0.881821i
\(848\) −5.00000 −0.171701
\(849\) −15.8927 + 1.64380i −0.545436 + 0.0564149i
\(850\) −10.4846 + 11.8353i −0.359618 + 0.405946i
\(851\) 10.3251 + 5.96123i 0.353942 + 0.204348i
\(852\) 1.23341 + 11.9250i 0.0422560 + 0.408543i
\(853\) 31.2891 1.07132 0.535659 0.844434i \(-0.320063\pi\)
0.535659 + 0.844434i \(0.320063\pi\)
\(854\) 0.369657 + 9.15769i 0.0126494 + 0.313370i
\(855\) 9.47723 + 1.49395i 0.324114 + 0.0510921i
\(856\) 2.73861 + 4.74342i 0.0936039 + 0.162127i
\(857\) −13.0455 7.53185i −0.445627 0.257283i 0.260354 0.965513i \(-0.416161\pi\)
−0.705982 + 0.708230i \(0.749494\pi\)
\(858\) 6.86646 4.97143i 0.234417 0.169722i
\(859\) −26.4772 + 15.2866i −0.903391 + 0.521573i −0.878299 0.478112i \(-0.841321\pi\)
−0.0250924 + 0.999685i \(0.507988\pi\)
\(860\) 11.9886 9.78866i 0.408808 0.333790i
\(861\) 1.77635 4.44495i 0.0605380 0.151484i
\(862\) 7.66374i 0.261028i
\(863\) −13.2386 22.9299i −0.450648 0.780545i 0.547779 0.836623i \(-0.315474\pi\)
−0.998426 + 0.0560787i \(0.982140\pi\)
\(864\) 1.10557 5.07718i 0.0376122 0.172729i
\(865\) −0.404780 2.49051i −0.0137629 0.0846797i
\(866\) 0 0
\(867\) −4.94975 + 11.0680i −0.168102 + 0.375888i
\(868\) 15.5241 + 8.14637i 0.526924 + 0.276506i
\(869\) 53.7772i 1.82427i
\(870\) 18.9104 19.0008i 0.641122 0.644188i
\(871\) 12.9089 + 7.45296i 0.437401 + 0.252534i
\(872\) −10.2158 + 17.6944i −0.345952 + 0.599206i
\(873\) 11.2272 34.1685i 0.379984 1.15643i
\(874\) 6.40345i 0.216600i
\(875\) 25.6190 + 14.7875i 0.866079 + 0.499908i
\(876\) 2.47723 5.53924i 0.0836977 0.187154i
\(877\) −48.2359 + 27.8490i −1.62881 + 0.940394i −0.644361 + 0.764721i \(0.722877\pi\)
−0.984449 + 0.175673i \(0.943790\pi\)
\(878\) −7.69306 4.44159i −0.259628 0.149896i
\(879\) −11.3029 + 8.18352i −0.381239 + 0.276023i
\(880\) 9.79642 + 3.71515i 0.330237 + 0.125238i
\(881\) 18.7544 0.631853 0.315926 0.948784i \(-0.397685\pi\)
0.315926 + 0.948784i \(0.397685\pi\)
\(882\) 4.92609 20.4141i 0.165870 0.687377i
\(883\) 24.3833i 0.820564i 0.911959 + 0.410282i \(0.134570\pi\)
−0.911959 + 0.410282i \(0.865430\pi\)
\(884\) 2.86064 1.65159i 0.0962136 0.0555489i
\(885\) 10.5054 39.5841i 0.353135 1.33061i
\(886\) 7.52277 13.0298i 0.252733 0.437746i
\(887\) −3.00000 + 1.73205i −0.100730 + 0.0581566i −0.549519 0.835481i \(-0.685189\pi\)
0.448789 + 0.893638i \(0.351856\pi\)
\(888\) 4.21043 + 1.88296i 0.141293 + 0.0631881i
\(889\) 19.5228 12.3473i 0.654773 0.414115i
\(890\) −6.95445 8.51743i −0.233114 0.285505i
\(891\) −16.8966 38.6370i −0.566059 1.29439i
\(892\) 10.9441 18.9557i 0.366434 0.634682i
\(893\) −8.02277 + 13.8959i −0.268472 + 0.465007i
\(894\) −0.436492 4.22013i −0.0145985 0.141142i
\(895\) 33.5715 27.4110i 1.12217 0.916248i
\(896\) −1.22938 + 2.34278i −0.0410709 + 0.0782667i
\(897\) 3.30694 7.39453i 0.110415 0.246896i
\(898\) −22.4104 + 12.9386i −0.747844 + 0.431768i
\(899\) −22.9327 + 39.7205i −0.764847 + 1.32475i
\(900\) 0.0715641 + 14.9998i 0.00238547 + 0.499994i
\(901\) −13.6931 + 7.90569i −0.456182 + 0.263377i
\(902\) 4.89433i 0.162963i
\(903\) 29.4540 + 11.7708i 0.980166 + 0.391707i
\(904\) 17.4772 0.581284
\(905\) −6.61160 2.50735i −0.219777 0.0833471i
\(906\) −2.03151 2.80588i −0.0674923 0.0932192i
\(907\) −8.48528 4.89898i −0.281749 0.162668i 0.352466 0.935825i \(-0.385343\pi\)
−0.634215 + 0.773157i \(0.718677\pi\)
\(908\) 9.00000 5.19615i 0.298675 0.172440i
\(909\) −22.6274 25.2982i −0.750504 0.839089i
\(910\) −4.09826 4.62523i −0.135856 0.153325i
\(911\) 24.0681i 0.797410i 0.917079 + 0.398705i \(0.130540\pi\)
−0.917079 + 0.398705i \(0.869460\pi\)
\(912\) −0.254862 2.46408i −0.00843933 0.0815939i
\(913\) −9.52984 + 16.5062i −0.315392 + 0.546274i
\(914\) 9.59425 + 5.53924i 0.317350 + 0.183222i
\(915\) 9.46418 9.50944i 0.312876 0.314372i
\(916\) 13.5546i 0.447856i
\(917\) −16.9317 + 32.2659i −0.559133 + 1.06551i
\(918\) −5.00000 15.6525i −0.165025 0.516609i
\(919\) −0.215838 0.373843i −0.00711985 0.0123319i 0.862444 0.506153i \(-0.168933\pi\)
−0.869563 + 0.493821i \(0.835600\pi\)
\(920\) 9.88171 1.60607i 0.325790 0.0529505i
\(921\) −12.1775 16.8193i −0.401261 0.554215i
\(922\) −15.8938 27.5289i −0.523434 0.906615i
\(923\) 7.23003i 0.237979i
\(924\) 3.06871 + 21.2515i 0.100953 + 0.699123i
\(925\) −13.0455 2.66291i −0.428935 0.0875560i
\(926\) 19.5497 11.2871i 0.642444 0.370916i
\(927\) 14.4403 3.01945i 0.474282 0.0991718i
\(928\) −5.99430 3.46081i −0.196773 0.113607i
\(929\) −7.96300 13.7923i −0.261258 0.452512i 0.705319 0.708890i \(-0.250804\pi\)
−0.966576 + 0.256379i \(0.917471\pi\)
\(930\) −6.70141 24.7735i −0.219748 0.812354i
\(931\) −0.806936 9.97902i −0.0264463 0.327049i
\(932\) 4.00000 0.131024
\(933\) 30.2897 3.13289i 0.991640 0.102566i
\(934\) 24.2614 + 14.0073i 0.793857 + 0.458333i
\(935\) 32.7028 5.31516i 1.06950 0.173824i
\(936\) 0.978218 2.97707i 0.0319741 0.0973087i
\(937\) −53.6757 −1.75351 −0.876754 0.480938i \(-0.840296\pi\)
−0.876754 + 0.480938i \(0.840296\pi\)
\(938\) −31.9089 + 20.1810i −1.04186 + 0.658932i
\(939\) 16.4317 36.7423i 0.536228 1.19904i
\(940\) −23.4561 8.89538i −0.765054 0.290135i
\(941\) 10.2369 17.7309i 0.333715 0.578011i −0.649522 0.760343i \(-0.725031\pi\)
0.983237 + 0.182331i \(0.0583644\pi\)
\(942\) −14.6750 20.2688i −0.478136 0.660394i
\(943\) 2.33836 + 4.05015i 0.0761474 + 0.131891i
\(944\) −10.5744 −0.344167
\(945\) −26.8190 + 15.0246i −0.872423 + 0.488751i
\(946\) −32.4317 −1.05444
\(947\) 16.4317 + 28.4605i 0.533958 + 0.924842i 0.999213 + 0.0396654i \(0.0126292\pi\)
−0.465255 + 0.885177i \(0.654037\pi\)
\(948\) −11.6580 16.1019i −0.378635 0.522965i
\(949\) 1.82971 3.16915i 0.0593949 0.102875i
\(950\) 2.26471 + 6.78305i 0.0734770 + 0.220071i
\(951\) −7.00665 + 15.6674i −0.227206 + 0.508049i
\(952\) 0.337449 + 8.35979i 0.0109368 + 0.270942i
\(953\) −46.9545 −1.52100 −0.760502 0.649336i \(-0.775047\pi\)
−0.760502 + 0.649336i \(0.775047\pi\)
\(954\) −4.68246 + 14.2504i −0.151600 + 0.461375i
\(955\) 5.84452 + 35.9598i 0.189124 + 1.16363i
\(956\) 0 0
\(957\) −55.8752 + 5.77923i −1.80619 + 0.186816i
\(958\) 42.3620 1.36865
\(959\) −9.19239 + 0.371058i −0.296838 + 0.0119821i
\(960\) 3.73861 1.01132i 0.120663 0.0326403i
\(961\) 6.45445 + 11.1794i 0.208208 + 0.360627i
\(962\) 2.40890 + 1.39078i 0.0776661 + 0.0448406i
\(963\) 16.0838 3.36311i 0.518294 0.108375i
\(964\) 18.4545 10.6547i 0.594378 0.343164i
\(965\) −12.7279 + 10.3923i −0.409726 + 0.334540i
\(966\) 12.6927 + 16.1199i 0.408382 + 0.518649i
\(967\) 7.23690i 0.232723i 0.993207 + 0.116361i \(0.0371231\pi\)
−0.993207 + 0.116361i \(0.962877\pi\)
\(968\) −5.47723 9.48683i −0.176045 0.304918i
\(969\) −4.59402 6.34519i −0.147581 0.203837i
\(970\) 26.4601 4.30055i 0.849584 0.138082i
\(971\) 18.8748 + 32.6922i 0.605723 + 1.04914i 0.991937 + 0.126733i \(0.0404492\pi\)
−0.386214 + 0.922409i \(0.626217\pi\)
\(972\) −13.4350 7.90569i −0.430929 0.253575i
\(973\) −45.1260 + 28.5402i −1.44667 + 0.914956i
\(974\) 17.0349i 0.545832i
\(975\) −0.887744 + 9.00246i −0.0284306 + 0.288309i
\(976\) −3.00000 1.73205i −0.0960277 0.0554416i
\(977\) 1.95445 3.38521i 0.0625284 0.108302i −0.833067 0.553173i \(-0.813417\pi\)
0.895595 + 0.444870i \(0.146750\pi\)
\(978\) −2.61895 25.3208i −0.0837448 0.809669i
\(979\) 23.0414i 0.736407i
\(980\) 15.1971 3.74812i 0.485453 0.119729i
\(981\) 40.8634 + 45.6866i 1.30467 + 1.45866i
\(982\) 11.9886 6.92163i 0.382572 0.220878i
\(983\) 45.7158 + 26.3941i 1.45811 + 0.841840i 0.998918 0.0464984i \(-0.0148062\pi\)
0.459190 + 0.888338i \(0.348140\pi\)
\(984\) 1.06101 + 1.46545i 0.0338238 + 0.0467169i
\(985\) 7.13604 18.8169i 0.227373 0.599557i
\(986\) −21.8881 −0.697059
\(987\) −7.34757 50.8836i −0.233876 1.61964i
\(988\) 1.49395i 0.0475290i
\(989\) −26.8378 + 15.4948i −0.853394 + 0.492707i
\(990\) 19.7628 24.4414i 0.628102 0.776800i
\(991\) −5.26139 + 9.11299i −0.167133 + 0.289484i −0.937411 0.348225i \(-0.886784\pi\)
0.770277 + 0.637709i \(0.220118\pi\)
\(992\) −5.73861 + 3.31319i −0.182201 + 0.105194i
\(993\) −15.1545 + 33.8865i −0.480913 + 1.07535i
\(994\) −16.2158 8.50934i −0.514335 0.269900i
\(995\) −26.8634 + 21.9338i −0.851626 + 0.695349i
\(996\) 0.724861 + 7.00816i 0.0229681 + 0.222062i
\(997\) 7.74597 13.4164i 0.245317 0.424902i −0.716904 0.697172i \(-0.754441\pi\)
0.962221 + 0.272270i \(0.0877745\pi\)
\(998\) 0.954451 1.65316i 0.0302126 0.0523298i
\(999\) 9.30964 10.2367i 0.294544 0.323875i
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 210.2.t.f.59.2 yes 8
3.2 odd 2 210.2.t.e.59.4 yes 8
5.2 odd 4 1050.2.s.i.101.1 16
5.3 odd 4 1050.2.s.i.101.8 16
5.4 even 2 210.2.t.e.59.3 8
7.3 odd 6 1470.2.d.e.1469.6 8
7.4 even 3 1470.2.d.e.1469.3 8
7.5 odd 6 inner 210.2.t.f.89.1 yes 8
15.2 even 4 1050.2.s.i.101.7 16
15.8 even 4 1050.2.s.i.101.2 16
15.14 odd 2 inner 210.2.t.f.59.1 yes 8
21.5 even 6 210.2.t.e.89.3 yes 8
21.11 odd 6 1470.2.d.f.1469.2 8
21.17 even 6 1470.2.d.f.1469.7 8
35.4 even 6 1470.2.d.f.1469.6 8
35.12 even 12 1050.2.s.i.551.7 16
35.19 odd 6 210.2.t.e.89.4 yes 8
35.24 odd 6 1470.2.d.f.1469.3 8
35.33 even 12 1050.2.s.i.551.2 16
105.47 odd 12 1050.2.s.i.551.1 16
105.59 even 6 1470.2.d.e.1469.2 8
105.68 odd 12 1050.2.s.i.551.8 16
105.74 odd 6 1470.2.d.e.1469.7 8
105.89 even 6 inner 210.2.t.f.89.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.e.59.3 8 5.4 even 2
210.2.t.e.59.4 yes 8 3.2 odd 2
210.2.t.e.89.3 yes 8 21.5 even 6
210.2.t.e.89.4 yes 8 35.19 odd 6
210.2.t.f.59.1 yes 8 15.14 odd 2 inner
210.2.t.f.59.2 yes 8 1.1 even 1 trivial
210.2.t.f.89.1 yes 8 7.5 odd 6 inner
210.2.t.f.89.2 yes 8 105.89 even 6 inner
1050.2.s.i.101.1 16 5.2 odd 4
1050.2.s.i.101.2 16 15.8 even 4
1050.2.s.i.101.7 16 15.2 even 4
1050.2.s.i.101.8 16 5.3 odd 4
1050.2.s.i.551.1 16 105.47 odd 12
1050.2.s.i.551.2 16 35.33 even 12
1050.2.s.i.551.7 16 35.12 even 12
1050.2.s.i.551.8 16 105.68 odd 12
1470.2.d.e.1469.2 8 105.59 even 6
1470.2.d.e.1469.3 8 7.4 even 3
1470.2.d.e.1469.6 8 7.3 odd 6
1470.2.d.e.1469.7 8 105.74 odd 6
1470.2.d.f.1469.2 8 21.11 odd 6
1470.2.d.f.1469.3 8 35.24 odd 6
1470.2.d.f.1469.6 8 35.4 even 6
1470.2.d.f.1469.7 8 21.17 even 6