Properties

Label 966.2.i.b.415.1
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $1$
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] = [966,2,Mod(277,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (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: \(7.71354883526\)
Analytic rank: \(1\)
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 415.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.b.277.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -6.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-2.50000 + 0.866025i) q^{21} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(3.00000 - 5.19615i) q^{26} +1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} +9.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +5.00000 q^{34} +1.00000 q^{36} +(-3.00000 + 5.19615i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(3.00000 + 5.19615i) q^{39} -6.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -6.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-5.50000 + 9.52628i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -5.00000 q^{50} +(-2.50000 + 4.33013i) q^{51} +(3.00000 + 5.19615i) q^{52} +(-7.00000 - 12.1244i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +6.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(1.00000 - 1.73205i) q^{61} -6.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-5.00000 - 8.66025i) q^{67} +(-2.50000 + 4.33013i) q^{68} +1.00000 q^{69} -3.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.50000 + 4.33013i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(2.50000 - 4.33013i) q^{75} +6.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} -6.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -8.00000 q^{83} +(2.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-3.00000 + 15.5885i) q^{91} +1.00000 q^{92} +(3.00000 - 5.19615i) q^{93} +(-5.50000 - 9.52628i) q^{94} +(-0.500000 + 0.866025i) q^{96} -4.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{11} - q^{12} - 12 q^{13} + 4 q^{14} - q^{16} - 5 q^{17} - q^{18} - 6 q^{19} - 5 q^{21} + 2 q^{22} - q^{23} - q^{24} + 5 q^{25} + 6 q^{26} + 2 q^{27} - 5 q^{28} + 18 q^{29} + 6 q^{31} - q^{32} - q^{33} + 10 q^{34} + 2 q^{36} - 6 q^{37} - 6 q^{38} + 6 q^{39} - 12 q^{41} + q^{42} - 12 q^{43} - q^{44} - q^{46} - 11 q^{47} + 2 q^{48} - 13 q^{49} - 10 q^{50} - 5 q^{51} + 6 q^{52} - 14 q^{53} - q^{54} + q^{56} + 12 q^{57} - 9 q^{58} + 2 q^{61} - 12 q^{62} + 4 q^{63} + 2 q^{64} - q^{66} - 10 q^{67} - 5 q^{68} + 2 q^{69} - 6 q^{71} - q^{72} + 5 q^{73} - 6 q^{74} + 5 q^{75} + 12 q^{76} - 5 q^{77} - 12 q^{78} - 5 q^{79} - q^{81} + 6 q^{82} - 16 q^{83} + 4 q^{84} + 6 q^{86} - 9 q^{87} - q^{88} - 10 q^{89} - 6 q^{91} + 2 q^{92} + 6 q^{93} - 11 q^{94} - q^{96} - 8 q^{97} + 11 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −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
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 0 0
\(21\) −2.50000 + 0.866025i −0.545545 + 0.188982i
\(22\) 1.00000 0.213201
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 3.00000 5.19615i 0.588348 1.01905i
\(27\) 1.00000 0.192450
\(28\) −2.50000 + 0.866025i −0.472456 + 0.163663i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 5.00000 0.857493
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) 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
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −5.50000 + 9.52628i −0.802257 + 1.38955i 0.115870 + 0.993264i \(0.463035\pi\)
−0.918127 + 0.396286i \(0.870299\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −5.00000 −0.707107
\(51\) −2.50000 + 4.33013i −0.350070 + 0.606339i
\(52\) 3.00000 + 5.19615i 0.416025 + 0.720577i
\(53\) −7.00000 12.1244i −0.961524 1.66541i −0.718677 0.695344i \(-0.755252\pi\)
−0.242846 0.970065i \(-0.578081\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 6.00000 0.794719
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) −6.00000 −0.762001
\(63\) 2.00000 + 1.73205i 0.251976 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) −2.50000 + 4.33013i −0.303170 + 0.525105i
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 2.50000 + 4.33013i 0.292603 + 0.506803i 0.974424 0.224716i \(-0.0721453\pi\)
−0.681822 + 0.731519i \(0.738812\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 2.50000 4.33013i 0.288675 0.500000i
\(76\) 6.00000 0.688247
\(77\) −2.50000 + 0.866025i −0.284901 + 0.0986928i
\(78\) −6.00000 −0.679366
\(79\) −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
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 2.00000 + 1.73205i 0.218218 + 0.188982i
\(85\) 0 0
\(86\) 3.00000 5.19615i 0.323498 0.560316i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 0 0
\(91\) −3.00000 + 15.5885i −0.314485 + 1.63411i
\(92\) 1.00000 0.104257
\(93\) 3.00000 5.19615i 0.311086 0.538816i
\(94\) −5.50000 9.52628i −0.567282 0.982561i
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −4.00000 −0.406138 −0.203069 0.979164i \(-0.565092\pi\)
−0.203069 + 0.979164i \(0.565092\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 1.00000 0.100504
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −3.50000 6.06218i −0.348263 0.603209i 0.637678 0.770303i \(-0.279895\pi\)
−0.985941 + 0.167094i \(0.946562\pi\)
\(102\) −2.50000 4.33013i −0.247537 0.428746i
\(103\) −5.50000 + 9.52628i −0.541931 + 0.938652i 0.456862 + 0.889538i \(0.348973\pi\)
−0.998793 + 0.0491146i \(0.984360\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 14.0000 1.35980
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i \(-0.120775\pi\)
−0.785203 + 0.619238i \(0.787442\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −3.00000 + 5.19615i −0.280976 + 0.486664i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) 0 0
\(119\) −12.5000 + 4.33013i −1.14587 + 0.396942i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) 0 0
\(126\) −2.50000 + 0.866025i −0.222718 + 0.0771517i
\(127\) −14.0000 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 3.00000 + 5.19615i 0.264135 + 0.457496i
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 1.00000 0.0870388
\(133\) 12.0000 + 10.3923i 1.04053 + 0.901127i
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) −2.50000 4.33013i −0.214373 0.371305i
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 11.0000 0.926367
\(142\) 1.50000 2.59808i 0.125877 0.218026i
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −5.00000 −0.413803
\(147\) 1.00000 + 6.92820i 0.0824786 + 0.571429i
\(148\) 6.00000 0.493197
\(149\) 4.00000 6.92820i 0.327693 0.567581i −0.654361 0.756182i \(-0.727062\pi\)
0.982054 + 0.188602i \(0.0603956\pi\)
\(150\) 2.50000 + 4.33013i 0.204124 + 0.353553i
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) −3.00000 + 5.19615i −0.243332 + 0.421464i
\(153\) 5.00000 0.404226
\(154\) 0.500000 2.59808i 0.0402911 0.209359i
\(155\) 0 0
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) −6.50000 11.2583i −0.518756 0.898513i −0.999762 0.0217953i \(-0.993062\pi\)
0.481006 0.876717i \(-0.340272\pi\)
\(158\) −2.50000 4.33013i −0.198889 0.344486i
\(159\) −7.00000 + 12.1244i −0.555136 + 0.961524i
\(160\) 0 0
\(161\) 2.00000 + 1.73205i 0.157622 + 0.136505i
\(162\) 1.00000 0.0785674
\(163\) −9.50000 + 16.4545i −0.744097 + 1.28881i 0.206518 + 0.978443i \(0.433787\pi\)
−0.950615 + 0.310372i \(0.899546\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) −2.50000 + 0.866025i −0.192879 + 0.0668153i
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 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
\(175\) 12.5000 4.33013i 0.944911 0.327327i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −5.00000 8.66025i −0.374766 0.649113i
\(179\) −11.0000 19.0526i −0.822179 1.42406i −0.904057 0.427413i \(-0.859425\pi\)
0.0818780 0.996642i \(-0.473908\pi\)
\(180\) 0 0
\(181\) −23.0000 −1.70958 −0.854788 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) −12.0000 10.3923i −0.889499 0.770329i
\(183\) −2.00000 −0.147844
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 3.00000 + 5.19615i 0.219971 + 0.381000i
\(187\) −2.50000 + 4.33013i −0.182818 + 0.316650i
\(188\) 11.0000 0.802257
\(189\) 0.500000 2.59808i 0.0363696 0.188982i
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 13.0000 + 22.5167i 0.935760 + 1.62078i 0.773272 + 0.634074i \(0.218619\pi\)
0.162488 + 0.986710i \(0.448048\pi\)
\(194\) 2.00000 3.46410i 0.143592 0.248708i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 13.0000 0.926212 0.463106 0.886303i \(-0.346735\pi\)
0.463106 + 0.886303i \(0.346735\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) −5.00000 + 8.66025i −0.352673 + 0.610847i
\(202\) 7.00000 0.492518
\(203\) 4.50000 23.3827i 0.315838 1.64114i
\(204\) 5.00000 0.350070
\(205\) 0 0
\(206\) −5.50000 9.52628i −0.383203 0.663727i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 3.00000 5.19615i 0.208013 0.360288i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 9.00000 0.619586 0.309793 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(212\) −7.00000 + 12.1244i −0.480762 + 0.832704i
\(213\) 1.50000 + 2.59808i 0.102778 + 0.178017i
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 15.0000 5.19615i 1.01827 0.352738i
\(218\) −3.00000 −0.203186
\(219\) 2.50000 4.33013i 0.168934 0.292603i
\(220\) 0 0
\(221\) 15.0000 + 25.9808i 1.00901 + 1.74766i
\(222\) −3.00000 + 5.19615i −0.201347 + 0.348743i
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) −5.00000 −0.333333
\(226\) −9.00000 + 15.5885i −0.598671 + 1.03693i
\(227\) −8.50000 14.7224i −0.564165 0.977162i −0.997127 0.0757500i \(-0.975865\pi\)
0.432962 0.901412i \(-0.357468\pi\)
\(228\) −3.00000 5.19615i −0.198680 0.344124i
\(229\) −10.5000 + 18.1865i −0.693860 + 1.20180i 0.276704 + 0.960955i \(0.410758\pi\)
−0.970564 + 0.240845i \(0.922576\pi\)
\(230\) 0 0
\(231\) 2.00000 + 1.73205i 0.131590 + 0.113961i
\(232\) 9.00000 0.590879
\(233\) −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i \(-0.917731\pi\)
0.704737 + 0.709468i \(0.251065\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 2.50000 12.9904i 0.162051 0.842041i
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 18.0000 31.1769i 1.14531 1.98374i
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) 0 0
\(251\) −17.0000 −1.07303 −0.536515 0.843891i \(-0.680260\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(252\) 0.500000 2.59808i 0.0314970 0.163663i
\(253\) 1.00000 0.0628695
\(254\) 7.00000 12.1244i 0.439219 0.760750i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.00000 12.1244i 0.436648 0.756297i −0.560781 0.827964i \(-0.689499\pi\)
0.997429 + 0.0716680i \(0.0228322\pi\)
\(258\) −6.00000 −0.373544
\(259\) 12.0000 + 10.3923i 0.745644 + 0.645746i
\(260\) 0 0
\(261\) −4.50000 + 7.79423i −0.278543 + 0.482451i
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) −15.0000 + 5.19615i −0.919709 + 0.318597i
\(267\) 10.0000 0.611990
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i \(-0.600397\pi\)
0.978406 0.206691i \(-0.0662693\pi\)
\(272\) 5.00000 0.303170
\(273\) 15.0000 5.19615i 0.907841 0.314485i
\(274\) 3.00000 0.181237
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) −16.0000 27.7128i −0.961347 1.66510i −0.719125 0.694881i \(-0.755457\pi\)
−0.242222 0.970221i \(-0.577876\pi\)
\(278\) −7.50000 + 12.9904i −0.449820 + 0.779111i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 5.00000 0.298275 0.149137 0.988816i \(-0.452350\pi\)
0.149137 + 0.988816i \(0.452350\pi\)
\(282\) −5.50000 + 9.52628i −0.327520 + 0.567282i
\(283\) 6.00000 + 10.3923i 0.356663 + 0.617758i 0.987401 0.158237i \(-0.0505811\pi\)
−0.630738 + 0.775996i \(0.717248\pi\)
\(284\) 1.50000 + 2.59808i 0.0890086 + 0.154167i
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) −3.00000 + 15.5885i −0.177084 + 0.920158i
\(288\) 1.00000 0.0589256
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) 2.00000 + 3.46410i 0.117242 + 0.203069i
\(292\) 2.50000 4.33013i 0.146301 0.253402i
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) −6.50000 2.59808i −0.379088 0.151523i
\(295\) 0 0
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 4.00000 + 6.92820i 0.231714 + 0.401340i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) −5.00000 −0.288675
\(301\) −3.00000 + 15.5885i −0.172917 + 0.898504i
\(302\) 12.0000 0.690522
\(303\) −3.50000 + 6.06218i −0.201070 + 0.348263i
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 0 0
\(306\) −2.50000 + 4.33013i −0.142915 + 0.247537i
\(307\) −33.0000 −1.88341 −0.941705 0.336440i \(-0.890777\pi\)
−0.941705 + 0.336440i \(0.890777\pi\)
\(308\) 2.00000 + 1.73205i 0.113961 + 0.0986928i
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 6.50000 + 11.2583i 0.368581 + 0.638401i 0.989344 0.145597i \(-0.0465103\pi\)
−0.620763 + 0.783998i \(0.713177\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) 10.0000 17.3205i 0.565233 0.979013i −0.431795 0.901972i \(-0.642119\pi\)
0.997028 0.0770410i \(-0.0245472\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) −1.00000 + 1.73205i −0.0561656 + 0.0972817i −0.892741 0.450570i \(-0.851221\pi\)
0.836576 + 0.547852i \(0.184554\pi\)
\(318\) −7.00000 12.1244i −0.392541 0.679900i
\(319\) −4.50000 7.79423i −0.251952 0.436393i
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) −2.50000 + 0.866025i −0.139320 + 0.0482617i
\(323\) 30.0000 1.66924
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −15.0000 25.9808i −0.832050 1.44115i
\(326\) −9.50000 16.4545i −0.526156 0.911330i
\(327\) 1.50000 2.59808i 0.0829502 0.143674i
\(328\) −6.00000 −0.331295
\(329\) 22.0000 + 19.0526i 1.21290 + 1.05040i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 4.00000 + 6.92820i 0.219529 + 0.380235i
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) 4.00000 6.92820i 0.218870 0.379094i
\(335\) 0 0
\(336\) 0.500000 2.59808i 0.0272772 0.141737i
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) −11.5000 + 19.9186i −0.625518 + 1.08343i
\(339\) −9.00000 15.5885i −0.488813 0.846649i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 6.00000 0.324443
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 11.0000 + 19.0526i 0.590511 + 1.02279i 0.994164 + 0.107883i \(0.0344071\pi\)
−0.403653 + 0.914912i \(0.632260\pi\)
\(348\) −4.50000 + 7.79423i −0.241225 + 0.417815i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −2.50000 + 12.9904i −0.133631 + 0.694365i
\(351\) −6.00000 −0.320256
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 7.00000 + 12.1244i 0.372572 + 0.645314i 0.989960 0.141344i \(-0.0451425\pi\)
−0.617388 + 0.786659i \(0.711809\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 10.0000 + 8.66025i 0.529256 + 0.458349i
\(358\) 22.0000 1.16274
\(359\) 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 11.5000 19.9186i 0.604427 1.04690i
\(363\) −10.0000 −0.524864
\(364\) 15.0000 5.19615i 0.786214 0.272352i
\(365\) 0 0
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) −35.0000 + 12.1244i −1.81711 + 0.629465i
\(372\) −6.00000 −0.311086
\(373\) 11.5000 19.9186i 0.595447 1.03135i −0.398036 0.917370i \(-0.630308\pi\)
0.993484 0.113975i \(-0.0363585\pi\)
\(374\) −2.50000 4.33013i −0.129272 0.223906i
\(375\) 0 0
\(376\) −5.50000 + 9.52628i −0.283641 + 0.491280i
\(377\) −54.0000 −2.78114
\(378\) 2.00000 + 1.73205i 0.102869 + 0.0890871i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 7.00000 + 12.1244i 0.358621 + 0.621150i
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) 2.00000 + 3.46410i 0.101535 + 0.175863i
\(389\) 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 0 0
\(391\) 5.00000 0.252861
\(392\) −6.50000 2.59808i −0.328300 0.131223i
\(393\) −12.0000 −0.605320
\(394\) −6.50000 + 11.2583i −0.327465 + 0.567186i
\(395\) 0 0
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) 19.0000 32.9090i 0.953583 1.65165i 0.216004 0.976392i \(-0.430698\pi\)
0.737579 0.675261i \(-0.235969\pi\)
\(398\) 7.00000 0.350878
\(399\) 3.00000 15.5885i 0.150188 0.780399i
\(400\) −5.00000 −0.250000
\(401\) 15.5000 26.8468i 0.774033 1.34066i −0.161303 0.986905i \(-0.551570\pi\)
0.935336 0.353760i \(-0.115097\pi\)
\(402\) −5.00000 8.66025i −0.249377 0.431934i
\(403\) −18.0000 31.1769i −0.896644 1.55303i
\(404\) −3.50000 + 6.06218i −0.174132 + 0.301605i
\(405\) 0 0
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) 6.00000 0.297409
\(408\) −2.50000 + 4.33013i −0.123768 + 0.214373i
\(409\) −6.50000 11.2583i −0.321404 0.556689i 0.659374 0.751815i \(-0.270822\pi\)
−0.980778 + 0.195127i \(0.937488\pi\)
\(410\) 0 0
\(411\) −1.50000 + 2.59808i −0.0739895 + 0.128154i
\(412\) 11.0000 0.541931
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) −7.50000 12.9904i −0.367277 0.636142i
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) −25.0000 −1.22133 −0.610665 0.791889i \(-0.709098\pi\)
−0.610665 + 0.791889i \(0.709098\pi\)
\(420\) 0 0
\(421\) −21.0000 −1.02348 −0.511739 0.859141i \(-0.670998\pi\)
−0.511739 + 0.859141i \(0.670998\pi\)
\(422\) −4.50000 + 7.79423i −0.219057 + 0.379417i
\(423\) −5.50000 9.52628i −0.267419 0.463184i
\(424\) −7.00000 12.1244i −0.339950 0.588811i
\(425\) 12.5000 21.6506i 0.606339 1.05021i
\(426\) −3.00000 −0.145350
\(427\) −4.00000 3.46410i −0.193574 0.167640i
\(428\) −4.00000 −0.193347
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i \(-0.212826\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −3.00000 + 15.5885i −0.144005 + 0.748270i
\(435\) 0 0
\(436\) 1.50000 2.59808i 0.0718370 0.124425i
\(437\) −3.00000 5.19615i −0.143509 0.248566i
\(438\) 2.50000 + 4.33013i 0.119455 + 0.206901i
\(439\) −10.0000 + 17.3205i −0.477274 + 0.826663i −0.999661 0.0260459i \(-0.991708\pi\)
0.522387 + 0.852709i \(0.325042\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) −30.0000 −1.42695
\(443\) 10.0000 17.3205i 0.475114 0.822922i −0.524479 0.851423i \(-0.675740\pi\)
0.999594 + 0.0285009i \(0.00907336\pi\)
\(444\) −3.00000 5.19615i −0.142374 0.246598i
\(445\) 0 0
\(446\) −5.00000 + 8.66025i −0.236757 + 0.410075i
\(447\) −8.00000 −0.378387
\(448\) 0.500000 2.59808i 0.0236228 0.122748i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 2.50000 4.33013i 0.117851 0.204124i
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) −9.00000 15.5885i −0.423324 0.733219i
\(453\) −6.00000 + 10.3923i −0.281905 + 0.488273i
\(454\) 17.0000 0.797850
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −6.00000 + 10.3923i −0.280668 + 0.486132i −0.971549 0.236837i \(-0.923889\pi\)
0.690881 + 0.722968i \(0.257223\pi\)
\(458\) −10.5000 18.1865i −0.490633 0.849801i
\(459\) −2.50000 4.33013i −0.116690 0.202113i
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −2.50000 + 0.866025i −0.116311 + 0.0402911i
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 0 0
\(466\) −4.00000 6.92820i −0.185296 0.320943i
\(467\) −15.5000 + 26.8468i −0.717254 + 1.24232i 0.244829 + 0.969566i \(0.421268\pi\)
−0.962084 + 0.272755i \(0.912065\pi\)
\(468\) −6.00000 −0.277350
\(469\) −25.0000 + 8.66025i −1.15439 + 0.399893i
\(470\) 0 0
\(471\) −6.50000 + 11.2583i −0.299504 + 0.518756i
\(472\) 0 0
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) −2.50000 + 4.33013i −0.114829 + 0.198889i
\(475\) −30.0000 −1.37649
\(476\) 10.0000 + 8.66025i 0.458349 + 0.396942i
\(477\) 14.0000 0.641016
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i \(-0.926308\pi\)
0.287954 0.957644i \(-0.407025\pi\)
\(480\) 0 0
\(481\) 18.0000 31.1769i 0.820729 1.42154i
\(482\) −14.0000 −0.637683
\(483\) 0.500000 2.59808i 0.0227508 0.118217i
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 7.00000 + 12.1244i 0.317200 + 0.549407i 0.979903 0.199476i \(-0.0639239\pi\)
−0.662702 + 0.748883i \(0.730591\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) 19.0000 0.859210
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) −22.5000 38.9711i −1.01335 1.75517i
\(494\) 18.0000 + 31.1769i 0.809858 + 1.40272i
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) −1.50000 + 7.79423i −0.0672842 + 0.349619i
\(498\) −8.00000 −0.358489
\(499\) −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i \(-0.883413\pi\)
0.776989 + 0.629515i \(0.216746\pi\)
\(500\) 0 0
\(501\) 4.00000 + 6.92820i 0.178707 + 0.309529i
\(502\) 8.50000 14.7224i 0.379374 0.657094i
\(503\) 18.0000 0.802580 0.401290 0.915951i \(-0.368562\pi\)
0.401290 + 0.915951i \(0.368562\pi\)
\(504\) 2.00000 + 1.73205i 0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) −0.500000 + 0.866025i −0.0222277 + 0.0384995i
\(507\) −11.5000 19.9186i −0.510733 0.884615i
\(508\) 7.00000 + 12.1244i 0.310575 + 0.537931i
\(509\) −20.5000 + 35.5070i −0.908647 + 1.57382i −0.0927004 + 0.995694i \(0.529550\pi\)
−0.815946 + 0.578128i \(0.803783\pi\)
\(510\) 0 0
\(511\) 12.5000 4.33013i 0.552967 0.191554i
\(512\) 1.00000 0.0441942
\(513\) −3.00000 + 5.19615i −0.132453 + 0.229416i
\(514\) 7.00000 + 12.1244i 0.308757 + 0.534782i
\(515\) 0 0
\(516\) 3.00000 5.19615i 0.132068 0.228748i
\(517\) 11.0000 0.483779
\(518\) −15.0000 + 5.19615i −0.659062 + 0.228306i
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) −9.00000 + 15.5885i −0.393543 + 0.681636i −0.992914 0.118835i \(-0.962084\pi\)
0.599371 + 0.800471i \(0.295417\pi\)
\(524\) −12.0000 −0.524222
\(525\) −10.0000 8.66025i −0.436436 0.377964i
\(526\) −12.0000 −0.523225
\(527\) 15.0000 25.9808i 0.653410 1.13174i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) 0 0
\(531\) 0 0
\(532\) 3.00000 15.5885i 0.130066 0.675845i
\(533\) 36.0000 1.55933
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) 0 0
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) −11.0000 + 19.0526i −0.474685 + 0.822179i
\(538\) −3.00000 −0.129339
\(539\) 1.00000 + 6.92820i 0.0430730 + 0.298419i
\(540\) 0 0
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 11.0000 + 19.0526i 0.472490 + 0.818377i
\(543\) 11.5000 + 19.9186i 0.493512 + 0.854788i
\(544\) −2.50000 + 4.33013i −0.107187 + 0.185653i
\(545\) 0 0
\(546\) −3.00000 + 15.5885i −0.128388 + 0.667124i
\(547\) 13.0000 0.555840 0.277920 0.960604i \(-0.410355\pi\)
0.277920 + 0.960604i \(0.410355\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) −27.0000 + 46.7654i −1.15024 + 1.99227i
\(552\) 1.00000 0.0425628
\(553\) 10.0000 + 8.66025i 0.425243 + 0.368271i
\(554\) 32.0000 1.35955
\(555\) 0 0
\(556\) −7.50000 12.9904i −0.318071 0.550915i
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) 36.0000 1.52264
\(560\) 0 0
\(561\) 5.00000 0.211100
\(562\) −2.50000 + 4.33013i −0.105456 + 0.182655i
\(563\) 10.5000 + 18.1865i 0.442522 + 0.766471i 0.997876 0.0651433i \(-0.0207504\pi\)
−0.555354 + 0.831614i \(0.687417\pi\)
\(564\) −5.50000 9.52628i −0.231592 0.401129i
\(565\) 0 0
\(566\) −12.0000 −0.504398
\(567\) −2.50000 + 0.866025i −0.104990 + 0.0363696i
\(568\) −3.00000 −0.125877
\(569\) −1.00000 + 1.73205i −0.0419222 + 0.0726113i −0.886225 0.463255i \(-0.846681\pi\)
0.844303 + 0.535866i \(0.180015\pi\)
\(570\) 0 0
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) 3.00000 5.19615i 0.125436 0.217262i
\(573\) 12.0000 0.501307
\(574\) −12.0000 10.3923i −0.500870 0.433766i
\(575\) −5.00000 −0.208514
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −16.5000 28.5788i −0.686904 1.18975i −0.972834 0.231502i \(-0.925636\pi\)
0.285930 0.958250i \(-0.407697\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 13.0000 22.5167i 0.540262 0.935760i
\(580\) 0 0
\(581\) −4.00000 + 20.7846i −0.165948 + 0.862291i
\(582\) −4.00000 −0.165805
\(583\) −7.00000 + 12.1244i −0.289910 + 0.502140i
\(584\) 2.50000 + 4.33013i 0.103451 + 0.179182i
\(585\) 0 0
\(586\) 6.00000 10.3923i 0.247858 0.429302i
\(587\) −24.0000 −0.990586 −0.495293 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) 5.50000 4.33013i 0.226816 0.178571i
\(589\) −36.0000 −1.48335
\(590\) 0 0
\(591\) −6.50000 11.2583i −0.267374 0.463106i
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) 11.0000 19.0526i 0.451716 0.782395i −0.546777 0.837278i \(-0.684145\pi\)
0.998493 + 0.0548835i \(0.0174787\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −8.00000 −0.327693
\(597\) −3.50000 + 6.06218i −0.143245 + 0.248108i
\(598\) 3.00000 + 5.19615i 0.122679 + 0.212486i
\(599\) 3.50000 + 6.06218i 0.143006 + 0.247694i 0.928627 0.371014i \(-0.120990\pi\)
−0.785621 + 0.618708i \(0.787656\pi\)
\(600\) 2.50000 4.33013i 0.102062 0.176777i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −12.0000 10.3923i −0.489083 0.423559i
\(603\) 10.0000 0.407231
\(604\) −6.00000 + 10.3923i −0.244137 + 0.422857i
\(605\) 0 0
\(606\) −3.50000 6.06218i −0.142178 0.246259i
\(607\) −3.00000 + 5.19615i −0.121766 + 0.210905i −0.920464 0.390827i \(-0.872189\pi\)
0.798698 + 0.601732i \(0.205522\pi\)
\(608\) 6.00000 0.243332
\(609\) −22.5000 + 7.79423i −0.911746 + 0.315838i
\(610\) 0 0
\(611\) 33.0000 57.1577i 1.33504 2.31235i
\(612\) −2.50000 4.33013i −0.101057 0.175035i
\(613\) −3.50000 6.06218i −0.141364 0.244849i 0.786647 0.617403i \(-0.211815\pi\)
−0.928010 + 0.372554i \(0.878482\pi\)
\(614\) 16.5000 28.5788i 0.665886 1.15335i
\(615\) 0 0
\(616\) −2.50000 + 0.866025i −0.100728 + 0.0348932i
\(617\) 33.0000 1.32853 0.664265 0.747497i \(-0.268745\pi\)
0.664265 + 0.747497i \(0.268745\pi\)
\(618\) −5.50000 + 9.52628i −0.221242 + 0.383203i
\(619\) −4.00000 6.92820i −0.160774 0.278468i 0.774373 0.632730i \(-0.218066\pi\)
−0.935146 + 0.354262i \(0.884732\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) −13.0000 −0.521253
\(623\) 20.0000 + 17.3205i 0.801283 + 0.693932i
\(624\) −6.00000 −0.240192
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 10.0000 + 17.3205i 0.399680 + 0.692267i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) −6.50000 + 11.2583i −0.259378 + 0.449256i
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) −41.0000 −1.63218 −0.816092 0.577922i \(-0.803864\pi\)
−0.816092 + 0.577922i \(0.803864\pi\)
\(632\) −2.50000 + 4.33013i −0.0994447 + 0.172243i
\(633\) −4.50000 7.79423i −0.178859 0.309793i
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) 0 0
\(636\) 14.0000 0.555136
\(637\) 39.0000 + 15.5885i 1.54524 + 0.617637i
\(638\) 9.00000 0.356313
\(639\) 1.50000 2.59808i 0.0593391 0.102778i
\(640\) 0 0
\(641\) −10.5000 18.1865i −0.414725 0.718325i 0.580674 0.814136i \(-0.302789\pi\)
−0.995400 + 0.0958109i \(0.969456\pi\)
\(642\) 2.00000 3.46410i 0.0789337 0.136717i
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0.500000 2.59808i 0.0197028 0.102379i
\(645\) 0 0
\(646\) −15.0000 + 25.9808i −0.590167 + 1.02220i
\(647\) −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i \(-0.261938\pi\)
−0.974951 + 0.222419i \(0.928605\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 0 0
\(650\) 30.0000 1.17670
\(651\) −12.0000 10.3923i −0.470317 0.407307i
\(652\) 19.0000 0.744097
\(653\) −24.5000 + 42.4352i −0.958759 + 1.66062i −0.233238 + 0.972420i \(0.574932\pi\)
−0.725521 + 0.688200i \(0.758401\pi\)
\(654\) 1.50000 + 2.59808i 0.0586546 + 0.101593i
\(655\) 0 0
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) −5.00000 −0.195069
\(658\) −27.5000 + 9.52628i −1.07206 + 0.371373i
\(659\) −33.0000 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 0 0
\(661\) −3.50000 6.06218i −0.136134 0.235791i 0.789896 0.613241i \(-0.210135\pi\)
−0.926030 + 0.377450i \(0.876801\pi\)
\(662\) −16.0000 27.7128i −0.621858 1.07709i
\(663\) 15.0000 25.9808i 0.582552 1.00901i
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −4.50000 + 7.79423i −0.174241 + 0.301794i
\(668\) 4.00000 + 6.92820i 0.154765 + 0.268060i
\(669\) −5.00000 8.66025i −0.193311 0.334825i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) 2.00000 + 1.73205i 0.0771517 + 0.0668153i
\(673\) −35.0000 −1.34915 −0.674575 0.738206i \(-0.735673\pi\)
−0.674575 + 0.738206i \(0.735673\pi\)
\(674\) 9.00000 15.5885i 0.346667 0.600445i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 7.00000 12.1244i 0.269032 0.465977i −0.699580 0.714554i \(-0.746630\pi\)
0.968612 + 0.248577i \(0.0799630\pi\)
\(678\) 18.0000 0.691286
\(679\) −2.00000 + 10.3923i −0.0767530 + 0.398820i
\(680\) 0 0
\(681\) −8.50000 + 14.7224i −0.325721 + 0.564165i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) 20.0000 + 34.6410i 0.765279 + 1.32550i 0.940099 + 0.340901i \(0.110732\pi\)
−0.174820 + 0.984600i \(0.555934\pi\)
\(684\) −3.00000 + 5.19615i −0.114708 + 0.198680i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 21.0000 0.801200
\(688\) 3.00000 5.19615i 0.114374 0.198101i
\(689\) 42.0000 + 72.7461i 1.60007 + 2.77141i
\(690\) 0 0
\(691\) −6.50000 + 11.2583i −0.247272 + 0.428287i −0.962768 0.270330i \(-0.912867\pi\)
0.715496 + 0.698617i \(0.246201\pi\)
\(692\) −21.0000 −0.798300
\(693\) 0.500000 2.59808i 0.0189934 0.0986928i
\(694\) −22.0000 −0.835109
\(695\) 0 0
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 8.00000 0.302588
\(700\) −10.0000 8.66025i −0.377964 0.327327i
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 3.00000 5.19615i 0.113228 0.196116i
\(703\) −18.0000 31.1769i −0.678883 1.17586i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −14.0000 −0.526897
\(707\) −17.5000 + 6.06218i −0.658155 + 0.227992i
\(708\) 0 0
\(709\) 18.5000 32.0429i 0.694782 1.20340i −0.275472 0.961309i \(-0.588834\pi\)
0.970254 0.242089i \(-0.0778325\pi\)
\(710\) 0 0
\(711\) −2.50000 4.33013i −0.0937573 0.162392i
\(712\) −5.00000 + 8.66025i −0.187383 + 0.324557i
\(713\) −6.00000 −0.224702
\(714\) −12.5000 + 4.33013i −0.467801 + 0.162051i
\(715\) 0 0
\(716\) −11.0000 + 19.0526i −0.411089 + 0.712028i
\(717\) −4.50000 7.79423i −0.168056 0.291081i
\(718\) 8.00000 + 13.8564i 0.298557 + 0.517116i
\(719\) 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i \(-0.565365\pi\)
0.949785 0.312903i \(-0.101301\pi\)
\(720\) 0 0
\(721\) 22.0000 + 19.0526i 0.819323 + 0.709554i
\(722\) 17.0000 0.632674
\(723\) 7.00000 12.1244i 0.260333 0.450910i
\(724\) 11.5000 + 19.9186i 0.427394 + 0.740268i
\(725\) 22.5000 + 38.9711i 0.835629 + 1.44735i
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) 25.0000 0.927199 0.463599 0.886045i \(-0.346558\pi\)
0.463599 + 0.886045i \(0.346558\pi\)
\(728\) −3.00000 + 15.5885i −0.111187 + 0.577747i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.0000 + 25.9808i 0.554795 + 0.960933i
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) 18.5000 + 32.0429i 0.680534 + 1.17872i 0.974818 + 0.223001i \(0.0715853\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) −36.0000 −1.32249
\(742\) 7.00000 36.3731i 0.256978 1.33530i
\(743\) −20.0000 −0.733729 −0.366864 0.930274i \(-0.619569\pi\)
−0.366864 + 0.930274i \(0.619569\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 0 0
\(746\) 11.5000 + 19.9186i 0.421045 + 0.729271i
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) 5.00000 0.182818
\(749\) −8.00000 6.92820i −0.292314 0.253151i
\(750\) 0 0
\(751\) 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) −5.50000 9.52628i −0.200564 0.347388i
\(753\) 8.50000 + 14.7224i 0.309757 + 0.536515i
\(754\) 27.0000 46.7654i 0.983282 1.70309i
\(755\) 0 0
\(756\) −2.50000 + 0.866025i −0.0909241 + 0.0314970i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) −0.500000 0.866025i −0.0181489 0.0314347i
\(760\) 0 0
\(761\) −6.00000 + 10.3923i −0.217500 + 0.376721i −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) −14.0000 −0.507166
\(763\) 7.50000 2.59808i 0.271518 0.0940567i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) 0 0
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 26.0000 0.937584 0.468792 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) 13.0000 22.5167i 0.467880 0.810392i
\(773\) −20.0000 34.6410i −0.719350 1.24595i −0.961258 0.275651i \(-0.911106\pi\)
0.241908 0.970299i \(-0.422227\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) −15.0000 + 25.9808i −0.538816 + 0.933257i
\(776\) −4.00000 −0.143592
\(777\) 3.00000 15.5885i 0.107624 0.559233i
\(778\) −12.0000 −0.430221
\(779\) 18.0000 31.1769i 0.644917 1.11703i
\(780\) 0 0
\(781\) 1.50000 + 2.59808i 0.0536742 + 0.0929665i
\(782\) −2.50000 + 4.33013i −0.0893998 + 0.154845i
\(783\) 9.00000 0.321634
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 0 0
\(786\) 6.00000 10.3923i 0.214013 0.370681i
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) −6.50000 11.2583i −0.231553 0.401061i
\(789\) 6.00000 10.3923i 0.213606 0.369976i
\(790\) 0 0
\(791\) 9.00000 46.7654i 0.320003 1.66279i
\(792\) 1.00000 0.0355335
\(793\) −6.00000 + 10.3923i −0.213066 + 0.369042i
\(794\) 19.0000 + 32.9090i 0.674285 + 1.16790i
\(795\) 0 0
\(796\) −3.50000 + 6.06218i −0.124054 + 0.214868i
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 12.0000 + 10.3923i 0.424795 + 0.367884i
\(799\) 55.0000 1.94576
\(800\) 2.50000 4.33013i 0.0883883 0.153093i
\(801\) −5.00000 8.66025i −0.176666 0.305995i
\(802\) 15.5000 + 26.8468i 0.547324 + 0.947993i
\(803\) 2.50000 4.33013i 0.0882231 0.152807i
\(804\) 10.0000 0.352673
\(805\) 0 0
\(806\) 36.0000 1.26805
\(807\) 1.50000 2.59808i 0.0528025 0.0914566i
\(808\) −3.50000 6.06218i −0.123130 0.213267i
\(809\) 17.0000 + 29.4449i 0.597688 + 1.03523i 0.993161 + 0.116749i \(0.0372472\pi\)
−0.395473 + 0.918477i \(0.629419\pi\)
\(810\) 0 0
\(811\) −27.0000 −0.948098 −0.474049 0.880498i \(-0.657208\pi\)
−0.474049 + 0.880498i \(0.657208\pi\)
\(812\) −22.5000 + 7.79423i −0.789595 + 0.273524i
\(813\) −22.0000 −0.771574
\(814\) −3.00000 + 5.19615i −0.105150 + 0.182125i
\(815\) 0 0
\(816\) −2.50000 4.33013i −0.0875175 0.151585i
\(817\) 18.0000 31.1769i 0.629740 1.09074i
\(818\) 13.0000 0.454534
\(819\) −12.0000 10.3923i −0.419314 0.363137i
\(820\) 0 0
\(821\) −1.50000 + 2.59808i −0.0523504 + 0.0906735i −0.891013 0.453978i \(-0.850005\pi\)
0.838663 + 0.544651i \(0.183338\pi\)
\(822\) −1.50000 2.59808i −0.0523185 0.0906183i
\(823\) 19.0000 + 32.9090i 0.662298 + 1.14713i 0.980010 + 0.198947i \(0.0637522\pi\)
−0.317712 + 0.948187i \(0.602914\pi\)
\(824\) −5.50000 + 9.52628i −0.191602 + 0.331864i
\(825\) −5.00000 −0.174078
\(826\) 0 0
\(827\) −9.00000 −0.312961 −0.156480 0.987681i \(-0.550015\pi\)
−0.156480 + 0.987681i \(0.550015\pi\)
\(828\) −0.500000 + 0.866025i −0.0173762 + 0.0300965i
\(829\) −1.00000 1.73205i −0.0347314 0.0601566i 0.848137 0.529777i \(-0.177724\pi\)
−0.882869 + 0.469620i \(0.844391\pi\)
\(830\) 0 0
\(831\) −16.0000 + 27.7128i −0.555034 + 0.961347i
\(832\) −6.00000 −0.208013
\(833\) 5.00000 + 34.6410i 0.173240 + 1.20024i
\(834\) 15.0000 0.519408
\(835\) 0 0
\(836\) −3.00000 5.19615i −0.103757 0.179713i
\(837\) 3.00000 + 5.19615i 0.103695 + 0.179605i
\(838\) 12.5000 21.6506i 0.431805 0.747909i
\(839\) −48.0000 −1.65714 −0.828572 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 10.5000 18.1865i 0.361854 0.626749i
\(843\) −2.50000 4.33013i −0.0861046 0.149137i
\(844\) −4.50000 7.79423i −0.154896 0.268288i
\(845\) 0 0
\(846\) 11.0000 0.378188
\(847\) −20.0000 17.3205i −0.687208 0.595140i
\(848\) 14.0000 0.480762
\(849\) 6.00000 10.3923i 0.205919 0.356663i
\(850\) 12.5000 + 21.6506i 0.428746 + 0.742611i
\(851\) −3.00000 5.19615i −0.102839 0.178122i
\(852\) 1.50000 2.59808i 0.0513892 0.0890086i
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 5.00000 1.73205i 0.171096 0.0592696i
\(855\) 0 0
\(856\) 2.00000 3.46410i 0.0683586 0.118401i
\(857\) 9.00000 + 15.5885i 0.307434 + 0.532492i 0.977800 0.209539i \(-0.0671963\pi\)
−0.670366 + 0.742030i \(0.733863\pi\)
\(858\) 3.00000 + 5.19615i 0.102418 + 0.177394i
\(859\) 8.50000 14.7224i 0.290016 0.502323i −0.683797 0.729672i \(-0.739673\pi\)
0.973813 + 0.227349i \(0.0730059\pi\)
\(860\) 0 0
\(861\) 15.0000 5.19615i 0.511199 0.177084i
\(862\) 6.00000 0.204361
\(863\) −18.5000 + 32.0429i −0.629747 + 1.09075i 0.357855 + 0.933777i \(0.383508\pi\)
−0.987602 + 0.156977i \(0.949825\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) 0 0
\(866\) −1.00000 + 1.73205i −0.0339814 + 0.0588575i
\(867\) 8.00000 0.271694
\(868\) −12.0000 10.3923i −0.407307 0.352738i
\(869\) 5.00000 0.169613
\(870\) 0 0
\(871\) 30.0000 + 51.9615i 1.01651 + 1.76065i
\(872\) 1.50000 + 2.59808i 0.0507964 + 0.0879820i
\(873\) 2.00000 3.46410i 0.0676897 0.117242i
\(874\) 6.00000 0.202953
\(875\) 0 0
\(876\) −5.00000 −0.168934
\(877\) 12.0000 20.7846i 0.405211 0.701846i −0.589135 0.808035i \(-0.700531\pi\)
0.994346 + 0.106188i \(0.0338646\pi\)
\(878\) −10.0000 17.3205i −0.337484 0.584539i
\(879\) 6.00000 + 10.3923i 0.202375 + 0.350524i
\(880\) 0 0
\(881\) −39.0000 −1.31394 −0.656972 0.753915i \(-0.728163\pi\)
−0.656972 + 0.753915i \(0.728163\pi\)
\(882\) 1.00000 + 6.92820i 0.0336718 + 0.233285i
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 15.0000 25.9808i 0.504505 0.873828i
\(885\) 0 0
\(886\) 10.0000 + 17.3205i 0.335957 + 0.581894i
\(887\) 1.50000 2.59808i 0.0503651 0.0872349i −0.839744 0.542983i \(-0.817295\pi\)
0.890109 + 0.455748i \(0.150628\pi\)
\(888\) 6.00000 0.201347
\(889\) −7.00000 + 36.3731i −0.234772 + 1.21991i
\(890\) 0 0
\(891\) −0.500000 + 0.866025i −0.0167506 + 0.0290129i
\(892\) −5.00000 8.66025i −0.167412 0.289967i
\(893\) −33.0000 57.1577i −1.10430 1.91271i
\(894\) 4.00000 6.92820i 0.133780 0.231714i
\(895\) 0 0
\(896\) 2.00000 + 1.73205i 0.0668153 + 0.0578638i
\(897\) −6.00000 −0.200334
\(898\) 0 0
\(899\) 27.0000 + 46.7654i 0.900500 + 1.55971i
\(900\) 2.50000 + 4.33013i 0.0833333 + 0.144338i
\(901\) −35.0000 + 60.6218i −1.16602 + 2.01960i
\(902\) −6.00000 −0.199778
\(903\) 15.0000 5.19615i 0.499169 0.172917i
\(904\) 18.0000 0.598671
\(905\) 0 0
\(906\) −6.00000 10.3923i −0.199337 0.345261i
\(907\) −2.00000 3.46410i −0.0664089 0.115024i 0.830909 0.556408i \(-0.187821\pi\)
−0.897318 + 0.441384i \(0.854488\pi\)
\(908\) −8.50000 + 14.7224i −0.282082 + 0.488581i
\(909\) 7.00000 0.232175
\(910\) 0 0
\(911\) −16.0000 −0.530104 −0.265052 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) −3.00000 + 5.19615i −0.0993399 + 0.172062i
\(913\) 4.00000 + 6.92820i 0.132381 + 0.229290i
\(914\) −6.00000 10.3923i −0.198462 0.343747i
\(915\) 0 0
\(916\) 21.0000 0.693860
\(917\) −24.0000 20.7846i −0.792550 0.686368i
\(918\) 5.00000 0.165025
\(919\) −25.5000 + 44.1673i −0.841167 + 1.45694i 0.0477411 + 0.998860i \(0.484798\pi\)
−0.888908 + 0.458085i \(0.848536\pi\)
\(920\) 0 0
\(921\) 16.5000 + 28.5788i 0.543693 + 0.941705i
\(922\) −7.00000 + 12.1244i −0.230533 + 0.399294i
\(923\) 18.0000 0.592477
\(924\) 0.500000 2.59808i 0.0164488 0.0854704i
\(925\) −30.0000 −0.986394
\(926\) 10.0000 17.3205i 0.328620 0.569187i
\(927\) −5.50000 9.52628i −0.180644 0.312884i
\(928\) −4.50000 7.79423i −0.147720 0.255858i
\(929\) 3.00000 5.19615i 0.0984268 0.170480i −0.812607 0.582812i \(-0.801952\pi\)
0.911034 + 0.412332i \(0.135286\pi\)
\(930\) 0 0
\(931\) 33.0000 25.9808i 1.08153 0.851485i
\(932\) 8.00000 0.262049
\(933\) 6.50000 11.2583i 0.212800 0.368581i
\(934\) −15.5000 26.8468i −0.507175 0.878454i
\(935\) 0 0
\(936\) 3.00000 5.19615i 0.0980581 0.169842i
\(937\) 34.0000 1.11073 0.555366 0.831606i \(-0.312578\pi\)
0.555366 + 0.831606i \(0.312578\pi\)
\(938\) 5.00000 25.9808i 0.163256 0.848302i
\(939\) −20.0000 −0.652675
\(940\) 0 0
\(941\) 3.00000 + 5.19615i 0.0977972 + 0.169390i 0.910773 0.412908i \(-0.135487\pi\)
−0.812975 + 0.582298i \(0.802154\pi\)
\(942\) −6.50000 11.2583i −0.211781 0.366816i
\(943\) 3.00000 5.19615i 0.0976934 0.169210i
\(944\) 0 0
\(945\) 0 0
\(946\) −6.00000 −0.195077
\(947\) 5.00000 8.66025i 0.162478 0.281420i −0.773279 0.634066i \(-0.781385\pi\)
0.935757 + 0.352646i \(0.114718\pi\)
\(948\) −2.50000 4.33013i −0.0811962 0.140636i
\(949\) −15.0000 25.9808i −0.486921 0.843371i
\(950\) 15.0000 25.9808i 0.486664 0.842927i
\(951\) 2.00000 0.0648544
\(952\) −12.5000 + 4.33013i −0.405127 + 0.140340i
\(953\) 1.00000 0.0323932 0.0161966 0.999869i \(-0.494844\pi\)
0.0161966 + 0.999869i \(0.494844\pi\)
\(954\) −7.00000 + 12.1244i −0.226633 + 0.392541i
\(955\) 0 0
\(956\) −4.50000 7.79423i −0.145540 0.252083i
\(957\) −4.50000 + 7.79423i −0.145464 + 0.251952i
\(958\) 30.0000 0.969256
\(959\) −7.50000 + 2.59808i −0.242188 + 0.0838963i
\(960\) 0 0
\(961\) −2.50000 + 4.33013i −0.0806452 + 0.139682i
\(962\) 18.0000 + 31.1769i 0.580343 + 1.00518i
\(963\) 2.00000 + 3.46410i 0.0644491 + 0.111629i
\(964\) 7.00000 12.1244i 0.225455 0.390499i
\(965\) 0 0
\(966\) 2.00000 + 1.73205i 0.0643489 + 0.0557278i
\(967\) 22.0000 0.707472 0.353736 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) 5.00000 8.66025i 0.160706 0.278351i
\(969\) −15.0000 25.9808i −0.481869 0.834622i
\(970\) 0 0
\(971\) 7.50000 12.9904i 0.240686 0.416881i −0.720224 0.693742i \(-0.755961\pi\)
0.960910 + 0.276861i \(0.0892941\pi\)
\(972\) 1.00000 0.0320750
\(973\) 7.50000 38.9711i 0.240439 1.24936i
\(974\) −14.0000 −0.448589
\(975\) −15.0000 + 25.9808i −0.480384 + 0.832050i
\(976\) 1.00000 + 1.73205i 0.0320092 + 0.0554416i
\(977\) −17.0000 29.4449i −0.543878 0.942025i −0.998677 0.0514302i \(-0.983622\pi\)
0.454798 0.890594i \(-0.349711\pi\)
\(978\) −9.50000 + 16.4545i −0.303777 + 0.526156i
\(979\) 10.0000 0.319601
\(980\) 0 0
\(981\) −3.00000 −0.0957826
\(982\) 12.0000 20.7846i 0.382935 0.663264i
\(983\) −3.00000 5.19615i −0.0956851 0.165732i 0.814209 0.580572i \(-0.197171\pi\)
−0.909894 + 0.414840i \(0.863838\pi\)
\(984\) 3.00000 + 5.19615i 0.0956365 + 0.165647i
\(985\) 0 0
\(986\) 45.0000 1.43309
\(987\) 5.50000 28.5788i 0.175067 0.909674i
\(988\) −36.0000 −1.14531
\(989\) 3.00000 5.19615i 0.0953945 0.165228i
\(990\) 0 0
\(991\) −12.0000 20.7846i −0.381193 0.660245i 0.610040 0.792370i \(-0.291153\pi\)
−0.991233 + 0.132125i \(0.957820\pi\)
\(992\) 3.00000 5.19615i 0.0952501 0.164978i
\(993\) 32.0000 1.01549
\(994\) −6.00000 5.19615i −0.190308 0.164812i
\(995\) 0 0
\(996\) 4.00000 6.92820i 0.126745 0.219529i
\(997\) −16.0000 27.7128i −0.506725 0.877674i −0.999970 0.00778294i \(-0.997523\pi\)
0.493245 0.869891i \(-0.335811\pi\)
\(998\) −3.50000 6.06218i −0.110791 0.191895i
\(999\) −3.00000 + 5.19615i −0.0949158 + 0.164399i
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 966.2.i.b.415.1 yes 2
7.2 even 3 6762.2.a.bk.1.1 1
7.4 even 3 inner 966.2.i.b.277.1 2
7.5 odd 6 6762.2.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.i.b.277.1 2 7.4 even 3 inner
966.2.i.b.415.1 yes 2 1.1 even 1 trivial
6762.2.a.ba.1.1 1 7.5 odd 6
6762.2.a.bk.1.1 1 7.2 even 3