Properties

Label 418.2.e.d.45.1
Level $418$
Weight $2$
Character 418.45
Analytic conductor $3.338$
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] = [418,2,Mod(45,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.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: \(3.33774680449\)
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 45.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 418.45
Dual form 418.2.e.d.353.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{6} +2.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{6} +2.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{11} -2.00000 q^{12} +(0.500000 - 0.866025i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(1.00000 + 1.73205i) q^{24} +(2.50000 - 4.33013i) q^{25} -1.00000 q^{26} +4.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(-4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(3.00000 - 5.19615i) q^{34} +(-0.500000 - 0.866025i) q^{36} -10.0000 q^{37} +(4.00000 + 1.73205i) q^{38} +2.00000 q^{39} +(3.00000 + 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{42} +(-2.50000 - 4.33013i) q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 1.73205i) q^{48} -3.00000 q^{49} -5.00000 q^{50} +(-6.00000 + 10.3923i) q^{51} +(0.500000 + 0.866025i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-2.00000 - 3.46410i) q^{54} +2.00000 q^{56} +(-8.00000 - 3.46410i) q^{57} +9.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(-4.00000 - 6.92820i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{66} +(5.00000 - 8.66025i) q^{67} -6.00000 q^{68} +(-4.50000 - 7.79423i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.00000 + 3.46410i) q^{73} +(5.00000 + 8.66025i) q^{74} +10.0000 q^{75} +(-0.500000 - 4.33013i) q^{76} +2.00000 q^{77} +(-1.00000 - 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(5.50000 + 9.52628i) q^{81} +(3.00000 - 5.19615i) q^{82} -9.00000 q^{83} -4.00000 q^{84} +(-2.50000 + 4.33013i) q^{86} -18.0000 q^{87} +1.00000 q^{88} +(-7.50000 + 12.9904i) q^{89} +(1.00000 - 1.73205i) q^{91} +(8.00000 + 13.8564i) q^{93} -3.00000 q^{94} -2.00000 q^{96} +(0.500000 + 0.866025i) q^{97} +(1.50000 + 2.59808i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} + 2 q^{11} - 4 q^{12} + q^{13} - 2 q^{14} - q^{16} + 6 q^{17} + 2 q^{18} - 7 q^{19} + 4 q^{21} - q^{22} + 2 q^{24} + 5 q^{25} - 2 q^{26} + 8 q^{27} - 2 q^{28} - 9 q^{29} + 16 q^{31} - q^{32} + 2 q^{33} + 6 q^{34} - q^{36} - 20 q^{37} + 8 q^{38} + 4 q^{39} + 6 q^{41} + 4 q^{42} - 5 q^{43} - q^{44} + 3 q^{47} + 2 q^{48} - 6 q^{49} - 10 q^{50} - 12 q^{51} + q^{52} + 6 q^{53} - 4 q^{54} + 4 q^{56} - 16 q^{57} + 18 q^{58} - 6 q^{59} + 13 q^{61} - 8 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{66} + 10 q^{67} - 12 q^{68} - 9 q^{71} - q^{72} + 4 q^{73} + 10 q^{74} + 20 q^{75} - q^{76} + 4 q^{77} - 2 q^{78} - 8 q^{79} + 11 q^{81} + 6 q^{82} - 18 q^{83} - 8 q^{84} - 5 q^{86} - 36 q^{87} + 2 q^{88} - 15 q^{89} + 2 q^{91} + 16 q^{93} - 6 q^{94} - 4 q^{96} + q^{97} + 3 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 1.00000 1.73205i 0.408248 0.707107i
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −2.00000 −0.577350
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) −1.00000 1.73205i −0.267261 0.462910i
\(15\) 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 0.235702
\(19\) −3.50000 + 2.59808i −0.802955 + 0.596040i
\(20\) 0 0
\(21\) 2.00000 + 3.46410i 0.436436 + 0.755929i
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 1.00000 + 1.73205i 0.204124 + 0.353553i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −1.00000 −0.196116
\(27\) 4.00000 0.769800
\(28\) −1.00000 + 1.73205i −0.188982 + 0.327327i
\(29\) −4.50000 + 7.79423i −0.835629 + 1.44735i 0.0578882 + 0.998323i \(0.481563\pi\)
−0.893517 + 0.449029i \(0.851770\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.00000 + 1.73205i 0.174078 + 0.301511i
\(34\) 3.00000 5.19615i 0.514496 0.891133i
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 + 1.73205i 0.648886 + 0.280976i
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 2.00000 3.46410i 0.308607 0.534522i
\(43\) −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i \(-0.291172\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 0 0
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) 1.00000 1.73205i 0.144338 0.250000i
\(49\) −3.00000 −0.428571
\(50\) −5.00000 −0.707107
\(51\) −6.00000 + 10.3923i −0.840168 + 1.45521i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) −2.00000 3.46410i −0.272166 0.471405i
\(55\) 0 0
\(56\) 2.00000 0.267261
\(57\) −8.00000 3.46410i −1.05963 0.458831i
\(58\) 9.00000 1.18176
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) −4.00000 6.92820i −0.508001 0.879883i
\(63\) −1.00000 + 1.73205i −0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −4.50000 7.79423i −0.534052 0.925005i −0.999209 0.0397765i \(-0.987335\pi\)
0.465157 0.885228i \(-0.345998\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) 5.00000 + 8.66025i 0.581238 + 1.00673i
\(75\) 10.0000 1.15470
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) 2.00000 0.227921
\(78\) −1.00000 1.73205i −0.113228 0.196116i
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −2.50000 + 4.33013i −0.269582 + 0.466930i
\(87\) −18.0000 −1.92980
\(88\) 1.00000 0.106600
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 1.00000 1.73205i 0.104828 0.181568i
\(92\) 0 0
\(93\) 8.00000 + 13.8564i 0.829561 + 1.43684i
\(94\) −3.00000 −0.309426
\(95\) 0 0
\(96\) −2.00000 −0.204124
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) −0.500000 + 0.866025i −0.0502519 + 0.0870388i
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 12.0000 1.18818
\(103\) −19.0000 −1.87213 −0.936063 0.351833i \(-0.885559\pi\)
−0.936063 + 0.351833i \(0.885559\pi\)
\(104\) 0.500000 0.866025i 0.0490290 0.0849208i
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) −10.0000 17.3205i −0.949158 1.64399i
\(112\) −1.00000 1.73205i −0.0944911 0.163663i
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 1.00000 + 8.66025i 0.0936586 + 0.811107i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) −3.00000 + 5.19615i −0.276172 + 0.478345i
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −13.0000 −1.17696
\(123\) −6.00000 + 10.3923i −0.541002 + 0.937043i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 5.00000 8.66025i 0.440225 0.762493i
\(130\) 0 0
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) −2.00000 −0.174078
\(133\) −7.00000 + 5.19615i −0.606977 + 0.450564i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −4.50000 + 7.79423i −0.377632 + 0.654077i
\(143\) 0.500000 0.866025i 0.0418121 0.0724207i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) −3.00000 5.19615i −0.247436 0.428571i
\(148\) 5.00000 8.66025i 0.410997 0.711868i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) −5.00000 8.66025i −0.408248 0.707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −3.50000 + 2.59808i −0.283887 + 0.210732i
\(153\) −6.00000 −0.485071
\(154\) −1.00000 1.73205i −0.0805823 0.139573i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 5.50000 9.52628i 0.432121 0.748455i
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −3.00000 + 5.19615i −0.232147 + 0.402090i −0.958440 0.285295i \(-0.907908\pi\)
0.726293 + 0.687386i \(0.241242\pi\)
\(168\) 2.00000 + 3.46410i 0.154303 + 0.267261i
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) −0.500000 4.33013i −0.0382360 0.331133i
\(172\) 5.00000 0.381246
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 9.00000 + 15.5885i 0.682288 + 1.18176i
\(175\) 5.00000 8.66025i 0.377964 0.654654i
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) 15.0000 1.12430
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 8.00000 13.8564i 0.594635 1.02994i −0.398963 0.916967i \(-0.630630\pi\)
0.993598 0.112972i \(-0.0360369\pi\)
\(182\) −2.00000 −0.148250
\(183\) 26.0000 1.92198
\(184\) 0 0
\(185\) 0 0
\(186\) 8.00000 13.8564i 0.586588 1.01600i
\(187\) 3.00000 + 5.19615i 0.219382 + 0.379980i
\(188\) 1.50000 + 2.59808i 0.109399 + 0.189484i
\(189\) 8.00000 0.581914
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 1.00000 + 1.73205i 0.0721688 + 0.125000i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 0.500000 0.866025i 0.0358979 0.0621770i
\(195\) 0 0
\(196\) 1.50000 2.59808i 0.107143 0.185577i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 1.00000 0.0710669
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 20.0000 1.41069
\(202\) −3.00000 −0.211079
\(203\) −9.00000 + 15.5885i −0.631676 + 1.09410i
\(204\) −6.00000 10.3923i −0.420084 0.727607i
\(205\) 0 0
\(206\) 9.50000 + 16.4545i 0.661896 + 1.14644i
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −3.50000 + 2.59808i −0.242100 + 0.179713i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 9.00000 15.5885i 0.616670 1.06810i
\(214\) 4.50000 + 7.79423i 0.307614 + 0.532803i
\(215\) 0 0
\(216\) 4.00000 0.272166
\(217\) 16.0000 1.08615
\(218\) −5.50000 + 9.52628i −0.372507 + 0.645201i
\(219\) −4.00000 + 6.92820i −0.270295 + 0.468165i
\(220\) 0 0
\(221\) 6.00000 0.403604
\(222\) −10.0000 + 17.3205i −0.671156 + 1.16248i
\(223\) 3.50000 + 6.06218i 0.234377 + 0.405953i 0.959092 0.283096i \(-0.0913615\pi\)
−0.724714 + 0.689050i \(0.758028\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 2.50000 + 4.33013i 0.166667 + 0.288675i
\(226\) −4.50000 7.79423i −0.299336 0.518464i
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 7.00000 5.19615i 0.463586 0.344124i
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) 2.00000 + 3.46410i 0.131590 + 0.227921i
\(232\) −4.50000 + 7.79423i −0.295439 + 0.511716i
\(233\) −6.00000 10.3923i −0.393073 0.680823i 0.599780 0.800165i \(-0.295255\pi\)
−0.992853 + 0.119342i \(0.961921\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) 8.00000 13.8564i 0.519656 0.900070i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 6.50000 + 11.2583i 0.416120 + 0.720741i
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 0.500000 + 4.33013i 0.0318142 + 0.275519i
\(248\) 8.00000 0.508001
\(249\) −9.00000 15.5885i −0.570352 0.987878i
\(250\) 0 0
\(251\) 9.00000 15.5885i 0.568075 0.983935i −0.428681 0.903456i \(-0.641022\pi\)
0.996756 0.0804789i \(-0.0256450\pi\)
\(252\) −1.00000 1.73205i −0.0629941 0.109109i
\(253\) 0 0
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) −10.0000 −0.622573
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) −4.50000 7.79423i −0.278543 0.482451i
\(262\) 1.50000 2.59808i 0.0926703 0.160510i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 1.00000 + 1.73205i 0.0615457 + 0.106600i
\(265\) 0 0
\(266\) 8.00000 + 3.46410i 0.490511 + 0.212398i
\(267\) −30.0000 −1.83597
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 3.00000 5.19615i 0.181902 0.315063i
\(273\) 4.00000 0.242091
\(274\) −9.00000 −0.543710
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −4.00000 −0.239904
\(279\) −4.00000 + 6.92820i −0.239474 + 0.414781i
\(280\) 0 0
\(281\) −6.00000 + 10.3923i −0.357930 + 0.619953i −0.987615 0.156898i \(-0.949851\pi\)
0.629685 + 0.776851i \(0.283184\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 9.00000 0.534052
\(285\) 0 0
\(286\) −1.00000 −0.0591312
\(287\) 6.00000 + 10.3923i 0.354169 + 0.613438i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) −1.00000 + 1.73205i −0.0586210 + 0.101535i
\(292\) −4.00000 −0.234082
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) −3.00000 + 5.19615i −0.174964 + 0.303046i
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 4.00000 0.232104
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) 0 0
\(300\) −5.00000 + 8.66025i −0.288675 + 0.500000i
\(301\) −5.00000 8.66025i −0.288195 0.499169i
\(302\) −4.00000 6.92820i −0.230174 0.398673i
\(303\) 6.00000 0.344691
\(304\) 4.00000 + 1.73205i 0.229416 + 0.0993399i
\(305\) 0 0
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) 3.50000 + 6.06218i 0.199756 + 0.345987i 0.948449 0.316929i \(-0.102652\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(308\) −1.00000 + 1.73205i −0.0569803 + 0.0986928i
\(309\) −19.0000 32.9090i −1.08087 1.87213i
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 2.00000 0.113228
\(313\) −8.50000 + 14.7224i −0.480448 + 0.832161i −0.999748 0.0224310i \(-0.992859\pi\)
0.519300 + 0.854592i \(0.326193\pi\)
\(314\) −7.00000 + 12.1244i −0.395033 + 0.684217i
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −15.0000 + 25.9808i −0.842484 + 1.45922i 0.0453045 + 0.998973i \(0.485574\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(318\) −6.00000 10.3923i −0.336463 0.582772i
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) 0 0
\(321\) −9.00000 15.5885i −0.502331 0.870063i
\(322\) 0 0
\(323\) −24.0000 10.3923i −1.33540 0.578243i
\(324\) −11.0000 −0.611111
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) −1.00000 1.73205i −0.0553849 0.0959294i
\(327\) 11.0000 19.0526i 0.608301 1.05361i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 4.50000 7.79423i 0.246970 0.427764i
\(333\) 5.00000 8.66025i 0.273998 0.474579i
\(334\) 6.00000 0.328305
\(335\) 0 0
\(336\) 2.00000 3.46410i 0.109109 0.188982i
\(337\) 17.0000 + 29.4449i 0.926049 + 1.60396i 0.789865 + 0.613280i \(0.210150\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 9.00000 + 15.5885i 0.488813 + 0.846649i
\(340\) 0 0
\(341\) 8.00000 0.433224
\(342\) −3.50000 + 2.59808i −0.189258 + 0.140488i
\(343\) −20.0000 −1.07990
\(344\) −2.50000 4.33013i −0.134791 0.233465i
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 16.5000 + 28.5788i 0.885766 + 1.53419i 0.844833 + 0.535031i \(0.179700\pi\)
0.0409337 + 0.999162i \(0.486967\pi\)
\(348\) 9.00000 15.5885i 0.482451 0.835629i
\(349\) 5.00000 0.267644 0.133822 0.991005i \(-0.457275\pi\)
0.133822 + 0.991005i \(0.457275\pi\)
\(350\) −10.0000 −0.534522
\(351\) 2.00000 3.46410i 0.106752 0.184900i
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −7.50000 12.9904i −0.397499 0.688489i
\(357\) −12.0000 + 20.7846i −0.635107 + 1.10004i
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i \(0.124121\pi\)
−0.133263 + 0.991081i \(0.542545\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) −16.0000 −0.840941
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 1.00000 + 1.73205i 0.0524142 + 0.0907841i
\(365\) 0 0
\(366\) −13.0000 22.5167i −0.679521 1.17696i
\(367\) 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i \(-0.774850\pi\)
0.942799 + 0.333363i \(0.108183\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) −16.0000 −0.829561
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 3.00000 5.19615i 0.155126 0.268687i
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 4.50000 + 7.79423i 0.231762 + 0.401423i
\(378\) −4.00000 6.92820i −0.205738 0.356348i
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) −1.50000 2.59808i −0.0767467 0.132929i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 1.00000 1.73205i 0.0510310 0.0883883i
\(385\) 0 0
\(386\) 8.00000 13.8564i 0.407189 0.705273i
\(387\) 5.00000 0.254164
\(388\) −1.00000 −0.0507673
\(389\) 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −3.00000 −0.151523
\(393\) −3.00000 + 5.19615i −0.151330 + 0.262111i
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) 0 0
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) −19.0000 −0.952384
\(399\) −16.0000 6.92820i −0.801002 0.346844i
\(400\) −5.00000 −0.250000
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) −10.0000 17.3205i −0.498755 0.863868i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 1.50000 + 2.59808i 0.0746278 + 0.129259i
\(405\) 0 0
\(406\) 18.0000 0.893325
\(407\) −10.0000 −0.495682
\(408\) −6.00000 + 10.3923i −0.297044 + 0.514496i
\(409\) 2.00000 3.46410i 0.0988936 0.171289i −0.812333 0.583193i \(-0.801803\pi\)
0.911227 + 0.411905i \(0.135136\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 9.50000 16.4545i 0.468031 0.810654i
\(413\) −6.00000 10.3923i −0.295241 0.511372i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 8.00000 0.391762
\(418\) 4.00000 + 1.73205i 0.195646 + 0.0847174i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 14.0000 + 24.2487i 0.682318 + 1.18181i 0.974272 + 0.225377i \(0.0723615\pi\)
−0.291953 + 0.956433i \(0.594305\pi\)
\(422\) −10.0000 + 17.3205i −0.486792 + 0.843149i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 30.0000 1.45521
\(426\) −18.0000 −0.872103
\(427\) 13.0000 22.5167i 0.629114 1.08966i
\(428\) 4.50000 7.79423i 0.217516 0.376748i
\(429\) 2.00000 0.0965609
\(430\) 0 0
\(431\) 18.0000 31.1769i 0.867029 1.50174i 0.00201168 0.999998i \(-0.499360\pi\)
0.865018 0.501741i \(-0.167307\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) −5.50000 + 9.52628i −0.264313 + 0.457804i −0.967383 0.253317i \(-0.918479\pi\)
0.703070 + 0.711120i \(0.251812\pi\)
\(434\) −8.00000 13.8564i −0.384012 0.665129i
\(435\) 0 0
\(436\) 11.0000 0.526804
\(437\) 0 0
\(438\) 8.00000 0.382255
\(439\) −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 0 0
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) −3.00000 5.19615i −0.142695 0.247156i
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 20.0000 0.949158
\(445\) 0 0
\(446\) 3.50000 6.06218i 0.165730 0.287052i
\(447\) 6.00000 10.3923i 0.283790 0.491539i
\(448\) 2.00000 0.0944911
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 2.50000 4.33013i 0.117851 0.204124i
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) −4.50000 + 7.79423i −0.211662 + 0.366610i
\(453\) 8.00000 + 13.8564i 0.375873 + 0.651031i
\(454\) 6.00000 + 10.3923i 0.281594 + 0.487735i
\(455\) 0 0
\(456\) −8.00000 3.46410i −0.374634 0.162221i
\(457\) −40.0000 −1.87112 −0.935561 0.353166i \(-0.885105\pi\)
−0.935561 + 0.353166i \(0.885105\pi\)
\(458\) −10.0000 17.3205i −0.467269 0.809334i
\(459\) 12.0000 + 20.7846i 0.560112 + 0.970143i
\(460\) 0 0
\(461\) 1.50000 + 2.59808i 0.0698620 + 0.121004i 0.898840 0.438276i \(-0.144411\pi\)
−0.828978 + 0.559281i \(0.811077\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 10.0000 17.3205i 0.461757 0.799787i
\(470\) 0 0
\(471\) 14.0000 24.2487i 0.645086 1.11732i
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) −2.50000 4.33013i −0.114950 0.199099i
\(474\) −16.0000 −0.734904
\(475\) 2.50000 + 21.6506i 0.114708 + 0.993399i
\(476\) −12.0000 −0.550019
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 0 0
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 0 0
\(481\) −5.00000 + 8.66025i −0.227980 + 0.394874i
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) 10.0000 0.453609
\(487\) −7.00000 −0.317200 −0.158600 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(488\) 6.50000 11.2583i 0.294241 0.509641i
\(489\) 2.00000 + 3.46410i 0.0904431 + 0.156652i
\(490\) 0 0
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) −6.00000 10.3923i −0.270501 0.468521i
\(493\) −54.0000 −2.43204
\(494\) 3.50000 2.59808i 0.157472 0.116893i
\(495\) 0 0
\(496\) −4.00000 6.92820i −0.179605 0.311086i
\(497\) −9.00000 15.5885i −0.403705 0.699238i
\(498\) −9.00000 + 15.5885i −0.403300 + 0.698535i
\(499\) −13.0000 22.5167i −0.581960 1.00798i −0.995247 0.0973833i \(-0.968953\pi\)
0.413287 0.910601i \(-0.364381\pi\)
\(500\) 0 0
\(501\) −12.0000 −0.536120
\(502\) −18.0000 −0.803379
\(503\) 15.0000 25.9808i 0.668817 1.15842i −0.309418 0.950926i \(-0.600134\pi\)
0.978235 0.207499i \(-0.0665323\pi\)
\(504\) −1.00000 + 1.73205i −0.0445435 + 0.0771517i
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 + 20.7846i −0.532939 + 0.923077i
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 4.00000 + 6.92820i 0.176950 + 0.306486i
\(512\) 1.00000 0.0441942
\(513\) −14.0000 + 10.3923i −0.618115 + 0.458831i
\(514\) −18.0000 −0.793946
\(515\) 0 0
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) 1.50000 2.59808i 0.0659699 0.114263i
\(518\) 10.0000 + 17.3205i 0.439375 + 0.761019i
\(519\) −18.0000 + 31.1769i −0.790112 + 1.36851i
\(520\) 0 0
\(521\) 39.0000 1.70862 0.854311 0.519763i \(-0.173980\pi\)
0.854311 + 0.519763i \(0.173980\pi\)
\(522\) −4.50000 + 7.79423i −0.196960 + 0.341144i
\(523\) −17.5000 + 30.3109i −0.765222 + 1.32540i 0.174908 + 0.984585i \(0.444037\pi\)
−0.940129 + 0.340818i \(0.889296\pi\)
\(524\) −3.00000 −0.131056
\(525\) 20.0000 0.872872
\(526\) 0 0
\(527\) 24.0000 + 41.5692i 1.04546 + 1.81078i
\(528\) 1.00000 1.73205i 0.0435194 0.0753778i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −1.00000 8.66025i −0.0433555 0.375470i
\(533\) 6.00000 0.259889
\(534\) 15.0000 + 25.9808i 0.649113 + 1.12430i
\(535\) 0 0
\(536\) 5.00000 8.66025i 0.215967 0.374066i
\(537\) −12.0000 20.7846i −0.517838 0.896922i
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) 11.0000 19.0526i 0.472927 0.819133i −0.526593 0.850118i \(-0.676531\pi\)
0.999520 + 0.0309841i \(0.00986412\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) 32.0000 1.37325
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) −2.00000 3.46410i −0.0855921 0.148250i
\(547\) −14.5000 + 25.1147i −0.619975 + 1.07383i 0.369514 + 0.929225i \(0.379524\pi\)
−0.989490 + 0.144604i \(0.953809\pi\)
\(548\) 4.50000 + 7.79423i 0.192230 + 0.332953i
\(549\) 6.50000 + 11.2583i 0.277413 + 0.480494i
\(550\) −5.00000 −0.213201
\(551\) −4.50000 38.9711i −0.191706 1.66023i
\(552\) 0 0
\(553\) −8.00000 13.8564i −0.340195 0.589234i
\(554\) −8.50000 14.7224i −0.361130 0.625496i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −10.5000 + 18.1865i −0.444899 + 0.770588i −0.998045 0.0624962i \(-0.980094\pi\)
0.553146 + 0.833084i \(0.313427\pi\)
\(558\) 8.00000 0.338667
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) −6.00000 + 10.3923i −0.253320 + 0.438763i
\(562\) 12.0000 0.506189
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 0 0
\(566\) 2.00000 3.46410i 0.0840663 0.145607i
\(567\) 11.0000 + 19.0526i 0.461957 + 0.800132i
\(568\) −4.50000 7.79423i −0.188816 0.327039i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 0.500000 + 0.866025i 0.0209061 + 0.0362103i
\(573\) 3.00000 + 5.19615i 0.125327 + 0.217072i
\(574\) 6.00000 10.3923i 0.250435 0.433766i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 19.0000 0.790296
\(579\) −16.0000 + 27.7128i −0.664937 + 1.15171i
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) 2.00000 0.0829027
\(583\) 3.00000 5.19615i 0.124247 0.215203i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) 6.00000 0.247436
\(589\) −28.0000 + 20.7846i −1.15372 + 0.856415i
\(590\) 0 0
\(591\) −15.0000 25.9808i −0.617018 1.06871i
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) −2.00000 3.46410i −0.0820610 0.142134i
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 38.0000 1.55524
\(598\) 0 0
\(599\) 4.50000 7.79423i 0.183865 0.318464i −0.759328 0.650708i \(-0.774472\pi\)
0.943193 + 0.332244i \(0.107806\pi\)
\(600\) 10.0000 0.408248
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) −5.00000 + 8.66025i −0.203785 + 0.352966i
\(603\) 5.00000 + 8.66025i 0.203616 + 0.352673i
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 0 0
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −0.500000 4.33013i −0.0202777 0.175610i
\(609\) −36.0000 −1.45879
\(610\) 0 0
\(611\) −1.50000 2.59808i −0.0606835 0.105107i
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) 3.50000 6.06218i 0.141249 0.244650i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −10.5000 + 18.1865i −0.422714 + 0.732162i −0.996204 0.0870504i \(-0.972256\pi\)
0.573490 + 0.819213i \(0.305589\pi\)
\(618\) −19.0000 + 32.9090i −0.764292 + 1.32379i
\(619\) 38.0000 1.52735 0.763674 0.645601i \(-0.223393\pi\)
0.763674 + 0.645601i \(0.223393\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 7.50000 + 12.9904i 0.300723 + 0.520867i
\(623\) −15.0000 + 25.9808i −0.600962 + 1.04090i
\(624\) −1.00000 1.73205i −0.0400320 0.0693375i
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 17.0000 0.679457
\(627\) −8.00000 3.46410i −0.319489 0.138343i
\(628\) 14.0000 0.558661
\(629\) −30.0000 51.9615i −1.19618 2.07184i
\(630\) 0 0
\(631\) 6.50000 11.2583i 0.258761 0.448187i −0.707149 0.707064i \(-0.750019\pi\)
0.965910 + 0.258877i \(0.0833525\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) 20.0000 34.6410i 0.794929 1.37686i
\(634\) 30.0000 1.19145
\(635\) 0 0
\(636\) −6.00000 + 10.3923i −0.237915 + 0.412082i
\(637\) −1.50000 + 2.59808i −0.0594322 + 0.102940i
\(638\) 9.00000 0.356313
\(639\) 9.00000 0.356034
\(640\) 0 0
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) −9.00000 + 15.5885i −0.355202 + 0.615227i
\(643\) −13.0000 22.5167i −0.512670 0.887970i −0.999892 0.0146923i \(-0.995323\pi\)
0.487222 0.873278i \(-0.338010\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.00000 + 25.9808i 0.118033 + 1.02220i
\(647\) 21.0000 0.825595 0.412798 0.910823i \(-0.364552\pi\)
0.412798 + 0.910823i \(0.364552\pi\)
\(648\) 5.50000 + 9.52628i 0.216060 + 0.374228i
\(649\) −3.00000 5.19615i −0.117760 0.203967i
\(650\) −2.50000 + 4.33013i −0.0980581 + 0.169842i
\(651\) 16.0000 + 27.7128i 0.627089 + 1.08615i
\(652\) −1.00000 + 1.73205i −0.0391630 + 0.0678323i
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) −22.0000 −0.860268
\(655\) 0 0
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) −4.00000 −0.156055
\(658\) −6.00000 −0.233904
\(659\) 19.5000 33.7750i 0.759612 1.31569i −0.183436 0.983032i \(-0.558722\pi\)
0.943049 0.332655i \(-0.107945\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) 14.0000 + 24.2487i 0.544125 + 0.942453i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 0 0
\(668\) −3.00000 5.19615i −0.116073 0.201045i
\(669\) −7.00000 + 12.1244i −0.270636 + 0.468755i
\(670\) 0 0
\(671\) 6.50000 11.2583i 0.250930 0.434623i
\(672\) −4.00000 −0.154303
\(673\) 38.0000 1.46479 0.732396 0.680879i \(-0.238402\pi\)
0.732396 + 0.680879i \(0.238402\pi\)
\(674\) 17.0000 29.4449i 0.654816 1.13417i
\(675\) 10.0000 17.3205i 0.384900 0.666667i
\(676\) −12.0000 −0.461538
\(677\) 15.0000 0.576497 0.288248 0.957556i \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) 9.00000 15.5885i 0.345643 0.598671i
\(679\) 1.00000 + 1.73205i 0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) −12.0000 20.7846i −0.459841 0.796468i
\(682\) −4.00000 6.92820i −0.153168 0.265295i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 4.00000 + 1.73205i 0.152944 + 0.0662266i
\(685\) 0 0
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 20.0000 + 34.6410i 0.763048 + 1.32164i
\(688\) −2.50000 + 4.33013i −0.0953116 + 0.165085i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −18.0000 −0.684257
\(693\) −1.00000 + 1.73205i −0.0379869 + 0.0657952i
\(694\) 16.5000 28.5788i 0.626331 1.08484i
\(695\) 0 0
\(696\) −18.0000 −0.682288
\(697\) −18.0000 + 31.1769i −0.681799 + 1.18091i
\(698\) −2.50000 4.33013i −0.0946264 0.163898i
\(699\) 12.0000 20.7846i 0.453882 0.786146i
\(700\) 5.00000 + 8.66025i 0.188982 + 0.327327i
\(701\) −7.50000 12.9904i −0.283271 0.490640i 0.688917 0.724840i \(-0.258086\pi\)
−0.972188 + 0.234200i \(0.924753\pi\)
\(702\) −4.00000 −0.150970
\(703\) 35.0000 25.9808i 1.32005 0.979883i
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 10.5000 + 18.1865i 0.395173 + 0.684459i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 6.00000 + 10.3923i 0.225494 + 0.390567i
\(709\) −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
\(711\) 8.00000 0.300023
\(712\) −7.50000 + 12.9904i −0.281074 + 0.486835i
\(713\) 0 0
\(714\) 24.0000 0.898177
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 0 0
\(721\) −38.0000 −1.41519
\(722\) −18.5000 + 4.33013i −0.688499 + 0.161151i
\(723\) −52.0000 −1.93390
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 22.5000 + 38.9711i 0.835629 + 1.44735i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i \(-0.0891678\pi\)
−0.719948 + 0.694028i \(0.755834\pi\)
\(728\) 1.00000 1.73205i 0.0370625 0.0641941i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 15.0000 25.9808i 0.554795 0.960933i
\(732\) −13.0000 + 22.5167i −0.480494 + 0.832240i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −7.00000 −0.258375
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) −11.5000 19.9186i −0.423034 0.732717i 0.573200 0.819415i \(-0.305702\pi\)
−0.996235 + 0.0866983i \(0.972368\pi\)
\(740\) 0 0
\(741\) −7.00000 + 5.19615i −0.257151 + 0.190885i
\(742\) −12.0000 −0.440534
\(743\) −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i \(-0.273775\pi\)
−0.982547 + 0.186017i \(0.940442\pi\)
\(744\) 8.00000 + 13.8564i 0.293294 + 0.508001i
\(745\) 0 0
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) 4.50000 7.79423i 0.164646 0.285176i
\(748\) −6.00000 −0.219382
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −11.5000 + 19.9186i −0.419641 + 0.726839i −0.995903 0.0904254i \(-0.971177\pi\)
0.576262 + 0.817265i \(0.304511\pi\)
\(752\) −3.00000 −0.109399
\(753\) 36.0000 1.31191
\(754\) 4.50000 7.79423i 0.163880 0.283849i
\(755\) 0 0
\(756\) −4.00000 + 6.92820i −0.145479 + 0.251976i
\(757\) −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i \(-0.924028\pi\)
0.281086 0.959683i \(-0.409305\pi\)
\(758\) −1.00000 1.73205i −0.0363216 0.0629109i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 2.00000 + 3.46410i 0.0724524 + 0.125491i
\(763\) −11.0000 19.0526i −0.398227 0.689749i
\(764\) −1.50000 + 2.59808i −0.0542681 + 0.0939951i
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) −2.00000 −0.0721688
\(769\) 11.0000 19.0526i 0.396670 0.687053i −0.596643 0.802507i \(-0.703499\pi\)
0.993313 + 0.115454i \(0.0368323\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) −16.0000 −0.575853
\(773\) 27.0000 46.7654i 0.971123 1.68203i 0.278944 0.960307i \(-0.410016\pi\)
0.692179 0.721726i \(-0.256651\pi\)
\(774\) −2.50000 4.33013i −0.0898606 0.155643i
\(775\) 20.0000 34.6410i 0.718421 1.24434i
\(776\) 0.500000 + 0.866025i 0.0179490 + 0.0310885i
\(777\) −20.0000 34.6410i −0.717496 1.24274i
\(778\) −24.0000 −0.860442
\(779\) −24.0000 10.3923i −0.859889 0.372343i
\(780\) 0 0
\(781\) −4.50000 7.79423i −0.161023 0.278899i
\(782\) 0 0
\(783\) −18.0000 + 31.1769i −0.643268 + 1.11417i
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) 0 0
\(786\) 6.00000 0.214013
\(787\) 35.0000 1.24762 0.623808 0.781578i \(-0.285585\pi\)
0.623808 + 0.781578i \(0.285585\pi\)
\(788\) 7.50000 12.9904i 0.267176 0.462763i
\(789\) 0 0
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) −0.500000 + 0.866025i −0.0177667 + 0.0307729i
\(793\) −6.50000 11.2583i −0.230822 0.399795i
\(794\) −1.00000 + 1.73205i −0.0354887 + 0.0614682i
\(795\) 0 0
\(796\) 9.50000 + 16.4545i 0.336719 + 0.583214i
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 2.00000 + 17.3205i 0.0707992 + 0.613139i
\(799\) 18.0000 0.636794
\(800\) 2.50000 + 4.33013i 0.0883883 + 0.153093i
\(801\) −7.50000 12.9904i −0.264999 0.458993i
\(802\) 9.00000 15.5885i 0.317801 0.550448i
\(803\) 2.00000 + 3.46410i 0.0705785 + 0.122245i
\(804\) −10.0000 + 17.3205i −0.352673 + 0.610847i
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) −18.0000 + 31.1769i −0.633630 + 1.09748i
\(808\) 1.50000 2.59808i 0.0527698 0.0914000i
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) 3.50000 6.06218i 0.122902 0.212872i −0.798009 0.602645i \(-0.794113\pi\)
0.920911 + 0.389774i \(0.127447\pi\)
\(812\) −9.00000 15.5885i −0.315838 0.547048i
\(813\) 2.00000 3.46410i 0.0701431 0.121491i
\(814\) 5.00000 + 8.66025i 0.175250 + 0.303542i
\(815\) 0 0
\(816\) 12.0000 0.420084
\(817\) 20.0000 + 8.66025i 0.699711 + 0.302984i
\(818\) −4.00000 −0.139857
\(819\) 1.00000 + 1.73205i 0.0349428 + 0.0605228i
\(820\) 0 0
\(821\) −3.00000 + 5.19615i −0.104701 + 0.181347i −0.913616 0.406578i \(-0.866722\pi\)
0.808915 + 0.587925i \(0.200055\pi\)
\(822\) −9.00000 15.5885i −0.313911 0.543710i
\(823\) 6.50000 11.2583i 0.226576 0.392441i −0.730215 0.683217i \(-0.760580\pi\)
0.956791 + 0.290776i \(0.0939136\pi\)
\(824\) −19.0000 −0.661896
\(825\) 10.0000 0.348155
\(826\) −6.00000 + 10.3923i −0.208767 + 0.361595i
\(827\) −22.5000 + 38.9711i −0.782402 + 1.35516i 0.148137 + 0.988967i \(0.452672\pi\)
−0.930539 + 0.366193i \(0.880661\pi\)
\(828\) 0 0
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) 0 0
\(831\) 17.0000 + 29.4449i 0.589723 + 1.02143i
\(832\) 0.500000 0.866025i 0.0173344 0.0300240i
\(833\) −9.00000 15.5885i −0.311832 0.540108i
\(834\) −4.00000 6.92820i −0.138509 0.239904i
\(835\) 0 0
\(836\) −0.500000 4.33013i −0.0172929 0.149761i
\(837\) 32.0000 1.10608
\(838\) −6.00000 10.3923i −0.207267 0.358996i
\(839\) −4.50000 7.79423i −0.155357 0.269087i 0.777832 0.628473i \(-0.216320\pi\)
−0.933189 + 0.359386i \(0.882986\pi\)
\(840\) 0 0
\(841\) −26.0000 45.0333i −0.896552 1.55287i
\(842\) 14.0000 24.2487i 0.482472 0.835666i
\(843\) −24.0000 −0.826604
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) 1.50000 2.59808i 0.0515711 0.0893237i
\(847\) 2.00000 0.0687208
\(848\) −6.00000 −0.206041
\(849\) −4.00000 + 6.92820i −0.137280 + 0.237775i
\(850\) −15.0000 25.9808i −0.514496 0.891133i
\(851\) 0 0
\(852\) 9.00000 + 15.5885i 0.308335 + 0.534052i
\(853\) −1.00000 1.73205i −0.0342393 0.0593043i 0.848398 0.529359i \(-0.177568\pi\)
−0.882637 + 0.470055i \(0.844234\pi\)
\(854\) −26.0000 −0.889702
\(855\) 0 0
\(856\) −9.00000 −0.307614
\(857\) 15.0000 + 25.9808i 0.512390 + 0.887486i 0.999897 + 0.0143666i \(0.00457319\pi\)
−0.487507 + 0.873119i \(0.662093\pi\)
\(858\) −1.00000 1.73205i −0.0341394 0.0591312i
\(859\) 17.0000 29.4449i 0.580033 1.00465i −0.415442 0.909620i \(-0.636373\pi\)
0.995475 0.0950262i \(-0.0302935\pi\)
\(860\) 0 0
\(861\) −12.0000 + 20.7846i −0.408959 + 0.708338i
\(862\) −36.0000 −1.22616
\(863\) −33.0000 −1.12333 −0.561667 0.827364i \(-0.689840\pi\)
−0.561667 + 0.827364i \(0.689840\pi\)
\(864\) −2.00000 + 3.46410i −0.0680414 + 0.117851i
\(865\) 0 0
\(866\) 11.0000 0.373795
\(867\) −38.0000 −1.29055
\(868\) −8.00000 + 13.8564i −0.271538 + 0.470317i
\(869\) −4.00000 6.92820i −0.135691 0.235023i
\(870\) 0 0
\(871\) −5.00000 8.66025i −0.169419 0.293442i
\(872\) −5.50000 9.52628i −0.186254 0.322601i
\(873\) −1.00000 −0.0338449
\(874\) 0 0
\(875\) 0 0
\(876\) −4.00000 6.92820i −0.135147 0.234082i
\(877\) −19.0000 32.9090i −0.641584 1.11126i −0.985079 0.172102i \(-0.944944\pi\)
0.343495 0.939155i \(-0.388389\pi\)
\(878\) −10.0000 + 17.3205i −0.337484 + 0.584539i
\(879\) −9.00000 15.5885i −0.303562 0.525786i
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) −3.00000 −0.101015
\(883\) −10.0000 + 17.3205i −0.336527 + 0.582882i −0.983777 0.179396i \(-0.942586\pi\)
0.647250 + 0.762278i \(0.275919\pi\)
\(884\) −3.00000 + 5.19615i −0.100901 + 0.174766i
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 6.00000 10.3923i 0.201460 0.348939i −0.747539 0.664218i \(-0.768765\pi\)
0.948999 + 0.315279i \(0.102098\pi\)
\(888\) −10.0000 17.3205i −0.335578 0.581238i
\(889\) −2.00000 + 3.46410i −0.0670778 + 0.116182i
\(890\) 0 0
\(891\) 5.50000 + 9.52628i 0.184257 + 0.319142i
\(892\) −7.00000 −0.234377
\(893\) 1.50000 + 12.9904i 0.0501956 + 0.434707i
\(894\) −12.0000 −0.401340
\(895\) 0 0
\(896\) −1.00000 1.73205i −0.0334077 0.0578638i
\(897\) 0 0
\(898\) 9.00000 + 15.5885i 0.300334 + 0.520194i
\(899\) −36.0000 + 62.3538i −1.20067 + 2.07962i
\(900\) −5.00000 −0.166667
\(901\) 36.0000 1.19933
\(902\) 3.00000 5.19615i 0.0998891 0.173013i
\(903\) 10.0000 17.3205i 0.332779 0.576390i
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) 8.00000 13.8564i 0.265782 0.460348i
\(907\) 5.00000 + 8.66025i 0.166022 + 0.287559i 0.937018 0.349281i \(-0.113574\pi\)
−0.770996 + 0.636841i \(0.780241\pi\)
\(908\) 6.00000 10.3923i 0.199117 0.344881i
\(909\) 1.50000 + 2.59808i 0.0497519 + 0.0861727i
\(910\) 0 0
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 1.00000 + 8.66025i 0.0331133 + 0.286770i
\(913\) −9.00000 −0.297857
\(914\) 20.0000 + 34.6410i 0.661541 + 1.14582i
\(915\) 0 0
\(916\) −10.0000 + 17.3205i −0.330409 + 0.572286i
\(917\) 3.00000 + 5.19615i 0.0990687 + 0.171592i
\(918\) 12.0000 20.7846i 0.396059 0.685994i
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) −7.00000 + 12.1244i −0.230658 + 0.399511i
\(922\) 1.50000 2.59808i 0.0493999 0.0855631i
\(923\) −9.00000 −0.296239
\(924\) −4.00000 −0.131590
\(925\) −25.0000 + 43.3013i −0.821995 + 1.42374i
\(926\) −8.50000 14.7224i −0.279327 0.483809i
\(927\) 9.50000 16.4545i 0.312021 0.540436i
\(928\) −4.50000 7.79423i −0.147720 0.255858i
\(929\) 10.5000 + 18.1865i 0.344494 + 0.596681i 0.985262 0.171054i \(-0.0547172\pi\)
−0.640768 + 0.767735i \(0.721384\pi\)
\(930\) 0 0
\(931\) 10.5000 7.79423i 0.344124 0.255446i
\(932\) 12.0000 0.393073
\(933\) −15.0000 25.9808i −0.491078 0.850572i
\(934\) 6.00000 + 10.3923i 0.196326 + 0.340047i
\(935\) 0 0
\(936\) 0.500000 + 0.866025i 0.0163430 + 0.0283069i
\(937\) −10.0000 + 17.3205i −0.326686 + 0.565836i −0.981852 0.189648i \(-0.939265\pi\)
0.655166 + 0.755485i \(0.272599\pi\)
\(938\) −20.0000 −0.653023
\(939\) −34.0000 −1.10955
\(940\) 0 0
\(941\) −9.00000 + 15.5885i −0.293392 + 0.508169i −0.974609 0.223912i \(-0.928117\pi\)
0.681218 + 0.732081i \(0.261451\pi\)
\(942\) −28.0000 −0.912289
\(943\) 0 0
\(944\) −3.00000 + 5.19615i −0.0976417 + 0.169120i
\(945\) 0 0
\(946\) −2.50000 + 4.33013i −0.0812820 + 0.140785i
\(947\) 9.00000 + 15.5885i 0.292461 + 0.506557i 0.974391 0.224860i \(-0.0721926\pi\)
−0.681930 + 0.731417i \(0.738859\pi\)
\(948\) 8.00000 + 13.8564i 0.259828 + 0.450035i
\(949\) 4.00000 0.129845
\(950\) 17.5000 12.9904i 0.567775 0.421464i
\(951\) −60.0000 −1.94563
\(952\) 6.00000 + 10.3923i 0.194461 + 0.336817i
\(953\) −24.0000 41.5692i −0.777436 1.34656i −0.933415 0.358799i \(-0.883186\pi\)
0.155979 0.987760i \(-0.450147\pi\)
\(954\) 3.00000 5.19615i 0.0971286 0.168232i
\(955\) 0 0
\(956\) 0 0
\(957\) −18.0000 −0.581857
\(958\) −36.0000 −1.16311
\(959\) 9.00000 15.5885i 0.290625 0.503378i
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 10.0000 0.322413
\(963\) 4.50000 7.79423i 0.145010 0.251166i
\(964\) −13.0000 22.5167i −0.418702 0.725213i
\(965\) 0 0
\(966\) 0 0
\(967\) 8.00000 + 13.8564i 0.257263 + 0.445592i 0.965508 0.260375i \(-0.0838461\pi\)
−0.708245 + 0.705967i \(0.750513\pi\)
\(968\) 1.00000 0.0321412
\(969\) −6.00000 51.9615i −0.192748 1.66924i
\(970\) 0 0
\(971\) −21.0000 36.3731i −0.673922 1.16727i −0.976783 0.214232i \(-0.931275\pi\)
0.302861 0.953035i \(-0.402058\pi\)
\(972\) −5.00000 8.66025i −0.160375 0.277778i
\(973\) 4.00000 6.92820i 0.128234 0.222108i
\(974\) 3.50000 + 6.06218i 0.112147 + 0.194245i
\(975\) 5.00000 8.66025i 0.160128 0.277350i
\(976\) −13.0000 −0.416120
\(977\) −9.00000 −0.287936 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(978\) 2.00000 3.46410i 0.0639529 0.110770i
\(979\) −7.50000 + 12.9904i −0.239701 + 0.415174i
\(980\) 0 0
\(981\) 11.0000 0.351203
\(982\) 6.00000 10.3923i 0.191468 0.331632i
\(983\) −16.5000 28.5788i −0.526268 0.911523i −0.999532 0.0306024i \(-0.990257\pi\)
0.473263 0.880921i \(-0.343076\pi\)
\(984\) −6.00000 + 10.3923i −0.191273 + 0.331295i
\(985\) 0 0
\(986\) 27.0000 + 46.7654i 0.859855 + 1.48931i
\(987\) 12.0000 0.381964
\(988\) −4.00000 1.73205i −0.127257 0.0551039i
\(989\) 0 0
\(990\) 0 0
\(991\) −2.50000 4.33013i −0.0794151 0.137551i 0.823583 0.567196i \(-0.191972\pi\)
−0.902998 + 0.429645i \(0.858639\pi\)
\(992\) −4.00000 + 6.92820i −0.127000 + 0.219971i
\(993\) −28.0000 48.4974i −0.888553 1.53902i
\(994\) −9.00000 + 15.5885i −0.285463 + 0.494436i
\(995\) 0 0
\(996\) 18.0000 0.570352
\(997\) −19.0000 + 32.9090i −0.601736 + 1.04224i 0.390822 + 0.920466i \(0.372191\pi\)
−0.992558 + 0.121771i \(0.961143\pi\)
\(998\) −13.0000 + 22.5167i −0.411508 + 0.712752i
\(999\) −40.0000 −1.26554
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 418.2.e.d.45.1 2
19.7 even 3 7942.2.a.l.1.1 1
19.11 even 3 inner 418.2.e.d.353.1 yes 2
19.12 odd 6 7942.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.e.d.45.1 2 1.1 even 1 trivial
418.2.e.d.353.1 yes 2 19.11 even 3 inner
7942.2.a.j.1.1 1 19.12 odd 6
7942.2.a.l.1.1 1 19.7 even 3