Properties

Label 74.2.e.a.27.1
Level $74$
Weight $2$
Character 74.27
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
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] = [74,2,Mod(11,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 27.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 74.27
Dual form 74.2.e.a.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000i q^{8} +(-2.23205 + 3.86603i) q^{9} +1.73205 q^{10} +1.26795 q^{11} +(1.36603 - 2.36603i) q^{12} +(5.19615 - 3.00000i) q^{13} +4.00000i q^{14} +(4.09808 + 2.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(3.86603 - 2.23205i) q^{18} +(4.09808 - 2.36603i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-5.46410 + 9.46410i) q^{21} +(-1.09808 - 0.633975i) q^{22} +4.73205i q^{23} +(-2.36603 + 1.36603i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} -7.73205i q^{29} +(-2.36603 - 4.09808i) q^{30} -4.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.73205 - 3.00000i) q^{33} +(0.866025 + 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} -4.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -4.73205 q^{38} +(-14.1962 - 8.19615i) q^{39} +(0.866025 + 1.50000i) q^{40} +(3.23205 + 5.59808i) q^{41} +(9.46410 - 5.46410i) q^{42} +2.53590i q^{43} +(0.633975 + 1.09808i) q^{44} -7.73205i q^{45} +(2.36603 - 4.09808i) q^{46} -5.66025 q^{47} +2.73205 q^{48} +(-4.50000 + 7.79423i) q^{49} +(1.73205 - 1.00000i) q^{50} +4.73205i q^{51} +(5.19615 + 3.00000i) q^{52} +(4.73205 - 8.19615i) q^{53} +(-3.46410 - 2.00000i) q^{54} +(-1.90192 + 1.09808i) q^{55} +(-3.46410 + 2.00000i) q^{56} +(-11.1962 - 6.46410i) q^{57} +(-3.86603 + 6.69615i) q^{58} +(8.19615 + 4.73205i) q^{59} +4.73205i q^{60} +(2.30385 - 1.33013i) q^{61} +(-2.36603 + 4.09808i) q^{62} +17.8564 q^{63} -1.00000 q^{64} +(-5.19615 + 9.00000i) q^{65} +3.46410i q^{66} +(2.09808 + 3.63397i) q^{67} -1.73205i q^{68} +(11.1962 - 6.46410i) q^{69} +(-3.46410 - 6.00000i) q^{70} +(-4.73205 - 8.19615i) q^{71} +(3.86603 + 2.23205i) q^{72} +8.39230 q^{73} +(3.46410 - 5.00000i) q^{74} +5.46410 q^{75} +(4.09808 + 2.36603i) q^{76} +(-2.53590 - 4.39230i) q^{77} +(8.19615 + 14.1962i) q^{78} +(-1.90192 + 1.09808i) q^{79} -1.73205i q^{80} +(1.23205 + 2.13397i) q^{81} -6.46410i q^{82} +(2.83013 - 4.90192i) q^{83} -10.9282 q^{84} +3.00000 q^{85} +(1.26795 - 2.19615i) q^{86} +(-18.2942 + 10.5622i) q^{87} -1.26795i q^{88} +(4.50000 + 2.59808i) q^{89} +(-3.86603 + 6.69615i) q^{90} +(-20.7846 - 12.0000i) q^{91} +(-4.09808 + 2.36603i) q^{92} +(-11.1962 + 6.46410i) q^{93} +(4.90192 + 2.83013i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(-2.36603 - 1.36603i) q^{96} -5.19615i q^{97} +(7.79423 - 4.50000i) q^{98} +(-2.83013 + 4.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −1.36603 2.36603i −0.788675 1.36603i −0.926779 0.375608i \(-0.877434\pi\)
0.138104 0.990418i \(-0.455899\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 2.73205i 1.11536i
\(7\) −2.00000 3.46410i −0.755929 1.30931i −0.944911 0.327327i \(-0.893852\pi\)
0.188982 0.981981i \(-0.439481\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.23205 + 3.86603i −0.744017 + 1.28868i
\(10\) 1.73205 0.547723
\(11\) 1.26795 0.382301 0.191151 0.981561i \(-0.438778\pi\)
0.191151 + 0.981561i \(0.438778\pi\)
\(12\) 1.36603 2.36603i 0.394338 0.683013i
\(13\) 5.19615 3.00000i 1.44115 0.832050i 0.443227 0.896410i \(-0.353834\pi\)
0.997927 + 0.0643593i \(0.0205004\pi\)
\(14\) 4.00000i 1.06904i
\(15\) 4.09808 + 2.36603i 1.05812 + 0.610905i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 0.866025i −0.363803 0.210042i 0.306944 0.951727i \(-0.400693\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(18\) 3.86603 2.23205i 0.911231 0.526099i
\(19\) 4.09808 2.36603i 0.940163 0.542803i 0.0501517 0.998742i \(-0.484030\pi\)
0.890011 + 0.455938i \(0.150696\pi\)
\(20\) −1.50000 0.866025i −0.335410 0.193649i
\(21\) −5.46410 + 9.46410i −1.19236 + 2.06524i
\(22\) −1.09808 0.633975i −0.234111 0.135164i
\(23\) 4.73205i 0.986701i 0.869831 + 0.493350i \(0.164228\pi\)
−0.869831 + 0.493350i \(0.835772\pi\)
\(24\) −2.36603 + 1.36603i −0.482963 + 0.278839i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −6.00000 −1.17670
\(27\) 4.00000 0.769800
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) 7.73205i 1.43581i −0.696143 0.717903i \(-0.745102\pi\)
0.696143 0.717903i \(-0.254898\pi\)
\(30\) −2.36603 4.09808i −0.431975 0.748203i
\(31\) 4.73205i 0.849901i −0.905216 0.424951i \(-0.860291\pi\)
0.905216 0.424951i \(-0.139709\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −1.73205 3.00000i −0.301511 0.522233i
\(34\) 0.866025 + 1.50000i 0.148522 + 0.257248i
\(35\) 6.00000 + 3.46410i 1.01419 + 0.585540i
\(36\) −4.46410 −0.744017
\(37\) −0.500000 + 6.06218i −0.0821995 + 0.996616i
\(38\) −4.73205 −0.767640
\(39\) −14.1962 8.19615i −2.27320 1.31243i
\(40\) 0.866025 + 1.50000i 0.136931 + 0.237171i
\(41\) 3.23205 + 5.59808i 0.504762 + 0.874273i 0.999985 + 0.00550690i \(0.00175291\pi\)
−0.495223 + 0.868766i \(0.664914\pi\)
\(42\) 9.46410 5.46410i 1.46034 0.843129i
\(43\) 2.53590i 0.386721i 0.981128 + 0.193360i \(0.0619387\pi\)
−0.981128 + 0.193360i \(0.938061\pi\)
\(44\) 0.633975 + 1.09808i 0.0955753 + 0.165541i
\(45\) 7.73205i 1.15263i
\(46\) 2.36603 4.09808i 0.348851 0.604228i
\(47\) −5.66025 −0.825633 −0.412816 0.910814i \(-0.635455\pi\)
−0.412816 + 0.910814i \(0.635455\pi\)
\(48\) 2.73205 0.394338
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 1.73205 1.00000i 0.244949 0.141421i
\(51\) 4.73205i 0.662620i
\(52\) 5.19615 + 3.00000i 0.720577 + 0.416025i
\(53\) 4.73205 8.19615i 0.649997 1.12583i −0.333126 0.942882i \(-0.608103\pi\)
0.983123 0.182946i \(-0.0585633\pi\)
\(54\) −3.46410 2.00000i −0.471405 0.272166i
\(55\) −1.90192 + 1.09808i −0.256455 + 0.148065i
\(56\) −3.46410 + 2.00000i −0.462910 + 0.267261i
\(57\) −11.1962 6.46410i −1.48297 0.856191i
\(58\) −3.86603 + 6.69615i −0.507634 + 0.879248i
\(59\) 8.19615 + 4.73205i 1.06705 + 0.616061i 0.927373 0.374137i \(-0.122061\pi\)
0.139675 + 0.990197i \(0.455394\pi\)
\(60\) 4.73205i 0.610905i
\(61\) 2.30385 1.33013i 0.294977 0.170305i −0.345207 0.938527i \(-0.612191\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −2.36603 + 4.09808i −0.300486 + 0.520456i
\(63\) 17.8564 2.24970
\(64\) −1.00000 −0.125000
\(65\) −5.19615 + 9.00000i −0.644503 + 1.11631i
\(66\) 3.46410i 0.426401i
\(67\) 2.09808 + 3.63397i 0.256321 + 0.443961i 0.965253 0.261316i \(-0.0841563\pi\)
−0.708933 + 0.705276i \(0.750823\pi\)
\(68\) 1.73205i 0.210042i
\(69\) 11.1962 6.46410i 1.34786 0.778186i
\(70\) −3.46410 6.00000i −0.414039 0.717137i
\(71\) −4.73205 8.19615i −0.561591 0.972704i −0.997358 0.0726447i \(-0.976856\pi\)
0.435767 0.900060i \(-0.356477\pi\)
\(72\) 3.86603 + 2.23205i 0.455615 + 0.263050i
\(73\) 8.39230 0.982245 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(74\) 3.46410 5.00000i 0.402694 0.581238i
\(75\) 5.46410 0.630940
\(76\) 4.09808 + 2.36603i 0.470082 + 0.271402i
\(77\) −2.53590 4.39230i −0.288992 0.500550i
\(78\) 8.19615 + 14.1962i 0.928032 + 1.60740i
\(79\) −1.90192 + 1.09808i −0.213983 + 0.123543i −0.603161 0.797619i \(-0.706092\pi\)
0.389178 + 0.921163i \(0.372759\pi\)
\(80\) 1.73205i 0.193649i
\(81\) 1.23205 + 2.13397i 0.136895 + 0.237108i
\(82\) 6.46410i 0.713841i
\(83\) 2.83013 4.90192i 0.310647 0.538056i −0.667856 0.744291i \(-0.732788\pi\)
0.978503 + 0.206235i \(0.0661210\pi\)
\(84\) −10.9282 −1.19236
\(85\) 3.00000 0.325396
\(86\) 1.26795 2.19615i 0.136726 0.236817i
\(87\) −18.2942 + 10.5622i −1.96135 + 1.13238i
\(88\) 1.26795i 0.135164i
\(89\) 4.50000 + 2.59808i 0.476999 + 0.275396i 0.719165 0.694839i \(-0.244525\pi\)
−0.242166 + 0.970235i \(0.577858\pi\)
\(90\) −3.86603 + 6.69615i −0.407515 + 0.705836i
\(91\) −20.7846 12.0000i −2.17882 1.25794i
\(92\) −4.09808 + 2.36603i −0.427254 + 0.246675i
\(93\) −11.1962 + 6.46410i −1.16099 + 0.670296i
\(94\) 4.90192 + 2.83013i 0.505595 + 0.291905i
\(95\) −4.09808 + 7.09808i −0.420454 + 0.728247i
\(96\) −2.36603 1.36603i −0.241481 0.139419i
\(97\) 5.19615i 0.527589i −0.964579 0.263795i \(-0.915026\pi\)
0.964579 0.263795i \(-0.0849741\pi\)
\(98\) 7.79423 4.50000i 0.787336 0.454569i
\(99\) −2.83013 + 4.90192i −0.284438 + 0.492662i
\(100\) −2.00000 −0.200000
\(101\) 6.46410 0.643202 0.321601 0.946875i \(-0.395779\pi\)
0.321601 + 0.946875i \(0.395779\pi\)
\(102\) 2.36603 4.09808i 0.234271 0.405770i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 18.9282i 1.84720i
\(106\) −8.19615 + 4.73205i −0.796081 + 0.459617i
\(107\) −2.19615 3.80385i −0.212310 0.367732i 0.740127 0.672467i \(-0.234765\pi\)
−0.952437 + 0.304735i \(0.901432\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 3.69615 + 2.13397i 0.354027 + 0.204398i 0.666458 0.745543i \(-0.267810\pi\)
−0.312430 + 0.949941i \(0.601143\pi\)
\(110\) 2.19615 0.209395
\(111\) 15.0263 7.09808i 1.42623 0.673720i
\(112\) 4.00000 0.377964
\(113\) 6.80385 + 3.92820i 0.640052 + 0.369534i 0.784635 0.619958i \(-0.212851\pi\)
−0.144582 + 0.989493i \(0.546184\pi\)
\(114\) 6.46410 + 11.1962i 0.605419 + 1.04862i
\(115\) −4.09808 7.09808i −0.382148 0.661899i
\(116\) 6.69615 3.86603i 0.621722 0.358951i
\(117\) 26.7846i 2.47624i
\(118\) −4.73205 8.19615i −0.435621 0.754517i
\(119\) 6.92820i 0.635107i
\(120\) 2.36603 4.09808i 0.215988 0.374101i
\(121\) −9.39230 −0.853846
\(122\) −2.66025 −0.240848
\(123\) 8.83013 15.2942i 0.796186 1.37903i
\(124\) 4.09808 2.36603i 0.368018 0.212475i
\(125\) 12.1244i 1.08444i
\(126\) −15.4641 8.92820i −1.37765 0.795388i
\(127\) −10.2942 + 17.8301i −0.913465 + 1.58217i −0.104332 + 0.994543i \(0.533270\pi\)
−0.809133 + 0.587625i \(0.800063\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 6.00000 3.46410i 0.528271 0.304997i
\(130\) 9.00000 5.19615i 0.789352 0.455733i
\(131\) −1.90192 1.09808i −0.166172 0.0959394i 0.414608 0.910000i \(-0.363919\pi\)
−0.580780 + 0.814061i \(0.697252\pi\)
\(132\) 1.73205 3.00000i 0.150756 0.261116i
\(133\) −16.3923 9.46410i −1.42139 0.820642i
\(134\) 4.19615i 0.362492i
\(135\) −6.00000 + 3.46410i −0.516398 + 0.298142i
\(136\) −0.866025 + 1.50000i −0.0742611 + 0.128624i
\(137\) 7.39230 0.631567 0.315784 0.948831i \(-0.397733\pi\)
0.315784 + 0.948831i \(0.397733\pi\)
\(138\) −12.9282 −1.10052
\(139\) −6.09808 + 10.5622i −0.517232 + 0.895872i 0.482568 + 0.875859i \(0.339704\pi\)
−0.999800 + 0.0200135i \(0.993629\pi\)
\(140\) 6.92820i 0.585540i
\(141\) 7.73205 + 13.3923i 0.651156 + 1.12784i
\(142\) 9.46410i 0.794210i
\(143\) 6.58846 3.80385i 0.550954 0.318094i
\(144\) −2.23205 3.86603i −0.186004 0.322169i
\(145\) 6.69615 + 11.5981i 0.556085 + 0.963168i
\(146\) −7.26795 4.19615i −0.601500 0.347276i
\(147\) 24.5885 2.02802
\(148\) −5.50000 + 2.59808i −0.452097 + 0.213561i
\(149\) −9.92820 −0.813350 −0.406675 0.913573i \(-0.633312\pi\)
−0.406675 + 0.913573i \(0.633312\pi\)
\(150\) −4.73205 2.73205i −0.386370 0.223071i
\(151\) 6.09808 + 10.5622i 0.496254 + 0.859538i 0.999991 0.00431966i \(-0.00137499\pi\)
−0.503736 + 0.863857i \(0.668042\pi\)
\(152\) −2.36603 4.09808i −0.191910 0.332398i
\(153\) 6.69615 3.86603i 0.541352 0.312550i
\(154\) 5.07180i 0.408697i
\(155\) 4.09808 + 7.09808i 0.329165 + 0.570131i
\(156\) 16.3923i 1.31243i
\(157\) −5.69615 + 9.86603i −0.454602 + 0.787395i −0.998665 0.0516500i \(-0.983552\pi\)
0.544063 + 0.839045i \(0.316885\pi\)
\(158\) 2.19615 0.174717
\(159\) −25.8564 −2.05055
\(160\) −0.866025 + 1.50000i −0.0684653 + 0.118585i
\(161\) 16.3923 9.46410i 1.29189 0.745876i
\(162\) 2.46410i 0.193598i
\(163\) 8.19615 + 4.73205i 0.641972 + 0.370643i 0.785374 0.619022i \(-0.212471\pi\)
−0.143402 + 0.989665i \(0.545804\pi\)
\(164\) −3.23205 + 5.59808i −0.252381 + 0.437136i
\(165\) 5.19615 + 3.00000i 0.404520 + 0.233550i
\(166\) −4.90192 + 2.83013i −0.380463 + 0.219660i
\(167\) −6.00000 + 3.46410i −0.464294 + 0.268060i −0.713848 0.700301i \(-0.753049\pi\)
0.249554 + 0.968361i \(0.419716\pi\)
\(168\) 9.46410 + 5.46410i 0.730171 + 0.421565i
\(169\) 11.5000 19.9186i 0.884615 1.53220i
\(170\) −2.59808 1.50000i −0.199263 0.115045i
\(171\) 21.1244i 1.61542i
\(172\) −2.19615 + 1.26795i −0.167455 + 0.0966802i
\(173\) −1.96410 + 3.40192i −0.149328 + 0.258643i −0.930979 0.365072i \(-0.881044\pi\)
0.781651 + 0.623716i \(0.214378\pi\)
\(174\) 21.1244 1.60143
\(175\) 8.00000 0.604743
\(176\) −0.633975 + 1.09808i −0.0477876 + 0.0827706i
\(177\) 25.8564i 1.94349i
\(178\) −2.59808 4.50000i −0.194734 0.337289i
\(179\) 23.3205i 1.74306i 0.490345 + 0.871528i \(0.336871\pi\)
−0.490345 + 0.871528i \(0.663129\pi\)
\(180\) 6.69615 3.86603i 0.499102 0.288157i
\(181\) −2.69615 4.66987i −0.200403 0.347109i 0.748255 0.663411i \(-0.230892\pi\)
−0.948658 + 0.316302i \(0.897559\pi\)
\(182\) 12.0000 + 20.7846i 0.889499 + 1.54066i
\(183\) −6.29423 3.63397i −0.465283 0.268631i
\(184\) 4.73205 0.348851
\(185\) −4.50000 9.52628i −0.330847 0.700386i
\(186\) 12.9282 0.947942
\(187\) −1.90192 1.09808i −0.139082 0.0802993i
\(188\) −2.83013 4.90192i −0.206408 0.357510i
\(189\) −8.00000 13.8564i −0.581914 1.00791i
\(190\) 7.09808 4.09808i 0.514949 0.297306i
\(191\) 6.58846i 0.476724i −0.971176 0.238362i \(-0.923390\pi\)
0.971176 0.238362i \(-0.0766105\pi\)
\(192\) 1.36603 + 2.36603i 0.0985844 + 0.170753i
\(193\) 12.1244i 0.872730i 0.899770 + 0.436365i \(0.143734\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) −2.59808 + 4.50000i −0.186531 + 0.323081i
\(195\) 28.3923 2.03322
\(196\) −9.00000 −0.642857
\(197\) 4.16025 7.20577i 0.296406 0.513390i −0.678905 0.734226i \(-0.737545\pi\)
0.975311 + 0.220836i \(0.0708786\pi\)
\(198\) 4.90192 2.83013i 0.348365 0.201128i
\(199\) 18.9282i 1.34178i −0.741555 0.670892i \(-0.765911\pi\)
0.741555 0.670892i \(-0.234089\pi\)
\(200\) 1.73205 + 1.00000i 0.122474 + 0.0707107i
\(201\) 5.73205 9.92820i 0.404308 0.700281i
\(202\) −5.59808 3.23205i −0.393879 0.227406i
\(203\) −26.7846 + 15.4641i −1.87991 + 1.08537i
\(204\) −4.09808 + 2.36603i −0.286923 + 0.165655i
\(205\) −9.69615 5.59808i −0.677209 0.390987i
\(206\) −3.46410 + 6.00000i −0.241355 + 0.418040i
\(207\) −18.2942 10.5622i −1.27154 0.734122i
\(208\) 6.00000i 0.416025i
\(209\) 5.19615 3.00000i 0.359425 0.207514i
\(210\) −9.46410 + 16.3923i −0.653085 + 1.13118i
\(211\) −8.39230 −0.577750 −0.288875 0.957367i \(-0.593281\pi\)
−0.288875 + 0.957367i \(0.593281\pi\)
\(212\) 9.46410 0.649997
\(213\) −12.9282 + 22.3923i −0.885826 + 1.53430i
\(214\) 4.39230i 0.300252i
\(215\) −2.19615 3.80385i −0.149776 0.259420i
\(216\) 4.00000i 0.272166i
\(217\) −16.3923 + 9.46410i −1.11278 + 0.642465i
\(218\) −2.13397 3.69615i −0.144531 0.250335i
\(219\) −11.4641 19.8564i −0.774672 1.34177i
\(220\) −1.90192 1.09808i −0.128228 0.0740323i
\(221\) −10.3923 −0.699062
\(222\) −16.5622 1.36603i −1.11158 0.0916816i
\(223\) 8.58846 0.575126 0.287563 0.957762i \(-0.407155\pi\)
0.287563 + 0.957762i \(0.407155\pi\)
\(224\) −3.46410 2.00000i −0.231455 0.133631i
\(225\) −4.46410 7.73205i −0.297607 0.515470i
\(226\) −3.92820 6.80385i −0.261300 0.452585i
\(227\) 4.09808 2.36603i 0.271999 0.157039i −0.357797 0.933799i \(-0.616472\pi\)
0.629796 + 0.776761i \(0.283139\pi\)
\(228\) 12.9282i 0.856191i
\(229\) 9.50000 + 16.4545i 0.627778 + 1.08734i 0.987997 + 0.154475i \(0.0493686\pi\)
−0.360219 + 0.932868i \(0.617298\pi\)
\(230\) 8.19615i 0.540438i
\(231\) −6.92820 + 12.0000i −0.455842 + 0.789542i
\(232\) −7.73205 −0.507634
\(233\) −25.3923 −1.66351 −0.831753 0.555146i \(-0.812662\pi\)
−0.831753 + 0.555146i \(0.812662\pi\)
\(234\) 13.3923 23.1962i 0.875482 1.51638i
\(235\) 8.49038 4.90192i 0.553851 0.319766i
\(236\) 9.46410i 0.616061i
\(237\) 5.19615 + 3.00000i 0.337526 + 0.194871i
\(238\) 3.46410 6.00000i 0.224544 0.388922i
\(239\) 16.3923 + 9.46410i 1.06033 + 0.612182i 0.925524 0.378690i \(-0.123625\pi\)
0.134807 + 0.990872i \(0.456959\pi\)
\(240\) −4.09808 + 2.36603i −0.264530 + 0.152726i
\(241\) 15.5885 9.00000i 1.00414 0.579741i 0.0946700 0.995509i \(-0.469820\pi\)
0.909471 + 0.415768i \(0.136487\pi\)
\(242\) 8.13397 + 4.69615i 0.522872 + 0.301880i
\(243\) 9.36603 16.2224i 0.600831 1.04067i
\(244\) 2.30385 + 1.33013i 0.147489 + 0.0851527i
\(245\) 15.5885i 0.995910i
\(246\) −15.2942 + 8.83013i −0.975124 + 0.562988i
\(247\) 14.1962 24.5885i 0.903280 1.56453i
\(248\) −4.73205 −0.300486
\(249\) −15.4641 −0.979998
\(250\) −6.06218 + 10.5000i −0.383406 + 0.664078i
\(251\) 18.9282i 1.19474i −0.801967 0.597369i \(-0.796213\pi\)
0.801967 0.597369i \(-0.203787\pi\)
\(252\) 8.92820 + 15.4641i 0.562424 + 0.974147i
\(253\) 6.00000i 0.377217i
\(254\) 17.8301 10.2942i 1.11876 0.645917i
\(255\) −4.09808 7.09808i −0.256631 0.444499i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.696152 0.401924i −0.0434248 0.0250713i 0.478130 0.878289i \(-0.341315\pi\)
−0.521555 + 0.853218i \(0.674648\pi\)
\(258\) −6.92820 −0.431331
\(259\) 22.0000 10.3923i 1.36701 0.645746i
\(260\) −10.3923 −0.644503
\(261\) 29.8923 + 17.2583i 1.85029 + 1.06826i
\(262\) 1.09808 + 1.90192i 0.0678394 + 0.117501i
\(263\) 5.66025 + 9.80385i 0.349026 + 0.604531i 0.986077 0.166291i \(-0.0531791\pi\)
−0.637051 + 0.770822i \(0.719846\pi\)
\(264\) −3.00000 + 1.73205i −0.184637 + 0.106600i
\(265\) 16.3923i 1.00697i
\(266\) 9.46410 + 16.3923i 0.580281 + 1.00508i
\(267\) 14.1962i 0.868790i
\(268\) −2.09808 + 3.63397i −0.128160 + 0.221980i
\(269\) −28.3923 −1.73111 −0.865555 0.500814i \(-0.833034\pi\)
−0.865555 + 0.500814i \(0.833034\pi\)
\(270\) 6.92820 0.421637
\(271\) −8.29423 + 14.3660i −0.503839 + 0.872674i 0.496152 + 0.868236i \(0.334746\pi\)
−0.999990 + 0.00443801i \(0.998587\pi\)
\(272\) 1.50000 0.866025i 0.0909509 0.0525105i
\(273\) 65.5692i 3.96843i
\(274\) −6.40192 3.69615i −0.386754 0.223293i
\(275\) −1.26795 + 2.19615i −0.0764602 + 0.132433i
\(276\) 11.1962 + 6.46410i 0.673929 + 0.389093i
\(277\) 14.8923 8.59808i 0.894792 0.516608i 0.0192850 0.999814i \(-0.493861\pi\)
0.875507 + 0.483206i \(0.160528\pi\)
\(278\) 10.5622 6.09808i 0.633477 0.365738i
\(279\) 18.2942 + 10.5622i 1.09525 + 0.632341i
\(280\) 3.46410 6.00000i 0.207020 0.358569i
\(281\) 0.696152 + 0.401924i 0.0415290 + 0.0239768i 0.520621 0.853788i \(-0.325701\pi\)
−0.479092 + 0.877765i \(0.659034\pi\)
\(282\) 15.4641i 0.920874i
\(283\) −8.19615 + 4.73205i −0.487211 + 0.281291i −0.723417 0.690412i \(-0.757429\pi\)
0.236206 + 0.971703i \(0.424096\pi\)
\(284\) 4.73205 8.19615i 0.280796 0.486352i
\(285\) 22.3923 1.32641
\(286\) −7.60770 −0.449852
\(287\) 12.9282 22.3923i 0.763128 1.32178i
\(288\) 4.46410i 0.263050i
\(289\) −7.00000 12.1244i −0.411765 0.713197i
\(290\) 13.3923i 0.786423i
\(291\) −12.2942 + 7.09808i −0.720700 + 0.416097i
\(292\) 4.19615 + 7.26795i 0.245561 + 0.425325i
\(293\) −2.30385 3.99038i −0.134592 0.233121i 0.790849 0.612011i \(-0.209639\pi\)
−0.925442 + 0.378890i \(0.876306\pi\)
\(294\) −21.2942 12.2942i −1.24190 0.717014i
\(295\) −16.3923 −0.954397
\(296\) 6.06218 + 0.500000i 0.352357 + 0.0290619i
\(297\) 5.07180 0.294295
\(298\) 8.59808 + 4.96410i 0.498073 + 0.287563i
\(299\) 14.1962 + 24.5885i 0.820985 + 1.42199i
\(300\) 2.73205 + 4.73205i 0.157735 + 0.273205i
\(301\) 8.78461 5.07180i 0.506336 0.292334i
\(302\) 12.1962i 0.701810i
\(303\) −8.83013 15.2942i −0.507278 0.878630i
\(304\) 4.73205i 0.271402i
\(305\) −2.30385 + 3.99038i −0.131918 + 0.228489i
\(306\) −7.73205 −0.442012
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 2.53590 4.39230i 0.144496 0.250275i
\(309\) −16.3923 + 9.46410i −0.932526 + 0.538394i
\(310\) 8.19615i 0.465510i
\(311\) 3.80385 + 2.19615i 0.215696 + 0.124532i 0.603956 0.797018i \(-0.293590\pi\)
−0.388260 + 0.921550i \(0.626924\pi\)
\(312\) −8.19615 + 14.1962i −0.464016 + 0.803699i
\(313\) 8.30385 + 4.79423i 0.469361 + 0.270986i 0.715972 0.698129i \(-0.245984\pi\)
−0.246611 + 0.969115i \(0.579317\pi\)
\(314\) 9.86603 5.69615i 0.556772 0.321452i
\(315\) −26.7846 + 15.4641i −1.50914 + 0.871303i
\(316\) −1.90192 1.09808i −0.106992 0.0617716i
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) 22.3923 + 12.9282i 1.25570 + 0.724978i
\(319\) 9.80385i 0.548910i
\(320\) 1.50000 0.866025i 0.0838525 0.0484123i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) −18.9282 −1.05483
\(323\) −8.19615 −0.456046
\(324\) −1.23205 + 2.13397i −0.0684473 + 0.118554i
\(325\) 12.0000i 0.665640i
\(326\) −4.73205 8.19615i −0.262084 0.453943i
\(327\) 11.6603i 0.644814i
\(328\) 5.59808 3.23205i 0.309102 0.178460i
\(329\) 11.3205 + 19.6077i 0.624120 + 1.08101i
\(330\) −3.00000 5.19615i −0.165145 0.286039i
\(331\) 14.7846 + 8.53590i 0.812636 + 0.469175i 0.847870 0.530204i \(-0.177885\pi\)
−0.0352347 + 0.999379i \(0.511218\pi\)
\(332\) 5.66025 0.310647
\(333\) −22.3205 15.4641i −1.22316 0.847428i
\(334\) 6.92820 0.379094
\(335\) −6.29423 3.63397i −0.343890 0.198545i
\(336\) −5.46410 9.46410i −0.298091 0.516309i
\(337\) 3.50000 + 6.06218i 0.190657 + 0.330228i 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) −19.9186 + 11.5000i −1.08343 + 0.625518i
\(339\) 21.4641i 1.16577i
\(340\) 1.50000 + 2.59808i 0.0813489 + 0.140900i
\(341\) 6.00000i 0.324918i
\(342\) 10.5622 18.2942i 0.571137 0.989239i
\(343\) 8.00000 0.431959
\(344\) 2.53590 0.136726
\(345\) −11.1962 + 19.3923i −0.602781 + 1.04405i
\(346\) 3.40192 1.96410i 0.182889 0.105591i
\(347\) 28.0526i 1.50594i −0.658055 0.752970i \(-0.728620\pi\)
0.658055 0.752970i \(-0.271380\pi\)
\(348\) −18.2942 10.5622i −0.980674 0.566192i
\(349\) 13.6962 23.7224i 0.733138 1.26983i −0.222397 0.974956i \(-0.571388\pi\)
0.955535 0.294877i \(-0.0952785\pi\)
\(350\) −6.92820 4.00000i −0.370328 0.213809i
\(351\) 20.7846 12.0000i 1.10940 0.640513i
\(352\) 1.09808 0.633975i 0.0585277 0.0337910i
\(353\) −5.08846 2.93782i −0.270831 0.156364i 0.358434 0.933555i \(-0.383311\pi\)
−0.629265 + 0.777191i \(0.716644\pi\)
\(354\) −12.9282 + 22.3923i −0.687126 + 1.19014i
\(355\) 14.1962 + 8.19615i 0.753454 + 0.435007i
\(356\) 5.19615i 0.275396i
\(357\) 16.3923 9.46410i 0.867573 0.500893i
\(358\) 11.6603 20.1962i 0.616264 1.06740i
\(359\) 26.5359 1.40051 0.700256 0.713892i \(-0.253069\pi\)
0.700256 + 0.713892i \(0.253069\pi\)
\(360\) −7.73205 −0.407515
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 5.39230i 0.283413i
\(363\) 12.8301 + 22.2224i 0.673407 + 1.16638i
\(364\) 24.0000i 1.25794i
\(365\) −12.5885 + 7.26795i −0.658910 + 0.380422i
\(366\) 3.63397 + 6.29423i 0.189951 + 0.329005i
\(367\) 10.1962 + 17.6603i 0.532235 + 0.921858i 0.999292 + 0.0376305i \(0.0119810\pi\)
−0.467057 + 0.884227i \(0.654686\pi\)
\(368\) −4.09808 2.36603i −0.213627 0.123338i
\(369\) −28.8564 −1.50220
\(370\) −0.866025 + 10.5000i −0.0450225 + 0.545869i
\(371\) −37.8564 −1.96541
\(372\) −11.1962 6.46410i −0.580493 0.335148i
\(373\) −10.8923 18.8660i −0.563982 0.976846i −0.997144 0.0755294i \(-0.975935\pi\)
0.433161 0.901316i \(-0.357398\pi\)
\(374\) 1.09808 + 1.90192i 0.0567802 + 0.0983461i
\(375\) −28.6865 + 16.5622i −1.48137 + 0.855267i
\(376\) 5.66025i 0.291905i
\(377\) −23.1962 40.1769i −1.19466 2.06922i
\(378\) 16.0000i 0.822951i
\(379\) 8.39230 14.5359i 0.431084 0.746659i −0.565883 0.824485i \(-0.691465\pi\)
0.996967 + 0.0778265i \(0.0247980\pi\)
\(380\) −8.19615 −0.420454
\(381\) 56.2487 2.88171
\(382\) −3.29423 + 5.70577i −0.168547 + 0.291933i
\(383\) 1.60770 0.928203i 0.0821494 0.0474290i −0.458363 0.888765i \(-0.651564\pi\)
0.540512 + 0.841336i \(0.318231\pi\)
\(384\) 2.73205i 0.139419i
\(385\) 7.60770 + 4.39230i 0.387724 + 0.223853i
\(386\) 6.06218 10.5000i 0.308557 0.534436i
\(387\) −9.80385 5.66025i −0.498358 0.287727i
\(388\) 4.50000 2.59808i 0.228453 0.131897i
\(389\) −9.69615 + 5.59808i −0.491614 + 0.283834i −0.725244 0.688492i \(-0.758273\pi\)
0.233630 + 0.972326i \(0.424940\pi\)
\(390\) −24.5885 14.1962i −1.24508 0.718850i
\(391\) 4.09808 7.09808i 0.207249 0.358965i
\(392\) 7.79423 + 4.50000i 0.393668 + 0.227284i
\(393\) 6.00000i 0.302660i
\(394\) −7.20577 + 4.16025i −0.363022 + 0.209591i
\(395\) 1.90192 3.29423i 0.0956962 0.165751i
\(396\) −5.66025 −0.284438
\(397\) −5.00000 −0.250943 −0.125471 0.992097i \(-0.540044\pi\)
−0.125471 + 0.992097i \(0.540044\pi\)
\(398\) −9.46410 + 16.3923i −0.474393 + 0.821672i
\(399\) 51.7128i 2.58888i
\(400\) −1.00000 1.73205i −0.0500000 0.0866025i
\(401\) 26.7846i 1.33756i 0.743461 + 0.668780i \(0.233183\pi\)
−0.743461 + 0.668780i \(0.766817\pi\)
\(402\) −9.92820 + 5.73205i −0.495174 + 0.285889i
\(403\) −14.1962 24.5885i −0.707161 1.22484i
\(404\) 3.23205 + 5.59808i 0.160801 + 0.278515i
\(405\) −3.69615 2.13397i −0.183663 0.106038i
\(406\) 30.9282 1.53494
\(407\) −0.633975 + 7.68653i −0.0314250 + 0.381007i
\(408\) 4.73205 0.234271
\(409\) 2.08846 + 1.20577i 0.103268 + 0.0596216i 0.550744 0.834674i \(-0.314344\pi\)
−0.447477 + 0.894296i \(0.647677\pi\)
\(410\) 5.59808 + 9.69615i 0.276469 + 0.478859i
\(411\) −10.0981 17.4904i −0.498101 0.862737i
\(412\) 6.00000 3.46410i 0.295599 0.170664i
\(413\) 37.8564i 1.86279i
\(414\) 10.5622 + 18.2942i 0.519103 + 0.899112i
\(415\) 9.80385i 0.481252i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) 33.3205 1.63171
\(418\) −6.00000 −0.293470
\(419\) −18.9282 + 32.7846i −0.924703 + 1.60163i −0.132665 + 0.991161i \(0.542354\pi\)
−0.792038 + 0.610472i \(0.790980\pi\)
\(420\) 16.3923 9.46410i 0.799863 0.461801i
\(421\) 20.6603i 1.00692i 0.864019 + 0.503460i \(0.167940\pi\)
−0.864019 + 0.503460i \(0.832060\pi\)
\(422\) 7.26795 + 4.19615i 0.353798 + 0.204266i
\(423\) 12.6340 21.8827i 0.614285 1.06397i
\(424\) −8.19615 4.73205i −0.398040 0.229809i
\(425\) 3.00000 1.73205i 0.145521 0.0840168i
\(426\) 22.3923 12.9282i 1.08491 0.626373i
\(427\) −9.21539 5.32051i −0.445964 0.257477i
\(428\) 2.19615 3.80385i 0.106155 0.183866i
\(429\) −18.0000 10.3923i −0.869048 0.501745i
\(430\) 4.39230i 0.211816i
\(431\) 13.9019 8.02628i 0.669632 0.386612i −0.126305 0.991991i \(-0.540312\pi\)
0.795937 + 0.605379i \(0.206979\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −33.3923 −1.60473 −0.802366 0.596832i \(-0.796426\pi\)
−0.802366 + 0.596832i \(0.796426\pi\)
\(434\) 18.9282 0.908583
\(435\) 18.2942 31.6865i 0.877141 1.51925i
\(436\) 4.26795i 0.204398i
\(437\) 11.1962 + 19.3923i 0.535585 + 0.927660i
\(438\) 22.9282i 1.09555i
\(439\) −8.19615 + 4.73205i −0.391181 + 0.225848i −0.682672 0.730725i \(-0.739182\pi\)
0.291491 + 0.956574i \(0.405849\pi\)
\(440\) 1.09808 + 1.90192i 0.0523487 + 0.0906707i
\(441\) −20.0885 34.7942i −0.956593 1.65687i
\(442\) 9.00000 + 5.19615i 0.428086 + 0.247156i
\(443\) −2.53590 −0.120484 −0.0602421 0.998184i \(-0.519187\pi\)
−0.0602421 + 0.998184i \(0.519187\pi\)
\(444\) 13.6603 + 9.46410i 0.648287 + 0.449146i
\(445\) −9.00000 −0.426641
\(446\) −7.43782 4.29423i −0.352191 0.203338i
\(447\) 13.5622 + 23.4904i 0.641469 + 1.11106i
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) −21.5885 + 12.4641i −1.01882 + 0.588217i −0.913763 0.406249i \(-0.866837\pi\)
−0.105060 + 0.994466i \(0.533503\pi\)
\(450\) 8.92820i 0.420880i
\(451\) 4.09808 + 7.09808i 0.192971 + 0.334235i
\(452\) 7.85641i 0.369534i
\(453\) 16.6603 28.8564i 0.782767 1.35579i
\(454\) −4.73205 −0.222086
\(455\) 41.5692 1.94880
\(456\) −6.46410 + 11.1962i −0.302709 + 0.524308i
\(457\) 17.3038 9.99038i 0.809440 0.467330i −0.0373215 0.999303i \(-0.511883\pi\)
0.846761 + 0.531973i \(0.178549\pi\)
\(458\) 19.0000i 0.887812i
\(459\) −6.00000 3.46410i −0.280056 0.161690i
\(460\) 4.09808 7.09808i 0.191074 0.330950i
\(461\) −29.1962 16.8564i −1.35980 0.785081i −0.370204 0.928951i \(-0.620712\pi\)
−0.989597 + 0.143869i \(0.954045\pi\)
\(462\) 12.0000 6.92820i 0.558291 0.322329i
\(463\) −12.5885 + 7.26795i −0.585035 + 0.337770i −0.763132 0.646243i \(-0.776339\pi\)
0.178097 + 0.984013i \(0.443006\pi\)
\(464\) 6.69615 + 3.86603i 0.310861 + 0.179476i
\(465\) 11.1962 19.3923i 0.519209 0.899297i
\(466\) 21.9904 + 12.6962i 1.01868 + 0.588138i
\(467\) 30.2487i 1.39974i 0.714269 + 0.699872i \(0.246760\pi\)
−0.714269 + 0.699872i \(0.753240\pi\)
\(468\) −23.1962 + 13.3923i −1.07224 + 0.619060i
\(469\) 8.39230 14.5359i 0.387521 0.671205i
\(470\) −9.80385 −0.452218
\(471\) 31.1244 1.43413
\(472\) 4.73205 8.19615i 0.217810 0.377258i
\(473\) 3.21539i 0.147844i
\(474\) −3.00000 5.19615i −0.137795 0.238667i
\(475\) 9.46410i 0.434243i
\(476\) −6.00000 + 3.46410i −0.275010 + 0.158777i
\(477\) 21.1244 + 36.5885i 0.967218 + 1.67527i
\(478\) −9.46410 16.3923i −0.432878 0.749767i
\(479\) −8.19615 4.73205i −0.374492 0.216213i 0.300927 0.953647i \(-0.402704\pi\)
−0.675419 + 0.737434i \(0.736037\pi\)
\(480\) 4.73205 0.215988
\(481\) 15.5885 + 33.0000i 0.710772 + 1.50467i
\(482\) −18.0000 −0.819878
\(483\) −44.7846 25.8564i −2.03777 1.17651i
\(484\) −4.69615 8.13397i −0.213461 0.369726i
\(485\) 4.50000 + 7.79423i 0.204334 + 0.353918i
\(486\) −16.2224 + 9.36603i −0.735864 + 0.424852i
\(487\) 28.0526i 1.27118i 0.772026 + 0.635591i \(0.219244\pi\)
−0.772026 + 0.635591i \(0.780756\pi\)
\(488\) −1.33013 2.30385i −0.0602120 0.104290i
\(489\) 25.8564i 1.16927i
\(490\) −7.79423 + 13.5000i −0.352107 + 0.609868i
\(491\) 28.9808 1.30788 0.653942 0.756545i \(-0.273114\pi\)
0.653942 + 0.756545i \(0.273114\pi\)
\(492\) 17.6603 0.796186
\(493\) −6.69615 + 11.5981i −0.301580 + 0.522351i
\(494\) −24.5885 + 14.1962i −1.10629 + 0.638715i
\(495\) 9.80385i 0.440650i
\(496\) 4.09808 + 2.36603i 0.184009 + 0.106238i
\(497\) −18.9282 + 32.7846i −0.849046 + 1.47059i
\(498\) 13.3923 + 7.73205i 0.600124 + 0.346481i
\(499\) 1.90192 1.09808i 0.0851418 0.0491566i −0.456825 0.889557i \(-0.651013\pi\)
0.541966 + 0.840400i \(0.317680\pi\)
\(500\) 10.5000 6.06218i 0.469574 0.271109i
\(501\) 16.3923 + 9.46410i 0.732354 + 0.422825i
\(502\) −9.46410 + 16.3923i −0.422404 + 0.731624i
\(503\) 16.0981 + 9.29423i 0.717778 + 0.414409i 0.813934 0.580957i \(-0.197322\pi\)
−0.0961565 + 0.995366i \(0.530655\pi\)
\(504\) 17.8564i 0.795388i
\(505\) −9.69615 + 5.59808i −0.431473 + 0.249111i
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) −62.8372 −2.79070
\(508\) −20.5885 −0.913465
\(509\) 18.8205 32.5981i 0.834204 1.44488i −0.0604722 0.998170i \(-0.519261\pi\)
0.894677 0.446714i \(-0.147406\pi\)
\(510\) 8.19615i 0.362932i
\(511\) −16.7846 29.0718i −0.742507 1.28606i
\(512\) 1.00000i 0.0441942i
\(513\) 16.3923 9.46410i 0.723738 0.417850i
\(514\) 0.401924 + 0.696152i 0.0177281 + 0.0307060i
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) 6.00000 + 3.46410i 0.264135 + 0.152499i
\(517\) −7.17691 −0.315640
\(518\) −24.2487 2.00000i −1.06543 0.0878750i
\(519\) 10.7321 0.471085
\(520\) 9.00000 + 5.19615i 0.394676 + 0.227866i
\(521\) −16.7321 28.9808i −0.733044 1.26967i −0.955576 0.294745i \(-0.904765\pi\)
0.222532 0.974925i \(-0.428568\pi\)
\(522\) −17.2583 29.8923i −0.755377 1.30835i
\(523\) 16.0981 9.29423i 0.703920 0.406408i −0.104886 0.994484i \(-0.533448\pi\)
0.808806 + 0.588076i \(0.200114\pi\)
\(524\) 2.19615i 0.0959394i
\(525\) −10.9282 18.9282i −0.476946 0.826095i
\(526\) 11.3205i 0.493598i
\(527\) −4.09808 + 7.09808i −0.178515 + 0.309197i
\(528\) 3.46410 0.150756
\(529\) 0.607695 0.0264215
\(530\) 8.19615 14.1962i 0.356018 0.616641i
\(531\) −36.5885 + 21.1244i −1.58780 + 0.916719i
\(532\) 18.9282i 0.820642i
\(533\) 33.5885 + 19.3923i 1.45488 + 0.839974i
\(534\) −7.09808 + 12.2942i −0.307164 + 0.532023i
\(535\) 6.58846 + 3.80385i 0.284844 + 0.164455i
\(536\) 3.63397 2.09808i 0.156964 0.0906231i
\(537\) 55.1769 31.8564i 2.38106 1.37471i
\(538\) 24.5885 + 14.1962i 1.06008 + 0.612040i
\(539\) −5.70577 + 9.88269i −0.245765 + 0.425677i
\(540\) −6.00000 3.46410i −0.258199 0.149071i
\(541\) 27.5885i 1.18612i −0.805158 0.593060i \(-0.797920\pi\)
0.805158 0.593060i \(-0.202080\pi\)
\(542\) 14.3660 8.29423i 0.617074 0.356268i
\(543\) −7.36603 + 12.7583i −0.316106 + 0.547512i
\(544\) −1.73205 −0.0742611
\(545\) −7.39230 −0.316652
\(546\) 32.7846 56.7846i 1.40305 2.43016i
\(547\) 18.5885i 0.794785i 0.917649 + 0.397393i \(0.130085\pi\)
−0.917649 + 0.397393i \(0.869915\pi\)
\(548\) 3.69615 + 6.40192i 0.157892 + 0.273477i
\(549\) 11.8756i 0.506840i
\(550\) 2.19615 1.26795i 0.0936443 0.0540655i
\(551\) −18.2942 31.6865i −0.779360 1.34989i
\(552\) −6.46410 11.1962i −0.275130 0.476540i
\(553\) 7.60770 + 4.39230i 0.323512 + 0.186780i
\(554\) −17.1962 −0.730595
\(555\) −16.3923 + 23.6603i −0.695815 + 1.00432i
\(556\) −12.1962 −0.517232
\(557\) 29.8923 + 17.2583i 1.26658 + 0.731259i 0.974339 0.225086i \(-0.0722665\pi\)
0.292239 + 0.956345i \(0.405600\pi\)
\(558\) −10.5622 18.2942i −0.447133 0.774456i
\(559\) 7.60770 + 13.1769i 0.321771 + 0.557324i
\(560\) −6.00000 + 3.46410i −0.253546 + 0.146385i
\(561\) 6.00000i 0.253320i
\(562\) −0.401924 0.696152i −0.0169541 0.0293654i
\(563\) 42.5885i 1.79489i 0.441127 + 0.897445i \(0.354579\pi\)
−0.441127 + 0.897445i \(0.645421\pi\)
\(564\) −7.73205 + 13.3923i −0.325578 + 0.563918i
\(565\) −13.6077 −0.572480
\(566\) 9.46410 0.397806
\(567\) 4.92820 8.53590i 0.206965 0.358474i
\(568\) −8.19615 + 4.73205i −0.343903 + 0.198552i
\(569\) 16.5167i 0.692414i 0.938158 + 0.346207i \(0.112531\pi\)
−0.938158 + 0.346207i \(0.887469\pi\)
\(570\) −19.3923 11.1962i −0.812254 0.468955i
\(571\) 18.4904 32.0263i 0.773798 1.34026i −0.161669 0.986845i \(-0.551688\pi\)
0.935467 0.353413i \(-0.114979\pi\)
\(572\) 6.58846 + 3.80385i 0.275477 + 0.159047i
\(573\) −15.5885 + 9.00000i −0.651217 + 0.375980i
\(574\) −22.3923 + 12.9282i −0.934637 + 0.539613i
\(575\) −8.19615 4.73205i −0.341803 0.197340i
\(576\) 2.23205 3.86603i 0.0930021 0.161084i
\(577\) −27.5885 15.9282i −1.14852 0.663100i −0.199996 0.979797i \(-0.564093\pi\)
−0.948527 + 0.316697i \(0.897426\pi\)
\(578\) 14.0000i 0.582323i
\(579\) 28.6865 16.5622i 1.19217 0.688301i
\(580\) −6.69615 + 11.5981i −0.278043 + 0.481584i
\(581\) −22.6410 −0.939308
\(582\) 14.1962 0.588449
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 8.39230i 0.347276i
\(585\) −23.1962 40.1769i −0.959043 1.66111i
\(586\) 4.60770i 0.190342i
\(587\) 13.9019 8.02628i 0.573794 0.331280i −0.184869 0.982763i \(-0.559186\pi\)
0.758663 + 0.651483i \(0.225853\pi\)
\(588\) 12.2942 + 21.2942i 0.507005 + 0.878159i
\(589\) −11.1962 19.3923i −0.461329 0.799046i
\(590\) 14.1962 + 8.19615i 0.584446 + 0.337430i
\(591\) −22.7321 −0.935072
\(592\) −5.00000 3.46410i −0.205499 0.142374i
\(593\) 30.4641 1.25101 0.625505 0.780220i \(-0.284893\pi\)
0.625505 + 0.780220i \(0.284893\pi\)
\(594\) −4.39230 2.53590i −0.180218 0.104049i
\(595\) −6.00000 10.3923i −0.245976 0.426043i
\(596\) −4.96410 8.59808i −0.203338 0.352191i
\(597\) −44.7846 + 25.8564i −1.83291 + 1.05823i
\(598\) 28.3923i 1.16105i
\(599\) −0.633975 1.09808i −0.0259035 0.0448662i 0.852783 0.522265i \(-0.174913\pi\)
−0.878687 + 0.477399i \(0.841580\pi\)
\(600\) 5.46410i 0.223071i
\(601\) −7.89230 + 13.6699i −0.321934 + 0.557606i −0.980887 0.194578i \(-0.937666\pi\)
0.658953 + 0.752184i \(0.271000\pi\)
\(602\) −10.1436 −0.413422
\(603\) −18.7321 −0.762828
\(604\) −6.09808 + 10.5622i −0.248127 + 0.429769i
\(605\) 14.0885 8.13397i 0.572777 0.330693i
\(606\) 17.6603i 0.717399i
\(607\) −34.6865 20.0263i −1.40788 0.812842i −0.412699 0.910867i \(-0.635414\pi\)
−0.995184 + 0.0980258i \(0.968747\pi\)
\(608\) 2.36603 4.09808i 0.0959550 0.166199i
\(609\) 73.1769 + 42.2487i 2.96528 + 1.71200i
\(610\) 3.99038 2.30385i 0.161566 0.0932801i
\(611\) −29.4115 + 16.9808i −1.18986 + 0.686968i
\(612\) 6.69615 + 3.86603i 0.270676 + 0.156275i
\(613\) −16.6962 + 28.9186i −0.674351 + 1.16801i 0.302307 + 0.953211i \(0.402243\pi\)
−0.976658 + 0.214800i \(0.931090\pi\)
\(614\) 3.46410 + 2.00000i 0.139800 + 0.0807134i
\(615\) 30.5885i 1.23345i
\(616\) −4.39230 + 2.53590i −0.176971 + 0.102174i
\(617\) 5.66025 9.80385i 0.227873 0.394688i −0.729304 0.684189i \(-0.760156\pi\)
0.957178 + 0.289501i \(0.0934895\pi\)
\(618\) 18.9282 0.761404
\(619\) −41.1769 −1.65504 −0.827520 0.561436i \(-0.810249\pi\)
−0.827520 + 0.561436i \(0.810249\pi\)
\(620\) −4.09808 + 7.09808i −0.164583 + 0.285066i
\(621\) 18.9282i 0.759563i
\(622\) −2.19615 3.80385i −0.0880577 0.152520i
\(623\) 20.7846i 0.832718i
\(624\) 14.1962 8.19615i 0.568301 0.328109i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) −4.79423 8.30385i −0.191616 0.331888i
\(627\) −14.1962 8.19615i −0.566940 0.327323i
\(628\) −11.3923 −0.454602
\(629\) 6.00000 8.66025i 0.239236 0.345307i
\(630\) 30.9282 1.23221
\(631\) 10.6865 + 6.16987i 0.425424 + 0.245619i 0.697395 0.716687i \(-0.254342\pi\)
−0.271971 + 0.962305i \(0.587676\pi\)
\(632\) 1.09808 + 1.90192i 0.0436791 + 0.0756545i
\(633\) 11.4641 + 19.8564i 0.455657 + 0.789221i
\(634\) 7.79423 4.50000i 0.309548 0.178718i
\(635\) 35.6603i 1.41513i
\(636\) −12.9282 22.3923i −0.512637 0.887913i
\(637\) 54.0000i 2.13956i
\(638\) −4.90192 + 8.49038i −0.194069 + 0.336137i
\(639\) 42.2487 1.67133
\(640\) −1.73205 −0.0684653
\(641\) 23.4282 40.5788i 0.925358 1.60277i 0.134375 0.990931i \(-0.457097\pi\)
0.790984 0.611837i \(-0.209569\pi\)
\(642\) 10.3923 6.00000i 0.410152 0.236801i
\(643\) 9.12436i 0.359829i −0.983682 0.179915i \(-0.942418\pi\)
0.983682 0.179915i \(-0.0575822\pi\)
\(644\) 16.3923 + 9.46410i 0.645947 + 0.372938i
\(645\) −6.00000 + 10.3923i −0.236250 + 0.409197i
\(646\) 7.09808 + 4.09808i 0.279270 + 0.161237i
\(647\) −8.19615 + 4.73205i −0.322224 + 0.186036i −0.652383 0.757889i \(-0.726231\pi\)
0.330159 + 0.943925i \(0.392897\pi\)
\(648\) 2.13397 1.23205i 0.0838304 0.0483995i
\(649\) 10.3923 + 6.00000i 0.407934 + 0.235521i
\(650\) 6.00000 10.3923i 0.235339 0.407620i
\(651\) 44.7846 + 25.8564i 1.75525 + 1.01339i
\(652\) 9.46410i 0.370643i
\(653\) 5.89230 3.40192i 0.230584 0.133128i −0.380258 0.924881i \(-0.624165\pi\)
0.610841 + 0.791753i \(0.290831\pi\)
\(654\) −5.83013 + 10.0981i −0.227976 + 0.394866i
\(655\) 3.80385 0.148629
\(656\) −6.46410 −0.252381
\(657\) −18.7321 + 32.4449i −0.730807 + 1.26579i
\(658\) 22.6410i 0.882639i
\(659\) −7.26795 12.5885i −0.283119 0.490377i 0.689032 0.724731i \(-0.258036\pi\)
−0.972151 + 0.234354i \(0.924703\pi\)
\(660\) 6.00000i 0.233550i
\(661\) 25.2846 14.5981i 0.983457 0.567799i 0.0801452 0.996783i \(-0.474462\pi\)
0.903312 + 0.428984i \(0.141128\pi\)
\(662\) −8.53590 14.7846i −0.331757 0.574620i
\(663\) 14.1962 + 24.5885i 0.551333 + 0.954937i
\(664\) −4.90192 2.83013i −0.190232 0.109830i
\(665\) 32.7846 1.27133
\(666\) 11.5981 + 24.5526i 0.449416 + 0.951392i
\(667\) 36.5885 1.41671
\(668\) −6.00000 3.46410i −0.232147 0.134030i
\(669\) −11.7321 20.3205i −0.453587 0.785636i
\(670\) 3.63397 + 6.29423i 0.140393 + 0.243167i
\(671\) 2.92116 1.68653i 0.112770 0.0651079i
\(672\) 10.9282i 0.421565i
\(673\) 6.19615 + 10.7321i 0.238844 + 0.413690i 0.960383 0.278684i \(-0.0898982\pi\)
−0.721539 + 0.692374i \(0.756565\pi\)
\(674\) 7.00000i 0.269630i
\(675\) −4.00000 + 6.92820i −0.153960 + 0.266667i
\(676\) 23.0000 0.884615
\(677\) 7.14359 0.274551 0.137275 0.990533i \(-0.456165\pi\)
0.137275 + 0.990533i \(0.456165\pi\)
\(678\) −10.7321 + 18.5885i −0.412162 + 0.713885i
\(679\) −18.0000 + 10.3923i −0.690777 + 0.398820i
\(680\) 3.00000i 0.115045i
\(681\) −11.1962 6.46410i −0.429037 0.247705i
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) 26.7846 + 15.4641i 1.02488 + 0.591717i 0.915515 0.402284i \(-0.131783\pi\)
0.109370 + 0.994001i \(0.465117\pi\)
\(684\) −18.2942 + 10.5622i −0.699497 + 0.403855i
\(685\) −11.0885 + 6.40192i −0.423668 + 0.244605i
\(686\) −6.92820 4.00000i −0.264520 0.152721i
\(687\) 25.9545 44.9545i 0.990225 1.71512i
\(688\) −2.19615 1.26795i −0.0837275 0.0483401i
\(689\) 56.7846i 2.16332i
\(690\) 19.3923 11.1962i 0.738252 0.426230i
\(691\) 5.90192 10.2224i 0.224520 0.388880i −0.731655 0.681675i \(-0.761252\pi\)
0.956175 + 0.292795i \(0.0945853\pi\)
\(692\) −3.92820 −0.149328
\(693\) 22.6410 0.860061
\(694\) −14.0263 + 24.2942i −0.532430 + 0.922196i
\(695\) 21.1244i 0.801292i
\(696\) 10.5622 + 18.2942i 0.400358 + 0.693441i
\(697\) 11.1962i 0.424085i
\(698\) −23.7224 + 13.6962i −0.897907 + 0.518407i
\(699\) 34.6865 + 60.0788i 1.31197 + 2.27239i
\(700\) 4.00000 + 6.92820i 0.151186 + 0.261861i
\(701\) 22.3923 + 12.9282i 0.845746 + 0.488291i 0.859213 0.511618i \(-0.170954\pi\)
−0.0134675 + 0.999909i \(0.504287\pi\)
\(702\) −24.0000 −0.905822
\(703\) 12.2942 + 26.0263i 0.463686 + 0.981600i
\(704\) −1.26795 −0.0477876
\(705\) −23.1962 13.3923i −0.873618 0.504383i
\(706\) 2.93782 + 5.08846i 0.110566 + 0.191507i
\(707\) −12.9282 22.3923i −0.486215 0.842149i
\(708\) 22.3923 12.9282i 0.841554 0.485872i
\(709\) 30.0000i 1.12667i −0.826227 0.563337i \(-0.809517\pi\)
0.826227 0.563337i \(-0.190483\pi\)
\(710\) −8.19615 14.1962i −0.307596 0.532772i
\(711\) 9.80385i 0.367673i
\(712\) 2.59808 4.50000i 0.0973670 0.168645i
\(713\) 22.3923 0.838598
\(714\) −18.9282 −0.708370
\(715\) −6.58846 + 11.4115i −0.246394 + 0.426768i
\(716\) −20.1962 + 11.6603i −0.754766 + 0.435764i
\(717\) 51.7128i 1.93125i
\(718\) −22.9808 13.2679i −0.857634 0.495155i
\(719\) −13.2224 + 22.9019i −0.493114 + 0.854098i −0.999969 0.00793367i \(-0.997475\pi\)
0.506855 + 0.862031i \(0.330808\pi\)
\(720\) 6.69615 + 3.86603i 0.249551 + 0.144078i
\(721\) −24.0000 + 13.8564i −0.893807 + 0.516040i
\(722\) −2.93782 + 1.69615i −0.109334 + 0.0631243i
\(723\) −42.5885 24.5885i −1.58388 0.914455i
\(724\) 2.69615 4.66987i 0.100202 0.173554i
\(725\) 13.3923 + 7.73205i 0.497378 + 0.287161i
\(726\) 25.6603i 0.952341i
\(727\) −22.3923 + 12.9282i −0.830485 + 0.479481i −0.854019 0.520243i \(-0.825842\pi\)
0.0235340 + 0.999723i \(0.492508\pi\)
\(728\) −12.0000 + 20.7846i −0.444750 + 0.770329i
\(729\) −43.7846 −1.62165
\(730\) 14.5359 0.537998
\(731\) 2.19615 3.80385i 0.0812276 0.140690i
\(732\) 7.26795i 0.268631i
\(733\) −18.1962 31.5167i −0.672090 1.16409i −0.977310 0.211813i \(-0.932063\pi\)
0.305220 0.952282i \(-0.401270\pi\)
\(734\) 20.3923i 0.752694i
\(735\) −36.8827 + 21.2942i −1.36044 + 0.785449i
\(736\) 2.36603 + 4.09808i 0.0872129 + 0.151057i
\(737\) 2.66025 + 4.60770i 0.0979917 + 0.169727i
\(738\) 24.9904 + 14.4282i 0.919909 + 0.531110i
\(739\) −44.9808 −1.65464 −0.827322 0.561728i \(-0.810137\pi\)
−0.827322 + 0.561728i \(0.810137\pi\)
\(740\) 6.00000 8.66025i 0.220564 0.318357i
\(741\) −77.5692 −2.84958
\(742\) 32.7846 + 18.9282i 1.20356 + 0.694876i
\(743\) −11.9545 20.7058i −0.438567 0.759621i 0.559012 0.829160i \(-0.311181\pi\)
−0.997579 + 0.0695386i \(0.977847\pi\)
\(744\) 6.46410 + 11.1962i 0.236985 + 0.410471i
\(745\) 14.8923 8.59808i 0.545612 0.315009i
\(746\) 21.7846i 0.797591i
\(747\) 12.6340 + 21.8827i 0.462253 + 0.800646i
\(748\) 2.19615i 0.0802993i
\(749\) −8.78461 + 15.2154i −0.320983 + 0.555958i
\(750\) 33.1244 1.20953
\(751\) −15.6077 −0.569533 −0.284766 0.958597i \(-0.591916\pi\)
−0.284766 + 0.958597i \(0.591916\pi\)
\(752\) 2.83013 4.90192i 0.103204 0.178755i
\(753\) −44.7846 + 25.8564i −1.63204 + 0.942260i
\(754\) 46.3923i 1.68951i
\(755\) −18.2942 10.5622i −0.665795 0.384397i
\(756\) 8.00000 13.8564i 0.290957 0.503953i
\(757\) −6.69615 3.86603i −0.243376 0.140513i 0.373352 0.927690i \(-0.378209\pi\)
−0.616727 + 0.787177i \(0.711542\pi\)
\(758\) −14.5359 + 8.39230i −0.527968 + 0.304822i
\(759\) 14.1962 8.19615i 0.515288 0.297501i
\(760\) 7.09808 + 4.09808i 0.257474 + 0.148653i
\(761\) 1.16025 2.00962i 0.0420592 0.0728486i −0.844229 0.535982i \(-0.819942\pi\)
0.886289 + 0.463133i \(0.153275\pi\)
\(762\) −48.7128 28.1244i −1.76468 1.01884i
\(763\) 17.0718i 0.618041i
\(764\) 5.70577 3.29423i 0.206428 0.119181i
\(765\) −6.69615 + 11.5981i −0.242100 + 0.419329i
\(766\) −1.85641 −0.0670747
\(767\) 56.7846 2.05037
\(768\) −1.36603 + 2.36603i −0.0492922 + 0.0853766i
\(769\) 33.7128i