Properties

Label 1470.2.i.a.361.1
Level $1470$
Weight $2$
Character 1470.361
Analytic conductor $11.738$
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] = [1470,2,Mod(361,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (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: \(11.7380090971\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.a.961.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} -4.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{46} +1.00000 q^{48} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{52} +(5.00000 - 8.66025i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} -8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-5.00000 - 8.66025i) q^{89} +1.00000 q^{90} -8.00000 q^{92} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + 2 q^{8} - q^{9} - q^{10} + 4 q^{11} - q^{12} - 4 q^{13} + 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + 2 q^{20} - 8 q^{22} + 8 q^{23} - q^{24} - q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{29} - q^{30} - q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} - q^{40} - 12 q^{41} - 8 q^{43} + 4 q^{44} - q^{45} + 8 q^{46} + 2 q^{48} + 2 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} - q^{54} - 8 q^{55} + 8 q^{57} + 2 q^{58} - 12 q^{59} - q^{60} - 14 q^{61} + 2 q^{64} + 2 q^{65} + 4 q^{66} + 12 q^{67} - 2 q^{68} - 16 q^{69} - 16 q^{71} - q^{72} - 10 q^{73} - 6 q^{74} - q^{75} + 8 q^{76} - 4 q^{78} - 16 q^{79} - q^{80} - q^{81} + 6 q^{82} - 24 q^{83} + 4 q^{85} + 4 q^{86} + 2 q^{87} + 4 q^{88} - 10 q^{89} + 2 q^{90} - 16 q^{92} - 4 q^{95} - q^{96} + 4 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.00000 + 3.46410i 0.348155 + 0.603023i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) −2.00000 + 3.46410i −0.324443 + 0.561951i
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 1.00000 + 1.73205i 0.131306 + 0.227429i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i \(-0.812942\pi\)
−0.0640184 0.997949i \(-0.520392\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 2.00000 3.46410i 0.246183 0.426401i
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −8.00000 13.8564i −0.900070 1.55897i −0.827401 0.561611i \(-0.810182\pi\)
−0.0726692 0.997356i \(-0.523152\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 1.00000 1.73205i 0.107211 0.185695i
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) 0 0
\(94\) 0 0
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) −1.00000 + 1.73205i −0.0990148 + 0.171499i
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 2.00000 + 3.46410i 0.190693 + 0.330289i
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −7.00000 + 12.1244i −0.633750 + 1.09769i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 1.00000 1.73205i 0.0877058 0.151911i
\(131\) −10.0000 17.3205i −0.873704 1.51330i −0.858137 0.513421i \(-0.828378\pi\)
−0.0155672 0.999879i \(-0.504955\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 4.00000 + 6.92820i 0.340503 + 0.589768i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) −4.00000 + 6.92820i −0.334497 + 0.579365i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.00000 + 1.73205i 0.0830455 + 0.143839i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 + 1.73205i 0.0800641 + 0.138675i
\(157\) 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i \(-0.578264\pi\)
0.961681 0.274169i \(-0.0884028\pi\)
\(158\) −8.00000 + 13.8564i −0.636446 + 1.10236i
\(159\) 5.00000 + 8.66025i 0.396526 + 0.686803i
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 2.00000 3.46410i 0.155700 0.269680i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −1.00000 1.73205i −0.0766965 0.132842i
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −6.00000 10.3923i −0.450988 0.781133i
\(178\) −5.00000 + 8.66025i −0.374766 + 0.649113i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 4.00000 + 6.92820i 0.294884 + 0.510754i
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 8.00000 + 13.8564i 0.578860 + 1.00261i 0.995610 + 0.0935936i \(0.0298354\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) 12.0000 20.7846i 0.850657 1.47338i −0.0299585 0.999551i \(-0.509538\pi\)
0.880616 0.473831i \(-0.157129\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 6.00000 + 10.3923i 0.423207 + 0.733017i
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 4.00000 6.92820i 0.278019 0.481543i
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 5.00000 + 8.66025i 0.343401 + 0.594789i
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 2.00000 3.46410i 0.134840 0.233550i
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) −3.00000 5.19615i −0.201347 0.348743i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) −2.00000 + 3.46410i −0.132745 + 0.229920i −0.924734 0.380615i \(-0.875712\pi\)
0.791989 + 0.610535i \(0.209046\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 11.0000 + 19.0526i 0.720634 + 1.24817i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.240112 + 0.970745i \(0.577184\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 7.00000 12.1244i 0.450910 0.780998i −0.547533 0.836784i \(-0.684433\pi\)
0.998443 + 0.0557856i \(0.0177663\pi\)
\(242\) −2.50000 + 4.33013i −0.160706 + 0.278351i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 32.0000 2.01182
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) −1.00000 + 1.73205i −0.0626224 + 0.108465i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.00000 + 12.1244i 0.436648 + 0.756297i 0.997429 0.0716680i \(-0.0228322\pi\)
−0.560781 + 0.827964i \(0.689499\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) 1.00000 + 1.73205i 0.0618984 + 0.107211i
\(262\) −10.0000 + 17.3205i −0.617802 + 1.07006i
\(263\) −4.00000 + 6.92820i −0.246651 + 0.427211i −0.962594 0.270947i \(-0.912663\pi\)
0.715944 + 0.698158i \(0.245997\pi\)
\(264\) 2.00000 + 3.46410i 0.123091 + 0.213201i
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 6.00000 + 10.3923i 0.366508 + 0.634811i
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 4.00000 6.92820i 0.240772 0.417029i
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) 2.00000 + 3.46410i 0.119952 + 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) 4.00000 6.92820i 0.237356 0.411113i
\(285\) −2.00000 3.46410i −0.118470 0.205196i
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 1.00000 1.73205i 0.0587220 0.101710i
\(291\) −1.00000 + 1.73205i −0.0586210 + 0.101535i
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) −3.00000 5.19615i −0.174371 0.302020i
\(297\) 2.00000 3.46410i 0.116052 0.201008i
\(298\) 5.00000 8.66025i 0.289642 0.501675i
\(299\) −8.00000 13.8564i −0.462652 0.801337i
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) −7.00000 + 12.1244i −0.400819 + 0.694239i
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 5.00000 8.66025i 0.280386 0.485643i
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) −4.00000 −0.220193
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) −3.00000 + 5.19615i −0.164399 + 0.284747i
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) −9.00000 + 15.5885i −0.488813 + 0.846649i
\(340\) −1.00000 + 1.73205i −0.0542326 + 0.0939336i
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 4.00000 + 6.92820i 0.215353 + 0.373002i
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 2.00000 3.46410i 0.107366 0.185963i −0.807337 0.590091i \(-0.799092\pi\)
0.914702 + 0.404128i \(0.132425\pi\)
\(348\) 1.00000 + 1.73205i 0.0536056 + 0.0928477i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 2.00000 + 3.46410i 0.106600 + 0.184637i
\(353\) 7.00000 12.1244i 0.372572 0.645314i −0.617388 0.786659i \(-0.711809\pi\)
0.989960 + 0.141344i \(0.0451425\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −3.00000 5.19615i −0.157676 0.273104i
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) −7.00000 12.1244i −0.365896 0.633750i
\(367\) 16.0000 27.7128i 0.835193 1.44660i −0.0586798 0.998277i \(-0.518689\pi\)
0.893873 0.448320i \(-0.147978\pi\)
\(368\) 4.00000 6.92820i 0.208514 0.361158i
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 6.00000 0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) 8.00000 13.8564i 0.409316 0.708955i
\(383\) −8.00000 13.8564i −0.408781 0.708029i 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 1.00000 + 1.73205i 0.0506370 + 0.0877058i
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 20.0000 1.00887
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) −8.00000 + 13.8564i −0.402524 + 0.697191i
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −15.0000 25.9808i −0.752828 1.30394i −0.946447 0.322860i \(-0.895356\pi\)
0.193618 0.981077i \(-0.437978\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 7.00000 + 12.1244i 0.349563 + 0.605461i 0.986172 0.165726i \(-0.0529966\pi\)
−0.636609 + 0.771187i \(0.719663\pi\)
\(402\) 6.00000 10.3923i 0.299253 0.518321i
\(403\) 0 0
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) −1.00000 1.73205i −0.0495074 0.0857493i
\(409\) 19.0000 32.9090i 0.939490 1.62724i 0.173064 0.984911i \(-0.444633\pi\)
0.766426 0.642333i \(-0.222033\pi\)
\(410\) 3.00000 5.19615i 0.148159 0.256620i
\(411\) −5.00000 8.66025i −0.246632 0.427179i
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) 8.00000 + 13.8564i 0.391293 + 0.677739i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 6.00000 + 10.3923i 0.292075 + 0.505889i
\(423\) 0 0
\(424\) 5.00000 8.66025i 0.242821 0.420579i
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) −4.00000 6.92820i −0.193122 0.334497i
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 16.0000 27.7128i 0.765384 1.32568i
\(438\) −5.00000 + 8.66025i −0.238909 + 0.413803i
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −4.00000 −0.190693
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) −3.00000 + 5.19615i −0.142374 + 0.246598i
\(445\) −5.00000 + 8.66025i −0.237023 + 0.410535i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) −9.00000 + 15.5885i −0.423324 + 0.733219i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) 4.00000 + 6.92820i 0.186501 + 0.323029i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) 11.0000 19.0526i 0.509565 0.882593i
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −8.00000 + 13.8564i −0.367840 + 0.637118i
\(474\) −8.00000 13.8564i −0.367452 0.636446i
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 0 0
\(479\) −16.0000 + 27.7128i −0.731059 + 1.26623i 0.225372 + 0.974273i \(0.427640\pi\)
−0.956431 + 0.291958i \(0.905693\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) −14.0000 −0.637683
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −1.00000 1.73205i −0.0454077 0.0786484i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) −7.00000 12.1244i −0.316875 0.548844i
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 4.00000 6.92820i 0.179969 0.311715i
\(495\) 2.00000 + 3.46410i 0.0898933 + 0.155700i
\(496\) 0 0
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 6.00000 + 10.3923i 0.268597 + 0.465223i 0.968500 0.249015i \(-0.0801067\pi\)
−0.699903 + 0.714238i \(0.746773\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) −6.00000 10.3923i −0.267793 0.463831i
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) −16.0000 27.7128i −0.711287 1.23198i
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 2.00000 0.0885615
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −2.00000 3.46410i −0.0883022 0.152944i
\(514\) 7.00000 12.1244i 0.308757 0.534782i
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 1.00000 + 1.73205i 0.0438529 + 0.0759555i
\(521\) 3.00000 5.19615i 0.131432 0.227648i −0.792797 0.609486i \(-0.791376\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) 2.00000 3.46410i 0.0870388 0.150756i
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 5.00000 + 8.66025i 0.217186 + 0.376177i
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −2.00000 3.46410i −0.0863064 0.149487i
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) −3.00000 + 5.19615i −0.128742 + 0.222988i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −5.00000 8.66025i −0.213589 0.369948i
\(549\) −7.00000 + 12.1244i −0.298753 + 0.517455i
\(550\) 2.00000 3.46410i 0.0852803 0.147710i
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) −3.00000 5.19615i −0.127343 0.220564i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 3.00000 + 5.19615i 0.126547 + 0.219186i
\(563\) −10.0000 + 17.3205i −0.421450 + 0.729972i −0.996082 0.0884397i \(-0.971812\pi\)
0.574632 + 0.818412i \(0.305145\pi\)
\(564\) 0 0
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 28.0000 1.17693
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) −14.0000 + 24.2487i −0.585882 + 1.01478i 0.408883 + 0.912587i \(0.365918\pi\)
−0.994765 + 0.102190i \(0.967415\pi\)
\(572\) −4.00000 6.92820i −0.167248 0.289683i
\(573\) −16.0000 −0.668410
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −17.0000 + 29.4449i −0.707719 + 1.22581i 0.257982 + 0.966150i \(0.416942\pi\)
−0.965701 + 0.259656i \(0.916391\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) −2.00000 −0.0830455
\(581\) 0 0
\(582\) 2.00000 0.0829027
\(583\) −20.0000 34.6410i −0.828315 1.43468i
\(584\) −5.00000 + 8.66025i −0.206901 + 0.358364i
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) −3.00000 5.19615i −0.123929 0.214651i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −6.00000 10.3923i −0.247016 0.427844i
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) −3.00000 + 5.19615i −0.123299 + 0.213561i
\(593\) 15.0000 + 25.9808i 0.615976 + 1.06690i 0.990212 + 0.139569i \(0.0445716\pi\)
−0.374236 + 0.927333i \(0.622095\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 12.0000 + 20.7846i 0.491127 + 0.850657i
\(598\) −8.00000 + 13.8564i −0.327144 + 0.566631i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) −2.50000 + 4.33013i −0.101639 + 0.176045i
\(606\) −3.00000 + 5.19615i −0.121867 + 0.211079i
\(607\) −8.00000 13.8564i −0.324710 0.562414i 0.656744 0.754114i \(-0.271933\pi\)
−0.981454 + 0.191700i \(0.938600\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 14.0000 0.566843
\(611\) 0 0
\(612\) −1.00000 + 1.73205i −0.0404226 + 0.0700140i
\(613\) −3.00000 + 5.19615i −0.121169 + 0.209871i −0.920229 0.391381i \(-0.871998\pi\)
0.799060 + 0.601251i \(0.205331\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 0 0
\(621\) 4.00000 + 6.92820i 0.160514 + 0.278019i
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) 8.00000 13.8564i 0.319489 0.553372i
\(628\) 9.00000 + 15.5885i 0.359139 + 0.622047i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −8.00000 13.8564i −0.318223 0.551178i
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) 1.00000 1.73205i 0.0397151 0.0687885i
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) −10.0000 −0.396526
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) 4.00000 + 6.92820i 0.158238 + 0.274075i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −17.0000 + 29.4449i −0.671460 + 1.16300i 0.306031 + 0.952022i \(0.400999\pi\)
−0.977490 + 0.210981i \(0.932334\pi\)
\(642\) −6.00000 10.3923i −0.236801 0.410152i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) −4.00000 6.92820i −0.157378 0.272587i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 24.0000 + 41.5692i 0.942082 + 1.63173i
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) −10.0000 + 17.3205i −0.390732 + 0.676768i
\(656\) 3.00000 + 5.19615i 0.117130 + 0.202876i
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 2.00000 + 3.46410i 0.0778499 + 0.134840i
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −6.00000 + 10.3923i −0.233197 + 0.403908i
\(663\) 2.00000 + 3.46410i 0.0776736 + 0.134535i
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) −56.0000 −2.16186
\(672\) 0 0
\(673\) −30.0000 −1.15642 −0.578208 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 13.0000 + 22.5167i 0.499631 + 0.865386i 1.00000 0.000426509i \(-0.000135762\pi\)
−0.500369 + 0.865812i \(0.666802\pi\)
\(678\) 18.0000 0.691286
\(679\) 0 0
\(680\) 2.00000 0.0766965
\(681\) −2.00000 3.46410i −0.0766402 0.132745i
\(682\) 0 0
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 10.0000 0.382080
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −10.0000 + 17.3205i −0.380970 + 0.659859i
\(690\) 4.00000 6.92820i 0.152277 0.263752i
\(691\) −18.0000 31.1769i −0.684752 1.18603i −0.973515 0.228625i \(-0.926577\pi\)
0.288762 0.957401i \(-0.406756\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) 1.00000 1.73205i 0.0379049 0.0656532i
\(697\) 6.00000 10.3923i 0.227266 0.393637i
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) −22.0000 −0.832116
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 1.00000 + 1.73205i 0.0377426 + 0.0653720i
\(703\) −12.0000 + 20.7846i −0.452589 + 0.783906i
\(704\) 2.00000 3.46410i 0.0753778 0.130558i
\(705\) 0 0
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 13.0000 + 22.5167i 0.488225 + 0.845631i 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) 4.00000 6.92820i 0.150117 0.260011i
\(711\) −8.00000 + 13.8564i −0.300023 + 0.519656i
\(712\) −5.00000 8.66025i −0.187383 0.324557i
\(713\) 0 0
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 0 0
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 8.00000 + 13.8564i 0.298350 + 0.516757i 0.975759 0.218850i \(-0.0702305\pi\)
−0.677409 + 0.735607i \(0.736897\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 7.00000 + 12.1244i 0.260333 + 0.450910i
\(724\) −3.00000 + 5.19615i −0.111494 + 0.193113i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) −7.00000 + 12.1244i −0.258727 + 0.448129i
\(733\) −23.0000 39.8372i −0.849524 1.47142i −0.881633 0.471935i \(-0.843556\pi\)
0.0321090 0.999484i \(-0.489778\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) −24.0000 41.5692i −0.884051 1.53122i
\(738\) 3.00000 5.19615i 0.110432 0.191273i
\(739\) 14.0000 24.2487i 0.514998 0.892003i −0.484850 0.874597i \(-0.661126\pi\)
0.999849 0.0174060i \(-0.00554079\pi\)
\(740\) −3.00000 5.19615i −0.110282 0.191014i
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 5.00000 8.66025i 0.183186 0.317287i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 6.00000 + 10.3923i 0.219529 + 0.380235i
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −8.00000 13.8564i −0.291924 0.505627i 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) 0 0
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) −2.00000 3.46410i −0.0728357 0.126155i
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) −16.0000 + 27.7128i −0.580763 + 1.00591i
\(760\) −2.00000 + 3.46410i −0.0725476 + 0.125656i
\(761\) −5.00000 8.66025i −0.181250 0.313934i 0.761057 0.648686i \(-0.224681\pi\)
−0.942306 + 0.334752i \(0.891348\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −1.00000 1.73205i −0.0361551 0.0626224i
\(766\) −8.00000 + 13.8564i −0.289052 + 0.500652i
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) 13.0000 22.5167i 0.467578 0.809868i −0.531736 0.846910i \(-0.678460\pi\)
0.999314 + 0.0370420i \(0.0117935\pi\)
\(774\) 2.00000 3.46410i 0.0718885 0.124515i
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) 12.0000 + 20.7846i 0.429945 + 0.744686i
\(780\) 1.00000 1.73205i 0.0358057 0.0620174i
\(781\) −16.0000 + 27.7128i −0.572525 + 0.991642i
\(782\) 8.00000 + 13.8564i 0.286079 + 0.495504i
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) −18.0000 −0.642448
\(786\) −10.0000 17.3205i −0.356688 0.617802i
\(787\) −10.0000 + 17.3205i −0.356462 + 0.617409i −0.987367 0.158450i \(-0.949350\pi\)
0.630905 + 0.775860i \(0.282684\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) −4.00000 6.92820i −0.142404 0.246651i
\(790\) 16.0000 0.569254
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 14.0000 + 24.2487i 0.497155 + 0.861097i
\(794\) −15.0000 + 25.9808i −0.532330 + 0.922023i
\(795\) 5.00000 8.66025i 0.177332 0.307148i
\(796\) 12.0000 + 20.7846i 0.425329 + 0.736691i
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) −5.00000 + 8.66025i −0.176666 + 0.305995i
\(802\) 7.00000 12.1244i 0.247179 0.428126i
\(803\) 20.0000 + 34.6410i 0.705785 + 1.22245i
\(804\) −12.0000 −0.423207
\(805\) 0 0
\(806\) 0 0
\(807\) 9.00000 + 15.5885i 0.316815 + 0.548740i
\(808\) −3.00000 + 5.19615i −0.105540 + 0.182800i
\(809\) 11.0000 19.0526i 0.386739 0.669852i −0.605269 0.796021i \(-0.706935\pi\)
0.992009 + 0.126168i \(0.0402680\pi\)
\(810\) −0.500000 0.866025i −0.0175682 0.0304290i
\(811\) 28.0000 0.983213 0.491606 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 12.0000 + 20.7846i 0.420600 + 0.728500i
\(815\) −10.0000 + 17.3205i −0.350285 + 0.606711i
\(816\) −1.00000 + 1.73205i −0.0350070 + 0.0606339i
\(817\) 8.00000 + 13.8564i 0.279885 + 0.484774i
\(818\) −38.0000 −1.32864
\(819\) 0 0
\(820\) −6.00000 −0.209529
\(821\) −11.0000 19.0526i −0.383903 0.664939i 0.607714 0.794156i \(-0.292087\pi\)
−0.991616 + 0.129217i \(0.958754\pi\)
\(822\) −5.00000 + 8.66025i −0.174395 + 0.302061i
\(823\) 12.0000 20.7846i 0.418294 0.724506i −0.577474 0.816409i \(-0.695962\pi\)
0.995768 + 0.0919029i \(0.0292950\pi\)
\(824\) 4.00000 + 6.92820i 0.139347 + 0.241355i
\(825\) −4.00000 −0.139262
\(826\) 0 0
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) 4.00000 + 6.92820i 0.139010 + 0.240772i
\(829\) 9.00000 15.5885i 0.312583 0.541409i −0.666338 0.745650i \(-0.732139\pi\)
0.978921 + 0.204240i \(0.0654725\pi\)
\(830\) 6.00000 10.3923i 0.208263 0.360722i
\(831\) −11.0000 19.0526i −0.381586 0.660926i
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 4.00000 + 6.92820i 0.138426 + 0.239760i
\(836\) 8.00000 13.8564i 0.276686 0.479234i
\(837\) 0 0
\(838\) −10.0000 17.3205i −0.345444 0.598327i
\(839\) 8.00000 0.276191 0.138095 0.990419i \(-0.455902\pi\)
0.138095 + 0.990419i \(0.455902\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 13.0000 + 22.5167i 0.448010 + 0.775975i
\(843\) 3.00000 5.19615i 0.103325 0.178965i
\(844\) 6.00000 10.3923i 0.206529 0.357718i
\(845\) 4.50000 + 7.79423i 0.154805 + 0.268130i
\(846\) 0 0
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −14.0000 24.2487i −0.480479 0.832214i
\(850\) −1.00000 + 1.73205i −0.0342997 + 0.0594089i
\(851\) 24.0000 41.5692i 0.822709 1.42497i
\(852\) 4.00000 + 6.92820i 0.137038 + 0.237356i
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) 4.00000 0.136797
\(856\) −6.00000 10.3923i −0.205076 0.355202i
\(857\) 11.0000 19.0526i 0.375753 0.650823i −0.614687 0.788771i \(-0.710717\pi\)
0.990439 + 0.137948i \(0.0440508\pi\)
\(858\) −4.00000 + 6.92820i −0.136558 + 0.236525i
\(859\) 10.0000 + 17.3205i 0.341196 + 0.590968i 0.984655 0.174512i \(-0.0558348\pi\)
−0.643459 + 0.765480i \(0.722501\pi\)
\(860\) −4.00000 −0.136399
\(861\) 0 0
\(862\) 0 0
\(863\) −16.0000 27.7128i −0.544646 0.943355i −0.998629 0.0523446i \(-0.983331\pi\)
0.453983 0.891010i \(-0.350003\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 9.00000 15.5885i 0.306009 0.530023i
\(866\) 7.00000 + 12.1244i 0.237870 + 0.412002i
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) −64.0000 −2.17105
\(870\) 1.00000 + 1.73205i 0.0339032 + 0.0587220i
\(871\) −12.0000 + 20.7846i −0.406604 + 0.704260i
\(872\) −7.00000 + 12.1244i −0.237050 + 0.410582i
\(873\) −1.00000 1.73205i −0.0338449 0.0586210i
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) 10.0000 0.337869
\(877\) −7.00000 12.1244i −0.236373 0.409410i 0.723298 0.690536i \(-0.242625\pi\)
−0.959671 + 0.281126i \(0.909292\pi\)
\(878\) 4.00000 6.92820i 0.134993 0.233816i
\(879\) −3.00000 + 5.19615i −0.101187 + 0.175262i
\(880\) 2.00000 + 3.46410i 0.0674200 + 0.116775i
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 0 0
\(883\) −28.0000 −0.942275 −0.471138 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) 2.00000 + 3.46410i 0.0672673 + 0.116510i
\(885\) −6.00000 + 10.3923i −0.201688 + 0.349334i
\(886\) 18.0000 31.1769i 0.604722 1.04741i
\(887\) −4.00000 6.92820i −0.134307 0.232626i 0.791026 0.611783i \(-0.209547\pi\)
−0.925332 + 0.379157i \(0.876214\pi\)
\(888\) 6.00000 0.201347
\(889\) 0 0
\(890\) 10.0000 0.335201
\(891\) 2.00000 + 3.46410i 0.0670025 + 0.116052i
\(892\) 8.00000 13.8564i 0.267860 0.463947i
\(893\) 0 0
\(894\) 5.00000 + 8.66025i 0.167225 + 0.289642i
\(895\) 4.00000 0.133705
\(896\) 0 0
\(897\) 16.0000 0.534224
\(898\) −1.00000 1.73205i −0.0333704 0.0577993i
\(899\) 0 0
\(900\) −0.500000 + 0.866025i −0.0166667 + 0.0288675i
\(901\) 10.0000 + 17.3205i 0.333148 + 0.577030i
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) −3.00000 5.19615i −0.0997234 0.172726i
\(906\) 4.00000 6.92820i 0.132891 0.230174i
\(907\) −14.0000 + 24.2487i −0.464862 + 0.805165i −0.999195 0.0401089i \(-0.987230\pi\)
0.534333 + 0.845274i \(0.320563\pi\)
\(908\) −2.00000 3.46410i −0.0663723 0.114960i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 32.0000 1.06021 0.530104 0.847933i \(-0.322153\pi\)
0.530104 + 0.847933i \(0.322153\pi\)
\(912\) −2.00000 3.46410i −0.0662266 0.114708i
\(913\) −24.0000 + 41.5692i −0.794284 + 1.37574i
\(914\) −5.00000 + 8.66025i −0.165385 + 0.286456i
\(915\) −7.00000 12.1244i −0.231413 0.400819i
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) 4.00000 + 6.92820i 0.131948 + 0.228540i 0.924427 0.381358i \(-0.124544\pi\)
−0.792480 + 0.609898i \(0.791210\pi\)
\(920\) 4.00000 6.92820i 0.131876 0.228416i
\(921\) −10.0000 + 17.3205i −0.329511 + 0.570730i
\(922\) −7.00000 12.1244i −0.230533 0.399294i
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 0 0
\(927\) 4.00000 6.92820i 0.131377 0.227552i
\(928\) 1.00000 1.73205i 0.0328266 0.0568574i
\(929\) 7.00000 + 12.1244i 0.229663 + 0.397787i 0.957708 0.287742i \(-0.0929044\pi\)
−0.728046 + 0.685529i \(0.759571\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −22.0000 −0.720634
\(933\) 4.00000 + 6.92820i 0.130954 + 0.226819i
\(934\) 6.00000 10.3923i 0.196326 0.340047i
\(935\) 4.00000 6.92820i 0.130814 0.226576i
\(936\) 1.00000 + 1.73205i 0.0326860 + 0.0566139i
\(937\) 10.0000 0.326686 0.163343 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) 0 0
\(939\) −6.00000 −0.195803
\(940\) 0 0
\(941\) 9.00000 15.5885i 0.293392 0.508169i −0.681218 0.732081i \(-0.738549\pi\)
0.974609 + 0.223912i \(0.0718827\pi\)
\(942\) 9.00000 15.5885i 0.293236 0.507899i
\(943\) −24.0000 41.5692i −0.781548 1.35368i
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) −26.0000 45.0333i −0.844886 1.46339i −0.885720 0.464220i \(-0.846335\pi\)
0.0408333 0.999166i \(-0.486999\pi\)
\(948\) −8.00000 + 13.8564i −0.259828 + 0.450035i
\(949\) 10.0000 17.3205i 0.324614 0.562247i
\(950\) −2.00000 3.46410i −0.0648886 0.112390i
\(951\) −2.00000 −0.0648544
\(952\) 0 0
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) 5.00000 + 8.66025i 0.161881 + 0.280386i
\(955\) 8.00000 13.8564i 0.258874 0.448383i
\(956\) 0 0
\(957\) −4.00000 6.92820i −0.129302 0.223957i
\(958\) 32.0000 1.03387
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) 15.5000 + 26.8468i 0.500000 + 0.866025i
\(962\) 6.00000 10.3923i 0.193448 0.335061i
\(963\) −6.00000 + 10.3923i −0.193347 + 0.334887i
\(964\) 7.00000 + 12.1244i 0.225455 + 0.390499i
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) −2.50000 4.33013i −0.0803530 0.139176i
\(969\) −4.00000 + 6.92820i −0.128499 + 0.222566i
\(970\) −1.00000 + 1.73205i −0.0321081 + 0.0556128i
\(971\) −14.0000 24.2487i −0.449281 0.778178i 0.549058 0.835784i \(-0.314987\pi\)
−0.998339 + 0.0576061i \(0.981653\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −8.00000 −0.256337
\(975\) 1.00000 + 1.73205i 0.0320256 + 0.0554700i
\(976\) −7.00000 + 12.1244i −0.224065 + 0.388091i
\(977\) −9.00000 + 15.5885i −0.287936 + 0.498719i −0.973317 0.229465i \(-0.926302\pi\)
0.685381 + 0.728184i \(0.259636\pi\)
\(978\) −10.0000 17.3205i −0.319765 0.553849i
\(979\) −40.0000 −1.27841
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) 18.0000 + 31.1769i 0.574403 + 0.994895i
\(983\) 12.0000 20.7846i 0.382741 0.662926i −0.608712 0.793391i \(-0.708314\pi\)
0.991453 + 0.130465i \(0.0416470\pi\)
\(984\) 3.00000 5.19615i 0.0956365 0.165647i
\(985\) −3.00000 5.19615i −0.0955879 0.165563i
\(986\) −4.00000 −0.127386
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) −16.0000 27.7128i −0.508770 0.881216i
\(990\) 2.00000 3.46410i 0.0635642 0.110096i
\(991\) 16.0000 27.7128i 0.508257 0.880327i −0.491698 0.870766i \(-0.663623\pi\)
0.999954 0.00956046i \(-0.00304324\pi\)
\(992\) 0 0
\(993\) 12.0000 0.380808
\(994\) 0 0
\(995\) −24.0000 −0.760851
\(996\) 6.00000 + 10.3923i 0.190117 + 0.329293i
\(997\) −11.0000 + 19.0526i −0.348373 + 0.603401i −0.985961 0.166978i \(-0.946599\pi\)
0.637587 + 0.770378i \(0.279933\pi\)
\(998\) 6.00000 10.3923i 0.189927 0.328963i
\(999\) −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 1470.2.i.a.361.1 2
7.2 even 3 inner 1470.2.i.a.961.1 2
7.3 odd 6 1470.2.a.j.1.1 1
7.4 even 3 210.2.a.e.1.1 1
7.5 odd 6 1470.2.i.j.961.1 2
7.6 odd 2 1470.2.i.j.361.1 2
21.11 odd 6 630.2.a.a.1.1 1
21.17 even 6 4410.2.a.t.1.1 1
28.11 odd 6 1680.2.a.j.1.1 1
35.4 even 6 1050.2.a.c.1.1 1
35.18 odd 12 1050.2.g.g.799.1 2
35.24 odd 6 7350.2.a.w.1.1 1
35.32 odd 12 1050.2.g.g.799.2 2
56.11 odd 6 6720.2.a.bq.1.1 1
56.53 even 6 6720.2.a.j.1.1 1
84.11 even 6 5040.2.a.k.1.1 1
105.32 even 12 3150.2.g.q.2899.1 2
105.53 even 12 3150.2.g.q.2899.2 2
105.74 odd 6 3150.2.a.bp.1.1 1
140.39 odd 6 8400.2.a.ce.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.a.e.1.1 1 7.4 even 3
630.2.a.a.1.1 1 21.11 odd 6
1050.2.a.c.1.1 1 35.4 even 6
1050.2.g.g.799.1 2 35.18 odd 12
1050.2.g.g.799.2 2 35.32 odd 12
1470.2.a.j.1.1 1 7.3 odd 6
1470.2.i.a.361.1 2 1.1 even 1 trivial
1470.2.i.a.961.1 2 7.2 even 3 inner
1470.2.i.j.361.1 2 7.6 odd 2
1470.2.i.j.961.1 2 7.5 odd 6
1680.2.a.j.1.1 1 28.11 odd 6
3150.2.a.bp.1.1 1 105.74 odd 6
3150.2.g.q.2899.1 2 105.32 even 12
3150.2.g.q.2899.2 2 105.53 even 12
4410.2.a.t.1.1 1 21.17 even 6
5040.2.a.k.1.1 1 84.11 even 6
6720.2.a.j.1.1 1 56.53 even 6
6720.2.a.bq.1.1 1 56.11 odd 6
7350.2.a.w.1.1 1 35.24 odd 6
8400.2.a.ce.1.1 1 140.39 odd 6