Properties

Label 630.2.i.g.121.6
Level $630$
Weight $2$
Character 630.121
Analytic conductor $5.031$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} - 81 x^{3} + 567 x^{2} - 729 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.6
Root \(-0.778860 + 1.54705i\) of defining polynomial
Character \(\chi\) \(=\) 630.121
Dual form 630.2.i.g.151.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.72922 + 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.72922 + 0.0990147i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 + 0.342436i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.72922 + 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.72922 + 0.0990147i) q^{6} +(1.40545 + 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 + 0.342436i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.357242 + 0.618760i) q^{11} +(1.72922 + 0.0990147i) q^{12} +(-0.823772 + 1.42682i) q^{13} +(1.40545 + 2.24159i) q^{14} +(-0.778860 - 1.54705i) q^{15} +1.00000 q^{16} +(-1.61526 - 2.79771i) q^{17} +(2.98039 + 0.342436i) q^{18} +(-0.0769447 + 0.133272i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.20837 + 4.01536i) q^{21} +(-0.357242 + 0.618760i) q^{22} +(-1.43903 - 2.49247i) q^{23} +(1.72922 + 0.0990147i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.823772 + 1.42682i) q^{26} +(5.11984 + 0.887250i) q^{27} +(1.40545 + 2.24159i) q^{28} +(-0.602632 - 1.04379i) q^{29} +(-0.778860 - 1.54705i) q^{30} -6.40096 q^{31} +1.00000 q^{32} +(-0.679015 + 1.03460i) q^{33} +(-1.61526 - 2.79771i) q^{34} +(1.23855 - 2.33795i) q^{35} +(2.98039 + 0.342436i) q^{36} +(4.69842 - 8.13791i) q^{37} +(-0.0769447 + 0.133272i) q^{38} +(-1.56576 + 2.38571i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.09435 - 5.35958i) q^{41} +(2.20837 + 4.01536i) q^{42} +(4.80435 + 8.32137i) q^{43} +(-0.357242 + 0.618760i) q^{44} +(-1.19364 - 2.75231i) q^{45} +(-1.43903 - 2.49247i) q^{46} -6.29469 q^{47} +(1.72922 + 0.0990147i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.51612 - 4.99778i) q^{51} +(-0.823772 + 1.42682i) q^{52} +(-0.576945 - 0.999298i) q^{53} +(5.11984 + 0.887250i) q^{54} +0.714483 q^{55} +(1.40545 + 2.24159i) q^{56} +(-0.146250 + 0.222838i) q^{57} +(-0.602632 - 1.04379i) q^{58} +1.24707 q^{59} +(-0.778860 - 1.54705i) q^{60} -9.20709 q^{61} -6.40096 q^{62} +(3.42118 + 7.16209i) q^{63} +1.00000 q^{64} +1.64754 q^{65} +(-0.679015 + 1.03460i) q^{66} -12.4936 q^{67} +(-1.61526 - 2.79771i) q^{68} +(-2.24160 - 4.45251i) q^{69} +(1.23855 - 2.33795i) q^{70} -3.71448 q^{71} +(2.98039 + 0.342436i) q^{72} +(-1.45160 - 2.51424i) q^{73} +(4.69842 - 8.13791i) q^{74} +(-0.950358 + 1.44804i) q^{75} +(-0.0769447 + 0.133272i) q^{76} +(-1.88909 + 0.0688459i) q^{77} +(-1.56576 + 2.38571i) q^{78} -2.44228 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.76547 + 2.04119i) q^{81} +(3.09435 - 5.35958i) q^{82} +(2.21659 + 3.83925i) q^{83} +(2.20837 + 4.01536i) q^{84} +(-1.61526 + 2.79771i) q^{85} +(4.80435 + 8.32137i) q^{86} +(-0.938732 - 1.86461i) q^{87} +(-0.357242 + 0.618760i) q^{88} +(-5.52854 + 9.57571i) q^{89} +(-1.19364 - 2.75231i) q^{90} +(-4.35610 + 0.158753i) q^{91} +(-1.43903 - 2.49247i) q^{92} +(-11.0687 - 0.633789i) q^{93} -6.29469 q^{94} +0.153889 q^{95} +(1.72922 + 0.0990147i) q^{96} +(-4.23213 - 7.33026i) q^{97} +(-3.04944 + 6.30087i) q^{98} +(-1.27661 + 1.72182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) 1.72922 + 0.0990147i 0.998365 + 0.0571662i
\(4\) 1.00000 0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.72922 + 0.0990147i 0.705950 + 0.0404226i
\(7\) 1.40545 + 2.24159i 0.531209 + 0.847241i
\(8\) 1.00000 0.353553
\(9\) 2.98039 + 0.342436i 0.993464 + 0.114145i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −0.357242 + 0.618760i −0.107712 + 0.186563i −0.914843 0.403809i \(-0.867686\pi\)
0.807131 + 0.590373i \(0.201019\pi\)
\(12\) 1.72922 + 0.0990147i 0.499182 + 0.0285831i
\(13\) −0.823772 + 1.42682i −0.228473 + 0.395727i −0.957356 0.288911i \(-0.906707\pi\)
0.728883 + 0.684639i \(0.240040\pi\)
\(14\) 1.40545 + 2.24159i 0.375621 + 0.599090i
\(15\) −0.778860 1.54705i −0.201101 0.399448i
\(16\) 1.00000 0.250000
\(17\) −1.61526 2.79771i −0.391757 0.678543i 0.600924 0.799306i \(-0.294799\pi\)
−0.992681 + 0.120763i \(0.961466\pi\)
\(18\) 2.98039 + 0.342436i 0.702485 + 0.0807130i
\(19\) −0.0769447 + 0.133272i −0.0176523 + 0.0305747i −0.874717 0.484635i \(-0.838953\pi\)
0.857064 + 0.515209i \(0.172286\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 2.20837 + 4.01536i 0.481906 + 0.876223i
\(22\) −0.357242 + 0.618760i −0.0761641 + 0.131920i
\(23\) −1.43903 2.49247i −0.300058 0.519716i 0.676091 0.736818i \(-0.263673\pi\)
−0.976149 + 0.217103i \(0.930339\pi\)
\(24\) 1.72922 + 0.0990147i 0.352975 + 0.0202113i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.823772 + 1.42682i −0.161555 + 0.279821i
\(27\) 5.11984 + 0.887250i 0.985314 + 0.170751i
\(28\) 1.40545 + 2.24159i 0.265604 + 0.423620i
\(29\) −0.602632 1.04379i −0.111906 0.193827i 0.804633 0.593773i \(-0.202362\pi\)
−0.916539 + 0.399946i \(0.869029\pi\)
\(30\) −0.778860 1.54705i −0.142200 0.282452i
\(31\) −6.40096 −1.14965 −0.574823 0.818278i \(-0.694929\pi\)
−0.574823 + 0.818278i \(0.694929\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.679015 + 1.03460i −0.118201 + 0.180101i
\(34\) −1.61526 2.79771i −0.277014 0.479803i
\(35\) 1.23855 2.33795i 0.209353 0.395185i
\(36\) 2.98039 + 0.342436i 0.496732 + 0.0570727i
\(37\) 4.69842 8.13791i 0.772416 1.33786i −0.163819 0.986490i \(-0.552381\pi\)
0.936235 0.351374i \(-0.114285\pi\)
\(38\) −0.0769447 + 0.133272i −0.0124821 + 0.0216196i
\(39\) −1.56576 + 2.38571i −0.250722 + 0.382019i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 3.09435 5.35958i 0.483257 0.837026i −0.516558 0.856252i \(-0.672787\pi\)
0.999815 + 0.0192264i \(0.00612034\pi\)
\(42\) 2.20837 + 4.01536i 0.340759 + 0.619583i
\(43\) 4.80435 + 8.32137i 0.732656 + 1.26900i 0.955744 + 0.294199i \(0.0950530\pi\)
−0.223088 + 0.974798i \(0.571614\pi\)
\(44\) −0.357242 + 0.618760i −0.0538562 + 0.0932817i
\(45\) −1.19364 2.75231i −0.177937 0.410291i
\(46\) −1.43903 2.49247i −0.212173 0.367495i
\(47\) −6.29469 −0.918175 −0.459087 0.888391i \(-0.651824\pi\)
−0.459087 + 0.888391i \(0.651824\pi\)
\(48\) 1.72922 + 0.0990147i 0.249591 + 0.0142915i
\(49\) −3.04944 + 6.30087i −0.435635 + 0.900124i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −2.51612 4.99778i −0.352327 0.699829i
\(52\) −0.823772 + 1.42682i −0.114237 + 0.197864i
\(53\) −0.576945 0.999298i −0.0792495 0.137264i 0.823677 0.567059i \(-0.191919\pi\)
−0.902926 + 0.429795i \(0.858586\pi\)
\(54\) 5.11984 + 0.887250i 0.696722 + 0.120739i
\(55\) 0.714483 0.0963409
\(56\) 1.40545 + 2.24159i 0.187811 + 0.299545i
\(57\) −0.146250 + 0.222838i −0.0193713 + 0.0295156i
\(58\) −0.602632 1.04379i −0.0791295 0.137056i
\(59\) 1.24707 0.162354 0.0811772 0.996700i \(-0.474132\pi\)
0.0811772 + 0.996700i \(0.474132\pi\)
\(60\) −0.778860 1.54705i −0.100550 0.199724i
\(61\) −9.20709 −1.17885 −0.589423 0.807824i \(-0.700645\pi\)
−0.589423 + 0.807824i \(0.700645\pi\)
\(62\) −6.40096 −0.812922
\(63\) 3.42118 + 7.16209i 0.431028 + 0.902339i
\(64\) 1.00000 0.125000
\(65\) 1.64754 0.204353
\(66\) −0.679015 + 1.03460i −0.0835810 + 0.127350i
\(67\) −12.4936 −1.52634 −0.763170 0.646198i \(-0.776358\pi\)
−0.763170 + 0.646198i \(0.776358\pi\)
\(68\) −1.61526 2.79771i −0.195879 0.339272i
\(69\) −2.24160 4.45251i −0.269857 0.536019i
\(70\) 1.23855 2.33795i 0.148035 0.279438i
\(71\) −3.71448 −0.440828 −0.220414 0.975406i \(-0.570741\pi\)
−0.220414 + 0.975406i \(0.570741\pi\)
\(72\) 2.98039 + 0.342436i 0.351243 + 0.0403565i
\(73\) −1.45160 2.51424i −0.169896 0.294269i 0.768487 0.639866i \(-0.221010\pi\)
−0.938383 + 0.345596i \(0.887677\pi\)
\(74\) 4.69842 8.13791i 0.546181 0.946013i
\(75\) −0.950358 + 1.44804i −0.109738 + 0.167205i
\(76\) −0.0769447 + 0.133272i −0.00882616 + 0.0152874i
\(77\) −1.88909 + 0.0688459i −0.215282 + 0.00784571i
\(78\) −1.56576 + 2.38571i −0.177287 + 0.270128i
\(79\) −2.44228 −0.274778 −0.137389 0.990517i \(-0.543871\pi\)
−0.137389 + 0.990517i \(0.543871\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 8.76547 + 2.04119i 0.973942 + 0.226799i
\(82\) 3.09435 5.35958i 0.341714 0.591867i
\(83\) 2.21659 + 3.83925i 0.243303 + 0.421413i 0.961653 0.274269i \(-0.0884358\pi\)
−0.718350 + 0.695682i \(0.755102\pi\)
\(84\) 2.20837 + 4.01536i 0.240953 + 0.438111i
\(85\) −1.61526 + 2.79771i −0.175199 + 0.303454i
\(86\) 4.80435 + 8.32137i 0.518066 + 0.897317i
\(87\) −0.938732 1.86461i −0.100643 0.199907i
\(88\) −0.357242 + 0.618760i −0.0380821 + 0.0659601i
\(89\) −5.52854 + 9.57571i −0.586024 + 1.01502i 0.408723 + 0.912659i \(0.365974\pi\)
−0.994747 + 0.102365i \(0.967359\pi\)
\(90\) −1.19364 2.75231i −0.125820 0.290119i
\(91\) −4.35610 + 0.158753i −0.456643 + 0.0166419i
\(92\) −1.43903 2.49247i −0.150029 0.259858i
\(93\) −11.0687 0.633789i −1.14777 0.0657209i
\(94\) −6.29469 −0.649248
\(95\) 0.153889 0.0157887
\(96\) 1.72922 + 0.0990147i 0.176488 + 0.0101056i
\(97\) −4.23213 7.33026i −0.429707 0.744275i 0.567140 0.823622i \(-0.308050\pi\)
−0.996847 + 0.0793465i \(0.974717\pi\)
\(98\) −3.04944 + 6.30087i −0.308040 + 0.636484i
\(99\) −1.27661 + 1.72182i −0.128304 + 0.173049i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 5.82008 10.0807i 0.579120 1.00306i −0.416461 0.909154i \(-0.636730\pi\)
0.995581 0.0939111i \(-0.0299370\pi\)
\(102\) −2.51612 4.99778i −0.249133 0.494854i
\(103\) 4.24519 + 7.35289i 0.418291 + 0.724501i 0.995768 0.0919058i \(-0.0292959\pi\)
−0.577477 + 0.816407i \(0.695963\pi\)
\(104\) −0.823772 + 1.42682i −0.0807775 + 0.139911i
\(105\) 2.37321 3.92019i 0.231602 0.382571i
\(106\) −0.576945 0.999298i −0.0560378 0.0970604i
\(107\) 1.76107 3.05026i 0.170249 0.294880i −0.768258 0.640140i \(-0.778876\pi\)
0.938507 + 0.345261i \(0.112210\pi\)
\(108\) 5.11984 + 0.887250i 0.492657 + 0.0853756i
\(109\) 5.21434 + 9.03150i 0.499443 + 0.865061i 1.00000 0.000642856i \(-0.000204627\pi\)
−0.500557 + 0.865704i \(0.666871\pi\)
\(110\) 0.714483 0.0681233
\(111\) 8.93037 13.6070i 0.847633 1.29152i
\(112\) 1.40545 + 2.24159i 0.132802 + 0.211810i
\(113\) −2.85715 + 4.94874i −0.268779 + 0.465538i −0.968547 0.248832i \(-0.919953\pi\)
0.699768 + 0.714370i \(0.253287\pi\)
\(114\) −0.146250 + 0.222838i −0.0136976 + 0.0208707i
\(115\) −1.43903 + 2.49247i −0.134190 + 0.232424i
\(116\) −0.602632 1.04379i −0.0559530 0.0969134i
\(117\) −2.94376 + 3.97038i −0.272150 + 0.367062i
\(118\) 1.24707 0.114802
\(119\) 4.00115 7.55276i 0.366785 0.692361i
\(120\) −0.778860 1.54705i −0.0710999 0.141226i
\(121\) 5.24476 + 9.08419i 0.476796 + 0.825835i
\(122\) −9.20709 −0.833570
\(123\) 5.88149 8.96150i 0.530316 0.808031i
\(124\) −6.40096 −0.574823
\(125\) 1.00000 0.0894427
\(126\) 3.42118 + 7.16209i 0.304783 + 0.638050i
\(127\) 9.02973 0.801259 0.400629 0.916240i \(-0.368792\pi\)
0.400629 + 0.916240i \(0.368792\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.48383 + 14.8652i 0.658914 + 1.30881i
\(130\) 1.64754 0.144499
\(131\) −9.17401 15.8899i −0.801537 1.38830i −0.918604 0.395179i \(-0.870682\pi\)
0.117067 0.993124i \(-0.462651\pi\)
\(132\) −0.679015 + 1.03460i −0.0591007 + 0.0900504i
\(133\) −0.406883 + 0.0148284i −0.0352812 + 0.00128579i
\(134\) −12.4936 −1.07928
\(135\) −1.79154 4.87754i −0.154191 0.419792i
\(136\) −1.61526 2.79771i −0.138507 0.239901i
\(137\) 8.94199 15.4880i 0.763966 1.32323i −0.176825 0.984242i \(-0.556583\pi\)
0.940791 0.338986i \(-0.110084\pi\)
\(138\) −2.24160 4.45251i −0.190818 0.379023i
\(139\) −0.436114 + 0.755372i −0.0369907 + 0.0640698i −0.883928 0.467623i \(-0.845111\pi\)
0.846937 + 0.531693i \(0.178444\pi\)
\(140\) 1.23855 2.33795i 0.104677 0.197593i
\(141\) −10.8849 0.623267i −0.916673 0.0524886i
\(142\) −3.71448 −0.311712
\(143\) −0.588571 1.01944i −0.0492188 0.0852495i
\(144\) 2.98039 + 0.342436i 0.248366 + 0.0285364i
\(145\) −0.602632 + 1.04379i −0.0500459 + 0.0866820i
\(146\) −1.45160 2.51424i −0.120135 0.208080i
\(147\) −5.89703 + 10.5936i −0.486379 + 0.873748i
\(148\) 4.69842 8.13791i 0.386208 0.668932i
\(149\) −0.571398 0.989690i −0.0468107 0.0810786i 0.841671 0.539991i \(-0.181572\pi\)
−0.888481 + 0.458913i \(0.848239\pi\)
\(150\) −0.950358 + 1.44804i −0.0775964 + 0.118232i
\(151\) 0.158200 0.274011i 0.0128741 0.0222987i −0.859517 0.511108i \(-0.829235\pi\)
0.872391 + 0.488809i \(0.162569\pi\)
\(152\) −0.0769447 + 0.133272i −0.00624104 + 0.0108098i
\(153\) −3.85606 8.89138i −0.311744 0.718826i
\(154\) −1.88909 + 0.0688459i −0.152227 + 0.00554776i
\(155\) 3.20048 + 5.54339i 0.257069 + 0.445256i
\(156\) −1.56576 + 2.38571i −0.125361 + 0.191010i
\(157\) −13.7530 −1.09761 −0.548805 0.835950i \(-0.684917\pi\)
−0.548805 + 0.835950i \(0.684917\pi\)
\(158\) −2.44228 −0.194297
\(159\) −0.898718 1.78513i −0.0712730 0.141570i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 3.56462 6.72874i 0.280931 0.530299i
\(162\) 8.76547 + 2.04119i 0.688681 + 0.160371i
\(163\) 2.04615 3.54404i 0.160267 0.277590i −0.774698 0.632332i \(-0.782098\pi\)
0.934964 + 0.354742i \(0.115431\pi\)
\(164\) 3.09435 5.35958i 0.241628 0.418513i
\(165\) 1.23550 + 0.0707444i 0.0961833 + 0.00550744i
\(166\) 2.21659 + 3.83925i 0.172041 + 0.297984i
\(167\) 3.13912 5.43712i 0.242913 0.420737i −0.718630 0.695393i \(-0.755230\pi\)
0.961543 + 0.274656i \(0.0885638\pi\)
\(168\) 2.20837 + 4.01536i 0.170380 + 0.309791i
\(169\) 5.14280 + 8.90759i 0.395600 + 0.685199i
\(170\) −1.61526 + 2.79771i −0.123884 + 0.214574i
\(171\) −0.274963 + 0.370855i −0.0210269 + 0.0283600i
\(172\) 4.80435 + 8.32137i 0.366328 + 0.634499i
\(173\) −15.1441 −1.15139 −0.575694 0.817665i \(-0.695268\pi\)
−0.575694 + 0.817665i \(0.695268\pi\)
\(174\) −0.938732 1.86461i −0.0711651 0.141356i
\(175\) −2.64400 + 0.0963576i −0.199867 + 0.00728395i
\(176\) −0.357242 + 0.618760i −0.0269281 + 0.0466408i
\(177\) 2.15645 + 0.123478i 0.162089 + 0.00928118i
\(178\) −5.52854 + 9.57571i −0.414382 + 0.717730i
\(179\) 10.3341 + 17.8993i 0.772410 + 1.33785i 0.936239 + 0.351365i \(0.114282\pi\)
−0.163829 + 0.986489i \(0.552384\pi\)
\(180\) −1.19364 2.75231i −0.0889685 0.205145i
\(181\) −24.3018 −1.80634 −0.903168 0.429288i \(-0.858765\pi\)
−0.903168 + 0.429288i \(0.858765\pi\)
\(182\) −4.35610 + 0.158753i −0.322896 + 0.0117676i
\(183\) −15.9211 0.911637i −1.17692 0.0673902i
\(184\) −1.43903 2.49247i −0.106087 0.183747i
\(185\) −9.39685 −0.690870
\(186\) −11.0687 0.633789i −0.811593 0.0464717i
\(187\) 2.30815 0.168788
\(188\) −6.29469 −0.459087
\(189\) 5.20681 + 12.7236i 0.378740 + 0.925503i
\(190\) 0.153889 0.0111643
\(191\) 17.5658 1.27102 0.635510 0.772093i \(-0.280790\pi\)
0.635510 + 0.772093i \(0.280790\pi\)
\(192\) 1.72922 + 0.0990147i 0.124796 + 0.00714577i
\(193\) 26.1637 1.88331 0.941653 0.336585i \(-0.109272\pi\)
0.941653 + 0.336585i \(0.109272\pi\)
\(194\) −4.23213 7.33026i −0.303849 0.526282i
\(195\) 2.84896 + 0.163131i 0.204019 + 0.0116821i
\(196\) −3.04944 + 6.30087i −0.217817 + 0.450062i
\(197\) −19.1886 −1.36713 −0.683564 0.729890i \(-0.739571\pi\)
−0.683564 + 0.729890i \(0.739571\pi\)
\(198\) −1.27661 + 1.72182i −0.0907244 + 0.122364i
\(199\) 12.6145 + 21.8489i 0.894216 + 1.54883i 0.834771 + 0.550597i \(0.185600\pi\)
0.0594449 + 0.998232i \(0.481067\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −21.6042 1.23705i −1.52384 0.0872550i
\(202\) 5.82008 10.0807i 0.409499 0.709274i
\(203\) 1.49278 2.81784i 0.104773 0.197774i
\(204\) −2.51612 4.99778i −0.176163 0.349914i
\(205\) −6.18871 −0.432238
\(206\) 4.24519 + 7.35289i 0.295776 + 0.512300i
\(207\) −3.43536 7.92131i −0.238774 0.550569i
\(208\) −0.823772 + 1.42682i −0.0571183 + 0.0989318i
\(209\) −0.0549757 0.0952207i −0.00380275 0.00658655i
\(210\) 2.37321 3.92019i 0.163767 0.270518i
\(211\) −10.0339 + 17.3793i −0.690763 + 1.19644i 0.280825 + 0.959759i \(0.409392\pi\)
−0.971588 + 0.236678i \(0.923941\pi\)
\(212\) −0.576945 0.999298i −0.0396247 0.0686320i
\(213\) −6.42315 0.367789i −0.440107 0.0252005i
\(214\) 1.76107 3.05026i 0.120384 0.208511i
\(215\) 4.80435 8.32137i 0.327654 0.567513i
\(216\) 5.11984 + 0.887250i 0.348361 + 0.0603697i
\(217\) −8.99620 14.3483i −0.610702 0.974027i
\(218\) 5.21434 + 9.03150i 0.353160 + 0.611690i
\(219\) −2.26118 4.49140i −0.152796 0.303500i
\(220\) 0.714483 0.0481704
\(221\) 5.32241 0.358024
\(222\) 8.93037 13.6070i 0.599367 0.913243i
\(223\) −2.32770 4.03170i −0.155875 0.269983i 0.777503 0.628880i \(-0.216486\pi\)
−0.933377 + 0.358897i \(0.883153\pi\)
\(224\) 1.40545 + 2.24159i 0.0939053 + 0.149772i
\(225\) −1.78675 + 2.40988i −0.119117 + 0.160658i
\(226\) −2.85715 + 4.94874i −0.190055 + 0.329185i
\(227\) 8.25676 14.3011i 0.548020 0.949199i −0.450390 0.892832i \(-0.648715\pi\)
0.998410 0.0563672i \(-0.0179518\pi\)
\(228\) −0.146250 + 0.222838i −0.00968565 + 0.0147578i
\(229\) 2.67044 + 4.62535i 0.176468 + 0.305651i 0.940668 0.339327i \(-0.110199\pi\)
−0.764200 + 0.644979i \(0.776866\pi\)
\(230\) −1.43903 + 2.49247i −0.0948867 + 0.164349i
\(231\) −3.27347 0.0679983i −0.215378 0.00447396i
\(232\) −0.602632 1.04379i −0.0395647 0.0685281i
\(233\) −0.625333 + 1.08311i −0.0409669 + 0.0709568i −0.885782 0.464102i \(-0.846377\pi\)
0.844815 + 0.535059i \(0.179710\pi\)
\(234\) −2.94376 + 3.97038i −0.192439 + 0.259552i
\(235\) 3.14735 + 5.45136i 0.205310 + 0.355608i
\(236\) 1.24707 0.0811772
\(237\) −4.22324 0.241822i −0.274329 0.0157080i
\(238\) 4.00115 7.55276i 0.259356 0.489573i
\(239\) 0.665842 1.15327i 0.0430698 0.0745990i −0.843687 0.536836i \(-0.819620\pi\)
0.886757 + 0.462237i \(0.152953\pi\)
\(240\) −0.778860 1.54705i −0.0502752 0.0998619i
\(241\) 8.51454 14.7476i 0.548470 0.949978i −0.449910 0.893074i \(-0.648544\pi\)
0.998380 0.0569036i \(-0.0181228\pi\)
\(242\) 5.24476 + 9.08419i 0.337146 + 0.583954i
\(243\) 14.9553 + 4.39757i 0.959384 + 0.282104i
\(244\) −9.20709 −0.589423
\(245\) 6.98143 0.509538i 0.446027 0.0325532i
\(246\) 5.88149 8.96150i 0.374990 0.571364i
\(247\) −0.126770 0.219572i −0.00806617 0.0139710i
\(248\) −6.40096 −0.406461
\(249\) 3.45283 + 6.85838i 0.218814 + 0.434632i
\(250\) 1.00000 0.0632456
\(251\) 19.1121 1.20635 0.603174 0.797610i \(-0.293903\pi\)
0.603174 + 0.797610i \(0.293903\pi\)
\(252\) 3.42118 + 7.16209i 0.215514 + 0.451169i
\(253\) 2.05632 0.129280
\(254\) 9.02973 0.566575
\(255\) −3.07014 + 4.67791i −0.192260 + 0.292942i
\(256\) 1.00000 0.0625000
\(257\) −15.5139 26.8709i −0.967733 1.67616i −0.702085 0.712093i \(-0.747747\pi\)
−0.265648 0.964070i \(-0.585586\pi\)
\(258\) 7.48383 + 14.8652i 0.465923 + 0.925465i
\(259\) 24.8452 0.905458i 1.54381 0.0562624i
\(260\) 1.64754 0.102176
\(261\) −1.43865 3.31726i −0.0890501 0.205334i
\(262\) −9.17401 15.8899i −0.566772 0.981679i
\(263\) 10.4507 18.1011i 0.644417 1.11616i −0.340019 0.940419i \(-0.610433\pi\)
0.984436 0.175745i \(-0.0562333\pi\)
\(264\) −0.679015 + 1.03460i −0.0417905 + 0.0636752i
\(265\) −0.576945 + 0.999298i −0.0354414 + 0.0613864i
\(266\) −0.406883 + 0.0148284i −0.0249476 + 0.000909188i
\(267\) −10.5082 + 16.0111i −0.643091 + 0.979863i
\(268\) −12.4936 −0.763170
\(269\) 10.4350 + 18.0740i 0.636234 + 1.10199i 0.986252 + 0.165247i \(0.0528421\pi\)
−0.350018 + 0.936743i \(0.613825\pi\)
\(270\) −1.79154 4.87754i −0.109030 0.296838i
\(271\) −6.19759 + 10.7345i −0.376477 + 0.652077i −0.990547 0.137175i \(-0.956198\pi\)
0.614070 + 0.789251i \(0.289531\pi\)
\(272\) −1.61526 2.79771i −0.0979393 0.169636i
\(273\) −7.54837 0.156799i −0.456848 0.00948990i
\(274\) 8.94199 15.4880i 0.540206 0.935664i
\(275\) −0.357242 0.618760i −0.0215425 0.0373127i
\(276\) −2.24160 4.45251i −0.134929 0.268010i
\(277\) 5.24812 9.09000i 0.315329 0.546165i −0.664179 0.747574i \(-0.731219\pi\)
0.979507 + 0.201409i \(0.0645519\pi\)
\(278\) −0.436114 + 0.755372i −0.0261564 + 0.0453042i
\(279\) −19.0774 2.19192i −1.14213 0.131227i
\(280\) 1.23855 2.33795i 0.0740175 0.139719i
\(281\) 15.8173 + 27.3964i 0.943582 + 1.63433i 0.758565 + 0.651597i \(0.225901\pi\)
0.185017 + 0.982735i \(0.440766\pi\)
\(282\) −10.8849 0.623267i −0.648186 0.0371150i
\(283\) 12.8565 0.764241 0.382120 0.924113i \(-0.375194\pi\)
0.382120 + 0.924113i \(0.375194\pi\)
\(284\) −3.71448 −0.220414
\(285\) 0.266108 + 0.0152373i 0.0157629 + 0.000902581i
\(286\) −0.588571 1.01944i −0.0348029 0.0602805i
\(287\) 16.3629 0.596329i 0.965873 0.0352002i
\(288\) 2.98039 + 0.342436i 0.175621 + 0.0201782i
\(289\) 3.28190 5.68441i 0.193053 0.334377i
\(290\) −0.602632 + 1.04379i −0.0353878 + 0.0612934i
\(291\) −6.59247 13.0947i −0.386457 0.767623i
\(292\) −1.45160 2.51424i −0.0849482 0.147135i
\(293\) −14.3055 + 24.7778i −0.835735 + 1.44754i 0.0576951 + 0.998334i \(0.481625\pi\)
−0.893430 + 0.449202i \(0.851708\pi\)
\(294\) −5.89703 + 10.5936i −0.343922 + 0.617833i
\(295\) −0.623534 1.07999i −0.0363035 0.0628796i
\(296\) 4.69842 8.13791i 0.273090 0.473006i
\(297\) −2.37802 + 2.85099i −0.137986 + 0.165431i
\(298\) −0.571398 0.989690i −0.0331002 0.0573312i
\(299\) 4.74173 0.274221
\(300\) −0.950358 + 1.44804i −0.0548690 + 0.0836026i
\(301\) −11.9008 + 22.4646i −0.685954 + 1.29484i
\(302\) 0.158200 0.274011i 0.00910340 0.0157675i
\(303\) 11.0623 16.8554i 0.635514 0.968318i
\(304\) −0.0769447 + 0.133272i −0.00441308 + 0.00764368i
\(305\) 4.60354 + 7.97357i 0.263598 + 0.456565i
\(306\) −3.85606 8.89138i −0.220436 0.508286i
\(307\) 34.6549 1.97786 0.988930 0.148382i \(-0.0474067\pi\)
0.988930 + 0.148382i \(0.0474067\pi\)
\(308\) −1.88909 + 0.0688459i −0.107641 + 0.00392286i
\(309\) 6.61282 + 13.1351i 0.376190 + 0.747229i
\(310\) 3.20048 + 5.54339i 0.181775 + 0.314843i
\(311\) 17.6573 1.00125 0.500626 0.865664i \(-0.333103\pi\)
0.500626 + 0.865664i \(0.333103\pi\)
\(312\) −1.56576 + 2.38571i −0.0886436 + 0.135064i
\(313\) 1.25714 0.0710578 0.0355289 0.999369i \(-0.488688\pi\)
0.0355289 + 0.999369i \(0.488688\pi\)
\(314\) −13.7530 −0.776127
\(315\) 4.49196 6.54387i 0.253093 0.368705i
\(316\) −2.44228 −0.137389
\(317\) −4.91403 −0.275999 −0.138000 0.990432i \(-0.544067\pi\)
−0.138000 + 0.990432i \(0.544067\pi\)
\(318\) −0.898718 1.78513i −0.0503976 0.100105i
\(319\) 0.861141 0.0482146
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 3.34729 5.10019i 0.186828 0.284665i
\(322\) 3.56462 6.72874i 0.198648 0.374978i
\(323\) 0.497142 0.0276617
\(324\) 8.76547 + 2.04119i 0.486971 + 0.113399i
\(325\) −0.823772 1.42682i −0.0456947 0.0791455i
\(326\) 2.04615 3.54404i 0.113326 0.196286i
\(327\) 8.12248 + 16.1337i 0.449174 + 0.892198i
\(328\) 3.09435 5.35958i 0.170857 0.295933i
\(329\) −8.84685 14.1101i −0.487743 0.777915i
\(330\) 1.23550 + 0.0707444i 0.0680119 + 0.00389435i
\(331\) 30.0766 1.65316 0.826579 0.562821i \(-0.190284\pi\)
0.826579 + 0.562821i \(0.190284\pi\)
\(332\) 2.21659 + 3.83925i 0.121651 + 0.210706i
\(333\) 16.7899 22.6452i 0.920079 1.24095i
\(334\) 3.13912 5.43712i 0.171765 0.297506i
\(335\) 6.24681 + 10.8198i 0.341300 + 0.591149i
\(336\) 2.20837 + 4.01536i 0.120477 + 0.219056i
\(337\) 8.27039 14.3247i 0.450517 0.780318i −0.547901 0.836543i \(-0.684573\pi\)
0.998418 + 0.0562251i \(0.0179065\pi\)
\(338\) 5.14280 + 8.90759i 0.279731 + 0.484509i
\(339\) −5.43064 + 8.27455i −0.294952 + 0.449412i
\(340\) −1.61526 + 2.79771i −0.0875996 + 0.151727i
\(341\) 2.28669 3.96066i 0.123831 0.214482i
\(342\) −0.274963 + 0.370855i −0.0148683 + 0.0200535i
\(343\) −18.4098 + 2.01993i −0.994035 + 0.109066i
\(344\) 4.80435 + 8.32137i 0.259033 + 0.448658i
\(345\) −2.73519 + 4.16754i −0.147257 + 0.224373i
\(346\) −15.1441 −0.814154
\(347\) 5.80220 0.311478 0.155739 0.987798i \(-0.450224\pi\)
0.155739 + 0.987798i \(0.450224\pi\)
\(348\) −0.938732 1.86461i −0.0503213 0.0999535i
\(349\) −12.5953 21.8157i −0.674211 1.16777i −0.976699 0.214615i \(-0.931150\pi\)
0.302487 0.953153i \(-0.402183\pi\)
\(350\) −2.64400 + 0.0963576i −0.141328 + 0.00515053i
\(351\) −5.48353 + 6.57418i −0.292689 + 0.350904i
\(352\) −0.357242 + 0.618760i −0.0190410 + 0.0329800i
\(353\) −1.97987 + 3.42924i −0.105378 + 0.182520i −0.913893 0.405956i \(-0.866939\pi\)
0.808515 + 0.588476i \(0.200272\pi\)
\(354\) 2.15645 + 0.123478i 0.114614 + 0.00656278i
\(355\) 1.85724 + 3.21684i 0.0985721 + 0.170732i
\(356\) −5.52854 + 9.57571i −0.293012 + 0.507512i
\(357\) 7.66670 12.6642i 0.405765 0.670261i
\(358\) 10.3341 + 17.8993i 0.546176 + 0.946005i
\(359\) −6.99027 + 12.1075i −0.368932 + 0.639010i −0.989399 0.145223i \(-0.953610\pi\)
0.620467 + 0.784233i \(0.286943\pi\)
\(360\) −1.19364 2.75231i −0.0629102 0.145060i
\(361\) 9.48816 + 16.4340i 0.499377 + 0.864946i
\(362\) −24.3018 −1.27727
\(363\) 8.16986 + 16.2278i 0.428807 + 0.851741i
\(364\) −4.35610 + 0.158753i −0.228322 + 0.00832094i
\(365\) −1.45160 + 2.51424i −0.0759800 + 0.131601i
\(366\) −15.9211 0.911637i −0.832207 0.0476520i
\(367\) −3.52613 + 6.10743i −0.184062 + 0.318805i −0.943260 0.332055i \(-0.892258\pi\)
0.759198 + 0.650860i \(0.225591\pi\)
\(368\) −1.43903 2.49247i −0.0750145 0.129929i
\(369\) 11.0577 14.9140i 0.575641 0.776393i
\(370\) −9.39685 −0.488519
\(371\) 1.42915 2.69773i 0.0741978 0.140059i
\(372\) −11.0687 0.633789i −0.573883 0.0328604i
\(373\) −14.5747 25.2441i −0.754649 1.30709i −0.945548 0.325481i \(-0.894474\pi\)
0.190899 0.981610i \(-0.438860\pi\)
\(374\) 2.30815 0.119351
\(375\) 1.72922 + 0.0990147i 0.0892965 + 0.00511310i
\(376\) −6.29469 −0.324624
\(377\) 1.98573 0.102270
\(378\) 5.20681 + 12.7236i 0.267810 + 0.654430i
\(379\) 31.6713 1.62684 0.813422 0.581673i \(-0.197602\pi\)
0.813422 + 0.581673i \(0.197602\pi\)
\(380\) 0.153889 0.00789436
\(381\) 15.6144 + 0.894076i 0.799948 + 0.0458049i
\(382\) 17.5658 0.898747
\(383\) −2.29736 3.97914i −0.117389 0.203325i 0.801343 0.598205i \(-0.204119\pi\)
−0.918732 + 0.394881i \(0.870786\pi\)
\(384\) 1.72922 + 0.0990147i 0.0882438 + 0.00505282i
\(385\) 1.00417 + 1.60158i 0.0511771 + 0.0816239i
\(386\) 26.1637 1.33170
\(387\) 11.4693 + 26.4461i 0.583017 + 1.34433i
\(388\) −4.23213 7.33026i −0.214854 0.372138i
\(389\) −17.0012 + 29.4470i −0.861997 + 1.49302i 0.00800198 + 0.999968i \(0.497453\pi\)
−0.869999 + 0.493054i \(0.835880\pi\)
\(390\) 2.84896 + 0.163131i 0.144263 + 0.00826047i
\(391\) −4.64880 + 8.05195i −0.235100 + 0.407205i
\(392\) −3.04944 + 6.30087i −0.154020 + 0.318242i
\(393\) −14.2905 28.3854i −0.720863 1.43185i
\(394\) −19.1886 −0.966706
\(395\) 1.22114 + 2.11508i 0.0614422 + 0.106421i
\(396\) −1.27661 + 1.72182i −0.0641519 + 0.0865245i
\(397\) 3.56605 6.17658i 0.178975 0.309994i −0.762555 0.646924i \(-0.776055\pi\)
0.941530 + 0.336930i \(0.109389\pi\)
\(398\) 12.6145 + 21.8489i 0.632306 + 1.09519i
\(399\) −0.705058 0.0146459i −0.0352970 0.000733210i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 5.20071 + 9.00790i 0.259711 + 0.449833i 0.966165 0.257927i \(-0.0830393\pi\)
−0.706453 + 0.707760i \(0.749706\pi\)
\(402\) −21.6042 1.23705i −1.07752 0.0616986i
\(403\) 5.27293 9.13298i 0.262663 0.454946i
\(404\) 5.82008 10.0807i 0.289560 0.501532i
\(405\) −2.61502 8.61172i −0.129941 0.427920i
\(406\) 1.49278 2.81784i 0.0740854 0.139847i
\(407\) 3.35694 + 5.81440i 0.166398 + 0.288209i
\(408\) −2.51612 4.99778i −0.124566 0.247427i
\(409\) 8.13727 0.402362 0.201181 0.979554i \(-0.435522\pi\)
0.201181 + 0.979554i \(0.435522\pi\)
\(410\) −6.18871 −0.305639
\(411\) 16.9962 25.8967i 0.838361 1.27739i
\(412\) 4.24519 + 7.35289i 0.209146 + 0.362251i
\(413\) 1.75269 + 2.79541i 0.0862440 + 0.137553i
\(414\) −3.43536 7.92131i −0.168839 0.389311i
\(415\) 2.21659 3.83925i 0.108808 0.188462i
\(416\) −0.823772 + 1.42682i −0.0403888 + 0.0699554i
\(417\) −0.828929 + 1.26302i −0.0405928 + 0.0618504i
\(418\) −0.0549757 0.0952207i −0.00268895 0.00465740i
\(419\) −6.88164 + 11.9194i −0.336190 + 0.582298i −0.983713 0.179748i \(-0.942472\pi\)
0.647523 + 0.762046i \(0.275805\pi\)
\(420\) 2.37321 3.92019i 0.115801 0.191285i
\(421\) −8.52205 14.7606i −0.415339 0.719389i 0.580125 0.814528i \(-0.303004\pi\)
−0.995464 + 0.0951387i \(0.969671\pi\)
\(422\) −10.0339 + 17.3793i −0.488443 + 0.846009i
\(423\) −18.7606 2.15553i −0.912174 0.104805i
\(424\) −0.576945 0.999298i −0.0280189 0.0485302i
\(425\) 3.23051 0.156703
\(426\) −6.42315 0.367789i −0.311203 0.0178194i
\(427\) −12.9401 20.6385i −0.626214 0.998767i
\(428\) 1.76107 3.05026i 0.0851244 0.147440i
\(429\) −0.916829 1.82110i −0.0442649 0.0879237i
\(430\) 4.80435 8.32137i 0.231686 0.401292i
\(431\) −3.94159 6.82703i −0.189860 0.328847i 0.755344 0.655329i \(-0.227470\pi\)
−0.945203 + 0.326482i \(0.894137\pi\)
\(432\) 5.11984 + 0.887250i 0.246329 + 0.0426878i
\(433\) 15.3356 0.736983 0.368491 0.929631i \(-0.379874\pi\)
0.368491 + 0.929631i \(0.379874\pi\)
\(434\) −8.99620 14.3483i −0.431831 0.688741i
\(435\) −1.14543 + 1.74527i −0.0549193 + 0.0836793i
\(436\) 5.21434 + 9.03150i 0.249722 + 0.432530i
\(437\) 0.442902 0.0211869
\(438\) −2.26118 4.49140i −0.108043 0.214607i
\(439\) 11.4596 0.546937 0.273469 0.961881i \(-0.411829\pi\)
0.273469 + 0.961881i \(0.411829\pi\)
\(440\) 0.714483 0.0340616
\(441\) −11.2462 + 17.7348i −0.535532 + 0.844515i
\(442\) 5.32241 0.253161
\(443\) −29.9668 −1.42377 −0.711883 0.702298i \(-0.752157\pi\)
−0.711883 + 0.702298i \(0.752157\pi\)
\(444\) 8.93037 13.6070i 0.423817 0.645760i
\(445\) 11.0571 0.524156
\(446\) −2.32770 4.03170i −0.110220 0.190907i
\(447\) −0.890077 1.76797i −0.0420992 0.0836220i
\(448\) 1.40545 + 2.24159i 0.0664011 + 0.105905i
\(449\) 3.37658 0.159351 0.0796754 0.996821i \(-0.474612\pi\)
0.0796754 + 0.996821i \(0.474612\pi\)
\(450\) −1.78675 + 2.40988i −0.0842284 + 0.113603i
\(451\) 2.21086 + 3.82933i 0.104106 + 0.180316i
\(452\) −2.85715 + 4.94874i −0.134389 + 0.232769i
\(453\) 0.300694 0.458160i 0.0141278 0.0215262i
\(454\) 8.25676 14.3011i 0.387509 0.671185i
\(455\) 2.31553 + 3.69312i 0.108554 + 0.173136i
\(456\) −0.146250 + 0.222838i −0.00684879 + 0.0104353i
\(457\) −25.0722 −1.17283 −0.586415 0.810011i \(-0.699461\pi\)
−0.586415 + 0.810011i \(0.699461\pi\)
\(458\) 2.67044 + 4.62535i 0.124782 + 0.216128i
\(459\) −5.78759 15.7569i −0.270142 0.735471i
\(460\) −1.43903 + 2.49247i −0.0670950 + 0.116212i
\(461\) 18.4429 + 31.9440i 0.858970 + 1.48778i 0.872912 + 0.487878i \(0.162229\pi\)
−0.0139415 + 0.999903i \(0.504438\pi\)
\(462\) −3.27347 0.0679983i −0.152295 0.00316357i
\(463\) 14.7697 25.5818i 0.686405 1.18889i −0.286588 0.958054i \(-0.592521\pi\)
0.972993 0.230835i \(-0.0741456\pi\)
\(464\) −0.602632 1.04379i −0.0279765 0.0484567i
\(465\) 4.98545 + 9.90263i 0.231195 + 0.459223i
\(466\) −0.625333 + 1.08311i −0.0289680 + 0.0501740i
\(467\) −17.8292 + 30.8810i −0.825035 + 1.42900i 0.0768575 + 0.997042i \(0.475511\pi\)
−0.901893 + 0.431960i \(0.857822\pi\)
\(468\) −2.94376 + 3.97038i −0.136075 + 0.183531i
\(469\) −17.5591 28.0056i −0.810805 1.29318i
\(470\) 3.14735 + 5.45136i 0.145176 + 0.251453i
\(471\) −23.7820 1.36175i −1.09582 0.0627462i
\(472\) 1.24707 0.0574009
\(473\) −6.86525 −0.315665
\(474\) −4.22324 0.241822i −0.193980 0.0111072i
\(475\) −0.0769447 0.133272i −0.00353047 0.00611495i
\(476\) 4.00115 7.55276i 0.183392 0.346180i
\(477\) −1.37733 3.17587i −0.0630634 0.145413i
\(478\) 0.665842 1.15327i 0.0304549 0.0527495i
\(479\) 7.13005 12.3496i 0.325780 0.564268i −0.655890 0.754857i \(-0.727706\pi\)
0.981670 + 0.190589i \(0.0610397\pi\)
\(480\) −0.778860 1.54705i −0.0355499 0.0706130i
\(481\) 7.74086 + 13.4076i 0.352953 + 0.611332i
\(482\) 8.51454 14.7476i 0.387827 0.671736i
\(483\) 6.83024 11.2825i 0.310787 0.513372i
\(484\) 5.24476 + 9.08419i 0.238398 + 0.412918i
\(485\) −4.23213 + 7.33026i −0.192171 + 0.332850i
\(486\) 14.9553 + 4.39757i 0.678387 + 0.199478i
\(487\) 20.1589 + 34.9163i 0.913488 + 1.58221i 0.809101 + 0.587670i \(0.199955\pi\)
0.104387 + 0.994537i \(0.466712\pi\)
\(488\) −9.20709 −0.416785
\(489\) 3.88915 5.92581i 0.175874 0.267974i
\(490\) 6.98143 0.509538i 0.315389 0.0230186i
\(491\) −5.36192 + 9.28713i −0.241980 + 0.419122i −0.961278 0.275580i \(-0.911130\pi\)
0.719298 + 0.694702i \(0.244464\pi\)
\(492\) 5.88149 8.96150i 0.265158 0.404015i
\(493\) −1.94681 + 3.37197i −0.0876799 + 0.151866i
\(494\) −0.126770 0.219572i −0.00570364 0.00987900i
\(495\) 2.12944 + 0.244665i 0.0957112 + 0.0109969i
\(496\) −6.40096 −0.287411
\(497\) −5.22051 8.32634i −0.234172 0.373488i
\(498\) 3.45283 + 6.85838i 0.154725 + 0.307332i
\(499\) −13.2928 23.0237i −0.595066 1.03068i −0.993538 0.113504i \(-0.963793\pi\)
0.398472 0.917181i \(-0.369541\pi\)
\(500\) 1.00000 0.0447214
\(501\) 5.96659 9.09115i 0.266567 0.406163i
\(502\) 19.1121 0.853016
\(503\) 14.8056 0.660147 0.330074 0.943955i \(-0.392926\pi\)
0.330074 + 0.943955i \(0.392926\pi\)
\(504\) 3.42118 + 7.16209i 0.152391 + 0.319025i
\(505\) −11.6402 −0.517980
\(506\) 2.05632 0.0914147
\(507\) 8.01104 + 15.9124i 0.355783 + 0.706694i
\(508\) 9.02973 0.400629
\(509\) −19.2566 33.3534i −0.853535 1.47837i −0.877998 0.478665i \(-0.841121\pi\)
0.0244632 0.999701i \(-0.492212\pi\)
\(510\) −3.07014 + 4.67791i −0.135948 + 0.207141i
\(511\) 3.59575 6.78751i 0.159067 0.300262i
\(512\) 1.00000 0.0441942
\(513\) −0.512191 + 0.614063i −0.0226138 + 0.0271116i
\(514\) −15.5139 26.8709i −0.684291 1.18523i
\(515\) 4.24519 7.35289i 0.187065 0.324007i
\(516\) 7.48383 + 14.8652i 0.329457 + 0.654403i
\(517\) 2.24872 3.89491i 0.0988988 0.171298i
\(518\) 24.8452 0.905458i 1.09164 0.0397835i
\(519\) −26.1875 1.49949i −1.14951 0.0658205i
\(520\) 1.64754 0.0722496
\(521\) 17.8768 + 30.9636i 0.783199 + 1.35654i 0.930069 + 0.367384i \(0.119747\pi\)
−0.146870 + 0.989156i \(0.546920\pi\)
\(522\) −1.43865 3.31726i −0.0629679 0.145193i
\(523\) −12.2253 + 21.1749i −0.534576 + 0.925912i 0.464608 + 0.885517i \(0.346195\pi\)
−0.999184 + 0.0403960i \(0.987138\pi\)
\(524\) −9.17401 15.8899i −0.400769 0.694152i
\(525\) −4.58159 0.0951713i −0.199957 0.00415362i
\(526\) 10.4507 18.1011i 0.455672 0.789247i
\(527\) 10.3392 + 17.9080i 0.450382 + 0.780084i
\(528\) −0.679015 + 1.03460i −0.0295503 + 0.0450252i
\(529\) 7.35840 12.7451i 0.319930 0.554135i
\(530\) −0.576945 + 0.999298i −0.0250609 + 0.0434067i
\(531\) 3.71675 + 0.427041i 0.161293 + 0.0185320i
\(532\) −0.406883 + 0.0148284i −0.0176406 + 0.000642893i
\(533\) 5.09809 + 8.83014i 0.220823 + 0.382476i
\(534\) −10.5082 + 16.0111i −0.454734 + 0.692868i
\(535\) −3.52213 −0.152275
\(536\) −12.4936 −0.539642
\(537\) 16.0977 + 31.9750i 0.694667 + 1.37982i
\(538\) 10.4350 + 18.0740i 0.449885 + 0.779224i
\(539\) −2.80934 4.13780i −0.121007 0.178228i
\(540\) −1.79154 4.87754i −0.0770956 0.209896i
\(541\) 0.930823 1.61223i 0.0400192 0.0693153i −0.845322 0.534257i \(-0.820591\pi\)
0.885341 + 0.464942i \(0.153925\pi\)
\(542\) −6.19759 + 10.7345i −0.266209 + 0.461088i
\(543\) −42.0230 2.40623i −1.80338 0.103261i
\(544\) −1.61526 2.79771i −0.0692535 0.119951i
\(545\) 5.21434 9.03150i 0.223358 0.386867i
\(546\) −7.54837 0.156799i −0.323040 0.00671037i
\(547\) −12.3911 21.4620i −0.529805 0.917649i −0.999396 0.0347649i \(-0.988932\pi\)
0.469591 0.882884i \(-0.344402\pi\)
\(548\) 8.94199 15.4880i 0.381983 0.661614i
\(549\) −27.4407 3.15284i −1.17114 0.134560i
\(550\) −0.357242 0.618760i −0.0152328 0.0263840i
\(551\) 0.185477 0.00790160
\(552\) −2.24160 4.45251i −0.0954089 0.189511i
\(553\) −3.43249 5.47459i −0.145964 0.232803i
\(554\) 5.24812 9.09000i 0.222971 0.386197i
\(555\) −16.2492 0.930426i −0.689740 0.0394944i
\(556\) −0.436114 + 0.755372i −0.0184954 + 0.0320349i
\(557\) 0.357368 + 0.618980i 0.0151422 + 0.0262270i 0.873497 0.486829i \(-0.161847\pi\)
−0.858355 + 0.513056i \(0.828513\pi\)
\(558\) −19.0774 2.19192i −0.807609 0.0927913i
\(559\) −15.8308 −0.669570
\(560\) 1.23855 2.33795i 0.0523383 0.0987963i
\(561\) 3.99129 + 0.228540i 0.168512 + 0.00964899i
\(562\) 15.8173 + 27.3964i 0.667213 + 1.15565i
\(563\) 19.3941 0.817362 0.408681 0.912677i \(-0.365989\pi\)
0.408681 + 0.912677i \(0.365989\pi\)
\(564\) −10.8849 0.623267i −0.458337 0.0262443i
\(565\) 5.71431 0.240403
\(566\) 12.8565 0.540400
\(567\) 7.74390 + 22.5174i 0.325213 + 0.945641i
\(568\) −3.71448 −0.155856
\(569\) −25.2785 −1.05973 −0.529864 0.848082i \(-0.677757\pi\)
−0.529864 + 0.848082i \(0.677757\pi\)
\(570\) 0.266108 + 0.0152373i 0.0111461 + 0.000638221i
\(571\) −31.3342 −1.31129 −0.655647 0.755067i \(-0.727604\pi\)
−0.655647 + 0.755067i \(0.727604\pi\)
\(572\) −0.588571 1.01944i −0.0246094 0.0426247i
\(573\) 30.3752 + 1.73928i 1.26894 + 0.0726593i
\(574\) 16.3629 0.596329i 0.682975 0.0248903i
\(575\) 2.87806 0.120023
\(576\) 2.98039 + 0.342436i 0.124183 + 0.0142682i
\(577\) −2.14572 3.71650i −0.0893277 0.154720i 0.817899 0.575361i \(-0.195139\pi\)
−0.907227 + 0.420641i \(0.861805\pi\)
\(578\) 3.28190 5.68441i 0.136509 0.236440i
\(579\) 45.2428 + 2.59059i 1.88023 + 0.107661i
\(580\) −0.602632 + 1.04379i −0.0250229 + 0.0433410i
\(581\) −5.49073 + 10.3646i −0.227794 + 0.429994i
\(582\) −6.59247 13.0947i −0.273267 0.542791i
\(583\) 0.824434 0.0341446
\(584\) −1.45160 2.51424i −0.0600675 0.104040i
\(585\) 4.91033 + 0.564179i 0.203017 + 0.0233259i
\(586\) −14.3055 + 24.7778i −0.590954 + 1.02356i
\(587\) −8.63045 14.9484i −0.356217 0.616985i 0.631109 0.775694i \(-0.282600\pi\)
−0.987325 + 0.158709i \(0.949267\pi\)
\(588\) −5.89703 + 10.5936i −0.243189 + 0.436874i
\(589\) 0.492520 0.853069i 0.0202939 0.0351501i
\(590\) −0.623534 1.07999i −0.0256705 0.0444626i
\(591\) −33.1812 1.89995i −1.36489 0.0781535i
\(592\) 4.69842 8.13791i 0.193104 0.334466i
\(593\) −3.11040 + 5.38737i −0.127729 + 0.221233i −0.922796 0.385288i \(-0.874102\pi\)
0.795067 + 0.606521i \(0.207435\pi\)
\(594\) −2.37802 + 2.85099i −0.0975712 + 0.116978i
\(595\) −8.54146 + 0.311284i −0.350166 + 0.0127614i
\(596\) −0.571398 0.989690i −0.0234054 0.0405393i
\(597\) 19.6498 + 39.0306i 0.804213 + 1.59741i
\(598\) 4.74173 0.193904
\(599\) −33.9612 −1.38762 −0.693808 0.720160i \(-0.744069\pi\)
−0.693808 + 0.720160i \(0.744069\pi\)
\(600\) −0.950358 + 1.44804i −0.0387982 + 0.0591160i
\(601\) −19.1838 33.2273i −0.782522 1.35537i −0.930468 0.366373i \(-0.880599\pi\)
0.147946 0.988995i \(-0.452734\pi\)
\(602\) −11.9008 + 22.4646i −0.485042 + 0.915589i
\(603\) −37.2359 4.27827i −1.51636 0.174225i
\(604\) 0.158200 0.274011i 0.00643707 0.0111493i
\(605\) 5.24476 9.08419i 0.213230 0.369325i
\(606\) 11.0623 16.8554i 0.449376 0.684704i
\(607\) 3.83103 + 6.63554i 0.155497 + 0.269328i 0.933240 0.359254i \(-0.116969\pi\)
−0.777743 + 0.628582i \(0.783636\pi\)
\(608\) −0.0769447 + 0.133272i −0.00312052 + 0.00540490i
\(609\) 2.86035 4.72486i 0.115907 0.191461i
\(610\) 4.60354 + 7.97357i 0.186392 + 0.322840i
\(611\) 5.18539 8.98136i 0.209778 0.363347i
\(612\) −3.85606 8.89138i −0.155872 0.359413i
\(613\) −20.9889 36.3539i −0.847735 1.46832i −0.883225 0.468950i \(-0.844633\pi\)
0.0354902 0.999370i \(-0.488701\pi\)
\(614\) 34.6549 1.39856
\(615\) −10.7016 0.612773i −0.431531 0.0247094i
\(616\) −1.88909 + 0.0688459i −0.0761136 + 0.00277388i
\(617\) −17.4083 + 30.1520i −0.700832 + 1.21388i 0.267343 + 0.963601i \(0.413854\pi\)
−0.968175 + 0.250274i \(0.919479\pi\)
\(618\) 6.61282 + 13.1351i 0.266007 + 0.528371i
\(619\) 1.32726 2.29888i 0.0533471 0.0923998i −0.838119 0.545488i \(-0.816344\pi\)
0.891466 + 0.453088i \(0.149678\pi\)
\(620\) 3.20048 + 5.54339i 0.128534 + 0.222628i
\(621\) −5.15615 14.0378i −0.206909 0.563319i
\(622\) 17.6573 0.707992
\(623\) −29.2349 + 1.06543i −1.17127 + 0.0426857i
\(624\) −1.56576 + 2.38571i −0.0626805 + 0.0955048i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 1.25714 0.0502455
\(627\) −0.0856367 0.170101i −0.00342000 0.00679317i
\(628\) −13.7530 −0.548805
\(629\) −30.3566 −1.21040
\(630\) 4.49196 6.54387i 0.178964 0.260714i
\(631\) −1.91702 −0.0763152 −0.0381576 0.999272i \(-0.512149\pi\)
−0.0381576 + 0.999272i \(0.512149\pi\)
\(632\) −2.44228 −0.0971487
\(633\) −19.0716 + 29.0590i −0.758029 + 1.15499i
\(634\) −4.91403 −0.195161
\(635\) −4.51486 7.81997i −0.179167 0.310326i
\(636\) −0.898718 1.78513i −0.0356365 0.0707850i
\(637\) −6.47813 9.54147i −0.256673 0.378047i
\(638\) 0.861141 0.0340929
\(639\) −11.0706 1.27197i −0.437947 0.0503185i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −9.24750 + 16.0171i −0.365254 + 0.632639i −0.988817 0.149134i \(-0.952351\pi\)
0.623563 + 0.781773i \(0.285685\pi\)
\(642\) 3.34729 5.10019i 0.132107 0.201288i
\(643\) −1.74128 + 3.01599i −0.0686694 + 0.118939i −0.898316 0.439350i \(-0.855209\pi\)
0.829646 + 0.558289i \(0.188542\pi\)
\(644\) 3.56462 6.72874i 0.140466 0.265150i
\(645\) 9.13171 13.9138i 0.359561 0.547854i
\(646\) 0.497142 0.0195598
\(647\) −10.5425 18.2602i −0.414469 0.717881i 0.580904 0.813972i \(-0.302699\pi\)
−0.995373 + 0.0960910i \(0.969366\pi\)
\(648\) 8.76547 + 2.04119i 0.344340 + 0.0801855i
\(649\) −0.445504 + 0.771636i −0.0174876 + 0.0302894i
\(650\) −0.823772 1.42682i −0.0323110 0.0559643i
\(651\) −14.1357 25.7021i −0.554022 1.00735i
\(652\) 2.04615 3.54404i 0.0801334 0.138795i
\(653\) 2.86772 + 4.96703i 0.112222 + 0.194375i 0.916666 0.399654i \(-0.130870\pi\)
−0.804444 + 0.594029i \(0.797536\pi\)
\(654\) 8.12248 + 16.1337i 0.317614 + 0.630879i
\(655\) −9.17401 + 15.8899i −0.358458 + 0.620868i
\(656\) 3.09435 5.35958i 0.120814 0.209256i
\(657\) −3.46536 7.99049i −0.135197 0.311739i
\(658\) −8.84685 14.1101i −0.344886 0.550069i
\(659\) −5.52636 9.57194i −0.215276 0.372870i 0.738082 0.674711i \(-0.235732\pi\)
−0.953358 + 0.301842i \(0.902399\pi\)
\(660\) 1.23550 + 0.0707444i 0.0480917 + 0.00275372i
\(661\) 2.36825 0.0921144 0.0460572 0.998939i \(-0.485334\pi\)
0.0460572 + 0.998939i \(0.485334\pi\)
\(662\) 30.0766 1.16896
\(663\) 9.20361 + 0.526997i 0.357439 + 0.0204669i
\(664\) 2.21659 + 3.83925i 0.0860205 + 0.148992i
\(665\) 0.216283 + 0.344957i 0.00838711 + 0.0133769i
\(666\) 16.7899 22.6452i 0.650594 0.877486i
\(667\) −1.73441 + 3.00408i −0.0671566 + 0.116319i
\(668\) 3.13912 5.43712i 0.121456 0.210369i
\(669\) −3.62591 7.20217i −0.140186 0.278452i
\(670\) 6.24681 + 10.8198i 0.241335 + 0.418005i
\(671\) 3.28915 5.69698i 0.126976 0.219929i
\(672\) 2.20837 + 4.01536i 0.0851898 + 0.154896i
\(673\) 0.952561 + 1.64988i 0.0367185 + 0.0635984i 0.883801 0.467864i \(-0.154976\pi\)
−0.847082 + 0.531462i \(0.821643\pi\)
\(674\) 8.27039 14.3247i 0.318563 0.551768i
\(675\) −3.32830 + 3.99029i −0.128106 + 0.153586i
\(676\) 5.14280 + 8.90759i 0.197800 + 0.342600i
\(677\) −9.45575 −0.363414 −0.181707 0.983353i \(-0.558162\pi\)
−0.181707 + 0.983353i \(0.558162\pi\)
\(678\) −5.43064 + 8.27455i −0.208563 + 0.317782i
\(679\) 10.4834 19.7890i 0.402316 0.759431i
\(680\) −1.61526 + 2.79771i −0.0619422 + 0.107287i
\(681\) 15.6938 23.9122i 0.601386 0.916319i
\(682\) 2.28669 3.96066i 0.0875618 0.151661i
\(683\) −0.925204 1.60250i −0.0354019 0.0613179i 0.847782 0.530346i \(-0.177938\pi\)
−0.883184 + 0.469028i \(0.844604\pi\)
\(684\) −0.274963 + 0.370855i −0.0105135 + 0.0141800i
\(685\) −17.8840 −0.683312
\(686\) −18.4098 + 2.01993i −0.702889 + 0.0771213i
\(687\) 4.15980 + 8.26265i 0.158706 + 0.315240i
\(688\) 4.80435 + 8.32137i 0.183164 + 0.317249i
\(689\) 1.90108 0.0724255
\(690\) −2.73519 + 4.16754i −0.104127 + 0.158656i
\(691\) −23.3344 −0.887682 −0.443841 0.896106i \(-0.646384\pi\)
−0.443841 + 0.896106i \(0.646384\pi\)
\(692\) −15.1441 −0.575694
\(693\) −5.65381 0.441705i −0.214770 0.0167790i
\(694\) 5.80220 0.220248
\(695\) 0.872228 0.0330855
\(696\) −0.938732 1.86461i −0.0355825 0.0706778i
\(697\) −19.9927 −0.757277
\(698\) −12.5953 21.8157i −0.476739 0.825737i
\(699\) −1.18858 + 1.81101i −0.0449563 + 0.0684988i
\(700\) −2.64400 + 0.0963576i −0.0999337 + 0.00364197i
\(701\) −43.6091 −1.64709 −0.823546 0.567249i \(-0.808008\pi\)
−0.823546 + 0.567249i \(0.808008\pi\)
\(702\) −5.48353 + 6.57418i −0.206962 + 0.248126i
\(703\) 0.723038 + 1.25234i 0.0272699 + 0.0472328i
\(704\) −0.357242 + 0.618760i −0.0134640 + 0.0233204i
\(705\) 4.90268 + 9.73823i 0.184646 + 0.366763i
\(706\) −1.97987 + 3.42924i −0.0745134 + 0.129061i
\(707\) 30.7765 1.12162i 1.15747 0.0421828i
\(708\) 2.15645 + 0.123478i 0.0810444 + 0.00464059i
\(709\) −6.20185 −0.232915 −0.116458 0.993196i \(-0.537154\pi\)
−0.116458 + 0.993196i \(0.537154\pi\)
\(710\) 1.85724 + 3.21684i 0.0697010 + 0.120726i
\(711\) −7.27895 0.836325i −0.272982 0.0313646i
\(712\) −5.52854 + 9.57571i −0.207191 + 0.358865i
\(713\) 9.21116 + 15.9542i 0.344961 + 0.597489i
\(714\) 7.66670 12.6642i 0.286919 0.473946i
\(715\) −0.588571 + 1.01944i −0.0220113 + 0.0381247i
\(716\) 10.3341 + 17.8993i 0.386205 + 0.668927i
\(717\) 1.26558 1.92833i 0.0472639 0.0720149i
\(718\) −6.99027 + 12.1075i −0.260875 + 0.451848i
\(719\) −8.23612 + 14.2654i −0.307155 + 0.532009i −0.977739 0.209825i \(-0.932710\pi\)
0.670583 + 0.741834i \(0.266044\pi\)
\(720\) −1.19364 2.75231i −0.0444842 0.102573i
\(721\) −10.5158 + 19.8501i −0.391627 + 0.739255i
\(722\) 9.48816 + 16.4340i 0.353113 + 0.611609i
\(723\) 16.1837 24.6588i 0.601879 0.917070i
\(724\) −24.3018 −0.903168
\(725\) 1.20526 0.0447624
\(726\) 8.16986 + 16.2278i 0.303212 + 0.602272i
\(727\) 10.1772 + 17.6274i 0.377450 + 0.653763i 0.990690 0.136134i \(-0.0434677\pi\)
−0.613240 + 0.789896i \(0.710134\pi\)
\(728\) −4.35610 + 0.158753i −0.161448 + 0.00588379i
\(729\) 25.4256 + 9.08516i 0.941688 + 0.336487i
\(730\) −1.45160 + 2.51424i −0.0537260 + 0.0930561i
\(731\) 15.5205 26.8823i 0.574047 0.994278i
\(732\) −15.9211 0.911637i −0.588459 0.0336951i
\(733\) 20.0756 + 34.7719i 0.741509 + 1.28433i 0.951808 + 0.306694i \(0.0992228\pi\)
−0.210299 + 0.977637i \(0.567444\pi\)
\(734\) −3.52613 + 6.10743i −0.130152 + 0.225429i
\(735\) 12.1229 0.189838i 0.447159 0.00700229i
\(736\) −1.43903 2.49247i −0.0530433 0.0918737i
\(737\) 4.46324 7.73056i 0.164406 0.284759i
\(738\) 11.0577 14.9140i 0.407040 0.548993i
\(739\) −2.20683 3.82234i −0.0811795 0.140607i 0.822577 0.568653i \(-0.192535\pi\)
−0.903757 + 0.428046i \(0.859202\pi\)
\(740\) −9.39685 −0.345435
\(741\) −0.197472 0.392240i −0.00725431 0.0144093i
\(742\) 1.42915 2.69773i 0.0524657 0.0990369i
\(743\) 20.4036 35.3401i 0.748536 1.29650i −0.199988 0.979798i \(-0.564090\pi\)
0.948524 0.316705i \(-0.102576\pi\)
\(744\) −11.0687 0.633789i −0.405796 0.0232358i
\(745\) −0.571398 + 0.989690i −0.0209344 + 0.0362594i
\(746\) −14.5747 25.2441i −0.533618 0.924253i
\(747\) 5.29162 + 12.2015i 0.193610 + 0.446430i
\(748\) 2.30815 0.0843942
\(749\) 9.31251 0.339384i 0.340272 0.0124008i
\(750\) 1.72922 + 0.0990147i 0.0631421 + 0.00361551i
\(751\) −11.2580 19.4995i −0.410811 0.711546i 0.584168 0.811633i \(-0.301421\pi\)
−0.994979 + 0.100087i \(0.968088\pi\)
\(752\) −6.29469 −0.229544
\(753\) 33.0491 + 1.89238i 1.20437 + 0.0689623i
\(754\) 1.98573 0.0723159
\(755\) −0.316400 −0.0115150
\(756\) 5.20681 + 12.7236i 0.189370 + 0.462752i
\(757\) 8.79446 0.319640 0.159820 0.987146i \(-0.448909\pi\)
0.159820 + 0.987146i \(0.448909\pi\)
\(758\) 31.6713 1.15035
\(759\) 3.55583 + 0.203606i 0.129068 + 0.00739044i
\(760\) 0.153889 0.00558216
\(761\) −13.8254 23.9462i −0.501169 0.868050i −0.999999 0.00135035i \(-0.999570\pi\)
0.498830 0.866700i \(-0.333763\pi\)
\(762\) 15.6144 + 0.894076i 0.565649 + 0.0323890i
\(763\) −12.9164 + 24.3817i −0.467607 + 0.882677i
\(764\) 17.5658 0.635510
\(765\) −5.77213 + 7.78514i −0.208692 + 0.281472i
\(766\) −2.29736 3.97914i −0.0830069 0.143772i
\(767\) −1.02730 + 1.77933i −0.0370936 + 0.0642480i
\(768\) 1.72922 + 0.0990147i 0.0623978 + 0.00357289i
\(769\) −1.97706 + 3.42437i −0.0712947 + 0.123486i −0.899469 0.436985i \(-0.856046\pi\)
0.828174 + 0.560471i \(0.189380\pi\)
\(770\) 1.00417 + 1.60158i 0.0361877 + 0.0577168i
\(771\) −24.1664 48.0018i −0.870331 1.72874i
\(772\) 26.1637 0.941653
\(773\) −13.4193 23.2429i −0.482658 0.835989i 0.517143 0.855899i \(-0.326995\pi\)
−0.999802 + 0.0199099i \(0.993662\pi\)
\(774\) 11.4693 + 26.4461i 0.412256 + 0.950587i
\(775\) 3.20048 5.54339i 0.114965 0.199124i
\(776\) −4.23213 7.33026i −0.151925 0.263141i
\(777\) 43.0525 + 0.894310i 1.54450 + 0.0320832i
\(778\) −17.0012 + 29.4470i −0.609524 + 1.05573i
\(779\) 0.476188 + 0.824783i 0.0170612 + 0.0295509i
\(780\) 2.84896 + 0.163131i 0.102009 + 0.00584103i
\(781\) 1.32697 2.29838i 0.0474826 0.0822423i
\(782\) −4.64880 + 8.05195i −0.166241 + 0.287937i
\(783\) −2.15928 5.87872i −0.0771664 0.210088i
\(784\) −3.04944 + 6.30087i −0.108909 + 0.225031i
\(785\) 6.87651 + 11.9105i 0.245433 + 0.425103i
\(786\) −14.2905 28.3854i −0.509727 1.01247i
\(787\) 2.52940 0.0901635 0.0450817 0.998983i \(-0.485645\pi\)
0.0450817 + 0.998983i \(0.485645\pi\)
\(788\) −19.1886 −0.683564
\(789\) 19.8638 30.2660i 0.707170 1.07750i
\(790\) 1.22114 + 2.11508i 0.0434462 + 0.0752511i
\(791\) −15.1086 + 0.550617i −0.537200 + 0.0195777i
\(792\) −1.27661 + 1.72182i −0.0453622 + 0.0611821i
\(793\) 7.58454 13.1368i 0.269335 0.466502i
\(794\) 3.56605 6.17658i 0.126554 0.219199i
\(795\) −1.09661 + 1.67088i −0.0388927 + 0.0592599i
\(796\) 12.6145 + 21.8489i 0.447108 + 0.774414i
\(797\) −16.6824 + 28.8948i −0.590922 + 1.02351i 0.403187 + 0.915118i \(0.367902\pi\)
−0.994109 + 0.108389i \(0.965431\pi\)
\(798\) −0.705058 0.0146459i −0.0249588 0.000518458i
\(799\) 10.1675 + 17.6107i 0.359702 + 0.623021i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) −19.7563 + 26.6462i −0.698054 + 0.941497i
\(802\) 5.20071 + 9.00790i 0.183644 + 0.318080i
\(803\) 2.07428 0.0731998
\(804\) −21.6042 1.23705i −0.761921 0.0436275i
\(805\) −7.60957 + 0.277323i −0.268202 + 0.00977434i
\(806\) 5.27293 9.13298i 0.185731 0.321696i
\(807\) 16.2548 + 32.2871i 0.572197 + 1.13656i
\(808\) 5.82008 10.0807i 0.204750 0.354637i
\(809\) −3.78183 6.55033i −0.132962 0.230297i 0.791855 0.610709i \(-0.209116\pi\)
−0.924817 + 0.380412i \(0.875782\pi\)
\(810\) −2.61502 8.61172i −0.0918823 0.302585i
\(811\) 47.1553 1.65585 0.827923 0.560843i \(-0.189523\pi\)
0.827923 + 0.560843i \(0.189523\pi\)
\(812\) 1.49278 2.81784i 0.0523863 0.0988869i
\(813\) −11.7799 + 17.9487i −0.413138 + 0.629489i
\(814\) 3.35694 + 5.81440i 0.117661 + 0.203795i
\(815\) −4.09230 −0.143347
\(816\) −2.51612 4.99778i −0.0880817 0.174957i
\(817\) −1.47868 −0.0517324
\(818\) 8.13727 0.284513
\(819\) −13.0373 1.01854i −0.455558 0.0355906i
\(820\) −6.18871 −0.216119
\(821\) −8.88841 −0.310208 −0.155104 0.987898i \(-0.549571\pi\)
−0.155104 + 0.987898i \(0.549571\pi\)
\(822\) 16.9962 25.8967i 0.592811 0.903252i
\(823\) −36.1929 −1.26161 −0.630803 0.775943i \(-0.717275\pi\)
−0.630803 + 0.775943i \(0.717275\pi\)
\(824\) 4.24519 + 7.35289i 0.147888 + 0.256150i
\(825\) −0.556482 1.10534i −0.0193742 0.0384831i
\(826\) 1.75269 + 2.79541i 0.0609837 + 0.0972648i
\(827\) −37.6461 −1.30908 −0.654542 0.756026i \(-0.727138\pi\)
−0.654542 + 0.756026i \(0.727138\pi\)
\(828\) −3.43536 7.92131i −0.119387 0.275285i
\(829\) 5.59846 + 9.69681i 0.194442 + 0.336784i 0.946718 0.322065i \(-0.104377\pi\)
−0.752275 + 0.658849i \(0.771044\pi\)
\(830\) 2.21659 3.83925i 0.0769391 0.133262i
\(831\) 9.97518 15.1990i 0.346035 0.527246i
\(832\) −0.823772 + 1.42682i −0.0285592 + 0.0494659i
\(833\) 22.5536 1.64607i 0.781436 0.0570329i
\(834\) −0.828929 + 1.26302i −0.0287035 + 0.0437348i
\(835\) −6.27825 −0.217268
\(836\) −0.0549757 0.0952207i −0.00190137 0.00329328i
\(837\) −32.7719 5.67925i −1.13276 0.196303i
\(838\) −6.88164 + 11.9194i −0.237722 + 0.411747i
\(839\) −12.3118 21.3247i −0.425052 0.736212i 0.571373 0.820690i \(-0.306411\pi\)
−0.996425 + 0.0844785i \(0.973078\pi\)
\(840\) 2.37321 3.92019i 0.0818837 0.135259i
\(841\) 13.7737 23.8567i 0.474954 0.822645i
\(842\) −8.52205 14.7606i −0.293689 0.508685i
\(843\) 24.6390 + 48.9405i 0.848611 + 1.68560i
\(844\) −10.0339 + 17.3793i −0.345382 + 0.598218i
\(845\) 5.14280 8.90759i 0.176918 0.306430i
\(846\) −18.7606 2.15553i −0.645004 0.0741086i
\(847\) −12.9918 + 24.5239i −0.446403 + 0.842652i
\(848\) −0.576945 0.999298i −0.0198124 0.0343160i
\(849\) 22.2317 + 1.27298i 0.762991 + 0.0436887i
\(850\) 3.23051 0.110806
\(851\) −27.0447 −0.927079
\(852\) −6.42315 0.367789i −0.220054 0.0126002i
\(853\) 25.6906 + 44.4975i 0.879630 + 1.52356i 0.851747 + 0.523953i \(0.175543\pi\)
0.0278834 + 0.999611i \(0.491123\pi\)
\(854\) −12.9401 20.6385i −0.442800 0.706235i
\(855\) 0.458651 + 0.0526973i 0.0156855 + 0.00180221i
\(856\) 1.76107 3.05026i 0.0601920 0.104256i
\(857\) 9.80966 16.9908i 0.335092 0.580396i −0.648411 0.761291i \(-0.724566\pi\)
0.983502 + 0.180895i \(0.0578993\pi\)
\(858\) −0.916829 1.82110i −0.0313000 0.0621714i
\(859\) 4.82699 + 8.36059i 0.164695 + 0.285260i 0.936547 0.350542i \(-0.114003\pi\)
−0.771852 + 0.635802i \(0.780669\pi\)
\(860\) 4.80435 8.32137i 0.163827 0.283757i
\(861\) 28.3541 + 0.588987i 0.966306 + 0.0200726i
\(862\) −3.94159 6.82703i −0.134251 0.232530i
\(863\) 18.1910 31.5077i 0.619227 1.07253i −0.370400 0.928872i \(-0.620779\pi\)
0.989627 0.143661i \(-0.0458874\pi\)
\(864\) 5.11984 + 0.887250i 0.174181 + 0.0301848i
\(865\) 7.57207 + 13.1152i 0.257458 + 0.445931i
\(866\) 15.3356 0.521125
\(867\) 6.23796 9.50463i 0.211852 0.322794i
\(868\) −8.99620 14.3483i −0.305351 0.487013i
\(869\) 0.872484 1.51119i 0.0295970 0.0512635i
\(870\) −1.14543 + 1.74527i −0.0388338 + 0.0591702i
\(871\) 10.2919 17.8261i 0.348728 0.604014i
\(872\) 5.21434 + 9.03150i 0.176580 + 0.305845i
\(873\) −10.1033 23.2963i −0.341943 0.788460i
\(874\) 0.442902 0.0149814
\(875\) 1.40545 + 2.24159i 0.0475128 + 0.0757795i
\(876\) −2.26118 4.49140i −0.0763982 0.151750i
\(877\) −16.3082 28.2467i −0.550690 0.953823i −0.998225 0.0595569i \(-0.981031\pi\)
0.447535 0.894267i \(-0.352302\pi\)
\(878\) 11.4596 0.386743
\(879\) −27.1907 + 41.4298i −0.917119 + 1.39739i
\(880\) 0.714483 0.0240852
\(881\) 38.3849 1.29322 0.646611 0.762820i \(-0.276186\pi\)
0.646611 + 0.762820i \(0.276186\pi\)
\(882\) −11.2462 + 17.7348i −0.378679 + 0.597162i
\(883\) −14.2675 −0.480139 −0.240070 0.970756i \(-0.577170\pi\)
−0.240070 + 0.970756i \(0.577170\pi\)
\(884\) 5.32241 0.179012
\(885\) −0.971291 1.92928i −0.0326496 0.0648521i
\(886\) −29.9668 −1.00675
\(887\) 16.4739 + 28.5337i 0.553141 + 0.958068i 0.998046 + 0.0624901i \(0.0199042\pi\)
−0.444905 + 0.895578i \(0.646762\pi\)
\(888\) 8.93037 13.6070i 0.299684 0.456621i
\(889\) 12.6908 + 20.2409i 0.425636 + 0.678859i
\(890\) 11.0571 0.370634
\(891\) −4.39440 + 4.69453i −0.147218 + 0.157273i
\(892\) −2.32770 4.03170i −0.0779373 0.134991i
\(893\) 0.484343 0.838907i 0.0162079 0.0280730i
\(894\) −0.890077 1.76797i −0.0297686 0.0591296i
\(895\) 10.3341 17.8993i 0.345432 0.598306i
\(896\) 1.40545 + 2.24159i 0.0469527 + 0.0748862i
\(897\) 8.19948 + 0.469501i 0.273773 + 0.0156762i
\(898\) 3.37658 0.112678
\(899\) 3.85742 + 6.68125i 0.128652 + 0.222832i
\(900\) −1.78675 + 2.40988i −0.0595585 + 0.0803292i
\(901\) −1.86383 + 3.22824i −0.0620931 + 0.107548i
\(902\) 2.21086 + 3.82933i 0.0736137 + 0.127503i
\(903\) −22.8035 + 37.6679i −0.758853 + 1.25351i
\(904\) −2.85715 + 4.94874i −0.0950276 + 0.164593i
\(905\) 12.1509 + 21.0459i 0.403909 + 0.699591i
\(906\) 0.300694 0.458160i 0.00998988 0.0152214i
\(907\) −22.6310 + 39.1980i −0.751450 + 1.30155i 0.195670 + 0.980670i \(0.437312\pi\)
−0.947120 + 0.320880i \(0.896021\pi\)
\(908\) 8.25676 14.3011i 0.274010 0.474600i
\(909\) 20.7981 28.0514i 0.689830 0.930405i
\(910\) 2.31553 + 3.69312i 0.0767592 + 0.122426i
\(911\) 2.92689 + 5.06952i 0.0969722 + 0.167961i 0.910430 0.413663i \(-0.135751\pi\)
−0.813458 + 0.581624i \(0.802418\pi\)
\(912\) −0.146250 + 0.222838i −0.00484283 + 0.00737890i
\(913\) −3.16744 −0.104827
\(914\) −25.0722 −0.829316
\(915\) 7.17103 + 14.2439i 0.237067 + 0.470888i
\(916\) 2.67044 + 4.62535i 0.0882340 + 0.152826i
\(917\) 22.7249 42.8967i 0.750444 1.41657i
\(918\) −5.78759 15.7569i −0.191019 0.520057i
\(919\) 0.192401 0.333248i 0.00634671 0.0109928i −0.862835 0.505486i \(-0.831313\pi\)
0.869181 + 0.494494i \(0.164646\pi\)
\(920\) −1.43903 + 2.49247i −0.0474434 + 0.0821743i
\(921\) 59.9259 + 3.43135i 1.97463 + 0.113067i
\(922\) 18.4429 + 31.9440i 0.607384 + 1.05202i
\(923\) 3.05989 5.29988i 0.100717 0.174448i
\(924\) −3.27347 0.0679983i −0.107689 0.00223698i
\(925\) 4.69842 + 8.13791i 0.154483 + 0.267573i
\(926\) 14.7697 25.5818i 0.485362 0.840671i
\(927\) 10.1344 + 23.3682i 0.332859 + 0.767512i
\(928\) −0.602632 1.04379i −0.0197824 0.0342641i
\(929\) 16.6050 0.544792 0.272396 0.962185i \(-0.412184\pi\)
0.272396 + 0.962185i \(0.412184\pi\)
\(930\) 4.98545 + 9.90263i 0.163479 + 0.324720i
\(931\) −0.605091 0.891224i −0.0198311 0.0292087i
\(932\) −0.625333 + 1.08311i −0.0204835 + 0.0354784i
\(933\) 30.5333 + 1.74833i 0.999614 + 0.0572377i
\(934\) −17.8292 + 30.8810i −0.583388 + 1.01046i
\(935\) −1.15407 1.99891i −0.0377422 0.0653714i
\(936\) −2.94376 + 3.97038i −0.0962197 + 0.129776i
\(937\) 19.5361 0.638218 0.319109 0.947718i \(-0.396616\pi\)
0.319109 + 0.947718i \(0.396616\pi\)
\(938\) −17.5591 28.0056i −0.573325 0.914414i
\(939\) 2.17387 + 0.124476i 0.0709416 + 0.00406211i
\(940\) 3.14735 + 5.45136i 0.102655 + 0.177804i
\(941\) 16.4586 0.536536 0.268268 0.963344i \(-0.413549\pi\)
0.268268 + 0.963344i \(0.413549\pi\)
\(942\) −23.7820 1.36175i −0.774858 0.0443682i
\(943\) −17.8115 −0.580021
\(944\) 1.24707 0.0405886
\(945\) 8.41552 10.8710i 0.273757 0.353634i
\(946\) −6.86525 −0.223209
\(947\) −16.7012 −0.542715 −0.271357 0.962479i \(-0.587473\pi\)
−0.271357 + 0.962479i \(0.587473\pi\)
\(948\) −4.22324 0.241822i −0.137164 0.00785401i
\(949\) 4.78314 0.155267
\(950\) −0.0769447 0.133272i −0.00249642 0.00432392i
\(951\) −8.49743 0.486562i −0.275548 0.0157778i
\(952\) 4.00115 7.55276i 0.129678 0.244786i
\(953\) −42.5993 −1.37993 −0.689963 0.723845i \(-0.742373\pi\)
−0.689963 + 0.723845i \(0.742373\pi\)
\(954\) −1.37733 3.17587i −0.0445926 0.102822i
\(955\) −8.78292 15.2125i −0.284209 0.492264i
\(956\) 0.665842 1.15327i 0.0215349 0.0372995i
\(957\) 1.48910 + 0.0852656i 0.0481358 + 0.00275625i
\(958\) 7.13005 12.3496i 0.230361 0.398998i
\(959\) 47.2852 1.72326i 1.52692 0.0556469i
\(960\) −0.778860 1.54705i −0.0251376 0.0499310i
\(961\) 9.97224 0.321685
\(962\) 7.74086 + 13.4076i 0.249575 + 0.432277i
\(963\) 6.29319 8.48791i 0.202795 0.273519i
\(964\) 8.51454 14.7476i 0.274235 0.474989i
\(965\) −13.0819 22.6585i −0.421120 0.729401i
\(966\) 6.83024 11.2825i 0.219760 0.363009i
\(967\) 6.13289 10.6225i 0.197221 0.341596i −0.750406 0.660978i \(-0.770142\pi\)
0.947626 + 0.319382i \(0.103475\pi\)
\(968\) 5.24476 + 9.08419i 0.168573 + 0.291977i
\(969\) 0.859666 + 0.0492244i 0.0276165 + 0.00158131i
\(970\) −4.23213 + 7.33026i −0.135885 + 0.235360i
\(971\) −12.7923 + 22.1570i −0.410525 + 0.711050i −0.994947 0.100399i \(-0.967988\pi\)
0.584422 + 0.811450i \(0.301321\pi\)
\(972\) 14.9553 + 4.39757i 0.479692 + 0.141052i
\(973\) −2.30617 + 0.0840458i −0.0739323 + 0.00269438i
\(974\) 20.1589 + 34.9163i 0.645933 + 1.11879i
\(975\) −1.28321 2.54884i −0.0410955 0.0816282i
\(976\) −9.20709 −0.294712
\(977\) 18.7484 0.599813 0.299907 0.953969i \(-0.403044\pi\)
0.299907 + 0.953969i \(0.403044\pi\)
\(978\) 3.88915 5.92581i 0.124361 0.189487i
\(979\) −3.95005 6.84168i −0.126244 0.218661i
\(980\) 6.98143 0.509538i 0.223014 0.0162766i
\(981\) 12.4481 + 28.7030i 0.397436 + 0.916416i
\(982\) −5.36192 + 9.28713i −0.171106 + 0.296364i
\(983\) 21.3371 36.9570i 0.680548 1.17874i −0.294265 0.955724i \(-0.595075\pi\)
0.974814 0.223021i \(-0.0715917\pi\)
\(984\) 5.88149 8.96150i 0.187495 0.285682i
\(985\) 9.59428 + 16.6178i 0.305699 + 0.529487i
\(986\) −1.94681 + 3.37197i −0.0619991 + 0.107386i
\(987\) −13.9010 25.2754i −0.442474 0.804526i
\(988\) −0.126770 0.219572i −0.00403309 0.00698551i
\(989\) 13.8272 23.9494i 0.439679 0.761546i
\(990\) 2.12944 + 0.244665i 0.0676780 + 0.00777596i
\(991\) 10.5017 + 18.1894i 0.333597 + 0.577807i 0.983214 0.182454i \(-0.0584042\pi\)
−0.649617 + 0.760261i \(0.725071\pi\)
\(992\) −6.40096 −0.203231
\(993\) 52.0089 + 2.97802i 1.65045 + 0.0945047i
\(994\) −5.22051 8.32634i −0.165584 0.264096i
\(995\) 12.6145 21.8489i 0.399906 0.692657i
\(996\) 3.45283 + 6.85838i 0.109407 + 0.217316i
\(997\) 3.72215 6.44696i 0.117882 0.204177i −0.801046 0.598602i \(-0.795723\pi\)
0.918928 + 0.394425i \(0.129056\pi\)
\(998\) −13.2928 23.0237i −0.420775 0.728804i
\(999\) 31.2755 37.4961i 0.989514 1.18633i
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.g.121.6 12
3.2 odd 2 1890.2.i.g.1171.3 12
7.4 even 3 630.2.l.g.571.2 yes 12
9.2 odd 6 1890.2.l.g.1801.4 12
9.7 even 3 630.2.l.g.331.2 yes 12
21.11 odd 6 1890.2.l.g.361.4 12
63.11 odd 6 1890.2.i.g.991.3 12
63.25 even 3 inner 630.2.i.g.151.6 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.i.g.121.6 12 1.1 even 1 trivial
630.2.i.g.151.6 yes 12 63.25 even 3 inner
630.2.l.g.331.2 yes 12 9.7 even 3
630.2.l.g.571.2 yes 12 7.4 even 3
1890.2.i.g.991.3 12 63.11 odd 6
1890.2.i.g.1171.3 12 3.2 odd 2
1890.2.l.g.361.4 12 21.11 odd 6
1890.2.l.g.1801.4 12 9.2 odd 6