Properties

Label 1078.2.e.d.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
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] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not 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: \(8.60787333789\)
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: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.d.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -5.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{18} +(1.00000 + 1.73205i) q^{19} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(2.50000 + 4.33013i) q^{26} +5.00000 q^{27} +3.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-2.50000 + 4.33013i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.00000 + 5.19615i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-2.50000 - 4.33013i) q^{54} +2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-3.50000 - 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(6.50000 - 11.2583i) q^{67} +(3.00000 + 5.19615i) q^{68} -6.00000 q^{69} -12.0000 q^{71} +(1.00000 + 1.73205i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.50000 - 4.33013i) q^{75} -2.00000 q^{76} +5.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(2.00000 + 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +6.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(3.00000 - 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + q^{11} + q^{12} - 10 q^{13} - q^{16} + 6 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{22} - 6 q^{23} + q^{24} + 5 q^{25} + 5 q^{26} + 10 q^{27} + 6 q^{29} + 8 q^{31} - q^{32} - q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} + 2 q^{38} - 5 q^{39} + 12 q^{41} - 8 q^{43} + q^{44} - 6 q^{46} + 6 q^{47} - 2 q^{48} - 10 q^{50} - 6 q^{51} + 5 q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} - 3 q^{58} - 3 q^{59} - 7 q^{61} - 16 q^{62} + 2 q^{64} - q^{66} + 13 q^{67} + 6 q^{68} - 12 q^{69} - 24 q^{71} + 2 q^{72} - 10 q^{73} - 2 q^{74} - 5 q^{75} - 4 q^{76} + 10 q^{78} + q^{79} - q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{86} + 3 q^{87} + q^{88} + 6 q^{89} + 12 q^{92} - 8 q^{93} + 6 q^{94} + q^{96} + 26 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −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 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 1.00000 1.73205i 0.235702 0.408248i
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) −3.00000 5.19615i −0.420084 0.727607i
\(52\) 2.50000 4.33013i 0.346688 0.600481i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) −2.50000 4.33013i −0.340207 0.589256i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) 6.50000 11.2583i 0.794101 1.37542i −0.129307 0.991605i \(-0.541275\pi\)
0.923408 0.383819i \(-0.125391\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −2.50000 4.33013i −0.288675 0.500000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.00000 5.19615i −0.331295 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 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 \(0.118979\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −2.50000 + 4.33013i −0.240563 + 0.416667i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) −1.50000 + 2.59808i −0.139272 + 0.241225i
\(117\) −5.00000 8.66025i −0.462250 0.800641i
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −3.50000 + 6.06218i −0.316875 + 0.548844i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 0 0
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 0 0
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) −13.0000 −1.12303
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −7.50000 + 12.9904i −0.640768 + 1.10984i 0.344493 + 0.938789i \(0.388051\pi\)
−0.985262 + 0.171054i \(0.945283\pi\)
\(138\) 3.00000 + 5.19615i 0.255377 + 0.442326i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) −2.50000 + 4.33013i −0.204124 + 0.353553i
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 0 0
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i \(-0.884359\pi\)
0.775113 + 0.631822i \(0.217693\pi\)
\(158\) 0.500000 0.866025i 0.0397779 0.0688973i
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −8.50000 14.7224i −0.665771 1.15315i −0.979076 0.203497i \(-0.934769\pi\)
0.313304 0.949653i \(-0.398564\pi\)
\(164\) −3.00000 + 5.19615i −0.234261 + 0.405751i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i \(-0.973527\pi\)
0.426329 0.904568i \(-0.359807\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 1.50000 + 2.59808i 0.112747 + 0.195283i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −4.50000 + 7.79423i −0.336346 + 0.582568i −0.983742 0.179585i \(-0.942524\pi\)
0.647397 + 0.762153i \(0.275858\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 0 0
\(186\) −4.00000 + 6.92820i −0.293294 + 0.508001i
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 11.0000 19.0526i 0.791797 1.37143i −0.133056 0.991109i \(-0.542479\pi\)
0.924853 0.380325i \(-0.124188\pi\)
\(194\) −6.50000 11.2583i −0.466673 0.808301i
\(195\) 0 0
\(196\) 0 0
\(197\) −9.00000 −0.641223 −0.320612 0.947211i \(-0.603888\pi\)
−0.320612 + 0.947211i \(0.603888\pi\)
\(198\) −1.00000 1.73205i −0.0710669 0.123091i
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) −6.50000 11.2583i −0.458475 0.794101i
\(202\) −3.00000 −0.211079
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) −2.00000 + 3.46410i −0.139347 + 0.241355i
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 2.50000 + 4.33013i 0.173344 + 0.300240i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) −6.00000 + 10.3923i −0.411113 + 0.712069i
\(214\) 0 0
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 5.00000 + 8.66025i 0.337869 + 0.585206i
\(220\) 0 0
\(221\) −15.0000 + 25.9808i −1.00901 + 1.74766i
\(222\) 1.00000 + 1.73205i 0.0671156 + 0.116248i
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 0 0
\(225\) 10.0000 0.666667
\(226\) −4.50000 7.79423i −0.299336 0.518464i
\(227\) −3.00000 + 5.19615i −0.199117 + 0.344881i −0.948242 0.317547i \(-0.897141\pi\)
0.749125 + 0.662428i \(0.230474\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i \(0.0631241\pi\)
−0.319582 + 0.947559i \(0.603543\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) 15.0000 + 25.9808i 0.982683 + 1.70206i 0.651813 + 0.758380i \(0.274009\pi\)
0.330870 + 0.943676i \(0.392658\pi\)
\(234\) −5.00000 + 8.66025i −0.326860 + 0.566139i
\(235\) 0 0
\(236\) −1.50000 2.59808i −0.0976417 0.169120i
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 21.0000 1.35838 0.679189 0.733964i \(-0.262332\pi\)
0.679189 + 0.733964i \(0.262332\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 7.00000 0.448129
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) 4.00000 6.92820i 0.254000 0.439941i
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 6.50000 + 11.2583i 0.407846 + 0.706410i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.5000 + 23.3827i 0.842107 + 1.45857i 0.888110 + 0.459631i \(0.152018\pi\)
−0.0460033 + 0.998941i \(0.514648\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) 1.50000 2.59808i 0.0924940 0.160204i −0.816066 0.577959i \(-0.803849\pi\)
0.908560 + 0.417755i \(0.137183\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 6.50000 + 11.2583i 0.397051 + 0.687712i
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) −12.5000 21.6506i −0.759321 1.31518i −0.943197 0.332233i \(-0.892198\pi\)
0.183876 0.982949i \(-0.441135\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 15.0000 0.906183
\(275\) −2.50000 4.33013i −0.150756 0.261116i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 16.0000 0.957895
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) −11.0000 + 19.0526i −0.653882 + 1.13256i 0.328291 + 0.944577i \(0.393527\pi\)
−0.982173 + 0.187980i \(0.939806\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 6.50000 11.2583i 0.381037 0.659975i
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 15.0000 + 25.9808i 0.867472 + 1.50251i
\(300\) 5.00000 0.288675
\(301\) 0 0
\(302\) −1.00000 −0.0575435
\(303\) −1.50000 2.59808i −0.0861727 0.149256i
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) 0 0
\(306\) −6.00000 10.3923i −0.342997 0.594089i
\(307\) −32.0000 −1.82634 −0.913168 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) −2.50000 + 4.33013i −0.141535 + 0.245145i
\(313\) −3.50000 6.06218i −0.197832 0.342655i 0.749993 0.661445i \(-0.230057\pi\)
−0.947825 + 0.318791i \(0.896723\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) −6.00000 + 10.3923i −0.336463 + 0.582772i
\(319\) 1.50000 2.59808i 0.0839839 0.145464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −12.5000 + 21.6506i −0.693375 + 1.20096i
\(326\) −8.50000 + 14.7224i −0.470771 + 0.815400i
\(327\) 7.00000 + 12.1244i 0.387101 + 0.670478i
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) 4.50000 + 7.79423i 0.246229 + 0.426481i
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 4.50000 7.79423i 0.244406 0.423324i
\(340\) 0 0
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −7.50000 + 12.9904i −0.403202 + 0.698367i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 1.50000 + 2.59808i 0.0804084 + 0.139272i
\(349\) 34.0000 1.81998 0.909989 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) 0 0
\(351\) −25.0000 −1.33440
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 1.50000 2.59808i 0.0797241 0.138086i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 9.00000 0.475665
\(359\) 4.50000 + 7.79423i 0.237501 + 0.411364i 0.959997 0.280012i \(-0.0903384\pi\)
−0.722496 + 0.691375i \(0.757005\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) 3.50000 + 6.06218i 0.182948 + 0.316875i
\(367\) 19.0000 32.9090i 0.991792 1.71783i 0.385164 0.922848i \(-0.374145\pi\)
0.606628 0.794986i \(-0.292522\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 6.00000 + 10.3923i 0.312348 + 0.541002i
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) −3.00000 + 5.19615i −0.155126 + 0.268687i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) −6.50000 + 11.2583i −0.333005 + 0.576782i
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −6.50000 + 11.2583i −0.329988 + 0.571555i
\(389\) −6.00000 + 10.3923i −0.304212 + 0.526911i −0.977086 0.212847i \(-0.931726\pi\)
0.672874 + 0.739758i \(0.265060\pi\)
\(390\) 0 0
\(391\) −36.0000 −1.82060
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 4.50000 + 7.79423i 0.226707 + 0.392668i
\(395\) 0 0
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) 1.00000 + 1.73205i 0.0501886 + 0.0869291i 0.890028 0.455905i \(-0.150684\pi\)
−0.839840 + 0.542834i \(0.817351\pi\)
\(398\) −14.0000 −0.701757
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 4.50000 + 7.79423i 0.224719 + 0.389225i 0.956235 0.292599i \(-0.0945202\pi\)
−0.731516 + 0.681824i \(0.761187\pi\)
\(402\) −6.50000 + 11.2583i −0.324191 + 0.561514i
\(403\) −20.0000 + 34.6410i −0.996271 + 1.72559i
\(404\) 1.50000 + 2.59808i 0.0746278 + 0.129259i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) −3.00000 5.19615i −0.148522 0.257248i
\(409\) −2.00000 + 3.46410i −0.0988936 + 0.171289i −0.911227 0.411905i \(-0.864864\pi\)
0.812333 + 0.583193i \(0.198197\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) 4.00000 0.197066
\(413\) 0 0
\(414\) −12.0000 −0.589768
\(415\) 0 0
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) −1.00000 1.73205i −0.0489116 0.0847174i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) −13.0000 22.5167i −0.632830 1.09609i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) −15.0000 25.9808i −0.727607 1.26025i
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 0 0
\(429\) 2.50000 + 4.33013i 0.120701 + 0.209061i
\(430\) 0 0
\(431\) −7.50000 + 12.9904i −0.361262 + 0.625725i −0.988169 0.153370i \(-0.950987\pi\)
0.626907 + 0.779094i \(0.284321\pi\)
\(432\) −2.50000 4.33013i −0.120281 0.208333i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 6.00000 10.3923i 0.287019 0.497131i
\(438\) 5.00000 8.66025i 0.238909 0.413803i
\(439\) −9.50000 16.4545i −0.453410 0.785330i 0.545185 0.838316i \(-0.316459\pi\)
−0.998595 + 0.0529862i \(0.983126\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 1.00000 1.73205i 0.0474579 0.0821995i
\(445\) 0 0
\(446\) −5.00000 8.66025i −0.236757 0.410075i
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −5.00000 8.66025i −0.235702 0.408248i
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) −4.50000 + 7.79423i −0.211662 + 0.366610i
\(453\) −0.500000 0.866025i −0.0234920 0.0406894i
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) 2.00000 0.0936586
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) 10.0000 17.3205i 0.467269 0.809334i
\(459\) 15.0000 25.9808i 0.700140 1.21268i
\(460\) 0 0
\(461\) −39.0000 −1.81641 −0.908206 0.418524i \(-0.862547\pi\)
−0.908206 + 0.418524i \(0.862547\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) 15.0000 25.9808i 0.694862 1.20354i
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) 10.0000 0.462250
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 + 3.46410i 0.0921551 + 0.159617i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) −2.00000 + 3.46410i −0.0919601 + 0.159280i
\(474\) −0.500000 0.866025i −0.0229658 0.0397779i
\(475\) 10.0000 0.458831
\(476\) 0 0
\(477\) 24.0000 1.09888
\(478\) −10.5000 18.1865i −0.480259 0.831833i
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 8.00000 13.8564i 0.362887 0.628539i
\(487\) 2.00000 3.46410i 0.0906287 0.156973i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(488\) −3.50000 6.06218i −0.158438 0.274422i
\(489\) −17.0000 −0.768767
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −5.00000 + 8.66025i −0.224961 + 0.389643i
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) −4.00000 6.92820i −0.179065 0.310149i 0.762496 0.646993i \(-0.223974\pi\)
−0.941560 + 0.336844i \(0.890640\pi\)
\(500\) 0 0
\(501\) −4.50000 + 7.79423i −0.201045 + 0.348220i
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 6.50000 11.2583i 0.288391 0.499508i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 5.00000 + 8.66025i 0.220755 + 0.382360i
\(514\) 13.5000 23.3827i 0.595459 1.03137i
\(515\) 0 0
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) 0 0
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) −0.500000 + 0.866025i −0.0217597 + 0.0376889i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) −30.0000 −1.29944
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) 0 0
\(536\) 6.50000 11.2583i 0.280757 0.486286i
\(537\) 4.50000 + 7.79423i 0.194189 + 0.336346i
\(538\) 24.0000 1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) −2.50000 4.33013i −0.107483 0.186167i 0.807267 0.590187i \(-0.200946\pi\)
−0.914750 + 0.404020i \(0.867613\pi\)
\(542\) −12.5000 + 21.6506i −0.536921 + 0.929974i
\(543\) 5.00000 8.66025i 0.214571 0.371647i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −7.50000 12.9904i −0.320384 0.554922i
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) −2.50000 + 4.33013i −0.106600 + 0.184637i
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) −6.00000 −0.255377
\(553\) 0 0
\(554\) −1.00000 −0.0424859
\(555\) 0 0
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 3.00000 5.19615i 0.127114 0.220168i −0.795443 0.606028i \(-0.792762\pi\)
0.922557 + 0.385860i \(0.126095\pi\)
\(558\) −8.00000 13.8564i −0.338667 0.586588i
\(559\) 20.0000 0.845910
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 3.00000 + 5.19615i 0.126547 + 0.219186i
\(563\) 9.00000 15.5885i 0.379305 0.656975i −0.611656 0.791123i \(-0.709497\pi\)
0.990961 + 0.134148i \(0.0428299\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −2.50000 4.33013i −0.104530 0.181052i
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i \(-0.879879\pi\)
0.783930 + 0.620850i \(0.213212\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) −11.0000 19.0526i −0.457144 0.791797i
\(580\) 0 0
\(581\) 0 0
\(582\) −13.0000 −0.538867
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −5.00000 + 8.66025i −0.206901 + 0.358364i
\(585\) 0 0
\(586\) −9.00000 15.5885i −0.371787 0.643953i
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −4.50000 + 7.79423i −0.185105 + 0.320612i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 12.0000 + 20.7846i 0.492781 + 0.853522i 0.999965 0.00831589i \(-0.00264706\pi\)
−0.507184 + 0.861838i \(0.669314\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −7.00000 12.1244i −0.286491 0.496217i
\(598\) 15.0000 25.9808i 0.613396 1.06243i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) −2.50000 4.33013i −0.102062 0.176777i
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 26.0000 1.05880
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) 0 0
\(606\) −1.50000 + 2.59808i −0.0609333 + 0.105540i
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 25.9808i −0.606835 1.05107i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i \(0.342626\pi\)
−0.999574 + 0.0291886i \(0.990708\pi\)
\(614\) 16.0000 + 27.7128i 0.645707 + 1.11840i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 0.845428 0.422714 0.906263i \(-0.361077\pi\)
0.422714 + 0.906263i \(0.361077\pi\)
\(618\) 2.00000 + 3.46410i 0.0804518 + 0.139347i
\(619\) 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i \(-0.488000\pi\)
0.846566 0.532284i \(-0.178666\pi\)
\(620\) 0 0
\(621\) −15.0000 25.9808i −0.601929 1.04257i
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) 5.00000 0.200160
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −3.50000 + 6.06218i −0.139888 + 0.242293i
\(627\) 1.00000 1.73205i 0.0399362 0.0691714i
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0.500000 + 0.866025i 0.0198889 + 0.0344486i
\(633\) 13.0000 22.5167i 0.516704 0.894957i
\(634\) 12.0000 20.7846i 0.476581 0.825462i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) −3.00000 −0.118771
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) 0 0
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) 19.0000 0.749287 0.374643 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 18.0000 31.1769i 0.707653 1.22569i −0.258073 0.966126i \(-0.583087\pi\)
0.965726 0.259565i \(-0.0835793\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 25.0000 0.980581
\(651\) 0 0
\(652\) 17.0000 0.665771
\(653\) 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) −20.0000 −0.780274
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −17.0000 + 29.4449i −0.661223 + 1.14527i 0.319071 + 0.947731i \(0.396629\pi\)
−0.980294 + 0.197542i \(0.936704\pi\)
\(662\) 6.50000 11.2583i 0.252630 0.437567i
\(663\) 15.0000 + 25.9808i 0.582552 + 1.00901i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 4.50000 7.79423i 0.174110 0.301568i
\(669\) 5.00000 8.66025i 0.193311 0.334825i
\(670\) 0 0
\(671\) −7.00000 −0.270232
\(672\) 0 0
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 11.0000 + 19.0526i 0.423704 + 0.733877i
\(675\) 12.5000 21.6506i 0.481125 0.833333i
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 21.0000 + 36.3731i 0.807096 + 1.39793i 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) −9.00000 −0.345643
\(679\) 0 0
\(680\) 0 0
\(681\) 3.00000 + 5.19615i 0.114960 + 0.199117i
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) 22.5000 38.9711i 0.860939 1.49119i −0.0100856 0.999949i \(-0.503210\pi\)
0.871024 0.491240i \(-0.163456\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) 20.0000 0.763048
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −30.0000 + 51.9615i −1.14291 + 1.97958i
\(690\) 0 0
\(691\) 17.5000 + 30.3109i 0.665731 + 1.15308i 0.979086 + 0.203445i \(0.0652137\pi\)
−0.313355 + 0.949636i \(0.601453\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) 1.50000 2.59808i 0.0568574 0.0984798i
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) −17.0000 29.4449i −0.643459 1.11450i
\(699\) 30.0000 1.13470
\(700\) 0 0
\(701\) −3.00000 −0.113308 −0.0566542 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 12.5000 + 21.6506i 0.471782 + 0.817151i
\(703\) 2.00000 3.46410i 0.0754314 0.130651i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 0 0
\(708\) −3.00000 −0.112747
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −1.00000 + 1.73205i −0.0375029 + 0.0649570i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) −48.0000 −1.79761
\(714\) 0 0
\(715\) 0 0
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) 10.5000 18.1865i 0.392130 0.679189i
\(718\) 4.50000 7.79423i 0.167939 0.290878i
\(719\) −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 −0.558242
\(723\) 5.00000 + 8.66025i 0.185952 + 0.322078i
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) 7.50000 12.9904i 0.278543 0.482451i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) −50.0000 −1.85440 −0.927199 0.374570i \(-0.877790\pi\)
−0.927199 + 0.374570i \(0.877790\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) −21.5000 37.2391i −0.794121 1.37546i −0.923396 0.383849i \(-0.874598\pi\)
0.129275 0.991609i \(-0.458735\pi\)
\(734\) −38.0000 −1.40261
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −6.50000 11.2583i −0.239431 0.414706i
\(738\) 6.00000 10.3923i 0.220863 0.382546i
\(739\) −1.00000 + 1.73205i −0.0367856 + 0.0637145i −0.883832 0.467804i \(-0.845045\pi\)
0.847046 + 0.531519i \(0.178379\pi\)
\(740\) 0 0
\(741\) −10.0000 −0.367359
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) 0 0
\(746\) −5.50000 + 9.52628i −0.201369 + 0.348782i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 6.00000 0.219382
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) 7.50000 + 12.9904i 0.273134 + 0.473082i
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 12.5000 + 21.6506i 0.454020 + 0.786386i
\(759\) −3.00000 + 5.19615i −0.108893 + 0.188608i
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 13.0000 0.470940
\(763\) 0 0
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 6.00000 10.3923i 0.216789 0.375489i
\(767\) 7.50000 12.9904i 0.270809 0.469055i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 27.0000 0.972381
\(772\) 11.0000 + 19.0526i 0.395899 + 0.685717i
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) −20.0000 34.6410i −0.718421 1.24434i
\(776\) 13.0000 0.466673
\(777\) 0 0
\(778\) 12.0000 0.430221
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 18.0000 + 31.1769i 0.643679 + 1.11488i
\(783\) 15.0000 0.536056
\(784\) 0 0
\(785\) 0 0
\(786\) −3.00000 5.19615i −0.107006 0.185341i
\(787\) 7.00000 12.1244i 0.249523 0.432187i −0.713871 0.700278i \(-0.753059\pi\)
0.963394 + 0.268091i \(0.0863928\pi\)
\(788\) 4.50000 7.79423i 0.160306 0.277658i
\(789\) −1.50000 2.59808i −0.0534014 0.0924940i
\(790\) 0 0
\(791\) 0 0
\(792\) 2.00000 0.0710669
\(793\) 17.5000 + 30.3109i 0.621443 + 1.07637i
\(794\) 1.00000 1.73205i 0.0354887 0.0614682i
\(795\) 0 0
\(796\) 7.00000 + 12.1244i 0.248108 + 0.429736i
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 36.0000 1.27359
\(800\) 2.50000 + 4.33013i 0.0883883 + 0.153093i
\(801\) −6.00000 + 10.3923i −0.212000 + 0.367194i
\(802\) 4.50000 7.79423i 0.158901 0.275224i
\(803\) 5.00000 + 8.66025i 0.176446 + 0.305614i
\(804\) 13.0000 0.458475
\(805\) 0 0
\(806\) 40.0000 1.40894
\(807\) 12.0000 + 20.7846i 0.422420 + 0.731653i
\(808\) 1.50000 2.59808i 0.0527698 0.0914000i
\(809\) −18.0000 + 31.1769i −0.632846 + 1.09612i 0.354121 + 0.935200i \(0.384780\pi\)
−0.986967 + 0.160922i \(0.948553\pi\)
\(810\) 0 0
\(811\) 16.0000 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) 0 0
\(813\) −25.0000 −0.876788
\(814\) 1.00000 + 1.73205i 0.0350500 + 0.0607083i
\(815\) 0 0
\(816\) −3.00000 + 5.19615i −0.105021 + 0.181902i
\(817\) −4.00000 6.92820i −0.139942 0.242387i
\(818\) 4.00000 0.139857
\(819\) 0 0
\(820\) 0 0
\(821\) −13.5000 23.3827i −0.471153 0.816061i 0.528302 0.849056i \(-0.322829\pi\)
−0.999456 + 0.0329950i \(0.989495\pi\)
\(822\) 7.50000 12.9904i 0.261593 0.453092i
\(823\) −13.0000 + 22.5167i −0.453152 + 0.784881i −0.998580 0.0532760i \(-0.983034\pi\)
0.545428 + 0.838157i \(0.316367\pi\)
\(824\) −2.00000 3.46410i −0.0696733 0.120678i
\(825\) −5.00000 −0.174078
\(826\) 0 0
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) −8.00000 + 13.8564i −0.277851 + 0.481253i −0.970851 0.239686i \(-0.922956\pi\)
0.692999 + 0.720938i \(0.256289\pi\)
\(830\) 0 0
\(831\) −0.500000 0.866025i −0.0173448 0.0300421i
\(832\) −5.00000 −0.173344
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) −1.00000 + 1.73205i −0.0345857 + 0.0599042i
\(837\) 20.0000 34.6410i 0.691301 1.19737i
\(838\) 6.00000 + 10.3923i 0.207267 + 0.358996i
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 8.00000 + 13.8564i 0.275698 + 0.477523i
\(843\) −3.00000 + 5.19615i −0.103325 + 0.178965i
\(844\) −13.0000 + 22.5167i −0.447478 + 0.775055i
\(845\) 0 0
\(846\) 12.0000 0.412568
\(847\) 0 0
\(848\) −12.0000 −0.412082
\(849\) 11.0000 + 19.0526i 0.377519 + 0.653882i
\(850\) −15.0000 + 25.9808i −0.514496 + 0.891133i
\(851\) −6.00000 + 10.3923i −0.205677 + 0.356244i
\(852\) −6.00000 10.3923i −0.205557 0.356034i
\(853\) 58.0000 1.98588 0.992941 0.118609i \(-0.0378434\pi\)
0.992941 + 0.118609i \(0.0378434\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.0000 41.5692i 0.819824 1.41998i −0.0859870 0.996296i \(-0.527404\pi\)
0.905811 0.423681i \(-0.139262\pi\)
\(858\) 2.50000 4.33013i 0.0853486 0.147828i
\(859\) 17.5000 + 30.3109i 0.597092 + 1.03419i 0.993248 + 0.116011i \(0.0370107\pi\)
−0.396156 + 0.918183i \(0.629656\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) −3.00000 5.19615i −0.102121 0.176879i 0.810437 0.585826i \(-0.199230\pi\)
−0.912558 + 0.408946i \(0.865896\pi\)
\(864\) −2.50000 + 4.33013i −0.0850517 + 0.147314i
\(865\) 0 0
\(866\) 7.00000 + 12.1244i 0.237870 + 0.412002i
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) 1.00000 0.0339227
\(870\) 0 0
\(871\) −32.5000 + 56.2917i −1.10122 + 1.90737i
\(872\) −7.00000 + 12.1244i −0.237050 + 0.410582i
\(873\) 13.0000 + 22.5167i 0.439983 + 0.762073i
\(874\) −12.0000 −0.405906
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) 18.5000 + 32.0429i 0.624701 + 1.08201i 0.988599 + 0.150574i \(0.0481123\pi\)
−0.363898 + 0.931439i \(0.618554\pi\)
\(878\) −9.50000 + 16.4545i −0.320609 + 0.555312i
\(879\) 9.00000 15.5885i 0.303562 0.525786i
\(880\) 0 0
\(881\) 15.0000 0.505363 0.252681 0.967550i \(-0.418688\pi\)
0.252681 + 0.967550i \(0.418688\pi\)
\(882\) 0 0
\(883\) −19.0000 −0.639401 −0.319700 0.947519i \(-0.603582\pi\)
−0.319700 + 0.947519i \(0.603582\pi\)
\(884\) −15.0000 25.9808i −0.504505 0.873828i
\(885\) 0 0
\(886\) −6.00000 + 10.3923i −0.201574 + 0.349136i
\(887\) 28.5000 + 49.3634i 0.956936 + 1.65746i 0.729873 + 0.683582i \(0.239579\pi\)
0.227063 + 0.973880i \(0.427088\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 0 0
\(890\) 0 0
\(891\) 0.500000 + 0.866025i 0.0167506 + 0.0290129i
\(892\) −5.00000 + 8.66025i −0.167412 + 0.289967i
\(893\) −6.00000 + 10.3923i −0.200782 + 0.347765i
\(894\) −3.00000 5.19615i −0.100335 0.173785i
\(895\) 0 0
\(896\) 0 0
\(897\) 30.0000 1.00167
\(898\) −15.0000 25.9808i −0.500556 0.866989i
\(899\) 12.0000 20.7846i 0.400222 0.693206i
\(900\) −5.00000 + 8.66025i −0.166667 + 0.288675i
\(901\) −36.0000 62.3538i −1.19933 2.07731i
\(902\) −6.00000 −0.199778
\(903\) 0 0
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) −0.500000 + 0.866025i −0.0166114 + 0.0287718i
\(907\) −22.0000 + 38.1051i −0.730498 + 1.26526i 0.226173 + 0.974087i \(0.427379\pi\)
−0.956671 + 0.291172i \(0.905955\pi\)
\(908\) −3.00000 5.19615i −0.0995585 0.172440i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) −1.00000 1.73205i −0.0331133 0.0573539i
\(913\) −3.00000 + 5.19615i −0.0992855 + 0.171968i
\(914\) 11.0000 19.0526i 0.363848 0.630203i
\(915\) 0 0
\(916\) −20.0000 −0.660819
\(917\) 0 0
\(918\) −30.0000 −0.990148
\(919\) 8.00000 + 13.8564i 0.263896 + 0.457081i 0.967274 0.253735i \(-0.0816592\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(920\) 0 0
\(921\) −16.0000 + 27.7128i −0.527218 + 0.913168i
\(922\) 19.5000 + 33.7750i 0.642198 + 1.11232i
\(923\) 60.0000 1.97492
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) −13.0000 22.5167i −0.427207 0.739943i
\(927\) 4.00000 6.92820i 0.131377 0.227552i
\(928\) −1.50000 + 2.59808i −0.0492399 + 0.0852860i
\(929\) 7.50000 + 12.9904i 0.246067 + 0.426201i 0.962431 0.271526i \(-0.0875283\pi\)
−0.716364 + 0.697727i \(0.754195\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −30.0000 −0.982683
\(933\) −12.0000 20.7846i −0.392862 0.680458i
\(934\) −6.00000 + 10.3923i −0.196326 + 0.340047i
\(935\) 0 0
\(936\) −5.00000 8.66025i −0.163430 0.283069i
\(937\) 52.0000 1.69877 0.849383 0.527777i \(-0.176974\pi\)
0.849383 + 0.527777i \(0.176974\pi\)
\(938\) 0 0
\(939\) −7.00000 −0.228436
\(940\) 0 0
\(941\) −13.5000 + 23.3827i −0.440087 + 0.762254i −0.997695 0.0678506i \(-0.978386\pi\)
0.557608 + 0.830104i \(0.311719\pi\)
\(942\) 2.00000 3.46410i 0.0651635 0.112867i
\(943\) −18.0000 31.1769i −0.586161 1.01526i
\(944\) 3.00000 0.0976417
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 12.0000 + 20.7846i 0.389948 + 0.675409i 0.992442 0.122714i \(-0.0391598\pi\)
−0.602494 + 0.798123i \(0.705826\pi\)
\(948\) −0.500000 + 0.866025i −0.0162392 + 0.0281272i
\(949\) 25.0000 43.3013i 0.811534 1.40562i
\(950\) −5.00000 8.66025i −0.162221 0.280976i
\(951\) 24.0000 0.778253
\(952\) 0 0
\(953\) 24.0000 0.777436 0.388718 0.921357i \(-0.372918\pi\)
0.388718 + 0.921357i \(0.372918\pi\)
\(954\) −12.0000 20.7846i −0.388514 0.672927i
\(955\) 0 0
\(956\) −10.5000 + 18.1865i −0.339594 + 0.588195i
\(957\) −1.50000 2.59808i −0.0484881 0.0839839i
\(958\) 3.00000 0.0969256
\(959\) 0 0
\(960\) 0 0
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 5.00000 8.66025i 0.161206 0.279218i
\(963\) 0 0
\(964\) −5.00000 8.66025i −0.161039 0.278928i
\(965\) 0 0
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) −0.500000 0.866025i −0.0160706 0.0278351i
\(969\) 6.00000 10.3923i 0.192748 0.333849i
\(970\) 0 0
\(971\) −16.5000 28.5788i −0.529510 0.917139i −0.999408 0.0344175i \(-0.989042\pi\)
0.469897 0.882721i \(-0.344291\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) −4.00000 −0.128168
\(975\) 12.5000 + 21.6506i 0.400320 + 0.693375i
\(976\) −3.50000 + 6.06218i −0.112032 + 0.194046i
\(977\) 9.00000 15.5885i 0.287936 0.498719i −0.685381 0.728184i \(-0.740364\pi\)
0.973317 + 0.229465i \(0.0736978\pi\)
\(978\) 8.50000 + 14.7224i 0.271800 + 0.470771i
\(979\) 6.00000 0.191761
\(980\) 0 0
\(981\) −28.0000 −0.893971
\(982\) 15.0000 + 25.9808i 0.478669 + 0.829079i
\(983\) −3.00000 + 5.19615i −0.0956851 + 0.165732i −0.909894 0.414840i \(-0.863838\pi\)
0.814209 + 0.580572i \(0.197171\pi\)
\(984\) 3.00000 5.19615i 0.0956365 0.165647i
\(985\) 0 0
\(986\) −18.0000 −0.573237
\(987\) 0 0
\(988\) 10.0000 0.318142
\(989\) 12.0000 + 20.7846i 0.381578 + 0.660912i
\(990\) 0 0
\(991\) 8.00000 13.8564i 0.254128 0.440163i −0.710530 0.703667i \(-0.751545\pi\)
0.964658 + 0.263504i \(0.0848781\pi\)
\(992\) 4.00000 + 6.92820i 0.127000 + 0.219971i
\(993\) 13.0000 0.412543
\(994\) 0 0
\(995\) 0 0
\(996\) −3.00000 5.19615i −0.0950586 0.164646i
\(997\) −23.0000 + 39.8372i −0.728417 + 1.26166i 0.229135 + 0.973395i \(0.426410\pi\)
−0.957552 + 0.288261i \(0.906923\pi\)
\(998\) −4.00000 + 6.92820i −0.126618 + 0.219308i
\(999\) −5.00000 8.66025i −0.158193 0.273998i
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 1078.2.e.d.67.1 2
7.2 even 3 inner 1078.2.e.d.177.1 2
7.3 odd 6 1078.2.a.k.1.1 1
7.4 even 3 1078.2.a.i.1.1 1
7.5 odd 6 154.2.e.b.23.1 2
7.6 odd 2 154.2.e.b.67.1 yes 2
21.5 even 6 1386.2.k.n.793.1 2
21.11 odd 6 9702.2.a.l.1.1 1
21.17 even 6 9702.2.a.o.1.1 1
21.20 even 2 1386.2.k.n.991.1 2
28.3 even 6 8624.2.a.l.1.1 1
28.11 odd 6 8624.2.a.t.1.1 1
28.19 even 6 1232.2.q.c.177.1 2
28.27 even 2 1232.2.q.c.529.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.e.b.23.1 2 7.5 odd 6
154.2.e.b.67.1 yes 2 7.6 odd 2
1078.2.a.i.1.1 1 7.4 even 3
1078.2.a.k.1.1 1 7.3 odd 6
1078.2.e.d.67.1 2 1.1 even 1 trivial
1078.2.e.d.177.1 2 7.2 even 3 inner
1232.2.q.c.177.1 2 28.19 even 6
1232.2.q.c.529.1 2 28.27 even 2
1386.2.k.n.793.1 2 21.5 even 6
1386.2.k.n.991.1 2 21.20 even 2
8624.2.a.l.1.1 1 28.3 even 6
8624.2.a.t.1.1 1 28.11 odd 6
9702.2.a.l.1.1 1 21.11 odd 6
9702.2.a.o.1.1 1 21.17 even 6