Properties

Label 1274.2.e.d.165.1
Level $1274$
Weight $2$
Character 1274.165
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 165.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1274.165
Dual form 1274.2.e.d.471.1

$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −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 −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) −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 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 5.00000 8.66025i 0.898027 1.55543i 0.0680129 0.997684i \(-0.478334\pi\)
0.830014 0.557743i \(-0.188333\pi\)
\(32\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) −3.00000 −0.442326
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) −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 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 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 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) −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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 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 0.941201 0.337846i \(-0.109698\pi\)
−0.763184 + 0.646181i \(0.776365\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −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 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) −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 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 3.00000 + 5.19615i 0.297044 + 0.514496i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) −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 −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 0 0
\(111\) −4.00000 6.92820i −0.379663 0.657596i
\(112\) 0 0
\(113\) 9.00000 + 15.5885i 0.846649 + 1.46644i 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 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 −0.999905 0.0137486i \(-0.995624\pi\)
0.511859 + 0.859069i \(0.328957\pi\)
\(128\) −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 −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 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 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) −4.00000 −0.326599
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) −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 −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) −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 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 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 −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) −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 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) −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 0.00454614 0.999990i \(-0.498553\pi\)
0.863743 0.503932i \(-0.168114\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 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 −0.996649 0.0818013i \(-0.973933\pi\)
0.569166 + 0.822222i \(0.307266\pi\)
\(198\) 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 −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) −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 −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 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 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 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 0.910968 0.412477i \(-0.135336\pi\)
−0.812700 + 0.582683i \(0.802003\pi\)
\(234\) 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 0.814795 0.579748i \(-0.196849\pi\)
−0.909475 + 0.415759i \(0.863516\pi\)
\(252\) 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 0.896093 + 0.443866i \(0.146393\pi\)
−0.0636476 + 0.997972i \(0.520273\pi\)
\(264\) 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 0.797283 + 0.603606i \(0.206270\pi\)
0.124096 + 0.992270i \(0.460397\pi\)
\(284\) 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 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 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 −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 3.50000 + 0.866025i 0.198148 + 0.0490290i
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) 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 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) −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 −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 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 0.157969 + 0.987444i \(0.449505\pi\)
−0.934136 + 0.356917i \(0.883828\pi\)
\(350\) 0 0
\(351\) −12.5000 + 12.9904i −0.667201 + 0.693375i
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 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 0.959997 0.280012i \(-0.0903384\pi\)
−0.722496 + 0.691375i \(0.757005\pi\)
\(360\) 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 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) 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 0.0708063 + 0.997490i \(0.477443\pi\)
−0.899255 + 0.437425i \(0.855891\pi\)
\(374\) 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 −0.242213 0.970223i \(-0.577873\pi\)
0.961344 0.275349i \(-0.0887935\pi\)
\(380\) −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 −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) 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 −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) −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 −0.764730 0.644351i \(-0.777127\pi\)
0.940389 + 0.340099i \(0.110461\pi\)
\(398\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 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 0.922981 + 0.384846i \(0.125746\pi\)
−0.128204 + 0.991748i \(0.540921\pi\)
\(432\) −5.00000 −0.240563
\(433\) 2.00000 + 3.46410i 0.0961139 + 0.166474i 0.910073 0.414448i \(-0.136025\pi\)
−0.813959 + 0.580922i \(0.802692\pi\)
\(434\) 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 0.569057 0.822298i \(-0.307309\pi\)
−0.996660 + 0.0816684i \(0.973975\pi\)
\(444\) −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 0.740087 0.672511i \(-0.234784\pi\)
−0.952455 + 0.304679i \(0.901451\pi\)
\(450\) −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 0.510887 0.859648i \(-0.329317\pi\)
−0.999920 + 0.0126168i \(0.995984\pi\)
\(462\) 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 0.898642 0.438682i \(-0.144554\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) −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 −0.973321 0.229447i \(-0.926308\pi\)
0.287954 0.957644i \(-0.407025\pi\)
\(480\) 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 −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) 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 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) −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 −0.772220 0.635355i \(-0.780854\pi\)
−0.164124 0.986440i \(-0.552480\pi\)
\(504\) 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 −0.138234 0.990400i \(-0.544143\pi\)
0.926828 0.375486i \(-0.122524\pi\)
\(522\) −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 −0.907975 0.419025i \(-0.862372\pi\)
0.0911008 0.995842i \(-0.470961\pi\)
\(542\) −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 −0.999952 0.00979220i \(-0.996883\pi\)
0.491496 0.870880i \(-0.336450\pi\)
\(558\) 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 −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) 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 −0.412315 0.911041i \(-0.635280\pi\)
0.995142 0.0984456i \(-0.0313871\pi\)
\(578\) −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 −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 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 −0.895042 0.445983i \(-0.852854\pi\)
0.833753 + 0.552137i \(0.186188\pi\)
\(600\) −4.00000 −0.163299
\(601\) −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i \(0.344580\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 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 −0.746532 0.665350i \(-0.768282\pi\)
0.949476 + 0.313841i \(0.101616\pi\)
\(608\) −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 0.998002 0.0631797i \(-0.0201241\pi\)
−0.553716 + 0.832705i \(0.686791\pi\)
\(614\) 13.0000 0.524637
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) 7.00000 12.1244i 0.281581 0.487713i
\(619\) 18.5000 32.0429i 0.743578 1.28791i −0.207279 0.978282i \(-0.566461\pi\)
0.950856 0.309633i \(-0.100206\pi\)
\(620\) −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 0.811964 0.583707i \(-0.198398\pi\)
−0.911487 + 0.411328i \(0.865065\pi\)
\(632\) −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 −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) 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 0.965726 + 0.259565i \(0.0835793\pi\)
−0.258073 + 0.966126i \(0.583087\pi\)
\(648\) 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 0.801660 0.597781i \(-0.203951\pi\)
−0.918523 + 0.395367i \(0.870617\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) −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 −0.753420 0.657539i \(-0.771597\pi\)
0.946156 + 0.323711i \(0.104931\pi\)
\(674\) −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 0.662169 + 0.749355i \(0.269636\pi\)
0.317876 + 0.948132i \(0.397030\pi\)
\(678\) −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 −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) −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 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) −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 −0.983982 0.178270i \(-0.942950\pi\)
0.337604 0.941288i \(-0.390383\pi\)
\(734\) −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 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) −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 −0.0296605 + 0.999560i \(0.509443\pi\)
−0.850814 + 0.525467i \(0.823891\pi\)
\(744\) 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 0.189207 0.981937i \(-0.439408\pi\)
0.755779 0.654827i \(-0.227258\pi\)
\(758\) −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 −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) −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 −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 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 0.967737 0.251961i \(-0.0810756\pi\)
−0.702074 + 0.712104i \(0.747742\pi\)
\(798\) 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 0.953251 + 0.302180i \(0.0977142\pi\)
−0.214930 + 0.976629i \(0.568952\pi\)
\(810\) 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 0.997225 0.0744432i \(-0.0237179\pi\)
−0.563082 + 0.826401i \(0.690385\pi\)
\(830\) 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 0.779650 + 0.626215i \(0.215397\pi\)
0.152493 + 0.988304i \(0.451270\pi\)
\(840\) 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 −0.670366 0.742030i \(-0.733863\pi\)
0.977800 + 0.209539i \(0.0671963\pi\)
\(858\) 0 0
\(859\) 2.00000 + 3.46410i 0.0682391 + 0.118194i 0.898126 0.439738i \(-0.144929\pi\)
−0.829887 + 0.557931i \(0.811595\pi\)
\(860\) −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 0.695087 + 0.718925i \(0.255366\pi\)
0.275064 + 0.961426i \(0.411301\pi\)
\(864\) 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 −0.618344 0.785907i \(-0.712196\pi\)
0.989788 + 0.142548i \(0.0455296\pi\)
\(878\) −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 −0.811054 0.584971i \(-0.801106\pi\)
0.912127 + 0.409908i \(0.134439\pi\)
\(882\) 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 0.726092 0.687598i \(-0.241335\pi\)
−0.958523 + 0.285015i \(0.908001\pi\)
\(908\) −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 −0.802507 0.596643i \(-0.796501\pi\)
0.917961 + 0.396670i \(0.129834\pi\)
\(920\) 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 −0.975050 0.221985i \(-0.928746\pi\)
0.679770 + 0.733426i \(0.262080\pi\)
\(930\) −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 −0.961989 0.273088i \(-0.911955\pi\)
0.717496 + 0.696563i \(0.245288\pi\)
\(942\) −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 0.961553 0.274620i \(-0.0885520\pi\)
−0.718604 + 0.695419i \(0.755219\pi\)
\(954\) −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 −0.889090 0.457732i \(-0.848662\pi\)
0.840953 + 0.541108i \(0.181995\pi\)
\(972\) −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 −0.988760 0.149511i \(-0.952230\pi\)
0.364900 0.931047i \(-0.381103\pi\)
\(978\) −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 −0.521268 0.853393i \(-0.674541\pi\)
0.999694 + 0.0247352i \(0.00787426\pi\)
\(984\) 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 0.698853 0.715265i \(-0.253694\pi\)
−0.968864 + 0.247592i \(0.920361\pi\)
\(992\) −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.165.1 2
7.2 even 3 1274.2.h.j.373.1 2
7.3 odd 6 1274.2.g.g.295.1 2
7.4 even 3 182.2.g.b.113.1 yes 2
7.5 odd 6 1274.2.h.i.373.1 2
7.6 odd 2 1274.2.e.i.165.1 2
13.3 even 3 1274.2.h.j.263.1 2
21.11 odd 6 1638.2.r.c.1387.1 2
28.11 odd 6 1456.2.s.e.113.1 2
91.3 odd 6 1274.2.g.g.393.1 2
91.4 even 6 2366.2.a.n.1.1 1
91.16 even 3 inner 1274.2.e.d.471.1 2
91.32 odd 12 2366.2.d.f.337.2 2
91.46 odd 12 2366.2.d.f.337.1 2
91.55 odd 6 1274.2.h.i.263.1 2
91.68 odd 6 1274.2.e.i.471.1 2
91.74 even 3 2366.2.a.f.1.1 1
91.81 even 3 182.2.g.b.29.1 2
273.263 odd 6 1638.2.r.c.757.1 2
364.263 odd 6 1456.2.s.e.1121.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.g.b.29.1 2 91.81 even 3
182.2.g.b.113.1 yes 2 7.4 even 3
1274.2.e.d.165.1 2 1.1 even 1 trivial
1274.2.e.d.471.1 2 91.16 even 3 inner
1274.2.e.i.165.1 2 7.6 odd 2
1274.2.e.i.471.1 2 91.68 odd 6
1274.2.g.g.295.1 2 7.3 odd 6
1274.2.g.g.393.1 2 91.3 odd 6
1274.2.h.i.263.1 2 91.55 odd 6
1274.2.h.i.373.1 2 7.5 odd 6
1274.2.h.j.263.1 2 13.3 even 3
1274.2.h.j.373.1 2 7.2 even 3
1456.2.s.e.113.1 2 28.11 odd 6
1456.2.s.e.1121.1 2 364.263 odd 6
1638.2.r.c.757.1 2 273.263 odd 6
1638.2.r.c.1387.1 2 21.11 odd 6
2366.2.a.f.1.1 1 91.74 even 3
2366.2.a.n.1.1 1 91.4 even 6
2366.2.d.f.337.1 2 91.46 odd 12
2366.2.d.f.337.2 2 91.32 odd 12