Properties

Label 630.2.j.i.211.1
Level $630$
Weight $2$
Character 630.211
Analytic conductor $5.031$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(211,630)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.211");
 
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.j (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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(1.71903 + 0.211943i\) of defining polynomial
Character \(\chi\) \(=\) 630.211
Dual form 630.2.j.i.421.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.71903 + 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.04307 + 1.38276i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.71903 + 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.04307 + 1.38276i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +1.00000 q^{10} +(-0.0430651 - 0.0745909i) q^{11} +(0.675970 - 1.59470i) q^{12} +(1.89500 - 3.28224i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.675970 - 1.59470i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.82032 q^{17} +(-2.08613 - 2.15594i) q^{18} -1.64806 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.04307 - 1.38276i) q^{21} +(-0.0430651 + 0.0745909i) q^{22} +(-3.98113 + 6.89553i) q^{23} +(-1.71903 + 0.211943i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.79001 q^{26} +(-4.84823 + 1.86940i) q^{27} -1.00000 q^{28} +(4.54307 + 7.86882i) q^{29} +(-1.71903 + 0.211943i) q^{30} +(-1.08613 + 1.88123i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0898394 + 0.119097i) q^{33} +(2.91016 + 5.04055i) q^{34} -1.00000 q^{35} +(-0.824030 + 2.88461i) q^{36} -4.43807 q^{37} +(0.824030 + 1.42726i) q^{38} +(-2.56193 + 6.04392i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.69113 - 2.92912i) q^{41} +(-0.675970 + 1.59470i) q^{42} +(4.23419 + 7.33383i) q^{43} +0.0861302 q^{44} +(-0.824030 + 2.88461i) q^{45} +7.96227 q^{46} +(-5.17226 - 8.95862i) q^{47} +(1.04307 + 1.38276i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(10.0053 - 1.23357i) q^{51} +(1.89500 + 3.28224i) q^{52} -12.7826 q^{53} +(4.04307 + 3.26399i) q^{54} +0.0861302 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.83307 - 0.349294i) q^{57} +(4.54307 - 7.86882i) q^{58} +(-6.43436 + 11.1446i) q^{59} +(1.04307 + 1.38276i) q^{60} +(-0.219035 - 0.379379i) q^{61} +2.17226 q^{62} +(2.08613 + 2.15594i) q^{63} +1.00000 q^{64} +(1.89500 + 3.28224i) q^{65} +(0.0582214 - 0.137352i) q^{66} +(0.527909 - 0.914365i) q^{67} +(2.91016 - 5.04055i) q^{68} +(5.38225 - 12.6974i) q^{69} +(0.500000 + 0.866025i) q^{70} -16.0181 q^{71} +(2.91016 - 0.728674i) q^{72} -7.17226 q^{73} +(2.21903 + 3.84348i) q^{74} +(1.04307 + 1.38276i) q^{75} +(0.824030 - 1.42726i) q^{76} +(0.0430651 - 0.0745909i) q^{77} +(6.51516 - 0.803265i) q^{78} +(6.52420 + 11.3002i) q^{79} +1.00000 q^{80} +(7.93807 - 4.24111i) q^{81} -3.38225 q^{82} +(4.43807 + 7.68696i) q^{83} +(1.71903 - 0.211943i) q^{84} +(2.91016 - 5.04055i) q^{85} +(4.23419 - 7.33383i) q^{86} +(-9.47743 - 12.5639i) q^{87} +(-0.0430651 - 0.0745909i) q^{88} -2.00000 q^{89} +(2.91016 - 0.728674i) q^{90} +3.79001 q^{91} +(-3.98113 - 6.89553i) q^{92} +(1.46838 - 3.46410i) q^{93} +(-5.17226 + 8.95862i) q^{94} +(0.824030 - 1.42726i) q^{95} +(0.675970 - 1.59470i) q^{96} +(-3.96838 - 6.87344i) q^{97} +1.00000 q^{98} +(-0.179679 - 0.185691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + 7 q^{11} + 2 q^{12} + 3 q^{14} + 2 q^{15} - 3 q^{16} - 10 q^{17} + 2 q^{18} - 14 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} + 2 q^{23} - q^{24} - 3 q^{25} + 2 q^{27} - 6 q^{28} + 20 q^{29} - q^{30} + 8 q^{31} - 3 q^{32} + 13 q^{33} + 5 q^{34} - 6 q^{35} - 7 q^{36} - 8 q^{37} + 7 q^{38} - 34 q^{39} - 3 q^{40} + 7 q^{41} - 2 q^{42} + 15 q^{43} - 14 q^{44} - 7 q^{45} - 4 q^{46} - 2 q^{47} - q^{48} - 3 q^{49} - 3 q^{50} + q^{51} + 17 q^{54} - 14 q^{55} + 3 q^{56} - 13 q^{57} + 20 q^{58} + 7 q^{59} - q^{60} + 8 q^{61} - 16 q^{62} - 2 q^{63} + 6 q^{64} - 8 q^{66} - 3 q^{67} + 5 q^{68} + 26 q^{69} + 3 q^{70} - 32 q^{71} + 5 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 7 q^{76} - 7 q^{77} + 38 q^{78} + 6 q^{79} + 6 q^{80} + 29 q^{81} - 14 q^{82} + 8 q^{83} + q^{84} + 5 q^{85} + 15 q^{86} - 4 q^{87} + 7 q^{88} - 12 q^{89} + 5 q^{90} + 2 q^{92} - 12 q^{93} - 2 q^{94} + 7 q^{95} + 2 q^{96} - 3 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.71903 + 0.211943i −0.992485 + 0.122365i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 1.04307 + 1.38276i 0.425830 + 0.564508i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 2.91016 0.728674i 0.970054 0.242891i
\(10\) 1.00000 0.316228
\(11\) −0.0430651 0.0745909i −0.0129846 0.0224900i 0.859460 0.511203i \(-0.170800\pi\)
−0.872445 + 0.488713i \(0.837467\pi\)
\(12\) 0.675970 1.59470i 0.195136 0.460350i
\(13\) 1.89500 3.28224i 0.525580 0.910331i −0.473976 0.880538i \(-0.657182\pi\)
0.999556 0.0297931i \(-0.00948484\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0.675970 1.59470i 0.174535 0.411750i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −5.82032 −1.41164 −0.705818 0.708394i \(-0.749420\pi\)
−0.705818 + 0.708394i \(0.749420\pi\)
\(18\) −2.08613 2.15594i −0.491706 0.508159i
\(19\) −1.64806 −0.378091 −0.189046 0.981968i \(-0.560539\pi\)
−0.189046 + 0.981968i \(0.560539\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −1.04307 1.38276i −0.227615 0.301742i
\(22\) −0.0430651 + 0.0745909i −0.00918151 + 0.0159028i
\(23\) −3.98113 + 6.89553i −0.830124 + 1.43782i 0.0678156 + 0.997698i \(0.478397\pi\)
−0.897939 + 0.440119i \(0.854936\pi\)
\(24\) −1.71903 + 0.211943i −0.350896 + 0.0432626i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.79001 −0.743282
\(27\) −4.84823 + 1.86940i −0.933042 + 0.359767i
\(28\) −1.00000 −0.188982
\(29\) 4.54307 + 7.86882i 0.843626 + 1.46120i 0.886809 + 0.462136i \(0.152917\pi\)
−0.0431831 + 0.999067i \(0.513750\pi\)
\(30\) −1.71903 + 0.211943i −0.313851 + 0.0386953i
\(31\) −1.08613 + 1.88123i −0.195075 + 0.337879i −0.946925 0.321455i \(-0.895828\pi\)
0.751850 + 0.659334i \(0.229162\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.0898394 + 0.119097i 0.0156390 + 0.0207321i
\(34\) 2.91016 + 5.04055i 0.499088 + 0.864447i
\(35\) −1.00000 −0.169031
\(36\) −0.824030 + 2.88461i −0.137338 + 0.480768i
\(37\) −4.43807 −0.729614 −0.364807 0.931083i \(-0.618865\pi\)
−0.364807 + 0.931083i \(0.618865\pi\)
\(38\) 0.824030 + 1.42726i 0.133675 + 0.231533i
\(39\) −2.56193 + 6.04392i −0.410237 + 0.967802i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 1.69113 2.92912i 0.264109 0.457451i −0.703220 0.710972i \(-0.748255\pi\)
0.967330 + 0.253521i \(0.0815886\pi\)
\(42\) −0.675970 + 1.59470i −0.104304 + 0.246067i
\(43\) 4.23419 + 7.33383i 0.645708 + 1.11840i 0.984137 + 0.177407i \(0.0567710\pi\)
−0.338429 + 0.940992i \(0.609896\pi\)
\(44\) 0.0861302 0.0129846
\(45\) −0.824030 + 2.88461i −0.122839 + 0.430012i
\(46\) 7.96227 1.17397
\(47\) −5.17226 8.95862i −0.754452 1.30675i −0.945646 0.325197i \(-0.894570\pi\)
0.191195 0.981552i \(-0.438764\pi\)
\(48\) 1.04307 + 1.38276i 0.150553 + 0.199584i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 10.0053 1.23357i 1.40103 0.172735i
\(52\) 1.89500 + 3.28224i 0.262790 + 0.455165i
\(53\) −12.7826 −1.75582 −0.877912 0.478822i \(-0.841064\pi\)
−0.877912 + 0.478822i \(0.841064\pi\)
\(54\) 4.04307 + 3.26399i 0.550191 + 0.444173i
\(55\) 0.0861302 0.0116138
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 2.83307 0.349294i 0.375250 0.0462652i
\(58\) 4.54307 7.86882i 0.596534 1.03323i
\(59\) −6.43436 + 11.1446i −0.837682 + 1.45091i 0.0541453 + 0.998533i \(0.482757\pi\)
−0.891828 + 0.452375i \(0.850577\pi\)
\(60\) 1.04307 + 1.38276i 0.134659 + 0.178513i
\(61\) −0.219035 0.379379i −0.0280445 0.0485745i 0.851663 0.524091i \(-0.175595\pi\)
−0.879707 + 0.475516i \(0.842261\pi\)
\(62\) 2.17226 0.275877
\(63\) 2.08613 + 2.15594i 0.262828 + 0.271622i
\(64\) 1.00000 0.125000
\(65\) 1.89500 + 3.28224i 0.235046 + 0.407112i
\(66\) 0.0582214 0.137352i 0.00716656 0.0169068i
\(67\) 0.527909 0.914365i 0.0644943 0.111707i −0.831975 0.554813i \(-0.812790\pi\)
0.896470 + 0.443105i \(0.146123\pi\)
\(68\) 2.91016 5.04055i 0.352909 0.611256i
\(69\) 5.38225 12.6974i 0.647947 1.52859i
\(70\) 0.500000 + 0.866025i 0.0597614 + 0.103510i
\(71\) −16.0181 −1.90100 −0.950499 0.310729i \(-0.899427\pi\)
−0.950499 + 0.310729i \(0.899427\pi\)
\(72\) 2.91016 0.728674i 0.342966 0.0858750i
\(73\) −7.17226 −0.839450 −0.419725 0.907651i \(-0.637873\pi\)
−0.419725 + 0.907651i \(0.637873\pi\)
\(74\) 2.21903 + 3.84348i 0.257958 + 0.446796i
\(75\) 1.04307 + 1.38276i 0.120443 + 0.159667i
\(76\) 0.824030 1.42726i 0.0945228 0.163718i
\(77\) 0.0430651 0.0745909i 0.00490772 0.00850043i
\(78\) 6.51516 0.803265i 0.737696 0.0909518i
\(79\) 6.52420 + 11.3002i 0.734030 + 1.27138i 0.955148 + 0.296130i \(0.0956961\pi\)
−0.221118 + 0.975247i \(0.570971\pi\)
\(80\) 1.00000 0.111803
\(81\) 7.93807 4.24111i 0.882008 0.471235i
\(82\) −3.38225 −0.373507
\(83\) 4.43807 + 7.68696i 0.487141 + 0.843754i 0.999891 0.0147847i \(-0.00470630\pi\)
−0.512749 + 0.858538i \(0.671373\pi\)
\(84\) 1.71903 0.211943i 0.187562 0.0231248i
\(85\) 2.91016 5.04055i 0.315651 0.546724i
\(86\) 4.23419 7.33383i 0.456585 0.790828i
\(87\) −9.47743 12.5639i −1.01609 1.34699i
\(88\) −0.0430651 0.0745909i −0.00459075 0.00795142i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 2.91016 0.728674i 0.306758 0.0768089i
\(91\) 3.79001 0.397301
\(92\) −3.98113 6.89553i −0.415062 0.718908i
\(93\) 1.46838 3.46410i 0.152264 0.359211i
\(94\) −5.17226 + 8.95862i −0.533478 + 0.924011i
\(95\) 0.824030 1.42726i 0.0845437 0.146434i
\(96\) 0.675970 1.59470i 0.0689909 0.162758i
\(97\) −3.96838 6.87344i −0.402928 0.697892i 0.591150 0.806562i \(-0.298674\pi\)
−0.994078 + 0.108670i \(0.965341\pi\)
\(98\) 1.00000 0.101015
\(99\) −0.179679 0.185691i −0.0180584 0.0186627i
\(100\) 1.00000 0.100000
\(101\) −0.734191 1.27166i −0.0730547 0.126535i 0.827184 0.561931i \(-0.189941\pi\)
−0.900239 + 0.435397i \(0.856608\pi\)
\(102\) −6.07097 8.04809i −0.601116 0.796879i
\(103\) −3.74323 + 6.48347i −0.368832 + 0.638835i −0.989383 0.145330i \(-0.953576\pi\)
0.620551 + 0.784166i \(0.286909\pi\)
\(104\) 1.89500 3.28224i 0.185820 0.321850i
\(105\) 1.71903 0.211943i 0.167761 0.0206835i
\(106\) 6.39130 + 11.0700i 0.620777 + 1.07522i
\(107\) −0.351939 −0.0340232 −0.0170116 0.999855i \(-0.505415\pi\)
−0.0170116 + 0.999855i \(0.505415\pi\)
\(108\) 0.805165 5.13339i 0.0774770 0.493961i
\(109\) 8.38225 0.802874 0.401437 0.915887i \(-0.368511\pi\)
0.401437 + 0.915887i \(0.368511\pi\)
\(110\) −0.0430651 0.0745909i −0.00410610 0.00711197i
\(111\) 7.62920 0.940616i 0.724131 0.0892794i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 2.76210 4.78410i 0.259836 0.450050i −0.706361 0.707851i \(-0.749665\pi\)
0.966198 + 0.257801i \(0.0829980\pi\)
\(114\) −1.71903 2.27887i −0.161002 0.213435i
\(115\) −3.98113 6.89553i −0.371243 0.643011i
\(116\) −9.08613 −0.843626
\(117\) 3.12308 10.9327i 0.288729 1.01073i
\(118\) 12.8687 1.18466
\(119\) −2.91016 5.04055i −0.266774 0.462066i
\(120\) 0.675970 1.59470i 0.0617073 0.145575i
\(121\) 5.49629 9.51985i 0.499663 0.865441i
\(122\) −0.219035 + 0.379379i −0.0198305 + 0.0343474i
\(123\) −2.28630 + 5.39367i −0.206149 + 0.486331i
\(124\) −1.08613 1.88123i −0.0975374 0.168940i
\(125\) 1.00000 0.0894427
\(126\) 0.824030 2.88461i 0.0734105 0.256981i
\(127\) −5.85063 −0.519160 −0.259580 0.965722i \(-0.583584\pi\)
−0.259580 + 0.965722i \(0.583584\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.83307 11.7097i −0.777709 1.03098i
\(130\) 1.89500 3.28224i 0.166203 0.287872i
\(131\) −3.02791 + 5.24449i −0.264550 + 0.458213i −0.967446 0.253079i \(-0.918557\pi\)
0.702896 + 0.711293i \(0.251890\pi\)
\(132\) −0.148061 + 0.0182547i −0.0128870 + 0.00158886i
\(133\) −0.824030 1.42726i −0.0714525 0.123759i
\(134\) −1.05582 −0.0912087
\(135\) 0.805165 5.13339i 0.0692976 0.441812i
\(136\) −5.82032 −0.499088
\(137\) 3.98484 + 6.90195i 0.340448 + 0.589674i 0.984516 0.175295i \(-0.0560879\pi\)
−0.644068 + 0.764968i \(0.722755\pi\)
\(138\) −13.6874 + 1.68754i −1.16515 + 0.143653i
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 0.500000 0.866025i 0.0422577 0.0731925i
\(141\) 10.7900 + 14.3040i 0.908683 + 1.20461i
\(142\) 8.00904 + 13.8721i 0.672104 + 1.16412i
\(143\) −0.326434 −0.0272978
\(144\) −2.08613 2.15594i −0.173844 0.179661i
\(145\) −9.08613 −0.754562
\(146\) 3.58613 + 6.21136i 0.296790 + 0.514056i
\(147\) 0.675970 1.59470i 0.0557530 0.131529i
\(148\) 2.21903 3.84348i 0.182404 0.315932i
\(149\) 5.38225 9.32233i 0.440931 0.763715i −0.556828 0.830628i \(-0.687982\pi\)
0.997759 + 0.0669128i \(0.0213149\pi\)
\(150\) 0.675970 1.59470i 0.0551927 0.130207i
\(151\) −2.70388 4.68325i −0.220039 0.381118i 0.734781 0.678305i \(-0.237285\pi\)
−0.954819 + 0.297187i \(0.903952\pi\)
\(152\) −1.64806 −0.133675
\(153\) −16.9381 + 4.24111i −1.36936 + 0.342874i
\(154\) −0.0861302 −0.00694057
\(155\) −1.08613 1.88123i −0.0872401 0.151104i
\(156\) −3.95323 5.24066i −0.316511 0.419588i
\(157\) −5.80887 + 10.0613i −0.463599 + 0.802976i −0.999137 0.0415345i \(-0.986775\pi\)
0.535538 + 0.844511i \(0.320109\pi\)
\(158\) 6.52420 11.3002i 0.519037 0.898999i
\(159\) 21.9737 2.70918i 1.74263 0.214852i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −7.96227 −0.627515
\(162\) −7.64195 4.75401i −0.600408 0.373510i
\(163\) 5.86872 0.459674 0.229837 0.973229i \(-0.426181\pi\)
0.229837 + 0.973229i \(0.426181\pi\)
\(164\) 1.69113 + 2.92912i 0.132055 + 0.228726i
\(165\) −0.148061 + 0.0182547i −0.0115265 + 0.00142112i
\(166\) 4.43807 7.68696i 0.344461 0.596624i
\(167\) 8.00904 13.8721i 0.619758 1.07345i −0.369771 0.929123i \(-0.620564\pi\)
0.989530 0.144330i \(-0.0461027\pi\)
\(168\) −1.04307 1.38276i −0.0804742 0.106682i
\(169\) −0.682083 1.18140i −0.0524679 0.0908771i
\(170\) −5.82032 −0.446398
\(171\) −4.79612 + 1.20090i −0.366769 + 0.0918350i
\(172\) −8.46838 −0.645708
\(173\) 3.25839 + 5.64370i 0.247731 + 0.429082i 0.962896 0.269873i \(-0.0869818\pi\)
−0.715165 + 0.698956i \(0.753648\pi\)
\(174\) −6.14195 + 14.4896i −0.465620 + 1.09846i
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) −0.0430651 + 0.0745909i −0.00324615 + 0.00562250i
\(177\) 8.69886 20.5217i 0.653847 1.54251i
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) −1.00742 −0.0752980 −0.0376490 0.999291i \(-0.511987\pi\)
−0.0376490 + 0.999291i \(0.511987\pi\)
\(180\) −2.08613 2.15594i −0.155491 0.160694i
\(181\) 19.9852 1.48549 0.742743 0.669577i \(-0.233525\pi\)
0.742743 + 0.669577i \(0.233525\pi\)
\(182\) −1.89500 3.28224i −0.140467 0.243296i
\(183\) 0.456935 + 0.605743i 0.0337776 + 0.0447778i
\(184\) −3.98113 + 6.89553i −0.293493 + 0.508345i
\(185\) 2.21903 3.84348i 0.163147 0.282578i
\(186\) −3.73419 + 0.460395i −0.273804 + 0.0337578i
\(187\) 0.250653 + 0.434143i 0.0183295 + 0.0317477i
\(188\) 10.3445 0.754452
\(189\) −4.04307 3.26399i −0.294090 0.237420i
\(190\) −1.64806 −0.119563
\(191\) −1.61033 2.78917i −0.116519 0.201817i 0.801867 0.597503i \(-0.203840\pi\)
−0.918386 + 0.395685i \(0.870507\pi\)
\(192\) −1.71903 + 0.211943i −0.124061 + 0.0152956i
\(193\) 7.50904 13.0060i 0.540513 0.936196i −0.458362 0.888766i \(-0.651564\pi\)
0.998875 0.0474299i \(-0.0151031\pi\)
\(194\) −3.96838 + 6.87344i −0.284913 + 0.493484i
\(195\) −3.95323 5.24066i −0.283096 0.375291i
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 3.48647 0.248401 0.124200 0.992257i \(-0.460363\pi\)
0.124200 + 0.992257i \(0.460363\pi\)
\(198\) −0.0709739 + 0.248452i −0.00504390 + 0.0176567i
\(199\) −8.30679 −0.588853 −0.294426 0.955674i \(-0.595129\pi\)
−0.294426 + 0.955674i \(0.595129\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −0.713701 + 1.68371i −0.0503406 + 0.118760i
\(202\) −0.734191 + 1.27166i −0.0516575 + 0.0894734i
\(203\) −4.54307 + 7.86882i −0.318861 + 0.552283i
\(204\) −3.93436 + 9.28166i −0.275460 + 0.649846i
\(205\) 1.69113 + 2.92912i 0.118113 + 0.204578i
\(206\) 7.48647 0.521607
\(207\) −6.56115 + 22.9680i −0.456032 + 1.59639i
\(208\) −3.79001 −0.262790
\(209\) 0.0709739 + 0.122930i 0.00490937 + 0.00850327i
\(210\) −1.04307 1.38276i −0.0719783 0.0954193i
\(211\) −14.1723 + 24.5471i −0.975659 + 1.68989i −0.297914 + 0.954593i \(0.596291\pi\)
−0.677744 + 0.735298i \(0.737042\pi\)
\(212\) 6.39130 11.0700i 0.438956 0.760294i
\(213\) 27.5356 3.39492i 1.88671 0.232616i
\(214\) 0.175970 + 0.304788i 0.0120290 + 0.0208349i
\(215\) −8.46838 −0.577539
\(216\) −4.84823 + 1.86940i −0.329880 + 0.127197i
\(217\) −2.17226 −0.147463
\(218\) −4.19113 7.25924i −0.283859 0.491658i
\(219\) 12.3294 1.52011i 0.833141 0.102719i
\(220\) −0.0430651 + 0.0745909i −0.00290345 + 0.00502892i
\(221\) −11.0295 + 19.1037i −0.741927 + 1.28505i
\(222\) −4.62920 6.13677i −0.310691 0.411873i
\(223\) 1.24935 + 2.16393i 0.0836625 + 0.144908i 0.904820 0.425793i \(-0.140005\pi\)
−0.821158 + 0.570701i \(0.806672\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −2.08613 2.15594i −0.139075 0.143729i
\(226\) −5.52420 −0.367464
\(227\) 7.62549 + 13.2077i 0.506121 + 0.876628i 0.999975 + 0.00708274i \(0.00225452\pi\)
−0.493854 + 0.869545i \(0.664412\pi\)
\(228\) −1.11404 + 2.62816i −0.0737790 + 0.174054i
\(229\) −12.4471 + 21.5590i −0.822528 + 1.42466i 0.0812653 + 0.996693i \(0.474104\pi\)
−0.903794 + 0.427968i \(0.859229\pi\)
\(230\) −3.98113 + 6.89553i −0.262508 + 0.454678i
\(231\) −0.0582214 + 0.137352i −0.00383069 + 0.00903708i
\(232\) 4.54307 + 7.86882i 0.298267 + 0.516613i
\(233\) 28.9474 1.89641 0.948205 0.317660i \(-0.102897\pi\)
0.948205 + 0.317660i \(0.102897\pi\)
\(234\) −11.0295 + 2.76168i −0.721023 + 0.180537i
\(235\) 10.3445 0.674802
\(236\) −6.43436 11.1446i −0.418841 0.725454i
\(237\) −13.6103 18.0428i −0.884086 1.17200i
\(238\) −2.91016 + 5.04055i −0.188638 + 0.326730i
\(239\) 15.2584 26.4283i 0.986983 1.70951i 0.354215 0.935164i \(-0.384748\pi\)
0.632769 0.774341i \(-0.281918\pi\)
\(240\) −1.71903 + 0.211943i −0.110963 + 0.0136808i
\(241\) −10.8913 18.8643i −0.701570 1.21515i −0.967915 0.251277i \(-0.919149\pi\)
0.266345 0.963878i \(-0.414184\pi\)
\(242\) −10.9926 −0.706630
\(243\) −12.7469 + 8.97304i −0.817717 + 0.575621i
\(244\) 0.438069 0.0280445
\(245\) −0.500000 0.866025i −0.0319438 0.0553283i
\(246\) 5.81421 0.716844i 0.370700 0.0457043i
\(247\) −3.12308 + 5.40934i −0.198717 + 0.344188i
\(248\) −1.08613 + 1.88123i −0.0689693 + 0.119458i
\(249\) −9.25839 12.2735i −0.586727 0.777804i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −5.17226 −0.326470 −0.163235 0.986587i \(-0.552193\pi\)
−0.163235 + 0.986587i \(0.552193\pi\)
\(252\) −2.91016 + 0.728674i −0.183323 + 0.0459021i
\(253\) 0.685792 0.0431154
\(254\) 2.92532 + 5.06680i 0.183551 + 0.317919i
\(255\) −3.93436 + 9.28166i −0.246379 + 0.581240i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.72808 15.1175i 0.544443 0.943002i −0.454199 0.890900i \(-0.650075\pi\)
0.998642 0.0521020i \(-0.0165921\pi\)
\(258\) −5.72437 + 13.5045i −0.356384 + 0.840755i
\(259\) −2.21903 3.84348i −0.137884 0.238822i
\(260\) −3.79001 −0.235046
\(261\) 18.9549 + 19.5891i 1.17328 + 1.21254i
\(262\) 6.05582 0.374130
\(263\) 13.0114 + 22.5365i 0.802320 + 1.38966i 0.918085 + 0.396383i \(0.129735\pi\)
−0.115765 + 0.993277i \(0.536932\pi\)
\(264\) 0.0898394 + 0.119097i 0.00552923 + 0.00732992i
\(265\) 6.39130 11.0700i 0.392614 0.680028i
\(266\) −0.824030 + 1.42726i −0.0505245 + 0.0875111i
\(267\) 3.43807 0.423885i 0.210406 0.0259414i
\(268\) 0.527909 + 0.914365i 0.0322472 + 0.0558537i
\(269\) 22.1297 1.34927 0.674636 0.738150i \(-0.264300\pi\)
0.674636 + 0.738150i \(0.264300\pi\)
\(270\) −4.84823 + 1.86940i −0.295054 + 0.113768i
\(271\) −2.13453 −0.129663 −0.0648317 0.997896i \(-0.520651\pi\)
−0.0648317 + 0.997896i \(0.520651\pi\)
\(272\) 2.91016 + 5.04055i 0.176454 + 0.305628i
\(273\) −6.51516 + 0.803265i −0.394315 + 0.0486158i
\(274\) 3.98484 6.90195i 0.240733 0.416962i
\(275\) −0.0430651 + 0.0745909i −0.00259692 + 0.00449800i
\(276\) 8.30516 + 11.0099i 0.499912 + 0.662717i
\(277\) −0.883557 1.53037i −0.0530878 0.0919508i 0.838260 0.545270i \(-0.183573\pi\)
−0.891348 + 0.453320i \(0.850240\pi\)
\(278\) −7.00000 −0.419832
\(279\) −1.79001 + 6.26612i −0.107165 + 0.375143i
\(280\) −1.00000 −0.0597614
\(281\) −9.11404 15.7860i −0.543698 0.941713i −0.998688 0.0512158i \(-0.983690\pi\)
0.454990 0.890497i \(-0.349643\pi\)
\(282\) 6.99258 16.4964i 0.416402 0.982346i
\(283\) 6.78259 11.7478i 0.403183 0.698334i −0.590925 0.806726i \(-0.701237\pi\)
0.994108 + 0.108393i \(0.0345704\pi\)
\(284\) 8.00904 13.8721i 0.475249 0.823156i
\(285\) −1.11404 + 2.62816i −0.0659900 + 0.155679i
\(286\) 0.163217 + 0.282700i 0.00965123 + 0.0167164i
\(287\) 3.38225 0.199648
\(288\) −0.824030 + 2.88461i −0.0485565 + 0.169977i
\(289\) 16.8761 0.992714
\(290\) 4.54307 + 7.86882i 0.266778 + 0.462073i
\(291\) 8.27856 + 10.9746i 0.485298 + 0.643343i
\(292\) 3.58613 6.21136i 0.209862 0.363492i
\(293\) −11.6218 + 20.1295i −0.678951 + 1.17598i 0.296346 + 0.955081i \(0.404232\pi\)
−0.975297 + 0.220898i \(0.929101\pi\)
\(294\) −1.71903 + 0.211943i −0.100256 + 0.0123607i
\(295\) −6.43436 11.1446i −0.374623 0.648866i
\(296\) −4.43807 −0.257958
\(297\) 0.348230 + 0.281128i 0.0202064 + 0.0163127i
\(298\) −10.7645 −0.623571
\(299\) 15.0885 + 26.1341i 0.872592 + 1.51137i
\(300\) −1.71903 + 0.211943i −0.0992485 + 0.0122365i
\(301\) −4.23419 + 7.33383i −0.244055 + 0.422715i
\(302\) −2.70388 + 4.68325i −0.155591 + 0.269491i
\(303\) 1.53162 + 2.03041i 0.0879892 + 0.116644i
\(304\) 0.824030 + 1.42726i 0.0472614 + 0.0818591i
\(305\) 0.438069 0.0250838
\(306\) 12.1419 + 12.5482i 0.694109 + 0.717335i
\(307\) −12.3700 −0.705995 −0.352997 0.935624i \(-0.614838\pi\)
−0.352997 + 0.935624i \(0.614838\pi\)
\(308\) 0.0430651 + 0.0745909i 0.00245386 + 0.00425021i
\(309\) 5.06063 11.9387i 0.287889 0.679167i
\(310\) −1.08613 + 1.88123i −0.0616880 + 0.106847i
\(311\) −4.64806 + 8.05068i −0.263567 + 0.456512i −0.967187 0.254064i \(-0.918232\pi\)
0.703620 + 0.710577i \(0.251566\pi\)
\(312\) −2.56193 + 6.04392i −0.145041 + 0.342170i
\(313\) 10.2621 + 17.7745i 0.580048 + 1.00467i 0.995473 + 0.0950454i \(0.0302996\pi\)
−0.415425 + 0.909628i \(0.636367\pi\)
\(314\) 11.6177 0.655627
\(315\) −2.91016 + 0.728674i −0.163969 + 0.0410561i
\(316\) −13.0484 −0.734030
\(317\) 12.7358 + 22.0591i 0.715315 + 1.23896i 0.962838 + 0.270079i \(0.0870500\pi\)
−0.247523 + 0.968882i \(0.579617\pi\)
\(318\) −13.3331 17.6752i −0.747682 0.991176i
\(319\) 0.391295 0.677743i 0.0219083 0.0379463i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0.604996 0.0745909i 0.0337676 0.00416326i
\(322\) 3.98113 + 6.89553i 0.221860 + 0.384273i
\(323\) 9.59224 0.533727
\(324\) −0.296122 + 8.99513i −0.0164512 + 0.499729i
\(325\) −3.79001 −0.210232
\(326\) −2.93436 5.08246i −0.162519 0.281491i
\(327\) −14.4094 + 1.77656i −0.796841 + 0.0982438i
\(328\) 1.69113 2.92912i 0.0933768 0.161733i
\(329\) 5.17226 8.95862i 0.285156 0.493905i
\(330\) 0.0898394 + 0.119097i 0.00494550 + 0.00655608i
\(331\) −4.43807 7.68696i −0.243938 0.422514i 0.717894 0.696152i \(-0.245106\pi\)
−0.961833 + 0.273639i \(0.911773\pi\)
\(332\) −8.87614 −0.487141
\(333\) −12.9155 + 3.23390i −0.707765 + 0.177217i
\(334\) −16.0181 −0.876471
\(335\) 0.527909 + 0.914365i 0.0288427 + 0.0499571i
\(336\) −0.675970 + 1.59470i −0.0368772 + 0.0869980i
\(337\) −6.21292 + 10.7611i −0.338439 + 0.586194i −0.984139 0.177397i \(-0.943232\pi\)
0.645700 + 0.763591i \(0.276566\pi\)
\(338\) −0.682083 + 1.18140i −0.0371004 + 0.0642598i
\(339\) −3.73419 + 8.80944i −0.202813 + 0.478463i
\(340\) 2.91016 + 5.04055i 0.157826 + 0.273362i
\(341\) 0.187097 0.0101319
\(342\) 3.43807 + 3.55311i 0.185910 + 0.192130i
\(343\) −1.00000 −0.0539949
\(344\) 4.23419 + 7.33383i 0.228292 + 0.395414i
\(345\) 8.30516 + 11.0099i 0.447135 + 0.592752i
\(346\) 3.25839 5.64370i 0.175172 0.303407i
\(347\) 6.35565 11.0083i 0.341189 0.590957i −0.643465 0.765476i \(-0.722504\pi\)
0.984654 + 0.174519i \(0.0558370\pi\)
\(348\) 15.6194 1.92574i 0.837286 0.103230i
\(349\) −12.7991 22.1686i −0.685118 1.18666i −0.973400 0.229113i \(-0.926417\pi\)
0.288282 0.957545i \(-0.406916\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −3.05158 + 19.4556i −0.162881 + 1.03846i
\(352\) 0.0861302 0.00459075
\(353\) 3.90776 + 6.76843i 0.207989 + 0.360247i 0.951081 0.308942i \(-0.0999749\pi\)
−0.743092 + 0.669189i \(0.766642\pi\)
\(354\) −22.1218 + 2.72743i −1.17576 + 0.144961i
\(355\) 8.00904 13.8721i 0.425076 0.736253i
\(356\) 1.00000 1.73205i 0.0529999 0.0917985i
\(357\) 6.07097 + 8.04809i 0.321310 + 0.425950i
\(358\) 0.503709 + 0.872450i 0.0266219 + 0.0461104i
\(359\) −35.5981 −1.87880 −0.939398 0.342828i \(-0.888615\pi\)
−0.939398 + 0.342828i \(0.888615\pi\)
\(360\) −0.824030 + 2.88461i −0.0434302 + 0.152032i
\(361\) −16.2839 −0.857047
\(362\) −9.99258 17.3077i −0.525198 0.909670i
\(363\) −7.43065 + 17.5299i −0.390008 + 0.920079i
\(364\) −1.89500 + 3.28224i −0.0993252 + 0.172036i
\(365\) 3.58613 6.21136i 0.187707 0.325117i
\(366\) 0.296122 0.698589i 0.0154785 0.0365158i
\(367\) −3.13290 5.42635i −0.163536 0.283253i 0.772598 0.634895i \(-0.218957\pi\)
−0.936135 + 0.351642i \(0.885623\pi\)
\(368\) 7.96227 0.415062
\(369\) 2.78708 9.75648i 0.145090 0.507902i
\(370\) −4.43807 −0.230724
\(371\) −6.39130 11.0700i −0.331820 0.574728i
\(372\) 2.26581 + 3.00371i 0.117477 + 0.155735i
\(373\) −8.66615 + 15.0102i −0.448716 + 0.777199i −0.998303 0.0582376i \(-0.981452\pi\)
0.549587 + 0.835437i \(0.314785\pi\)
\(374\) 0.250653 0.434143i 0.0129609 0.0224490i
\(375\) −1.71903 + 0.211943i −0.0887706 + 0.0109447i
\(376\) −5.17226 8.95862i −0.266739 0.462005i
\(377\) 34.4365 1.77357
\(378\) −0.805165 + 5.13339i −0.0414132 + 0.264033i
\(379\) 17.9549 0.922279 0.461139 0.887328i \(-0.347441\pi\)
0.461139 + 0.887328i \(0.347441\pi\)
\(380\) 0.824030 + 1.42726i 0.0422719 + 0.0732170i
\(381\) 10.0574 1.24000i 0.515258 0.0635271i
\(382\) −1.61033 + 2.78917i −0.0823916 + 0.142707i
\(383\) 3.26581 5.65655i 0.166875 0.289036i −0.770445 0.637507i \(-0.779966\pi\)
0.937320 + 0.348471i \(0.113299\pi\)
\(384\) 1.04307 + 1.38276i 0.0532287 + 0.0705635i
\(385\) 0.0430651 + 0.0745909i 0.00219480 + 0.00380151i
\(386\) −15.0181 −0.764400
\(387\) 17.6661 + 18.2573i 0.898021 + 0.928070i
\(388\) 7.93676 0.402928
\(389\) 4.22808 + 7.32325i 0.214372 + 0.371303i 0.953078 0.302724i \(-0.0978962\pi\)
−0.738706 + 0.674028i \(0.764563\pi\)
\(390\) −2.56193 + 6.04392i −0.129728 + 0.306046i
\(391\) 23.1715 40.1342i 1.17183 2.02967i
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 4.09355 9.65721i 0.206492 0.487142i
\(394\) −1.74323 3.01937i −0.0878229 0.152114i
\(395\) −13.0484 −0.656536
\(396\) 0.250653 0.0627608i 0.0125958 0.00315385i
\(397\) −22.4791 −1.12819 −0.564096 0.825709i \(-0.690775\pi\)
−0.564096 + 0.825709i \(0.690775\pi\)
\(398\) 4.15339 + 7.19389i 0.208191 + 0.360597i
\(399\) 1.71903 + 2.27887i 0.0860594 + 0.114086i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −7.90776 + 13.6966i −0.394895 + 0.683977i −0.993088 0.117375i \(-0.962552\pi\)
0.598193 + 0.801352i \(0.295886\pi\)
\(402\) 1.81499 0.223773i 0.0905233 0.0111608i
\(403\) 4.11644 + 7.12989i 0.205055 + 0.355165i
\(404\) 1.46838 0.0730547
\(405\) −0.296122 + 8.99513i −0.0147144 + 0.446971i
\(406\) 9.08613 0.450937
\(407\) 0.191126 + 0.331040i 0.00947376 + 0.0164090i
\(408\) 10.0053 1.23357i 0.495338 0.0610710i
\(409\) −8.95693 + 15.5139i −0.442892 + 0.767111i −0.997903 0.0647318i \(-0.979381\pi\)
0.555011 + 0.831843i \(0.312714\pi\)
\(410\) 1.69113 2.92912i 0.0835188 0.144659i
\(411\) −8.31290 11.0201i −0.410045 0.543583i
\(412\) −3.74323 6.48347i −0.184416 0.319418i
\(413\) −12.8687 −0.633228
\(414\) 23.1715 5.80190i 1.13882 0.285148i
\(415\) −8.87614 −0.435713
\(416\) 1.89500 + 3.28224i 0.0929102 + 0.160925i
\(417\) −4.73179 + 11.1629i −0.231717 + 0.546649i
\(418\) 0.0709739 0.122930i 0.00347145 0.00601272i
\(419\) −3.02791 + 5.24449i −0.147923 + 0.256210i −0.930460 0.366394i \(-0.880592\pi\)
0.782537 + 0.622605i \(0.213925\pi\)
\(420\) −0.675970 + 1.59470i −0.0329839 + 0.0778133i
\(421\) −7.10500 12.3062i −0.346276 0.599768i 0.639308 0.768950i \(-0.279221\pi\)
−0.985585 + 0.169182i \(0.945887\pi\)
\(422\) 28.3445 1.37979
\(423\) −21.5800 22.3021i −1.04926 1.08437i
\(424\) −12.7826 −0.620777
\(425\) 2.91016 + 5.04055i 0.141164 + 0.244502i
\(426\) −16.7079 22.1491i −0.809501 1.07313i
\(427\) 0.219035 0.379379i 0.0105998 0.0183594i
\(428\) 0.175970 0.304788i 0.00850581 0.0147325i
\(429\) 0.561152 0.0691853i 0.0270927 0.00334030i
\(430\) 4.23419 + 7.33383i 0.204191 + 0.353669i
\(431\) −15.5800 −0.750463 −0.375232 0.926931i \(-0.622437\pi\)
−0.375232 + 0.926931i \(0.622437\pi\)
\(432\) 4.04307 + 3.26399i 0.194522 + 0.157039i
\(433\) −36.6768 −1.76258 −0.881288 0.472580i \(-0.843323\pi\)
−0.881288 + 0.472580i \(0.843323\pi\)
\(434\) 1.08613 + 1.88123i 0.0521359 + 0.0903021i
\(435\) 15.6194 1.92574i 0.748892 0.0923321i
\(436\) −4.19113 + 7.25924i −0.200719 + 0.347655i
\(437\) 6.56115 11.3642i 0.313862 0.543626i
\(438\) −7.48113 9.91749i −0.357462 0.473876i
\(439\) 8.85727 + 15.3412i 0.422735 + 0.732198i 0.996206 0.0870279i \(-0.0277369\pi\)
−0.573471 + 0.819226i \(0.694404\pi\)
\(440\) 0.0861302 0.00410610
\(441\) −0.824030 + 2.88461i −0.0392395 + 0.137362i
\(442\) 22.0591 1.04924
\(443\) −18.9307 32.7888i −0.899422 1.55785i −0.828234 0.560382i \(-0.810654\pi\)
−0.0711883 0.997463i \(-0.522679\pi\)
\(444\) −3.00000 + 7.07739i −0.142374 + 0.335878i
\(445\) 1.00000 1.73205i 0.0474045 0.0821071i
\(446\) 1.24935 2.16393i 0.0591583 0.102465i
\(447\) −7.27648 + 17.1661i −0.344166 + 0.811931i
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −38.6965 −1.82620 −0.913099 0.407737i \(-0.866318\pi\)
−0.913099 + 0.407737i \(0.866318\pi\)
\(450\) −0.824030 + 2.88461i −0.0388452 + 0.135982i
\(451\) −0.291314 −0.0137174
\(452\) 2.76210 + 4.78410i 0.129918 + 0.225025i
\(453\) 5.64064 + 7.47761i 0.265020 + 0.351329i
\(454\) 7.62549 13.2077i 0.357882 0.619869i
\(455\) −1.89500 + 3.28224i −0.0888392 + 0.153874i
\(456\) 2.83307 0.349294i 0.132671 0.0163572i
\(457\) 0.488553 + 0.846198i 0.0228535 + 0.0395835i 0.877226 0.480078i \(-0.159392\pi\)
−0.854372 + 0.519661i \(0.826058\pi\)
\(458\) 24.8942 1.16323
\(459\) 28.2183 10.8805i 1.31712 0.507859i
\(460\) 7.96227 0.371243
\(461\) 12.6194 + 21.8574i 0.587743 + 1.01800i 0.994527 + 0.104476i \(0.0333166\pi\)
−0.406785 + 0.913524i \(0.633350\pi\)
\(462\) 0.148061 0.0182547i 0.00688841 0.000849284i
\(463\) 8.61775 14.9264i 0.400501 0.693688i −0.593286 0.804992i \(-0.702170\pi\)
0.993786 + 0.111304i \(0.0355029\pi\)
\(464\) 4.54307 7.86882i 0.210907 0.365301i
\(465\) 2.26581 + 3.00371i 0.105074 + 0.139294i
\(466\) −14.4737 25.0692i −0.670482 1.16131i
\(467\) 8.71935 0.403484 0.201742 0.979439i \(-0.435340\pi\)
0.201742 + 0.979439i \(0.435340\pi\)
\(468\) 7.90645 + 8.17102i 0.365476 + 0.377705i
\(469\) 1.05582 0.0487531
\(470\) −5.17226 8.95862i −0.238579 0.413230i
\(471\) 7.85324 18.5268i 0.361858 0.853670i
\(472\) −6.43436 + 11.1446i −0.296165 + 0.512974i
\(473\) 0.364692 0.631665i 0.0167685 0.0290440i
\(474\) −8.82032 + 20.8083i −0.405131 + 0.955755i
\(475\) 0.824030 + 1.42726i 0.0378091 + 0.0654873i
\(476\) 5.82032 0.266774
\(477\) −37.1994 + 9.31434i −1.70324 + 0.426474i
\(478\) −30.5168 −1.39581
\(479\) 2.89500 + 5.01429i 0.132276 + 0.229109i 0.924554 0.381052i \(-0.124438\pi\)
−0.792277 + 0.610161i \(0.791105\pi\)
\(480\) 1.04307 + 1.38276i 0.0476092 + 0.0631139i
\(481\) −8.41016 + 14.5668i −0.383470 + 0.664190i
\(482\) −10.8913 + 18.8643i −0.496085 + 0.859244i
\(483\) 13.6874 1.68754i 0.622799 0.0767859i
\(484\) 5.49629 + 9.51985i 0.249831 + 0.432721i
\(485\) 7.93676 0.360390
\(486\) 14.1444 + 6.55266i 0.641601 + 0.297235i
\(487\) 38.1574 1.72908 0.864539 0.502566i \(-0.167611\pi\)
0.864539 + 0.502566i \(0.167611\pi\)
\(488\) −0.219035 0.379379i −0.00991523 0.0171737i
\(489\) −10.0885 + 1.24383i −0.456219 + 0.0562480i
\(490\) −0.500000 + 0.866025i −0.0225877 + 0.0391230i
\(491\) 2.06356 3.57418i 0.0931270 0.161301i −0.815698 0.578477i \(-0.803647\pi\)
0.908825 + 0.417177i \(0.136980\pi\)
\(492\) −3.52791 4.67683i −0.159050 0.210848i
\(493\) −26.4421 45.7991i −1.19089 2.06269i
\(494\) 6.24616 0.281028
\(495\) 0.250653 0.0627608i 0.0112660 0.00282089i
\(496\) 2.17226 0.0975374
\(497\) −8.00904 13.8721i −0.359255 0.622247i
\(498\) −6.00000 + 14.1548i −0.268866 + 0.634290i
\(499\) −8.68371 + 15.0406i −0.388736 + 0.673311i −0.992280 0.124019i \(-0.960422\pi\)
0.603544 + 0.797330i \(0.293755\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −10.8277 + 25.5440i −0.483748 + 1.14122i
\(502\) 2.58613 + 4.47931i 0.115425 + 0.199921i
\(503\) 2.47099 0.110176 0.0550881 0.998481i \(-0.482456\pi\)
0.0550881 + 0.998481i \(0.482456\pi\)
\(504\) 2.08613 + 2.15594i 0.0929236 + 0.0960330i
\(505\) 1.46838 0.0653421
\(506\) −0.342896 0.593913i −0.0152436 0.0264027i
\(507\) 1.42291 + 1.88631i 0.0631938 + 0.0837739i
\(508\) 2.92532 5.06680i 0.129790 0.224803i
\(509\) 11.5710 20.0415i 0.512874 0.888325i −0.487014 0.873394i \(-0.661914\pi\)
0.999889 0.0149304i \(-0.00475268\pi\)
\(510\) 10.0053 1.23357i 0.443044 0.0546236i
\(511\) −3.58613 6.21136i −0.158641 0.274774i
\(512\) 1.00000 0.0441942
\(513\) 7.99018 3.08089i 0.352775 0.136025i
\(514\) −17.4562 −0.769958
\(515\) −3.74323 6.48347i −0.164947 0.285696i
\(516\) 14.5574 1.79481i 0.640856 0.0790122i
\(517\) −0.445488 + 0.771608i −0.0195925 + 0.0339353i
\(518\) −2.21903 + 3.84348i −0.0974988 + 0.168873i
\(519\) −6.79743 9.01112i −0.298374 0.395544i
\(520\) 1.89500 + 3.28224i 0.0831014 + 0.143936i
\(521\) −0.425843 −0.0186565 −0.00932827 0.999956i \(-0.502969\pi\)
−0.00932827 + 0.999956i \(0.502969\pi\)
\(522\) 7.48725 26.2099i 0.327708 1.14718i
\(523\) 13.8081 0.603786 0.301893 0.953342i \(-0.402381\pi\)
0.301893 + 0.953342i \(0.402381\pi\)
\(524\) −3.02791 5.24449i −0.132275 0.229107i
\(525\) −0.675970 + 1.59470i −0.0295017 + 0.0695984i
\(526\) 13.0114 22.5365i 0.567326 0.982638i
\(527\) 6.32163 10.9494i 0.275374 0.476962i
\(528\) 0.0582214 0.137352i 0.00253376 0.00597747i
\(529\) −20.1989 34.9855i −0.878211 1.52111i
\(530\) −12.7826 −0.555240
\(531\) −10.6042 + 37.1212i −0.460184 + 1.61092i
\(532\) 1.64806 0.0714525
\(533\) −6.40938 11.1014i −0.277621 0.480854i
\(534\) −2.08613 2.76551i −0.0902757 0.119675i
\(535\) 0.175970 0.304788i 0.00760783 0.0131771i
\(536\) 0.527909 0.914365i 0.0228022 0.0394945i
\(537\) 1.73179 0.213515i 0.0747321 0.00921385i
\(538\) −11.0649 19.1649i −0.477040 0.826258i
\(539\) 0.0861302 0.00370989
\(540\) 4.04307 + 3.26399i 0.173986 + 0.140460i
\(541\) 25.0484 1.07691 0.538457 0.842653i \(-0.319007\pi\)
0.538457 + 0.842653i \(0.319007\pi\)
\(542\) 1.06726 + 1.84856i 0.0458429 + 0.0794023i
\(543\) −34.3552 + 4.23571i −1.47432 + 0.181772i
\(544\) 2.91016 5.04055i 0.124772 0.216112i
\(545\) −4.19113 + 7.25924i −0.179528 + 0.310952i
\(546\) 3.95323 + 5.24066i 0.169182 + 0.224279i
\(547\) −4.85194 8.40381i −0.207454 0.359321i 0.743458 0.668783i \(-0.233184\pi\)
−0.950912 + 0.309462i \(0.899851\pi\)
\(548\) −7.96969 −0.340448
\(549\) −0.913870 0.944450i −0.0390030 0.0403081i
\(550\) 0.0861302 0.00367260
\(551\) −7.48725 12.9683i −0.318967 0.552468i
\(552\) 5.38225 12.6974i 0.229084 0.540438i
\(553\) −6.52420 + 11.3002i −0.277437 + 0.480535i
\(554\) −0.883557 + 1.53037i −0.0375387 + 0.0650190i
\(555\) −3.00000 + 7.07739i −0.127343 + 0.300418i
\(556\) 3.50000 + 6.06218i 0.148433 + 0.257094i
\(557\) 16.0968 0.682043 0.341022 0.940055i \(-0.389227\pi\)
0.341022 + 0.940055i \(0.389227\pi\)
\(558\) 6.32163 1.58287i 0.267616 0.0670082i
\(559\) 32.0952 1.35748
\(560\) 0.500000 + 0.866025i 0.0211289 + 0.0365963i
\(561\) −0.522894 0.693183i −0.0220766 0.0292662i
\(562\) −9.11404 + 15.7860i −0.384453 + 0.665891i
\(563\) 11.5418 19.9909i 0.486427 0.842517i −0.513451 0.858119i \(-0.671633\pi\)
0.999878 + 0.0156023i \(0.00496656\pi\)
\(564\) −17.7826 + 2.19245i −0.748782 + 0.0923186i
\(565\) 2.76210 + 4.78410i 0.116202 + 0.201268i
\(566\) −13.5652 −0.570187
\(567\) 7.64195 + 4.75401i 0.320932 + 0.199650i
\(568\) −16.0181 −0.672104
\(569\) −14.6550 25.3832i −0.614370 1.06412i −0.990495 0.137551i \(-0.956077\pi\)
0.376124 0.926569i \(-0.377257\pi\)
\(570\) 2.83307 0.349294i 0.118664 0.0146303i
\(571\) 10.1497 17.5798i 0.424751 0.735691i −0.571646 0.820500i \(-0.693695\pi\)
0.996397 + 0.0848098i \(0.0270283\pi\)
\(572\) 0.163217 0.282700i 0.00682445 0.0118203i
\(573\) 3.35936 + 4.45339i 0.140339 + 0.186043i
\(574\) −1.69113 2.92912i −0.0705862 0.122259i
\(575\) 7.96227 0.332050
\(576\) 2.91016 0.728674i 0.121257 0.0303614i
\(577\) 35.5726 1.48091 0.740453 0.672108i \(-0.234611\pi\)
0.740453 + 0.672108i \(0.234611\pi\)
\(578\) −8.43807 14.6152i −0.350977 0.607911i
\(579\) −10.1518 + 23.9493i −0.421893 + 0.995300i
\(580\) 4.54307 7.86882i 0.188641 0.326735i
\(581\) −4.43807 + 7.68696i −0.184122 + 0.318909i
\(582\) 5.36501 12.6568i 0.222387 0.524639i
\(583\) 0.550484 + 0.953465i 0.0227987 + 0.0394885i
\(584\) −7.17226 −0.296790
\(585\) 7.90645 + 8.17102i 0.326892 + 0.337830i
\(586\) 23.2436 0.960182
\(587\) 2.80757 + 4.86285i 0.115881 + 0.200711i 0.918131 0.396276i \(-0.129698\pi\)
−0.802251 + 0.596987i \(0.796364\pi\)
\(588\) 1.04307 + 1.38276i 0.0430153 + 0.0570239i
\(589\) 1.79001 3.10039i 0.0737560 0.127749i
\(590\) −6.43436 + 11.1446i −0.264898 + 0.458818i
\(591\) −5.99336 + 0.738932i −0.246534 + 0.0303956i
\(592\) 2.21903 + 3.84348i 0.0912018 + 0.157966i
\(593\) 3.86872 0.158869 0.0794347 0.996840i \(-0.474688\pi\)
0.0794347 + 0.996840i \(0.474688\pi\)
\(594\) 0.0693490 0.442140i 0.00284542 0.0181412i
\(595\) 5.82032 0.238610
\(596\) 5.38225 + 9.32233i 0.220466 + 0.381858i
\(597\) 14.2797 1.76056i 0.584428 0.0720551i
\(598\) 15.0885 26.1341i 0.617016 1.06870i
\(599\) 21.1648 36.6586i 0.864772 1.49783i −0.00250139 0.999997i \(-0.500796\pi\)
0.867273 0.497832i \(-0.165870\pi\)
\(600\) 1.04307 + 1.38276i 0.0425830 + 0.0564508i
\(601\) −4.71663 8.16944i −0.192395 0.333239i 0.753648 0.657278i \(-0.228292\pi\)
−0.946044 + 0.324039i \(0.894959\pi\)
\(602\) 8.46838 0.345145
\(603\) 0.870026 3.04562i 0.0354302 0.124027i
\(604\) 5.40776 0.220039
\(605\) 5.49629 + 9.51985i 0.223456 + 0.387037i
\(606\) 0.992582 2.34163i 0.0403209 0.0951221i
\(607\) −18.3445 + 31.7736i −0.744581 + 1.28965i 0.205809 + 0.978592i \(0.434017\pi\)
−0.950390 + 0.311060i \(0.899316\pi\)
\(608\) 0.824030 1.42726i 0.0334188 0.0578831i
\(609\) 6.14195 14.4896i 0.248884 0.587150i
\(610\) −0.219035 0.379379i −0.00886846 0.0153606i
\(611\) −39.2058 −1.58610
\(612\) 4.79612 16.7894i 0.193872 0.678669i
\(613\) 6.70388 0.270767 0.135384 0.990793i \(-0.456773\pi\)
0.135384 + 0.990793i \(0.456773\pi\)
\(614\) 6.18501 + 10.7128i 0.249607 + 0.432332i
\(615\) −3.52791 4.67683i −0.142259 0.188588i
\(616\) 0.0430651 0.0745909i 0.00173514 0.00300535i
\(617\) 2.10870 3.65238i 0.0848933 0.147039i −0.820452 0.571715i \(-0.806278\pi\)
0.905346 + 0.424675i \(0.139612\pi\)
\(618\) −12.8695 + 1.58670i −0.517687 + 0.0638265i
\(619\) 1.96838 + 3.40934i 0.0791160 + 0.137033i 0.902869 0.429916i \(-0.141457\pi\)
−0.823753 + 0.566949i \(0.808124\pi\)
\(620\) 2.17226 0.0872401
\(621\) 6.41094 40.8734i 0.257262 1.64019i
\(622\) 9.29612 0.372741
\(623\) −1.00000 1.73205i −0.0400642 0.0693932i
\(624\) 6.51516 0.803265i 0.260815 0.0321563i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 10.2621 17.7745i 0.410156 0.710411i
\(627\) −0.148061 0.196279i −0.00591298 0.00783864i
\(628\) −5.80887 10.0613i −0.231799 0.401488i
\(629\) 25.8310 1.02995
\(630\) 2.08613 + 2.15594i 0.0831134 + 0.0858946i
\(631\) 6.62517 0.263744 0.131872 0.991267i \(-0.457901\pi\)
0.131872 + 0.991267i \(0.457901\pi\)
\(632\) 6.52420 + 11.3002i 0.259519 + 0.449500i
\(633\) 19.1600 45.2010i 0.761543 1.79658i
\(634\) 12.7358 22.0591i 0.505804 0.876078i
\(635\) 2.92532 5.06680i 0.116088 0.201070i
\(636\) −8.64064 + 20.3844i −0.342624 + 0.808293i
\(637\) 1.89500 + 3.28224i 0.0750828 + 0.130047i
\(638\) −0.782590 −0.0309830
\(639\) −46.6152 + 11.6720i −1.84407 + 0.461736i
\(640\) 1.00000 0.0395285
\(641\) 17.1382 + 29.6843i 0.676920 + 1.17246i 0.975904 + 0.218201i \(0.0700189\pi\)
−0.298984 + 0.954258i \(0.596648\pi\)
\(642\) −0.367095 0.486646i −0.0144881 0.0192064i
\(643\) 5.21292 9.02905i 0.205578 0.356071i −0.744739 0.667356i \(-0.767426\pi\)
0.950317 + 0.311285i \(0.100759\pi\)
\(644\) 3.98113 6.89553i 0.156879 0.271722i
\(645\) 14.5574 1.79481i 0.573199 0.0706706i
\(646\) −4.79612 8.30713i −0.188701 0.326840i
\(647\) 35.0155 1.37660 0.688300 0.725426i \(-0.258357\pi\)
0.688300 + 0.725426i \(0.258357\pi\)
\(648\) 7.93807 4.24111i 0.311837 0.166607i
\(649\) 1.10839 0.0435079
\(650\) 1.89500 + 3.28224i 0.0743282 + 0.128740i
\(651\) 3.73419 0.460395i 0.146354 0.0180443i
\(652\) −2.93436 + 5.08246i −0.114918 + 0.199045i
\(653\) 17.5168 30.3400i 0.685485 1.18729i −0.287800 0.957691i \(-0.592924\pi\)
0.973284 0.229604i \(-0.0737430\pi\)
\(654\) 8.74323 + 11.5906i 0.341888 + 0.453229i
\(655\) −3.02791 5.24449i −0.118310 0.204919i
\(656\) −3.38225 −0.132055
\(657\) −20.8724 + 5.22624i −0.814311 + 0.203895i
\(658\) −10.3445 −0.403271
\(659\) −14.4610 25.0471i −0.563319 0.975697i −0.997204 0.0747290i \(-0.976191\pi\)
0.433885 0.900968i \(-0.357143\pi\)
\(660\) 0.0582214 0.137352i 0.00226626 0.00534641i
\(661\) −3.61775 + 6.26612i −0.140714 + 0.243724i −0.927766 0.373163i \(-0.878273\pi\)
0.787052 + 0.616887i \(0.211607\pi\)
\(662\) −4.43807 + 7.68696i −0.172490 + 0.298762i
\(663\) 14.9113 35.1776i 0.579105 1.36618i
\(664\) 4.43807 + 7.68696i 0.172230 + 0.298312i
\(665\) 1.64806 0.0639091
\(666\) 9.25839 + 9.56819i 0.358755 + 0.370760i
\(667\) −72.3462 −2.80126
\(668\) 8.00904 + 13.8721i 0.309879 + 0.536726i
\(669\) −2.60630 3.45509i −0.100765 0.133581i
\(670\) 0.527909 0.914365i 0.0203949 0.0353250i
\(671\) −0.0188655 + 0.0326760i −0.000728295 + 0.00126144i
\(672\) 1.71903 0.211943i 0.0663132 0.00817587i
\(673\) 11.4939 + 19.9080i 0.443057 + 0.767397i 0.997915 0.0645483i \(-0.0205607\pi\)
−0.554858 + 0.831945i \(0.687227\pi\)
\(674\) 12.4258 0.478626
\(675\) 4.04307 + 3.26399i 0.155618 + 0.125631i
\(676\) 1.36417 0.0524679
\(677\) 5.78337 + 10.0171i 0.222273 + 0.384988i 0.955498 0.294998i \(-0.0953191\pi\)
−0.733225 + 0.679986i \(0.761986\pi\)
\(678\) 9.49629 1.17081i 0.364703 0.0449648i
\(679\) 3.96838 6.87344i 0.152293 0.263778i
\(680\) 2.91016 5.04055i 0.111600 0.193296i
\(681\) −15.9078 21.0884i −0.609587 0.808108i
\(682\) −0.0935486 0.162031i −0.00358216 0.00620449i
\(683\) −2.06804 −0.0791315 −0.0395657 0.999217i \(-0.512597\pi\)
−0.0395657 + 0.999217i \(0.512597\pi\)
\(684\) 1.35805 4.75401i 0.0519264 0.181774i
\(685\) −7.96969 −0.304506
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 16.8277 39.6988i 0.642018 1.51460i
\(688\) 4.23419 7.33383i 0.161427 0.279600i
\(689\) −24.2231 + 41.9556i −0.922825 + 1.59838i
\(690\) 5.38225 12.6974i 0.204899 0.483383i
\(691\) −10.5316 18.2413i −0.400642 0.693932i 0.593162 0.805083i \(-0.297879\pi\)
−0.993803 + 0.111152i \(0.964546\pi\)
\(692\) −6.51678 −0.247731
\(693\) 0.0709739 0.248452i 0.00269608 0.00943791i
\(694\) −12.7113 −0.482514
\(695\) 3.50000 + 6.06218i 0.132763 + 0.229952i
\(696\) −9.47743 12.5639i −0.359241 0.476234i
\(697\) −9.84290 + 17.0484i −0.372826 + 0.645754i
\(698\) −12.7991 + 22.1686i −0.484451 + 0.839094i
\(699\) −49.7616 + 6.13520i −1.88216 + 0.232054i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 26.3068 0.993594 0.496797 0.867867i \(-0.334509\pi\)
0.496797 + 0.867867i \(0.334509\pi\)
\(702\) 18.3748 7.08505i 0.693513 0.267408i
\(703\) 7.31421 0.275861
\(704\) −0.0430651 0.0745909i −0.00162308 0.00281125i
\(705\) −17.7826 + 2.19245i −0.669731 + 0.0825723i
\(706\) 3.90776 6.76843i 0.147070 0.254733i
\(707\) 0.734191 1.27166i 0.0276121 0.0478256i
\(708\) 13.4229 + 17.7943i 0.504464 + 0.668751i
\(709\) 2.85727 + 4.94894i 0.107307 + 0.185861i 0.914678 0.404182i \(-0.132444\pi\)
−0.807371 + 0.590044i \(0.799111\pi\)
\(710\) −16.0181 −0.601148
\(711\) 27.2207 + 28.1315i 1.02085 + 1.05501i
\(712\) −2.00000 −0.0749532
\(713\) −8.64806 14.9789i −0.323872 0.560963i
\(714\) 3.93436 9.28166i 0.147240 0.347357i
\(715\) 0.163217 0.282700i 0.00610397 0.0105724i
\(716\) 0.503709 0.872450i 0.0188245 0.0326050i
\(717\) −20.6284 + 48.6651i −0.770382 + 1.81743i
\(718\) 17.7991 + 30.8289i 0.664255 + 1.15052i
\(719\) 5.07129 0.189127 0.0945637 0.995519i \(-0.469854\pi\)
0.0945637 + 0.995519i \(0.469854\pi\)
\(720\) 2.91016 0.728674i 0.108455 0.0271561i
\(721\) −7.48647 −0.278811
\(722\) 8.14195 + 14.1023i 0.303012 + 0.524832i
\(723\) 22.7207 + 30.1200i 0.844990 + 1.12018i
\(724\) −9.99258 + 17.3077i −0.371371 + 0.643234i
\(725\) 4.54307 7.86882i 0.168725 0.292241i
\(726\) 18.8966 2.32980i 0.701320 0.0864669i
\(727\) 13.8597 + 24.0057i 0.514027 + 0.890321i 0.999868 + 0.0162734i \(0.00518021\pi\)
−0.485841 + 0.874047i \(0.661486\pi\)
\(728\) 3.79001 0.140467
\(729\) 20.0107 18.1266i 0.741136 0.671355i
\(730\) −7.17226 −0.265457
\(731\) −24.6444 42.6853i −0.911504 1.57877i
\(732\) −0.753056 + 0.0928456i −0.0278338 + 0.00343167i
\(733\) −19.0854 + 33.0568i −0.704934 + 1.22098i 0.261782 + 0.965127i \(0.415690\pi\)
−0.966716 + 0.255854i \(0.917643\pi\)
\(734\) −3.13290 + 5.42635i −0.115638 + 0.200290i
\(735\) 1.04307 + 1.38276i 0.0384740 + 0.0510037i
\(736\) −3.98113 6.89553i −0.146747 0.254173i
\(737\) −0.0909378 −0.00334974
\(738\) −9.84290 + 2.46456i −0.362322 + 0.0907216i
\(739\) 31.3068 1.15164 0.575819 0.817577i \(-0.304683\pi\)
0.575819 + 0.817577i \(0.304683\pi\)
\(740\) 2.21903 + 3.84348i 0.0815733 + 0.141289i
\(741\) 4.22222 9.96075i 0.155107 0.365917i
\(742\) −6.39130 + 11.0700i −0.234632 + 0.406394i
\(743\) −20.7523 + 35.9440i −0.761327 + 1.31866i 0.180839 + 0.983513i \(0.442119\pi\)
−0.942167 + 0.335145i \(0.891215\pi\)
\(744\) 1.46838 3.46410i 0.0538335 0.127000i
\(745\) 5.38225 + 9.32233i 0.197190 + 0.341544i
\(746\) 17.3323 0.634580
\(747\) 18.5168 + 19.1364i 0.677494 + 0.700164i
\(748\) −0.501305 −0.0183295
\(749\) −0.175970 0.304788i −0.00642979 0.0111367i
\(750\) 1.04307 + 1.38276i 0.0380874 + 0.0504911i
\(751\) 5.61937 9.73304i 0.205054 0.355164i −0.745096 0.666957i \(-0.767596\pi\)
0.950150 + 0.311794i \(0.100930\pi\)
\(752\) −5.17226 + 8.95862i −0.188613 + 0.326687i
\(753\) 8.89130 1.09622i 0.324017 0.0399486i
\(754\) −17.2183 29.8229i −0.627052 1.08609i
\(755\) 5.40776 0.196808
\(756\) 4.84823 1.86940i 0.176328 0.0679895i
\(757\) 7.61294 0.276697 0.138349 0.990384i \(-0.455821\pi\)
0.138349 + 0.990384i \(0.455821\pi\)
\(758\) −8.97743 15.5494i −0.326075 0.564778i
\(759\) −1.17890 + 0.145349i −0.0427914 + 0.00527582i
\(760\) 0.824030 1.42726i 0.0298907 0.0517723i
\(761\) −20.1648 + 34.9265i −0.730975 + 1.26609i 0.225492 + 0.974245i \(0.427601\pi\)
−0.956467 + 0.291841i \(0.905732\pi\)
\(762\) −6.10259 8.09000i −0.221074 0.293070i
\(763\) 4.19113 + 7.25924i 0.151729 + 0.262802i
\(764\) 3.22066 0.116519
\(765\) 4.79612 16.7894i 0.173404 0.607020i
\(766\) −6.53162 −0.235997
\(767\) 24.3863 + 42.2383i 0.880538 + 1.52514i
\(768\) 0.675970 1.59470i 0.0243920 0.0575437i
\(769\) 12.2863 21.2805i 0.443055 0.767394i −0.554859 0.831944i \(-0.687228\pi\)
0.997914 + 0.0645500i \(0.0205612\pi\)
\(770\) 0.0430651 0.0745909i 0.00155196 0.00268807i
\(771\) −11.7998 + 27.8373i −0.424961 + 1.00254i
\(772\) 7.50904 + 13.0060i 0.270256 + 0.468098i
\(773\) −11.4455 −0.411666 −0.205833 0.978587i \(-0.565990\pi\)
−0.205833 + 0.978587i \(0.565990\pi\)
\(774\) 6.97820 24.4280i 0.250826 0.878046i
\(775\) 2.17226 0.0780299
\(776\) −3.96838 6.87344i −0.142457 0.246742i
\(777\) 4.62920 + 6.13677i 0.166071 + 0.220155i
\(778\) 4.22808 7.32325i 0.151584 0.262551i
\(779\) −2.78708 + 4.82736i −0.0998574 + 0.172958i
\(780\) 6.51516 0.803265i 0.233280 0.0287615i
\(781\) 0.689820 + 1.19480i 0.0246837 + 0.0427535i
\(782\) −46.3430 −1.65722
\(783\) −36.7358 29.6570i −1.31283 1.05986i
\(784\) 1.00000 0.0357143
\(785\) −5.80887 10.0613i −0.207328 0.359102i
\(786\) −10.4102 + 1.28349i −0.371318 + 0.0457804i
\(787\) 19.1419 33.1548i 0.682337 1.18184i −0.291929 0.956440i \(-0.594297\pi\)
0.974266 0.225402i \(-0.0723695\pi\)
\(788\) −1.74323 + 3.01937i −0.0621002 + 0.107561i
\(789\) −27.1436 35.9833i −0.966337 1.28104i
\(790\) 6.52420 + 11.3002i 0.232121 + 0.402045i
\(791\) 5.52420 0.196418
\(792\) −0.179679 0.185691i −0.00638461 0.00659825i
\(793\) −1.66029 −0.0589585
\(794\) 11.2395 + 19.4674i 0.398876 + 0.690873i
\(795\) −8.64064 + 20.3844i −0.306452 + 0.722960i
\(796\) 4.15339 7.19389i 0.147213 0.254981i
\(797\) −7.72677 + 13.3832i −0.273696 + 0.474056i −0.969805 0.243880i \(-0.921580\pi\)
0.696109 + 0.717936i \(0.254913\pi\)
\(798\) 1.11404 2.62816i 0.0394366 0.0930359i
\(799\) 30.1042 + 52.1420i 1.06501 + 1.84465i
\(800\) 1.00000 0.0353553
\(801\) −5.82032 + 1.45735i −0.205651 + 0.0514928i
\(802\) 15.8155 0.558465
\(803\) 0.308874 + 0.534986i 0.0108999 + 0.0188792i
\(804\) −1.10129 1.45994i −0.0388394 0.0514881i
\(805\) 3.98113 6.89553i 0.140317 0.243035i
\(806\) 4.11644 7.12989i 0.144996 0.251140i
\(807\) −38.0418 + 4.69023i −1.33913 + 0.165104i
\(808\) −0.734191 1.27166i −0.0258287 0.0447367i
\(809\) −30.8539 −1.08476 −0.542382 0.840132i \(-0.682478\pi\)
−0.542382 + 0.840132i \(0.682478\pi\)
\(810\) 7.93807 4.24111i 0.278915 0.149018i
\(811\) 18.9804 0.666490 0.333245 0.942840i \(-0.391856\pi\)
0.333245 + 0.942840i \(0.391856\pi\)
\(812\) −4.54307 7.86882i −0.159430 0.276141i
\(813\) 3.66933 0.452398i 0.128689 0.0158663i
\(814\) 0.191126 0.331040i 0.00669896 0.0116029i
\(815\) −2.93436 + 5.08246i −0.102786 + 0.178031i
\(816\) −6.07097 8.04809i −0.212527 0.281739i
\(817\) −6.97820 12.0866i −0.244136 0.422857i
\(818\) 17.9139 0.626344
\(819\) 11.0295 2.76168i 0.385403 0.0965009i
\(820\) −3.38225 −0.118113
\(821\) −3.59888 6.23345i −0.125602 0.217549i 0.796366 0.604815i \(-0.206753\pi\)
−0.921968 + 0.387266i \(0.873420\pi\)
\(822\) −5.38727 + 12.7093i −0.187902 + 0.443286i
\(823\) −14.1460 + 24.5015i −0.493098 + 0.854070i −0.999968 0.00795179i \(-0.997469\pi\)
0.506871 + 0.862022i \(0.330802\pi\)
\(824\) −3.74323 + 6.48347i −0.130402 + 0.225862i
\(825\) 0.0582214 0.137352i 0.00202701 0.00478197i
\(826\) 6.43436 + 11.1446i 0.223880 + 0.387772i
\(827\) −4.46096 −0.155123 −0.0775615 0.996988i \(-0.524713\pi\)
−0.0775615 + 0.996988i \(0.524713\pi\)
\(828\) −16.6103 17.1661i −0.577249 0.596565i
\(829\) −10.8613 −0.377229 −0.188614 0.982051i \(-0.560400\pi\)
−0.188614 + 0.982051i \(0.560400\pi\)
\(830\) 4.43807 + 7.68696i 0.154048 + 0.266818i
\(831\) 1.84322 + 2.44349i 0.0639404 + 0.0847637i
\(832\) 1.89500 3.28224i 0.0656975 0.113791i
\(833\) 2.91016 5.04055i 0.100831 0.174645i
\(834\) 12.0332 1.48360i 0.416677 0.0513728i
\(835\) 8.00904 + 13.8721i 0.277164 + 0.480063i
\(836\) −0.141948 −0.00490937
\(837\) 1.74903 11.1511i 0.0604552 0.385437i
\(838\) 6.05582 0.209195
\(839\) 0.981134 + 1.69937i 0.0338725 + 0.0586689i 0.882465 0.470379i \(-0.155883\pi\)
−0.848592 + 0.529048i \(0.822549\pi\)
\(840\) 1.71903 0.211943i 0.0593123 0.00731272i
\(841\) −26.7789 + 46.3824i −0.923410 + 1.59939i
\(842\) −7.10500 + 12.3062i −0.244854 + 0.424100i
\(843\) 19.0131 + 25.2050i 0.654845 + 0.868106i
\(844\) −14.1723 24.5471i −0.487829 0.844945i
\(845\) 1.36417 0.0469287
\(846\) −8.52420 + 29.8399i −0.293068 + 1.02592i
\(847\) 10.9926 0.377710
\(848\) 6.39130 + 11.0700i 0.219478 + 0.380147i
\(849\) −9.16965 + 21.6324i −0.314702 + 0.742421i
\(850\) 2.91016 5.04055i 0.0998177 0.172889i
\(851\) 17.6686 30.6028i 0.605670 1.04905i
\(852\) −10.8277 + 25.5440i −0.370952 + 0.875124i
\(853\) 10.3216 + 17.8776i 0.353406 + 0.612117i 0.986844 0.161677i \(-0.0516902\pi\)
−0.633438 + 0.773793i \(0.718357\pi\)
\(854\) −0.438069 −0.0149904
\(855\) 1.35805 4.75401i 0.0464444 0.162584i
\(856\) −0.351939 −0.0120290
\(857\) −11.2305 19.4518i −0.383626 0.664460i 0.607952 0.793974i \(-0.291991\pi\)
−0.991578 + 0.129514i \(0.958658\pi\)
\(858\) −0.340492 0.451379i −0.0116242 0.0154098i
\(859\) −13.0070 + 22.5287i −0.443792 + 0.768670i −0.997967 0.0637301i \(-0.979700\pi\)
0.554175 + 0.832400i \(0.313034\pi\)
\(860\) 4.23419 7.33383i 0.144385 0.250082i
\(861\) −5.81421 + 0.716844i −0.198148 + 0.0244300i
\(862\) 7.79001 + 13.4927i 0.265329 + 0.459563i
\(863\) −56.3052 −1.91665 −0.958326 0.285676i \(-0.907782\pi\)
−0.958326 + 0.285676i \(0.907782\pi\)
\(864\) 0.805165 5.13339i 0.0273923 0.174642i
\(865\) −6.51678 −0.221577
\(866\) 18.3384 + 31.7631i 0.623164 + 1.07935i
\(867\) −29.0107 + 3.57677i −0.985254 + 0.121474i
\(868\) 1.08613 1.88123i 0.0368657 0.0638532i
\(869\) 0.561931 0.973292i 0.0190622 0.0330167i
\(870\) −9.47743 12.5639i −0.321315 0.425956i
\(871\) −2.00078 3.46545i −0.0677938 0.117422i
\(872\) 8.38225 0.283859
\(873\) −16.5571 17.1112i −0.560374 0.579125i
\(874\) −13.1223 −0.443869
\(875\) 0.500000 + 0.866025i 0.0169031 + 0.0292770i
\(876\) −4.84823 + 11.4376i −0.163807 + 0.386441i
\(877\) −21.2297 + 36.7709i −0.716876 + 1.24167i 0.245355 + 0.969433i \(0.421095\pi\)
−0.962231 + 0.272233i \(0.912238\pi\)
\(878\) 8.85727 15.3412i 0.298918 0.517742i
\(879\) 15.7119 37.0665i 0.529950 1.25022i
\(880\) −0.0430651 0.0745909i −0.00145172 0.00251446i
\(881\) 45.6358 1.53751 0.768755 0.639543i \(-0.220876\pi\)
0.768755 + 0.639543i \(0.220876\pi\)
\(882\) 2.91016 0.728674i 0.0979902 0.0245357i
\(883\) −3.19190 −0.107416 −0.0537081 0.998557i \(-0.517104\pi\)
−0.0537081 + 0.998557i \(0.517104\pi\)
\(884\) −11.0295 19.1037i −0.370963 0.642527i
\(885\) 13.4229 + 17.7943i 0.451206 + 0.598149i
\(886\) −18.9307 + 32.7888i −0.635988 + 1.10156i
\(887\) 24.4487 42.3465i 0.820908 1.42185i −0.0840984 0.996457i \(-0.526801\pi\)
0.905007 0.425397i \(-0.139866\pi\)
\(888\) 7.62920 0.940616i 0.256019 0.0315650i
\(889\) −2.92532 5.06680i −0.0981120 0.169935i
\(890\) −2.00000 −0.0670402
\(891\) −0.658202 0.409464i −0.0220506 0.0137176i
\(892\) −2.49869 −0.0836625
\(893\) 8.52420 + 14.7643i 0.285251 + 0.494070i
\(894\) 18.5046 2.28146i 0.618885 0.0763034i
\(895\) 0.503709 0.872450i 0.0168371 0.0291628i
\(896\) 0.500000 0.866025i 0.0167038 0.0289319i
\(897\) −31.4766 41.7275i −1.05097 1.39324i
\(898\) 19.3482 + 33.5121i 0.645659 + 1.11831i
\(899\) −19.7374 −0.658281
\(900\) 2.91016 0.728674i 0.0970054 0.0242891i
\(901\) 74.3988 2.47858
\(902\) 0.145657 + 0.252285i 0.00484985 + 0.00840018i
\(903\) 5.72437 13.5045i 0.190495 0.449402i
\(904\) 2.76210 4.78410i 0.0918661 0.159117i
\(905\) −9.99258 + 17.3077i −0.332165 + 0.575326i
\(906\) 3.65548 8.62374i 0.121445 0.286505i
\(907\) −3.35565 5.81215i −0.111422 0.192989i 0.804922 0.593381i \(-0.202207\pi\)
−0.916344 + 0.400392i \(0.868874\pi\)
\(908\) −15.2510 −0.506121
\(909\) −3.06324 3.16574i −0.101601 0.105001i
\(910\) 3.79001 0.125638
\(911\) −13.5029 23.3878i −0.447372 0.774871i 0.550842 0.834610i \(-0.314307\pi\)
−0.998214 + 0.0597384i \(0.980973\pi\)
\(912\) −1.71903 2.27887i −0.0569229 0.0754608i
\(913\) 0.382252 0.662080i 0.0126507 0.0219116i
\(914\) 0.488553 0.846198i 0.0161599 0.0279898i
\(915\) −0.753056 + 0.0928456i −0.0248953 + 0.00306938i
\(916\) −12.4471 21.5590i −0.411264 0.712330i
\(917\) −6.05582 −0.199981
\(918\) −23.5319 18.9975i −0.776670 0.627010i
\(919\) −46.7167 −1.54104 −0.770522 0.637414i \(-0.780004\pi\)
−0.770522 + 0.637414i \(0.780004\pi\)
\(920\) −3.98113 6.89553i −0.131254 0.227339i
\(921\) 21.2645 2.62174i 0.700689 0.0863892i
\(922\) 12.6194 21.8574i 0.415597 0.719835i
\(923\) −30.3543 + 52.5753i −0.999125 + 1.73054i
\(924\) −0.0898394 0.119097i −0.00295550 0.00391801i
\(925\) 2.21903 + 3.84348i 0.0729614 + 0.126373i
\(926\) −17.2355 −0.566394
\(927\) −6.16908 + 21.5955i −0.202619 + 0.709291i
\(928\) −9.08613 −0.298267
\(929\) −5.38225 9.32233i −0.176586 0.305856i 0.764123 0.645071i \(-0.223172\pi\)
−0.940709 + 0.339215i \(0.889839\pi\)
\(930\) 1.46838 3.46410i 0.0481501 0.113592i
\(931\) 0.824030 1.42726i 0.0270065 0.0467766i
\(932\) −14.4737 + 25.0692i −0.474102 + 0.821169i
\(933\) 6.28390 14.8245i 0.205726 0.485333i
\(934\) −4.35968 7.55118i −0.142653 0.247082i
\(935\) −0.501305 −0.0163944
\(936\) 3.12308 10.9327i 0.102081 0.357346i
\(937\) −20.7449 −0.677705 −0.338853 0.940840i \(-0.610039\pi\)
−0.338853 + 0.940840i \(0.610039\pi\)
\(938\) −0.527909 0.914365i −0.0172368 0.0298551i
\(939\) −21.4081 28.3800i −0.698626 0.926145i
\(940\) −5.17226 + 8.95862i −0.168701 + 0.292198i
\(941\) −19.3142 + 33.4532i −0.629625 + 1.09054i 0.358002 + 0.933721i \(0.383458\pi\)
−0.987627 + 0.156822i \(0.949875\pi\)
\(942\) −19.9713 + 2.46230i −0.650701 + 0.0802260i
\(943\) 13.4652 + 23.3224i 0.438487 + 0.759482i
\(944\) 12.8687 0.418841
\(945\) 4.84823 1.86940i 0.157713 0.0608117i
\(946\) −0.729383 −0.0237143
\(947\) 6.93807 + 12.0171i 0.225457 + 0.390503i 0.956456 0.291875i \(-0.0942792\pi\)
−0.730999 + 0.682378i \(0.760946\pi\)
\(948\) 22.4307 2.76551i 0.728514 0.0898197i
\(949\) −13.5915 + 23.5411i −0.441198 + 0.764177i
\(950\) 0.824030 1.42726i 0.0267351 0.0463065i
\(951\) −26.5686 35.2211i −0.861545 1.14212i
\(952\) −2.91016 5.04055i −0.0943188 0.163365i
\(953\) −15.9500 −0.516673 −0.258336 0.966055i \(-0.583174\pi\)
−0.258336 + 0.966055i \(0.583174\pi\)
\(954\) 26.6661 + 27.5584i 0.863348 + 0.892238i
\(955\) 3.22066 0.104218
\(956\) 15.2584 + 26.4283i 0.493492 + 0.854753i
\(957\) −0.529007 + 1.24800i −0.0171004 + 0.0403420i
\(958\) 2.89500 5.01429i 0.0935333 0.162005i
\(959\) −3.98484 + 6.90195i −0.128677 + 0.222876i
\(960\) 0.675970 1.59470i 0.0218168 0.0514687i
\(961\) 13.1406 + 22.7603i 0.423892 + 0.734202i
\(962\) 16.8203 0.542309
\(963\) −1.02420 + 0.256449i −0.0330044 + 0.00826395i
\(964\) 21.7826 0.701570
\(965\) 7.50904 + 13.0060i 0.241725 + 0.418679i
\(966\) −8.30516 11.0099i −0.267214 0.354237i
\(967\) −24.7268 + 42.8280i −0.795159 + 1.37726i 0.127579 + 0.991828i \(0.459280\pi\)
−0.922738 + 0.385428i \(0.874054\pi\)
\(968\) 5.49629 9.51985i 0.176657 0.305980i
\(969\) −16.4894 + 2.03301i −0.529716 + 0.0653096i
\(970\) −3.96838 6.87344i −0.127417 0.220693i
\(971\) 10.2477 0.328865 0.164433 0.986388i \(-0.447421\pi\)
0.164433 + 0.986388i \(0.447421\pi\)
\(972\) −1.39741 15.5257i −0.0448219 0.497987i
\(973\) 7.00000 0.224410
\(974\) −19.0787 33.0453i −0.611321 1.05884i
\(975\) 6.51516 0.803265i 0.208652 0.0257251i
\(976\) −0.219035 + 0.379379i −0.00701113 + 0.0121436i
\(977\) −3.21292 + 5.56494i −0.102790 + 0.178038i −0.912833 0.408332i \(-0.866110\pi\)
0.810043 + 0.586371i \(0.199444\pi\)
\(978\) 6.12146 + 8.11501i 0.195743 + 0.259489i
\(979\) 0.0861302 + 0.149182i 0.00275273 + 0.00476787i
\(980\) 1.00000 0.0319438
\(981\) 24.3937 6.10793i 0.778831 0.195011i
\(982\) −4.12711 −0.131701
\(983\) −20.1723 34.9394i −0.643395 1.11439i −0.984670 0.174429i \(-0.944192\pi\)
0.341274 0.939964i \(-0.389141\pi\)
\(984\) −2.28630 + 5.39367i −0.0728846 + 0.171944i
\(985\) −1.74323 + 3.01937i −0.0555441 + 0.0962051i
\(986\) −26.4421 + 45.7991i −0.842088 + 1.45854i
\(987\) −6.99258 + 16.4964i −0.222576 + 0.525086i
\(988\) −3.12308 5.40934i −0.0993585 0.172094i
\(989\) −67.4275 −2.14407
\(990\) −0.179679 0.185691i −0.00571057 0.00590165i
\(991\) 16.5168 0.524673 0.262336 0.964976i \(-0.415507\pi\)
0.262336 + 0.964976i \(0.415507\pi\)
\(992\) −1.08613 1.88123i −0.0344847 0.0597292i
\(993\) 9.25839 + 12.2735i 0.293806 + 0.389489i
\(994\) −8.00904 + 13.8721i −0.254031 + 0.439995i
\(995\) 4.15339 7.19389i 0.131671 0.228062i
\(996\) 15.2584 1.88123i 0.483481 0.0596091i
\(997\) −3.72938 6.45948i −0.118111 0.204574i 0.800908 0.598787i \(-0.204350\pi\)
−0.919019 + 0.394213i \(0.871017\pi\)
\(998\) 17.3674 0.549756
\(999\) 21.5168 8.29654i 0.680761 0.262491i
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.j.i.211.1 6
3.2 odd 2 1890.2.j.k.631.3 6
9.2 odd 6 1890.2.j.k.1261.3 6
9.4 even 3 5670.2.a.bs.1.3 3
9.5 odd 6 5670.2.a.bo.1.1 3
9.7 even 3 inner 630.2.j.i.421.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.j.i.211.1 6 1.1 even 1 trivial
630.2.j.i.421.1 yes 6 9.7 even 3 inner
1890.2.j.k.631.3 6 3.2 odd 2
1890.2.j.k.1261.3 6 9.2 odd 6
5670.2.a.bo.1.1 3 9.5 odd 6
5670.2.a.bs.1.3 3 9.4 even 3