Properties

Label 154.2.e.d.23.1
Level $154$
Weight $2$
Character 154.23
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 23.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 154.23
Dual form 154.2.e.d.67.1

$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 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 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 3.00000 + 5.19615i 0.707107 + 1.22474i
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) −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 −0.742732 0.669588i \(-0.766471\pi\)
0.951247 + 0.308431i \(0.0998038\pi\)
\(24\) −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 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 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 −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 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 −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) −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 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) −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 −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) −6.00000 10.3923i −0.774597 1.34164i
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) −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 0.998290 + 0.0584478i \(0.0186151\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(68\) −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 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −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 −0.0428296 0.999082i \(-0.513637\pi\)
0.886646 0.462450i \(-0.153029\pi\)
\(80\) 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 −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 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 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) 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 −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) 4.50000 + 7.79423i 0.433013 + 0.750000i
\(109\) −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i \(-0.325636\pi\)
−0.999708 + 0.0241802i \(0.992302\pi\)
\(110\) 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 −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 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 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 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 −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) −16.5000 28.5788i −1.34722 2.33345i
\(151\) −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i \(-0.286010\pi\)
−0.988969 + 0.148124i \(0.952676\pi\)
\(152\) 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 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) −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 0.490825 + 0.871258i \(0.336695\pi\)
−0.999944 + 0.0105623i \(0.996638\pi\)
\(164\) 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 −0.755202 0.655492i \(-0.772461\pi\)
0.945274 + 0.326278i \(0.105795\pi\)
\(174\) 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 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) 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 0.493469 + 0.869763i \(0.335728\pi\)
−0.999972 + 0.00752447i \(0.997605\pi\)
\(192\) 1.50000 + 2.59808i 0.108253 + 0.187500i
\(193\) 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i \(0.124188\pi\)
−0.133056 + 0.991109i \(0.542479\pi\)
\(194\) −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 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) 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 0.651015 0.759065i \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 9.00000 + 15.5885i 0.596040 + 1.03237i
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) −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 −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −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 −0.706260 0.707953i \(-0.749619\pi\)
−0.259975 0.965615i \(-0.583714\pi\)
\(242\) 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 −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) 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 0.816066 0.577959i \(-0.196151\pi\)
−0.908560 + 0.417755i \(0.862817\pi\)
\(264\) 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 0.623082 0.782157i \(-0.285880\pi\)
−0.988908 + 0.148527i \(0.952547\pi\)
\(270\) 18.0000 + 31.1769i 1.09545 + 1.89737i
\(271\) −12.5000 + 21.6506i −0.759321 + 1.31518i 0.183876 + 0.982949i \(0.441135\pi\)
−0.943197 + 0.332233i \(0.892198\pi\)
\(272\) 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 0.907564 0.419914i \(-0.137940\pi\)
−0.817438 + 0.576017i \(0.804606\pi\)
\(278\) 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 0.941309 0.337546i \(-0.109597\pi\)
−0.762978 + 0.646425i \(0.776263\pi\)
\(284\) −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 0.923556 + 0.383464i \(0.125269\pi\)
−0.129689 + 0.991555i \(0.541398\pi\)
\(312\) 1.50000 + 2.59808i 0.0849208 + 0.147087i
\(313\) −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) −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 −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 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 −0.946038 0.324057i \(-0.894953\pi\)
0.753660 + 0.657264i \(0.228286\pi\)
\(332\) 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 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) 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 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) −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 −0.0890519 0.996027i \(-0.528384\pi\)
0.907111 0.420892i \(-0.138283\pi\)
\(360\) −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 0.988840 0.148983i \(-0.0475999\pi\)
−0.623443 + 0.781869i \(0.714267\pi\)
\(368\) 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 −0.761074 0.648665i \(-0.775328\pi\)
0.942297 + 0.334777i \(0.108661\pi\)
\(374\) −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 −0.949938 0.312437i \(-0.898855\pi\)
0.745548 + 0.666452i \(0.232188\pi\)
\(384\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) −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 −0.193618 0.981077i \(-0.562022\pi\)
0.946447 0.322860i \(-0.104644\pi\)
\(398\) −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 −0.990257 0.139253i \(-0.955530\pi\)
0.615725 + 0.787961i \(0.288863\pi\)
\(402\) 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 0.925256 + 0.379344i \(0.123850\pi\)
−0.134107 + 0.990967i \(0.542817\pi\)
\(410\) 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 0.853732 0.520712i \(-0.174334\pi\)
−0.877816 + 0.478997i \(0.841000\pi\)
\(432\) 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 −0.800179 0.599761i \(-0.795262\pi\)
0.919498 + 0.393095i \(0.128596\pi\)
\(440\) −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 −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) −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 −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) −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 −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) −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 0.885372 + 0.464883i \(0.153904\pi\)
−0.0400855 + 0.999196i \(0.512763\pi\)
\(480\) 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 0.907776 0.419456i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(488\) −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 −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) 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 −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) −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 0.996611 + 0.0822547i \(0.0262121\pi\)
−0.427071 + 0.904218i \(0.640455\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) −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 −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 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 −0.916253 0.400599i \(-0.868802\pi\)
0.111198 0.993798i \(-0.464531\pi\)
\(558\) 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 −0.998419 0.0562051i \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) 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 0.190974 + 0.981595i \(0.438835\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(570\) 36.0000 + 62.3538i 1.50787 + 2.61171i
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) −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 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) −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 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) −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 −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −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 0.553716 0.832705i \(-0.313209\pi\)
−0.998002 + 0.0631797i \(0.979876\pi\)
\(614\) 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 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 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 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) −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 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 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 −0.996913 0.0785119i \(-0.974983\pi\)
0.566450 + 0.824096i \(0.308316\pi\)
\(654\) −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 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 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 0.226556 + 0.973998i \(0.427253\pi\)
−0.956785 + 0.290796i \(0.906080\pi\)
\(678\) 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 0.987275 + 0.159022i \(0.0508342\pi\)
−0.355920 + 0.934516i \(0.615832\pi\)
\(684\) −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 −0.972685 0.232128i \(-0.925431\pi\)
0.687372 + 0.726306i \(0.258764\pi\)
\(692\) −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 −0.916845 0.399244i \(-0.869273\pi\)
0.804178 + 0.594389i \(0.202606\pi\)
\(710\) −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 −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) −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 −0.856644 0.515908i \(-0.827454\pi\)
0.875112 + 0.483921i \(0.160788\pi\)
\(734\) 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 0.651652 0.758518i \(-0.274076\pi\)
−0.982722 + 0.185088i \(0.940743\pi\)
\(740\) −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 −0.114981 0.993368i \(-0.536681\pi\)
0.917772 0.397108i \(-0.129986\pi\)
\(752\) −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 −0.311787 + 0.950152i \(0.600927\pi\)
−0.666962 + 0.745091i \(0.732406\pi\)
\(762\) 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 0.997012 0.0772449i \(-0.0246123\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(774\) 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 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) 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 0.886664 + 0.462415i \(0.153017\pi\)
−0.0428684 + 0.999081i \(0.513650\pi\)
\(810\) −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 −0.704956 0.709251i \(-0.749033\pi\)
0.966708 + 0.255884i \(0.0823665\pi\)
\(822\) 13.5000 + 23.3827i 0.470867 + 0.815565i
\(823\) −19.0000 32.9090i −0.662298 1.14713i −0.980010 0.198947i \(-0.936248\pi\)
0.317712 0.948187i \(-0.397086\pi\)
\(824\) 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 0.692999 0.720938i \(-0.256289\pi\)
−0.970851 + 0.239686i \(0.922956\pi\)
\(830\) 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 0.898161 0.439666i \(-0.144903\pi\)
−0.829843 + 0.557998i \(0.811570\pi\)
\(858\) −1.50000 2.59808i −0.0512092 0.0886969i
\(859\) 8.50000 14.7224i 0.290016 0.502323i −0.683797 0.729672i \(-0.739673\pi\)
0.973813 + 0.227349i \(0.0730059\pi\)
\(860\) −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 −0.938490 0.345305i \(-0.887775\pi\)
0.768288 + 0.640104i \(0.221109\pi\)
\(864\) −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 −0.996144 0.0877308i \(-0.972038\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) −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 −0.687305 0.726369i \(-0.741206\pi\)
0.972707 + 0.232038i \(0.0745395\pi\)
\(888\) −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 −0.956671 0.291172i \(-0.905955\pi\)
0.226173 0.974087i \(-0.427379\pi\)
\(908\) −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 −0.597365 0.801970i \(-0.703786\pi\)
0.993208 + 0.116348i \(0.0371189\pi\)
\(920\) 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 −0.457480 0.889220i \(-0.651248\pi\)
0.998827 0.0484211i \(-0.0154190\pi\)
\(930\) −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 −0.831969 0.554822i \(-0.812786\pi\)
−0.0645052 0.997917i \(-0.520547\pi\)
\(942\) −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 −0.706267 0.707945i \(-0.749622\pi\)
0.966232 + 0.257673i \(0.0829556\pi\)
\(948\) −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 −0.742677 0.669650i \(-0.766444\pi\)
0.951272 + 0.308353i \(0.0997776\pi\)
\(972\) 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 0.732054 0.681247i \(-0.238562\pi\)
−0.956004 + 0.293354i \(0.905229\pi\)
\(978\) −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 0.686050 0.727554i \(-0.259343\pi\)
−0.973106 + 0.230360i \(0.926010\pi\)
\(984\) 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 0.979999 0.199000i \(-0.0637695\pi\)
−0.662339 + 0.749204i \(0.730436\pi\)
\(992\) 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 0.979265 + 0.202586i \(0.0649345\pi\)
−0.314188 + 0.949361i \(0.601732\pi\)
\(998\) −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.23.1 2
3.2 odd 2 1386.2.k.a.793.1 2
4.3 odd 2 1232.2.q.a.177.1 2
7.2 even 3 1078.2.a.a.1.1 1
7.3 odd 6 1078.2.e.g.67.1 2
7.4 even 3 inner 154.2.e.d.67.1 yes 2
7.5 odd 6 1078.2.a.f.1.1 1
7.6 odd 2 1078.2.e.g.177.1 2
21.2 odd 6 9702.2.a.cg.1.1 1
21.5 even 6 9702.2.a.bb.1.1 1
21.11 odd 6 1386.2.k.a.991.1 2
28.11 odd 6 1232.2.q.a.529.1 2
28.19 even 6 8624.2.a.d.1.1 1
28.23 odd 6 8624.2.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.e.d.23.1 2 1.1 even 1 trivial
154.2.e.d.67.1 yes 2 7.4 even 3 inner
1078.2.a.a.1.1 1 7.2 even 3
1078.2.a.f.1.1 1 7.5 odd 6
1078.2.e.g.67.1 2 7.3 odd 6
1078.2.e.g.177.1 2 7.6 odd 2
1232.2.q.a.177.1 2 4.3 odd 2
1232.2.q.a.529.1 2 28.11 odd 6
1386.2.k.a.793.1 2 3.2 odd 2
1386.2.k.a.991.1 2 21.11 odd 6
8624.2.a.d.1.1 1 28.19 even 6
8624.2.a.bd.1.1 1 28.23 odd 6
9702.2.a.bb.1.1 1 21.5 even 6
9702.2.a.cg.1.1 1 21.2 odd 6