Properties

Label 1274.2.e.d.471.1
Level $1274$
Weight $2$
Character 1274.471
Analytic conductor $10.173$
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] = [1274,2,Mod(165,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1274.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.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: \(10.1729412175\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1274.471
Dual form 1274.2.e.d.165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(2.50000 + 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +1.00000 q^{16} +6.00000 q^{17} +(-1.00000 - 1.73205i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +3.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 - 2.59808i) q^{26} -5.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} +(1.50000 + 2.59808i) q^{30} +(5.00000 + 8.66025i) q^{31} -1.00000 q^{32} -6.00000 q^{34} +(1.00000 + 1.73205i) q^{36} +8.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(-3.50000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-4.00000 + 6.92820i) q^{43} -6.00000 q^{45} -3.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(2.50000 + 2.59808i) q^{52} +(-6.00000 - 10.3923i) q^{53} +5.00000 q^{54} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +3.00000 q^{59} +(-1.50000 - 2.59808i) q^{60} +(-5.50000 - 9.52628i) q^{61} +(-5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(-10.5000 + 2.59808i) q^{65} +(-1.00000 + 1.73205i) q^{67} +6.00000 q^{68} +(-1.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(-1.00000 - 1.73205i) q^{73} -8.00000 q^{74} +4.00000 q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 0.866025i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.00000 + 15.5885i) q^{85} +(4.00000 - 6.92820i) q^{86} +6.00000 q^{87} -6.00000 q^{89} +6.00000 q^{90} +3.00000 q^{92} -10.0000 q^{93} +(3.00000 - 5.19615i) q^{94} -12.0000 q^{95} +(0.500000 - 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} + q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} + q^{6} - 2 q^{8} + 2 q^{9} + 3 q^{10} - q^{12} + 5 q^{13} - 3 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + 4 q^{19} - 3 q^{20} + 6 q^{23} + q^{24} - 4 q^{25} - 5 q^{26} - 10 q^{27} - 6 q^{29} + 3 q^{30} + 10 q^{31} - 2 q^{32} - 12 q^{34} + 2 q^{36} + 16 q^{37} - 4 q^{38} - 7 q^{39} + 3 q^{40} - 8 q^{43} - 12 q^{45} - 6 q^{46} - 6 q^{47} - q^{48} + 4 q^{50} - 6 q^{51} + 5 q^{52} - 12 q^{53} + 10 q^{54} - 8 q^{57} + 6 q^{58} + 6 q^{59} - 3 q^{60} - 11 q^{61} - 10 q^{62} + 2 q^{64} - 21 q^{65} - 2 q^{67} + 12 q^{68} - 3 q^{69} + 3 q^{71} - 2 q^{72} - 2 q^{73} - 16 q^{74} + 8 q^{75} + 4 q^{76} + 7 q^{78} + 4 q^{79} - 3 q^{80} - q^{81} - 18 q^{85} + 8 q^{86} + 12 q^{87} - 12 q^{89} + 12 q^{90} + 6 q^{92} - 20 q^{93} + 6 q^{94} - 24 q^{95} + q^{96} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) 0 0
\(15\) −1.50000 2.59808i −0.387298 0.670820i
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) −3.50000 + 0.866025i −0.560449 + 0.138675i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) −3.00000 −0.442326
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 0 0
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 2.50000 + 2.59808i 0.346688 + 0.360288i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 3.00000 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) −5.00000 8.66025i −0.635001 1.09985i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −10.5000 + 2.59808i −1.30236 + 0.322252i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 6.00000 0.727607
\(69\) −1.50000 + 2.59808i −0.180579 + 0.312772i
\(70\) 0 0
\(71\) 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i \(-0.776365\pi\)
0.941201 + 0.337846i \(0.109698\pi\)
\(72\) −1.00000 1.73205i −0.117851 0.204124i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −8.00000 −0.929981
\(75\) 4.00000 0.461880
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 0 0
\(78\) 3.50000 0.866025i 0.396297 0.0980581i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −9.00000 + 15.5885i −0.976187 + 1.69081i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 3.00000 0.312772
\(93\) −10.0000 −1.03695
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) −12.0000 −1.23117
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 0 0
\(106\) 6.00000 + 10.3923i 0.582772 + 1.00939i
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −5.00000 −0.481125
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) −4.00000 + 6.92820i −0.379663 + 0.657596i
\(112\) 0 0
\(113\) 9.00000 15.5885i 0.846649 1.46644i −0.0375328 0.999295i \(-0.511950\pi\)
0.884182 0.467143i \(-0.154717\pi\)
\(114\) 4.00000 0.374634
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) −2.00000 + 6.92820i −0.184900 + 0.640513i
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 5.50000 + 9.52628i 0.497947 + 0.862469i
\(123\) 0 0
\(124\) 5.00000 + 8.66025i 0.449013 + 0.777714i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −5.50000 9.52628i −0.488046 0.845321i 0.511859 0.859069i \(-0.328957\pi\)
−0.999905 + 0.0137486i \(0.995624\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 10.5000 2.59808i 0.920911 0.227866i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) 7.50000 12.9904i 0.645497 1.11803i
\(136\) −6.00000 −0.514496
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 1.50000 2.59808i 0.127688 0.221163i
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) 0 0
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 18.0000 1.49482
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) −4.00000 −0.326599
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 6.00000 + 10.3923i 0.485071 + 0.840168i
\(154\) 0 0
\(155\) −30.0000 −2.40966
\(156\) −3.50000 + 0.866025i −0.280224 + 0.0693375i
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 12.0000 0.951662
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) 0 0
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 9.00000 15.5885i 0.690268 1.19558i
\(171\) −4.00000 + 6.92820i −0.305888 + 0.529813i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) 0 0
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 6.00000 0.449719
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) −6.00000 −0.447214
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 11.0000 0.813143
\(184\) −3.00000 −0.221163
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 3.00000 10.3923i 0.214834 0.744208i
\(196\) 0 0
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) 0 0
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) −1.00000 1.73205i −0.0705346 0.122169i
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 3.00000 + 5.19615i 0.208514 + 0.361158i
\(208\) 2.50000 + 2.59808i 0.173344 + 0.180144i
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 1.50000 + 2.59808i 0.102778 + 0.178017i
\(214\) 18.0000 1.23045
\(215\) −12.0000 20.7846i −0.818393 1.41750i
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) −8.00000 13.8564i −0.541828 0.938474i
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 15.0000 + 15.5885i 1.00901 + 1.04859i
\(222\) 4.00000 6.92820i 0.268462 0.464991i
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 4.00000 6.92820i 0.266667 0.461880i
\(226\) −9.00000 + 15.5885i −0.598671 + 1.03693i
\(227\) −15.0000 −0.995585 −0.497792 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) −4.00000 −0.264906
\(229\) 11.0000 19.0526i 0.726900 1.25903i −0.231287 0.972886i \(-0.574293\pi\)
0.958187 0.286143i \(-0.0923732\pi\)
\(230\) 4.50000 7.79423i 0.296721 0.513936i
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 2.00000 6.92820i 0.130744 0.452911i
\(235\) −9.00000 15.5885i −0.587095 1.01688i
\(236\) 3.00000 0.195283
\(237\) 2.00000 + 3.46410i 0.129914 + 0.225018i
\(238\) 0 0
\(239\) 21.0000 1.35838 0.679189 0.733964i \(-0.262332\pi\)
0.679189 + 0.733964i \(0.262332\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) −28.0000 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) −5.50000 9.52628i −0.353553 0.612372i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −5.50000 9.52628i −0.352101 0.609858i
\(245\) 0 0
\(246\) 0 0
\(247\) −4.00000 + 13.8564i −0.254514 + 0.881662i
\(248\) −5.00000 8.66025i −0.317500 0.549927i
\(249\) 0 0
\(250\) 3.00000 0.189737
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 5.50000 + 9.52628i 0.345101 + 0.597732i
\(255\) −9.00000 15.5885i −0.563602 0.976187i
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 4.00000 + 6.92820i 0.249029 + 0.431331i
\(259\) 0 0
\(260\) −10.5000 + 2.59808i −0.651182 + 0.161126i
\(261\) 6.00000 10.3923i 0.371391 0.643268i
\(262\) 7.50000 12.9904i 0.463352 0.802548i
\(263\) 13.5000 23.3827i 0.832446 1.44184i −0.0636476 0.997972i \(-0.520273\pi\)
0.896093 0.443866i \(-0.146393\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) 0 0
\(267\) 3.00000 5.19615i 0.183597 0.317999i
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) −7.50000 + 12.9904i −0.456435 + 0.790569i
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −8.00000 + 13.8564i −0.479808 + 0.831052i
\(279\) −10.0000 + 17.3205i −0.598684 + 1.03695i
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) 15.5000 26.8468i 0.921379 1.59588i 0.124096 0.992270i \(-0.460397\pi\)
0.797283 0.603606i \(-0.206270\pi\)
\(284\) 1.50000 2.59808i 0.0890086 0.154167i
\(285\) 6.00000 10.3923i 0.355409 0.615587i
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 1.73205i −0.0589256 0.102062i
\(289\) 19.0000 1.11765
\(290\) −18.0000 −1.05700
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i \(-0.777256\pi\)
0.940252 + 0.340480i \(0.110589\pi\)
\(294\) 0 0
\(295\) −4.50000 + 7.79423i −0.262000 + 0.453798i
\(296\) −8.00000 −0.464991
\(297\) 0 0
\(298\) 0 0
\(299\) 7.50000 + 7.79423i 0.433736 + 0.450752i
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) −0.500000 0.866025i −0.0287718 0.0498342i
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 33.0000 1.88957
\(306\) −6.00000 10.3923i −0.342997 0.594089i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) −7.00000 12.1244i −0.398216 0.689730i
\(310\) 30.0000 1.70389
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 3.50000 0.866025i 0.198148 0.0490290i
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 1.00000 + 1.73205i 0.0564333 + 0.0977453i
\(315\) 0 0
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 9.00000 15.5885i 0.502331 0.870063i
\(322\) 0 0
\(323\) 12.0000 + 20.7846i 0.667698 + 1.15649i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 4.00000 13.8564i 0.221880 0.768615i
\(326\) 10.0000 + 17.3205i 0.553849 + 0.959294i
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 0 0
\(333\) 8.00000 + 13.8564i 0.438397 + 0.759326i
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) −3.00000 5.19615i −0.163908 0.283896i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) 9.00000 + 15.5885i 0.488813 + 0.846649i
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) 0 0
\(342\) 4.00000 6.92820i 0.216295 0.374634i
\(343\) 0 0
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) −4.50000 7.79423i −0.242272 0.419627i
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 6.00000 0.321634
\(349\) −14.5000 25.1147i −0.776167 1.34436i −0.934136 0.356917i \(-0.883828\pi\)
0.157969 0.987444i \(-0.449505\pi\)
\(350\) 0 0
\(351\) −12.5000 12.9904i −0.667201 0.693375i
\(352\) 0 0
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 1.50000 2.59808i 0.0797241 0.138086i
\(355\) 4.50000 + 7.79423i 0.238835 + 0.413675i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) 4.50000 7.79423i 0.237501 0.411364i −0.722496 0.691375i \(-0.757005\pi\)
0.959997 + 0.280012i \(0.0903384\pi\)
\(360\) 6.00000 0.316228
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −5.00000 −0.262794
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) −11.0000 −0.574979
\(367\) 5.00000 8.66025i 0.260998 0.452062i −0.705509 0.708700i \(-0.749282\pi\)
0.966507 + 0.256639i \(0.0826151\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 12.0000 20.7846i 0.623850 1.08054i
\(371\) 0 0
\(372\) −10.0000 −0.518476
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) 0 0
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 6.00000 20.7846i 0.309016 1.07046i
\(378\) 0 0
\(379\) 14.0000 + 24.2487i 0.719132 + 1.24557i 0.961344 + 0.275349i \(0.0887935\pi\)
−0.242213 + 0.970223i \(0.577873\pi\)
\(380\) −12.0000 −0.615587
\(381\) 11.0000 0.563547
\(382\) −12.0000 20.7846i −0.613973 1.06343i
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) 2.50000 4.33013i 0.127247 0.220398i
\(387\) −16.0000 −0.813326
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) −3.00000 + 10.3923i −0.151911 + 0.526235i
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) −7.50000 12.9904i −0.378325 0.655278i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 6.00000 + 10.3923i 0.301893 + 0.522894i
\(396\) 0 0
\(397\) 3.50000 + 6.06218i 0.175660 + 0.304252i 0.940389 0.340099i \(-0.110461\pi\)
−0.764730 + 0.644351i \(0.777127\pi\)
\(398\) −14.0000 −0.701757
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 1.00000 + 1.73205i 0.0498755 + 0.0863868i
\(403\) −10.0000 + 34.6410i −0.498135 + 1.72559i
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) −1.50000 2.59808i −0.0745356 0.129099i
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000 5.19615i 0.148522 0.257248i
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) −1.50000 + 2.59808i −0.0739895 + 0.128154i
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) 0 0
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) 8.00000 + 13.8564i 0.391762 + 0.678551i
\(418\) 0 0
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) −12.0000 −0.583460
\(424\) 6.00000 + 10.3923i 0.291386 + 0.504695i
\(425\) −12.0000 20.7846i −0.582086 1.00820i
\(426\) −1.50000 2.59808i −0.0726752 0.125877i
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 12.0000 + 20.7846i 0.578691 + 1.00232i
\(431\) 16.5000 28.5788i 0.794777 1.37659i −0.128204 0.991748i \(-0.540921\pi\)
0.922981 0.384846i \(-0.125746\pi\)
\(432\) −5.00000 −0.240563
\(433\) 2.00000 3.46410i 0.0961139 0.166474i −0.813959 0.580922i \(-0.802692\pi\)
0.910073 + 0.414448i \(0.136025\pi\)
\(434\) 0 0
\(435\) −9.00000 + 15.5885i −0.431517 + 0.747409i
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) −2.00000 −0.0955637
\(439\) 14.0000 0.668184 0.334092 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −15.0000 15.5885i −0.713477 0.741467i
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) −4.00000 + 6.92820i −0.189832 + 0.328798i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) 0 0
\(449\) −4.50000 + 7.79423i −0.212368 + 0.367832i −0.952455 0.304679i \(-0.901451\pi\)
0.740087 + 0.672511i \(0.234784\pi\)
\(450\) −4.00000 + 6.92820i −0.188562 + 0.326599i
\(451\) 0 0
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) −1.00000 −0.0469841
\(454\) 15.0000 0.703985
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 29.0000 1.35656 0.678281 0.734802i \(-0.262725\pi\)
0.678281 + 0.734802i \(0.262725\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) −30.0000 −1.40028
\(460\) −4.50000 + 7.79423i −0.209814 + 0.363408i
\(461\) −10.5000 + 18.1865i −0.489034 + 0.847031i −0.999920 0.0126168i \(-0.995984\pi\)
0.510887 + 0.859648i \(0.329317\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 15.0000 25.9808i 0.695608 1.20483i
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) −2.00000 + 6.92820i −0.0924500 + 0.320256i
\(469\) 0 0
\(470\) 9.00000 + 15.5885i 0.415139 + 0.719042i
\(471\) 2.00000 0.0921551
\(472\) −3.00000 −0.138086
\(473\) 0 0
\(474\) −2.00000 3.46410i −0.0918630 0.159111i
\(475\) 8.00000 13.8564i 0.367065 0.635776i
\(476\) 0 0
\(477\) 12.0000 20.7846i 0.549442 0.951662i
\(478\) −21.0000 −0.960518
\(479\) −15.0000 + 25.9808i −0.685367 + 1.18709i 0.287954 + 0.957644i \(0.407025\pi\)
−0.973321 + 0.229447i \(0.926308\pi\)
\(480\) 1.50000 + 2.59808i 0.0684653 + 0.118585i
\(481\) 20.0000 + 20.7846i 0.911922 + 0.947697i
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) −13.0000 −0.589086 −0.294543 0.955638i \(-0.595167\pi\)
−0.294543 + 0.955638i \(0.595167\pi\)
\(488\) 5.50000 + 9.52628i 0.248973 + 0.431234i
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 0 0
\(493\) −18.0000 31.1769i −0.810679 1.40414i
\(494\) 4.00000 13.8564i 0.179969 0.623429i
\(495\) 0 0
\(496\) 5.00000 + 8.66025i 0.224507 + 0.388857i
\(497\) 0 0
\(498\) 0 0
\(499\) 11.0000 19.0526i 0.492428 0.852910i −0.507534 0.861632i \(-0.669443\pi\)
0.999962 + 0.00872186i \(0.00277629\pi\)
\(500\) −3.00000 −0.134164
\(501\) −12.0000 −0.536120
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) −21.0000 + 36.3731i −0.936344 + 1.62179i −0.164124 + 0.986440i \(0.552480\pi\)
−0.772220 + 0.635355i \(0.780854\pi\)
\(504\) 0 0
\(505\) 9.00000 + 15.5885i 0.400495 + 0.693677i
\(506\) 0 0
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) −5.50000 9.52628i −0.244023 0.422660i
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −10.0000 17.3205i −0.441511 0.764719i
\(514\) 6.00000 0.264649
\(515\) −21.0000 36.3731i −0.925371 1.60279i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 0 0
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) −6.00000 + 10.3923i −0.262613 + 0.454859i
\(523\) −1.00000 −0.0437269 −0.0218635 0.999761i \(-0.506960\pi\)
−0.0218635 + 0.999761i \(0.506960\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) −13.5000 + 23.3827i −0.588628 + 1.01953i
\(527\) 30.0000 + 51.9615i 1.30682 + 2.26348i
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −36.0000 −1.56374
\(531\) 3.00000 + 5.19615i 0.130189 + 0.225494i
\(532\) 0 0
\(533\) 0 0
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 27.0000 46.7654i 1.16731 2.02184i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) −9.00000 −0.388018
\(539\) 0 0
\(540\) 7.50000 12.9904i 0.322749 0.559017i
\(541\) −19.0000 + 32.9090i −0.816874 + 1.41487i 0.0911008 + 0.995842i \(0.470961\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) −2.00000 −0.0859074
\(543\) −2.50000 + 4.33013i −0.107285 + 0.185824i
\(544\) −6.00000 −0.257248
\(545\) −48.0000 −2.05609
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 3.00000 0.128154
\(549\) 11.0000 19.0526i 0.469469 0.813143i
\(550\) 0 0
\(551\) 12.0000 20.7846i 0.511217 0.885454i
\(552\) 1.50000 2.59808i 0.0638442 0.110581i
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) −12.0000 20.7846i −0.509372 0.882258i
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i \(0.336450\pi\)
−0.999952 + 0.00979220i \(0.996883\pi\)
\(558\) 10.0000 17.3205i 0.423334 0.733236i
\(559\) −28.0000 + 6.92820i −1.18427 + 0.293032i
\(560\) 0 0
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 27.0000 + 46.7654i 1.13590 + 1.96743i
\(566\) −15.5000 + 26.8468i −0.651514 + 1.12845i
\(567\) 0 0
\(568\) −1.50000 + 2.59808i −0.0629386 + 0.109013i
\(569\) −45.0000 −1.88650 −0.943249 0.332086i \(-0.892248\pi\)
−0.943249 + 0.332086i \(0.892248\pi\)
\(570\) −6.00000 + 10.3923i −0.251312 + 0.435286i
\(571\) −4.00000 6.92820i −0.167395 0.289936i 0.770108 0.637913i \(-0.220202\pi\)
−0.937503 + 0.347977i \(0.886869\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 0 0
\(575\) −6.00000 10.3923i −0.250217 0.433389i
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) 14.0000 + 24.2487i 0.582828 + 1.00949i 0.995142 + 0.0984456i \(0.0313871\pi\)
−0.412315 + 0.911041i \(0.635280\pi\)
\(578\) −19.0000 −0.790296
\(579\) −2.50000 4.33013i −0.103896 0.179954i
\(580\) 18.0000 0.747409
\(581\) 0 0
\(582\) 1.00000 + 1.73205i 0.0414513 + 0.0717958i
\(583\) 0 0
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) −15.0000 15.5885i −0.620174 0.644503i
\(586\) −3.00000 + 5.19615i −0.123929 + 0.214651i
\(587\) −1.50000 2.59808i −0.0619116 0.107234i 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 0 0
\(589\) −20.0000 + 34.6410i −0.824086 + 1.42736i
\(590\) 4.50000 7.79423i 0.185262 0.320883i
\(591\) 12.0000 0.493614
\(592\) 8.00000 0.328798
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.00000 + 12.1244i −0.286491 + 0.496217i
\(598\) −7.50000 7.79423i −0.306698 0.318730i
\(599\) −1.50000 2.59808i −0.0612883 0.106155i 0.833753 0.552137i \(-0.186188\pi\)
−0.895042 + 0.445983i \(0.852854\pi\)
\(600\) −4.00000 −0.163299
\(601\) −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i \(-0.988753\pi\)
0.469095 0.883148i \(-0.344580\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) −33.0000 −1.34164
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) 5.00000 + 8.66025i 0.202944 + 0.351509i 0.949476 0.313841i \(-0.101616\pi\)
−0.746532 + 0.665350i \(0.768282\pi\)
\(608\) −2.00000 3.46410i −0.0811107 0.140488i
\(609\) 0 0
\(610\) −33.0000 −1.33613
\(611\) −21.0000 + 5.19615i −0.849569 + 0.210214i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 13.0000 0.524637
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 7.00000 + 12.1244i 0.281581 + 0.487713i
\(619\) 18.5000 + 32.0429i 0.743578 + 1.28791i 0.950856 + 0.309633i \(0.100206\pi\)
−0.207279 + 0.978282i \(0.566461\pi\)
\(620\) −30.0000 −1.20483
\(621\) −15.0000 −0.601929
\(622\) −3.00000 5.19615i −0.120289 0.208347i
\(623\) 0 0
\(624\) −3.50000 + 0.866025i −0.140112 + 0.0346688i
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 4.00000 6.92820i 0.159872 0.276907i
\(627\) 0 0
\(628\) −1.00000 1.73205i −0.0399043 0.0691164i
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) −2.50000 + 4.33013i −0.0995234 + 0.172380i −0.911487 0.411328i \(-0.865065\pi\)
0.811964 + 0.583707i \(0.198398\pi\)
\(632\) −2.00000 + 3.46410i −0.0795557 + 0.137795i
\(633\) −4.00000 −0.158986
\(634\) −6.00000 + 10.3923i −0.238290 + 0.412731i
\(635\) 33.0000 1.30957
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) −9.00000 + 15.5885i −0.355202 + 0.615227i
\(643\) −20.5000 + 35.5070i −0.808441 + 1.40026i 0.105502 + 0.994419i \(0.466355\pi\)
−0.913943 + 0.405842i \(0.866978\pi\)
\(644\) 0 0
\(645\) 24.0000 0.944999
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 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
\(649\) 0 0
\(650\) −4.00000 + 13.8564i −0.156893 + 0.543493i
\(651\) 0 0
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 16.0000 0.625650
\(655\) −22.5000 38.9711i −0.879148 1.52273i
\(656\) 0 0
\(657\) 2.00000 3.46410i 0.0780274 0.135147i
\(658\) 0 0
\(659\) −3.00000 + 5.19615i −0.116863 + 0.202413i −0.918523 0.395367i \(-0.870617\pi\)
0.801660 + 0.597781i \(0.203951\pi\)
\(660\) 0 0
\(661\) −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i \(-0.980947\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(662\) −5.00000 8.66025i −0.194331 0.336590i
\(663\) −21.0000 + 5.19615i −0.815572 + 0.201802i
\(664\) 0 0
\(665\) 0 0
\(666\) −8.00000 13.8564i −0.309994 0.536925i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 8.00000 0.309298
\(670\) 3.00000 + 5.19615i 0.115900 + 0.200745i
\(671\) 0 0
\(672\) 0 0
\(673\) 5.00000 + 8.66025i 0.192736 + 0.333828i 0.946156 0.323711i \(-0.104931\pi\)
−0.753420 + 0.657539i \(0.771597\pi\)
\(674\) −14.0000 −0.539260
\(675\) 10.0000 + 17.3205i 0.384900 + 0.666667i
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 25.5000 44.1673i 0.980045 1.69749i 0.317876 0.948132i \(-0.397030\pi\)
0.662169 0.749355i \(-0.269636\pi\)
\(678\) −9.00000 15.5885i −0.345643 0.598671i
\(679\) 0 0
\(680\) 9.00000 15.5885i 0.345134 0.597790i
\(681\) 7.50000 12.9904i 0.287401 0.497792i
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −4.00000 + 6.92820i −0.152944 + 0.264906i
\(685\) −4.50000 + 7.79423i −0.171936 + 0.297802i
\(686\) 0 0
\(687\) 11.0000 + 19.0526i 0.419676 + 0.726900i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 12.0000 41.5692i 0.457164 1.58366i
\(690\) 4.50000 + 7.79423i 0.171312 + 0.296721i
\(691\) −1.00000 −0.0380418 −0.0190209 0.999819i \(-0.506055\pi\)
−0.0190209 + 0.999819i \(0.506055\pi\)
\(692\) −4.50000 7.79423i −0.171064 0.296292i
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 24.0000 + 41.5692i 0.910372 + 1.57681i
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) 14.5000 + 25.1147i 0.548833 + 0.950607i
\(699\) 1.50000 + 2.59808i 0.0567352 + 0.0982683i
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 12.5000 + 12.9904i 0.471782 + 0.490290i
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) 0 0
\(705\) 18.0000 0.677919
\(706\) −3.00000 + 5.19615i −0.112906 + 0.195560i
\(707\) 0 0
\(708\) −1.50000 + 2.59808i −0.0563735 + 0.0976417i
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) −4.50000 7.79423i −0.168882 0.292512i
\(711\) 8.00000 0.300023
\(712\) 6.00000 0.224860
\(713\) 15.0000 + 25.9808i 0.561754 + 0.972987i
\(714\) 0 0
\(715\) 0 0
\(716\) −3.00000 + 5.19615i −0.112115 + 0.194189i
\(717\) −10.5000 + 18.1865i −0.392130 + 0.679189i
\(718\) −4.50000 + 7.79423i −0.167939 + 0.290878i
\(719\) 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) −6.00000 −0.223607
\(721\) 0 0
\(722\) −1.50000 + 2.59808i −0.0558242 + 0.0966904i
\(723\) 14.0000 24.2487i 0.520666 0.901819i
\(724\) 5.00000 0.185824
\(725\) −12.0000 + 20.7846i −0.445669 + 0.771921i
\(726\) 11.0000 0.408248
\(727\) −52.0000 −1.92857 −0.964287 0.264861i \(-0.914674\pi\)
−0.964287 + 0.264861i \(0.914674\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −6.00000 −0.222070
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 11.0000 0.406572
\(733\) −17.5000 + 30.3109i −0.646377 + 1.11956i 0.337604 + 0.941288i \(0.390383\pi\)
−0.983982 + 0.178270i \(0.942950\pi\)
\(734\) −5.00000 + 8.66025i −0.184553 + 0.319656i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) −12.0000 + 20.7846i −0.441129 + 0.764057i
\(741\) −10.0000 10.3923i −0.367359 0.381771i
\(742\) 0 0
\(743\) −24.0000 41.5692i −0.880475 1.52503i −0.850814 0.525467i \(-0.823891\pi\)
−0.0296605 0.999560i \(-0.509443\pi\)
\(744\) 10.0000 0.366618
\(745\) 0 0
\(746\) 16.0000 + 27.7128i 0.585802 + 1.01464i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.50000 + 2.59808i −0.0547723 + 0.0948683i
\(751\) 17.0000 0.620339 0.310169 0.950681i \(-0.399614\pi\)
0.310169 + 0.950681i \(0.399614\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) −1.50000 2.59808i −0.0546630 0.0946792i
\(754\) −6.00000 + 20.7846i −0.218507 + 0.756931i
\(755\) −3.00000 −0.109181
\(756\) 0 0
\(757\) 26.0000 + 45.0333i 0.944986 + 1.63676i 0.755779 + 0.654827i \(0.227258\pi\)
0.189207 + 0.981937i \(0.439408\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i \(-0.236457\pi\)
−0.954043 + 0.299670i \(0.903123\pi\)
\(762\) −11.0000 −0.398488
\(763\) 0 0
\(764\) 12.0000 + 20.7846i 0.434145 + 0.751961i
\(765\) −36.0000 −1.30158
\(766\) −3.00000 5.19615i −0.108394 0.187745i
\(767\) 7.50000 + 7.79423i 0.270809 + 0.281433i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i \(-0.108958\pi\)
−0.761680 + 0.647954i \(0.775625\pi\)
\(770\) 0 0
\(771\) 3.00000 5.19615i 0.108042 0.187135i
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) −30.0000 −1.07903 −0.539513 0.841978i \(-0.681391\pi\)
−0.539513 + 0.841978i \(0.681391\pi\)
\(774\) 16.0000 0.575108
\(775\) 20.0000 34.6410i 0.718421 1.24434i
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) 0 0
\(778\) −15.0000 25.9808i −0.537776 0.931455i
\(779\) 0 0
\(780\) 3.00000 10.3923i 0.107417 0.372104i
\(781\) 0 0
\(782\) −18.0000 −0.643679
\(783\) 15.0000 + 25.9808i 0.536056 + 0.928477i
\(784\) 0 0
\(785\) 6.00000 0.214149
\(786\) 7.50000 + 12.9904i 0.267516 + 0.463352i
\(787\) 53.0000 1.88925 0.944623 0.328158i \(-0.106428\pi\)
0.944623 + 0.328158i \(0.106428\pi\)
\(788\) −6.00000 10.3923i −0.213741 0.370211i
\(789\) 13.5000 + 23.3827i 0.480613 + 0.832446i
\(790\) −6.00000 10.3923i −0.213470 0.369742i
\(791\) 0 0
\(792\) 0 0
\(793\) 11.0000 38.1051i 0.390621 1.35315i
\(794\) −3.50000 6.06218i −0.124210 0.215139i
\(795\) −18.0000 + 31.1769i −0.638394 + 1.10573i
\(796\) 14.0000 0.496217
\(797\) 7.50000 12.9904i 0.265664 0.460143i −0.702074 0.712104i \(-0.747742\pi\)
0.967737 + 0.251961i \(0.0810756\pi\)
\(798\) 0 0
\(799\) −18.0000 + 31.1769i −0.636794 + 1.10296i
\(800\) 2.00000 + 3.46410i 0.0707107 + 0.122474i
\(801\) −6.00000 10.3923i −0.212000 0.367194i
\(802\) −6.00000 −0.211867
\(803\) 0 0
\(804\) −1.00000 1.73205i −0.0352673 0.0610847i
\(805\) 0 0
\(806\) 10.0000 34.6410i 0.352235 1.22018i
\(807\) −4.50000 + 7.79423i −0.158408 + 0.274370i
\(808\) −3.00000 + 5.19615i −0.105540 + 0.182800i
\(809\) 21.0000 36.3731i 0.738321 1.27881i −0.214930 0.976629i \(-0.568952\pi\)
0.953251 0.302180i \(-0.0977142\pi\)
\(810\) 1.50000 + 2.59808i 0.0527046 + 0.0912871i
\(811\) −19.0000 −0.667180 −0.333590 0.942718i \(-0.608260\pi\)
−0.333590 + 0.942718i \(0.608260\pi\)
\(812\) 0 0
\(813\) −1.00000 + 1.73205i −0.0350715 + 0.0607457i
\(814\) 0 0
\(815\) 60.0000 2.10171
\(816\) −3.00000 + 5.19615i −0.105021 + 0.181902i
\(817\) −32.0000 −1.11954
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) 12.0000 0.418803 0.209401 0.977830i \(-0.432848\pi\)
0.209401 + 0.977830i \(0.432848\pi\)
\(822\) 1.50000 2.59808i 0.0523185 0.0906183i
\(823\) −13.0000 −0.453152 −0.226576 0.973994i \(-0.572753\pi\)
−0.226576 + 0.973994i \(0.572753\pi\)
\(824\) 7.00000 12.1244i 0.243857 0.422372i
\(825\) 0 0
\(826\) 0 0
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 3.00000 + 5.19615i 0.104257 + 0.180579i
\(829\) 12.5000 21.6506i 0.434143 0.751958i −0.563082 0.826401i \(-0.690385\pi\)
0.997225 + 0.0744432i \(0.0237179\pi\)
\(830\) 0 0
\(831\) −13.0000 + 22.5167i −0.450965 + 0.781094i
\(832\) 2.50000 + 2.59808i 0.0866719 + 0.0900721i
\(833\) 0 0
\(834\) −8.00000 13.8564i −0.277017 0.479808i
\(835\) −36.0000 −1.24583
\(836\) 0 0
\(837\) −25.0000 43.3013i −0.864126 1.49671i
\(838\) 0 0
\(839\) 27.0000 46.7654i 0.932144 1.61452i 0.152493 0.988304i \(-0.451270\pi\)
0.779650 0.626215i \(-0.215397\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) −26.0000 −0.896019
\(843\) −9.00000 + 15.5885i −0.309976 + 0.536895i
\(844\) 2.00000 + 3.46410i 0.0688428 + 0.119239i
\(845\) −33.0000 20.7846i −1.13523 0.715012i
\(846\) 12.0000 0.412568
\(847\) 0 0
\(848\) −6.00000 10.3923i −0.206041 0.356873i
\(849\) 15.5000 + 26.8468i 0.531959 + 0.921379i
\(850\) 12.0000 + 20.7846i 0.411597 + 0.712906i
\(851\) 24.0000 0.822709
\(852\) 1.50000 + 2.59808i 0.0513892 + 0.0890086i
\(853\) 17.0000 0.582069 0.291034 0.956713i \(-0.406001\pi\)
0.291034 + 0.956713i \(0.406001\pi\)
\(854\) 0 0
\(855\) −12.0000 20.7846i −0.410391 0.710819i
\(856\) 18.0000 0.615227
\(857\) 9.00000 + 15.5885i 0.307434 + 0.532492i 0.977800 0.209539i \(-0.0671963\pi\)
−0.670366 + 0.742030i \(0.733863\pi\)
\(858\) 0 0
\(859\) 2.00000 3.46410i 0.0682391 0.118194i −0.829887 0.557931i \(-0.811595\pi\)
0.898126 + 0.439738i \(0.144929\pi\)
\(860\) −12.0000 20.7846i −0.409197 0.708749i
\(861\) 0 0
\(862\) −16.5000 + 28.5788i −0.561992 + 0.973399i
\(863\) 28.5000 49.3634i 0.970151 1.68035i 0.275064 0.961426i \(-0.411301\pi\)
0.695087 0.718925i \(-0.255366\pi\)
\(864\) 5.00000 0.170103
\(865\) 27.0000 0.918028
\(866\) −2.00000 + 3.46410i −0.0679628 + 0.117715i
\(867\) −9.50000 + 16.4545i −0.322637 + 0.558824i
\(868\) 0 0
\(869\) 0 0
\(870\) 9.00000 15.5885i 0.305129 0.528498i
\(871\) −7.00000 + 1.73205i −0.237186 + 0.0586883i
\(872\) −8.00000 13.8564i −0.270914 0.469237i
\(873\) −4.00000 −0.135379
\(874\) −6.00000 10.3923i −0.202953 0.351525i
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 11.0000 + 19.0526i 0.371444 + 0.643359i 0.989788 0.142548i \(-0.0455296\pi\)
−0.618344 + 0.785907i \(0.712196\pi\)
\(878\) −14.0000 −0.472477
\(879\) 3.00000 + 5.19615i 0.101187 + 0.175262i
\(880\) 0 0
\(881\) 3.00000 + 5.19615i 0.101073 + 0.175063i 0.912127 0.409908i \(-0.134439\pi\)
−0.811054 + 0.584971i \(0.801106\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 15.0000 + 15.5885i 0.504505 + 0.524297i
\(885\) −4.50000 7.79423i −0.151266 0.262000i
\(886\) 9.00000 15.5885i 0.302361 0.523704i
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 4.00000 6.92820i 0.134231 0.232495i
\(889\) 0 0
\(890\) −9.00000 + 15.5885i −0.301681 + 0.522526i
\(891\) 0 0
\(892\) −4.00000 6.92820i −0.133930 0.231973i
\(893\) −24.0000 −0.803129
\(894\) 0 0
\(895\) −9.00000 15.5885i −0.300837 0.521065i
\(896\) 0 0
\(897\) −10.5000 + 2.59808i −0.350585 + 0.0867472i
\(898\) 4.50000 7.79423i 0.150167 0.260097i
\(899\) 30.0000 51.9615i 1.00056 1.73301i
\(900\) 4.00000 6.92820i 0.133333 0.230940i
\(901\) −36.0000 62.3538i −1.19933 2.07731i
\(902\) 0 0
\(903\) 0 0
\(904\) −9.00000 + 15.5885i −0.299336 + 0.518464i
\(905\) −7.50000 + 12.9904i −0.249308 + 0.431815i
\(906\) 1.00000 0.0332228
\(907\) −7.00000 + 12.1244i −0.232431 + 0.402583i −0.958523 0.285015i \(-0.908001\pi\)
0.726092 + 0.687598i \(0.241335\pi\)
\(908\) −15.0000 −0.497792
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 21.0000 0.695761 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) −29.0000 −0.959235
\(915\) −16.5000 + 28.5788i −0.545473 + 0.944787i
\(916\) 11.0000 19.0526i 0.363450 0.629514i
\(917\) 0 0
\(918\) 30.0000 0.990148
\(919\) 3.50000 + 6.06218i 0.115454 + 0.199973i 0.917961 0.396670i \(-0.129834\pi\)
−0.802507 + 0.596643i \(0.796501\pi\)
\(920\) 4.50000 7.79423i 0.148361 0.256968i
\(921\) 6.50000 11.2583i 0.214182 0.370975i
\(922\) 10.5000 18.1865i 0.345799 0.598942i
\(923\) 10.5000 2.59808i 0.345612 0.0855167i
\(924\) 0 0
\(925\) −16.0000 27.7128i −0.526077 0.911192i
\(926\) 31.0000 1.01872
\(927\) −28.0000 −0.919641
\(928\) 3.00000 + 5.19615i 0.0984798 + 0.170572i
\(929\) −9.00000 15.5885i −0.295280 0.511441i 0.679770 0.733426i \(-0.262080\pi\)
−0.975050 + 0.221985i \(0.928746\pi\)
\(930\) −15.0000 + 25.9808i −0.491869 + 0.851943i
\(931\) 0 0
\(932\) 1.50000 2.59808i 0.0491341 0.0851028i
\(933\) −6.00000 −0.196431
\(934\) −1.50000 + 2.59808i −0.0490815 + 0.0850117i
\(935\) 0 0
\(936\) 2.00000 6.92820i 0.0653720 0.226455i
\(937\) 8.00000 0.261349 0.130674 0.991425i \(-0.458286\pi\)
0.130674 + 0.991425i \(0.458286\pi\)
\(938\) 0 0
\(939\) −4.00000 6.92820i −0.130535 0.226093i
\(940\) −9.00000 15.5885i −0.293548 0.508439i
\(941\) −7.50000 12.9904i −0.244493 0.423474i 0.717496 0.696563i \(-0.245288\pi\)
−0.961989 + 0.273088i \(0.911955\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 0 0
\(944\) 3.00000 0.0976417
\(945\) 0 0
\(946\) 0 0
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) 2.00000 + 3.46410i 0.0649570 + 0.112509i
\(949\) 2.00000 6.92820i 0.0649227 0.224899i
\(950\) −8.00000 + 13.8564i −0.259554 + 0.449561i
\(951\) 6.00000 + 10.3923i 0.194563 + 0.336994i
\(952\) 0 0
\(953\) 7.50000 12.9904i 0.242949 0.420800i −0.718604 0.695419i \(-0.755219\pi\)
0.961553 + 0.274620i \(0.0885520\pi\)
\(954\) −12.0000 + 20.7846i −0.388514 + 0.672927i
\(955\) −72.0000 −2.32987
\(956\) 21.0000 0.679189
\(957\) 0 0
\(958\) 15.0000 25.9808i 0.484628 0.839400i
\(959\) 0 0
\(960\) −1.50000 2.59808i −0.0484123 0.0838525i
\(961\) −34.5000 + 59.7558i −1.11290 + 1.92760i
\(962\) −20.0000 20.7846i −0.644826 0.670123i
\(963\) −18.0000 31.1769i −0.580042 1.00466i
\(964\) −28.0000 −0.901819
\(965\) −7.50000 12.9904i −0.241434 0.418175i
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) −5.50000 9.52628i −0.176777 0.306186i
\(969\) −24.0000 −0.770991
\(970\) 3.00000 + 5.19615i 0.0963242 + 0.166838i
\(971\) −1.50000 2.59808i −0.0481373 0.0833762i 0.840953 0.541108i \(-0.181995\pi\)
−0.889090 + 0.457732i \(0.848662\pi\)
\(972\) −8.00000 13.8564i −0.256600 0.444444i
\(973\) 0 0
\(974\) 13.0000 0.416547
\(975\) 10.0000 + 10.3923i 0.320256 + 0.332820i
\(976\) −5.50000 9.52628i −0.176051 0.304929i
\(977\) −19.5000 + 33.7750i −0.623860 + 1.08056i 0.364900 + 0.931047i \(0.381103\pi\)
−0.988760 + 0.149511i \(0.952230\pi\)
\(978\) −20.0000 −0.639529
\(979\) 0 0
\(980\) 0 0
\(981\) −16.0000 + 27.7128i −0.510841 + 0.884802i
\(982\) 6.00000 + 10.3923i 0.191468 + 0.331632i
\(983\) 15.0000 + 25.9808i 0.478426 + 0.828658i 0.999694 0.0247352i \(-0.00787426\pi\)
−0.521268 + 0.853393i \(0.674541\pi\)
\(984\) 0 0
\(985\) 36.0000 1.14706
\(986\) 18.0000 + 31.1769i 0.573237 + 0.992875i
\(987\) 0 0
\(988\) −4.00000 + 13.8564i −0.127257 + 0.440831i
\(989\) −12.0000 + 20.7846i −0.381578 + 0.660912i
\(990\) 0 0
\(991\) −8.50000 + 14.7224i −0.270011 + 0.467673i −0.968864 0.247592i \(-0.920361\pi\)
0.698853 + 0.715265i \(0.253694\pi\)
\(992\) −5.00000 8.66025i −0.158750 0.274963i
\(993\) −10.0000 −0.317340
\(994\) 0 0
\(995\) −21.0000 + 36.3731i −0.665745 + 1.15310i
\(996\) 0 0
\(997\) 35.0000 1.10846 0.554231 0.832363i \(-0.313013\pi\)
0.554231 + 0.832363i \(0.313013\pi\)
\(998\) −11.0000 + 19.0526i −0.348199 + 0.603098i
\(999\) −40.0000 −1.26554
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1274.2.e.d.471.1 2
7.2 even 3 182.2.g.b.29.1 2
7.3 odd 6 1274.2.h.i.263.1 2
7.4 even 3 1274.2.h.j.263.1 2
7.5 odd 6 1274.2.g.g.393.1 2
7.6 odd 2 1274.2.e.i.471.1 2
13.9 even 3 1274.2.h.j.373.1 2
21.2 odd 6 1638.2.r.c.757.1 2
28.23 odd 6 1456.2.s.e.1121.1 2
91.2 odd 12 2366.2.d.f.337.2 2
91.9 even 3 182.2.g.b.113.1 yes 2
91.16 even 3 2366.2.a.f.1.1 1
91.23 even 6 2366.2.a.n.1.1 1
91.37 odd 12 2366.2.d.f.337.1 2
91.48 odd 6 1274.2.h.i.373.1 2
91.61 odd 6 1274.2.g.g.295.1 2
91.74 even 3 inner 1274.2.e.d.165.1 2
91.87 odd 6 1274.2.e.i.165.1 2
273.191 odd 6 1638.2.r.c.1387.1 2
364.191 odd 6 1456.2.s.e.113.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.g.b.29.1 2 7.2 even 3
182.2.g.b.113.1 yes 2 91.9 even 3
1274.2.e.d.165.1 2 91.74 even 3 inner
1274.2.e.d.471.1 2 1.1 even 1 trivial
1274.2.e.i.165.1 2 91.87 odd 6
1274.2.e.i.471.1 2 7.6 odd 2
1274.2.g.g.295.1 2 91.61 odd 6
1274.2.g.g.393.1 2 7.5 odd 6
1274.2.h.i.263.1 2 7.3 odd 6
1274.2.h.i.373.1 2 91.48 odd 6
1274.2.h.j.263.1 2 7.4 even 3
1274.2.h.j.373.1 2 13.9 even 3
1456.2.s.e.113.1 2 364.191 odd 6
1456.2.s.e.1121.1 2 28.23 odd 6
1638.2.r.c.757.1 2 21.2 odd 6
1638.2.r.c.1387.1 2 273.191 odd 6
2366.2.a.f.1.1 1 91.16 even 3
2366.2.a.n.1.1 1 91.23 even 6
2366.2.d.f.337.1 2 91.37 odd 12
2366.2.d.f.337.2 2 91.2 odd 12