Properties

Label 154.2.e.d.67.1
Level $154$
Weight $2$
Character 154.67
Analytic conductor $1.230$
Analytic rank $0$
Dimension $2$
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] = [154,2,Mod(23,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (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: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 154.67
Dual form 154.2.e.d.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +3.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +3.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{12} -1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +12.0000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{18} +(-3.00000 - 5.19615i) q^{19} -4.00000 q^{20} +(-6.00000 + 5.19615i) q^{21} +1.00000 q^{22} +(1.00000 + 1.73205i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(-0.500000 - 0.866025i) q^{26} -9.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +1.00000 q^{29} +(6.00000 + 10.3923i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -2.00000 q^{34} +(-2.00000 - 10.3923i) q^{35} +6.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.50000 + 2.59808i) q^{39} +(-2.00000 - 3.46410i) q^{40} -2.00000 q^{41} +(-7.50000 - 2.59808i) q^{42} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(12.0000 - 20.7846i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-1.00000 - 1.73205i) q^{47} -3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -11.0000 q^{50} +(3.00000 + 5.19615i) q^{51} +(0.500000 - 0.866025i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-4.50000 - 7.79423i) q^{54} +4.00000 q^{55} +(2.50000 + 0.866025i) q^{56} -18.0000 q^{57} +(0.500000 + 0.866025i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-6.00000 + 10.3923i) q^{60} +(2.50000 + 4.33013i) q^{61} -4.00000 q^{62} +(3.00000 + 15.5885i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(1.50000 - 2.59808i) q^{66} +(4.50000 - 7.79423i) q^{67} +(-1.00000 - 1.73205i) q^{68} +6.00000 q^{69} +(8.00000 - 6.92820i) q^{70} +4.00000 q^{71} +(3.00000 + 5.19615i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(16.5000 + 28.5788i) q^{75} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} -3.00000 q^{78} +(7.50000 + 12.9904i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.00000 - 1.73205i) q^{82} -6.00000 q^{83} +(-1.50000 - 7.79423i) q^{84} -8.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +24.0000 q^{90} +(2.50000 + 0.866025i) q^{91} -2.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(1.00000 - 1.73205i) q^{94} +(12.0000 - 20.7846i) q^{95} +(-1.50000 - 2.59808i) q^{96} -5.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 6 q^{6} - 5 q^{7} - 2 q^{8} - 6 q^{9} - 4 q^{10} + q^{11} + 3 q^{12} - 2 q^{13} - q^{14} + 24 q^{15} - q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} - 8 q^{20} - 12 q^{21} + 2 q^{22} + 2 q^{23} - 3 q^{24} - 11 q^{25} - q^{26} - 18 q^{27} + 4 q^{28} + 2 q^{29} + 12 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} + 12 q^{36} + 2 q^{37} + 6 q^{38} - 3 q^{39} - 4 q^{40} - 4 q^{41} - 15 q^{42} + 8 q^{43} + q^{44} + 24 q^{45} - 2 q^{46} - 2 q^{47} - 6 q^{48} + 11 q^{49} - 22 q^{50} + 6 q^{51} + q^{52} + 12 q^{53} - 9 q^{54} + 8 q^{55} + 5 q^{56} - 36 q^{57} + q^{58} - 9 q^{59} - 12 q^{60} + 5 q^{61} - 8 q^{62} + 6 q^{63} + 2 q^{64} - 4 q^{65} + 3 q^{66} + 9 q^{67} - 2 q^{68} + 12 q^{69} + 16 q^{70} + 8 q^{71} + 6 q^{72} + 2 q^{73} - 2 q^{74} + 33 q^{75} + 12 q^{76} - 4 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} - 9 q^{81} - 2 q^{82} - 12 q^{83} - 3 q^{84} - 16 q^{85} + 4 q^{86} + 3 q^{87} - q^{88} - 6 q^{89} + 48 q^{90} + 5 q^{91} - 4 q^{92} + 12 q^{93} + 2 q^{94} + 24 q^{95} - 3 q^{96} - 10 q^{97} - 2 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 1.50000 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 3.00000 1.22474
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) −2.00000 + 3.46410i −0.632456 + 1.09545i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 1.50000 + 2.59808i 0.433013 + 0.750000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 12.0000 3.09839
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 3.00000 5.19615i 0.707107 1.22474i
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) −4.00000 −0.894427
\(21\) −6.00000 + 5.19615i −1.30931 + 1.13389i
\(22\) 1.00000 0.213201
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) −9.00000 −1.73205
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 6.00000 + 10.3923i 1.09545 + 1.89737i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) −2.00000 −0.342997
\(35\) −2.00000 10.3923i −0.338062 1.75662i
\(36\) 6.00000 1.00000
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) −1.50000 + 2.59808i −0.240192 + 0.416025i
\(40\) −2.00000 3.46410i −0.316228 0.547723i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) −7.50000 2.59808i −1.15728 0.400892i
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 12.0000 20.7846i 1.78885 3.09839i
\(46\) −1.00000 + 1.73205i −0.147442 + 0.255377i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) −3.00000 −0.433013
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −11.0000 −1.55563
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) −4.50000 7.79423i −0.612372 1.06066i
\(55\) 4.00000 0.539360
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) −18.0000 −2.38416
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) −6.00000 + 10.3923i −0.774597 + 1.34164i
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) −4.00000 −0.508001
\(63\) 3.00000 + 15.5885i 0.377964 + 1.96396i
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) 4.50000 7.79423i 0.549762 0.952217i −0.448528 0.893769i \(-0.648052\pi\)
0.998290 0.0584478i \(-0.0186151\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) 6.00000 0.722315
\(70\) 8.00000 6.92820i 0.956183 0.828079i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 3.00000 + 5.19615i 0.353553 + 0.612372i
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 16.5000 + 28.5788i 1.90526 + 3.30000i
\(76\) 6.00000 0.688247
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) −3.00000 −0.339683
\(79\) 7.50000 + 12.9904i 0.843816 + 1.46153i 0.886646 + 0.462450i \(0.153029\pi\)
−0.0428296 + 0.999082i \(0.513637\pi\)
\(80\) 2.00000 3.46410i 0.223607 0.387298i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.50000 7.79423i −0.163663 0.850420i
\(85\) −8.00000 −0.867722
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 24.0000 2.52982
\(91\) 2.50000 + 0.866025i 0.262071 + 0.0907841i
\(92\) −2.00000 −0.208514
\(93\) 6.00000 + 10.3923i 0.622171 + 1.07763i
\(94\) 1.00000 1.73205i 0.103142 0.178647i
\(95\) 12.0000 20.7846i 1.23117 2.13246i
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) −6.00000 −0.603023
\(100\) −5.50000 9.52628i −0.550000 0.952628i
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) −6.00000 10.3923i −0.591198 1.02398i −0.994071 0.108729i \(-0.965322\pi\)
0.402874 0.915255i \(-0.368011\pi\)
\(104\) 1.00000 0.0980581
\(105\) −30.0000 10.3923i −2.92770 1.01419i
\(106\) 12.0000 1.16554
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 4.50000 7.79423i 0.433013 0.750000i
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 2.00000 + 3.46410i 0.190693 + 0.330289i
\(111\) 6.00000 0.569495
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 17.0000 1.59923 0.799613 0.600516i \(-0.205038\pi\)
0.799613 + 0.600516i \(0.205038\pi\)
\(114\) −9.00000 15.5885i −0.842927 1.45999i
\(115\) −4.00000 + 6.92820i −0.373002 + 0.646058i
\(116\) −0.500000 + 0.866025i −0.0464238 + 0.0804084i
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) −9.00000 −0.828517
\(119\) 4.00000 3.46410i 0.366679 0.317554i
\(120\) −12.0000 −1.09545
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.50000 + 4.33013i −0.226339 + 0.392031i
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) −24.0000 −2.14663
\(126\) −12.0000 + 10.3923i −1.06904 + 0.925820i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 6.00000 10.3923i 0.528271 0.914991i
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 3.00000 0.261116
\(133\) 3.00000 + 15.5885i 0.260133 + 1.35169i
\(134\) 9.00000 0.777482
\(135\) −18.0000 31.1769i −1.54919 2.68328i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 3.00000 + 5.19615i 0.255377 + 0.442326i
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 10.0000 + 3.46410i 0.845154 + 0.292770i
\(141\) −6.00000 −0.505291
\(142\) 2.00000 + 3.46410i 0.167836 + 0.290701i
\(143\) −0.500000 + 0.866025i −0.0418121 + 0.0724207i
\(144\) −3.00000 + 5.19615i −0.250000 + 0.433013i
\(145\) 2.00000 + 3.46410i 0.166091 + 0.287678i
\(146\) 2.00000 0.165521
\(147\) 19.5000 7.79423i 1.60833 0.642857i
\(148\) −2.00000 −0.164399
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) −16.5000 + 28.5788i −1.34722 + 2.33345i
\(151\) −4.50000 + 7.79423i −0.366205 + 0.634285i −0.988969 0.148124i \(-0.952676\pi\)
0.622764 + 0.782410i \(0.286010\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) 12.0000 0.970143
\(154\) −2.50000 0.866025i −0.201456 0.0697863i
\(155\) −16.0000 −1.28515
\(156\) −1.50000 2.59808i −0.120096 0.208013i
\(157\) −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i \(-0.884359\pi\)
0.775113 + 0.631822i \(0.217693\pi\)
\(158\) −7.50000 + 12.9904i −0.596668 + 1.03346i
\(159\) −18.0000 31.1769i −1.42749 2.47249i
\(160\) 4.00000 0.316228
\(161\) −1.00000 5.19615i −0.0788110 0.409514i
\(162\) −9.00000 −0.707107
\(163\) −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i \(-0.996638\pi\)
0.490825 0.871258i \(-0.336695\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) 6.00000 10.3923i 0.467099 0.809040i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −17.0000 −1.31550 −0.657750 0.753237i \(-0.728492\pi\)
−0.657750 + 0.753237i \(0.728492\pi\)
\(168\) 6.00000 5.19615i 0.462910 0.400892i
\(169\) −12.0000 −0.923077
\(170\) −4.00000 6.92820i −0.306786 0.531369i
\(171\) −18.0000 + 31.1769i −1.37649 + 2.38416i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 2.50000 + 4.33013i 0.190071 + 0.329213i 0.945274 0.326278i \(-0.105795\pi\)
−0.755202 + 0.655492i \(0.772461\pi\)
\(174\) 3.00000 0.227429
\(175\) 22.0000 19.0526i 1.66304 1.44024i
\(176\) −1.00000 −0.0753778
\(177\) 13.5000 + 23.3827i 1.01472 + 1.75755i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 12.0000 + 20.7846i 0.894427 + 1.54919i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0.500000 + 2.59808i 0.0370625 + 0.192582i
\(183\) 15.0000 1.10883
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) −6.00000 + 10.3923i −0.439941 + 0.762001i
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 2.00000 0.145865
\(189\) 22.5000 + 7.79423i 1.63663 + 0.566947i
\(190\) 24.0000 1.74114
\(191\) −7.00000 12.1244i −0.506502 0.877288i −0.999972 0.00752447i \(-0.997605\pi\)
0.493469 0.869763i \(-0.335728\pi\)
\(192\) 1.50000 2.59808i 0.108253 0.187500i
\(193\) 11.0000 19.0526i 0.791797 1.37143i −0.133056 0.991109i \(-0.542479\pi\)
0.924853 0.380325i \(-0.124188\pi\)
\(194\) −2.50000 4.33013i −0.179490 0.310885i
\(195\) −12.0000 −0.859338
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) 5.50000 9.52628i 0.388909 0.673610i
\(201\) −13.5000 23.3827i −0.952217 1.64929i
\(202\) 15.0000 1.05540
\(203\) −2.50000 0.866025i −0.175466 0.0607831i
\(204\) −6.00000 −0.420084
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) 6.00000 10.3923i 0.418040 0.724066i
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) −6.00000 −0.415029
\(210\) −6.00000 31.1769i −0.414039 2.15141i
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 6.00000 10.3923i 0.411113 0.712069i
\(214\) 4.00000 6.92820i 0.273434 0.473602i
\(215\) 8.00000 + 13.8564i 0.545595 + 0.944999i
\(216\) 9.00000 0.612372
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) −10.0000 −0.677285
\(219\) −3.00000 5.19615i −0.202721 0.351123i
\(220\) −2.00000 + 3.46410i −0.134840 + 0.233550i
\(221\) 1.00000 1.73205i 0.0672673 0.116510i
\(222\) 3.00000 + 5.19615i 0.201347 + 0.348743i
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 66.0000 4.40000
\(226\) 8.50000 + 14.7224i 0.565412 + 0.979322i
\(227\) −5.00000 + 8.66025i −0.331862 + 0.574801i −0.982877 0.184263i \(-0.941010\pi\)
0.651015 + 0.759065i \(0.274343\pi\)
\(228\) 9.00000 15.5885i 0.596040 1.03237i
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) −8.00000 −0.527504
\(231\) 1.50000 + 7.79423i 0.0986928 + 0.512823i
\(232\) −1.00000 −0.0656532
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 4.00000 6.92820i 0.260931 0.451946i
\(236\) −4.50000 7.79423i −0.292925 0.507361i
\(237\) 45.0000 2.92306
\(238\) 5.00000 + 1.73205i 0.324102 + 0.112272i
\(239\) 19.0000 1.22901 0.614504 0.788914i \(-0.289356\pi\)
0.614504 + 0.788914i \(0.289356\pi\)
\(240\) −6.00000 10.3923i −0.387298 0.670820i
\(241\) −15.0000 + 25.9808i −0.966235 + 1.67357i −0.259975 + 0.965615i \(0.583714\pi\)
−0.706260 + 0.707953i \(0.749619\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) −5.00000 −0.320092
\(245\) −4.00000 + 27.7128i −0.255551 + 1.77051i
\(246\) −6.00000 −0.382546
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) −9.00000 + 15.5885i −0.570352 + 0.987878i
\(250\) −12.0000 20.7846i −0.758947 1.31453i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −15.0000 5.19615i −0.944911 0.327327i
\(253\) 2.00000 0.125739
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) −12.0000 + 20.7846i −0.751469 + 1.30158i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 12.0000 0.747087
\(259\) −1.00000 5.19615i −0.0621370 0.322873i
\(260\) 4.00000 0.248069
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) −9.00000 + 15.5885i −0.556022 + 0.963058i
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 48.0000 2.94862
\(266\) −12.0000 + 10.3923i −0.735767 + 0.637193i
\(267\) −18.0000 −1.10158
\(268\) 4.50000 + 7.79423i 0.274881 + 0.476108i
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) 18.0000 31.1769i 1.09545 1.89737i
\(271\) −12.5000 21.6506i −0.759321 1.31518i −0.943197 0.332233i \(-0.892198\pi\)
0.183876 0.982949i \(-0.441135\pi\)
\(272\) 2.00000 0.121268
\(273\) 6.00000 5.19615i 0.363137 0.314485i
\(274\) 9.00000 0.543710
\(275\) 5.50000 + 9.52628i 0.331662 + 0.574456i
\(276\) −3.00000 + 5.19615i −0.180579 + 0.312772i
\(277\) 1.50000 2.59808i 0.0901263 0.156103i −0.817438 0.576017i \(-0.804606\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(278\) 4.00000 + 6.92820i 0.239904 + 0.415526i
\(279\) 24.0000 1.43684
\(280\) 2.00000 + 10.3923i 0.119523 + 0.621059i
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 3.00000 5.19615i 0.178331 0.308879i −0.762978 0.646425i \(-0.776263\pi\)
0.941309 + 0.337546i \(0.109597\pi\)
\(284\) −2.00000 + 3.46410i −0.118678 + 0.205557i
\(285\) −36.0000 62.3538i −2.13246 3.69352i
\(286\) −1.00000 −0.0591312
\(287\) 5.00000 + 1.73205i 0.295141 + 0.102240i
\(288\) −6.00000 −0.353553
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −2.00000 + 3.46410i −0.117444 + 0.203419i
\(291\) −7.50000 + 12.9904i −0.439658 + 0.761510i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 16.5000 + 12.9904i 0.962300 + 0.757614i
\(295\) −36.0000 −2.09600
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) −4.50000 + 7.79423i −0.261116 + 0.452267i
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) −33.0000 −1.90526
\(301\) −10.0000 3.46410i −0.576390 0.199667i
\(302\) −9.00000 −0.517892
\(303\) −22.5000 38.9711i −1.29259 2.23883i
\(304\) −3.00000 + 5.19615i −0.172062 + 0.298020i
\(305\) −10.0000 + 17.3205i −0.572598 + 0.991769i
\(306\) 6.00000 + 10.3923i 0.342997 + 0.594089i
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) −36.0000 −2.04797
\(310\) −8.00000 13.8564i −0.454369 0.786991i
\(311\) 14.0000 24.2487i 0.793867 1.37502i −0.129689 0.991555i \(-0.541398\pi\)
0.923556 0.383464i \(-0.125269\pi\)
\(312\) 1.50000 2.59808i 0.0849208 0.147087i
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) −4.00000 −0.225733
\(315\) −48.0000 + 41.5692i −2.70449 + 2.34216i
\(316\) −15.0000 −0.843816
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 18.0000 31.1769i 1.00939 1.74831i
\(319\) 0.500000 0.866025i 0.0279946 0.0484881i
\(320\) 2.00000 + 3.46410i 0.111803 + 0.193649i
\(321\) −24.0000 −1.33955
\(322\) 4.00000 3.46410i 0.222911 0.193047i
\(323\) 12.0000 0.667698
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 5.50000 9.52628i 0.305085 0.528423i
\(326\) 6.50000 11.2583i 0.360002 0.623541i
\(327\) 15.0000 + 25.9808i 0.829502 + 1.43674i
\(328\) 2.00000 0.110432
\(329\) 1.00000 + 5.19615i 0.0551318 + 0.286473i
\(330\) 12.0000 0.660578
\(331\) −3.50000 6.06218i −0.192377 0.333207i 0.753660 0.657264i \(-0.228286\pi\)
−0.946038 + 0.324057i \(0.894953\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 6.00000 10.3923i 0.328798 0.569495i
\(334\) −8.50000 14.7224i −0.465099 0.805576i
\(335\) 36.0000 1.96689
\(336\) 7.50000 + 2.59808i 0.409159 + 0.141737i
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 25.5000 44.1673i 1.38497 2.39884i
\(340\) 4.00000 6.92820i 0.216930 0.375735i
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) −36.0000 −1.94666
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −4.00000 −0.215666
\(345\) 12.0000 + 20.7846i 0.646058 + 1.11901i
\(346\) −2.50000 + 4.33013i −0.134401 + 0.232789i
\(347\) 14.0000 24.2487i 0.751559 1.30174i −0.195507 0.980702i \(-0.562635\pi\)
0.947067 0.321037i \(-0.104031\pi\)
\(348\) 1.50000 + 2.59808i 0.0804084 + 0.139272i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 27.5000 + 9.52628i 1.46994 + 0.509201i
\(351\) 9.00000 0.480384
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) −13.5000 + 23.3827i −0.717517 + 1.24278i
\(355\) 8.00000 + 13.8564i 0.424596 + 0.735422i
\(356\) 6.00000 0.317999
\(357\) −3.00000 15.5885i −0.158777 0.825029i
\(358\) −13.0000 −0.687071
\(359\) 15.5000 + 26.8468i 0.818059 + 1.41692i 0.907111 + 0.420892i \(0.138283\pi\)
−0.0890519 + 0.996027i \(0.528384\pi\)
\(360\) −12.0000 + 20.7846i −0.632456 + 1.09545i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −11.0000 19.0526i −0.578147 1.00138i
\(363\) −3.00000 −0.157459
\(364\) −2.00000 + 1.73205i −0.104828 + 0.0907841i
\(365\) 8.00000 0.418739
\(366\) 7.50000 + 12.9904i 0.392031 + 0.679018i
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) 1.00000 1.73205i 0.0521286 0.0902894i
\(369\) 6.00000 + 10.3923i 0.312348 + 0.541002i
\(370\) −8.00000 −0.415900
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) −12.0000 −0.622171
\(373\) 3.50000 + 6.06218i 0.181223 + 0.313888i 0.942297 0.334777i \(-0.108661\pi\)
−0.761074 + 0.648665i \(0.775328\pi\)
\(374\) −1.00000 + 1.73205i −0.0517088 + 0.0895622i
\(375\) −36.0000 + 62.3538i −1.85903 + 3.21994i
\(376\) 1.00000 + 1.73205i 0.0515711 + 0.0893237i
\(377\) −1.00000 −0.0515026
\(378\) 4.50000 + 23.3827i 0.231455 + 1.20268i
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 12.0000 + 20.7846i 0.615587 + 1.06623i
\(381\) 7.50000 12.9904i 0.384237 0.665517i
\(382\) 7.00000 12.1244i 0.358151 0.620336i
\(383\) −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i \(-0.232188\pi\)
−0.949938 + 0.312437i \(0.898855\pi\)
\(384\) 3.00000 0.153093
\(385\) −10.0000 3.46410i −0.509647 0.176547i
\(386\) 22.0000 1.11977
\(387\) −12.0000 20.7846i −0.609994 1.05654i
\(388\) 2.50000 4.33013i 0.126918 0.219829i
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) −6.00000 10.3923i −0.303822 0.526235i
\(391\) −4.00000 −0.202289
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) 54.0000 2.72394
\(394\) −1.50000 2.59808i −0.0755689 0.130889i
\(395\) −30.0000 + 51.9615i −1.50946 + 2.61447i
\(396\) 3.00000 5.19615i 0.150756 0.261116i
\(397\) 15.0000 + 25.9808i 0.752828 + 1.30394i 0.946447 + 0.322860i \(0.104644\pi\)
−0.193618 + 0.981077i \(0.562022\pi\)
\(398\) −10.0000 −0.501255
\(399\) 45.0000 + 15.5885i 2.25282 + 0.780399i
\(400\) 11.0000 0.550000
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 13.5000 23.3827i 0.673319 1.16622i
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 7.50000 + 12.9904i 0.373139 + 0.646296i
\(405\) −36.0000 −1.78885
\(406\) −0.500000 2.59808i −0.0248146 0.128940i
\(407\) 2.00000 0.0991363
\(408\) −3.00000 5.19615i −0.148522 0.257248i
\(409\) 16.0000 27.7128i 0.791149 1.37031i −0.134107 0.990967i \(-0.542817\pi\)
0.925256 0.379344i \(-0.123850\pi\)
\(410\) 4.00000 6.92820i 0.197546 0.342160i
\(411\) −13.5000 23.3827i −0.665906 1.15338i
\(412\) 12.0000 0.591198
\(413\) 18.0000 15.5885i 0.885722 0.767058i
\(414\) 12.0000 0.589768
\(415\) −12.0000 20.7846i −0.589057 1.02028i
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 12.0000 20.7846i 0.587643 1.01783i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 24.0000 20.7846i 1.17108 1.01419i
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −7.00000 12.1244i −0.340755 0.590204i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) −11.0000 19.0526i −0.533578 0.924185i
\(426\) 12.0000 0.581402
\(427\) −2.50000 12.9904i −0.120983 0.628649i
\(428\) 8.00000 0.386695
\(429\) 1.50000 + 2.59808i 0.0724207 + 0.125436i
\(430\) −8.00000 + 13.8564i −0.385794 + 0.668215i
\(431\) −0.500000 + 0.866025i −0.0240842 + 0.0417150i −0.877816 0.478997i \(-0.841000\pi\)
0.853732 + 0.520712i \(0.174334\pi\)
\(432\) 4.50000 + 7.79423i 0.216506 + 0.375000i
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 10.0000 + 3.46410i 0.480015 + 0.166282i
\(435\) 12.0000 0.575356
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 6.00000 10.3923i 0.287019 0.497131i
\(438\) 3.00000 5.19615i 0.143346 0.248282i
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) −4.00000 −0.190693
\(441\) 6.00000 41.5692i 0.285714 1.97949i
\(442\) 2.00000 0.0951303
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) −3.00000 + 5.19615i −0.142374 + 0.246598i
\(445\) 12.0000 20.7846i 0.568855 0.985285i
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 30.0000 1.41895
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 33.0000 + 57.1577i 1.55563 + 2.69444i
\(451\) −1.00000 + 1.73205i −0.0470882 + 0.0815591i
\(452\) −8.50000 + 14.7224i −0.399806 + 0.692485i
\(453\) 13.5000 + 23.3827i 0.634285 + 1.09861i
\(454\) −10.0000 −0.469323
\(455\) 2.00000 + 10.3923i 0.0937614 + 0.487199i
\(456\) 18.0000 0.842927
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) −8.00000 + 13.8564i −0.373815 + 0.647467i
\(459\) 9.00000 15.5885i 0.420084 0.727607i
\(460\) −4.00000 6.92820i −0.186501 0.323029i
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) −6.00000 + 5.19615i −0.279145 + 0.241747i
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) −24.0000 + 41.5692i −1.11297 + 1.92773i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) −6.00000 −0.277350
\(469\) −18.0000 + 15.5885i −0.831163 + 0.719808i
\(470\) 8.00000 0.369012
\(471\) 6.00000 + 10.3923i 0.276465 + 0.478852i
\(472\) 4.50000 7.79423i 0.207129 0.358758i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 22.5000 + 38.9711i 1.03346 + 1.79000i
\(475\) 66.0000 3.02829
\(476\) 1.00000 + 5.19615i 0.0458349 + 0.238165i
\(477\) −72.0000 −3.29665
\(478\) 9.50000 + 16.4545i 0.434520 + 0.752611i
\(479\) 18.5000 32.0429i 0.845287 1.46408i −0.0400855 0.999196i \(-0.512763\pi\)
0.885372 0.464883i \(-0.153904\pi\)
\(480\) 6.00000 10.3923i 0.273861 0.474342i
\(481\) −1.00000 1.73205i −0.0455961 0.0789747i
\(482\) −30.0000 −1.36646
\(483\) −15.0000 5.19615i −0.682524 0.236433i
\(484\) 1.00000 0.0454545
\(485\) −10.0000 17.3205i −0.454077 0.786484i
\(486\) 0 0
\(487\) 2.00000 3.46410i 0.0906287 0.156973i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(488\) −2.50000 4.33013i −0.113170 0.196016i
\(489\) −39.0000 −1.76364
\(490\) −26.0000 + 10.3923i −1.17456 + 0.469476i
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) −1.00000 + 1.73205i −0.0450377 + 0.0780076i
\(494\) −3.00000 + 5.19615i −0.134976 + 0.233786i
\(495\) −12.0000 20.7846i −0.539360 0.934199i
\(496\) 4.00000 0.179605
\(497\) −10.0000 3.46410i −0.448561 0.155386i
\(498\) −18.0000 −0.806599
\(499\) 8.00000 + 13.8564i 0.358129 + 0.620298i 0.987648 0.156687i \(-0.0500814\pi\)
−0.629519 + 0.776985i \(0.716748\pi\)
\(500\) 12.0000 20.7846i 0.536656 0.929516i
\(501\) −25.5000 + 44.1673i −1.13926 + 1.97325i
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) −3.00000 15.5885i −0.133631 0.694365i
\(505\) 60.0000 2.66996
\(506\) 1.00000 + 1.73205i 0.0444554 + 0.0769991i
\(507\) −18.0000 + 31.1769i −0.799408 + 1.38462i
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i \(-0.180780\pi\)
−0.887336 + 0.461123i \(0.847447\pi\)
\(510\) −24.0000 −1.06274
\(511\) −4.00000 + 3.46410i −0.176950 + 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 27.0000 + 46.7654i 1.19208 + 2.06474i
\(514\) −10.5000 + 18.1865i −0.463135 + 0.802174i
\(515\) 24.0000 41.5692i 1.05757 1.83176i
\(516\) 6.00000 + 10.3923i 0.264135 + 0.457496i
\(517\) −2.00000 −0.0879599
\(518\) 4.00000 3.46410i 0.175750 0.152204i
\(519\) 15.0000 0.658427
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) 13.0000 22.5167i 0.569540 0.986473i −0.427071 0.904218i \(-0.640455\pi\)
0.996611 0.0822547i \(-0.0262121\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) −18.0000 −0.786334
\(525\) −16.5000 85.7365i −0.720119 3.74185i
\(526\) −3.00000 −0.130806
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 24.0000 + 41.5692i 1.04249 + 1.80565i
\(531\) 54.0000 2.34340
\(532\) −15.0000 5.19615i −0.650332 0.225282i
\(533\) 2.00000 0.0866296
\(534\) −9.00000 15.5885i −0.389468 0.674579i
\(535\) 16.0000 27.7128i 0.691740 1.19813i
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) 19.5000 + 33.7750i 0.841487 + 1.45750i
\(538\) −12.0000 −0.517357
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 36.0000 1.54919
\(541\) 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 12.5000 21.6506i 0.536921 0.929974i
\(543\) −33.0000 + 57.1577i −1.41617 + 2.45287i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) −40.0000 −1.71341
\(546\) 7.50000 + 2.59808i 0.320970 + 0.111187i
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 4.50000 + 7.79423i 0.192230 + 0.332953i
\(549\) 15.0000 25.9808i 0.640184 1.10883i
\(550\) −5.50000 + 9.52628i −0.234521 + 0.406202i
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) −6.00000 −0.255377
\(553\) −7.50000 38.9711i −0.318932 1.65722i
\(554\) 3.00000 0.127458
\(555\) 12.0000 + 20.7846i 0.509372 + 0.882258i
\(556\) −4.00000 + 6.92820i −0.169638 + 0.293821i
\(557\) −19.0000 + 32.9090i −0.805056 + 1.39440i 0.111198 + 0.993798i \(0.464531\pi\)
−0.916253 + 0.400599i \(0.868802\pi\)
\(558\) 12.0000 + 20.7846i 0.508001 + 0.879883i
\(559\) −4.00000 −0.169182
\(560\) −8.00000 + 6.92820i −0.338062 + 0.292770i
\(561\) 6.00000 0.253320
\(562\) −5.00000 8.66025i −0.210912 0.365311i
\(563\) −13.0000 + 22.5167i −0.547885 + 0.948964i 0.450535 + 0.892759i \(0.351233\pi\)
−0.998419 + 0.0562051i \(0.982100\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) 34.0000 + 58.8897i 1.43039 + 2.47751i
\(566\) 6.00000 0.252199
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) −4.00000 −0.167836
\(569\) −18.0000 31.1769i −0.754599 1.30700i −0.945573 0.325409i \(-0.894498\pi\)
0.190974 0.981595i \(-0.438835\pi\)
\(570\) 36.0000 62.3538i 1.50787 2.61171i
\(571\) 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916910i \(0.0292272\pi\)
\(572\) −0.500000 0.866025i −0.0209061 0.0362103i
\(573\) −42.0000 −1.75458
\(574\) 1.00000 + 5.19615i 0.0417392 + 0.216883i
\(575\) −22.0000 −0.917463
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) 3.50000 6.06218i 0.145707 0.252372i −0.783930 0.620850i \(-0.786788\pi\)
0.929636 + 0.368478i \(0.120121\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) −33.0000 57.1577i −1.37143 2.37539i
\(580\) −4.00000 −0.166091
\(581\) 15.0000 + 5.19615i 0.622305 + 0.215573i
\(582\) −15.0000 −0.621770
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) −12.0000 + 20.7846i −0.496139 + 0.859338i
\(586\) −3.00000 5.19615i −0.123929 0.214651i
\(587\) −3.00000 −0.123823 −0.0619116 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(588\) −3.00000 + 20.7846i −0.123718 + 0.857143i
\(589\) 24.0000 0.988903
\(590\) −18.0000 31.1769i −0.741048 1.28353i
\(591\) −4.50000 + 7.79423i −0.185105 + 0.320612i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) −9.00000 −0.369274
\(595\) 20.0000 + 6.92820i 0.819920 + 0.284029i
\(596\) −10.0000 −0.409616
\(597\) 15.0000 + 25.9808i 0.613909 + 1.06332i
\(598\) 1.00000 1.73205i 0.0408930 0.0708288i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −16.5000 28.5788i −0.673610 1.16673i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −2.00000 10.3923i −0.0815139 0.423559i
\(603\) −54.0000 −2.19905
\(604\) −4.50000 7.79423i −0.183102 0.317143i
\(605\) 2.00000 3.46410i 0.0813116 0.140836i
\(606\) 22.5000 38.9711i 0.914000 1.58309i
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) −6.00000 −0.243332
\(609\) −6.00000 + 5.19615i −0.243132 + 0.210559i
\(610\) −20.0000 −0.809776
\(611\) 1.00000 + 1.73205i 0.0404557 + 0.0700713i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) −11.0000 + 19.0526i −0.444286 + 0.769526i −0.998002 0.0631797i \(-0.979876\pi\)
0.553716 + 0.832705i \(0.313209\pi\)
\(614\) 16.0000 + 27.7128i 0.645707 + 1.11840i
\(615\) −24.0000 −0.967773
\(616\) 2.00000 1.73205i 0.0805823 0.0697863i
\(617\) −27.0000 −1.08698 −0.543490 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) −18.0000 31.1769i −0.724066 1.25412i
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) 8.00000 13.8564i 0.321288 0.556487i
\(621\) −9.00000 15.5885i −0.361158 0.625543i
\(622\) 28.0000 1.12270
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) 3.00000 0.120096
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) 0.500000 0.866025i 0.0199840 0.0346133i
\(627\) −9.00000 + 15.5885i −0.359425 + 0.622543i
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) −4.00000 −0.159490
\(630\) −60.0000 20.7846i −2.39046 0.828079i
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −7.50000 12.9904i −0.298334 0.516730i
\(633\) −21.0000 + 36.3731i −0.834675 + 1.44570i
\(634\) −6.00000 + 10.3923i −0.238290 + 0.412731i
\(635\) 10.0000 + 17.3205i 0.396838 + 0.687343i
\(636\) 36.0000 1.42749
\(637\) −5.50000 4.33013i −0.217918 0.171566i
\(638\) 1.00000 0.0395904
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) −2.00000 + 3.46410i −0.0790569 + 0.136931i
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) −12.0000 20.7846i −0.473602 0.820303i
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 5.00000 + 1.73205i 0.197028 + 0.0682524i
\(645\) 48.0000 1.89000
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 4.50000 + 7.79423i 0.176640 + 0.305950i
\(650\) 11.0000 0.431455
\(651\) −6.00000 31.1769i −0.235159 1.22192i
\(652\) 13.0000 0.509119
\(653\) −11.0000 19.0526i −0.430463 0.745584i 0.566450 0.824096i \(-0.308316\pi\)
−0.996913 + 0.0785119i \(0.974983\pi\)
\(654\) −15.0000 + 25.9808i −0.586546 + 1.01593i
\(655\) −36.0000 + 62.3538i −1.40664 + 2.43637i
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) −12.0000 −0.468165
\(658\) −4.00000 + 3.46410i −0.155936 + 0.135045i
\(659\) −32.0000 −1.24654 −0.623272 0.782006i \(-0.714197\pi\)
−0.623272 + 0.782006i \(0.714197\pi\)
\(660\) 6.00000 + 10.3923i 0.233550 + 0.404520i
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 3.50000 6.06218i 0.136031 0.235613i
\(663\) −3.00000 5.19615i −0.116510 0.201802i
\(664\) 6.00000 0.232845
\(665\) −48.0000 + 41.5692i −1.86136 + 1.61199i
\(666\) 12.0000 0.464991
\(667\) 1.00000 + 1.73205i 0.0387202 + 0.0670653i
\(668\) 8.50000 14.7224i 0.328875 0.569628i
\(669\) −39.0000 + 67.5500i −1.50783 + 2.61163i
\(670\) 18.0000 + 31.1769i 0.695401 + 1.20447i
\(671\) 5.00000 0.193023
\(672\) 1.50000 + 7.79423i 0.0578638 + 0.300669i
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) −15.0000 25.9808i −0.577778 1.00074i
\(675\) 49.5000 85.7365i 1.90526 3.30000i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −19.0000 32.9090i −0.730229 1.26479i −0.956785 0.290796i \(-0.906080\pi\)
0.226556 0.973998i \(-0.427253\pi\)
\(678\) 51.0000 1.95864
\(679\) 12.5000 + 4.33013i 0.479706 + 0.166175i
\(680\) 8.00000 0.306786
\(681\) 15.0000 + 25.9808i 0.574801 + 0.995585i
\(682\) −2.00000 + 3.46410i −0.0765840 + 0.132647i
\(683\) 16.5000 28.5788i 0.631355 1.09354i −0.355920 0.934516i \(-0.615832\pi\)
0.987275 0.159022i \(-0.0508342\pi\)
\(684\) −18.0000 31.1769i −0.688247 1.19208i
\(685\) 36.0000 1.37549
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 48.0000 1.83131
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) −12.0000 + 20.7846i −0.456832 + 0.791257i
\(691\) −7.50000 12.9904i −0.285313 0.494177i 0.687372 0.726306i \(-0.258764\pi\)
−0.972685 + 0.232128i \(0.925431\pi\)
\(692\) −5.00000 −0.190071
\(693\) 15.0000 + 5.19615i 0.569803 + 0.197386i
\(694\) 28.0000 1.06287
\(695\) 16.0000 + 27.7128i 0.606915 + 1.05121i
\(696\) −1.50000 + 2.59808i −0.0568574 + 0.0984798i
\(697\) 2.00000 3.46410i 0.0757554 0.131212i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) −18.0000 −0.680823
\(700\) 5.50000 + 28.5788i 0.207880 + 1.08018i
\(701\) 39.0000 1.47301 0.736505 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 4.50000 + 7.79423i 0.169842 + 0.294174i
\(703\) 6.00000 10.3923i 0.226294 0.391953i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −12.0000 20.7846i −0.451946 0.782794i
\(706\) 18.0000 0.677439
\(707\) −30.0000 + 25.9808i −1.12827 + 0.977107i
\(708\) −27.0000 −1.01472
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) −8.00000 + 13.8564i −0.300235 + 0.520022i
\(711\) 45.0000 77.9423i 1.68763 2.92306i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) −8.00000 −0.299602
\(714\) 12.0000 10.3923i 0.449089 0.388922i
\(715\) −4.00000 −0.149592
\(716\) −6.50000 11.2583i −0.242916 0.420744i
\(717\) 28.5000 49.3634i 1.06435 1.84351i
\(718\) −15.5000 + 26.8468i −0.578455 + 1.00191i
\(719\) 13.0000 + 22.5167i 0.484818 + 0.839730i 0.999848 0.0174426i \(-0.00555244\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(720\) −24.0000 −0.894427
\(721\) 6.00000 + 31.1769i 0.223452 + 1.16109i
\(722\) −17.0000 −0.632674
\(723\) 45.0000 + 77.9423i 1.67357 + 2.89870i
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) −5.50000 + 9.52628i −0.204265 + 0.353797i
\(726\) −1.50000 2.59808i −0.0556702 0.0964237i
\(727\) −34.0000 −1.26099 −0.630495 0.776193i \(-0.717148\pi\)
−0.630495 + 0.776193i \(0.717148\pi\)
\(728\) −2.50000 0.866025i −0.0926562 0.0320970i
\(729\) −27.0000 −1.00000
\(730\) 4.00000 + 6.92820i 0.148047 + 0.256424i
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) −7.50000 + 12.9904i −0.277208 + 0.480138i
\(733\) 0.500000 + 0.866025i 0.0184679 + 0.0319874i 0.875112 0.483921i \(-0.160788\pi\)
−0.856644 + 0.515908i \(0.827454\pi\)
\(734\) 14.0000 0.516749
\(735\) 66.0000 + 51.9615i 2.43445 + 1.91663i
\(736\) 2.00000 0.0737210
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) −9.00000 + 15.5885i −0.331070 + 0.573431i −0.982722 0.185088i \(-0.940743\pi\)
0.651652 + 0.758518i \(0.274076\pi\)
\(740\) −4.00000 6.92820i −0.147043 0.254686i
\(741\) 18.0000 0.661247
\(742\) −30.0000 10.3923i −1.10133 0.381514i
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) −6.00000 10.3923i −0.219971 0.381000i
\(745\) −20.0000 + 34.6410i −0.732743 + 1.26915i
\(746\) −3.50000 + 6.06218i −0.128144 + 0.221952i
\(747\) 18.0000 + 31.1769i 0.658586 + 1.14070i
\(748\) −2.00000 −0.0731272
\(749\) 4.00000 + 20.7846i 0.146157 + 0.759453i
\(750\) −72.0000 −2.62907
\(751\) 22.0000 + 38.1051i 0.802791 + 1.39048i 0.917772 + 0.397108i \(0.129986\pi\)
−0.114981 + 0.993368i \(0.536681\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) 18.0000 31.1769i 0.655956 1.13615i
\(754\) −0.500000 0.866025i −0.0182089 0.0315388i
\(755\) −36.0000 −1.31017
\(756\) −18.0000 + 15.5885i −0.654654 + 0.566947i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −14.5000 25.1147i −0.526664 0.912208i
\(759\) 3.00000 5.19615i 0.108893 0.188608i
\(760\) −12.0000 + 20.7846i −0.435286 + 0.753937i
\(761\) −27.0000 46.7654i −0.978749 1.69524i −0.666962 0.745091i \(-0.732406\pi\)
−0.311787 0.950152i \(-0.600927\pi\)
\(762\) 15.0000 0.543393
\(763\) 20.0000 17.3205i 0.724049 0.627044i
\(764\) 14.0000 0.506502
\(765\) 24.0000 + 41.5692i 0.867722 + 1.50294i
\(766\) 4.00000 6.92820i 0.144526 0.250326i
\(767\) 4.50000 7.79423i 0.162486 0.281433i
\(768\) 1.50000 + 2.59808i 0.0541266 + 0.0937500i
\(769\) −38.0000 −1.37032 −0.685158 0.728395i \(-0.740267\pi\)
−0.685158 + 0.728395i \(0.740267\pi\)
\(770\) −2.00000 10.3923i −0.0720750 0.374513i
\(771\) 63.0000 2.26889
\(772\) 11.0000 + 19.0526i 0.395899 + 0.685717i
\(773\) 12.0000 20.7846i 0.431610 0.747570i −0.565402 0.824815i \(-0.691279\pi\)
0.997012 + 0.0772449i \(0.0246123\pi\)
\(774\) 12.0000 20.7846i 0.431331 0.747087i
\(775\) −22.0000 38.1051i −0.790263 1.36878i
\(776\) 5.00000 0.179490
\(777\) −15.0000 5.19615i −0.538122 0.186411i
\(778\) 0 0
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 6.00000 10.3923i 0.214834 0.372104i
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) −2.00000 3.46410i −0.0715199 0.123876i
\(783\) −9.00000 −0.321634
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) −16.0000 −0.571064
\(786\) 27.0000 + 46.7654i 0.963058 + 1.66807i
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) 1.50000 2.59808i 0.0534353 0.0925526i
\(789\) 4.50000 + 7.79423i 0.160204 + 0.277482i
\(790\) −60.0000 −2.13470
\(791\) −42.5000 14.7224i −1.51113 0.523469i
\(792\) 6.00000 0.213201
\(793\) −2.50000 4.33013i −0.0887776 0.153767i
\(794\) −15.0000 + 25.9808i −0.532330 + 0.922023i
\(795\) 72.0000 124.708i 2.55358 4.42292i
\(796\) −5.00000 8.66025i −0.177220 0.306955i
\(797\) 38.0000 1.34603 0.673015 0.739629i \(-0.264999\pi\)
0.673015 + 0.739629i \(0.264999\pi\)
\(798\) 9.00000 + 46.7654i 0.318597 + 1.65548i
\(799\) 4.00000 0.141510
\(800\) 5.50000 + 9.52628i 0.194454 + 0.336805i
\(801\) −18.0000 + 31.1769i −0.635999 + 1.10158i
\(802\) 7.50000 12.9904i 0.264834 0.458706i
\(803\) −1.00000 1.73205i −0.0352892 0.0611227i
\(804\) 27.0000 0.952217
\(805\) 16.0000 13.8564i 0.563926 0.488374i
\(806\) 4.00000 0.140894
\(807\) 18.0000 + 31.1769i 0.633630 + 1.09748i
\(808\) −7.50000 + 12.9904i −0.263849 + 0.457000i
\(809\) 24.0000 41.5692i 0.843795 1.46150i −0.0428684 0.999081i \(-0.513650\pi\)
0.886664 0.462415i \(-0.153017\pi\)
\(810\) −18.0000 31.1769i −0.632456 1.09545i
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 2.00000 1.73205i 0.0701862 0.0607831i
\(813\) −75.0000 −2.63036
\(814\) 1.00000 + 1.73205i 0.0350500 + 0.0607083i
\(815\) 26.0000 45.0333i 0.910740 1.57745i
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) −12.0000 20.7846i −0.419827 0.727161i
\(818\) 32.0000 1.11885
\(819\) −3.00000 15.5885i −0.104828 0.544705i
\(820\) 8.00000 0.279372
\(821\) 7.50000 + 12.9904i 0.261752 + 0.453367i 0.966708 0.255884i \(-0.0823665\pi\)
−0.704956 + 0.709251i \(0.749033\pi\)
\(822\) 13.5000 23.3827i 0.470867 0.815565i
\(823\) −19.0000 + 32.9090i −0.662298 + 1.14713i 0.317712 + 0.948187i \(0.397086\pi\)
−0.980010 + 0.198947i \(0.936248\pi\)
\(824\) 6.00000 + 10.3923i 0.209020 + 0.362033i
\(825\) 33.0000 1.14891
\(826\) 22.5000 + 7.79423i 0.782875 + 0.271196i
\(827\) −22.0000 −0.765015 −0.382507 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) −8.00000 + 13.8564i −0.277851 + 0.481253i −0.970851 0.239686i \(-0.922956\pi\)
0.692999 + 0.720938i \(0.256289\pi\)
\(830\) 12.0000 20.7846i 0.416526 0.721444i
\(831\) −4.50000 7.79423i −0.156103 0.270379i
\(832\) −1.00000 −0.0346688
\(833\) −13.0000 + 5.19615i −0.450423 + 0.180036i
\(834\) 24.0000 0.831052
\(835\) −34.0000 58.8897i −1.17662 2.03796i
\(836\) 3.00000 5.19615i 0.103757 0.179713i
\(837\) 18.0000 31.1769i 0.622171 1.07763i
\(838\) −10.0000 17.3205i −0.345444 0.598327i
\(839\) 54.0000 1.86429 0.932144 0.362089i \(-0.117936\pi\)
0.932144 + 0.362089i \(0.117936\pi\)
\(840\) 30.0000 + 10.3923i 1.03510 + 0.358569i
\(841\) −28.0000 −0.965517
\(842\) −10.0000 17.3205i −0.344623 0.596904i
\(843\) −15.0000 + 25.9808i −0.516627 + 0.894825i
\(844\) 7.00000 12.1244i 0.240950 0.417338i
\(845\) −24.0000 41.5692i −0.825625 1.43002i
\(846\) −12.0000 −0.412568
\(847\) 0.500000 + 2.59808i 0.0171802 + 0.0892710i
\(848\) −12.0000 −0.412082
\(849\) −9.00000 15.5885i −0.308879 0.534994i
\(850\) 11.0000 19.0526i 0.377297 0.653497i
\(851\) −2.00000 + 3.46410i −0.0685591 + 0.118748i
\(852\) 6.00000 + 10.3923i 0.205557 + 0.356034i
\(853\) 50.0000 1.71197 0.855984 0.517003i \(-0.172952\pi\)
0.855984 + 0.517003i \(0.172952\pi\)
\(854\) 10.0000 8.66025i 0.342193 0.296348i
\(855\) −144.000 −4.92470
\(856\) 4.00000 + 6.92820i 0.136717 + 0.236801i
\(857\) 2.00000 3.46410i 0.0683187 0.118331i −0.829843 0.557998i \(-0.811570\pi\)
0.898161 + 0.439666i \(0.144903\pi\)
\(858\) −1.50000 + 2.59808i −0.0512092 + 0.0886969i
\(859\) 8.50000 + 14.7224i 0.290016 + 0.502323i 0.973813 0.227349i \(-0.0730059\pi\)
−0.683797 + 0.729672i \(0.739673\pi\)
\(860\) −16.0000 −0.545595
\(861\) 12.0000 10.3923i 0.408959 0.354169i
\(862\) −1.00000 −0.0340601
\(863\) −5.00000 8.66025i −0.170202 0.294798i 0.768288 0.640104i \(-0.221109\pi\)
−0.938490 + 0.345305i \(0.887775\pi\)
\(864\) −4.50000 + 7.79423i −0.153093 + 0.265165i
\(865\) −10.0000 + 17.3205i −0.340010 + 0.588915i
\(866\) −5.00000 8.66025i −0.169907 0.294287i
\(867\) 39.0000 1.32451
\(868\) 2.00000 + 10.3923i 0.0678844 + 0.352738i
\(869\) 15.0000 0.508840
\(870\) 6.00000 + 10.3923i 0.203419 + 0.352332i
\(871\) −4.50000 + 7.79423i −0.152477 + 0.264097i
\(872\) 5.00000 8.66025i 0.169321 0.293273i
\(873\) 15.0000 + 25.9808i 0.507673 + 0.879316i
\(874\) 12.0000 0.405906
\(875\) 60.0000 + 20.7846i 2.02837 + 0.702648i
\(876\) 6.00000 0.202721
\(877\) −12.5000 21.6506i −0.422095 0.731090i 0.574049 0.818821i \(-0.305372\pi\)
−0.996144 + 0.0877308i \(0.972038\pi\)
\(878\) −2.50000 + 4.33013i −0.0843709 + 0.146135i
\(879\) −9.00000 + 15.5885i −0.303562 + 0.525786i
\(880\) −2.00000 3.46410i −0.0674200 0.116775i
\(881\) 9.00000 0.303218 0.151609 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) 39.0000 15.5885i 1.31320 0.524891i
\(883\) 1.00000 0.0336527 0.0168263 0.999858i \(-0.494644\pi\)
0.0168263 + 0.999858i \(0.494644\pi\)
\(884\) 1.00000 + 1.73205i 0.0336336 + 0.0582552i
\(885\) −54.0000 + 93.5307i −1.81519 + 3.14400i
\(886\) −6.00000 + 10.3923i −0.201574 + 0.349136i
\(887\) 8.50000 + 14.7224i 0.285402 + 0.494331i 0.972707 0.232038i \(-0.0745395\pi\)
−0.687305 + 0.726369i \(0.741206\pi\)
\(888\) −6.00000 −0.201347
\(889\) −12.5000 4.33013i −0.419237 0.145228i
\(890\) 24.0000 0.804482
\(891\) 4.50000 + 7.79423i 0.150756 + 0.261116i
\(892\) 13.0000 22.5167i 0.435272 0.753914i
\(893\) −6.00000 + 10.3923i −0.200782 + 0.347765i
\(894\) 15.0000 + 25.9808i 0.501675 + 0.868927i
\(895\) −52.0000 −1.73817
\(896\) −0.500000 2.59808i −0.0167038 0.0867956i
\(897\) −6.00000 −0.200334
\(898\) 15.0000 + 25.9808i 0.500556 + 0.866989i
\(899\) −2.00000 + 3.46410i −0.0667037 + 0.115534i
\(900\) −33.0000 + 57.1577i −1.10000 + 1.90526i
\(901\) 12.0000 + 20.7846i 0.399778 + 0.692436i
\(902\) −2.00000 −0.0665927
\(903\) −24.0000 + 20.7846i −0.798670 + 0.691669i
\(904\) −17.0000 −0.565412
\(905\) −44.0000 76.2102i −1.46261 2.53331i
\(906\) −13.5000 + 23.3827i −0.448507 + 0.776838i
\(907\) −22.0000 + 38.1051i −0.730498 + 1.26526i 0.226173 + 0.974087i \(0.427379\pi\)
−0.956671 + 0.291172i \(0.905955\pi\)
\(908\) −5.00000 8.66025i −0.165931 0.287401i
\(909\) −90.0000 −2.98511
\(910\) −8.00000 + 6.92820i −0.265197 + 0.229668i
\(911\) −54.0000 −1.78910 −0.894550 0.446968i \(-0.852504\pi\)
−0.894550 + 0.446968i \(0.852504\pi\)
\(912\) 9.00000 + 15.5885i 0.298020 + 0.516185i
\(913\) −3.00000 + 5.19615i −0.0992855 + 0.171968i
\(914\) 1.00000 1.73205i 0.0330771 0.0572911i
\(915\) 30.0000 + 51.9615i 0.991769 + 1.71780i
\(916\) −16.0000 −0.528655
\(917\) −9.00000 46.7654i −0.297206 1.54433i
\(918\) 18.0000 0.594089
\(919\) 12.0000 + 20.7846i 0.395843 + 0.685621i 0.993208 0.116348i \(-0.0371189\pi\)
−0.597365 + 0.801970i \(0.703786\pi\)
\(920\) 4.00000 6.92820i 0.131876 0.228416i
\(921\) 48.0000 83.1384i 1.58165 2.73950i
\(922\) −1.50000 2.59808i −0.0493999 0.0855631i
\(923\) −4.00000 −0.131662
\(924\) −7.50000 2.59808i −0.246732 0.0854704i
\(925\) −22.0000 −0.723356
\(926\) −7.00000 12.1244i −0.230034 0.398431i
\(927\) −36.0000 + 62.3538i −1.18240 + 2.04797i
\(928\) 0.500000 0.866025i 0.0164133 0.0284287i
\(929\) 16.5000 + 28.5788i 0.541347 + 0.937641i 0.998827 + 0.0484211i \(0.0154190\pi\)
−0.457480 + 0.889220i \(0.651248\pi\)
\(930\) −48.0000 −1.57398
\(931\) 6.00000 41.5692i 0.196642 1.36238i
\(932\) 6.00000 0.196537
\(933\) −42.0000 72.7461i −1.37502 2.38160i
\(934\) −6.00000 + 10.3923i −0.196326 + 0.340047i
\(935\) −4.00000 + 6.92820i −0.130814 + 0.226576i
\(936\) −3.00000 5.19615i −0.0980581 0.169842i
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) −22.5000 7.79423i −0.734651 0.254491i
\(939\) −3.00000 −0.0979013
\(940\) 4.00000 + 6.92820i 0.130466 + 0.225973i
\(941\) −27.5000 + 47.6314i −0.896474 + 1.55274i −0.0645052 + 0.997917i \(0.520547\pi\)
−0.831969 + 0.554822i \(0.812786\pi\)
\(942\) −6.00000 + 10.3923i −0.195491 + 0.338600i
\(943\) −2.00000 3.46410i −0.0651290 0.112807i
\(944\) 9.00000 0.292925
\(945\) 18.0000 + 93.5307i 0.585540 + 3.04256i
\(946\) 4.00000 0.130051
\(947\) 8.00000 + 13.8564i 0.259965 + 0.450273i 0.966232 0.257673i \(-0.0829556\pi\)
−0.706267 + 0.707945i \(0.749622\pi\)
\(948\) −22.5000 + 38.9711i −0.730766 + 1.26572i
\(949\) −1.00000 + 1.73205i −0.0324614 + 0.0562247i
\(950\) 33.0000 + 57.1577i 1.07066 + 1.85444i
\(951\) 36.0000 1.16738
\(952\) −4.00000 + 3.46410i −0.129641 + 0.112272i
\(953\) 56.0000 1.81402 0.907009 0.421111i \(-0.138360\pi\)
0.907009 + 0.421111i \(0.138360\pi\)
\(954\) −36.0000 62.3538i −1.16554 2.01878i
\(955\) 28.0000 48.4974i 0.906059 1.56934i
\(956\) −9.50000 + 16.4545i −0.307252 + 0.532176i
\(957\) −1.50000 2.59808i −0.0484881 0.0839839i
\(958\) 37.0000 1.19542
\(959\) −18.0000 + 15.5885i −0.581250 + 0.503378i
\(960\) 12.0000 0.387298
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 1.00000 1.73205i 0.0322413 0.0558436i
\(963\) −24.0000 + 41.5692i −0.773389 + 1.33955i
\(964\) −15.0000 25.9808i −0.483117 0.836784i
\(965\) 88.0000 2.83282
\(966\) −3.00000 15.5885i −0.0965234 0.501550i
\(967\) 56.0000 1.80084 0.900419 0.435023i \(-0.143260\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(968\) 0.500000 + 0.866025i 0.0160706 + 0.0278351i
\(969\) 18.0000 31.1769i 0.578243 1.00155i
\(970\) 10.0000 17.3205i 0.321081 0.556128i
\(971\) 6.50000 + 11.2583i 0.208595 + 0.361297i 0.951272 0.308353i \(-0.0997776\pi\)
−0.742677 + 0.669650i \(0.766444\pi\)
\(972\) 0 0
\(973\) −20.0000 6.92820i −0.641171 0.222108i
\(974\) 4.00000 0.128168
\(975\) −16.5000 28.5788i −0.528423 0.915255i
\(976\) 2.50000 4.33013i 0.0800230 0.138604i
\(977\) −7.00000 + 12.1244i −0.223950 + 0.387893i −0.956004 0.293354i \(-0.905229\pi\)
0.732054 + 0.681247i \(0.238562\pi\)
\(978\) −19.5000 33.7750i −0.623541 1.08001i
\(979\) −6.00000 −0.191761
\(980\) −22.0000 17.3205i −0.702764 0.553283i
\(981\) 60.0000 1.91565
\(982\) 9.00000 + 15.5885i 0.287202 + 0.497448i
\(983\) −9.00000 + 15.5885i −0.287055 + 0.497195i −0.973106 0.230360i \(-0.926010\pi\)
0.686050 + 0.727554i \(0.259343\pi\)
\(984\) 3.00000 5.19615i 0.0956365 0.165647i
\(985\) −6.00000 10.3923i −0.191176 0.331126i
\(986\) −2.00000 −0.0636930
\(987\) 15.0000 + 5.19615i 0.477455 + 0.165395i
\(988\) −6.00000 −0.190885
\(989\) 4.00000 + 6.92820i 0.127193 + 0.220304i
\(990\) 12.0000 20.7846i 0.381385 0.660578i
\(991\) 10.0000 17.3205i 0.317660 0.550204i −0.662339 0.749204i \(-0.730436\pi\)
0.979999 + 0.199000i \(0.0637695\pi\)
\(992\) 2.00000 + 3.46410i 0.0635001 + 0.109985i
\(993\) −21.0000 −0.666415
\(994\) −2.00000 10.3923i −0.0634361 0.329624i
\(995\) −40.0000 −1.26809
\(996\) −9.00000 15.5885i −0.285176 0.493939i
\(997\) 21.0000 36.3731i 0.665077 1.15195i −0.314188 0.949361i \(-0.601732\pi\)
0.979265 0.202586i \(-0.0649345\pi\)
\(998\) −8.00000 + 13.8564i −0.253236 + 0.438617i
\(999\) −9.00000 15.5885i −0.284747 0.493197i
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 154.2.e.d.67.1 yes 2
3.2 odd 2 1386.2.k.a.991.1 2
4.3 odd 2 1232.2.q.a.529.1 2
7.2 even 3 inner 154.2.e.d.23.1 2
7.3 odd 6 1078.2.a.f.1.1 1
7.4 even 3 1078.2.a.a.1.1 1
7.5 odd 6 1078.2.e.g.177.1 2
7.6 odd 2 1078.2.e.g.67.1 2
21.2 odd 6 1386.2.k.a.793.1 2
21.11 odd 6 9702.2.a.cg.1.1 1
21.17 even 6 9702.2.a.bb.1.1 1
28.3 even 6 8624.2.a.d.1.1 1
28.11 odd 6 8624.2.a.bd.1.1 1
28.23 odd 6 1232.2.q.a.177.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.e.d.23.1 2 7.2 even 3 inner
154.2.e.d.67.1 yes 2 1.1 even 1 trivial
1078.2.a.a.1.1 1 7.4 even 3
1078.2.a.f.1.1 1 7.3 odd 6
1078.2.e.g.67.1 2 7.6 odd 2
1078.2.e.g.177.1 2 7.5 odd 6
1232.2.q.a.177.1 2 28.23 odd 6
1232.2.q.a.529.1 2 4.3 odd 2
1386.2.k.a.793.1 2 21.2 odd 6
1386.2.k.a.991.1 2 3.2 odd 2
8624.2.a.d.1.1 1 28.3 even 6
8624.2.a.bd.1.1 1 28.11 odd 6
9702.2.a.bb.1.1 1 21.17 even 6
9702.2.a.cg.1.1 1 21.11 odd 6