Properties

Label 154.2.e.c.23.1
Level $154$
Weight $2$
Character 154.23
Analytic conductor $1.230$
Analytic rank $0$
Dimension $2$
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.c.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-0.500000 + 0.866025i) q^{26} -5.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} +9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} -6.00000 q^{41} +(0.500000 + 2.59808i) q^{42} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{54} +(0.500000 + 2.59808i) q^{56} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +4.00000 q^{62} +(-5.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +(-1.00000 + 1.73205i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{75} +2.00000 q^{76} +(2.00000 - 1.73205i) q^{77} +1.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -6.00000 q^{83} +(2.50000 + 0.866025i) q^{84} +(-2.00000 + 3.46410i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(9.00000 - 15.5885i) q^{89} +(0.500000 + 2.59808i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -13.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} + q^{11} - q^{12} - 2 q^{13} - 5 q^{14} - q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{21} + 2 q^{22} + 6 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} - 4 q^{28} + 18 q^{29} + 4 q^{31} + q^{32} + q^{33} + 12 q^{34} - 4 q^{36} - 2 q^{37} + 2 q^{38} + q^{39} - 12 q^{41} + q^{42} - 8 q^{43} + q^{44} - 6 q^{46} + 6 q^{47} + 2 q^{48} - 13 q^{49} + 10 q^{50} + 6 q^{51} + q^{52} - 5 q^{54} + q^{56} + 4 q^{57} + 9 q^{58} + 3 q^{59} - 11 q^{61} + 8 q^{62} - 10 q^{63} + 2 q^{64} - q^{66} - 11 q^{67} + 6 q^{68} - 12 q^{69} - 2 q^{72} - 2 q^{73} + 2 q^{74} + 5 q^{75} + 4 q^{76} + 4 q^{77} + 2 q^{78} - 5 q^{79} - q^{81} - 6 q^{82} - 12 q^{83} + 5 q^{84} - 4 q^{86} - 9 q^{87} - q^{88} + 18 q^{89} + q^{91} - 12 q^{92} + 4 q^{93} - 6 q^{94} + q^{96} - 26 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 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
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) −1.00000 −0.408248
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 1.00000 0.213201
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) −5.00000 −0.962250
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.500000 0.866025i 0.0870388 0.150756i
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0.500000 + 2.59808i 0.0771517 + 0.400892i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 5.00000 0.707107
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 0 0
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 2.00000 0.264906
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 4.00000 0.508001
\(63\) −5.00000 1.73205i −0.629941 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 2.50000 4.33013i 0.288675 0.500000i
\(76\) 2.00000 0.229416
\(77\) 2.00000 1.73205i 0.227921 0.197386i
\(78\) 1.00000 0.113228
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 2.50000 + 0.866025i 0.272772 + 0.0944911i
\(85\) 0 0
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 9.00000 15.5885i 0.953998 1.65237i 0.217354 0.976093i \(-0.430258\pi\)
0.736644 0.676280i \(-0.236409\pi\)
\(90\) 0 0
\(91\) 0.500000 + 2.59808i 0.0524142 + 0.272352i
\(92\) −6.00000 −0.625543
\(93\) 2.00000 3.46410i 0.207390 0.359211i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 2.00000 0.201008
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 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
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 3.00000 0.276172
\(119\) 12.0000 10.3923i 1.10004 0.952661i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 5.50000 + 9.52628i 0.497947 + 0.862469i
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) −4.00000 + 3.46410i −0.356348 + 0.308607i
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 5.00000 + 1.73205i 0.433555 + 0.150188i
\(134\) −11.0000 −0.950255
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 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 \(0.389818\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −0.500000 0.866025i −0.0418121 0.0724207i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 5.50000 + 4.33013i 0.453632 + 0.357143i
\(148\) 2.00000 0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −2.50000 4.33013i −0.204124 0.353553i
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 12.0000 0.970143
\(154\) −0.500000 2.59808i −0.0402911 0.209359i
\(155\) 0 0
\(156\) 0.500000 0.866025i 0.0400320 0.0693375i
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 5.19615i −1.18217 0.409514i
\(162\) −1.00000 −0.0785674
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 2.00000 1.73205i 0.154303 0.133631i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) −9.00000 −0.682288
\(175\) 10.0000 8.66025i 0.755929 0.654654i
\(176\) −1.00000 −0.0753778
\(177\) 1.50000 2.59808i 0.112747 0.195283i
\(178\) −9.00000 15.5885i −0.674579 1.16840i
\(179\) 7.50000 + 12.9904i 0.560576 + 0.970947i 0.997446 + 0.0714220i \(0.0227537\pi\)
−0.436870 + 0.899525i \(0.643913\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.50000 + 0.866025i 0.185312 + 0.0641941i
\(183\) 11.0000 0.813143
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) −6.00000 −0.437595
\(189\) 2.50000 + 12.9904i 0.181848 + 0.944911i
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −6.50000 + 11.2583i −0.466673 + 0.808301i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) −5.50000 + 9.52628i −0.387940 + 0.671932i
\(202\) 15.0000 1.05540
\(203\) −4.50000 23.3827i −0.315838 1.64114i
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) −6.00000 10.3923i −0.417029 0.722315i
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) −2.00000 −0.135457
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 1.00000 1.73205i 0.0671156 0.116248i
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 10.0000 0.666667
\(226\) 4.50000 7.79423i 0.299336 0.518464i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) −2.50000 0.866025i −0.164488 0.0569803i
\(232\) −9.00000 −0.590879
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) 0 0
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) 5.00000 0.324785
\(238\) −3.00000 15.5885i −0.194461 1.01045i
\(239\) −9.00000 −0.582162 −0.291081 0.956698i \(-0.594015\pi\)
−0.291081 + 0.956698i \(0.594015\pi\)
\(240\) 0 0
\(241\) −13.0000 22.5167i −0.837404 1.45043i −0.892058 0.451920i \(-0.850739\pi\)
0.0546547 0.998505i \(-0.482594\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 11.0000 0.704203
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 1.00000 + 5.19615i 0.0629941 + 0.327327i
\(253\) 6.00000 0.377217
\(254\) −3.50000 + 6.06218i −0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 4.00000 0.249029
\(259\) 5.00000 + 1.73205i 0.310685 + 0.107624i
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) −18.0000 −1.10158
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) −6.00000 10.3923i −0.365826 0.633630i 0.623082 0.782157i \(-0.285880\pi\)
−0.988908 + 0.148527i \(0.952547\pi\)
\(270\) 0 0
\(271\) −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i \(0.509669\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −6.00000 −0.363803
\(273\) 2.00000 1.73205i 0.121046 0.104828i
\(274\) 9.00000 0.543710
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −14.5000 25.1147i −0.871221 1.50900i −0.860735 0.509053i \(-0.829996\pi\)
−0.0104855 0.999945i \(-0.503338\pi\)
\(278\) 4.00000 6.92820i 0.239904 0.415526i
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.00000 −0.0591312
\(287\) 3.00000 + 15.5885i 0.177084 + 0.920158i
\(288\) 2.00000 0.117851
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 6.50000 + 11.2583i 0.381037 + 0.659975i
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 6.50000 2.59808i 0.379088 0.151523i
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) −5.00000 −0.288675
\(301\) 2.00000 + 10.3923i 0.115278 + 0.599002i
\(302\) 19.0000 1.09333
\(303\) 7.50000 12.9904i 0.430864 0.746278i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −2.50000 0.866025i −0.142451 0.0493464i
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) −8.50000 + 14.7224i −0.480448 + 0.832161i −0.999748 0.0224310i \(-0.992859\pi\)
0.519300 + 0.854592i \(0.326193\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) −12.0000 + 10.3923i −0.668734 + 0.579141i
\(323\) −12.0000 −0.667698
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) 8.50000 + 14.7224i 0.470771 + 0.815400i
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) 6.00000 0.331295
\(329\) −15.0000 5.19615i −0.826977 0.286473i
\(330\) 0 0
\(331\) −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i \(0.578503\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) 0 0
\(336\) −0.500000 2.59808i −0.0272772 0.141737i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) −4.50000 7.79423i −0.244406 0.423324i
\(340\) 0 0
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 4.00000 0.216295
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) −4.50000 + 7.79423i −0.241225 + 0.417815i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −2.50000 12.9904i −0.133631 0.694365i
\(351\) 5.00000 0.266880
\(352\) −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 \(0.674325\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) −15.0000 5.19615i −0.793884 0.275010i
\(358\) 15.0000 0.792775
\(359\) 1.50000 2.59808i 0.0791670 0.137121i −0.823724 0.566991i \(-0.808107\pi\)
0.902891 + 0.429870i \(0.141441\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 1.00000 0.0524864
\(364\) 2.00000 1.73205i 0.104828 0.0907841i
\(365\) 0 0
\(366\) 5.50000 9.52628i 0.287490 0.497947i
\(367\) 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) −6.00000 + 10.3923i −0.312348 + 0.541002i
\(370\) 0 0
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) 15.5000 26.8468i 0.802560 1.39007i −0.115367 0.993323i \(-0.536804\pi\)
0.917926 0.396751i \(-0.129862\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −9.00000 −0.463524
\(378\) 12.5000 + 4.33013i 0.642931 + 0.222718i
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) 3.50000 + 6.06218i 0.179310 + 0.310575i
\(382\) 3.00000 + 5.19615i 0.153493 + 0.265858i
\(383\) 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 6.50000 + 11.2583i 0.329988 + 0.571555i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 18.0000 0.907980
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 0 0
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) −14.0000 −0.701757
\(399\) −1.00000 5.19615i −0.0500626 0.260133i
\(400\) −5.00000 −0.250000
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) 5.50000 + 9.52628i 0.274315 + 0.475128i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 7.50000 12.9904i 0.373139 0.646296i
\(405\) 0 0
\(406\) −22.5000 7.79423i −1.11666 0.386821i
\(407\) −2.00000 −0.0991363
\(408\) −3.00000 + 5.19615i −0.148522 + 0.257248i
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −16.0000 −0.788263
\(413\) 6.00000 5.19615i 0.295241 0.255686i
\(414\) −12.0000 −0.589768
\(415\) 0 0
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) −4.00000 6.92820i −0.195881 0.339276i
\(418\) −1.00000 + 1.73205i −0.0489116 + 0.0847174i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −5.00000 + 8.66025i −0.243396 + 0.421575i
\(423\) −6.00000 10.3923i −0.291730 0.505291i
\(424\) 0 0
\(425\) −15.0000 + 25.9808i −0.727607 + 1.26025i
\(426\) 0 0
\(427\) 27.5000 + 9.52628i 1.33082 + 0.461009i
\(428\) 12.0000 0.580042
\(429\) −0.500000 + 0.866025i −0.0241402 + 0.0418121i
\(430\) 0 0
\(431\) 1.50000 + 2.59808i 0.0722525 + 0.125145i 0.899888 0.436121i \(-0.143648\pi\)
−0.827636 + 0.561266i \(0.810315\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −2.00000 10.3923i −0.0960031 0.498847i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 0 0
\(441\) −2.00000 + 13.8564i −0.0952381 + 0.659829i
\(442\) −6.00000 −0.285391
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) 0 0
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 6.00000 0.283790
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 5.00000 8.66025i 0.235702 0.408248i
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) −4.50000 7.79423i −0.211662 0.366610i
\(453\) 9.50000 16.4545i 0.446349 0.773099i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) −8.00000 13.8564i −0.373815 0.647467i
\(459\) −15.0000 25.9808i −0.700140 1.21268i
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) −2.00000 + 1.73205i −0.0930484 + 0.0805823i
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 2.00000 0.0924500
\(469\) −22.0000 + 19.0526i −1.01587 + 0.879765i
\(470\) 0 0
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) −1.50000 2.59808i −0.0690431 0.119586i
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) 2.50000 4.33013i 0.114829 0.198889i
\(475\) −10.0000 −0.458831
\(476\) −15.0000 5.19615i −0.687524 0.238165i
\(477\) 0 0
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) −26.0000 −1.18427
\(483\) 3.00000 + 15.5885i 0.136505 + 0.709299i
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i \(-0.316364\pi\)
−0.998579 + 0.0532853i \(0.983031\pi\)
\(488\) 5.50000 9.52628i 0.248973 0.431234i
\(489\) 17.0000 0.768767
\(490\) 0 0
\(491\) 42.0000 1.89543 0.947717 0.319113i \(-0.103385\pi\)
0.947717 + 0.319113i \(0.103385\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) 27.0000 + 46.7654i 1.21602 + 2.10621i
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) 0 0
\(501\) −1.50000 2.59808i −0.0670151 0.116073i
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) −33.0000 −1.47140 −0.735699 0.677309i \(-0.763146\pi\)
−0.735699 + 0.677309i \(0.763146\pi\)
\(504\) 5.00000 + 1.73205i 0.222718 + 0.0771517i
\(505\) 0 0
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) −4.00000 + 3.46410i −0.176950 + 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 8.66025i 0.220755 0.382360i
\(514\) 1.50000 + 2.59808i 0.0661622 + 0.114596i
\(515\) 0 0
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 6.00000 0.263880
\(518\) 4.00000 3.46410i 0.175750 0.152204i
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) 18.0000 0.786334
\(525\) −12.5000 4.33013i −0.545545 0.188982i
\(526\) 9.00000 0.392419
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) 0.500000 + 0.866025i 0.0217597 + 0.0376889i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −1.00000 5.19615i −0.0433555 0.225282i
\(533\) 6.00000 0.259889
\(534\) −9.00000 + 15.5885i −0.389468 + 0.674579i
\(535\) 0 0
\(536\) 5.50000 + 9.52628i 0.237564 + 0.411473i
\(537\) 7.50000 12.9904i 0.323649 0.560576i
\(538\) −12.0000 −0.517357
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 14.5000 + 25.1147i 0.622828 + 1.07877i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 0 0
\(546\) −0.500000 2.59808i −0.0213980 0.111187i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 11.0000 + 19.0526i 0.469469 + 0.813143i
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) −9.00000 + 15.5885i −0.383413 + 0.664091i
\(552\) 6.00000 0.255377
\(553\) 12.5000 + 4.33013i 0.531554 + 0.184136i
\(554\) −29.0000 −1.23209
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 4.00000 6.92820i 0.169334 0.293294i
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 0 0
\(566\) 10.0000 0.420331
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) −0.500000 + 0.866025i −0.0209061 + 0.0362103i
\(573\) 6.00000 0.250654
\(574\) 15.0000 + 5.19615i 0.626088 + 0.216883i
\(575\) 30.0000 1.25109
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 0 0
\(581\) 3.00000 + 15.5885i 0.124461 + 0.646718i
\(582\) 13.0000 0.538867
\(583\) 0 0
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) −15.0000 + 25.9808i −0.619644 + 1.07326i
\(587\) 9.00000 0.371470 0.185735 0.982600i \(-0.440533\pi\)
0.185735 + 0.982600i \(0.440533\pi\)
\(588\) 1.00000 6.92820i 0.0412393 0.285714i
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −18.0000 + 31.1769i −0.739171 + 1.28028i 0.213697 + 0.976900i \(0.431449\pi\)
−0.952869 + 0.303383i \(0.901884\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −7.00000 + 12.1244i −0.286491 + 0.496217i
\(598\) 3.00000 + 5.19615i 0.122679 + 0.212486i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 10.0000 + 3.46410i 0.407570 + 0.141186i
\(603\) −22.0000 −0.895909
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0 0
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i \(-0.531835\pi\)
0.911621 0.411033i \(-0.134832\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −18.0000 + 15.5885i −0.729397 + 0.631676i
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) −6.00000 10.3923i −0.242536 0.420084i
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) 0 0
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) 21.0000 0.845428 0.422714 0.906263i \(-0.361077\pi\)
0.422714 + 0.906263i \(0.361077\pi\)
\(618\) −8.00000 + 13.8564i −0.321807 + 0.557386i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 0 0
\(621\) −15.0000 + 25.9808i −0.601929 + 1.04257i
\(622\) −24.0000 −0.962312
\(623\) −45.0000 15.5885i −1.80289 0.624538i
\(624\) −1.00000 −0.0400320
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 8.50000 + 14.7224i 0.339728 + 0.588427i
\(627\) 1.00000 + 1.73205i 0.0399362 + 0.0691714i
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 2.50000 4.33013i 0.0994447 0.172243i
\(633\) 5.00000 + 8.66025i 0.198732 + 0.344214i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) 9.00000 0.356313
\(639\) 0 0
\(640\) 0 0
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) 6.00000 10.3923i 0.236801 0.410152i
\(643\) 5.00000 0.197181 0.0985904 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) 3.00000 + 15.5885i 0.118217 + 0.614271i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) −5.00000 −0.196116
\(651\) −10.0000 3.46410i −0.391931 0.135769i
\(652\) 17.0000 0.665771
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) 0 0
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) −4.00000 −0.156055
\(658\) −12.0000 + 10.3923i −0.467809 + 0.405134i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 17.5000 + 30.3109i 0.680157 + 1.17807i
\(663\) −3.00000 + 5.19615i −0.116510 + 0.201802i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) −1.50000 2.59808i −0.0580367 0.100523i
\(669\) −13.0000 22.5167i −0.502609 0.870544i
\(670\) 0 0
\(671\) −11.0000 −0.424650
\(672\) −2.50000 0.866025i −0.0964396 0.0334077i
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) −12.5000 21.6506i −0.481125 0.833333i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) −9.00000 −0.345643
\(679\) 6.50000 + 33.7750i 0.249447 + 1.29617i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) 0 0
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) −16.0000 −0.610438
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 0 0
\(690\) 0 0
\(691\) −5.50000 + 9.52628i −0.209230 + 0.362397i −0.951472 0.307735i \(-0.900429\pi\)
0.742242 + 0.670132i \(0.233762\pi\)
\(692\) −21.0000 −0.798300
\(693\) −1.00000 5.19615i −0.0379869 0.197386i
\(694\) 0 0
\(695\) 0 0
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) 1.00000 1.73205i 0.0378506 0.0655591i
\(699\) −6.00000 −0.226941
\(700\) −12.5000 4.33013i −0.472456 0.163663i
\(701\) 39.0000 1.47301 0.736505 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 2.50000 4.33013i 0.0943564 0.163430i
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 30.0000 25.9808i 1.12827 0.977107i
\(708\) −3.00000 −0.112747
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) 24.0000 0.898807
\(714\) −12.0000 + 10.3923i −0.449089 + 0.388922i
\(715\) 0 0
\(716\) 7.50000 12.9904i 0.280288 0.485473i
\(717\) 4.50000 + 7.79423i 0.168056 + 0.291081i
\(718\) −1.50000 2.59808i −0.0559795 0.0969593i
\(719\) 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i \(-0.546936\pi\)
0.930087 0.367338i \(-0.119731\pi\)
\(720\) 0 0
\(721\) −40.0000 13.8564i −1.48968 0.516040i
\(722\) 15.0000 0.558242
\(723\) −13.0000 + 22.5167i −0.483475 + 0.837404i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 22.5000 + 38.9711i 0.835629 + 1.44735i
\(726\) 0.500000 0.866025i 0.0185567 0.0321412i
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) −0.500000 2.59808i −0.0185312 0.0962911i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) −5.50000 9.52628i −0.203286 0.352101i
\(733\) 12.5000 21.6506i 0.461698 0.799684i −0.537348 0.843361i \(-0.680574\pi\)
0.999046 + 0.0436764i \(0.0139070\pi\)
\(734\) 10.0000 0.369107
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 5.50000 9.52628i 0.202595 0.350905i
\(738\) 6.00000 + 10.3923i 0.220863 + 0.382546i
\(739\) −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −15.5000 26.8468i −0.567495 0.982931i
\(747\) −6.00000 + 10.3923i −0.219529 + 0.380235i
\(748\) 6.00000 0.219382
\(749\) 30.0000 + 10.3923i 1.09618 + 0.379727i
\(750\) 0 0
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) 0 0
\(756\) 10.0000 8.66025i 0.363696 0.314970i
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 11.5000 19.9186i 0.417699 0.723476i
\(759\) −3.00000 5.19615i −0.108893 0.188608i
\(760\) 0 0
\(761\) 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 7.00000 0.253583
\(763\) −4.00000 + 3.46410i −0.144810 + 0.125409i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) −18.0000 31.1769i −0.650366 1.12647i
\(767\) −1.50000 2.59808i −0.0541619 0.0938111i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i \(-0.308721\pi\)
−0.997012 + 0.0772449i \(0.975388\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) 13.0000 0.466673
\(777\) −1.00000 5.19615i