Properties

Label 630.2.i.i.151.6
Level $630$
Weight $2$
Character 630.151
Analytic conductor $5.031$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(121,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.i (of order \(3\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + 243 x^{7} - 315 x^{6} + 54 x^{5} + 405 x^{4} - 972 x^{3} + 1458 x^{2} - 2187 x + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.6
Root \(-0.803168 - 1.53458i\) of defining polynomial
Character \(\chi\) \(=\) 630.151
Dual form 630.2.i.i.121.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.927397 + 1.46285i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.927397 - 1.46285i) q^{6} +(0.832221 + 2.51146i) q^{7} -1.00000 q^{8} +(-1.27987 + 2.71329i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.927397 + 1.46285i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.927397 - 1.46285i) q^{6} +(0.832221 + 2.51146i) q^{7} -1.00000 q^{8} +(-1.27987 + 2.71329i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.189632 - 0.328453i) q^{11} +(0.927397 + 1.46285i) q^{12} +(-0.308106 - 0.533656i) q^{13} +(-0.832221 - 2.51146i) q^{14} +(1.73057 - 0.0717234i) q^{15} +1.00000 q^{16} +(-1.97521 + 3.42117i) q^{17} +(1.27987 - 2.71329i) q^{18} +(2.57037 + 4.45201i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.90209 + 3.54653i) q^{21} +(0.189632 + 0.328453i) q^{22} +(-1.37042 + 2.37364i) q^{23} +(-0.927397 - 1.46285i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.308106 + 0.533656i) q^{26} +(-5.15609 + 0.644035i) q^{27} +(0.832221 + 2.51146i) q^{28} +(3.69460 - 6.39923i) q^{29} +(-1.73057 + 0.0717234i) q^{30} +2.37926 q^{31} -1.00000 q^{32} +(0.304613 - 0.582010i) q^{33} +(1.97521 - 3.42117i) q^{34} +(2.59109 + 0.535003i) q^{35} +(-1.27987 + 2.71329i) q^{36} +(3.99026 + 6.91133i) q^{37} +(-2.57037 - 4.45201i) q^{38} +(0.494922 - 0.945624i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.63844 - 6.30196i) q^{41} +(2.90209 - 3.54653i) q^{42} +(-2.57500 + 4.46002i) q^{43} +(-0.189632 - 0.328453i) q^{44} +(1.70984 + 2.46504i) q^{45} +(1.37042 - 2.37364i) q^{46} +7.44508 q^{47} +(0.927397 + 1.46285i) q^{48} +(-5.61482 + 4.18017i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.83647 + 0.283338i) q^{51} +(-0.308106 - 0.533656i) q^{52} +(-0.998199 + 1.72893i) q^{53} +(5.15609 - 0.644035i) q^{54} -0.379264 q^{55} +(-0.832221 - 2.51146i) q^{56} +(-4.12888 + 7.88885i) q^{57} +(-3.69460 + 6.39923i) q^{58} +0.231761 q^{59} +(1.73057 - 0.0717234i) q^{60} -11.5356 q^{61} -2.37926 q^{62} +(-7.87944 - 0.956281i) q^{63} +1.00000 q^{64} -0.616212 q^{65} +(-0.304613 + 0.582010i) q^{66} +13.4063 q^{67} +(-1.97521 + 3.42117i) q^{68} +(-4.74320 + 0.196583i) q^{69} +(-2.59109 - 0.535003i) q^{70} -11.2870 q^{71} +(1.27987 - 2.71329i) q^{72} +(-3.58534 + 6.20999i) q^{73} +(-3.99026 - 6.91133i) q^{74} +(0.803168 - 1.53458i) q^{75} +(2.57037 + 4.45201i) q^{76} +(0.667078 - 0.749598i) q^{77} +(-0.494922 + 0.945624i) q^{78} +6.03527 q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.72387 - 6.94531i) q^{81} +(3.63844 + 6.30196i) q^{82} +(4.29143 - 7.43298i) q^{83} +(-2.90209 + 3.54653i) q^{84} +(1.97521 + 3.42117i) q^{85} +(2.57500 - 4.46002i) q^{86} +(12.7875 - 0.529979i) q^{87} +(0.189632 + 0.328453i) q^{88} +(6.26653 + 10.8540i) q^{89} +(-1.70984 - 2.46504i) q^{90} +(1.08384 - 1.21791i) q^{91} +(-1.37042 + 2.37364i) q^{92} +(2.20652 + 3.48051i) q^{93} -7.44508 q^{94} +5.14074 q^{95} +(-0.927397 - 1.46285i) q^{96} +(-0.792120 + 1.37199i) q^{97} +(5.61482 - 4.18017i) q^{98} +(1.13389 - 0.0941502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.927397 + 1.46285i 0.535433 + 0.844578i
\(4\) 1.00000 0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −0.927397 1.46285i −0.378608 0.597207i
\(7\) 0.832221 + 2.51146i 0.314550 + 0.949241i
\(8\) −1.00000 −0.353553
\(9\) −1.27987 + 2.71329i −0.426623 + 0.904429i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −0.189632 0.328453i −0.0571763 0.0990322i 0.836021 0.548698i \(-0.184876\pi\)
−0.893197 + 0.449666i \(0.851543\pi\)
\(12\) 0.927397 + 1.46285i 0.267716 + 0.422289i
\(13\) −0.308106 0.533656i −0.0854533 0.148009i 0.820131 0.572176i \(-0.193901\pi\)
−0.905584 + 0.424166i \(0.860567\pi\)
\(14\) −0.832221 2.51146i −0.222420 0.671215i
\(15\) 1.73057 0.0717234i 0.446830 0.0185189i
\(16\) 1.00000 0.250000
\(17\) −1.97521 + 3.42117i −0.479060 + 0.829756i −0.999712 0.0240132i \(-0.992356\pi\)
0.520652 + 0.853769i \(0.325689\pi\)
\(18\) 1.27987 2.71329i 0.301668 0.639528i
\(19\) 2.57037 + 4.45201i 0.589684 + 1.02136i 0.994274 + 0.106864i \(0.0340809\pi\)
−0.404590 + 0.914498i \(0.632586\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) −2.90209 + 3.54653i −0.633287 + 0.773917i
\(22\) 0.189632 + 0.328453i 0.0404297 + 0.0700263i
\(23\) −1.37042 + 2.37364i −0.285752 + 0.494938i −0.972791 0.231683i \(-0.925577\pi\)
0.687039 + 0.726621i \(0.258910\pi\)
\(24\) −0.927397 1.46285i −0.189304 0.298603i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.308106 + 0.533656i 0.0604246 + 0.104658i
\(27\) −5.15609 + 0.644035i −0.992289 + 0.123945i
\(28\) 0.832221 + 2.51146i 0.157275 + 0.474620i
\(29\) 3.69460 6.39923i 0.686070 1.18831i −0.287029 0.957922i \(-0.592668\pi\)
0.973099 0.230386i \(-0.0739989\pi\)
\(30\) −1.73057 + 0.0717234i −0.315957 + 0.0130948i
\(31\) 2.37926 0.427329 0.213664 0.976907i \(-0.431460\pi\)
0.213664 + 0.976907i \(0.431460\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.304613 0.582010i 0.0530263 0.101315i
\(34\) 1.97521 3.42117i 0.338746 0.586726i
\(35\) 2.59109 + 0.535003i 0.437975 + 0.0904320i
\(36\) −1.27987 + 2.71329i −0.213312 + 0.452215i
\(37\) 3.99026 + 6.91133i 0.655994 + 1.13621i 0.981644 + 0.190724i \(0.0610837\pi\)
−0.325650 + 0.945491i \(0.605583\pi\)
\(38\) −2.57037 4.45201i −0.416969 0.722212i
\(39\) 0.494922 0.945624i 0.0792510 0.151421i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −3.63844 6.30196i −0.568229 0.984201i −0.996741 0.0806654i \(-0.974295\pi\)
0.428512 0.903536i \(-0.359038\pi\)
\(42\) 2.90209 3.54653i 0.447802 0.547242i
\(43\) −2.57500 + 4.46002i −0.392683 + 0.680147i −0.992802 0.119763i \(-0.961786\pi\)
0.600119 + 0.799911i \(0.295120\pi\)
\(44\) −0.189632 0.328453i −0.0285881 0.0495161i
\(45\) 1.70984 + 2.46504i 0.254888 + 0.367467i
\(46\) 1.37042 2.37364i 0.202058 0.349974i
\(47\) 7.44508 1.08598 0.542988 0.839740i \(-0.317293\pi\)
0.542988 + 0.839740i \(0.317293\pi\)
\(48\) 0.927397 + 1.46285i 0.133858 + 0.211144i
\(49\) −5.61482 + 4.18017i −0.802117 + 0.597168i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −6.83647 + 0.283338i −0.957298 + 0.0396753i
\(52\) −0.308106 0.533656i −0.0427266 0.0740047i
\(53\) −0.998199 + 1.72893i −0.137113 + 0.237487i −0.926403 0.376534i \(-0.877116\pi\)
0.789290 + 0.614021i \(0.210449\pi\)
\(54\) 5.15609 0.644035i 0.701654 0.0876421i
\(55\) −0.379264 −0.0511400
\(56\) −0.832221 2.51146i −0.111210 0.335607i
\(57\) −4.12888 + 7.88885i −0.546884 + 1.04490i
\(58\) −3.69460 + 6.39923i −0.485125 + 0.840261i
\(59\) 0.231761 0.0301727 0.0150864 0.999886i \(-0.495198\pi\)
0.0150864 + 0.999886i \(0.495198\pi\)
\(60\) 1.73057 0.0717234i 0.223415 0.00925945i
\(61\) −11.5356 −1.47699 −0.738494 0.674260i \(-0.764463\pi\)
−0.738494 + 0.674260i \(0.764463\pi\)
\(62\) −2.37926 −0.302167
\(63\) −7.87944 0.956281i −0.992716 0.120480i
\(64\) 1.00000 0.125000
\(65\) −0.616212 −0.0764317
\(66\) −0.304613 + 0.582010i −0.0374953 + 0.0716404i
\(67\) 13.4063 1.63784 0.818919 0.573909i \(-0.194574\pi\)
0.818919 + 0.573909i \(0.194574\pi\)
\(68\) −1.97521 + 3.42117i −0.239530 + 0.414878i
\(69\) −4.74320 + 0.196583i −0.571015 + 0.0236658i
\(70\) −2.59109 0.535003i −0.309695 0.0639451i
\(71\) −11.2870 −1.33952 −0.669758 0.742580i \(-0.733602\pi\)
−0.669758 + 0.742580i \(0.733602\pi\)
\(72\) 1.27987 2.71329i 0.150834 0.319764i
\(73\) −3.58534 + 6.20999i −0.419632 + 0.726824i −0.995902 0.0904348i \(-0.971174\pi\)
0.576270 + 0.817259i \(0.304508\pi\)
\(74\) −3.99026 6.91133i −0.463858 0.803425i
\(75\) 0.803168 1.53458i 0.0927419 0.177197i
\(76\) 2.57037 + 4.45201i 0.294842 + 0.510681i
\(77\) 0.667078 0.749598i 0.0760206 0.0854246i
\(78\) −0.494922 + 0.945624i −0.0560389 + 0.107071i
\(79\) 6.03527 0.679021 0.339510 0.940602i \(-0.389739\pi\)
0.339510 + 0.940602i \(0.389739\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −5.72387 6.94531i −0.635985 0.771701i
\(82\) 3.63844 + 6.30196i 0.401799 + 0.695935i
\(83\) 4.29143 7.43298i 0.471046 0.815876i −0.528405 0.848992i \(-0.677210\pi\)
0.999452 + 0.0331163i \(0.0105432\pi\)
\(84\) −2.90209 + 3.54653i −0.316644 + 0.386958i
\(85\) 1.97521 + 3.42117i 0.214242 + 0.371078i
\(86\) 2.57500 4.46002i 0.277669 0.480937i
\(87\) 12.7875 0.529979i 1.37096 0.0568197i
\(88\) 0.189632 + 0.328453i 0.0202149 + 0.0350132i
\(89\) 6.26653 + 10.8540i 0.664251 + 1.15052i 0.979488 + 0.201504i \(0.0645828\pi\)
−0.315237 + 0.949013i \(0.602084\pi\)
\(90\) −1.70984 2.46504i −0.180233 0.259838i
\(91\) 1.08384 1.21791i 0.113617 0.127672i
\(92\) −1.37042 + 2.37364i −0.142876 + 0.247469i
\(93\) 2.20652 + 3.48051i 0.228806 + 0.360912i
\(94\) −7.44508 −0.767901
\(95\) 5.14074 0.527429
\(96\) −0.927397 1.46285i −0.0946520 0.149302i
\(97\) −0.792120 + 1.37199i −0.0804276 + 0.139305i −0.903434 0.428728i \(-0.858962\pi\)
0.823006 + 0.568033i \(0.192295\pi\)
\(98\) 5.61482 4.18017i 0.567182 0.422261i
\(99\) 1.13389 0.0941502i 0.113960 0.00946245i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 6.03331 + 10.4500i 0.600337 + 1.03981i 0.992770 + 0.120033i \(0.0383001\pi\)
−0.392433 + 0.919781i \(0.628367\pi\)
\(102\) 6.83647 0.283338i 0.676912 0.0280547i
\(103\) 5.73449 9.93243i 0.565036 0.978672i −0.432010 0.901869i \(-0.642196\pi\)
0.997046 0.0768027i \(-0.0244712\pi\)
\(104\) 0.308106 + 0.533656i 0.0302123 + 0.0523292i
\(105\) 1.62034 + 4.28655i 0.158129 + 0.418324i
\(106\) 0.998199 1.72893i 0.0969537 0.167929i
\(107\) 2.31889 + 4.01643i 0.224175 + 0.388283i 0.956072 0.293133i \(-0.0946979\pi\)
−0.731896 + 0.681416i \(0.761365\pi\)
\(108\) −5.15609 + 0.644035i −0.496145 + 0.0619723i
\(109\) 6.78033 11.7439i 0.649438 1.12486i −0.333820 0.942637i \(-0.608338\pi\)
0.983257 0.182222i \(-0.0583290\pi\)
\(110\) 0.379264 0.0361614
\(111\) −6.40969 + 12.2467i −0.608381 + 1.16240i
\(112\) 0.832221 + 2.51146i 0.0786375 + 0.237310i
\(113\) −7.78805 13.4893i −0.732638 1.26897i −0.955752 0.294174i \(-0.904956\pi\)
0.223114 0.974792i \(-0.428378\pi\)
\(114\) 4.12888 7.88885i 0.386705 0.738859i
\(115\) 1.37042 + 2.37364i 0.127792 + 0.221343i
\(116\) 3.69460 6.39923i 0.343035 0.594154i
\(117\) 1.84230 0.152971i 0.170320 0.0141422i
\(118\) −0.231761 −0.0213353
\(119\) −10.2359 2.11349i −0.938327 0.193743i
\(120\) −1.73057 + 0.0717234i −0.157978 + 0.00654742i
\(121\) 5.42808 9.40171i 0.493462 0.854701i
\(122\) 11.5356 1.04439
\(123\) 5.84456 11.1669i 0.526986 1.00689i
\(124\) 2.37926 0.213664
\(125\) −1.00000 −0.0894427
\(126\) 7.87944 + 0.956281i 0.701956 + 0.0851922i
\(127\) 8.57545 0.760948 0.380474 0.924792i \(-0.375761\pi\)
0.380474 + 0.924792i \(0.375761\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.91240 + 0.369375i −0.784693 + 0.0325217i
\(130\) 0.616212 0.0540454
\(131\) 6.90931 11.9673i 0.603669 1.04559i −0.388591 0.921410i \(-0.627038\pi\)
0.992260 0.124175i \(-0.0396286\pi\)
\(132\) 0.304613 0.582010i 0.0265132 0.0506574i
\(133\) −9.04192 + 10.1604i −0.784033 + 0.881021i
\(134\) −13.4063 −1.15813
\(135\) −2.02029 + 4.78732i −0.173879 + 0.412027i
\(136\) 1.97521 3.42117i 0.169373 0.293363i
\(137\) −4.66480 8.07967i −0.398541 0.690293i 0.595005 0.803722i \(-0.297150\pi\)
−0.993546 + 0.113429i \(0.963817\pi\)
\(138\) 4.74320 0.196583i 0.403768 0.0167342i
\(139\) −4.87554 8.44469i −0.413538 0.716269i 0.581736 0.813378i \(-0.302374\pi\)
−0.995274 + 0.0971088i \(0.969041\pi\)
\(140\) 2.59109 + 0.535003i 0.218987 + 0.0452160i
\(141\) 6.90454 + 10.8910i 0.581467 + 0.917191i
\(142\) 11.2870 0.947181
\(143\) −0.116854 + 0.202397i −0.00977180 + 0.0169253i
\(144\) −1.27987 + 2.71329i −0.106656 + 0.226107i
\(145\) −3.69460 6.39923i −0.306820 0.531427i
\(146\) 3.58534 6.20999i 0.296725 0.513943i
\(147\) −11.3221 4.33696i −0.933834 0.357707i
\(148\) 3.99026 + 6.91133i 0.327997 + 0.568107i
\(149\) 3.12699 5.41611i 0.256173 0.443705i −0.709040 0.705168i \(-0.750872\pi\)
0.965214 + 0.261463i \(0.0842049\pi\)
\(150\) −0.803168 + 1.53458i −0.0655784 + 0.125298i
\(151\) −10.9945 19.0431i −0.894723 1.54971i −0.834147 0.551542i \(-0.814040\pi\)
−0.0605755 0.998164i \(-0.519294\pi\)
\(152\) −2.57037 4.45201i −0.208485 0.361106i
\(153\) −6.75461 9.73798i −0.546078 0.787269i
\(154\) −0.667078 + 0.749598i −0.0537547 + 0.0604043i
\(155\) 1.18963 2.06050i 0.0955536 0.165504i
\(156\) 0.494922 0.945624i 0.0396255 0.0757105i
\(157\) 15.9599 1.27374 0.636869 0.770972i \(-0.280229\pi\)
0.636869 + 0.770972i \(0.280229\pi\)
\(158\) −6.03527 −0.480140
\(159\) −3.45490 + 0.143189i −0.273991 + 0.0113556i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −7.10178 1.46636i −0.559699 0.115565i
\(162\) 5.72387 + 6.94531i 0.449709 + 0.545675i
\(163\) −3.60765 6.24864i −0.282573 0.489431i 0.689444 0.724339i \(-0.257855\pi\)
−0.972018 + 0.234907i \(0.924521\pi\)
\(164\) −3.63844 6.30196i −0.284114 0.492101i
\(165\) −0.351729 0.554808i −0.0273820 0.0431917i
\(166\) −4.29143 + 7.43298i −0.333080 + 0.576911i
\(167\) 5.11565 + 8.86057i 0.395861 + 0.685652i 0.993211 0.116329i \(-0.0371128\pi\)
−0.597350 + 0.801981i \(0.703779\pi\)
\(168\) 2.90209 3.54653i 0.223901 0.273621i
\(169\) 6.31014 10.9295i 0.485395 0.840730i
\(170\) −1.97521 3.42117i −0.151492 0.262392i
\(171\) −15.3693 + 1.27616i −1.17532 + 0.0975903i
\(172\) −2.57500 + 4.46002i −0.196342 + 0.340074i
\(173\) 4.25750 0.323692 0.161846 0.986816i \(-0.448255\pi\)
0.161846 + 0.986816i \(0.448255\pi\)
\(174\) −12.7875 + 0.529979i −0.969417 + 0.0401776i
\(175\) 1.75887 1.97645i 0.132958 0.149406i
\(176\) −0.189632 0.328453i −0.0142941 0.0247580i
\(177\) 0.214934 + 0.339032i 0.0161555 + 0.0254832i
\(178\) −6.26653 10.8540i −0.469696 0.813538i
\(179\) 1.87410 3.24604i 0.140077 0.242621i −0.787448 0.616381i \(-0.788598\pi\)
0.927525 + 0.373760i \(0.121932\pi\)
\(180\) 1.70984 + 2.46504i 0.127444 + 0.183734i
\(181\) 19.5320 1.45180 0.725899 0.687801i \(-0.241424\pi\)
0.725899 + 0.687801i \(0.241424\pi\)
\(182\) −1.08384 + 1.21791i −0.0803395 + 0.0902778i
\(183\) −10.6981 16.8749i −0.790828 1.24743i
\(184\) 1.37042 2.37364i 0.101029 0.174987i
\(185\) 7.98051 0.586739
\(186\) −2.20652 3.48051i −0.161790 0.255203i
\(187\) 1.49826 0.109563
\(188\) 7.44508 0.542988
\(189\) −5.90847 12.4133i −0.429778 0.902935i
\(190\) −5.14074 −0.372949
\(191\) 7.73641 0.559787 0.279893 0.960031i \(-0.409701\pi\)
0.279893 + 0.960031i \(0.409701\pi\)
\(192\) 0.927397 + 1.46285i 0.0669291 + 0.105572i
\(193\) 1.20249 0.0865569 0.0432784 0.999063i \(-0.486220\pi\)
0.0432784 + 0.999063i \(0.486220\pi\)
\(194\) 0.792120 1.37199i 0.0568709 0.0985033i
\(195\) −0.571473 0.901427i −0.0409241 0.0645525i
\(196\) −5.61482 + 4.18017i −0.401058 + 0.298584i
\(197\) −18.2839 −1.30268 −0.651339 0.758787i \(-0.725792\pi\)
−0.651339 + 0.758787i \(0.725792\pi\)
\(198\) −1.13389 + 0.0941502i −0.0805821 + 0.00669096i
\(199\) −4.34213 + 7.52079i −0.307806 + 0.533135i −0.977882 0.209157i \(-0.932928\pi\)
0.670076 + 0.742292i \(0.266261\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 12.4329 + 19.6114i 0.876953 + 1.38328i
\(202\) −6.03331 10.4500i −0.424502 0.735259i
\(203\) 19.1461 + 3.95324i 1.34379 + 0.277463i
\(204\) −6.83647 + 0.283338i −0.478649 + 0.0198376i
\(205\) −7.27688 −0.508239
\(206\) −5.73449 + 9.93243i −0.399541 + 0.692025i
\(207\) −4.68640 6.75630i −0.325728 0.469595i
\(208\) −0.308106 0.533656i −0.0213633 0.0370024i
\(209\) 0.974850 1.68849i 0.0674318 0.116795i
\(210\) −1.62034 4.28655i −0.111814 0.295800i
\(211\) −7.54299 13.0648i −0.519281 0.899421i −0.999749 0.0224087i \(-0.992866\pi\)
0.480468 0.877012i \(-0.340467\pi\)
\(212\) −0.998199 + 1.72893i −0.0685566 + 0.118744i
\(213\) −10.4675 16.5111i −0.717221 1.13133i
\(214\) −2.31889 4.01643i −0.158516 0.274557i
\(215\) 2.57500 + 4.46002i 0.175613 + 0.304171i
\(216\) 5.15609 0.644035i 0.350827 0.0438210i
\(217\) 1.98007 + 5.97542i 0.134416 + 0.405638i
\(218\) −6.78033 + 11.7439i −0.459222 + 0.795396i
\(219\) −12.4093 + 0.514306i −0.838545 + 0.0347536i
\(220\) −0.379264 −0.0255700
\(221\) 2.43430 0.163749
\(222\) 6.40969 12.2467i 0.430190 0.821944i
\(223\) 11.1346 19.2857i 0.745629 1.29147i −0.204271 0.978914i \(-0.565482\pi\)
0.949900 0.312553i \(-0.101184\pi\)
\(224\) −0.832221 2.51146i −0.0556051 0.167804i
\(225\) 2.98971 0.248244i 0.199314 0.0165496i
\(226\) 7.78805 + 13.4893i 0.518053 + 0.897295i
\(227\) −1.45201 2.51496i −0.0963734 0.166924i 0.813808 0.581134i \(-0.197391\pi\)
−0.910181 + 0.414211i \(0.864058\pi\)
\(228\) −4.12888 + 7.88885i −0.273442 + 0.522452i
\(229\) −7.40450 + 12.8250i −0.489303 + 0.847498i −0.999924 0.0123082i \(-0.996082\pi\)
0.510621 + 0.859806i \(0.329415\pi\)
\(230\) −1.37042 2.37364i −0.0903629 0.156513i
\(231\) 1.71520 + 0.280661i 0.112852 + 0.0184662i
\(232\) −3.69460 + 6.39923i −0.242562 + 0.420130i
\(233\) 9.63735 + 16.6924i 0.631364 + 1.09355i 0.987273 + 0.159034i \(0.0508379\pi\)
−0.355909 + 0.934521i \(0.615829\pi\)
\(234\) −1.84230 + 0.152971i −0.120435 + 0.0100000i
\(235\) 3.72254 6.44763i 0.242832 0.420597i
\(236\) 0.231761 0.0150864
\(237\) 5.59709 + 8.82870i 0.363570 + 0.573486i
\(238\) 10.2359 + 2.11349i 0.663497 + 0.136997i
\(239\) 5.41490 + 9.37888i 0.350261 + 0.606669i 0.986295 0.164991i \(-0.0527597\pi\)
−0.636034 + 0.771661i \(0.719426\pi\)
\(240\) 1.73057 0.0717234i 0.111708 0.00462973i
\(241\) 3.49332 + 6.05061i 0.225025 + 0.389754i 0.956327 0.292300i \(-0.0944204\pi\)
−0.731302 + 0.682054i \(0.761087\pi\)
\(242\) −5.42808 + 9.40171i −0.348930 + 0.604365i
\(243\) 4.85167 14.8142i 0.311235 0.950333i
\(244\) −11.5356 −0.738494
\(245\) 0.812728 + 6.95266i 0.0519233 + 0.444189i
\(246\) −5.84456 + 11.1669i −0.372636 + 0.711977i
\(247\) 1.58389 2.74339i 0.100781 0.174557i
\(248\) −2.37926 −0.151083
\(249\) 14.8532 0.615593i 0.941284 0.0390116i
\(250\) 1.00000 0.0632456
\(251\) 17.4193 1.09950 0.549749 0.835330i \(-0.314723\pi\)
0.549749 + 0.835330i \(0.314723\pi\)
\(252\) −7.87944 0.956281i −0.496358 0.0602400i
\(253\) 1.03950 0.0653530
\(254\) −8.57545 −0.538072
\(255\) −3.17286 + 6.06223i −0.198692 + 0.379632i
\(256\) 1.00000 0.0625000
\(257\) −6.55702 + 11.3571i −0.409016 + 0.708436i −0.994780 0.102046i \(-0.967461\pi\)
0.585764 + 0.810482i \(0.300795\pi\)
\(258\) 8.91240 0.369375i 0.554862 0.0229963i
\(259\) −14.0367 + 15.7731i −0.872199 + 0.980093i
\(260\) −0.616212 −0.0382159
\(261\) 12.6344 + 18.2147i 0.782047 + 1.12746i
\(262\) −6.90931 + 11.9673i −0.426859 + 0.739341i
\(263\) 2.40150 + 4.15951i 0.148083 + 0.256487i 0.930519 0.366244i \(-0.119357\pi\)
−0.782436 + 0.622731i \(0.786023\pi\)
\(264\) −0.304613 + 0.582010i −0.0187476 + 0.0358202i
\(265\) 0.998199 + 1.72893i 0.0613189 + 0.106207i
\(266\) 9.04192 10.1604i 0.554395 0.622976i
\(267\) −10.0662 + 19.2329i −0.616039 + 1.17704i
\(268\) 13.4063 0.818919
\(269\) −4.56270 + 7.90283i −0.278193 + 0.481844i −0.970936 0.239341i \(-0.923069\pi\)
0.692743 + 0.721185i \(0.256402\pi\)
\(270\) 2.02029 4.78732i 0.122951 0.291347i
\(271\) −13.2680 22.9808i −0.805973 1.39599i −0.915632 0.402017i \(-0.868309\pi\)
0.109659 0.993969i \(-0.465024\pi\)
\(272\) −1.97521 + 3.42117i −0.119765 + 0.207439i
\(273\) 2.78678 + 0.456007i 0.168663 + 0.0275988i
\(274\) 4.66480 + 8.07967i 0.281811 + 0.488111i
\(275\) −0.189632 + 0.328453i −0.0114353 + 0.0198064i
\(276\) −4.74320 + 0.196583i −0.285507 + 0.0118329i
\(277\) 1.17060 + 2.02754i 0.0703347 + 0.121823i 0.899048 0.437850i \(-0.144260\pi\)
−0.828713 + 0.559673i \(0.810927\pi\)
\(278\) 4.87554 + 8.44469i 0.292416 + 0.506479i
\(279\) −3.04515 + 6.45563i −0.182308 + 0.386488i
\(280\) −2.59109 0.535003i −0.154848 0.0319725i
\(281\) 8.99372 15.5776i 0.536520 0.929280i −0.462568 0.886584i \(-0.653072\pi\)
0.999088 0.0426963i \(-0.0135948\pi\)
\(282\) −6.90454 10.8910i −0.411159 0.648552i
\(283\) −7.92530 −0.471110 −0.235555 0.971861i \(-0.575691\pi\)
−0.235555 + 0.971861i \(0.575691\pi\)
\(284\) −11.2870 −0.669758
\(285\) 4.76751 + 7.52014i 0.282403 + 0.445455i
\(286\) 0.116854 0.202397i 0.00690970 0.0119680i
\(287\) 12.7991 14.3824i 0.755508 0.848967i
\(288\) 1.27987 2.71329i 0.0754171 0.159882i
\(289\) 0.697058 + 1.20734i 0.0410034 + 0.0710200i
\(290\) 3.69460 + 6.39923i 0.216954 + 0.375776i
\(291\) −2.74163 + 0.113627i −0.160717 + 0.00666094i
\(292\) −3.58534 + 6.20999i −0.209816 + 0.363412i
\(293\) 13.3538 + 23.1294i 0.780135 + 1.35123i 0.931863 + 0.362811i \(0.118183\pi\)
−0.151728 + 0.988422i \(0.548484\pi\)
\(294\) 11.3221 + 4.33696i 0.660320 + 0.252937i
\(295\) 0.115881 0.200711i 0.00674683 0.0116858i
\(296\) −3.99026 6.91133i −0.231929 0.401713i
\(297\) 1.18929 + 1.57140i 0.0690099 + 0.0911819i
\(298\) −3.12699 + 5.41611i −0.181142 + 0.313747i
\(299\) 1.68894 0.0976739
\(300\) 0.803168 1.53458i 0.0463709 0.0885987i
\(301\) −13.3441 2.75526i −0.769142 0.158811i
\(302\) 10.9945 + 19.0431i 0.632665 + 1.09581i
\(303\) −9.69153 + 18.5171i −0.556764 + 1.06378i
\(304\) 2.57037 + 4.45201i 0.147421 + 0.255340i
\(305\) −5.76782 + 9.99016i −0.330264 + 0.572035i
\(306\) 6.75461 + 9.73798i 0.386135 + 0.556683i
\(307\) 17.6963 1.00998 0.504991 0.863125i \(-0.331496\pi\)
0.504991 + 0.863125i \(0.331496\pi\)
\(308\) 0.667078 0.749598i 0.0380103 0.0427123i
\(309\) 19.8478 0.822595i 1.12910 0.0467958i
\(310\) −1.18963 + 2.06050i −0.0675666 + 0.117029i
\(311\) 16.4249 0.931372 0.465686 0.884950i \(-0.345808\pi\)
0.465686 + 0.884950i \(0.345808\pi\)
\(312\) −0.494922 + 0.945624i −0.0280195 + 0.0535354i
\(313\) −11.8959 −0.672394 −0.336197 0.941792i \(-0.609141\pi\)
−0.336197 + 0.941792i \(0.609141\pi\)
\(314\) −15.9599 −0.900669
\(315\) −4.76788 + 6.34565i −0.268640 + 0.357537i
\(316\) 6.03527 0.339510
\(317\) −25.7886 −1.44843 −0.724216 0.689573i \(-0.757798\pi\)
−0.724216 + 0.689573i \(0.757798\pi\)
\(318\) 3.45490 0.143189i 0.193741 0.00802962i
\(319\) −2.80246 −0.156908
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −3.72491 + 7.11701i −0.207904 + 0.397233i
\(322\) 7.10178 + 1.46636i 0.395767 + 0.0817170i
\(323\) −20.3081 −1.12997
\(324\) −5.72387 6.94531i −0.317993 0.385851i
\(325\) −0.308106 + 0.533656i −0.0170907 + 0.0296019i
\(326\) 3.60765 + 6.24864i 0.199810 + 0.346080i
\(327\) 23.4676 0.972617i 1.29776 0.0537858i
\(328\) 3.63844 + 6.30196i 0.200899 + 0.347968i
\(329\) 6.19595 + 18.6980i 0.341594 + 1.03085i
\(330\) 0.351729 + 0.554808i 0.0193620 + 0.0305412i
\(331\) −0.0260656 −0.00143269 −0.000716347 1.00000i \(-0.500228\pi\)
−0.000716347 1.00000i \(0.500228\pi\)
\(332\) 4.29143 7.43298i 0.235523 0.407938i
\(333\) −23.8594 + 1.98112i −1.30749 + 0.108564i
\(334\) −5.11565 8.86057i −0.279916 0.484829i
\(335\) 6.70314 11.6102i 0.366232 0.634332i
\(336\) −2.90209 + 3.54653i −0.158322 + 0.193479i
\(337\) −9.33400 16.1670i −0.508455 0.880671i −0.999952 0.00979108i \(-0.996883\pi\)
0.491497 0.870879i \(-0.336450\pi\)
\(338\) −6.31014 + 10.9295i −0.343226 + 0.594486i
\(339\) 12.5102 23.9027i 0.679462 1.29822i
\(340\) 1.97521 + 3.42117i 0.107121 + 0.185539i
\(341\) −0.451185 0.781476i −0.0244330 0.0423193i
\(342\) 15.3693 1.27616i 0.831078 0.0690068i
\(343\) −15.1711 10.6225i −0.819162 0.573563i
\(344\) 2.57500 4.46002i 0.138834 0.240468i
\(345\) −2.20136 + 4.20603i −0.118517 + 0.226445i
\(346\) −4.25750 −0.228885
\(347\) −33.8993 −1.81981 −0.909904 0.414819i \(-0.863845\pi\)
−0.909904 + 0.414819i \(0.863845\pi\)
\(348\) 12.7875 0.529979i 0.685481 0.0284098i
\(349\) 3.64339 6.31054i 0.195026 0.337796i −0.751883 0.659297i \(-0.770854\pi\)
0.946909 + 0.321501i \(0.104187\pi\)
\(350\) −1.75887 + 1.97645i −0.0940157 + 0.105646i
\(351\) 1.93231 + 2.55314i 0.103139 + 0.136277i
\(352\) 0.189632 + 0.328453i 0.0101074 + 0.0175066i
\(353\) −2.78042 4.81582i −0.147987 0.256320i 0.782497 0.622655i \(-0.213946\pi\)
−0.930483 + 0.366335i \(0.880613\pi\)
\(354\) −0.214934 0.339032i −0.0114236 0.0180194i
\(355\) −5.64348 + 9.77479i −0.299525 + 0.518792i
\(356\) 6.26653 + 10.8540i 0.332126 + 0.575258i
\(357\) −6.40105 16.9337i −0.338779 0.896226i
\(358\) −1.87410 + 3.24604i −0.0990495 + 0.171559i
\(359\) 0.698378 + 1.20963i 0.0368590 + 0.0638416i 0.883866 0.467739i \(-0.154931\pi\)
−0.847007 + 0.531581i \(0.821598\pi\)
\(360\) −1.70984 2.46504i −0.0901166 0.129919i
\(361\) −3.71361 + 6.43217i −0.195453 + 0.338535i
\(362\) −19.5320 −1.02658
\(363\) 18.7873 0.778641i 0.986077 0.0408680i
\(364\) 1.08384 1.21791i 0.0568086 0.0638361i
\(365\) 3.58534 + 6.20999i 0.187665 + 0.325046i
\(366\) 10.6981 + 16.8749i 0.559200 + 0.882067i
\(367\) 14.0446 + 24.3260i 0.733123 + 1.26981i 0.955542 + 0.294855i \(0.0952713\pi\)
−0.222419 + 0.974951i \(0.571395\pi\)
\(368\) −1.37042 + 2.37364i −0.0714381 + 0.123734i
\(369\) 21.7558 1.80644i 1.13256 0.0940397i
\(370\) −7.98051 −0.414887
\(371\) −5.17286 1.06808i −0.268561 0.0554519i
\(372\) 2.20652 + 3.48051i 0.114403 + 0.180456i
\(373\) −5.61261 + 9.72133i −0.290610 + 0.503352i −0.973954 0.226745i \(-0.927192\pi\)
0.683344 + 0.730097i \(0.260525\pi\)
\(374\) −1.49826 −0.0774730
\(375\) −0.927397 1.46285i −0.0478906 0.0755413i
\(376\) −7.44508 −0.383951
\(377\) −4.55332 −0.234508
\(378\) 5.90847 + 12.4133i 0.303899 + 0.638471i
\(379\) −13.2661 −0.681435 −0.340718 0.940166i \(-0.610670\pi\)
−0.340718 + 0.940166i \(0.610670\pi\)
\(380\) 5.14074 0.263715
\(381\) 7.95285 + 12.5446i 0.407437 + 0.642680i
\(382\) −7.73641 −0.395829
\(383\) −8.76220 + 15.1766i −0.447727 + 0.775487i −0.998238 0.0593417i \(-0.981100\pi\)
0.550510 + 0.834828i \(0.314433\pi\)
\(384\) −0.927397 1.46285i −0.0473260 0.0746508i
\(385\) −0.315632 0.952506i −0.0160861 0.0485442i
\(386\) −1.20249 −0.0612050
\(387\) −8.80567 12.6950i −0.447617 0.645321i
\(388\) −0.792120 + 1.37199i −0.0402138 + 0.0696523i
\(389\) −4.71220 8.16178i −0.238918 0.413818i 0.721486 0.692429i \(-0.243459\pi\)
−0.960404 + 0.278611i \(0.910126\pi\)
\(390\) 0.571473 + 0.901427i 0.0289377 + 0.0456455i
\(391\) −5.41375 9.37689i −0.273785 0.474210i
\(392\) 5.61482 4.18017i 0.283591 0.211131i
\(393\) 23.9140 0.991119i 1.20630 0.0499953i
\(394\) 18.2839 0.921132
\(395\) 3.01763 5.22670i 0.151834 0.262984i
\(396\) 1.13389 0.0941502i 0.0569802 0.00473122i
\(397\) 3.03378 + 5.25466i 0.152261 + 0.263724i 0.932058 0.362308i \(-0.118011\pi\)
−0.779797 + 0.626032i \(0.784678\pi\)
\(398\) 4.34213 7.52079i 0.217651 0.376983i
\(399\) −23.2486 3.80423i −1.16389 0.190450i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 19.5894 33.9298i 0.978246 1.69437i 0.309466 0.950910i \(-0.399850\pi\)
0.668779 0.743461i \(-0.266817\pi\)
\(402\) −12.4329 19.6114i −0.620099 0.978128i
\(403\) −0.733066 1.26971i −0.0365166 0.0632486i
\(404\) 6.03331 + 10.4500i 0.300168 + 0.519907i
\(405\) −8.87675 + 1.48436i −0.441089 + 0.0737583i
\(406\) −19.1461 3.95324i −0.950206 0.196196i
\(407\) 1.51336 2.62122i 0.0750146 0.129929i
\(408\) 6.83647 0.283338i 0.338456 0.0140273i
\(409\) 0.807364 0.0399216 0.0199608 0.999801i \(-0.493646\pi\)
0.0199608 + 0.999801i \(0.493646\pi\)
\(410\) 7.27688 0.359380
\(411\) 7.49324 14.3170i 0.369614 0.706204i
\(412\) 5.73449 9.93243i 0.282518 0.489336i
\(413\) 0.192876 + 0.582058i 0.00949083 + 0.0286412i
\(414\) 4.68640 + 6.75630i 0.230324 + 0.332054i
\(415\) −4.29143 7.43298i −0.210658 0.364871i
\(416\) 0.308106 + 0.533656i 0.0151061 + 0.0261646i
\(417\) 7.83176 14.9638i 0.383523 0.732779i
\(418\) −0.974850 + 1.68849i −0.0476815 + 0.0825868i
\(419\) 15.1172 + 26.1838i 0.738524 + 1.27916i 0.953160 + 0.302467i \(0.0978104\pi\)
−0.214635 + 0.976694i \(0.568856\pi\)
\(420\) 1.62034 + 4.28655i 0.0790646 + 0.209162i
\(421\) −13.5938 + 23.5451i −0.662519 + 1.14752i 0.317432 + 0.948281i \(0.397179\pi\)
−0.979951 + 0.199236i \(0.936154\pi\)
\(422\) 7.54299 + 13.0648i 0.367187 + 0.635987i
\(423\) −9.52873 + 20.2006i −0.463303 + 0.982189i
\(424\) 0.998199 1.72893i 0.0484769 0.0839644i
\(425\) 3.95043 0.191624
\(426\) 10.4675 + 16.5111i 0.507152 + 0.799968i
\(427\) −9.60021 28.9713i −0.464587 1.40202i
\(428\) 2.31889 + 4.01643i 0.112088 + 0.194141i
\(429\) −0.404446 + 0.0167623i −0.0195268 + 0.000809291i
\(430\) −2.57500 4.46002i −0.124177 0.215081i
\(431\) −18.3346 + 31.7564i −0.883145 + 1.52965i −0.0353190 + 0.999376i \(0.511245\pi\)
−0.847826 + 0.530275i \(0.822089\pi\)
\(432\) −5.15609 + 0.644035i −0.248072 + 0.0309861i
\(433\) −24.3601 −1.17067 −0.585336 0.810791i \(-0.699037\pi\)
−0.585336 + 0.810791i \(0.699037\pi\)
\(434\) −1.98007 5.97542i −0.0950466 0.286829i
\(435\) 5.93477 11.3393i 0.284550 0.543677i
\(436\) 6.78033 11.7439i 0.324719 0.562430i
\(437\) −14.0900 −0.674014
\(438\) 12.4093 0.514306i 0.592941 0.0245745i
\(439\) 22.4590 1.07191 0.535956 0.844246i \(-0.319951\pi\)
0.535956 + 0.844246i \(0.319951\pi\)
\(440\) 0.379264 0.0180807
\(441\) −4.15578 20.5847i −0.197894 0.980223i
\(442\) −2.43430 −0.115788
\(443\) −18.5159 −0.879718 −0.439859 0.898067i \(-0.644972\pi\)
−0.439859 + 0.898067i \(0.644972\pi\)
\(444\) −6.40969 + 12.2467i −0.304191 + 0.581202i
\(445\) 12.5331 0.594124
\(446\) −11.1346 + 19.2857i −0.527240 + 0.913206i
\(447\) 10.8229 0.448557i 0.511907 0.0212160i
\(448\) 0.832221 + 2.51146i 0.0393188 + 0.118655i
\(449\) −27.6845 −1.30651 −0.653257 0.757136i \(-0.726598\pi\)
−0.653257 + 0.757136i \(0.726598\pi\)
\(450\) −2.98971 + 0.248244i −0.140936 + 0.0117023i
\(451\) −1.37993 + 2.39011i −0.0649784 + 0.112546i
\(452\) −7.78805 13.4893i −0.366319 0.634483i
\(453\) 17.6609 33.7439i 0.829783 1.58543i
\(454\) 1.45201 + 2.51496i 0.0681463 + 0.118033i
\(455\) −0.512825 1.54759i −0.0240416 0.0725521i
\(456\) 4.12888 7.88885i 0.193353 0.369429i
\(457\) −11.3805 −0.532355 −0.266178 0.963924i \(-0.585761\pi\)
−0.266178 + 0.963924i \(0.585761\pi\)
\(458\) 7.40450 12.8250i 0.345989 0.599271i
\(459\) 7.98102 18.9120i 0.372522 0.882735i
\(460\) 1.37042 + 2.37364i 0.0638962 + 0.110671i
\(461\) −11.2662 + 19.5136i −0.524720 + 0.908841i 0.474866 + 0.880058i \(0.342496\pi\)
−0.999586 + 0.0287830i \(0.990837\pi\)
\(462\) −1.71520 0.280661i −0.0797982 0.0130576i
\(463\) −8.51644 14.7509i −0.395793 0.685533i 0.597409 0.801936i \(-0.296197\pi\)
−0.993202 + 0.116404i \(0.962863\pi\)
\(464\) 3.69460 6.39923i 0.171517 0.297077i
\(465\) 4.11747 0.170649i 0.190943 0.00791366i
\(466\) −9.63735 16.6924i −0.446442 0.773260i
\(467\) 3.14018 + 5.43895i 0.145310 + 0.251685i 0.929489 0.368851i \(-0.120249\pi\)
−0.784178 + 0.620535i \(0.786915\pi\)
\(468\) 1.84230 0.152971i 0.0851602 0.00707109i
\(469\) 11.1570 + 33.6693i 0.515182 + 1.55470i
\(470\) −3.72254 + 6.44763i −0.171708 + 0.297407i
\(471\) 14.8012 + 23.3470i 0.682001 + 1.07577i
\(472\) −0.231761 −0.0106677
\(473\) 1.95321 0.0898086
\(474\) −5.59709 8.82870i −0.257083 0.405516i
\(475\) 2.57037 4.45201i 0.117937 0.204272i
\(476\) −10.2359 2.11349i −0.469163 0.0968717i
\(477\) −3.41353 4.92121i −0.156295 0.225327i
\(478\) −5.41490 9.37888i −0.247672 0.428980i
\(479\) −1.48483 2.57181i −0.0678438 0.117509i 0.830108 0.557602i \(-0.188279\pi\)
−0.897952 + 0.440093i \(0.854945\pi\)
\(480\) −1.73057 + 0.0717234i −0.0789891 + 0.00327371i
\(481\) 2.45884 4.25884i 0.112114 0.194187i
\(482\) −3.49332 6.05061i −0.159116 0.275598i
\(483\) −4.44110 11.7487i −0.202077 0.534587i
\(484\) 5.42808 9.40171i 0.246731 0.427350i
\(485\) 0.792120 + 1.37199i 0.0359683 + 0.0622989i
\(486\) −4.85167 + 14.8142i −0.220076 + 0.671987i
\(487\) 7.50526 12.9995i 0.340096 0.589063i −0.644354 0.764727i \(-0.722874\pi\)
0.984450 + 0.175664i \(0.0562071\pi\)
\(488\) 11.5356 0.522194
\(489\) 5.79511 11.0724i 0.262064 0.500713i
\(490\) −0.812728 6.95266i −0.0367153 0.314089i
\(491\) −6.41840 11.1170i −0.289658 0.501703i 0.684070 0.729417i \(-0.260208\pi\)
−0.973728 + 0.227714i \(0.926875\pi\)
\(492\) 5.84456 11.1669i 0.263493 0.503444i
\(493\) 14.5953 + 25.2797i 0.657337 + 1.13854i
\(494\) −1.58389 + 2.74339i −0.0712628 + 0.123431i
\(495\) 0.485409 1.02905i 0.0218175 0.0462525i
\(496\) 2.37926 0.106832
\(497\) −9.39325 28.3467i −0.421345 1.27152i
\(498\) −14.8532 + 0.615593i −0.665588 + 0.0275854i
\(499\) 11.6783 20.2273i 0.522791 0.905500i −0.476857 0.878981i \(-0.658224\pi\)
0.999648 0.0265196i \(-0.00844245\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −8.21746 + 15.7007i −0.367129 + 0.701456i
\(502\) −17.4193 −0.777463
\(503\) 18.9067 0.843007 0.421503 0.906827i \(-0.361503\pi\)
0.421503 + 0.906827i \(0.361503\pi\)
\(504\) 7.87944 + 0.956281i 0.350978 + 0.0425961i
\(505\) 12.0666 0.536958
\(506\) −1.03950 −0.0462116
\(507\) 21.8402 0.905170i 0.969958 0.0402000i
\(508\) 8.57545 0.380474
\(509\) −17.4056 + 30.1473i −0.771487 + 1.33626i 0.165260 + 0.986250i \(0.447154\pi\)
−0.936748 + 0.350005i \(0.886180\pi\)
\(510\) 3.17286 6.06223i 0.140497 0.268440i
\(511\) −18.5799 3.83634i −0.821927 0.169709i
\(512\) −1.00000 −0.0441942
\(513\) −16.1203 21.2996i −0.711729 0.940398i
\(514\) 6.55702 11.3571i 0.289218 0.500940i
\(515\) −5.73449 9.93243i −0.252692 0.437675i
\(516\) −8.91240 + 0.369375i −0.392346 + 0.0162608i
\(517\) −1.41183 2.44535i −0.0620920 0.107547i
\(518\) 14.0367 15.7731i 0.616738 0.693030i
\(519\) 3.94839 + 6.22809i 0.173315 + 0.273383i
\(520\) 0.616212 0.0270227
\(521\) 17.3804 30.1037i 0.761449 1.31887i −0.180655 0.983546i \(-0.557822\pi\)
0.942104 0.335321i \(-0.108845\pi\)
\(522\) −12.6344 18.2147i −0.552991 0.797236i
\(523\) −15.7294 27.2442i −0.687800 1.19130i −0.972548 0.232702i \(-0.925243\pi\)
0.284748 0.958602i \(-0.408090\pi\)
\(524\) 6.90931 11.9673i 0.301835 0.522793i
\(525\) 4.52243 + 0.740015i 0.197375 + 0.0322969i
\(526\) −2.40150 4.15951i −0.104710 0.181363i
\(527\) −4.69956 + 8.13987i −0.204716 + 0.354578i
\(528\) 0.304613 0.582010i 0.0132566 0.0253287i
\(529\) 7.74389 + 13.4128i 0.336691 + 0.583166i
\(530\) −0.998199 1.72893i −0.0433590 0.0751000i
\(531\) −0.296624 + 0.628835i −0.0128724 + 0.0272891i
\(532\) −9.04192 + 10.1604i −0.392017 + 0.440511i
\(533\) −2.24205 + 3.88335i −0.0971140 + 0.168206i
\(534\) 10.0662 19.2329i 0.435605 0.832290i
\(535\) 4.63777 0.200508
\(536\) −13.4063 −0.579063
\(537\) 6.48652 0.268834i 0.279914 0.0116011i
\(538\) 4.56270 7.90283i 0.196712 0.340715i
\(539\) 2.43774 + 1.05151i 0.105001 + 0.0452916i
\(540\) −2.02029 + 4.78732i −0.0869395 + 0.206013i
\(541\) −14.7606 25.5662i −0.634609 1.09918i −0.986598 0.163171i \(-0.947828\pi\)
0.351989 0.936004i \(-0.385506\pi\)
\(542\) 13.2680 + 22.9808i 0.569909 + 0.987112i
\(543\) 18.1139 + 28.5724i 0.777341 + 1.22616i
\(544\) 1.97521 3.42117i 0.0846866 0.146682i
\(545\) −6.78033 11.7439i −0.290437 0.503052i
\(546\) −2.78678 0.456007i −0.119263 0.0195153i
\(547\) 10.2744 17.7958i 0.439301 0.760892i −0.558334 0.829616i \(-0.688559\pi\)
0.997636 + 0.0687237i \(0.0218927\pi\)
\(548\) −4.66480 8.07967i −0.199270 0.345147i
\(549\) 14.7641 31.2995i 0.630117 1.33583i
\(550\) 0.189632 0.328453i 0.00808594 0.0140053i
\(551\) 37.9860 1.61826
\(552\) 4.74320 0.196583i 0.201884 0.00836711i
\(553\) 5.02268 + 15.1573i 0.213586 + 0.644554i
\(554\) −1.17060 2.02754i −0.0497342 0.0861421i
\(555\) 7.40110 + 11.6743i 0.314159 + 0.495547i
\(556\) −4.87554 8.44469i −0.206769 0.358135i
\(557\) −12.1130 + 20.9803i −0.513243 + 0.888963i 0.486639 + 0.873603i \(0.338223\pi\)
−0.999882 + 0.0153595i \(0.995111\pi\)
\(558\) 3.04515 6.45563i 0.128911 0.273289i
\(559\) 3.17349 0.134224
\(560\) 2.59109 + 0.535003i 0.109494 + 0.0226080i
\(561\) 1.38948 + 2.19173i 0.0586638 + 0.0925348i
\(562\) −8.99372 + 15.5776i −0.379377 + 0.657100i
\(563\) −14.5914 −0.614954 −0.307477 0.951556i \(-0.599485\pi\)
−0.307477 + 0.951556i \(0.599485\pi\)
\(564\) 6.90454 + 10.8910i 0.290734 + 0.458596i
\(565\) −15.5761 −0.655291
\(566\) 7.92530 0.333125
\(567\) 12.6793 20.1553i 0.532481 0.846442i
\(568\) 11.2870 0.473590
\(569\) 6.71655 0.281572 0.140786 0.990040i \(-0.455037\pi\)
0.140786 + 0.990040i \(0.455037\pi\)
\(570\) −4.76751 7.52014i −0.199689 0.314984i
\(571\) −35.8252 −1.49924 −0.749619 0.661870i \(-0.769763\pi\)
−0.749619 + 0.661870i \(0.769763\pi\)
\(572\) −0.116854 + 0.202397i −0.00488590 + 0.00846263i
\(573\) 7.17472 + 11.3172i 0.299728 + 0.472783i
\(574\) −12.7991 + 14.3824i −0.534225 + 0.600310i
\(575\) 2.74084 0.114301
\(576\) −1.27987 + 2.71329i −0.0533279 + 0.113054i
\(577\) −5.90753 + 10.2321i −0.245934 + 0.425970i −0.962394 0.271659i \(-0.912428\pi\)
0.716460 + 0.697628i \(0.245761\pi\)
\(578\) −0.697058 1.20734i −0.0289938 0.0502187i
\(579\) 1.11518 + 1.75906i 0.0463454 + 0.0731040i
\(580\) −3.69460 6.39923i −0.153410 0.265714i
\(581\) 22.2390 + 4.59186i 0.922630 + 0.190503i
\(582\) 2.74163 0.113627i 0.113644 0.00471000i
\(583\) 0.757163 0.0313585
\(584\) 3.58534 6.20999i 0.148362 0.256971i
\(585\) 0.788672 1.67196i 0.0326076 0.0691271i
\(586\) −13.3538 23.1294i −0.551639 0.955466i
\(587\) −7.21091 + 12.4897i −0.297626 + 0.515503i −0.975592 0.219590i \(-0.929528\pi\)
0.677966 + 0.735093i \(0.262862\pi\)
\(588\) −11.3221 4.33696i −0.466917 0.178853i
\(589\) 6.11559 + 10.5925i 0.251989 + 0.436457i
\(590\) −0.115881 + 0.200711i −0.00477073 + 0.00826314i
\(591\) −16.9565 26.7467i −0.697496 1.10021i
\(592\) 3.99026 + 6.91133i 0.163998 + 0.284054i
\(593\) −15.5047 26.8549i −0.636701 1.10280i −0.986152 0.165844i \(-0.946965\pi\)
0.349451 0.936955i \(-0.386368\pi\)
\(594\) −1.18929 1.57140i −0.0487974 0.0644753i
\(595\) −6.94830 + 7.80783i −0.284853 + 0.320090i
\(596\) 3.12699 5.41611i 0.128087 0.221853i
\(597\) −15.0287 + 0.622865i −0.615083 + 0.0254922i
\(598\) −1.68894 −0.0690659
\(599\) 47.2701 1.93140 0.965701 0.259656i \(-0.0836092\pi\)
0.965701 + 0.259656i \(0.0836092\pi\)
\(600\) −0.803168 + 1.53458i −0.0327892 + 0.0626488i
\(601\) −21.3039 + 36.8994i −0.869004 + 1.50516i −0.00598892 + 0.999982i \(0.501906\pi\)
−0.863015 + 0.505178i \(0.831427\pi\)
\(602\) 13.3441 + 2.75526i 0.543866 + 0.112296i
\(603\) −17.1583 + 36.3751i −0.698740 + 1.48131i
\(604\) −10.9945 19.0431i −0.447361 0.774853i
\(605\) −5.42808 9.40171i −0.220683 0.382234i
\(606\) 9.69153 18.5171i 0.393691 0.752207i
\(607\) 0.311071 0.538791i 0.0126260 0.0218688i −0.859643 0.510895i \(-0.829314\pi\)
0.872269 + 0.489026i \(0.162648\pi\)
\(608\) −2.57037 4.45201i −0.104242 0.180553i
\(609\) 11.9730 + 31.6742i 0.485172 + 1.28350i
\(610\) 5.76782 9.99016i 0.233532 0.404490i
\(611\) −2.29387 3.97311i −0.0928002 0.160735i
\(612\) −6.75461 9.73798i −0.273039 0.393635i
\(613\) −16.3060 + 28.2428i −0.658593 + 1.14072i 0.322387 + 0.946608i \(0.395515\pi\)
−0.980980 + 0.194108i \(0.937819\pi\)
\(614\) −17.6963 −0.714165
\(615\) −6.74856 10.6450i −0.272128 0.429248i
\(616\) −0.667078 + 0.749598i −0.0268773 + 0.0302022i
\(617\) −5.77847 10.0086i −0.232632 0.402931i 0.725950 0.687748i \(-0.241401\pi\)
−0.958582 + 0.284817i \(0.908067\pi\)
\(618\) −19.8478 + 0.822595i −0.798397 + 0.0330896i
\(619\) 15.1903 + 26.3104i 0.610551 + 1.05750i 0.991148 + 0.132764i \(0.0423852\pi\)
−0.380597 + 0.924741i \(0.624281\pi\)
\(620\) 1.18963 2.06050i 0.0477768 0.0827518i
\(621\) 5.53730 13.1213i 0.222204 0.526539i
\(622\) −16.4249 −0.658580
\(623\) −22.0441 + 24.7710i −0.883177 + 0.992429i
\(624\) 0.494922 0.945624i 0.0198127 0.0378553i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 11.8959 0.475455
\(627\) 3.37408 0.139839i 0.134748 0.00558464i
\(628\) 15.9599 0.636869
\(629\) −31.5264 −1.25704
\(630\) 4.76788 6.34565i 0.189957 0.252817i
\(631\) 38.4859 1.53210 0.766050 0.642781i \(-0.222219\pi\)
0.766050 + 0.642781i \(0.222219\pi\)
\(632\) −6.03527 −0.240070
\(633\) 12.1166 23.1506i 0.481591 0.920153i
\(634\) 25.7886 1.02420
\(635\) 4.28773 7.42656i 0.170153 0.294714i
\(636\) −3.45490 + 0.143189i −0.136996 + 0.00567780i
\(637\) 3.96073 + 1.70844i 0.156930 + 0.0676909i
\(638\) 2.80246 0.110950
\(639\) 14.4458 30.6248i 0.571469 1.21150i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 24.1078 + 41.7559i 0.952201 + 1.64926i 0.740647 + 0.671894i \(0.234519\pi\)
0.211553 + 0.977366i \(0.432148\pi\)
\(642\) 3.72491 7.11701i 0.147011 0.280886i
\(643\) 13.1515 + 22.7790i 0.518643 + 0.898316i 0.999765 + 0.0216625i \(0.00689593\pi\)
−0.481122 + 0.876653i \(0.659771\pi\)
\(644\) −7.10178 1.46636i −0.279849 0.0577826i
\(645\) −4.13631 + 7.90305i −0.162867 + 0.311182i
\(646\) 20.3081 0.799013
\(647\) 10.4110 18.0323i 0.409298 0.708924i −0.585514 0.810663i \(-0.699107\pi\)
0.994811 + 0.101738i \(0.0324404\pi\)
\(648\) 5.72387 + 6.94531i 0.224855 + 0.272838i
\(649\) −0.0439494 0.0761225i −0.00172516 0.00298807i
\(650\) 0.308106 0.533656i 0.0120849 0.0209317i
\(651\) −6.90483 + 8.43814i −0.270622 + 0.330717i
\(652\) −3.60765 6.24864i −0.141287 0.244716i
\(653\) 11.4960 19.9117i 0.449874 0.779205i −0.548503 0.836148i \(-0.684802\pi\)
0.998377 + 0.0569437i \(0.0181356\pi\)
\(654\) −23.4676 + 0.972617i −0.917656 + 0.0380323i
\(655\) −6.90931 11.9673i −0.269969 0.467600i
\(656\) −3.63844 6.30196i −0.142057 0.246050i
\(657\) −12.2607 17.6760i −0.478336 0.689608i
\(658\) −6.19595 18.6980i −0.241543 0.728923i
\(659\) 1.13866 1.97221i 0.0443557 0.0768263i −0.842995 0.537921i \(-0.819210\pi\)
0.887351 + 0.461095i \(0.152543\pi\)
\(660\) −0.351729 0.554808i −0.0136910 0.0215959i
\(661\) 49.2670 1.91626 0.958132 0.286326i \(-0.0924340\pi\)
0.958132 + 0.286326i \(0.0924340\pi\)
\(662\) 0.0260656 0.00101307
\(663\) 2.25756 + 3.56102i 0.0876766 + 0.138299i
\(664\) −4.29143 + 7.43298i −0.166540 + 0.288456i
\(665\) 4.27823 + 12.9107i 0.165903 + 0.500657i
\(666\) 23.8594 1.98112i 0.924534 0.0767666i
\(667\) 10.1263 + 17.5393i 0.392092 + 0.679124i
\(668\) 5.11565 + 8.86057i 0.197931 + 0.342826i
\(669\) 38.5384 1.59723i 1.48998 0.0617523i
\(670\) −6.70314 + 11.6102i −0.258965 + 0.448541i
\(671\) 2.18753 + 3.78891i 0.0844486 + 0.146269i
\(672\) 2.90209 3.54653i 0.111950 0.136810i
\(673\) 23.7608 41.1550i 0.915913 1.58641i 0.110355 0.993892i \(-0.464801\pi\)
0.805559 0.592516i \(-0.201865\pi\)
\(674\) 9.33400 + 16.1670i 0.359532 + 0.622728i
\(675\) 3.13579 + 4.14328i 0.120697 + 0.159475i
\(676\) 6.31014 10.9295i 0.242698 0.420365i
\(677\) −22.1895 −0.852813 −0.426406 0.904532i \(-0.640221\pi\)
−0.426406 + 0.904532i \(0.640221\pi\)
\(678\) −12.5102 + 23.9027i −0.480452 + 0.917977i
\(679\) −4.10492 0.847573i −0.157532 0.0325269i
\(680\) −1.97521 3.42117i −0.0757460 0.131196i
\(681\) 2.33242 4.45644i 0.0893785 0.170771i
\(682\) 0.451185 + 0.781476i 0.0172768 + 0.0299242i
\(683\) 9.12399 15.8032i 0.349120 0.604693i −0.636974 0.770886i \(-0.719814\pi\)
0.986093 + 0.166192i \(0.0531473\pi\)
\(684\) −15.3693 + 1.27616i −0.587661 + 0.0487952i
\(685\) −9.32960 −0.356466
\(686\) 15.1711 + 10.6225i 0.579235 + 0.405570i
\(687\) −25.6279 + 1.06215i −0.977766 + 0.0405236i
\(688\) −2.57500 + 4.46002i −0.0981708 + 0.170037i
\(689\) 1.23021 0.0468671
\(690\) 2.20136 4.20603i 0.0838042 0.160121i
\(691\) −26.5381 −1.00956 −0.504779 0.863248i \(-0.668426\pi\)
−0.504779 + 0.863248i \(0.668426\pi\)
\(692\) 4.25750 0.161846
\(693\) 1.18010 + 2.76936i 0.0448284 + 0.105199i
\(694\) 33.8993 1.28680
\(695\) −9.75109 −0.369880
\(696\) −12.7875 + 0.529979i −0.484709 + 0.0200888i
\(697\) 28.7468 1.08886
\(698\) −3.64339 + 6.31054i −0.137904 + 0.238858i
\(699\) −15.4808 + 29.5785i −0.585539 + 1.11876i
\(700\) 1.75887 1.97645i 0.0664792 0.0747029i
\(701\) −11.5095 −0.434708 −0.217354 0.976093i \(-0.569743\pi\)
−0.217354 + 0.976093i \(0.569743\pi\)
\(702\) −1.93231 2.55314i −0.0729305 0.0963622i
\(703\) −20.5129 + 35.5293i −0.773658 + 1.34001i
\(704\) −0.189632 0.328453i −0.00714703 0.0123790i
\(705\) 12.8842 0.533986i 0.485247 0.0201111i
\(706\) 2.78042 + 4.81582i 0.104642 + 0.181246i
\(707\) −21.2237 + 23.8491i −0.798198 + 0.896938i
\(708\) 0.214934 + 0.339032i 0.00807773 + 0.0127416i
\(709\) −13.2023 −0.495825 −0.247912 0.968782i \(-0.579744\pi\)
−0.247912 + 0.968782i \(0.579744\pi\)
\(710\) 5.64348 9.77479i 0.211796 0.366841i
\(711\) −7.72436 + 16.3754i −0.289686 + 0.614126i
\(712\) −6.26653 10.8540i −0.234848 0.406769i
\(713\) −3.26059 + 5.64751i −0.122110 + 0.211501i
\(714\) 6.40105 + 16.9337i 0.239553 + 0.633728i
\(715\) 0.116854 + 0.202397i 0.00437008 + 0.00756920i
\(716\) 1.87410 3.24604i 0.0700385 0.121310i
\(717\) −8.69815 + 16.6191i −0.324838 + 0.620653i
\(718\) −0.698378 1.20963i −0.0260632 0.0451428i
\(719\) 21.8952 + 37.9237i 0.816555 + 1.41431i 0.908206 + 0.418523i \(0.137452\pi\)
−0.0916513 + 0.995791i \(0.529215\pi\)
\(720\) 1.70984 + 2.46504i 0.0637220 + 0.0918668i
\(721\) 29.7172 + 6.13594i 1.10673 + 0.228514i
\(722\) 3.71361 6.43217i 0.138206 0.239381i
\(723\) −5.61145 + 10.7215i −0.208692 + 0.398738i
\(724\) 19.5320 0.725899
\(725\) −7.38920 −0.274428
\(726\) −18.7873 + 0.778641i −0.697262 + 0.0288981i
\(727\) 14.4786 25.0776i 0.536980 0.930076i −0.462085 0.886836i \(-0.652898\pi\)
0.999065 0.0432406i \(-0.0137682\pi\)
\(728\) −1.08384 + 1.21791i −0.0401698 + 0.0451389i
\(729\) 26.1704 6.64140i 0.969275 0.245978i
\(730\) −3.58534 6.20999i −0.132699 0.229842i
\(731\) −10.1723 17.6190i −0.376237 0.651662i
\(732\) −10.6981 16.8749i −0.395414 0.623715i
\(733\) −17.8667 + 30.9460i −0.659920 + 1.14302i 0.320715 + 0.947176i \(0.396077\pi\)
−0.980636 + 0.195840i \(0.937257\pi\)
\(734\) −14.0446 24.3260i −0.518396 0.897888i
\(735\) −9.41699 + 7.63677i −0.347351 + 0.281687i
\(736\) 1.37042 2.37364i 0.0505144 0.0874935i
\(737\) −2.54226 4.40333i −0.0936455 0.162199i
\(738\) −21.7558 + 1.80644i −0.800841 + 0.0664961i
\(739\) 5.27465 9.13596i 0.194031 0.336072i −0.752551 0.658534i \(-0.771177\pi\)
0.946582 + 0.322462i \(0.104510\pi\)
\(740\) 7.98051 0.293369
\(741\) 5.48206 0.227205i 0.201389 0.00834657i
\(742\) 5.17286 + 1.06808i 0.189902 + 0.0392104i
\(743\) −9.55767 16.5544i −0.350637 0.607321i 0.635724 0.771916i \(-0.280702\pi\)
−0.986361 + 0.164595i \(0.947368\pi\)
\(744\) −2.20652 3.48051i −0.0808950 0.127602i
\(745\) −3.12699 5.41611i −0.114564 0.198431i
\(746\) 5.61261 9.72133i 0.205492 0.355923i
\(747\) 14.6753 + 21.1572i 0.536943 + 0.774100i
\(748\) 1.49826 0.0547817
\(749\) −8.15726 + 9.16634i −0.298060 + 0.334931i
\(750\) 0.927397 + 1.46285i 0.0338637 + 0.0534158i
\(751\) −5.66425 + 9.81078i −0.206692 + 0.358000i −0.950670 0.310203i \(-0.899603\pi\)
0.743979 + 0.668203i \(0.232936\pi\)
\(752\) 7.44508 0.271494
\(753\) 16.1546 + 25.4819i 0.588708 + 0.928612i
\(754\) 4.55332 0.165822
\(755\) −21.9891 −0.800264
\(756\) −5.90847 12.4133i −0.214889 0.451467i
\(757\) 11.7276 0.426248 0.213124 0.977025i \(-0.431636\pi\)
0.213124 + 0.977025i \(0.431636\pi\)
\(758\) 13.2661 0.481847
\(759\) 0.964032 + 1.52064i 0.0349922 + 0.0551957i
\(760\) −5.14074 −0.186474
\(761\) 1.80014 3.11794i 0.0652551 0.113025i −0.831552 0.555447i \(-0.812547\pi\)
0.896807 + 0.442422i \(0.145881\pi\)
\(762\) −7.95285 12.5446i −0.288101 0.454443i
\(763\) 35.1370 + 7.25499i 1.27204 + 0.262648i
\(764\) 7.73641 0.279893
\(765\) −11.8106 + 0.980671i −0.427015 + 0.0354562i
\(766\) 8.76220 15.1766i 0.316591 0.548352i
\(767\) −0.0714070 0.123681i −0.00257836 0.00446585i
\(768\) 0.927397 + 1.46285i 0.0334646 + 0.0527861i
\(769\) −19.2146 33.2806i −0.692896 1.20013i −0.970885 0.239546i \(-0.923001\pi\)
0.277989 0.960584i \(-0.410332\pi\)
\(770\) 0.315632 + 0.952506i 0.0113746 + 0.0343259i
\(771\) −22.6947 + 0.940584i −0.817330 + 0.0338743i
\(772\) 1.20249 0.0432784
\(773\) 12.7904 22.1536i 0.460038 0.796810i −0.538924 0.842354i \(-0.681169\pi\)
0.998962 + 0.0455446i \(0.0145023\pi\)
\(774\) 8.80567 + 12.6950i 0.316513 + 0.456311i
\(775\) −1.18963 2.06050i −0.0427329 0.0740155i
\(776\) 0.792120 1.37199i 0.0284354 0.0492516i
\(777\) −36.0913 5.90570i −1.29477 0.211866i
\(778\) 4.71220 + 8.16178i 0.168941 + 0.292614i
\(779\) 18.7043 32.3968i 0.670150 1.16073i
\(780\) −0.571473 0.901427i −0.0204620 0.0322763i
\(781\) 2.14037 + 3.70723i 0.0765885 + 0.132655i
\(782\) 5.41375 + 9.37689i 0.193595 + 0.335317i
\(783\) −14.9283 + 35.3745i −0.533495 + 1.26418i
\(784\) −5.61482 + 4.18017i −0.200529 + 0.149292i
\(785\) 7.97995 13.8217i 0.284817 0.493317i
\(786\) −23.9140 + 0.991119i −0.852985 + 0.0353520i
\(787\) −36.3100 −1.29431 −0.647155 0.762358i \(-0.724041\pi\)
−0.647155 + 0.762358i \(0.724041\pi\)
\(788\) −18.2839 −0.651339
\(789\) −3.85761 + 7.37055i −0.137335 + 0.262399i
\(790\) −3.01763 + 5.22670i −0.107363 + 0.185958i
\(791\) 27.3964 30.7854i 0.974103 1.09460i
\(792\) −1.13389 + 0.0941502i −0.0402911 + 0.00334548i
\(793\) 3.55420 + 6.15606i 0.126213 + 0.218608i
\(794\) −3.03378 5.25466i −0.107665 0.186481i
\(795\) −1.60344 + 3.06362i −0.0568683 + 0.108656i
\(796\) −4.34213 + 7.52079i −0.153903 + 0.266567i
\(797\) −25.0226 43.3404i −0.886345 1.53520i −0.844164 0.536085i \(-0.819903\pi\)
−0.0421813 0.999110i \(-0.513431\pi\)
\(798\) 23.2486 + 3.80423i 0.822993 + 0.134668i
\(799\) −14.7056 + 25.4709i −0.520247 + 0.901095i
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −37.4702 + 3.11126i −1.32395 + 0.109931i
\(802\) −19.5894 + 33.9298i −0.691724 + 1.19810i
\(803\) 2.71958 0.0959720
\(804\) 12.4329 + 19.6114i 0.438476 + 0.691641i
\(805\) −4.82079 + 5.41714i −0.169911 + 0.190929i
\(806\) 0.733066 + 1.26971i 0.0258212 + 0.0447235i
\(807\) −15.7921 + 0.654505i −0.555908 + 0.0230397i
\(808\) −6.03331 10.4500i −0.212251 0.367630i
\(809\) 19.2324 33.3115i 0.676175 1.17117i −0.299949 0.953955i \(-0.596970\pi\)
0.976124 0.217215i \(-0.0696971\pi\)
\(810\) 8.87675 1.48436i 0.311897 0.0521550i
\(811\) −3.66567 −0.128719 −0.0643595 0.997927i \(-0.520500\pi\)
−0.0643595 + 0.997927i \(0.520500\pi\)
\(812\) 19.1461 + 3.95324i 0.671897 + 0.138732i
\(813\) 21.3129 40.7215i 0.747475 1.42816i
\(814\) −1.51336 + 2.62122i −0.0530433 + 0.0918737i
\(815\) −7.21531 −0.252741
\(816\) −6.83647 + 0.283338i −0.239324 + 0.00991882i
\(817\) −26.4748 −0.926235
\(818\) −0.807364 −0.0282288
\(819\) 1.91738 + 4.49954i 0.0669986 + 0.157227i
\(820\) −7.27688 −0.254120
\(821\) −49.6735 −1.73362 −0.866809 0.498640i \(-0.833833\pi\)
−0.866809 + 0.498640i \(0.833833\pi\)
\(822\) −7.49324 + 14.3170i −0.261357 + 0.499362i
\(823\) −23.4653 −0.817949 −0.408974 0.912546i \(-0.634113\pi\)
−0.408974 + 0.912546i \(0.634113\pi\)
\(824\) −5.73449 + 9.93243i −0.199770 + 0.346013i
\(825\) −0.656342 + 0.0272021i −0.0228509 + 0.000947057i
\(826\) −0.192876 0.582058i −0.00671103 0.0202524i
\(827\) −7.31763 −0.254459 −0.127230 0.991873i \(-0.540608\pi\)
−0.127230 + 0.991873i \(0.540608\pi\)
\(828\) −4.68640 6.75630i −0.162864 0.234797i
\(829\) −3.79583 + 6.57457i −0.131835 + 0.228344i −0.924384 0.381464i \(-0.875420\pi\)
0.792549 + 0.609808i \(0.208753\pi\)
\(830\) 4.29143 + 7.43298i 0.148958 + 0.258003i
\(831\) −1.88038 + 3.59276i −0.0652298 + 0.124631i
\(832\) −0.308106 0.533656i −0.0106817 0.0185012i
\(833\) −3.21062 27.4660i −0.111241 0.951640i
\(834\) −7.83176 + 14.9638i −0.271192 + 0.518153i
\(835\) 10.2313 0.354069
\(836\) 0.974850 1.68849i 0.0337159 0.0583977i
\(837\) −12.2677 + 1.53233i −0.424033 + 0.0529651i
\(838\) −15.1172 26.1838i −0.522216 0.904504i
\(839\) −24.3324 + 42.1449i −0.840047 + 1.45500i 0.0498072 + 0.998759i \(0.484139\pi\)
−0.889854 + 0.456245i \(0.849194\pi\)
\(840\) −1.62034 4.28655i −0.0559071 0.147900i
\(841\) −12.8001 22.1705i −0.441384 0.764499i
\(842\) 13.5938 23.5451i 0.468472 0.811417i
\(843\) 31.1284 1.29012i 1.07212 0.0444341i
\(844\) −7.54299 13.0648i −0.259640 0.449711i
\(845\) −6.31014 10.9295i −0.217075 0.375986i
\(846\) 9.52873 20.2006i 0.327604 0.694512i
\(847\) 28.1293 + 5.80808i 0.966535 + 0.199568i
\(848\) −0.998199 + 1.72893i −0.0342783 + 0.0593718i
\(849\) −7.34990 11.5935i −0.252248 0.397889i
\(850\) −3.95043 −0.135499
\(851\) −21.8733 −0.749808
\(852\) −10.4675 16.5111i −0.358610 0.565663i
\(853\) 17.4299 30.1895i 0.596790 1.03367i −0.396502 0.918034i \(-0.629776\pi\)
0.993292 0.115636i \(-0.0368907\pi\)
\(854\) 9.60021 + 28.9713i 0.328512 + 0.991376i
\(855\) −6.57948 + 13.9483i −0.225014 + 0.477022i
\(856\) −2.31889 4.01643i −0.0792579 0.137279i
\(857\) −8.06035 13.9609i −0.275336 0.476896i 0.694884 0.719122i \(-0.255456\pi\)
−0.970220 + 0.242226i \(0.922122\pi\)
\(858\) 0.404446 0.0167623i 0.0138076 0.000572255i
\(859\) −2.93110 + 5.07681i −0.100008 + 0.173218i −0.911688 0.410884i \(-0.865220\pi\)
0.811680 + 0.584103i \(0.198553\pi\)
\(860\) 2.57500 + 4.46002i 0.0878066 + 0.152086i
\(861\) 32.9092 + 5.38500i 1.12154 + 0.183520i
\(862\) 18.3346 31.7564i 0.624478 1.08163i
\(863\) 5.81678 + 10.0750i 0.198006 + 0.342956i 0.947882 0.318623i \(-0.103220\pi\)
−0.749876 + 0.661578i \(0.769887\pi\)
\(864\) 5.15609 0.644035i 0.175414 0.0219105i
\(865\) 2.12875 3.68710i 0.0723797 0.125365i
\(866\) 24.3601 0.827790
\(867\) −1.11971 + 2.13938i −0.0380273 + 0.0726570i
\(868\) 1.98007 + 5.97542i 0.0672081 + 0.202819i
\(869\) −1.14448 1.98230i −0.0388239 0.0672449i
\(870\) −5.93477 + 11.3393i −0.201208 + 0.384438i
\(871\) −4.13056 7.15434i −0.139959 0.242416i
\(872\) −6.78033 + 11.7439i −0.229611 + 0.397698i
\(873\) −2.70880 3.90522i −0.0916789 0.132172i
\(874\) 14.0900 0.476600
\(875\) −0.832221 2.51146i −0.0281342 0.0849027i
\(876\) −12.4093 + 0.514306i −0.419272 + 0.0173768i
\(877\) −25.1865 + 43.6243i −0.850487 + 1.47309i 0.0302826 + 0.999541i \(0.490359\pi\)
−0.880770 + 0.473545i \(0.842974\pi\)
\(878\) −22.4590 −0.757956
\(879\) −21.4506 + 40.9847i −0.723512 + 1.38238i
\(880\) −0.379264 −0.0127850
\(881\) 17.7576 0.598269 0.299135 0.954211i \(-0.403302\pi\)
0.299135 + 0.954211i \(0.403302\pi\)
\(882\) 4.15578 + 20.5847i 0.139932 + 0.693123i
\(883\) 43.0049 1.44723 0.723614 0.690204i \(-0.242479\pi\)
0.723614 + 0.690204i \(0.242479\pi\)
\(884\) 2.43430 0.0818745
\(885\) 0.401078 0.0166227i 0.0134821 0.000558766i
\(886\) 18.5159 0.622055
\(887\) −17.4531 + 30.2297i −0.586018 + 1.01501i 0.408730 + 0.912655i \(0.365972\pi\)
−0.994748 + 0.102357i \(0.967362\pi\)
\(888\) 6.40969 12.2467i 0.215095 0.410972i
\(889\) 7.13667 + 21.5369i 0.239356 + 0.722323i
\(890\) −12.5331 −0.420109
\(891\) −1.19578 + 3.19707i −0.0400600 + 0.107106i
\(892\) 11.1346 19.2857i 0.372815 0.645734i
\(893\) 19.1366 + 33.1456i 0.640382 + 1.10917i
\(894\) −10.8229 + 0.448557i −0.361973 + 0.0150020i
\(895\) −1.87410 3.24604i −0.0626444 0.108503i
\(896\) −0.832221 2.51146i −0.0278026 0.0839018i
\(897\) 1.56632 + 2.47067i 0.0522978 + 0.0824932i
\(898\) 27.6845 0.923845
\(899\) 8.79043 15.2255i 0.293177 0.507798i
\(900\) 2.98971 0.248244i 0.0996570 0.00827480i
\(901\) −3.94332 6.83002i −0.131371 0.227541i
\(902\) 1.37993 2.39011i 0.0459467 0.0795820i
\(903\) −8.34475 22.0757i −0.277696 0.734633i
\(904\) 7.78805 + 13.4893i 0.259027 + 0.448647i
\(905\) 9.76598 16.9152i 0.324632 0.562279i
\(906\) −17.6609 + 33.7439i −0.586745 + 1.12107i
\(907\) 17.2147 + 29.8168i 0.571606 + 0.990051i 0.996401 + 0.0847615i \(0.0270128\pi\)
−0.424795 + 0.905290i \(0.639654\pi\)
\(908\) −1.45201 2.51496i −0.0481867 0.0834618i
\(909\) −36.0757 + 2.99547i −1.19656 + 0.0993534i
\(910\) 0.512825 + 1.54759i 0.0170000 + 0.0513021i
\(911\) 10.1847 17.6405i 0.337436 0.584456i −0.646514 0.762902i \(-0.723774\pi\)
0.983950 + 0.178446i \(0.0571071\pi\)
\(912\) −4.12888 + 7.88885i −0.136721 + 0.261226i
\(913\) −3.25518 −0.107731
\(914\) 11.3805 0.376432
\(915\) −19.9632 + 0.827376i −0.659962 + 0.0273522i
\(916\) −7.40450 + 12.8250i −0.244651 + 0.423749i
\(917\) 35.8054 + 7.39300i 1.18240 + 0.244138i
\(918\) −7.98102 + 18.9120i −0.263413 + 0.624188i
\(919\) 21.3909 + 37.0501i 0.705619 + 1.22217i 0.966468 + 0.256789i \(0.0826644\pi\)
−0.260848 + 0.965380i \(0.584002\pi\)
\(920\) −1.37042 2.37364i −0.0451814 0.0782565i
\(921\) 16.4115 + 25.8871i 0.540777 + 0.853008i
\(922\) 11.2662 19.5136i 0.371033 0.642648i
\(923\) 3.47758 + 6.02335i 0.114466 + 0.198261i
\(924\) 1.71520 + 0.280661i 0.0564258 + 0.00923309i
\(925\) 3.99026 6.91133i 0.131199 0.227243i
\(926\) 8.51644 + 14.7509i 0.279868 + 0.484745i
\(927\) 19.6101 + 28.2715i 0.644082 + 0.928560i
\(928\) −3.69460 + 6.39923i −0.121281 + 0.210065i
\(929\) 19.6430 0.644464 0.322232 0.946661i \(-0.395567\pi\)
0.322232 + 0.946661i \(0.395567\pi\)
\(930\) −4.11747 + 0.170649i −0.135017 + 0.00559580i
\(931\) −33.0423 14.2526i −1.08292 0.467111i
\(932\) 9.63735 + 16.6924i 0.315682 + 0.546777i
\(933\) 15.2324 + 24.0272i 0.498687 + 0.786616i
\(934\) −3.14018 5.43895i −0.102750 0.177968i
\(935\) 0.749128 1.29753i 0.0244991 0.0424337i
\(936\) −1.84230 + 0.152971i −0.0602174 + 0.00500002i
\(937\) 25.9493 0.847726 0.423863 0.905726i \(-0.360674\pi\)
0.423863 + 0.905726i \(0.360674\pi\)
\(938\) −11.1570 33.6693i −0.364289 1.09934i
\(939\) −11.0322 17.4019i −0.360022 0.567889i
\(940\) 3.72254 6.44763i 0.121416 0.210298i
\(941\) −6.02152 −0.196296 −0.0981479 0.995172i \(-0.531292\pi\)
−0.0981479 + 0.995172i \(0.531292\pi\)
\(942\) −14.8012 23.3470i −0.482248 0.760685i
\(943\) 19.9448 0.649491
\(944\) 0.231761 0.00754318
\(945\) −13.7045 1.08977i −0.445806 0.0354501i
\(946\) −1.95321 −0.0635043
\(947\) 48.1819 1.56570 0.782850 0.622210i \(-0.213765\pi\)
0.782850 + 0.622210i \(0.213765\pi\)
\(948\) 5.59709 + 8.82870i 0.181785 + 0.286743i
\(949\) 4.41866 0.143436
\(950\) −2.57037 + 4.45201i −0.0833938 + 0.144442i
\(951\) −23.9163 37.7249i −0.775538 1.22331i
\(952\) 10.2359 + 2.11349i 0.331749 + 0.0684986i
\(953\) −9.73496 −0.315346 −0.157673 0.987491i \(-0.550399\pi\)
−0.157673 + 0.987491i \(0.550399\pi\)
\(954\) 3.41353 + 4.92121i 0.110517 + 0.159330i
\(955\) 3.86820 6.69992i 0.125172 0.216804i
\(956\) 5.41490 + 9.37888i 0.175130 + 0.303335i
\(957\) −2.59899 4.09958i −0.0840135 0.132521i
\(958\) 1.48483 + 2.57181i 0.0479728 + 0.0830914i
\(959\) 16.4096 18.4395i 0.529893 0.595443i
\(960\) 1.73057 0.0717234i 0.0558538 0.00231486i
\(961\) −25.3391 −0.817390
\(962\) −2.45884 + 4.25884i −0.0792763 + 0.137311i
\(963\) −13.8656 + 1.15130i −0.446813 + 0.0371001i
\(964\) 3.49332 + 6.05061i 0.112512 + 0.194877i
\(965\) 0.601243 1.04138i 0.0193547 0.0335233i
\(966\) 4.44110 + 11.7487i 0.142890 + 0.378010i
\(967\) 5.59665 + 9.69367i 0.179976 + 0.311728i 0.941872 0.335972i \(-0.109065\pi\)
−0.761896 + 0.647699i \(0.775731\pi\)
\(968\) −5.42808 + 9.40171i −0.174465 + 0.302182i
\(969\) −18.8337 29.7078i −0.605026 0.954352i
\(970\) −0.792120 1.37199i −0.0254334 0.0440520i
\(971\) 27.9680 + 48.4420i 0.897535 + 1.55458i 0.830635 + 0.556817i \(0.187977\pi\)
0.0668998 + 0.997760i \(0.478689\pi\)
\(972\) 4.85167 14.8142i 0.155617 0.475167i
\(973\) 17.1509 19.2726i 0.549834 0.617850i
\(974\) −7.50526 + 12.9995i −0.240484 + 0.416531i
\(975\) −1.06640 + 0.0441969i −0.0341520 + 0.00141543i
\(976\) −11.5356 −0.369247
\(977\) −51.9665 −1.66256 −0.831279 0.555856i \(-0.812391\pi\)
−0.831279 + 0.555856i \(0.812391\pi\)
\(978\) −5.79511 + 11.0724i −0.185307 + 0.354057i
\(979\) 2.37667 4.11652i 0.0759588 0.131564i
\(980\) 0.812728 + 6.95266i 0.0259616 + 0.222095i
\(981\) 23.1866 + 33.4276i 0.740290 + 1.06726i
\(982\) 6.41840 + 11.1170i 0.204819 + 0.354758i
\(983\) 7.65401 + 13.2571i 0.244125 + 0.422837i 0.961885 0.273454i \(-0.0881660\pi\)
−0.717760 + 0.696290i \(0.754833\pi\)
\(984\) −5.84456 + 11.1669i −0.186318 + 0.355988i
\(985\) −9.14197 + 15.8344i −0.291287 + 0.504525i
\(986\) −14.5953 25.2797i −0.464807 0.805070i
\(987\) −21.6063 + 26.4042i −0.687735 + 0.840455i
\(988\) 1.58389 2.74339i 0.0503904 0.0872787i
\(989\) −7.05766 12.2242i −0.224420 0.388708i
\(990\) −0.485409 + 1.02905i −0.0154273 + 0.0327055i
\(991\) 9.70464 16.8089i 0.308278 0.533953i −0.669708 0.742625i \(-0.733581\pi\)
0.977986 + 0.208672i \(0.0669140\pi\)
\(992\) −2.37926 −0.0755417
\(993\) −0.0241731 0.0381301i −0.000767111 0.00121002i
\(994\) 9.39325 + 28.3467i 0.297936 + 0.899103i
\(995\) 4.34213 + 7.52079i 0.137655 + 0.238425i
\(996\) 14.8532 0.615593i 0.470642 0.0195058i
\(997\) −4.95260 8.57815i −0.156850 0.271673i 0.776881 0.629648i \(-0.216801\pi\)
−0.933731 + 0.357975i \(0.883467\pi\)
\(998\) −11.6783 + 20.2273i −0.369669 + 0.640285i
\(999\) −25.0252 33.0655i −0.791763 1.04615i
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 630.2.i.i.151.6 yes 16
3.2 odd 2 1890.2.i.i.991.5 16
7.2 even 3 630.2.l.i.331.1 yes 16
9.4 even 3 630.2.l.i.571.1 yes 16
9.5 odd 6 1890.2.l.i.361.1 16
21.2 odd 6 1890.2.l.i.1801.1 16
63.23 odd 6 1890.2.i.i.1171.5 16
63.58 even 3 inner 630.2.i.i.121.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.i.i.121.6 16 63.58 even 3 inner
630.2.i.i.151.6 yes 16 1.1 even 1 trivial
630.2.l.i.331.1 yes 16 7.2 even 3
630.2.l.i.571.1 yes 16 9.4 even 3
1890.2.i.i.991.5 16 3.2 odd 2
1890.2.i.i.1171.5 16 63.23 odd 6
1890.2.l.i.361.1 16 9.5 odd 6
1890.2.l.i.1801.1 16 21.2 odd 6